Observation and analysis of lunar occultations of stars with an ...

THE OBSERVATION AND ANALYSIS OF LUNAR OCCULTAT IONS OFSTARS WITH AN EMPHASIS ON IMPROVEMENTS TO DATAACQUISITION INSTRUMENTATION AND REDUCTION TECHNIQUESByGLENN HSCHNEIDERA DISSERTATION PRESENTED TO THE GRADUATE SCHOOLOF THE UNIVERSITY OF FLORIDA INPARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THEDEGREE OF DOCTOR OF PHILOSOPHYUNIVERSITY OFFLORIDA1985

Without his assistance and guidance throughout my years atthe University of Florida, this dissertation would never havebeen. I also thank my other committee members, Heinrich K.Eichhorn, Howard L. Cohen, Haywood C. Smith, and Ralph 6.Sel -fridge, -for their help, valuable suggestions, and at timesmuch needed criticisms as this study progressed. To thelatter, and to the University's Center for IntelligentMachines and Robotics I offer additional thanks for securingthe use of the computational resources required for thisinvestigation. I would also like to thank Ben Adenbaum andWarner Computer Systems, Inc., for granting the use of theirfacilities during the early stages of this project.My personal thanks extend to Frank B. Wood, and Kwan-YuChen, both of whom often provided much needed informationrelated to this study. In addition, through their efforts Iwas afforded the unique opportunity to hone my fledglingskills as an instrumentalist by actively working on thedevelopment of the South Pole Observatory.My fellow graduate students proved to be a source of awealth of information and ideas. To them I offer not only mythanks but the hope that there may indeed be life aftergraduate school. In particular, I would like to acknowledgethe support I received from Roger Ball, Joseph T. Pollock(who have already realized this hope), and Gregory L.Fitzgibbons. To Elaine Reeves, who soon will enter intoindentured servitude as a graduate student herself, go my

v Ithanks -for proo-f reading the manuscript o-f this dissertation,and -for helping "bag" Pallas.For their -fabrication o-f the mechanical componentsrequired

calcales.onTABLE OF CONTENTSACKNOWLEDGEMENTS ivLI ST OF TABLES x i iLIST OF FIGURES xviiABSTRACTxxvCHAPTERSI INTRODUCTION 1Lunar Occul tat i ons: A Historical Synopsis 1Information Which May Be Learned From theAnalysis of Lunar Occul tations 3Goals o-f the Program of Occul tat ion Observat i . . . .5II INSTRUMENTATION 8Opt i Equ i pment 8The Seventy-Six Centimeter Telescope 8Location and description 8The telescope light baffle 8Photoel ec tr i c Photometers. 13The Astromechan i cs photometer 18Opt i f i 1 ters 1?The portabl e photometer 20Data Acquisition Electronics 20The SPICA-IV/LODAS System 20Design criteria for a new SPICA 20The SPICA-IV digital electronics 22Anc i 1 1 ary equ i pment 27Power suppl i 23SPICA-IV system configuration 29Portabl e use .2?An a 1 og E 1 e c t r on i c s 40The WWVB receiver 40Radi o antennas 4?The photometer amplifier 50Limitations of the Occul tation PhotometricSystem 52The Lunar Occul tat ion Data Acquisition SystemSof tware 55Software Design Considerations 55System t imi ng 56Memory usage 57VIII

spheralonngval'. ~.iSuplementary program documentation 58Per iInput/Output 62User (Observer) I/O 62The video "strip chart recorder" 71Data arch 73iIII NUMERICAL MODELING OF LUNAR OCCULTATIONS 76~.The Physical Characterization o-f an OccultationIntensity Curve......... 76The Generation o-f a Model Occultation IntensityCurve 78Monochromatic Point Source Approximation 78Lunar Limb Effects 79A Monochromatic Extended Source and LimbDarken i31Polychromatic Intensity Curve 36The E-f-fects o-f Discrete Modeling 90The E-f-fects of Instrumental Optical Response ... .91The Polychromatic Extended Source IntensityCurve 93Model s o-f Doubl e Stars 94The Di -f-ferent i al Corrections

ance-covaroncornanceThe Two-Star Di f f eren t i al CorrectionsProcedure (DC2) 154Global parameters -for DC2 154The APL function DC2 155Preprocessing of the Observational Data 158Presentation o-f the Results o-f the DC Run 158K> THE OCCULTATION OBSERVATIONS AND RESULTS OFTHEIR ANALYSIS 162Pre sen tat i on Format 162Format and Content o-f the Tables 162The occultation summary table.. 162Uar i i , correlation, anddl/dPj 167Observed and computed intensity values 168Format and Content of the Graphs 169Graph of the entire event, RAWPLOT 169The integration plot, INTPLOT 170Graphic depiction of the best fit, FITPL0T..171Noise statistics of the observation,NOI SEPLOT 1 72Power spectra, POWERRPLOT 174Sensitivity of solution to variation ofparameters, PDPLOT 176Discussion of Individual Occultation Events 177ZC0916

x IAPPENDICESX07202 337X07247 396X09514 401ZC1030 (Epsilon Geminorum) 413Summary of the Occultation Observations 416Future Directions for the Occultation Program. . . .424A LODAS/E07 ASSEMBLY LISTING 434B OCCTRANS ASSEMBLY LISTING 470C LISTING OF THE APL WORKSPACE OCCPREP 475D LISTING OF THE APL WORKSPACE OCCRED 477E LISTING OF THE APL WORKSPACE OCCPLOTS 489LI ST OF REFERENCES 497BIOGRAPHICAL SKETCH 503

LIST OF TABLES2-1 SPECIFICATIONS FOR THE 76-CM. OPTICAL BAFFLE TUBE... 162-2 DETERMINATION OF THE PRIMARY MIRROR FOCAL LENGTH 172-3 DIAPHRAGM DESIGNATIONS, LINEAR, AND ANGULAR FIELDSIZES 192-4 DESIGN CRITERIA FOR SPI CA-IV/LODAS 212-5 STELLAR INTENSITY READINGS WITH THE RHOSP I CA-IV/LODAS 532-6 LODAS/E07 SUBROUTINES 632-7 LODAS/E07 DATA TABLES *52-8 LODAS/E07 KEYBOARD COMMANDS 663-1 PARAMETERS CHARACTERIZING AN OCCULTATIONINTENSITY CURVE 763-2 PARAMETERS AFFECTING THE OBSERVED INTENSITY CURVE... 773-3 BRIGHTNESS DISTRIBUTION FOR A MODEL STAR WITHGRID PARAMETERS 333-4 BRIGHTNESS DISTRIBUTION FOR A MODEL STAR WITHGRID PARAMETERS AND A LIMB DARKENINGCOEFFICIENT OF 1.0 343-5 PARAMETERS FOR GENERATING THE INITIAL MODEL 983-6 COMPARATIVE SAMPLE OF DC FITTING TO SYNTHETICCURVE 1163-7 COMPARATIVE SAMPLE OF DC2 FITTING TO SYNTHETICCURVE 1134-1 GLOBAL VARIABLES CREATED BY THE APL FUNCTIONINPUT 1 404-2 GLOBAL VARIABLES RESIDENT IN THE OCCRED WORKSPACE .. 1 414-3 GLOBAL VARIABLES CREATED BY THE APL FUNCTION DC 1534-4 INFORMATION PRESENTED BY THE APL FUNCTION OUTPUT... 160x I 1

4-5 TWO-STAR QUANTITIES PRESENTED BY THE APL FUNCTIONDC21 615-1 THE OCCULTATION OBSERVATI ON OF ZC0916 (1 GEM) 17?5-2 TWO-STAR SOLUTION FOR 1 GEM A 1835-3 TWO-STAR SOLUTI ON FOR 1 GEM B 1 885-4 RELATIVE BRIGHTNESSES AND MAGNITUDES OF THEINDIVIDUAL COMPONENTS OF 1 GEM 1925-5 TIMES OF GEOMETRICAL OCCULTATI ONS OF THECOMPONENTS OF 1 GEM 1 955-6 ZC0916: OBSERVED, COMPUTED, AND RESIDUAL VALUES 2015-7 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE 1 GEM A SOLUTION 2025-8 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE 1 GEM B SOLUTI ON 2035-9 THE OCCULTATION SUMMARY TABLE FOR 2C1221 2055-10 ZC1221: OBSERVED, COMPUTED AND RESIDUAL VALUES 2125-11 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE ZC1221 SOLUTION 2135-12 THE OCCULTATION SUMMARY TABLE FOR ZC1222 2165-13 ZC1222: OBSERVED, COMPUTED, AND RESIDUAL VALUES 2205-14 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE ZC1222 SOLUTION 2215-15 THE OCCULTATION SUMMARY TABLE FOR X07589 2255-16 X07589: OBSERVED, COMPUTED, AND RESIDUAL VALUES 2325-17 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE X07589 SOLUTI ON 2335-18 THE OCCULTATION SUMMARY TABLE FOR X07598 2365-19 X07598: OBSERVED, COMPUTED, AND RESIDUAL VALUES 2405-20 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE X07598 SOLUTION 2425-21 THE OCCULTATION SUMMARY TABLE FOR XI 3534 2465-22 XI 3534: OBSERVED, COMPUTED, AND RESIDUAL VALUES 252XIII

5-23 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE XI 3534 SOLUTION 2545-24 THE OCCULTATION SUMMARY TABLE FOR XI 3607 2575-25 XI 3607: OBSERVED, COMPUTED, AND RESIDUAL VALUES 2625-26 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE XI 3607 SOLUTION 2635-27 THE OCCULTATION SUMMARY TABLE FOR ZC1462 2705-28 2C1462: OBSERVED, COMPUTED, AND RESIDUAL VALUES 2745-2? VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE 2C1 462 SOLUTI ON 2755-30 THE OCCULTATION SUMMARY TABLE FOR X13067 2795-31 X18067: OBSERVED, COMPUTED, AND RESIDUAL VALUES 2845-32 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE XI 8067 SOLUTI ON 2875-33 THE OCCULTATION SUMMARY TABLE FOR ZC2209 2895-34 2C2209: OBSERVED, COMPUTED, AND RESIDUAL VALUES 2975-35 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE ZC2209 SOLUTION 2985-36 THE OCCULTATION SUMMARY TABLE FOR 2C3214 2995-37 ZC3214: OBSERVED, COMPUTED, AND RESIDUAL VALUES 3045-38 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE ZC321 4 SOLUTI ON 3055-39 THE OCCULTATION SUMMARY TABLE FOR X31590 3085-40 X31590: OBSERVED, COMPUTED, AND RESIDUAL VALUES 3115-41 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE X31590 SOLUTION 3145-42 THE OCCULTATION SUMMARY TABLE FOR X01217 3205-43 X01217: OBSERVED, COMPUTED, AND RESIDUAL VALUES 3235-44 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE XO 1 21 7 SOLUTI ON 3255-45 THE OCCULTATION SUMMARY TABLE FOR X01246 330x i v

5-46 X01246: OBSERVED, COMPUTED, AND RESIDUAL VALUES 3335-47 UARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE X01246 SOLUTION 3355-48 THE OCCULTATION SUMMARY TABLE FOR ZC0126 3405-4? ZCO 126: OBSERVED, COMPUTED, AND RESIDUAL VALUESRESI DUALS 3455-50 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE ZCO 1 26 SOLUTI ON 3475-51 THE OCCULTATION SUMMARY TABLE FOR X0130? 3515-52 X0130?: OBSERVED, COMPUTED, AND RESIDUAL VALUES 3545-53 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE X0130? SOLUTION 3565-54 THE OCCULTATION SUMMARY TABLE FOR ZC3158 35?5-55 ZC3158: OBSERVED, COMPUTED, AND RESIDUAL VALUES 3645-56 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE ZC3158 SOLUTION 3665-57 THE OCCULTATION SUMMARY TABLE FOR ZCO 835 3705-58 ZC0835: OBSERVED, COMPUTED, AND RESIDUAL VALUES 3725-5? VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE ZC0835 SOLUTION 3765-60 THE OCCULTATION SUMMARY TABLE FOR X07145 3805-61 X07145: OBSERVED, COMPUTED, AND RESIDUAL VALUES 3815-62 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE X071 45 SOLUTI ON 3845-63 THE OCCULTATION SUMMARY TABLE FOR X07202 3885-64 X07202: OBSERVED, COMPUTED, AND RESIDUAL VALUES 3?35-65 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE X07202 SOLUTI ON 3?45-66 THE OCCULTATION SUMMARY TABLE FOR X07247 3?75-67 X07247: OBSERVED, COMPUTED, AND RESIDUAL VALUES 400xv

5-63 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE X07247 SOLUTION 4035-69 THE OCCULTATION SUMMARY TABLE FOR X09514 4075-70 X09514: OBSERVED, COMPUTED, AND RESIDUAL VALUES 4095-71 VARIANCE-COVARIANCE AND CORRELATION MATRICES FORTHE X95147 SOLUTION 4115-72 DERIVED QUANTITIES FOR THE OCCULTATION BINARIES 4185-73 STELLAR ANGULAR DIAMETERS 4185-74 COORDINATED UNIVERSAL TIMES OF GEOMETRICALOCCULTATIONS 419XV I

ILIST OF FIGURES2-1 The Rosemary Hill Observatory 76-cm. telescope 102-2 Layout of the occultation baffle system 122-3 The occultation 1 i ght-baf 4 1 e tube and ring 152-4 Schematic diagram of SPICA-IV/LODAS clock 262-5 Schematic diagram o-f A-to-D circuit 262-6 The SPICA-IV/LODAS 8-inch disk drive package 312-7 SPICA-IV/LODAS system con-figuration 322-8 The A-to-D Converter/Clock board 342-9 SPICA-IV/LODAS backplate and connector layout 362-10 The SPICA-IV/LODAS rolling rack and photometricequ i pment 382-11 Photograph o-f SPICA-IM/LODAS at Macon, Georgia 422-12 Photograph o-f SPICA-IU/LODAS in the Everglades 442-13 The WwVB and WwV receivers, and HU power supply.... 482-14 LODAS -foreground program logic flow chart 592-15 LODAS background program logic flow chart 602-16 LODAS 20-character LED status display format 712-17 The SPICA-IV/LODAS video "strip chart recorder" 753-1 Lunar occultation intensity curve for amonochromatic point source ...803-2 An example of a stellar quadrant grid. 803-3 Stellar limb darkening 353-4 Modeling an extended source from intensityweighted monochromatic point sources 87XV I

3-5 Modeling a polychromatic source -from intensityweighted monochromatic extended sources 893-6 The effect of discrete modeling on a 10-mi 1 1 i second-of-arc source 923-7 Sample two-star intensity curve used -forinitial parameter selection 1053-8 Iterative convergence o-f the DC -fitting process. .. 1 123-9 Iterative convergence o-f the DC2 fitting process.. 1203-10 Eight-point unweighted smoothing of raw data 1263-11 Power spectra of selected synthetic curves 1293-12 windowing effects of Fourier smoothing 1315-1 ZC0916

5-17 ZC1221 - FITPLOT 2085-18 ZC12215-1? ZC12215-20 ZC12215-21 ZC12225-22 ZC12225-23 ZC12225-24 ZC12225-25 ZC12225-26 ZC12225-27 X0758?5-28 X0758?5-2? X0758?5-30 X0758?5-31 X0758?5-32 X0758?5-33 X0758?5-34 X075?85-35 X075?85-34 X075?85-37 X075?85-38 X075?85-3? X075?85-40 XI 35345-41 XI 35345-42 XI 35345-43 XI 3534- PDPLOT 210- NOISEPLOT 210- POWERPLOT 214- RAWPLOT 217- INTPLOT 217- FITPLOT 21?- PDPLOT 222- NOISEPLOT 222- POUERPLOT 224- RAWPLOT 226- INTPLOT 226- FITPLOT 22?- Detailed FITPLOT 22?- PDPLOT 231- NOISEPLOT 231- POWERPLOT 234- RAWPLOT 237- INTPLOT 237- FITPLOT 23?- PDPLOT 243- NOI SEPLOT 243- POWERPLOT 244- RAWPLOT 248- INTPLOT 248- FITPLOT 250- PDPLOT 253x i x

5-44 XI 3534 - NOI SEPLOT 2535-45 XI 3534 - POWERPLOT 2555-46 XI 360? - RAWPLOT 2595-4? XI 360? - INTPLOT 25?5-48 XI 360? - FITPLOT 2605-4? XI 360? - PDPLOT 2645-50 XI 360? - NOI SEPLOT 2645-51 XI 3607 - POWERPLOT 2665-52 2C1 462 - RAWPLOT 26?5-53 2C1462 - INTPLOT 26?5-54 ZC1 462 - FITPLOT 26?5-55 ZC1462 - FITPLOT of the occultation with Fouriersmoothed data. 26?5-56 2C1 462 - POWERPLOT 2?15-57 ZC1 462 - PDPLOT 2765-58 ZC1462 - NOI SEPLOT 2765-5? XI 8607 - RAWPLOT 2805-60 XI 8607 - INTPLOT 2805-61 X18067 - Detailed INTPLOT with 5-point smooth ing. .2815-62 XI 8067 - FITPLOT 2835-63 XI 8067 - PDPLOT 2865-64 XI 8067 - NOI SEPLOT 2865-65 XI 8067 - POWERPLOT 2885-66 ZC220?

5-71 ZC2209 - POWERPLOT 2955-72 ZC3214 - RAWPLOT 3005-73 2C3214 - INTPLOT 3005-74 ZC3214 - FITPLOT 3015-75 ZC321 4 - POPLOT 3035-76 ZC3214 - NOISEPLOT 3035-77 ZC321 4 - POWERPLOT 3065-78 X31 590 - RAWPLOT 3095-79 X31590 - INTPLOT 3095-80 X31590 - FITPLOT 3105-81 X31590 - PDPLOT 3135-82 X31 590 - NOI SEPLOT 3135-83 X31 590 - POWERPLOT*.3155-84 ZC3458

I5-98 XO 1 246 - POWERPLOT 3385-9? ZC0126 - RAWPLOT 3415-100 ZC0126 - INTPLOT 3425-101 ZCG126 - INTPLOT o-f the secondary event 3425-102 ZC0126 - FITPLOT 3445-103 ZC0126i- Detailed FITPLOT with 5-point smoothno. .3445-104 ZC0 1 26 - PDPLOT 3485-105 ZC0126 - NOISEPLOT 3485-106 ZC0126 - POWERPLOT 34?5-107 X01309 - RAWPLOT 3525-108 X01309 - INTPLOT 3525-109 X01309 - FITPLOT 3535-1 10 XO 1 309 - PDPLOT 3555-111 XO 1 309 - NOI SEPLOT 3555-112 XO 1 309 - POWERPLOT 3575-113 ZC3158

5-1 25 XO 1 745 - RAWPLOT 3795-126 X01745 - INTPLOT 3795-127 X07145 - FITPLOT 3835-1 28 X071 45 - PDPLOT 3855-129 X07145 - NOISEPLOT 3855-130 X07145 - POWERPLOT 3865-131 X07202 - RAWPLOT 3895-132 X07202 - INTPLOT 3895-133 X07202 - FITPLOT 3905-134 X07202 - Detailed FITPLOT with 5-point smooth ino. 390.5-1 35 X07202 - PDPLOT 3925-1 36 X07202 - NOI SEPLOT 3925-137 X07202 - POUERPLOT 3955-138 X07247 - RAWPLOT 3985-1 39 X07247 - INTPLOT 3985-140 X07247 - FITPLOT 3995-141 X07247 - PDPLOT 4025-142 X07247 - NOISEPLOT 4025-143 X07247 - POWERPLOT 4045-144 X09514 - RAWPLOT 4065-145 X09514 - INTPLOT 4065-146 X09514 - FITPLOT 4085-147 X09514 - PDPLOT 4105-148 X09514 - NOISEPLOT 4105-149 X09514 - POWERPLOT 4125-150 2C1030

5-152 Distribution function of observed lunar limbsi opes. . .423xx iv

Abstract of Dissertation Presented to the Graduate School ofthe University of Florida in Partial Fulfillment of theRequirements for the Degree of Doctor of PhilosophyTHE OBSERVATION AND ANALYSIS OF LUNAR OCCULTAT IONS OFSTARS WITH AN EMPHASIS ON IMPROVEMENTS TO DATAACQUISITION INSTRUMENTATION AND REDUCTION TECHNIQUESChairman: John P. OliverMajor Department: AstronomyByGlenn H SchneiderAugust 1985A program of observation and analysis of lunaroccultations was conceived, developed, and carried out usingthe facilities of the University of Florida's Rosemary HillObservatory . The successful implementation of theprogram required investigation into several related areas.First, after an upgrade to the RHO 76-cm. reflectingtelescope, a microprocessor controlled fast photoelectricdata acquisition system was designed and built for theoccultation data acquisition task. Second, the currentlyavailable model -f itt ing techniques used in the analysis ofoccultation observations were evaluated. A number ofnumerical experiments on synthesized and observational datawere carried out to improve the performance of the numericaltechniques. Among the numerical methods investigated werexxv

solution schemes employing partial parametric adjustment,parametric grouping into computational subsets (randomly andon the basis the correlation coefficients), and preprocessingof the observational data by a number of smoothing techniquesfor a variety of noise conditions. Third, a turn-keycomputational software system, incorporating data transfer,reduction, graphics and dislplay, was developed to carry outall the necessary and related computational tasks in aninteractive environment.Twenty-four occultation observations were obtainedduring the period March 1983 to March 1934. Theobservational data and the solutions resulting from thesubsequent reductions are presented graphically and tabularlyfor each of the occultation events. Several angular diameterdeterminations were made. Among those of particular interestwere 32 Librae

CHAPTER IINTRODUCTIONLunar Occul tat ions; A Historical SynopsisWhen the moon, as a result o-f its orbital motion, movesin -front o-f a star as viewed by an Earth-based observer, thelight -from the star is obscured. Such an event is known as alunar occultation. At the time o-f the star's disappearance(or reappearance) the moon's 1 imb is seen to move across thestellar disc. MacMahon

2requiring -fast photometric observations. Whit-ford ,reported on observations of occul tat ions o-f Nu Aquarii andBeta Capricorni using a photocell with a Cesium-Oxygen-Silvercathode on the 100-inch telescope. Neither o-f these eventsshowed any deviation in the di -f -f rac t i on pattern -from a pointsource, as his instrumental detection limit was approximately5 mi 1 1 i seconds-o-f-arc . Yet the foundation for a powerful newtechnique for the acquisition of fundamental astronomicalinformation, i.e. stellar diameters, was laid.Over the ensuing three decades additional photoelectricoccul tat ion observations were carried out. The first angulardiameter measurement was reported by Evans (1951) for thestar Antares. This was followed, also by Evans (1959), withthe determination of the angular diameter of Mu Geminorum.Over the next two decades other observations had been made,and additional theoretical work on the extraction ofinformation from lunar occul tat ion observations progressed.It was not until the advent of electronic computers andreliable fast photometric equipment that occul tationobservations could truly begin to be exploited. In a nowclassic series of papers by Nather and Evans (1970), Nather(1970), Evans

3Only in the last few years, with the revolution in bothmicrocomputer and op to-el ec tron i c technology, have the toolsessential to bringing the observation and analysis of lunaroccul tat ions come to -fruition. The problems are still many,but the instrumental hurdle, at least, may now be cleared.Information UJhich May Be Learned From the Analysis o-fLunar Occul tat ionsThe analysis of the lunar occul tation intensity curve,obtained from a fast photoelectric record of an occul tationevent can yield, in principle, a wealth of information. Thedegree to which any observation can be exploited depends upona large number of variables. The geometry of the relativeposition of the moon and the star, the quality of the skyduring the observation (seeing and scintillation), thephysical nature of the source, and the response of theinstrumental system, to mention only a few, can help orhinder the discovery of information hidden in the intensitycurveIn the case of an occul tation of a single star theangular diameter of the star can be determined. Coupled witheither a knowledge of the stellar parallax, or the V and Rstellar flux (Barnes and Evans, 1976) this angularmeasurement can be transformed into an actual lineardiameter. The observational techniques for directmeasurement of stellar diameters are severely limited.Speckle i nterf erometry (Lohman and Weige 1 t , 1980), PhaseCorrelation In terf erometry (Brown, 1968), and Michelson

In terf erome try (Brown, 1980), are the only other currently,ia binary (Evans, 1971) or multiple system (Evans et al .available techniques. All of these are restricted,nstrumen tal 1 y , to the measurement o-f diameters o-f verybright stars.The size o-f extended non-stellar sources such as theemission shells o-f Be stars can be determined (White andSlettebak, 1980) as was investigated in the case o-f ZetaTauri (Schmidtke and A-fricano, 1984). In ideal cases, withmultiple observations the brightness distributions o-f suchsources could be -found.The angular optical resolution achievable throughoccultation observations, on the order o-fmi 1 1 i seconds-o-f-arc , o-f ten leads to the discovery o-f stellarduplicity o-f stars previously thought to be single. Anaccurate determination o-f the separation o-f the components in1977) can be found -from simultaneous observations -from morethan one site (or a projected separation -from a singleobservation). The individual brightnesses o-f otherwise"unresolved" binaries, or multiple systems, can bedetermi ned.The -field o-f chronometry is dependent upon, and enhancedenormously by, the precise measurement o-f the times o-foccultation events. These event timings lead to an accuratedetermination o-f the moon's longitude -from which EphemerisTime is derived. Time intervals are easily obtained with aprecision o-f one part in 10 trillion through the use of

5atomic clocks. The observation of dynamical phenomena musthave a zero point reference to couple dynamical events toatomic time

6dictated the types of stars for which the occultation methodwould be fruitful. The general nature of these constraintshas been addressed by Taylor

7to the United States Naval Observatory, and the InternationalLunar Occultation Center.An outgrowth o-f the lunar occultation program has beenthe observation and analysis o-f occultations o-f stars byasteroids. Such observations typically yield in-f ormat i onabout the size and shape o-f the occulting body, as well asbetter astrometric positions o-f the occulted stars. Over twothousand asteroids are known and have been catalogued(Bender, 1979), and several hundred have orbits determinedwith a su-f-ficient degree o-f precision to allow topocentricpredictions o-f asteroidal occultations to be carried out wellin advance of the anticipated event. Hence, the third aspecto-f this investigation o-f high speed occultation photometryextended the observational domain to asteroidal, as well aslunar occultations.

,CHAPTER IIINSTRUMENTATIONOptical EquipmentThe Seventy-Six Centimeter TelescopeLocation and description . All observations, unlessotherwise noted, were carried out at the University ofFlorida's Rosemary Hill Observatory

Figure 2-1. The seventy-six centimeter Tinsley relectingtelescope at the University o-f Florida's Rosemary HillObservatory.

11optical baffling -for the seventy-six centimeter re-Hectorcould be improved upon greatly. A redesign of the opticalbaffle permitted a reduction in light scattered by thetelescope optics and supporting structure. In addition, atighter baffle system enabled the rejection o-f off-axis rays,preventing them -from reaching the -focal plane.The primary design considerations -for a new baf-flesystem were two—fold. First, any ba-f-fles and/or field stopswould have to be easily removable, so as not to impact on thetelescope configuration required by concurrently runningobserving programs. Second, the unvignetted field of view atthe focal plane had to marginally exceed the field obtainedwith the available diaphragm while minimizing extraneouslight. An Astromechan ics dual channel photometer was theprimary instrument to be used for observing lunaroccul tat ions. This instrument has a maximum diaphragmopening corresponding to a field of view with a diameter ofthirty two seconds of arc.Many designs wereconsidered by constructing models ofthe optical path, and ray tracing paraxial and marginal rays.It became quite obvious early in this investigation that nosingle tube/field stop design would be satisfactory for thetask. The new baffle system would have to consist of twomajor elements: a tube with concentric annular field stops(rings), and an annular ring placed around the Cassegrainsecondary mirror. A schematic representation of the opticalpath is presented in Figure 2-2.

111 (15124uQ.c 01— c-TS—c LenOi nUl c«U OiJDo< 3JZ -w•+•c .

13To satisfy the -first design objective a system of -fieldstops was built into a baffle tube identical at the mountingbase to the existing tube. This would allow easy change-overto either the new or old ba-f-fle tube. The Cassegrainsecondary ring would be be installed on the already existinglocking pins on the secondary mirror ba-f-fle, which serve tohold the mirror cover in place. The new ba-f-fle tube, withthe inner concentric rings removed to show its construction,is shown in Figure 2-3 along with the secondary ring.Since the position o-f the -focal plane varies withrespect to the -fixed position o-f the telescope superstructureand ba-f-fle assembly as a -function o-f temperature, some degreeo-f tolerance had to be allowed in the placement and size o-ffield stops in the baffle tube. The system as designed wouldallow a one minute of arc unvignetted field of view at thefocal plane at 15 degrees Celsius. This rather liberaltolerance was felt prudent considering the wide variation ofclimatic conditions experienced in northern Florida.Table 2-1 gives the specifications for the spacing and sizesof the inner ring stack. The secondary baffle ring has anoutside diameter of 11.375 inches.To actually perform the ray tracing, the optical path ofthe telescope had to be determined. Although the blueprintsfrom Tinsley Laboratories claim the primary is an f/4paraboloid this had to be tested as the engineeringspecifications did not necessarily represent the state of thecompleted telescope.

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16TABLE 2-1SPECIFICATIONS FOR THE OPTICAL BAFFLE TUBERinq Hole Diameter Ring Hole Diameter1 3.56 5 2.242 3.23 6 1.913 2.90 7 1.674 2.57 8 1.24Outside diameter or ring 1: 5.000Outside diameter of rings 2-7: 4.812Thickness o-f rings 1-8: 0.0625Spacing between rings: 5.938Bevel angle -for all 8 holes: 45 degreesNote: All linear measurements are in inches.Using photographic plates o-f regions routinely monitoredby the quasar research program, the plate scale o-f theprimary mirror was -found to be 67.065 (S.E. 0.06) seconds o-farc per millimeter, corresponding to a -focal length o-f117.505 (S.E. 0.11) inches. The scale was determined byPollock

will loosen its seating. When unscrewing the old ba-ffle tubeone hand is kept below the lower end o-f the tube to preventit -from hitting the primary mirror when it is completelyreleased. When screwing the occultation ba-f-fle tube intoTABLE 2-2DETERMINATION OF THE PRIMARY MIRROR FOCAL LENGTH17PLATE DATE S to Q Q to S MEAN DIFF SCALE(mm) (mm) (mm) "/mm4/2-3/72 9.21212.9889.2089.21512.9879.21712.982 12.991 3.774 67.011/30-31/73 10.0241 3 . 79210.02610.03213.79310.02813.796 13.796 3.767 67.142/27-28/76 7.94011 .7407.9797.98811 .7587.98511 .750 11 .753 3.769 67.102/27-28/76 2.7826.5552.7882.7916.5672.7906.560 6.567 3.774 67.012/13-14/77 3.9957.7754.0004.0007.7764.0057.769 7.778 3.774 67.011/28-29/79 19.97222.74918.97118.97222.73618.97522.735 22.742 3.768MEAN67.1267.065(0.06)

position, care must also be taken to assure the tube is notbeing cross-threaded. To switch back to the old tube (whichmust be done if using the infra-red photometer available atRHO) the process is reversed. The Cassegrain secondarybaffle ring slips over the end o-f the secondary containmentcylinder after it has been aligned with the cylinder's threepositioning pins. A small rotation will secure the ringposition insets against the pins.PhotoelectricPhotometersThe Astromechan i13cs photometer . Unless otherwise stated,the photometer used throughout this investigation was a dualchannel instrument manufactured by Astromechan ics. Thisinstrument splits the light path into two beams by means o-fdichroic filters so two wavelengths can be monitoredsimultaneously. Though the instrument can be used in dualchannel mode, observations of lunar occultations obtainedthus far at RHO have been observed only in one color. Thephotometer employs two dry ice cooled photomul t ipi i er tubes

i?TABLE 2-3DIAPHRAGM DESIGNATIONS. LINEAR AND ANGULAR FIELD SIZESLetter Desionation Diameter (mm) Field (arc-sees.)G 1.98 32.5H 1.52 25.00.93 15.2IJ 0.51 8.3Opt ical fi 1 ters . Occultation observations made with theAstromechan i cs photometer employed Johnson V and B -filters,as well as intermediate bandwidth yellow and blueinterference -filters. One inch diameter interference filterswere obtained from Pomfret Research Optics, and aredesignated "y" and "b" respectively. The "y" filter, Pomfretpart number 20-5400-1, has a peak spectral transmission at5400 Angstroms and a Full Width at Half Maximum (FUHM) of100 Angstroms. The "b" filter, Pomfret part number 20-4700-1has a peak spectral transmission at 4700 Angstroms and a FWHMalso of 100 Angstroms. These filters were selected inspectral regions for which M and K stars are relatively freeof major absorption features. Of course, late type stars areriddled with a myriad of spectral lines. Hence the choice ofthese particular filters was somewhat of a compromise.Spectra typical G, K, and M, stars presented by Keenan andMcNeil (1976) were examined, and on average were found leastplagued with absorption lines at wavelengths of 4716 and5408 Angstroms. These would have been the ideal centralwavelengths for selected filters, but the cost of custom madefilters was prohibitive. The filters procured were selected

1to be as close to these wavelengths as possible -from a stocklist. The H-Beta line at 4861 Angstroms is outside of the"b" -filter passband. While other lines are -found at 4716 and4670 Angstroms, the integrated passband is less subject toabsorption losses than adjacent regions. The TiO band at5448 Angstroms enters into the "y" filter passband, but it iscentered close to the lower hal-f-power point.While an actual set o-f narrow band -filters was notavailable, a digital spectrum scanner employing Ebert-Fastieoptics (Parise, 1978) is part o-f the standard equipment atRHO. The scanner can be used in a non-scanning mode as avar iabl e-passband tunable filter. This in fact was done withgreat success in observing the occultation of Zeta Taur i inthe passband of its H-Alpha emission.The portable photometer . A small, lightweightphotometer employing a 1P21 photomul t ipi i er tube and built-inJohnson U, B, and V filters was used exclusively for eventsobserved from remote sites. This instrument is discussed indetail by Chen and Rekenthaler (1966).20TheSPICA-IV/LODAS SystemData AcquisitionElectronicsPes ion criteria for a new SPICA . The concept of a SmalPortable Interactive Computer for Astronomy (SPICA) was firstconceived by Dr. John P. Oliver. The first SPICA system wasimplemented on a KIM-1 computer, and is the precursor to thethree generations of SPICAs which have followed. The common

21thread linking the -first SPICA to the latest version, theSPICA-IV, is the use o-f a 6502 microprocessor. Though eachmajor upgrade to the SPICA systems has involved more hardwarean e-f-fort has been made in SPICA-IV to retain portability, orat the very least transportability.The Lunar Occultation Data Acquisition System (LODAS) isthe so-ftware control program designed to carry out the tasko-f fast photometric data acquisition on SPICA-IV. It is, inactuality, inaccurate to say that LODAS was designed -forSPICA-IV, or SPICA-IV -for LODAS. The system requirementswere such that the hardware and so-ftware grew together in acomplementary -fashion. The major design criteria -forSPICA-IV/LODAS are listed in Table 2-4.TABLE 2-4DESIGN CRITERIA FOR SPICA-IV/LODAS1. Data acquisition rates up to and including 1 kiloHertzmust be supported.2. The system must support a minimum o-f two simultaneousdata acquisition channels.3. Memory space must be provided to hold a minimum o-f twoseconds o-f data in each channel, at a rate o-f 1kHz.4. 12-bit sample resolution should be used, to give a largedynamic range and eliminate last minute gain switching.5. The system should retain easy transportability.6. The system must -function in the abscence o-f a diskdrive, or a disk operating system.7. A user -friendly command structure and display must beimpl emented.8. The control program must reside in Read Only Memory.

In all cases these criteria were met, and in the -firstthree cases they were exceeded.The SPICA-IV digital electronics . The heart of theSPICA-IV/LODAS system is an Advanced InteractiveMicrocomputer, model AIM-65, manufactured by RockwellInternational. The AIM-65 has proven to be an invaluabledesign and development tool -for the LODAS system as well asfor several other astronomical data acquisition systemsimplemented at the Rosemary Hill Observatory. The AIM-65 isan 8-bit microcomputer with sixteen address linesincorporating a 6502 microprocessor chip. Up to 4-kilobyteso-f Random Access Memory (RAM), in the -form o-f paired lK-by-4bit chips (i.e. 2114's> can be accommodated on the AIM board.A 6522 Versatile Inter-face Adaptor (VIA), which is aprogrammable chip holding 16 bidirectional I/O lines, -fourcontrol lines, and two timers, serves as an inter-face to the"outside world" through an expansion connector on back of theAIM board. A standard ASCII keyboard, a 20 characteralphanumeric LED display, and a thermal printer are provided-for user I/O. The AIM-65 accomodates 24-kilobytes o-f ROMspace in five 4-kilobyte Read Only Memory (ROM) sockets,memory mapped in the areas of *B000 to *FFFF. The AIM-65operating system is normally resident in two ROM's occupyingthe uppermost 8-kilobytes of address space.The SPICA-IV/LODAS system uses three boards manufacturedby Micro-Technology Unlimited (MTU) to expand its RAM memoryand to support peripheral devices. The first of these is a

2316-kilobyte dynamic RAM board, model number K-1016

.24The CODOS and its associated programs occupy addressspace in the range of *5000 to *5FFF , and *8000 to *9FFFThe DDDC board also provides an additional 4-kilobytes o-f RAMwhich is mapped in the address range *4000 to *4FFF.Although the disk/CODOS system is an integral part o-fSPICA-IV/LODAS, it is modular. Both the disk drive and theDDDC board may be removed from the system without impairingthe data acquisition capability o-f the LODAS.The -final MTU board is a bit-mapped dynamic 8-kilobyte"visual" RAM high resolution display, model number K-1008

25An additional board, re-ferred to as theAnalog-to-Digi tal Converter/Clock

265.1KI11!w\Hh200K 2 Opt-12#-1N9Uimld"*+ S V 51 K (7)^F ic i rcugurei t2-4. Schematic diaoram o-f the SPICA-IY/LODAS clockFigure 2-5. Schematic diagram o-f one o-f the threeSPICA-IV/LODAS analoo-to-dToi tal converter circuits.

27combination. For ease of operation the clock chip wasinter-faced to the SPICA-IV system through a 6522 on theprotoboard. Thus the LODAS control software commands theclock through the protoboard VIA rather than controlling itdirectly. A schematic diagram showing the implementation ofthe clock circuit is presented in Figure 2-4.The ADCC board also holds three 12-bit Analog DevicesAD-574 analog-to-digital converters, each o-f these memorymapped into two contiguous bytes. A voltage conversion isinitiated by writing to the A-to-D's. A digitizedrepresentation o-f the presented input voltage is obtained byreading the two memory mapped data bytes. The settling timefor these A-to-D's is 35 microseconds. All three A-to-D'smay be used in either a bipolar or unipolar mode, as selectedby switches placed on the front-left edge o-f the ADCC board.In the unipolar mode the dynamic input range o-f the A-to-D'sis zero to 10 Volts. In the bipolar mode the range is-5 to +5 Volts. Since the DC output of the photometeramplifiers used at RHO produce a zero-to-1 Volt negativegoing signal, buffer amplifiers

protocard. In addition inputs to each o-f the A-to-D's may beprovided through miniature phone plugs mounted on the•front-left side o-f the ADCC board.The AIM-45, the three MTU boards and the A-to-D/cl ockboard are mounted on an MTU K-1005 Card File and 5-S1 otMotherboard

along with the disk drive, is packaged separately -fromSPICA-IV/LODAS. For use at RHO the disk drive/power supplyunit is mounted on the bottom shelf of a rolling equipmentcart (see Figure 2-6).2?SPICA-IV system con-f i ourat i on . Figure 2-7 indicates theoverall system con-figuration. All major components includingperipheral I/O devices are shown. Figure 2-8 is a photographo-f the ADCC board. The polarity-mode switches for theA-to-D's are mounted on the top o-f the board, as is a trimcapacitor to adjust the MM-58167 clock rate.The MTU K-1005 card -file holding the digital electronicsboards and the HBB-512 power supply, which comprise the majorcomponents of the SPICA-IV/LODAS system, are packaged in asmall aluminum chassis. All signal and power cables arebrought into the system through connectors on the back plateso as not to be obtrusive during operation. A cooling fan,which can be disabled on cold nights, is also mounted on theback plate of the chassis. Figure 2-9 shows the placementand fucntion of each signal and power connector found on theback plate of the chassis. Figure 2-10 shows the assembledSPICA-IV/LODAS system on its rolling cart in operation atRHO.Portable use . A key element in the system design wasthe need for relatively low power utilization. The portableaspect of the SPICA system had to be retained in order to useSPICA-IV/LODAS in the field. Observations of lunar grazingor asteroidal occultations often require setting up a

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39portable photoelectric station in a dark, secluded site wherethe availability of AC electric power is often non-existent.Thus one reason -for using dynamic < as opposed to static) RAMis its lower overall power utilization, drawing highercurrent only during periods o-f active write cycles.For observing at a remote site AC power is required tooperate not only the SPICA-IV/LODAS system, but a Kepco modelABC-2500M high voltage power supply, an Astronomical TimeMechanisms model 240V DC electrometer amplifier, and a TrueTime Instruments WwVB receiver as well. To provide AC powera Nova model 1260-24 DC-to-AC inverter, running on two12 Volt DC automobile batteries, has sufficient capacity tooperate the entire photoelectric station for 35 hours. TheAC inverter can supply approximately one Ampere at120 Volts AC. Thus, to conserve power, the DDDC board andthe Shugart 801 disk drive are not used. Data are saved tocassette tape after an observed event. Although the invertercan also provide power for the ZDS 12-inch monitor, thisadditional load reduces the working life of the portablepower supply system considerably. Hence, for field use aGold Star 12-inch black and white television with an RFmodulator that had been built-in is used in its place.Though the power required for the television is no less thanthat of the ZDS monitor, it can be run directly on 12 VoltsDC. The source of 12 Volts can be derived from one of thetwo batteries supplying the DC-to-AC inverter. In practice,however, the transporting vehicle's 12 Volt car battery is

.used to power the television as well as the telescope drivecorrector, slewing motors, electric dew cap, and ancillaryequ ipmen tFigure 2-11 shows the SPI CA-IV/LODAS system in -field usewhile observing the asteroidal occultation of 14 Piscium byNemausa on September 11, 1983 (Dunham et al . , 1984). In thiscase AC power was available at the observing site.Figure 2-12, taken on November 13, 1984, shows theSPICA-IV/LODAS system when it was powered by the portablesupply system while observing the asteroidal occultation ofBD +08 471 by Ceres -from the middle o-f the FloridaEvergl ades.Analog ElectronicsThe UJwVB receiver . Nather and Evans (1970) have pointedout that the reduction of photoelectric observations, inprinciple, can yield the times of geometrical occultationwith an uncertainty of only one or two milliseconds. AsTable 2-4 has shown, a primary design criterion ofSPICA-IV/LODAS was to have a data acquisition rate of leastone point per millisecond. The inherent degree of accuracyin overall system timing depends upon both the AIM-65 phase-2clock and the clock on the ADCC board. Thus, in order torealize absolute timing accuracy of one millisecond astandard time calibration source must be employed.This requirement precludes the idea of using HighFreguency (HF) transmissions from the National Bureau ofStandards' radio station WwV (located in Fort Collins,40

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i45Colorado) as a suitable time base reference. The uncertaintyin the HF propagation path arising -from variability inionospheric conditions between Fort Collins and Bronson canlead to timing uncertainties as large as a severalmil I seconds.Fortunately, NBS provides a Very Low FrequencyCoordinated Universal Time broadcast, via radio stationWwVB, which transmits at a standard carrier frequency ofsixty KiloHertz (Kamas, 1977). At sixty kiloHertz the modeof propagation is strictly by ground waves; hence, thevariability in propagation time is removed (Department of theArmy, 1953). The propagation path will simply follow a greatcircle from transmitter to receiver, amounting to a fixedlight-time delay of 7.4 milliseconds at the RHO.WwVB transmits timing information in a tristated timecode. The strength of the carrier wave is modulated byreducing output power for 0.2, 0.5, or 0.8 seconds eachsecond. Encoded in this modulation envelope are the time,date, and current UT1 correction. Each ten-second period andthe start of each new minute are identified by encodedframing references.Detection and interpretation of this signal areprecisely what is needed to provide the timing accuracydesired. Several avenues of approach were debated. Ratherthan having a receiver built, a commercially available unitwell suited to the task was procured. The unit, a True TimeInstruments model 60-T receiver provides not only a detectedcarrier output, but a TTL compatible code output as well.

46A small modification made to the TTL output, dividingit down to 0.3 Volts, permits feeding the code signaldirectly into one of the three A-to-D converters available inthe SPICA-IV/LODAS system. The digitized time code issampled simultaneously along with the photometric channels.The receiver is mounted on a 19-inch equipment rack, shown inFigure 2-13, along with a WwV receiver and the high voltagepower supply used by the PMT's.In actual use the LODAS system clock is set manually bythe observer to an audio wwV signal. This procedure resultsin a clock setting accuracy of a few tenths of a second. Itis then noted if the clock was set fast or slow. DigitizedWwVB second transitions then provide a correction to thenearest millisecond.The signal strength at RHO rarely exceeds 125 microvoltsper meter (True Time Instruments, 1974). An active antenna,model A-60FS, also manufactured by True Time instruments iscurrently used at the observatory. This is marginal undercircumstances of unfavorable reception, and an alternateantenna design is being considered for future use at theobservatory. However, it has been found that eighty percentof the time a decodable signal is available while observing.During nights of signal fading, time code is digitized beforeand after the event as conditions permit and time correctionsto the computer's internal clock are interpolated inpost-observationalreduction.The receiver introduces a measured electronic delay timeof 19 milliseconds from the time of reception of the wWB

Figure 2-13. The wW and WwVB receivers, and PMT highvoltage power supply.

4?carrier to code output. This, however, varies slightly as afunction of signal strength. By attenuating the input signalfrom the antenna it was -found the delay is lengthened to 21milliseconds at a level where the time code cannot bereliably detected. This then sets the limit of the absolutetiming determination to +/- 1 millisecond, meeting theoccultation program's allowable tolerance. All reductionsthen have a final correction of 27.4 milliseconds subtractedfrom the determined time of geometrical occultation, with anadditional error of +/- 1 millisecond added to the formalerror of the solution.Radio antennas . For use at the observatory the receiveris mounted in the telescope main-power distribution rack,immediately above the WwV receiver. These two receiversshare an antenna cable, so only one receiver can be used at atime. The antenna connector must be switched from the WwVreceiver to the WWVB receiver before use. Approximately oneminute is required by the WwVB receiver after being poweredup to lock onto the time code and produce a readable decodedoutput. A twenty-five foot cable terminated at one end witha BNC connector and a three conductor phono plug on the otheris kept on the rolling cart with the SPICA-IV/LODAS system.The BNC end is connected to the CODE output of the WwVBreceiver, and the phono plug end connected to one of theSPICA-IV/LODAS signal inputs. The input channel selected toreceive the time code should be switched to unipolar mode.

50Because of the frequent lightning strikes, unavoidableon one o-f the highest hills in Florida, the U)wV and WwVBantennas are disconnected at the base o-f the antenna tower atthe end o-f a night's observing. A PL-259 connector can befound at the tower base to which the WwVB active antennaconnects via a plug, and the WwV long wire antenna connectsby means o-f an alligator clip. The WwVB antenna and its15-foot antenna cable are removed from its 6-foot highmounting stand and stored above the desk on the first floorof the observatory building.The photometer amplifier . Since millisecond timeresolution is desired, the photometer amplifier used musthave a response at least as fast at a range of gains usefulto the occultation observing program. An Astronomical TimeMechanisms model 240 fast photometric DC electrometeramplifier was choosen. This amplifier described byAstronomical Time Mechanisms (1980) is based on a circuit byUliver (1976) designed specifically with lunar occultationobservations in mind. Amplification is achieved in twostages: first in a current-to-voltage conversion stage; andsecond in a buffer amplifier. A similar amplifier had beenin use at the Rosemary Hill Observatory fourty-six centimetertelescope for several years. Caton

..feedback resistance in the -first ampl i51-f i cat i on stage. Usingthe seventy-six centimeter telescope would yield a gain o-fapproximately one magnitude over the -forty-six centimetertel esc opeThe effective time constant o-f the amplifier is limitedby the high precision megohm feedback resistors and thecapacitance of the input signal cable (added to a capacitanceof 5 pf . , the value of the feedback capacitor used on thesignal input). In order to observe ninth magnitude starswith a 2 kHz half power response, twice that of the targettime resolution, the capacitance of the input signal cablecannot exceed 45 pf . RG-58 A/AU co-axial cable has acapacitance of 28.5 pf./foot. Thus, to achieve this timeresolution for stars of ninth magnitude a cable of this typeno longer than 18 inches must be used. Rather than RG-58,which is commonly used as a signal cable, the occultationprogram uses RG-71/U, with a measured capacitance of 13.1pf ./footFor practicality, the amplifier is mounted on the sideof the photometer cold box as may be seen in Figure 2-9.This allows a short cable run (only eight inches is needed),and is in an extremely convienient place for an observeroperating the photometer. Having the amplifier fixed to thephotometer also permits the signal cable from the PMT to besecurely fastened down thus preventing any possible cableflexure. Such flexure would result in charge redistributionalong the signal cable leading to erroneous fluctuations inthe observed signal level.

52The amplifier coarse gain steps are in increments of 2.5magnitudes, and -fine gain steps in increments o-f 0.5magnitudes. After initial use at the telescope the ampli-fierwas modified to provide a 0.25 magnitude gain switch to boostthe effective gain at any coarse and -fine combination. Thiswas done to provide the observer with a bi t more -flexibilityin chosing the amplification -factor used -for the purpose o-freal-time photometric data display.The output o-f the amplifier is connected to theSPICA-IV/LODAS system by means of a fifteen foot signal cableterminated on both ends with phono plugs. This cable is kepton the rolling cart along with the wWB signal cable. Oneend is connected to the amplifier output marked RECORDER, andthe other end is connected to a SPICA-IV/LODAS input switchedto unipolar mode.Limitations of the Qccultation Photometric SystemOnce obtained, the new amplifier was used to assess thelimitations of the seventy-six centimeter telescopephotometric system and to confirm that stars of reasonablefaintness could be observed while preserving a system timeconstant on the order of a millisecond. Stars over a rangeof six magnitudes were observed on the moonless night of May23, 1981 U.T. with the Astromechan ics photometer, cooled withdry ice, and a Johnson V filter. Measurements were taken atboth the nominal operating voltage of the PMT of1200 Volts DC, and at the maximum operating voltage of

531600 Volts DC. Five minutes of settling time was allowedafter switching voltages before readings were taken. Theobservations, listed in Table 2-5, give the star name, U.T.o-f observation, the star's V magnitude, the photometerdiaphragm used. For both voltages the amplifier coarse andfine gains, and the signal level due to the star (normalizedto a full scale value of 255) are listed. In all cases thedark current and sky background have been subtracted from thestar-plus-sky readings. Gain settings were adjusted to givereadings as close to 65 percent of full scale as possible.TABLE 2-5STELLAR INTENSITY READINGS UITH RHO SPI CA-IV/LODAS1200 Vol ts 1600 Vol tsStar Name U.T. mV Dia. Gain Star Gain StarGamma Leo-a 0315 2.6 J B7 193 B2 17357 UMa 0338 5.2 J C7 173 B7 15388 Leo-a 0401 6.1 J C? 165 B9 14388 Leo-b 0413 8.6 J D10 158 C10 136The fine gain steps of 0.5 magnitude run from "1" to"11". Hence stars with a V-magn itude as faint asapproximately 7 can be observed at a coarse gain setting of"C", at a PMT voltage of 1200 Volts DC. In order to gain onemagnitude observations can be made at 25 percent of fullscale. With twelve bit digitization this is still roughlyone part in one-thousand, or a photometric precision of 0.001magnitude. Alternatively, a gain can be achieved byincreasing the PMT voltage. As can be seen from Table 2-5increasing the PMT voltage to 1600 Volts provides a gain ofapproximately 2.4 magnitudes. However, the penalty of

54increased thermal noise (dark current) must be paid i -f thisoption is taken. Fortunately, the RMS amplitude of the darkcurrent -for the 1600 Volt observation of 88 Leo-b was only2 percent of the star signal level .These observations tend to lead to over-optimisticresults, as occultation observations will not be made in darkskies; indeed the telescope will be pointed in the directionof the moon. To assess a "worse case" condition, the starSAO 098723

55The Lunar Qccultation Data Acquisition System SoftwareSoftware Desion ConsiderationsThe design criteria specified in Table 2-4 were bindingnot only -for the choice of hardware to be used the SPICA-IVsystem, but applied equally, if not even to a greater extent,to the design of the data acquisition and process controlsoftware. The execution of a repetitive task at a preciselydefined rate, which must interact in real-time with the"outside-world" is best accomplished by the technique ofinterrupt processing. Thus, the major process control taskof the LODAS software, real-time data acquisition at a rateof at least one-thousand 12-bit samples per second, in atleast two channels, was relegated to an interrupt serviceroutine. Yet, some functions of LODAS do not have the needfor either repetitive or regularly scheduled execution. Forexample, scanning the keyboard for user requests, or updatingthe 20-character alphanumeric display with system statusinformation can be done at the microprocessor's leisure.Hence LODAS actually operates two concurrent programs. Aforeground program handling all input to, and output fromthe observer runs continuously in a relatively quiescentmode, calling upon system services only when required by theobserver or program logic. This program is repeatedlyinterrupted by the aforementioned interrupt service routine,referred to as the background task, on a regularly scheduledbasis.*

56System timino . The limiting factor which played a majorrole in the development of the LODAS operating concepts wasthe execution speed of the 6502 microprocessor. The system(i.e. microprocessor) clock rate for the AIM-65, as for all6502 systems, is 1-megaHertz. A sampling rate of 1-kiloHertzwould require the evocation of the interrupt service routineevery millisecond. This constrains the process control tasksto a maximum of one-thousand system clock cycles. However,the system cannot spend all of its available clock cyclesexecuting the interrupt service requests. Some percentage ofthe total system throughput must be allocated to theforeground task. Fortunately, the reaction time of anyperson is much longer than the cycle time of a 1-MegaHertzcomputer. This undeniable physiological fact allows a \/erylow bias in time-slicing for the foreground routine. Acomfortable allowance of a minimum of 10 percent was deemedmore than adequate.On average, the execution cycle time for a typicalmachine instruction on a 6502 microprocessor is3.5 microseconds. This means that approximatelythree hundred instructions, at most, could be issued in theinterrupt service routine before interrupt pile-up wouldoccur. The need for rapid execution speed is clear. Forthis reason the LODAS software was implemented in 6502machine language, rather than a more user-oriented, butslower, high level language.

57It was -found that while the task o-f data acquisitionand storage requires less than a half-millisecond, otherinterrupt service requests (such as servicing a video "stripchart" display) would demand a total number of machineinstructions well in excess of the three hundred maximum.Because of this the interrupt service routine wasmul t -phased, handling data acquisition and storage i in eachphase, and pieces of other service requests in successivephases. In breaking the background task into four phases theexecution time for any one phase required less than450-mi croseconds. Hence, the basic system interrupt rate wasdefined as 500-mi croseconds. This allows data to be sampledin successive pairs and averaged together in real-time beforebeing stored. Thus a 1-kiloHertz data sample is actuallycomprised of two 500-mi crosecond pair-averaged samples. Thisnot only effectively increases the signal-to-noise ratio ofthe acquired data by 41 percent, but the stored 1-kiloHertzsamples have a Nyquist cut-off frequency of 1-kiloHertz (halfthe actual data sampling rate) as well.Memory usaoe . The area available for storing data in acirculating event buffer is 18-kilobytes in length. In orderto optimize the use of this limited (but sufficient)resource, two 12-bit acquired and averaged data samples arebit-packed into three 8-bit bytes. This packing,accomplished by the interrupt service routine, saves25 percent over storing the 12-bit data, unpacked, into two8-bit bytes. The 18-kilobytes of available fV*1 are

58partitioned into three 6-kilobyte regions, each to hold onechannel's data. Four seconds of pair-averaged data, acquiredat an effective rate o-f 1-kilohertz, can be stored in each6-kilobyte region. Hence, the system as built and programmedis capable o-f holding twice the amount o-f data originallyenvisioned, and in an additional data channel as well.A modi-fied version o-f the LODAS program, called FASTDAS(Fast Asteroidal Data Acquisition System) partitions RAM intoonly two data storage areas, thereby gaining 50 percent inthe data bu-f-fer circulation length. This program has beenused in observing asteroidal occultations o-f stars fromremote sites (Dunham et. al , 1984).The L0DAS/E07 program has been assembled to reside inROM at an address space o-f *D000 . This allows co-residencywith AIM-65/F0RTH, which is o-f ten used on RHO SPICA systems.Supplementary prooram documentation . The overall logicflow for the LODAS foreground and background (interruptservice) programs, as well as the program initializationprocedure are shown on the operational flow charts presentedas Figures 2-13 and 2-14. A fully annotated assembly listingof the LODAS program is contained in Appendix A. Thislisting reflects LODAS program revision number E07, theseventeenth incarnation of LODAS since its inception. Theassembly listing is preceeded by a detailed accounting of theLODAS memory space in terms of I/O addressing, AIM-65 monitorutilization, program variable space, and an overall systemmemory map. Following the assembly listing is a symbol -table

[—— —60Label Description o-f Program Step( INTERRUPT SERVICE ROUTINE )4INTRCV C Save A, X. and Y-Reqisters on the Stack ]4SNAPCK < Did a Quit A-fter Delay Just Occur? )—NO4 4

STEP1STEP2SETSNP3TEP2BSTEP3STPENDSTPND1STPND2RGET—[[

.62and re-ference list. The LODAS makes extensive use o-finternal subroutines and data tables. Tables 2-6 and 2-7provide a synopsis o-f these routines and data tablesrespect ivel yPeripheralInput/QutputUser (Observer) I/O . The LODAS program was written withease o-f operation in mind. An observer at the telescopeo-f ten has enough problems con-fronting him or her, and anun-friendly computer need not be among them. After poweringup the SPICA-IV, and evoking LODAS, the observer is promptedon the 20-character alphanumeric display to enter theparameters salient to the observing session. The date, dataacquisition rate and channel assignments are among theseinput requests. These parameters may be changed at any timeby issuance o-f a LODAS command. The LODAS commands areactuated by a single keystroke (or -for sa-fety, by depressingthe CTRL key simultaneously with the command key). Thecommand-key assignments are, in most cases, mnemonic to thecommand request. A list o-f LODAS commands is given inTable 2-8. Some o-f the LODAS commands are acted uponimmediately (as in the case o-f EXIT) and some requireadditional in-formation -from the observer. Examination o-fTable 2-8 will reveal the proper responses to any LODAScommand request prompt. These responses are identical tothose required on system initialization when the parametersare -first established.Once the LODAS system initialization is completed theobserver is kept abreast o-f system status on the 20-character

..63TABLE 2-6LODAS/E07 SUBROUTINESNameDescription of SubroutineCLENUP Post tape writing clean-up. Reset interrupt count,clear VIA interrupt -flags, re-enable 0.1 secondinterrupts, restore "Action Code*.CLEAR Clear the 20-character alphanumeric display.COMENT Input comment -from user, up to 40-charac ters inlenoth. Display, print, and store in the tape headerbuffer,

64Table 2-6. Continued.Name Description o-f SubroutineLHWOFA Hal-fword sh i f t to A-register to the right. Zero outthe le-ft hal-fword o-f A-register.OBHXAS Convert a one-digit hex decimal number to ASCII.PACK2 Get two digit BDC number -from keyboard, displaynumber, store as packed BCD in A-register.PNDM Print and display an in-line message.RDCLIN Set up clock to accept a read request.RDCLK Read current time -from clock and store in MILSEC.A, X, and Y registers una-f ected.ROLACT Clear the 20-character alphanumeric display andrestore old "Action Code".TICSET Set up tics, data channel markers and screen lines onvideo display.TIMEGO Start clock running -from keyboard command.i -fTIMSET Interactive clock setting routine. Getcommanded.time anddate -from keyboard. Start clockValidity o-f entry is checked.TOGPRT Toggle AIM-65 printer on/o-f -f .TAPINT Write occultation observation to cassette tape,interrupt request servicing disabled.TUCLEA Clear the video display.TUDISP Output next hi and 1o resolution data points on videodi spl ayTVSET Interactive set-up o-f video display parameters. Getchannel assignments and display rate from keyboard.TVSETX Clear video display and redraw background.WRCLIN Set up clock to accept a write request.WRTAPE Trans-fer a contiguous block o-f data to tape.

65TABLE 2-7LODAS/E07 DATA TABLESName Description o-f Data TableCLCTBL A table o-f packed BCD numbers -from decimal 00 to 99,inclusive. Used by clock and intensity displayroutines to 20-character LED display.TVTICS A bi t mapped data table containing the video displaybackground pattern.TUTBLH The hi byte o-f the address o-f each video displayline as mapped on the visual memory.1 iTVTBLL The lo byte o-f the address o-f each video displayne as mapped on the visual memory.

66TABLE 2-8LODAS/E07 KEYBOARD COMMANDSKey=5LODAS Cold Start:This command, if executed -from the AIM-65 monitor, willtransfer control to the Lunar Occultation Data AcquisitionSystem and begin execution. The system will respond byflashing LODAS R65/E07 on the alphanumeric display andlogging this on the printer. Program de-fault parameterswill be established, and the observer asked -for variable setup parameters. This command is val id only -from the AIM-65monitor and will be ignored once LODAS is in control andrunn i ng.Key=6LODAS Warm Start:To re-enter LODAS -from the AIM-65 monitor while preservingpreviously set parameters use this command. It is assumedthat LODAS was previously cold started, and exited (i.e. toCODOS or the AIM-65 monitor). Warm start will not requireresetting the internal cl ock/cal ander , selecting dataacquisition rates, display channels or the "video stripchart" display rate.Key=Cc Enter a COMMENT:This command will allow the observer to enter a comment ofup to 40 characters in length (two lines) on the printedobserving log. The most recent comment is also retained inthe data buffer header to be saved on disk or tape oncommand. Entering a RETURN in the comment -field willterminate comment entry.Key=Dc Exit To The DISK Operating System (CODOS):This command will terminate LODAS and boot the ChannelOriented Disk Operating System. If a CODOS system disketteis not in the disk drive, and the drive door closed thesystem will -freeze up. CODOS must be entered in order tosave observing data to a data diskette, or load anotherobserving program -from the system diskette. Note: To go•from CODOS to the AIM-65 monitor strike the ESC key. To gofrom the AIM-65 monitor to CODOS, after CODOS had beenpreviously booted strike the F3 key.

67Table 2-8. Continued.Key=Fc Save FILE On Cassette tapeData may be sawed on cassette tape instead o-f a CODOS diskby issuing this command. Be sure the cassette tape recorderis set to RECORD, and that a non-wr i te protected cassette isin the tape recorder. LODAS will ask -for a data FILE name.Any name up to -five characters in length may be entered.Data trans-fer to tape will begin immediately a-fter the entryo-f the -file name. As each block is writen the current blockcount will be presented on the alphanumeric display. Uhenal 1 data has been transferred the message TAPE WRITECOMPLETED will be displayed.Key=Gc Restart System U.T. Clock To Preset Time:

68Table 2-8. Continued.Key=Q QUIT Data Taking:Upon receipt of this command LODAS will cease data takingafter the previously specified delay time. When data takingstops all system status information related to data takingwill be sawed in the data header buffer for possiblesubsequent storage to disk or tape.Key=Rc Select Data Taking RATE:This command is used to select the data acquisition rate.LODAS will ask for the desired rate, which is to be enteredin milliseconds per point. Three digits must be entered.Thus if data is to be taken at five points per millisecondthe entry should be 005. Data may be taken at any rate fromone to 256 milliseconds per point. An entry of 000 willresult in the 256 millisecond per point rate. Data willactually be taken at twice the specified rate and pairaveraged before being stored.Key=Tc Set Delay TIME:The Delay TIME parameter set by this command affects thesystem response time to a QUIT command. LODAS will promptfor the desired time delay to be waited before the systemwill QUIT data taking when commanded to do so. Delay timesare entered in units of 100 times the data acquisition ratein milliseconds. Two digits

69Table 2-8. Continued.Key=Uc Set The UNIVERSAL Time Clock/Calendar:This command will allow the observe to manually reset theinternal U.T. Clock. LODAS will -first prompt -for the theyear, month, and day to which the clock should be seeded.Entry must be in the form of a six digit number. Forexample 850118 will seed the calendar to January 18, 1985.LODAS will then ask -for the day o-f the week, as a singledigit number. Day 1 is Sunday and day 7 is Saturday. LODASwill then request the hour and minute to be entered as afour digit number. Thus 1820 will seed the clock to 18hours and 20 minutes. After these entries are made LODASwill prompt by displaying START=ANY EXIT=CR. If any keyother than RETURN is struck, the clock/calendar willimmediately start running with the seeded values. If RETURNis hit, the seeded values will be stored and theclock/calendar can be commanded to start running at a latertime by issuing a GO command.Key=Vc Set Up VIDEO Display Parameters:This command allows the observer to select which of thethree input data channels is be displayed on the HiResolution Graphics Display, and which is to be displayed onthe Lo Resolution Graphics Display. LODAS first asks forthe input channel number to be assigned to the A

70Table 2-8. Continued,Key=XcEXIT To The AIM-65 Monitor:isThis command will terminate LODAS and return control to theAIM-65 monitor. LODAS may then be restarted with either aCOLD or WARM start. This command should be used i -f CODOSto be re-entered rather than booted. A-fter exiting toAIM-65 monitor use the F3 key to re-enter a previouslythebooted CODOS system.NOTE: A letter designation o-f "c" post-fixing the command key

.alphanumeric display. Figure 2-16 shows the -format o-f thisdi spl ay71HHMMSS M 000 000 128Intensity on A-to-D channel #3:Intensity on A-to-D channel #2Intensity on A-to-D channel Ml: Current (or Last) Command CodeUniversal TimeFigure 2-16. Format o-f the LODAS 20-characteralphanumeric system status display.The A-to-D channel intensities are scaled -from zero to 255.With no input on an A-to-D channel the display will read 000i -f that channel is set to unipolar mode, or 128 i-f thatchannel is set to bipolar mode.All observer commands, command responses, and the currentstatus display are logged on the 20-character thermal printerwhenever a command is issued. The printer can be disabled byan observer command.The video 'strip chart recorder" . Without a doubt,strip chart recorders are the bane o-f photoelectric observersworldwide. Renowned -for clogging up, dripping ink, jammingpaper or spewing it -forth in voluminous quantities, thesedevices, while undoubtedly use-ful, often seem moretroublesome than they are worth. Since the LODAS saves allobservational data in a digital -format on disk or tape thereis no need -for a printed chart record o-f the observations.

72Yet, a chart recorder is an extraordinarily handy tool (whenworking) on the observing -floor, even if used simply tovisually monitor the ongoing photoelectric observations. Anideal chart recorder -for use with SPI CA-IV/LODAS wouldprovide a graphic display o-f the event -for the observer'simmediate inspection, without the necessity o-f plotting itout on reams o-f paper. A -further ideal would be such adevice with no mechanical parts to fail, as they invariablydo, while observing.These ideals were trans-formed to reality with theintroduction of what is now referred to as the video "stripchart recorder". Rather than having the photoelectric and/ortiming signals drawn on a paper chart with an inkingmechanism, data are displayed on a video monitor. The screenis divided into two halves. The left half, called thehi-res, or A-channel display, has a resolution of0.25 percent

The video "strip chart recorder" is best thought o-f aseither a vertical two-channel programmable storageoscilloscope, or a chart recorder with a -fixed paper andmoving pen. When the pen hits the bottom o-f the page, thenext point will be plotted on the top o-f the page as thepoint previously there is erased.The LODAS activates the video "strip chart recorder"when an Integrate command is issued, and -freezes the displaywhen a Quit command times out. A sample video "strip chartrecorder" display is seen in Figure 2-17. The number o-fshort dashes at the top le-ft and top right o-f the displayindicate which A-to-D channels have been assigned to thehi-res and lo-res portions o-f the screen respectively. Theshort horizontal dashes (on the same line -for both hi andlo-res) indicate where the cursor ("chart pen") was when dataacquisition stopped. Tic marks on top and bottom indicatethe 25, 50, and 75 percent signal levels for the hi-resdisplay, and the 50 percent level -for the lo-res display.Data arch ival . Post-event observing data may be storedon either 8-inch -floppy disks or on cassette tapes. To savedata to disk the observer should command LODAS to enter thedisk operating system (CODOS), save the observing data byissuing the command: SAVE -filename 0700 4FFF, and thenre-enter LODAS (if more observations are to be made) with awarm-start. To save data to cassette tape the LODAS Fccommand is used. Approximately 10 minutes are required tosave the observing data to cassette tape.73

Figure 2-17. The SPICA-IV/LODAS and the video "strip chartrecorder" display.

calCHAPTER IIINUMERICAL MODELING OF LUNAR OCCULTATIONSThe Physical Characterization ofan Occultation Intensity CurveWhen the moon occults a star the lunar limb acts as adiffracting aperture. As the moon's limb approaches the star(as seen topocen tr i cal 1 y) the intensity of the starlight isseen to vary as a result of this diffraction. Atopocentr ical 1 y stationary observer sees the diffractionpattern projected onto the Earth's surface moving due to theorbital motion of the moon and rotation of the Earth. Thetime variation of the intensity of starlight diffractedaround the lunar limb under ideal conditions would becharacterized by the parameters listed in Table 3-1.TABLE 3-1PARAMETERS CHARACTERIZING AN OCCULTATION INTENSITY CURVE1. The topocentric distance to the limb contact point.2. The angular velocity of the lunar limb, as measuredtopocentr i 1 y, projected onto a line joining thestar and the point of contact on the limb.3. The peak wavelength, or spectral energy distribution ofthe star

i rreguThe actual observed diffraction pattern, referred to asan occultation intensity curve, is affected by severalnon-idealized distorting effects. These effects are listedin Tabl e 3-2.TABLE 3-2PARAMETERS AFFECTING THE OBSERVED INTENSITY CURVE771. The contribution o-f background skylight due to bothatmospherically scattered moonlight, and Earthshinealong the lunar limb.2. The local slope o-f the lunar limb due to surface1 ar i ties.3. Noise in the observation due to both scintillation andphoton statistics.4. The spectral response characteristics o-f the opticalsystem (mirrors, windows, lenses, -filter, and PMT).5. Instrumental e-f-fects such as PMT dark current and theelectrical bandpass of the electrometer amplifier.The observed occultation intensity curve results -from acombination o-f the e-f-fects o-f the parameters given in bothTables 3-1 and 3-2. The process o-f "solving" a lunaroccultation intensity curve involves isolating or removingthe distorting e-f-fects and determining the individualparameters intrinsic to the star. The topocentric lunardistance and projected angular velocity (referred to as theR-Rate) can be computed from the moon's orbit. Theinstrumental parameters can be determined through calibrationof the instrumental system. The other intrinsic parametersare determined by a process of fitting an intensity curve,computed from a set of model parameters, to the observedintensity curve. The generation of the computed intensity

curve and the fitting procedure will be addressed in detail73in this chapter .The Generation of a Model Occultation Intensity CurveMonochromatic Point Source ApproximationThe process o-f the -formation of a model occultationintensity curve adopted in this study essentially follows themethod as outlined by Nather and McCants

i7?straight-edge to observer distance. A typical intensitycurve resulting -from the de-fining equations,

i80STARD'4321 13-1-2 j iFRESNEL NUMBERFigure 3-1. Lunar occul tat ion intensity curve -for amonochromatic point source.U-3 -4Figure 3-2. Example o-f a two dimensional grid used todiscretely model a stellar quadrant.

81distorting effects on the occultation intensity curve arediscussed in detail by Evans (1970). Morbey hascompiled an catalog showing the nature o-f these e-f-fects -for avariety o-f sur-face discontinuities.The e-f-fect upon occultation intensity curves by lunarsur-face structure along the line o-f sight was investigated byMurdin < 1 971 > and found to be negligible.A Monochromatic Extended Source and Limb Darken i noA star, however, is not a true point source, but has a•finite angular diameter. I-f the star is assumed to bespherically symmetric then the visible disc projected ontothe plane o-f the sky will have a circular cross-section. Inmost cases spherical symmetry is certainly a valid assumptionto make. The vast majority o-f stars which can yield sensiblediameters are o-f late spectral type and hence are not likelyto be rotationally distorted out o-f spheroidicity (Tassoul,1978). In the special case of occultations of close binariesthe tidal distortions and effects of possibly rapid rotationacting on the component stars would cause the sphericalsymmetry argument to break down.The computation of the diffraction intensity for anextended circular source is handled by dividing the disc intoa series of discrete elements as shown in Figure 3-2. Thetwo dimensional grid used to partition the model stellar discis linear in one dimension and radial in the other. Thepartitioning of the model disc into radial zones allows theeffects of limb darkening to be modeled discretely. The

A

For convenience, the degree of the partitioning of themodel stellar grid is referred to as the grid parameter.The grid parameter is the square root o-f the number o-fsurface elements per quadrant on the model stellar disc.Thus a grid parameter of 6 would refer to a grid containing36 elements. Since the grid elements are actuallyrepresented in a rectangular coordinate system, thoseelements which fall outside of the stellar disc have zerointensity. Table 3-3 shows the elemental contribution ofeach surface element as a percentage of the total intensityof the entire model disc. This is a non-limb darkened starwith a grid parameter of 6. In this table element is closest to the center of the stellar disc. Thetotal intensity of this quadrant has been normalized to25 percent.TABLE 3-3BRIGHTNESS DISTRIBUTION FOR MODEL STAR UITH GRID PARMETER=633S# Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Sum6 0.88918 0.89174 0.89697 0.91095 0.99722 0.69444 5.280505 0.00000 0.92110 0.94177 0.98906 1.19189 1.08612 5.129934 0.00000 0.00000 0.99725 1.07606 1.37182 1.36939 4.814513 0.00000 0.00000 0.00000 1.16089 1.53335 1.60326 4.297502 0.00000 0.00000 0.00000 0.00000 1.68034 1.80708 3.487431 0.00000 0.00000 0.00000 0.00000 0.00000 1.99012 1.99012The relative attenuation of the zonal intensity due tolimb darkening is modeled by a simple linear limb darkeningfunction of the formI/I = + ycos(O) [3-6]where Y is the limb darkening coefficient, and is the angle

etween the star's radius vector and the line of sight.Table 3-4, which is similar to Table 3-3, shows the relativeintensity o-f the surface elements o-f a fully limb darkeneddisc with a grid parameter o-f 6. The e-f-fects o-f limbdarkening coe-f -f i c i ents o-f values 0.0, 0.2, 0.4, 0.6, 0.3 and1.0 are depicted in Figure 3-3. This -figure shows therelative intensity o-f each linear strip on the model discfrom the center o-f disc to the edge. A grid parameter o-f 100was used in this illustration. The maximum variation -foundin the intensity distributions was -for limb darkeningcoe-f -f i c i ents o-f 0.0 and 1.0, and was only 13 percent.TABLE 3-4BRIGHTNESS DISTRIBUTION FOR MODEL STAR WITHGRID PAREMETER=6 AND A LIMB DARKENING COEFFICIENT OF 1.034Stt Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Sum6 0.52257 0.86735 1.07134 1.21774 1.41985 1.01764 6.116485 0.00000 0.54132 0.91601 1.18132 1.59329 1.54643 5.778384 0.00000 0.00000 0.58608 1.04663 1.63850 1.83057 5.101773 0.00000 0.00000 0.00000 0.68225 1.49142 1.91493 4.088592 0.00000 0.00000 0.00000 0.00000 0.98753 1.75766 2.745191 0.00000 0.00000 0.00000 0.00000 0.00000 1.16958 1.16958The observed di -f -f ract i on intensity o-f a monochromaticpoint source o-f intensity unity at a -fixed distance -from theobserver is dependent only on the distance of the source fromthe diffracting aperture. In the limit, each surface elementis essentially a point source. Those point sourcesequidistant from the lunar limb (i.e., along the same strip)will result in an observed diffraction intensity whose totalintensity is the linear sum of the individual intensities.Hence, the strip itself can be treated as a point source.

85«01 LAUSN3_LNICBZriVWUON— j:

Equation 3-1 may be computed -for each linear strip, S. TheFresnel numbers, U s, for the points o-f evaluation of eachstrip will be of-fset by an amount corresponding to theseparation of the center of each strip and the occultingaperture. The intensities, I ,sare the fractional normalizedintensities for the corresponding strips. Thus, theintensity curve resulting from a grid of individual elementsis computed as the linear superposition of strip intensitycurves, F S. This is shown graphically in Figure 3-4.The uppermost curve is the linear sum of the individualcurves shown. The sum curve is shown at a reduced scale sothe details of the component curves can be seen on the samefigure. In this example the resultant curve is that of a10-mi 1 1 i second-of-arc source, at a distance of 375,000Kilometers, and an angular velocity of 0.3 seconds-of -arc persecond.PolychromaticIntensity CurvesThe monochromatic approximation to the occultationintensity curve is sufficient to model observations takenwith a narrow bandwidth filter (less than 50 Angstrom FWI-W) .In order to model intensity curves over a broader bandwidthindividual model curves, of the monochromatic type describedabove, must be computed for a number of discrete spectralregions, approximating the contiguous spectral energydistribution of the source. Each individual curve, computedfor a specific wavelength, is intensity weighted by the86

ifi•37OP*»£ a—OiinCM.CMJSIS.CM?X-M._tfcu a>— 4->*> cits—i- L1 3U. TJ UCa>• u uq- a, L.1 U1 Z>en —wmm L. — -m3 E c0) •—1— OU. — a.

88relative total power of the source in that particularspectral region.In the actual case o-f stellar modeling, a blackbodyspectral energy distribution is assumed. The total powerradiated by the star -for a spectral region centered at awavelength, Xj , and o-f spectral bandwidth 2B isE:1=Xi+ 5 1 -*f f26729X

I3?T3Oj^-CO

.fractional contribution o-f Ej

The effect of choosing too -few strips to represent thedisc is easily seen in Figure 3-6. This -figure shows afamily of model occultation intensity curves for a10-mi 1 1 i second-of-arc star, similar to the model shown inFiqure 3-4 for a variety of grid parameters (as indicated onthe vertical axis). In this example the bandpass provided bythe intermediate bandwidth "y" filter was used. Choosinggrid parameters of 8 or larger caused no discernibledifference in the intensity curves.The model fitting procedure, which will be discussed,generally would use a grid parameter of 8, sufficient for allbut the very largest sources. If the fitting procedureindicated a source larger than 5 mi 1 1 i seconds-of-arc , are-fit was attempted using the roughly determined parametersand a finer grid parameter.In order to determine the appropriate spectral width touse in discretely modeling an observed optical passband,model intensity curves were generated for sources of 0, 5,10, and 20 mi 1 1 i seconds-of-arc with a grid parameter of 20.Each of these were "observed" with a Johnson V filter whosebandpass was modeled in spectral regions of 500, 200, 100,50, and 10 Angstrom widths. In all cases 50 Angstrom stepsacross the bandpass were required to achieve a worst caseprecision of 0.05 percent.The Effects of Instrumental Optical ResponseThe instrumental response of the optical system affectsthe measured spectral energy distribution of the source, and91

i9250 100 150TIME IN MILLISECONDS200 250Figure 3-6. The effect of discrete modeling on a10-tni 1 1 isecond-of arc curve for the grid parametersndicated.

)93hence must be included in the -formation o-f the modelintensity curve. Thus, the relative power in each spectralregion -from the source, Ej(Xj), computed by Equation 3-7 mustbe modified by the instrumental response -function. Theintensity o-f light measured in a wavelength regimecontributes -fractionally to the light passing through theintegrated bandpass -for a given -filter. Tables o-finstrumental response, reflecting the -filter -function -foreach of the filters actually used in the observations, wereconstructed for this purpose. The model un-occultedintensity of the bl ackbody source, Ij, in a given spectralregion, Xj , corrected for the instrumental response is simplyIj= E,

94simple case of F

95through the analysis o-f lunar occultation observations, themore conventionally held concepts o-f "wide" and "close"binaries are not applicable. In the context o-f discussingoccultation binaries the term "close" does not necessarilyrefer to contact, or semi -detatched systems. Rather, there-ference here is to the apparent angular separation o-f thecomponents. Occultation binaries which are considered "wide"undergo disappearances which are well separated in time.Spec i -f i cal 1 y, i -f the intensity curve resulting -from the thedisappearance o-f the -first star has essentially converged toits post-occul tat i on level be-fore any significant -fringinge-f-fects are seen due to the disappearance o-f the second star,then the system is considered "wide". Typically, wideoccultation binaries are separated by more than 50milliseconds o-f arc. Widely separated double stars

component stars and linearly superimposing them (along with aconstant sky background).A model intensity curve computed -for close occultationbinaries (referred to as the two-star case) uses the same•filter and systemic response matrix, as well as backgroundsky level -for both stars. Individual stellar diameters,times of geometrical occultation, pre-occul tat ion stellarintensities, and velocity parameters are employed. Thevelocity parameters, in principle, would be the same -for bothstars, i-f the lunar limb were smooth. However, since thelunar surface undulates, the contact points o-f geometricaloccultation for the individual stars may have differentslopes and therefore different projected angular velocitiesof lunar limb passage. If the individual spectral types ofthe component stars are known, then different effectivephotospheric color temperatures should be employed incomputing the stellar spectral energy distributions.96The Differential Corrections

time of geometrical occultation is unknown, and indeed is oneof the parameters -for which a solution is sought. Thus,throughout the -fitting process times are referenced to thetime o-f the -first point in the observed data set. Units oftime are referred to in milliseconds as this is mostcommensurable with the time-scale of the occultationphenomenon. All observations to which the fitting procedurehas been applied have been made with 1 -mi 1 1 i second sampling.Thus, for convenience, the term "bin number" is often usedinterchangeably with "time with respect to data sample numberzero". After the time of geometrical occultation has beenfound by the fitting procedure it is referenced toCoordinated UniversalTime.Choosing, Initial Parameters for the DC ProcedureThe fitting procedure is basically an iterative,non-linear least squares, differential corrections processfollowing the method outlined by Nather and McCants (1970).Initially, a model curve is generated from physicalquantities and model parameters listed in Table 3-5.The choice of initial parameters in some cases is quiteobvious. The number of points to be generated in the modelmust be the same as the length (i.e. number of data points)extracted from the 4096 milliseconds of observational datawhich is to be fit to a model curve. The selection of thisextracted data set must be done by visual inspection, androughly centering the subset on the apparent time ofoccultation. The specification of the filter response table97

98TABLE 3-5PARAMETERS FOR GENERATING THE INITIAL MODELModel Generating and Control lino Parameters1. The number o-f points to be generated in the modeloccultation intensity curve.2. Specification o-f the filter/systemic response table.3. Maximum number o-f iterations to executed in thecorrections procedure.4. Fraction o-f computed adjustments to be applied at eachiterative adjustment step.Fixed PhysicalParameters1. The topocentric distance to the lunar limb.2. The predicted R-rate, based on a smooth limb (seconds o-farc per second)Normally Fixed PhysicalParameters1. The e-f-fective color temperature o-f the stellarphotosphere2. The stellar limb darkening coe-f -f i c i entAdjustableParameters1. The stellar angular diameter.2. The pre-occul tat i on intensity o-f the star plus thebackground skylight.3. The velocity o-f lunar limb passage.4. The time o-f geometrical occultation.5. The post-occul tat i on intensity o-f the backgroundskyl ight .

9?must obviously match the instrumental set-up used inobtaining the observational data.The next two parameters are concerned not with theinitial model generation, but with control of the adjustmentprocedure. The number o-f iterations required -for aconvergent solution depends strongly on the signal-to-noiseratio o-f the observations. Experimentation with thenumerical and computational processes suggests that a maximumo-f 10 to 20 iterations is usually su-f -f i c i en t . The -fractiono-f computed adjustments will be discussed in the section onthe application o-f partial parametric adjustments.The -fixed parameters have already been addressed. Inprinciple, there is no reason why the two parameters listedas "normally -fixed" could not be treated as adjustableparameters as well. However, the model is rather insensitiveto the effects of limb darkening, and as previously indicatedstellar temperature (within the normal accuracy determinedfrom the spectral type, and if available luminosity class).Unless there is an astrophysi cal 1 y compelling reason, a limbdarkening coefficient of 0.5 is suitable in virtually allcases.The stellar angular diameter, unless previouslydetermined by another occultation, or in rare cases byi nterf erome tr i c methods, is unknown. As already mentioned aninitial guess can be made on the basis of the star's parallaxand spectral type, or by application of the Barnes-Evansrelation. However, an initial guess of a

100"mi ddl e-of-the-road" value such as 5 mi 1 1 i seconds-of-arc willbe adjusted rather quickly even i-f grossly wrong.The initial ouess -for the velocity of lunar limb passageshould be the R-Rate, as any variation -from the predictedrate would be due to a local slope o-f the lunar limb. Thisslope, in -fact is derived -from the difference between thepredicted and observed velocities. The numerical procedureactually works with a linear, rather than an angular rate.Thus the lunar limb distance is used in conjunction with theR-Rate to compute the L-Rate, the linear rate o-f the motionof the geometrical shadow across the telescope in units o-fmeters permillisecond.Initial values -for the pre and post-occul tat i onintensities can be determined by averaging the intensity o-f afew hundred milliseconds of data before and after the time ofgeometrical occultation. The time of geometrical occultationcan be estimated from visual inspection of the observedi ntensi ty curveParametric AdjustmentOnce an initial model curve is computed, each of theadjustable parameters in turn is varied by a small percentagein order to numerically compute the partial derivatives ofthe intensity curve with respect to each of the parameters.Analytic evaluation of the partial derivatives is obviouslyimpossible as the intensity curve itself is determined fromdiscrete numerical functions. Due to different degrees ofsensitivity of the intensity curve to numerical variation of

101the parameters, and indeed to the values of the parametersthemselves, experimentation was required to ascertain anoptimal percentage variation to use. This would present noproblem if an analytic -form -for the computation o-f thederivatives existed. Choosing a variation which is too smallresults in computational truncation errors anddiscontinuities in the partial derivatives. Too large avariation results in a loss of computation precision. It wasfound that -for most ranges in the values of the parametersthat a numerical variation (multiplicative -factor) o-f 1.001was applicable -for the intensities and time of geometricaloccultation. The partial derivative o-f the intensity curveproved better behaved with a variation o-f 1.005 for thevelocity parameter, and 1.02 -for the stellar diameter.Since the diameter can go to zero -for a point source,numerical limits must be put on the variation procedure toassure no computational singularites arise. This is alsotrue, conceptually -for the velocity parameter as well (and inthe unrealistic case o-f no background sky contribution thepost-occul tat i on intensity). However, this would beimportant only for true grazing incidence which is virtuallynever seen. Hence, as the angular diameter or the projectedvelocity (or both) approach zero the variation of theseparameters in computing the numerical partial derivativesshould be increased accordingly.

.iOnce the partial derivaties have been computed a matrixof residual equations o-f the -form102n £C:- = - AP-. 0: C: 2 — 13-93iJ J j=1 &Pcan be established. The Pj's are the varied parameters,n is the number o-f parameters in the model (normally 5), theC: s are the computed intensity values, and the 0j s are theobserved values. The .dPj's are the adjustments to be appliedto each o-f the parameters. These adjustments are determinedby solving the residual equations by the method o-f leastsquares and is discussed in a general -formulation by Brown(1955)Eichhorn and Clary (1974) have suggested that when theadjustment parameters derived -from non-linear equations ofcondition are not significantly larger than the adjustmentresiduals, then the second order terms should be included inthe adjustment residuals. However, as can be seen,Equation 3-9 has been linearized, and hence does not includehigher order terms to represent the non-linear equations.This was done primarily -for a practical reason. Thenumerical evaluation o-f the -first derivatives o-f thenon-linear, non-analytic equations alone is alreadycomputationally extensive. The actual computer time requiredto arrive at a solution is discussed in the section oncomputational procedures. The additional computationsrequired -for the inclusion of the higher order terms in the

103solution were computationally prohibitive with the computerresources available.As a result of this linearization the derivedadjustments are not completely correct. Thus, theadjustments must be applied to the parameters, and theprocess repeated until convergence is achieved. Fortunately,the least squares process is suff i c i ent 1 y robust thatconvergent solutions (with less than 1 percent change insuccessive adjustment attempts) were usually achieved for allparameters in less than a dozen iterations of the adjustmentprocedureThe DC Fitting Procedure for Close Double StarsA procedure analogous to the single star DC fittingprocess previously discussed is followed in the case of aclose double star. In this case, refered to as the DC2procedure, if the limb darkening coefficients of the stars,and photospheric temperatures are held constant, then themodel is parameterized by nine adjustable quantities. Theseare listed in Table 3-5 as "Adjustable Parameters" numbers 1through 4 (for each star) and the background skylightintensity (item 5). Hence, Equation 3-9 is the same as inthe single star case, with n=9 instead of n=5.The choice of initial parameters for the two-starfitting procedure is similar to that of the single star case,though "good guesses" for the starting values of someparameters are more difficult to select than for the fittingof a single star model. Since the observed curve is actually

,the linear combination of the two single star curves, theapproximate times o-f geometrical occultation and theindividual pre-occul tat i104on stellar intensities are not easilydetermined by visual inspection. Though the DC procedure isquite forgiving -for even wildly disparate initial parameters,the required computation time -for convergence can be reducedby giving some thought to the starting parameter selection.To serve as a guide to selecting the initial time andintensity parameters, a -family o-f model curves was generatedfor a series o-f monochromatic double stars considered aspoint sources. The curves covered the range of stellarseparation in Fresnel space from U = -2.5 to U = +2.5 insteps of 0.2, and a range of magnitude differences of 0.0 to2.5 in steps 0.5 magnitudes. By comparing these against theobserved intensity curve, a reasonable match could usually befound. The parameters used to generate the selected modelcurve were then applied to the particular two-star DCsolution under consideration.The task of generating the simple monochromatic two-starmodels from point sources was relegated to a desk-topmicrocomputer (Commodore SP9000) . The computation of theFresnel intensity curves (Equation 3-1), by the numericalintegration of the Fresnel integrals (Equations 3-2a and b>and the production of the 306 graphs of the two-starintensity curves required 25 hours. However, this only hadto be done once, and a compendium for future guidance inparameter selection was created. Figure 3-7 is a sample of a

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106two-star curve extracted -from this compendium. In this casethe star which disappeared -first is the -fainter star

107parametric guesses for the adjustable parameters weredeliberately chosen to be far from the correct values. Inevery case the DC fitting process converged rapidly

terms of relative amplitudes) of the noise, and the temporal108variation in the stochastic noise on time-scales shorter thanthe length o-f the synthetic data set. Rather than make suchassumptions, noise which was actually observed, as extractedfrom a pre-occul tat ithe synthetic curves.on observational record, was applied toThe character o-f the observational noise would bedi-f-ferent -for each observed occultation, and in fact is a-function o-f the local seeing and scintillation e-f-fects andphotometric signal-to-noise ratio (as will be discussed inChapter 5). Thus, ideally, it would have been pre-ferable toconsider all o-f the above synthetic cases under a variety o-fobserved noise conditions. However, due to the limitedsystem throughput on the computer employed in thisinvestigation, a compromise had to be made.The noise characteristics o-f the occultation observationo-f ZC0835 were found to be nicely representative in terms ofthe noise figures and power spectra seen in most of theobservational records. The distribution function of theobservational noise obtained from this observation wasapplied to the synthetic models, and the noisy models thenre-reduced by DC and DC2, with the same initial startingparameters used in the first trials.Once again, the model parameters were essentiallyrecovered; however, three effects were noticed. First, andsomewhat expected, the formal errors of the solution weresignificantly worse than in the "clean" synthetic cases.

10?Second, the number of iterations required -for the DC model toconverge was increased by roughly a -factor of -four. Andthird, -for the corresponding trials where DC2 solutions werepreviously obtained, the DC2 procedure would notasymptotically converge to recovering the solutionparameters. Rather, after initial movement towardconvergence, oscillation about some set of final values wouldset in. The amplitudes of these oscillations were often asoreat as 100 percent of the mean values about which theparameters were oscillating. This effect was also seen, butto a much smaller degree, in the DC solutions.While this behavior (except for the recalcitrant DC2solutions) was not unacceptable it lead to a number ofnumerical experiments in an attempt to improve the basic DCand DC2 fitting procedures.Numerical Experiments to Improve the Fitting ProcedureTwo types of improvements were sought to enhance boththe utility of the fitting procedures and the statisticalsignificance of the numerical results. First, from apractical standpoint, it was desired to reduce the amount ofcomputation time required to achieve a convergent solution.Second, the DC procedure, (and usually DC2 as well), couldsuccessfully recover the physical parameters intrinsic to theintensity curve in question; it was of interest to see if theformal errors of the solution parameters could be reduced.

110Addressing the first point, it was noticed that thefittinq process would approach convergent solutions ratherrapidly in most cases. But, on occasion, rather than smoothlyapproaching the true parametric values (i.e., those used togenerate the synthetic curves), the numerical values o-f theadjustable parameters would oscillate about someundetermined, final values. This effect was usualy small forthe five parameter DC fitting process but often was quitepronounced for the nine parameter DC2 routine.Since the residual equations had been linearized, aspreviously discussed, the adjustments applied at the end ofeach iteration step tended to overcompensate for the factthat the higher order terms had been omitted. Thus, as thesolution was approached, the adjustments to the parameterscomputed from the residual equations would overcorrect theinterim values of the adjustable parameters, and thereby leadto the noted oscillations.The uppermost set of graphs in Figure 3-8 shows theprogress of the DC fitting process as the adjustableparameters approached their final values through twentyiterations of parametric adjustments. From left to right theparameters presented are the angular diameter,pre-occul tat ion intensity, post-occul tat i on intensity, timeof geometrical occultation and L-Rate. The correct values(those used in generating the synthetic curve) are indicatedby the dashed lines. This example is from the DC fitting ofan 8 millisecond of arc star, with observational noise addedto the synthetic curve as specified in the previous section.

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113In this case, the noise was taken from the residual amplitudedistribution -function for the occultation observation of2C1221 (see Figure 5-19). The mean value of thisdistribution function is skewed negatively by 1.706 percent.(The physical reasons for this skewing, and the Poissoncharacter of some of the observed residual distributions areaddressed in Chapter 5.)The negative bias (or offset) in the noise was notcorrected before application to the synthetic curve. Hence,there was an expectation that the pre-occul tat ion andpost-occul tat i on intensities would be underestimated, and theL-Rate overestimated by this amount. This expectation wasindeed borne out, within the one sigma uncertainties of thefinal parametric solution values.The model generating parameters, and parameters for thebest solution determined by the DC procedure, are presentedin Table 3-6. The table indicates that the best solution, asdetermined by the smallest value of the sum of the squares ofthe residuals, was achieved on the fourteenth iteration. Theparenthetical values are the one sigma uncertainties in theformal errors of the solutions. It should be noted thatwhile the best solution required fourteen iterations, afteronly four iterations the interim values for all theadjustable parameters were not significantly different fromthe later determined best parametric solutions.Application of Partial Parametric AdjustmentsTo reduce the degree of oscillation about the finallydetermined values of the solution parameters, the DC process.

'114starting with the same initial values, was run again with oneminor change. Rather than applying the -full correctionsderived -from the linearized residual equations, only partialcorrections were made at each iteration step. The initialtests o-f the partial corrections procedure applied afractional correction factor, denoted ^, of 0.5 (i.e. onlyhalf of the computed adjustments were applied to each of theinterim values of the parameters at the end of each iterationstep. If the adjustments at the end of each step had beenabsolutely correct (which they were not) then the solutionswould be approached asymptotically. In that case, aftern-iteration steps the current value of a given parameter, Pjwou 1 d bePj,n * p i,s+ "» " * n >'< p i,0 " p i,s>l C3 " 10]where Pj is the initial guess for the i tn parameter, andP: _ is the true value of the tni parameter.Thus, after ten iterations the interim solutionparameters would converge to better than 0.1 percent of theirtrue values. Of course, s need not be given a value of 0.5.If a larger value is used the true parameter values areapproached more quickly, but larger amplitude oscillationsset in after initial convergence has begun.The middle set of graphs in Figure 3-8 shows a typicalhistorical run of the solution parameters with a partialadjustment of s = 0.5. As may have been expected, the bestsolution was obtained on the last iteration. By that time,however, the variations in the parameters from one iteration

115to the next were insignificant. Table 3-6 shows that theparametric solutions obtained -for the DC -fitting with partialadjustments (^=0.5) were essentially identical to thoseobtained using the -full parametric adjustments

116TABLE 3-6COMPARATIVE SAMPLE OF DC FITTING TO SYNTHETIC CURVEPARAMETERS FOR SYNTHETIC INTENSITY CURVEDistance (km): 375000 Diameter (ms. o-f arc): 8.0# of Points (msec): 200 Time (milliseconds): 101.0Temperature: 4500 Pre-Event Intensity: 1495.4Limb Darkening 0.5 Post-Event Intensity: 498.5Filter: Johnson V L-Rate (meters/s.>: 545.4Grid Parameter: 8Smoothing Raw Raw 150 Hertz^ 1.0 0.5 0.5-METHOD OF DC SOLUTION--SOLUTIONS-Iterations 14 20 20Diameter 8.10 (1.28) 8.12 (1.28) 8.10 (0.75)Time (msec) 101.2 (0.65) 101.2 (0.65) 101.2 (0.38)Pre-Event 1471.3 (10.3) 1471.2 (10.3) 1471.2 ( 6.3)Post-Event 489.4 (10.4) 489.2 (10.4) 489.2 ( 6.1)Velocity 572.8 (18.6) 571.4 (18.8) 572.6 (10.7)

117It was of interest, however, to evaluate a computationalprocedure discussed by Wilson (1976), and to determine itsapplicability to -fitting lunar occultation intensity curvesby non-linear least squares, differential corrections. Indetermining his solution to the light curve of the eclipsingbinary TX UMa, Wilson encountered similar difficulties. Theapproach he suggested, of dividing the adjustable parametersinto two subsets which were adjusted independently, wastried. When coupled with the procedure of using only partialparametric adjustment, this parametric subgroup ing method wasfound to yield convergent solutions, but not as rapidly as byadjusting all nine parameters simultaneously.The variations in the methods of DC2 fitting werecompared by attempting solutions to a variety of syntheticcurves. Table 3-7 is an example of the comparative resultsobtained after twenty iterations of an illustrative casestudied. The synthetic parameters for generating thetwo-star model curve are given in the table. This was a casefor which full parametric adjustment (£=1.0) in the DC2fitting process could yield no convergent solution. In bothcases shown where the Wilson method was tried (for £=0.5and 4*1.0) the process was still heading toward convergencewhere the DC2 process, with %=0.5, had already obtainedconvergent solutions. As can be seen, after 20 iterations,the formal errors of the solution parameters are much betterin the case of partial adjustments with the DC2 procedure.Figure 3-9 (similar to Figure 3-8) shows the history of the

::::118TABLE 3-7COMPARATIVE SAMPLE OF DC2 FITTING TO SYNTHETIC CURVE-PARAMETERS FOR SYNTHETIC INTENSITY CURVE-Di stance (km) : 375000# o-f Points (msec): 201Temperature Star 1 : 4500Temperature Star 2: 5000Limb Darkening (1 & 2): 0.5Grid Parameter: 8Iterations: 40Monochromatic, 5500 Anostroms1 :Diameter Star 1Diameter Star 2:Intensi ty Star 1Intensi ty StarTime StarTime Star1 :2L-Rate StarL-Rate Star 2:Sky Background:5.0010.001000.00800.0090.00101 .00400.00545.41400.00•INITIAL PARAMETRIC "GUESSES" (STARTING VALUES)Di ameter Star 1Intensi ty Star 1Time Star 1L-Rate Star 1Background:8.262120095500600Diameter Star 2: 0.206Intensi ty Star 2: 500Time Star 2: 105L-Rate Star 2: 600-SOLUTIONS-MethodsGrouped1 .0Grouped0.5Unqrouped0.5Diameter 1Diameter 2Intensi ty 1ntensi ty 2Time 1Time 2L-Rate 1L-Rate 2BackgroundComment6.40 (0.14)6.98 (0.18)1 1 66 . 5 (11.1)631 .691 .103.7392.2494.0394.5(7.2)(0.4)(0.1)(2.7)(2.0)(8.8)6.486.8 71176.6629.191 .3103.9391 .7489.4394.1(1 .08)(0.21)(141 .7)(7.0)(1 .5)(0.2)(10.1)(2.4)(2.4)5.0010.001000.00800.0090.00101 .00400.00545.41400.00(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)Rejected Rejected AcceptedNote: No convergent solution -for ungrouped, %=1 case

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120

121interim solutions -for these three cases. Similar resultswere seen in all the synthetic trials considered.Uniqueness of the SolutionThe iterative di f f erent i al correction process cannotabsolutely guarantee, in a rigorous sense, that the set o-fsolution parameters obtained is unique. To verify that theset of solution parameters is correct one must -first con-firmthat they are physically meaningful, within the context o-fthe observation. Clearly, solutions with astrophysi cal 1improbable implications

iterations o-f subsequent runs o-f the DC or DC2 procedures,with widely differing starting values, it is apparent thatthe parameters are being adjusted toward the same -finalval ues.The basic DC method was adopted -for the initialiterative adjustments in the case o-f single stars. Theapplication of partial parametric corrections were employedin the two-star DC2 -fitting process and in the the -finaliteration steps for the DC single star -fitting procedure.122The validity o-f the solutions was checked by multiple runs o-fthe initial corrections steps with very di-f-ferent startingval ues.Smooth ino o-f the Observational DataAs previously mentioned, the second area whereimprovements to the basic -fitting procedure seemed possiblewas in obtaining more realistic error estimates o-f thesolution parameters. The -formal errors o-f the solutionparameters were derived -from the var iance-covar i ance matrixo-f the -final set o-f residual equations. These errors reflectthe magnitude o-f the squares of the residuals. If theresidual amplitudes were smaller, then the error estimateswould have been tighter as well.Observational ly, this problem is addressed by trying toimprove the signal-to-noise ratio. This can be done byrejection of erroneous background light through a goodoptical baffle (see Chapter 1) and selection of a filter wellsuited to the spectral energy distribution of the star under

123study. Once data are acquired, the characteristics o-f thenoise in the raw observational record are -fixed; however,this does not preclude the possibility o-f the raw data beingpreprocessed be-fore being submitted to the -fitting procedure.The question which naturally arises is: can the data bepreprocessed in such a manner as to effectively improve thesignal-to-noise ratio, without degrading the underlyingoccultation record itself?The time scale o-f variation o-f an occultation intensitycurve is typically 10 to 50 milliseconds. This suggests thatsome type o-f time dependent smoothing might be applied to thedata, which were acquired at a pair-averaged rate o-f onesample per millisecond. To see i -f this in-ference was indeedtrue the previously generated synthetic intensity curves,with noise added as be-fore, were subjected to severaldi-f-ferent smoothing algorithms. The smoothed, syntheticobservations were then re—f i t by DC and DC2, as appropriateto the model in question.N-point unweighted smoothing . Each o-f the syntheticcurves previously considered was -first smoothed by a simpleN-point unweighted moving average. Values o-f N=3 and N=8were considered, corresponding to sampling -frequencies o-f 330and 125 Hertz respectively. This method o-f smoothing has theadvantage o-f reducing the e-f-fect o-f spurious single-samplevalues within the smoothing window, at the expense o-f losinginformation associated with level transitions which are -fastcompared to the smoothing length.

fThe application of N-point smoothing to the syntheticintensity curves resulted in solutions determined by the DCand DC2 procedures that were si on iican 1 1 y worse in some o-fthe parameters than those obtained in the unsmoothed trials.In every case the angular diameters of the stars wereoverestimated. In the case o-f 8-point smoothing, thedetermined angular diameters were typically too large byfactors o-f 2 to 5. The times o-f geometrical occultations124were shi-fted, by a smaller degree, to times earlier than usedin generating the synthetic models. The L-rate wasconsistently low, but only to a small degree; however, theformal error attached to the determined L-rate in some caseswas even worse than in the unsmoothed trials. Only therecovery o-f the true values o-f the pre-occul tat i on andpost-occul tat ion signal levels were unhampered by N-pointsmoothing. Since the determination o-f the primary parameterso-f astrophysi cal interest

125passive -filter network to set the 1/e -folding time o-f theamplifier response. Hence, investigating the use o-f anexponentially decaying weighting -function would mimic thee-f-fect of observing with various instrumental time constants.To be commensurable with the trials attempted in theinvestigation of unweighted smoothing, decay constants werechosen to provide an effective FUHM in the smoothing functionof 330 and 125 Hertz. The results of the DC and DC2 fittingwere similar to, though not quite as bad, as fitting to thedata which were smoothed with the unweighted functions.Here, too, the effect of increasing the smoothing widthresulted in an overest imat i on of the stellar angulardi ameterBoth N-point smoothing techniques proved unusable asmethods to preprocess the data in an attempt to reduce theresidual amplitudes. These smoothing methods, however, wereuseful in the visual inspection of the observed intensitycurves. It is difficult for the eye to see structure innoisy data, and N-point smoothing helped bring out detailswhich would otherwise would have been visually obscured.Figure 3-10 is a 200 millisecond extract from the observingrecord of the occultation of ZC1222, centered roughly on thetime of geometrical occultation. Eight-point (125 Hertz)unweighted smoothing was applied to these data, and thesmoothed curve is superimposed on the raw data.Smooth ino by forward and inverse Fourier transformation .Since the background noise was superimposed on the synthetic(and observational) data, the simple N-point smoothing

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algorithms acted with equal e-f-fect in not only smoothing outthe noise, but the underlying occultation intensity curve aswell. What was needed was a method o-f smoothing only thebackground noise, while leaving the character o-f theintensity curve itself ef f ect ivel y undistorted.Examination o-f the raw occultation data records seemedto indicate that the temporal characteristics o-f thevariation in background noise were, generally, quite a bit-faster than the 10 to 50 millisecond time-scale o-f variationtypical of the intensity curves. This implied that anumerical analog to active low-pass filtering of the datamight improve the effective signal-to-noise ratio andsubsequently the statistical certainty of the recoveredsolution parameters.To see if this implication was true, the power spectra127of synthetic "clean" intensity curves had to be compared withthe power spectra of actual observed background noise.Several additional synthetic curves were generated andFourier transformed into the frequency domain. In additionto the synthetic curves already available, point source and10 milliseconds of arc sources were modeled applying thespectral response of the intermediate bandwidth "y" (as wellas the Johnson-V) filter which would actually be used in theobservations. The synthetic curves consisted of 1024 datapoints, evenly spaced in time by one-millisecond. Actually,2048 data points, spaced one-half millisecond apart weregenerated and pair averaged to model more appropriately the

.implemented data acquistion scheme. The length of thesesynthetic data sets allowed the examination o-f their powerspectra up to a frequency o-f 512 Hertz.Figure 3-11 shows three representative power spectra.Only the -first 150 integral -frequency components (roughly upto 150 Hertz) are shown. At -frequencies higher than this,the power spectra continue to smoothly decay. The amplitudeo-f the power contributions -for each o-f the -frequencycomponents has been normalized so that the total powerassociated with all -frequency components up to 512 Hertz isun i tyIt was -found that as either the source diameter or thespectral bandwidth o-f the optical -filters was increased, thepower contributions o-f the higher frequency componentsdiminished. More importantly, in every case, the powerassociated with the frequency components higher than 150Hertz contributed less than 0.001 percent to the total power128of the intensity curve. The power spectra scale in frequencylinearly with the R-rate. The power spectra shown were forR-rates of 0.3 seconds of arc per second, which is a typicalvalue for most occul tat i ons.Examination of the power spectra of the pre-occul tat i onstar+sky intensity (shown for each event in Chapter 5) showthat, in general, at frequencies above about 150 Hertz thebackground noise dominates the observational occul tat ionrecords. But, in almost all cases, at low frequencies it isthe signature of the occultation curve itself which is

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dominant. This is exemplified quite nicely in the130comparative power spectra shown -for the occupation of ZC0835(Figure 5-124). These findings were significant. Theyimplied that better DC solutions might be obtained bysubjecting the observational data to Fourier smoothing.Here, Fourier smoothing means transforming the raw data intothe frequency domain, removing the high frequency componentscharacteristic of only the background noise (i.e. greaterthan 150 Hertz), and inversely transforming thefrequency-truncated data back into the spatial domain.Whenever such transformations are applied, carefulconsideration must be given to the inverse transformationprocess. Since these numerical transformations do notoperate on infinite data sets, spurious results can beobtained due to edge effects. The endpoints of thetransformed functions (i.e. ends of the observational datasets) appear as di scont i nu ites in the numerical functions,and often cause "ringing", or high frequency oscillation, tobe seen in the re-transformed data. This effect can be seenin Figure 3-12. The upper curve shows the synthetic curve ofa 10 millisecond of arc star observed with a Johnson-Vfilter. This is the curve whose power spectra is shown asthe bottom graph in Figure 3-11. The "ringing" effects ofinverse transformation, after the high frequency componentshave been removed from the data in the frequency domain, areshown in Figure 3-12.

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.The "rinQinQ" e-f-fects due to data windowing are oftenef f ect i vel y suppressed by the judicious application of anapodizing -function, as discussed by Bracewell (1965). In132practice, however, the intensity curves fit by the DC and DC2processes are small subsets of the observational data

133cases had arisen where fitting to smoothed and unsmootheddata -from the same observation yielded significantlydifferent results, -further investigation would have beenneeded. Fortunately, in all the observations reduced andanalyzed this problem never arose.

yCHAPTER IUCOMPUTATIONAL DATA REDUCTION PROCEDURESA Choice o-f ProoramminQ Lanouaoes; The APL DecisionThe data uploading and preprocessing programs, datareduction algorithms, graphics display software, and allnumerical experimentation employed in this investigation wereimplemented and carried out in APL. APL, an understatedlmodest acronym -for A Programming Language, is a power-fulalgebraic notation which was invented by Iverson (1962). Aninterpreter -for this notation was developed by InternationalBusiness Machines and first released as programming productXM/6 (Falkoff and Iverson, 1968 and 1970), more commonlyreferred to as APLX360 . Since that time, numerous releasesof APL interpreters and translators have become available forvirtually every mainframe and mi n -computer as well as foriquite a few microcomputers. Brenner

135as primitive) -functions enable easy array manipulation. Anumber o-f operators which act on the primitive functionscreate, in effect, new -functions and enhance the power o-fthis notation dramatically. In addition, APL allows -for thecreation o-f 'user de-fined -functions" extending the scope o-fits inherent capabilities only to the limits o-f theimagination o-f the user. Excellent treatments of APL as acomputer language, including the practical limitations of thenotation as implemented on finite machines, are addressed byPakin and Polvka (1975) and by 6i 1 lman and Rose

136required by virtually all other computer languages areneeded. Given the above, the decision to employ APL in thenumerical computations and associated data processing in thisproject was an easy one to make. It remains a mystery tothis investigator why any researcher involved in dataprocessing would make any other choice.The discussion of the algorithms developed for thesolution of lunar occultation intensity curves refers both tothe APL functions which have implemented these algorithms(Appendices C, D, and E) and to the underlying equationswhich have already been presented. This duality inpresentation is made to guide the reader unfamiliar with APLnotation to an understanding of both the overall datareduction scheme and the computer programs.Downloading and Uploadino of Observational DataOnce the observational data are saved as a contiguousmemory image on a CODOS disk file, these data must betransferred to the computer which will be used to perform thecomputational data reduction. The numerical computationsperformed on the observations during the course of thisinvestigation were carried out, for the most part, on fourmainframe computers. Warner Computer Systems, Inc. (NewYork) provided access to their Xerox Sigma-9 computer wherethe initial computational algorithms and basic reductionprocedures were developed and tested. A small amount ofnumerical experimentation was carried out on the Northeast

137Regional Data Center's Amdahl 470/V6 and IBM 4341. Thelatter was done when the MVS operating system was -firstestablished and computing was -free -for a limited time. Themajority of computing and the final reduction of allobservations was done on the Harris-500 computer operated bythe University of Florida's Center for Intelligent Machinesand Robotics.The process of moving data from CODOS disk files ontoany of the above mainframes was accomplished by a datatransfer program called OCCTRANS. This program (listed inAppendix B) is a 6502 machine language program written to runon a SPICA-IV system equipped with an RS-232 serial port. ASPICA-IV computer, similar to the SPICA-IV/LODAS with theaddition of a 6850 asynchronous communications adapterinterface (ACIA) , which also serves as a backup system forthe RHO SPICA-IV/LODAS, was used for this purpose. Thecommunication protocols in terms of baud rates, number ofstart and stop bits, parity, character prompting, andhandshaking are different for each of these machines. As aresult OCCTRANS must be modified slightly to establish theproper communications interface for different mainframecomputers. The version of the OCCTRANS program listed inAppendix B is for communication with the HARRIS-500 computer.This program converts the CODOS file which contains thefile header and three channel data buffers to ASCII before itis sent to the mainframe computer. Data are transferred inblocks whose size is appropriate to the length of the input

138buffer on the receiving computer. Data are received directlyinto APL via a very simple receiving program called READ,given in the listing of the APL workspace OCCPREP(Appendix C) . The OCCTRANS and READ programs "talk" to eachother, handshaking and transferring the data. The data, oncetransferred into the APL OCCPREP workspace, exist as a textvector o-f length 37376.This vector is then submitted as the right argument tothe function TRANSLATE. TRANSLATE unpacks the ASCIIrepresentation of the 12-bit observing data and headerinformation and stores this information as global variablesin the workspace. The variables CHI, CH2, and CH3, eachnumeric vectors of length 4096, hold the contiguous intensityreadings taken on each of the three data channels. Thesedata have been "unfolded" from each channel's circulatingbuffer so that the first element in each vector is the firstsample taken in the wraparound data windows. The time anddate of the last data sample, the "foldpoinf (sample pointerto the position of the last sample taken in the circulatingbuffer), and the last comment entered by the observer beforesaving the data to CODOS disk are also saved in theworkspace. The function TRANSLATE and subordinate functionsare shown in the OCCPREP workspace listing.The Qccultation Reduction workspace (OCCRED)The APL workspace OCCRED (OCCultation REDuction) listedin Appendix D contains the complete set of functions and

.139global variables needed to reduce a lunar occultationobservation. This workspace listing should be consulted inorder to elucidate the discussion of the computationalprocedures which -follow.Global Variables Used by QCCREDParameters -for the reduction run o-f the occultationsolution are established interactively by the -function INPUT.INPUT is monadic and takes as a right argument the globalvector o-f raw observational data (i.e. CHI, CH2, or CH3)created by the -function TRANSLATE. The entry o-f eachparameter is prompted -for conversationally, and on completionINPUT leaves the established parameters as global variablesin the active workspace. A convention o-f using underscoredvariable names -for parameters passed globally between APL-functions is used throughout this and other supporting APLworkspaces. Table 4-1 lists the global variables created byINPUT and brie-fly describes their content. The listing o-fthe function INPUT should be consulted -for the physical unitso-f the numerical values. The use o-f these variables isaddressed in the explanation o-f the di -f-f erent i al correctionsprocedureTypically, a maximum of about 250 points (except in thecase of very low R-Rates which occur for occul tat ions ofnear-grazing incidence) is appropriate. The global variableslisted in Table 4-2 also reside in the OCCRED workspace andare required by the differential corrections procedure. Thenames of the filter response matrices are the only global

.140variables employed whose names are not underscored. The FRENvector is explained in the discussion of the FRESNELf unc t i on .TABLE 4-1GLOBAL VARIABLES CREATED BY THE APL FUNCTION INPUTName Shape Type DescriptionBIN Scalar NUM Estimated Bin Number o-f GeometricalOccul tat i onCONNDATEFILTMARMARMARLIMS 2 6NAMEOBSMARMARPM 14TEXT Any Applicable Comments o-f Special NoteTEXT U. T. Date o-f the ObservationTEXT Name o-f Filter Matrix to UseParametric Limitation Matrix, First RowAre Upper Limits, Last Row are LowerLimits, Malues are Limits for PMElements 161 to [11]TEXT Name or Catalog Number o-f the StarNUM Subset o-f Observational Data to be UsedNUM The Parameter Mector Indexed as follows:CI] Central Wavelength of Passband[23 Lunar Limb DistanceC3] Number of Observation PointsExtracted for Solution.[43 Effective Stellar Temperature[53 Square Root of the Number of GRIDPoints per Stellar Quadrant[63 Stellar Angular Diameter[7] Pre-Event Signal Level[8] Post-Event Signal Level[?] Time of Geometrical Occul tation[103 L-Rate[113 Limb Darkening Coefficient[123 Maximum Number of Iterationsfor DC[133 Spectral Width of Filter Matrix[143 Fraction of Adjustments to ApplyNotes: An Index Origin of 1 is used in this table.MAR indicates a variable lenoth vector.

141TABLE 4-2GLOBAL (VARIABLES RESIDENT IN THE OCCRED WORKSPACENameNARROW^FILTERVFILTNARROUBBFILTERBFILTFRENShape Type5,2 NUM53,2 NUM6,2 NUM5,2 NUM42 , NUM5,2 NUM4001 NUMDescr i pt i on"y" -filter -fractional response,normalized, 100 Angstrom stepsJohnson V -filter fractional response,normalized, 50 Angstrom stepsJohnson V -filter fractional response,normalized, 500 Angstrom steps"b" filter fractional response,normalized, 100 Angstrom stepsJohnson B filter fractional response,normalized, 50 Angstrom stepsJohnson B filter fractional response,normalized, 500 Angstrom stepsDiffraction intensity values orderedin decreasing Fresnel unitsThe Computational Differential Corrections ProcedureThe primary function, which sets up and controls theflow of program logic for the solution of occultationintensity curves, is the differential corrections routinecalled DC. Minor modifications to DC can be made prior toits execution depending upon the nature of the parametricmodel. For example, the limb darkening coefficient of thestellar atmosphere can be treated as a free parameter. Asnoted earlier, however, in most cases the model is ratherinsensitive to changes in limb darkening; hence, it isusually held fixed. Because of the relatively long amountsof CPU time required for computation, "fine-tuning" of the DC

142procedure to -fit the needs o-f a given observation is -feltwarranted. A general computational approach may seem moreaesthetically pleasing -from a programming point o-f view butis somewhat less efficient computationally. Fortunately, theinteractive nature of APL allows variations in the basic DCprocedure to be implemented without any special effort.Indeed, alternate execution paths through DC and severalsubordinate functions are realized by simply turning certainexecutable statements into comments and vice-versa.Several global variables are created in the process ofdetermining the occultation solution. In most cases theseglobals provide information on the solution after completionof the reduction run. A few computational parameters arepassed between functions by global variables (though in mostcases variables are passed as functional arguments).The DC solution, in its basic form, is passed theparameter vector as an argument called P. DCL3] begins byestablishing two global variables and one local variable. Asexecution proceeds, the variable SOLS accumulates theadjusted parameter vectors after each iteration step. Whenexecution of DC is completed, SOLS provides an historicalrecord of the various parameter combinations used at eachstep on the way to arriving at the final solution. Thevariable SSE , similarly, is an historical record of thesum-of-squares of the residuals from the O-Cs after eachcorrection step. DI is a vector containing the fractionalvariation to be applied to each of the parameters in

143numerically computing the partial derivatives of theintensity curve. The index position of each entry in thisvector corresponds to the index position of the associatedparameters in PV. As an example, the intensity curve isfairly insensitive to a small variation in stellar diameterfor small diameter sources, hence, DU61 is typicallyassigned the moderately large value of 1.02.DC[4] sets up the iteration counter ITER and theparameter variation control vector CVEC. The first elementin CVEC, at any time, determines which parameter is to bevaried next in the corrections process. DCC5] computes thespectral response function, R. This response function,corresponding to Equation 3-8, is dependent upon both thespectral energy distribution of the source and theinstrumental spectral response function. In order to computethe spectral energy distribution of the source Equation 3-7is evaluated by the function BBDY.BBDY takes two arguments. The right argument, L, is atwo element vector. LI 1 ] specifies the blackbody temperature,and LE23 specifies the number of terms (i.e. width of eachspectral region in Angstroms) to be used in the numericalintegration of Equation 3-7. The left argument, W, is avector giving a list of wavelengths for which the blackbodyfunction is to be computed. BBDY normalizes the integratedblackbody function and returns a vector conformable in lengthto W, whose elements give the fractional contribution to the

144total blackbody power distribution function -for thewavelength regions evaluated.The arguments passed to BBDY are computed by DCE53. Thetemperature is taken -from the local parameter vector PE43 andthe spectral width computed -from the -first difference of thewavelength specifications of the first two entries in thefilter matrix specified by FILT . The wavelengths forevaluation are taken directly from the same filter matrix.After the blackbody distribution function is computed, eachwavelength regime is attenuated by an amount representing thefilter function also given by the FILT matrix. The modifiedspectral energy distribution function is the spectralresponse function, R.The model strip brightness distribution of the projectedquadrant of the stellar disc, as previously discussed, iscomputed in DCC63. The computation of the non-limb-darkenedgrid, which represents surface elements on the stellar disc,is handled by the function GRID. GRID takes a scalar rightargument specifying the square root of the number of gridpoints to be computed for each quadrant on the model stellardisc. DCC63 is passed this value from the parameter vector.GRID carries out the analytic solution (Equation 3-5) for theintegration of Equation 3-4 for each projected surfaceelement. The result is a normalized matrix where eachelement gives the fractional brightness contribution of aprojected surface element in the grid coordinate system whoseorigin is centered at the upper right corner of the matrix.

145as shown in Figure 3-2. Only one quarter o-f the stellar discis computed, as spherical symmetry is assumed.The stellar arid is then limb darkened by the -functionLDARKEN. LDARKEN takes two arguments. The right argument isthe stellar grid quadrant as computed by GRID. The le-ftargument is the limb darkening coe-f -f i c i ent to be applied.The linear limb darkening law given in Equation 3-6 isapplied. The limb darkened quadrant is renormalized andpassed as the resulting matrix.Since spherical symmetry is assumed, the hemisphericalstrip brightness distribution is computed by DCC63 bydoubling the values and summing the matrix along the lastcoordinate axis. Again applying symmetry, the vectorresulting -from the previous step when rotated andconcatenated onto itsel-f yields the total strip brightnessdistribution. The normalized limb-darkened strip brightnessdistribution is stored in the variable S.DCE73, labeled LO , is the entry point -for the outeriterative loop o-f the di -f -ferent i al corrections procedure.This point is re-entered a-fter all parameters have beenvaried and parametric corrections have been applied to allparameters on the basis o-f the partial derivatives o-f theresidual matrix. DC[5] establishes a matrix, X, which willhold the numerical partial derivatives o-f the intensitycurve .DCC83 calculates the computed intensity curve on thebasis o-f the current parameters in P. To do this, the

,146normalized polychromatic intensity curve must be computedfrom the linear superposition o-f monochromatic curves. Thisis carried out by the -function WIDE.WIDE takes two arguments. The parameter vector ispassed as the right argument. The left argument, R, is thepreviously computed spectral response -function. WIDE -firstcalculates the individual monochromatic curve (as anapproximation to each spectral region), then sums thesecurves. The normalized monochromatic curves, which aredependent upon the stellar diameter, velocity parameter andlimb darkening coe-f -f i c i en t are computed prior to summation,by WIDEC6D. In the case where the limb darkening coefficientis not held constant, the stellar grid brightnessdistribution must be recomputed at this step. Then WIDEE5]would be uncommented" and the variable S recomputed in thesame manner as it had been in DC161.The computation o-f the series o-f normalizedmonochromatic curves which eventually forms the polychromaticcurve is carried out in Fresnel space. Thus, the parametersgiven in physical units o-f kilometers, mi 1 1 i seconds-o-f-arcAngstroms and so on, are converted by the -function FNOS intoFresnel numbers. At each step through the iterative WIDE-function, one monochromatic curve is computed. FNOS takes asits right argument the parameter vector with the -firstelement replaced by the wavelength, in Angstroms, o-f theparticular monochromatic curve sought in the currentiteration step. FNOS returns a matrix o-f Fresnel numbers

147corresponding to the points of evaluation in time and space-for the wavelength and parameter vector specified. Thecolumns o-f this matrix correspond to the strip segments, S,uniformly separated in space in accordance with the stellardiameter and number o-f strips. The rows o-f the matrixcorrespond to the temporally separated points determined -fromthe data acquisition rate (i.e. one millisecond per point)and the velocity parameter. The zero point references arethe center o-f the stellar disc -for the columns, and the timeo-f geometrical occultation for the rows.It is a simple matter to compute the normalizeddiffraction intensity for a given Fresnel number bynumerically integrating Equations 3-2a and 3-2b and applyingEquation 3-1. If this were done for each pass through theWIDE function, both the Fresnel sine and cosine integralswould each have to be numerically integrated approximately 50million times for a typical DC solution. This is, needlessto say, prohibitive. Rather, the diffraction intensities, asa function of Fresnel numbers, in the range of Fresnelnumbers from -20 to +20 were computed by the function FRESNELonce and stored as a global vector called FREN in theworkspace. FRESNEL performed the numerical integration byrectangular approximation to a precision of approximately onepart in 5000. Diffraction intensities are stored in FREN inserial order starting with the intensity for a Frenel numberof -20 and incremented by 0.01.

148Once the Fresnel numbers are computed by FNOS, thecorresponding intensities are -found by linear interpolationo-f the FREN vector by the -function NPOL. The right argumento-f NPOL is the array o-f Fresnel numbers and the result,con-formable in shape to the argument array, is an array o-fcorresponding intensities. It was -found that simple linearinterpolation would produce values correct to one part in2000 in the worst case.The matrix product o-f the intensity array with the stripbrightness distribution yields the normalized monochromaticcurve. WIDEC63 then applies the response -function -for thewavelength evaluated to each point in the curve andaccumulates a sum o-f successive curves. The iterativeprocess is completed when all spectral regions have beencomputed. The execution o-f WIDE results in a normalizedintensity curve with the spectral response -function included.It should be noted that, in principle, WIDE could havebeen de-fined non-i terat i vel y ; however, the amount o-f memoryspace required was -far in excess o-f that available.DCC8] scales the polychromatic wideband curve for theparametric value o-f the signal level

149of iteration zero) is accumulated in the variable SSE as partof the iterative solution history. The current localparameter vector P is saved in a vector o-f tentativesolutions called SOL .It may be noted that DCC8] displays both the currentparametric values and the sum of the squares of the errors ofthe just completed iteration step. This output, in general,is somewhat superfluous. However, the Harr is-500 computer onwhich most computations were performed was unreliable andoften would crash before a DC run would go to completion.Having this information displayed periodically allowed theprocedure to be restarted after the computer was brought backup. At that time, the last iteration values which had beendisplayed were used as new starting parameters.The inner iterative loop labeled LI is entered at DCC9],During the process of computing numerical partial derivativesof the intensity curve, numerical singularities may occur fordomains in which the intensity curve is insensitive tovariation of a particular parameter. This problem isparticularly acute as the angular diameter of the starapproaches zero. Hence DC[9] determines what value of dD(variation in diameter) should be used in computing thenumerical partial derivative dl/dD. The values were chosenafter some computational experimentation. For sourcesecond of arc, a variation factordiameters less than 1 -mi 1 1 iof 1.4 is used in the source diameter. Sources larger than1-mi 1 1 i second of arc but less than 2-mi 1 1 i seconds of arc have

their diameters varied by a factor of 1.2. Sources largerthan 2-mi 1 1 i seconds o-f arc but less than 3-mi 1 1 i seconds ofarc are varied by a -factor o-f 1.03, and sources with anyangular diameter larger than this are varied by 2-percent.DCC103 begins the process o-f parametric variation andadjustment. CVEC is rotated by one to point to thesuccessive parameters in each pass through the LI procedure.The parameter is then varied by the amount specified by DIand resaved back in the P vector. In order to preventfurther numerical singularities due to the finitecomputational precision of the computer, the variedparameters are never allowed to be fuzzed to zero but are-12limited to a minimum value of 10DCC11] recomputes the intensity curve in the samemanner as DCE8] using the varied parametric value. Theinitial model curve, CQMP . is subtracted from this resultantcurve and the residuals stored in the vector D.DCE13] computes the partial derivative of the intensitycurve as a function of the just-varied parameter. Eachpartial derivative, as it is computed, is saved as a columnin the matrix X. The P vector is restored to its previousvalue which was tentatively retained in SQL . The variation150procedure and computation of partial derivatives is continueduntil all the parameters whose adjustments are sought havebeen handled.

151In the case where a previous DC run resulted in aparticularly recalcitrant solution

The L2 procedure at DCC13] is entered on completion ofall iterations through the LO loop. The solution history152Qiving the iteration number, ranking o-f the solution in termso-f the sums-of-squares o-f the residuals and the successivelytried parameter vectors are displayed.The var iance/covar i ance array o-f the -final adjustments,computed -from the residual vector Y, and the partialderivative matrix X are computed by DCC19I. The standarderrors o-f the estimates are -found -from thevar iance/covar i ance array, and displayed. The algorithms -forthese computations are taken -from Smillie . The DCfunction concludes by assigning the last partial derivativematrix to the global variable PDER . On completion DC leavesa number o-f global variables in the workspace re-flecting thefinal solution and the history o-f the DC run. A summary o-fthese variables is given in Table 4-3.In most cases the last iteration has the lowest ranking,that is, it is the solution which has the smallestsum-o-f-squares o-f the residuals. I -f the variations insuccessive solutions were small, so that near-asymptoticconvergence had been reached, then no -further execution isrequ i red.The last iteration, however, need not produce the lowestranked solution. Meyer

ance/Covar153TABLE 4-3GLOBAL VARIABLES CREATED BY THE APL FUNCTION DCName Shape Type DescriptionCQMP PVC3] NUM Computed Intensity CurveiCOV 5 5 NUM Var i ance Matrix -for theLast Adjustments Made by DCER 5 NUM Standard Errors of the EstimatesPDER PU[123,5 NUM Partial Derivatives o-f the ComputedIntensi ty CurveSQL 14 NUM Last Adjusted Parameter VectorUsed by DCSOLS 1+PVE12] ,14 NUM Sol u t i ons Matr ix, a Chronol ogi calHistory o-f Successively AdjustedParameter VectorsSSE 1+PVC12] NUM Chronological History o-f the Sum-Square-Errors o-f QBS-COMP -forSuccessive COMP / s Generated.the parameter vector. I-f the DC procedure is not invokeddirectly, but controlled by the -function START, then this isdone automatically. This is normally done in all reductionruns.The solution history must be examined to determine ifthe last computed set o-f parameters is su-f-f i c i ent 1 y nearconvergence as to not require any -further adjustment. Thisevaluation is le-ft to human judgement rather than to apreprogrammed algorithmic decision. If it is desired tocontinue the DC process then the best solution may beextracted from SOLS and these parametric values used inestablishing a new PV. DC may then be re-executed with theadjusted parameters as the new starting values. It may be

154desirable to reduce the iteration maximum on subsequent runsof DC.The DC procedure will attempt to -fit any data presentedto a model occultation curve. Thus the raw observed data maybe preprocessed be-fore being submitted to DC without anyvariation in the operation o-f the computational DC procedure.This was done in the numerical experimentation per-formed toevaluate the e-ffects of removing high -frequency components inthe observed data by -foward and inverse Fouriertransformation, as well as applying simple N-point andexponential and smoothing to the observational data.The Two-Star Differential Corrections Procedure (DC2)Global parameters for DC2 . The APL function DC2 is atwo star analog to DC. The numerical procedures discussed inChapter 3 have been implemented and are carried out by DC2.Uhere DC was defined monadicaly, DC2 is defined dyadically.The right argument is a parameter vector, identical in shapeand analagous in content to that which would be passed to DC.This parameter vector, PM, would hold the initial parametricguesses for one of the component stars (arbitrarily referredto as star 1> in the two-star system. Here, the pre-eventsignal level PVC73, is the out-of-occul tat i on signal level ofthe first star only. The post-event signal level, PyC8]refers to the background sky level, not the star 2 plus sky1 evel .The left argument passed to DC2 is a similar parametervector, which will be denoted PV2, and holds the parameter

specifications for the second star. The shape and content155are similar to PV with a few minor exceptions. The pre-eventsignal level, PV2E73 refers to the out-of-occul tat ion signallevel of star 2 only. PVE8] is an unused element in theparameter vector, as the background sky level is assumedconstant throughout the event. Therefore, the background skylevel specified for star 1 is used for star 2 as well.Some of the elements in PV2 are redundant, as they areidentical to those in PV (i.e., the lunar limb distance,number of data points extracted for solution, etc.).Structuring FV2 in a manner similar to PV, however, allowedthe same previously defined subordinate functions to beemployed withno modifications.The APL function INPUT2, listed in Appendix D, is used tointeractively establish the two parameter vectors used byDC2. In addition to the global variables created by the APLfunction INPUT (see Table 4-1), INPUT2 creates the variablesPVE2I and LIMS 2. The latter of these is the parametricadjustment limitations matrix for star 2, and has the samearrangement of elements as the LI MS matrix.The APL function DC2 . The function DC2, given inAppendix-D, was developed from DC and has a great resemblanceto the one-star function. The variable names and algorithmicprocedures, where applicable, were retained from the DCfunction and include the second star. Variables related tostar 2 have names which are postfixed with a "2": P2, DI2,

156R2, X2, SQLS 2, and SQL 2 . They have the same meaning inalgorithmic context as the related variables -for star 1.As can be seen, the structure and content of DC2resembles DC closely. The version o-f the DC2 -function shownretains the capability o-f either using the Wilson parametergrouping method or solving for all nine parameterssimultaneously. The -function as shown uses the latterapproach. To implement the parameter grouping method thosefunction lines which are preceded by double comment symbolsshould be unconsented and those lines which are -followed bydouble comments should be turned into comments.The function shown here defines the same stripbrightness vector, S (on DC2C7]), to be used for both stars.If different limb darkening coefficients or grid parameterspecifications are desired for the two stars, a separatestrip brightness distribution, S2, for star 2 should becomputed as well. This information must be passed to WIDEwhich currently uses S for computing the model intensitycurve. The simplest approach is to create a functionidentical to WIDE, called WIDE2, which refers to S2 insteadof S. WIDE2 would then be called, instead of WIDE, in thecomputation of the polychromatic model curve for star 2.The interim model for the two-star

157The adjustment procedure has been partitioned into twosections labeled LI and LIB. LI handles the variation o-f themodel parameters of star 1 -for the numerical computation o-fthe partial derivatives. LIB is the same -for star 2. InLIB, FV2C8] is skipped as it does not enter into the model.In the usual -fitting process, the labeling o-f LIB has nosi gn i -f cance as it is not a line that is enterediconditionally. I-f the parametric grouping code is activated,however, this becomes an entry point -for the parametricadjustment o-f the subset o-f parameters associated only withstar 2. In that case, the computation o-f the adjustmentsafter the computation o-f the partial derivatives -for eachstar is handled by DC2C16] and DC2C17], respectively.After the iterative adjustment process is completed, DC2concludes in the same manner as DC. Four additional columnsare added to the historical synopsis matrix SOLS (defined onDC2C29J) which are not present on the SOLS matrix created byDC. These contain, for each iteration, the interim values ofthe adjustable parameters for star 2. The variance/covariance array, CW , is a ?-by-9 matrix, rather than a5-by-5. Similarly, the vector of error estimates of thesolution parameters, ER, is of length 9. These twovariables are computed on DCC303. The 9 column matrix, PDER,contains the numerical partial derivatives of each of theparameters evaluated for every point of observation.

.158Preprocessi no of the Observational DataBe-fore submitting the raw observational data to eitherDC or DC2, Fourier smoothing (as discussed in Chapter 3) maybe applied. The dyadic APL -function FTSMOOTH carries out theFourier smoothing. The raw observational data, storedglobally in the workspace under the name CHI, must beresident. The right argument is a two element vector. The•first element is the bin number of the time of geometricaloccultation. In the case o-f a one star event the variableBIN , created by INPUT, should be used. For a two-star eventthe mean of BIN and BIN2 is more appropriate. The secondelement is the number of points centered on the specifiedtime to be included in the Fourier smoothed data set. Theleft argument, a scalar, is the cutoff frequency

159the global variables created by both INPUT and DC. Theinformation presented by the OUTPUT -function is listed inTable 4-4.The APL function 0UTPUT2 produces a similar report -forthe results obtained -from a DC2 -fit. In addition to thein-formation presented -for DC -fitting, the parameters andderived quantities salient to the two-star model are given.These additional items are listed in Table 4-5.A number o-f APL -functions have been assembled to presenta graphical depiction o-f the solution and other salientinformation relating to the fitting process. These functionsare discussed in detail in Chapter 5.

ance/covar160TABLE 4-4INFORMATION PRESENTED BY THE APL FUNCTION OUTPUTGeneralInformation1 . Name of the star2. U. T. Date o-f the occultation3. Any significant comments to head the outputInputParameters1. Central wavelength o-f the passband (Angstroms)2. Topocentic lunar limb distance (kilometers)3. Effective photospheric color temperature (Kelvins)4. Limb darkenino coefficientModelParameters1. Number of data points used in the solution2. Number of grid points on the model stellar grid3. Number of discrete spectral regions modeled4. Width of each of the spectral regions (Angstoms)5. Number of iterations of the DC adjustment procedureSol ut i ons1. Stellar angular diameter (mi 1 1 i seconds-of-arc)2. Bin number of geometrical occultation3. Pre-event (stai—plus-sky) signal level (counts)4. Post-event (limb-plus-sky) signal level (counts)5. Observed lunar shadow velocity (kilometers/second)6. Predicted lunar shadow velocity (kilometers/second)7. Local slope of the lunar limb (degrees)Statistics of the Solution1. The var i i ance matrix2. The correlation matrix3. The sum of the squares of the residuals4. Sigma (one standard error)5. The normalized standard error6. The photometric (Si gnal -pi us-Noi se)/Noi se ratio7. The (Change in Intensi ty)/Background Intensity8. The change in magnitudeTabulation of the Observation and the Solution1. Time from start of solution subset (milliseconds)2. Observed Intensity (counts)3. Computed Intensity (counts)4. Observed-Computed Intensity (counts)

161TABLE 4-5TWO-STAR QUANTITIES PRESENTED BY THE APL FUNCTION DC2Sol ut i ons1. Stellar angular diameters for each of the components2. Bin numbers o-f geometrical occultation -for each star3. Intensity

.CHAPTER VTHE OCCULTATION OBSERVATIONS AND RESULTS OF THEIR ANALYSISPresentation FormatTo -facilitate the discussion of the occultationobservations and the results o-f their subsequent analysis,the observations, their solutions, and related in-formationare presented in both tabular and graphical -form. The ordero-f presentation is chronological, based on the time and dateo-f the observations, beginning with the occultation o-f ZC0916< 1 Gemi norum)Format and Content o-f the TablesThe occultation summary table . A synopsis o-f each eventis presented on a table re-f erred to as an occultation summarytable. Table 5-9 is an example o-f an occultation summarytable. Each o-f these tables, headed by the name o-f theocculted star is divided into six sections. The -first o-fthese sections, labeled "Stellar and Observing In-formation",conveys both the primary characteristics for classifying thestar and in-formation with regard to the instrumentalcon-figuration employed while making the observation. Theprimary reference given for the star is either itsRobertsons' (1940) Zodiacal Catalog number or UnitedStates Naval Observatory (USNO) Extended Catalog number.The Smithsonian Astrophysi cal Observatory , Bonner162

.Durchmusterung (DM), and other pertinent catalog numbers orstar names are also given. Following these are the RightAscension and Declination of the star, precessed to theequinox and equator of the date o-f observation. Also listedare the star's apparent V magnitude, spectral type, and163cat i onsluminosity class ( i -f known). The instrumental spec i -f iinclude the filter (designated U, B, "y", or "b"), thediaphragm (designated by the letter codes given inTable 2-3), the amplifier gain setting, and the PMT voltage.The second section, labeled "Lunar Information",presents the lunar geometry and characteristics which areunique to each occultation event. These data refer to thetime of geometrical occultation. The percentage of the lunardisc illuminated

next. A negative hour angle indicates a pre-transit event.164The sel enocentri c geometry o-f the occultation, de-fined by theposition angle, cusp angle, contact angle, and Watts angle,(Uan Flandern, 1973) o-f the star concludes this section.Both the lunar and event information presented are derivedfrom data supplied by Lukac (1983, and 1984).The fourth section, labeled "Model Parameters", presentsthe -fixed computational model parameters and assumed stellarcharacteristics used in the -final di -f -f erent i al correctionssolution. Listed -first is the number o-f data points(milliseconds o-f data) extracted -from the observation databu-f-fer that were used in the reduction. The number o-f gridpoints used to represent the stellar disc o-f the star, thenumber o-f discrete spectral regions employed to model thestellar blackbody -function, the instrumental spectralresponse, and the width (in Angstroms) o-f those spectralregions are listed next. The instrumental spectral response-function used in all cases corresponds to the -filteremployed. These response -functions are given in Appendix D.The assumed stellar limb darkening coe-f -f i c i ent and e-f-fectivephotospheric temperature (based on the star's spectral andluminosity classes) are the last entries in this section.The -fifth section, labeled "Solutions", shows theprincipal computational results obtained -from the model•fitting procedure. Each solution parameter also has itsformal standard error presented alongside in parentheses.The stellar diameter (in milliseconds o-f arc), and time o-f

165geometrical occultation (in milliseconds) relative to thesample number of the -first intensity point taken in theextracted observational subset used in the reduction, aregiven -first. Listed next are the out-o-f-occul tat i onintensity levels, in raw "counts" (with a -full scale value o-f4095), be-fore and a-fter the disappearance. The observedtopocentric linear velocity o-f the lunar shadow and the lunarlimb slope derived -from this velocity are given next. I-f adecodable WwVB time signal was obtained for the occultationevent, the Universal Time o-f geometrical occultation ispresented and is the last entry in this section.The sixth, and -final section o-f the Occultation Summarytables, labeled "Photometric Noise In-f ormat i on" , containsinformation useful in assessing the photometric quality ofthe sky during the event. The sum of the square of theresiduals is given in raw counts, as is the standard error(Sigma) of the residuals. The absolute unsealed values ofthese numbers depend both on the number of samples used inthe reduction and on the arbitrary full scale intensity valueused. To aid in the i ntercompar i son of differentobservations, a normalized standard error, adjusted for boththe size of the data sample and full scale intensity, is alsogiven. The si gnal -pi us-noi se to noise (S+N/N) ratio duringthe time of the observation subset is presented.Out-of-occul tat ion , the S+N/N would be essentially constant

166over time intervals short enough not to affect the integratedtransparency -function of the sky.The amplitude o-f scintillation noise, which is thedominant noise source -for bright stars, varies linearly withthe signal level. Scintillation noise affects only theintensity of the source and not that of the background sky.Photon shot noise, which varies as the square root of theintensity, is normally much less important in the observationof bright stars. Yet during an occultation disappearance theintensity of the source itself is diminished rapidly. Thephoton arrival statistics are even worse for fast photometrywhen the arrival time between photons can approach the sampleinterval. Fortunately, this is in the region of theoccultation curve which is well into the asymptotic falloffand is insensitive to these effects.The sky, however, is typically bright due to scatteredmoonlight. The noise statistics of this background tend tohave a Poisson distribution. Henden and Kai tchuck (1982)discuss a method of observat i onal 1 y determining the noiseassociated with this background. Due to the stellardisappearance at the time of occultation the dominant noisesource changes rapidly from being scintillation dominatedGaussian noise, to background dominated Poisson noise.Hence, the S+N/N ratio would also change. A propercomputation of the S+N/N ratio must allow for the switchoverin dominant noise sources, and in fact must consider both ofthem. The scintillation noise is easily measured, and the

noise due to the background is determined as suggested by167Henden and Kaitchuck (1982). The noise sources are then addedin quadrature to determine the -final figure presented as theS+N/N ratio.The time-averaged sky background is, for the purpose ofconsidering tht noise sources in an occultation event, simplya zero offset. This offset level varies enormously fordifferent events, depending on the lunar phase and theposition angle of the event geometry. Thus, an indication ofthe quality of the degree of detection is the ratio of thechange in intensity (the pre-occul tat ion and post-occul tat i onsignal levels) compared to the background sky level. Thisratio, listed in this section, is independent of thesuperimposed scintillation noise. This change in intensity,expressed as a stellar magnitude difference, is the lastentry in an Occultation Summary table.An additional section is inserted into the occultationsummary tables, in the case of solutions of "close" binarystars. The derived quantities which are listed in Table 4-5are presented in this additional section.Var i ance-covar i ance . correlation, and dl/dPj. Theformal errors of the solution parameters, as listed in theoccultation summary tables, are derived from thevar i ance-covar i ance matrix of the residual matrix. In thecase where high correlations exist between the modelparameters, the formal errors of these parameters are ofteninsufficient for judging the quality of the solution

168(Bevington, 1969). This is the case -for occultationobservations where some of the physical parameters describingthe occultation intensity curve have a high degree o-fcoupling. The degree o-f coupling is a -function o-f thescintillation noise, expressed as the photometric S+N/N, thedynamic range o-f the signal decrease (change in magnitude),and the timescale o-f the event (projected lunar velocity) incomparison to the data acquisition rate. Thus, thecorrelation between the parameters is o-f interest. Thecorrelation coe-f-f i c i en ts indicate the degree o-f sensitivityo-f a solution parameter to a change in the other parameters.The var i ance-covar i ance and correlation matrices -for thedetermined solution parameters are presented on tables o-fnumerical and statistical significance. Table 5-6 is anexample o-f this type o-f table.As previously discussed, the regions o-f sensitivity tovariation o-f the intensity curve with respect to changes ineach o-f the parameters are reflected by the partialderivatives of the intensity curve (dl/dPj). It is notedhere, however, that while a list of the partial derivativestabulated at each point of evaluation is too lengthy topresent for each observation, the range of values for each ofthe partial derivatives are given at the bottom of thesetabl es.Observed and computed intensity values . A 1 i st of theactual observations, computed intensities, and theirresiduals, are also tabulated. The data presented on these

169tables are -for the subset of observations used in the DCsolution. As an example of this type of table see Table 5-6.The first entry corresponds to the first data point in the DCsolution subset. These tables are organized in a verticalfashion, and are read from top to bottom within each columnof figures.Format and Content of the GraphsThe graphical representation of the occultations arealso of a standard form and are produced by APL functions inthe workspace OCCPLOTS listed in Appendix E. As may be seen,the generating functions employ subordinate functions to drawaxes, labels, plot points, and perform similar tasks. Thesefunctions are not shown here but are discussed by Sel fridge. For clarity, each graph will be referred to by thename of its APL generating function. The informationpresented on each type of graph is discussed here.Graph of the entire event. RAUIPLOT . The first type ofgraph shows the entire 4096 milliseconds of acquired data foreach event. These graphs are produced by the APL functionRAWPLOT, an example of which is Figure 5-1. On each RAWPLOTthe horizontal axis gives the time of each acquired datapoint, in milliseconds, relative to the time of the firstintensity value (time 0000). The right hand vertical axisgives the actual number of recorded counts scaled from zeroto 4096 for each millisecond of observed data. The left handvertical axis indicates the counts normalized on a scale fromzero to one. The plotting device used to draw these graphs

170(a Houston Instruments digital incremental plotter) has aresolution of 0.01 inches. Hence, trying to depict all4096 points on the RAWPLOT would result in several retracesalong each step in the horizontal direction. Thus, RAWPLOTdisplays only every fourth point (1024 in all) of theacquired data.A cursory examination of a RAWPLOT will give apreliminary indication of the quality of the photometricdata. The scatter in the data from point to point resultsfrom high frequency scintillation noise. Longer periodvariation in overall signal intensity comes about from theslower variation in the atmospheric transparency. Theapproximate time of geometrical occultation relative to timezero can be seen where the intensity data takes a suddendownward step. The relative amount of background light fromsky and lunar limb brightness can be seen by noting thepost-event intensity above the zero count level. Thecontribution to the total intensity due to the starlight isnoted by comparing the intensity of the signal before andafter geometrical occultation.The integration plot. INTPLOT . The second type ofgraph, produced by the APL function INTPLOT, is anintegration plot of the entire 4096 milliseconds of observeddata. These graphs are typified by Figure 5-3. This type ofplot was first suggested by Dunham et al . (1973), and may beused to examine the occultation record for evidence ofstellar duplicity. The mean intensity taken over all

171observed data points is computed and this mean is thensubtracted -from each observed point. A running sum is thenproduced -from this di f f erence . When plotted against time, asingle star disappearance will ascend to a maximum anddescend back to zero. A double star, however, will giveitsel-f away by the presence of a change in slope in theascending or descending branches o-f the curve. Some suchdetections, as in the case o-f 1 Geminorum, are obvious. If,however, the second star is o-f considerably lesserbrightness, the detection might pe quite subtle, as isevidenced in the INTPLOT of ZC0126. In these cases thechange in in-flection can be enhanced by choosing a subset o-fthe data, centered on the time o-f disappearance of thesuspected second star to be processed by the INTPLOT functionover a shorter time interval. Several of these shorterINTPLOT figures have been generated and included.Graphic depiction of the best fit. FITPLQT . Graphs suchas Figure 5-13, generated by the APL function FITPLOT, eachshow the best theoretical fit to the observation for thesubset of contiguous data points used in the reduction. Thisfit is superimposed on the observed data. The bottomhorizontal axis, as in the case of RAWPLOT ,gives the time inmilliseconds relative to time zero. The recorded counts areonce again presented on the right hand vertical axis. Theleft hand vertical axis has been normalized such that zerocorresponds to the smallest intensity in the data subset, andone to the largest. The relative time of geometrical

172occul tat i on is indicated by a dashed vertical line. Thistime corresponds to an intensity level which is 25 percentabove the post-occul tat ion intensity with respect to thepre-occul tat i on intensity. A second dashed line appears inthe case of two-star solutions. The computed pre-occul tat i onintensity level (due to starlight, skylight, and lunar limbbrightness) is indicated by a short horizontal line extendingto the right -from the le-ft hand vertical axis. The computedpost-occul tat ion intensity level (due only to skylight andlunar limb brightness) is indicated by a short horizontalline extending to the left from the right hand vertical axis.Across the top of the graph is an additional horizontalaxis, scaling the event linearly. This axis gives thedistance, in meters, of the projection (along the Earth'ssurface) of the geometrical shadow from the telescope. Thezero reference is taken at the point of geometricaloccultation. Negative values along this axis correspond topre-occul tat ion intensities.Noise statistics of the observation. NQISEPLQT . Thefourth type of graph (of which Figure 5-6 is an example) isgenerated by the APL function NOISEPLOT and shows the noisefigure of the event throughout the entire 4096 millisecondsof data. The observed intensity values are subtracted fromthe computed values and the residuals binned into fiftyclasses. Each class width is two percent of the range of theresiduals. The binned residuals are plotted against thenumber of residuals per bin. The horizontal axis indicates

173the value of the residuals as a percentage of the mean value.The vertical axis indicates the number o-f residuals per bin.A dashed vertical line shows where the mean o-f thedistribution -falls. The one sigma width o-f the distributionis shown as a horizontal error bar centered on the 1 inerepresenting the mean value.The non-linear least squares, di -f -f erent i al correctionprocedure, employed to obtain the occultation solutionparameters, assumes that the residuals are randomlydistributed. Thus, the noise figure should be essentiallyGaussian. O-ften, the distribution -function o-f the residuals,taken across the entire data set, seems to have a smallnegative-going Poisson tail. This results from an increasein background light during the 4096 milliseconds of dataacquisition. The two major sources contributing to a timevarying background are: Earthshine along the lunar limb(dominant for events of small solar elongation), and theradial brightness distribution of the lunar aureole (dominantfor events occur ing at large solar elongations). Thebackground sky intensity determined as one of the solutionparameters reflects the light-level at the time of the event,and typically, is somewhat higher than the backgroundobserved earlier in the observation. The Poisson tailarising in the residual distribution functions due to theseeffects is usually inconsequential, as the effect is verysmall over the short timescale of the occultation itself.

174Power spectra. PQUJERPLQT . While the character of thedistribution -function of the residual amplitudes is importantin con-firming that the -fundamental assumption o-f stochasticnoise implicit in the reduction process is true, so too isthe distribution of the power components associated with theobserved data. The question of an optimum data acquisitionrate, effective system time constant for the analogelectronics, and their relation to scintillation noise andthe power spectrum of an occultation observation is discussedin Chapter 3. Figures generated by the APL functionPCWERPLOT contain three power spectra for each occultation,and show the relative power contributions for all frequencycomponents up to 500 Hertz.Figure 5-7 is an example of a P0WERPL0T. The lowerpower spectrum in a POWERPLOT results from a discrete Fouriertransformation of 1000 millisecond observations centered onthe time of geometrical occultation. These may be comparedwith the middle spectrum, which for the same event shows thepre-occul tat i on power spectrum derived from 1024 millisecondobservations typically centered 1500 milliseconds from thetime of geometrical occultation. The 512 millisecondseparation in time between the endpoints of thepre-occul tat i on and occultation power spectra aresufficiently separated in time so diffraction fringingeffects will not corrupt the pre-occul tat i on data. Also, inthis short time interval the atmospheric conditions cannotappreciably change and thereby affect the character of the

175seeing or scintillation. The upper power spectrum is that ofthe computed occultation curve, also centered on the time ofgeometrical occultation. In a -few cases the data acquisitionprocess was halted too late to to preserve 1024 millisecondso-f pre-occul tat ion data. In these cases theout-of-occul tat i on data subset is shorter, and hence, thepower spectrum is generated to correspondingly lowerf requenc i es.The horizontal axes give the frequency components inHertz. The power spectra are plotted on a logarithmic(base 10) scale. Each decade is marked along the verticalaxes. All three power spectra, on each POWERPLOT, arenormalized to the same logarithmic power scale. Most of theFourier transformations were carried out using the APLfunctions FFT and FFTI (listed in Appendix E) , supplied bySelf ridge (1984). These are "fast" Fourier transformationsand require data to be transformed to have a number ofelements evenly divisible by a power of two. In cases wherethis was not possible or practical, the discrete Fouriertransformation functions FT and INVFT were used. Thesefunctions are discussed in detail by Schneider

176occultation curve itself. These graphs also allow one toquickly spot any induced artificial noise, such as a 60Hzcomponent (which could result from improper electricalshielding or loss of a ground or other source of AC pickup inthe analog electronics).Sensitivity of solution to variation of parameters,PDPLQT . Of interest in the final solution to an occultationobservation is the sensitivity of the computed curve tovariations in the solution parameters. In the computationalprocess of determining differential corrections, numericalpartial derivatives of the intensity curve at each observedpoint are computed for each parameter considered in themodel. These derivatives, dl/dPj , are retained for the bestdetermined theoretical fit. Where each of these derivativesis at a maximum corresponds to an area of the computedintensity curve of high sensitivity to perturbations in thecorresponding parameter.Graphs, such as Figure 5-14, generated by the APLfunction PDPLOT , show dl/dPj for the variation of thesolution parameters. The partial derivative curves arelabeled as follows: PREI Pre-event Intensity ;POST = Post-event Intensity ; TIME " Time of GeometricalOccultation ; DIAM = Angular Diameter of Stellar Disk : andVELO = Velocity of Lunar Shadow Passage. In the case oftwo-star solutions the labeling of the derivative curves arepostfixed with a "1" or "2" as is appropriate. Each curvehas been normalized from -1 to 1 , with the line corresDondi ng

177to dl/dPj = drawn in. The actual values of dl/dPj differby orders o-f magnitude -for the -five parameters. Thus, therelative degree o-f sensitivity o-f the intensity curve is noteasily seen. The maximum and minimum values -for dl/dPj aregiven in the tables o-f supplementary statistical information.Discussion o-f Individual Qccultation EventsZ CQ916

i..178visual micrometer observations. More recent observations byMcAlister (Worley, 1984) have been via specklen terf erome tryHeintz -found a period for the visual pair o-f 13.17years, as reported by Muller (1961). The orbital elements hedetermined, along with the associated Thiele-Innes constants,were listed by Finsen and Worley (1970).Abt and Kallarakal

question of -final determination of spectral types may still17?beopen.The observation . On 22 March 1933, a lunar occultationo-f the K0III/G8III-VII

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181complete or detailed integration plots. Figures 5-3 and 5-4,shows no evidence o-f any disappearances other than those ofthe A and B visual components.Reduction and analysis o-f the 1 Geminorum A observation .The di -f-fract i on curves resulting -from the occultations o-f theA and B components were sufficiently separated to allowtreating each of these independently. It can be seen from theextracted data set that the B star is so far into theasymptotic falloff of the A star curve that the A starcontribution is negligable.Inspection of the A star curve immediately revealsi rregul ar i tes unanticipated in the disapearance of a singlestar, but of the sort commonly seen in the occultation of aclose double star. Attributing this to rapid atmosphericvariations is difficult, as the sky was well behaved throughthe other 3900 milliseconds of data taken.Despite the fact that there was an appearance ofduplicity, an attempt was first made to fit the A curve to asingle star model with the single-star DC program. Thoughliberal constraints were applied to the differentialcorrections, no solution could be obtained. An attempt wasthen made to fit the data to a two-star model, using the DC2program.The initial run of the two-star model allowed for thevariation of nine parameters: the diameters of the twosuspected stars, their times of geometrical occultation,their unoccul ted intensity, the local slopes of the lunar

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ve::limb (actually the projected component o-f the lunar velocity183vector) at the contact points o-f geometrical occultation. andthe background skylight. The slopes were presumed to beindependent as the to-be-determined separation might besu-f -f i c i entl y large to allow this.One hundred milliseconds o-f data were used in thereduction o-f 1 Gem A, as indicated in Table 5-2.TABLE 5-2TWO-STAR SOLUTION OF THE OCCULTATION OF 1 GEMINORUM AMODEL PARAMETERSNumber o-f Data Points:Number o-f Grid Points:Number o-f Spectral Regions:Width o-f Spectral Regions:Limb Darkening Coe-f -f i c i entE-f-fective Stellar Temperature:SOLUTIONSBrighter Star1014096550 Angstroms0.55400 KFainterStariStellar Diameter (ams)Time : < Re 1 at ) :Pre-Event Signal:Velocity :Lunar Limb Slope 0.73 (2.42)54.82 372.60

truncated so as not to include significant effects -from the1 Gem B curve. Additional reduction runs containing earlierdata points in the sample did not si gn i i cant 1 y alter thesolutions. The solution obtained by the DC2 procedure134indicated that both stars were essentially point sources, buta large formal error was attached to the diameter of thefainter star. This is understandable when one notes that thefainter star contributes only 1/3 of the total light to theA curve. Hence, the solution is, unfortunately, insensitiveto the diameter of the fainter star. With this in mind theprogram was re-run, but this time holding the diameter of thesecond star fixed as a point source. It was found, as mighthave been anticipated, that the resulting solutions werechanged insignificantly, though the formal errors werewidened slightly in most of the parameters.The parametric solutions are also presented inTable 5-2. The difference in time between the geometricaloccultations for the two A stars was 20.8

18!DISTANCE TO THE GEOMETRICAL SHADOW IN METERSj-40 -30 -20 -10 ^3362 3382 3402 3422" 3442TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWFi gure 5-5. FITPLOT o-f the 1 Gem A two-star solutionDISTANCE TO THE GEOMETRICAL SHADOV DM METERSi.n -40 -30 -9 -j0 a 10 20 5503451 3471 3481 3511 ~^STIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWFigure 5-6. FITPLOT o-f the 1 Gem 8 two-star solution

136of each of the parameters (i.e., the -first derivatives of theintensity curve) is shown on the PDPLOT , Figure 5-7.Reduction and analysis o-f the 1 Geminorum B observation .A similar approach was taken -for the solution o-f 1 Gem B.Here, however, DC2 was modified to determine dynamically if aone, or two-star solution would represent a better choice.This decision was made at the end of each differentialcorrection step. It was felt, in the light of the fact thatthe fainter component of 1 Gem B had never been detected,that a one star solution would be more appropriate.Nevertheless, the model would invariably return tore-entering the additional parameters necessary for atwo-star solution. Forcing a one star model resulted in aquasi -convergent solution; that is, the parameters exhibitedlarge amplitude oscillations about some mean values, ratherthan asymptotically approaching final values. The formalerrors and the sum square error of this "solution", and avisual inspection of the best obtainable fit weresignificantly worse than the two-star model. The two-starsolutions for 1 Gem B is presented in Table 5-3, andgraphically in Figure 5-6.Note here that the fainter, previously undetected,spectroscopic component of 1 Gem B is almost ten timesfainter than the brighter star. This led to a completei nsensi t i v i ty of the solution to the diameter of the fainterstar. Its detection, however, is quite evident, and the fitis made possible only with the change in level provided by

137COMP< VELiP% TTM1Q.INTiDIMrWWW\z3362 3382 3402 3422 3442TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-7. PDPLOT of the 1 Gem A two-star solution.COMP< VELi< TIM1INTI:ww\z""./VWv3451 3471 3491-*fc'3510 '3530TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-8. PDPLOT o-f the 1 Gem B two-star soluti on

the occul tation of the -fainter B star component. The PDPLOTfor the 1 Gem B solution is presented as figure 5-8.TABLE 5-3.TWO-STAR SOLUTION OF THE OCCULTATION OF 1 GEMINORUM B188MODEL PARAMETERSNumber of Data Points: 101Number of Grid Points: 4096Number of Spectral Regions: 5Width of Spectral Regions: 50 AngstromsLimb Darkening Coefficient: 0.5Effective Stellar Temperature: 5400 KSOLUTIONSBrighter Star Fainter StarStellar Diameter : 5.8? (0.84) Point SourceTime: (Relative): 61.00 (0.45) 52.6? (3.05)Pre-Event Signal: 301.30 (15.1) 33.50 (15.0)Velocity (m/sec): 773.5 (?.0) 787.5 (72.6)Lunar Limb Slope (deg): -11.1 (1.1) +12.3 (5.8)Background Sky Level: 115.? (3.3)Separation in Time (milliseconds): 8.31 (3.08)Projected Spatial Separation (ams): 3.34 (1.24)PHOTOMETRIC NOISEINFORMATIONSum-of-Squares of Residuals: 348100Sigma (Standard Error): 18.754Normalized Standard Error: 0.0857Photometric (S+N)/N Ratio: 12.68Total Intensity/Background: 2.8?Change in Magnitude: 1.15A discussion of the 1 Geminorum results . Thedistribution function of the residuals of the four-star fitto the observed data is shown in the NOISEPLOT, Figure 5-?.The power spectra of the observed and computed four-star fit,as well as the power spectrum of the pre-occul tat i on signal,can be seen on the POWERPLOT, Figure 5-10.

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11'1«1190MODEL CURVETOCCULTATION"0'1005012?FREQUENCY INI300" 400HERTZFigure 5-10. POUERPLOT o-f the ZC0916 occupation.

191For purposes of clarity in this discussion the brightercomponent o-f 1 Gem A is referred to as Al and the -fainter asA2. Similarly denoted is the brighter member o-f 1 Gem B asBl and its unseen spectroscopic companion as B2. Theintention in doing so is not necessarily to imply that theA stars are actually a physical pair

192system, it is quite understandable that its spectralsignature does not make itsel-f readily apparent.TABLE 5-41 GEM: COMPONENT CONTRIBUTION TO TOTAL SYSTEM INTENSITYStar Intensi ty XTotalmV^mVAl 372.6 45.02A2 120.3 14.535.05 (+/- 0.02)6.27 < +0.1 2, -0.10) 1 .22A1+A2 492.9 59.55Bl 301 .3 36.40B2 33.5 4.054.745.28 (+0.06,-0.05)7.66 ( +0.64, -0.40) 2.40B1+B2 334.8 40.45 5.19 0.43As to its e-f-fect on the long period radial velocitycurve o-f 1 Gem A, it need have none i-f Al and A2 are aphysical pair with an inclination near zero degrees. Itwould, however, be presumptuous to assume, a priori, thatthis is the case. I-f A2 has an independent orbit about thebarycenter o-f the system, one still might see an e-f-fect inthe long period radial velocity curve o-f the AB system. Toresolve this question one will have to look care-fully at theavailable radial velocity data, with an eye to the idea thata -fourth component most probably exists. This is a matterfor -future investigation. It is of interest to note that intheir exposition o-f 1 Geminorum, Abt and Kallarakal concludethat "the astrometric and spectroscopic observations areconsistent with a multiple system in which the primary is aK0III star that may be single"

.193not rule out the existance o-f this newely discoveredcomponentIn principle an occultation observation itself canprovide a constraint on the orbit o-f a visual binary. Theposition angle, P, and angular separation 0, are inseparablefrom a single occultation observation alone. Only aprojected separation, along a line in space can be -found.However, given an orbit with its associated errors, theintersection o-f that line with the orbit provides anindependent, highly accurate (though only solitary)observation. Un-f ortunatel y , with the addition o-f a fourthmember in the 1 Gem system the situation is not quite asclearcut.If 1 Gem A is assumed to be a physical pair, that is tosay a hierarchy 2 quadruple system a la Evans (1968), thenthe visual observations of the AB pair would have been madenot with respect to the AB positions, but with respect to thecenters-of-1 ight (CL's) of the A and B component systemsrespectively. In the case of 1 Gem B the difference isnegligible, but not necessarily so for 1 Gem A.Figure 5-11 shows the chords both in time and spacecontaining the A and B stars. The figure is oriented so thetopocentric radial direction of approach of each star to thesmooth lunar limb is vertical. Thus, the stars lie somewherealong the horizontal chords. The intersection of thehorizontal chords with the time scale on the left is simplythe relative times of geometrical occultation. The bottom

—194— X3 a4 c+• Ti ft nC JZ "0 4imilliarcsecondsa> +> Oi .N 0) £ L Oi— C — •*• D nn 3 ft X4i — — 1 LH ^£ CO £ flj XM • 4-> o Oin JZ Ui Oi *>•+• CM *- O'T) wo * F— c — -^* •— Ol-H * * en CO c— .0 ^ •c —1 fli Oi "0 «in — ui L C — pi•M flj * -^ Q.Oi 1/1

)195line is both the chord of A2 (which disappeared first) andthe smooth lunar limb at the time of A2's geometricaloccultation. The top line corresponds to Bl's disappearance,which happened last. From the measured intensities of eachof the four stars, the CL's of the Al ,A2 and Bl ,B2 pairs werecomputed as the intensity and time-weighted-means of therespective components. Hence, the time of geometricaloccultation of the CL of the A system isCL(A)=C (54.82x372. 6) +

then the projected angular separation, D, is 31.5

197Figure 5-12 shows the observed and computed residuals -forboth P and e.There is no intention to suggest that there is anyphysical meaning to any o-f the particular coe-f-f i c i ents.Rather, the -fitting was done to provide a reasonable methodo-f extrapolation, on the basis o-f the O-C's -for the orbit,for corrections to be applied to predicted values o-f P and S•for the date o-f the occultation observation. In doing socorrections o-f -22°099 -for 0, and +01004547 -for P werefound. The corrected quantities are denoted 9' = 4

on1980.09pRESIDUALS-0.04$12.09r» n n r8 RESIDUALS-43.04-i1948.82 1983.219Fiqure 5-12. The 3 and P residuals based on Heintz'sdetermination o-f the 1 Geminorum visual orbit are shown -for58 observations as listed by Worley. The best fit to theresiduals (a third order polynomial) is also shown. Thenumbers or letters indicate the -following observers:0-Kuiper 1 -Wilson 2-Muller 3-Van Beisbroeck4-Finsen 5-Heintz 6-Couteau 7-Worley8-Uan Den Bos 9-Baize A-McAlister B-TokovininC-Morel D-Ex trapol at i to 1983.219

199radial direction of lunar approach. Since the inclination o-fthe orbit (as well as the orientation o-f the major axis o-fthe projected orbital ellipse) is unknown, the relativepositions of the individual components cannot be determined.Since, however, the fainter star disappeared first, it musthave been essentially to the west of Bl . Knowing the lunarPA of the event, one can then say that the Bl star was at aposition angle greater than 24 , but less than 204 , measuredeastward from North of the B2 star. Finally, it is notedfrom Griffin's period and

'I'I'II'I'I200COUNTSa.CD GO CD LO& Q St SI0) (D N ffl in*SCOQCMQ

TABLE 5-6Z CO 91 6: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 3362201NUM OBS COMP RESID NUM OBS COMP RESID NUM OBS COMP RESID891 920.3 -29.31 905 925.5 -20.52 928 933.0 -5.03 974 937.5 36.54 990 934.9 55.15 1015 927.7 87.36 978 921.2 56.87 983 917.4 65.68 967 913.8 53.29 936 910.2 25.810 968 910.6 57.411 1001 918.2 82.812 1004 930.4 73.613 1060 939.9 120.114 963 942.3 20.715 916 940.2 -24.216 890 938.8 -48.817 891 939.5 -48.518 869 937.3 -68.319 825 926.8 -101.820 881 909.6 -28.621 803 894.2 -91.222 866 889.9 -23.923 896 899.1 -3.124 867 914.5 -47.525 888 925.5 -37.526 884 926.0 -42.027 933 919.2 13.828 890 915.2 -25.229 896 923.4 -27.430 945 945.5 -0.531 98 9 974.0 15.032 991 996.3 -5.333 1081 1001.9 79.134 1112 987.6 124.435 975 959.8 15.236 931 930.1 0.937 924 910.4 13.638 911 907.4 3.639 880 920.4 -40.440 965 941.9 23.141 950 961.3 -11.342 956 969.1 -13.143 971 959.7 11.344 998 933.1 64.945 951 894.3 56.746 845 851.3 -6.347 765 812.8 -47.848 723 786.0 -63.049 716 774.9 -58.950 810 780.5 29.551 840 800.4 39.652 768 830.2 -62.253 835 864.6 -29.654 917 8 98.3 18.755 896 926.6 -30.656 932 946.4 -14.457 928 955.8 -27.858 936 954.3 -18.359 958 942.6 15.460 962 922.0 40.061 959 894.4 64.662 937 861.8 75.263 909 826.2 82.864 808 789.1 18.965 750 752.2 -2.266 731 716.5 14.567 663 682.9 -19.968 603 651.7 -48.769 598 623.4 -25.470 568 598.0 -30.071 542 575.5 -33.572 500 555.8 -55.873 504 538.6 -34.674 503 523.7 -20.775 460 510.9 -50.976 441 499.9 -58.977 448 490.5 -42.578 452 482.5 -30.579 464 475.6 -11.680 459 469.8 -10.881 487 464.8 22.282 462 460.5 1.583 487 456.9 30.184 466 453.8 12.285 460 451.1 8.986 440 448.8 -8.887 474 446.9 27.188 490 445.1 44.989 440 454.5 -14.590 463 450.2 12.891 437 446.7 -9.792 429 447.3 -18.393 461 452.4 8.694 456 458.1 -2.195 465 459.5 5.596 457 454.4 2.697 409 446.2 -37.298 3 90 441.4 -51.499 400 444.7 -44.7100 453 454.5 -1.5101 467 464.1 2.9102 436 466.1 -30.1103 458 458.3 -0.3104 489 445.4 43.6105 467 435.7 31.3106 470 435.8 34.2107 478 446.2 31.8108 478 461.3 16.7109 498 472.7 25.3110 482 474.0 8.0111 519 464.4 54.6112 480 448.4 31.6113 419 433.8 -14.8114 406 427.4 -21.4115 402 432.1 -30.1116 449 446.0 3.0117 479 463.6 15.4118 443 478.4 -35.4119 483 484.8 -1.8120 485 480.8 4.2121 432 467.6 -35.6122 457 449.3 7.7123 431 431.3 -0.3124 409 418.6 -9.6125 436 414.7 21.3126 401 420.7 -19.7127 461 435.8 25.2128 480 457.4 22.6129 493 481.8 11.2130 507 505.3 1.7131 507 524.6 -17.6132 540 537.3 2.7133 524 541.9 -17.9134 541 538.2 2.8135 550 526.5 23.5136 462 508.0 -46.0137 477 484.2 -7.2138 447 456.6 -9.6139 429 426.9 2.1140 411 396.3 14.7141 356 366.1 -10.1142 332 337.1 -5.1143 334 309.9 24.1144 304 284.9 19.1145 273 262.4 10.6146 271 242.4 28.6147 226 224.7 1.3148 181 209.3 -28.3149 196 196.0 0.0150 182 184.6 -2.6151 179 174.8 4.2152 168 166.5 1.5153 152 159.4 -7.4154 160 153.4 6.6155 157 148.4 8.6156 150 144.1 5.9157 139 140.4 -1.4158 133 137.3 -4.3159 119 134.7 -15.7160 131 132.5 -1.5161 125 130.6 -5.6162 151 128.9 22.1163 133 127.5 5.5164 116 126.3 -10.3165 113 125.2 -12.2166 109 124.3 -15.3167 122 123.5 -1.5168 141 122.8 18.2169 126 122.2 3.8170 133 121.7 11.3171 124 121.2 2.8172 121 120.8 0.2173 108 120.4 -12.4174 111 120.1 -9.1175 102 119.8 -17.8176 117 119.5 -2.5177 132 119.3 12.7178 118 119.1 -1.1179 129 118.8 10.2180 115 118.7 -3.7181 122 118.5 3.5182 107 118.3 -11.3183 113 118.2 -5.2184 136 118.1 17.9185 123 117.9 5.1186 114 117.8 -3.8187 101 117.7 -16.7188 106 117.7 -11.7

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)204The contention that the lack o-f any detectable spectralfeatures -from the spectroscopic component o-f 1 Gem B is dueto a considerably lower intrinsic luminosity seems consistentwith the V magnitude -found -for this component.ZC1221 (9 CancriThe moderately bright M3-1 1 1 star ZC1221(9 Cancri) was occulted under -favorable conditions onMarch 24, 1983. Table 5-9 gives a synopsis o-f theoccultation observation. The RAWPLOT, Figure 5-14, shows theraw observational data. Data acquisition was haltedapproximately 800 milliseconds be-fore the end o-f the datawi ndow.A care-ful examination o-f the integration plot,Figure 5-15, indicates a slight downward de-flection at2300 milliseconds. This change in integrated level, duepossibly to the presence o-f a second star, is rather subtle.In order to more easily see this level change, an integrationplot approximately 1200 milliseconds in length, centeredroughly at the suspected time o-f secondary disappearance andexcluding the primary occultation, was plotted and is shownin Figure 5-16. From the cusp seen at 2280 milliseconds, itis evident that a secondary event did occur.The best -fit to the primary occultation event, showngraphically in Figure 5-17, places the relative time o-fgeometrical occultation close to 3426 milliseconds. Thus,the -fainter star disappeared 1146 milliseconds be-fore thebrighter one. The angular velocity o-f lunar limb passage was

.205ZC1221:TABLE 5-9LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: ZC1221, (9 Cancr i , SAO 079940, DM +23 1887)RA: 080518 DEC: +224106 mV: 6.24 Sp : M3-IIIFilter: V Diaphragm: I Gain: C7+ Voltage: 1000LUNARINFORMATIONSurface Illumination:Elongation from Sun:Altitude Above Horizon:Lunar Limb Distance:Predicted Shadow Velocity:Predicted Angular Rate:EVENTINFORMATION72 percent116 deorees78 decrees1038 k i 1 ometers657 2 meters/sec3756 arcsec/sec.Date: March 24, 1983 UT of Event: 00:44:56USNO V/0 Code: 17 HA of Event: -114426Position Angle: 110.4 Cusp Angle: 83SContact Angle: -11.0 Watts Angle: 97.4MODEL PARAMETERSNumber of Data Points: 201Number of Grid Points: 1600Number of Spectral Regions: 53Width of Spectral Regions: 50 AngstromsLimb Darkening Coefficient: 0.5Effective Stellar Temperature: 3300KSOLUTIONSStellar Diameter

206COUNTSCO CO Is * h* 00 OD0) CO s CD \n^>Q CO CM CD

207COz111QLilN

i203COUNTSr^ in CO s enCO Tfto s ^r CO -*-i LO njr* ID CM CD h* rf •*H03 0) 0) CNJ CM CM CMCMCO0)0)COCONONs-c3uuo_lQ.hinL03 N (D ID t (D•**•••(\l•S S SI Si S 5} SA±ISN3_LNI QHZIlVWaON

y•found to be 0.3881 seconds of arc per second. The projected20?separation between the two stars, there-fore, was 0.44 secondso-f arc .The actual change in mean signal level due to thefainter star's disappearance, as determined -from the500-mi 1 1 i second samples be-fore and a-fter the secondary event,was 29.5 counts. This is only 0.022 o-f the intensity o-f thebrighter star. Hence, the fainter star is approximately 4magnitudes fainter in Kf than the brighter star. While thereis always the possibility of a second star coi nc idental 1being in the field of view under study, in an 15.2 arcseconddiaphragm

|I I i i|i i i i|i i i i|i i i illi|2103315 3355 3395 3435 '3475"TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-18. PDPLOT o-f the occultation o-f ZC1221(0UJQZ 0263 _ SIGMA 0.058821LUen 0232 _q:DU 0197uo0165u.occUJ(DD2032S_0296 _ MEAN -0.017060132009S_0066 _0033 _0002, ii Ii_LL44.1 -37.6 -31.1 -24.8H.8.1 -U.6 -5.1 L4 7.9 14.4NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-19. NOISEPLOT o-f the occultation o-f ZC1221.

211Figure 5-18, the best -fit to the observed data, in thisregion, is quite good.Figure 5-19 shows the residuals of the -fit to the4096 milliseconds o-f the observation. The Gaussian nature o-fthe residuals

TABLE 5-10ZC1221: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 3315RDM OBS COMP RES ID NUM OBS COMP RES ID2770 2935.4 -165.4 67 2958 2963.2 -5.21 2868 2935.6 -67.6 68 3036 2888.3 147.72 3016 2935.5 80.5 69 2855 2825.4 29.63 2753 2935.3 -182.3 70 2528 2799.7 -271.74 2801 2935.3 -134.3 71 3095 2823.0 272.05 2914 2935.4 -21.4 72 2873 28 90.1 -17.16 2991 2935.5 55.5 73 2900 2981.2 -81.27 2918 2935.5 -17.5 74 2887 3069.2 -182.28 3065 2935.4 129.6 75 3377 3128.4 248.69 2910 2935.2 -25.2 76 2918 3141.7 -223.710 3054 2935.3 118.7 77 3175 3104.5 70.511 2971 2935.8 35.2 78 3411 3025.2 385.812 3018 2935.7 82.3 79 3328 2921.4 406.613 2683 2935.2 -252.2 80 2919 2815.6 103.414 2917 2935.1 -18.1 81 2747 2729.3 17.715 3080 2935.6 144.4 82 2754 2679.0 75.016 3183 2935.8 247.2 83 2641 2673.9 -32.917 2763 2935.4 -172.4 84 2617 2714.6 -97.618 2787 2935.3 -148.3 85 2722 2795.0 -73.019 3245 2935.7 309.3 86 3185 2903.4 281.620 3071 2935.6 135.4 87 3167 3025.7 141.321 2820 2935.0 -115.0 88 3239 3147.3 91.722 2943 2935.4 7.6 89 3363 3255.4 107.623 3162 2936.5 225.5 90 3319 3340.0 -21.024 2815 2936.4 -121.4 91 3363 3394.5 -31.525 2975 2934.7 40.3 92 3767 3416.0 351.026 3095 2934.0 161.0 93 3344 3404.5 -60.527 2655 2935.9 -280.9 94 3259 3362.6 -103.628 2693 2938.0 -245.0 95 2975 3294.6 -319.629 2941 2937.1 3.9 96 3482 3205.8 276.230 2689 2933.8 -244.8 97 3172 3101.6 70.431 2601 2932.9 -331.9 98 2833 2987.6 -154.632 2782 2936.0 -154.0 99 2741 2868.7 -127.733 3106 2939.2 166.8 100 2582 2748.9 -166.934 2872 2938.2 -66.2 101 2579 2631.6 -52.635 2779 2934.1 -155.1 102 2505 2519.5 -14.536 2942 2932.3 9.7 103 2737 2414.2 322.837 2883 2935.2 -52.2 104 2575 2317.0 258.038 2857 2939.2 -82.2 105 2335 2228.3 106.739 2831 2939.1 -108.1 106 2307 2148.4 158.640 2815 2935.3 -120.3 107 1916 2077.0 -161.041 2488 2932.9 -444.9 108 1777 2013.7 -236.742 2478 2935.4 -457.4 109 1769 1958.0 -189.043 2834 2939.9 -105.9 110 1839 1909.3 -70.344 2723 2940.3 -217.3 111 1965 1866.8 98.245 2927 2934.8 -7.8 112 1933 1829.9 103.146 298 9 2929.2 59.8 113 1837 1798.0 39.047 2631 2931.0 -300.0 114 1559 1770.4 -211.448 2819 2941.1 -122.1 115 1747 1746.6 0.449 3003 2951.0 52.0 116 1947 1726.0 221.050 3063 2950.0 113.0 117 1799 1708.3 90.751 3357 2935.5 421.5 118 1998 1693.1 304.952 2654 2917.2 -263.2 119 1621 1679.9 -58.953 2967 2910.7 56.3 120 1535 1668.5 -133.554 303 9 2924.7 114.3 121 1426 1658.6 -232.655 2862 2953.2 -91.2 122 1739 1650.0 89.056 3007 2977.6 29.4 123 1769 1642.6 126.457 3221 2979.6 241.4 124 1845 1636.1 208.958 2523 2953.3 -430.3 125 1859 1630.4 228.659 2863 2911.3 -48.3 126 1687 1625.5 61.560 30 93 2877.5 215.5 127 1552 1621.1 -69.161 3293 2873.5 419.5 128 1489 1617.2 -128.262 3174 2905.9 268.1 129 1602 1613.8 -11.863 3067 2961.9 105.1 130 1580 1610.8 -30.864 3243 3015.5 227.5 131 1505 1608.1 -103.165 3204 3039.9 164.1 132 1526 1605.7 -79.766 2892 3020.9 -128.9 133 1640 1603.5 36.5212NUM OBS COMP RES ID135 1145 1599.9 -454.9136 1403 1598.4 -195.4137 1405 1597.0 -192.0138 1354 1595.8 -241.8139 1531 1594.7140 1548 1593.7141 1645 1592.7142 1685 1591.9143 1811 1591.1144 1506 1590.3145 1492 1589.6146 1391 1589.0147 1485 1588.4148 1665 1587.8149 1579 1587.3150 1574 1586.9151 1684 1586.5152 1746 1586.2153 1577 1585.8154 1696 1585.5155 1754 1585.1156 1638 1584.8157 1639 1584.5158 1598 1584.2159 1387 1584.0160 1560 1583.8161 1497 1583.6162 1603 1583.4163 1636 1583.2-63.7-45.752.393.1219.9-84.3-97.6-198.0-103.477.2-8.3-12.997.5159.8-8.8110.5168.953.254.513.8-197.0-23.8-86.619.652.8164 1408 1583.0 -175.0165 1512 1582.8 -70.8166 1423 1582.6 -159.6167 1502 1582.4 -80.4168 1508 1582.3 -74.3169 1830 1582.2 247.8170 1475 1582.0 -107.0171 1728 1581.9 146.1172 1587 1581.8 5.2173 1755 1581.6 173.4174 1610 1581.5 28.5175 1735 1581.4 153.6176 1751 1581.3 169.7177 1577 1581.2 -4.2178 1655 1581.1 73.9179 1736 1581.0 155.0180 1446 1581.0 -135.0181 1456 1580.9 -124.9182 1627 1580.8 46.2183 1632 1580.7 51.3184 1488 1580.6 -92.6185 1599 1580.6 18.4186 1658 1580.5 77.5187 1629 1580.4 48.6188 1728 1580.4 147.6189 1660 1580.3 79.7190 1498 1580.3 -82.3191 1548 1580.2 -32.2192 1551 1580.2 -29.2193 1676 1580.1 95.9194 1807 1580.1 226.9195 1455 1580.0 -125.0196 1359 1580.0 -221.0197 1465 1579.9 -114.9198 1615 1579.9 35.1199 1719 1579.8 139.2200 1775 1579.8 195.2

213TABLE 5-11ZC1221: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO-VARIANCEMATRIXDIAM PREI POST TIME VELO2.463E~16 3.103E~08 -2.809E 08 -7.701E 10 2.575E~113.103E~08 2.781E02 8.816E00 -1.967E00 4.594E_02-2.809E"08 8.816E00 3.423E02 -2.411E00 5.674E_02-7.701E"10 -1.967E00 -2.411E00 3.342E_01 -7.973E032.575E~11 4.594E"02 5.674E 02 -7.973E 03 2.643E~04CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.797793 -0.744069 0.077028 -0.081285PREI 0.797793 1.000000 -0.191055 -0.535414 0.531644POST -0.744069 -0.191055 1.000000 -0.721129 0.723939TIME 0.077028 -0.535414 -0.721129 1.000000 -0.999988VELO -0.081285 0.531644 0.723939 -0.999988 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMIN IMUMDIAM 2 .730E09 -2.742E09PREI 1.358E00 1 .324E"03POST 9.987E~01 -3.578E 01TIME 1 .200E02 -1 .243E02VELO 4.841E03 -5.026E03

214MODELCURVEi rSTAR + SKYOCCULTATION 1'100" '200' "3 00' '400FREQUENCY INHERTZFigure 5-20. POUERPLOT of the occultation of ZC1221.

215M3— 1 1 1 star to be on the order of 50 solar diameters. At adistance o-f 250 parsecs this corresponds to an angulardiameter of 1.9 milliseconds of arc. Hence, theobservat i onal 1 y determined diameter seems entirely reasonableand in accord with the previously known stellar data.A rather good internal precision o-f the time o-fgeometrical occultation, with a -formal error o-f only0.58 milliseconds, was achieved in the reduction process.However, the radio signal carrying the WwVB time code wasunusually noisy, leading to a large one sigma error in theCoordinated Universal Time o-f 0.012 seconds. The CoordinatedUniversal Time o-f geometrical occultation was determined tobe 00:44:55.87? (+/- 0.012 seconds).ZC1222As indicated on the occultation summary -for the SO starZC1222 (Table 5-12>, this event occured only one hal-f houra-fter the previously discussed occultation o-f 9 Cancri. Thephotometric conditions -for these two events were nearlyidentical. This is evidenced by an in tercompar ison o-f thenormalized standard errors, and the photometric

'.16TABLE 5-122 CI 222: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: ZC1222, (SAO 079948, DM +22 1854)RA: 080535 DEC: +223024 mV: 7.22 Sp : GOFilter: V Diaphragm: I Gain: CIO Voltage: 1200LUNARINFORMATIONSur-face Illumination: 72 percentElongation -from Sun: 116 degreesAltitude Above Horizon: 82 degreesLunar Limb Distance: 360913 kilometersPredicted Shadow Velocity: 336.9 meters/sec.Predicted Angular Rate: 0.2467 arcsec/secEVENTINFORMATIONDate: March 24, 1983 UT o-f Event : 01:14:46USNO V/O Code: 26 HA of Event : -042030Position Angle: 150.8 Cusp Angle: 42SContact Angle: -49.6 Watts Anol e : 137.8MODEL PARAMETERSNumber o-f Data Points:201Number o-f Grid Points: 256Number of Spectral Regions: 53Width o-f Spectral Regions: 50 AnostromsLimb Darkening Coe-f -f i c i en t 0.5E-f-fective Stellar Temperature: 5900 KSOLUTIONSStellar Diameter (ams): Poi nt SourceTime: (relative to Bin 0): 2923.3 (2.1)Pre-Event Sional: 2117.4 (20.7)Background Sky Level : 1305.0 (44.8)Velocity (meters/sec . ) : 431.7 (12.5)Lunar Limb Slope (degrees): +19.34 U.T. o-f Occultation: 01:14:46.177 (0.004)PHOTOMETRIC NOISEINFORMATIONSum-o-f-Squares o-f Residuals: 13498450Sigma (Standard Error): 259.7927Normalized Standard Error: 0.31979Photometric (S+N)/N Ratio: 4.12699(Change in In tensi ty)/Background: 0.62251Chanoe in Maonitude: 0.52547

217^4096k>12 1024 1536 '2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-21. RAUPLOT o-f the occultation o-f ZC1222.fe12 1024 1536 2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-22. INTPLOT o-f the occultation o-f 2C1222.

218of data subsets, show no compelling evidence of "wide"stel 1 ar dupl i c i tyThe best model fit to the observations indicated thatthe star was a point source (or at least below the detectionthreshold of approximately 1 millisecond of arc). This wasas expected, considering the spectral type and apparentV magnitude of the star. The graphic depiction of the fit isshown in Figure 5-23. The observational data, the solutioncurve intensities and the residuals are given in Table 5-13.The formal statistics of the solution parameters< var iance-covar i ance , correlation matrices, and range ofpartial derivatives) can be found in Table 5-14. The PDPLOT,showing the sensitivity of the model intensity curve to thevariation of the solution parameters, is presented asFigure 5-24.The internal formal error of the time of geometricaloccultation was not quite as good as one might have expected,if that expectation were based solely on the noise statisticsof the observation. It should be noted that the determinedL-rate for this event (431.7 meters/second) is 63 percentslower than the L-rate determined for the ZC1221 event (691.0meters/second). Under identical photometric conditions thiswould widen the uncertainty in the time of geometricaloccultation by the same amount. Fortunately, in theintervening half hour between these two events, the signalstrength of the WwVB time code improved dramatically. Theone sigma error of the WwVB time reference was a reasonable

I!1?(J)m-»-lCD r^co COr.Haa.LOsQQQQSlsisiSlSlSlajjsn3_lni aaznvwwoN

TABLE 5-13ZC1222: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALSFROM BIN 2760220NUM OBS COMP RESID NUM OBS COMP RESID NUM OBS COMP RESID2145 2115.9 29.1 67 1851 2134.5 -283.51 2634 2115.9 518.1 68 2020 2156.3 -136.32 2574 2117.4 456.6 69 2126 2175.3 -49.33 2107 2119.9 -12.9 70 2559 2189.1 369.94 2287 2122.6 164.4 71 3111 2195.8 915.25 2125 2124.3 0.7 72 2540 2194.7 345.36 1903 2124.6 -221.6 73 2186 2185.5 0.57 1745 2123.1 -378.1 74 2344 2169.0 175.08 2151 2120.4 30.6 75 2413 2146.9 266.19 2031 2117.4 -86.4 76 2335 2121.1 213.910 2164 2115.3 48.7 77 2019 2094.3 -75.311 1918 2114.6 -196.6 78 1840 2069.0 -229.012 1830 2115.8 -285.8 79 1964 2047.7 -83.713 2182 2118.6 63.4 80 1703 2032.5 -329.514 1971 2121.9 -150.9 81 2073 2024.8 48.215 2571 2124.7 446.3 82 1903 2025.6 -122.616 2335 2126.0 209.0 83 2310 2034.8 275.217 2166 2125.3 40.7 84 2329 2051.8 277.218 2032 2122.8 -90.8 85 1931 2075.3 -144.319 1873 2119.3 -246.3 86 2107 2103.7 3.320 2213 2116.0 97.0 87 2049 2134.7 -85.721 2415 2113.7 301.3 88 2551 2166.1 384.922 2303 2113.4 189.6 89 2660 2195.5 464.523 2508 2115.4 3 92.6 90 2329 2220.8 108.224 2155 2119.1 35.9 91 2174 2240.4 -66.425 1738 2123.3 -385.3 92 2500 2252.9 247.126 2353 2127.0 226.0 93 2067 2257.3 -190.327 2267 2128.8 138.2 94 1819 2253.5 -434.528 2460 2128.3 331.7 95 1783 2241.7 -458.729 2279 2125.1 153.9 96 2283 2222.4 60.630 2602 2120.3 481.7 97 2138 2197.0 -59.031 2040 2115.0 -75.0 98 2541 2166.8 374.232 1894 2110.5 -216.5 99 2047 2133.4 -86.433 2026 2108.4 -82.4 100 1780 2098.7 -318.734 2139 2109.3 29.7 101 1759 2064.5 -305.535 1694 2113.2 -419.2 102 1741 2032.4 -291.436 2412 2119.5 292.5 103 2074 2004.0 70.037 2307 2126.8 180.2 104 1790 1980.7 -190.738 2859 2133.4 725.6 105 1831 1963.4 -132.439 2696 2137.6 558.4 106 1734 1952.9 -218.940 1866 2138.2 -272.2 107 1687 1949.5 -262.541 1589 2134.9 -545.9 108 1603 1953.4 -350.442 2215 2127.9 87.1 109 1759 1964.4 -205.443 2303 2118.6 184.4 110 1767 1981.9 -214.944 2175 2108.7 66.3 111 1951 2005.4 -54.445 2239 2100.3 138.7 112 2169 2033.9 135.146 1667 2095.2 -428.2 113 2126 2066.5 59.547 1197 2094.8 -897.8 114 2203 2102.0 101.048 1801 2099.4 -298.4 115 1967 2139.4 -172.449 2232 2108.6 123.4 116 1991 2177.6 -186.650 2211 2120.9 90.1 117 2152 2215.5 -63.551 2607 2134.5 472.5 118 2031 2252.0 -221.052 2535 2146.8 388.2 119 2011 2286.3 -275.353 2615 2155.7 459.3 120 2102 2317.7 -215.754 2055 2159.5 -104.5 121 2361 2345.3 15.755 1821 2157.2 -336.2 122 2263 2368.8 -105.856 2466 2148.9 317.1 123 2204 2387.8 -183.857 2104 2135.5 -31.5 124 2399 2401.8 -2.858 2043 2118.8 -75.8 125 2590 2410.9 179.159 2207 2101.3 105.7 126 2296 2415.0 -119.060 2156 2085.4 70.6 127 2592 2414.2 177.861 1763 2073.7 -310.7 128 2385 2408.6 -23.662 1635 2068.0 -433.0 129 2623 2398.4 224.663 2198 206 9.3 128.7 130 2450 2384.0 66.064 1871 2077.8 -206.8 131 2083 2365.8 -282.865 2145 2092.8 52.2 132 2228 2344.0 -116.066 1881 2112.4 -231.4 133 2583 2319.1 263.9134 2245135 2365136 2081137 2151138 2611139 2100140 1814141 1975142 1628143 1871144 1553145 1775146 1606147 1796148 1747149 1848150 1998151 2128152 2193153 1727154 1598155 1749156 1620157 1624158 1391159 1534160 1611161 1935162 1759163 1730164 1434165 1425166 1759167 1662168 1396169 1456170 1175171 1299172 1095173 1263174 1787175 1492176 1066177 1165178 1388179 933180 1483181 1385182 1562183 1200184 1496185 1161186 1071187 1227188 974189 1183190 1535191 1380192 1557193 1864194 1540195 1224196 1048197 1146198 16 97199 1351200 14552291.52261.62229.82196.52162.12127.02091.42055.62019.91984.61949.81915.81882.61850.41819.31789.41760.61733.21707.01682.11658.51636.11615.01595.11576.31558.71542.21526.71512.31498.71486.11474.31463.31453.01443.41434.61426.31418.61411.41404.813 98.613 92.81387.51382.51377.91373.61369.61365.81362.41359.21356.11353.31350.71348.31346.01343.91341.91340.01338.31336.71335.11333.71332.41331.11329.91328.81327.8-46.5103.4-148.8-45.5448.9-27.0-277.4-80.6-391.9-113.6-396.8-140.8-276.6-54.4-72.358.6237.43 94.8486.044.9-60.5112.95.028.9-185.3-24.768.8408.3246.7231.3-52.1-49.3295.7209.0-47.421.4-251.3-119.6-316.4-141.8388.499.2-321.5-217.510.1-440.6113.419.2199.6-159.2139.9-192.3-279.7-121.3-372.0-160.9193.140.0218.7527.3204.9-109.7-284.4-185.1367.122.2127.2

221TABLE 5-14ZC1222: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO- VARIANCE MATRIXDIAM PREI POST TIME VELO2.849E"15 1.373E"07 -5.788E~07 7.215E 10 1.217E 111.373E"07 4.349E02 7.193E01 -1.093E01 5.701E~025.788E~07 7.193E01 2.154E03 -4.181E01 2.091E~017.215E~10 -1.093E01 -4.181E01 4.480E00 -2.315E_021.217E"11 5.701E~02 2.091E 01 -2.315E 02 1.587E 04CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.288964 -0.968314 0.871718 -0.865589PREI 0.288964 1.000000 -0.040942 -0.210200 0.221926POST -0.968314 -0.040942 1.000000 -0.965427 0.962118TIME 0.871718 -0.210200 -0.965427 1.000000 -0.999923VELO -0.865589 0.221926 0.962118 -0.999923 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 8.475E08 -8.332E08PREI 1.366E00 2.803E_02POST 9.720E"01 -3.664E 01TIME 3.576E01 -3.819E01VELO 6.809E03 -7.093E03

2222760 2800 '2840 2880 '2920TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-24. PDPLOT o-f the occupation o-f ZC1222.(0UJo2LJceoQO0331-0296 _ MEAN -0.002560265 _ SIGMA 0.1066900232 _01990166O 0132uj009S_03D 0066 _20032 _0002 JJJJ M-84.9-72.9-60.8-48.7-36.7-24.6-12.5 -0.4 U.6 23.7NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-25. NOISEPLOT o-f the occultation o-f ZC1222.

2233.1 milliseconds. The Universal Time o-f geometricaloccultation was -found to be 01:14:50.125

224MODELCURVEOCCULTATION"0'100' *200 •300" '400FREQUENCY INHERTZFigure 5-26. POUERPLOT o-f the occultation o-f ZC1222.

:.225TABLE 5-15X07589: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X07589

226*512 '1024 1536 2048 2560 '3072 '3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-27. RAWPLOT o-f the occupation o-f X0758?L0 _12 1024 1536 2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-28. INTPLOT o-f the occultation o-f X07589.

.227deflecting the curve in a downward direction. The intrusionof increasing Earthshine midway through the data windowcaused a decrease in the integrated intensity (subtractedfrom the mean) -for data taken be-fore the moon's 1 imb enteredthe diaphragm.Fortunately, since the star was held close to the centerof the f iel d-of-v iew (as called -for by standard observingprocedures), the increase in background illumination was veryclose to linear over the short timescale of the occultationevent. The lunar angular velocity -for this event was 0.4720seconds o-f arc per second. Thus, in the 200 milliseconds o-fdata extracted for the DC solution, the lunar limb traversedan angular distance o-f only about 100 milliseconds o-f arc.This is only 1/150 o-f the diameter o-f the -f i el d-o-f-v i ew givenby the diaphragm employed in the observation. (SeeTable 2-3)The assumption o-f linearity in the increase inbackground light is indeed proven correct by examination ofthe integration plot. The non-linear change in intensity(due to Earthshine) begins at roughly 2200 milliseconds. Theslope of the descending branch of the integration plotchanges here. The time at which the change in intensity dueto contributed Earthlight is greatest, is at the minumum ofthe integration plot, at approximately 2700 milliseconds.While still increasing, the change in Earthlight isessentially linear by millisecond 3600, where the slope of

228the integration plot remains constant until the decreasecaused by the occultation itself sets in.The result of a linear increase in background lightcauses an effective tilt in the observed occultationintensity curve. Rather than modeling the slope o-f this tiltas an additional free parameter in the DC solution, a simplerapproach was taken. A linear least squares -fit was done toboth the pre-occul tat ion and post-occul tat i on observations,each containing 100 samples of data bordering the solutiondata subset. The characteristic slopes obtained were foundto be in good agreement and were averaged. The occultationdata were then "detilted" by the appropriate amount beforebeing submitted to the DC solution process.The only time this method of removing increasingmoonlight from the occultation data set would not be validare in the cases of near-grazing incidence, or if the starwere near the eastern or western extreme of thef i el d-of-v iew. In either of these cases, the increase ofmoonlight at the time of occultation would be non-linear.In this case, within the linear portions of theintegration plot examined in detail, there was no indicationof a secondary stellar component.The solution to the intensity curve is presentedgraphically on Figure 5-29. The geometry of this event ledto a rather rapid L-rate, and as a result the intensityvariation of the solution curve is a bit obscured inFigure 5-29. A detailed depiction of the region of interest

I I I I I I I I I I I I II22?DISTANCE TO THE GEOMETRICAL SHADOW IN METERSia -140-120-100-80 -60 -40 -20 20 40 60 80 100 3402x* )° —i—i—i—i—i—i—n —i—i—i—i—I—i—i—i—I—I—I—I—1—I—I—1—I—I—3678 3918 3958 3998 4038TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-29. FITPLOT of the occultation o-f X87589.DISTANCE TO THE GEOMETRICAL SHADOW IN METERS-70 -50 -30 -10 10 30 50 34023928 3948 3968 3988 4008TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-39. 188 millisecond detailed FITPLOT -for X87589

230(covering only 100 milliseconds o-f the observation) ispresented in Figure 5-30.The diameter o-f X07589 was below the detectionthreshold, and hence, was indistinguishable -from a pointsource. The PDPLOT -for the solution curve is presented asFigure 5-31. The observational data subset used in thesolution determination and the computed intensity values, andtheir residuals are listed in Table 5-16. Thevar i ance-covar i ance and correlation matrices, and the rangesof the partial derivatives are given on Table 5-17.No attempt was made to fit the non-linear increase inthe sky background as the moon entered the diaphragm. Hence,the noise statistics for this event, as well as thedistribution function (Figure 5-32) of the noise, reflectonly the first 1600 milliseconds of pre-occul tat i on data anddetilted occultation data. Even the early part of thepre-occul tat ion record contains an increase in the backgroundlevel. This is evidenced by the skewed nature of theNOISEPLOT, Figure 5-32.The power spectra of the event, the star-plus-skysignal, and the solution intensity curve are shown onFigure 5-33. The observed power spectra (occultation andstar-plus-sky) reflect the actual observation with theincreasing sky backgroundincluded.A formal internal error for the time of geometricaloccultation of only 1.1 milliseconds was obtained for thisevent. As had been seen from previous experience, the signal

111 1 1 111 1 1 111 1 1 111 1 1 111 12313928 3946 3968 3988 4008TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFiqure 5-31 PDPLOT of the occultation of X07589.0119 - MEAN -0.03665U) 0106 - SIGMA 0.157721UJZ 0092l_UJ% 0079J_[j 006$_O005= _O0042 _aeCO3z002e_0013nnno\j LU4UM±UJdH±a-83.5 -66.0 -48.5 -3L0 '-13.5 4.1 Sl6kNOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYXruxLnFigure 5-32. NOISEPLOT of the first 1600 milliseconds ofdata taken for the occultation observation of X07589.

232TABLE 5-16X07589: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 3878NUM OBS COMP RES ID NUM OBS COMP RES ID NUM OBS COMP RES ID2023 1981.0 41.8 67 1816 1986.4 -170.4 134 474 1131.8 -657.81 2270 1981.1 289.3 68 2115 1978.7 136.8 135 996 1131.6 -136.12 1774 1981.0 -207.1 69 2310 1977.0 333.0 136 1551 1131.4 419.63 2352 1981.3 371.2 70 2354 1990.0 363.5 137 711 1131.3 -420.74 1244 1980.9 -736.9 71 1853 1974.4 -121.3 138 902 1131.2 -229.05 2514 1980.9 532.6 72 1649 1974.4 -325.8 139 1282 1131.0 150.66 2035 1981.1 53.9 73 1773 1999.4 -226.2 140 1545 1130.9 414.37 2482 1980.9 500.7 74 2092 1979.1 112.6 141 785 1130.8 -346.18 1765 1980.7 -215.6 75 2455 1954.3 501.0 142 429 1130.7 -701.49 1486 1980.7 -495.0 76 2011 1994.2 16.6 143 1129 1130.6 -1.810 2434 1980.8 453.4 77 2098 2020.5 77.8 144 1348 1130.6 217.811 1467 1980.8 -514.1 78 2278 1965.4 312.4 145 865 1130.5 -265.612 1878 1980.8 -102.5 79 1153 1926.5 -773.1 146 1168 1130.4 38.013 1888 1980.8 -93.0 80 2217 1987.4 229.5 147 1750 1130.3 619.614 2367 1980.8 386.5 81 2322 2058.0 264.5 148 1386 1130.3 255.215 1562 1980.8 -418.9 82 2040 2020.6 19.4 149 1170 1130.2 39.816 2166 1980.7 185.7 83 2217 1916.6 299.9 150 1014 1130.2 -116.617 2310 1980.9 329.1 84 1767 1884.8 -117.7 151 728 1130.1 -402.018 1846 1980.8 -135.3 85 1918 1974.3 -56.7 152 724 1130.1 -406.419 1498 1980.6 -482.6 86 2140 2092.3 47.8 153 1047 1130.0 -82.820 1606 1980.7 -375.1 87 2131 2118.3 12.4 154 1112 1130.0 -18.321 1580 1980.6 -400.4 88 1356 2024.4 -668.2 155 1871 1130.0 741.322 1748 1980.7 -233.0 89 2023 1886.3 136.4 156 971 1129.9 -159.123 2176 1980.7 195.6 90 1564 1805.8 -241.5 157 1274 1129.9 144.524 2179 1980.5 198.3 91 2232 1835.7 396.1 158 1123 1129.9 -7.025 1971 1980.5 -9.2 92 1717 1958.4 -241.0 159 909 1129.8 -220.426 2043 1980.4 62.5 93 2099 2112.9 -14.0 160 964 1129.8 -165.827 1821 1980.6 -159.2 94 2411 2235.8 175.6 161 804 1129.8 -326.328 1114 1980.7 -866.8 95 2173 2288.3 -115.4 162 1243 1129.7 113.329 1945 1980.8 -35.3 96 1650 2262.2 -612.7 163 971 1129.7 -159.1-180.7 164 1238 1129.7 108.430 2064 1980.4 83.6 97 1991 2171.731 2767 1980.4 786.1 98 3402 2041.4 1360.2 165 1098 1129.7 -32.033 2384 1980.3 403.3 100 2400 1752.7 647.0 167 86632 2302 1980.7 321.4 99 1496 1895.5 -399.4 166 1321 1129.71129.6191.6-263.934 1809 1980.4 -171.3 101 1271 1624.3 -353.1 168 1520 1129.6 3 90.735 2178 1980.5 197.2 102 1318 1515.7 -197.9 169 1625 1129.6 495.236 1882 1980.2 -98.0 103 802 1427.5 -625.2 170 924 1129.6 -205.237 2412 1980.5 431.3 104 1386 1358.0 27.8 171 1571 1129.6 441.338 2024 1980.5 43.8 105 1185 1304.6 -119.2 172 1218 1129.5 88.939 1896 1980.4 -84.5 106 1230 1264.0 -34.0 173 1207 1129.5 77.440 1823 1980.3 -157.0 107 1468 1233.3 235.1 174 1603 1129.5 473.041 1826 1980.7 -154.8 108 1460 1210.4 249.6 175 1322 1129.5 192.542 1847 1980.2 -132.8 109 932 1193.1 -261.6 176 957 1129.5 -172.943 1586 1980.6 -394.6 110 1063 1180.1 -117.0 177 1216 1129.5 86.744 2203 1980.3 222.2 111 865 1170.2 -305.6 178 916 1129.5 -213.845 1918 1980.3 -62.2 112 1163 1162.7 0.5 179 1052 1129.5 -77.246 2645 1980.3 664.3 113 842 1156.8 -315.1 180 1269 1129.4 139.347 2123 1980.1 143.0 114 1329 1152.2 177.0 181 1160 1129.4 30.948 1729 1980.5 -251.8 115 860 1148.6 -288.8 182 923 1129.4 -206.649 2007 1980.2 27.0 116 824 1145.7 -321.4 183 809 1129.4 -320.050 1365 1980.1 -615.4 117 1400 1143.3 256.5 184 465 1129.4 -664.551 2034 1980.6 53.7 118 1234 1141.4 92.9 185 1592 1129.4 463.052 2103 1980.0 122.9 119 1520 1139.9 380.0 186 1127 1129.4 -2.453 1633 1980.8 -347.5 120 1078 1138.7 -60.2 187 1254 1129.4 124.154 2319 1979.7 339.2 121 1154 1137.6 16.3 188 935 1129.4 -194.355 1944 1980.8 -36.4 122 6 91 1136.7 -446.2 189 775 1129.4 -354.856 2200 1979.7 220.3 123 1373 1135.9 237.2 190 1329 1129.3 199.857 2436 1981.0 454.5 124 1033 1135.2 -102.6 191 772 1129.3 -357.758 1820 1979.9 -159.8 125 760 1134.6 -374.5 192 1365 1129.3 235.959 1923 1980.7 -58.1 126 1140 1134.2 5.5 193 641 1129.3 -488.660 1848 1981.2 -133.0 127 2063 1133.8 929.5 194 1332 1129.3 203.061 2038 1978.4 59.3 128 1377 1133.3 243.4 195 1380 1129.3 250.562 1297 1984.1 -686.9 129 1190 1132.9 57.3 196 1227 1129.3 98.163 1505 1976.8 -472.0 130 947 1132.7 -185.8 197 1221 1129.3 91.664 2050 1982.4 67.9 131 2210 1132.4 1077.9 198 1578 1129.3 449.165 2108 1982.4 125.4 132 7 91 1132.2 -341.3 199 1451 1129.3 321.766 2759 1975.5 783.9 133 1038 1131.9 -93.5 200 923 1129.3 -206.8

TABLE 5-17X07589: SUPPLEMENTAL STATISTICAL INFORMATION233VARIANCE/CO-VARIANCE MATRIXDIAM PREI POST TIME VELO1.143E 16 -4.465E 08 -5.040E~09 1.273E~09 -1.521E"10-4.465E~08 1.212E03 2.450E01 -5.787E00 4.580E _ 01-5.040E_09 2.450E01 1.303E03 -5.392E00 3.745E"011.273E09 -5.787E00 -5.392E00 1.196E00 -8.278E"02-1.521E"10 4.580E~01 3.745E 01 -8.278E"02 9.180E~03CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 -0.994887 0.113292 0.727451 -0.778838PREI -0.994887 1.000000 -0.210486 -0.654490 0.711548POST 0.113292 -0.210486 1.000000 -0.587384 0.523549TIME 0.727451 -0.654490 -0.587384 1.000000 -0.996928VELO -0.778838 0.711548 0.523549 -0.996928 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 8.781E08 -8.462E08PREI 1.366E00 3.206E~04POST 9.997E 01 -3.656E"01TIME 1.469E02 -1.496E02VELO 1.601E03 -1.799E03

234MODEL CURVEmm^STAR +SKYOCCULTATION•0" '100" l200" n '30tJFREQUENCY INHERTZWFigure 5-33. POWERPLOT o-f the occultation o-f X07589,

.235strength of the WwVB radio signal during and shortly afterevening twilight tends to be quite low. As a result, no WwVBtime code was available at the time of the event.Fortunately, the signal strength had improved sufficientlythirty seven minutes later to reliably detect the digitaltime code. The crystal controlled clock circuit o-f theSPICA-IV/LODAS system has been -found to have a cumulativetiming error o-f at most two seconds per day. Taking this asa worst case condition, the time o-f the event reckoned -fromthe SPICA-IV/LODAS clock and synchronized to WwVB a hal-f houra-fter occultation would have a one sigma error ofapproximately 0.025 seconds. The Universal Time ofgeometrical occultation was 01:35:12.17

:236TABLE 5-18X07598: LUNAR OCCULTA!" I ON SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X07598 (SAO 077559, DM + 22 1032)RA: 054627 DEC: +225501 mV: 7.5 Sp : KOFilter: V Diaphram: I Gain: C8+ Voltage: 1200LUNARINFORMATIONSurface Illumination: 25 percentElongation -from Sun: 59 degreesAltitude Above Horizon: 23 degreesLunar Limb Distance: 369285 kilometersPredicted Shadow Velocity: 153.1 meters/sec.Predicted Angular Rate: 0.0855 arcsec/secEVENTDate: Apri 1 18, 1983USNO V/O Code: 47Position Angle: 172.1Contact Angle: -80.3INFORMATIONMODEL PARAMETERSUT of Event: 02:12:03HA of Event: +692638Cusp Angle: 7SWat ts Angl e 172.3Number of Data Points: 401Number of Grid Points: 256Number of Spectral Regions: 53Width of Spectral Regions: 50 AngstromsLimb Darkening Coefficient: 0.5Effective Stellar Temperature: 5100 KSOLUTIONSStellar Diameter : 5.45

237512 1024 1536 '2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-34. RAWPLOT of the occultation of X07598.fe12 1024 1536 2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-35. INTPLOT of the occultation of X07598.

.not span a large enough portion of the intensity curve to bewarranted as significant. The observation was re-reducedconsidering 400 milliseconds o-f data centered on theestimated time o-f geometrical occultation.The solution obtained -from the 400 millisecond data set238is presented graphically in the FITPLOT, Figure 5-36. Exceptfor the anomalous depression in the zero order diffractionmaximum, the fit is quite good. This depression is not tootroublesome, remembering that the time-scale is elongated bya factor of roughly four. It is unfortunate that variationin atmospheric transparency took its toll at this point, butit was not unduly critical in the determination of thesol ut i onThe observational data used in the solution, thecomputed intensities and their residuals are given inTable 5-19. The usual supplementary statistical informationis listed in Table 5-20.An angular diameter for this K0

23?COUNTSCO oQ-J IS sssisssiaiaiaausnhini aaznvwaoN

X07598 : OBSERVATIONS, COMPUTED'VALUES, AND RESIDUALS FROM BIN 2350240NUM OBS COMP RES ID NUM OBS COMP RES ID NUM OBS COMP RES ID2240 2244.0 -4.0 67 2576 2325.6 250.4 134 2155 2292.4 -137.41 2449 2242.7 206.3 68 23 96 2323.9 72.1 135 2319 2277.3 41.72 2383 2241.9 141.1 69 2303 2321.0 -18.0 136 2016 2261.8 -245.83 2355 2241.5 113.5 70 2357 2316.9 40.1 137 2324 2246.1 77.94 2305 2241.6 63.4 71 2077 2311.8 -234.8 138 2439 2230.4 208.65 2066 2242.2 -176.2 72 1979 2305.6 -326.6 139 2585 2214.6 370.46 2356 2243.3 112.7 73 1879 2298.6 -419.6 140 2086 2199.1 -113.17 2143 2244.9 -101.9 74 1875 2290.7 -415.7 141 1876 2183.8 -307.88 2263 2247.0 16.0 75 2181 2282.1 -101.1 142 1311 2168.9 -857.99 2156 2249.5 -93.5 76 1890 2272.8 -382.8 143 1631 2154.5 -523.510 2115 2252.4 -137.4 77 1975 2263.2 -288.2 144 1975 2140.8 -165.811 2649 2255.6 3 93.4 78 2191 2253.2 -62.2 145 2009 2127.9 -118.912 1885 2259.0 -374.0 79 2139 2243.1 -104.1 146 1792 2115.7 -323.713 1885 2262.5 -377.5 80 2437 2233.0 204.0 147 2219 2104.5 114.514 2146 2266.2 -120.2 81 2578 2223.0 355.0 148 2256 2094.4 161.615 2159 2269.8 -110.8 82 1784 2213.4 -429.4 149 2391 2085.3 305.716 2632 2273.2 358.8 83 1691 2204.2 -513.2 150 2357 2077.4 279.617 2575 2276.4 2 98.6 84 1879 2195.7 -316.7 151 2647 2070.7 576.318 2451 2279.2 171.8 85 2743 2187.9 555.1 152 1981 2065.3 -84.319 2099 2281.6 -182.6 86 1942 2181.0 -239.0 153 1775 2061.2 -286.220 3023 2283.5 739.5 87 2290 2175.1 114.9 154 2411 2058.4 352.621 2571 2284.8 286.2 88 2843 2170.3 672.7 155 2324 2057.0 267.022 3423 2285.5 1137.5 89 2867 2166.6 700.4 156 1539 2056.9 -517.923 2995 2285.4 709.6 90 23 91 2164.2 226.8 157 2938 2058.2 879.824 20 95 2284.7 -189.7 91 1988 2163.1 -175.1 158 2305 2060.9 244.125 2107 2283.3 -176.3 92 2087 2163.4 -76.4 159 1628 2065.0 -437.026 2735 2281.2 453.8 93 2307 2165.0 142.0 160 1709 2070.4 -361.427 1512 2278.3 -766.3 94 2196 2167.9 28.1 161 1573 2077.0 -504.028 2919 2274.9 644.1 95 2027 2172.2 -145.2 162 2006 2085.0 -79.029 2772 2270.9 501.1 96 2081 2177.8 -96.8 163 1878 2094.1 -216.130 2280 2266.5 13.5 97 2138 2184.6 -46.6 164 2012 2104.4 -92.431 2407 2261.6 145.4 98 2431 2192.5 238.5 165 2127 2115.9 11.132 2240 2256.5 -16.5 99 2383 2201.6 181.4 166 1627 2128.3 -501.333 2825 2251.2 573.8 100 2721 2211.6 509.4 167 1658 2141.8 -483.834 2407 2245.9 161.1 101 2576 2222.4 353.6 168 2018 2156.1 -138.135 1920 2240.6 -320.6 102 3079 2234.0 845.0 169 2257 2171.3 85.736 1584 2235.6 -651.6 103 2506 2246.2 259.8 170 1807 2187.3 -380.337 1743 2230.8 -487.8 104 2559 2258.8 300.2 171 2431 2203.9 227.138 2219 2226.6 -7.6 105 2813 2271.8 541.2 172 2111 2221.1 -110.139 1506 2222.8 -716.8 106 2499 2284.9 214.1 173 1960 2238.8 -278.840 1833 2219.8 -386.8 107 1991 22 98.0 -307.0 174 1831 2256.9 -425.941 2015 2217.5 -202.5 108 1847 2310.9 -463.9 175 2748 2275.4 472.642 2445 2216.0 229.0 109 1836 2323.6 -487.6 176 2172 2294.1 -122.143 2195 2215.4 -20.4 110 1640 2335.8 -6 95.8 177 2431 2312.9 118.144 2195 2215.8 -20.8 111 1835 2347.5 -512.5 178 3136 2331.9 804.145 2655 2217.0 438.0 112 2300 2358.4 -58.4 179 3607 2350.8 1256.246 2105 2219.2 -114.2 113 2427 2368.4 58.6 180 2967 2369.7 597.347 1864 2222.4 -358.4 114 2347 2377.6 -30.6 181 2711 2388.3 322.748 1664 2226.4 -562.4 115 2144 2385.6 -241.6 182 2463 2406.8 56.249 1550 2231.2 -681.2 116 2579 23 92.5 186.5 183 2935 2424.9 510.150 2471 2236.8 234.2 117 2112 2398.1 -286.1 184 2744 2442.6 301.451 2530 2243.0 287.0 118 1872 2402.4 -530.4 185 2605 2459.8 145.252 2036 2249.7 -213.7 119 1863 2405.4 -542.4 186 2680 2476.6 203.453 2223 2256.9 -33.9 120 2191 2406.9 -215.9 187 2475 2492.7 -17.754 2191 2264.4 -73.4 121 2714 2407.1 306.9 188 2567 2508.2 58.855 2079 2272.0 -193.0 122 2736 2405.8 330.2 189 2352 2523.1 -171.156 2179 2279.6 -100.6 123 2435 2403.0 32.0 190 2528 2537.1 -9.157 1928 2287.1 -359.1 124 2243 23 98.8 -155.8 191 2421 2550.4 -129.458 2261 22 94.3 -33.3 125 2495 23 93.3 101.7 192 2512 2562.9 -50.959 1785 2301.0 -516.0 126 2345 2386.4 -41.4 193 2459 2574.4 -115.460 1911 2307.2 -396.2 127 2222 2378.3 -156.3 194 22 98 2585.1 -287.161 2091 2312.7 -221.7 128 2479 2368.9 110.1 195 2032 2594.9 -562.962 1996 2317.4 -321.4 129 2257 2358.4 -101.4 196 1909 2603.7 -694.763 1967 2321.1 -354.1 130 2207 2346.8 -139.8 197 2368 2611.5 -243.564 2024 2323.9 -299.9 131 1857 2334.4 -477.4 198 1963 2618.4 -655.465 2205 2325.6 -120.6 132 2203 2321.0 -118.0 199 2338 2624.2 -286.266 2597 2326.2 270.8 133 2248 2307.0 -59.0 200 2451 2629.0 -178.0

TABLE 5-19.CONTINUED.>41NUM OBS COMP RES ID NUM OBS COMP RES ID NUM OBS COMP RES ID201 2332 2632.8 -300.8 268 1771 1700.5 70.5 335 1296 1236.9 59.1202 2079 2635.6 -556.6 269 1523 1686.6 -163.6 336 1225 1234.5 -9.5203 2116 2637.4 -521.4 270 1641 1673.0 -32.0 337 1297 1232.3 64.7204 2321 2638.2 -317.2 271 1775 1659.6 115.4 338 1303 1230.1 72.9205 2017 2637.9 -620.9 272 1239 1646.5 -407.5 339 1310 1227.9 82.1206 2465 2636.7 -171.7 273 1576 1633.6 -57.6 340 774 1225.8 -451.8207 2897 2634.4 262.6 274 1574 1621.1 -47.1 341 886 1223.8 -337.8208 3099 2631.3 467.7 275 1073 1608.8 -535.8 342 983 1221.8 -238.8209 3580 2627.1 952.9 276 1487 1596.8 -109.8 343 1201 1219.9 -18.9210 2739 2622.0 117.0 277 1551 1585.0 -34.0 344 860 1218.1 -358.1211 2650 2616.1 33.9 278 1185 1573.5 -388.5 345 1077 1216.2 -139.2212 2404 2609.2 -205.2 279 1519 1562.3 -43.3 346 1095 1214.5 -119.5213 2555 2601.5 -46.5 280 1359 1551.3 -192.3 347 1087 1212.8 -125.8214 3047 2593.0 454.0 281 1299 1540.6 -241.6 348 1139 1211.1 -72.1215 3363 2583.6 779.4 282 1263 1530.1 -267.1 349 1121 1209.5 -88.5216 3643 2573.5 1069.5 283 1397 1519.9 -122.9 350 1056 1207.9 -151.9217 3221 2562.6 658.4 284 1464 1509.9 -45.9 351 1451 1206.4 244.6218 2885 2551.1 333.9 285 1912 1500.1 411.9 352 1178 1204.9 -26.9219 3296 2538.8 757.2 286 1695 1490.6 204.4 353 1367 1203.5 163.5220 2889 2525.9 363.1 287 1450 1481.4 -31.4 354 1294 1202.1 91.9221 2575 2512.4 62.6 288 1620 1472.4 147.6 355 1599 1200.7 3 98.3222 2619 2498.3 120.7 289 1380 1463.6 -83.6 356 1768 1199.4 568.6223 3123 2483.7 639.3 290 945 1455.0 -510.0 357 1423 1198.1 224.9224 3487 2468.6 1018.4 291 1243 1446.6 -203.6 358 1534 1196.8 337.2225 3583 2452.9 1130.1 292 1420 1438.5 -18.5 359 1440 1195.6 244.4226 3267 2436.9 830.1 293 1399 1430.5 -31.5 360 1207 1194.4 12.6227 2691 2420.4 270.6 294 1603 1422.8 180.2 361 1405 1193.2 211.8228 2337 2403.5 -66.5 295 1331 1415.3 -84.3 362 1387 1192.1 194.9229 2531 2386.3 144.7 296 1151 1408.0 -257.0 363 1127 1191.0 -64.0230 2351 2368.8 -17.8 297 1615 1400.8 214.2 364 1152 1189.9 -37.9231 2821 2351.0 470.0 298 995 1393.9 -398.9 365 1251 1188.9 62.1232 2802 2332.9 469.1 299 1022 1387.1 -365.1 366 1457 1187.9 269.1233 2307 2314.7 -7.7 300 1015 1380.6 -365.6 367 1042 1186.9 -144.9234 23 93 2296.2 96.8 301 1353 1374.2 -21.2 368 1269 1185.9 83.1235 2030 2277.5 -247.5 302 1757 1368.0 389.0 369 1141 1185.0 -44.0236 2407 2258.8 148.2 303 1476 1361.9 114.1 370 1224 1184.1 39.9237 2361 2239.9 121.1 304 1103 1356.1 -253.1 371 1548 1183.2 364.8238 2151 2220.9 -69.9 305 1208 1350.3 -142.3 372 1258 1182.3 75.723 9 2595 2201.8 3 93.2 306 1949 1344.8 604.2 373 1002 1181.5 -179.5240 2702 2182.8 519.2 307 1778 1339.4 438.6 374 1107 1180.7 -73.7241 2153 2163.7 -10.7 308 1767 1334.1 432.9 375 1348 1179.9 168.1242 2059 2144.6 -85.6 309 1085 1329.0 -244.0 376 1171 1179.1 -8.1243 1680 2125.5 -445.5 310 930 1324.0 -394.0 377 1645 1178.3 466.7244 2311 2106.5 204.5 311 1082 1319.2 -237.2 378 1152 1177.6 -25.6245 1903 2087.6 -184.6 312 1594 1314.5 279.5 379 817 1176.9 -359.9246 1938 2068.7 -130.7 313 1243 1310.0 -67.0 380 1111 1176.2 -65.2247 203 9 2050.0 -11.0 314 1303 1305.6 -2.6 381 1247 1175.5 71.5248 2104 2031.3 72.7 315 1224 1301.3 -77.3 382 1431 1174.8 256.2249 1737 2012.8 -275.8 316 1247 1297.1 -50.1 383 1343 1174.1 168.9250 1783 1994.5 -211.5 317 1061 1293.0 -232.0 384 1471 1173.5 297.5251 1615 1976.3 -361.3 318 1178 1289.1 -111.1 385 1277 1172.9 104.1252 1127 1958.2 -831.2 319 1343 1285.2 57.8 386 1215 1172.3 42.7253 1087 1940.4 -853.4 320 1487 1281.5 205.5 387 1759 1171.7 587.3254 1490 1922.8 -432.8 321 1186 1277.9 -91.9 388 1365 1171.1 193.9255 1404 1905.3 -501.3 322 1169 1274.4 -105.4 389 1600 1170.5 429.5256 1787 1888.1 -101.1 323 1131 1271.0 -140.0 3 90 1364 1170.0 194.0257 1797 1871.1 -74.1 324 1334 1267.7 66.3 3 91 1415 1169.4 245.6258 1955 1854.3 100.7 325 1112 1264.4 -152.4 3 92 1336 1168.9259 1577 1837.8 -260.8 326 1007 1261.3 -254.3 3 93 1124 1168.4167.1-44.4260 1737 1821.5 -84.5 327 1007 1258.3 -251.3 3 94 973 1167.9 -194.9261 2287 1805.5 481.5 328 1255 1255.3 -0.3 3 95 1103 1167.4 -64.4262 1857 1789.7 67.3 329 1920 1252.5 667.5 3 96 5 91 1166.9 -575.9263 1275 1774.2 -499.2 330 1381 1249.7 131.3 3 97 1149 1166.4 -17.4264 1222 1758.9 -536.9 331 1458 1247.0 211.0 3 98 1102 1166.0 -64.0265 2100 1743.9 356.1 332 1576 1244.3 331.7 399 1392 1165.5 226.5266 1935 1729.2 205.8 333 1411 1241.8 169.2267 1705 1714.7 -9.7 334 1307 1239.3 67.7400 1157 1165.1 -8.1

TABLE 5-20X07598: SUPPLEMENTAL STATISTICAL INFORMATION242VARIANCE/ CO- VARIANCEMATRIXDIAM PREI POST TIME VELO1.447E 16 3.947E"08 -9.496E 08 -1.637E~09 3.319E"123.947E~08 4.785E02 8.940E01 -2.714E01 2.714E~029.496E 08 8.940E01 1.517E03 -6.788E01 6.483E"021.637E~09 -2.714E01 -6.788E01 1.463E01 -1.444E~023.319E~12 2.714E"02 6.483E02 -1.444E"02 1.891E~05CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.394094 -0.908842 0.681148 -0.667250PREI 0.394094 1.000000 0.024095 -0.389071 0.405659POST -0.908842 0.024095 1.000000 -0.921565 0.914093TIME 0.681148 -0.389071 -0.921565 1.000000 -0.999822VELO -0.667250 0.405659 0.914093 -0.999822 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 3.271E09 -3.408E09PREI 1.346E00 2.314E~02POST 9.769E~01 -3.458E~01TIME 1.910E01 -1.897E01VELO 1.805E04 -1.822E04

2432350 2430 2510 '2590 "2670^TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-37. PDPLOT o-f the occultation o-f X07598.0313 _-96.0 -8L4 -66.8 -52.3 -37.7 -23.2 -8.6 5.9 20.5 35.0NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-38. NOISEPLOT o-f the occultation o-f X07598.

''1244MODEL CURVEtrtSTAR +•"SKY0 100' "200" 300 '400"FREQUENCY IN HERTZFigure 5-39. POJERPLOT o-f the occultation o-f X07598

..245point source. No convergent solution could be -forced on apoint source model. The determined angular diameter doesindeed seem to be realBecause o-f the relatively slow disappearance (due to thesmall R-rate) the internal formal error in the time o-fgeometrical occultation was not very well determined (+/- 4.4milliseconds). The Coordinated Universal Time o-f geometricaloccultation was -found to be 02:12:04.713 (+/- 0.0049seconds)XI 3534The occultation o-f the K0 star X13534 on April 21, 1933U. T., (as noted in the occultation summary. Table 5-21) wasthe -first o-f two events observed on that night.Interestingly enough, these two events both gave rise to thediscovery o-f previously unknown "close" companions. Otherthan the recognition o-f 1 Geminorum Al (ZC0916-A1 ) , these twowere the only such discoveries made in the reduction andanalysis o-f the twenty-two observations where "close"duplicity could have been uncovered.Even -from the plot o-f the raw occultation data(Figure 5-40), one can note a diminution o-f thepositive-going signal spiking (due to scintillation noise)immediately before occultation. While this is onlymarginally noticeable on the presented RAWPLOT, this was seenquite easily when examined at the -four-times greaterresolution obtained by using a high resolution graphicsdisplay terminal. This diminution in the noise spiking (as

246TABLE 5-21XI 3534: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X13534, (SAO 080497, DM +21 1939)RA: 085323 DEC: +203905 mV: 8.4 Sp : KOFilter: V Diaphragm: I Gain: 08 Voltage: 1200LUNARINFORMATIONSur-face Illumination:Elongation from Sun:Altitude Above Horizon:Lunar Limb Distance:Predicted Shadow Velocity:Predicted Angular Rate:EVENT58 percent100 degrees58 deorees364349 K i 1 ome ters661 ,,7 meters/sec0,,3746 arcsec/secINFORMATIONDate: April 21, 1983 UT of Event: 02:46:31USNO V/O Code: 15 HA of Event: +342042Position Angle: 143.4 Cusp Angle: 53SContact Angle: -30.0 Watts Angle: 126.7TWO-STAR MODEL PARAMETERSNumber of Data Points: 201Number of Grid Points: 256, 256Number of Spectral Regions: 53Width of Spectral Regions: 50 AngstromsLimb Darkening Coefficients: 0.5, 0.05Effective Stellar Temperatures: 5100 K, 5100 KSOLUTIONSSky Level: 1336.5 (39.2)STAR 1 STAR 2Stellar Diameter (ams>: Point Source Point SourceTime (relative to Bin 0): 2389.2 (2.2) 2372.3 (7.2)Stellar Intensity: 649.5 (100.2) 229.9 (98.7)Velocity (meters/sec): 666.9 (49.4) 559.0 (116.3)Lunar Limb Slope (degrees) -3.58 (4.28) -16.3 (10.1)U.T. of Occultation: 02:46:29.632 (0.003) :29.594 (0.008)

247Table 5-21. Continued,TWO-STAR DERIVED QUANTITIESTemporal Separation (milliseconds): 16.9 (7.6)Intensity Weighted Mean L-Rate (meters/sec): 634.7 (48.4)Intensity Weighted Mean R-Rate (arcsec/sec) : 0.359 (0.027)Projected Spatial Separation,Based on Predicted R-Rate:Based on Weighted Mean R-Rate:Brightness Ratio (Brighter/Fainter):Magnitude Di -f i erence :mU o-f Star 1 :mV o-f Star 2:PHOTOMETRIC NOISE6.32 arc-ms6.07 (2.74) arc-ms2.82 (1 .289)1 .13 (+0.66. -0.41)8.73 (0.14)9.86 (0.37)INFORMATIONSum-o-f -Squares o-f Residuals: 17673786Sigma (Standard Error): 297.269Normalized Standard Error: 0.33803Photometric (S+N)/N Ratio: 3.9583(Change in In tensi ty)/Background: 0.6580Change in Magnitude: 0.5490

248^4096TIMEFi gure-k312 1024 '1536 2048 2560 3072 '3564IN MILLISECONDS FROM BEGINNING OF DATA VINDOV5-40. RAWPLOT of the occultation o-f XI 3534.512 1024 1536 2048 2560 '3072 '3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-41. INTPLOT o-f the occultation of X13534.

24?it so appears when plotted at this scale) was actually due toa reduction in the zero order di f f rac t i on -fringe maximumbrought about by a second star.The presence of a second star was uncovered by the DC2fitting process. No "wide" stellar components are indicatedby the integration plot, Figure 5-41. An initial attempt tofit the observational data to a one star model -failed, andthe divergence o-f the fitting procedure indicated that atwo-star model was the appropriate one to use. The FITPLOTof the two-star solution is presented as Figure 5-42. Thetimes of geometrical occultation of the individual componentsare noted by the dashed vertical lines. The arbitrary zeropoint reference on the linear distance scale coincides withthe point of geometrical occultation of the brighter star.Neither of the two stars had resolvable stellardiameters, and hence, led to point source solutions. Theprojected spatial separation of the components was found tobe 6.07

'I250^CMH IinCOUNTS00OCMOCO Q(u10 (0 ^HCM CM CM CM' ICMCDCDXit^^4^fCOQB 2 9 8> s_.CM< s-Q oA_LISN3_LNI QBTIlVWaON

251components would have corresponding V magnitudes of 8.73

252TABLE 5-22X13534 : OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 2250NUM OBS COMP RES ID NUM OBS COMP RES ID NUM OBS COMP RES ID2137 2218.7 -81.7 67 2572 2233.3 338.7 134 1334 1633.7 -299.71 2223 2218.4 4.6 68 1995 2229.9 -234.9 135 1551 1598.2 -47.22 2451 2218.1 232.9 69 1993 2224.0 -231.0 136 1403 1566.6 -163.63 2330 2218.5 111.5 70 2387 2212.5 174.5 137 1337 1538.6 -201.64 2767 2218.6 548.4 71 2217 2196.8 20.2 138 1284 1513.9 -229.95 2941 2218.6 722.4 72 2116 2185.1 -69.1 139 1325 1492.3 -167.36 2365 2218.4 146.6 73 1800 2185.7 -385.7 140 1554 1473.4 80.67 2235 2218.1 16.9 74 1685 2200.9 -515.9 141 1093 1456.9 -363.98 2213 2218.6 -5.6 75 2017 2223.5 -206.5 142 1431 1442.6 -11.69 2004 2218.7 -214.7 76 2455 2241.9 213.1 143 1321 1430.1 -109.110 2443 2218.4 224.6 77 2314 2248.4 65.6 144 1537 1419.3 117.711 2925 2218.1 706.9 78 2093 2244.5 -151.5 145 1503 1409.9 93.112 2566 2218.3 347.7 79 2215 2238.7 -23.7 146 1368 1401.7 -33.713 2488 2218.3 269.7 80 1960 2239.3 -279.3 147 1027 1394.6 -367.614 2679 2218.6 460.4 81 2269 2247.3 21.7 148 1665 1388.5 276.515 2526 2219.0 307.0 82 2399 2255.2 143.8 149 1743 1383.1 359.916 2617 2218.4 3 98.6 83 2333 2251.8 81.2 150 1447 1378.4 68.617 1802 2217.7 -415.7 84 2179 2230.4 -51.4 151 1157 1374.3 -217.318 1715 2217.8 -502.8 85 2057 2194.3 -137.3 152 1123 1370.7 -247.719 2207 2218.6 -11.6 86 1951 2156.4 -205.4 153 1310 1367.5 -57.5-172.6 154 1221 1364.8 -143.820 2579 2219.2 359.8 87 1960 2132.621 2359 2219.2 139.8 88 1414 2133.9 -719.9 155 1173 1362.3 -189.322 1879 2218.2 -339.2 89 1905 2161.1 -256.1 156 1083 1360.1 -277.123 2291 2217.2 73.8 90 2009 2203.9 -194.9 157 1123 1358.2 -235.224 2215 2217.6 -2.6 91 1975 2246.4 -271.4 158 888 1356.5 -468.525 2712 2218.9 493.1 92 1568 2273.7 -705.7 159 1235 1354.9 -119.926 2341 2219.5 121.5 93 2353 2278.4 74.6 160 1270 1353.5 -83.527 2150 2219.3 -69.3 94 2423 2262.9 160.1 161 1476 1352.3 123.728 2044 2218.5 -174.5 95 1930 2238.0 -308.0 162 1028 1351.2 -323.229 2388 2217.4 170.6 96 2146 2217.8 -71.8 163 1641 1350.1 290.930 2139 2217.0 -78.0 97 1524 2214.3 -690.3 164 1591 1349.2 241.831 2259 2218.2 40.8 98 1939 2232.7 -293.7 165 1455 1348.4 106.632 2107 2219.9 -112.9 99 2191 2270.2 -79.2 166 1509 1347.7 161.333 2259 2219.9 39.1 100 2638 2317.4 320.6 167 1121 1347.0 -226.034 2351 2218.7 132.3 101 2167 2360.9 -193.9 168 1103 1346.4 -243.435 2054 2217.5 -163.5 102 2703 2388.4 314.6 169 1983 1345.8 637.236 2179 2217.3 -38.3 103 2360 2391.0 -31.0 170 2048 1345.3 702.737 2363 2217.5 145.5 104 2211 2366.2 -155.2 171 1881 1344.9 536.138 2426 2218.5 207.5 105 2399 2317.1 81.9 172 1421 1344.4 76.639 1815 2220.5 -405.5 106 1863 2252.0 -389.0 173 1318 1344.0 -26.040 2642 2221.2 420.8 107 1986 2181.7 -195.7 174 1151 1343.6 -192.641 2008 2219.0 -211.0 108 2292 2117.1 174.9 175 1156 1343.3 -187.342 2007 2216.0 -209.0 109 1803 2067.3 -264.3 176 1733 1342.9 3 90.143 2116 2215.1 -99.1 110 2927 2038.1 888.9 177 1433 1342.6 90.444 2006 2217.1 -211.1 111 1984 2031.7 -47.7 178 13 95 1342.3 52.745 23 91 2219.6 171.4 112 1558 2046.6 -488.6 179 1870 1342.0 528.046 2791 2221.4 569.6 113 1811 2078.5 -267.5 180 1176 1341.8 -165.847 2168 2222.7 -54.7 114 1783 2121.4 -338.4 181 1071 1341.6 -270.648 1725 2222.7 -497.7 115 2271 2168.7 102.3 182 987 1341.4 -354.449 2290 2219.4 70.6 116 2367 2214.1 152.9 183 1488 1341.2 146.850 2216 2213.4 2.6 117 243 9 2252.2 186.8 184 1178 1341.0 -163.051 1951 2209.6 -258.6 118 2136 2279.0 -143.0 185 1171 1340.8 -169.852 1616 2212.4 -596.4 119 2274 22 92.1 -18.1 186 1431 1340.7 90.353 1811 2219.8 -408.8 120 2799 2290.7 508.3 187 1126 1340.5 -214.554 2099 2225.9 -126.9 121 2093 2275.1 -182.1 188 1234 1340.3 -106.355 2232 2227.5 4.5 122 1893 2246.6 -353.6 189 1979 1340.2 638.856 2951 2226.2 724.8 123 1804 2207.3 -403.3 190 1711 1340.1 370.957 2403 2224.7 178.3 124 2483 2159.5 323.5 191 1720 1340.0 380.058 2361 2221.4 139.6 125 2328 2105.6 222.4 192 1699 1339.8 359.259 2887 2214.3 672.7 126 1612 2047.9 -435.9 193 1463 1339.7 123.360 2119 2205.1 -86.1 127 2338 1988.5 349.5 194 1179 1339.6 -160.661 2338 2200.7 137.3 128 2207 1929.3 277.7 195 1077 1339.5 -262.562 2091 2206.2 -115.2 129 2165 1871.6 293.4 196 1478 1339.4 138.663 2502 2219.4 282.6 130 2047 1816.5 230.5 197 1023 1339.3 -316.364 2487 2232.1 254.9 131 1587 1764.9 -177.9 198 1123 1339.2 -216.265 2279 2238.0 41.0 132 1720 1717.0 3.0 199 1255 1339.2 -84.266 2867 2237.0 630.0 133 1795 1673.3 121.7 200 1039 1339.1 -300.1

—[1 1 111 1 n1 1 1 111 1 1 111 1 1 111 1 h253COMPVEL2LU> TTM2> INT2KW 0IA2•:< VEU^W\;v .»»*M/\/\/\^W\AA?«„», St* « ,.».»>«-MA/VVDIA1«v2250 2290 2330 2370 2410TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-43. PDPLOT o-f the occultation o-f X13534.0296L.0266 _ MEAN -0.08527W 0237 - SIGMA 0.150196O£Ji1-92.9 -78.2 -63.5-48.8-34.1 -19.4 -4.7 h10.0 24.8NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-44. NOISEPLOT o-f the occultation of X13534.

IiIIIIIIIIIIiiiiiiiliiIIiiiiIIiiiiIIIIIIiiiiiiiiIIiiIIIIiiIIIIIIiiiiIIiiIIiiIIIIIIIIIIIIIIIIIIIIIIIIIIIIiiIIIIIIIIIIiiIIIIIIiiiiIIIIIIIIIIiiIIIIiiIIiiIIIIIIIIiiIIIIIIIIiiiiiiiiiiIIiiiiIIIIIIIIII—III I OIIIII I OOCXtIII OIIiIIi I oooiIIIIIIII I OOOIIIiII I OOOOIIiIIIIII I I I II I I I I I I I III I I I II I I I I I I I I IIIIiiIiiIIIiiIIiIIIIiiIiIIiIIIIIIiiIIIIIIIIiIi ONvoovooo^o-tf-aIiIIIIIIIiIIII I I I III1I1i1254SHouWuoooooooooI I I OI IWWWWWWWWWION ,-|CM«*ON "-ItSlomuiOHOintOHcm i inin>—tONooONuoomcMoocMcovocNsr-^coW I> icM^Tcocoini—i-3t-^i—IIIONHOOONHOWWWWWWWWWr-» csioo -hOOlONoOr-»cO«-HCMCM.—100CM I stoOCOvO-*NOCM-tfOOmMr-vO*(«lNhOi-ir^coinOCMONOOr^OON^HONOcoONvO^HvOCMsOMS•h i or~-ONcocomvoooooQHH>COCOoo*S-«3-WWCM cMr~-1 CM^HW • •> -Hi—OO WWON— -1§ vO00vOr~.l-l • •H1-1035EQ09ECM vOCOH CO NO• •B -HCMCOw>M ON 00H oo -HCMi-igoomOSON CMw M • •a Q -nm3McocoH oo WW%CMP^Ph -H 1 -HCO1 P~00W w 1 • •> 1 CMCMRwo 1 f-Hi-H1 OOCO 1 WWmoow iu t—s 1s? M11 CM«*vOON• •M H i mm53u 1 ooH 1 ooas 1 WWW 1 ooS 1 oo3 >" 1 ooZ w * *0011H 1037EQ07E-H 1 vOCMCOO

'1'—255MODELCURVEi r TOCCULTATION"0 '100'"200'l300" '400'FREQUENCY INHERTZFigure 5-45. POUERPLOT o-f the occultation o-f XI 3534,

.02:46:29.594

257TABLE 5-24XI 360 7: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X13607,

258Table 5-24. Continued.TWO-STAR DERIVED QUANTITIESTemporal Separation (milliseconds): 53.4 (7.7)Intensi ty Weighted Mean L-Rate (me ters/sec) : 436.8 (37.6)Intensi ty Weighted Mean R-Rate < arcsec/sec) : 0.244

.25?TIMEk112 1024 1536 2048 2560 3072 3584IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-46. RAWPLOT o-f the occultation o-f XI 3607.L00.9 10)z 0.8^ 0.7sQ 0.6LU0.5

i260CO t^ CMfs 0) CMCO ^ OCM CM CMCOUNTSco q in o)^ N 2 £co -h ^r coT{ CD N CO^ CMCM -«-i *-• -»n —--iCM0)COa> oQzin-lw

.261unknown "close" stellar companion. Indeed, this was the caseand was verified by the DC2 -fit to the observed intensitycurveBecause o-f the early spectral type o-f the star

262TABLE 5-25X13607: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 23 95NUM OBS COMP RES ID1845 2116.3 -271.31 2330 2115.2 214.82 2404 2114.3 289.73 2207 2114.2 92.84 1950 2114.9 -164.95 2082 2116.0 -34.06 2135 2116.7 18.37 2495 2116.6 378.48 2007 2115.6 -108.69 1628 2114.5 -486.510 2176 2113.9 62.111 2090 2114.5 -24.512 2231 2115.9 115.113 2222 2117.5 104.514 1748 2118.3 -370.315 1830 2117.6 -287.616 2062 2115.5 -53.517 1827 2112.8 -285.818 2019 2111.0 -92.019 2023 2111.1 -88.120 2104 2113.6 -9.621 1658 2117.8 -459.822 1891 2122.0 -231.023 2287 2124.5 162.524 1943 2123.8 -180.825 1879 2119.5 -240.526 1871 2112.9 -241.927 1961 2106.1 -145.128 2143 2101.9 41.129 1567 2102.0 -535.030 2143 2107.3 35.731 2474 2116.5 357.532 2446 2126.9 319.133 2238 2135.3 102.734 2137 2138.8 -1.835 2034 2135.8 -101.836 1935 2126.6 -191.637 1909 2113.6 -204.638 2295 2100.2 194.839 2208 2090.1 117.940 2191 2086.1 104.941 2103 2089.5 13.542 1805 2099.6 -294.643 2250 2113.9 136.144 2198 2129.1 68.945 1916 2141.7 -225.746 2293 2149.2 143.847 2136 2150.3 -14.348 2193 2145.4 47.649 1863 2136.2 -273.250 2173 2125.0 48.051 2415 2114.2 300.852 2041 2105.6 -64.653 1882 2100.1 -218.154 2047 2097.4 -50.455 2589 2096.5 492.556 2234 2096.4 137.657 2250 2095.8 154.258 1642 2094.2 -452.259 1903 2092.1 -189.160 1899 2090.4 -191.461 2064 2090.8 -26.862 2339 2094.9 244.163 1901 2103.9 -202.964 2156 2118.3 37.765 2453 2137.6 315.466 2253 2160.2 92.8NUM OBS COMP RES ID67 2647 2183.6 463.468 2499 2204.9 294.169 2198 2221.3 -23.370 2529 2230.4 298.671 2271 2230.5 40.572 2186 2221.0 -35.073 2203 2202.9 0.174 2296 2177.6 118.475 2448 2147.9 300.176 2474 2116.7 357.377 2287 2087.0 200.078 2299 2061.5 237.579 2121 2042.2 78.880 1822 2030.3 -208.381 1883 2025.8 -142.882 2059 2027.9 31.183 1919 2035.2 -116.284 1807 2045.6 -238.685 2091 2056.8 34.286 1993 2066.4 -73.487 1879 2072.4 -193.488 2127 2073.2 53.889 1943 2068.0 -125.090 1752 2056.3 -304.391 2321 2038.5 282.592 1819 2015.5 -196.593 2382 1988.8 3 93.294 2126 1959.9 166.195 1990 1930.7 59.396 1443 1903.0 -460.097 1968 1878.5 89.598 1595 1858.5 -263.599 1759 1844.1 -85.1100 1815 1836.0 -21.0101 1573 1834.4 -261.4102 1739 1839.2 -100.2103 1935 1850.0 85.0104 1606 1866.0 -260.0105 1897 1886.3 10.7106 1863 1909.8 -46.8107 2301 1935.3 365.7108 2496 1961.6 534.4109 2263 1987.5 275.5110 1744 2012.2 -268.2111 1800 2034.6 -234.6112 1759 2054.1 -295.1113 2281 2070.0 211.0114 1920 2081.9 -161.9115 2239 2089.7 149.3116 2122 2093.1 28.9117 2015 2092.3 -77.3118 2179 2087.5 91.5119 2311 2078.7 232.3120 2047 2066.5 -19.5121 2047 2051.2 -4.2122 2343 2033.1 309.9123 2407 2012.7 394.3124 2673 1990.5 682.5125 2343 1966.9 376.1126 1743 1942.2 -199.2127 1858 1916.8 -58.8128 1926 1891.1 34.9129 1962 1865.3 96.7130 1552 1839.7 -287.7131 1623 1814.6 -191.6132 1448 1790.2 -342.2133 1775 1766.5 8.5NUM OBS COMP RES ID134 1832 1743.7 88.3135 1621 1721.9 -100.9136 1313 1701.1 -388.1137 1662 1681.5 -19.5138 1639 1662.9 -23.9139 1563 1645.5 -82.5140 1463 1629.2 -166.2141 1000 1613.9 -613.9142 1218 1599.7 -381.7143 1300 1586.5 -286.5144 1467 1574.3 -107.3145 2092 1563.0 529.0146 2488 1552.6 935.4147 1815 1543.0 272.0148 1800 1534.1 265.9149 1637 1526.0 111.0150 1915 1518.5 396.5151 1363 1511.7 -148.7152 939 1505.4 -566.4153 985 1499.6 -514.6154 1145 1494.3 -349.3155 1913 1489.5 423.5156 1614 1485.0 129.0157 1199 1481.0 -282.0158 1738 1477.2 260.8159 1683 1473.8 209.2160 1824 1470.7 353.3161 1350 1467.9 -117.9162 1518 1465.2 52.8163 1595 1462.8 132.2164 1264 1460.6 -196.6165 1296 1458.6 -162.6166 1171 1456.7 -285.7167 1607 1455.0 152.0168 1686 1453.4 232.6169 1417 1451.9 -34.9170 1171 1450.6 -279.6171 1643 1449.4 193.6172 1554 1448.2 105.8173 1600 1447.1 152.9174 1626 1446.2 179.8175 916 1445.2 -529.2176 1001 1444.4 -443.4177 1362 1443.6 -81.6178 1566 1442.9 123.1179 1610 1442.2 167.8180 1064 1441.5 -377.5181 1747 1440.9 306.1182 2028 1440.4 587.6183 2035 1439.9 595.1184 1230 1439.4 -209.4185 1143 1438.9 -295.9186 1742 1438.5 303.5187 1559 1438.1 120.9188 1147 1437.7 -290.7189 1307 1437.3 -130.3190 1373 1437.0 -64.0191 1207 1436.7 -229.7192 1520 1436.4 83.6193 1351 1436.2 -85.2194 1625 1435.9 189.1195 1524 1435.7 88.3196 1245 1435.4 -190.4197 1249 1435.2 -186.2198 1864 1435.0 429.0199 1571 1434.8 136.2200 1379 1434.6 -55.6

IIIIIIIIIIIIIIIIIIIIIIIIII11IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXIIIIIIIIIIWIIIIIIIIIIIIIIIIIIMIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIiiI OIIiIIii1 1 ooaIiIImI I I I Ii i ii i i i i1 1 I I I I I I I IiiiiiiiIi i i i iI I I I I i i I i IIiI1 1 ooaIIII I ooaIiiiIIiIIIiii i i i iI I ImiiIIIIiIII OOvOCNvOStcOCOOC? 1iiIIIiIIIiIIIiIiiiiiIiIIIiiIIIiIiiIII I I I IIooooMi1 COCO II1 ooi aw1 CNCN• • II1 OO1 UH1 ooo11IIIIIIIIIIcost II• • II1 OO1IIIIIIII1 Ol IIi awi mooCOvOIIIIIIII0000 IIooaaCNSt IIIIII• • II1IIIIII11COCO IIooi aw1 Ost1 COO• • IICOCO IIII(H oo IIMi cocoi ooi WW1IIIIII11IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIi r*.o> IIVOV0 II• • II1IIIIIIIIIIIIIIIIIIIIII263§ IIIIH< IIsOa IIs1M1H IIIu3MvOH331U 1IIIICNCO1 H giin Eh II H< II1II 53!l-JOO II> iO 1U 1H II^ 1W 13a§§J II0*P*ii1II 23!D > II ico••r~ IIovT>CO-H IIX—ICNStOi-Hi—ICS.-HOOOO-HOOOII Ol IUHHEdUMHUHin oi in cNst cnocn i -JmNOoovo-JOi-3 i cNCN-Hcostcticocr>ow> iin -h ^h sf co vo r-«m—i oo csoo ^HONOOOOHHOII OOOI I OOiWWWWWWWWWvoco-H^ocnoostr-»ocs i mi—tcr>\ocoi—icriostooovo*HcicNoor-«cr>S iH IH Iwicoi-ir-»cocNcoinstmill ii ioniNHOOMHOii r~» i—ivo i-iooiWHWWWWWWWmooovooor^stcNcs i oomn^op^mo>voCNI^stcyivOOvOOOCO\Oi—iHin«*i-icNinr~»vOvOJ—COOStvOOOOhOOOhhOOhwawHwwawwcN-HCAomnooomo>vomi—iOoor»HO% Oi—ip~oocsster>cso>••••••••co i ^h^h co co com st cncoillOHHHOOHOOI CO CNCO CNiaaaaaaaaaooistOCOCNvOOvOvOCNt-i i >—io\oovor^i—icy>vooS iH iomm«—i cocoon •—icoM| •••••••••csi-Kti-HcommcosfOC1MHOOCSOOI t»» i-HI"- rHI ooiaaaaaaaaa i^HcO'—lO^ooi-immcocr>cocoincoo>cN>* i vocostmsti-^stvOi—uico i cOi-ii-HocOi—ion*cNstcooimvomi—imO-ncomcNi—ir^ocNICO-IrtvONOOOvONOOO-HOOO'H'-iOO—taaaaaaaaaII I I I I I I I ImoststmcNmvom»-j i cscNini—ico ci coco st1 ostCT>oi-l i oo oo st in moo co cr>oa |> I•••••••••OOOOOOOO^HII IIIstooMncoini—ior^\OCOvOCOvOOi-lOCN0VH00>HOrsHOC«isinioNcoo^to*oo oo st in in oo oo oo>OOOOOOO-HOII I ICT>CNmmCTOi—ICNCTistsOOCOCNO'-HCNor^ocNvomorHstr^ooo-nCTips.ococNcn i mi-tr-ooooCTioststH i oooocNi-^r--cr>ooooo£T|•••••••••P* i oooooo^oosaQ III IrHCOCNOOi-HOCTMnoOCN h« st o> co Ocn Oooostoststoinr-co(nnOOoOOrscocoCNOOCNi—!•—IOCTiOOI 001^ CNCO 00 OCT* 00 00•••••••••OOOOO—tOOOII I Ioocomcoo-HCTicovovo CO 00OO CO CO vO cy>r^stooiostvoocomvo voc^oooctisto—I I CriCNStCTlO-HOOOOCii-i i co co codoco r^ in ina l> I•••••••••OOOO—IOOOOIIIvooocNOcooommONr~r-~cr*ooo > iOcoo-Nmoostoo>stcNi-HmC0C000O0">O-Hv0CNrH i coHinocfiHooisMS I coco coo cricoid in inM| •••••••••H I 000--HOOOOOONstocNmcNincticN00000>cO* I I^I^OCOCOCNCNStst^ •••••••••I00 I OOi-IOOOOOO IIIo>o st oo cocoes ocncNOOr^coi—*cor~CNOSt00Ststr-»^Hi-HP^OvOCr>ocNCNinr~oocr>voONcs com co rococoi-j i oo>cNoocr*cNmp~r~» rococo oo oo oo ooa i-hooooooooii iii-^T" 1 ^ rH'-HCNCNCNCN£ Z « M W M Z h-1 WQH03H>QHH>IIIIIICN 1 00--I IIhJ 1 0.-I IIw 1> 1 ^H-H1 -Hi—IIIIIICN I r-»in IIS I IH 1i-Hi—COIIIIIICN 1 vOCN IIH 1 II1 • •s 1 ~*r-lOlW> II1H 1 II< i II> 1H1 OStOS 5 1 \0\0H 1 1COCOQ Q 1^1H 15gPh t—H w1IIIIIIIIH-l 1 cost IIpa > 1H 1taO i—l i-H IIOOaUmcN II•-HS*£>COmr~IIS H • • IIOd H CNCN53uM«W |S I5 iZ1OOOO WW• •1—1 1—1IIIIIIIIIIIIII wCNooOlWWvOOOi-t i vOCO IIH ICOO IIH! • •-Hi-«< 1^ 1aiIIIIII^H 1 vOvO IIcocossSs§HH3ssa

264COMP2395 2435 2475 '2515 2555TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-49. PDPLOT o-f the occultation o-f X13607.0313^.0282_ MEAN -0.06553UJ 025Z_ SIGMA 0.141783o zLUCCX5o yoU.oUJCOz DZ0002,-86.2-72.2-58.2-44.2-30.2-16.2-2.2 11.8 25.8NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-50. N0ISEPL0T o-f the occultation o-f X13407

,The NOISEPLOT o-f the 4096 milliseconds of observationaldata (Figure 5-26), as well as the mean offset and one sigmavalues, are nearly identical to those obtained -for theearlier occultation o-f X13567. This was expected as bothstars were nearly the same apparent V magnitude, and theobserv ing condi t i ons were essen t ially identical.Finally, the power spectra of the observation centeredon the event, the pre-occul tat i265on and star-plus-sky signals,and the two-star model curve are shown in the POUIERPLOTFi gure 5-51 .Since the UwVB time signal was of lower quality for thisevent, the Coordinated Universal Times of geometricaloccultation were not quite as well determined as for theX13534 event. The fainter star underwent disappearance at04:33:58.773

'266MODELCURVEir1 •"1STAR + SKYOCCULTATION'100' £00' 300" '400'FREQUENCY IN HERTZFigure 5-51. POWERPLOT o-f the occultation o-f X13687.

267n 40961 3686*512 1024 1536 '2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-52. RAWPLOT o-f the occupation of 2C1462.k512 1024 1536 2048 2560 '3072 '358 4TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-53. INTPLOT o-f the occupation o-f 2C1462.

263The integration plot, Figure 5-53, shows noevidence o-f stellar duplicity. Though there is anapparent change in slope at approximately 1800milliseconds, it is a gradual change in level, ratherthan a sharp discontinuity typical o-f a second star. Inaddition, the original slope o-f the integration curvereturns at approximately 2200 milliseconds. Thisbehavior is due only to variations in atmospherictransparency.The -formal solution to the observed intensity curveis shown on the FITPLOT, Figure 5-54. As may be seenfrom the -figure, or from the occultation summary, Table5-27, the best fit to the raw data calls for a sourcediameter of roughly 9 milliseconds of arc. Thisanomalously large angular diameter is quite unexpectedconsidering the relative faintness of this star, and isbelieved to be spurious.The power spectrum of the star-plus-sky signaldetermined from 1000 millisecond data samples takenbetween 1.5 ond 0.5 seconds preceeding the determinedtime of geometrical occultation is shown on Figure 5-56.Contributions to the background noise due to the lowfrequency power components are quite important. Indeed,in the range of 10 to 70 Hertz these are dominant overthe power spectral signature of the solution curve byone to two orders of magnitude, respectively. It isprecisely, however, in this power spectral region that

,26?1.0DIfT C f,,T° THE GEOMETRICAL SHADOV IN^0-70^5^40-30-20-^* METERS

:170ZC1462:TABLE 5-27LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: ZC1462

'1111l11271MODELCURVE!JSTAR +SKYiOCCULTATION0Figure 5-56,'100" "200' •300"FREQUENCY IN400HERTZPOUERPLOT o-f the occupation o-f ZC1462.

.272the signature of the occultation curve is mostimportant. Hence, the observed data are corrupted byintensity variations due to atmospheric noise whichmimic the variations seen in an occultation curve.This effect is seen rather dramatically in thesecond FITPLOT presented (Figure 5-55). Here, theobserved data were Fourier transformed and all powercomponents o-f -frequency higher than 150 Hertz removed.A-fter inverse trans-formation, the Fourier smoothed datawere fit by the DC procedure. The solutions obtained ina fit to the smoothed data, as expected, are nearlyidentical to the fit to the raw data. What is obviousfrom visual inspection is that the undulating characterof the data, in terms of both frequency and amplitude,is very similar to the fringing effects expected due tothe occul tat i onIt is therefore apparent that the noisecharacteristics of the sky, at the time of this event,were such that the formal solution of the angulardiameter is highly suspect, and in fact most probablyerroneous. Under these conditions, with presentreduction and analysis techniques, it is almostcertainly impossible to ascertain the true angulardiameter of the star. Though a formally determineddiameter is presented here, a strong "caveat emptor" isplaced on the result.

The observations extracted -from the raw data set(as well as the computed intensity curve and theresiduals) are listed in Table 5-28. Thevar iance-covar i ance and correlation matrices of the•formal solution are given in Table 5-29. Also -found on273this table are the ranges o-f the numerical values o-f thepartial derivatives o-f the intensity curve, as depictedon the PDPLOT, Figure 5-57.The photometrically poor conditions -foroccultation photometry are -further noted by anexamination o-f the NOISEPLOT o-f the 4096 milliseconds o-fobservational data presented in Figure 5-58. The meansignal level does correspond with the peak o-f thedistribution -function o-f the residuals, but thedistribution function itsel-f is highly skewed. The meansignal level over the entire data window is more than2 percent down -from the mean level during the 201milliseconds centered on the time o-f the event, and theone sigma level o-f the distribution -function isapproximately11.5 percent.A -final note on observations, such as this one,taken under photometrically noisy conditions iswarranted. In this case, the noise associated with theraw data has a one sigma level of 21.4 percent of themean intensity. This by itself is not sufficient todismiss the possibility of obtaining a meaningfulsolution from the observed intensity curve. What is

274TABLE 5-28ZC1462: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 2500NUM = 6BS == COMP === RESiD "" NuTfoBS COMP RESID NUM OBS_ C0MP__ RESID_2682 2311.0 371.01 2111 2311.1 -200.12 2648 2311.0 337.03 1923 2311.0 -388.04 2155 2311.0 -156.05 2095 2311.0 -216.06 2555 2311.0 244.07 2800 2311.0 489.08 2979 2311.0 668.09 2619 2311.0 308.010 2507 2311.0 196.011 1767 2311.0 -544.012 1882 2311.0 -429.013 2111 2311.0 -200.014 2050 2311.0 -261.015 1691 2311.0 -620.016 1779 2311.0 -532.017 1683 2310.9 -627.918 2115 2311.0 -196.019 2583 2311.0 272.020 2671 2311.0 360.021 3067 2311.0 756.022 2194 2311.0 -117.023 2387 2311.0 76.024 2755 2311.0 444.025 2641 2311.1 329.926 2783 2311.0 472.027 2216 2311.0 -95.028 2043 2311.2 -268.229 2573 2311.1 261.930 2343 2311.0 32.031 2426 2311.1 114.932 2403 2311.3 91.733 2083 2311.2 -228.234 2559 2311.0 248.035 2247 2311.2 -64.236 2498 2311.4 186.637 2175 2311.4 -136.438 2102 2311.2 -209.239 2075 2311.3 -236.340 2246 2311.5 -65.541 1692 2311.6 -619.642 2237 2311.4 -74.443 2175 2311.3 -136.344 2339 2311.7 27.345 2582 2312.2 269.846 2591 2311.8 279.247 2604 2310.9 293.148 2527 2311.2 215.849 2673 2313.0 360.050 2503 2314.2 188.851 2217 2312.7 -95.752 2331 2309.7 21.353 2233 2309.1 -76.154 2140 2312.4 -172.455 2369 2316.9 52.156 2080 2317.9 -237.957 2294 2314.1 -20.158 2107 2308.6 -201.659 2367 2306.1 60.960 2202 2308.7 -106.761 2010 2314.8 -304.862 2367 2320.9 46.163 2237 2324.3 -87.364 2647 2323.3 323.765 2539 2317.7 221.366 23 90 2308.4 81.667 2321 2298.5 22.568 2173 2293.2 -120.269 2250 2297.6 -47.670 2193 2313.8 -120.871 2553 2338.1 214.972 2244 2361.7 -117.773 2117 2373.5 -256.574 2503 2365.0 138.075 2607 2334.8 272.276 2423 2290.0 133.077 2029 2243.6 -214.678 2226 2210.8 15.279 2371 2204.0 167.080 2311 2229.1 81.981 2095 2284.2 -189.282 1797 2360.7 -563.783 2639 2445.5 193.584 2996 2524.4 471.685 2478 2584.9 -106.986 2471 2618.1 -147.187 2641 2619.4 21.688 2543 2588.7 -45.789 2496 2529.3 -33.390 1643 2446.6 -803.691 2203 2347.3 -144.392 2313 2238.3 74.793 2411 2125.6 285.494 2218 2014.3 203.795 1920 1908.3 11.796 1553 1810.0 -257.097 1691 1721.1 -30.198 1608 1642.2 -34.299 1844 1573.2 270.8100 1599 1513.6 85.4101 1475 1462.8 12.2102 1605 1419.8 185.2103 1229 1383.6 -154.6104 1457 1353.2 103.8105 1515 1327.9 187.1106 1318 1306.9 11.1107 1090 1289.3 -199.3108 1308 1274.8 33.2109 1183 1262.6 -79.6110 1407 1252.5 154.5111 1631 1244.0 387.0112 1015 1236.8 -221.8113 1331 1230.8 100.2114 1739 1225.7 513.3115 1460 1221.4 238.6116 1073 1217.7 -144.7117 1301 1214.5 86.5118 1182 1211.8 -29.8119 1309 1209.4 99.6120 1167 1207.3 -40.3121 1224 1205.5 18.5122 902 1204.0 -302.0123 999 1202.6 -203.6124 1045 1201.4 -156.4125 1367 1200.4 166.6126 1119 1199.4 -80.4127 1115 1198.6 -83.6128 1125 1197.8 -72.8129 1345 1197.1 147.9130 1051 1196.5 -145.5131 1273 1195.9 77.1132 913 1195.4 -282.4133 1079 1194.9 -115.9134 1458 1194.5 263.5135 1361 1194.1 166.9136 858 1193.7 -335.7137 870 1193.4 -323.4138 1379 1193.1 185.9139 1403 1192.8 210.2140 1324 1192.6 131.4141 1104 1192.3 -88.3142 1074 1192.1 -118.1143 1183 1191.9 -8.9144 1370 1191.7 178.3145 778 1191.5 -413.5146 1014 1191.3 -177.3147 1143 1191.2 -48.2148 1257 1191.0 66.0149 1269 1190.9 78.1150 1109 1190.8 -81.8151 1182 1190.6 -8.6152 1464 1190.5 273.5153 1336 1190.4 145.6154 1271 1190.3 80.7155 1247 1190.2 56.8156 1065 1190.1 -125.1157 1203 1190.0 13.0158 968 1190.0 -222.0159 986 1189.9 -203.9160 1415 1189.8 225.2161 1278 1189.7 88.3162 1241 1189.7 51.3163 1357 1189.6 167.4164 1087 1189.5 -102.5165 1032 1189.5 -157.5166 1119 1189.4 -70.4167 924 1189.4 -265.4168 936 1189.3 -253.3169 1139 1189.3 -50.3170 1343 1189.2 153.8171 1387 1189.2 197.8172 1219 1189.1 29.9173 1516 1189.1 326.9174 1139 1189.1 -50.1175 868 1189.0 -321.0176 767 1189.0 -422.0177 1027 1188.9 -161.9178 1403 1188.9 214.1179 1451 1188.9 262.1180 965 1188.8 -223.8181 1467 1188.8 278.2182 1047 1188.8 -141.8183 1121 1188.8 -67.8184 1139 1188.7 -49.7185 1166 1188.7 -22.7186 1242 1188.7 53.3187 1126 1188.7 -62.7188 1291 1188.6 102.4189 1075 1188.6 -113.6190 1231 1188.6 42.4191 1033 1188.6 -155.6192 1315 1188.6 126.4193 1209 1188.5 20.5194 1515 1188.5 326.5195 954 1188.5 -234.5196 856 1188.5 -332.5197 1117 1188.5 -71.5198 1367 1188.4 178.6199 1401 1188.4 212.6200 1325 1188.4 136.6

275TABLE 5-29ZC1462: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO-VARIANCEMATRIXDIAM PREI POST TIME VELO3.207E~16 6.839E 08 -2.060E"08 -4.716E"09 3.890E~106.839E 08 6.296E02 2.217E01 -6.631E00 3.594E"012.060E_08 2.217E01 6.404E02 -7.124E00 3.994E"014.716E_09 -6.631E00 -7.124E00 1.306E00 -7.414E"023.890E 10 3.594E 01 3.994E 01 -7.414E"02 6.182E"03CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.959624 -0.441850 -0.367280 0.348224PREI 0.959624 1.000000 -0.176967 -0.603263 0.586464POST -0.441850 -0.176967 1.000000 -0.669212 0.683702TIME -0.367280 -0.603263 -0.669212 1.000000 -0.999770VELO 0.348224 0.586464 0.683702 -0.999770 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 4.426E09 -3.867E09PREI 1.278E00 6.941E"04POST 9.993E~01 -2.781E"01TIME 1.127E02 -8.438E01VELO 1.411E03 -1.846E03

_|2762500 2540 2580 2620 '2660TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWFigure 5-57. PDPLOT o-f the occultation of ZC1462.032Z_(0UJozUJXcc0288_ MEAN -0.021910256 _ SIGMA 0.1146200224 _3 0192 _o 0160 _O 012821 0096(03 0064 _Z0032 _0002 J I I II I IH-9L8 -78.7 -65.6 -52.5 -39.5 -26.4-13.3 -0.2~ '12.8 '25 9NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-58. NOISEPLOT of the occultation o-f 2C1442

277important is whether the noise is dominant in the low orhigh -frequency regime . To -further verify that this isindeed true, a computational test was performed. Amodel intensity curve was needed -for the test. Forconvenience, the solution curve -for this occultation wasused. To this model curve, noise

.278Martin England who (as noted in the occultation summary,Table 5-30) employed a Johnson K> filter for theobservat ionThe integration plot o-f the observational data(Figure 5-60) hints at a possible "wide" stellarduplicity approximately 150 milliseconds before theobvious disappearance. To ascertain if this drop (alsoseen on the RAWPLOT) was real, a detailed integrationplot was produced containing the data -from 3100 to 3625milliseconds. To aid in the visual interpretation o-fthe graph, the integrated data were subjected to 5-oointunweighted smoothing before being plotted. It isapparent in Figure 5-61 that a real, sharp change ofslope does occur at approximately millisecond 3265.The mean intensity (averaged over 125 milliseconds)prior to this was 2515 counts, and afterward, 2488counts. This drop of 27 counts represents a lowering ofthe signal intensity by approximately 0.011 magnitudes.This seems like a rather small amount. However, as wi 11be seen, the formal error of the pre-occul tat i onintensity found by the DC fitting process at the time oftheprimary event was only roughly 0.007 magnitudes.Hence, the one s igma certainty of detection of a "wide"component is 64 percent better than the determination ofthe mean star-pl us-sky level. Therefore, one can

:.279XI 8067:TABLE 5-30LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X18067 (SAO 119227, DM +05 2587)RA: 120641 DEC: +043627 mV: 7.9 Sp : KOFilter: V Diaphragm: I Gain: B10+ Voltage: 1200LUNARSurface Illumination:Elongation from Sun:Altitude Above Horizon:Lunar Limb Distance:Predicted Shadow Velocity:Predicted Angular Rate:EVENTINFORMATION53 percent93 deorees48 decrees370414 K i 1 ome ters364 91 meters/sec2032 arcsec/secINFORMATIONDate: June 18, 1983 UT of Event: 02:16:54USNO V/O Code: 26 HA o+" Event: +354352Position Angle: 63.8 Cusp Angle: 40NContact Angle: +61.5 Watts Angle: 40.6MODEL PARAMETERSNumber of Data Points: 201Number of Grid Points: 4096Number of Spectral Regions: 53Width of Spectral Regions: 50 AngstromsLimb Darkening Coefficient: 0.5Effective Stellar Temperature: 5100KSOLUTIONSStellar Diameter (ams): Point SourceTime: (relative to Bin 0): 3422.1 Pre-Event Signal: 2459.2

280^4096i512 1024 1536 '2048 2560 '3072 '3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-59. RAUPLOT o-f the occupation o-f X18067.L0 ^-fe 512 1024 1538 2048 2560 3072 '3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-60. INTPLOT o-f the occupation o-f X18067.

281Q CD CO [^ (D in ^-* m • 9 « «Q S Q Q s Q Q CM QAUSN31NI a32HVWaON

282ascribe a confidence level to the detection of a "wide"secondary component of 90 percent.The best solution for the observation of theprimary occultation of X18067 (depicted graphically inFigure 5-62) found the star to be a point source. Thiswas not unexpected as X18067 has been classified as amain sequence star, thus giving it a distance modulus ofapproximately 2.0, and an anticipated diameter of 0.85solar radii. At this distance the corresponding angulardiameter would be only 1/25 millisecond of arc, wellbelow the detection threshold of roughly one millisecondofarc.From the determined R-rate of 0.2036

233COUNTS8 °> co t^q in ^ o) cj ^A-LISNH1NI aaznvHdON

TABLE 5-31X18067: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 3300NUM OBS COMP RES ID2297 2452.3 -155.31 2216 2452.4 -236.42 2672 2455.4 216.63 2512 2460.8 51.24 2207 2467.3 -260.35 2197 2473.2 -276.26 23 98 2476.5 -78.57 2534 2476.4 57.68 2572 2472.5 99.59 2550 2465.3 84.710 2561 2456.4 104.611 2607 2447.9 159.112 2256 2441.8 -185.813 2231 2439.7 -208.714 2405 2442.5 -37.515 2448 2450.0 -2.016 2699 2460.9 238.117 2333 2473.3 -140.318 2681 2484.8 196.219 2415 2492.8 -77.820 2324 2495.7 -171.721 2427 2492.5 -65.522 2744 2483.5 260.523 2734 2469.9 264.124 2575 2453.8 121.225 2858 2437.9 420.126 2566 2425.0 141.027 2255 2417.3 -162.328 2335 2416.3 -81.329 2309 2422.6 -113.630 2220 2435.5 -215.531 2317 2453.4 -136.432 2539 2474.0 65.033 2703 2494.4 208.634 2891 2511.8 379.235 2704 2523.8 180.236 2427 2528.5 -101.537 2384 2525.2 -141.238 2292 2513.9 -221.939 2679 2495.9 183.140 2452 2473.1 -21.141 2212 2448.0 -236.042 2203 2423.4 -220.443 2571 2402.1 168.944 2530 2386.4 143.645 2364 2378.0 -14.046 2251 2378.1 -127.147 2347 2386.7 -39.748 2063 2403.2 -340.249 2217 2426.1 -209.150 2753 2453.6 299.451 2729 2483.1 245.952 2782 2512.4 269.653 2872 2538.8 333.254 2818 2560.4 257.655 2647 2575.3 71.756 2586 2582.4 3.657 2464 2581.2 -117.258 2648 2571.9 76.159 2409 2554.7 -145.760 2428 2531.2 -103.261 2271 2502.7 -231.762 2623 2471.1 151.963 2459 2438.2 20.864 2599 2406.0 193.065 2315 2376.4 -61.466 2488 2351.0 137.0NUM OBS COMP RES ID67 2479 2330.9 148.168 2497 2317.4 179.669 2270 2311.0 -41.070 2284 2311.9 -27.971 2421 2320.1 100.972 2496 2335.1 160.973 2663 2356.3 306.774 2407 2382.8 24.275 1967 2413.5 -446.576 2320 2447.2 -127.277 2292 2482.8 -190.878 2543 2519.0 24.079 2552 2554.7 -2.780 2579 2588.8 -9.881 2452 2620.4 -168.482 2669 2648.7 20.383 2613 2673.0 -60.084 2535 2692.8 -157.885 2479 2707.9 -228.986 2821 2717.9 103.187 2653 2722.8 -69.888 2671 2722.7 -51.789 2895 2717.7 177.390 2551 2708.1 -157.191 2679 2694.3 -15.392 2835 2676.5 158.593 3118 2655.2 462.894 2639 2630.9 8.195 2449 2603.9 -154.996 2322 2574.8 -252.897 2499 2543.9 -44.998 2456 2511.7 -55.799 2284 2478.6 -194.6100 2505 2444.9 60.1101 2218 2411.0 -193.0102 2040 2377.1 -337.1103 2663 2343.6 319.4104 2348 2310.6 37.4105 2108 2278.3 -170.3106 1999 2246.9 -247.9107 2094 2216.6 -122.6108 2015 2187.3 -172.3109 2427 2159.3 267.7110 2299 2132.5 166.5111 2108 2107.0 1.0112 2127 2082.8 44.2113 2180 2059.8 120.2114 2285 2038.2 246.8115 2059 2017.9 41.1116 1966 1998.8 -32.8117 1848 1980.8 -132.8118 2056 1964.1 91.9119 2007 1948.4 58.6120 1779 1933.8 -154.8121 1887 1920.2 -33.2122 2062 1907.5 154.5123 2031 1895.8 135.2124 1872 1884.9 -12.9125 1863 1874.7 -11.7126 1995 1865.3 129.7127 1874 1856.6 17.4128 1787 1848.6 -61.6129 2055 1841.1 213.9130 2000 1834.2 165.8131 1888 1827.8 60.2132 1741 1821.9 -80.9133 1703 1816.5 -113.5284NUM OBS COMP RES ID134 1635 1811.4 -176.4135 1723 1806.7 -83.7136 1775 1802.4 -27.4137 2036 1798.4 237.6138 1657 1794.7 -137.7139 1779 1791.3 -12.3140 1831 1788.1 42.9141 2049 1785.1 263.9142 1641 1782.4 -141.4143 2067 1779.9 287.1144 1627 1777.5 -150.5145 2119 1775.3 343.7146 2039 1773.3 265.7147 1768 1771.4 -3.4148 1583 1769.6 -186.6149 2096 1768.0 328.0150 1734 1766.5 -32.5151 1723 1765.0 -42.0152 1755 1763.7 -8.7153 1536 1762.5 -226.5154 1257 1761.3 -504.3155 1484 1760.2 -276.2156 1639 1759.2 -120.2157 1658 1758.2 -100.2158 1946 1757.3 188.7159 1899 1756.5 142.5160 1689 1755.7 -66.7161 1640 1754.9 -114.9162 1546 1754.2 -208.2163 1311 1753.6 -442.6164 1727 1752.9 -25.9165 1819 1752.3 66.7166 1825 1751.8 73.2167 1665 1751.3 -86.3168 1791 1750.8 40.2169 1505 1750.3 -245.3170 2115 1749.9 365.1171 1843 1749.4 93.6172 1984 1749.0 235.0173 1727 1748.7 -21.7174 1872 1748.3 123.7175 1536 1748.0 -212.0176 1728 1747.7 -19.7177 1498 1747.4 -249.4178 1611 1747.1 -136.1179 1718 1746.9 -28.9180 1743 1746.6 -3.6181 1680 1746.4 -66.4182 1783 1746.1 36.9183 1676 1745.9 -69.9184 1841 1745.7 95.3185 1819 1745.5 73.5186 1756 1745.2 10.8187 1772 1745.0 27.0188 1973 1744.8 228.2189 1850 1744.7 105.3190 1592 1744.5 -152.5191 1585 1744.3 -159.3192 1768 1744.1 23.9193 2008 1744.0 264.0194 1579 1743.8 -164.8195 1680 1743.7 -63.7196 1808 1743.6 64.4197 1596 1743.4 -147.4198 1762 1743.3 18.7199 1711 1743.2 -32.2200 1895 1743.1 151.9

285range of the partial derivatives presented on the PDPLOT(Figure 5-63) are given in Table 5-32.A cursory examination o-f the raw intensity plotreveals that while the expected high -frequencyscintillation and photon noise sources are present,there is virtually no variation in atmospherictransparency on longer time-scales. This led to arapidly convergent solution with very low -formalstatistical errors. The distribution -function o-f theobservational noise is shown in Figure 5-64. The usualoccultation power spectra are displayed in Figure 5-65.The Coordinated Universal Time o-f geometricaloccultation was determined to be 02:16:52.406 (+/- 0.007seconds)ZC22Q9 star ZC220? was occulted onJune 22, 1983. 2C2209 is o-f spectral type K0 and hasbeen classified as a giant (luminosity class III). Theoccultation event was observed by John P. Oliver, MartinEngland, and Howard L. Cohen with the instrumentalcon-figuration specified in Table 5-33. The observinglog indicates that clouds appeared seven minutes afterthe event. Oliver, however, has indicated that prior tothis the transparency of the sky was quite good and theseeing steady and calm. The post-event cloud cover wasof the low patchy cumulus type, which is common in northFlorida during the summer. Therefore, the onset of

2863300 3340 3380 3420 3480TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-63. PDPLOT o-f the occultation o-f X18067.-39.5-33.0-26.6-20.1 -13.7 -7.3 -0.8 5.8 12.0 18.5NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-64. NOISEPLOT o-f the occultation o-f X18067.

287TABLE 5-32X18067: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO- VARIANCE MATRIXDIAM PREI POST TIME VELO1.008E~14 2.581E~07 -3.101E07 -1.077E"08 9.371E~112.581E~07 2.874E02 1.917E01 -7.082E00 4.368E"02•3.101E_07 1.917E01 4.509E02 -1.010E01 5.972E"021.077E~08 -7.082E00 -1.010E01 2.379E0O -1.439E"029.371E 11 4.368E 02 5.972E 02 -1.439E"02 1.171E~04CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.701669 -0.797370 0.254354 -0.231840PREI 0.701669 1.000000 -0.130101 -0.498781 0.518495POST -0.797370 -0.130101 1.000000 -0.781331 0.766733TIME 0.254354 -0.498781 -0.781331 1.000000 -0.999731VELO -0.231840 0.518495 0.766733 -0.999731 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 3.274E08 -3.212E08PREI 1.366E00 6.222E"03POST 9.938E 01 -3.659E~01TIME 3.393E01 -3.612E01VELO 6.036E03 -6.035E03

I111288MODELCURVEt 1 rSTAR + SKY!% Pflfjf^^ftr*OCCULTATIONFigure 5-65,'100" *200" •300 '400FREQUENCY IN HERTZPOWERPLOT o-f the occultation o-f X18067.

289ZC2209:TABLE 5-33LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: ZC 2209, (32 Librae, SAO 159280, DM -16 4089)RA: 152719 DEC: -163935 mV: 5.92 Sp : KO-IIIFilter: V Diaphragm: I Gain: B8 Voltage: 1000LUNARINFORMATIONSur-face Illumination: 90 percentElongation -from Sun: 143 degreesAltitude Above Horizon: 44 degreesLunar Limb Distance: 386528 kilometersPredicted Shadow Velocity: 625.71 meters/sec.Predicted Angular Rate: 0.3339 arcsec/sec.EVENTINFORMATIONDate: June 22, 1983 UT o-f Event: 03:12:54USNO V/O Code: 76 HA o-f Event: +033323Position Angle: 111.6 Cusp Angle: 85SContact Angle: +8.3 Uatts Angle: 98.8MODEL PARAMETERSNumber o-f Data Points: 201Number o-f Grid Points: 256Number o-f Spectral Regions: 53Width o-f Spectral Regions: 50 AngstromsLimb Darkening Coe-f-f i c i ent 0.5E-f-fective Stellar Temperature: 5100 KSOLUTIONSStellar Diameter (ams): 12.18 (1.86)Time: (relative to Bin 0): 631.2 (0.8)Pre-Event Signal: 3020.2 (12.2)Background Sky Level: 2025.8 (12.2)Velocity (meters/sec): 673.7 (45.5)Lunar Limb Slope (degrees): -10.88 (4.16)U.T. o-f Occultation: 03:12:53.356 (0.007)PHOTOMETRIC NOISESum-o-f-Squares o-f Residuals:Sigma (Standard Error):Normalized Standard Error:Photometric (S+N)/N Ratio:Intensity Change/Background:Change in Magnitude:INFORMATION2494300111 .68.112319 .904.49086.43359

290cloud cover after the event did not adversley affect theobservat ionThe digital photoelectric record obtained ispresented in Figure 5-66. As can be seen, the sky wasquite well behaved throughout the 4096 milliseconds o-fdata acquisition. The observation is seen early in thedata window. One o-f the observers, who was using theLODAS system -for the -first time, nearly forgot to stopthe data acquisition process after the event. Theintegration plot of the occultation record (Figure 5-67)shows no indication of stellar duplicity.The solution to the observed intensity curve isdepicted graphically in Figure 5-68. As indicated, arather large angular diameter (12.18 +/- 1.86milliseconds of arc) was determined by the differentialcorrections fitting procedure. Assuming the spectraltype and luminosity classification for ZC2209 arecorrect, they would indicate a distance on the order of115 parsecs; hence, the diameter found is an order ofmagnitude larger than one would expect. This disparityremains unresolved, as the fit is rather good anddifficult to dismiss. Examination of the PDPLOT(Figure 5-69) clearly indicates that the region ofsensitivity of the observed curve to variations in allthe parameters was well considered and that numericalnoise was minimal.

2914096J 3686327728672458 8 C2048 hen16381229819410i,__l i__ i.512 1024 1536 2048 2560 3072 3584IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-66. RAUPLOT o-f the occultation o-f ZC2289.CO2iQuM—I

292COUNTSCMCM(X)COCD en CO Q 05 rsCM CO V) CD rf COS CO r^ ID ^r CMm CM CM CM CM CMSCMLOGO. i . i i . i .-L -L L^Q CON(Olf)t(l)OJ^Q0)ausn3_lni aazuvwaoN

293The distribution -function of the residuals shown inthe NOISEPLOT (Figure 5-70) is obviously Gaussian innature. The mean observed intensity is down only0.1 percent from the computed intensity, with a onesigma width in the distribution -function o-f only4 percent. In addition, the photometric

294520 560 '600 640 '680TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-69. PDPLOT of the occultation of ZC2209.(0UJo 2UJcc£Oyou.ocrUJcQz>2022£_ MEAN 0.001U020SJ_ SIGMA 0.03993501780152012701020078 _0051 _002E_000411114. j4 j-h~ktT-20.4 -16.9 -13.4 -9.9 -6.4 -2.9 0.6 4.0 vt 7.5 1L0NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-70. NOISEPLOT of the occultation of ZC2209,

'•295MODELCURVEW#»^irSTAR +SKYi 11rOCCULTATIONIfHft^^^l50~ r ~'100' '150' '200FREQUENCY INHERTZFigure 5-71. POWERPLOT o-f the occultation o-f 2C2289.

eason -for the disparity between the anticipated smallangular diameter and the larger diameter in-ferred -fromthe observation could lie in an erroneous spectralcl assi f i cat i on . However, this tentatve suggestion isput -forth without much -force, and the question at thistime remains open.The Coordinated Universal Time o-f geometricaloccultation for this event was -found to be 03:12:53.356

297TABLE 5-34ZC2209: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 520NUM OBS COMP RES ID NUM OBS COMP RES ID NUM OBS COMP RES ID2949 3023.0 -74.01 2853 3023.0 -170.02 3089 3023.0 66.03 3176 3023.0 153.04 3085 3022.9 62.15 3082 3022.9 59.16 3042 3023.1 18.97 30 93 3023.1 69.98 2969 3023.1 -54.19 2954 3023.0 -69.010 3142 3023.0 119.011 3009 3023.1 -14.112 3034 3023.2 10.813 3322 3023.3 298.714 3119 3023.2 95.815 2983 3023.1 -40.116 3003 3023.1 -20.117 3182 3023.2 158.818 3199 3023.4 175.619 3191 3023.4 167.620 2984 3023.3 -39.321 3094 3023.2 70.822 2954 3023.3 -69.323 3160 3023.5 136.524 3109 3023.7 85.325 3060 3023.7 36.326 3011 3023.3 -12.327 2924 3023.1 -99.128 2816 3023.2 -207.229 2971 3023.8 -52.830 3012 3024.6 -12.631 2705 3024.8 -319.832 2694 3024.2 -330.233 2899 3023.2 -124.234 3084 3022.4 61.635 3071 3022.6 48.436 3285 3023.7 261.337 3052 3025.3 26.738 3000 3026.5 -26.539 3034 3026.7 7.340 3080 3025.8 54.241 3071 3024.1 46.942 2936 3022.1 -86.143 3131 3020.9 110.144 2985 3021.0 -36.045 2733 3022.9 -289.946 2967 3026.3 -59.347 2955 3030.1 -75.148 32 93 3032.8 260.249 3227 3033.1 193.950 2989 3030.3 -41.351 3037 3025.1 11.952 2971 3019.2 -48.253 3188 3014.7 173.354 3019 3013.5 5.555 2902 3016.3 -114.356 3235 3022.6 212.457 3307 3030.7 276.358 3168 3038.4 129.659 3070 3044.1 25.960 3272 3046.6 225.461 3076 3045.9 30.162 2947 3042.4 -95.463 3207 3037.0 170.064 3043 3030.4 12.665 2969 3023.1 -54.166 2737 3015.4 •-278.467 266168 284869 314570 288471 301972 287073 287374 290075 307476 305077 301578 314779 319580 312781 310982 318483 328184 327185 312786 317787 313288 295989 292590 273791 285992 273693 267594 271295 261196 247097 244998 218899 2163100 2343101 2374102 23 91103 2273104 2060105 2179106 2228107 2228108 2089109 2006110 2075111 2334112 2245113 2156114 2147115 1966116 1976117 1956118 1913119 1994120 1976121 2145122 2006123 1998124 2252125 2133126 2190127 2114128 2024129 1965130 2015131 1959132 1983133 21343007.63000.22994.22991.02992.12999.03012.83033.73061.03093.13127.53161.23191.13214.33228.23231.13222.03200.73167.73124.23071.93012.52948.22880.72812.12743.82677.22613.42553.12496.92445.12397.72354.92316.42282.12251.62224.72201.02180.12161.92146.02132.22120.12109.52100.32092.32085.32079.22073.92069.22065.12061.42058.22055.42052.92050.62048.72046.92045.32043.92042.62041.42040.42039.42038.62037.82037.1-346.6-152.2150.8-107.026.9-129.0-139.8-133.713.0-43.1-112.5-14.23.9-87.3-119.2-47.159.070.3-40.752.860.1-53.5-23.2-143.746.9-7.8-2.298.657.9-26.93.9-209.7-191.926.691.9139.448.3-141.0-1.166.182.0-43.2-114.1-34.5233.7152.770.767.8-107.9-93.2-109.1-148.4-64.2-79.492.1-44.6-50.7205.187.7146.171.4-17.4-75.4-24.4-79.6-54.896.913413513613713813914014114214314414514614714814915015115215315415515615715815916016116216316416516616716816917017117217317417517617717817918018118218318418518618718818919019119219319419519619719819920018 94187419592151206821552050192920282080193719832031217520331857194819791936198621112161212520201930210120231907205521272027216819661987205619712115213020211949188218822047204820731873208 92071193 9203 9204520872147201920941994196919941916222720872043207120312112201120532036.42035.82035.32034.82034.32033.92033.52033.12032.72032.42032.12031.82031.62031.32031.12030.92030.72030.52030.32030.12030.02029.82029.72029.52029.42029.32029.22029.02028.92028.82028.72028.62028.62028.52028.42028.32028.32028.22028.12028.12028.02027.92027.92027.82027.82027.72027.72027.62027.62027.52027.52027.52027.42027.42027.32027.32027.32027.22027.22027.22027.12027.12027.12027.12027.02027.02027.0-142.4-161.8-76.3116.233.7121.116.5-104.1-4.747.6-95.1-48.8-0.6143.71.9-173.9-82.7-51.5-94.3-44.181.0131.295.3-9.5-99.471.7-6.2-122.026.198.2-1.7139.4-62.6-41.527.6-57.386.7101.8-7.1-79.1-146.0-145.919.120.245.2-154.761.343.4-88.611.517.559.5119.6-8.466.7-33.3-58.3-33.2-111.2199.859.915.943.93.985.0-16.026.0

TABLE 5-35ZC2209: SUPPLEMENTAL STATISTICAL INFORMATION298VARIANCE/ CO- VARIANCE MATRIXDIAM PREI POST TIME VELO8.149E 17 2.649E"08 2.525E 10 -2.870E"09 1.899E~102.649E 08 1.476E02 9.753E00 -3.250E00 1.445E~012.525E~10 9.753E00 1.478E02 -3.257E00 1.454E01-2.870E 09 -3.250E00 -3.257E00 6.850E~01 -3.114E~021.899E 10 1.445E 01 1.454E 01 -3.114E 02 2.066E 03CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.996428 -0.137148 -0.647710 0.645788PREI 0.996428 1.000000 -0.109177 -0.661815 0.659550POST -0.137148 -0.109177 1.000000 -0.663632 0.665138TIME -0.647710 -0.661815 -0.663632 1.000000 -0.999983VELO 0.645788 0.659550 0.665138 -0.999983 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 3.608E09 -4.206E09PREI 1.212E00 1 .209E~03POST 9.988E~01 -2.122E 01TIME 6.867E01 -3.459E01VELO 1 .120E03 -1 .217E03

i299TABLE 5-36ZC3214: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: 2C3214 (SAO 164756, DM -18 6037)RA: 215551 DEC: -175835 mV: 6.6 Sp : AOFilter: V Diaphragm: I Gain: C5+ Voltage: 1200LUNARINFORMATIONSurface Illumination: 54 percentElongation -from Sun: 95 degreesAltitude Above Horizon: 20 degreesLunar Limb Distance: 402184 k i 1 ome tersPredicted Shadow Velocity: 694 .7 meters/secPredicted Angular Rate: ,3563 arcsec/sec.EVENTINFORMATIONDate: November 13, 1983 UT o-f Event: 03:35:44USNO V/O Code: 28 HA o-f Event 540443Position Angle: 31.0 Cu sp Anole: 51NContact Angle: +28.4 Wa tts Angle: 51.8MODEL PARAMETERSNumber o-f Data Points:201Number o-f Grid Points: 256Number o-f Spectral Regions: 53Width o-f Spectral Regions: 50 Angs tromsLimb Darkening Coe-f -f i c i en t 0.5E-f-fective Stellar Temperature: 10800 KSOLUTIONSStellar Diameter (ams): Point Souro?Time: (relative to Bin 0): 2255.7 (0 .8)Pre-Event Signal: 2481.5 (18 .6)Background Sky Level 1484.8 (18 .3)Velocity (me ters/sec . > : 732.3 (20 .4)Lunar Limb Slope (degrees): -9.22 (1 .68)U.T. o-f Occultation: 03: 35:43.107 (0 .018)PHOTOMETRIC NOISEINFORMATION!Sum-o-f -Squares o-f Residuals: 6385000Sigma (Standard Error): 178 .68Normalized Standard Error: .17927Photometric (S+N)/N Ratio: 6 .5781(Change in In tensi ty)/Background: .67124Change in Magnitude: .5576

300^4096%512 1024 1536 2048 2560 3072 '3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-72. RAWPLOT o-f the occultation o-f 2C3214.CO2GLUN

301COUNTSS • •••••••AJJSN3J_NIl.l.l -L.CMCfim 5LU.CM.?a32HVHdON

302measurable angular diameter. The -fit of the modelintensity curve to the observations appears to be quitegood. This is reflected in the low -formal errors o-f thesolution parameters and is seen by visual inspection o-fthe FITPLOT even as far out as the fourth orderdiffraction minimum.As evidenced by the PDPLOT , Figure 5-75, theportions of the intensity curve most sensitive toparametric variation were well covered in the solutionprocess. The model intensity curve was fit to the datapresented in Table 5-37. The usual supplementalstatistical information is compiled in Table 5-38.The NOISEPLOT of the observation is presented asFigure 5-76. As noted, the RMS background noise throughthe 4096 milliseconds of the observation wasapproximately 8 percent. The power spectra of theoccultation event, the star-plus-sky signal, and thebest fit model curve are shown on the POWERPLOTFigure 5-77.As in the case of the occultation of ZC1221, a finedetermination of the time of geometrical occultation,made possible by the small (0.8 millisecond) error ofthe formal solution, was thwarted by a noisy UwVB radiosignal. The Coordinated Universal Time of geometricaloccultation was 03:35:43.929

3032215 2255 2295 2335 2375TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-75. PDPLOT o-f the occultation o-f ZC3214.0288-0002 -50.7-42-6-34.5-26.4-18.3 -10.2 -2.1 6.0 14.1 22.2NOISE LEVEL AS APERCENTAGE OF COMPUTED INTENSITYFigure 5-76. NOISEPLOT o-f the occultation o-f 2C3214.

304TABLE 5-37ZC3214: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 2215NUM OBS COMP RES ID NUM OBS COMP RES ID NUM OBS COMP RES ID2527 2484.1 42.91 2756 2485.3 270.72 2335 2484.4 -149.43 2454 2483.1 -29.14 2752 2484.3 267.75 2436 2485.7 -49.76 2643 2484.3 158.77 2472 2482.8 -10.88 2683 2484.4 198.69 2643 2486.2 156.810 2766 2484.4 281.611 2701 2482.1 218.912 2968 2483.9 484.113 2815 2487.2 327.814 2781 2485.9 295.115 2433 2481.5 -48.516 2164 2481.4 -317.417 2612 2486.7 125.318 2333 2489.2 -156.219 2443 2484.4 -41.420 2405 2478.9 -73.921 2327 2481.4 -154.422 3047 2489.0 558.023 2540 2491.0 49.024 2289 2483.9 -194.925 2380 2477.1 -97.126 2243 2480.2 -237.227 2384 2489.8 -105.828 2460 2493.7 -33.729 2200 2486.1 -286.130 2265 2475.9 -210.931 2705 2475.9 229.132 2448 2487.5 -39.533 2407 2498.0 -91.034 2318 2494.6 -176.635 2266 2479.3 -213.336 2445 2467.4 -22.437 2373 2472.7 -99.738 2185 2492.6 -307.639 2434 2509.4 -75.440 2436 2506.4 -70.441 2507 2483.2 23.842 2521 2457.2 63.843 2174 2450.5 -276.544 2322 2471.4 -149.445 2348 2507.6 -159.646 2588 2534.1 53.947 2705 2530.7 174.348 2437 2496.3 -59.349 2003 2450.2 -447.250 2239 2419.9 -180.951 2413 2425.2 -12.252 2315 2466.3 -151.353 2503 2523.9 -20.954 2563 2569.4 -6.455 2728 2579.7 148.356 3179 2547.7 631.357 2628 2485.6 142.458 2281 2418.5 -137.559 2265 2373.3 -108.360 2427 2368.5 58.561 2668 2407.3 260.762 2477 2477.7 -0.763 2722 2557.5 164.564 2482 2622.4 -140.465 2765 2653.5 111.566 2487 2641.8 -154.867 2646 2590.3 55.768 2491 2511.5 -20.569 2478 2423.6 54.470 2134 2345.4 -211.471 2050 2292.6 -242.672 2142 2274.9 -132.973 2276 2294.9 -18.974 2309 2349.0 -40.075 2195 2428.6 -233.676 2690 2522.4 167.677 2534 2618.5 -84.578 2767 2706.0 61.079 2591 2776.4 -185.480 2763 2824.0 -61.081 2960 2845.7 114.382 3027 2841.6 185.483 2848 2813.4 34.684 2713 2764.3 -51.385 2923 2698.6 224.486 2694 2620.7 73.387 2717 2534.9 182.188 2920 2445.1 474.989 2244 2354.5 -110.590 2052 2265.9 -213.991 2343 2181.3 161.792 2181 2102.0 79.093 1999 2028.9 -29.994 1789 1962.4 -173.495 1894 1902.6 -8.696 1647 1849.3 -202.397 1779 1802.3 -23.398 1549 1761.0 -212.099 1785 1725.0 60.0100 1634 1693.8 -59.8101 1261 1666.7 -405.7102 1443 1643.3 -200.3103 1611 1623.2 -12.2104 1568 1605.8 -37.8105 1470 1590.9 -120.9106 1331 1578.1 -247.1107 1240 1567.1 -327.1108 1627 1557.5 69.5109 1860 1549.3 310.7110 1575 1542.3 32.7111 1546 1536.1 9.9112 1474 1530.8 -56.8113 1645 1526.1 118.9114 1654 1522.1 131.9115 1677 1518.6 158.4116 1771 1515.4 255.6117 1607 1512.7 94.3118 1503 1510.3 -7.3119 1560 1508.1 51.9120 1416 1506.2 -90.2121 1363 1504.5 -141.5122 1455 1502.9 -47.9123 1468 1501.6 -33.6124 1089 1500.4 -411.4125 1195 1499.3 -304.3126 1612 1498.3 113.7127 1503 1497.4 5.6128 1552 1496.7 55.3129 1451 1496.0 -45.0130 1564 1495.3 68.7131 1513 1494.7 18.3132 1527 1494.1 32.9133 1614 1493.6 120.4134 1387 1493.1 -106.1135 1499 1492.6 6.4136 1465 1492.2 -27.2137 1723 1491.8 231.2138 2165 1491.5 673.5139 1667 1491.2 175.8140 1416 1490.9 -74.9141 1373 1490.7 -117.7142 1717 1490.4 226.6143 1716 1490.1 225.9144 1456 1489.9 -33.9145 1560 1489.6 70.4146 1392 1489.4 -97.4147 1503 1489.2 13.8148 1478 1489.1 -11.1149 1335 1488.9 -153.9150 1503 1488.8 14.2151 1552 1488.6 63.4152 1476 1488.5 -12.5153 1631 1488.3 142.7154 1595 1488.2 106.8155 1396 1488.1 -92.1156 1523 1488.0 35.0157 1349 1487.9 -138.9158 1434 1487.8 -53.8159 1440 1487.7 -47.7160 1315 1487.6 -172.6161 1152 1487.5 -335.5162 1459 1487.4 -28.4163 1487 1487.3 -0.3164 1361 1487.3 -126.3165 1379 1487.2 -108.2166 1586 1487.1 98.9167 1515 1487.0 28.0168 1306 1487.0 -181.0169 1411 1486.9 -75.9170 1620 1486.9 133.1171 1386 1486.8 -100.8172 1378 1486.8 -108.8173 1511 1486.7 24.3174 1384 1486.7 -102.7175 1335 1486.6 -151.6176 1439 1486.6 -47.6177 1795 1486.5 308.5178 1670 1486.5 183.5179 1463 1486.4 -23.4180 1523 1486.4 36.6181 1644 1486.4 157.6182 1563 1486.3 76.7183 1498 1486.3 11.7184 1351 1486.3 -135.3185 1523 1486.2 36.8186 1387 1486.2 -99.2187 1560 1486.2 73.8188 1287 1486.1 -199.1189 1303 1486.1 -183.1190 1379 1486.1 -107.1191 1495 1486.0 9.0192 1892 1486.0 406.0193 1718 1486.0 232.0194 1698 1486.0 212.0195 1527 1485.9 41.1196 1449 1485.9 -36.9197 1311 1485.9 -174.9198 1526 1485.9 40.1199 1623 1485.9 137.1200 1721 1485.8 235.2

305TABLE 5-38ZC3214: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/CO-VARIANCE MATRIXDIAM PREI POST TIME VELO5.694E"16 5.662E 08 -4.205E 08 -1.344E~09 4.047E~115.662E"08 3.371E02 7.832E00 -2.875E00 6.537E_02-4.205E"08 7.832E00 3.262E02 -2.672E00 5.986E 02-1.344E"09 -2.875E00 -2.672E00 5.657E 01 -1.283E~024.047E"11 6.537E 02 5.986E 02 -1.283E~02 4.051E 04CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.845265 -0.692455 -0.164543 0.173361PREI 0.845265 1.000000 -0.200047 -0.660013 0.666554POST -0.692455 -0.200047 1.000000 -0.592852 0.585544TIME -0.164543 -0.660013 -0.592852 1.000000 -0.999958VELO 0.173361 0.666554 0.585544 -0.999958 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 1.811E09 -1.802E09PREI 1.365E00 1.019E_03POST 9.990E 01 -3 .655E 01TIME 9.068E01 -9.686E01VELO 3.942E03 -3.974E03

1I'1'1306MODEL CURVETSTAR +•"SKY*Vww^OCCULTATIONFigure 5-77.'100' "200"FREQUENCY INl300" '400HERTZPOWERPLOT o-f the occultation o-f ZC3214,

307X31590The rather slow occultation disappearance o-f the K0star X31590 is apparent on the plot o-f the 4096milliseconds o-f raw observational data shown inFigure 5-73. The relative -faintness o-f the star(.wf^=8.7> and the high sky brightness, due to a72 percent illuminated moon, resulted in a -finalphotometric S+N/N of only 2.55. Fortunately, the seeingwas unusually good, and the photometer J diaphragm (asnoted in the occultation summary, Table 5-39) wassel ec ted.The integration plot o-f the event, Figure 5-79,shows no indication o-f any disappearances other thanthat o-f X31590 itself .The graphical depiction o-f the solution is shown inFigure 5-80. Three hundred and -fi-fty milliseconds o-fdata (given in Table 5-40) were included to be -fit bythe DC process. This rather lengthy data set wasnecessary due to the somewhat lengthened time-scale o-fthe event. Not unexpectedly, given the poor S+N/N ratioand the -faintness o-f the star, no detectable stellardisc was -found.The partial derivatives of the intensity curve,with respect to each of the solution parameters, areshown graphically in Figure 5-81. The numerical rangesof these derivatives are listed, along with the otherusual supplemental statistics, in Table 5-41.

308TABLE 5-39X31590: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X31590,

309512 1024 1538 2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWFigure 5-78. RAWPLOT o-f the occultation of X31590.zQLUN

illI310COUNTSomCOxco3UujZO_lCLOCOin

311TABLE 5-40X31590 : OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 2140NUM OBS COMP RESID NUM OBS COMP RESID NUM OBS COMP RESID2529 23 97.5 131.5 67 2719 2400.2 318.8 134 2199 2353.0 -154.01 2570 23 98.1 171.9 68 2303 2402.3 -99.3 135 2160 2351.1 -191.12 23 98 23 98.5 -0.5 69 2128 2404.0 -276.0 136 1941 2351.0 -410.03 2643 23 98.8 244.2 70 2267 2405.3 -138.3 137 2517 2352.6 164.44 2495 23 98 .8 96.2 71 2184 2405.8 -221.8 138 23 90 2355.9 34.15 2041 23 98.5 -357.5 72 1800 2405.6 -605.6 139 2010 2360.9 -350.96 2359 23 98.0 -39.0 73 1981 2404.6 -423.6 140 23 91 2367.3 23.77 2291 23 97.3 -106.3 74 2600 2402.8 197.2 141 2316 2374.9 -58.98 2681 23 96.6 284.4 75 2751 2400.5 350.5 142 2354 2383.5 -29.59 2517 23 96.0 121.0 76 2403 2397.7 5.3 143 2218 23 92.9 -174.910 2463 23 95.5 67.5 77 3080 2394.7 685.3 144 2110 2402.7 -292.711 2211 23 95.3 -184.3 78 2831 2391.7 43 9.3 145 23 95 2412.7 -17.712 23 91 23 95.5 -4.5 79 3002 2389.1 612.9 146 2775 2422.4 352.613 2156 23 95.9 -239.9 80 2317 2387.0 -70.0 147 2436 2431.7 4.314 2408 23 96.5 11.5 81 2132 2385.7 -253.7 148 1913 2440.2 -527.215 2175 23 97.3 -222.3 82 2303 2385.4 -82.4 149 2183 2447.8 -264.816 2271 23 98.1 -127.1 83 2619 2386.0 233.0 150 2151 2454.1 -303.117 2321 23 98.8 -77.8 84 2573 2387.6 185.4 151 2076 2458.9 -382.918 2591 23 99.3 191.7 85 1699 2390.1 -691.1 152 2255 2462.3 -207.319 2744 23 99.5 344.5 86 2681 2393.4 287.6 153 3051 2463.9 587.120 2388 2399.3 -11.3 87 2400 2397.3 2.7 154 2719 2463.9 255.121 2553 23 98 .8 154.2 88 2495 2401.4 93.6 155 2637 2462.2 174.822 2632 23 98.1 233.9 89 2243 2405.5 -162.5 156 2157 2458.9 -301.923 2400 23 97.2 2.8 90 2151 2409.3 -258.3 157 2262 2453.9 -191.924 2281 23 96.3 -115.3 91 2436 2412.5 23.5 158 2539 2447.6 91.425 2455 23 95.6 59.4 92 2200 2414.8 -214.8 159 2444 2439.9 4.126 2843 23 95.1 447.9 93 2725 2416.0 309.0 160 2248 2431.1 -183.127 2717 23 94.9 322.1 94 2883 2416.0 467.0 161 2872 2421.5 450.528 2256 23 95.0 -139.0 95 2831 2414.7 416.3 162 2146 2411.1 -265.129 2019 23 95.5 -376.5 96 2586 2412.3 173.7 163 2177 2400.3 -223.330 2655 23 96.3 258.7 97 2707 2408 .8 2 98.2 164 2706 2389.4 316.631 2160 23 97.3 -237.3 98 2802 2404.3 397.7 165 2565 2378.4 186.632 2331 23 98.2 -67.2 99 2515 2399.2 115.8 166 1954 2367.8 -413.833 2570 2399.1 170.9 100 2496 23 93.8 102.2 167 2156 2357.6 -201.634 2236 2399.7 -163.7 101 1960 2388.4 -428.4 168 2303 2348.1 -45.135 2375 2400.0 -25.0 102 2507 2383.3 123.7 169 2477 2339.6 137.436 2131 23 99.9 -268.9 103 2423 2378.9 44.1 170 2105 2332.1 -227.137 2777 23 99.4 377.6 104 2112 2375.4 -263.4 171 247 9 2325.7 153.338 2476 23 98.7 77.3 105 2265 2373.1 -108.1 172 2070 2320.7 -250.739 2639 23 97.7 241.3 106 2410 2372.2 37.8 173 2019 2317.1 -298.140 2851 23 96.6 454.4 107 1872 2372.8 -500.8 174 2405 2314.9 90.141 2346 23 95.7 -49.7 108 2203 2374.8 -171.8 175 2304 2314.2 -10.242 2435 23 94.9 40.1 109 2239 2378.2 -139.2 176 23 94 2315.0 79.043 2380 23 94.5 -14.5 110 2423 2382.9 40.1 177 2150 2317.3 -167.344 2372 23 94.4 -22.4 111 2881 2388.6 492.4 178 2231 2321.0 -90.045 2443 23 94.8 48.2 112 2486 23 95.1 90.9 179 2178 2326.1 -148.146 2644 23 95.6 248.4 113 2098 2402.0 -304.0 180 1995 2332.5 -337.547 2169 23 96.6 -227.6 114 2655 2408.9 246.1 181 1797 2340.0 -543.048 2280 23 97.9 -117.9 115 2512 2415.6 96.4 182 2127 2348.6 -221.649 2516 2399.1 116.9 116 2231 2421.7 -190.7 183 26 91 2358.1 332.950 2599 2400.1 198.9 117 2184 2426.8 -242.8 184 3139 2368.4 770.651 2431 2400.9 30.1 118 2219 2430.8 -211.8 185 2450 2379.4 70.652 3137 2401.3 735.7 119 2531 2433.3 97.7 186 2257 23 90.9 -133.953 2900 2401.1 498.9 120 2084 2434.2 -350.2 187 2307 2402.7 -95.754 2933 2400.5 532.5 121 2328 2433.5 -105.5 188 2466 2414.7 51.355 223 5 23 99.4 -164.4 122 2771 2431.1 339.9 189 23 96 2426.8 -30.856 2317 23 98.1 -81.1 123 2802 2427.2 374.8 190 2313 2438.8 -125.857 2509 23 96.5 112.5 124 2572 2421 .8 150.2 191 2787 2450.6 336.458 2195 23 95.0 -200.0 125 2600 2415.3 184.7 192 2578 2462.1 115.959 2495 23 93.6 101.4 126 2148 2407.8 -259.8 193 2242 2473.0 -231.060 2471 23 92.6 78.4 127 2029 2399.7 -370.7 194 2223 2483.5 -260.561 2743 23 92.1 350.9 128 2356 23 91.3 -35.3 195 1887 2493.3 -606.362 2654 23 92.2 261.8 129 2335 2382.9 -47.9 196 2579 2502.3 76.763 2089 23 92.9 -303.9 130 2679 2374.9 304.1 197 2746 2510.5 235.564 2250 23 94.2 -144.2 131 2407 2367.7 39.3 198 2482 2517.8 -35.865 2380 23 96.0 -16.0 132 2157 2361.4 -204.4 199 2589 2524.2 64.866 2111 23 98.0 -287.0 133 2599 2356.5 242.5 200 2670 2529.6 140.4

TABLE 5-40.CONTINUED.312NUM OBS COMP RES ID NUM OBS COMP RES ID NUM OBS COMP RES ID201 2623 2534.0 89.0 251 2075 2147.9 -72.9 301 2067 2018.7 48.3202 2297 2537.4 -240.4 252 2383 2141.7 241.3 302 2655 2018.1 636.9203 2730 2539.8 190.2 253 2751 2135.7 615.3 303 1765 2017.5 -252.5204 2251 2541.1 -290.1 254 2006 2129.9 -123.9 304 2101 2016.9 84.1205 2471 2541.4 -70.4 255 1732 2124.3 -392.3 305 1863 2016.3 -153.3206 2143 2540.7 -397.7 256 1980 2119.0 -139.0 306 1876 2015.8 -139.8207 2599 2539.1 59.9 257 1843 2113.9 -270.9 307 1729 2015.2 -286.2208 2867 2536.5 330.5 258 2098 2109.0 -11.0 308 1695 2014.7 -319.7209 3021 2532.9 488.1 259 2427 2104.3 322.7 309 2064 2014.3 49.7210 2451 2528.6 -77.6 260 2499 2099.8 399.2 310 2029 2013.8 15.2211 2149 2523.3 -374.3 261 222 9 2095.5 133.5 311 2153 2013.4 139.6212 2403 2517.4 -114.4 262 2559 2091.4 467.6 312 1803 2012.9 -209.9213 2685 2510.7 174.3 263 2383 2087.4 295.6 313 1993 2012.5 -19.5214 2445 2503.3 -58.3 264 1911 2083.7 -172.7 314 1937 2012.1 -75.1215 23 99 2495.3 -96.3 265 1915 2080.1 -165.1 315 2184 2011.8 172.2216 2611 2486.8 124.2 266 2153 2076.6 76.4 316 2016 2011.4 4.6217 2530 2477.7 52.3 267 1953 2073.4 -120.4 317 1934 2011.0 -77.0218 2634 2468.2 165.8 268 2407 2070.2 336.8 318 1809 2010.7 -201.7219 2643 2458.3 184.7 269 1715 2067.2 -352.2 319 22 93 2010.4 282.6220 2576 2448.0 128.0 270 1666 2064.4 -398.4 320 1751 2010.1 -259.1221 2580 2437.5 142.5 271 1631 2061.6 -430.6 321 1721 2009.8 -288.8222 2207 2426.7 -219.7 272 1727 2059.0 -332.0 322 1933 2009.5 -76.5223 1955 2415.7 -460.7 273 1966 2056.6 -90.6 323 2137 2009.2 127.8224 2098 2404.6 -306.6 274 2060 2054.2 5.8 324 2083 2008.9 74.1225 2663 23 93.4 269.6 275 1945 2051.9 -106.9 325 2112 2008.7 103.3226 2184 2382.1 -198.1 276 2018 2049.8 -31.8 326 1900 2008.4 -108.4227 2099 2370.8 -271.8 277 1861 2047.7 -186.7 327 2231 2008.2 222.8228 1942 2359.4 -417.4 278 1835 2045.7 -210.7 328 2351 2008.0 343.0229 2013 2348.2 -335.2 279 1626 2043.9 -417.9 329 2335 2007.7 327.3230 2260 2337.0 -77.0 280 1535 2042.1 -507.1 330 1961 2007.5 -46.5231 2559 2325.9 233.1 281 1884 2040.4 -156.4 331 1819 2007.3 -188.3232 23 99 2314.9 84.1 282 2159 2038.8 120.2 332 1904 2007.1 -103.1233 2381 2304.0 77.0 283 2127 2037.2 89.8 333 1788 2006.9 -218.9234 2544 2293.4 250.6 284 2197 2035.7 161.3 334 1523 2006.7 -483.7235 2470 2282.9 187.1 285 1936 2034.3 -98.3 335 2201 2006.6 194.4236 2486 2272.6 213.4 286 1772 2033.0 -261.0 336 2362 2006.4 355.6237 2604 2262.5 341.5 287 2215 2031.7 183.3 337 1977 2006.2 -29.2238 2128 2252.7 -124.7 288 2114 2030.5 83.5 338 1779 2006.1 -227.123 9 2302 2243.1 58.9 289 1978 2029.3 -51.3 339 1881 2005.9 -124.9240 2416 2233.7 182.3 290 2084 2028.2 55.8 340 1621 2005.8 -384.8241 2205 2224.6 -19.6 291 227 9 2027.1 251.9 341 1988 2005.6 -17.6242 2173 2215.8 -42.8 292 2284 2026.1 257.9 342 1992 2005.5 -13.5243 2562 2207.2 354.8 293 2224 2025.1 198.9 343 1962 2005.3 -43.3244 2000 2198.9 -198.9 294 2378 2024.2 353.8 344 1904 2005.2 -101.2245 1897 21 90 .8 -293.8 295 2231 2023.3 207.7 345 1886 2005.1 -119.1246 2312 2183.0 129.0 296 2069 2022.5 46.5 346 2005 2005.0247 2207 2175.5 31.5 297 1807 2021.6 -214.6 347 2032 2004.9 27.1248 2115 2168.2 -53.2 298 1871 2020.9 -149.9 348 1983 2004.7 -21.7249 1888 2161.2 -273.2 299 2747 2020.1 726.9 349 2151 2004.6 146.4250 2099 2154.5 -55.5 300 2123 2019.4 103.6 350 2580 2004.5 575.5

3132140 2210 '2280 2350 '2420"TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-81. PDPLOT o-f the occultation o-f X31590.0282-0000_ -6L5 -52.4-43.2-34.1 -25-0-15.8 -6.7 2.5 1L6 '20.7NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-82. NOISEPLOT o-f the occultation of X31590

TABLE 5-41X31590: SUPPLEMENTAL STATISTICAL INFORMATION314VARIANCE/ CO-VARIANCE MATRIXDIAM PREI POST TIME VELO3.067E"14 3.795E~07 -9.342E 07 -2.879E~08 1.217E 103.795E"07 2.716E02 2.809E01 -2.066E01 4.788E029.342E"07 2.809E01 8.649E02 -5.633E01 1.270E012.879E"08 -2.066E01 -5.633E01 2.765E01 -6.389E021.217E"10 4.788E"02 1.270E01 -6.389E~02 1.983E04CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.463093 -0.915775 0.629985 -0.621074PREI 0.463093 1.000000 -0.071425 -0.330036 0.338810POST -0.915775 -0.071425 1.000000 -0.874404 0.868639TIME 0.629985 -0.330036 -0.874404 1.000000 -0.999931VELO -0.621074 0.338810 0.868639 -0.999931 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 2.073E08 -2.086E08PREI 1.367E00 1.276E"02POST 9.872E 01 -3.666E~01TIME 1.133E01 -1.208E01VELO 4.875E03 -5.024E03

1r1.1IMODELCURVE315-i1rSTAR +SKYmMM~>r-i11OCCULTATIONT1100 200 300FREQUENCY IN HERTZ1 1. IFigure 5-83. POWERPLOT o-f the occultation o-f X31598

316The distribution function of the residualintensities is shown in the NOISEPLOT, Figure 5-32.Despite the weakness of the stellar signal against thebackground sky, the noise characteristics o-f the skyitself were well behaved.The POWERPLOT showing the usual Fourier powerspectra is presented as Figure 5-83. As typical withlonger duration events, the power components importantto the occultation curve are shifted toward lowerf requenc ies.The Coordinated Universal Time of geometricaloccultation was determined to be 001:02:40.703, with arelatively large one sigma uncertainty of 0.014 seconds.ZC3458 (336 B. Aquarii)The second occultation observed on the night ofNovember 15, 1983 was that of the moderately bright K0star ZC3458 (336 B. Aquarii). Even with the moon73 percent illuminated, this event was quite promising,given the good seeing conditions which continued toprevail since the early part of the evening.Disaster (literally, "bad star", appropriatelyenough), however, usually strikes at the best of times.Blow attests that observers at the University of Texashave "... found at least 57 ways to foul up anoccultation [observation] . . ." (1983, p. 9-14). Afifty-eighth may now be contributed by the University ofFl or i da.

317The loss of a high speed photoelectric record o-fthe ZC3458 event was due to a mechanical failure,resulting in two sel -f-cancel 1 i ng errors as -far as theLODAS video strip chart display was concerned. The "0"key on the LODAS command keyboard had becomemechanically sticky and electrically "bouncy". As aresult, the data acquisition rate, which should havebeen entered as 001 samples per millisecond was enteredas 010 samples per millisecond. Similarly, the videostrip chart recorder display rate which was typed in as010 display points per two acquisition times was takenas 001. Hence, the video display was updating at a rateindicative o-f millisecond data acquisition, while datawere actually being sampled and stored at a slow rate o-f100 samples per second.The observer -freely admits his error -for notchecking the printed observing log at the time o-fsetting up the instrumental system. The RAWPLOT o-f the40.96 seconds o-f data obtained >,is shown in Figure 5-84. The integration plot o-f theevent, Figure 5-85, has no indication of any very widelyseparated components.All, however, was not lost as the time ofoccultation was determined to an accuracy as well ascould be obtained at this sampling rate. The

3186.56 10.86 15.16 19.46 23.76 '28.06 32.36 36.66TIME IN SECONDS FROM BEGINNING OF DATA VINDOVFigure 5-84. RAWPLOT o-f the occultation o-f ZC3458.zDLUNoz'6.56 10.86 15.16 19.46 23.76 28.06 32.36 36.66TIME IN SECONDS FROM BEGINNING OF DATA VINDOVFigure 5-85. INTPLOT o-f the occultation o-f ZC3458.

31?Coordinated Universal Time o-f "geometrical " occultationwas seen at 03:37:57.996

: i::320TABLE 5-42X01217: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X01217, < SAO 129029, DM -00 0139)RA: 005444 DEC: -000404 mV : 7.7 Sp : KOFilter: V Diaphragm: I Gain: B10+ Voltage: 1200LUNARINFORMATIONSurface Illumination: 87 percentElongation -from Sun: 138 degreesAltitude Above Horizon: 42 degreesLunar Limb Distance: 391396 kilometersPredicted Shadow Velocity: 516.3 meters/sec.Predicted Angular Rate: 0.2721 arcsec/sec.EVENTINFORMATIONDate: November 17, 1983 UT o-f Event 00 :02: 09USNO V/0 Code: 74 HA o-f Event -401416Posi t i on Anol e 99.0 Cusp Angle: 52SContact Angle: -44.6 Watts Angl e 121 .4MODEL PARAMETERSNumber o-f Da ta Points:351Number o-f Gr id Poi nts: 256Number o-f Sp ectral Regions: 53Width o-f Spectral Regions: 50 An ostromsLimb Darken0.5no Coe-f -f i c i en tE-f-fective St ellar Temperature: 5100 KSOLUTIONSStellar Diameter (ams): 2.88 (4.98)Time: (relative to Bin 0): 2091.6 (3.5)Pre-Event Signal: 2927.6 (13.5)Background Sky Level: 2495.6 (20.7)Velocity (meters/sec.) 284.8 (16.0)Lunar Limb Slope (degrees): +28.3 (1.8)U.T. o-f Occultation: 00:02:07.790 (0.004)PHOTOMETRIC NOISEINFORMATIONSum-o-f -Squares o-f Residuals: 14186840Sigma (Standard Error): 201.330Normalized Standard Error: 0.46613Photometric (S+N)/N Ratio: 3.1453(Change in Intensi ty)/Background: 0.1730Change in Magnitude: 0.1733

1•321_4096_3686512 1024 1536 2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-86. RAWPLOT o-f the occultation o-f X01217.L.U r-0.9 _hU) 0.8z^0.7g—Q 0.6LUi—0.5

322COUNTScoinconCDCOCMon-»H *H CM CM\D CD CO isS GO fs mCO CM CM CMCMCMCMIf)CMCMCMCDSCMCMCOCD•cq in ^co cmAjjsNaiNiaaznvwaoN

9TABLE 5-43X01217: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 1850323NUM OBS COMP RES ID NUM OBS COMP RES ID NUM OBS COMP RES ID1234562823287129643049312832533048309678 30639 286110 268011 285212 274613 321114 296615 353116 299417 291118 315919 296520 269421 296922 279123 287924 272025 296626 302127 256828 248429 276530 289531 278232 288133 281534 308735 324736 294837 309538 270239 312440 331741 28 9042 259843 274344 28 9445 258346 274847 305548 317149 296750 295951 282452 292553 285554 260455 335056 311257 2 90358 317159 280060 301361 274162 299163 302364 262965 282366 28632928.82928.92928.92928.92928.92928.82928.72928.72928.72928.72928.82928.92928.92928.92928.92928.82928.72928.62928.62928.72928.82929.02929.12929.22929.12929.02928.72928.52928.32928.32928.42928.72929.02929.32929.62929.62929.52929.22928.82928.32928.02927.92928.12928.42928.92929.42929.82930.12930.02929.72929.22928.62928.12927.72927.62927.92928.32929.02929.62930.22930.42930.42930.02929.42928.72928.02927.5-105.8-57.935.1120.1199.1324.2119.3167.3134.3-67.7-248.8-76.9-182.9282.137.1602.265.3-17.6230.436.3-234.840.0-138.1-50.2-209.137.092.3-360.5-444.3-163.3-33.4-146.7-48.0-114.3157.4317.418.5165.8-226.8195.7389.0-37.9-330.1-185.4-34.9-346.4-181.8124.9241.037.329.8-104.6-3.1-72.7-323.6422.1183.7-26.0241.4-130.282.6-189.461.093.6-299.7-105.0-64.567 336368 295169 278070 329671 311772 2 94073 294874 286375 258076 276777 256578 270379 288780 283781 288782 286983 286284 306685 310486 294387 285588 28 9389 288790 284991 317592 309193 284094 256995 2 90396 281797 322098 335999 3039100 2879101 2809102 3089103 2780104 3159105 3069106 2696107 2906108 3071109 2901110 2986111 3204112 3343113 3073114 2624115 2671116 2953117 2703118 3051119 2867120 2620121 2999122 2844123 2957124 3227125 2969126 2960127 3239128 3166129 3209130 2886131 2722132 2524133 27992927.42927.52928.12928.92929.82930.72931.22931.42931.12930.32929.22 928.02926.82926.02925.62925.92926.82928.22930.02931.92933.52934.72935.12934.72933.42931.42 928.82926.02923.42921.42 920.22920.12921.22923.42926.62930.52934.62938.42941.62943.72944.32 943.52941.02937.22932.32926.82921.12915.92911.72 908 .2907.82908.62911.42916.02922.12929.12936.72944.22951.02956.52960.32 962.02 961.52958.72953.72946.82 938.5435.623.5-148.1367.1187.29.316.8-68.4-351.1-163.3-364.2-225.0-39.8-89.0-38.6-56.9-64.8137.8174.011.1-78.5-41.7-48.1-85.7241.6159.6-88.8-357.0-20.4-104.4299.8438.9117.8-44.4-117.6158.5-154.6220.6127.4-247.7-38.3127.5-40.048.8271.7416.2151.9-291.9-240.744.1-204.8142.4-44.4-296.076.9-85.120.3282.818.03.5278.7204.0247.5-72.7-231.7-422.8-139.5134 3125135 2996136 3347137 3071138 2559139 2777140 2607141 2900142 2701143 2755144 2697145 3163146 2792147 2660148 2 946149 2723150 3175151 2855152 2761153 2759154 3120155 2911156 3043157 3048158 2883159 2911160 2815161 2871162 2885163 2788164 2819165 2795166 2815167 3015168 2900169 2950170 3193171 2704172 2721173 3007174 2799175 2971176 3296177 3083178 3264179 2735180 2895181 2806182 2475183 2753184 3327185 3245186 3039187 2663188 3071189 3084190 3212191 3015192 3367193 2983194 3172195 3135196 3012197 3108198 2927199 2974200 28 952929.22919.62910.32901.82894.72889.52886.52886.02888.02892.52899.22908.02918.22929.52941.42953.12964.22974.12982.52 988.82992.82994.32993.22989.62983.62975.42965.22953.62940.82927.42913.82900.42887.72876.12865.92857.62851.22847.02845.22845.72848.52853.62860.92870.12881.028 93.52907.22921.82937.02952.62 968.32983.72998.63012.83026.13038.23049.13058.53066.33072.63077.23080.13081.43080.93078.93075.33070.2195.876.4436.7169.2-335.7-112.5-279.514.0-187.0-137.5-202.2255.0-126.2-269.54.6-230.1210.8-119.1-221.5-229.8127.2-83.349.858.4-100.6-64.4-150.2-82.6-55.8-139.4-94.8-105.4-72.7138.934.192.4341.8-143.0-124.2161.3-49.5117.4435.1212.9383.0-158.5-12.2-115.8-462.0-199.6358.7261.340.4-349.844.945.8162.9-43.5300.7-89.694.854.9-69.427.1-151.9-101.3-175.2

324TABLE 5-43.CONTINUED.NUM OBS COMP RES ID201 2971 3063.6 -92.6202 3039 3055.8 -16.8203 2807 3046.8 -239.8204 3007 3036.7 -29.7205 3263 3025.6 237.4206 2987 3013.6 -26.6207 3068 3000.8 67.2208 3171 2987.4 183.6209 2952 2973.5 -21.5210 3117 2959.1 157.9211 3319 2944.4 374.6212 3283 2929.4 353.6213 3155 2914.3 240.7214 2712 2899.1 -187.1215 2544 2883.8 -339.8216 2837 2868.7 -31.7217 2743 2853.7 -110.7218 2701 2838.9 -137.9219 3007 2824.3 182.7220 3188 2810.0 378.0221 3088 2796.0 292.0222 2960 2782.3 177.7223 2560 2769.1 -209.1224 2892 2756.2 135.8225 2615 2743.8 -128.8226 2724 2731.7 -7.7227 2851 2720.1 130.9228 2775 2709.0 66.0229 2535 2698.2 -163.2230 2630 2688.0 -58.0231 2559 2678.1 -119.1232 2856 2668.7 187.3233 2272 2659.7 -387.7234 2255 2651.2 -396.2235 2577 2643.0 -66.0236 2859 2635.2 223.8237 2615 2627.9 -12.9238 2489 2620.9 -131.9239 2983 2614.2 368.8240 2512 2607.9 -95.9241 2476 2601.9 -125.9242 2338 2596.3 -258.3243 2119 2590.9 -471.9244 2525 2585.9 -60.9245 2739 2581.1 157.9246 2695 2576.6 118.4247 2576 2572.3 3.7248 2433 2568.3 -135.3249 2749 2564.5 184.5250 2527 2560.9 -33.9NUM OBS COMP RES ID251 2568 2557.5 10.5252 2487 2554.3 -67.3253 2466 2551.3 -85.3254 2439 2548.5 -109.5255 2375 2545.8 -170.8256 2351 2543.3 -192.3257 2363 2540.9 -177.9258 2468 2538.7 -70.7259 2524 2536.6 -12.6260 2227 2534.6 -307.6261 2559 2532.7 26.3262 2487 2530.9 -43.9263 2451 2529.3 -78.3264 2340 2527.7 -187.7265 2639 2526.2 112.8266 2954 2524.8 429.2267 2655 2523.5 131.5268 2537 2522.2 14.8269 2663 2521.0 142.0270 2323 2519.9 -196.9271 2328 2518.9 -190.9272 2719 2517.9 201.1273 2762 2516.9 245.1274 2735 2516.0 219.0275 2423 2515.2 -92.2276 2318 2514.4 -196.4277 2598 2513.6 84.4278 2872 2512.9 359.1279 2340 2512.2 -172.2280 1932 2511.6 -579.6281 2223 2511.0 -288.0282 2309 2510.4 -201.4283 2207 2509.8 -302.8284 2481 2509.3 -28.3285 2342 2508.8 -166.8286 2564 2508.3 55.7287 2492 2507.8 -15.8288 2399 2507.4 -108.4289 2652 2507.0 145.0290 2440 2506.6 -66.6291 2544 2506.2 37.8292 2655 2505.9 149.1293 2753 2505.5 247.5294 2408 2505.2 -97.2295 2631 2504.9 126.1296 2383 2504.6 -121.6297 2783 2504.3 278.7298 2535 2504.0 31.0299 2355 2503.8 -148.8300 2591 2503.5 87.5NUM OBS COMP RESID301 2364 2503.3 -139.3302 2925 2503.0 422.0303 2639 2502.8 136.2304 2230 2502.6 -272.6305 2227 2502.4 -275.4306 2367 2502.2 -135.2307 2569 2502.0 67.0308 2472 2501.9 -29.9309 2579 2501.7 77.3310 2251 2501.5 -250.5311 2504 2501.4 2.6312 2944 2501.2 442.8313 3133 2501.1 631.9314 2502 2500.9 1.1315 2351 2500.8 -149.8316 2551 2500.7 50.3317 2836 2500.6 335.4318 3010 2500.5 509.5319 2355 2500.3 -145.3320 2600 2500.2 99.8321 2511 2500.1 10.9322 2618 2500.0 118.0323 2459 2499.9 -40.9324 2621 2499.8 121.2325 2527 2499.7 27.3326 2288 2499.6 -211.6327 2208 2499.5 -291.5328 2319 2499.4 -180.4329 2631 2499.4 131.6330 2426 2499.3 -73.3331 2650 2499.2 150.8332 2640 2499.1 140.9333 2507 2499.0 8.0334 2581 2499.0 82.0335 2525 2498.9 26.1336 2705 2498.8 206.2337 2828 2498.7 329.3338 2367 2498.7 -131.7339 2519 2498.6 20.4340 2743 2498.6 244.4341 2351 2498.5 -147.5342 2653 2498.5 154.5343 2830 2498.4 331.6344 2239 2498.4 -259.4345 2159 2498.3 -339.3346 2197 2498.3 -301.3347 2431 2498.2 -67.2348 2411 2498.2 -87.2349 2644 2498.1 145.9350 2684 2498.1 185.9

325TABLE 5-44X01217: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO- VARIANCE MATRIXDIAM PREI POST TIME VELO9.193E~16 5.253E~08 -8.800E~08 -6.868E~09 3.992E~115.253E"08 1.835E02 1.329E01 -1.093E01 4.225E028.800E 08 1.329E01 4.297E02 -2.321E01 8.805E~026.868E09 -1.093E01 -2.321E01 1.239E01 -4.798E~023.992E"11 4.225E~02 8.805E~02 -4.798E 02 2.552E 04CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.609252 -0.854026 0.443445 -0.435567PREI 0.609252 1.000000 -0.113136 -0.372319 0.378780POST -0.854026 -0.113136 1.000000 -0.826759 0.821489TIME 0.443445 -0.372319 -0.826759 1.000000 -0.999956VELO -0.435567 0.378780 0.821489 -0.999956 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 1.063E09 -1.063E09PREI 1.356E00 5.680E"03POST 9.943E"01 -3.561E"01TIME 1.522E01 -1.567E01VELO 3.706E03 -3.855E03

326only 3.15. The solution yielded an angular diameter o-fo-f 2.38 milliseconds o-f arc. However, the one sigmauncertainty in this value o-f 4.98 milliseconds o-f arc isquite high, and hence, the diameter must be viewed withcaution. This large -formal error was partially due tothe low S+N/N ratio and partially to the small dynamicrange o-f the change in signal level in comparison to thebackground level

1 I| II I I1I I I32?DIAM1850 1920 1990 2060 2130TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFioure 5-89. PDPLOT o-f the occultation o-f X01217.0241_0217COLU 0193ozLU 0169(X

11111328MODELCURVET 1STAR +1 r-SKYOCCULTATION'100' l200" '300' '400FREQUENCY IN HERTZFigure 5-91. POWERPLOT o-f the occultation of X81217.

.32?XQ1246This relatively early (spectral class FO) star wasocculted 78 minutes after X01217. In the interveningtime, the seeing conditions improved considerably, andthe "J" diaphragm was selected -for this observation (asnoted in the occultation summary, Table 5-45). Neitherthe trace of the raw intensity data (Figure 5-92) northe integration plot (Figure 5-93) show any signs o-fstel 1 ar dupl i c i tyThree hundred milliseconds o-f data were used in theDC fitting process, and the best solution curve is shownin Figure 5-95. As it turned out, this was more datathan was needed to be considered -for a proper solution.To enable a better visualization o-f the -fit, a detailedFITPLOT is presented as Figure 5-95. In this -figure,covering only 100 milliseconds, 5-point smoothing wasapplied to the raw data be-fore being plotted along withthe fit to unsmoothed data.The star was, not unexpectedly, indistinguishablefrom a point source. The 300 milliseconds of datasubjected to DC fitting are listed (with the computedintensities and the residuals) on Table 5-46.Table 5-47 contains the var i ance/covar i ance andcorrelation matrices for the solution parameters, aswell as the ranges of the numerical values of thepartial derivatives of the intensity curve (which areshown in Figure 5-92).

.330TABLE 5-45X01246: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X01246, (SAO 109548, DM -00 0145)RA: 005610 DEC: +002154 mV: 8.2 Sp :FOFilter: V Diaphragm: J Gain: B10+ Voltage: 1200LUNARINFORMATIONSur-face Illumination: 88 percentElongation -from Sun: 139 degreesAltitude Above Horizon: 55 degreesLunar Limb Distance: 390238 k i 1 ometersPredicted Shadow Velocity: 648 ,2 meters/secPredicted Angular Rate: .3426 arcsec/sec.EVENTINFORMATIONDate: November 17, 1983 UT o-f Event: 01:20:02USNO V/0 Code: 53 HA of Event: -210352Position Angle: 66.1 Cusp Angle:Contact Angle: -15.2 Watts Angle: 88.5MODEL PARAMETERSNumber of Data Points: 301Number of Grid Points: 256Number of Spectral Regions: 53Width of Spectral Regions: 50 AnqstromsLimb Darkening Coefficient: 0.5Effective Stellar Temperature: 7300 KSOLUTIONSStellar Diameter (ams) : Point SourceTime: (relative to Bin 0): 1920.4 (3.3)Pre-Event Signal: 2716.5

331"1512 1024 1536 2048 '2560 '3072 '3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-92. RAUPLOT o-f the occultation o-f X01246.1536 '2048 '2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-93. INTPLOT o-f the occultation o-f X01246.

332DISTANCE TO THE GEOMETRICAL SHADOW IN METERSL0 -110 -90 -70 -50 -30 -10 10 30 50 70 agflta1750 1810 '1870 1930 1980TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWFigure 5-94. FITPLOT of the occul tat i on of X01246,DISTANCE TO THE GEOMETRICAL SHADOW IN METERSL0 -60 -50 -40 -30 -20 -10 10 20 ,28871825 1855 '1885 1915 1945TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWFigure 5-95. FITPLOT of the occultation of X01246 showinothe raw fit to a smoothed data set.

X01246: OBSERVATIONS,TABLE 5-46COMPUTED VALUES, AND RESIDUALS FROM BIN 1750NUM OBS COMP RESID NUM OBS COMP RESID NUM OBS COMP RESID1234562421290026632732292129443161297278 31459 280910 277111 270412 280713 283514 291915 265916 255117 285118 266419 281520 260821 258722 242323 271124 244625 281926 284427 255528 264829 285030 257531 269732 266333 267134 310335 297536 237137 276638 272239 230640 247141 227442 203043 251144 273545 271146 268747 287248 315949 290150 286751 275252 268553 279554 2 94355 280056 271957 280158 275259 270460 292361 286062 273863 283864 252365 273966 24312717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.32717.22717.32717.32717.22717.32717.32717.22717.32717.32717.22717.32717.32717.22717.32717.32717.22717.32717.32717.22717.32717.32717.22717.22717.32717.32717.22717.22717.22717.22717.32717.22717.12717.22717.32717.22717.12717.32717.32717.12717.22717.42717.22717.02717.2-296.3182.7-54.314.7203.7226.7443.7254.7427.791.753.7-13.389.7117.7201.7-58.3-166.3133.7-53.397.7-109.3-130.3-294.3-6.2-271.3101.7126.8-162.3-69.3132.8-142.3-20.3-54.2-46.3385.7257.8-346.348.74.8-411.3-246.3-443 .2-687.3-206.317.8-6.2-30.3154.7441.8183.8149.834.8-32.377.8225.982.81.783.834.9-13.3205.7142.920.8120.6-194.222.0-286.267 247468 285569 258470 228871 278272 260373 266374 293175 284776 280777 275578 274579 300780 255281 275282 270383 273284 233585 255986 259187 252888 272789 262190 2 93291 259692 261093 258194 303995 253996 265497 262798 267799 2827100 3023101 2966102 2841103 2575104 2367105 2652106 2627107 2768108 2567109 2679110 2824111 2600112 2752113 2798114 2961115 3096116 3015117 2656118 2587119 2620120 2465121 2619122 2551123 2540124 2563125 2582126 2646127 2374128 2507129 2865130 2888131 2465132 2964133 27402717.52717.22717.02717.22717.62717.32716.92717.12717.62717.52716.82716.92717.72717.92717.12716.32717.02718.22718.32716.92715.92716.82718.52718.92717.22715.52716.12718.32719.52718.32715.82714.92716.92719.82720.52717.92714.22713.22716.32721.32723.92721.42715.12709.52709.12715.02723.92730.12729.32721.12709.72701.22700.62709.12723.02736.22742.72739.12726.42709.32693.92685.92688.52701.02720.02740.02755.6-243.5137.8-133.0-429.264.4-114.3-53.9213.9129.489.538.228.1289.3-165.934.9-13.315.0-383.2-159.3-125.9-187.910.2-97.5213.1-121.2-105.5-135.1320.7-180.5-64.3-88.8-37.9110.1303.2245.5123.1-139.2-346.2-64.3-94.344.1-154.4-36.1114.5-109.137.074.1230.9366.7293.9-53.7-114.2-80.6-244.1-104.0-185.2-202.7-176.1-144.4-63.3-319.9-178.9176.5187.0-255.0224.0-15.6134 2735135 2703136 3280137 2675138 3028139 2680140 2652141 2191142 2607143 2851144 2680145 3023146 3191147 2959148 3039149 2417150 2777151 2563152 2524153 2786154 2747155 3016156 293 9157 3131158 2776159 2473160 2591161 2887162 2479163 2383164 2666165 2639166 2864167 2769168 2559169 2011170 2461171 2603172 2387173 2656174 2416175 2470176 2392177 2618178 2527179 2493180 2341181 2536182 2358183 2418184 2345185 2091186 2228187 2079188 2823189 2292190 2120191 2531192 2236193 2324194 2362195 2170196 2527197 2431198 2442199 2315200 23332762.62759.22746.12726.32703.92683.32668.32661.42663.72674.72692.82715.62740.22764.02784.82800.82810.92814.62812.12803.927 90.82773.72753.72731.82708.82685.72662.92641.02620.42601.22583.62567.62553.32540.52529.22519.22510.42502.82496.12490.32485.32481.02477.22473.92471.12468.62466.52464.62463.02461.62460.42459.32458.32457.52456.72456.12455.52454.92454.52454.02453.72453.32453.02452.72452.52452.32452.1333-27.6-56.2533.9-51.3324.1-3.3-16.3-470.4-56.7176.3-12.8307.4450.8195.0254.2-383.8-33.9-251.6-288.1-17.9-43.8242.3185.3399.267.2-212.7-71.9246.0-141.4-218.282.471.4310.7228.529.8-508.2-49.4100.2-109.1165.7-69.3-11.0-85.2144.155.924.4-125.571.4-105.0-43.6-115.4-368.3-230.3-378.5366.3-164.1-335.576.1-218.5-130.0-91.7-283.374.0-21.7-10.5-137.3-119.1

334TABLE 5-46.CONTINUED.NUM~0BS"~C0MP RESID NUM OBS COMP RESID NUM OBS COMP RESID_201 2099202 2291203 2447204 2495205 2477206 2639207 2192208 2283209 2716210 2824211 2707212 2321213 2331214 2480215 2284216 2331217 2464218 2376219 2407220 2479221 2327222 2864223 2552224 2228225 2461226 2684227 2260228 2585229 2644230 2507231 2487232 2751233 2583234 25592451.92451.72451.62451.42451.32451.12451.02450.92450.82450.72450.62450.52450.52450.42450.32450.32450.22450.22450.12450.12450.02450.02449.92449.92449.92449.82449.82449.82449.72449.72449.72449.72449.62449.6-352.9-160.7-4.643.625.7187.9-259.0-167.9265.2373.3256.4-129.5-119.529.6-166.3-119.313.8-74.2-43.128.9-123.0414.0102.1-221.911.1234.2-189.8135.2194.357.337.3301.3133.4109.4235 2572236 2648237 2516238 2242239 2201240 2146241 2329242 2270243 2495244 280 9245 2522246 2459247 2477248 2468249 2228250 2219251 2216252 2771253 2725254 2214255 2407256 2575257 2415258 2345259 2262260 2144261 2365262 2543263 2993264 2986265 2593266 2555267 2367268 24472449.62449.62449.52449.52449.52449.52449.52449.42449.42449.42449.42449.42449.42449.42449.42449.32449.32449.32449.32449.32449.32449.32449.32449.32449.22449.22449.22449.22449.22449.22449.22449.22449.22449.2122.4198.466.5-207.5-248.5-303.5-120.5-179.445.6359.672.69.627.618.6-221.4-230.3-233.3321.7275.7-235.3-42.3125.7-34.3-104.3-187.2-305.2-84.293.8543.8536.8143.8105.8-82.2-2.2269 2607270 2640271 2559272 2453273 2583274 2337275 2596276 2210277 2191278 2125279 2435280 2270281 2338282 2476283 2095284 2384285 2 902286 2294287 2235288 244628 9 2443290 2744291 2432292 2895293 2667294 2455295 2615296 2479297 2618298 2576299 2334300 28122449.22449.22449.22449.22449.22449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.12449.02449.0157.8190.8109.83.8133.8-112.1146.9-239.1-258.1-324.1-14.1-179.1-111.126.9-354.1-65.1452.9-155.1-214.1-3.1-6.1294.9-17.1445.9217.95.9165.929.9168.9126.9-115.0363.0

TABLE 5-47X01246: SUPPLEMENTAL STATISTICAL INFORMATION335VARIANCE/ CO-VARIANCEMATRIXDIAM PREI POST TIME VELO3.372E"14 2.876E 07 -2.754E"07 -4.922E - 08 1.347E_092.876E"07 2.534E02 5.360E00 -8.449E00 1.733E012.754E~07 5.360E00 3.316E02 -1.072E01 2.183E~014.922E~08 -8.449E00 -1.072E01 1.079E01 -2.223E_011.347E~09 1.733E~01 2.183E"01 -2.223E~01 6.409E~03CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.806934 -0.727659 -0.010259 0.013761PREI 0.806934 1.000000 -0.193646 -0.481362 0.482215POST -0.727659 -0.193646 1.000000 -0.623821 0.619762TIME -0.010259 -0.481362 -0.623821 1.000000 -0.999972VELO 0.013761 0.482215 0.619762 -0.999972 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 2.617E08 -2.596E08PREI 1.367E00 6.770E"04POST 9.993E~01 -3.667E"01TIME 2.315E01 -2.468E01VELO 1.092E03 -1.140E03

I II | I M|I I I I|M3361750 '1810 1870 1930 1990TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFioure 5-96. PDPLOT o-f the occupation o-f X01246.COLUUzLUa.cc3 0152Uo 0127enLUin0255 _022e_020* _0177u.o 01010078L-XD 0051Z0025 _II0002., IN M I I 1 I I II 1 i II33.3 -27.5 -2L8 -16.1 -10.4 -4.6 LI 6.8 12.5NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-97. NOISEPLOT o-f the occultation of X01246,

337The steadiness of the sky, in terms of atmospherictransparency, is attested to by the NOISEPLOT, Figure5-97. The mean o-f the residual distribution is only 0.8percent below that o-f the computed intensities, with aone sigma width o-f 6.5 percent. Despite the prevailingobserving conditions, the -faintness o-f the stellarsignal in comparison to the bright sky background (10.9percent, or 5.5 percent o-f full scale) led to a very lowS+N/N ratio o-f only 2.32. This in turn was the primarycause -for the large statistical uncertainties in thetime o-f geometrical occultation (3.3 milliseconds) andthe L-rate (11.6 percent o-f the determined value o-f688.2 meters/second).The characteristics o-f the comparative powerspectra (Figure 5-98) are very similar to those seen -forthe previous occultation. The change in scale, withcontributing power components more important at somewhathigher -frequencies, is due to the di-f-ferent time-scaleso-f the two events.The occultation disappearance was determined tohave occurred at 01:20:01.938 (+/- 0.011 seconds),Coordinated UniversalTime.ZC0126The occultation o-f ZC0126 -followed that o-f X01246by only eight minutes. This star was o-f later spectraltype than X01246 (G5 in comparison to F0) , as well ashal-f a magnitude brighter in V. These two differences

.338MODELCURVESTAR +SKY1 r-'100' "200" ^300" '4FREQUENCY IN HERTZFigure 5-98. POUERPLOT o-f the occultation o-f X81246.

.in characteristics led to a somewhat better occultationsignal, with a S+N/N ratio o-f 3.45 < as noted inTable 5-48)The raw intensity data are presented inFigure 5-99. The integration plot, Figure 5-100,suggests a possible secondary disappearance atapproximately 1200 milliseconds. To see this suddenchange in the integrated signal level more clearly,Figure 5-101 details the supposed secondarydisappearance only. As is apparent, there is indeed asharp decline in the integrated signal level atapproximately 1205 milliseconds. No other such abruptchanges in the signal level (except, o-f course at the33?time o-f the primary disappearance) are seen in the data.Hence, a -fainter "wide" secondary component was detectedat 1205 mi 1 1 i seconds.The ascending and decending branches o-f theintegrated data, presented in Figure 5-101, were -fit vialeast squares to linear equations. The statisticaluncertainty in the intersection o-f the two regressionlines was 0.008 seconds, which is, there-fore, theuncertainty in the time o-f secondary disappearance.Four hundred milliseconds o-f intensity datacentered on the estimated time o-f primary occultationwere fit via the DC process. This, in retrospect, wasroughly 100 milliseconds longer than needed in thepost-occul tat ion portion o-f the data. The best -fit to

:.340ZC0126:TABLE 5-48LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: ZC0126, < SAO 109552, DM -00 0146)RA: 005623 DEC: -001517 mV: 7.71 Sp: G5Filter: V Diaphragm: J Gain: BIO Voltage: 1200LUNARINFORMATIONSurface Illumination: 88 percentElongation -from Sun: 139 degreesAltitude Above Horizon: 56 degreesLunar Limb Distance: 390149 k i 1 ome tersPredicted Shadow Velocity: 449 8 meters/secPredicted Angular Rate: 2378 arcsec/sec.EVENTINFORMATIONDate: November 17, 1983 UT o-f Event 01 -.28:05USNO V/0 Code: 64 HA o-f Event: -190552-Position Angle: 98.3 Cusp Angle: 53SContact Angle: -47.6 Watts Angle: 120.7MODEL PARAMETERSNumber o-f Data Points:401Number o-f Grid Points: 266Number o-f Spectral Regions: 53Ulidth o-f Spectral Regions: 50 AnostromsLimb Darkening Coefficient: 0.5E-f-fective Stellar Temperature: 5700 KSOLUTIONSStellar Diameter : Point SourceTime: (relative to Bin 0): 982.4 (2.7)Pre-Event Signal: 2721.6 (14.0)Background Sky Level: 2279.2 (12. 6)Velocity (meter s/sec . ) : 322.4 (14.3)Lunar Limb Slope (degrees): +22.11 (1.83)U.T. o-f Occultation: 01:28:01.981 (0.010)PHOTOMETRIC NOISEINFORMATIONSum-o-f-Squares o-f Residuals: 13087870Sigma (Standard Error): 180.886Normalized Standard Error: 0.40882Photometric (S+N)/N Ratio: 3.4461(Change in Intensi ty)/Background: 0.19413Change in Magnitude: 0.19263

I' I ' I ' I'I'I''341CO0)3CO00COCDINhCMCDCDCOCMCOUNTS00LOCMSCM00CDCOCDCM CDCMin3:00I3sI'coLO_.cdCMS.COLlO13COCDID.CMOaz

i3421.0E 0.9z 0.8^0.79.n 0.6HINi—0.5

343the data is shown in Figure 5-102. A detail o-f thedisappearance is plotted, along with the data subjectedto 5-point smoothing, in Figure 5-103.The solution -found ZC0126 to have no detectabledisc, and hence has been classed as a point sourcesolution. The intensity data, computed intensities andresiduals are compiled in Table 5-49. The usualsupplemental statistics are presented on Table 5-50.The PDPLOT, Figure 5-104 exhibits no anomalousbehavior. It does indicate, however, that a better datasample might have been selected -from data pointsbeginning roughly 50 milliseconds earlier. But, giventhe point source nature o-f the solution and the -factthat the regions o-f sensitivity to parametric variationare well covered, this selection would not have made asignificant di-f-ference in the solution.The NOISEPLOT and the POWERPLOT for thisobservation are presented as Figures 5-105 and 5-106,respectively. Here, too, there is no unusual behavior.The Coordinated Universal Time o-f geometricaloccultation -for the primary event was 01:28:01.981

344DISTANCE TO THE GEOMETRICAL SHADOW IN METERSL0 -50 -4 -30 -20 -10 10 20 30 40 50 60 g^g800 880 '960 1040 4QPITIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-162. FITPLOT o-f the occultation o-f ZC8126.DISTANCE TO THE GEOMETRICAL SHADOV IN METERSL0 -40 -30 -20 -10 10 3036850 '890 930 '970 "" 1010TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-183. FITPLOT o-f the occultation o-f ZC8126 showingthe raw -fit to a smoothed data set.

TABLE 5-49ZC0126: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 800345NUM OBS COMP RES ID2826 2724.8 101.21 2883 2724.6 158.42 2573 2723.8 -150.83 2864 2722.7 141.34 2703 2721.6 -18.65 2595 2720.9 -125.96 2628 2720.8 -92.87 2597 2721.5 -124.58 2767 2722.7 44.39 2706 2724.0 -18.010 2303 2725.1 -422.111 2575 2725.6 -150.612 2652 2725.3 -73.313 2257 2724.3 -467.314 2824 2722.8 101.215 3103 2721.4 381.616 2681 2720.4 -39.417 2573 2720.2 -147.218 2434 2720.8 -286.819 2666 2722.1 -56.120 2778 2723.7 54.321 2890 2725.2 164.822 3134 2726.1 407.923 2766 2726.2 39.824 2788 2725.4 62.625 3260 2723.9 536.126 2923 2722.1 200.927 2339 2720.5 -381.528 2654 2719.6 -65.629 2379 2719.6 -340.630 2679 2720.6 -41.631 2831 2722.4 108.632 2871 2724.5 146.533 2864 2726.4 137.634 2639 2727.6 -88.635 2456 2727.7 -271.736 2657 2726.7 -69.737 2685 2724.7 -39.738 2497 2722.2 -225.239 2495 2719.6 -224.640 2587 2717.7 -130.741 2823 2716.8 106.242 2904 2717.4 186.643 2543 2719.4 -176.444 2731 2722.4 8.645 2774 2726.0 48.046 2699 2729.4 -30.447 2636 2731.9 -95.948 2682 2733.0 -51.049 2585 2732.3 -147.350 2776 2729.7 46.351 2391 2725.7 -334.752 2651 2720.8 -69.853 2327 2716.0 -389.054 2503 2712.1 -209.155 2698 2709.7 -11.756 2738 2709.4 28.657 2899 2711.5 187.558 2739 2715.7 23.359 3043 2721.5 321.560 2637 2728.1 -91.161 2836 2734.7 101.362 2600 2740.1 -140.163 2815 2743.6 71.464 2819 2744.4 74.665 2844 2742.5 101.566 2728 2737.8 -9.8NUM OBS COMP RES ID67 2831 2730.9 100.168 2565 2722.6 -157.669 2925 2713.8 211.270 3183 2705.7 477.371 2551 2699.3 -148.372 2738 2695.5 42.573 2657 2694.8 -37.874 3015 2697.4 317.675 3035 2703.2 331.876 2567 2711.7 -144.777 2820 2722.0 98.078 2779 2733.1 45.979 2705 2743.9 -38.980 2567 2753.3 -186.381 3047 2760.2 286.882 2971 2764.0 207.083 3126 2764.2 361.884 2783 2760.6 22.485 2565 2753.5 -188.586 2952 2743.5 208.587 2762 2731.4 30.688 2795 2718.1 76.989 2819 2704.8 114.290 2751 2692.6 58.491 2790 2682.4 107.692 2645 2675.1 -30.193 2579 2671.4 -92.494 2564 2671.4 -107.495 2395 2675.5 -280.596 2343 2683.1 -340.197 2599 2694.0 -95.098 3108 2707.4 400.699 2760 2722.5 37.5100 2545 2738.2 -193.2101 2634 2753.7 -119.7102 2879 2767.9 111.1103 2859 2780.1 78.9104 2826 2789.5 36.5105 2591 2795.5 -204.5106 2622 2797.8 -175.8107 2847 2796.3 50.7108 2855 2791.1 63.9109 2807 2782.4 24.6110 2724 2770.6 -46.6111 2511 2756.4 -245.4112 2775 2740.4 34.6113 2963 2723.3 239.7114 2581 2705.9 -124.9115 2935 2688.9 246.1116 3066 2673.1 392.9117 2881 2659.2 221.8118 2935 2647.5 287.5119 2389 2638.6 -249.6120 2131 2632.8 -501.8121 2403 2630.3 -227.3122 2470 2631.2 -161.2123 2889 2635.3 253.7124 2567 2642.6 -75.6125 2775 2652.8 122.2126 2936 2665.6 270.4127 2551 2680.5 -129.5128 2777 2697.2 79.8129 2665 2715.1 -50.1130 3059 2733.9 325.1131 2567 2753.0 -186.0132 2629 2772.0 -143.0133 2572 2790.5 -218.5NUM OBS COMP RES ID134 2770 2808.0 -38.0135 3419 2824.3 594.7136 2905 2839.0 66.0137 2863 2851.9 11.1138 2971 2862.7 108.3139 2721 2871.4 -150.4140 2886 2877.8 8.2141 2716 2882.0 -166.0142 2779 2883.8 -104.8143 2607 2883.3 -276.3144 2959 2880.7 78.3145 3287 2875.9 411.1146 2949 2869.2 79.8147 3132 2860.6 271.4148 2851 2850.4 0.6149 2936 2838.6 97.4150 2522 2825.5 -303.5151 2527 2811.2 -284.2152 2619 2795.9 -176.9153 2619 2779.8 -160.8154 2819 2763.1 55.9155 2597 2745.8 -148.8156 2882 2728.2 153.8157 2806 2710.4 95.6158 2928 2692.5 235.5159 2759 2674.6 84.4160 2666 2656.8 9.2161 2535 2639.3 -104.3162 2591 2622.0 -31.0163 2487 2605.1 -118.1164 2566 2588.7 -22.7165 2505 2572.7 -67.7166 2360 2557.2 -197.2167 2385 2542.2 -157.2168 2602 2527.8 74.2169 2720 2514.0 206.0170 2363 2500.8 -137.8171 2503 2488.2 14.8172 2395 2476.2 -81.2173 2399 2464.7 -65.7174 2471 2453.8 17.2175 2271 2443.5 -172.5176 2350 2433.8 -83.8177 2263 2424.5 -161.5178 2531 2415.8 115.2179 2833 2407.6 425.4180 2531 2399.9 131.1181 2706 2392.6 313.4182 2434 2385.8 48.2183 2316 2379.4 -63.4184 2403 2373.3 29.7185 2335 2367.7 -32.7186 2258 2362.4 -104.4187 2307 2357.4 -50.4188 2433 2352.8 80.2189 2537 2348.4 188.6190 2387 2344.3 42.7191 2551 2340.5 210.5192 2184 2337.0 -153.0193 2456 2333.6 122.4194 2528 2330.5 197.5195 2135 2327.6 -192.6196 2287 2324.9 -37.9197 2496 2322.3 173.7198 2300 2319.9 -19.9199 2499 2317.7 181.3200 2514 2315.6 198.4

346TABLE 5-49.CONTINUED.BUM OBS COMP RE SID NUM OBS COMP RESID NUM OBS COMP RESID201 2241 2313.7 -72.7 268 2366 2282.2 83.8 335 2180 2280.1 -100.1202 1949 2311.8 -362.8 269 2463 2282.1 180.9 336 2487 2280.1 206.9203 2183 2310.1 -127.1 270 2352 2282.1 69.9 337 2451 2280.1 170.9204 2255 2308.5 -53.5 271 2231 2282.0 -51.0 338 2162 2280.1 -118.1205 2688 2307.0 381.0 272 2220 2282.0 -62.0 339 2493 2280.1 212.9206 2375 2305.6 69.4 273 2393 2281.9 111.1 340 2164 2280.1 -116.1207 2358 2304.3 53.7 274 2040 2281.9 -241.9 341 2165 2280.1 -115.1208 2407 2303.1 103.9 275 2047 2281.8 -234.8 342 2079 2280.1 -201.1209 2308 2301.9 6.1 276 2251 2281.8 -30.8 343 2163 2280.1 -117.1210 2112 2300.8 -188.8 277 2467 2281.7 185.3 344 2127 2280.0 -153.0211 2265 2299.8 -34.8 278 2343 2281.7 61.3 345 2319 2280.0 39.0212 2443 2298.8 144.2 279 2020 2281.6 -261.6 346 2386 2280.0 106.0213 2304 2297.9 6.1 280 2175 2281.6 -106.6 347 2173 2280.0 -107.0214 2136 22 97.1 -161.1 281 2308 2281.5 26.5 348 2391 2280.0 111.0215 2235 2296.3 -61.3 282 2137 2281.5 -144.5 349 2250 2280.0 -30.0216 2287 2295.5 -8.5 283 2376 2281.4 94.6 350 2131 2280.0 -149.0217 2611 2294.8 316.2 284 2207 2281.4 -74.4 351 2164 2280.0 -116.0218 2460 2294.1 165.9 285 2463 2281.3 181.7 352 2059 2280.0 -221.0219 2319 2293.5 25.5 286 2490 2281.3 208.7 353 2409 2280.0 129.0220 2243 2292.9 -49.9 287 2257 2281.2 -24.2 354 2211 2279.9 -68.9221 2603 2292.3 310.7 288 2279 2281.2 -2.2 355 2531 2279.9 251.1222 2362 2291.8 70.2 289 2157 2281.1 -124.1 356 2381 2279.9 101.1223 2417 2291.3 125.7 290 2259 2281.1 -22.1 357 2475 2279.9 195.1224 2253 2290.8 -37.8 291 2427 2281.1 145.9 358 2688 2279.9 408.1225 2331 2290.3 40.7 292 2127 2281.1 -154.1 359 1921 2279.9 -358.9226 2199 2289.9 -90.9 293 2086 2281.0 -195.0 360 2223 2279.9 -56.9227 2206 2289.5 -83.5 294 2238 2281.0 -43.0 361 22 96 2279.9 16.1228 2207 2289.1 -82.1 295 2455 2281.0 174.0 362 2512 2279.9 232.1229 23 94 2288.7 105.3 296 2119 2280.9 -161.9 363 2063 2279.9 -216.9230 2160 2288.4 -128.4 297 2299 2280.9 18.1 364 2003 2279.9 -276.9231 2326 2288.0 38.0 298 2522 2280.9 241.1 365 2143 2279.9 -136.9232 2130 2287.7 -157.7 299 2047 2280.9 -233.9 366 2500 2279.8 220.2233 2131 2287.4 -156.4 300 2495 2280.8 214.2 367 2111 2279.8 -168.8234 2191 2287.1 -96.1 301 22 96 2280.8 15.2 368 2135 2279.8 -144.8235 2237 2286.8 -49.8 302 22 95 2280.8 14.2 369 2238 2279.8 -41.8236 2135 2286.6 -151.6 303 2243 2280.7 -37.7 370 2230 2279.8 -49.8237 2234 2286.3 -52.3 304 2616 2280.7 335.3 371 2581 2279.8 301.2238 2367 2286.1 80.9 305 2207 2280.7 -73.7 372 2542 2279.8 262.223 9 2412 2285.9 126.1 306 2431 2280.6 150.4 373 2393 2279.8 113.2240 2459 2285.7 173.3 307 2360 2280.6 79.4 374 2528 2279.8 248.2241 2070 2285.5 -215.5 308 2305 2280.6 24.4 375 2463 2279.8 183.2242 1859 2285.3 -426.3 309 2424 2280.6 143.4 376 2204 2279.8 -75.8243 2275 2285.1 -10.1 310 2124 2280.6 -156.6 377 2115 2279.8 -164.8244 2582 2284.9 297.1 311 2236 2280.6 -44.6 378 2223 2279.8 -56.8245 2307 2284.8 22.2 312 2423 2280.5 142.5 379 2360 2279.8 80.2246 2455 2284.6 170.4 313 2399 2280.5 118.5 380 2480 2279.8 200.2247 2151 2284.4 -133.4 314 2672 2280.5 391.5 381 2767 2279.7 487.3248 2183 2284.3 -101.3 315 2203 2280.5 -77.5 382 2166 2279.7 -113.7249 2058 2284.2 -226.2 316 2068 2280.4 -212.4 383 2208 2279.7 -71.7250 2235 2284.0 -49.0 317 2118 2280.4 -162.4 384 2214 2279.7 -65.7251 2260 2283.9 -23.9 318 2361 2280.4 80.6 385 2451 2279.7 171.3252 2040 2283.8 -243.8 319 2496 2280.4 215.6 386 2071 2279.7 -208.7253 2138 2283.7 -145.7 320 2336 2280.4 55.6 387 2311 2279.7 31.3254 1965 2283.5 -318.5 321 2210 2280.3 -70.3 388 2047 2279.7 -232.7255 2159 2283.4 -124.4 322 2237 2280.3 -43.3 389 2337 2279.7 57.3256 2374 2283.3 90.7 323 2540 2280.3 259.7 390 2445 2279.7 165.3257 2495 2283.2 211.8 324 27 90 2280.3 509.7 391 1975 2279.7 -304.7258 2248 2283.1 -35.1 325 2353 2280.3 72.7 3 92 2195 2279.7 -84.7259 2327 2283.0 44.0 326 2243 2280.3 -37.3 3 93 2246 2279.7 -33.7260 2029 2282.9 -253.9 327 2076 2280.3 -204.3 3 94 2147 2279.7 -132.7261 2103 2282.8 -179.8 328 2123 2280.2 -157.2 3 95 2137 2279.7 -142.7262 23 91 2282.7 108.3 329 2075 2280.2 -205.2 3 96 22 91 2279.7 11.3263 253 9 2282.6 256.4 330 1800 2280.2 -480.2 397 2185 2279.7 -94.7264 2285 2282.5 2.5 331 2407 2280.2 126.8 398 2128 2279.7 -151.7265 2360 2282.4 77.6 332 2219 2280.2 -61.2 399 2099 2279.7 -180.7266 2511 2282.4 228.6 333 22 95 2280.2 14.8 400 2227 2279.6 -52.6267 2116 2282.3 -166.3 334 2228 2280.2 -52.2

347TABLE 5-50ZC0126: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO- VARIANCE MATRIXDIAM PREI POST TIME VELO3.719E~15 1.224E"07 -7.310E _ 08 -1.376E"08 8.217E_111.224E"07 1.970E02 5.010E00 -8.764E00 4.015E027.310E~08 5.010E00 1.600E02 -6.918E00 3.135E~02•1.376E~08 -8.764E00 -6.918E00 7.146E00 -3.278E028.217E"11 4.015E"02 3.135E 02 -3.278E"02 2.070E 04CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.891094 -0.591950 -0.334484 0.338583PREI 0.891094 1.000000 -0.167240 -0.663298 0.665761POST -0.591950 -0.167240 1.000000 -0.509287 0.504986TIME -0.334484 -0.663298 -0.509287 1.000000 -0.999987VELO 0.338583 0.665761 0.504986 -0.999987 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 4.982E08 -4.917E08PREI 1.367E00 1.104E_03POST 9.989E 01 -3.665E 01TIME 1.793E01 -1.914E01VELO 3.912E03 -3.984E03

11 1 11 1 1n1111 1 11 1i 1 111 1 11 1 irpi11348800 880 '960 '1040 1120TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFiqure 5-104. PDPLOT o-f the occultation o-f ZC0126.COLUO zLU(X.

' I00T1111111'111—34?MODELCURVE-1 1STAR +SKY1 r_11OCCULTATIONl200"FREQUENCY IN1300" ' '400HERTZFigure 5-106. POWERPLOT o-f the occupation o-f 2C8126,

350this K0 star (11*^=7.8) were virtually unchanged -fromthose which prevailed at the times o-f the two previousoccul tat ions. As noted on Table 5-51, the instrumentalconfiguration was the same as that used -for the ZC0126eventThe RAWPLOT and INTPLOT (Figures 5-107 and 5-108,respectively) typify those o-f a single stardisappearance, with no indication o-f stellar duplicity.A DC -fit to 200 milliseconds o-f data was performed, andthe resulting best fit is depicted in Figure 5-109. Nodiscernible stellar disc could be detected for thisstarThe observations, computed intensities and theresiduals for the solution are listed in Table 5-52.The PDPLOT, Figure 5-110, shows nothing unusual in thenumerical partial derivatives. Table 5-32 contains thenumerical ranges of these partial derivatives along withthe var i ance/covar i ance and correlation matrices of thesolutionparameters.As might have been expected both the NOISEPLOT andPOUERPLQT for this event (Figures 5-111, and 5-112,respectively) are very similar to those seen for theobservations of ZC0126 and X01246.The Coordinated Universal Time of geometricaloccul tation was 03:32:06.631 (+/- 0.005 seconds).

.351TABLE 5-51X01309: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X01309,

352TIME512 1024 1536 204S 2560 3072 3584IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-197. RAWPLOT o-f the occultation o-f X81389.0.9en—T»sGUJNJ_1

i353COUNTSh* CD «t CD •«-»CM** CO U)

TABLE 5-52X01309: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 1830354NUM OBS COMP RES ID NUM OBS COMP RES ID NUM OBS COMP RESID1234562804338029603155332830602943335378 31449 28 9610 288911 289812 323113 299614 341415 325116 317917 306118 300319 319520 278921 287922 334023 345124 286325 312826 330327 315728 305029 328730 313131 346732 319933 350834 340135 302636 287137 331138 312039 299440 332841 295742 283 943 326344 314845 349246 301147 336348 292849 295150 320751 333952 332853 355154 315955 293756 282457 312658 345859 355560 349461 333762 348963 321564 325965 303066 33123135.43135.33136.13137.13137.23136.23135.03134.63135.63137.33138.23137.43135.53133.93134.03135.93138.23139.13137.93135.33133.43133.43135.53138.33139.73138.83136.03133.33132.63134.43137.93140.83141.13138.43134.03130.33129.83133.23139.13144.83147.23144.73137.73129.03122.43121.03126.23136.53148.53157.73160.53155.23143.03127.33113.03104.73105.43115.53132.93153.13171.13182.13183.13173.33154.63130.83106.8-331.4244.7-176.117.9190.8-76.2-192.0218.48.4-241.3-249.2-239.495.5-137.9280.0115.140.8-78.1-134.959.7-344.4-254.4204.5312.7-276.7-10.8167.023.7-82.6152.6-6.9326.257.9369.6267.0-104.3-258.8177.8-19.1-150.8180.8-187.7-298.7134.025.6371.0-115.2226.5-220.5-206.746.5183.8185.0423.746.0-167.7-281.410.5325.1401.9322.9154.9305.941.7104.4-100.8205.267 299668 356869 310170 288771 290072 307873 304974 314075 335676 332977 295278 314279 286580 315581 294782 303283 286484 295985 285086 275487 275988 315989 315190 312691 282592 288193 311494 341795 307596 345597 333198 325999 3447100 3294101 3747102 3052103 3548104 3379105 3215106 2783107 3006108 3163109 3164110 3303111 2994112 3065113 2749114 2635115 2998116 3068117 3283118 2832119 2659120 2600121 2575122 2651123 2635124 2711125 2648126 2939127 2804128 2747129 2912130 2848131 2814132 2517133 26153087.63077.23077.93089.93111.23138.53167.43193.43212.53222.03220.43208.03186.23157.83126.13094.63066.73045.33032.33028.93035.33050.93074.43103.93137.43172.63207.43239.83268.33291.53308.63319.03322.63319.63310.33295.33275.43251.43224.03194.13162.53129.83096.73063.73031.32999.82969.62940.92913.72888.32864.62842.62822.42803.82786.82771.32757.22744.42732.82722.42713.02704.52696.92690.02683.92678.32673.4-91.6490.823.1-202.9-211.2-60.5-118.4-53.4143.5107.0-268.4-66.0-321.2-2.8-179.1-62.6-202.7-86.3-182.3-274.9-276.3108.176.622.1-312.4-291.6-93.4177.2-193.3163.522.4-60.0124.4-25.6436.7-243.3272.6127.6-9.0-411.1-156.533.267.3239.3-37.365.2-220.6-305.984.3179.7418.4-10.6-163.4-203.8-211.8-120.3-122.2-33.4-84.8216.691.042.5215.1158.0130.1-161.3-58.4134 2689135 2807136 2449137 2842138 3183139 2592140 2472141 2511142 2575143 243 9144 2681145 2556146 2519147 2668148 2639149 2530150 2655151 2495152 2399153 2815154 2541155 2455156 2683157 2737158 2847159 2723160 2351161 2759162 2759163 2756164 2759165 2622166 2560167 2943168 2878169 2877170 2732171 2687172 2599173 2371174 2483175 2329176 2611177 2589178 2819179 3003180 2 936181 27 98182 2667183 2403184 2760185 2347186 2561187 2594188 2596189 2234190 2452191 2401192 2548193 2575194 2624195 3093196 2407197 2383198 2871199 2528200 25112668.92664.92661.32658.02655.12652.42650.02647.92645.92644.22642.62641.12639.82638.62637.52636.52635.62634.72633.92633.22632.52631.92631.42630.92630.42629.92629.52629.22628.82628.52628.22627.92627.72627.42627.22627.02626.82626.62626.42626.22626.02625.82625.72625.52625.42625.32625.22625.12625.02624.92624.82624.72624.62624.52624.42624.32624.32624.22624.12624.12624.02624.02623.92623.92623.82623.82623.720.1142.1-212.3184.0527.9-60.4-178.0-136.9-70.9-205.238.4-85.1-120.829.41.5-106.519.4-139.7-234.9181.8-91.5-176.951.6106.1216.693.1-278.5129.8130.2127.5130.8-5.9-67.7315.6250.8250.0105.260.4-27.4-255.2-143.0-296.8-14.7-36.5193.6377.7310.8172.942.0-221.9135.2-277.7-63.6-30.5-28.4-390.3-172.3-223.2-76.1-49.10.0469.0-216.9-240.9247.2-95.8-112.7

^7111 1 1 111 1 1 11I1 1 1 111 11 1 in111 113551830 1870 1910 1950 1990TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFi Qure 5-1 10 PDPLOT o-f the occultation o-f X01309.3245_0221 [_ MEAN -0.001080)g 0196 _ SIGMA 0.056689Zg 0172 _g0147oO 0123O 009SLlu 0073|_a3 004£_20025 _rlA\3002 Lf t 1 1-27.1tu^' IiH-THi-22.1 -17.1 -12.2 -7.2 -2.2 2.7 7.7 12.7 17.7NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-111. NOISEPLOT o-f the occultation o-f X01309,

356TABLE 5-53X01309: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO-VARIANCEMATRIXDIAM PREI POST TIME VELO3.004E~14 4.253E"07 -5.242E"07 -2.350E~08 3.963E_104.253E"07 3.435E02 1.772E01 -8.716E00 1.041E_015.242E"07 1.772E01 5.679E02 -1.309E01 1.504E 01•2 350E"08 -8.716E00 -1.309E01 4.109E00 -4.807E_023.963E"10 1.041E"01 1.504E01 -4.807E~02 7.689E04CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.707272 -0.807680 0.275065 -0.255759PREI 0.707272 1.000000 -0.155474 -0.463281 0.480530POST -0.807680 -0.155474 1.000000 -0.779561 0.767024TIME 0.275065 -0.463281 -0.779561 1.000000 -0.999799VELO -0.255759 0.480530 0.767024 -0.999799 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 2.403E08 -2.322E08PREI 1.367E00 3.510E_03POST 9.965E"01 -3.667E 01TIME 3.313E01 -3.536E01VELO 2.824E03 -2.852E03

357MODELCURVEOCCULTATION"0 '100' "200' §00 '4FREQUENCY INHERTZFigure 5-112. POWERPLOT of the occultation o-f X8138?

358ZC3159 (37 Capricorni)The bright (mU=5.79) F5 star 2C3158 was occultedunder very -favorable circumstances on the night o-fDecember 10, 1983. Though the event occurred early inthe evening (approximately 00:07 U. T.), astronomicaltwilight had been over -for approximately ten minutes.Thus, despite the relatively small solar elongation o-f62 degrees, the event was seen in dark skies. Thepenalty for this was a moderately low lunar altitude,though still above two air masses. The darkened portiono-f the 27 percent illuminated lunar disc was quite dark,and virtually no Earthshine could be seen, even in a6-inch -finding telescope.The seeing was unusually good for RHO and estimatedat 2 seconds o-f arc or better. These almostextraordinary combinations o-f -fortuitous circumstancesallowed the observation to be made with the narrowbandwidth "b" -filter. Though the integrated bandpass o-fthis -filter is less than 1/10 that o-f a Johnson B•filter, the S+N/N ratio obtained -for this observation(given in Table 5-54) was still a respectable 5.52.As easily seen on the RAWPLOT, Figure 5-113, thestellar signal was highly dominant (by a -factor o-f 6.5)over the background sky brightness. The integrationplot o-f the 4096 milliseconds o-f raw data (Figure 5-114)shows no evidence o-f any secondary disappearances.

::359ZC3158:TABLE 5-54LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: 2C3158, (37 Cap, SAO 190461, DM -20 6237)RA: 213355 DEC: -200935 mV: 5.79 Sp :F5Filter: "b u Diaphragm: I Sain: C9+ Voltage: 1200LUNARINFORMATIONSurface Illumination: 27 percentElongation -from Sun: 62 degreesAltitude Above Horizon: 31 degreesLunar Limb Distance: 400741 kilometersPredicted Shadow Velocity: 355.7 meters/sec.Predicted Angul ar Rate: 0.1831 arcsec/secEVENTINFORMATIONDate: December 10, 1983 UT o-f Event : 00:06:42USNO V/0 Code: 59 HA o-f Event : +334727Position Anale: 118.3 Cu sp Angle: 46SContact Angle: -58.9 Wa tts Angle : 137.9MODEL PARAMETERSNumber o-f Data Points: 301Number o-f Grid Points: 256Number o-f Spectral Regions: 5Width o-f Spectral Regions: 50 AnostromsLimb Darkening Coe-f i c i en t-f 0.5E-f-fective Stellar Temperature: 6600KSOLUTIONSStellar Diameter (ams): 1 .74 (1 .68)Time: (relative to Bin 0): 1521.9 (1 .6)Pre-Event Signal: 1509.9 (23.7)Backoround Sky Level231 .7 (49.3)Velocity (meters/sec.): 269.9 (3.34)Lunar Limb Slope (degrees): + 20.3 (0.5)U.T. o-f Occultation: 00: 06:39.731 (0.004)PHOTOMETRIC NOISEINFORMATIONSum-o-f-Squares o-f Residuals: 38293450Sigma (Standard Error): 357.274Normalized Standard Error: 0.2795Photometric (S+N)/N Ratio: 4.5775(Change in Intensi ty)/Background: 5.5159Change in Magnitude: 2.0349

360kS12 1024 1536 2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-113. RAWPLOT o-f the occultation o-f ZC3158.6Q UN»—_i

361Because o-f the somewhat slower R-rate -for this event(predicted to be 0.1831 arc seconds per second), 300milliseconds o-f data were used in the DC -fittingprocess. The resulting best -fit is shown graphically inFigure 5-115 and as can be seen is rather good. Theslowly decaying di -f -f ract i on fringes arose -from the nearmonochromat i c i ty o-f the optical bandpass. This isre-flected in the PDPLOT (Figure 5-116) as wel 1 .Examination o-f the PDPLOT (see Table 5-56 for the rangeso-f numerical values in the partial derivatives) showsthat the sensitivity of the solution curve to variationsin the stellar diameter and velocity parameter (and to alesser extent time of geometrical occultation) continuesto be high before the start of the choosen data set.While this is true, because of the decaying amplitude ofthe diffraction fringes in the occultation curve itself,to include data from times earlier than considered wouldnot be helpful. Data extracted from times before about1280 milliseconds would be dominated by variations dueto scintillation noise rather than intrinsic variationsin the intensity curve.A stellar angular diameter of 1.74 (+/- 1.68)milliseconds of arc was determined by the DC fittingprocedure, for ZC3158. This star, according toSchlesinger and Jenkins (1940), has a parallax of 0.032arc seconds, or a corresponding distance of 31 parsecs.

362COUNTSs °> «,3 S Q rs co in "t

363COMP1280 1340 1400 1460 1520TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFiqure 5-116. PDPLOT o-f the occultation o-f ZC3158.HIozUJcrQC3auo0548_0491 - MEAN 0.05540O 0218- SIGMA 0.375851-563 -499 '-438 -372 -308 -245 -181 -U7 -54 10NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-117. NOISEPLOT o-f the occultation of ZC3158,

TABLE 5-55zc : 3158 : OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 1280364NUM OBS COMP RESID NUM OBS COMP RESID NUM OBS COMP RESID1677 1466.6 210.4 67 1671 1491.4 179.6 134 1447 1332.2 114.81 1300 1490.2 -190.2 68 1248 1455.9 -207.9 135 1367 1323.6 43.42 1544 1519.5 24.5 69 1145 1427.2 -282.2 136 1955 1324.7 630.33 2103 1548.0 555.0 70 1735 1410.5 324.5 137 2049 1335.6 713.44 2103 1568.1 534.9 71 1752 1406.8 345.2 138 2083 1355.4 727.65 1489 1575.3 -86.3 72 1696 1416.7 279.3 139 1462 1383.6 78.46 1335 1566.9 -231.9 73 991 1439.7 -448.7 140 1104 1418.4 -314.47 1343 1545.9 -202.9 74 1346 1471.7 -125.7 141 1058 1458.2 -400.28 1232 1516.5 -284.5 75 2004 1510.0 494.0 142 1121 1501.4 -380.49 1087 1485.9 -398.9 76 1745 1548.9 196.1 143 1121 1546.0 -425.010 1258 1461.6 -203.6 77 1770 1584.5 185.5 144 963 1590.0 -627.011 1210 1449.5 -239.5 78 1378 1611.7 -233.7 145 1343 1631.6 -288.612 1219 1451.5 -232.5 79 1263 1628.5 -365.5 146 805 1669.3 -864.313 1151 1468.5 -317.5 80 1647 1631.2 15.8 147 2111 1701.2 409.814 1443 1496.1 -53.1 81 1832 1621.2 210.8 148 1705 1726.7 -21.715 1791 1527.7 263.3 82 1980 1598.6 381.4 149 2035 1744.0 291.016 1775 1556.8 218.2 83 1280 1566.3 -286.3 150 1680 1753.2 -73.217 2131 1576.8 554.2 84 147 9 1528.2 -49.2 151 1335 1754.1 -419.118 2185 1582.6 602.4 85 2270 1488.1 781.9 152 1368 1746.1 -378.119 1923 1573.5 349.5 86 2871 1450.4 1420.6 153 1495 1730.6 -235.620 856 1551.5 -695.5 87 1759 1419.3 339.7 154 1466 1706.9 -240.921 422 1520.7 ****** 88 1170 1398.1 -228.1 155 1363 1677.0 -314.022 1799 1488.1 310.9 89 1654 1388.6 265.4 156 1226 1641.5 -415.523 1122 1460.6 -338.6 90 1311 1392.5 -81.5 157 1337 1601.5 -264.524 1747 1443.9 303.1 91 914 1408.5 -494.5 158 795 1558.7 -763.725 1595 1441.4 153.6 92 906 1435.8 -529.8 159 1684 1514.1 169.926 1717 1453.9 263.1 93 2183 1471.2 711.8 160 1592 1469.3 122.727 1023 1478.7 -455.7 94 1641 1511.2 129.8 161 1519 1425.5 93.528 1081 1511.0 -430.0 95 2079 1552.1 526.9 162 1604 1384.1 219.929 1463 1544.2 -81.2 96 2276 1590.1 685.9 163 1585 1345.9 239.130 991 1571.9 -580.9 97 1671 1621.4 49.6 164 1471 1312.5 158.531 892 1588.4 -696.4 98 2307 1643.3 663.7 165 8 98 1284.2 -386.232 1081 1590.7 -509.7 99 1740 1653.9 86.1 166 1591 1262.0 329.033 1619 1578.0 41.0 100 1384 1652.0 -268.0 167 1560 1246.4 313.634 1618 1552.9 65.1 101 1744 1638.1 105.9 168 1484 1237.3 246.735 1327 1519.9 -192.9 102 2003 1613.2 389.8 169 1795 1235.6 559.436 2263 1485.5 777.5 103 1791 1579.6 211.4 170 938 1240.5 -302.537 1728 1455.8 272.2 104 1804 1540.4 263.6 171 1186 1252.4 -66.438 1778 1436.6 341.4 105 2008 1498.6 509.4 172 1003 1270.7 -267.739 1109 1431.2 -322.2 106 2072 1457.8 614.2 173 1037 1294.8 -257.840 1875 1440.8 434.2 107 82 9 1421.4 -592.4 174 1172 1324.6 -152.641 1923 1463.7 459.3 108 789 1392.2 -603.2 175 1675 1358.9 316.142 1455 1495.5 -40.5 109 1189 1372.4 -183.4 176 1423 1397.3 25.743 1843 1531.1 311.9 110 1260 1363.7 -103.7 177 1323 1439.0 -116.044 1071 1564.1 -493.1 111 950 1366.5 -416.5 178 981 1483.0 -502.045 2176 1589.1 586.9 112 1139 1380.9 -241.9 179 1687 1528.8 158.246 1543 1601.2 -58.2 113 1223 1405.6 -182.6 180 1278 1575.4 -297.447 1631 1599.0 32.0 114 1460 1438.7 21.3 181 1327 1622.0 -295.048 1791 1582.5 208.5 115 1448 1477.8 -29.8 182 1733 1668.0 65.049 13 95 1554.6 -159.6 116 1567 1520.2 46.8 183 1521 1712.6 -191.650 1463 1519.5 -56.5 117 1703 1562.8 140.2 184 2471 1755.2 715.851 1433 1483.3 -50.3 118 1179 1602.7 -423.7 185 1676 1795.2 -119.252 1536 1451.4 84.6 119 1851 1637.3 213.7 186 1511 1832.1 -321.153 1355 1429.4 -74.4 120 1633 1664.3 -31.3 187 1368 1865.4 -497.454 1435 1420.0 15.0 121 2424 1682.0 742.0 188 1359 1894.9 -535.955 1428 1425.6 2.4 122 1992 1689.3 302.7 189 1441 1920.2 -479.256 1781 1444.7 336.3 123 1499 1685.7 -186.7 190 1763 1941.1 -178.157 1527 1474.5 52.5 124 1639 1671.5 -32.5 191 1779 1957.4 -178.458 1544 1510.8 33.2 125 1232 1647.7 -415.7 192 2431 1969.1 461.959 774 1548.0 -774.0 126 1441 1615.9 -174.9 193 1928 1976.1 -48.160 1163 1580.6 -417.6 127 1468 1577.9 -109.9 194 1935 1978.6 -43.661 2350 1603.8 746.2 128 1351 1535.9 -184.9 195 2095 1976.5 118.562 16 96 1614.8 81.2 129 1175 1492.4 -317.4 196 2338 1969.9 368.163 1920 1611.0 309.0 130 879 1449.9 -570.9 197 1985 1959.1 25.964 1570 1594.4 -24.4 131 146 9 1410.7 58.3 198 2628 1944.4 683.665 1780 1565.5 214.5 132 1327 1376.9 -49.9 199 1791 1925.8 -134.866 1535 1529.9 5.1 133 1431 1350.2 80.8 200 3150 1903.7 1246.3

TABLE 5-55.CONTINUED.365NUM~0BS"C0MP RESID NUM OBS COMP RESID NUM OBS COMP RESID201 2927 1878.3 1048.7202 2975 1849.8 1125.2203 2554 1818.7 735.3204 1548 1785.2 -237.2205 1414 1749.5 -335.5206 1744 1712.0 32.0207 1354 1672.9 -318.9208 1378 1632.6 -254.6209 1407 1591.2 -184.2210 1258 1549.1 -291.1211 1169 1506.4 -337.4212 1231 1463.4 -232.4213 736 1420.3 -684.3214 1009 1377.3 -368.3215 1379 1334.5 44.5216 1539 1292.1 246.9217 1349 1250.2 98.8218 1092 1208.9 -116.9219 1020 1168.5 -148.5220 1109 1128.9 -19.9221 872 1090.2 -218.2222 467 1052.5 -585.5223 473 1015.9 -542.9224 787 980.4 -193.4225 610 946.0 -336.0226 1243 912.8 330.2227 1215 880.7 334.3228 948 849.9 98.1229 517 820.2 -303.2230 779 791.7 -12.7231 757 764.4 -7.4232 510 738.2 -228.2233 510 713.2 -203.2234 418 689.3 -271.3235 514 666.5 -152.5236 523 644.7 -121.7237 266 623.9 -357.9238 345 604.2 -259.2239 782 585.4 196.6240 548 567.5 -19.5241 546 550.5 -4.5242 265 534.4 -269.4243 247 519.1 -272.1244 704 504.6 199.4245 461 490.8 -29.8246 999 477.8 521.2247 640 465.5 174.5248 174 453.8 -279.8249 159 442.7 -283.7250 193 432.2 -239.2251 463 422.3 40.7252 330 412.9 -82.9253 356 404.1 -48.1254 380 395.7 -15.7255 595 387.8 207.2256 611 380.3 230.7257 200 373.2 -173.2258 432 366.5 65.5259 598 360.1 237.9260 754 354.1 399.9261 199 348.5 -149.5262 93 343.1 -250.1263 138 338.0 -200.0264 401 333.2 67.8265 525 328.7 196.3266 264 324.4 -60.4267 439 320.3 118.7268 336 316.5 19.5269 118 312.8 -194.8270 130 309.4 -179.4271 231 306.1 -75.1272 487 303.0 184.0273 309 300.1 8.9274 634 297.3 336.7275 631 294.6 336.4276 352 292.1 59.9277 553 289.7 263.3278 337 287.5 49.5279 382 285.3 96.7280 651 283.3 367.7281 324 281.3 42.7282 212 279.5 -67.5283 317 277.7 39.3284 184 276.0 -92.0285 41 274.4 -233.4286 454 272.9 181.1287 352 271.5 80.5288 434 270.1 163.9289 302 268.7 33.3290 219 267.5 -48.5291 211 266.3 -55.3292 216 265.1 -49.1293 305 264.0 41.0294 184 263.0 -79.0295 247 261.9 -14.9296 234 261.0 -27.0297 165 260.1 -95.1298 294 259.2 34.8299 440 258.3 181.7300 766 257.5 508.5

366TABLE 5-56ZC 3158: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO-VARIANCEMATRIXDIAM PREI POST TIME VELO4.209E"16 1.051E"07 -1.973E - 07 -4.960E"10 2.342E 121.051E"07 8.947E02 8.525E01 -1.498E01 3.970E_02-1.973E"07 8.525E01 2.254E03 -3.618E01 1.069E_01-4.960E"10 -1.498E01 -3.618E01 3.897E00 -1.164E022.342E"12 3.970E"02 1.069E 01 -1.164E 02 4.462E~05CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.548987 -0.891538 0.642859 -0.673466PREI 0.548987 1.000000 -0.110924 -0.283453 0.243923POST -0.891538 -0.110924 1.000000 -0.918646 0.933638TIME 0.642859 -0.283453 -0.918646 1.000000 -0.999159VELO -0.673466 0.243923 0.933638 -0.999159 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 4.690E09 -4.917E09PREI 1.367E00 2.017E"02POST 9.798E"01 -3.667E _ 01TIME 4.488E01 -4.674E01VELO 2.702E04 -2.786E04

367This then gives a linear diameter for the star ofapproximately 6 solar radii. This is entirelyconsistent with the spectral and luminositycharacteristics of ZC3158. Again, assuming a distanceof 31 parsecs, an F5 star would have an absolute Vmagnitude of -0.4. This value, according to Allen, would place it between luminosity classes II andIII. Also, interpolating from Allen's tables, an F5star of this luminosity class would have a diameter ofroughly 8 solar diameters. Hence, a "ballpark" estimateof the anticipated diameter of the star shows theobservat ional 1 y determined angular diameter to be ingood agreement with what might have been inferred fromthe previously known physical properties of ZC3158.The NOISEPLOT of the raw data is presented asFigure 5-117. As can be seen in the RAWPLOT itself, thedispersion of the residual amplitudes about the meanintensity level is quite high. This is to be expectedfor photometric data whose dominant noise source is, asin this case, determined by photon arrival statistics.The POWERPLOT of the comparative power spectra(Figure 5-118) does indeed show that the background skylevel had no significant effect on the observations.The flat nature of the stai—plus-sky power spectrum istypical of photon shot noise. The only low frequencycomponents in the occultation power spectrum of anysignificance are due to diffraction fringing effects.

,368MODELCURVE]STAR + SKY, r-'100' £00 '300" '400FREQUENCY INHERTZFigure 5-113. POWERPLOT o-f the occupation o-f ZC3158,

.with no contributions -from atmospheric scintillation ortransparency variations.The Coordinated Universal Time of geometricaloccultation was 00:06:42.333 .ZC083536?The night o-f March 11, 1984 U. T., gave rise to -fouroccul tat ions which were observed -from RHO. The -first ofthese, that o-f 2C0835, occurred at approximately 00:30 U. T,and hence was observed 25 minutes be-fore the end o-fastronomical twilight. Though the sky was not yet completelydark, the brightness o-f this star led to a S+N/Nratio o-f 11.81 with a Johnson B filter. The seeing was quitegood and enabled the use of the small "J" diaphragm, as notedin the occultation summary (Table 5-57).The photoelectric record of the event is presented inFigure 5-119. The rather clean signal and precipitous dropare attributed to the good seeing, small background noise,and the brightness of the star. The integration plot(Figure 5-120) is remarkably clean and attests to thesteadiness of the sky over time-scales of tenths of secondsto seconds. There is no indication of stellar duplicity inthis f i gureThe parametric solution obtained for the 200milliseconds of observational data f i t by the DC procedure,given in Table 5-58, did give rise to a value for the stellardiameter. However, the diameter determined is Kfery close tothe lower limit of detectabi 1 i ty due to both the finite

::.370TABLE 5-572 CO 835: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: ZC0835. (SAO 077252, DM +24 0854)RA: 053232 DEC: +243711 mV: 6.92 Sp : B8Filter: B Diaphragm: J Gain: B9 Voltage: 1200LUNARINFORMATIONSurface Illumination: 53 percentElongation from Sun: 93 degreesAltitude Above Horizon: 77 degreesLunar Limb Distance: 374852 k i 1 ometersPredicted Shadow Velocity: 385 ,64 meters/secPredicted Angular Rate: .2345 arcsec/sec.EVENTINFORMATIONDate: March 11 , 1984 UT of Event: 00:39:30USNO V/O Code: 17 HA of Event: +130138Position Angle: 33.7 Cusp Angle: 36NContact Angle: +47.3 Uatts Angle: 35.2MODEL PARAMETERSNumber of Data Points: 201Number of Grid Points: 256Number of Spectral Regions: 42Width of Spectral Regions: 50 AnostromsLimb Darkening Coefficient: 0.5Effective Stellar Temperature: 12000 KSOLUTIONSStellar Diameter : 1 .08 (1 .46)Time: (relative to Bin 0): 2238 .1 (0.6)Pre-Event Signal: 2441 .7 (15.0)Background Sky Level791 .1 (18.0)Velocity (meter s/sec . ) 388 .0 (5.5)Lunar Limb Slope (degrees) : -3 .15 (0.82)U.T. of Occultation: 00 : 39 : 28 .8 (0.1)PHOTOMETRIC NOISEINFORMATIONSum-of -Squares of Residu lis: 4660483Sigma (Standard Error): 153.6513Normalized Standard Error: 0.092524Photometric (S+N)/N Ratio: 11 .80804Intensity Change/Background: 2.083527Change in Magnitude: 1 .222619

•3711.00.9 10.8 12 0.7L0.6Q 0.5LaJN3 0.4

TABLE 5-58ZC0835: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 2120372NUM OBS COMP RESID NUM OBS COMP RESID NUM OBS COMP RESID2488 2443.7 44.31 2481 2451.3 29.72 2403 2457.7 -54.73 2303 2459.4 -156.44 2330 2455.3 -125.35 2167 2447.1 -280.16 2145 2438.4 -293.47 1923 2433.4 -510.48 2141 2434.4 -293.49 2021 2441.3 -420.310 2163 2451.0 -288.011 2123 2459.4 -336.412 2372 2462.8 -90.813 2319 2459.8 -140.814 2485 2451.7 33.315 2341 2442.2 -101.216 2224 2435.3 -211.317 2219 2434.1 -215.118 2138 2439.2 -301.219 2472 2448.4 23.620 2718 2457.9 260.121 2703 2463.5 239.522 2547 2462.6 84.423 2512 2454.8 57.224 26 90 2443.0 247.025 2651 2431.4 219.626 2837 2424.8 412.227 2672 2426.6 245.428 2280 2437.4 -157.429 2499 2454.7 44.330 2520 2473.8 46.231 2571 2488.4 82.632 2638 2493.6 144.433 2419 2486.3 -67.334 2499 2467.2 31.835 2443 2439.9 3.136 2560 2410.8 149.237 2549 2387.3 161.738 2215 2376.0 -161.039 2373 2380.7 -7.740 2467 2402.2 64.841 2480 2437.2 42.842 2630 2479.5 150.543 2823 2520.9 302.144 2626 2552.9 73.145 2647 2568.8 78.246 2558 2564.3 -6.347 2627 2539.0 88.048 2419 2496.1 -77.149 2473 2441.9 31.150 2135 2384.8 -249.851 2080 2333.7 -253.752 2140 2296.9 -156.953 2240 2280.5 -40.554 2360 2287.8 72.255 2060 2318.7 -258.756 2496 2370.0 126.057 2247 2435.6 -188.658 2193 2508.0 -315.059 2375 2578.4 -203.460 2928 2638.8 289.261 2986 2682.2 303.862 2780 2703.6 76.463 2599 2700.5 -101.564 2483 2672.8 -189.865 2411 2623.0 -212.066 2516 2555.5 -39.567 2487 2476.3 10.768 2561 2392.0 169.069 2598 2309.8 288.270 2472 2236.0 236.071 2540 2176.4 363.672 2413 2135.2 277.873 2191 2115.5 75.574 2103 2118.4 -15.475 2239 2143.7 95.376 2143 2189.8 -46.877 2474 2253.9 220.178 2280 2332.4 -52.479 2463 2421.2 41.880 2907 2515.8 391.281 2861 2611.8 249.282 2769 2705.0 64.083 2794 2791.6 2.484 2782 2868.5 -86.585 2855 2933.2 -78.286 2832 2983.6 -151.687 2905 3018.6 -113.688 2860 3037.6 -177.689 3040 3040.6 -0.690 3144 3028.2 115.891 2997 3001.1 -4.192 2978 2960.6 17.493 3040 2908.1 131.994 3071 2845.3 225.795 2846 2773.7 72.396 2789 2695.1 93.997 2899 2611.1 287.998 2683 2523.3 159.799 2531 2433.0 98.0100 2160 2341.6 -181.6101 1975 2250.2 -275.2102 2100 2159.8 -59.8103 2015 2071.2 -56.2104 1895 1985.1 -90.1105 1768 1902.2 -134.2106 1715 1822.7 -107.7107 1865 1747.0 118.0108 1955 1675.3 279.7109 1746 1607.7 138.3110 1529 1544.3 -15.3111 1335 1485.0 -150.0112 1206 1429.8 -223.8113 1093 1378.5 -285.5114 1419 1331.0 88.0115 1546 1287.1 258.9116 1368 1246.7 121.3117 1238 1209.5 28.5118 1061 1175.3 -114.3119 1186 1144.0 42.0120 1021 1115.3 -94.3121 1047 1089.0 -42.0122 974 1065.0 -91.0123 839 1043.1 -204.1124 1001 1023.1 -22.1125 966 1004.9 -38.9126 954 988.2 -34.2127 867 973.1 -106.1128 954 959.2 -5.212 9 940 946.6 -6.6130 1113 935.1 177.9131 917 924.6 -7.6132 1056 915.0 141.0133 938 906.2 31.81341351361371381391401411421431441451461471488579578478398439168851010768879828807784824871149 1007150 874151 767152 792153 712154 871155 816156 889157 839158 952159 1036160 840161 665162 799163 786164 789165 862166 840167 825168 768169 776170 82 9171 861172 92 9173 888174 1001175 871176177178179180181182183184m1871881891901911921931941951961971981992008208399128027676807996497036737268067188588997236658239537507148387468137118 98.2 -41.28 90.8 66.2884.1 -37.1878.0 -39.0872.3 -29.3867.2 48.8862.4 22.6858.0 152.0854.0 -86.0850.3 28.7846.9 -18.9843.7 -36.7840.8 -56.8838.1 -14.1835.5 35.5833.2 173.8831.0 43.0829.0 -62.0827.1 -35.1825.3 -113.3823.7 47.3822.2 -6.2820.7 68.3819.4 19.6818.2 133.8817.0 219.0815.9 24.1814.9 -149.9814.0 -15.0813.1 -27.1812.3 -23.3811.5 50.5810.8 29.2810.1 14.9809.4 -41.4808.8 -32.8808.2 20.8807.6 53.4807.0 122.0806.5 81.5805.9 195.1805.4 65.6805.0 15.0804.5 34.5804.1 107.9803.7 -1.7803.3 -36.3803.0 -123.0802.7 -3.7802.4 -153.4802.1 -99.1801.8 -128.8801.6 -75.6801.3 4.7801.0 -83.0800.8 57.2800.5 98.5800.3 77.3800.0 -135.0799.8799.6799.4799.2799.0798.9798.7798.623.2153.4-49.4-85.239.0-52.914.3-87.6

aperture of the telescope and the optical bandpass. This isreflected in the -formal error o-f the determined angulardiameter which was 1.08

374COUNTSS °2GOin ^ CO« •CMi »s s s s s ISa±isn3_lni aaznvwaoN

I IMi l iH-I I I I|I I HI I I INI I|I I Ii i i i|375COMP2120 '2160 2200 2240 2280TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFioure 5-122. PDPLOT o-f the occultation o-f 2C0835.LUO zLUCCDC3u uoLlo(ZLUCO0377033S_0302 _0264 _0226 _0189015101130075 _20036 _MEAN -0.00305SIGMA 0.087367|000CJ -"'|lI |-46.6-37.9 '-29.3 '-20.7 '-12.0 -3.4 5.3 '13.9 '22.5 3L2NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFioure 5-123. NOISEPLOT o-f the occultation o-f ZC0835,I

}?6TABLE 5-59ZC0835: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO-VARIANCEMATRIXDIAM PREI POST TIME VELO5.021E~17 1.821E"08 -1.885E08 -3.245E"10 3.783E~121.821E~08 2.259E02 1.218E01 -2.286E0O 1.933E_021.885E~08 1.218E01 3.239E02 -2.984E00 2.444E_023.245E~10 -2.286E00 -2.984E00 3.202E_01 -2.679E_033.783E"12 1.933E"02 2.444E 02 -2.679E 03 3.033E 05CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.749272 -0.771171 0.169356 -0.150545PREI 0.749272 1.000000 -0.156314 -0.523365 0.539440POST -0.771171 -0.156314 1.000000 -0.756773 0.744181TIME 0.169356 -0.523365 -0.756773 1.000000 -0.999818VELO -0.150545 0.539440 0.744181 -0.999818 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 4.426E09 -4.589E09PREI 1.363E00 4.073E~03POST 9.959E"01 -3.630E 01TIME 9.160E01 -9.600E01VELO 1.081E04 -1.121E04

1 1''377MODEL CURVE-I 1 1 1STAR +1•"SKYT 11 11"T*—1OCCULTATION5T- 1—!l300 '4FREQUENCY IN HERTZ: r100^ "200"Figure 5-124. POWERPLOT o-f the occultation o-f 2C0835.

378time of geometrical occultation was determined to be00:39:23.3

II37?4096368632772867J 2458 o C_ 2048 5en_16381 1229flwlfl^ww^512 '1024 '1536 2048 '2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWFigure 5-125. RAUPLOT o-f the occultation of X07145,i512 1024 1536 '2048 '2560 '3072 '3584TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWFigure 5-126. INTPLOT o-f the occultation o-f X07145.

.380TABLE 5-60X07145: LUNAR OCCULTA"!" I ON SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X07145

TABLE 5-61X07145: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 2025381_NUM~OBS~~COMP "iisiD " "~NUm"oBS COMP RESID NUM OBS COMP RESID_1885 1549.2 335.81 1539 1547.3 -8.32 1609 1547.7 61.33 1703 1550.4 152.64 1791 1553.1 237.95 1680 1553.0 127.06 1520 1550.0 -30.07 1527 1546.6 -19.68 1718 1545.8 172.29 1574 1548.6 25.410 1671 1552.8 118.211 1347 1555.0 -208.012 1256 1553.1 -297.113 1626 1548.6 77.414 1416 1545.0 -129.015 1447 1545.4 -98.416 1511 1549.5 -38.517 1701 1554.3 146.718 1409 1556.1 -147.119 1359 1553.4 -194.420 1387 1548.0 -161.021 1337 1544.0 -207.022 1458 1544.5 -86.523 1331 1549.5 -218.524 1555 1555.8 -0.825 1451 1558.9 -107.926 1477 1556.2 -79.227 1571 1548.9 22.128 1520 1541.3 -21.329 1543 1538.4 4.630 1760 1543.0 217.031 1552 1553.3 -1.332 1503 1564.0 -61.033 1589 1569.1 19.934 1647 1564.9 82.135 1652 1552.2 99.836 1408 1536.5 -128.537 1388 1525.2 -137.238 1291 1524.5 -233.539 1425 1535.9 -110.940 1613 1556.1 56.941 1735 1577.2 157.842 1629 1590.5 38.543 1565 1590.0 -25.044 1381 1574.5 -193.545 1367 1548.3 -181.346 1507 1520.0 -13.047 1363 1499.5 -136.548 1312 1494.3 -182.349 1424 1507.2 -83.250 1615 1535.6 79.451 1927 1571.9 355.152 1692 1606.0 86.053 1419 1628.1 -209.154 1544 1631.6 -87.655 1740 1614.7 125.356 1540 1580.8 -40.857 1401 1537.4 -136.458 1463 1494.4 -31.459 1481 1461.6 19.460 1620 1446.5 173.561 1484 1452.7 31.362 1405 1479.7 -74.763 1444 1522.8 -78.864 1721 1574.4 146.665 1611 1625.5 -14.566 1338 1667.5 -329.567 1438 1693.5 -255.568 1504 1699.3 -195.369 1679 1684.0 -5.070 1928 1649.7 278.371 1881 1601.1 279.972 1518 1544.4 -26.473 1673 1486.7 186.374 1703 1434.9 268.175 1446 1394.7 51.376 1409 1370.4 38.677 1232 1364.2 -132.278 1299 1376.7 -77.779 1401 1406.4 -5.480 1676 1450.8 225.281 1560 1506.0 54.082 1484 1567.9 -83.983 1438 1631.9 -193.984 1433 1694.0 -261.085 2038 1750.5 287.586 2201 1798.3 402.787 2143 1835.3 307.788 1956 1860.0 96.089 1516 1871.9 -355.990 1918 1870.9 47.191 2015 1857.8 157.292 1937 1833.5 103.593 1936 1799.4 136.694 1931 1757.1 173.995 1783 1708.2 74.896 1732 1654.4 77.697 1506 1597.0 -91.098 1448 1537.7 -89.799 1484 1477.6 6.4100 1471 1417.8 53.2101 1356 1359.2 -3.2102 1455 1302.5 152.5103 1185 1248.2 -63.2104 995 1196.8 -201.8105 1009 1148.6 -139.6106 871 1103.5 -232.5107 1079 1061.8 17.2108 752 1023.4 -271.4109 1160 988.2 171.8110 909 956.1 -47.1111 891 927.0 -36.0112 857 900.5 -43.5113 915 876.7 38.3114 785 855.2 -70.2115 749 835.8 -86.8116 864 818.5 45.5117 870 802.9 67.1118 758 789.0 -31.0119 772 776.6 -4.6120 736 765.4 -29.4121 695 755.5 -60.5122 719 746.6 -27.6123 841 738.6 102.4124 791 731.5 59.5125 719 725.1 -6.1126 752 719.4 32.6127 595 714.3 -119.3128 717 709.7 7.3129 712 705.6 6.4130 755 701.8 53.2131 840 698.5 141.5132 603 695.5 -92.5133 829 692.8 136.2134 735 690.3 44.7135 587 688.0 -101.0136 797 686.0 111.0137 677 684.1 -7.1138 628 682.5 -54.5139 655 680.9 -25.9140 672 679.5 -7.5141 819 678.2 140.8142 597 677.0 -80.0143 641 675.9 -34.9144 739 674.9 64.1145 742 674.0 68.0146 519 673.1 -154.1147 675 672.3 2.7148 712 671.6 40.4149 715 671.0 44.0150 787 670.4 116.6151 759 669.8 89.2152 740 669.3 70.7153 574 668.8 -94.8154 781 668.4 112.6155 574 667.9 -93.9156 687 667.5 19.5157 828 667.1 160.9158 847 666.8 180.2159 705 666.4 38.6160 507 666.1 -159.1161 558 665.8 -107.8162 591 665.5 -74.5163 749 665.2 83.8164 897 664.9 232.1165 593 664.7 -71.7166 709 664.5 44.5167 583 664.3 -81.3168 697 664.1 32.9169 617 664.0 -47.0170 728 663.8 64.2171 557 663.6 -106.6172 675 663.4 11.6173 814 663.3 150.7174 909 663.1 245.9175 668 662.9 5.1176 613 662.8 -49.8177 800 662.7 137.3178 653 662.6 -9.6179 644 662.5 -18.5180 472 662.4 -190.4181 577 662.3 -85.3182 597 662.2 -65.2183 622 662.1 -40.1184 671 662.0 9.0185 689 661.9 27.1186 631 661.8 -30.8187 638 661.7 -23.7188 613 661.6 -48.6189 643 661.5 -18.5190 673 661.5 11.5191 677 661.4 15.6192 569 661.3 -92.3193 461 661.3 -200.3194 644 661.2 -17.2195 595 661.1 -66.1196 731 661.1 69.9197 663 661.0 2.0198 679 661.0 18.0199 827 660.9 166.1200 661 660.9 0.1

382were -fewer observed points per diffraction fringe than forthe previous event. Nevertheless, the fit was quite good, asan examination of the FITPLOT will reveal. Thevari ance/covari ance and correlation matrices of the solutionparameters are given in Table 5-62.The PDPLOT for this event is shown as Figure 5-128. Asmall amount of numerical noise was present in thecomputation of the partial derivative of the intensity curvewith respect to the angular diameter. This numerical noise,however, was present only in the partial derivatives fortimes early in the solution space. At those times, as isapparent in the PDPLOT, the intensity curve was veryinsensitive to changes in the diameter. Hence, in this casethe numerical noise which arose did not adversely affect thefinal solution determination.The best fit to the observations was for the intensitycurve of a point source. Thus, the angular diameter ofX07145 was below the capability of detection by theoccultation method.The distribution function of the residual amplitudes,seen in Figure 5-192, is similar to that previously shown forthe previous event. In this case, due to a smaller stellarsignal in comparison to a slightly more variable background,a Poisson tail can be seen in the distribution function.The POWERPLOT (Figure 5-130) indicates that thefrequency components that are of most importance in the

383CMSCMCOUNTS00 CD ins-^tLfl rs 0?GO CD in COLDa_lisn3.lni a^ziivwaoN

384TABLE 5-62X07145: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO-VARIANCEMATRIXDIAM PREI POST TIME VELO1.430E"16 2.593E"08 -2.853E~08 -4.964E 10 8.640E 122.593E"08 1.703E02 4.570E00 -2.251E00 2.834E_02•2.853E~08 4.570E00 2.231E02 -2.817E00 3.503E_02•4.964E~10 -2.251E00 -2.817E00 5.799E_01 -7.327E 038.640E"12 2.834E"02 3.503E02 -7.327E03 1.271E04CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.750746 -0.795461 0.161136 -0.153926PREI 0.750746 1.000000 -0.197010 -0.523228 0.529208POST -0.795461 -0.197010 1.000000 -0.721394 0.716211TIME 0.161136 -0.523228 -0.721394 1.000000 -0.999972VELO -0.153926 0.529208 0.716211 -0.999972 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 2.566E09 -2.506E09PREI 1.365E00 2.485E"03POST 9.975E~01 -3.653E"01TIME 6.013E01 -6.378E01VELO 4.735E03 -4.868E03

III I I 1|I I I I|I II I[385COMP2025 2065 2105 2145 2185TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-128. PDPLOT o-f the occultation o-f X07145.LUO zUJcc30194uo 0162u.occUJ03•xr>03240292_ MEAN 0.00832025£_ SIGMA 0.0998120227 _01300097 _006E_20032 _10002 J-67.8-57.2-46.6-35.9-25.3-14.7-4.1 6.5 17.1 '27.8NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-129. NOISEPLOT of the occultation o-f X07145,

336MODELCURVESTARSKY">rOCCULTATION5~ '100' •200" 300~ '400'FREQUENCY IN HERTZFigure 5-130. POWERPLOT o-f the occultation o-f X07145,

387occultation spectral signature dominate oyer those in thestar-plus-sky signal.Geometrical occultation was -found to have occurred at01:28:05.604 (+/- 0.006 seconds) Coordinated Universal Time.XQ7202The third event observed on the night of March 11, 1933U. T., was the disappearance of X07202. This K2 star wassubstantially -fainter

388TABLE 5-63X07202: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X07202,

58?%512 1024 1536 2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-131. RAUPLOT o-f the occultation o-f X07202.52 0.8Go 21024 1536 2048 2560 3072 3584TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-132. INTPLOT o-f the occultation o-f X07202.

390DISTANCE TO THE GEOMETRICAL SHADOW IN METERSLq ^ -100 -80 -60 -40 -20 20 40 60 80 100 p^fl.q2125 2165 2205 2245 2285TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFioure 5-133. FITPLOT o-f the occultation o-f X07202.DISTANCE TO THE GEOMETRICAL SHADOW IN METERSU3 _ -50 -40 -30 -20 -10 10 20 30 40 ?d?d2175 21S5 2215 2235 2255TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-134. Detailed FITPLOT o-f the occultation o-f X0702showino the raw -fit to a smoothed data set.

meters/second, was considerably -faster. Thus, the observeddi -f-fract ion fringes were comprised o-f correspondi ngl y -fewer391observed data points than expected. This, in addition to thelower signal intensity, was responsible -for the somewhatlarger statistical uncertainties in the solution parameters.In order to allow a better visualization o-f thesolution, the computed intensity curve is shown in detail(over 100 milliseconds only) in Figure 5-134. The observeddata were subjected to 5-point smoothing be-fore being plottedon the detailed computed curve.As expected, no diameter was determined. The PDPLOTillustrating the partial derivatives o-f the computedintensity curve is shown in Figure 5-135. Unquestionably,the regions o-f sensitivity to parametric variation were wellcovered in the solution. The observed and computedintensities and the residuals are given in Table 5-64. Thevar iance/covar i ance and correlation matrices o-f the solutionparameters and the numerical ranges o-f the partialderivatives are contained in Table 5-65.The NOISEPLOT (Figure 5-136), as expected, is a bit moreskewed toward a Poisson distribution than that o-f theprevious event. Also, not unexpectedly, the one sigma widtho-f the distribution was increased to 11.98 percent.The POWERPLOT -for this event indicates that the powercomponents o-f the star-plus-sky signal at low -frequencieswere comparable to that o-f the occultation signal itself.Thus, any type o-f Fourier smoothing was out o-f the question.

,3922125 '2165 '2205 '2245 2285TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFioure 5-135. PDPLOT of the occultation o-f X07202.0002^-ii6.2'-iaL2'-ae.2 -7L2 '-56.2'-4L2 -26.1 -U.1 3.9 18.9NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYFigure 5-136. NOISEPLOT o-f the occultation o-f X07202,

TABLE 5-64X07202: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 2125393NUM OBS COMP RE SID1684 1680.8 3.21 1513 1680.7 -167.72 1321 1680.8 -359.83 1740 1680.7 59.34 1601 1680.7 -79.75 1584 1680.7 -96.76 1633 1680.7 -47.77 1620 1680.7 -60.78 1341 1680.7 -339.79 1757 1680.7 76.310 1747 1680.7 66.311 1763 1680.7 82.312 1800 1680.7 119.313 1815 1680.6 134.414 1633 1680.8 -47.815 1753 1680.6 72.416 1685 1680.7 4.317 1664 1680.6 -16.618 1571 1680.7 -109.719 1552 1680.6 -128.620 1711 1680.6 30.421 1797 1680.7 116.322 1639 1680.5 -41.523 1604 1680.7 -76.724 1771 1680.5 90.525 1423 1680.7 -257.726 1592 1680.6 -88.627 1445 1680.6 -235.628 1410 1680.6 -270.629 1665 1680.7 -15.730 2161 1680.5 480.531 1728 1680.8 47.232 1575 1680.5 -105.533 1912 1680.7 231.334 1983 1680.5 302.535 1587 1680.7 -93.736 1823 1680.4 142.637 1647 1680.7 -33.738 1300 1680.7 -380.739 2239 1680.4 558.640 1659 1681.0 -22.041 1602 1680.3 -78.342 1706 1680.9 25.143 1656 1680.6 -24.644 1667 1680.3 -13.345 1664 1681.5 -17.546 1655 1679.9 -24.947 1696 1680.5 15.548 1777 1682.1 94.949 1399 1679.4 -280.450 1668 1680.3 -12.351 1668 1682.8 -14.852 2054 1679.5 374.553 1652 1679.6 -27.654 1543 1683.2 -140.255 1419 1680.3 -261.356 1652 1678.5 -26.557 1904 1683.4 220.658 1649 1682.4 -33.459 1561 1676.3 -115.360 1775 1680.4 94.661 2063 1688.5 374.562 1770 1682.0 88.063 1443 1670.2 -227.264 1817 1676.7 140.365 1439 1694.9 -255.966 1662 1694.8 -32.8NUM OBS COMP RES ID67 1487 1671.7 -184.768 1496 1657.0 -161.069 1595 1674.3 -79.370 1979 1706.0 273.071 1511 1714.3 -203.372 1987 1686.4 300.673 1500 1648.5 -148.574 1418 1637.6 -219.675 1783 1666.2 116.876 1689 1713.0 -24.077 1631 1742.9 -111.978 1872 1734.3 137.779 2059 1692.0 367.080 1556 1640.1 -84.181 1325 1606.0 -281.082 1241 1605.7 -364.783 1660 1639.1 20.984 1568 1693.4 -125.485 2395 1750.6 644.486 2287 1795.0 492.087 1847 1817.1 29.988 1900 1814.0 86.089 1669 1788.6 -119.690 1825 1746.9 78.191 1534 1695.4 -161.492 1919 1640.5 278.593 1598 1586.7 11.394 1503 1537.1 -34.195 1316 1493.5 -177.596 1608 1456.4 151.697 1319 1425.6 -106.698 1581 1400.5 180.599 1497 1380.4 116.6100 1575 1364.4 210.6101 1561 1351.7 209.3102 1476 1341.8 134.2103 1216 1333.9 -117.9104 1315 1327.8 -12.8105 1257 1322.9 -65.9106 1295 1319.1 -24.1107 1287 1316.0 -29.0108 1278 1313.5 -35.5109 1295 1311.5 -16.5110 1064 1309.9 -245.9111 1284 1308.5 -24.5112 1195 1307.4 -112.4113 1031 1306.5 -275.5114 1523 1305.7 217.3115 1428 1305.1 122.9116 1109 1304.5 -195.5117 1237 1304.1 -67.1118 1380 1303.7 76.3119 1219 1303.3 -84.3120 1149 1303.0 -154.0121 1268 1302.7 -34.7122 1004 1302.4 -298.4123 1235 1302.2 -67.2124 1567 1302.1 264.9125 1097 1301.9 -204.9126 1296 1301.7 -5.7127 1405 1301.6 103.4128 1228 1301.5 -73.5129 1365 1301.4 63.6130 1321 1301.3 19.7131 1447 1301.2 145.8132 1427 1301.1 125.9133 1092 1301.0 -209.0NUM OBS COMP RESID134 1067 1300.9 233.9135 1382 1300.9 81.1136 1421137 1499 1188:1 HH138 1112 1300.7 -188.7139 1453 1300.7 152.3140 1708 1300.6 407.4141 1405 1300.6 104.4142 1631 1300.5 330.5143 1448 1300.5 147.5144 1127 1300.5 -173.5145 1151 1300.4 -149.4146 1220 1300.4 -80.4147 1333 1300.4 32.6148 1181 1300.4 -119.4149 1345 1300.3 44.7150 1209 1300.3 -91.3151 1428 1300.3 127.7152 1177 1300.3 -123.3153 1145 1300.2 -155.2154 1059 1300.2 -241.2155 979 1300.2 -321.2156 1332 1300.2 31.8157 1386 1300.2 85.8158 1178 1300.2 -122.2159 1432 1300.1 131.9160 1252 1300.1161 1047 1300.1162 1167 1300.1163 1281 1300.1164 1323 1300.1165 1206 1300.1166 1479 1300.1167 1637 1300.1168 1157 1300.0169 1088 1300.0170 1343 1300.0171 1331 1300.0172 1607 1300.0173 1280 1300.0174 1539 1300.0175 1370 1300.0176 1563 1300.0177 1224 1300.0178 1278 1300.048.1253.1133.1-19.122.9-94.1178.9336.9143.0212.043.031.0307.0-20.0239.070.0263.076.022.0179 950 1300.0 -350.0180 1145 1300.0 -155.0181 1526 1300.0 226.0182 1116 1299.9 -183.9183 1028 1299.9 -271.9184 1301 1299.9 1.1185 1451 1299.9 151.1186 1609 1299.9 309.1187 1691 1299.9 391.1188 1336 1299.9 36.1189 1370 1299.9 70.1190 1152 1299.9 -147.9191 1117 1299.9 -182.9192 1547 1299.9 247.1193 1214 1299.9 -85.9194 1207 1299.9 -92.9195 1326 1299.9 26.1196 1141 1299.9 -158.9197 1380 1299.9 80.1198 1423 1299.9 123.1199 1405 1299.9 105.1200 1349 1299.9 49.1

394TABLE 5-65X07202: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO- VARIANCE MATRIXDIAM PREI POST TIME VELO4.401E"13 1.328E"06 -8.203E 07 -7.665E 08 5.838E 091.328E"06 3.429E02 5.490E00 -4.822E00 2.791E_018.203E"07 5.490E00 3.303E02 -4.658E00 2.704E017.665E"08 -4.822E00 -4.658E00 2.549E00 -1.489E_015.838E"09 2.791E"01 2.704E"01 -1.489E01 1.218E02CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.886113 -0.638250 -0.216493 0.214986PREI 0.886113 1.000000 -0.210694 -0.610273 0.607797POST -0.638250 -0.210694 1.000000 -0.582763 0.582383TIME -0.216493 -0.610273 -0.582763 1.000000 -0.999953VELO 0.214986 0.607797 0.582383 -0.999953 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 6.264E08 -6.116E08PREI 1.362E00 4.004E~04POST 9.996E"01 -3.620E~01TIME 5.504E01 -5.869E01VELO 9.125E02 -8.903E02

SSiT"395MODEL CURVE5'"1200 §00^ 400 "1FREQUENCY IN HERTZFigure 5-137. POWERPLOT o-f the occultation o-f X07202.

396The determined Coordinated Universal Time o-f geometricaloccultation was 02:15:30.346 (+/- 0.012) seconds.XQ7247The relatively -faint

:397TABLE 5-66X07247: LUNAR OCCULTATI ON SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X07247, (SAO 077341, DM +24 0895)RA: 053708 DEC: +241825 mV: 8.9 Sp:B9Filter: B Diaphragm: J Gain: C7+ Voltage: 1100LUNARINFORMATIONSurface Illumination:54 percentElongation -from Sun:94 degreesAltitude Above Horizon:44 deoreesLunar Limb Distance: 375983 k i 1 ometersPredicted Shadow Velocity: 618.7 meters/sec.Predicted Angular Rate: 0.3394 arcsec/sec.EVENTINFORMATIONDate: March 11, 1984 UT of Event 03:17:08USNO V/O Code: 14 HA of Event +512416Position Angle: 126.3 Cusp Anole: 51SContact Angle: -36.1 Uatts Angl e 127.5MODEL PARAMETERSNumber of Data Points:201Number of Grid Points: 256Number of Spectral Reoions: 50Uidth of Spectral Regions: 42 An QstromsLimb Darkening Coefficient: 0.5Effective Stellar Temperature: 5100 KSOLUTIONSStellar Diameter : Point SourceTime: (relative to Bin 0): 1218.9 (3.4)Pre-Event Signal: 1967.4 (15.4)Background Sky Level: 1647.7 (31.3)Velocity (meters/second): 444.3 (44.1)Lunar Limb Slope (degrees): -20.1 (7.4)U.T. of Occultation: 03:17:07.618 (0.004)PHOTOMETRIC NOISEINFORMATIONSum-of-Squares of Residuals: 7116248Sigma (Standard Error): 188.6304Normalized Standard Error: 0.59007Photometric (S+N)/N Ratio: 2.6937(Change in Intensi ty)/Background: 0.19401Change in Magnitude: 0.19252

1398TIME%112 1024 1536 '2048 '2560 3072 3584IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-138. RAWPLOT o-f the occultation of X07247,L0 r-£ 0.9 -0.82_LU^$ 0.7t—c 0.6uN 0.5

399COaoOJCDinOJCMCOOJISOJOJCOUNTSOJ \S) 00 -r^LO OJ CD [NCD 00 CO LHOJ zit15 ^A_LISN3J_NICBZUVWdON

X07247: OBSERVATIONS,400TABLE 5-67COMPUTED VALUES, AND RESIDUALS FROM BIN 1060NUM OBS COMP RES ID NUM OBS COMP RES ID NUM OBS COMP RES ID1948 1968.4 -20.4 67 2013 1969.6 43.4 134 2202 2083.5 118.51 1696 1968.2 -272.2 68 1856 1970.9 -114.9 135 2330 2079.3 250.72 1781 1968.2 -187.2 69 1981 1971.0 10.0 136 2171 2071.5 99.53 1872 1968.4 -96.4 70 2505 1969.8 535.2 137 2453 2060.3 3 92.74 1928 1968.4 -40.4 71 1873 1968.3 -95.3 138 2118 2046.4 71.65 1925 1968.2 -43.2 72 1867 1967.2 -100.2 139 1760 2030.1 -270.16 1872 1968.2 -96.2 73 1973 1967.2 5.8 140 1861 2012.0 -151.07 2009 1968.3 40.7 74 2320 1968.0 352.0 141 2032 1992.6 39.48 1835 1968.5 -133.5 75 2137 1969.0 168.0 142 2093 1972.4 120.69 1949 1968.3 -19.3 76 2107 1969.6 137.4 143 2092 1951.8 140.210 1669 1968.1 -299.1 77 1911 1969.1 -58.1 144 2139 1931.1 207.911 1701 1968.1 -267.1 78 2231 1967.9 263.1 145 1880 1910.7 -30.712 1708 1968.5 -260.5 79 1888 1966.7 -78.7 146 1688 1890.8 -202.813 2157 1968.7 188.3 80 2120 1966.4 153.6 147 1925 1871.6 53.414 1904 1968.4 -64.4 81 1670 1967.6 -297.6 148 1923 1853.3 69.715 1847 1968.0 -121.0 82 1561 1970.1 -409.1 149 18 90 1835.9 54.116 2586 1968.0 618.0 83 1914 1973.2 -59.2 150 1433 1819.6 -386.617 2056 1968.4 87.6 84 1952 1975.3 -23.3 151 1785 1804.4 -19.418 1912 1968.8 -56.8 85 2145 1975.4 169.6 152 1724 1790.3 -66.319 1989 1968.6 20.4 86 1821 1972.8 -151.8 153 1805 1777.2 27.8-57.0 1885 1765.2 119.820 1950 1968.1 -18.1 87 1911 1968.0 15421 1955 1967.9 -12.9 88 1732 1962.4 -230.4 155 1611 1754.2 -143.222 1829 1968.2 -139.2 89 1815 1957.7 -142.7 156 1527 1744.2 -217.223 2141 1968.6 172.4 90 1873 1955.9 -82.9 157 1905 1735.1 169.924 2271 1968.6 302.4 91 2252 1957.9 294.1 158 1483 1726.8 -243 .825 2040 1968.2 71.8 92 22 97 1963.7 333.3 159 1923 1719.3 203.726 2163 1967.9 195.1 93 1781 1972.1 -191.1 160 1664 1712.6 -48.627 1995 1968.2 26.8 94 1595 1981.1 -386.1 161 1721 1706.5 14.528 1914 1968.6 -54.6 95 2004 1988.2 15.8 162 1768 1701.0 67.029 1996 1968.8 27.2 96 2348 1991.4 356.6 163 1317 1696.1 -379.11989.4 -85.4 164 1509 1691.6 -182.630 1969 1968.3 0.7 97 190431 2177 1967.8 209.2 98 1967 1982.4 -15.4 165 1743 1687.6 55.432 2100 1967.8 132.2 99 2120 1971.5 148.5 166 1550 1684.0 -134.033 2027 1968.4 58.6 100 1866 1958.9 -92.9 167 1646 1680.8 -34.834 1746 1969.1 -223.1 101 1714 1947.3 -233.3 168 1718 1677.9 40.135 1855 1969.1 -114.1 102 2117 1939.2 177.8 169 1514 1675.3 -161.336 1896 1968.3 -72.3 103 2161 1936.4 224.6 170 1519 1673.0 -154.037 1774 1967.5 -193.5 104 2088 1939.8 148.2 171 1769 1670.9 98.138 1928 1967.4 -39.4 105 1935 1949.0 -14.0 172 2107 1669.0 438.039 1681 1968.1 -287.1 106 1888 1962.7 -74.7 173 1907 1667.3 239.740 2059 1969.1 89.9 107 2242 1978.8 263.2 174 1528 1665.7 -137.741 1919 1969.4 -50.4 108 1988 1994.6 -6.6 175 1496 1664.4 -168.442 2048 1968.9 79.1 109 1807 2007.8 -200.8 176 1875 1663.1 211.943 2127 1968.0 159.0 110 2191 2016.2 174.8 177 1640 1662.0 -22.044 2182 1967.5 214.5 111 1927 2018.5 -91.5 178 1383 1660.9 -277.945 2011 1967.8 43.2 112 2099 2014.4 84.6 179 1653 1660.0 -7.046 1991 1968.5 22.5 113 2180 2004.2 175.8 180 1679 1659.2 19.847 1614 1969.0 -355.0 114 2096 1989.1 106.9 181 2031 1658.4 372.648 2143 1968.8 174.2 115 1771 1971.0 -200.0 182 1602 1657.7 -55.749 2227 1968.2 258.8 116 1687 1952.0 -265.0 183 1707 1657.0 50.050 2278 1968.0 310.0 117 1642 1934.0 -292.0 184 1756 1656.4 99.651 16 96 1968.3 -272.3 118 1675 1919.1 -244.1 185 1617 1655.9 -38.952 2037 1968.9 68.1 119 2024 1908.7 115.3 186 1907 1655.4 251.653 2071 1969.3 101.7 120 1965 1903.8 61.2 187 1571 1654.9 -83.954 2280 1968.9 311.1 121 1701 1904.9 -203.9 188 1539 1654.5 -115.555 2141 1967.9 173.1 122 1696 1911.9 -215.9 189 16 96 1654.1 41.956 1715 1967.1 -252.1 123 2087 1924.1 162.9 190 1695 1653.8 41.257 1834 1967.1 -133.1 124 2149 1940.6 208.4 191 1746 1653.4 92.658 1784 1968.2 -184.2 125 2059 1960.2 98.8 192 1656 1653.1 2.959 2347 1969.7 377.3 126 1969 1981.6 -12.6 193 1736 1652.8 83.260 2212 1970.7 241.3 127 1900 2003.3 -103.3 194 1759 1652.6 106.461 223 9 1970.4 268.6 128 1571 2024.2 -453.2 195 1663 1652.3 10.762 1997 1969.0 28.0 129 1769 2043.0 -274.0 196 1655 1652.1 2.963 1971 1967.1 3.9 130 1852 2058.9 -206.9 197 1696 1651.9 44.164 1787 1966.0 -179.0 131 2308 2071.2 236.8 198 1696 1651.7 44.365 1684 1966.2 -282.2 132 1965 2079.5 -114.5 199 1402 1651.5 -249.566 2095 1967.7 127.3 133 1774 2083.6 -309.6 200 1640 1651.4 -11.4

401The PDPLOT of the solution intensity curve(Figure 5-141) shows nothing unusual or o-f concern in thefinal numerical computations o-f the partial derivatives. Thenumerical ranges o-f the partial derivatives, as well as theusual supplementary statistics, are listed in Table 5-48.The stellar signal itsel-f was only 319.7 counts, or only19.4 percent of the background level. Hence, the slow rise(over 4096 milliseconds) in the now strongly dominantbackground contribution resulted in a stronger Poisson tailin the distribution function of the residuals (seeFigure 5-142).The Coordinated Universal Time of geometricaloccultation for X07247 was 03:17:07.618 (+/0.004 seconds).The four events which occurred on this night were ofprogressively fainter stars, observed under similarconditions. It i s of interest to compare the degradation ofthe solutions (in terms of the formal errors of thedetermined parameters), the broadening and increasing Poissonnature of the residual amplitude distributions, and theincreasing dominance of the low frequency power contributionsin the pre-occul tat ion (stai—plus-sky) signal. The lattercan be seen for X07202 in Figure 5-143.X09514The first of two occul tat ions observed on the night ofMarch 12, 1984 U. T., was that of the K5 star X09514. Due toan intermittent problem in the A-to-D converter inputselected for this event, approximately half of the data which

II I I III I I III I I I|I I I I|I I I I | I I I I | I H4021060 1100 U40 U80 1220TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-141. PDPLOT o-f the occultation of X07247.U)0242_0218 _ MEAN -0.02316UJo2LU0194 _0169.SIGMA 0.094275enaDUo000CRH UJdJXWJ Ilj-53.3-45.1-38.8-28.6-20.4-12.1 -3.9 4.4 12.6 20.8NOISE LEVEL AS A PERCENTAGE OF COMPLTTED INTENSITYFigure 5-142. NOISEPLOT o-f the occultation o-f X07247.

403TABLE 5-68X07247: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO-VARIANCE MATRIXDIAM PREI POST TIME VELO1.371E"14 2.264E 07 -6.947E 07 -1.822E _ 08 3.630E_102.264E"07 2.457E02 2.824E01 -1.200E01 1.398E 01•6.947E"07 2.824E01 1.031E03 -4.002E01 4.384E - 011.822E"08 -1.200E01 -4.002E01 1.149E01 -1.297E~013.630E"10 1.398E 01 4.384E 01 -1.297E _ 01 1.972E 03CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.405449 -0.944025 0.762444 -0.749555PREI 0.405449 1.000000 -0.083764 -0.242888 0.260790POST -0.944025 -0.083764 1.000000 -0.927240 0.919840TIME 0.762444 -0.242888 -0.927240 1.000000 -0.999806VELO -0.749555 0.260790 0.919840 -0.999806 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 3.548E08 -3.771E08PREI 1.363E00 1.138E 02POST 9.886E"01 -3.634E 01TIME 2.070E01 -2.166E01VELO 1.838E03 -1.876E03

''300'1'404MODELCURVE"" 1 'STAR +1"SKYT1rOCCULTATION'100 £00" "FREQUENCY IN'400'HERTZFigure 5-143. POWERPLOT o-f the occultation o-f X07247,

405should have been acquired were not. This problem was notknown to exist at the time of the event but came to lighta-fter the -fact. Fortunately, data dropouts did not occurduring the occultation event itself, and hence, did notadversely affect the solution process. The RAWPLOT

4062177 2417 2857 '2897 '3137 '3377 '3617 '3857TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFigure 5-144. RAWPLOT o-f the occupation o-f X89514.0)zLUDUl•— ._l

407TABLE 5-69X09514: LUNAR OCCULTATION SUMMARYSTELLAR AND OBSERVINGINFORMATIONStar: X09514, (SAO 078598, DM +25 1364)RA: 063835 DEC: +253153 mV: 8.7 Sp : K5Filter: B Diaphragm: J Gain: C7+ Voltage: 1200LUNARSur-face Illumination:Elongation from Sun:Altitude Above Horizon:Lunar Limb Distance:Predicted Shadow Velocity:Predicted Angular Rate:EVENTDate: March 12, 1984USNO V/O Code: 14Position Angle: 61.2Contact Angle: +37.1INFORMATION65 percent107 decrees51 deorees369551 k i 1 ome ters606 .3 meters/sec.3384 arcsec/secINFORMATIONMODEL PARAMETERSUT o-f Event: 03:45:29HA of Event: +440653Cusp Angle: 57NWatts Anole: 56.4Number of Data Points: 201Number of Grid Points: 256Number of Spectral Regions: 53Width of Spectral Regions: 50 AngstromsLimb Darkening Coefficient: 0.5Effective Stellar Temperature: 4200 KSOLUTIONSStellar Diameter : Point SourceTime: (relative to Bin 0): 3918.4 (3.7)Pre-Event Signal: 2596.5 (21.8)Backoround Sky Level 2305.5 (26.3)Velocity (meters/sec): 621.6 (77.2)Lunar Limb Slope (degrees): -6.36 (7.29)U.T. of Occultation: 03:35:32.8 (0.1)PHOTOMETRIC NOISEINFORMATIONSum-of-Squares of Residuals: 10568390Sigma (Standard Error): 229.8738Normalized Standard Error: 0.78984Photometric (S+N)/N Ratio: 2.26608(Change in Intensi ty)/Background: 0.12624Change in Magnitude: 0.12908

403COUNTSQ \s) CD ^r CD ^r ccCMS ID S (D -r-l NCM S CO N CD ^r 0)(T) cu CM CM CM CM COCDCOCOCOQCMCMCDCO13 °>^5 S Sa±isn3-LniaaznvwdON

TABLE 5-70X09514: OBSERVATIONS, COMPUTED VALUES, AND RESIDUALS FROM BIN 380040?NUM OBS COMP RESID NUM OBS COMP RESID NUM OBS COMP RESID2815 2597.3 217.7 67 2529 2623.6 -94.6 134 1951 2317.1 -366.11 3014 2597.2 416.8 68 2623 2621.9 1.1 135 2599 2316.1 282.92 2716 2597.3 118.7 69 2733 2611.6 121.4 136 2651 2315.2 335.83 2515 2597.3 -82.3 70 2479 2595.6 -116.6 137 2368 2314.4 53.64 2520 2597.2 -77.2 71 2606 2579.1 26.9 138 2287 2313.7 -26.75 2575 2597.1 -22.1 72 2456 2567.2 -111.2 139 1996 2313.0 -317.06 2224 2597.3 -373.3 73 2272 2563.7 -291.7 140 2161 2312.5 -151.57 2327 2597.5 -270.5 74 25 91 2569.9 21.1 141 2847 2311.9 535.18 2725 2597.3 127.7 75 2619 2584.5 34.5 142 2699 2311.5 387.59 2383 2597.0 -214.0 76 2883 2604.0 279.0 143 2086 2311.0 -225.010 2859 2597.2 261.8 77 3010 2623.6 386.4 144 2395 2310.7 84.311 2956 2597.5 358.5 78 2527 2638.7 -111.7 145 2772 2310.3 461.712 2605 2597.5 7.5 79 2578 2645.9 -67.9 146 227 9 2310.0 -31.013 3063 2597.2 465.8 80 2659 2643.6 15.4 147 2583 2309.7 273.314 2044 2597.0 -553.0 81 2926 2632.2 2 93.8 148 243 9 2309.5 129.515 2479 2597.4 -118.4 82 2808 2613.9 194.1 149 2052 2309.2 -257.216 3200 2597.6 602.4 83 2600 2591.9 8.1 150 2512 2309.0 203.017 2870 2597.3 272.7 84 2531 2570.1 -39.1 151 2168 2308.8 -140.818 1747 2596.9 -849.9 85 2643 2551.9 91.1 152 2039 2308.6 -269.619 2451 2597.1 -146.1 86 2317 2540.2 -223.2 153 2135 2308.5 -173.520 2715 2597.7 117.3 87 2728 2536.5 191.5 154 2159 2308.3 -149.321 2666 2597.8 68.2 88 2502 2541.4 -39.4 155 2675 2308.2 366.822 2680 2597.1 82.9 89 2428 2554.0 -126.0 156 2191 2308.0 -117.023 2811 2596.5 214.5 90 2408 2572.8 -164.8 157 2024 2307.9 -283.924 2295 2596.9 -301.9 91 2513 2595.7 -82.7 158 2344 2307.8 36.225 2439 2598.0 -159.0 92 2432 2620.4 -188.4 159 2145 2307.7 -162.726 3084 2598.4 485.6 93 2460 2644.5 -184.5 160 2409 2307.5 101.527 2420 2597.5 -177.5 94 2772 2666.1 105.9 161 2879 2307.5 571.528 2490 2596.3 -106.3 95 3000 2683.5 316.5 162 2476 2307.4 168.629 2501 2596.2 -95.2 96 2883 2695.7 187.3 163 1875 2307.3 -432.330 2721 2597.5 123.5 97 2527 2702.1 -175.1 164 2133 2307.2 -174.231 2559 2598.7 -39.7 98 2727 2702.7 24.3 165 2265 2307.2 -42.232 2568 2598.5 -30.5 99 2697 2697.6 -0.6 166 18 94 2307.1 -413.133 2535 2597.1 -62.1 100 2543 2687.5 -144.5 167 2273 2307.0 -34.034 263 9 2595.9 43.1 101 2596 2673.1 -77.1 168 2084 2307.0 -223.035 2849 2596.3 252.7 102 2491 2655.3 -164.3 169 2694 2306.9 387.136 2755 2597.9 157.1 103 2953 2635.0 318.0 170 2232 2306.8 -74.837 2976 2599.1 376.9 104 27 98 2612.9 185.1 171 2351 2306.8 44.238 2775 2598.5 176.5 105 2559 2589.9 -30.9 172 2129 2306.7 -177.739 2416 2596.8 -180.8 106 2328 2566.7 -238.7 173 2235 2306.7 -71.740 2989 2595.6 393.4 107 2637 2543.7 93.3 174 2489 2306.6 182.441 2814 2596.4 217.6 108 2116 2521.5 -405.5 175 2112 2306.6 -194.642 2415 2598.4 -183.4 109 25 92 2500.3 91.7 176 2256 2306.6 -50.643 2900 2599.8 300.2 110 2520 2480.4 39.6 177 2116 2306.5 -190.544 2376 2599.0 -223.0 111 2385 2461.9 -76.9 178 2562 2306.5 255.545 2584 2596.5 -12.5 112 2407 2445.0 -38.0 179 2651 2306.4 344.646 2563 2594.3 -31.3 113 2499 2429.5 69.5 180 2304 2306.4 -2.447 3036 2594.7 441.3 114 2337 2415.5 -78.5 181 2043 2306.4 -263.448 2083 2597.8 -514.8 115 2828 2403.0 425.0 182 2320 2306.4 13.649 2671 2601.6 69.4 116 2362 2391.8 -29.8 183 2325 2306.3 18.750 2630 2603.0 27.0 117 2351 2381.8 -30.8 184 242 9 2306.3 122.751 2735 2600.5 134.5 118 2184 2373.0 -189.0 185 2405 2306.3 98.752 2643 2595.2 47.8 119 2319 2365.2 -46.2 186 2221 2306.3 -85.353 2149 2590.4 -441.4 120 2300 2358.4 -58.4 187 2394 2306.2 87.854 2281 2589.5 -308.5 121 2525 2352.3 172.7 188 2280 2306.2 -26.255 2599 2593.7 5.3 122 2244 2347.0 -103.0 189 1964 2306.2 -342.256 2620 2601.4 18.6 123 2127 2342.4 -215.4 190 2409 2306.2 102.857 2359 2608.4 -249.4 124 2227 2338.3 -111.3 191 2419 2306.1 112.958 2321 2610.6 -289.6 125 2517 2334.8 182.2 192 2340 2306.1 33.959 2722 2606.1 115.9 126 2273 2331.7 -58.7 193 2312 2306.1 5.960 2576 2596.5 -20.5 127 2386 2328.9 57.1 194 2311 2306.1 4.961 2303 2586.1 -283.1 128 246 9 2326.5 142.5 195 2001 2306.1 -305.162 2551 2579.9 -28.9 129 2484 2324.4 159.6 196 2511 2306.1 204.963 2588 2581.2 6.8 130 2183 2322.6 -139.6 197 2763 2306.0 457.064 2825 2590.2 234.8 131 2111 2320.9 -209.9 198 243 9 2306.0 133.065 2533 2603.7 -70.7 132 2307 2319.5 -12.5 199 2231 2306.0 -75.066 2092 2616.5 -524.5 133 2091 2318.2 -227.2 200 2063 2306.0 -243.0

i i i iIi i i i|i i i i|i i i i|i i i i|i i i i|i410COMP3800 3840 3880 3920 3960TIME IN MILLISECONDS FROM BEGINNING OF DATA VINDOVFioure 5-147. PDPLOT of the occultation o-f X09514.0124 _0112 - MEAN -0.00294wo009S_ SIGMA 0.075658zLU 0087 _3 0074 _o 0062 _o e2 0037,32 002S_ 0012\I000EJJ-47.9-40.6-33.3-26.1 -18.8 -ii.5 -4.2 3.1 10.4 17.6NOISE LEVEL AS A PERCENTAGE OF COMPUTED INTENSITYI I | I I I IHFigure 5-148. NOISEPLOT o-f the occultation o-f X09514

411TABLE 5-71X09514: SUPPLEMENTAL STATISTICAL INFORMATIONVARIANCE/ CO- VARIANCE MATRIXDIAM PREI POST TIME VELO3.254E~14 5.005E~07 -5.270E 07 -5.312E 08 1.290E 095.005E"07 4.841E02 1.686E01 -1.663E01 2.919E~01-5.270E"07 1.686E01 6.996E02 -2.319E01 4.042E~01-5.312E"08 -1.663E01 -2.319E01 1.380E01 -2.444E011.290E"09 2.919E 01 4.042E 01 -2.444E 01 5.961E"03CORRELATIONMATRIXDIAM PREI POST TIME VELODIAM 1.000000 0.766505 -0.761986 0.128535 -0.124485PREI 0.766505 1.000000 -0.172303 -0.479860 0.481833POST -0.761986 -0.172303 1.000000 -0.713209 0.709453TIME 0.128535 -0.479860 -0.713209 1.000000 -0.999975VELO -0.124485 0.481833 0.709453 -0.999975 1.000000NUMERICAL RANGES OF THE PARTIAL DERIVATIVESMAXIMUMMINIMUMDIAM 3.055E08 -3.000E08PREI 1.365E00 1 .974E"03POST 9.980E 01 -3.649E~01TIME 2.322E01 -2.477E01VELO 1.311E03 -1 .336E03

111'11141:MODELCURVE1 1-lSTAR +1 p "SKY-. 1 .OCCULTATION'100' *200' '300 '400'FREQUENCY INHERTZFiqure 5-149. POWERPLOT o-f the occultation of X09514,

.413Unf ortunatel y , as had occasionally happened inpreviously observed events, the signal strength of the wWBtime code was too low to provide a useful time reference atthe time o-f the event. A successful post-event calibrationof the SPICA-IY/LQDAS clock could not be obtained until 2hours after the event. Assuming a worst case internal clockdrift of 2 seconds per day, the Coordinated Universal Time ofoeometrical occultation was found to be 03:35:32.8 (+/- 0.1seconds)ZC1Q30 (Epsilon Geminorum)2C1030 (Epsilon Geminorum, Mebsuta, BS 2473) was a primecandidate for the occultation program. This G5 supergiant(luminosity class lb) is on the order of 6000 times asluminous as the sun. Its apparent V magnitude of 3.18 givesEpsilon Geminorum a corresponding distance of appoximately350 parsecs. To gauge the possibility of a diameterdetection for Epsilon Geminorum, Allen (1963) gives diametersof G5-I stars to be in excess of 120 solar diameters. Atthis distance this linear diameter corresponds to an angulardiameter on the order of 3 or 4 milliseconds of arc, wellabove the detection threshold. On April 7, 1976, EpsilonGeminorum was occulted by Mars. This wel -observed planetary1occultation has been discussed by LJasserman et al . (1977).The intermediate bandwidth "y" filter was initiallyselected for this observation. This star, brighter by farthan any other previously observed in the occultation

414program, should have produced an observation with anunprecedented si gnal -to-noi se ratio. Though X09514 had beenobserved under clear skies only two hours earlier, theweather conditions deteriorated rapidly. Twenty minutesbe-fore the predicted time o-f the event, the sky wascompletely covered with a heavy layer o-f cirrus clouds, andno stars could be seen with the unaided eye. Just prior tothe event, no sur-face markings could be distinguished on thelunar sur-face.

415'20.48 '23.04 '25.80 28.16 30.72 33.28 35.84 38.40TIME IN SECONDS FROM BEGINNING OF DATA VINDOVFigure 5-150. RAWPLOT o-f the occultation o-f 2C1030.zQLUMoz20.48 23.04 '25.60 28.16 30.72 33.28 35.84 38.40TIME IN SECONDS FROM BEGINNING OF DATA VINDOVFigure 5-151. INTPLOT o-f the occultation o-f 2C1030

i -f only the416event the selected -filter was changed to the "b" -filter, asthe stai—plus-sky/sky signal ratio was a approximately10 percent higher than with the V" -filter.The RAWPLOT o-f the event. Figure 5-150, shows the slowlyacquired photometric data. The integration plot. Figure5-151, is indicative o-f the variation in atmospherictransparency brought on by the layer o-f intervening cloudsand haze. As can be seen, the change in signal level due tothe occultation is unmistakable. No di-ffraction -fringes arecontained in the data (as expected) due to the slow dataacquisition rate. The data sample corresponding to the timeo-f disappearance was noted strictly by visual inspection.A-fter reduction o-f the UwVB time code the CoordinatedUniversal Time o-f geometrical occultation was -found to be05:50:06.77 (+/- 0.01 seconds).Under normal circumstances such an observation wouldhave been impossible, and the presence o-f a layer o-f heavycirrus clouds would have prevented any observing attempt.Yet, as was shown by the partial success o-f this observation,a bright star can yield some information (eventime o-f occultation to low precision) under adverseconditions. Occultation photometry, -for chronometric and lowprecision astrometric work, is quite -forgiving.Summary o-f the Occultation ObservationsThe observations which have been discussed in theprevious section were all made during the thirteen lunations

417spanning the time period -from March 1933, to March 1934.Durino this period, 67 occultation observations were planned.Of these, photometric data were obtained -for 24 occul tat i ons.The remainder, with the exception of two, were lost due toinclement weather. The two other events mentioned were notobserved due to a mechanical failure in the instrumentalsystem, which was remedied in time for the next night'sobserv ing.Of the 24 events for which data were obtained, two (theoccul tat ions of ZC3458 and ZC1030) were observed with a dataacquisition rate which was too slow to allow a completeanalysis to be carried out. If the observing year discussedwas typical (in terms of weather), then one might expectapproximately one fruitful occultation observation for everythree planned for the Rosemary Hill Observatory.The stars ZC0916-A, X13534, and X13607 were discoveredto be "close" occultation binaries. (The B component ofZC0916 was previously known to be a spectroscopic binary).Hence, though based on admittedly small number statistics, 14percent of the 22 observations which were fully analyzedresulted in the discovery of previously unknown "close"companions. Widely separated, though much fainter, companionstars were found for ZC1221, X18067, ZC0126. Thus, 14percent of the stars studied were revealed to have fainter"wide" components. Considering both "close" and "wide"systems, 27 percent of the stars studied turned out to havepreviously unknown companions. Table 5-72 summarizes the

413TABLE 5-72DERIVED QUANTITIES FOR THE OCCULTATION BINARIESSTAR T mV-T mV-1 mV-2 P. S.ZC0916-A C 4.74 5.05 6.27 3.34ZC0916-B C 5.19 5.28 7.66 8.41ZC0916-AB U) 4.30 4.74 5.19 31 .5ZC1221 w 440XI 3534 c 3.4 3.73 9.86 6.07XI 3607 c 3.2 8.53 9.52 13.15ZC0126 u 38.3Notes: 1. Type codes : W = wide, C = close.2. mV-T is combined mV for both stars.3. Projected Separation

TABLE 5-74COORDINATED UNIVERSAL TIM!IS OF GEOMETRICAL 0(;CULT*:*TI

420projected angular separations -found -for these double stars.In addition, the derived apparent K> magnitudes are given forthe "close" doubles.Stellar angular diameters were determined -for the starsZC0916-B1, ZC1221, X07598, ZC1462, 2C2209, X01217, ZC3158,and ZC0835. However, the uncertainties in the angulardiameters determined -for ZC1221 , ZC3158, ZC0835 and X01217

421post-occul tat ion signal intensities. A "quality index",denoted Q, has been assigned to each o-f these events. Q isde-fined as the product o-f the (S+N)/N and intensity ratiosdivided by the normalized standard error o-f the photometricO-Cs. The "quality index" is not de-fined -from any rigorousstandpoint. Rather, it is designed merely to give, in asinale quantity.:-.- indication o-f the overall photometricconditions -for a particular event. Thus, an i ntercompar i sono-f Q -for di-f-ferent events provides a relative scale forjudoing the quality o-f the observational data used in theparametricsolutions.The Coordinated Universal Times o-f geometricaloccultation were determined -for each o-f the 24 events. Inthe case o-f "close" doubles, the individual times o-fdisappearance o-f the components were -found. These times,which have been reported to the International LunarOccultation Center (in Japan), are summarized along withtheir one sigma uncertainties in Table 5-74. Thesestatistical uncertainties arise both -from the internal -formalerror in the DC solution -for the time parameter and the errorinherent in edge detection o-f the WwVB time code.For each individual event, the determined R and L ratesdepend upon the local slope o-f the lunar surface. Inprinciple, -for any one event the slope can assume any value.However, the likelihood o-f encountering an extremely largelocal slope should be quite small, as near-verticalprotuberances are rare in comparison to the total lunar

.422surface area which can be seen along the limb. Clearly,there should be a most likely value tor a lunar slope basedon the distribution -function o-f individual slopes. Thisdistribution -function could be -found by measuring the slopeso-f lunar sur-face -features -from the Lunar Orbi ten or Apollophotographs. However, this would be a -formidable task, asthe lunar sur-face would have to be treated as a grid o-f nomore than a -few meters on a side in order to obtain adistribution -function use-ful in the reduction and analysis o-foccultationobservations.I -f a detailed lunar slope distribution function wereknown, it could serve to assess the probability o-f a properdetermination of the slopes for an individual event. In thecourse of this investigation, 2? local lunar slopes weredetermined, and the derived distribution function is shown inFigure 5-152. This figure, binned into regions 3 degreeswide, shows the occurrences of the absolute values of thedetermined slopes.One would not expect a preferential alignment of lunarsurface features, and hence, the mean of all slopes shouldaverage to zero. (Indeed, the mean slope angle found for the27 observations was found to be -1.8 degrees). The meanabsolute slope was approximately 15 degrees. The largestslope encountered was just in excess of 33 degrees. Thisdistribution function is in good agreement with thedistribution of lunar slopes which have been reported fromobservations made at McDonald Observatory over the lastdecade

•1/1111i/iii/i423CO^cnUJCDUJ»83.COJ3*ID "m CMssCDUJUJaCDLl!QaCO»111ClO-JCDUJoCDCOcouj5roScQXI"0a.:>i.XIO enCMinaUlEC L3 nJQi c— 3u. —S30N3dd0000 dO U3QHnN

424Future Directions -for the Occultation ProgramIn order to meet the goals o-f the program of occultationobservation discussed in Chapter 1, an instrumental systemcapable o-f obtaining -fast photometric observations of lunaroccul tat ions was developed and implemented at the RosemaryHill Observatory. Further, careful consideration o-f themethods available -for the reduction and subsequent analyseso-f these observations led to improvements in the conventionalnumerical and computational procedures. These improvementswere incorporated into a set o-f algorithms, implemented asAPL -functions, to allow a routine program o-f analysis to becarried out.The systems and procedures developed have been provenviable as demonstrated by the success-ful determination o-fstellar angular diameters, the discovery o-f previouslyunsuspected multiplicity in several stellar systems, and inmeasuring the times o-f occultation events to a degree o-fprecision useful to ongoing astrometric programs. This isnot to say that there is not room for improvement. Indeed,on many levels the overall occultation program can beexpanded andimproved upon.Improvements to the instrumental system at RHO couldlead to the successful observation of at least twice as manyoccultations as are now currently possible. Specifically,all events observed to date were dark limb disappearances.For reappearance events, the star cannot be seen

425event), and must one rely on the pointing accuracy o-f thetelescope to acquire the unseen star. The 76-centimeterTinsley re-flector, however, lacks the pointing accuracyrequired to acquire a field typically o-f less than 15 arcseconds without visual reference.A 4-inch refracting telescope with a high power eyepiece

426brightness level o-f the background would literally swamp thestellar signal for even the brightest o-f sources if observedin the visible region of the spectrum. For a number of yearsobservations of lunar occul tat ions of late stars in theinfra-red have been made with great success (as in the caseof Aldeberan as reported by White and Kreidl, 1984). Whilesuch observations are not normally as effective from lowaltitude sites such as RHO as at high altitude sites, K-YChen (1985) has indicated that infrared observations,nevertheless, can be made rather effectively. Recently, P.Chen has been testing a new infrared photometric system onthe 76-centimeter telescope. Though the opportunities forinfra-red observations of lunar occul tat ions from RHO wouldbe more restrictive than from a high altitude site, on thebasis of previous work done at RHO there is reason to believethat such observations would be successful.Clearly, the next logical step to enhance theoccul tation program is to move in the direction ofsimultaneous multicolor observations. This could be done ata minimum expense, and the gain would certainly be worth thesmall additional effort. The Astromechan i cs photometer, aspreviously mentioned, can be used in two channels (i.e., blueand red) simultaneously. A three channel photometer built byFlesch

427code detection as all three 12-bit A-to-D's would be used -foracquisition o-f photometric data. However, the time signalcould be detected with only one bit (since it is digital innature), and this additional input could be added with littleimpact on the memory allocated -for photometric data storage.Multicolor observations would be advantageous from twoviewpoints. First, the simultaneous solution o-f the residualequations resulting -from multicolor observations would bemore highly constrained than in the case o-f one singleobservations. The time o-f geometrical occultation must bethe same for all colors. This condition, when enforced inthe parametric solution, would result in an improveddecoupling and, therefore, a more reliable determination ofthe solution parameters. In addition, while the diffractionfringe spacing scales linearly

428determination o-f the relative time of geometricaloccultation. This situation, brought on by poor radioreception, could probably be improved with a higher gain VLFantenna. A new antenna con-figuration should be investigatedas one of the -first items considered in making continuedimprovements to the occultation instrumental system.In terms o-f the numerical procedures used in determiningthe solution parameters, the consideration o-f second orderterms in the residual equations, as suggested by Eichhorn andClary

429be determined empirically. As more occultation observationsare made and solved, the better the knowledge of thisdistribution -function becomes. Thus, this is ase 1 -f- improv i no. process. I f one constrains the adjustment o-fthe L-rate on the basis o-f the observed slope distributionfunction, then each newly determined slope should be added tothe growing baseline data -for that distribution. Theinclusion o-f probabilistic constraints, like theconsideration o-f second order terms, is a refinement thatdeserves investigation and possible -future implementation.The currently discussed observations do leave a numbero-f questions unanswered, as pointed out earlier. As anexample, the detected -fourth component in the 1 Geminorumsystem remains a bi t of an enigma. Griffin (1984) notes thatthe probability of non-detection by use of his photoelectric"radial velocity meter" (due to a near zero inclination ofthe orbital plane) is approximately one part in 800. Yet,the evidence for the existence of the A2 component is quitestrong. Photoelectric radial velocity meter measurements,however, are sensitive to the spectral types of the componentstars. This instrument requires that a mask be employedwhose physical characteristics strongly depend on theanticipated spectral characteristics of the stars understudy. The analysis of the spectra of composite stellarsystems is enormously complex, and it is quite easy toimagine that a previously unsuspected component couldpossibly bias the interpretation of those spectra. In any

430event, the 1 Geminorum system is certainly one that bearsfurtherinvestigation.Also lurking in the relm of unanswered questions is theunexpectedly large diameter -found -for ZC2209. Corroborative

the movement of the di ff rac t i on pattern resulting -from theoccultation, as projected onto the spacecraft, would beslowed enormously. From a suitably equipped orbitalobserving platform, data acquisition sampling rates on theorder of 1 to 10 Hertz (as opposed to 1000 Hertz) could beemployed with no degradation (i.e., smearing) of the431diffraction pattern. Thus, from photon statistics alone, the(S+N)/N ratios could be improved by a factor of 10 to 30.This, of course, does not include the added gain ofeliminating the effects of atmospheric scintillation, seeing,and transparency variation. The observed intensity curvewould be adversely affected only by photon arrivalstat i st i cs.By the end of the next calendar year, the Hubble SpaceTelescope (HST) will be operational. The possibility ofusing a 94-inch orbital telescope, equipped with a high speedphotometer, for spaceborne occultation observations isintriguing. There are two problems which would have to beovercome. First, normal HST operation guidelines disallowthe pointing of the telescope in the vicinity of the moon dueto possible damage to the various light sensitive detectorsin the instruments. Second, HST requires two guide stars indifferent "pickles" (as described by Giacconi, 1982). Theprocess of guide star selection might prove, in most cases,to be almost impossible. If the target star is about to beocculted then at least one and a half of the three fineguidance sensor "pickles" would be in the moon's shadow,

432obscuring any possible guide stars. These are technicalproblems which need careful study. It may indeed turn outthat, despite the ideal environment -for occultationobservations, HST might not be suitable -for a majority ofcandidate events.One cannot help but reflect on the nearly mind bogglingarray o-f spaceborne and "new generation" astronomicalinstruments which will soon become a reality. The spectrumspanning network o-f the HST, the Space In-fra-Red TelescopeFacility, the Advanced X-Ray Astonomy Facility, the Gamma RayObservatory, as well as (K> and ELW telescopes will all be inorbit and operational in the not too distant -future. Newmulti -meter ground-based telescopes with state o-f the artsupport equipment are being planned and will be on-line wellbefore the turn o-f the century. The new 10-meter telescopeto be located on the summit o-f Mauna Kea would be anunparalled achievement in itsel-f, and even now, there is aglimmer o-f a possibility that two such instruments might bebuilt and operated as an optical nter-f erometer . These newiinstruments will open up new vistas as o-f yet unimagined.Some vocal proponents o-f spaceborne astronomical-facilities have remarked that the days o-f ground-basedobservatories are numbered. At the same time, other voiceshave remarked that ground-based astronomy will beaccomplished only by large (greater than approximately 3meter diameter) telescopes. With "competition" -from some o-fthe most sophisticated and finely built op to-el ec tron i

433instrumentation ever to be constructed, some ask if it is nowfolly to plan a program -for a small, ground based instrument.The answer to both the cynics and skeptics alike is anunequivocal no. It is a -fact that in terms o-f scientificreturn (expressed in the now-in-vogue units o-f photons perdollar), it is the small, research grade instruments whichcan be the most productive. Institution orientedastronomical sites, such as the University of Florida'sRosemary Hill Observatory, have the luxury of carrying outlong term projects, unthinkable and misplaced on large,heavily oversubscribedinstruments.Specifically, telescopes in the 1 meter class are idealfor carrying out occultation observations in the visible andperhaps even near IR wavelengths. In the case of RHO, itsother concurrent research programs require dark time, leavingmoonlit nights otherwise unused. Uhat better way to fill theunproductive hours than by adding to the knowledge offundamental astronomical data in the measurement of stellardiameters, elucidation of the geometry and physical makeup ofmultiple systems, and compilation of a long term baseline oftiming data for astrometric purposes?It is to this end that this program of the observationand analysis of lunar occultations was established. It ishoped that this program will continue in full force andperhaps similar programs implemented at other small,institution oriented astronomical facilities.

APPENDIX ALISTING OF THE 6502 PROGRAM LODAS (VERSION E07)This appendix contains the source code for the LunarOccultation Data Acquisition System so-ftware, which isdescribed in Chapter 2. The revision shown here (E07) iscurrently in use at the Rosemary Hill Observatory.The assembly o-f this program was carried out using theASM6502 cross-assembler, available at the Northeast RegionalData Center (NERDC) . The assembly directives seen in thissource listing are described by NERDC

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APPENDIX BLISTING OF THE 6502 PROGRAM OCCTRANSThis appendix contains an assembly language source codelisting for the 6502 machine language program calledOCCTRANS. This program is discussed in Chapter 4. Thisprogram was assembled with the ASM6502 cross-assemblermentioned in the introduction to Appendix A.470

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;APPENDIX CLISTING OF THE APL WORKSPACE OCCPREPV Y+BIT12 X[1] AUNPACKS 12 BIT BIT-PACKED LODAS DATA[2] Y«-2lfc?(12 ,.6666666667xpX)p$(8p2)TXVV IDENT[1][2] *** LUNAR OCCULTATION DATA PREPARATION WORKSPACE **[3][4]C5][6]VERSION: A02/HARRIS'REVISION DATE 18 JUNE 1984'NOTE: DIO-H)'[7] A GLENN SCHNEIDER DEPARTMENT OF ASTRONOMY[8] A UNIVERSITY OF FLORIDA GAINESVILLE, FL 32611VV READ;Y[1] AREADS IN A LODAS DATA FILE FROM A SPICA- IV/ CODOS DISK[2] ATHE SPICA- IV MUST RUN THE PROGRAM "HARRISTERM"[3] ATHE DOWNLOADED FILE IS IN THE TEXT VARIABLE "DATA"[4] DATA-«-iO[5] Ll:» •[6] -»-(v/(2 3p'6TLEND')A.=3 + Y-t-[!I)/L2[7] -»-Ll,pDATAf-DATA,Y,(72-pY)p •*'[8] L2 :ERRS-

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APPENDIX DLISTING OF THE APL WORKSPACE: OCCRED7 B-f-W BBDY L[1] AB=NORMALIZED RADIATED BLACKBODY POWER CONTRIBUTION[2] AL[1]=ASSUMED EFFECTIVE COLOR TEMPERATURE OF THE STAR[3] AL[2]=NUMBER OF TERMS USED IN THE NUMERICAL INTERGATION[4] A W=WAVELENGTH LIST[5] B+Bt+/B+-+/ .000037412r(W*5)x* 1 + 1 .438 7 9*L[ 1 ] xw«- . 00000001*w° .+(0,iL[2])-L[2]*2V7 R-eCM X;V[1] ACORRELATION MATRIX FOR THE MATRIX [2] V«-(Vo .xv«-l l$R-f-((5>R)+.xR«-x-(pX)p(+/X)*l + pX)*.5[3] APATCH FOR DIVISION SCALING PROBLEM ON THE HARRISC43 V[1;1>R[1;1][5] R«-R*V7 DC P;DI;CVEC;ITER;N;I;X;V;D;R;Y;£[1] ADIFFERENTIAL CORRECTIONS PROCEDURE FOR LUNAR OCCULTATIONS[2] AFIVERATUREPARAMETER MODEL, FIXED LIMB DARKENING AND TEMPEC3] ££L_£-«-l 14pP,.S_S_E/ITER)/3)A.*l + pX«-X,DW(Dl[l],l)xlE~12r(P+££Ii)[l])/Ll[13] *(5*l+pX*X.D*-/(DI[l].l)xlE"l2r(P*SfiL)[l])/Ll[14] -*(P[12](LlMS_[l;i5]LP[N] + P[14]xY@X)|"LIiL£[2; i5]477

473[16] -»L0. .SOLS^SOLS.niP[17] L2:'SOLUTION HISTORY: »[18] + £O_L.S«-(0,iP[12]) ,(Q£SE) t ll + pjSJSLE) .SSE.SOLS[19] 'STANDARD ERRORS: ',T£R.«-(1 l$COV«-( ( ( , Y-X+ . xylX) + . *2 ) *-/pX)xHINV($X)+.xD_I«-x)*.5[20] PDER"-XVV P2 DC2 P;DI;CVEC; ITER;N; I;X;V;D;R;Y;AD;.S_[1] ^DIFFERENTIAL CORRECTIONS PROCEDURE FOR LUNAR OCCULTATIONS[2] ANINE PARAMETER MODEL, FIXED LIMB DARKENING AND TEMPERATURE[3] SOLS2-*-SOLS--l 1 4p P ,£££«-() p DI«-DI2«-( 5p0 ) ,1 .02 1.0003,1.00l,(2pl 10003) ,1[4] CVEC«- lN«-5+l5+ITER-*-0[5] R*R* + /R-«-(iZlLl)[;2]x(i£XLl)C;l]BBDY P[4],(l+-/©2 2pJ>FXLX)*5[6] R2^R2T+/R2^(i£lLl)[;2]x(i£2LT)[;l]BBDY P2[ 4] . ( l+-/e22piZILl)*5[7] i-«-+/2xp[ll]LDARKEN GRID P[5][8] L0:X«-X2«-(2 + P[3])p0[9] £^^££E.,D+(Y+0^-COMP/1.02 + + /(P[6]1.02 + + /(P2[6]Dl[l]xlE~12rP[l«-l+CVEC«-lCVEC][14] D«--.C_0i!E-P[8]+(P2[7]xR WIDE P2)+P[7]xR WIDE P[15] *(5>l + pXH-X.D+-/(DI[l].l)xlE~12r(P+SIiL)Cl])/Ll[16] nn P[N]*(UHaClsi5]LP[N] + P[14]xYlX)rUliaC2;i5][17] CVEC«-~lN[18] LlB:P2[l]«-DI2[l]xlE"l2rP2[l«-l+CVEC«-lCVEC][19] -»-(l = 8)/LlB[20] D«--.CJ21LE-P[8]+(P2[7]xR WIDE P2) + P[7]xR WIDE P[21] -(9>l + pX-(4>l + pX2«-X2,DW(DI2[l],l)xlE~12r(P2-(L_IM_£2[l;S]LP2[5+S] + "4 + AD)rLIMjS_2[2;S(LJM_£2[l;S]LP2[5+S] + P[14]xYlX2)ri i IMS_2[2;S«-12 4 5][26] -*(P[12]

[1] flFAST FOURIER TRANSFORM OF X; FROM RGS[2] AX VECTOR OF REALS OR X[;0]=REAL X[ ; 1] = IMAG IN ARY[3] DIO+O[4] -K2=ppX)/L0C5] X«-X,[.5]0[6] L0:T^2ie(Gp2)TiI-»-2*G-t-r2®HpX[7] X«-((N«-I*2),2 2)p((I,2)tX*I*.5)[T;][8] T«-$2 lo.OO(N + T)42xN[9] Z+(+/[l]X),[.5]-/[l+l]X[10] LA:Z«-( (N-*-N*2) ,(2xi-»-ix2) ,2)pZ[11] X«-( 0,1,0 )IZ[12] Z«-(0,-I.0)+Z[13] Z«-(Z+Q),Z-Q«-( + /QxX) ,[1.5]-/(Qf(N,I,2)p(l,2) + T)xX[14] -»-(l

430C7] 0_B_S_-[8] 0_B_S_-C 9 ]V1024-K"512 + 5l4rx[0]L3 5 95) + CHl)*2-FFT-FFTI 1024 2+(F,2) + 0_B_.S_-X[l]-K512-L.5xX[l])+0_i£0_B_£-V Y«-GRID N ;R;R2;X[1] ^NORMALIZED RADIAL GRID AREA DISTRIBUTION (2D) SPHERICAL STAR[2] AN = SQUARE ROOT OF NUMBER OF GRID POINTS PER QUADRANT[3] X«-( iR) ,[.5]~l+iR«-l + pY«-(2pK)pO[4] Ll:R2«-(Xx((R*2)-X*2)*.5) + RxRx"loX*RC5] Y[;l+R]*Np-/R2-((Xx((R*2)-X*2)*.5)+RxRx lo(X«-(0 1+pX)+X)*R«-R-l) ,0[6][7]V-*-Llxil*l + pR2Y«-Y*4x+/ + /Y-«-(l- iN)Yx( iN) ° .*lNV Y«-H IN V X C[1] APATCH;FOR PROBLEM WITH MONADIC S IN HARRIS APL[2] C*10*.5xlO«X[l;l][3J X[;1>X[;1]*C[4] X[1;>X[1;] + C[5] Y^iX[6] Y[1;>Y[1;]*C[7] Y[;1>Y[;1]*C7 Y-X[;1 6]4C[4] X[l 6;]«-X[l 6;]tC5 ] Y-HBX[[6] Y[l 6;>Y[1 6;]tC[7] Y[;l 6]«-Y[;l 6]*CCI][2][3][4]C5][6][7][8]IDENTt*** LUNAR OCCULTATION DATA REDUCTION WORKSPACE ***'VERSION C03/HARRIS BATCH'REVISION DATE: 29 APRIL 1985 1NOTE: THIS WORKSPACE IS DlO«-l 'iA GLENN SCHNEIDER DEPARTMENT OF ASTRONOMYA UNIVERSITY OF FLORIDA GAINESVILLE, FL 32611CI]C2][3][4][5]INPUT2 X;PR;CAX IS RAW OBSERVING DATA (I.E. CHI)ACONVERSATIONAL ENTRY OF INITIAL DC2 PARAMETERSNAME/

431[6] Zl-'-D.OpD-*-* ENTER THE MONOCHROMATIC WAVELENGTH, OR ENTER TO USE FILTER TABLE'[7] l(_Py*0)/ 'F.ILT-*-' 'MONO' ' ' ,0pMONO-i-l 2p£V,l[8] +(£V*0)/I0[9] 'ENTER THE NAME OF THE FILTER TABLE TO BE USED:'C ] 1 F_ILI«-H[11] 10 : £l-' ENTER STARTING BIN NUMBER OF DATA TO BE USED'[13] P_V/«\EV,[],0pL>-' ENTER NUMBER OF DATA POINTS TO BE USED'[14] OJLS_«-("l + P_y.) + (B_ffl-l)+X[15] £V_«-ZZ,n,0pL"H-' ENTER THE EFFECTIVE COLOR TEMPERATURE OFTHE STAR'[16] P_i-' ENTER THE SQUARE ROOT OF THE NUMBER OF GRID PTS./ QUADRANT'[17] £V-f-P.V.,D*C-

i[2C3[4[5[6C7[8[9[10Cll[12[13[14[15[16[17[18[19[20[21[22[23[24[25[26[27[28[29[30[31flCONVERSATIONAL ENTRY OF INITIAL DC PARAMETERSN_AMi;«-3 2 4-E,0pE-PR-t-' ENTER UPPER AND LOWER LIMIT'P_£^£I,D,0p[]-

J*pT-*ul + pGV433V Y-«-NPOL V;T;I;QCT[1] ^INTERPOLATION OF FRESNEL INTENSITY VALUE FOR FRESNEL NUMBER [2] Yt-FREN m+(-/FREN[ 1 ° .+ I«-( 1+ . 5 xpFJIi) - 1 OOxT] ) x 100 xV-T-t-.01*L.5 + VxlOOV7 OUTPUT2 ;S;T;PM;CT;W;Q[1] AFORMATTED OUTPUT FOR DC2 SOLUTIONOF: ' .NAMET.'[2][3](20p'(20p f •) ,'OCCULTATION') ,M£.' U.[4] (20p» f ) .COMN[5] ' '[6] » INPUT PARAMETERS:'[7] ' '' , ( 0T + / x/j>F_ILT_) ANG, ' [8] 'CENTRAL WAVELENGTH OF PAS SB AN D :STROMS 1[9] 'LUNAR LIMB DISTANCE (KM): ',6 0T.S_O_L[ 2 ][10] 'EFFECTIVE TEMPERATURE STAR-1 : ',f.S_Q_L[4][11] 'EFFECTIVE TEMPERATURE STAR-2 : ' ,T.S_0_12 [ 4][12] 'LIMB DARKENING COEFFICIENT STAR-1: ' ,T.S_P_L.[ 11 ][13] 'LIMB DARKENING COEFFICIENT STAR-2: ' , T.S_0_L.2 [ 1 1 ][14] ' '[15] ' MODEL PARAMETERS:'[16] ' '[17] 'NUMBER OF DATA POINTS: * ,T.S_P_L.[ 3 ][18] 'NUMBER OF GRID POINTS: ' ,?(.S_0_L.[ 5 ] x2 ) *2[19] 'NUMBER OF SPECTRAL REGIONS: ' .Tl+pi FILT[20] 'WIDTH OF SPECTRAL REGIONS: ' . (?-/&( FILT ) T 1 .2 11-ho.BFHill 13) .' ANGSTROMS'[21] 'NUMBER OF ITERATIONS: » ,T JSjO_L[ 12 ][22] ' '[23] ' SOLUTIONS FOR STAR-1:'[24] ' '[25] PM-«-' +/-•[26] 'STELLAR DIAMETER ( ARC-MILLISECON DS ) : ',(6 2T.S_0_L.[ 6 ] x206264806) ,PM, 6 2TEJ&[ 1 ]x206264806[27] 'BIN OF GEOMETRICAL OCCULTATION : ',(7 lT.S_Q_L.[ 9] + B_I&) ,PM,4 1TE_R.[4][28] 'SIGNAL LEVEL OF STAR-1 (COUNTS) ',(6 lTJLQJL[ 7 ] ) ,PM.5 1TMC2][29] ST-

.5x-/QLQ«-(*o*180)x(££12[10]°[57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73]'SOLUTIONS FOR STAR-2 : ']::484t t|t',6[35][36][37] 'STELLAR DIAMETER ( ARC-MILL ISECON DS ) .(6 2T.£012[6]x206264806) ,PM,6 2t1£[ 6 x20626 4806[38] 'BIN OF GEOMETRICAL OCCULTATION,(7 lT.S_Q12[9] +BIN) ,PM,4 1TH[8][39] 'SIGNAL LEVEL OF STAR-2 (COUNTS),(6 1TS0L2[7]),PM,4 1TEJ£[7][40] •POST-EVENT LIMB+SKY SIGNAL LEVEL: ,(6 1T££1,[8]) ,PM.4 1TE_&[3][41] 'OBSERVED LUNAR SHADOW VELOCITY:(7 5tS£12[10]),PM,(7 5T£R.[9]),' KM/SEC[42] ST+x 1 - T-«-.S_P_12 [ 1 ] *P_y_[ 1 ][43] T-

)[74] (13p« *),,CT[75] ((U$A\CT='' )

:' ,TS-*-( -/.SJ2L[ 7486C VELOCITY'[39] ((1iS?a\CT=' »)CT) .'MQ-BFIO.S' DFMT CM M[40] 2 lp' '[41] 'SUM OF SQUARES OF RESIDUALS: ' ,TS

487[6] WO :Y-*-Y+R[I]x(NPOL FNOS P«-( iHLLl) C 1*1+ 1 ; 1 ] . 1 + P) + . x ( 4>T)[7] -»(l*ltpjFILT)/WOV

NAME: VFILxER NAME: BFILTER NAME: NARROWSHAPE: 53 2 SHAPE: 42 2 SHAPE: 5 24450 0.0001294 3600 0.0000953 5295 0.06211184500 0.0002588 3650 0.0004767 5345 0.22515534550 0.0003881 3700 0.0013347 5395 0.44875784600 0.0005175 3750 0.0023834 5445 0.22515534650 0.0006469 3800 0.0044809 5495 0.03881994700 0.0007763 3850 0.01153594750 0.0011644 3900 0.02078374800 0.0016820 3950 0.0397559 NAME: NARROWB4850 0.0023289 4000 0.0469063 SHAPE: 5 24900 0.0047872 4050 0.04890844950 0.0112563 4100 0.0499571 4600 0.06581065000 0.0208306 4150 0.0505291 4650 0.22471915050 0.0296287 4200 0.0511965 4700 0.45585875100 0.0380386 4250 0.0513872 4750 0.22471915150 0.0450252 4300 0.0514825 4800 0.02889255200 0.0513650 4350 0.05100585250 0.0548583 4400 0.04976645300 0.0555052 4450 0.04738305350 0.0553759 4500 0.04519025400 0.0545996 4550 0.04271145450 0.0534351 4600 0.04004195500 0.0507181 4650 0.03765855550 0.0481304 4700 0.03479845600 0.0452840 4750 0.03317765650 0.0426963 4800 0.02955485700 0.0398499 4850 0.02717135750 0.0364860 4900 0.02440655800 0.0337689 4950 0.02192775850 0.0307931 5000 0.01925835900 0.0282055 5050 0.01649355950 0.0252297 5100 0.01372876000 0.0225126 5150 0.01115456050 0.0194074 5200 0.00858046100 0.0166904 5250 0.00581566150 0.0142321 5300 0.00343226200 0.0122914 5350 0.00209746250 0.0104800 5400 0.00152546300 0.0087980 5450 0.00085806350 0.0071161 5500 0.00047676400 0.0054341 5550 0.00028606450 0.0041403 5600 0.00019076500 0.0029758 5650 0.00009536550 0.00245836600 0.00207016650 0.00168206700 0.00142326750 0.00129386800 0.00103516850 0.00077636900 0.00064696950 0.00038817000 0.00025887050 0.0001294433

APPENDIX ELISTING OF THE APL WORKSPACE OCCPLOTS7 Y+fl BIN D;DlO;T[1] ABIN DATA FOR INTO CLASSES FOR HISTOGRAM[2] flD IS DATA VECTOR; N IS NUMBER OF CLASSES[3] Dio+l[4] Y*(T+D[l]-.5xl + T) ,[1.5] + /( 1+ lN ) ° .= + /(( 1 1 D) + T«-+\N p (( [/D)-L/D)*N) ° .

)][12] Z«-(0,-I,0)+Z[13] Z+-(Z+Q) ,Z-Q«-(+/QxX) ,[1.5]-/(Q^(N,I,2)p(l,2) + T)xx[14] ->-(l-(2=ppX)/L0[5] X«-X,[0.5][6] L0:T^2xe(Gp2)TiI^2*G-»-r2®l + pX[7] X«-((N«-I*2) ,2 2)p((l,2)+X*I*.5)[T;][8] T-

) T491[25] 'ANGULAR SEPARATION IN MILLISECONDS OF ARC CENTER 19 6.75[26] (1 20p'NORMALIZED IN TEN S ITY ' ) LAB ELD 1 3pl.4 2.8 90[27] (1 6p'COUNTS')LABELD 1 3p9.8 4.9 270[28] N«-0[29] L1:AXISD ZRO,(2+.475xN) ,( .475*2) ,270[30] + (10*N-«-N + l)/Ll[31] 1 SPLINE(2 + 7x(ip£££)* l+p£££) ,1 . 7 5 + 4 . 7 5 x ( £££- L/ &2£) */M-L/flli[32] 1 SPLINE(2 + 7x( ip££Ml)* l + p£fiMl) . 1 • 7 5 + 4 . 7 5* (££M,.E- [/ 0M)*I7.QB.S_-L/0B_S_[33] AXISD 8.5,(1.75 + 4.75x(££L.[6]-L/.QM)*( I7jH£) - L/£B_&) ..5[34] AXISD 2,(1.75 + 4.75x(££i[7]-L/ja£S) + (l7Jia£)-L/fl££)..5[35] AXISD ZR0.6 .32 ,(X[4]x.lxSPA) ,0[36] PLOTENDVV FITPL0T2 X;QlO;ZRO; SPA; XPOS ; STV ;NUMN ;N[1] flPLOT OF THE FITTED TWO-STAR OCCULTATION CURVE[2] flX = STARTING BIN NUMBER; £££, £0.112., SQL MUST BE GLOBAL[3] DlO-f-0[4] X«-X,(X+i£i[2]) ,(££L[8] + X2«-X) ,££L.[9],££L[5]x206 2 6 4810[5] START[6] PLOTSET .3[7] AXISD 2 1.7570 .35 ^15[8] AXISD 2 1 .75 7 1.4 .05[9] AXISD 2 1 .75 4.75 90 .475 .15[10] AXISD 2,(1 .75+4.75*20) ,4.275 90,(4.75*10), .08[11] AXISD 9 1.75 4.75 90 .475 .15[12] AXISD 9,(1.75 + 4.75*20) ,4.275 90 .475 .08[13] ZRO«-2 + (-/X[2 0])x7*-/X[l 0][14] SPA-

T.492[30] -K10*N«-N + 1)/L1[31] 1 SPLINE(2 + 7x( ipflfifi)* 1+Pfll£) » 1 • 7 5 + 4 . 7 5 * (£££- L/££.S_) */.0_B.S_-L/OB£[32] 1 SPLIHE(2+7x( ip£XJH£)* l + p£Ml) .1 . 75 + 4 . 75x(££MP- L/ 0£S)^r/OB£-L/OB£[33] AXISD 8.5,(1.75+4.75x((££L[7]+££L2[6]+££L[6])-L/OB£)*(l7fl££)-L/fl££) ,.5[34] AXISD 2.(1.75+4.75x(££l[7]-L/flfi£)*(r/fll£)-L/fl££)..5[35] AXISD ZR0,6.32,(X[4]x.lxSPA) ,0[36] X+X2,(X2+£0i2[2]) , ( X2+££L2 [8 ] ) ,££12 [ 9] ,.££12 [ 5 ] x2 0626 4810[37] N-f-0xl + ZRO-*-2+(-/X[2 0])x7*-/X[l 0][38] SPA«-10x*X[3]x(-/X[l 0])*7[39] L2:AXISD ZRO , ( 2+ 475 xN ) , ( . 47 5*2 ) ,2 7[40] ->-(10*N-f-N + l)/L2[41] AXISD ZR0.6 .32 ,(X[4]x .lxSPA) ,0[42] PLOTENDVV R«-FT Y;M;N;DlO[1] ADISCRETE FOURIER TRANSFORMATION OF EVENLY SPACED REAL DATA[2] OIO«-0[3] M«-( i2xN)xo*N-*-(pY)*2[4] R«-l 2p,(+/Y)*2xN[5] Ll:R*R.[0](*N)x+/(l 1°.xY)x2 l°.o(l+pR)xM[6] *(N>~l+ltpR)/Ll[7] R[N;>.5 Ox,~l 2 + RVV FTPREP X;DlO;T[1] PiSETS UP GLOBAL FOR POWER SPECTRA ANALYSIS[2] ftX IS CENTER OF TRANSFORM WINDOW FROM DATA SET[3] DlO-f-0[4] FJTJ2k£*-.5x + /(FFT EXBAXA-«-1024+ ( "512 + 5 1 4TX1.3 5 95 ) + CHI ) *2[5] *(3595*X+1512)/'F_I£U-1-'- 1012+ ( X+l 512 ) + CHI '[6] J>(35 95

1Q493V[1][2][3][4][5][6][7][8][9][10][11][12][13][14]INTPLOT X;DlO^INTEGRATION PLOT OF THE DATA VECTOR XDIO+-0STARTAXISD 2 1.7570 .4375_. 15.875 .05_AXISD 2 1.7570AXISD 2 1 .75 4.75 90 .475 .15AXISD 2, (1.75+4. 75*20), 4. 275 90,(4.75*10), .08('ZF3.1' DFMT .lxiH )LABELD 1 .55 , ( 1 .75+ .475" ill ) »C .5 ]( »LI4' DFMT( (pX)*8)xi8)LABELD(2+.8 75*i8) ,1.55.[.5]8p0•TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOW'CENTER 1 9 1.3(1 20p 'NORMALIZED IN TEN S ITY ' ) LABELD 1 3pl.25 3.22 90X«-(L/X)-X«-+\X-(+/X)tpX«-X[2 3],2+X1 SPLINE (2+7x(i P X)* 1+pX) ,1 .75+4.75xX*T/XPLOTENDV[1][2][3][4]F«-X INVFT R;DI0flINVERSE FOURIER TRANSFORMATION FROM COEFFICIENT MATRIXD I O-K)l°.OXo.xl+ X+-2 1$2 l l + pRF"-,(l l+R)+ + / + /((pX)pl + R)xXVV NOISEPLOT X;OC;PD;R;MEAN ; SIGMA; Y;BR;N[1] ANOISE FIGURE FOR LUNAR OCCULTATION[2] AX IS BIN NUMBER OF START OF DATA USED IN SOLUTION[3] AMUST HAVE §,OL OBS AND COMP AS GLOBAL VARIABLES[4] I2!£A . =.Sjpj,[ 2 ] + ( X- 1 ) + CH[5] AX[1]=FIRST BIN OF DATA X[2]=LENGTH OF DATA[6] C«-( ( X- 1 ) + CH 1 ) -.S_P_L.[ 6 ][7] OC^OC.(OBS-COMP) ,(( 1+.SJ2L.[2]+X) + CH1)-.S_£L.[7][8] PD-

494[23] MEAN-f-(+/2 + 0C)*4094[24] SIGMA«-( (0O2)+.*.5)*4093[25] N^O[26] Ll:AXISD(2 + 7x(MEAN-l+L/BR)*l+R) .(2+.475XN) ,.2375 90[27] -KlO*N-

1 I[16] 1 SPLINE(2 + 2 .5x,(500 + X)o.xi 1 ) , 1 + 495[7] X«-X,[ .5]2 + ( (7t P £0MP)x ip C0M1) °.x9 P 1[8] N«-0[9] START[10] Ll:l SPLINE, W>X[;;N][11] AXISD 2,(1 .82+NX.52) ,.5 90 .5 .1[12] AXISD 2,(1 .82+NX.52) , .5 90 .5 .1[13] AXISD 9,(1 .82+Nx.52) , .5 90 .5 .1[14] AXISD 9,(1.82+Nx.52) ,.5 90 .5 .1[15] AXISD(2 + 7x££L2[8]t P 0££) , ( 2 . 56+N x . 52 ) , .04 90[16] AXISD(2 + 7x££L[8]t P 01£) , ( 2 . 56+N x . 52 ) ,.04 90[17] AXISD 2,(2.08+Nx.52) ,7[18] *(9*N-HJ + 1)/L1[19] AXISD(2 + 7x££L[8]* P 01£) ,1 .75 .07 90[20] AXISD(2 + 7x££L2[8]t P 0£!) ,1 .75 .07 90[21] AXISD 2 1.75 7 1.4 ;05[22] AXISD 2 1.75 7 1.4 .05[23] 'TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWCENTER 1 9 1.3[24] (99 4 P 'C0MPVEL2TIM2INT2DIA2VEL1TIM1INT1DIA1 )LABELD '.35,(2.02+.52x 1l 9) ,[ .5]9 P[25] (1 18 P 'PARTIAL DERIVATIVES ') LAB ELD 1 3pl.2 2.8 90[26] ('LI4' DFMT S+(i5)x.2x 1 + P C£MP) LABELD( 2 + 1 . 4x i 5 ) , 1 . 55 ,[.5]5 P[27] PLOTENDVV POWERPLOT;R;X; I;DlO[1] flPOWER SPECTRA OF MODEL CURVE, STAR+SKY, AND OCCULTATION[2] AEXECUTE FTPREP IN BEFORE POWERPLOT[3] DIO+-0[4] START[5] PLOTSET .3[6] AXISD 2 1 5 90 1 .1[7] AXISD 2 1 .5 4 90 1 .05[8] AXISD 4.66 1 5 90 1 .1[9] AXISD 4.66 1 .5 4 90 1 .05[10] AXISD 7.32 1 5 90 1 .1[11] AXISD 7.32 1 .5 4 90 1 .05[12] X«-(500+l+F_10_B_S_) ,( 500+1 + FJTC:U_l) .500+1 + FTMOD[13] R

A?6[27] (1 llp'OCCULTATION ')LAXISD 4.36 3 271[28] (1 lOp'STAR + SKY')LAXISD 7.02 3 271[29] (1 llp'MODEL CURVE' )LAXISD 9.68 3 271[30] PLOTENDVV RAWPLOT X;DlO;ZRO;SPA;NEG;POS;XPOS;STV;NUMM;N[1] flPLOT OF THE RAW DATA, X (EVERY 4 POINTS)[2] DlO+0[3] START[4] PLOTSET .4[5] AXISD 2 1.75 7 .4375_.15[6] AXISD 2 1.7570 .875 .05_[7] AXISD 2 1.75 4.75 90 .475 .15[8] AXISD 2,(1.75 + 4.75*20) ,4.275 90,(4.75*10), .08[9] AXISD 9 1.75 4.75 90 .475 .15[10] AXISD 9,(1.75+4.75*20) ,4.275 90 .475 .08[11] ('ZF3.1' DFMT .lxUl)LABELD 1 • 55 , ( 1 . 7 5+ . 47 5 * 1 1 1 ) , [ . 5 ][12] ('LI4* QFMT 4096x.lx;H)LABELD 9 . 5 , ( 1 . 7 5+ . 47 5 x il 1 ) , [.5]0[13] ('LI4' DFMT 512x;8)LABELD(2+.875xi8) ,1 .55 ,[ .5]8p0[14] 'TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWCENTER 1 9 1 .3[15] (1 20p 'NORMALIZED IN TEN SITY ' ) LABELD 1 3pl.4 2.8 90[16] (1 6p 'COUNTS')LABELD 1 3p9.8 4.9 270[17] 1 SPLINE(8192pO 1 ) / ( 2 + 7 x( t 40 96 ) *40 95 ) , 1 . 7 5 + 4 . 75xX*4095[18] PLOTENDVV Y«-N SMOOTH D;DlO[1] AN-POINT UNWEIGHTED SMOOTHING OF THE VECTOR D[2] DIO+-0[3] Y«-(pD)p((L.5xN) + D) ,((-N) + (+/( iN ) (N , p D) p D) *N ) , ( - T . 5 xN) + DV

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BIOGRAPHICAL SKETCHSchneider (no B . " after the Glenn H H, please note) wasborn to Elaine and Ira G. Schneider on October 12, 1955, anotherwise un-noteworthy day, except perhaps for the -fact thatit marked the 463rd anniversary of the discovery of America,as commonly reckoned. At the tender age o-f three he receivedhis -first telescope (Sears, 40X!), and learned early in lifethe meaning o-f light pollution.He attended public school 97 and J.H.S. 135 (also knownas the Frank D. Whalen Junior High School, though no one everknew who Frank D. Whalen was) in New York City. Thanks tothe closing o-f the school during the summer o-f 1969 he waspermitted to retain possession o-f the school library's copieso-f The Larousse Encyclopedia of Astronomy and Norton's StarAt 1 as . Later that year he became a member of the AmateurObservers' Society of New York. These two events foreverinfluenced his life and started him on the path to a careerinastronomy.He graduated from The Bronx High School of Science inJune of 1972. Shortly thereafter, he organized aninternational solar eclipse expedition, in hopes of observinghis second total solar eclipse. The clouds which hungominously over the Gaspe Peninsula that day served toreinforce his devotion to shadow chasing.503

504In June of 1976, he earned a Bachelor of Science degreein physics -from the New York Institute o-f Technology. Be-foreentering the graduate program in astronomy at the Universityo-f Florida in September o-f 1977, he worked as an APLtechnical analyst -for Warner Computer Systems, Inc.After eight years, two trips to the South Pole,seemingly endless commuting between Gainesville, Paris,Noordwijc and Bristol, statistically improbable stretches o-fcloudy weather during scheduled observing runs, and beingthwarted at every turn by wayward computers (micro andmacro), he expects, -finally, to receive the degree o-f Doctoro-f Philosophy in August o-f 1985. He has accepted positionaat the Space Telescope Science Institute, working -for theComputer Sciences Corporation as a Science and MissionOperations Astronomer.He has observed every total solar eclipse since March,1970, and intends to keep chasing the moon's shadow well intothe -future. He has a definite preference for Dr. Brown'sCelery Tonic (now called Cel-Ray Soda, alas), and egg creamsmade with Fox's U-Bet chocolate syrup and Good-Healthsel tzer .At the moment he is single, but this malady is expectedto be cured on June 7, 1985.

'I certify that I have read this study and that in myopinion it con-forms to acceptable standards of scholarlypresentation and is ful 1 y adequate , irT~sxope and quality, asa dissertation -for the degree, of Doctor ]of- PtM rpsophy./John P. Oliver, ChairmanAssociate Professor o-f AstronomyI certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality, asa dissertation for the degree of Doctor of Philosophy.C(/C

I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality, asa dissertation for the degree of Doctor of Philosophy.Ralpfl G. Sel fridgeProfessor of Computer andInformation SciencesThis dissertation was submitted to the Graduate Facultyof the Department of Astronomy in the College of Liberal Artsand Sciences and to the Graduate School and was accepted aspartial fulfillment of the requirements for the degree ofDoctor of Philosophy.Auoust 1985 Dean, Graduate School

i[2C3[4[5[6C7[8[9[10Cll[12[13[14[15[16[17[18[19[20[21[22[23[24[25[26[27[28[29[30[31flCONVERSATIONAL ENTRY OF INITIAL DC PARAMETERSN_AMi;«-3 2 4-E,0pE-PR-t-' ENTER UPPER AND LOWER LIMIT'P_£^£I,D,0p[]-

J*pT-*ul + pGV433V Y-«-NPOL V;T;I;QCT[1] ^INTERPOLATION OF FRESNEL INTENSITY VALUE FOR FRESNEL NUMBER [2] Yt-FREN m+(-/FREN[ 1 ° .+ I«-( 1+ . 5 xpFJIi) - 1 OOxT] ) x 100 xV-T-t-.01*L.5 + VxlOOV7 OUTPUT2 ;S;T;PM;CT;W;Q[1] AFORMATTED OUTPUT FOR DC2 SOLUTIONOF: ' .NAMET.'[2][3](20p'(20p f •) ,'OCCULTATION') ,M£.' U.[4] (20p» f ) .COMN[5] ' '[6] » INPUT PARAMETERS:'[7] ' '' , ( 0T + / x/j>F_ILT_) ANG, ' [8] 'CENTRAL WAVELENGTH OF PAS SB AN D :STROMS 1[9] 'LUNAR LIMB DISTANCE (KM): ',6 0T.S_O_L[ 2 ][10] 'EFFECTIVE TEMPERATURE STAR-1 : ',f.S_Q_L[4][11] 'EFFECTIVE TEMPERATURE STAR-2 : ' ,T.S_0_12 [ 4][12] 'LIMB DARKENING COEFFICIENT STAR-1: ' ,T.S_P_L.[ 11 ][13] 'LIMB DARKENING COEFFICIENT STAR-2: ' , T.S_0_L.2 [ 1 1 ][14] ' '[15] ' MODEL PARAMETERS:'[16] ' '[17] 'NUMBER OF DATA POINTS: * ,T.S_P_L.[ 3 ][18] 'NUMBER OF GRID POINTS: ' ,?(.S_0_L.[ 5 ] x2 ) *2[19] 'NUMBER OF SPECTRAL REGIONS: ' .Tl+pi FILT[20] 'WIDTH OF SPECTRAL REGIONS: ' . (?-/&( FILT ) T 1 .2 11-ho.BFHill 13) .' ANGSTROMS'[21] 'NUMBER OF ITERATIONS: » ,T JSjO_L[ 12 ][22] ' '[23] ' SOLUTIONS FOR STAR-1:'[24] ' '[25] PM-«-' +/-•[26] 'STELLAR DIAMETER ( ARC-MILLISECON DS ) : ',(6 2T.S_0_L.[ 6 ] x206264806) ,PM, 6 2TEJ&[ 1 ]x206264806[27] 'BIN OF GEOMETRICAL OCCULTATION : ',(7 lT.S_Q_L.[ 9] + B_I&) ,PM,4 1TE_R.[4][28] 'SIGNAL LEVEL OF STAR-1 (COUNTS) ',(6 lTJLQJL[ 7 ] ) ,PM.5 1TMC2][29] ST-

.5x-/QLQ«-(*o*180)x(££12[10]°[57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73]'SOLUTIONS FOR STAR-2 : ']::484t t|t',6[35][36][37] 'STELLAR DIAMETER ( ARC-MILL ISECON DS ) .(6 2T.£012[6]x206264806) ,PM,6 2t1£[ 6 x20626 4806[38] 'BIN OF GEOMETRICAL OCCULTATION,(7 lT.S_Q12[9] +BIN) ,PM,4 1TH[8][39] 'SIGNAL LEVEL OF STAR-2 (COUNTS),(6 1TS0L2[7]),PM,4 1TEJ£[7][40] •POST-EVENT LIMB+SKY SIGNAL LEVEL: ,(6 1T££1,[8]) ,PM.4 1TE_&[3][41] 'OBSERVED LUNAR SHADOW VELOCITY:(7 5tS£12[10]),PM,(7 5T£R.[9]),' KM/SEC[42] ST+x 1 - T-«-.S_P_12 [ 1 ] *P_y_[ 1 ][43] T-

)[74] (13p« *),,CT[75] ((U$A\CT='' )

:' ,TS-*-( -/.SJ2L[ 7486C VELOCITY'[39] ((1iS?a\CT=' »)CT) .'MQ-BFIO.S' DFMT CM M[40] 2 lp' '[41] 'SUM OF SQUARES OF RESIDUALS: ' ,TS

487[6] WO :Y-*-Y+R[I]x(NPOL FNOS P«-( iHLLl) C 1*1+ 1 ; 1 ] . 1 + P) + . x ( 4>T)[7] -»(l*ltpjFILT)/WOV

NAME: VFILxER NAME: BFILTER NAME: NARROWSHAPE: 53 2 SHAPE: 42 2 SHAPE: 5 24450 0.0001294 3600 0.0000953 5295 0.06211184500 0.0002588 3650 0.0004767 5345 0.22515534550 0.0003881 3700 0.0013347 5395 0.44875784600 0.0005175 3750 0.0023834 5445 0.22515534650 0.0006469 3800 0.0044809 5495 0.03881994700 0.0007763 3850 0.01153594750 0.0011644 3900 0.02078374800 0.0016820 3950 0.0397559 NAME: NARROWB4850 0.0023289 4000 0.0469063 SHAPE: 5 24900 0.0047872 4050 0.04890844950 0.0112563 4100 0.0499571 4600 0.06581065000 0.0208306 4150 0.0505291 4650 0.22471915050 0.0296287 4200 0.0511965 4700 0.45585875100 0.0380386 4250 0.0513872 4750 0.22471915150 0.0450252 4300 0.0514825 4800 0.02889255200 0.0513650 4350 0.05100585250 0.0548583 4400 0.04976645300 0.0555052 4450 0.04738305350 0.0553759 4500 0.04519025400 0.0545996 4550 0.04271145450 0.0534351 4600 0.04004195500 0.0507181 4650 0.03765855550 0.0481304 4700 0.03479845600 0.0452840 4750 0.03317765650 0.0426963 4800 0.02955485700 0.0398499 4850 0.02717135750 0.0364860 4900 0.02440655800 0.0337689 4950 0.02192775850 0.0307931 5000 0.01925835900 0.0282055 5050 0.01649355950 0.0252297 5100 0.01372876000 0.0225126 5150 0.01115456050 0.0194074 5200 0.00858046100 0.0166904 5250 0.00581566150 0.0142321 5300 0.00343226200 0.0122914 5350 0.00209746250 0.0104800 5400 0.00152546300 0.0087980 5450 0.00085806350 0.0071161 5500 0.00047676400 0.0054341 5550 0.00028606450 0.0041403 5600 0.00019076500 0.0029758 5650 0.00009536550 0.00245836600 0.00207016650 0.00168206700 0.00142326750 0.00129386800 0.00103516850 0.00077636900 0.00064696950 0.00038817000 0.00025887050 0.0001294433

APPENDIX ELISTING OF THE APL WORKSPACE OCCPLOTS7 Y+fl BIN D;DlO;T[1] ABIN DATA FOR INTO CLASSES FOR HISTOGRAM[2] flD IS DATA VECTOR; N IS NUMBER OF CLASSES[3] Dio+l[4] Y*(T+D[l]-.5xl + T) ,[1.5] + /( 1+ lN ) ° .= + /(( 1 1 D) + T«-+\N p (( [/D)-L/D)*N) ° .

)][12] Z«-(0,-I,0)+Z[13] Z+-(Z+Q) ,Z-Q«-(+/QxX) ,[1.5]-/(Q^(N,I,2)p(l,2) + T)xx[14] ->-(l-(2=ppX)/L0[5] X«-X,[0.5][6] L0:T^2xe(Gp2)TiI^2*G-»-r2®l + pX[7] X«-((N«-I*2) ,2 2)p((l,2)+X*I*.5)[T;][8] T-

) T491[25] 'ANGULAR SEPARATION IN MILLISECONDS OF ARC CENTER 19 6.75[26] (1 20p'NORMALIZED IN TEN S ITY ' ) LAB ELD 1 3pl.4 2.8 90[27] (1 6p'COUNTS')LABELD 1 3p9.8 4.9 270[28] N«-0[29] L1:AXISD ZRO,(2+.475xN) ,( .475*2) ,270[30] + (10*N-«-N + l)/Ll[31] 1 SPLINE(2 + 7x(ip£££)* l+p£££) ,1 . 7 5 + 4 . 7 5 x ( £££- L/ &2£) */M-L/flli[32] 1 SPLINE(2 + 7x( ip££Ml)* l + p£fiMl) . 1 • 7 5 + 4 . 7 5* (££M,.E- [/ 0M)*I7.QB.S_-L/0B_S_[33] AXISD 8.5,(1.75 + 4.75x(££L.[6]-L/.QM)*( I7jH£) - L/£B_&) ..5[34] AXISD 2,(1.75 + 4.75x(££i[7]-L/ja£S) + (l7Jia£)-L/fl££)..5[35] AXISD ZR0.6 .32 ,(X[4]x.lxSPA) ,0[36] PLOTENDVV FITPL0T2 X;QlO;ZRO; SPA; XPOS ; STV ;NUMN ;N[1] flPLOT OF THE FITTED TWO-STAR OCCULTATION CURVE[2] flX = STARTING BIN NUMBER; £££, £0.112., SQL MUST BE GLOBAL[3] DlO-f-0[4] X«-X,(X+i£i[2]) ,(££L[8] + X2«-X) ,££L.[9],££L[5]x206 2 6 4810[5] START[6] PLOTSET .3[7] AXISD 2 1.7570 .35 ^15[8] AXISD 2 1 .75 7 1.4 .05[9] AXISD 2 1 .75 4.75 90 .475 .15[10] AXISD 2,(1 .75+4.75*20) ,4.275 90,(4.75*10), .08[11] AXISD 9 1.75 4.75 90 .475 .15[12] AXISD 9,(1.75 + 4.75*20) ,4.275 90 .475 .08[13] ZRO«-2 + (-/X[2 0])x7*-/X[l 0][14] SPA-

T.492[30] -K10*N«-N + 1)/L1[31] 1 SPLINE(2 + 7x( ipflfifi)* 1+Pfll£) » 1 • 7 5 + 4 . 7 5 * (£££- L/££.S_) */.0_B.S_-L/OB£[32] 1 SPLIHE(2+7x( ip£XJH£)* l + p£Ml) .1 . 75 + 4 . 75x(££MP- L/ 0£S)^r/OB£-L/OB£[33] AXISD 8.5,(1.75+4.75x((££L[7]+££L2[6]+££L[6])-L/OB£)*(l7fl££)-L/fl££) ,.5[34] AXISD 2.(1.75+4.75x(££l[7]-L/flfi£)*(r/fll£)-L/fl££)..5[35] AXISD ZR0,6.32,(X[4]x.lxSPA) ,0[36] X+X2,(X2+£0i2[2]) , ( X2+££L2 [8 ] ) ,££12 [ 9] ,.££12 [ 5 ] x2 0626 4810[37] N-f-0xl + ZRO-*-2+(-/X[2 0])x7*-/X[l 0][38] SPA«-10x*X[3]x(-/X[l 0])*7[39] L2:AXISD ZRO , ( 2+ 475 xN ) , ( . 47 5*2 ) ,2 7[40] ->-(10*N-f-N + l)/L2[41] AXISD ZR0.6 .32 ,(X[4]x .lxSPA) ,0[42] PLOTENDVV R«-FT Y;M;N;DlO[1] ADISCRETE FOURIER TRANSFORMATION OF EVENLY SPACED REAL DATA[2] OIO«-0[3] M«-( i2xN)xo*N-*-(pY)*2[4] R«-l 2p,(+/Y)*2xN[5] Ll:R*R.[0](*N)x+/(l 1°.xY)x2 l°.o(l+pR)xM[6] *(N>~l+ltpR)/Ll[7] R[N;>.5 Ox,~l 2 + RVV FTPREP X;DlO;T[1] PiSETS UP GLOBAL FOR POWER SPECTRA ANALYSIS[2] ftX IS CENTER OF TRANSFORM WINDOW FROM DATA SET[3] DlO-f-0[4] FJTJ2k£*-.5x + /(FFT EXBAXA-«-1024+ ( "512 + 5 1 4TX1.3 5 95 ) + CHI ) *2[5] *(3595*X+1512)/'F_I£U-1-'- 1012+ ( X+l 512 ) + CHI '[6] J>(35 95

1Q493V[1][2][3][4][5][6][7][8][9][10][11][12][13][14]INTPLOT X;DlO^INTEGRATION PLOT OF THE DATA VECTOR XDIO+-0STARTAXISD 2 1.7570 .4375_. 15.875 .05_AXISD 2 1.7570AXISD 2 1 .75 4.75 90 .475 .15AXISD 2, (1.75+4. 75*20), 4. 275 90,(4.75*10), .08('ZF3.1' DFMT .lxiH )LABELD 1 .55 , ( 1 .75+ .475" ill ) »C .5 ]( »LI4' DFMT( (pX)*8)xi8)LABELD(2+.8 75*i8) ,1.55.[.5]8p0•TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOW'CENTER 1 9 1.3(1 20p 'NORMALIZED IN TEN S ITY ' ) LABELD 1 3pl.25 3.22 90X«-(L/X)-X«-+\X-(+/X)tpX«-X[2 3],2+X1 SPLINE (2+7x(i P X)* 1+pX) ,1 .75+4.75xX*T/XPLOTENDV[1][2][3][4]F«-X INVFT R;DI0flINVERSE FOURIER TRANSFORMATION FROM COEFFICIENT MATRIXD I O-K)l°.OXo.xl+ X+-2 1$2 l l + pRF"-,(l l+R)+ + / + /((pX)pl + R)xXVV NOISEPLOT X;OC;PD;R;MEAN ; SIGMA; Y;BR;N[1] ANOISE FIGURE FOR LUNAR OCCULTATION[2] AX IS BIN NUMBER OF START OF DATA USED IN SOLUTION[3] AMUST HAVE §,OL OBS AND COMP AS GLOBAL VARIABLES[4] I2!£A . =.Sjpj,[ 2 ] + ( X- 1 ) + CH[5] AX[1]=FIRST BIN OF DATA X[2]=LENGTH OF DATA[6] C«-( ( X- 1 ) + CH 1 ) -.S_P_L.[ 6 ][7] OC^OC.(OBS-COMP) ,(( 1+.SJ2L.[2]+X) + CH1)-.S_£L.[7][8] PD-

494[23] MEAN-f-(+/2 + 0C)*4094[24] SIGMA«-( (0O2)+.*.5)*4093[25] N^O[26] Ll:AXISD(2 + 7x(MEAN-l+L/BR)*l+R) .(2+.475XN) ,.2375 90[27] -KlO*N-

1 I[16] 1 SPLINE(2 + 2 .5x,(500 + X)o.xi 1 ) , 1 + 495[7] X«-X,[ .5]2 + ( (7t P £0MP)x ip C0M1) °.x9 P 1[8] N«-0[9] START[10] Ll:l SPLINE, W>X[;;N][11] AXISD 2,(1 .82+NX.52) ,.5 90 .5 .1[12] AXISD 2,(1 .82+NX.52) , .5 90 .5 .1[13] AXISD 9,(1 .82+Nx.52) , .5 90 .5 .1[14] AXISD 9,(1.82+Nx.52) ,.5 90 .5 .1[15] AXISD(2 + 7x££L2[8]t P 0££) , ( 2 . 56+N x . 52 ) , .04 90[16] AXISD(2 + 7x££L[8]t P 01£) , ( 2 . 56+N x . 52 ) ,.04 90[17] AXISD 2,(2.08+Nx.52) ,7[18] *(9*N-HJ + 1)/L1[19] AXISD(2 + 7x££L[8]* P 01£) ,1 .75 .07 90[20] AXISD(2 + 7x££L2[8]t P 0£!) ,1 .75 .07 90[21] AXISD 2 1.75 7 1.4 ;05[22] AXISD 2 1.75 7 1.4 .05[23] 'TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWCENTER 1 9 1.3[24] (99 4 P 'C0MPVEL2TIM2INT2DIA2VEL1TIM1INT1DIA1 )LABELD '.35,(2.02+.52x 1l 9) ,[ .5]9 P[25] (1 18 P 'PARTIAL DERIVATIVES ') LAB ELD 1 3pl.2 2.8 90[26] ('LI4' DFMT S+(i5)x.2x 1 + P C£MP) LABELD( 2 + 1 . 4x i 5 ) , 1 . 55 ,[.5]5 P[27] PLOTENDVV POWERPLOT;R;X; I;DlO[1] flPOWER SPECTRA OF MODEL CURVE, STAR+SKY, AND OCCULTATION[2] AEXECUTE FTPREP IN BEFORE POWERPLOT[3] DIO+-0[4] START[5] PLOTSET .3[6] AXISD 2 1 5 90 1 .1[7] AXISD 2 1 .5 4 90 1 .05[8] AXISD 4.66 1 5 90 1 .1[9] AXISD 4.66 1 .5 4 90 1 .05[10] AXISD 7.32 1 5 90 1 .1[11] AXISD 7.32 1 .5 4 90 1 .05[12] X«-(500+l+F_10_B_S_) ,( 500+1 + FJTC:U_l) .500+1 + FTMOD[13] R

A?6[27] (1 llp'OCCULTATION ')LAXISD 4.36 3 271[28] (1 lOp'STAR + SKY')LAXISD 7.02 3 271[29] (1 llp'MODEL CURVE' )LAXISD 9.68 3 271[30] PLOTENDVV RAWPLOT X;DlO;ZRO;SPA;NEG;POS;XPOS;STV;NUMM;N[1] flPLOT OF THE RAW DATA, X (EVERY 4 POINTS)[2] DlO+0[3] START[4] PLOTSET .4[5] AXISD 2 1.75 7 .4375_.15[6] AXISD 2 1.7570 .875 .05_[7] AXISD 2 1.75 4.75 90 .475 .15[8] AXISD 2,(1.75 + 4.75*20) ,4.275 90,(4.75*10), .08[9] AXISD 9 1.75 4.75 90 .475 .15[10] AXISD 9,(1.75+4.75*20) ,4.275 90 .475 .08[11] ('ZF3.1' DFMT .lxUl)LABELD 1 • 55 , ( 1 . 7 5+ . 47 5 * 1 1 1 ) , [ . 5 ][12] ('LI4* QFMT 4096x.lx;H)LABELD 9 . 5 , ( 1 . 7 5+ . 47 5 x il 1 ) , [.5]0[13] ('LI4' DFMT 512x;8)LABELD(2+.875xi8) ,1 .55 ,[ .5]8p0[14] 'TIME IN MILLISECONDS FROM BEGINNING OF DATA WINDOWCENTER 1 9 1 .3[15] (1 20p 'NORMALIZED IN TEN SITY ' ) LABELD 1 3pl.4 2.8 90[16] (1 6p 'COUNTS')LABELD 1 3p9.8 4.9 270[17] 1 SPLINE(8192pO 1 ) / ( 2 + 7 x( t 40 96 ) *40 95 ) , 1 . 7 5 + 4 . 75xX*4095[18] PLOTENDVV Y«-N SMOOTH D;DlO[1] AN-POINT UNWEIGHTED SMOOTHING OF THE VECTOR D[2] DIO+-0[3] Y«-(pD)p((L.5xN) + D) ,((-N) + (+/( iN ) (N , p D) p D) *N ) , ( - T . 5 xN) + DV

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BIOGRAPHICAL SKETCHSchneider (no B . " after the Glenn H H, please note) wasborn to Elaine and Ira G. Schneider on October 12, 1955, anotherwise un-noteworthy day, except perhaps for the -fact thatit marked the 463rd anniversary of the discovery of America,as commonly reckoned. At the tender age o-f three he receivedhis -first telescope (Sears, 40X!), and learned early in lifethe meaning o-f light pollution.He attended public school 97 and J.H.S. 135 (also knownas the Frank D. Whalen Junior High School, though no one everknew who Frank D. Whalen was) in New York City. Thanks tothe closing o-f the school during the summer o-f 1969 he waspermitted to retain possession o-f the school library's copieso-f The Larousse Encyclopedia of Astronomy and Norton's StarAt 1 as . Later that year he became a member of the AmateurObservers' Society of New York. These two events foreverinfluenced his life and started him on the path to a careerinastronomy.He graduated from The Bronx High School of Science inJune of 1972. Shortly thereafter, he organized aninternational solar eclipse expedition, in hopes of observinghis second total solar eclipse. The clouds which hungominously over the Gaspe Peninsula that day served toreinforce his devotion to shadow chasing.503

504In June of 1976, he earned a Bachelor of Science degreein physics -from the New York Institute o-f Technology. Be-foreentering the graduate program in astronomy at the Universityo-f Florida in September o-f 1977, he worked as an APLtechnical analyst -for Warner Computer Systems, Inc.After eight years, two trips to the South Pole,seemingly endless commuting between Gainesville, Paris,Noordwijc and Bristol, statistically improbable stretches o-fcloudy weather during scheduled observing runs, and beingthwarted at every turn by wayward computers (micro andmacro), he expects, -finally, to receive the degree o-f Doctoro-f Philosophy in August o-f 1985. He has accepted positionaat the Space Telescope Science Institute, working -for theComputer Sciences Corporation as a Science and MissionOperations Astronomer.He has observed every total solar eclipse since March,1970, and intends to keep chasing the moon's shadow well intothe -future. He has a definite preference for Dr. Brown'sCelery Tonic (now called Cel-Ray Soda, alas), and egg creamsmade with Fox's U-Bet chocolate syrup and Good-Healthsel tzer .At the moment he is single, but this malady is expectedto be cured on June 7, 1985.

'I certify that I have read this study and that in myopinion it con-forms to acceptable standards of scholarlypresentation and is ful 1 y adequate , irT~sxope and quality, asa dissertation -for the degree, of Doctor ]of- PtM rpsophy./John P. Oliver, ChairmanAssociate Professor o-f AstronomyI certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality, asa dissertation for the degree of Doctor of Philosophy.C(/C

I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality, asa dissertation for the degree of Doctor of Philosophy.Ralpfl G. Sel fridgeProfessor of Computer andInformation SciencesThis dissertation was submitted to the Graduate Facultyof the Department of Astronomy in the College of Liberal Artsand Sciences and to the Graduate School and was accepted aspartial fulfillment of the requirements for the degree ofDoctor of Philosophy.Auoust 1985 Dean, Graduate School