Properties of the surface detector data recorded by the Pierre Auger ...

Properties of the surfacedetector data recorded by thePierre Auger observatoryMASTERARBEITzur Erlangung des akademischen GradesMaster of Science(M.Sc.)dem Fachbereich Physik derUniversität Siegenvorgelegt vonStefan GrebeOktober 2008

CONTENTSContents1 Introduction 11.1 Cosmic rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.3 Extensive air showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.4 Detection methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Scope of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Pierre Auger observatory 72.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Surface detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Surface detector stations . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Calibration and monitoring . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.3 AMIGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Fluorescence detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 Radio detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 First results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Event reconstruction using the surface detector data 163.1 Trigger chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Tank trigger probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3 Event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.1 CDAS and Offline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.2 Angular reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.3 Energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.4 Fine-tuning of the LDF . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4.1 Variations on different time-scales . . . . . . . . . . . . . . . . . . . . . 253.4.2 Attributes of the array . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Stability of the reconstruction 284.1 Method and data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Reconstruction without individual stations . . . . . . . . . . . . . . . . . . . . . 294.2.1 Stability of events with E > 57EeV . . . . . . . . . . . . . . . . . . . . 294.2.2 Stability of events with E > 25EeV . . . . . . . . . . . . . . . . . . . . 334.2.3 Test of the asymmetry correction . . . . . . . . . . . . . . . . . . . . . . 354.2.4 The optimum ground parameter . . . . . . . . . . . . . . . . . . . . . . 36

IVCONTENTS4.3 Reconstruction without sets of detectors . . . . . . . . . . . . . . . . . . . . . . 404.3.1 Reconstruction with the unitary cell only . . . . . . . . . . . . . . . . . 404.3.2 Simulating borders of the array . . . . . . . . . . . . . . . . . . . . . . . 434.4 Less dense arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Azimuth angle distribution 495.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2 Azimuth angle distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.2.1 Hexagonal structure of the array . . . . . . . . . . . . . . . . . . . . . . 505.2.2 Direct light in inclined showers . . . . . . . . . . . . . . . . . . . . . . 545.2.3 Determination of amplitudes and phases . . . . . . . . . . . . . . . . . . 545.3 Model for the hexagonal effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.3.1 Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.3.2 Asymmetry correction . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.3.3 Signal fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.3.5 Limits of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.4 Description of the asymmetry in 2! . . . . . . . . . . . . . . . . . . . . . . . . 645.4.1 Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.4.2 Rayleigh analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.4.3 Energy and " dependency . . . . . . . . . . . . . . . . . . . . . . . . . 705.4.4 Different areas of the array . . . . . . . . . . . . . . . . . . . . . . . . . 735.4.5 Time dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.4.6 Events with less strict cuts . . . . . . . . . . . . . . . . . . . . . . . . . 765.4.7 Attributes of the effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.5 Origin of the asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.5.1 CDAS reconstruction algorithm . . . . . . . . . . . . . . . . . . . . . . 815.5.2 Border effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.5.3 Tilt of the array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.5.4 PMT effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.5.5 Terrestrial magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . 855.5.6 Solar panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866 Summary and outlook 88List of Figures 95List of Tables 97List of Acronyms 98Acknowledgment 103

Chapter 1Introduction1.1 Cosmic raysCosmic rays are particles with high energies coming from outer space. These particles are permanentlyhitting and penetrating the earth’s atmosphere, thereby initiating extensive air showers ofsecondary particles.Cosmic rays are mainly positively charged and their exact composition depends on the part of theenergy spectrum, which is observed. In general, about 85% of the particles arriving at the top ofthe atmosphere are protons, about 12% are helium nuclei, about 2% are electrons and about 1%are nuclei, which are heavier than helium [1]. Cosmic rays cover an energy range of 11 ordersof magnitude from 10 9 eV up to 10 20 eV. For energies below 10 14 eV, the best data have beenobtained from direct measurements in space experiments; for higher energies, the data are derivedfrom ground based experiments, which measure the secondary particles of extensive air showers,or interactions of the particles with the molecules in the atmosphere.In this chapter, a short historic introduction about the discovery of cosmic rays and the determinationof their properties is given. Then, the particles, their energy spectrum, the extensive airshowers produced, and the detection techniques used are described. In the last part, the scope ofthis thesis is defined.1.1.1 HistoryIn 1785, H. Coulomb found, that a simple electroscope looses its charge with time though beingwell insulated. After the discovery of radioactivity by H. Becquerel in 1896, it was believed, thatthe electric discharge is due to radioactivity in the soil or due to radioactive gases. In a series ofexperiments, the phenomenon and its dependence on the altitude above ground has been studied.In 1910, T. Wulf compared the radiation at the bottom and on the top of the Eiffel Tower and founda significant drop of the ionization rate at the top [2].The cosmic radiation has been discovered by V. Hess in 1912 [3], as he increased the distanceto the ground up to 5300 m by performing balloon flights. Hess measured the discharging effectswith electroscopes. He found a decrease of the effect up to an altitude of 1500 m, then it startedto increase again and became even larger at an altitude of 3600 m than on the ground. This measurementestablished the extraterrestrial origin of the radiation, which R. Milikan called ”cosmicrays”, after he had discovered in 1925, that the radiation interacts with the particles in the earth’satmosphere [4]. In the interactions, new particles are produced, which in turn may interact withatmospheric constituents. All particles produced in interactions in the atmosphere are called “sec-

2 Introductionondary particles”, which could for the first time be detected by cloud chambers and photographicplates.In 1938, P. Auger found, that cosmic radiation events were coincident in time, by measuring secondaryparticles with spatially separated detectors on ground level [5]. He postulated, that theywere associated with a single event, an “extensive air shower”. Today, the largest experiment tomeasure extensive air showers is named after their discoverer, the Pierre Auger observatory.1.1.2 Energy spectrumCosmic rays arriving at the top of the earth’s atmosphere cover a range of about 11 orders ofmagnitude in energy and of about 30 orders of magnitude in flux. The relation between the flux Iand the energy E is given by a power lawdIdE ∼ E−# , (1.1)where the spectral index # depends on the energy. For cosmic rays with energies between 10 11 eVand 10 15 eV # equals 2.7. For higher energies # changes to 3.1 and returns to the value of 2.7 atE ≈ 10 18 eV (see Figure 1.1). The regions, where the spectral index changes are referred to as theFigure 1.1: Primary cosmic ray spectrum [6].“knee” and the “ankle”.For energies beyond 6 · 10 19 eV, Greisen, Zatsepin and Kuzmin predicted a cut-off of the flux

1.1 Cosmic rays 3[7]. At the GZK cut-off, primary cosmic rays are expected to interact with cosmic microwavebackground photons. Up to now, the number of events with energies above the predicted energythreshold, detected with the Pierre Auger observatory, is compatible with the GZK cut-off.1.1.3 Extensive air showersWhen high energy primary cosmic rays enter the atmosphere, they collide with nuclei in the upperatmosphere and generate less energetic secondary particles. These secondary particles are also interactingwith constituents of the atmosphere and, thus, initiating cascades themselves. During thedevelopment of an extensive air shower, the secondary particles of each new generation carry lessenergy per particle than the generation before. The number of particles increases up to the showermaximum X max , where the energy of the particles becomes too small to produce new particles (seeFigure 1.2). Beyond the shower maximum, the number of particles decreases exponentially withFigure 1.2: Schematic drawing of the longitudinal development of an extensive air shower [8].the atmospheric depth. The altitude of the shower maximum depends on the energy and the typeof the primary particle, as well as on the mass densities in the atmosphere.The cascade of secondary particles comprises of three different components: the hadronic, themuonic, and the electromagnetic (see Figure 1.3). The hadronic component in extensive air showersis small (1%), but has a large impact on the shower development, as it feeds the other components.In strong interactions, mainly pions are generated and with smaller cross sections alsokaons, protons and neutrons. The charged pions perform most likely further hadronic interactions,whereas the neutral pions decay with high probability into two photons. Since the transversal momentaof the hadrons are very small, they propagate along the line of flight of the primary particleand form, together with other, only slightly deflected particles, the shower core.The muonic component rises mainly from weak interactions of the hadronic component. The crosssection decreases during the shower development, as the cross sections of the competing stronginteractions arise with increasing particle densities in lower atmosphere layers. The dominatingmechanisms for the production of muons are! ± −→ µ ± + $ µ ($ µ ),K ± −→ µ ± + $ µ ($ µ ),K ± −→ ! ± + ! 0 .

1.2 Scope of this thesis 5pends on the distance r to the shower axis% e (r)=( )& (4.5 − s)& (s) · & (4.5 − 2s) · N e r s−2 (2!r 2 · 1 + r ) s−4.5, (1.2)r M r Mwhere N e is the number of electrons at observation level, r M the Molière radius and s theparametrization of the shower age. At the point of the first interaction of the shower with a particleof the atmosphere, s equals 0. It reaches 1 at the shower maximum and s equals 2 at the point,where the shower dies out.1.1.4 Detection methodsFor the detection of cosmic rays, its various interactions with matter are used. Depending on theenergy and the particle type, the appropriate detector is selected. For charged particles, the dominatingmechanisms of energy loss are bremsstrahlung and ionization. They can be measured withgas detectors, scintillators and calorimeters. The emitted Cherenkov radiation can be measuredwith threshold counters or ring imaging Cherenkov counters [10].Cosmic rays can be detected by measuring the primary particle directly, or by measuring the secondaryparticles of extensive air showers. For energies below 10 14 eV, only small detectors arerequired to collect high statistics in a reasonable time, due to the high flux of particles. In thiscase, the cosmic rays can be detected directly by particle detectors flown aboard satellites or inhigh altitude balloons.For the detection of cosmic rays with E > 10 14 eV, two different techniques are common: theobservation of longitudinal shower profiles and the observation of lateral shower profiles on theground. The Pierre Auger observatory comprises both techniques and performs hybrid measurementsof extensive air showers with fluorescence telescopes and a ground array (see Figure 1.4)The secondary particles of extensive air showers excite the nitrogen atoms in the atmosphere.When the atoms fall back into their ground state, they emit ultraviolet fluorescence light. Theamount of emitted light is proportional to the number of secondary particles and thus, correlateswith the energy of the primary cosmic ray. This light is measured by fluorescence telescopes,which observe the atmosphere above the Pierre Auger observatory.The other technique uses the production of Cherenkov light in water-filled surface detector stations.The secondary particles are reaching the ground with almost the speed of light. When theycross the water, their speed is greater than the speed of light in that medium and this results in theemission of Cherenkov light, which is measured with photomultipliers. Arrays of surface detectorstations measure the lateral distribution of the particles at the ground.1.2 Scope of this thesisThe work on hand constitutes an effort to achieve a better understanding of the properties of thesurface detector data recorded by the Pierre Auger observatory. Since the construction phase ofthe regular surface detector array has been finished in the middle of 2008, more than 4500 eventsare recorded every day, in an energy range from 0.1 EeV to 100 EeV. The events are reconstructedwith two independent reconstruction algorithms, online (CDAS, central data acquisition system)and Offline, and analyzed by the members of the Pierre Auger collaboration. The aim is, to solvefundamental questions about the highest energetic cosmic rays with this data. Before these resultscome into reach, a detailed knowledge of the detector and its features is essential.Two main aspects have to be considered, the accuracy of the reconstruction for the individual

6 IntroductionFigure 1.4: Schematic view of the measurement of an extensive air shower by a fluorescence telescopeand surface detector stations [12].events, which fulfill the trigger conditions and the dependence of the trigger rate on the energy,the zenith angle, the azimuth angle or the core position in the array.In the following Chapter 2, the Pierre Auger observatory and its detector techniques are described.The focus is on the surface detector, its stations and its calibration. Chapter 3 contains a descriptionof the trigger chain and the reconstruction method for surface detector events. At the end of thechapter, several known properties of the data are presented.In Chapter 4, the stability of the CDAS reconstruction algorithm is checked for events with E >25EeV. The energies and arrival directions of highest-energy Auger surface detector events arecompared to the values, obtained with modified sets of detectors, used in the reconstruction.In Chapter 5, the azimuth angle distribution is analyzed in detail. In addition to the variations inthe number of events due to the hexagonal structure of the array, an asymmetry in the number ofevents with a period of 2!, is observed and investigated in more detail.Finally, Chapter 6 summarizes the contents of this thesis, including a brief outlook on possiblefurther studies.

Chapter 2Pierre Auger observatoryThe Pierre Auger observatory has been designed in order to answer fundamental questions abouthighest-energy cosmic rays. Nowadays, 100 years after their discovery by V. Hess [3], theirsources are still not identified and the acceleration mechanisms are not yet understood.2.1 OverviewThe observatory is named after Pierre Auger, who discovered extensive air showers in 1938 [13]with spatially separated detectors. These days, more than 300 physicists from universities andresearch institutes of 18 countries work with the observatory.The Pierre Auger observatory will have two sites, one in each hemisphere to be able to observeultra-high energy cosmic rays (UHECRs) over the entire sky. The northern site (Auger North) isplanned for southeast Colorado, USA, near the city of Lamar. It will be a hybrid detector consistingof water Cherenkov detectors and fluorescence telescopes. Studies for the design of thetelescopes, the surface stations and their spacing are under way. In this thesis, the focus is onAuger-South and its data. In all further chapters the word observatory is used instead of southernsite of the Pierre Auger observatory.The observatory is located in the Pampa Amarilla near the town of Malargüe in the province ofMendoza, Argentina. The assembling is almost finished and data taking started at the beginningof 2004. The observatory has a size of 3000km 2 and allows the detection of primary particles inan energy range from 10 17 eV to 10 21 eV.With its clear nights and minimal light pollution, the site in the Pampa Amarilla provides uniqueconditions for the detection of cosmic rays. The observatory is located at a plain plateau at an altitudeof 1420 m above sea-level, which reduces the distance to the shower maximum (see Chapter1.1.3), which is typically situated a few kilometers higher in the atmosphere. The surface detectorarray consists of 1600 water Cherenkov tanks, located at altitudes between 1340 m and 1610 m,and is surrounded by four fluorescence detector buildings. Each building, called eye, is equippedwith 6 telescopes, which survey the sky above the ground array in moonless and cloudless nights(see Figure 2.1) [15].The observatory combines two complementary observation techniques: the detection of the secondaryparticles at ground level and the observation of fluorescence light, produced by the airshower in the atmosphere. The detection of showers, using both techniques, allows to crosscalibratethe individual detectors. Events detected simultaneously with the surface detector andthe fluorescence detector are called hybrid events.

8 Pierre Auger observatoryFigure 2.1: The Pierre Auger observatory near the city of Malargüe. The circles illustrate the positionsof the 1600 water Cherenkov detectors forming the surface detector array. The array is overlookedby 24 fluorescence telescopes, situated in 4 buildings. The fields of view of the individualtelescopes are indicated by lines [14].After the first detection of a particle at an energy of about 10 20 eV reported by Linsley in 1963[16], many questions about these rare particles are still not answered. Due to the low flux of particlesin this energy range (one particle per century and km 2 for E ≈ 10 19 eV), a huge detectoris required to be able to collect a large amount of statistics, for an analysis in a reasonable time.After the completion of the two sites in the south and in the north, the Pierre Auger observatorywill measure the cosmic ray flux with more statistics, within 50 days of operation, than all datacombined of all the other experiments in the last 30 years.2.2 Surface detectorThe surface detector (SD) array of the Pierre Auger observatory (PAO) consists of 1600 waterCherenkov detectors, covering 3000km 2 with a spacing of 1500 m on a triangular grid. The distancebetween the stations is a compromise between cost considerations and the energy thresholdfor the detection of cosmic rays.In addition, 15 pair tanks and 7 triplets have been installed to study signal fluctuations. For pairtanks, a second detector is installed at a distance of 11 m next to another surface station. Tripletsare arranged in an equilateral triangle with a spacing of 11 m as well. In the reconstruction algorithm,only the signals of stations belonging to the regular grid are used.2.2.1 Surface detector stationsA schematic view of a surface detector station is shown in Figure 2.2. The main component of

2.2 Surface detector 9Figure 2.2: Schematic view of a surface detector station [17].each station is a cylindrical plastic water tank of 3.6 m in diameter. It is filled with 12 t of ultrapure water, which is required to achieve the lowest possible attenuation of the UV Cherenkov lightand to guarantee a stable operation over the running period of 20 years. The water is enclosed bya sealed liner with a diffusively reflecting inner surface.Three photomultipliers (PMTs), each nine inch in diameter, symmetrically mounted in a regularmanner at the upper side of the tank (1.2 m from the center), are looking down to the water and arecollecting the produced Cherenkov light. The height of a tank is 1.55 m and it is filled with waterup to a level of 1.2 m. The water absorbs on average 85% of the energy of the secondary particleshitting the station, if it has a distance of more then 100 m to the shower core.Two solar panels on top of the tank provide the power for the electronics. The energy is accumulatedin two batteries, hosted in a battery box in the south of the station, to protect them fromdirect sunlight. Each station has an antenna and communicates via a wireless system with thecentral data acquisition system (CDAS) in Malargüe. The location of each station is known withan accuracy of less than 1 m as measured by a differential GPS system.Each of the three PMTs in a station has two outputs: the signals of the anode and the last dynode,the latter amplified by a factor of 32. The two signals are filtered and digitized using 10 bit flashanalog-digital converters (FADC) in 1024 bins, each representing a time interval of 25 ns. Ringbuffer memories save the digitized data and allow first and second level triggers to be processed.The whole electronics, except for the front-end board, are implemented in a unified board (UB)[18].2.2.2 Calibration and monitoringThe time resolution of the surface detector is affected by two factors: the uncertainty of the synchronizationbetween the stations (8 ns, achieved with the differential GPS system) and the uncer-

10 Pierre Auger observatorytainty of the starting points of the FADC traces (7 ns). Therefore, the total time resolution of thesurface detector adds up to 10 ns [15].The measured signals of the FADCs have to be converted into physical units. The signal of aPMT depends on several parameters like the water quality, the liner reflectivity, the coupling ofthe PMT to the water, the gains of the PMT and the amplification factor. Each surface station iscalibrated individually and continuously by measuring the charge deposit of atmospheric muons.The signals caused by the muons are proportional to the track lengths in the water, as they arenot absorbed in the detector station. The energy deposited by a single vertically and centrallythrough-going muon is used as a reference and defined as 1 VEM (vertical equivalent muon). Asthe atmospheric muons arrive isotropically from all directions, they have different trace lengths inthe water. The charge distribution has a peak at (1.09 ± 0.02)VEM for the sum of the three PMTsFigure 2.3: Histograms of charge (left) and pulse height (right) for a single SD station, triggered by a3-fold coincidence from all 3 PMTs (solid line). The histogram with the dashed line showsthe spectrum of an external muon telescope for the same events. The first hump is due to thetriggering of low-energy particles from EAS and shows the typical exponential slope. Thesecond hump is caused by the atmospheric muons [19].and at (1.03 ± 0.02)VEM for individual PMTs, as they are only sensitive to the fraction of lightdeposited in their proximity.Switching a station on, the high voltage of each PMT is tuned until the signal rate is 100 Hz at150 channels above baseline. A pedestal of 50 channels is added to the signal to observe possiblefluctuations of the baseline.The calibration to VEM units is a three step process [19]:• The gains of the PMTs are set to have the peak I peakV EMin the pulse height histogram at50 channels for each individual PMT (see Figure 2.3).• The I peakV EMis monitored in units of channels and adjusted to the electronics-level trigger tocompensate for drifts, which occur after setting the value.• The peak in the charge histogram Q peakVEM (see Figure 2.3) is determined and used to get theconversion for the signal from Q peakV EMin units of VEM.

2.2 Surface detector 11During data taking the individual PMT rates are monitored by determining the events, with allworking PMTs in a station, above 1.75 VEM. The estimated rate is at 110 Hz. These T1 events areused to check, if each individual PMT has a counting rate of 70Hz above 2.3 VEM. An unmatchedPMT, with a too high baseline, would have a higher rate than 70Hz above 2.3 VEM. The VEMvalue for a PMT not conforming to the 70 Hz will be modified and matched in an iterative process[20].To determine the charge of a VEM, the signals of the PMTs are integrated over 625 ns, if the signalpeaks exactly at the threshold of 1.75 VEM. The obtained value is divided by a factor of 1.75 toget 1 VEM, which has now a precision better than 2%. This method is not applied at a thresholdof 1 VEM directly, because of a too high rate.2.2.3 AMIGAThere are clear indications that simulations underestimate the muon content of extensive air showersand, hence, are biasing the SD energy estimator. A direct measurement of the muons wouldreduce the systematic error of the reconstructed energies and, in addition, the muon fraction is anexcellent indicator of the type of the primary particle and might help to solve the question of thecomposition of cosmic rays [21].At the moment, the observatory is upgraded with a muon detector and additional surface detectorstations. AMIGA (Auger Muons and Infill for the Ground Array) is an enhancement of the existingsurface detector. In a hexagon with an area of 23.5km 2 , additional surface detectors havebeen installed, with a graded spacing of 433 m and 750 m (see Figure 2.2.3). The spacing allowsto measure primary particles down to an energy of 0.1 EeV. The expected number of detectedevents per year is given in Table 2.1. In 2009, 30m 2 muon scintillation counters will be buried in aE 0 [EeV] Area [ km 2] No. events year −10.1 5.9 160000.3 23.5 8500Table 2.1: Expected number of events per year with the completely installed AMIGA [22].depth of ∼ 3m next to 7 surface detector stations (one unitary cell). This prototype will take datafor one year and then muon counters will be deployed next to each of the 85 surface stations inthe 23.5km 2 hexagon (shown in Figure 2.2.3) to determine the muon component of extensive airshowers. The center of AMIGA will be located 6 km away from the Coihueco building and willbe overlooked by the fluorescence telescopes.Each muon counter will comprise 64 strips of a highly segmented plastic scintillator with opticalfibers ending on a 64-pixel multi-anode PMT. In the current design, the strips are 400 cm long,4.1 cm wide and have a height of 1.0 cm. At each tank, 3 or 4 counters will be installed and aprinted circuit board (PCB) with a data handling field programmable gate array (FPGA) will beattached to the PMTs. A micro-controller for monitoring and communication will process the dataand send it to a second FPGA above ground, if the corresponding surface detector station has beentriggered by an extensive air shower. A microcomputer will transmit the tank and muon counterdata to the central data acquisition system at the Auger campus.The aim is, to use the information of the number of muons at each station to calculate the estimatednumber of muons N µ (600) 600 m away from the shower axis, by using the parameterized muonlateral distribution function [23], currently used by KASCADE-Grande. In addition N µ (600) is an

12 Pierre Auger observatoryexcellent indicator for the type of the primary particle [22].Figure 2.4: The extensions near the Coihueco building: The dots illustrate the surface stations and thelines indicate the field of view of the HEAT and the former installed fluorescence telescopes.All stations indicated with a name belong to the 1.5 km grid, the others are spaced 750 m and433 m apart. All stations inside the huge hexagon will have in addition a 30m 2 buried muoncounter, after AMIGA is completed [24].2.3 Fluorescence detectorDuring the night, the atmosphere above the array is monitored by 24 Schmidt telescopes placed in4 buildings (eyes) at the border of the ground array (see Figure 2.1). Each telescope has a field ofview of 30 ◦ × 30 ◦ , resulting in a lateral view of 180 ◦ per eye, towards the center of the array, from1 ◦ to 31 ◦ above the horizon.The secondary particles of extensive air showers excite the nitrogen molecules in the atmospherealong their path. When the excited molecules fall back to ground state, fluorescence light is emitted.If the shower axis is in the field of view of a telescope, the produced light passes a UVtransmitting filter at the diaphragm with an aperture of 3.8m 2 . The filter is transparent for wavelengthsin the range of 300 nm to 400 nm, The optical aberrations are minimized, using a ringof corrector lenses installed around the diaphragm. The transmitted light is reflected by a 12m 2mirror and measured by a camera, equipped with 440 hexagonal PMTs. The PMTs are arrangedin a 22 × 20 matrix. Each PMT overlooks a region of the sky of 1.5 ◦ in diameter. The signals ofthe PMTs are amplified and filtered using an analog board, which is connected to a digital board.The fluorescence detector has a 4 level trigger and the real events are sent from the eye PCs (mainPC in each building) to the central data acquisition system (CDAS) [26].Before and after each run, a three step relative calibration is performed to observe any changesin the system. Firstly, the PMTs are illuminated directly with a laser located at the center of the

2.3 Fluorescence detector 13Figure 2.5: Schematic view of a fluorescence telescope unit [25].mirror, to check their responses. Secondly, a laser mounted at the top of the camera points at themirror and the reflected beam is used to test the mirror-camera system. In the third step, the lighthas to pass the diaphragm, before being reflected at the mirror and coming to the camera. This allowsto test the whole telescope system. The absolute calibration is performed only 3 or 4 times ayear by illuminating the cameras with a well known diffuse light source. The absolute calibrationhas an uncertainty of 12%.As the number of detected photons is strongly correlated with the atmospheric conditions, anatmospheric monitoring system is installed. In order to determine the aerosol content in the airbackscatter LIDARs (light detection and rangings) are constructed next to each telescope building.Each LIDAR consists of an UV-laser and a PMT, that detects the photons of the UV laser pulses,which are backscattered in the atmosphere. Furthermore, density and temperature profiles of theatmosphere are available from balloon measurements. The atmospheric monitoring data is used,to correct for attenuation effects.Another tool is the central laser facility (CLF), a strong laser located at the center of the array.The CLF is used to check the relative timing between the SD and the FD by inserting a signal viaa glass fiber into the closest SD station, at the same time as the laser shoots vertically in the sky.The well known position of the laser beam is used to test the angular reconstruction of the FD andto cross-check the calibration of the individual telescopes.At the moment, the FD is upgraded with three high elevation Auger telescopes (HEAT) nearthe Coihueco building. When the construction is being finished, they will observe the atmosphereabove the new infill detector area, with an elevated field of view from 30 ◦ to 60 ◦ above the horizon.Together with the telescopes hosted in the Coihueco building, the atmosphere can be monitored

14 Pierre Auger observatoryfrom the horizon up to an angle of 60 ◦ and this allows to measure the main part of the showerdevelopment in the atmosphere, for a sizable number of extensive air showers.Since all telescopes (normal FD and HEAT) are very sensitive to light, data taking is only possiblein periods of a bit more than two weeks around new moon, without rain and storm, as well as nottoo heavy clouds. The duty cycle is less than 12%. As the FD performs a calorimetric measurement,the longitudinal shower profile and the location of the shower maximum can be detected.The estimated systematic uncertainty in the reconstructed shower energy is 25% and the angularresolution is in the range of 0.5 ◦ [27].2.4 Radio detectorsThe charged particles of air showers passing through the terrestrial magnetic field emit electromagneticradiation, that can be detected by ground-based antennas [28] [29]. The radiation isemitted coherently and as the amount of radiation is proportional to the number of particles in theEAS, the energy of the primary particle and the shower maximum can be determined.The emission mechanism is still an open question and different models try to describe it. Onemodel is based on the fact, that the particles in the air shower travel faster than the speed oflight and emit coherent Cherenkov radiation in the range of radio frequency. In neutral showers,the signals of positively and negatively charged particles would cancel each other, but due to theenrichment of negative charge in the EAS, caused by the recombination of positrons with the electronsin the air, radiation at radio frequency is emitted in the forward direction.Another model assumes, that the geomagnetic field deflects the particles and induces synchrotronradiation. This process can also be interpreted as a transverse current, coming from the separationof positively and negatively charged particles by the geomagnetic field [30].The advantages of radio detectors are the possibility to measure the longitudinal profile of EAS,comparable to fluorescence measurements, but with a much higher duty cycle and the low costsetup.At the Pierre Auger observatory, different prototypes of radio detectors are tested. Currently, externaltriggers from the SD are used. The challenge is to develop a self-triggered system coveringan area of 20km 2 . In order to achieve this, several technical issues, like handling the data streamand installing a wireless system for the data transfer, have to be resolved.2.5 First resultsThe observatory is taking data in a stable mode since 1st of January 2004, starting with 154 surfacedetector stations. The construction has been finished in the middle of 2008. Since the starting ofdata taking more than 1.5 Mio. events have been detected and first results have been published.The most interesting recent observation is the “Correlation of the highest energy cosmic rays withnearby extragalactic objects” [31]. A brief summary of the results is given, as the stability of thereconstruction of exactly these events is analyzed in Chapter 4.In the study, which arouse public interest, the arrival directions of the highest-energy cosmic rays,detected by the Pierre Auger observatory, are compared with the positions of active galactic nuclei(AGN), listed in the 12th edition of the Véron-Cetty and Véron catalog [32]. The energies are soextreme, that the particle origins or places of acceleration have to be located in the most violentplaces in the universe. One possible location is within AGNs, compact regions at the centre ofgalaxies, which ejecting plasma jets into intergalactic space. The charged particles are deflected

2.5 First results 15Figure 2.6: Sky map of the celestial sphere in galactic coordinates. The asterisks illustrate the positionsof the 442 AGN (318 within the field of view of the observatory) with redshift z ≤ 0.017 (D ≤71Mpc) from the 12th edition of the Véron-Cetty and Véron catalog [32]. The black circlesof 3.1 ◦ in diameter are centered around the reconstructed arrival directions of the 27 eventswith a reconstructed energy above 57 EeV. Darker colors indicate higher relative exposure andthe solid line shows the limit of the field of view, for " < 60 ◦ . The dashed line displays thesuper-galactic plane [31].by intergalactic magnetic fields. For particles with energies above a few tens of EeV, the deflectionsare small enough to identify the sources.The study is performed with all events, recorded between 1 January 2004 and 31 August 2007,with a reconstructed energy above 40 EeV, a zenith angle smaller than 60 ◦ and satisfying predefinedquality criteria. A three-dimensional scan has been performed to compute the degree ofcorrelation between the arrival directions of the events and the positions of the AGN. The freeparameters are the maximum AGN redshift z max , the maximum angular separation ' and thethreshold for the energy of the cosmic rays E th . The minimum probability of the hypothesis ofisotropic arrival directions was found for z max = 0.017 (corresponding to a maximum distance ofthe source of D ∼ 71Mpc), ' = 3.1 ◦ and E th = 57EeV. With these parameters, 20 out of 27cosmic ray events correlate with at least one of the 442 selected AGN (see Figure 2.6). For anisotropic flux only 5.6 are expected.It is possible, that other sources emit and accelerate the UHECRs, but their local distributions haveto be similar to the positions of the AGN. The AGN are in this case only tracers to the real sources.The statistic of 27 events is not very high and limited by the threshold energy E th , which is necessarybecause lower energetic particles are deflected much more by the intergalactic magnetic fieldsand the detected arrival directions do not point to the sources of the CRs.The Auger collaboration showed for the first time, that astronomy of charged particles at highestenergies is practicable and that the identification of the sources as well as the comprehension of theaccelerating mechanisms come into reach. The next step is to detect more events to reach higherstatistics and to build the northern site to get full sky coverage.

Event reconstruction using the surface detector dataChapter 3Event reconstruction using the surfacedetector dataIn this chapter, the trigger chain, the reconstruction algorithm and the characteristics of the surfacedetector are described. The Cherenkov light, produced by secondary particles of extensive airshowers crossing the water of surface stations, is collected by three photomultiplier tubes (PMTs)and converted into electric signals. The integrated signals are proportional to the energy depositsin the water. If the signals of three or more stations conform to predefined trigger criteria, it ispossible to reconstruct the energy and the arrival direction of the primary particle.For each detected event, 13 histograms from each station, containing the information from thecalibration, are sent to the central data acquisition system (CDAS). As an example the signalsof one station are shown in Figure 3.1. The online calibration (described in Section 2.2.2) isperformed in order to obtain the same pulse height histograms for all PMTs in all stations. Thisdefinition of a uniform trigger condition for all stations ensures to achieve a uniform event rateover the whole array.3.1 Trigger chainThe Auger trigger chain is hierarchical and consists of the two local triggers (T1 and T2), the arraytrigger (T3), the physics event trigger (T4) and the quality trigger (T5).The local triggers are part of the electronics, installed in each surface detector. The T1 can besatisfied by two conditions:• Time-over-threshold (ToT): The amplitude of the signals of 2 PMTs have to be above thethreshold of 0.2 VEM, in at least 13 time bins of 25 ns, in an interval of 3 µs.• Single threshold (ST): The amplitudes of the signals of all three PMTs in one station exceedthe threshold of 1.75 VEM, in at least one time bin.The ToT trigger is very efficient for the detection signals, which are long and have small amplitudes,how they occur in low energy showers and in stations far off the core of high energyextensive air showers. The ToT trigger has a rate of 1.6 Hz and is not sensitive to the muoniccomponent, since their signals are too short (< 200ns and < 8 bins respectively). The muonsconform to the ST trigger demands and trigger with a rate of 100 Hz. The single threshold triggeris necessary to measure muons of horizontal showers. If a station conforms to both criteria, it is

3.1 Trigger chain 17Base PMT 1, LS 1640Base PMT 2, LS 1640Base PMT 3, LS 1640Charge PMT 1, LS 1640Charge PMT 2, LS 1640Charge PMT 3, LS 1640Charge PMT 4, LS 1640Peak PMT 1, LS 1640Shape PMT 1, LS 1640Figure 3.1: Raw histograms of station 1640, with an integrated signal of 10.3 VEM. The data belongs toevent 200821400018 and is a randomly picked example. Top: baseline histograms for all threedynode channels; middle: charge histograms of the three PMTs; bottom left: summed chargehistogram; bottom middle: pulse height (peak) histograms of the three PMTs; bottom right:average pulse shape of the three PMTs.

18 Event reconstruction using the surface detector dataflagged as a ToT and not as a ST triggered event.Signals passing the ToT trigger are directly promoted to the T2 trigger, whereas for ST signals thecrossing of a higher threshold of 3.2 VEM for all PMTs is required. The T2 trigger rate is reducedto 20 Hz and the data is transferred to the CDAS on the campus in Malargüe. The T2 trigger rateallows to monitor the performance of the array and to calculate the exposure [33].Coincidences of three or more stations, which passed the T2 trigger, satisfy the array trigger T3.It can be achieved by two different criteria:• The coincidence of three ToT triggered detectors in a compact position defines the 3ToT.One of the stations must have one of its closest and one of its second closest neighborstriggered. The 3ToT trigger selects 90% physics events and is very sensitive to verticalshowers.• If four T2 triggers are fired in coincidence and in moderate distance (up to 6 km in an appropriatetime window), the 3C1 trigger is set. This trigger is necessary in order to detecthorizontal showers with fast and wide-spread signals. Due to the less strict requirements,many accidental coincidences conform to the trigger condition and the fraction of real showersis only 2% [34].All T3 triggered events are stored and the physics trigger (T4) performs the real shower selectionoffline. Two different trigger modes are implemented on the T4 level. The first, called 3ToT T4trigger, requires a 3ToT trigger and a zenith angle below 60 degree. The other trigger condition iscalled 4C1 and is fulfilled, if at least one station and three of six direct neighbors have passed theT3 trigger. For both criteria the time difference between the signals has to be compatible with thespeed of light.By using only the 3ToT T4 trigger, less than 5% of the real showers below 60 ◦ are lost. The 4C1trigger ensures to detect these showers and is also sensitive to showers beyond 60 ◦ (see Figure3.2).Before reconstructing the events, the signals of stations, which are in accidental coincidence, haveFigure 3.2: Zenith angle (left) and energy (right) distribution for events passing the T4 trigger. Eventspassing the 3ToT are displayed in the red shaded area and 4C1 events in the blue dashed area.Events fulfilling both criteria are counted as 3ToT events [34].to be removed. Accidental tanks are triggered in the same time window as the stations triggered byan extensive air shower, but their signals are caused by atmospheric muons or other background

3.2 Tank trigger probability 19effects. The start times of the three stations with the highest signals are used to define a seed, that isan elementary triangle (one station with 2 neighbors in a non-aligned configuration). The signalsof the other triggered stations are added and kept, if they are compatible with a plane showerfront derived from the seed, otherwise the stations are classified as accidental and not used in thereconstruction [35]. If a station has no triggered neighbor within a circle of 1800 m, or only onetriggered neighbor within a circle of 5000 m, it is considered as isolated and the data is removedas well.From the obtained T4 events 99% are reconstructed and used for further studies. The events witha zenith angle above 60 degree are more difficult to handle and the development of a T4 is workin progress.The last element in the chain is the T5 quality trigger. It is used to select events with high energyand angular accuracy. Several studies have been performed to define a reasonable criterion [36].At the moment mainly two definitions are used (see Figure 3.3):• The strict-T5: The station with the highest signal is surrounded by 6 active stations. Theydo not have to be triggered, but have to be active at the time, when the shower is detected.• The ICRCT5: Five of six direct neighbors of the station with the highest signal have to beactive and the reconstructed shower core has to be inside an equilateral triangle of activestations.Figure 3.3: The ICRCT5 (left) requires five of six active stations in the first crown and a reconstructedcore position in an active triangle of detectors. Core positions inside the right triangle satisfythe ICRCT5, core positions inside the left triangle not. The right picture shows the conditionfor the strict-T5, an active unitary cell.3.2 Tank trigger probabilityIn the previous section the whole trigger chain has been discussed. The signals obtained in thetanks are used to reconstruct the arrival directions and the energies of the primary cosmic rays.Before the algorithm is described, it is worth to have a look at the tank trigger probability andshower fluctuations.The signal of each station is affected by several fluctuations, as the shower-to-shower fluctuations,the sampling of Cherenkov photons, production of photoelectrons and noise [37]. Due to thefluctuations, measured signals can be higher or lower, and signals above the trigger threshold canfall below the threshold and the other way around. This causes a bias, because in the thresholdregion, only signals with positive fluctuations are recorded.

20 Event reconstruction using the surface detector dataThe trigger probability P exp (S) is defined asP exp (S)= N T + (S)N on (S) ,where N T + (S) is the number of triggered stations with a signal S and N on (S) the number of activestations in the selected signal bin. An example of a lateral trigger probability (LTP) for " = 45 ◦and S 1000 = 4.5VEM is shown in Figure 3.4, whereas S 1000 is the signal, obtained at a distance of1000 m from the shower core (see Chaper 3.3.3). The efficiency to trigger a station decreases forincreasing zenith angles, decreasing signal size and increasing distance to the shower core.Figure 3.4: Left: Comparison between the experimental (symbols) and unbiased (solid line) trigger probabilityfor " = 45 ◦ and S 1000 = 4.5VEM. Right: Lateral trigger probability for three differentvalues of S 1000 (3 (boxes), 10 (circles) and 30 VEM (triangles)) and zenith angles of 0 ◦ and45 ◦ (closed and open symbols) [37].3.3 Event reconstruction3.3.1 CDAS and OfflineAuger has two independent reconstruction softwares available, the CDAS online reconstructionand the Auger Offline software. The Auger Offline software is able to perform SD and FD reconstruction,as well as the comparison with Monte Carlo simulations. The CDAS code is onlyfor SD data reconstruction. CDAS is used to generate the Herald file, which contains all reconstructedT4 events. This Herald file is used for anisotropy studies and source identifications. Themost interesting recent result, published by the Auger collaboration (see Chapter 2.5), is basedon the data reconstructed by CDAS. Therefore, it is important to check the stability of the CDASreconstruction algorithm (see Chapter 4).In this chapter the reconstruction algorithm of the CDAS code is described, as all steps of theanalysis in this thesis are performed with CDAS. The Offline reference manual for the SD reconstructioncan be found in [38]. A comparison of the different reconstruction softwares is presentedin [39] and a guideline for SD analysis is given in [40].For each day a ROOT file with all T4-events is available. These files contain the raw histogramsfrom each station, the FADC traces of each PMT, the time of detection and further informationssupplied by the detectors. The stored events can be reconstructed with the standard, or a modified

3.3 Event reconstruction 21algorithm.The most important parameters in order to characterize a shower, obtained by the standard CDASreconstruction, are stored in the Herald file. This file contains 39 informations like event-id, reconstructedenergy and arrival direction. The file and detailed informations can be found at [41].3.3.2 Angular reconstructionAll triggered stations used in the reconstruction are called selected stations. The determination ofthese stations has been described in Chapter 3.1 and a detailed description can be found in [42].The arrival times of the shower front at the selected stations are used to calculate the arrival directionof the primary cosmic ray. The times are extracted from the PMT FADC traces and thecoordinates of the stations are known at the level of 1 m from the GPS antennas mounted on thetanks. The data can be compared to different shower front models, like plane, spheric or parabolic.For a plane shower front, orthogonal to the shower axis, the time difference (t i between the predictedand measured arrival times at station i, can be written as [43]:(t i = t i −(T 0 − u(x i − x core )+v(y i − y core )c). (3.1)T 0 is the shower core arrival time at ground, c the speed of light, u equals sin" cos ) and v equalssin" sin). The predicted arrival time is calculated by assuming a plane shower front, given by thesignals of the three stations with the highest integrated signals. The angles in spherical coordinates,) for the azimuth angle and " for the zenith angle, are the common nomenclature for the arrivaldirection. The position of the shower core (x core ,y core ) is calculated from the barycenter of alltriggered tank positions (x i ,y i ), weighted by the square root of their signals (see Figure 3.6 right).The typical accuracy of the core position is better than 150 m. For a spherical shower front,ri 2/(2Rc) has to be added to Equation 3.1, with the shower curvature R and r i the distance betweenthe core and station i.is the uncertainty of the arrival time t i , the angles" and ) are determined. The uncertainties , ti depend on the distance of the station to the coreand increase from 20 ns at the core to 50 ns at a distance of 1000m. The parameterization of, ti =(22 + 0.03 · r)ns, with the distance r of the station to the shower core in meter, is included inthe reconstruction [43].The angular resolution is better than 1.8 ◦ for events below 3 EeV and decreases to 1.2 ◦ for eventsabove 3 EeV. Events with energies above 10 EeV are reconstructed with an angular accuracy betterthan 0.9 ◦ [44].By minimizing * 2 = + i ((t i ) 2 /, 2t i, where , ti3.3.3 Energy reconstructionThe reconstruction of the energy is a two step process. First the signal S(1000) at a distance of1000 m from an a priori unknown core position is estimated from the surface detector data andthen the energy E is calculated, using hybrid events (measured simultaneously with the SD andthe FD) to calibrate the surface detector.The primary particle interacts with the air molecules and produces an extensive air shower. A“pancake” of secondary particles arrives at ground level, whose number of secondary particlesscales roughly with the primary energy. As the surface detector samples only a small part of theparticles arriving at ground level, a fit of the lateral distribution has to be performed (see Figure3.6 left). The lateral dependence of the signals is modeled asS(r)=S(1000) · f LDF (r), (3.2)

22 Event reconstruction using the surface detector datawhere f LDF (r) is the parameterized lateral distribution function (LDF) normalized to the signalS(1000) with a distance of 1000 m from the shower axis. The shower front curvature and particledistribution depend on several parameters. High-developing showers have a flat lateral distribution,whereas low-developing showers produce steep lateral distributions. At a distance of 1000 mfrom the shower axis, the signal is almost independent of the primary mass and fluctuations [45].To obtain the lateral distribution function, the signals of the stations, converted into units of VEM,are plotted against the distances of the stations to the shower axis (see Figures 3.5 and 3.6). Beforeshower coreshower frontdDDthetadFigure 3.5: The distances d of the stations to the shower axis or shower core and the distances D to thepoint, where the shower core hits the ground. The left station is an early detector, as the stationis triggered before the core reaches the ground, whereas the right station is a late detector.performing the fit, the signals are corrected for the forward-backward asymmetry. Early and latetriggered stations, at the same distance to the shower core, exhibit a different behavior. AfterLateral distribution function fit310210101200 400 600 800 1000 1200 1400 1600 1800 2000 2200Figure 3.6: Pictures from the CDAS Event Display: event 200821400018,E = 12.03EeV, " = 51.5 ◦ . Theleft plot shows the signals of the triggered stations (rectangles), the silent stations (triangles)and the LDF with the error band. The right shows a top view of the triggered stations. Thesize of the circles is proportional to the logarithm of the detected signal. The stations markedwith a cross, are flagged as accidental and the two black stations at the right were not active,at the time the event was detected.reaching the shower maximum a few kilometers above the surface detector, extensive air showersthin out. The number of particles decreases and at the observation level early stations measurehigher signals than late detectors, as they detect the particles of a not so far developed shower

3.3 Event reconstruction 23[46].In CDAS several lateral distribution functions (LDF) are available. The standard one is the loglog-parabolaS(r)=S 1000 ×{ ( )r -1000m× ( r1000m() 2·#·lg(300m1000m)×( 300mr1000m1000m) -+#·lg( r1000m)) −#·lg( 300m1000m)r < 300mr > 300mwith r the distance between the station with the highest signal and the core. The parameterizationof the slope parameter is(3.3)- = 0.7 × arctan (6.0 × (0.65 − cos ")) − 3.0 (3.4)and # is a piecewise defined function (see Figure 3.7), whereas the single functions are all linear,but with different slopes. In the fit of the LDF the uncertainties of the signals are taken as [47], S (") = (0.32 + 0.42 · sec ") √ S. (3.5)After obtaining S(1000), which depends on the energy and the zenith angle only, the next stepis to separate these two dependencies. This is achieved with the Constant Intensity Cut (CIC)Figure 3.7: - (left) and # (right) as a function of the zenith angle. The light line represent the parameterizationof -.method [48]. The main assumption is the isotropic arrival of cosmic rays from the sky. Above fullacceptance the zenith angle distribution is of the form const · sin " cos ". The sine-term is causedby the increasing spherical element and the cosine term by the decreasing effective array size,with increasing zenith angle. By dividing the "-distribution in bins, whose borders are chosento contain the same number of events in each bin, the method of the CIC can be applied. Aftersorting the events in each bin according to their S(1000) values, the signals of constant intensity(e.g. the 500th event in each selected bin) are plotted against the mean " of each bin. The obtainedplot showsS(1000)=S 38 · f ( cos 2 (") ) = S 38 · (1+ ax + bx 2) , (3.6)with x = cos 2 " − cos 2 38 ◦ and the fit parameters a and b. Now the energy estimator S 38 , the valueof S(1000) at a reference angle of 38 ◦ , can be obtained:S 38 = S(1000)f (cos 2 ") . (3.7)

24 Event reconstruction using the surface detector dataThe selection of 38 ◦ is justified, as it is the mean value of the "-distribution (see Chapter 3.4). Theenergy estimator S 38 does not depend on " any longer and is only a function of the energy of theprimary particle.In a last step S 38 has to be linked with the energy. This can be achieved based on Monte Carlosimulations or by cross-calibrating with hybrid events. The energies obtained with both methodsare available in the Herald data set. With the FD calibration (see Figure 3.8) the energy of theFigure 3.8: Correlation between lgS 38 and lgE FD for the 661 hybrid events used in the fit. The solid lineis the best fit to the data [49].primary is calculated withE = p · (S 38 ) q . (3.8)The best fit yields p =(1.49 ± 0.06(stat) ± 0.12(syst)) × 10 17 eV and q = 1.08 ± 0.01(stat) ±0.04(syst) with a reduced * 2 of 1.1 [50].3.3.4 Fine-tuning of the LDFIn addition to the log-log parabola (Equation 3.3) two other LDFs describe the signal distribution.Firstly, a modified NKG-function is the standard LDF in the standard reconstruction software,called Offline(S(r)=S 1000 ×r1000m) ( )- r + 700m-+#× . (3.9)1700mSecondly, an LDF obtained by the Haverah Park experiment, which was a large air shower experimentnear Leeds/UK [51] with a dense array of water Cherenkov detectors in the center, can beused. The obtained LDF for air showers isS(r)=S 1000 ×{ (( 1800r1000m) #×() -+ r4000mr1000m) -+#+rr < 800m4000mr > 800m.(3.10)

3.4 Data 25In addition to the choice of different lateral distribution functions, it is possible to use a calculatedor a fitted slope parameter - for the energy reconstruction. Equation 3.4 shows the formula, whichis used to calculate the value of the slope parameter for a given zenith angle. If a shower triggersmany stations, the slope parameter of the LDF can be fitted to the data points. In the standardreconstruction the fit is performed, if a certain number of stations, with defined distances to theshower axis, have been triggered.3.4 DataThe surface detector is operating in a stable mode since 1st January 2004 and has detected morethan 1.5 · 10 6 events, out of which more than 20000 have an energy above 3 EeV. At 3 EeV thearray reaches full acceptance. Below this energy, the array is not fully efficient and the probabilityto detect an event depends of the zenith angle and the core position, in reference to the neareststation.The zenith and azimuth angle distributions are shown in Figure 3.9. The zenith angle distributiondiffers from the typical sin" cos"-distribution, as it is created without any energy cut. Due tothe absorption of inclined showers, the maximum is shifted to lower zenith angles, below fullacceptance. The azimuth angle distribution is analyzed in detail and the results are presented inChapter 5.2.counts41004000hPhicounts4000035000hTheta39003000038003700250002000015000360010000350050003400-150 -100 -50 0 50 100 150.00 10 20 30 40 50 60 70 80 90"Figure 3.9: Azimuth angle distribution (left) for all events with " < 60 ◦ and zenith angle distribution(right) without any cuts.3.4.1 Variations on different time-scalesThe data, recorded by the Pierre Auger observatory, is influenced by the temperature at the groundand the conditions in the atmosphere above the array. The T1 and T2 trigger rates are monitoredcontinuously and the gains of the PMTs are adjusted to reduce temperature effects. Anyhow theToT rates of the individual stations correlate with the temperature and the T5 trigger rate perhexagon varies from 1.1 event per day in winter, to 1.4 events per day in summer [41]. In addition,the ToT rates of the individual stations decrease with time and, thus, decrease the T5 rate of thewhole array. Figure 3.10 shows the decline of the ToT rate of station 119 and the development of

26 Event reconstruction using the surface detector datathe T5 rate in the sub-array, which is taking data since December 2004. The reason of this agingeffect of the array has to do with the water quality in the tanks, but is not yet entirely understood.Figure 3.10: The left plot demonstrates the development of the ToT rate of the Piuquen detector sinceits deployment. The right graph shows the decreasing T5 rate of the sub-array, which isoperating since December 2004 [52].3.4.2 Attributes of the arrayThe location in the Pampa Amarilla provides almost perfect conditions for the detection of extensiveair showers. To analyze the data, collected by the surface detector, it is important to considermany of the detector characteristics.The height of the tanks is defined by the topography. The whole array is tilted, with the higheststations located in the west (see Figure 3.11 left). This causes a large scale anisotropy in the data,as the effective size of the array, seen by the shower, depends on the azimuth angle [53]. Thedifferent ground altitudes affect the energy determination as well, since the showers are detectedat a different depth, but this effect is of little relevance, as shown in [54].In addition, the grid of the stations is not perfect, as many stations had to be installed displaced,due to rivers or rocks. Figure 3.12 shows the differences in size of the triangles, formed by threeneighboring stations, from the average of 0.975km 2 . The displacements lead to irregular triggercharacteristics and have to be considered in the analysis, using events with energies below fullacceptance.Due to the large distances between the stations and weather conditions, which allow the accessto the array in only one third of the days, some stations show problems. The worst case is a blacktank, a station, which sends no information to the central data acquisition system. The number ofblack tanks varies with time around ≈ 15.For cosmic rays with energies above ≈ 30EeV, the dynode and anode PMT signals of the closestto-the-coretanks are saturated in more than 50% of the events. A method has been developed torecover these signals. The effect on S(1000) is smaller than 1% at low energies and about 3% athigh values of S(1000) [55].An occurring and not yet solved problem is the so-called raining behavior of approximate halfof the PMTs [56]. In the summer the PMTs, marked in Figure 3.11 right, show a drop of theVEM value of the order of ≤ 30% and an increase of the ToT rate. The influence of this effect islimited to the acceptance of the detector and does not affect the reconstructed energies and arrivaldirections of the events.

3.4 Data 27altitude1005010050north - south40000300002000000-5010000-100-150-500-200300002000010000north -south0-10000-20000-30000 -20000-10000 0east - west300002000010000-100-150-10000-20000-30000-40000 -30000 -20000 -10000 0 10000 20000 30000east - westFigure 3.11: Left: The altitude of the stations in meter in reference to the center of the array. Right:Stations, which had one or more raining PMTs in March 2008, are visualized with asterisks.number of triangles210Entries 2638Mean -1.435e-13RMS 1.459101-15 -10 -5 0 5deviation / %Figure 3.12: Histogram of the triangle sizes for the surface detector. The deviations in percent are causedby displaced stations.

Stability of the reconstructionChapter 4Stability of the reconstructionThe accuracy and stability of the reconstruction algorithm are essential requirements for discoverieswith the Pierre Auger observatory. The goal of the studies presented here is to check thestability of the CDAS online reconstruction algorithm (see Chapter 3.3.1) for cosmic rays withE > 25EeV.The events are reconstructed with modified sets of detectors. The reconstructed energy and thearrival direction of the standard reconstruction are taken as a reference and compared to the resultsof the modified reconstructions. Leaving out individual surface detector stations in the reconstructionsimulates non-operational stations. In order to assess the influence of the border of the array,detectors in certain configurations are left out. In further steps the impact of the asymmetry correctionis evaluated and a study is performed to determine the optimum ground parameter r opt forextensive air showers with energies above 25 EeV. The optimum ground parameter is the distancefrom the shower axis, where the fluctuations of the signal S(r opt ) have the minimum. In the lastpart, less dense arrays are generated by leaving out whole sets of detectors. The results give hintswith respect to Auger North, as the spacing between the surface stations will be wider there.4.1 Method and data setThe reconstruction is performed using CDAS version v4r6p2. In the CDAS reconstruction code,all triggered stations used for the reconstruction are classified as selected stations. In the firstpart of the analysis, the reconstruction is performed repeatedly for each event, each time leavingout one selected station. The results are categorized according to the distance between the coreand the station, which has been left out in the reconstruction: the central tank, a tank of the firstcrown, of the second crown or a tank which is located farther away (see Figure 4.1). The reconstructedenergy and the arrival direction of the standard reconstruction are taken as a reference andcompared to the results of the modified reconstructions. For example, for an event with twelvetriggered stations, twelve tests are performed and twelve deviations in energy and arrival directionare obtained. In those parts of the analysis, where more then a detector is excluded, the number oftests per event depends on the number of selected detector sets.For the analysis, all events recorded by the Pierre Auger observatory between 1 January 2004 and4 April 2008, with a reconstructed zenith angle smaller than 60 ◦ , are used. In the reconstructionalgorithm, different LDF functions can be selected to determine S(1000), the signal at 1000 m coredistance (see Chapter 3.3.4). In addition, the slope parameter can be determined in different ways.In CDAS, log-log parabolas are used. In the standard option “LDFOptimal”, the slope parameter

4.2 Reconstruction without individual stations 29Figure 4.1: The station with the highest signal is called central tank. It is surrounded by the six stations ofthe first crown. The second crown consists of the twelve stations surrounding the first crown.Crown n is formed by 6 · n stations.- is extracted from the LDF fit, if enough stations are available in predefined bins of distance tothe shower axis. Otherwise, - is calculated from a function depending on the zenith angle. In theanalysis presented here, the use of the “LDFOptimal” option generates a systematic error. If thiscriterion of enough triggered stations in the predefined bins is fulfilled for an event, the exclusionof a detector may cause, that it is not satisfied any longer. In this case, the energy would first becalculated with a fitted - and after the removal with the calculated slope parameter. To avoid this,all events are reconstructed with the calculated -.The deviation in energy is always given as the percentage of the energy and is calculated from theformula:(EE = E Original − E Modified.E OriginalThe arrival direction is described by two angles, the zenith angle " and the azimuth angle ). Foreach event these two angles define a vector, which points back to the incoming direction of theprimary cosmic ray. The deviations in arrival direction are all positive, as they are defined as thespace angles between the two vectors, that are obtained by the reconstructions using the originaland the modified set of detectors, respectively.4.2 Reconstruction without individual stationsEvents with energies above 10 EeV trigger at least six surface stations and events with E > 25EeVtrigger seven surface stations (one unitary cell) or more, if the core positions are not nearby theborder of the array. The main assumption is, that the removal of one detector station should notchange fundamentally the results of the reconstruction.4.2.1 Stability of events with E > 57EeVEvents with energies above a few tens of EeV have a large rigidity and the search for correlationswith point sources is possible. The events with E > 57EeV recorded by the Pierre Augerobservatory show correlations with nearby AGN (see Chapter 2.5). Above this energy 33 eventshave been detected. Altogether, they triggered 514 surface detector stations. Figure 4.2 showsthe normalized deviations in energy and space angle between the original and the modifiedreconstruction. The RMS values of the distributions of the individual crowns are given in Table

30 Stability of the reconstructioncounts210Entries 514Mean 0.1092RMS 2.385Underflow 0Overflow 0counts210Entries 514Mean 0.1122RMS 0.1244Underflow 0Overflow 0101011-25 -20 -15 -10 -5 0 5 10 15 20 25Difference in energy [percent]0 0.2 0.4 0.6 0.8 1 1.2Difference in space angle [degree]Figure 4.2: Differences in energy (left) and space angle (right) between the original and modified reconstructionsfor events with E > 57EeV.4.1 and the RMS for all reconstructions is displayed in the legend of Figure 4.2. For 8 out ofthe 514 modified reconstructions the deviations in energy are larger than 10% (see Table 4.2).Stations leading to a change of the arrival direction of more than 0.6 ◦ are listed in Table 4.3. Thethresholds of 10% and 0.6 ◦ are chosen, as for such events, the deviations are a factor of 1.5 largerthan the errors of the reconstructed S(1000) and space angle (see Figure 4.3).counts80 Entries 369 45 Entries 36970counts4060504030201000 2 4 6 8 10 12 14( S(1000) [percent]353025201510500 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Space angle [degree]Figure 4.3: (S(1000) (left) and space angle between (),") and () + ()," + (") (right) for T5 triggerevents with E > 57EeV.The central stations and the stations of the first crown measure the largest signals. For thisreason the relative errors of their signals are smaller and their weighting in the LDF fit is higher,than for stations with a larger distance to the shower axis. The removal of a station of the unitarycell has therefore a stronger influence on the reconstruction of the energy than the removal of moredistant detectors. The obtained differences in energy show exactly this behavior. The removal ofstations of the unitary cell leads to deviations up to 15% and that of stations farther off leads todifferences of only up to 3%.

4.2 Reconstruction without individual stations 31crown 0 1 2 > 2energy mean -0.63 0.38 0.04 -0,01energy RMS 5.18 3.18 0.47 0.29space angle RMS 0.25 0.22 0.11 0.10Table 4.1: Properties of the energy and space angle distributions shown in Figure 4.2.event ID tank ID - crown (deviation in %)200629604873 370 - 1 (10,8%)200629900147 1061 - 1 (−11.5%), 1068 - 0 (−11.0%)200723401180 383 - 0 (10.1%)200729501686 145 - 0 (−12.3%), 149 - 1 (−13.8%), 192 - 1 (−10.6%)200734500536 1483 - 1 (11.2%)Table 4.2: Deviation in energy between the original and the modified reconstruction. All events for whichthe modification leads to a deviation in energy larger than 10% are listed. The number after thehyphen denotes the crown (0 = central station).event ID tank ID - crown (deviation in ◦ )200508101056 499 - 1 (0.65 ◦ )200529501100 950 - 0 (0.63 ◦ ), 957 - 1 (0.69 ◦ )200530605022 562 - 1 (0.70 ◦ )200605500287 133 - 1 (0.67 ◦ )200729501686 149 - 1 (0.69 ◦ )Table 4.3: Angular deviation between the original and the modified reconstruction. All events, for whichthe modification leads to a deviation larger than 0.6 ◦ , are listed.

32 Stability of the reconstructionThe removal of the central station decreases the reconstructed energy in average by 0.63% (seeTable 4.1) mainly due to saturation effects. For stations close to the shower core (< 100m forshowers in the EeV range and a few hundred meters for showers at higher energy) most PMT signalsare saturated. The integrated signal is smaller and the LDF is pulled down at small distancesto the shower axis. To avoid this, a saturation correction is implemented in the reconstructionalgorithm. The results show, that the correction can be improved for the highest-energy cosmicrays.For the differences in arrival direction the statement is similar, but not as distinct as for the energies.The angular deviations decrease with increasing distance of the removed station to theshower axis. In the angular reconstruction, the arrival direction is calculated from the positionsof the tanks and the arrival times of the signals detected by them. The errors of the arrival times, ti are estimated from the time residuals of the shower fit. At the core , ti is about 20ns [43] andit increases with the core distance r. In the reconstruction code the following parametrization isincluded:, t = 22ns + 0.03 ns · r with r in meter. (4.1)mThe maximum space angle differences for the selected events are 0.7 ◦ for stations of the unitarycell and up to 0.4 ◦ for stations farther off.The variations in energy and arrival direction are caused by changes in the LDF and the showerfront fit, as well as shifts of the core position, after leaving out individual stations. Figure 4.4shows the displacements of the cores. For the analyzed events, the displacements reach up tocounts102Entries 514Mean 7.555RMS 14.46Underflow 0Overflow 01010 20 40 60 80 100 120 140Displacement of core position [m]Figure 4.4: Shifts of the reconstructed core position between original and modified reconstruction forevents with E > 57EeV100 m.The analysis presented so far gives evidence that the CDAS reconstruction of ultra high energyevents is very robust against the removal of individual detectors. The influence of a single failingtank is negligible for the detection of particles with energies above 57EeV. No station removalinduces an angular deviation of more than 1 ◦ [31], which corresponds to the estimated resolutionof the SD. The absolute energy has an uncertainty of 22% for this energy range [31] and alldeviations are below this systematic uncertainty. There isno event, for which excluding one station

4.2 Reconstruction without individual stations 33from the reconstruction leads to an energy below 57EeV, the current energy cut for the search forcorrelations with source candidates. There is also no event with an reconstructed energy below57EeV, for which the removal of a single station leads to an energy above the energy threshold.4.2.2 Stability of events with E > 25EeVThe same test as described in the previous section is applied to all events above 25 EeV. In a firsttest, all events are used, regardless whether they satisfy the T5 trigger condition or not. In a secondstep, only events satisfying the ICRC-T5 trigger are used. An event is classified as a ICRC-T5event, if five stations of the first crown were active at the time of detection and if the reconstructedcore position is inside an equilateral triangle of active detectors. In the third step, the strict-T5trigger condition is required. The station with the highest signal has to be surrounded by six activestations. Figure 4.5 shows, from top to bottom: all events (including non-T5 events), ICRC-T5events and strict-T5 events. With each quality cut, the number of events decreases and the robustnessof the remaining events increases. This is clearly visible in Table 4.1. The RMS values ofT5 cut crown 0 1 2 > 2no cutenergy 10.04 7.71 3.76 2.71space angle 0.45 0.34 0.21 0.20ICRC-T5energy 7.88 5.51 1.38 1.41space angle 0.42 0.30 0.20 0.19strict-T5energy 7.51 4.22 0.96 1.42space angle 0.41 0.29 0.19 0.19Table 4.4: RMS values of the energy and space angle distributions shown in figure 4.5.the histograms shown in Figure 4.5 become smaller with increasing core distance and with eachquality cut applied.For all events, including those which fulfill no T5 trigger condition, 3% of the tests lead to deviationslarger than 22%, the uncertainty of the absolute energy scale. For non-T5 events, the removalof one tank results in a reconstruction without at least two stations, the subtracted and the inactiveone. If these missing detectors are neighbors, the core position, the LDF and hence the arrivaldirection and the energy are affected heavily.A check of all strict-T5 events shows, that deviations above 22% in energy (19 of 4650 modifiedreconstructions) and 1.6 ◦ in space angle (45 of 4650 modified reconstructions) occur, if at leastone of the following conditions is fulfilled:• one detector is saturated,• at least in one detector the signals of the three PMTs differ in more than 20%.To get a more quantitative result, Gaussian fits to the distributions of the strict-T5 events areperformed. As usual, the assignment of the stations to the crowns are considered and in additiondifferent energy cuts are implemented. The distributions of all events above four different energythresholds (E > 25EeV, 35EeV, 45EeV and 55EeV) are fitted. Table 4.5 shows all mean values Eand standard deviations , of the fits. The mean values E are the average differences of the energy,reconstructed with the original and modified set of detectors. The removal of the central stationincreases the energy. Omitting stations farther off induces a minimal shift to lower energies.

34 Stability of the reconstructioncounts310Entries 6943Mean 0.3785RMS 6.43Underflow 60Overflow 43counts310Entries 6943Mean 0.3261RMS 0.7285Underflow 0Overflow 22210210101011-60 -40 -20 0 20 40 60Difference in energy [percent]0 1 2 3 4 5 6 7 8 9 10Difference in space angle [degree]counts310Entries 5740Mean 0.166RMS 4.47Underflow 1Overflow 9counts310Entries 5740Mean 0.2259RMS 0.4422Underflow 0Overflow 721021010101-60 -40 -20 0 20 40 60Difference in energy [percent]10 1 2 3 4 5 6 7 8 9 10Difference in space angle [degree]counts310Entries 4650Mean -0.01543RMS 3.681Underflow 1Overflow 3counts310Entries 4650Mean 0.2019RMS 0.3334Underflow 0Overflow 3210210101011-60 -40 -20 0 20 40 60Difference in energy [percent]0 1 2 3 4 5 6 7 8 9 10Difference in space angle [degree]Figure 4.5: Differences in energy (left) and space angle (right) for all events above 25 EeV (top), ICRCT5events (middle) and strict-T5 events (bottom).

4.2 Reconstruction without individual stations 35crown E > 25EeV E > 35EeV E > 45EeV E > 55EeV0 E −1.40 ± 0.32 −1.13 ± 0.38 −0.74 ± 0.45 −0.33 ± 0.810 , 5.9 ± 0.24 5.43 ± 0.32 4.74 ± 0.58 5.57 ± 0.931 E 0.12 ± 0.04 0.14 ± 0.04 0.12 ± 0.06 0.04 ± 0.071 , 1.12 ± 0.02 1.18 ± 0.03 1.38 ± 0.08 1.23 ± 0.072 E 0.19 ± 0.04 0.18 ± 0.05 0.04 ± 0.07 0.11 ± 0.042 , 0.79 ± 0.02 0.80 ± 0.02 0.79 ± 0.02 0.77 ± 0.02> 2 E 0.11 ± 0.04 0.07 ± 0.04 0.03 ± 0.05 −0.09 ± 0.06> 2 , 0.77 ± 0.02 0.77 ± 0.02 0.78 ± 0.02 0.76 ± 0.03Table 4.5: Values of the Gaussian fits to the energy histograms.The Gaussian fits show the strong correlation between the stations core distances and theirimpact on the reconstructed energies and arrival directions. For the station with the highest signal, is around 5%, for the first crown it is around 1.2% and for the far-off detectors it is close to0.8%. Furthermore, the fit results show the independence of the , and E values from the energythreshold. Nevertheless, the comparison of the RMS values of Figure 4.2 and 4.5 (bottom) showsa smaller number of excessive deviations at high energies. This is no contradiction, as the RMSvalue is more sensitive to outliers than ,.4.2.3 Test of the asymmetry correctionIn this part, all strict-T5 events with zenith angles between 45 ◦ and 60 ◦ are analyzed. In orderto find out if these events are responsible for the large deviations, a comparison of the results excludingeither early or late triggered stations from the reconstruction has been performed. This isa check of the forward-backward correction, which is implemented in the CDAS reconstructionalgorithm (see Chapter 3.3.3). For the early part, all stations located in a range of ) ± 30 ◦ andfor the late part, all stations in the range of () + 180 ◦ ) ± 30 ◦ are selected. The analysis distinguishesbetween detectors of the first crown and those farther away. Figure 4.6 shows the fitteddistributions and Table 4.6 lists the parameters of the Gaussian fits.Fit x ,early and 1. crown 0.30 ± 0.24 1.56 ± 0.39early and > 1. crown −0.21 ± 0.04 0.48 ± 0.04late and 1. crown 1.25 ± 0.26 2.20 ± 0.28late and > 1. crown 0.11 ± 0.04 0.62 ± 0.04Table 4.6: Values of the fits to the distributions for the early and late part of the shower.For the early and the late part of the showers no bias is visible. Neither the mean nor the ,values have a systematic offset. There is no hint of a problem with the correction of the forwardbackwardasymmetry.

36 Stability of the reconstructioncounts12108Entries 105Mean 0.4769RMS 4.278Underflow 0Overflow 0counts120 Entries 283Mean -0.1191100RMS 1.23Underflow 0Overflow 0806604402200-25 -20 -15 -10 -5 0 5 10 15 20 25Difference in energy [%]0-25 -20 -15 -10 -5 0 5 10 15 20 25Difference in energy [%]counts10 Entries 105Mean -0.008773RMS 5.1368Underflow 0Overflow 06counts90 Entries 304Mean 0.202780RMS 1.03670Underflow 0Overflow 0605044030220100-25 -20 -15 -10 -5 0 5 10 15 20 25Difference in energy [%]0-25 -20 -15 -10 -5 0 5 10 15 20 25Difference in energy [%]Figure 4.6: Deviations in energy resulting from excluding individual stations of the first crown (left) andfarther off (right) for the early (top) and late part (bottom) of the showers.4.2.4 The optimum ground parameterIn order to reconstruct the energy of primary cosmic rays with the surface detector, the LDF isfitted to the signals of the stations and the signal S(1000), at a distance of 1000 m from the showeraxis, is determined. Monte Carlo simulations have shown, that the shower-by-shower fluctuationsare minimized for a distance of 1000 m from the shower axis, in the energy range of the PierreAuger observatory [57]. For the highest-energy events and for events with saturated stations, theoptimum ground parameter r opt differs from 1000 m. Studies presented in [58] and [59] show, thatr opt increases for increasing energies.In Figure 4.7, the deviations in S(1000) are compared to the deviations in S(1600) for all strict-T5events above 25 EeV and with " < 60 ◦ . The LDF fit is performed with a fitted slope parameter, asfor a fixed - the variations of S(1000) and S(1600) are the same. The selection of the fitted slopeparameter can be used, as the strict-T5 events have enough triggered stations for a reliable fit.The mean deviations of the S(1600) values are much smaller than for S(1000). The RMS valuedecreases from 6.0 to 3.2 and the mean value increases from −0.58 to 0.75. For S(1000), theremoval of the central station leads to an increase of S(1000) up to 60%. This is caused bysaturated stations, which pull the LDF down at distances near the core. To illustrate this further,only events with saturated stations are used to create Figure 4.8. The removal of the central stationleads to an increase of S(1000) and to a decrease of S(1600) in average. For an optimum groundparameter the mean value of such a distribution should be zero and the RMS should be as smallas possible. The estimation of a mean value close to zero is based on the assumption of the sameprobability for an increase or decrease of the energy, if reconstructing without individual stations.In the next step, the same procedure is applied again to all events above 25 EeV, excluding allevents with saturated stations. In the histograms in Figure 4.10, the deviations from S(1000) to

4.2 Reconstruction without individual stations 37counts310Entries 4650Mean -0.584RMS 6.008Underflow 15Overflow 1counts310Entries 4650Mean 0.7502RMS 3.227Underflow 2Overflow 4210210101011-60 -40 -20 0 20 40 60Difference in S1000 [percent]-60 -40 -20 0 20 40 60Difference in S1600 [percent]Figure 4.7: Deviations in S(1000) (left) and S(1600) (right) resulting from excluding individual stationsbefore the reconstruction.counts310Entries 1678Mean -0.5705RMS 7.437Underflow 10Overflow 1counts310Entries 1678Mean 0.8254RMS 3.631Underflow 0Overflow 2210210101011-60 -40 -20 0 20 40 60Difference in S1000 [percent]-60 -40 -20 0 20 40 60Difference in S1600 [percent]Figure 4.8: Deviations in S(1000) (left) and S(1600) (right) resulting from excluding individual stationsbefore the reconstruction from events with saturated detectors.

38 Stability of the reconstructionS(1800) are shown in steps of 50 m, each time leaving out the central station. For each groundparameter, the mean and the RMS of the histogram is calculated. The development of these valueswith increasing ground parameter are shown in Figure 4.9.RMS values of energy difference distributions14121086421000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Mean values of energy difference distributions420-2-4-6-8-101000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Figure 4.9: RMS (left) and mean values (right) of the histograms shown in Figure 4.10.The mean becomes zero for S(1500) and the RMS becomes minimal at the same distanceto the core. The optimum ground parameter seems to be found, but the removal of the centralstations induces a systematic bias. The core position is calculated as the barycenter of the signalsof the surface detector stations. The three stations, which measure the highest signals, form atriangle, which contains the shower core. The subtraction of a station, especially the one with thehighest signal, leads to a displacement of the core (see Figure 4.11 left). The movement of thecore changes the distances to the shower axis for all other stations. For the two stations, with thesecond and third highest signal, the core distances become smaller, for the other four stations ofthe first crown, the core distances increase. The arrows in Figure 4.11 (right) illustrate the shifts.The LDF fit of the modified set of detector signals results in higher signals at small core distancesand smaller signals at larger distances. This is exactly the behavior, which can be seen in Figures4.10 and 4.9. An LDF fitted with all stations and one fitted without the central station are differentwith respect to the slope parameter. The differences between the reconstructions become minimalat the intersection point of the different LDFs, which is at a distance of ≈ 1500m.To reduce the impact of the movement of the core, the same test is performed by eliminatingstations from the first crown. For each event, the reconstruction is performed six times, each timeleaving out one station of the first crown. The movements of the cores are of the same order ofmagnitude as for the central stations (see Figure 4.4), but the six removals per event result in sixdislocations in different directions. It is no longer valid, that the core distances of the stations withthe second and third highest signals always decrease.To check the statement, that the optimum ground parameter depends on the energy [58], the eventsare divided into three energy bins: 25EeV < E ≤ 30EeV, 30EeV < E ≤ 40EeV and E > 40EeV.The same type of histograms as in Figure 4.10 are plotted for these energy bins leaving out thecentral station and stations of the first crown. Figure 4.12 shows the development of the RMS andmean values of the distributions.The points of interest (minimum RMS and mean value equal to zero) are shifted to smaller

4.2 Reconstruction without individual stations 392222Energy101010101111-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 602222101010101111-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 602222101010101111-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 602222101010101111-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60Figure 4.10: Deviations in S(r) by comparing the signals of the events above 25 EeV reconstructed withall stations and without the central station. In the left plot of the first line, r is equal to 1000 mand increases by 50 m with each histogram up to 1800 m in the last histogram on the right inthe bottom row.

40 Stability of the reconstructionFigure 4.11: Direction of the core displacement after the removal of the central station (left) and theinfluence on the core distances for the other stations (right).distances for the removal of stations of the first crown. It has been explained, that the differencesin the minima are due to the shifts, caused by the displacements of the core positions, for the reconstructionsexcluding the central station. Furthermore, the choice of a ground parameter largerthan 1000 m improves the reconstruction for events with E > 25EeV. The optimum ground parameterincreases with increasing energy. Besides this qualitative results, the determination of theoptimum ground parameter is difficult with this method. A clue is given by the mean values of thedistributions, generated by alternatively leaving out the stations of the first crown. A mean valueof zero implies that positive and negative deviations are of the same frequency. For the selectedenergy ranges this yields the optimum ground parameters listed in Table 4.7.Energy range25EeV < E < 30EeV30EeV < E < 40EeVE > 40EeVr opt1100 m1200 m1250 mTable 4.7: Optimum ground parameters determined by reconstructing events without individual stationsof the first crown.4.3 Reconstruction without sets of detectors4.3.1 Reconstruction with the unitary cell onlyThe removal of individual stations of the second crown or farther away changes the energy byless than 2% for events with energies above 57 EeV. For events with energies down to 25 EeV thedifferences remain in the same region. In an additional test, the results of the original reconstructionare compared with the values obtained by reconstructing the showers with the unitary cellonly. The test is performed for all events with energies above 57 EeV and all strict-T5 events withE > 25EeV as before. The results are shown in Figure 4.13. The deviations in energy as well asin arrival direction are smaller than the detector resolution.The deviations are of the same magnitude as for the removal of individual stations. These results

4.3 Reconstruction without sets of detectors 41RMS values of energy difference distributions14121086421000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Mean values of energy difference distributions420-2-4-6-8-10-12-141000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]RMS values of energy difference distributions121086421000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Mean values of energy difference distributions20-2-4-6-81000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]RMS values of energy difference distributions1086421000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Mean values of energy difference distributions210-1-2-3-4-5-61000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Figure 4.12: Analog plot to Figure 4.9, RMS values (left) and mean values (right): The circles are usedto illustrate the development of the histograms of the central stations, the rectangles for thehistograms of the first crown stations. From top to bottom the energy range changes from25EeV < E ≤ 30EeV via 30EeV < E ≤ 40EeV to E > 40EeV.

42 Stability of the reconstructioncounts10Entries 32Mean -0.3065RMS 1.674Underflow 0countsEntries 32Mean 0.2427RMS 0.1821Underflow 0Overflow 1Overflow 111-20 -15 -10 -5 0 5 10 15 20Differences in energy [percent]0 0.2 0.4 0.6 0.8 1 1.2Differences in space angle [degree]counts102Entries 365Mean 0.706RMS 2.947Underflow 0Overflow 0counts210Entries 365Mean 0.2342RMS 0.2396Underflow 0Overflow 1101011-50 -40 -30 -20 -10 0 10 20 30 40 50Differences in energy [percent]0 0.5 1 1.5 2 2.5Differences in space angle [degree]Figure 4.13: Differences in energy in percent (left) and space angle in degrees (right) between the reconstructionwith all stations and the reconstruction with only the unitary cell for events withE > 57EeV (top) and E > 25EeV (bottom).

4.4 Less dense arrays 43show, that the signals of the seven highest signals suffice to guarantee a stable reconstruction. Itcan be concluded, that the reconstruction of strict-T5 events with E > 25EeV copes with the removalof all stations outside the unitary cell around the core. The accuracy for these events ismuch higher than for the majority of events, as they have only three or four stations with signals.4.3.2 Simulating borders of the arrayIn order to check, if the border of the array induces any bias in the reconstruction, the events arereconstructed leaving out sets of detectors located on one side of the core. The cut preserves thestrict-T5 criterion and only stations from the second crown and farther off are erased. Figure 4.14Figure 4.14: Stations beyond the unitary cell on two sides of the central tank are left out in the reconstruction.These detectors are marked with a cross.shows the highest-signal station in the center surrounded by the stations of the different crowns.The stations not used in the reconstruction are marked with a cross. The test is performed fourtimes for each event, each time leaving out all detectors of two neighboring sides of the array,as shown in Figure 4.14. The deviations (see Figure 4.15) are similar to the ones obtained byreconstructing with the unitary cell only. The RMS values of the distributions are smaller than inthe previous test. The asymmetric removal of detectors on one side of the core induces the largestdislocation of the core, as it is the barycenter of the signals of the stations. The small deviationsshow the robustness of the reconstruction algorithm. If an event passes the strict-T5 trigger, theeffect of the border on the reconstructed energy and the arrival direction is not significant.4.4 Less dense arraysIt is planned, that the Pierre Auger observatory will be completed with the northern side in theUnited States. The surface detector array will be similar to the one in the south, but with a widerspacing between the stations. With the data recorded by the existing array, the response of lessdense arrays can be simulated by using only the signals of sub-arrays in the reconstruction. Thereis no limitation in generating configurations with decreasing densities. One similar to the existingarray, is shown in Figure 4.16. The array is divided into three independent arrays (a, b, c), eachforming equilateral triangles of 2600 m (compare with results presented in [60]). The unitary cell(full hexagon) covers an area of 20.28km 2 and is by a factor of 3.5 bigger than in the regular array.For low multiplicity events, the distribution of tanks may cause the reconstruction to fail, even ifthree non-aligned stations are found. Consequently, the number of successful reconstructions is

44 Stability of the reconstructioncountsEntries 112Mean 0.04464RMS 1.209Underflow 0Overflow 0countsEntries 112Mean 0.1478RMS 0.1237Underflow 0Overflow 0101011-20 -15 -10 -5 0 5 10 15 20Differences in energy [percent]0 0.2 0.4 0.6 0.8 1 1.2Differences in space angle [degree]counts210Entries 1460Mean 0.1327RMS 2.4Underflow 0Overflow 1counts210Entries 1460Mean 0.1745RMS 0.2171Underflow 0Overflow 3101011-50 -40 -30 -20 -10 0 10 20 30 40 50Differences in energy [percent]0 0.5 1 1.5 2 2.5Differences in space angle [degree]Figure 4.15: Differences in energy in percent (left) and space angle in degrees (right) between the reconstructionwith all stations and modified sets of detectors simulating the border of the arrayfor events with E > 57EeV (top) and E > 25EeV (bottom).Figure 4.16: Triangle sub-array configurations.

4.5 Summary 45below 3·N, for N events. The reconstruction algorithm does not need to be modified. For the test,only strict-T5 events with E > 25EeV are used. In Figure 4.17, the deviations in energy and spaceangle are illustrated for different energy ranges.The deviations depend strongly on the energy. For events with E > 55EeV, most deviationsin energy are below 20% and in arrival direction they are large and have values up to 4 ◦ . Therequest of two working crowns around the central station does not enhance the stability of thereconstruction noticeable (see Figure 4.18).Using the sub-arrays for a less dense configuration, the quality of the shower reconstruction ofan Auger North-like array has been studied. For extensive air showers with high multiplicity andenergies above 35 EeV, the deviations in energy are comparable to those obtained by leaving outone individual station of the unitary cell around the core. A new definition of the T5 trigger andan optimum ground parameter for the wider spacing will improve the stability further.4.5 SummaryIn this chapter the stability of the CDAS reconstruction for events with energies above 25 EeV hasbeen analyzed. For these events the sets of detectors taking part in the reconstruction have beenmodified by leaving out individual stations or sets of detectors. For every event the reconstructionis repeated as many times as there are active detectors involved, each time leaving out anotherdetector station or set of stations in the reconstruction. The resulting energies and angles are thencompared to the original values obtained with all detectors.The removal of the highest signal station or a station of the first crown, leads for strict-T5 eventsto deviations of 20% in energy and of 3 ◦ in arrival direction. Leaving out a station with a largerdistance to the shower axis, changes the energy by less than 3% and the arrival direction by lessthan 1 ◦ , with very few exceptions. The sizes of the deviations show no correlation with the energyof the primary cosmic ray, but depend strongly on the distance of the removed station to theshower axis.For the subset of events with E > 57EeV no removal of an individual station changes the energymore than 15% and the arrival direction more than 0.8 ◦ . Both the deviations in energy and inarrival direction are smaller than the resolutions of the surface detector. They are 22% and 1 ◦ forthis energy range. No removal of a station results in a failing reconstruction or an energy below57EeV. This is the current energy cut for the search for correlations with source candidates. In afurther test using all events above 25 EeV the influence of removing stations from the early or latepart of a shower has been discussed. Neither the removal of early nor of late triggered stationsshifts the energy systematically in one direction. The correction implemented in the reconstructioncode, which corrects for the different signal sizes, seems to work well for the analyzed energyrange.In addition, it has been shown, that strict-T5 events detected near the border of the array are notbiased by the missing detectors in the second crown and farther away. The removal of sets of detectors,which simulate the border of the array changes the energy up to 10% and the reconstructedarrival direction up to 1.5 ◦ . Leaving out all stations except the unitary cell leads to deviations inthe same ranges.The results summarized so far are all obtained for strict-T5 events. A comparison with the ICRC-T5 events, all events without a T5 cut, and with E > 25EeV has shown, that the deviations causedby removing a station of the unitary cell around the core, grow up to 60% in energy and 10 ◦ in arrivaldirection. The largest deviations have been found for reconstructions, where the two missingdetectors (the not active one and the removed one) have a distance of 1500 m from each other.

46 Stability of the reconstructionFigure 4.17: Deviations in energy (top) and space angle (bottom) between events reconstructed with all stations and reconstructed with only the signals of onethird of the stations. From the left to right the energy threshold changes from E > 25EeV, then E > 35EeV, E > 45EeV and finally, E > 55EeVon the right. The filled histograms are used to display subsets with five or more stations.0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree111110101010210Overflow 26210Overflow 0Overflow 0Overflow 0countsUnderflow 0RMS 1.811countsUnderflow 0RMS 1.137countsUnderflow 0210RMS 0.9098countsUnderflow 0RMS 0.7183Mean 1.598Mean 1.137Mean 0.9758Mean 0.8459Entries 1044Entries 490Entries 259Entries 139-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]-50 -40 -30-20 -10 0 10 20 30 40 50Difference in Energy [EeV]000-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]Difference in Energy [EeV]0-50 -40 -30 -20 -10 0 10 20 30 40 5030201020151051056423040251510850352012Overflow 91Overflow 2Overflow 1Overflow 0counts60Underflow 0Underflow 0RMS 15.64counts40Underflow 0RMS 12.46countsUnderflow 025RMS 12.59counts1445RMS 9.451Mean 9.651Mean 3.327Mean 2.834Mean 2.835Entries 1044Entries 490Entries 259Entries 139

4.5 Summary 47Entries 564Entries 269Entries 145Entries 8840Mean 9.674RMS 15.33Underflow 0counts35302530Overflow 46 2520Mean 3.809RMS 11.82Underflow 014countsOverflow 21210Mean 3.259RMS 11.14Underflow 0countsOverflow 1Mean 3.597RMS 8.153Underflow 0counts108Overflow 020158661510410452520-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]0-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]0-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]0-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]Entries 564Entries 269Entries 145Entries 88Mean 1.675RMS 2.024Underflow 02counts10Overflow 1010Mean 1.0832RMS 0.9529Underflow 0countsOverflow 0Mean 0.9124RMS 0.7942Underflow 0countsOverflow 0Mean 0.8651RMS 0.7508Underflow 0countsOverflow 01010101011110 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degreeFigure 4.18: Deviations in energy (top) and space angle (bottom) between T5+-events reconstructed with all stations and reconstructed with only the signals ofone third of the stations. T5+-events are surrounded by two crowns of working stations. The energy threshold changes from the left to the right:E > 25EeV, E > 35EeV, E > 45EeV and E > 55EeV. The filled histogramms are used to display subsets with five or more stations.

48 Stability of the reconstructionIn addition to the checks of the stability of the reconstruction, the described method can give a hintof the optimum ground parameter. The analysis shows, that the distance of 1000 m is too smallfor cosmic rays with energies above 25 EeV. It has been demonstrated, that the optimum distanceincreases with the energy. The identification of the optimum distance with this method is difficult,as the shift of the core position induces a bias.In the last part, the method of reducing the number of detectors taking part in the reconstructionis used to generate less dense arrays. With a spacing of 2600 m between the stations in each subarray,the distances are in the range, which is beeing discussed for Auger North. The results show,that the accuracy of the reconstruction depends on the energy. For events with energies above55 EeV the angular deviations are below 4 ◦ for all reconstructions and in energy below 20% for135 of 139 reconstructions. For the rest see Figure 4.17.From the analysis presented in this chapter can be concluded, that the CDAS reconstruction of highenergy strict-T5 events is very robust. Excluding individual stations or sets of detectors changesthe reconstructed energy by less than 10% and the arrival direction by less than 1.5 ◦ for eventswith E > 25EeV.

Chapter 5Azimuth angle distributionIn the studies presented in this chapter, the focus is on the analysis of the properties of the azimuthangle distribution. Starting from the basic assumption of an isotropic particle flux from the cosmosfor events with energies below 57 EeV, the measured zenith and azimuth angle distributions areanalyzed in detail.In the first part of this chapter, the zenith angle and azimuth angle distributions are described.Then a model is developed to understand structures in the azimuth angle distribution for energiesbelow full acceptance. After this, the obtained asymmetry with a period of 2! in the azimuth angledistribution is analyzed and finally the search for the reason of this effect is presented.5.1 IntroductionThe analysis presented in this chapter is based on the Herald data [41] detected between 1. January2004 and 20. July 2008. The Herald file contains all reconstructed T4 events. The usual cuts forthe Herald data are: " < 60 ◦ , flag 22 > 0 and flag 23 > 1. Flag 22 > 0 declares the reconstructedarrival direction of the shower compatible with the estimation, obtained from the seed of the threestations with the highest signal. Flag 23 > 1 marks events as strict-T5. If the energy for an eventis needed, the value of column 38 is used, as the file contains different energy values. For furtherinformation see [41].Before the analysis of the azimuth distribution is presented, a short discussion of the zenith angledistribution is performed. The " distribution for events detected above full acceptance of thesurface detector can be described by the functionf (")=a · sin" cos". (5.1)The variable a increases with the number of detected events and an event with " = 0 ◦ comesexactly from above. The sine term is due to the increasing spherical segment and the cosine termis due to the decreasing effective detector area, seen by an air shower, for increasing zenith angle.The distribution of all events above 3 EeV is shown in Figure 5.1 and it has its maximum at 45 ◦ .The distribution complies with Function 5.1 and systematic deviations are not visible. Themedian of the distribution given by Function 5.1 is at " = 37.76 ◦ and for the measured data it isat the same value. The agreement of the data with the theoretical expectation means that there areno systematic deviations. " distributions, containing events at energies below the full acceptancethreshold of the detector, are shifted towards lower zenith angles (see Figure 3.9 right). Thereason is the higher absorption of energy for inclined showers on their longer way through the

50 Azimuth angle distributioncounts700600Entries 26539Mean 36.63RMS 14.1850040030020010000 10 20 30 40 50 60Figure 5.1: Measured zenith angle distribution up to 60 ◦ for events with E > 3EeV and the usual qualitycuts. The solid line is the sin" cos"-function."atmosphere. The particle density or the energy of the individual particles decreases, so showerswith large zenith angles drop below the trigger threshold and are not being detected.5.2 Azimuth angle distributionSince cosmic rays arrive isotropically from the cosmos, the azimuth angle distribution is expectedto be flat. Figure 5.2 shows the )-distribution for all events above full acceptance (E > 3EeV) andwith " < 60 ◦ . Zero degree points to the east, 90 ◦ to the north and −90 ◦ to the south. Taking theerrors into account, the distribution is in agreement with a flat distribution.Below full acceptance (E < 3EeV), things become more complicated. The probability of detectinga shower depends on the core position, the energy, the zenith angle and the azimuth angle. Dueto the hexagonal structure of the array and the distribution of the 3 PMTs in the tanks, deviationsfrom the flat distribution are expected. The modulations for all events with " < 60 ◦ and for allevents with 37.76 ◦ < " < 60 ◦ , respectively, are shown in Figure 5.3. In both diagrams, deviationsfrom the flat distribution are visible. The dominating oscillation has a period of 2!/6 and is causedby the hexagonal structure of the array. For the events with " > 37.76 ◦ the hexagonal structure ofthe array has a stronger impact. The effect is superimposed by an effect with a period of 2!. Thechallenge of this analysis is to identify the reason for the latter oscillation. In addition to theseoscillations, the three PMTs may induce a modulation with a period of 2!/3, as they are arrangedin a plane with an angle of 2!/3 between each pair of PMTs.5.2.1 Hexagonal structure of the arrayIn this section, the reason for the oscillation with a period of 2!/6 is explained. It is a puregeometric effect, caused by the hexagonal structure of the array.Primary cosmic rays produce a cascade of secondary particles, which reach the earth in the formof a “pancake”. At the core, the particle density is very high, farther away the density decreaseswith increasing distance. The signals are, except for fluctuations, constant on circles around the

Entries26539Mean -1.338RMS 104.25.2 Azimuth angle distribution 51hThetacounts200150100500-150 -100 -50 0 50 100 150)Figure 5.2: Measured azimuth angle distribution for events with E > 3EeV and " < 60 ◦ .counts640014000 Entries 1169971 Entries 4945026200counts600013500580013000125005600540052005000120004800-150 -100 -50 0 50 100 150)-150 -100 -50 0 50 100 150)Figure 5.3: Measured azimuth angle distribution for all events with " < 60 ◦ (left) and the events with37.76 ◦ < " < 60 ◦ (right).

52 Azimuth angle distributionshower axis. For a shower with " = 0 ◦ , the signal distribution on the ground is point symmetric tothe core. For inclined showers with " > 0 ◦ the circles of constant signals are deformed to ellipses.The particle density on the ground decreases, as the same number of particles is distributed on alarger area. The relation between the major axis S M and the minor axis S m of an ellipse dependson the zenith angle only and can be written asS m = S M · cos". (5.2)The orientation of the ellipse is defined by the azimuth angle ), with the major axis parallel tothe incoming direction of the shower. If the shower reaches the ground, its spread depends on theenergy of the primary particle. In addition, the asymmetry between the signals of early and latetriggered stations has to be considered for inclined showers (see Chapter 3.3.3).Neglecting all fluctuations, there is one ellipse around the core which encircles all positions, wherea station would be triggered, whereas for all positions outside the signals are to small to trigger astation. A shower is detected, if at least three stations are located inside this ellipse. For showerswith energies above full acceptance the ellipse sizes are sufficiently large to enclose more thantwo stations, independent of the core position. For showers with energies below 3 EeV, the ellipsesizes become so small, that the fact, whether three or less stations are located inside, depends onthe core position and the arrival direction of the shower. For small zenith angles, the major andminor axes of the ellipse have similar length and the probability to detect a shower depends of thedistance of the core to the closest station, only. With increasing zenith angle a dependency on theazimuth angle emerges. The array consists of equilateral triangles of detector stations. Since theheight h of an equilateral triangle is smaller than the length of one side, showers with the minoraxis parallel to the height can be triggered for smaller ellipses, than showers perpendicular to it(see Figure 5.4). This results in a sine variation of the number of events detected in the azimuthhFigure 5.4: Schematic view of two showers with the same energy and the same core position. The onewith ) = 0 ◦ (solid line) would be detected, as three stations are enclosed by the ellipses, theother one, with ) = 90 ◦ , would not be detected.angle distribution. The period of this hexagonal effect is 2!/6, due to the structure of the array.To achieve a better understanding of this geometric effect, it is interesting to examine not onlythe question, if an event is triggered or not, but also to determine the ratio between the number ofevents that trigger three stations and the number of events that trigger four or more stations. To dothis, the different configurations of triggered surface detector stations have to be determined for

5.2 Azimuth angle distribution 533-fold an 4-fold events. For 3-fold events two configurations of stations are possible: equilateraltriangles with the apex to the north or to the south and six isosceles triangles, as shown in Figure5.5 (left). For the isosceles triangles the azimuth angles are indicated, for which the maxima areexpected. At zero degree the )-distribution should have a minimum. In case of the equilateraltriangles, there is a difference in the trigger probability between showers arriving parallel to thedirect connecting line of two stations, with a length of 1500m, and showers arriving perpendicularto it (height of triangles ≈ 1300m). The maxima are expected to occur for ) = 0 ◦ ±60 ◦ , exactly atthe positions of the minima of the isosceles triangles. The maxima in the ) distribution are definedby the appearance frequency of the different types of triangles. Due to the structure of the arraythe extrema recur every 60 ◦ , with an angle of 30 ◦ between each maximum and the neighboringminima.The 4-fold events are dominated by the three compact configurations of triggered stations shownmaxmaxmaxFigure 5.5: Left: The six possible isosceles triangles for 3-fold events and the expected maxima in theazimuth angle distribution. The only difference between the triangles with solid lines and theones with dashed lines, are that they are rotated by 60 ◦ . Right: The dominating configurationsof stations for 4-fold events.in Figure 5.5 (right). All three have the same attributes, as they can be converted into each other,by rotating them by an angle of 60 ◦ . Therefore, the maxima and minima occur every 60 ◦ , witha minimum at 0 ◦ . The second possibility for 4-fold events are the twelve possibilities shown inFigure 5.6.It is not necessary to investigate the possible configurations of triggered stations for events withFigure 5.6: The twelve possible configurations for the non-compact adjustment of stations for 4-foldevents. The three stations of the solid triangle and one at the end of one dashed line aretriggered.more triggered stations. On the one hand these events are detected independently of their arrival

54 Azimuth angle distributiondirection and distance between the core and the shower axis and on the other hand all events withmore than four triggered stations amount to 7.2% of all detected events, only. The frequenciesof occurrence for all events determined from the data are listed in Table 5.1. The azimuth angle3-fold 4-fold 5-fold 6-fold > 6-fold77.0% 15.8% 4.3% 1.5% 1.3%Table 5.1: Fractions of events, which trigger three, four or more stations.distributions for 3-fold, 4-fold and 5-fold events are shown in Figure 5.7. Inclined showers exhibitdistinctive maxima with distances of 60 ◦ for the 3-fold and 4-fold events. For events with moretriggered stations, the distribution is flat, as shown in Figure 5.2.5.2.2 Direct light in inclined showersThree photomultipliers collect the Cherenkov light produced in the water of each surface detectorstation. In the CDAS reconstruction code, the signal of a station is calculated as the average ofthe signals, collected by its working PMTs. This is not correct, as the signal measured by theindividual PMTs depends on the azimuth angle of the extensive air shower. The Cherenkov lightis emitted by the secondary particles, which cross the station and propagate in the water. In thefirst 50 ns, the light is not completely diffusely distributed and the PMTs collect different amountsof direct light (without any reflection) and semi-direct light (after a small number of reflections).It is a completely geometrical effect, due to the overlapping areas between the PMTs’ field of viewand the Cherenkov cone [61, 62]. After a few reflections, the light is distributed uniformly, as thewater is enclosed by a sealed liner with a diffusively reflecting inner surface. Since all stationsare oriented in the same way, the signal of the individual PMTs correlate with the azimuth angle(see Figure 5.8). This figure is generated by adding the signals of all stations with three workingPMTs, of all detected events of 2007 for each PMT, in " bins of 20 ◦ . The sine structure is clearlyvisible and the average signals of the PMTs are equal.5.2.3 Determination of amplitudes and phasesBoth effects described above result in sine structures in the azimuth angle distribution. At firstsight, the effect with a period of 360 ◦ seems to show a sine structure as well (compare Figure 5.2).In this part of the analysis, the data is fitted with a sine function, in Chapter 5.4.3 this assumptionis checked. The function fitted to the azimuth angle distribution is given by:N( )=c + a 6 · sin( 6!180 · ) + b 6)+ a 3 · sin( 3!180 · ) + b 3)( !)+ a 1 · sin180 · ) + b 1 . (5.3)It has seven free parameters, the absolute term c, the amplitudes a 6 , a 3 , a 1 of the three sine functionsand their phases b 6 , b 3 , b 1 . The function is fitted to all 3-fold events, all 4-fold events andall events without a cut on the number of triggered stations, respectively. In all three cases, onlyevents, which fulfill the strict-T5 and the usual cuts, are used. The selection of strict-T5 events isnecessary in order to use only events with a well defined multiplicity.The parameters of the fits are shown in Table 5.2. From the fit parameters the relative differencebetween the maxima and minima can be determined withp = 2 · ac . (5.4)

5.2 Azimuth angle distribution 55counts90008800860084008200Entries 756608 Entries 2631223400counts320030002800800026007800-150 -100 -50 0 50 100 150)-150 -100 -50 0 50 100 150)counts21002000Entries 156927 1400 Entries 96866counts130019001200180011001700100016009001500800-150 -100 -50 0 50 100 150)-150 -100 -50 0 50 100 150)counts600550500450400Entries 43094500 Entries 31930counts450400350300250350-150 -100 -50 0 50 100 150)200-150 -100 -50 0 50 100 150)Figure 5.7: Measured azimuth angle distributions for strict-T5 events with (left) " < 60 ◦ and strict-T5events with 37.76 ◦ < " < 60 ◦ (right); top: 3-fold events, middle: 4-fold events, bottom: 5-fold events.c a 6 b 6 a 3 b 3 a 1 b 13-fold 8408.7 ± 5.8 49 ± 14 −80.5 ◦ 11 ± 14 −88.5 ◦ 133 ± 14 −133.5 ◦4-fold 1743.9 ± 4.5 73.6 ± 6.4 −93.0 ◦ 5.3 ± 6.3 180.4 ◦ 21.2 ± 6.2 −165.3 ◦all 10951 ± 12 113 ± 16 −87.1 ◦ 12 ± 16 −74.6 ◦ 155 ± 16 −143.3 ◦Table 5.2: Parameters of the fits with Function 5.3 shown in Figure 5.9.

56 Azimuth angle distributionSignal in %0.380.360.340.320.30.28-150 -100 -50 0 50 100 150)Figure 5.8: Fraction of the total signal as a function of ) detected by the three PMTs. The errors are sosmall, that they are not visible. The plot is generated by taking the siganls of all PMTs, usedfor the reconstruction of the T4 events, which have been detected in 2007.The error results from error propagation:√ √ (/ ) p 2 ( ) / p 2 ((a ) 2 ( ) a · (c 2( p =/a · (a +/c · (c = +c c 2 . (5.5)The differences in the number of detected events between the maxima and minima, for the differentcuts, are listed in Table 5.3.The fits show very clearly, that the influence of the different signals of the three PMTs in eachp 6 p 3 p 13-fold (1.17 ± 0.17)% (0.27 ± 0.17)% (3.15 ± 0.16)%4-fold (8.44 ± 0.37)% (0.61 ± 0.36)% (2.43 ± 0.36)%all (2.07 ± 0.15)% (0.22 ± 0.14)% (2.83 ± 0.14)%Table 5.3: Relative differences p 6 , p 3 and p 1 between the maxima and the minima of the oscillations withperiods of 2!/6, 2!/3 and 2!, in the )-distribution.station is not significant for the azimuth angle distribution. Therefore, in the following the focusof the analysis is put on the effects with periods of 2! and 2!/6.5.3 Model for the hexagonal effect5.3.1 LayoutTo study the effect of the hexagonal structure of the array, a model has been developed. Theunitary cell of the array is a hexagon, composed of seven stations. They form six triangles, threewith an apex pointing to the north and three with an apex to the south. The smallest unit, whichrepresents the whole array is formed by two triangles, one with the apex pointing to the northand one with an apex to the south. By dividing one triangle, a rectangular unitary cell can beconstructed, whose size is one third of the common unitary cell. In the rectangle (shown in Figure

5.3 Model for the hexagonal effect 57counts9200 Entries 75660890008800860084008200800078007600-150 -100 -50 0 50 100 150)counts220021002000Entries 1569271900180017001600150014001300-150 -100 -50 0 50 100 150)counts11800 Entries 9853671160011400112001100010800106001040010200-150 -100 -50 0 50 100 150)Figure 5.9: Azimuth distributions for the 3-fold (top), 4-fold events (middle) and all events (bottom),which fulfill the usual cuts. For the fits Equation 5.3 is used.

58 Azimuth angle distribution5.10) with edge lengths of 1500 m and 1300 m, a shower core is placed every ten meters in the x-y-plane, which adds up to 19500 core positions. Around each core position an ellipse is drawn. IfFigure 5.10: Model for the 2!/6-effect: The left picture shows the stations (dots) and the area (littlesquares), where the showers are simulated with a core positions on a ten meter grid. In theright picture, two ellipses are shown, one would trigger the surface detector, one would not,as only two stations, located at the apexes of the triangle, are inside the ellipse.three non-aligned stations (in the figure illustrated by little squares) are located inside the ellipse,the shower can be reconstructed, otherwise it cannot. In this model, stations inside the ellipseshave a trigger probability of one, stations outside have a probability of zero. Around the rectangleone row of stations is inserted. No further stations can be triggered by 3-fold and 4-fold events,since the ellipses are to small to encircle stations farther away.The model developed so far has two free parameters, the lengths of the semi-major axis S M and thesemi-minor axis S m of the ellipse. These two variables depend on the energy and the zenith angleof the simulated shower. For a given energy, the minor axis can be extracted from the LDF andthe major axis is given by Equation 5.2. By simulating showers with all energies and zenith anglesoccurring, normalized by the frequency of their appearance, it is possible to compare the numberof showers detected with two ellipses perpendicular to each other. One has its major axis parallelto the x-axis and corresponds to extensive air showers with ) = 0 ◦ ± n · 60 ◦ , the other one has itsmajor axis parallel to the y-axis and represents showers with ) = 30 ◦ ± n · 60 ◦ (see Figure 5.4.The orientations coincide with the maxima and minima determined from the fits for the hexagonaleffect.In the next steps, firstly, the connection between S(1000) and the semi-minor axis of the ellipsewill be described, then, secondly, the frequency of occurrence of the showers is presented, independency on their zenith angles and energies and, finally, asymmetries of the footprint of theshowers and fluctuations will be figured out.For the reconstruction of the energy, different types of LDFs can be selected. For this model, apower-law function [63] is used, as this is the standard LDF in the CDAS reconstruction code.The signal S depends on the distance r from the shower core:(r) −-S(r)=S(1000) ·, (5.6)1000mwith the slope parameter -- = 2.24 − 0.98(sec " − 1). (5.7)By transposing Equation 5.6, the distance to the core can be calculated, for a given S(1000) anda given signal S(r)=2.6VEM (TOT trigger condition: signal above 0.2 VEM in at least 13 time

5.3 Model for the hexagonal effect 59bins, see also Figure 3.4):( ) 2.6VEM − 1-r = 1000m ·. (5.8)S(1000) · cos"It is also possible to use a NKG-like function, which is the standard LDF in the offline reconstructionsoftware. The respective equations are[( r) (S(r)=S(1000) · 3.47 - · · 1 + r )] −-(5.9)700m 700mandr = − 700m2√ (700m ) 2 ( S(1000) · 3.47- · cos"++2S(r)) 1-(5.10)with the same slope parameter -.The cos"-term in Equations 5.8 and 5.10 is included to account for the fact, that the secondaryparticles of extensive air shower with large zenith angles are distributed on a wider area than theparticles of showers with small zenith angles. The sizes of the ellipses increase for a constantsemi-minor axis proportional to 1/cos ". With this correction, the signal S(r)/cos " is selected inthe LDF to have a signal of the same size on the ground as for vertical showers.To determine the ellipse, which encircles all triggered stations and leaves out all not triggeredstations, the threshold for triggering a station is needed. On the station level, two independenttrigger conditions are implemented. The single threshold trigger requires a signal of 3.2 VEM inone bin and for the time-over-threshold trigger, the signals in 13 time bins of 25 ns in an interval of3 µs have to be above 0.2 VEM each (see Chapter 3.1). This results in a signal of 2.6 VEM, whichis implemented in the model. This assumption is a very rough estimation and its consequenceswill be discussed in Chapter 5.3.5.For any given signal, the size of the corresponding ellipse can be calculated as a function ofS(1000) and ". The semi-minor axis has a length of S m = r and the semi-major axis can becalculated from Equation 5.2. For each configuration (" and S(1000) fixed) a map can be drawn,which illustrates the core positions (x,y) that would trigger an event. Such a map for S m = 1000and " = 40 ◦ can be seen in Figure 5.11. The ellipses with the major axis parallel to the x-axiswould trigger 5875 showers, the ones with the major axis parallel to the y-axis only 5806. Thesemaps are generated for all zenith angles up to 60 ◦ and for all occurring ellipse sizes.In the next step, the normalization factors for the showers with different S(1000) and " have to becalculated. With respect to ", the events arrive proportional to sin" cos". The scale factor isN(")=a · sin" cos ". (5.11)To obtain the distribution of the occurring ellipse sizes, the starting point is the energy spectrum.From the energy spectrum first the S 38 and then the S(1000) spectrum are calculated:N(E) ∼ E −# , (5.12)[N (S 38 ) ∼ a · (S 38 ) b] −#, (5.13)[ ( ) ]S(1000)b−#N (S(1000)) ∼ a(5.14)CICwith # = −3.0, a = 0.149 and b = 1.08 [50]. The CIC function used isCIC (")=1 + 0.94 ( cos 2 " − cos 2 38 ◦) − 0.48 ( cos 2 " − cos 2 38 ◦) 2. (5.15)

histEntries 5876Mean x 1493Mean y 649.9RMS x 441.4RMS y 189.50 0 01 5875 00 0 0hist2Entries 5807Mean x 1489Mean y 647.8RMS x 468.9RMS y 378.10 0 01 5806 00 0 060 Azimuth angle distributionsouth - north1200100050454035south - north120010005045403580030800306002520600252040015400152001052001050800 1000 1200 1400 1600 1800 2000 2200east -west00800 1000 1200 1400 1600 1800 2000 2200east - west0Figure 5.11: Number of triggered showers per bin for ellipses with the major axis parallel to the x-axis(left) and parallel to the y-axis (right) for showers with S m = 1000 and " = 40 ◦ .For a given shower size and a given zenith angle, 19500 ellipses are generated with the majoraxisparallel to the x-axis and the same number of ellipses with the major-axis parallel to they-axis. If the positions of the required number of stations are located inside the ellipse, a counteris incremented. After all possible positions are tested, the number of triggered events is multipliedwith the two scale factors N(") and N(E). For the calculation of the relative difference of triggeredevents with the two ellipses, 200 shower sizes are created, covering the whole spectrum, from thepoint where the triggering of three stations becomes possible for the first time, up to the energy,where 3 (4 for the 4-fold test) stations are triggered, independent of the core position. For eachshower size, showers for every zenith angle up to 60 ◦ are created in steps of 1 ◦ . In total19500 × 200 × 60 = 2.34 · 10 8 showersare simulated for both ellipses. For each shower size and zenith angle, the number of detectedshowers is counted and normalized with N (S(1000)). Finally, the number of showers N x with) = 0 ◦ (major axis parallel to x-axis) and N y with ) = 90 ◦ are calculated. The relative differenceis determined fromD = 2 · (N x − N y )N x + N y· 100. (5.16)5.3.2 Asymmetry correctionThe footprints of inclined showers are ellipses. As the detector level is below the shower maximum,the number of particles decreases, before the shower reaches the ground. In a first approximation,this can be taken into account by an inverted cone reaching the detector level. Theintersection is an ellipse, which is not centered around the core (see Figure 5.12). For a givencone, the half angle 0, the semi-major axis and the offset of the elliptical center from the cone axiscan be calculated. The distances from the conical axis to the edges of the ellipse along the major

5.3 Model for the hexagonal effect 61Figure 5.12: The intersection of a vertical cylinder, an inclined cylinder, and an inclined (inverted) conewith the ground plane [46].and minor axis areThe semi-major axis adds isr 1 = S msin(90 − 0)sin(90 + 0 − ") and r 2 = S msin(90 + 0)sin(90 − 0 − ") . (5.17)S M = r 1 + r 22and the offset d of the elliptic center is= S mcos"(5.18)d = r 2 − r 1. (5.19)2In order to consider this in the model, the core positions are shifted by d and the ellipses are drawnaround the new positions. After moving all cores by a constant term, the whole rectangle of corepositions is moved by this value and due to the regular shape of the array, this does not change thenumber of detected events. In the model, the influence has been tested for cone half angles up to10 ◦ and the number of events has not been affected.5.3.3 Signal fluctuationsIn studies dealing with trigger probabilities, it is essential to analyze signal fluctuations in detail.In the analysis presented here, the impact of fluctuations is small, since the comparison of thetwo orientations of the same ellipse guarantees that the fluctuations almost cancel each other.Nevertheless, a test has been performed to check the assumption.Without fluctuations, the trigger efficiency is one inside the ellipse and zero outside. In Chapter3.2, the trigger probability of individual surface detectors has been described. The continuousincrease of the trigger probability is simulated by softening the sharp transition from one to zeroby a Gaussian smearing (see Figure 5.13). At the former edge of the ellipse the trigger probabilityis 0.5. Up to 0.9r, the probability stays at one and for distances larger than 1.4r it becomes zero. Inbetween, a random number between 0 and 1 is picked from a uniform distribution and comparedto the value of the Gaussian distribution at this distance r. If the randomly chosen value is smallerthan the value of the Gauss smeared edge, the station has been triggered, otherwise not.In the next section, the results obtained with and without fluctuations are presented.

62 Azimuth angle distribution110.5r0.9r rFigure 5.13: Model with binary trigger probability (left) and with a continuously developing trigger probability(right).5.3.4 ResultsJust like for the data, the simulation is performed for all events and for the 3-fold and 4-fold events,separately. Table 5.4 lists the results. Figure 5.14 illustrates the number of showers triggering theModelDataD D f luc % of events D % of events3-fold 1.32% 1.20% 72.5 −1.17% 77.04-fold −14.23% −13.7% 20.6 −8.44% 15.8all −0.51% −0.52% 100 −2.07% 100Table 5.4: Oscillations with amplitude D/2 in the azimuth angle distribution with a period of 2!/6.detector, plotted against S(1000) and ". In the zenith angle plots, the measured " distributions areadded. The " distributions obtained from the data are normalized, so that the maxima of the zenithangle distributions have the same amplitude. As shown in Table 5.4, there are differences betweenthe values of the model and the data. For all events, the model and the data show a minimum at) = 0 ◦ , but with different amplitudes. In the data, the effect is four times larger. In the subset ofthe 3-fold events, the amplitudes are similar but the maxima of the model are at the positions ofthe minima in the data. For the 4-fold events, the minima are at the same azimuth angles (90 ◦ ) forthe model and the data, but the amplitude of the model is almost three times higher. At first viewthe model does not describe the data at all.3-fold events can trigger two types of triangle configurations, equilateral and stretched ones (seeChapter 5.2.1). In the model, the major part of the triggered triangles are equilateral triangles and,therefore, the minima are at 0 ◦ ± n · 60 ◦ , with n = 0,1,2,3. This compact configuration dominatesespecially for small zenith angles, as the footprints of theshowers on the ground are ellipses, wherethe differences between S M and S m are small. For inclined showers the ellipses are more stretchedand the stations at the corners of isosceles triangles are triggered more often. The " distributionof the model is shifted towards lower zenith angles and, therefore, the equilateral triangles occurwith a higher probability than in the data.Furthermore, the fraction of 3-fold events in the model is lower and the fraction of 4-fold eventsis higher than in the data. 5% of the events, which are 3-folds in the data, trigger four stations inthe model. The azimuth distribution of these events has a minimum at ) = 0 ◦ . They reduce theamplitude of the oscillation for the 4-fold events in the data, as they are measured as 3-fold events.Besides, their maxima are at the positions of the minima in the 3-fold " distribution. In the datathey reverse the direction of the effect.In the ) distribution of all events, the amplitudes in the data are four times more distinctive than

5.3 Model for the hexagonal effect 63N(S1000)120010003110counts10008003110DataModel ellipse 1Model ellipse 280060040060040020020000 20 40 60 80 100 120s0 10 20 30 40 50 60"N(S1000)1109008007006003counts7006005003110DataModel ellipse 1Model ellipse 25004003002001004003002001000 20 40 60 80 100 120s00 10 20 30 40 50 60"N(S1000)1108007006005003counts1801601401203110200DataModel ellipse 1Model ellipse 2400300200100100806040200 20 40 60 80 100 120s0 10 20 30 40 50 60"Figure 5.14: The number of triggered showers as a function of S(1000) (left) and the " distributions ofthe two ellipses and the measured events. The plot at the top is for all events, the one in themiddle for 3-fold events and the one at the bottom for 4-fold events. The major axis of ellipse1 is parallel to the east-west axis and the major axis of ellipse 2 is perpendicular.

64 Azimuth angle distributionin the model (see Table 5.4). The shift of the " distribution in the model enlarges the fraction oftriggered equilateral triangles. They reduce the amplitude of the hexagonal effect.5.3.5 Limits of the modelIt is important to remark, that creating this simple model helps to understand and visualize theeffect of the hexagonal structure of the array, but due to the simplifications a perfect agreementis not possible. The displacements of surface detector stations, the differences in the trigger ratesfor individual stations or the influences of not working stations are all not taken into account. TheLDF implemented in the CDAS code (see Equation 3.3) is simplified, as the entire LDF dependson the distance of the core to the nearest station and contains a second slope parameter #. All thesesimplifications could be implemented in the model, but their impact is small in comparison to theseverest simplification, which has been made for the trigger condition.In the surface detector stations, two different local triggers are implemented, the single thresholdtrigger, which requires a signal of more than 3.2 VEM in one signal bin, and the time-overthresholdtrigger (ToT), which requires signals above 0.2 VEM in 13 time bins of 25 ns in aninterval of 3µs. The minimum signal for the ToT is therefore only 2.6 VEM. These two signalscorrespond to two different ellipse sizes for the trigger threshold. Since the time-over-thresholdtrigger condition is the most frequent one and the single threshold trigger only contributes a smallfraction (see Figure 3.2), only ToT events are considered in the model. Since it is not possibleto implement a condition to distinguish between these two trigger criteria, this is the limit of themodel. For further analyses Monte Carlo simulations are essential. With them, the fractions ofsingle threshold and time-over-threshold triggered stations can be determined and the shift of themaximum in the zenith angle distribution for events with E < 3EeV can be analyzed in moredetail.5.4 Description of the asymmetry in 2!The azimuth angle distribution shows an oscillation with a period of 360 ◦ . The results of thefits, performed in Chapter 5.2.3, are summarized in Table 5.5. Neither in the amplitude nor inp ) min3-fold (3.15 ± 0.16)% 43.5 ◦4-fold (2.43 ± 0.36)% 75.3 ◦all (2.83 ± 0.14)% 53.3 ◦Table 5.5: Azimuth angles ) min and amplitudes p of the minima, obtained by the sine fits to the azimuthdistributions (see Section 5.2.3).the phase, the fits of the subsets agree with the values obtained for the whole data set. Whetherthe oscillation in 360 ◦ depends on the multiplicity of the events, is discussed as well as, whetherthe strength of the effect depends on the energy or the zenith angle. Afterwards possible timedependencies are analyzed.

5.4 Description of the asymmetry in 2! 655.4.1 RatiosIt has been shown, that the three PMTs induce no oscillation, or an oscillation with a very smallamplitude. From now on oscillations with a period of 120 ◦ are ignored and the focus is only onthe superposition of the two oscillations with periods of 360 ◦ and 60 ◦ , respectively. To determinethe amplitude and the phase of the 360 ◦ effect, ratios are calculated.The azimuth angle distribution is divided into equally sized bins of 60 ◦ . Each bin includes onefull period of the oscillation in 60 ◦ and, therefore, the number of entries in each bin is independentof the hexagonal effect. By comparing the two bins with mean values of ) and ) + 180 ◦ , for all) angles, the phase and the amplitude of the 360 ◦ effect can be determined. The ratio r i ( ) iscalculated as the fraction of the number of entries in the bins N 1i ∈ [) − 30 ◦ ,) + 30 ◦ ] and N 2i ∈[) + 180 ◦ − 30 ◦ ,) + 180 ◦ + 30 ◦ ]:The error is calculated by applying error propagationr i = N 1iN 2i. (5.20)(r i ==√ ( ) 2 ( ) 2 /ri/ri(N 1i + (N 2i (5.21)/N 1i /N 2i√ ( ) 1 √ 2 (N1i + − N )1i √ 2N2iN 2i N2i2 .(5.22)Figure 5.15 shows the ratio r i as a function of the azimuth angle. Although one half of the graphcontains the complete information, since r( ) is equal to 1/r() +180 ◦ ), the whole range is plottedto illustrate the sine structure. In the graph at the bottom of Figure 5.15 the ratios for the 3-fold and4-fold events are compared to the ratio for all events. For most azimuth angles the data points agreewithin 1,. A significant dependency on the number of triggered stations can not be confirmed.The sine behavior is clearly visible for all subsets of events. The amplitude and the phase areobtained by a sine-fit. The result for all events is( ))r( )=1.0 + 0.026 · sin180 − 144.38 . (5.23)As the ratios are determined by integrations, they have to be normalized, to be comparable withthe relative deviations obtained by the sine-fits (see Table 5.5). In this case, the scale factor is one,as the area below the integrated function is equal to one:∫ 2!3!3sinxdx = −cosx| 2! 3 !3= −[−0.5 − 0.5]=1. (5.24)The minimum for the plot with all events is at ) min = 54.4 ◦ and the amplitude is p = 2.64%. Thevalues are in agreement with the ones listed in Table 5.5.In order to analyze, up to which energy the effect is significant, a Rayleigh analysis is performed.With this method, it is possible to quantify the probability of an asymmetry, to be due to randomfluctuations. This is especially important for the energy range above full acceptance. All searchesfor large scale anisotropies and correlations with point sources start with the basic assumption ofa flat azimuth distribution for events with E > 3EeV.

0.02643p0 ±0.0002399p1 0.01745 ±0p2 -2.524 ±0.009115p3 1 ±066 Azimuth angle distributionratio1.041.031.021.0110.990.980.97all events0.96-150 -100 -50 0 50 100 150)ratio1.041.031.021.0110.990.980.970.96all events3-fold events4-fold events-150 -100 -50 0 50 100 150)Figure 5.15: Top: Ratios between all events measured in N 1i ∈ [) − 30 ◦ ,) + 30 ◦ ] and N 2i ∈[) + 180 ◦ − 30 ◦ ,) + 180 ◦ + 30 ◦ ]. Bottom: Comparison of the ratios of events with differentnumbers of triggered stations.5.4.2 Rayleigh analysisA Rayleigh analysis [64, 65] is a harmonic analysis, where the m-th order fits the distribution ofazimuths . i of the N events to a sine wave with period 2!/m. The amplitude r and the phase . r ofthe sine fit are given by√r = a 2 + b 2 and tan. r = b (5.25)awitha = 2 NN+i=1cos(m. i ) and b = 2 NN+i=1sin(m. i ). (5.26)The chance probability, for obtaining an amplitude larger than r for a uniform distribution, is givenbyP(≥ r)=exp(−k) (5.27)with k = Nr 2 /4. For the analysis of the oscillation with a period of 2! in the azimuth distribution,first order Rayleigh tests (m = 1) are performed. The first analysis (see Figure 5.16 left) isperformed by determining the amplitude, phase and probability for T5 events with energies abovegiven values, as a function of the threshold energy. The Rayleigh amplitude, phase and probabilityare calculated as a function of the threshold energy. The phase corresponds to the location of

5.4 Description of the asymmetry in 2! 67Rayleigh amplitude1-110Rayleigh amplitude-110-210-210-3-11010 1 10210E [EeV]10-3-110 1 10E [EeV]Rayleigh phase20015010050Rayleigh phase2001501005000-50-50-100-100-150-150-200-110 1 10210E [EeV]-200-110 1 10210E [EeV]Rayleigh probability-210-410-610-81010101-10-12-1410-1610-1810-2010-22-11010 1 10210E [EeV]Rayleigh probability-210-410-610-810-101010-12-1410-1610-1810-201010 -22-24-11010 1 10210E [EeV]Figure 5.16: Rayleigh amplitude, phase and probability for T5 events with " < 60 ◦ above a given energy(left) and below a given energy (right).

68 Azimuth angle distributionthe minimum of the sine wave, that fits the distribution best. For the data points up to an energyof 1 EeV, the amplitude is nearly constant at a value close to 10 −2 , the phase is constant at 55 ◦and the probability increases from 10 −21 to 10 −4 with increasing energy. The probability, that theasymmetry in the data is accidental is 10 −21 , if all events are taken. The decrease of the probabilityis due to the fact, that the number of events decreases with increasing energy threshold. For theevents above 1 EeV, the probability to measure such an effect by chance is still 10 −4 . For eventsabove 3 EeV, the Rayleigh probability is above 10 −2 , as the number of events decreases. Nevertheless,the phase remains at about 55 ◦ , except for a few data points, up to 20 EeV.In the second test (see Figure 5.16 right), the amplitude, phase and probability are calculated forthe events with energies below given values, again as a function of the threshold energy. The datapoint at the highest energy corresponds to the point at the lowest energy in the previous analysis.Both points are calculated using the whole data set. With decreasing energy threshold, thenumber of events is reduced. Down to an energy of 1 EeV, the amplitude (≈ 10 −2 ) , phase (55 ◦ )and probability (< 10 −22 ) are almost constant. Below 0.5 EeV, the phase is no longer constantand the probability reaches zero. The reason for this can be seen from Figure 5.16. In the regionaround 0.2 EeV, a few bins have a Rayleigh phase of −80 ◦ . The probability is close to zero, but itis sufficient to cause the dip in the phase diagram in Figure 5.16 (right).Two further Rayleigh tests have been performed. The events are once divided into seven separateenergy ranges, and once into energy bins of varying sizes, with the bin center changed from smallto high energies. The entries of bin i are in the energy range of(−1 + 0.01 · i) < log 10 E i ≤ (−1 + 0.01 · (i + 10)).The result for the test with the seven bins is displayed in Table 5.6, whereas Figure 5.17 shows theresult for the analysis with the bins of varying size.E [EeV] Entries Amplitude [%] Phase Probability< 0.5 396219 1.6 42.0 4.41 · 10 −110.5 − 1 366669 1.4 60.9 2.72 · 10 −81 − 2 165983 1.0 70.3 1.56 · 10 −22 − 3 32094 1.9 72.3 5.12 · 10 −23 − 5 14908 1.4 -74.8 5.05 · 10 −15 − 10 6605 2.6 58.8 3.31 · 10 −1> 10 2889 5.3 63.6 1.33 · 10 −1Table 5.6: Rayleigh amplitudes, phases and probabilities of T5 events, subdivided in six independentenergy bins. The phase corresponds to the location of the minimum of a sine wave.The plot in the middle of Figure 5.17 shows only small changes in the phase for the bins witha bin center less than 1 EeV. This energy range contains the majority of all detected events. Forabout 30 bins, the probability is below 10 −3 . For all bins with phases very different from 55 ◦ , theprobabilities are close to zero. Table 5.6 shows the phases, amplitudes and probabilities for sevennon-overlapping bins and the number of entries in the bins. Here, again the phase is close to 55 ◦for most bins.The Rayleigh analyses have established, that the azimuth asymmetry is not accidental. TheRayleigh probability for all events is 10 −21 with a phase of 55 ◦ . These results are in perfectagreement with the phase of 55 ◦ and the amplitude of 2.66% obtained by the ratio method.

5.4 Description of the asymmetry in 2! 69Rayleigh amplitude-11010-2Rayleigh phaseRayleigh probability-310 -110 1 10200150100500-50-100-150-200-110 1 10101-110-210-310-4-510-610-710-110 1 10210E [EeV]210E [EeV]210E [EeV]Figure 5.17: Rayleigh amplitude, phase and probability for T5 events with " < 60 ◦ in logarithmic energybins.

70 Azimuth angle distribution5.4.3 Energy and " dependencyUp to now, a sine structure of the asymmetry in the azimuth distribution has been assumed, as theform of the oscillation looks like a sine. By modifying the method presented in Chapter 5.4.1, ananalysis independent of this assumption is performed. The number of events detected in a 60 ◦ binin ) is compared to the total number of events. For a flat distribution, 1/6 of all events is expectedto be found in each bin, independent of its position. The bin size of 60 ◦ is chosen again to excludeany inpact from the hexagonal effect.With this method the same plot as in Figure 5.15 is generated. It is shown in Figure 5.18. Theratio0.030.02all events0.010-0.01-0.02-0.03-150 -100 -50 0 50 100 150)Figure 5.18: Relative deviations of the number of events detected in 60 ◦ bins, from a flat distribution.azimuth angle distribution has a defined maximum at ) =(−130 ± 5) ◦ , with an excess of (1.7 ±0.3)% and a minimum between 0 ◦ and 100 ◦ , with a deficit of (−1.0 ± 0.3)% in the number ofdetected events. The deviations are in agreement with the results obtained with the sine fit (seeFigure 5.15). The amplitude of 2.64% at ) max = −126.4 ◦ is calculated as the difference betweenthe number of events in the bin centered around ) max and the bin centered around ) min = ) max +180 ◦ and is therefore larger.Now, a two dimensional map in " and ) is created to find the maximum and minimum in ) andto figure out, if the strength or the location of the maximum depends on the zenith angle. At eachpoint (", ) in Figure 5.19 (upper left) the ratio between the events detected in [) − 30 ◦ ,) + 30 ◦ ]and [" − 5 ◦ ," + 5 ◦ ] and all events detected in [" − 5 ◦ ," + 5 ◦ ] for all azimuth angles, is calculated.These relative deviations p are by a factor of two smaller for a sine oscillation, compared to theones calculated in Chapter 5.4.1, where the difference between the maximum and minimum iscalculated.With respect to ", the plot is limited to a range from 5 ◦ to 55 ◦ , to use only events below 60 ◦ . Thechoice of the interval size in " is motivated by a compromise between having enough statistics anda not to large overlap between the individual bins.The obtained ratios are multiplied by a factor of six and afterwards a value of one is subtracted. Thenumerical values represent the differences in the number of detected events from a flat distributionin percent. The upper left plot in Figure 5.19 shows theses relative differences p and in the upperright plot the absolute errors ( p of the relative differences are shown. Their sizes depend on thenumber of the events in the bins. The plot on the bottom left shows the significance t = p/( p,

5.4 Description of the asymmetry in 2! 710.030.0130.030.020.010-0.01-0.02555045403530252015105-150 -100 -50 050100 1500.020.010-0.01-0.020.0140.0130.0120.0110.010.0090.0080.0070.0060.005555045403530252015105-150 -100 -50 050100 1500.0120.0110.010.0090.0080.0070.00640.06543210-1-2-35055 -445403530252015105-150 -100 -50 050100 1503210-1-2-30.080.060.040.020-0.02-0.04-0.06555045403530252015105-150 -100 -50 050100 1500.040.020-0.02-0.04Figure 5.19: Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): Relative deviations from a flat azimuth distribution (top left), errors of these values (topright), significances (bottom left) and fluctuated map of deviations (bottom right).

72 Azimuth angle distributioncalculated from the two plots in the upper row. The plot on the bottom right is the same map as inthe upper left, with each point (", ) fluctuated by its error. Every point in the map is obtained asa random value from a Gaussian distribution with the mean value p and the width ( p.Figure 5.19 shows, that the assumption of a sine structure might be incorrect and has to be analyzedin more detail. For the zenith angle region with the highest significances (" ≈ 50 ◦ ), the differencebetween the maximum ) max ≈−120 ◦ and the minimum ) min ≈ +100 ◦ is only 140 ◦ , not 180 ◦ .In addition to this, it seems that the position of largest negative deviation varies with the zenithangle. For " = 55 ◦ it is located at ) min ≈ 100 ◦ and shifts to ) min ≈−40 ◦ for " = 0 ◦ . As thestatistics are small for vertical showers, the significances are small for bins with bin centers below25 ◦ . Within its errors, it is also possible that the minimum is at ) ≈ 70 ◦ for all zenith angles. Tofigure this out and to determine any possible energy dependencies, the events are divided into sixenergy and six " bins, delimitated by the edges listed in Table 5.4.3. The bin edges are chosenin a way, that each bin contains the same number of events. The dependence of the variationsbin 1 2 3 4 5 6" [ ◦ ] < 20.5 20.5 − 28.5 28.5 − 35.0 35.0 − 41.0 41.0 − 47.5 > 47.5E [EeV] < 0.34 0.34 − 0.45 0.45 − 0.59 0.59 − 0.8 0.8 − 1.2 > 1.2Table 5.7: Borders of the " and energy bins.on the energy and on " are analyzed for bins around four selected azimuth angles: one at theposition of the maximum () = −120 ◦ ) and three in the region of the minimum () = 5 ◦ , ) = 55 ◦ ,) = 105 ◦ ). Figure 5.20 shows the results for ) = −120 ◦ . Neither an explicit zenith angle, norRatio0.050.04Ratio0.050.040.030.030.020.020.010.01-0-0-0.011 2 3 4 5 6"-0.011 2 3 4 5 6EnergyFigure 5.20: Relative differences in the number of events detected in a 60 ◦ bin around ) = −120 ◦ incomparison to a flat distribution. The left plot shows the zenith angle dependence, the rightplot the energy dependence.an explicite energy dependence can be gathered from the plots. Both graphs are compatible witha flat distribution. In the map in Figure 5.19, it seems that the strength of the effect increaseswith the zenith angle increasing. This apparent difference between the plots of Figures 5.19 and5.20 is caused by the fact, that the bins in the map at small zenith angles contain a relative small

5.4 Description of the asymmetry in 2! 73number of events. The significances are small and give the impression of a positive fluctuation. Itis possible, that the first data point in Figure 5.20 is in fact caused by a positive fluctuation, butthis has to be confirmed, when more events are detected.In the energy plot, no significant deviations from a flat distribution are found. As the first five binscontain only events with energies below 1.2 EeV and the last bin comprises the events with higherenergies, all events above full acceptance are included in this bin. The number of events is notsufficient to analyze the strength of the effect above full acceptance separately. The size of theerrors make every value compatible with zero.Figure 5.21 shows the same plots for bins around various azimuth angles in the range of theminimum. For the energy plot, it is not possible to make a statement, besides, that the three ratiosRatio0.01Ratio0.01Bin around 5àBin around 55àBin around 105à00-0.01-0.01-0.02-0.02-0.03-0.031 2 3 4 5 6"1 2 3 4 5 6EnergyFigure 5.21: Same as Figure 5.20 with 60 ◦ bins around ) = 5 ◦ , ) = 55 ◦ and ) = 105 ◦ .of the three positions agree with each other within their errors. For zenith angles above 40 ◦ therations do not agree within their errors. As for none of the three azimuth angles a tendency can bestated, neither a constant minimum nor a minimum varying with the zenith angle can be excluded.5.4.4 Different areas of the arrayIn this part, the array is divided into four spatial parts, north-west, north-east, south-west andsouth-east. The two cuts in north-south and east-west direction are such, that each quarter containsone fourth of the recorded events. In Figure 5.22, the deviations from an isotropic distribution andin Figure 5.23 their significances are plotted for each of the four parts. The ratios in the upperplots are again calculated for the events detected in [) − 30 ◦ ,) + 30 ◦ ] and [" − 5 ◦ ," + 5 ◦ ] andfor all events detected in [" − 5 ◦ ," + 5 ◦ ] with all azimuth angles. The significances represent thediscrepancies in units of ,. All four ratio and significance plots are normalized, so they can becompared by eye.The south-west part of the array shows less distinct deviations from a flat distribution than the otherparts. This is the oldest part of the array. In this quarter, the deviations for small zenith angles arenot significant, due to the small number of detected extensive air showers and the distribution iscompatible with a flat distribution. In the adjacent part in the east, the minimum and maximumare much more distinctive. In the region around ) = −120 ◦ , the strength of the effect is up to 4%

74 Azimuth angle distribution0.040.040.040.020.020.040.020.02-0-0-0.02-0-0-0.02-0.04-0.065040302010-150 -100 -50 0 50100 150-0.02-0.04-0.06-0.04-0.065040302010-150 -100 -50 0 50100 150-0.02-0.04-0.060.040.040.040.020.020.040.020.02-0-0.02-0.04-0-0.02-0-0.02-0.04-0-0.02-0.065040302010-150 -100 -50 0 50100 150-0.04-0.06-0.065040302010-150 -100 -50 0 50100 150-0.04-0.06Figure 5.22: Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): The four plots show the relative differences from an isotropic distribution. The plots arearranged according to the positions of the parts in the array they represent (north-west, north-east, south-west and south-east).

5.4 Description of the asymmetry in 2! 754404321-1-2-3-4-55040302010-150 -100 -50 0 50100 1503210-1-2-3-4-504321-1-2-3-4-55040302010-150 -100 -50 0 50100 1503210-1-2-3-4-54443210-1-2-3-4-55040302010-150-100 -50 0 50 100 1503210-1-2-3-4-543210-1-2-3-4-55040302010-150-100 -50 0 50 100 1503210-1-2-3-4-5Figure 5.23: Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): The four plots show the significances of the deviations shown in Figure 5.23. The plots arearranged according to the positions of the parts in the array they represent (north-west, north-east, south-west and south-east).

76 Azimuth angle distributionwith significances between 2.5 and 4. In the north-east part, the relative deviations have a similarsize, as in the south-east, with slightly smaller significances. In the north-west part, the maximaare less distinctive than in the eastern parts.5.4.5 Time dependenceTo find the reason for the asymmetry in the azimuth angle distribution, it is important to know, ifthe strength or the location of the maximum, respectively the minimum, varies with time. Variationsare conceivable on different time scales. In this part, it is restricted to the obvious oneswith a periode of a day and a year. The time scan in hours is sensitive to influences of the sunand all other variations with a daily periodicity. By sorting the events into time bins of months,the influence of the seasons can be determined. In addition both studies give hints for possibletemperature dependencies.For each of the two tests, the events are sorted into six time bins. For the analysis on a daily basis,each bin includes the events of a four hour period, for the second analysis each bins includes thedata of two months of the year. Each point in Figure 5.24, respectively 5.25, shows the relativedeviation in the number of events detected in a 60 ◦ bin centered around the plotted azimuth angleand all measured events, both in the denoted time bins.In the analysis of the daily variations (see Figure 5.24), there is a difference in the locations of themaxima, between the evens detected in the morning and those, detected in the afternoon. The plotof the events detected between 8 h and 12 h has the maximum at ) ≈−140 ◦ and for the followingfour hours, it is at ) ≈−70 ◦ . The data points from the other time bins show no distinctive featuresand in the region of the minimum the values of all time bins are all compatible with each other.In Figure 5.25 the differences form a flat distribution are plotted dependent of the month, in whichthey have been detected. There is no difference between summer and winter in the data. All valuesagree with each other, within their errors. This suggests that the effect does not vary with the temperatureor any other effects, like atmospheric conditions, which exhibit modulations in periods ofyears.5.4.6 Events with less strict cutsFor the analyses presented here, the number of detected events is too low to make explicit statementsof dependencies on other parameters. This will change, when more events will be recordedin the future. At the moment, it is only possible to increase the number of events by softening thequality cuts. Two possibilities are discussed here: taking into account events with " > 60 ◦ andevents, which do not fulfill the T5 trigger, respectively.Cosmic rays with zenith angles well above 60 ◦ have to penetrate more air, as the path throughthe atmosphere increases with ". The muon content increases and, therefore, the reconstructionalgorithm is changed at " = 70 ◦ . The angular reconstruction becomes challenging, as the timedifferences between the stations increases and the influence of the hexagonal structure is morepronounced. The reconstruction is not as accurate as for events with " < 60 ◦ . Nevertheless, thereis no obvious reason, why this should effect the number of events detected in 60 ◦ bins, as eachbin includes one period of the oscillation, caused by the hexagonal structure of the array and reconstructionuncertainties should be distributed randomly. The ratio and the significance plot areexpanded and exhibited in Figure 5.26.Up to 70 ◦ , the map confirms the tendencies of increasing amplitudes and significances with increasing". The maximum stays constant at ) ≈−120 ◦ and the minimum seems to shift furtherwith increasing " towards higher azimuth angles. Above 70 ◦ , the significances as well as the

5.4 Description of the asymmetry in 2! 77ratio0.040.030h - 4hratio0.040.034h - 8h0.020.020.010.0100-0.01-0.01-0.02-0.02-0.03-0.03-0.04-200 -150 -100 -50 0 50 100 150)-0.04-200 -150 -100 -50 0 50 100 150)ratio0.040.038h - 12hratio0.040.0312h - 16h0.020.020.010.0100-0.01-0.01-0.02-0.02-0.03-0.03-0.04-200 -150 -100 -50 0 50 100 150)-0.04-200 -150 -100 -50 0 50 100 150)ratio0.040.0316h - 20hratio0.040.0320h - 24h0.020.020.010.0100-0.01-0.01-0.02-0.02-0.03-0.03-0.04-200 -150 -100 -50 0 50 100 150)-0.04-200 -150 -100 -50 0 50 100 150)Figure 5.24: Relative deviations from a flat azimuth distribution in dependence on the time of the day,when the events were recorded.

78 Azimuth angle distributionratio0.040.030.020.010-0.01-0.02-0.03-0.04Month01 - 0203 - 0405 - 0607 - 0809 - 1011 - 12-150 -100 -50 0 50 100 150)Figure 5.25: Relative deviations from a flat azimuth distribution in dependence on the month, when theevents were recorded.relative differences grow. Above 75 ◦ , the azimuth angle distribution has two maxima and twominima. The minimum obtained below 60 ◦ moves further to higher azimuth angles. At " = 90 ◦ ,it is located at ) ≈ 180 ◦ . At " = 90 ◦ almost all measured events come from the north or the southand almost none form the east or the west. Although the significances are up to 11 respectively−10, the use of these events needs a very detailed knowledge of the modified reconstruction andthe trigger efficiencies. Within the scope of this thesis, it is not possible to perform such a comprehensiveanalysis.Another method to increase the number of events, is to repeat the analysis without the T5 qualitytrigger requirement. The trigger requires, that the station with the highest signal is surrounded bya crown of six active stations during the time of the detection of the event. Just like for the cut at" = 60 ◦ , there is no obvious reason, why the events should be biased without that cut, with respectto the occurrence in bins of 60 ◦ . The results for all events are shown in Figure 5.27. The result isqualitatively exactly the same as for the events, which fulfill the T5 trigger. The only differenceis, that higher significance can be obtained. The maximum in the azimuth angle distribution isat ) = −120 ◦ for all zenith angles. The largest excess of events (+3%) and a significance of 5is observed at ) ≈−120 ◦ and " = 55 ◦ ). The location of the minimum can not be specified asprecise as by the maximum. It is less pronounced and changes with the zenith angle. The absoluteminimum is at ) ≈ 100 ◦ and " = 55 ◦ with a deficit of events of −3% and a significance of 4.5.4.7 Attributes of the effectIn this section, the results of the tests performed to characterize the asymmetry in the azimuthangle distribution are summarized. In addition to the oscillation with a period of 60 ◦ a significantdeviation from a flat azimuth angle distribution has been found. The probability, that the azimuthangle distribution of all detected events with " < 60 ◦ , which fulfill the T5 trigger, is compatiblewith a flat distribution, is calculated as 10 −21 with a Rayleigh analysis. The effect has been

5.4 Description of the asymmetry in 2! 7911.210.80.60.40.20-0.2-0.4-0.68070605040302010-150 -100 -500501001500.80.60.40.20-0.2-0.4-0.61010550-50-10-58070605040302010-150 -100 -50050100150-10Figure 5.26: Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 85 ◦ ): Relative deviations from a flat distribution(top) and significance plot (bottom) for T5 events.

80 Azimuth angle distribution0.030.040.030.020.010.020.010-0.01-0.02-0.030-0.015040302010-150 -100 -50050100150-0.02-0.03564204321-20-4-15040302010-150 -100 -50 050100 150-2-3-4Figure 5.27: Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): Relative deviations from a flat distribution(top) and significance plot (bottom) for events, which fulfill the T5 requirement andthose which do not, for zenith angles up to 60 ◦ .

5.5 Origin of the asymmetry 81analyzed with and without the assumption of a sine behavior.With the assumption, the maximum is obtained at ) max = −125.6 ◦ and the difference between themaximum and minimum is 2.64%. Without the assumption the maximum is at ) =(−130 ± 5) ◦ ,with an excess of (1.7 ± 0.3)% and the minimum is located between 0 ◦ and 100 ◦ , with a deficit of(−1.0 ± 0.3)% in the number of detected events. Therefore, it is not clear, if the effect has a sinestructure, or not and will therefore be subject of further investigations.By creating bins in " and ), the absolut maximum is found at ) ≈−120 ◦ and " = 55 ◦ and theabsolute minimum is located at ) ≈ 100 ◦ and " = 55 ◦ , which complies with a phase differenceof 140 ◦ , and not 180 ◦ , as expected for a sine. At the maximum, the excess of particles amountsto +3% with a significance of 4 and at the absolute minimum, the deficit is around −2.5% witha significance of 3. The position of the maximum is constant in ) for all zenith angles ". For theminimum, the " dependence remains unclear. Within the recorded statistics, a variation in ) from) = 0 ◦ at " = 5 ◦ to ) = 100 ◦ at " = 55 ◦ is as well possible as a constant value.A correlation with the energy could neither be obtained for the maximum nor for the minimumand an explicit time dependence is not visible. The only distinctive feature is a differene in thelocation of the maximum for events measured between 8 h and 12h() max ≈−140 ◦ ) and and eventsmeasured in the following four hours () max ≈−70 ◦ ).By splitting the array into four areas, a variation in the strength is determined. In the east, theextrema are more distinctive than in the west. In the south-west, the significances of the deviationsfrom a flat ) distribution are below 2.5, for all extrema in the " − )−map.5.5 Origin of the asymmetryNow, as the extent of the effect and the locations of the maximum and the minimum have beenpresented, the next step is to find the origin of the effect. In the search for the reason, it is importantto consider, that the asymmetry has been found in the local coordinate system of the detectorand not in galactic coordinates. The causes are therefore limited to terrestrial impacts, detectoreffects and problems of the reconstruction algorithm. By assuming an isotropic flux for particles(with E < 57EeV) from outer space, the terrestrial effects could induce an asymmetry, bybiasing the development of extensive air shower in the atmosphere. Possible reasons are varyingatmospheric conditions above the surface detector array or the influence of the geomagnetic field,which deflects the particles. Here, a comparison with the azimuth distribution of the fluorescencedetector would be a useful tool. Unfortunately the recorded statistics of the telescopes are muchsmaller than for the surface detector and the ) distribution is influenced by many systematic effects.Therefore a comparison is of no help.It is only possible to stick to the data recorded by the surface detector or to compare it with MonteCarlo simulations. Monte Carlo simulation was not part of this thesis, so the search is limited totests of the measured events.5.5.1 CDAS reconstruction algorithmThe first test is to check, if the effect is also visible, if the events are reconstructed with the AugerOffline reconstruction software instead of the CDAS code. For individual events, the differencesin the reconstructed arrival direction are less than three degrees [39]. The reconstructed S(1000)value is in average about 5% larger, if an event is reconstructed with the CDAS code, than in areconstruction with the Offline algorithm. The azimuth angle distributions of both reconstructionsare displayed in Figure 5.28. In both distributions, the oscillations in 2! and 2!/6 are clearly

82 Azimuth angle distributioncounts960094009600Entries 1079166 Entries 1079166counts9400920092009000900088008800860086008400-150 -100 -50 0 50 100 150)8400-150 -100 -50 0 50 100 150)Figure 5.28: The azimuth angle distributions of all events reconstructed with the CDAS algorithm (left)and the Offline algorithm (right).visible. The agreement of the distributions does not exclude an error in the reconstruction software,but then the same error is in the two independent algorithms. E.g. such an error could be a wrongdefinition of the coordinate system, which is implemented in both algorithms.5.5.2 Border effectsDuring the construction phase the array took sometimes complicated shapes (see Figure 5.29).The influence of the form and the border is excluded by using only the data of events, where theFigure 5.29: Status of the surface detector array in November 2005: 1031 tanks are deployed (shadedregion), 1012 filled with water and 898 with electronics [66].station with the highest signal is surrounded by two crowns of active stations. The requirement ofthe T5+ trigger decreases the number of detected events from 985367 for the T5 trigger to 546140.The azimuth angle distribution shows still the same oscillations in 2! and 2!/6 as the plot of theevents, that conformed to the T5 trigger only. An influence of the border can thus be excludedfor the data taking period with a growing array size, as well as for the time afterwards, when theinstallation of stations has been finished.

5.5 Origin of the asymmetry 835.5.3 Tilt of the arrayThe stations of the surface detector cover an area of 3000km 2 . Although the region in the PampaAmarilla is rather flat, variations of the ground level of up to 300 m occur. The stations with thehighest altitudes are located in the west, the ones with the lowest altitudes in the north-east andthe south (see Figure 3.11). The tilt of the array is determined by calculating the normal vector ofeach equilateral triangle, formed by three stations, and adding them to an average normal vectorfor the whole array. This normal vector has changed, each time a new station has been deployed.In February 2008, 1547 stations of the regular grid were installed and the array was tilted by 0.16 ◦towards the south-east () = −22.2 ◦ ). This tilt influences the azimuth angle distribution, as theprobability to detect events with ) = −22.2 ◦ is higher than the probability to detect events fromthe opposite direction. From the measured zenith angle distribution the size of this asymmetry canbe calculated. The estimated difference in the number of events between the minimum and themaximum is 0.18%.As the size of the effect is by a factor of 10 too small and the positions of the extrema are displacedby ≈ 100 ◦ , the tilt of the array is not the cause of the asymmetry in the azimuth angle distribution.5.5.4 PMT effectsWhen an extensive air shower deposits energy in a station, the signal of the station is calculatedas the average of the signals detected by the working PMTs. The fraction of the signal of the individualPMTs depends on the azimuth angle (see Chapter 5.2.2). The performed fits of the azimuthangle distribution have shown no significant oscillation with a period of 120 ◦ , induced by the threePMTs. Nevertheless, it is checked, if the PMTs can induce an oscillation with a period of 2!.A difference between the three PMTs is their temperature. The electronics of the stations is locatedbelow an aluminum enclosure above PMT1 and heats the PMT. The development of the temperaturesmeasured by thermometers at the three PMTs and the electronics are plotted in Figure 5.30left. The temperature of the electronics is 10 ◦ higher across the day. To identify the temperaturetemp [degree]4035302520PMT 1PMT 2PMT 3Electronicstemp [degree]3210PMT 1 - PMT 2PMT 1 -PMT 3PMT 2 - PMT 315-110-250 2 4 6 8 10 12 14 16 18 20 22 24time [h]-30 2 4 6 8 10 12 14 16 18 20 22 24time [h]Figure 5.30: Temperatures of the electronics and the PMTs for one day (left) and differences betweenpairs of PMTs (right).

84 Azimuth angle distributionoffsets between the PMTs, their differences are calculated (see Figure 5.30 right). PMT 2 andPMT3 behave similar and have maximal differences of 1 ◦ . The temperature differences betweenPMT1 and the other two PMTs cover a range of 4 ◦ .In Chapter 5.4.5 the maxima obtained between 8 h and 16 h are a bit more distinctive then in theother hours of the day. This is the region, where the temperature differences between the PMTs isminimal, but more events have to be detected to demonstrate a definite dependenceAnother possible reason might be the raining behavior of many PMTs (see Chapter 3.4.2). Tocheck, if the raining PMTs are responsible for the asymmetry, the events are sorted into bins accordingto the number of triggered raining PMTs. Neither the amplitude, nor the phase of theasymmetry shows any correlation with the number of raining PMTs.The reconstruction algorithm is modified such, that the reconstruction is only performed with thesignal of one PMT. To achieve this, the signal of one PMT is copied to the other two PMTs priorto reconstruction. By applying this to all stations, three modified HERALD files are generated,one for each PMT. The three azimuth distributions from the modified reconstruction are shown inFigure 5.31. All three distributions show the oscillations with periods of 2! and 2!/6 and agreecounts100009800Entries 1137358counts100009800Entries 1112948960096009400940092009200900090008800-150 -100 -50 0 50 100 150)8800-150 -100 -50 0 50 100 150)counts100009800Entries 1116668960021solar panel9400920090003north8800-150 -100 -50 0 50 100 150)Figure 5.31: Azimuth angle distributions, obtained by reconstructing the events with the signals of onlyone of the three PMTs per station. The plot in the upper left corner is for PMT 2, the upperright for PMT 1 and the plot at the bottom right is for PMT 3. The drawing illustrates thepositions of the PMTs in the station.with each other. This check provides no further information about the cause of the asymmetry.All tests performed with respect to the PMTs provide no indication of the reason of the asymmetry.

5.5 Origin of the asymmetry 855.5.5 Terrestrial magnetic fieldPrimary cosmic rays are mainly positively charged. They are deflected systematically by the terrestrialmagnetic field. Especially at low geomagnetic latitudes, this leads to an enhancement ofcosmic rays hitting the atmosphere from the west. This so called east-west effect [67, 68] is aconsequence of the fact, that not all trajectories can reach the atmosphere from outside the geomagneticfield. To see, which trajectories are allowed, a standard procedure is to inject positivelyand negatively charged particles near the top of the atmosphere in various directions and simulatetheir paths back outward to their incoming directions. If their paths intersect with the surface ofthe earth, the respective directions are impossible.The magnitude of the deflection of charged particles in magnetic fields decreases with the energiesof the particles increasing. The horizontal component of the geomagnetic field at the Pierre Augerobservatory in Malargüe is B ≈ 20 µT. A proton at an energy E = 3 · 10 18 eV has a momentum of|⃗p| ≈ E/c = 1 · 1010 eV·s. The Lorentz force forces the particles to move on a circular path withthe radiusmr =peV·sq · B = 1 · 1010m1e· 20 · 10 −6 T = 5 · 1014 m. (5.28)The strength of the magnetic field decreases as the distance to the earth increases and in an altitudeof 100 km above ground the strength is reduced by 98%. As the radius of the circle, which wouldbe described by a particle deflected by the geomagnetic field, is about nine orders of magnitudelarger, than the region, where the geomagnetic field deflects the cosmic rays, the impact is verysmall. This rough calculation illustrates that the east-west effect is negligible for the energy rangecovered by the Pierre Auger observatory. The deflection of the secondary particles is not studiedand can be subject of further investigations.5.5.6 Solar panelThe power for the electronics is provided by a solar photovoltaic system, installed on top of eachstation. To optimize the exposure to sunlight in winter time, the solar panels are installed such, thatthey face north, at an inclination of 55 ◦ with respect to the upward-looking position [15]. Eachstation has two panels, with a total size of 1.26m 2 [69]. As the minimum in the ) distributionis located almost in the north, the question, if it could be caused by the absorption of secondaryparticles in the solar panel, has to be considered.Each surface detector station covers an area of 10m 2 , which is about eight times the size of thesolar panel. In a geometrical model, the effective area of a station, which is masked by the solarpanel, is calculated. Therefore, the scalar product of the normal vector of the solar panel and thevector of the incoming cosmic ray, is calculated. The result in dependency on " and ) is shownin Figure 5.32. The region, where the masked area is largest, coincides with the minimum in themap of the relative deviations from a flat distribution (see Figure 5.19). For cosmic rays comingfrom the position of the maximum, the masked area is zero. From this geometrical consideration,absorption of secondary particles in the solar panel could be the reason for the asymmetry in thedata.Solar panels are made of silicon, which has a radiation length of 9.4 cm. The installed solar panelshave a thickness of 3.2 cm, which is one third of a radiation length. The question is, whether thisis enough to absorb so much energy of the secondary particles of showers coming from the north,such that ≈ 2.5% of the events do not fulfill the event trigger conditions any longer. But this isbeyond the scope of this thesis. The best way to do this, is to simulate the signals, measured bythe surface detector stations with and without solar panels, if the secondary particles of extensive

86 Azimuth angle distribution0.910.80.80.70.60.60.40.50.20.460 050403020100-150-100-500501001500.30.20.10Figure 5.32: Area of a surface detector station masked by the solar panel as a function of " and ) andnormalized to one for the maximal masking.air showers reach the ground. If the number of triggered events, detected with the solar panelis by about 2.5% smaller than without, the solar panel would be identified as the cause of theasymmetry. Without this simulation, the hypothesis can neither be confirmed nor rejected.5.6 SummaryIn this chapter, the azimuth angle distribution has been analyzed in detail. For events with energiesbelow full acceptance of the array (3 EeV), the hexagonal structure leads to an oscillationin the number of detected events, with a period of 60 ◦ . The difference between the extrema is(2.07 ± 0.15)% with a minimum at ) = 0 ◦ , which corresponds to the east (see Section 5.2.3).The amplitude of the oscillation increases with zenith angle increasing. In a model, the effect issimulated (see Section 5.3), by comparing the number of events triggering the array for showerscoming from the directions of the extrema. With the model, the effect of the hexagonal structurecan be reproduced. The amplidude of the oscillation is in the model (0.51%) by a factor of foursmaller, than in the data. This is a result of the fact, that the model has only one fixed triggerthreshold, whereas the stations can be triggered, if one of two trigger conditions is met, the singlethreshold trigger or the time-over-threshold trigger. Since it is not possible to implement two triggercriteria in this kind of model, a detailed Monte Carlo study is necessary to analyze the effectin more detail.A possible oscillation in the ) distribution with a period of 120 ◦ , caused by the dependence of thePMT signals on ), could not be stated. Either there is no oscillation at all, or the amplitude is sosmall, that it is not observable (see Sections 5.2.2, 5.2.3 and 5.5.4).In Section 5.4, the asymmetry, found with a period of 360 ◦ in the azimuth angle distribution ofthe T5 events, is analyzed in detail. Firstly, the amplitude and the phase are calculated under theassumption of a sine structure of the asymmetry. The difference in the number of events is calculatedby comparing the number of events in 60 ◦ bins to exclude any influence of the oscillationwith a period of 60 ◦ . The difference between the minimum () min = 54.4 ◦ ) and the maximum

5.6 Summary 87() max = −125.6 ◦ ) is 2.64%. By comparing the number of events measured in a 60 ◦ bin, with theaverage of all azimuth angles, the maximum is at ) =(−130±5) ◦ , with an excess of (1.7±0.3)%and the minimum is located between 0 ◦ and 100 ◦ , with a deficit of (−1.0 ± 0.3)% in the numberof detected events (see Figure 5.18.In Rayleigh tests, the amplitude and phase were confirmed and the probability, that the recordedazimuth angle distribution is compatible with a flat distribution, is calculated, as 10 −21 . Furthermore,the method shows, that the phase sticks to ≈ 55 ◦ for all events above a given energythreshold, up to 10 EeV. Above 10 EeV, the phase is no longer constant.Secondly, the energy and " dependences are analyzed. The minimum and the maximum valuesare determined without the assumption of a sine behavior of the effect, by calculating the fractionof events, which are measured in 60 ◦ bins in ). The absolute maximum is found at ) ≈−120 ◦and " = 55 ◦ and the absolute minimum is located at ) ≈ 100 ◦ and " = 55 ◦ , which complies with aphase difference of 140 ◦ , and not 180 ◦ , as expected for a sine. At the maximum, the excess of particlesamounts to +3% with a significance of 4 and at the absolute minimum, the deficit is around−2.5% with a significance of 3. The position of the maximum is constant in ) for all zenith angles.For the minimum, the " dependence remains unclear. Within the recorded statistics, a variationin ) is as well possible as a constant value. The attempt to solve this question by increasing thestatistics by using also events, which do not fulfill the T5 trigger, provides no further information.A correlation with the energy could neither be obtained for the maximum nor for the minimum.By splitting the array into four areas, a variation in the strength is determined. In the east, theextrema are more distinctive than in the west. In the south-west, the significances of the deviationsfrom a flat ) distribution are below 2.5, for all extrema in the " − )−map. An explicit timedependence is not visible. The shift of the maximum between 8h and 16 h in the analysis of dailyvariations has to be analyzed with more statistics to judge, if this is a random fluctuation, or causedby a real dependency.Finally, in Section 5.5, several possible reasons are analyzed. A comparison of the results, obtainedby reconstructing the events with the two common reconstruction algorithms, CDAS andOffline, shows, that the azimuth angle distributions are similar. In further tests, border effects, thetilt of the array, effects of the individual PMTs and the influence of the geomagnetic field couldbe excluded as major causes. The solar panel could be a possible cause, since the position of theminimum agrees with the direction, where its absorption of secondary particles has a maximum.This might be by chance and has to be checked with Monte Carlo simulations. It has not beendiscussed, if the thickness of the panel is sufficient, to cause an effect of 2.5%. It is, furthermore,unclear, which effect could cause the maximum in this case, as the solar panel would only decreasethe energy of the secondary particles of extensive air showers coming from northern directions.This would reduce the number of detected events coming from the north, as some fall below thetrigger threshold of the surface detector stations.

Summary and outlookChapter 6Summary and outlookThe aim of this thesis was to analyze the properties of the surface detector data of the Pierre Augerobservatory. Two different aspects have been discussed, the stability of the CDAS online reconstructionalgorithm and the features of the azimuth angle distribution.In Chapter 4, events with reconstructed energies above 25 EeV and " < 60 ◦ are analyzed. For eachevent the set of detectors taking part in the reconstruction is modified by leaving out individualstations, or sets of detectors. The resulting energies and angles are then compared to the originalvalues, obtained with all detectors. For events, which fulfill the strict-T5 trigger condition, theexclusion of individual stations or sets of detectors changes the reconstructed energy by less than10% and the arrival direction by less than 1.5 ◦ . Furthermore, it has been shown, that strict-T5events, recorded near the border of the array, are not biased by the missing detectors in the secondcrown or farther away. It has also been shown, that the uncertainties of the signal at a distance of1000 m from the core are larger than for more distant core distances. The reconstruction of cosmicrays with E > 25EeV can be improved, by determining S(r > 1000m) instead of S(1000m)from the signals of the triggered stations and calculating the energy from this S(r > 1000m). Todetermine the optimum distance from the shower core, Monte Carlo simulation is an appropriatetool, but it is beyond the scope of this thesis. In the analysis presented here, it has been shown,that detectors of the second crown and farther away have almost no influence on the reconstructedproperties of the events. In addition, it has been evidenced, that the influence of one single failingdetector is negligible for the detection of high energy cosmic rays (see also [70]).In Chapter 5 an asymmetry in the azimuth angle distribution has been obtained. It has been shown,that the three PMTs in each station induce no significant oscillation in the zenith angle distribution.In addition to an oscillation with a period of 60 ◦ , which is purely due to the hexagonal structure ofthe array, a maximum and a minimum are found in the ) distribution, with a difference in phaseof approximatly 180 ◦ . In a two dimensional search in " and ), the absolute maximum is foundat () ≈−120 ◦ ," ≈ 55 ◦ ) with an excess of detected events of +3% and a significance of 4. Theabsolute minimum is located at () ≈ 100 ◦ ," ≈ 55 ◦ ), where the deficit of events amounts to −2.5%with a significance of 3. In an analysis independent of the zenith angle, the extrema are obtainedat ) min = 54.4 ◦ (north-east) and ) max = −125.6 ◦ (south-west) with a difference in the number ofdetected events of 2.64%. For the 985000 strict-T5 events, detected up to August 2008, these2.64% correspond to an excess of about 4300 detected events in a 60 ◦ bin in ), centered aroundthe maximum, compared to the showers in a bin of the same size, centered around the minimum.The reason for the effect is not found yet. Nevertheless, border effects, the tilt of the array, effectsof the individual PMTs and the influence of the geomagnetic field could be excluded as majorcauses. The effect might be caused by absorption of secondary particles in the solar panel. Due

to lack of time, the absolut absorption factor is not calculated in this thesis and will therefore besubject of further investigations.89

LIST OF FIGURESList of Figures1.1 Primary cosmic ray spectrum [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Schematic drawing of the longitudinal development of an extensive air shower [8]. 31.3 Schematic views of an extensive air shower [9]. . . . . . . . . . . . . . . . . . . 41.4 Schematic view of the measurement of an extensive air shower by a fluorescencetelescope and surface detector stations [12]. . . . . . . . . . . . . . . . . . . . . 62.1 The Pierre Auger observatory near the city of Malargüe. The circles illustratethe positions of the 1600 water Cherenkov detectors forming the surface detectorarray. The array is over-looked by 24 fluorescence telescopes, situated in 4buildings. The fields of view of the individual telescopes are indicated by lines [14]. 82.2 Schematic view of a surface detector station [17]. . . . . . . . . . . . . . . . . . 92.3 Histograms of charge (left) and pulse height (right) for a single SD station, triggeredby a 3-fold coincidence from all 3 PMTs (solid line). The histogram withthe dashed line shows the spectrum of an external muon telescope for the sameevents. The first hump is due to the triggering of low-energy particles from EASand shows the typical exponential slope. The second hump is caused by the atmosphericmuons [19]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 The extensions near the Coihueco building: The dots illustrate the surface stationsand the lines indicate the field of view of the HEAT and the former installed fluorescencetelescopes. All stations indicated with a name belong to the 1.5 km grid,the others are spaced 750 m and 433 m apart. All stations inside the huge hexagonwill have in addition a 30m 2 buried muon counter, after AMIGA is completed [24]. 122.5 Schematic view of a fluorescence telescope unit [25]. . . . . . . . . . . . . . . . 132.6 Sky map of the celestial sphere in galactic coordinates. The asterisks illustratethe positions of the 442 AGN (318 within the field of view of the observatory)with redshift z ≤ 0.017 (D ≤ 71Mpc) from the 12th edition of the Véron-Cettyand Véron catalog [32]. The black circles of 3.1 ◦ in diameter are centered aroundthe reconstructed arrival directions of the 27 events with a reconstructed energyabove 57 EeV. Darker colors indicate higher relative exposure and the solid lineshows the limit of the field of view, for " < 60 ◦ . The dashed line displays thesuper-galactic plane [31]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

92 LIST OF FIGURES3.1 Raw histograms of station 1640, with an integrated signal of 10.3 VEM. The databelongs to event 200821400018 and is a randomly picked example. Top: baselinehistograms for all three dynode channels; middle: charge histograms of thethree PMTs; bottom left: summed charge histogram; bottom middle: pulse height(peak) histograms of the three PMTs; bottom right: average pulse shape of thethree PMTs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Zenith angle (left) and energy (right) distribution for events passing the T4 trigger.Events passing the 3ToT are displayed in the red shaded area and 4C1 events inthe blue dashed area. Events fulfilling both criteria are counted as 3ToT events [34]. 183.3 The ICRCT5 (left) requires five of six active stations in the first crown and a reconstructedcore position in an active triangle of detectors. Core positions insidethe right triangle satisfy the ICRCT5, core positions inside the left triangle not.The right picture shows the condition for the strict-T5, an active unitary cell. . . . 193.4 Left: Comparison between the experimental (symbols) and unbiased (solid line)trigger probability for " = 45 ◦ and S 1000 = 4.5VEM. Right: Lateral trigger probabilityfor three different values of S 1000 (3 (boxes), 10 (circles) and 30 VEM (triangles))and zenith angles of 0 ◦ and 45 ◦ (closed and open symbols) [37]. . . . . . 203.5 The distances d of the stations to the shower axis or shower core and the distancesD to the point, where the shower core hits the ground. The left station is an earlydetector, as the station is triggered before the core reaches the ground, whereas theright station is a late detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.6 Pictures from the CDAS Event Display: event 200821400018, E = 12.03EeV," = 51.5 ◦ . The left plot shows the signals of the triggered stations (rectangles),the silent stations (triangles) and the LDF with the error band. The right showsa top view of the triggered stations. The size of the circles is proportional to thelogarithm of the detected signal. The stations marked with a cross, are flagged asaccidental and the two black stations at the right were not active, at the time theevent was detected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.7 - (left) and # (right) as a function of the zenith angle. The light line represent theparameterization of -. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.8 Correlation between lgS 38 and lgE FD for the 661 hybrid events used in the fit. Thesolid line is the best fit to the data [49]. . . . . . . . . . . . . . . . . . . . . . . . 243.9 Azimuth angle distribution (left) for all events with " < 60 ◦ and zenith angle distribution(right) without any cuts. . . . . . . . . . . . . . . . . . . . . . . . . . . 253.10 The left plot demonstrates the development of the ToT rate of the Piuquen detectorsince its deployment. The right graph shows the decreasing T5 rate of the subarray,which is operating since December 2004 [52]. . . . . . . . . . . . . . . . 263.11 Left: The altitude of the stations in meter in reference to the center of the array.Right: Stations, which had one or more raining PMTs in March 2008, are visualizedwith asterisks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.12 Histogram of the triangle sizes for the surface detector. The deviations in percentare caused by displaced stations. . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1 The station with the highest signal is called central tank. It is surrounded by thesix stations of the first crown. The second crown consists of the twelve stationssurrounding the first crown. Crown n is formed by 6 · n stations. . . . . . . . . . 29

LIST OF FIGURES 934.2 Differences in energy (left) and space angle (right) between the original and modifiedreconstructions for events with E > 57EeV. . . . . . . . . . . . . . . . . . 304.3 (S(1000) (left) and space angle between (),") and () + ()," + (") (right) forT5 trigger events with E > 57EeV. . . . . . . . . . . . . . . . . . . . . . . . . . 304.4 Shifts of the reconstructed core position between original and modified reconstructionfor events with E > 57EeV . . . . . . . . . . . . . . . . . . . . . . . . . . 324.5 Differences in energy (left) and space angle (right) for all events above 25 EeV(top), ICRCT5 events (middle) and strict-T5 events (bottom). . . . . . . . . . . . 344.6 Deviations in energy resulting from excluding individual stations of the first crown(left) and farther off (right) for the early (top) and late part (bottom) of the showers. 364.7 Deviations in S(1000) (left) and S(1600) (right) resulting from excluding individualstations before the reconstruction. . . . . . . . . . . . . . . . . . . . . . . . 374.8 Deviations in S(1000) (left) and S(1600) (right) resulting from excluding individualstations before the reconstruction from events with saturated detectors. . . . . 374.9 RMS (left) and mean values (right) of the histograms shown in Figure 4.10. . . . 384.10 Deviations in S(r) by comparing the signals of the events above 25 EeV reconstructedwith all stations and without the central station. In the left plot of the firstline, r is equal to 1000 m and increases by 50 m with each histogram up to 1800 min the last histogram on the right in the bottom row. . . . . . . . . . . . . . . . . 394.11 Direction of the core displacement after the removal of the central station (left)and the influence on the core distances for the other stations (right). . . . . . . . 404.12 Analog plot to Figure 4.9, RMS values (left) and mean values (right): The circlesare used to illustrate the development of the histograms of the central stations, therectangles for the histograms of the first crown stations. From top to bottom theenergy range changes from 25EeV < E ≤ 30EeV via 30EeV < E ≤ 40EeV toE > 40EeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.13 Differences in energy in percent (left) and space angle in degrees (right) betweenthe reconstruction with all stations and the reconstruction with only the unitarycell for events with E > 57EeV (top) and E > 25EeV (bottom). . . . . . . . . . 424.14 Stations beyond the unitary cell on two sides of the central tank are left out in thereconstruction. These detectors are marked with a cross. . . . . . . . . . . . . . 434.15 Differences in energy in percent (left) and space angle in degrees (right) betweenthe reconstruction with all stations and modified sets of detectors simulating theborder of the array for events with E > 57EeV (top) and E > 25EeV (bottom). . 444.16 Triangle sub-array configurations. . . . . . . . . . . . . . . . . . . . . . . . . . 444.17 Deviations in energy (top) and space angle (bottom) between events reconstructedwith all stations and reconstructed with only the signals of one third of the stations.From the left to right the energy threshold changes from E > 25EeV, then E >35EeV, E > 45EeV and finally, E > 55EeV on the right. The filled histogramsare used to display subsets with five or more stations. . . . . . . . . . . . . . . . 464.18 Deviations in energy (top) and space angle (bottom) between T5+-events reconstructedwith all stations and reconstructed with only the signals of one third ofthe stations. T5+-events are surrounded by two crowns of working stations. Theenergy threshold changes from the left to the right: E > 25EeV, E > 35EeV,E > 45EeV and E > 55EeV. The filled histogramms are used to display subsetswith five or more stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

94 LIST OF FIGURES5.1 Measured zenith angle distribution up to 60 ◦ for events with E > 3EeV and theusual quality cuts. The solid line is the sin" cos"-function. . . . . . . . . . . . . 505.2 Measured azimuth angle distribution for events with E > 3EeV and " < 60 ◦ . . . 515.3 Measured azimuth angle distribution for all events with " < 60 ◦ (left) and theevents with 37.76 ◦ < " < 60 ◦ (right). . . . . . . . . . . . . . . . . . . . . . . . 515.4 Schematic view of two showers with the same energy and the same core position.The one with ) = 0 ◦ (solid line) would be detected, as three stations are enclosedby the ellipses, the other one, with ) = 90 ◦ , would not be detected. . . . . . . . . 525.5 Left: The six possible isosceles triangles for 3-fold events and the expected maximain the azimuth angle distribution. The only difference between the triangleswith solid lines and the ones with dashed lines, are that they are rotated by 60 ◦ .Right: The dominating configurations of stations for 4-fold events. . . . . . . . . 535.6 The twelve possible configurations for the non-compact adjustment of stations for4-fold events. The three stations of the solid triangle and one at the end of onedashed line are triggered. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.7 Measured azimuth angle distributions for strict-T5 events with (left) " < 60 ◦ andstrict-T5 events with 37.76 ◦ < " < 60 ◦ (right); top: 3-fold events, middle: 4-foldevents, bottom: 5-fold events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.8 Fraction of the total signal as a function of ) detected by the three PMTs. Theerrors are so small, that they are not visible. The plot is generated by taking thesiganls of all PMTs, used for the reconstruction of the T4 events, which have beendetected in 2007. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.9 Azimuth distributions for the 3-fold (top), 4-fold events (middle) and all events(bottom), which fulfill the usual cuts. For the fits Equation 5.3 is used. . . . . . . 575.10 Model for the 2!/6-effect: The left picture shows the stations (dots) and the area(little squares), where the showers are simulated with a core positions on a tenmeter grid. In the right picture, two ellipses are shown, one would trigger thesurface detector, one would not, as only two stations, located at the apexes of thetriangle, are inside the ellipse. . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.11 Number of triggered showers per bin for ellipses with the major axis parallel tothe x-axis (left) and parallel to the y-axis (right) for showers with S m = 1000 and" = 40 ◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.12 The intersection of a vertical cylinder, an inclined cylinder, and an inclined (inverted)cone with the ground plane [46]. . . . . . . . . . . . . . . . . . . . . . . 615.13 Model with binary trigger probability (left) and with a continuously developingtrigger probability (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.14 The number of triggered showers as a function of S(1000) (left) and the " distributionsof the two ellipses and the measured events. The plot at the top is for allevents, the one in the middle for 3-fold events and the one at the bottom for 4-foldevents. The major axis of ellipse 1 is parallel to the east-west axis and the majoraxis of ellipse 2 is perpendicular. . . . . . . . . . . . . . . . . . . . . . . . . . . 635.15 Top: Ratios between all events measured in N 1i ∈ [) − 30 ◦ ,) + 30 ◦ ] and N 2i ∈[) + 180 ◦ − 30 ◦ ,) + 180 ◦ + 30 ◦ ]. Bottom: Comparison of the ratios of events withdifferent numbers of triggered stations. . . . . . . . . . . . . . . . . . . . . . . . 665.16 Rayleigh amplitude, phase and probability for T5 events with " < 60 ◦ above agiven energy (left) and below a given energy (right). . . . . . . . . . . . . . . . . 67

LIST OF FIGURES 955.17 Rayleigh amplitude, phase and probability for T5 events with " < 60 ◦ in logarithmicenergy bins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.18 Relative deviations of the number of events detected in 60 ◦ bins, from a flat distribution.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.19 Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): Relative deviations from aflat azimuth distribution (top left), errors of these values (top right), significances(bottom left) and fluctuated map of deviations (bottom right). . . . . . . . . . . . 715.20 Relative differences in the number of events detected in a 60 ◦ bin around ) =−120 ◦ in comparison to a flat distribution. The left plot shows the zenith angledependence, the right plot the energy dependence. . . . . . . . . . . . . . . . . . 725.21 Same as Figure 5.20 with 60 ◦ bins around ) = 5 ◦ , ) = 55 ◦ and ) = 105 ◦ . . . . . 735.22 Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): The four plots show therelative differences from an isotropic distribution. The plots are arranged accordingto the positions of the parts in the array they represent (north-west, north-east,south-west and south-east). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.23 Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): The four plots show the significancesof the deviations shown in Figure 5.23. The plots are arranged accordingto the positions of the parts in the array they represent (north-west, north-east,south-west and south-east). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.24 Relative deviations from a flat azimuth distribution in dependence on the time ofthe day, when the events were recorded. . . . . . . . . . . . . . . . . . . . . . . 775.25 Relative deviations from a flat azimuth distribution in dependence on the month,when the events were recorded. . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.26 Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 85 ◦ ): Relative deviations from aflat distribution (top) and significance plot (bottom) for T5 events. . . . . . . . . 795.27 Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): Relative deviations froma flat distribution (top) and significance plot (bottom) for events, which fulfill theT5 requirement and those which do not, for zenith angles up to 60 ◦ . . . . . . . . 805.28 The azimuth angle distributions of all events reconstructed with the CDAS algorithm(left) and the Offline algorithm (right). . . . . . . . . . . . . . . . . . . . . 825.29 Status of the surface detector array in November 2005: 1031 tanks are deployed(shaded region), 1012 filled with water and 898 with electronics [66]. . . . . . . 825.30 Temperatures of the electronics and the PMTs for one day (left) and differencesbetween pairs of PMTs (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.31 Azimuth angle distributions, obtained by reconstructing the events with the signalsof only one of the three PMTs per station. The plot in the upper left corner is forPMT 2, the upper right for PMT 1 and the plot at the bottom right is for PMT 3.The drawing illustrates the positions of the PMTs in the station. . . . . . . . . . 845.32 Area of a surface detector station masked by the solar panel as a function of " and) and normalized to one for the maximal masking. . . . . . . . . . . . . . . . . 86

LIST OF TABLESList of Tables2.1 Expected number of events per year with the completely installed AMIGA [22]. . 114.1 Properties of the energy and space angle distributions shown in Figure 4.2. . . . 314.2 Deviation in energy between the original and the modified reconstruction. Allevents for which the modification leads to a deviation in energy larger than 10%are listed. The number after the hyphen denotes the crown (0 = central station). . 314.3 Angular deviation between the original and the modified reconstruction. Allevents, for which the modification leads to a deviation larger than 0.6 ◦ , are listed. 314.4 RMS values of the energy and space angle distributions shown in figure 4.5. . . . 334.5 Values of the Gaussian fits to the energy histograms. . . . . . . . . . . . . . . . 354.6 Values of the fits to the distributions for the early and late part of the shower. . . . 354.7 Optimum ground parameters determined by reconstructing events without individualstations of the first crown. . . . . . . . . . . . . . . . . . . . . . . . . . . 405.1 Fractions of events, which trigger three, four or more stations. . . . . . . . . . . 545.2 Parameters of the fits with Function 5.3 shown in Figure 5.9. . . . . . . . . . . . 555.3 Relative differences p 6 , p 3 and p 1 between the maxima and the minima of theoscillations with periods of 2!/6, 2!/3 and 2!, in the )-distribution. . . . . . . . 565.4 Oscillations with amplitude D/2 in the azimuth angle distribution with a period of2!/6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.5 Azimuth angles ) min and amplitudes p of the minima, obtained by the sine fits tothe azimuth distributions (see Section 5.2.3). . . . . . . . . . . . . . . . . . . . . 645.6 Rayleigh amplitudes, phases and probabilities of T5 events, subdivided in six independentenergy bins. The phase corresponds to the location of the minimum ofa sine wave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.7 Borders of the " and energy bins. . . . . . . . . . . . . . . . . . . . . . . . . . . 72

List of AcronymsAcronymAGNAMIGACDASCICCLFCREASFADCFDGPSHEATLIDARLDFLTPMCPAOPMTRMSSDSTTOTUHECRVEMExplanationActive Galactic NucleusAuger Muons and Infill for the Ground ArrayCentral Data Acquisition SystemConstant Intensity CutCentral Laser FacilityCosmic RayExtensive Air ShowerFlash Analog-to-Digital ConverterFluorescence DetectorGlobal Positioning SystemHigh Elevation Auger TelescopesLIght Detection And RangingsLateral Distribution FunctionLateral Trigger ProbabilityMonte CarloPierre Auger ObservatoryPhoto Multiplier TubeRoot Mean SquareSurface DetectorSingle Threshold (first level trigger)Time Over Threshold (first level trigger)Ultra High Energy Cosmic RayVertical Equivalent Muon

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AcknowledgmentMy gratitude goes out to all those, who made this thesis possible.Firstly I would like to thank Isabell Steinseifer and Daniel Eiteneuer. You two kept me fromquitting my studies in the first semesters.Then I would like to thank Prof. Dr. Peter Buchholz for the opportunity to take part in the researchfor the Pierre Auger observatory and the support to spend half a year abroad.My thanks goes to all my friends in Bariloche, Argentina. It was a wonderful experience to staywith you. Thank you for your continuous support and especially for your warm hospitality. Iwould like to thank namely Hernán Asorey and Dr. Xavier Bertou. My special thanks goes toProf. Dr. Ingomar Allekotte for agreeing to revise this thesis and for being more a friend, than asupervisor.In addition, my gratitude goes to the members of the Siegen group, especially to ThomasBäcker and Dr. Dirk Kickelbick. I am indebted to you, for proofreading my thesis, sharing yourknowledge with me and for the many funny conversations, i.e. during lunch.Der größte Dank von allen, geht jedoch ohne Zweifel an meine gesamte Familie. Ich dankevor allem meiner Freundin Isabell: für deine Liebe, deine Unterstützung und dafür, dass du immerda warst. Genauso möchte ich meinen Eltern und meiner Schwester Nadine danken. Ihr habt michmeinen ganzen Lebensweg begleitet und mich immer unterstützt. Danke!

ErklärungHiermit erkläre ich, dass ich die vorliegende Masterarbeit selbstständig verfasst und keineanderen als die angegebenen Quellen und Hilfsmittel benutzt, sowie Zitate und ErgebnisseAnderer kenntlich gemacht habe.(Ort) (Datum) Stefan Grebe