(ed.). Gravitational waves (IOP, 2001)(422s).

More documents

Recommendations

Info

112 The Earth-based large interferometer Virgoa Nd-YAG, of the order of 10 −1 –10 −2 Hz/ √ Hz at 10 Hz has been obtained, forexample by the Nice-Virgo team [8]. A copy of this circuit provides the frequencystabilization for the LFF. It is already operational and has obtained a closed loopbehaviour similar to the Virgo prestabilization circuit. The technique to reducethe influence of power fluctuation is to extract signals from the Fabry–Perot withthe well known Pound–Drever–Hall, where the injected light is phase modulatedat high frequency (usually around 10 MHz, where the laser is shot noise limited).The signal is extracted in reflection, the noise is due to the shot noise, and theSNR for the cavity detuning δν is:SNR = P in8J 0 (m)J 1 (m)F(1 − A loss Fπ) 2L c δν2 √ . (9.9)ηP DC hν 0where P in represents the incident power on the cavity, A loss the total loss in thecavity during one round trip, P DC is the DC term of the power reflected fromthe cavity, √ 2ηP DC hν is the shot noise expression with η the quantum efficiencyof the photodiode, h is the Planck constant, ν 0 is the laser frequency, L is thecavity length, F is the finesse, c is the speed of light and J 0 and J 1 are Besselfunctions, functions of the modulation depth m. The LFF cavity parameters are:Finesse 3000, P 0 = 30 mW, cavity length L = 1 cm. With these parameters,the sensitivity at 10 Hz is limited by the frequency fluctuation, and a powerspectrum density of 10 −1 Hz/ √ Hz is necessary in order to reach the displacementsensitivity of 10 −18 m/ √ Hz at 10 Hz. A prototype of the SA, called R andD SA, has been assembled in Pisa, and has tested the assembly procedure anddeveloped the control loop. LFF will suspend to the R and D SA two mirrors,in a way to create a very high finesse Fabry–Perot; of whose element, one is thestandard Virgo mirror, with a mass above 20 kg, while the other [18], usuallycalled (AX), will be different. In the early phase of the experiment the auxiliarymirror will be a standard small mirror; the auxiliary mirror will be loaded withan extra mass, in order to reduce the displacement noise due to low-frequencyradiation pressure. The Fabry–Perot cavity will act as a displacement transducerand allow the measurement of the combined thermal noise of the two mirrors, andrelated suspension. Figure 9.7 shows the experimental apparatus: the R and D SAholding the two mirrors of the cavity and the table with the optical circuit, whichwill inject light into the cavity.9.4 ConclusionSeveral gravitational-wave interferometers will be operational in a few years,and a lot of effort is being concentrated in building and making them work.Expectations are great around such experiments, since they can give essentialinformation on general relativity, fundamental physics and astrophysics. TheVirgo antenna will be operational in 2–3 years from now. A large study is goingon around the SA suspension. A special prototype called R and D SA is under
Conclusion 113Figure 9.7. The R and D SA and the injection table of the LFF, inside vacuum tanks; theenlarged picture shows the two mirrors forming a Fabry–Perot cavity.
Page 1:
GRAVITATIONAL WAVES
Page 4 and 5:
c IOP Publishing Ltd 2001All righ
Page 6 and 7:
viContents4 Astrophysics of gravita
Page 8 and 9:
viiiContents11.3 Gravitational wave
Page 10 and 11:
xContents16.5 Cosmological perturba
Page 13 and 14:
PrefaceGravitational waves today re
Page 15 and 16:
2 Gravitational waves, theory and e
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
10 Gravitational waves, theory and
Page 26 and 27:
SynopsisGravitational waves and the
Page 28 and 29:
Chapter 2Elements of gravitational
Page 30 and 31:
Using the TT gauge to understand gr
Page 32 and 33:
Interaction of gravitational waves
Page 34 and 35:
Analysis of beam detectors 21This d
Page 36 and 37:
Exercises for chapter 2 232. Show t
Page 38 and 39:
Gravitational-wave detectors 25indi
Page 40 and 41:
Gravitational-wave observables 27th
Page 42 and 43:
The physics of interferometers 29
Page 44 and 45:
The physics of interferometers 31Dr
Page 46 and 47:
The physics of interferometers 33Fi
Page 48 and 49:
The physics of resonant mass detect
Page 50 and 51:
The physics of resonant mass detect
Page 52 and 53:
A detector in space 39LISA has been
Page 54 and 55:
Gravitational and electromagnetic w
Page 56 and 57:
Chapter 4Astrophysics of gravitatio
Page 58 and 59:
Sources detectable from ground and
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Variational principles and the ener
Page 66 and 67:
Variational principles and the ener
Page 68 and 69:
Practical applications of the Isaac
Page 70 and 71:
Exercises for chapter 5 57(f)This s
Page 72 and 73:
Expansion for the far field of a sl
Page 74 and 75: Application of the TT gauge to the
Page 82 and 83: 6.4.1 Mass-quadrupole radiationEner
Page 84 and 85: Chapter 7Source calculationsNow tha
Page 86 and 87: The r-modes 73As we mentioned in ch
Page 88 and 89: The r-modes 75instability. In an id
Page 90 and 91: The r-modes 77Table 7.1. Gravitatio
Page 92 and 93: The r-modes 79evolution turns out t
Page 94 and 95: ReferencesWe have divided the refer
Page 96 and 97: References 83[19] van der Klis M 19
Page 98 and 99: Solutions to exercises 85For this p
Page 100 and 101: Solutions to exercises 87The gauge
Page 103 and 104: Chapter 8Resonant detectors for gra
Page 105 and 106: Sensitivity and bandwidth of resona
Page 107 and 108: 8.2 Sensitivity for various GW sign
Page 109 and 110: Sensitivity for various GW signals
Page 111 and 112: Recent results obtained with the re
Page 113 and 114: Discussion and conclusions 101Figur
Page 115 and 116: Chapter 9The Earth-based large inte
Page 117 and 118: Introduction 105Figure 9.1. The sim
Page 119 and 120: h(sqrt(1/Hz))10 −610 −810 −10
Page 121 and 122: 18.5 cmThe SA suspension and requir
Page 123: A few words about the Low Frequency
Page 127 and 128: Chapter 10LISA: A proposed joint ES
Page 129 and 130: Description of the LISA mission 117
Page 145 and 146: Expected gravitational-wave results
Page 161 and 162: References 149[8] Folkner W M 1998
Page 163 and 164: References 151[68] Miralda-Escuda J
Page 165 and 166: Introduction 153detect GWs with a s
Page 167 and 168: Testing theories of gravity 155•
Page 169 and 170: 0Testing theories of gravity 157the
Page 171 and 172: Taking the scalar product we findGr
Page 173 and 174: Gravitational wave radiation in the
Page 175 and 176:
Gravitational wave radiation in the
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
The hollow sphere 169and introduced
Page 183 and 184:
Scalar-tensor cross sections 171mon
Page 185 and 186:
Scalar-tensor cross sections 173Tab
Page 187 and 188:
Scalar-tensor cross sections 175Tab
Page 189 and 190:
References 177Frossati G and Coccia
Page 192 and 193:
Chapter 12Generalities on the stoch
Page 194 and 195:
Introduction 183contribution to the
Page 196 and 197:
Definitions 185The value of H 0 is
Page 198 and 199:
Definitions 18712.2.2 The character
Page 200 and 201:
Definitions 189or, dividing by the
Page 202 and 203:
The overlap reduction function 191O
Page 204 and 205:
The overlap reduction function 193T
Page 206 and 207:
The overlap reduction function 195F
Page 208 and 209:
Achievable sensitivities to the SGW
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Observational bounds 207Table 12.10
Page 220 and 221:
equation gives immediately(ρgwρ
Page 222 and 223:
Chapter 13Sources of SGWBHere we re
Page 224 and 225:
Topological defects 213This correla
Page 226 and 227:
Topological defects 215It can be sh
Page 228 and 229:
Topological defects 217(i)A loop ra
Page 230 and 231:
Topological defects 219• A peak n
Page 232 and 233:
Topological defects 22113.1.2 Hybri
Page 234 and 235:
Inflation 223Hubble radius and when
Page 236 and 237:
Inflation 225as a first approximati
Page 238 and 239:
Inflation 227the lower bound to the
Page 240 and 241:
String cosmology 22913.3 String cos
Page 242 and 243:
String cosmology 231HPre-big bangPo
Page 244 and 245:
String cosmology 233Figure 13.6. h
Page 246 and 247:
First-order phase transitions 23580
Page 248 and 249:
Astrophysical sources 237which is t
Page 250 and 251:
References 239of [71]). However, fo
Page 252 and 253:
References 241[39] Liddle A R 2000
Page 254:
PART 4THEORETICAL DEVELOPMENTSHerma
Page 257 and 258:
246 Infinite-dimensional symmetries
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Chapter 15Gyroscopes and gravitatio
Page 281 and 282:
270 Gyroscopes and gravitational wa
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
Chapter 16Elementary introduction t
Page 293 and 294:
282 Elementary introduction to pre-
Page 295 and 296:
Page 297 and 298:
Page 299 and 300:
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
Page 307 and 308:
Page 309 and 310:
Page 311 and 312:
Page 313 and 314:
Page 315 and 316:
Page 317 and 318:
Page 319 and 320:
Page 321 and 322:
Page 323 and 324:
Page 325 and 326:
Page 327 and 328:
Page 329 and 330:
Page 331 and 332:
Page 333 and 334:
Page 335 and 336:
Page 337 and 338:
Page 339 and 340:
Page 341 and 342:
Page 343 and 344:
Page 345 and 346:
Page 347 and 348:
Page 349 and 350:
Chapter 17Post-Newtonian computatio
Page 351 and 352:
340 Post-Newtonian computation of b
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
Page 367 and 368:
Page 369:
PART 5NUMERICAL RELATIVITYEdward Se
Page 372 and 373:
362 Numerical relativityspite of mo
Page 374 and 375:
364 Numerical relativityterms, of m
Page 376 and 377:
366 Numerical relativityHere we hav
Page 378 and 379:
368 Numerical relativityinformation
Page 380 and 381:
370 Numerical relativityThe Palma,
Page 382 and 383:
372 Numerical relativityHyperbolic
Page 384 and 385:
374 Numerical relativityEinstein di
Page 386 and 387:
376 Numerical relativityare the abi
Page 388 and 389:
378 Numerical relativityeach cell i
Page 390 and 391:
380 Numerical relativityFigure 18.1
Page 392 and 393:
382 Numerical relativity1D code [45
Page 394 and 395:
384 Numerical relativityfunctions,
Page 396 and 397:
386 Numerical relativityto a very a
Page 398 and 399:
388 Numerical relativity18.5 Comput
Page 400 and 401:
390 Numerical relativitynumerics an
Page 402 and 403:
392 Numerical relativityinitial dis
Page 404 and 405:
Page 406 and 407:
396 Numerical relativityof these re
Page 408 and 409:
Page 410 and 411:
400 Numerical relativityof Einstein
Page 412 and 413:
402 Numerical relativity18.9.5.2 Co
Page 414 and 415:
404 Numerical relativity[23] Ashby
Page 416 and 417:
406 Numerical relativity[101] Shapi
Page 418 and 419:
408 Numerical relativity(Singapore:
Page 420 and 421:
410 IndexEhlers Lagrangian, 254Eins
Page 422:
412 Indexscalarspherical harmonics,
show all

(ed.). Gravitational waves (IOP, 2001)(422s).

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?