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102 Resonant detectors for gravitational waves and their bandwidththe sensitivity to bursts and other types of GW in a somewhat different manner,which improved our understanding of the role played by the electromechanicaltransducer and its associated electronics. The noise spectrum of the apparatus isexpressed by equation (8.11), which also directly gives the sensitivity for the GWbackground.We notice that the optimum sensitivity (at the resonance) depends essentiallyon the ratio T e /MQ and is independent of the transducer. In practice, thetransducer and electronics determine only the bandwidth of the apparatus,expressed by equation (8.14).For the measurement of the GW stochastic background, that should notchange drastically in a frequency band of a few hertz, it might therefore besufficient to make use of a very simple transducer and even small bandwidthelectronics. This makes the resonant detectors, in particular, well suited formeasuring the GW stochastic background.The use of a sophisticated transducer, with larger bandwidth, improves thesensitivity to GW bursts. As far as the search for monochromatic waves a largerbandwidth is better, in the sense that it allows a larger frequency region in whichto search.References[1] Astone P et al 1993 Phys. Rev. D 47 362[2] Mauceli E et al 1996 Phys. Rev. D 54 1264[3] Blair D G et al 1995 Phys. Rev. Lett. 74 1908[4] Astone P et al 1997 Astropart. Phys. 7 231–43[5] Cerdonio M et al 1995 Gravitational wave experiments Proc. First Edoardo AmaldiConf. (Frascati, 1994) ed E Coccia, G Pizzella and F Ronga (Singapore: WorldScientific)[6] Pizzella G 1975 Riv. Nuovo Cimento 5 369[7] Pallottino G V and Pizzella G 1998 Data Analysis in Astronomy vol III, ed V Di Gesuet al (New York: Plenum) p 361[8] Papoulis A 1984 Signal Analysis (Singapore: McGraw-Hill) pp 325–6[9] Pizzella G 1979 Nuovo Cimento 2 C209[10] Pallottino G V and Pizzella G 1984 Nuovo Cimento 7 C155[11] Bendat J S and Piersol A G 1966 Measurement and Analysis of Random Data (NewYork: Wiley)[12] Brustein R, Gasperini M, Giovannini M and Veneziano G 1995 Phys. Lett. B 36145–51[13] Astone P, Buttiglione C, Frasca S, Pallottino G V and Pizzella G 1997 Nuovo Cimento20 9[14] Astone P, Pallottino G P and Pizzella G 1998 Gen. Rel. Grav. 30 105[15] Astone P et al 1999 Astropart. Phys. 10 83–92[16] Astone P, Pallottino G V and Pizzella G 1997 Class. Quantum Grav. 14 2019–30[17] Astone P et al 1999 Astron. Astrophys. 351 811–14
Chapter 9The Earth-based large interferometer Virgoand the Low Frequency FacilityAngela Di VirgilioINFN Sezione di Pisa, via Vecchia Livornese 1265,56010 S. Piero a Grado (Pisa), ItalyE-mail: angela.divirgilio@pi.infn.itThe principle of the Earth-based interferometer and the parameters of Virgo, theCNRS-INFN antenna under construction in Cascina near Pisa, are presented. TheSuper-Attenuator (SA), the suspension ad hoc designed for Virgo, and the LowFrequency Facility, the project devoted to study the SA with a sensitivity close tothe Virgo one, are shortly described.9.1 IntroductionThe detection of gravitational waves (GW), produced in astrophysical processes,is one of the most challenging fields of modern physics, aimed at findinggravitational-wave astronomy. Lectures about GW production and expectedsources can be found in this book, but let me very briefly remind you ofthe essentials. General relativity predicts that accelerated matter producesgravitational waves, ripples of spacetime travelling with the speed of light. GWcan be defined as a perturbation of the metric, h αβ , and the observational effect ofits passage through the Earth is a change among the relative distance of massivebodies. If A and B are the space-state locations of the two testmasses and if weset AB = (x α ), the vector (x α ) obeys the equation of geodesic deviation in weakfield:d 2 x αdt 2 = 1 ∂ 2 h TTαβ2 ∂t 2 x β (9.1)103
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GRAVITATIONAL WAVES
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c IOP Publishing Ltd 2001All righ
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viContents4 Astrophysics of gravita
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viiiContents11.3 Gravitational wave
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xContents16.5 Cosmological perturba
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PrefaceGravitational waves today re
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2 Gravitational waves, theory and e
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10 Gravitational waves, theory and
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SynopsisGravitational waves and the
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Chapter 2Elements of gravitational
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Using the TT gauge to understand gr
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Interaction of gravitational waves
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Analysis of beam detectors 21This d
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Exercises for chapter 2 232. Show t
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Gravitational-wave detectors 25indi
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Gravitational-wave observables 27th
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The physics of interferometers 29
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The physics of interferometers 31Dr
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The physics of interferometers 33Fi
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The physics of resonant mass detect
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The physics of resonant mass detect
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A detector in space 39LISA has been
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Gravitational and electromagnetic w
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Chapter 4Astrophysics of gravitatio
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Sources detectable from ground and
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Page 64 and 65: Variational principles and the ener
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Page 100 and 101: Solutions to exercises 87The gauge
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Page 113: Discussion and conclusions 101Figur
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Page 125 and 126: Conclusion 113Figure 9.7. The R and
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Page 145 and 146: Expected gravitational-wave results
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Introduction 153detect GWs with a s
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Testing theories of gravity 155•
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0Testing theories of gravity 157the
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Taking the scalar product we findGr
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Gravitational wave radiation in the
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The hollow sphere 169and introduced
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Scalar-tensor cross sections 171mon
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Scalar-tensor cross sections 173Tab
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Scalar-tensor cross sections 175Tab
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References 177Frossati G and Coccia
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Chapter 12Generalities on the stoch
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Introduction 183contribution to the
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Definitions 185The value of H 0 is
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Definitions 18712.2.2 The character
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Definitions 189or, dividing by the
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The overlap reduction function 191O
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The overlap reduction function 193T
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The overlap reduction function 195F
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Achievable sensitivities to the SGW
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Observational bounds 207Table 12.10
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equation gives immediately(ρgwρ
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Chapter 13Sources of SGWBHere we re
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Topological defects 213This correla
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Topological defects 215It can be sh
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Topological defects 217(i)A loop ra
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Topological defects 219• A peak n
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Topological defects 22113.1.2 Hybri
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Inflation 223Hubble radius and when
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Inflation 225as a first approximati
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Inflation 227the lower bound to the
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String cosmology 22913.3 String cos
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String cosmology 231HPre-big bangPo
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String cosmology 233Figure 13.6. h
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First-order phase transitions 23580
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Astrophysical sources 237which is t
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References 239of [71]). However, fo
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References 241[39] Liddle A R 2000
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PART 4THEORETICAL DEVELOPMENTSHerma
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246 Infinite-dimensional symmetries
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Chapter 15Gyroscopes and gravitatio
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270 Gyroscopes and gravitational wa
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Chapter 16Elementary introduction t
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282 Elementary introduction to pre-
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Chapter 17Post-Newtonian computatio
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340 Post-Newtonian computation of b
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PART 5NUMERICAL RELATIVITYEdward Se
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362 Numerical relativityspite of mo
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364 Numerical relativityterms, of m
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366 Numerical relativityHere we hav
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368 Numerical relativityinformation
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370 Numerical relativityThe Palma,
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372 Numerical relativityHyperbolic
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374 Numerical relativityEinstein di
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376 Numerical relativityare the abi
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378 Numerical relativityeach cell i
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380 Numerical relativityFigure 18.1
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382 Numerical relativity1D code [45
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384 Numerical relativityfunctions,
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386 Numerical relativityto a very a
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388 Numerical relativity18.5 Comput
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390 Numerical relativitynumerics an
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392 Numerical relativityinitial dis
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396 Numerical relativityof these re
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400 Numerical relativityof Einstein
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402 Numerical relativity18.9.5.2 Co
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404 Numerical relativity[23] Ashby
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406 Numerical relativity[101] Shapi
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408 Numerical relativity(Singapore:
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410 IndexEhlers Lagrangian, 254Eins
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412 Indexscalarspherical harmonics,
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