Physics 879: Gravitational Wave Physics Week 1: Overview

Transcription

1 Physics 879: Gravitational Wave Physics Week 1: Overview Alessandra Buonanno Department of Physics, University of Maryland Ph 879: Gravitational Wave Physics

2 Nature of gravitational waves Matter tells spacetime how to curve, and spacetime tells matter how to move by John Achibald Wheeler The rapid motion of mass-energy generates ripples in spacetime curvature which radiate outward as gravitational waves Once generated, GWs propagate at the speed of light GWs push free-falling test-particles apart and together Newtonian tidal acceleration tensor A ξ0 B t = 0 t = 0 ξ t = t 1 1 t = t 1 Local inertial frames do not mesh in presence of spacetime curvature (or GWs) t = t ξ 2 2 t = t2 z y x Ph 879: Gravitational Wave Physics 1

3 A bit of history In 1916 Einstein realized the propagation effects at finite velocity in the gravitational equations and predicted the existence of wave-like solutions of the linearized vacuum field equations Works by Eddington, Einstein et al. in the 20-30s trying to understand whether the radiative degrees of freedom were physical Complications and subtleties: Non-linearities and invariance under coordinate transformations The work by Bondi in the mid 50s, applied to self-gravitating systems like binaries made of neutron stars and/or black holes, proved that gravitational waves carry off energy and angular-momentum Ph 879: Gravitational Wave Physics 2

4 Properties of gravitational waves Stretch and squeeze are transverse to direction of propagation L = h(t) L equal and opposite along orthogonal axis (trace-free) Gravitons are spin-2 particles Two polarizations: h + and h GW theory: polarizations rotated by 45 o EM theory: polarizations rotated by 90 o h + and h are double time integral of Riemann tensor ḧ ij R i0j0 2 ij Φ Φ non-static tidal potential Ph 879: Gravitational Wave Physics 3

5 Interaction between GW and ring of free-falling particles GW propagating along z-axis Case: h + 0 h = 0 λ GW Case: h 0 h + = 0 λ GW Ph 879: Gravitational Wave Physics 4

6 Force pattern for h and h + z z y y x x Force pattern of GWs are invariant under 180 o degree, by contrast force patterns of EM waves are invariant under 360 o degree Ph 879: Gravitational Wave Physics 5

7 How to measure gravitational waves Use light beams to measure the stretching and squeezing L = L h cm being L = 4km and h Ph 879: Gravitational Wave Physics 6

8 Multipolar decomposition of waves Multipole expansion in terms of mass moments (I L ) and mass-current moments (J L ) of the source h can toscillate {}}{ G I 0 c 2 r + G J 1 c 4 r + } {{ } can toscillate + can toscillate {}}{ G I 1 c 3 r G J2 } c 5 {{ r} + current quadrupole mass quadrupole {}}{ G Ï 2 c 4 r + + Typical strength: h G M c 4 L2 1 P 2 r G(E kin/c 2 ) c 2 r If E kin /c 2 1M, depending on r h Ph 879: Gravitational Wave Physics 7

9 Comparison between GW and EM luminosity L GW = G 5c 5 (... I 2) 2 I 2 ǫm R 2 R typical source s dimension, M source s mass, ǫ deviation from sphericity Ï ω 3 ǫ M R 2 with ω 1/P L GW G c 5 ǫ 2 ω 6 M 2 R 4 L GW ( ) c5 G ǫ2 G M ω 6 ( c 3 R c 2 G M ) 4 c 5 G = erg/sec (huge!) For a steel rod of M = 490 tons, R = 20 m and ω 28 rad/sec: GMω/c , Rc 2 /GM L GW erg/sec L EM sun! As Weber noticed in 1972, if we introduce R S = 2GM/c 2 and ω = (v/c) (c/r) L GW = ( ) ( ) c5 G ǫ2 v 6 RS c R }{{} v c, R R S L GW ǫ 2 5 c G 1026 L EM sun! Ph 879: Gravitational Wave Physics 8

10 GWs on the Earth: comparison with other kind of radiation Supernova at 20 kpc: From GWs: 400 erg cm 2 sec ( ) 2 fgw ( h ) 2 1kHz 10 during few msecs 21 From neutrino: 10 5 erg cm 2 sec during 10 secs From optical radiation: 10 4 erg cm 2 sec during one week Ph 879: Gravitational Wave Physics 9

11 Electromagnetic astronomy versus gravitational-wave astronomy EM astronomy GW astronomy accelerating charges; time changing dipole accelerating masses; time changing quadr. incoherent superposition of emissions from electrons, atoms and molecules direct information about thermodynamic state wavelength small compared to source absorbed, scattered, dispersed by matter frequency range: 10 MHz and up coherent superposition of radiation from bulk dynamics of dense source direct information of system s dynamics wavelength large compared to source very small interaction with matter frequency range: 10 khz and down Ph 879: Gravitational Wave Physics 10

12 GW frequency spectrum extends over many decades h LISA Pulsar timing CMB bars/ligo/virgo/ Hz Ph 879: Gravitational Wave Physics 11

13 Indirect observation of gravitational waves Neutron Binary System: PSR Timing Pulsars Hulse & Taylor discovery (1974) Separated by 10 6 Km, m 1 = 1.4M, m 2 = 1.36M, eccentricity = msec 8 hours Prediction from GR: rate of change of orbital period Emission of gravitational waves: due to loss of orbital energy orbital decay in very good agreement with GR Ph 879: Gravitational Wave Physics 12

14 Direct observation with resonant-mass detectors Pioneering work by Joe Weber at Maryland Resonant-transducer concept discovered by Ho-Jung Paik at Maryland; further developments by Jean-Paul Richard at Maryland Ph 879: Gravitational Wave Physics 13

15 Resonant-mass detectors in the world Resonant bar detectors (GW frequency 1 khz) Nautilus (Rome) Explorer (CERN) Allegro (Louisiana) Niobe (Perth) Auriga (Padova) Ph 879: Gravitational Wave Physics 14

16 International network of GW interferometers(frequency band Hz) LIGO at Livingston (Lousiana) LIGO at Hanford (Washington State) Ph 879: Gravitational Wave Physics 15

17 VIRGO (France-Italy) GEO 600 (UK-Germany) TAMA 300 (Japan) Ph 879: Gravitational Wave Physics 16

18 Sensitivity of LIGO during current run (S5) Sh f h h L/L f f S h 1/2 (Hz -1/2 ) Hanford 4km Hanford 2km Livingston 4km LIGO design (4km) f (Hz) Ph 879: Gravitational Wave Physics 17

19 Sensitivity of VIRGO Ph 879: Gravitational Wave Physics 18

20 A few LIGO/VIRGO/... specifications and technical challenges Monitor test masses ( 11 kg) with precision of cm with laser s wavelength of 10 4 cm Remove/subtract all non-gravitational forces such as thermal noise, seismic noise, suspension noise, etc. Beam tube vacuum level 10 9 torr Ph 879: Gravitational Wave Physics 19

21 Typical noises in ground-based detectors INITIAL INTERFEROMETER SENSITIVITY INITIAL LIGO SUSPENSION THERMAL SEISMIC GRAVITY GRADIENT NOISE RADIATION PRESSURE /2 h(f) [ Hz ] SHOT RESIDUAL GAS, 10-6 TORR H 2 TEST MASS INTERNAL STRAY LIGHT FACILITY RESIDUAL GAS, 10 Torr H Frequency (Hz) Ph 879: Gravitational Wave Physics 20

22 LIGO Scientific Collaboration LSC organizes scientific goals in data analysis and guides the research & development of future upgrades of LIGO 400 scientists and 25 institutions worldwide MIT, Univ. of Florida, Univ. of Louisiana, Univ. of Milwakee,... Stanford, Caltech, Cornell, Penn State, Univ. of Maryland,... at Maryland: myself and (postdoc) Jeremy Schnittman Spokesman: Peter y Saulson (Univ. of Syracuse) Ph 879: Gravitational Wave Physics 21

23 LISA: Laser Interferometer Space Antenna (frequency band: Hz) LISA science goals complementary to ground-based interferometer ones ESA/NASA mission in 2015? Ph 879: Gravitational Wave Physics 22

24 A few LISA specifications and technical challenges Distance between spacecraft 5 millions of km Monitor test masses inside spacecrafts with a precision of 10 9 cm (h ) Nd:YAG laser with wavelength 10 4 cm and power 1 Watt Drag-free system to guarantee that only gravitational forces outside the spacecraft act on the proof masses Draf-free performances m/sec 2 [LISA Pathfinder in 2009] Ph 879: Gravitational Wave Physics 23

25 Gravitational-wave sources Ph 879: Gravitational Wave Physics 24

26 Gravitational waves from compact binaries Mass-quadrupole approximation: h ij G rc 4 Ïij I ij = µ (X i X j R 2 δ ij ) h M5/3 ω 2/3 r cos 2Φ for quasi-circular orbits: ω 2 Φ 2 = GM R 3 h Chirp: The signal continuously changes chirp its frequency and the power emitted at any frequency is very small! time h M5/3 f 2/3 r for f 100 Hz, M = 20M r at 20 Mpc h Ph 879: Gravitational Wave Physics 25

27 Waveforms including spin effects Maximal spins M = 10M + 10M S 1 L Newt S h 0.00 h time time Ph 879: Gravitational Wave Physics 26

28 Inspiral signals are chirps GW signal: chirp [duration seconds to years] (f GW 10 4 Hz 1kHz) NS/NS, NS/BH and BH/BH MACHO binaries (m < 1M ) [MACHOs in galaxy halos < 3 5%] h GW GW frequency at end-of-inspiral (ISCO): f GW 4400 M M Hz inspiral waveform coalescence waveform "ringdown" time LIGO/VIRGO/GEO/TAMA: M = 1 50M ISCO Plunge LISA: M = M adiabatic inspiral Ph 879: Gravitational Wave Physics 27

29 Gravitational waves from stellar collapse GW signal: bursts [ few mseconds] or (quasi) periodic (f GW 1 khz 10kHz) Supernovae: Non-axisymmetric core collapse Material in the stellar core may form a rapidly rotating bar-like structure Collapse material may fragment into clumps which orbit as the collapse proceeds Pulsation modes of new-born NS; ring-down of new-born BH Dynamics of star very complicated GW amplitude and frequency estimated using mass- and current-quadrupole moments Numerical simulations Correlations with neutrino flux and/or EM counterparts Event rates in our galaxy and its companions < 30 yrs Ph 879: Gravitational Wave Physics 28

30 Gravitational-wave strain from non-axisymmetric collapse h GW η eff ( 1 msec τ τ duration of emission ) 1/2 ( efficiency η eff = E M c ) 1/2 ( ) ( ) M 10 kpc 1 khz M r f GW Ph 879: Gravitational Wave Physics 29

31 Gravitational waves from spinning neutron stars: pulsars GW signal: (quasi) periodic (f GW 10 Hz 1 khz) Pulsars: non-zero ellipticity (or oblateness) h GW ( ) ( ) ( 26 ǫ I kpc g cm 2 r ) ( ) 2 fgw 1 khz ǫ = I 11 I 22 I 33 ellipticity The crust contributes only 10% of total moment of inertia ǫ C is low Magnetic fields could induce stresses and generate ǫ M 0 Expected ellipticity rather low 10 7, unless exotic EOS are used search for known spinning neutron stars: Vela, Crab,... all sky search Ph 879: Gravitational Wave Physics 30

32 (screensaver) Partecipate in LIGO pulsar data analysis by signing up! (B Allen, Univ. of Winsconsin, Milwakee) Ph 879: Gravitational Wave Physics 31

33 Summary of sources with first-generation ground-based detectors S h 1/2 (Hz -1/2 ) VIRGO NS/NS at 20 Mpc Crab (upper limit) GEO TAMA bars LIGO known pulsar at 10kpc ε=10-5 ε= f (Hz) Upper bound for NS-NS (BH-BH) coalescence with LIGO: 1/3yr (1/yr) Ph 879: Gravitational Wave Physics 32

34 Advanced LIGO/VIRGO Higher laser power lower photon-fluctuation noise Heavier test masses 40 Kg lower radiation-pressure noise Better optics to reduce thermal noise Better suspensions and seismic isolation systems Signal-recycling cavity: reshaping noise curves Ph 879: Gravitational Wave Physics 33

35 Summary of sources for second-generation ground-based detectors Sensitivity improved by a factor 10 event rates by Vela (upper limit) Crab (upper limit) S h 1/2 (Hz -1/2 ) BH/BH at 100Mpc NS/NS at 300Mpc Advanced LIGO (narrowband) Advanced LIGO (wideband) Low-mass X-ray binaries pulsar ε =10-6 at 10kpc f (Hz) Advanced Bars SCOX-1 Upper bound for NS-NS binary with Advanced LIGO: a few/month Ph 879: Gravitational Wave Physics 34

36 LISA s orbital motion Wide variety of different sources scattered over all directions on the sky To distinguish different sources we use the different time evolution of their waveforms To determine each s source orientation we use the manner in which its waves amplitude and frequency are modulated by LISA s orbital motion Ph 879: Gravitational Wave Physics 35

37 Typical binary masses and radial separations LISA can probe f GW = 1 2π ω ( GW = 1 GM ) 1/2 π R 3 ( ) 1/2 ( 3/ M R 1M 1 10 m) Hz 8 R radial separation M binary total mass e.g., at f GW = 1 mhz M = 2.8M and R 10 5 NS s radius M = M and R 7 BH s radius Ph 879: Gravitational Wave Physics 36

38 Known, short-period binary stars in our galaxy There are currently a dozen galactic binaries with GW frequencies above 0.1 mhz Monochromatic gravity-wave signals These sources will provide an important test LISA is functioning as expected (verification binaries) Test of general relativistic theory of GW emission in weak-gravity limit Compare with predictions from optically measured orbital motion Ph 879: Gravitational Wave Physics 37

39 10-17 Three known galactic binaries (f S h ) 1/ * LISA noise WD * RXJ * 4U f (Hz) WD : WD-WD binary with masses 0.37M and 0.32M, at 100 pc from Earth and time to merger years RXJ (Am CVn binary): WD (0.6M ) accreting from low-mass, helium-star companion (0.07M ) at 100 pc from Earth 4U : star (< 0.1M ) orbiting a NS at 100 pc from Earth Ph 879: Gravitational Wave Physics 38

40 Astrophysical stochastic background There are an estimated galactic WD-WD binaries with GW frequencies f > 0.1 mhz At frequencies below 2mHz, there are too many binaries per resolvable frequency bin f = 1/T obs 10 8 Hz, to be fit and removed from LISA data confusion noise Science to be extracted: The WD-WD galactic background is anisotropic. The first two moments of the WD-WD distribution could be measured with few percent of accuracy Ph 879: Gravitational Wave Physics 39

41 Massive BH binaries Massive BH binaries form following the mergers of galaxies and pregalactic structures MS (cluster of galaxies) at z = 0.83: about 20% are merging! (a) 16 most luminous galaxies in the cluster (b) 8 fainter galaxies Masses and merger rates as function of redshift Ph 879: Gravitational Wave Physics 40

42 Image of NGC6240 taken by Chandra showing a butterfly shaped galaxy product of two smaller galaxies (two active giant BHs) Ph 879: Gravitational Wave Physics 41

43 Relativity: Massive BH binaries From inspiraling post-newtonian waveforms precision tests of GR From merger waveforms (num. relativity) tests of non-linear gravity Tests of cosmic censorship (is the final object a black hole?) and second law of BH mechanics (increase of horizon area) Astrophysics: Cosmic history of MBH s and IMBHs formation from very high redshift to the present time Very high S/N (very large z); high accuracy in determining binary parameters, but event rates uncertain yr 1 Ph 879: Gravitational Wave Physics 42

44 Massive BH binaries Mo / 106 Mo BH Inspiral at 3Gpc f (Hz) Ph 879: Gravitational Wave Physics 43 LISA noise (f S h ) 1/2 105 Mo / 105 Mo BH Inspiral at 3Gpc 104 Mo / 104 Mo BH Inspiral at 3Gpc

45 Extreme mass-ratio inspiraling binaries Small body spiraling into central body of M out to Gpc distance Relativity: Relativistic orbits (test of GR) Map of massive body s external spacetime geometry. Extract multiple moments. Test the BH no hair theorem (is it a black hole?) Astrophysics: Probe astrophysics of dense clusters around MBH s in galactic nuclei Existence and population of IMBH s in galactic nuclei Infer massive body s spin and mass with accuracy ; sky position determined within 1 o ; distance-to-source s accuracy of several 10% Ph 879: Gravitational Wave Physics 44

46 Ph 879: Gravitational Wave Physics 45

47 no spin Alessandra Buonanno January 26 & 31, 2006 Extreme mass-ratio binaries (f S h ) 1/ Mo BH into 106 Mo BH at 1Gpc maximal spin LISA noise f (Hz) Ph 879: Gravitational Wave Physics 46

48 Primordial stochastic backgrounds from inflation -4-6 Log 10 [ GW ] Ω LISA WD/WD stochastic background T/S= Log 10 [f (Hz)] T/S= Ph 879: Gravitational Wave Physics 47