Fundamental Physics, Astrophysics and Cosmology with ET B.S. Sathyaprakash (CU) and Bernard Schutz (CU, AEI) based on a Living Review article with a similar title (in preparation)
ET Science Summary Fundamental physics What are the different polarization states of gravitational waves? Are gravitons massless? Black hole spectroscopy and the no-hair theorem? Is general relativity the correct description of strong gravity? Cosmology Independent and accurate measurement of Hubble constant What is the nature of dark energy? How is matter organized on very large scales? What were the physical conditions in the early Universe? p2
ET Science Summary Astrophysics What is the origin of gamma ray bursts and what are the different populations? Are ULX sources IMBH? How and when did they form? How asymmetric are neutron stars and what is their equation-ofstate? What is the end state of gravitational collapse? p3
Fundamental physics
Counting the Polarization States Only two states in GR: h + and h x Plus polarization Cross polarization p5
Cliff Will Polarization States in a Scalar-Tensor Theory p6
Speed of Gravitational Waves Coincident observation of an electromagnetic event and the associated gravitational radiation can be used to constrain the speed of gravitational waves to a fantastic degree: If t is the time difference in the arrival times of GW and optical radiation and D is the distance to the source then the fractional difference in the speeds is Should be possible with coincident observation of gamma-ray bursts up to very high red-shifts p7
Dispersion of the waves and binary black hole Spectroscopy Massive gravitons suffer dispersion which will be imprint in the phasing of the waves Waveform currently known to 3.5 PN (i.e. to order v 7 /c 7 ) in phase and 2.5 in amplitude (up to seven harmonics of the orbital frequency) Should allow better tests of general relativity Harmonics PN corrections Blanchet et al (2002, 2004, 2005); Van Den Broeck and Sengupta (2006, 2007) p8
Black Hole Spectroscopy
Black Hole Quasi-Normal Modes p10
QNM Frequency and Damping Time (Echeverria, 1989) p11
Black Hole Spectroscopy Berti, Cardoso and Will p12
Quality Factor of BH QNMs Berti, Cardoso and Will p13
Testing the No-Hair Theorem By measuring a single (say l=2, m=2) quasi-normal mode s frequency and damping time one can determine the mass and spin of the black hole No-hair theorem: Frequencies and damping times of other modes also depend on the mass and spin of the BH If it is possible to measure the other modes then we would be basically testing the no-hair theorem p14
Strong-gravity GR Tests
Testing the tail effect Gravitational wave tails Testing the presence of tails Blanchet, Sathyaprakash Blanchet and Schaefer p16
Strong Field Tests of GR Arun et al p17
Fundamental questions on strong gravity and the nature of space-time From inspiral and ring down signals measure M and J before and after merger: test Hawking area theorem Is J/M 2 less than 1? Consistent with a BH or Naked singularity or Soliton/Boson stars? p18
Testing the merger dynamics p19
Adv LIGO Sensitivity to Inspirals p20
Strong field tests of gravity Jones and BSS p21
Cosmology
Binaries are Standard Sirens Luminosity L = (Asymm.) v 10 Luminosity is a strong function of velocity: A black hole binary source brightens up a million times during merger Amplitude h = (Asymm.) (M/R) (M/r) The amplitude gives strain caused in space as the wave propagates h = dl/l Frequency f = ρ Dynamical frequency in the system: e.g., in a binary twice the orb. freq. Binary chirp rate Many sources chirp during observation: chirp rate depends only on the chirp mass: M = (m 1 m 2 ) 3/5 (m 1 +m 2 ) -1/5 Chirping sources are standard sirens Schutz p23
Need coincident EM-GW observation for Cosmology Schutz Amplitude of gravitational waves depends on the combination of Chirp-mass/Effective-Distance Effective-Distance depends on the luminosity distance, source location and polarization Gravitational wave observations can independently measure the amplitude and the chirp-mass Therefore, binary inspirals are standard sirens: from the apparent luminosity (the strain) we can conclude the luminosity distance However, chirp-mass and luminosity distance both scale as (1+z) so GW observations alone cannot determine the redshift Joint GW (for luminosity distance) and optical observations (for red-shift) can facilitate a new cosmological tool p24
Cosmology with inspirals If a binary inspiral is associated with an EM event Knowledge of the direction to the source and the time of the event can be used to greatly improve the accuracy of the estimation of luminosity distance Can measure the Hubble constant to a good accuracy, as also other cosmological parameters Exploring the large-scale distribution of matter in the Universe A population of inspirals will act as markers with known luminosity distance and red-shift Will allow detailed study of dark matter distribution in the Universe via gravitational lensing. p25
* * * * * * * * * * * * * Image: WMAP p26
Massive Black Hole Merger Rates The rates depend on the specific scenario by which black hole seeds formed The rates would be 10 s per year if small black holes were the seeds The rates would be several 100 s per year if the seeds were in the region of 10 4 to 10 6 solar masses Observed merger rates will test models of formation of black hole seeds Sesana, Volonteri, Haardt, 2007 p27
Astrophysics p28
Astrophysics From Binary Coalescences Information carried: Masses (a few %), spins (few %), distance (~10%), location on sky (~10 s of degrees) NS/NS NS/BH BH/BH Search for EM counterpart, e.g. γ-burst. If found: Learn the nature of the trigger for that γ-burst Deduce relative speed of light and GW s to ~ 1 sec / 3x10 9 yrs ~ 10-17 Measure Neutron Star radius to 15% and deduce equation of state Relativistic effects are very strong, e.g. Frame dragging by spins precession modulation p29
Neutron Star-Black Hole Inspiral and NS Tidal Disruption 1.4Msun / 10 Msun NS/BH Binaries Merger involves general relativistic non-linearities, relativistic hydrodynamics, large magnetic fields, tidal disruption, etc., dictated by unknown physics at nuclear densities p30
What I haven t talked about Burst sources and multi-messenger astronomy Szabi Marka (this afternoon) Stochastic background of gravitational waves Marco Bruni (Thursday) Continuous waves from neutron stars A lot of microphysics to be learnt but much needs to be understood in terms of strengths of sources p31
Slide by: P Shellard p32