Testing GR with Ground-Based GW Detectors B.S. Sathyaprakash, Cardiff University, UK (based on a Living Reviews article with Schutz) at University of Birmingham, March 30-31, 2006

March 2, Testing GR with Gravitational Waves Plan Gravitational-wave spectrum –What might be observed from ground Gravitational-wave observables –amplitude, luminosity, frequency, chirp-rate Fundamental properties –speed, polarization, … Strong field tests of general relativity –merger dynamics, QNM Predictions of PN gravity –presence of log-terms Relativistic astrophysics –instabilities, normal modes Cosmology

March 2, Testing GR with Gravitational Waves Quantum Fluctuations in the Early Universe Merging super-massive black holes (SMBH) at galactic cores Phase transitions in the Early Universe Capture of black holes and compact stars by SMBH Merging binary neutron stars and black holes in distant galaxies Neutron star quakes and magnetars Gravitational Wave Spectrum

March 2, Testing GR with Gravitational Waves Compact Binary Inspirals Late-time dynamics of compact binaries is highly relativistic, dictated by non-linear general relativistic effects Post-Newtonian theory, which is used to model the evolution, is now known to O(v 7 ) The shape and strength of the emitted radiation depend on many parameters of binary system: masses, spins, distance, orientation, sky location, … Three archetypal systems –Double Neutron Stars (NS-NS) –Neutron Star-Black Hole (NS-BH) –Double Black Holes (BH-BH) Amplitude Time

March 2, Testing GR with Gravitational Waves Rotating Neutron Stars Wobbling neutron star R-modes “Mountain” on neutron star Accreting neutron star

March 2, Testing GR with Gravitational Waves Stochastic Sources Stochastic backgrounds –astrophysically generated and from the Big Bang –strength and spectrum of astrophysical backgrounds, production of early-universe radiation, relation to fundamental physics (string theory, branes, …)

March 2, Testing GR with Gravitational Waves Gravitational Wave Observables Frequency f = √  –Dynamical frequency in the system: twice the orb. freq. Binary chirp rate –Many sources chirp during observation: chirp rate depends only chirp mass –Chirping sources are standard candles Polarisation –In Einstein’s theory two polarisations - plus and cross 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 –For binaries the amplitude depends only on chirpmass 5/3 /distance

Fundamental Measurements

March 2, Testing GR with Gravitational Waves Speed of Gravitational Waves In general relativity gravitational waves travel on the light-cone How do we measure the speed of GW: –Coincident observation of gravitational waves and electromagnetic radiation from the same source –for a source at a distance D can test the speed of GW relative to EM to a relative accuracy of ~1/D x-ray/radio observations of compact objects, supernovae, gamma-ray bursts

March 2, Testing GR with Gravitational Waves Quadrupole formula Binary pulsars have already confirmed the quadrupole formula in weak-field regime GW observations will test the validity of the quadrupole formula in strong gravitational fields

March 2, Testing GR with Gravitational Waves Polarisation of Gravitational Waves Cross polarization Plus polarization

March 2, Testing GR with Gravitational Waves Cliff Will

Strong field tests of relativity

March 2, Testing GR with Gravitational Waves From inspiral and ringdown signals –measure M and J before and after merger: test Hawking area theorem –Measure J/M 2. Is it less than 1? Consistent with a central BH or Naked singularity or Soliton/Boson stars? Use parameters estimated from inspiral and ringdown to test models of merger dynamics –Effective one-body approach –Numerical relativity simulations Fundamental questions on strong gravity and the nature of space-time

March 2, Testing GR with Gravitational Waves Accurate measurements from inspirals Arun et al

March 2, Testing GR with Gravitational Waves Measurement from BH ringdowns Jones and Turner

March 2, Testing GR with Gravitational Waves From inspiral, merger and quasi-normal modes –Test analytical models of merger and numerical relativity simulations Effective one-body (Buonanno and Damour) –0.07% of total mass in GW Numerical relativity (Baker et al, AEI, Jena, PSU, UTB) –1-3% of total mass in GW Testing the Merger Dynamics

March 2, Testing GR with Gravitational Waves Analytical Vs Numerical Relativity

March 2, Testing GR with Gravitational Waves Adv LIGO Sensitivity to Inspirals

March 2, Testing GR with Gravitational Waves Strong field tests of gravity Consistency of Parameters Jones and BSS

Testing Post- Newtonian Gravity

March 2, Testing GR with Gravitational Waves GR two-body problem is ill-posed GW detectors are a tool to explore the two-body problem and tests the various predictions of general relativity

March 2, Testing GR with Gravitational Waves 1 event per two years several events per day 10 per day 1 per year

March 2, Testing GR with Gravitational Waves Phasing Formula for GW akin to Timing Formula for Binary PSRs Blanchet Damour Faye Farase Iyer Jaranowski Schaeffer Will Wiseman …

March 2, Testing GR with Gravitational Waves Signal in the Fourier Domain

March 2, Testing GR with Gravitational Waves post-Newtonian parameters

March 2, Testing GR with Gravitational Waves Testing PN Theory using EGO Arun et al

March 2, Testing GR with Gravitational Waves Testing PN Theory using LISA Arun et al

March 2, Testing GR with Gravitational Waves Consistency of PN Coefficients including log-terms Arun et al

March 2, Testing GR with Gravitational Waves Blanchet and Schaefer 95, Blanchet and Sathyaprakash 96 Gravitational wave tails

Relativistic Astrophysics with GW

March 2, Testing GR with Gravitational Waves Neutron Star-Black Hole Inspiral and NS Tidal Disruption Merger involves general relativistic non- linearities, relativistic hydrodynamics, large magnetic fields, tidal disruption, etc., dictated by unknown physics at nuclear densities 650 Mpc < ~ 43 Mpc inspiral NS disrupt 140 Mpc NS Radius to 15% -Nuclear Physics- NEED: Reshaped Noise, Numerical Simulations 1.4Msun / 10 Msun NS/BH Binaries Vallisneri

March 2, Testing GR with Gravitational Waves Neutron Stars Great interest in detecting radiation: physics of such stars is poorly understood. –After 40 years we still don’t know what makes pulsars pulse or glitch. –Interior properties not understood: equation of state, superfluidity, superconductivity, solid core, source of magnetic field. –May not even be neutron stars: could be made of strange matter!

March 2, Testing GR with Gravitational Waves Low-Mass X-ray Binaries Rotation rates –~250 to 700 rev/sec –Why not faster? –R-modes balancing accretion torque (Cutler et al) –Spin-up torque balanced by GW emission torque (Bildsten) If so and in steady state: – X-ray  GW strength –Combined GW & EM obs’s carry information about crust strength and structure, temperature dependence of viscosity,...

March 2, Testing GR with Gravitational Waves Stellar Modes G-modes or gravity-modes: buoyancy is the main restoring force P-modes or pressure-modes: main restoring force is the pressure F-mode or fundamental-mode: (surface waves) has an intermediate character of p- and g-mode W-modes: pure space-time modes (only in GR, space-time curvature is the restoring agent) Inertial modes (r-mode) : main restoring force is the Coriolis force (σ~2Ω/3) Superfluid modes: Deviation from chemical equilibrium provides the main restoring agent Andersson and Kokkotas

Cosmology

March 2, Testing GR with Gravitational Waves Inspirals can be seen to cosmological distances

March 2, Testing GR with Gravitational Waves Cosmology and Astronomy from Stellar Mass Binary Coalescences Search for EM counterpart, e.g.  -burst. If found: –Learn the nature of the trigger for that  -burst, deduce relative speed of light and GW’s to ~ 1 sec / 3x10 9 yrs ~ , measure Neutron Star radius to 15% and deduce equation of state Relativistic effects are very strong, e.g. –Frame dragging by spins  precession  modulation Cosmology –Measure luminosity distance to within 10% and, with the aid of EM observations of host galaxies, determine cosmological parameters; binary coalescences are standard candles, build a new distance ladder, measure d L (z); infer about dark matter/energy

In conclusion

March 2, Testing GR with Gravitational Waves 20 Mpc: Current interferometers Virgo Supercluster 300 Mpc Adv. Interferometers Coma cluster 3 Gpc 3 rd gen. interferometers Cosmological Dist Ground-Based Detectors: Nearby to High-z Universe

March 2, Testing GR with Gravitational Waves LISA: Fundamental Physics, Astrophysics and Cosmology

March 2, Testing GR with Gravitational Waves 0.1m 10m 1 Hz k 4x10 7 4x10 5 4x10 3 M  frequency f / binary black hole mass whose freq at merger=f Current detectors BBO 3 rd generation Adv detectors LISA /( √yr Hz) | 1/ √ Hz