Transcript Document
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 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, 2006 Testing GR with Gravitational Waves 2 Gravitational Wave Spectrum Phase Capture super-massive Quantum Fluctuations inMerging the Early Universe transitions of black black holes (SMBH) at holes and galactic coresin the Earlycompact Universe stars by SMBH March 2, 2006 Testing GR with Gravitational Waves Merging Neutron binary star neutron quakes stars and and black magnetars holes in distant galaxies 3 • 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(v7) • 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) March 2, 2006 Amplitude Compact Binary Inspirals Time Testing GR with Gravitational Waves 4 Rotating Neutron Stars “Mountain” on neutron star Accreting neutron star March 2, 2006 Wobbling neutron star R-modes Testing GR with Gravitational Waves 5 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, 2006 Testing GR with Gravitational Waves 6 Gravitational Wave Observables • Luminosity L = (Asymm.) v10 • Frequency f = √r – Luminosity is a strong function – Dynamical frequency in the of velocity: A black hole binary system: twice the orb. freq. source brightens up a million • Binary chirp rate times during merger – Many sources chirp during • Amplitude observation: chirp rate depends only chirp mass h = (Asymm.) (M/R) (M/r) – The amplitude gives strain caused in space as the wave propagates – For binaries the amplitude depends only on chirpmass5/3/distance March 2, 2006 – Chirping sources are standard candles • Polarisation – In Einstein’s theory two polarisations - plus and cross Testing GR with Gravitational Waves 7 Fundamental Measurements 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, 2006 Testing GR with Gravitational Waves 9 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, 2006 Testing GR with Gravitational Waves 10 Polarisation of Gravitational Waves Plus polarization March 2, 2006 Cross polarization Testing GR with Gravitational Waves 11 Cliff Will March 2, 2006 Testing GR with Gravitational Waves 12 Strong field tests of relativity Fundamental questions on strong gravity and the nature of space-time • From inspiral and ringdown signals – measure M and J before and after merger: test Hawking area theorem – Measure J/M2. 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 March 2, 2006 Testing GR with Gravitational Waves 14 Accurate measurements from inspirals Arun et al March 2, 2006 Testing GR with Gravitational Waves 15 Measurement from BH ringdowns Jones and Turner March 2, 2006 Testing GR with Gravitational Waves 16 Testing the Merger Dynamics • 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 March 2, 2006 Testing GR with Gravitational Waves 17 Analytical Vs Numerical Relativity March 2, 2006 Testing GR with Gravitational Waves 18 Adv LIGO Sensitivity to Inspirals March 2, 2006 Testing GR with Gravitational Waves 19 Strong field tests of gravity Consistency of Parameters Jones and BSS March 2, 2006 Testing GR with Gravitational Waves 20 Testing PostNewtonian Gravity 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, 2006 Testing GR with Gravitational Waves 22 10 per day several events per day 1 per year 1 event per two years March 2, 2006 Testing GR with Gravitational Waves 23 Phasing Formula for GW akin to Timing Formula for Binary PSRs Blanchet Damour Faye Farase Iyer Jaranowski Schaeffer Will Wiseman … March 2, 2006 Testing GR with Gravitational Waves 24 Signal in the Fourier Domain March 2, 2006 Testing GR with Gravitational Waves 25 post-Newtonian parameters March 2, 2006 Testing GR with Gravitational Waves 26 Testing PN Theory using EGO Arun et al March 2, 2006 Testing GR with Gravitational Waves 27 Testing PN Theory using LISA Arun et al March 2, 2006 Testing GR with Gravitational Waves 28 Consistency of PN Coefficients including log-terms Arun et al March 2, 2006 Testing GR with Gravitational Waves 29 Gravitational wave tails Blanchet and Schaefer 95, Blanchet and Sathyaprakash 96 March 2, 2006 Testing GR with Gravitational Waves 30 Relativistic Astrophysics with GW Neutron Star-Black Hole Inspiral and NS Tidal Disruption 1.4Msun / 10 Msun NS/BH Binaries Vallisneri • Merger involves general relativistic nonlinearities, relativistic hydrodynamics, large magnetic fields, tidal disruption, etc., dictated by unknown physics at nuclear densities March 2,< ~2006 NS disrupt NS Radius to 15% -Nuclear PhysicsNEED: Reshaped Noise, Numerical Simulations Testing GR with Gravitational Waves 32 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, 2006 Testing GR with Gravitational Waves 33 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-rayGW strength – Combined GW & EM obs’s carry information about crust strength and structure, temperature dependence of viscosity, ... March 2, 2006 Testing GR with Gravitational Waves 34 Stellar Modes Andersson and Kokkotas • 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 March 2, 2006 Testing GR with Gravitational Waves 35 Cosmology Inspirals can be seen to cosmological distances March 2, 2006 Testing GR with Gravitational Waves 37 Cosmology and Astronomy from Stellar Mass Binary Coalescences • 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 dL(z); infer about dark matter/energy • 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 / 3x109 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 March 2, 2006 Testing GR with Gravitational Waves 38 In conclusion Ground-Based Detectors: Nearby to High-z Universe 20 Mpc: Current interferometers Virgo Supercluster 300 Mpc Adv. Interferometers Coma cluster 3 Gpc 3rd gen. interferometers Cosmological Dist March 2, 2006 Testing GR with Gravitational Waves 40 LISA: Fundamental Physics, Astrophysics and Cosmology March 2, 2006 Testing GR with Gravitational Waves 41 5/(√yr Hz) | 1/√Hz 10-22 Current detectors LISA 10-23 BBO 10-24 Adv detectors 3rd generation 10-25 0.1m 10m 1 Hz 100 10k frequency f / binary black hole mass whose freq at merger=f 3M with Gravitational Waves 40 4x102,7 2006 4x105 Testing GR4x10 0.4 March 42