Testing GR with Ground-Based GW Detectors

1. 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

2. 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 Plan Testing GR with Gravitational Waves

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

4. Amplitude Time 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(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) Testing GR with Gravitational Waves

5. Wobbling neutron star Accreting neutron star “Mountain” on neutron star R-modes Rotating Neutron Stars Testing GR with Gravitational Waves

6. 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, …) Testing GR with Gravitational Waves

7. Frequency f = √r 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.) v10 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 chirpmass5/3/distance Gravitational Wave Observables Testing GR with Gravitational Waves

8. Fundamental Measurements

9. 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 Testing GR with Gravitational Waves

10. 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 Testing GR with Gravitational Waves

11. Cross polarization Plus polarization Polarisation of Gravitational Waves Testing GR with Gravitational Waves

12. Cliff Will Testing GR with Gravitational Waves

13. Strong field tests of relativity

14. Fundamental questions on strong gravity and the nature of space-time • From inspiral and ringdown signals • measureM 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 Testing GR with Gravitational Waves

15. Accurate measurements from inspirals Arun et al Testing GR with Gravitational Waves

16. Measurement from BH ringdowns Jones and Turner Testing GR with Gravitational Waves

17. 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 Testing GR with Gravitational Waves

18. Analytical Vs Numerical Relativity Testing GR with Gravitational Waves

19. Adv LIGO Sensitivity to Inspirals Testing GR with Gravitational Waves

20. Strong field tests of gravityConsistency of Parameters Jones and BSS Testing GR with Gravitational Waves

21. Testing Post-Newtonian Gravity

22. 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 Testing GR with Gravitational Waves

23. 10 per day several events per day 1 per year 1 event per two years Testing GR with Gravitational Waves

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

25. Signal in the Fourier Domain Testing GR with Gravitational Waves

26. post-Newtonian parameters Testing GR with Gravitational Waves

27. Testing PN Theory using EGO Arun et al Testing GR with Gravitational Waves

28. Testing PN Theory using LISA Arun et al Testing GR with Gravitational Waves

29. Consistency of PN Coefficients including log-terms Arun et al Testing GR with Gravitational Waves

30. Gravitational wave tails Blanchet and Schaefer 95, Blanchet and Sathyaprakash 96 Testing GR with Gravitational Waves

31. Relativistic Astrophysics with GW

32. < ~ 43 Mpc inspiral NS disrupt 140 Mpc 650 Mpc NS Radius to 15% -Nuclear Physics- NEED: Reshaped Noise, Numerical Simulations Neutron Star-Black Hole Inspiral and NS Tidal Disruption 1.4Msun / 10 Msun NS/BH Binaries Vallisneri • Merger involves general relativistic non-linearities, relativistic hydrodynamics, large magnetic fields, tidal disruption, etc., dictated by unknown physics at nuclear densities Testing GR with Gravitational Waves

33. 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! Testing GR with Gravitational Waves

34. 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, ... Testing GR with Gravitational Waves

35. 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 Testing GR with Gravitational Waves

36. Cosmology

37. Inspirals can be seen to cosmological distances Testing GR with Gravitational Waves

38. 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 / 3x109yrs ~ 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 Testing GR with Gravitational Waves

39. In conclusion

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

41. LISA: Fundamental Physics, Astrophysics and Cosmology Testing GR with Gravitational Waves

42. 10-22 10-23 10-24 10-25 Current detectors Adv detectors LISA 3rd generation BBO 5/(√yr Hz) | 1/√Hz 0.1m 10m 1 Hz 100 10k frequency f / binary black hole mass whose freq at merger=f Testing GR with Gravitational Waves 4x107 4x105 4x103 M 40 0.4