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Testing GR with Inspirals

Testing GR with Inspirals. B.S. Sathyaprakash, Cardiff University, UK based on work with Arun, Iyer, Qusailah, Jones, Turner, Broeck, Sengupta. Gravitational-wave spectrum What might be observed from ground and space Gravitational-wave observables

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Testing GR with Inspirals

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  1. Testing GR with Inspirals B.S. Sathyaprakash, Cardiff University, UK based on work with Arun, Iyer, Qusailah, Jones, Turner, Broeck, Sengupta

  2. Gravitational-wave spectrum What might be observed from ground and space 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 Cosmology Plan Testing GR with Inspirals

  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 Inspirals

  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 Inspirals

  5. 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 Inspirals

  6. Fundamental Measurements

  7. 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 • Gravitational potential F ~ 10-6 (v ~ 10-3) n radio binary pulsars while F ~ 0.1 (v ~ 0.3) in coalescing binaries • PN effects at order v7 are 1014 times more important in inpsiral observations than in radio pulsars Testing GR with Inspirals

  8. 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 Testing GR with Inspirals

  9. Constrain the mass of the graviton • If graviton is massive then it will lead to dispersion of the waves (Cliff Will) • Different waves travel at different speeds • The phasing of the waves changes • The matched filter will have an additional parameter (mass of the graviton) • Can constrain lg ~ 1.3 x 1013 in EGO and 7 x 1016 km in LISA (Arun et al) Testing GR with Inspirals

  10. Cross polarization Plus polarization Polarisation of Gravitational Waves Testing GR with Inspirals

  11. Cliff Will Testing GR with Inspirals

  12. Response of a GW Detector • R(t,q,f,y) = F+(q,f,y) h+(t)+ Fx(q,f,y) hX(t) • h+(t,i), hX(t,i) – The two different polarisations of the gravitational wave in GR • F+(q,f,y), Fx(q,f,y) antenna response to the two different polarisations • q, fDirection to the source • Polarization angle y Testing GR with Inspirals

  13. Beam Pattern Function • Beam pattern of a detector is the sensitivity of an antenna to un-polarized radiation as a function of the direction of the incoming wave • (i , i ) source coordinates wrt with i-th detector, and the factor Ciis a constant used to mimic the difference in the strain sensitivity of different antennas. • In order to compare different detectors it is necessary to choose a single coordinate system (, ) with respect to which we shall consider the various detector responses Testing GR with Inspirals

  14. LIGO Livingstone ACIGA VIRGO TAMA LIGO Hanford GEO 600 Testing GR with Inspirals

  15. Extracting the Polarisation in GR • Assuming that there are only two polarisations • We can extract the two polarizations using three or more detectors (three responses and two independent time delays to measure the fine unknowns) Testing GR with Inspirals

  16. Strong field tests of relativity

  17. 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? Testing GR with Inspirals

  18. Accurate measurements from inspirals Arun et al Testing GR with Inspirals

  19. Jones, Turner, BSS Testing GR with Inspirals

  20. 3 G pc 10-2 Jones, Turner, BSS; Berti et al 10-3 10-4 Testing GR with Inspirals

  21. 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) • 0.7% of total mass in GW • Numerical relativity (Baker et al, AEI, Jena, PSU, UTB) • 1-3% of total mass in GW Testing GR with Inspirals

  22. Analytical Vs Numerical Relativity Testing GR with Inspirals

  23. Adv LIGO Sensitivity to Inspirals Testing GR with Inspirals

  24. Strong field tests of gravityConsistency of Parameters Jones and BSS Testing GR with Inspirals

  25. Testing Post-Newtonian Gravity

  26. 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 Inspirals

  27. 10 per day several events per day 1 per year 1 event per two years Testing GR with Inspirals

  28. / Merger of supermassive black holes - no templates needed! a The high S/N at early times enables LISA to predict the time and position of the coalescence event, allowing the event to be observed simultaneously by other telescopes. Cutler and Vecchio Testing GR with Inspirals

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

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

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

  32. Signal in the Fourier Domain Testing GR with Inspirals

  33. post-Newtonian parameters Testing GR with Inspirals

  34. Testing PN Theory using EGO Arun et al Testing GR with Inspirals

  35. Testing PN Theory using LISA Arun et al Testing GR with Inspirals

  36. Testing other PN effects in LISA • In this test we re-expand the log-terms and absorb them into various post-Newtonian orders • The test can quite reliably test most PN parameters except y4 Testing GR with Inspirals

  37. Testing the presence of log terms • In this test we keep the log-terms as they appear but introduce new parameters corresponding to the log-terms • Greater number of parameters means that we have a weaker test Testing GR with Inspirals

  38. Consistency of PN Coefficients including log-terms Arun et al Testing GR with Inspirals

  39. Cosmology

  40. Inspirals can be seen to cosmological distances Testing GR with Inspirals

  41. 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: ~ 1 / 3x109yrs ~ 10-17 • measure Neutron Star radius to 15% and deduce equation of state • Deduce star formation rate from coalescence rates Testing GR with Inspirals

  42. In conclusion

  43. 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 Inspirals

  44. LISA: Fundamental Physics, Astrophysics and Cosmology Testing GR with Inspirals

  45. 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 Inspirals 4x107 4x105 4x103 M 40 0.4

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