Testing GR with Ground-Based GW Detectors

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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
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Plan

• 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

• Gravitational-wave spectrum
• What might be observed from ground
• Gravitational-wave observables
• amplitude, luminosity, frequency, chirp-rate

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Gravitational Wave Spectrum

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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)

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Rotating Neutron Stars
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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, )

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Gravitational Wave Observables

• Frequency f vr
• 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 Einsteins 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

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Fundamental Measurements
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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

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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

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Polarisation of Gravitational Waves
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Cliff Will
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Strong field tests of relativity
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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

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Accurate measurements from inspirals
Arun et al
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Measurement from BH ringdowns
Jones and Turner
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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

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Analytical Vs Numerical Relativity
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Adv LIGO Sensitivity to Inspirals
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Strong field tests of gravityConsistency of
Parameters
Jones and BSS
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Testing Post-Newtonian Gravity
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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

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10 per day
several events per day
1 per year
1 event per two years
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Phasing Formula for GW akin to Timing Formula
for Binary PSRs
Blanchet Damour Faye Farase Iyer Jaranowski Schaef
fer Will Wiseman
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Signal in the Fourier Domain
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post-Newtonian parameters
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Testing PN Theory using EGO
Arun et al
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Testing PN Theory using LISA
Arun et al
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Consistency of PN Coefficients including log-terms
Arun et al
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(No Transcript)
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Relativistic Astrophysics with GW
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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

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Neutron Stars

• Great interest in detecting radiation physics of
  such stars is poorly understood.
• After 40 years we still dont 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!

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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 obss carry information about
  crust strength and structure, temperature
  dependence of viscosity, ...

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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 (s2O/3)
• Superfluid modes Deviation from chemical
  equilibrium provides the main restoring agent

Andersson and Kokkotas
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Cosmology
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Inspirals can be seen to cosmological distances
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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 GWs 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

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In conclusion
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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
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LISA Fundamental Physics, Astrophysics and
Cosmology
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5/(vyr Hz) 1/vHz
0.1m 10m 1 Hz
100 10k
frequency f / binary black hole mass whose freq
at mergerf
4x107 4x105
4x103 M? 40 0.4