Testing GR with Ground-

Based GW DetectorsB.S. Sathyaprakash, Cardiff University, UK

(based on a Living Reviews article with Schutz)at University of Birmingham, March 30-31, 2006

March 2, 2006 2Testing 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, 2006 3Testing GR with Gravitational Waves

Quantum Fluctuations in the Early UniverseMerging 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, 2006 4Testing 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(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)

Am

plitu

de

Time

March 2, 2006 5Testing GR with Gravitational Waves

Rotating Neutron Stars

Wobbling neutron star

R-modes

“Mountain” on neutron star

Accreting neutron star

March 2, 2006 6Testing 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, 2006 7Testing 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.) 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

Fundamental

Measurements

March 2, 2006 9Testing 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, 2006 10Testing 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, 2006 11Testing GR with Gravitational Waves

Polarisation of Gravitational Waves

Cross polarizationPlus polarization

March 2, 2006 12Testing GR with Gravitational Waves

Cliff Will

Strong field tests of

relativity

March 2, 2006 14Testing GR with Gravitational Waves

• 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

Fundamental questions on strong gravity and the nature of space-

time

March 2, 2006 15Testing GR with Gravitational Waves

Accurate measurements from inspirals

Arun et al

March 2, 2006 16Testing GR with Gravitational Waves

Measurement from BH ringdowns

Jones and Turner

March 2, 2006 17Testing 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, 2006 18Testing GR with Gravitational Waves

Analytical Vs Numerical Relativity

March 2, 2006 19Testing GR with Gravitational Waves

Adv LIGO Sensitivity to Inspirals

March 2, 2006 20Testing GR with Gravitational Waves

Strong field tests of gravity

Consistency of Parameters

Jones and BSS

Testing Post-Newtonian

Gravity

March 2, 2006 22Testing 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, 2006 23Testing GR with Gravitational Waves

1 event per two years

several events per

day

10 per day

1 per year

March 2, 2006 24Testing GR with Gravitational Waves

Phasing Formula for GW akin to

Timing Formula for Binary PSRsBlanchet

Damour

Faye

Farase

Iyer

Jaranowski

Schaeffer Will

Wiseman

…

March 2, 2006 25Testing GR with Gravitational Waves

Signal in the Fourier Domain

March 2, 2006 26Testing GR with Gravitational Waves

post-Newtonian parameters

March 2, 2006 27Testing GR with Gravitational Waves

Testing PN Theory using EGO

Arun et al

March 2, 2006 28Testing GR with Gravitational Waves

Testing PN Theory using LISA

Arun et al

March 2, 2006 29Testing GR with Gravitational Waves

Consistency of PN Coefficients including log-terms

Arun et al

March 2, 2006 30Testing GR with Gravitational Waves

Blanchet and Schaefer 95, Blanchet and Sathyaprakash 96

Gravitational wave tails

Relativistic Astrophysics

with GW

March 2, 2006 32Testing 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, 2006 33Testing 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, 2006 34Testing 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-rayGW strength

– Combined GW & EM obs’s carry information about crust strength and structure, temperature dependence of viscosity, ...

March 2, 2006 35Testing 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, 2006 37Testing GR with Gravitational Waves

Inspirals can be seen to cosmological distances

March 2, 2006 38Testing 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 / 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

• 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

In conclusion

March 2, 2006 40Testing GR with Gravitational Waves

20 Mpc: Current interferometers

Virgo Supercluster

300 Mpc Adv. Interferometers Coma cluster

3 Gpc 3rd gen. interferometers Cosmological

Dist

Ground-Based Detectors: Nearby to High-z Universe

March 2, 2006 41Testing GR with Gravitational Waves

LISA: Fundamental Physics, Astrophysics and Cosmology

March 2, 2006 42Testing GR with Gravitational Waves

0.1m 10m 1 Hz 100 10k

4x107 4x105 4x103 M 40 0.4

frequency f / binary black hole mass whose freq at merger=f

Current detectors

BBO3rd generation

Adv detectors

LISA

10-22

10-23

10-24

10-25

5/(√yr Hz) | 1/√Hz