Testing GR with Inspirals B.S. Sathyaprakash, Cardiff University, UK based on work with Arun, Iyer,...
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Transcript of Testing GR with Inspirals B.S. Sathyaprakash, Cardiff University, UK based on work with Arun, Iyer,...
![Page 1: Testing GR with Inspirals B.S. Sathyaprakash, Cardiff University, UK based on work with Arun, Iyer, Qusailah, Jones, Turner, Broeck, Sengupta.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649e625503460f94b5eec2/html5/thumbnails/1.jpg)
Testing GR with Inspirals
B.S. Sathyaprakash, Cardiff University, UK based on work with Arun, Iyer, Qusailah, Jones, Turner, Broeck, Sengupta
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November 17, 2006 2Testing GR with Inspirals
Plan• 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
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November 17, 2006 3Testing GR with Inspirals
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
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November 17, 2006 4Testing GR with Inspirals
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
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November 17, 2006 5Testing GR with Inspirals
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
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Fundamental
Measurements
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November 17, 2006 7Testing GR with Inspirals
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 ~ 10-6 (v ~ 10-3) n radio binary pulsars while ~ 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
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November 17, 2006 8Testing GR with Inspirals
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
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November 17, 2006 9Testing GR with Inspirals
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 g ~ 1.3 x 1013 in EGO and 7 x 1016 km in LISA (Arun et al)
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November 17, 2006 10Testing GR with Inspirals
Polarisation of Gravitational Waves
Cross polarizationPlus polarization
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November 17, 2006 11Testing GR with Inspirals
Cliff Will
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November 17, 2006 12Testing GR with Inspirals
Response of a GW Detector
• R(t = F+() h+(t)+ Fx() hX(t)– h+(t,i), hX(t,i) – The two different polarisations
of the gravitational wave in GR
– F+(), Fx() antenna response to the two different polarisations
– Direction to the source
– Polarization angle
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November 17, 2006 13Testing GR with Inspirals
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 Ci is 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
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November 17, 2006 14Testing GR with Inspirals
VIRGO
TAMALIGO Hanford
ACIGALIGO Livingstone
GEO 600
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November 17, 2006 15Testing GR with Inspirals
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)
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Strong field tests of
relativity
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November 17, 2006 17Testing GR with Inspirals
• 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?
Fundamental questions on strong gravity and the nature of space-
time
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November 17, 2006 18Testing GR with Inspirals
Accurate measurements from inspirals
Arun et al
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November 17, 2006 19Testing GR with Inspirals
Jones, Turner, BSS
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November 17, 2006 20Testing GR with Inspirals
Jones, Turner, BSS; Berti et al
3 G pc10-2
10-3
10-4
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November 17, 2006 21Testing GR with Inspirals
• 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 the Merger Dynamics
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November 17, 2006 22Testing GR with Inspirals
Analytical Vs Numerical Relativity
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November 17, 2006 23Testing GR with Inspirals
Adv LIGO Sensitivity to Inspirals
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November 17, 2006 24Testing GR with Inspirals
Strong field tests of gravity
Consistency of Parameters
Jones and BSS
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Testing Post-Newtonian
Gravity
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November 17, 2006 26Testing GR with Inspirals
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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November 17, 2006 27Testing GR with Inspirals
1 event per two years
several events per
day
10 per day
1 per year
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November 17, 2006 28Testing GR with Inspirals
/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
Merger of supermassive black holes - no templates
needed!
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November 17, 2006 29Testing GR with Inspirals
Phasing Formula for GW akin to
Timing Formula for Binary PSRsBlanchet
Damour
Faye
Farase
Iyer
Jaranowski
Schaeffer Will
Wiseman
…
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November 17, 2006 30Testing GR with Inspirals
Blanchet and Schaefer 95, Blanchet and Sathyaprakash 96
Gravitational wave tails
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November 17, 2006 31Testing GR with Inspirals
Phasing Formula for GW akin to
Timing Formula for Binary PSRsBlanchet
Damour
Faye
Farase
Iyer
Jaranowski
Schaeffer Will
Wiseman
…
![Page 32: Testing GR with Inspirals B.S. Sathyaprakash, Cardiff University, UK based on work with Arun, Iyer, Qusailah, Jones, Turner, Broeck, Sengupta.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649e625503460f94b5eec2/html5/thumbnails/32.jpg)
November 17, 2006 32Testing GR with Inspirals
Signal in the Fourier Domain
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November 17, 2006 33Testing GR with Inspirals
post-Newtonian parameters
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November 17, 2006 34Testing GR with Inspirals
Testing PN Theory using EGO
Arun et al
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November 17, 2006 35Testing GR with Inspirals
Testing PN Theory using LISA
Arun et al
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November 17, 2006 36Testing GR with Inspirals
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 4
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November 17, 2006 37Testing GR with Inspirals
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
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November 17, 2006 38Testing GR with Inspirals
Consistency of PN Coefficients including log-terms
Arun et al
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Cosmology
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November 17, 2006 40Testing GR with Inspirals
Inspirals can be seen to cosmological distances
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November 17, 2006 41Testing GR with Inspirals
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: ~ 1 / 3x109 yrs ~ 10-17
– measure Neutron Star radius to 15% and deduce equation of state
• Deduce star formation rate from coalescence rates
• 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
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In conclusion
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November 17, 2006 43Testing GR with Inspirals
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
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November 17, 2006 44Testing GR with Inspirals
LISA: Fundamental Physics, Astrophysics and Cosmology
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November 17, 2006 45Testing GR with Inspirals
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