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Fundamental Physics,
Astrophysics and
Cosmology with ETB.S. Sathyaprakash (CU) and Bernard Schutz (CU, AEI)
based on a Living Review article with a similar title (in preparation)
Fundamental Physics, Astrophysics and Cosmology with ET
p2
ET Science Summary
Fundamental physics
What are the different polarization states of gravitational
waves?
Are gravitons massless?
Black hole spectroscopy and the no-hair theorem?
Is general relativity the correct description of strong gravity?
Cosmology
Independent and accurate measurement of Hubble constant
What is the nature of dark energy?
How is matter organized on very large scales?
What were the physical conditions in the early Universe?
Fundamental Physics, Astrophysics and Cosmology with ET
p3
ET Science Summary
Astrophysics
What is the origin of gamma ray bursts and what are the
different populations?
Are ULX sources IMBH? How and when did they form?
How asymmetric are neutron stars and what is their equation-of-
state?
What is the end state of gravitational collapse?
Fundamental physics
Fundamental Physics, Astrophysics and Cosmology with ET
p5
Counting the Polarization States
Cross polarizationPlus polarization
Only two states in GR: h+ and hx
Fundamental Physics, Astrophysics and Cosmology with ET
p6
Polarization States in a
Scalar-Tensor TheoryCliff Will
Fundamental Physics, Astrophysics and Cosmology with ET
p7
Speed of Gravitational Waves
Coincident observation of an electromagnetic event and the
associated gravitational radiation can be used to constrain the
speed of gravitational waves to a fantastic degree:
If ∆t is the time difference in the arrival times of GW and
optical radiation and D is the distance to the source then the
fractional difference in the speeds is
Should be possible with coincident observation of gamma-ray
bursts up to very high red-shifts
Fundamental Physics, Astrophysics and Cosmology with ET
p8
Dispersion of the waves and binary
black hole Spectroscopy
Massive gravitons suffer dispersion which will be imprint in the phasing of the waves
Waveform currently known to 3.5 PN (i.e. to order v7/c7) in phase and 2.5 in amplitude (up to seven harmonics of the orbital frequency)
Should allow better tests of general relativity
Harmonics PN corrections
Blanchet et al (2002, 2004, 2005); Van Den Broeck and Sengupta (2006, 2007)
Black Hole Spectroscopy
Fundamental Physics, Astrophysics and Cosmology with ET
p10
Black Hole Quasi-Normal Modes
Fundamental Physics, Astrophysics and Cosmology with ET
p11
QNM Frequency and Damping Time
(Echeverria, 1989)
Fundamental Physics, Astrophysics and Cosmology with ET
p12
Black Hole Spectroscopy
Berti, Cardoso and Will
Fundamental Physics, Astrophysics and Cosmology with ET
p13
Quality Factor of BH QNMs
Berti, Cardoso and Will
Fundamental Physics, Astrophysics and Cosmology with ET
p14
Testing the No-Hair Theorem
By measuring a single (say l=2, m=2) quasi-normal mode’s
frequency and damping time one can determine the mass
and spin of the black hole
No-hair theorem: Frequencies and damping times of other
modes also depend on the mass and spin of the BH
If it is possible to measure the other modes then we would
be basically testing the no-hair theorem
Strong-gravity GR Tests
Fundamental Physics, Astrophysics and Cosmology with ET
p16
Testing the tail effect
Gravitational wave tails Testing the presence of tails
Blanchet and Schaefer
Blanchet, Sathyaprakash
Fundamental Physics, Astrophysics and Cosmology with ET
p17
Strong Field Tests of GR
Arun et al
Fundamental Physics, Astrophysics and Cosmology with ET
p18
From inspiral and ring
down signals
measure M and J before
and after merger: test
Hawking area theorem
Is J/M2 less than 1?
Consistent with a BH or
Naked singularity or
Soliton/Boson stars?
Fundamental questions on strong gravity
and the nature of space-time
Fundamental Physics, Astrophysics and Cosmology with ET
p19
Testing the merger dynamics
Fundamental Physics, Astrophysics and Cosmology with ET
p20
Adv LIGO Sensitivity to Inspirals
Fundamental Physics, Astrophysics and Cosmology with ET
p21
Strong field tests of gravity
Jones and BSS
Cosmology
Fundamental Physics, Astrophysics and Cosmology with ET
p23
Binaries are Standard Sirens
Frequency f = √ρρρρ
Dynamical frequency in the
system: e.g., in a binary
twice the orb. freq.
Binary chirp rate
Many sources chirp during
observation: chirp rate
depends only on the chirp
mass:
M = (m1m2)3/5 (m1+m2)
-1/5
Chirping sources are
standard sirens
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 h = dL/L
Schutz
Fundamental Physics, Astrophysics and Cosmology with ET
p24
Need coincident EM-GW observation for
Cosmology
Amplitude of gravitational waves depends on the
combination of Chirp-mass/Effective-Distance
Effective-Distance depends on the luminosity distance, source
location and polarization
Gravitational wave observations can independently
measure the amplitude and the chirp-mass
Therefore, binary inspirals are standard sirens: from the apparent
luminosity (the strain) we can conclude the luminosity distance
However, chirp-mass and luminosity distance both scale as
(1+z) so GW observations alone cannot determine the red-
shift
Joint GW (for luminosity distance) and optical observations (for
red-shift) can facilitate a new cosmological tool
Schutz
Fundamental Physics, Astrophysics and Cosmology with ET
p25
Cosmology with inspirals
If a binary inspiral is associated with an EM event
Knowledge of the direction to the source and the time of the event
can be used to greatly improve the accuracy of the estimation of
luminosity distance
Can measure the Hubble constant to a good accuracy, as also other
cosmological parameters
Exploring the large-scale distribution of matter in the
Universe
A population of inspirals will act as markers with known luminosity
distance and red-shift
Will allow detailed study of dark matter distribution in the
Universe via gravitational lensing.
Fundamental Physics, Astrophysics and Cosmology with ET
p26
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Image: WMAP
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Fundamental Physics, Astrophysics and Cosmology with ET
p27
Massive Black Hole Merger Rates
The rates depend on the
specific scenario by which
black hole seeds formed
The rates would be 10’s
per year if small black
holes were the seeds
The rates would be several
100’s per year if the seeds
were in the region of 104
to 106 solar masses
Observed merger rates
will test models of
formation of black hole
seeds
Sesana, Volonteri, Haardt, 2007
Fundamental Physics, Astrophysics and Cosmology with ET
p28
Astrophysics
Fundamental Physics, Astrophysics and Cosmology with ET
p29
Information carried:
Masses (a few %), spins (few %),
distance (~10%), location on sky
(~10’s of degrees)
Astrophysics From Binary Coalescences
NS/NS NS/BH BH/BH
Search for EM counterpart, e.g. γ-burst. If found:Learn the nature of the trigger for that γ-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
Fundamental Physics, Astrophysics and Cosmology with ET
p30
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
1.4Msun / 10 Msun NS/BH Binaries
Fundamental Physics, Astrophysics and Cosmology with ET
p31
What I haven’t talked about
Burst sources and multi-messenger astronomy
Szabi Marka (this afternoon)
Stochastic background of gravitational waves
Marco Bruni (Thursday)
Continuous waves from neutron stars
A lot of microphysics to be learnt but much needs to be
understood in terms of strengths of sources
Fundamental Physics, Astrophysics and Cosmology with ET
p32
Slide by: P Shellard
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