-- Gravitational Waves -Sources and rates for LIGO
Hsinjung Lin
Class presentation
University of Florida, 2008.12.04
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Outline
Gravitational waves
Quadrupole approximation
Amplitude
Frequency
Polarization
Sources of gravitational waves for LIGO
What is LIGO and how does it work
Constraints and sensitivity curve
Sources
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Gravitational Waves
Accelerating objects with non-spherical symmetric
motions cause ripples in the curvature of spacetime.
The energy of the changing field propagates outward
at the speed of light.
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Gravitational Waves
Quadrupole approximation
Lowest order of the post-Newtonian approximation
Gives the first approximation to the radiation emitted
by a weakly relativistic system
Quadrupole moment tensor
I ij t=∫ y y T 00 t , y  d y
i
j
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Quadrupole formula
2
d I ij
2G
hij t , x =
t r 
2
r dt
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Gravitational Waves
Amplitude
The motion inside the source is highly non-spherical
2Mv
h≈
r
2
N.S.
where v N.S. is the non- spherical part velocity
and r is the distance between observer and source.
Binary system – using Newtonian approximation
R2S
h≈
rR
where
2 GM
RS=
2
c
is the Schwarzschild radius
For a binary black hole system with both M ≈10 solar mass
, R≈105 m and r≈10 24 m , the h is about 10−21
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Gravitational Waves
Frequency -- Decided by mass M and radius R
1 to 10^4 Hz for ground based detectors.
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Gravitational Waves
Polarization
for a plane wave in TT- gauge (transverse traceless gauge),
the solutions to the wave equation is
h
TT
v
=C  v e
ik  x

 
0
0
C  v=
0
0
0 0
h + hx
hx −h +
0 0
0
0
0
0
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What is LIGO?
LIGO(Laser Interferometer Gravitational Waves Observatory)
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Constraints for LIGO
Seismic noise
Thermal noise
Shot noise
Quantum effects
gravity gradient
Other effects :
Instrumental noises
coating noise...
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Sources for LIGO
Binary (inspiral) Systems
Binary black holes (BBH)
From 10M to 50M
−4
From ~100Mpc to z=2 ( 1Mpc z=2×10 )
Binary neutron stars (BNS)
From ~20 Mpc to ~350 Mpc
From 1/30y(<1/3y) to 1/2d(<5/d)
(data from LIGO-G060582-00-Z)
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Sources for LIGO
Spinning Neutron Stars
Emitted GW when asymmetry
Searching from Known pulsars
Ellipticity From 3x10-6 to 2x10-8
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Sources for LIGO
Short duration GW transient
-- less than 1 sec
Supernovae
Accreting /merging black holes
Gamma ray burst (GRB)
Other unknown sources
Zwerger and Muller, 1996
Burst
t~0.005 sec
Simulated gravitational wave from core collapse
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Sources for LIGO
Stochastic background
Cosmic background radiation and galaxy formation
Random radiation described by its spectrum
Big Bang
Way to search : Cross correlate from different detectors
From ΩGW ~3x10-6 to ~3x10-9
Low frequency spectrum
Energy density
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Thank you!!
NASA/GSFC
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