Fredrick A. Jenet Center for Gravitational Wave Astronomy
University of Texas at Brownsville
Pulsar timing and the properties of Gravitational Waves
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 2
Executive Summary of G-wave detection with Pulsar timing:
Number of gravitational wave sources detected by pulsar timing to date:
0
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 3
Collaborators Dick Manchester
ATNF/CSIRO Australia
George Hobbs ATNF/CSIRO
Australia
李柯伽
KJ Lee
CGWA/UTB
Joris Verbiest Swinburne Australia
文中略 Zhonglue Wen
Beijing Astronomical Observatory
Richard Price CGWA/UTB
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 4
Take home Pulsar timing is sensitive to the nanoHz
regime of the gravitational wave spectrum. If we get sensitive enough, we could see
supermassive black hole binaries out to large red shift.
We can test general relativity by measuring the polarization properties of GWs.
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 5
Radio Pulsars
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 6
Gravitational Waves
“Ripples in the fabric of space-time itself”
gµν = ηµν + hµν
- ∂2 hµν /∂2 t + ∇2 hµν = -16πTµν
Rυν[αβ;δ](g)=0 Rα
µ α ν - gµνRα µ
αµ/2= -8 π Tµ ν
6/26/08 7 Frequency, Hz
h
10-16 10-8 10-4 102 10-25
10-20
10-15
10-10
10-5
LF VLF
ELF
The Big Picture of G-wave Detection
HF
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 8
Science in the Nano-Hz Gravitational Wave Band
Binary Supermassive Black Hole formation and Evolution
Equation of State of the Early Universe (Quintessence)
Study of Cosmic Strings Testing GR by measuring the polarization
properties of GWs.
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 9
How do we detect/limit GW using radio pulsars?
Consider small perturbations from a flat space-time:
The slight change in the rate at which pulsar pulses arrive at Earth is given by:
Pulsar timing observations measure the timing residuals:
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 10
The Basic Strategy for GW detection
GWs will induce correlations between the timing residuals of different pulsars.
Exactly what correlations one is looking for depends on the type of signal.
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 11
Detecting a single supermassive black hole binary
The amplitude of a gravitational wave strain produced by a SMBH binary is given by:
Now, include the effects of cosmology:
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 12
文中略 (Zhonglue Wen)
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 13
Individual Supermassive Black Hole Binaries
Probability of detecting individual sources:
20 Pulsars, 100 ns: < 2% 5 Pulsars, 10 ns: > 90%
(Preliminary results by 文中略 (Zhonglue Wen))
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 14
Gravitational Waves The whole mess together says that we have 2 possible polarizations states.
If we remove the last equations, we can have up to 6 possible states.
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 15
Polarization Properties of GWs GR predicts only two
polarization modes. A general metric theory
has 4 more.
(Eardly, Lee, Lightman ‘73)
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 16
The Stochastic Background (Definitions of various quantities)
The stochastic background is made up of a sum of a large number of plane gravitational waves. The power spectrum of h is given by Sh(f) and satisfies:
hc(f) is the ‘characteristic strain’ spectrum and is defined by the above equation.
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 17
The Stochastic Background
hc(f) = A fα
Ωgw(f) = (2 π2/3 H02) f2 hc(f)2
Characterized by its “Characteristic Strain” Spectrum:
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 18
Detecting a Stochastic Background of GWs
Pulse arrival time fluctuations from different pulsars will be correlated:
C(θij) = <RI Rj>
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 19
Testing GR with the stochastic background
Different polarization modes will have different curves.
The actual correlation curve will be a weighted sum of these curves.
(Lee, Jenet, Price, 2008)
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 20
How well will pulsar timing be able to measure the polarization properties of
GW? Assume a background made up of GR +
another polarization class.
In order to have a hope of discriminating between different modes, one needs:
# pulsars Mode 40 Breathing 100 Longitudinal
500 Shear
6/26/08 Fredrick Jenet, Center for Gravitational Wave
Astronomy, UTB 21
Summary Pulsar timing can be used to study gravitational waves in
the nanoHz region of the GW spectrum. With current sensitivities, we can see SMBBHs with Mc =
1010 Msolar out to z=10. With rms timing residuals at 10 ns, we can see all Mc=109 SMBBHS in
the universe. We have analyzed the prospects of studying the polarization
properties of GWs in a stochastic background. We need at least 40 pulsars @ 100 ns to discriminate the breathing mode. For more info, see Lee, Jenet, Price, ApJ 2008.