Gravitational Wave Detection Using Pulsar Timing
Current Status and Future Progress
Fredrick A. Jenet
Center for Gravitational Wave Astronomy
University of Texas at Brownsville
Collaborators
Dick ManchesterATNF/CSIRO
Australia
George HobbsATNF/CSIRO
Australia
KJ LeePeking U.
China
Andrea LommenFranklin & Marshall
USA
Shane L. LarsonPenn State
USA
Linqing WenAEI
Germany
Teviet CreightonCaltech
USA
John ArmstrongJPLUSA
Main Points
• Radio pulsar can directly detect gravitational waves– How can you do that?
• What can we learn?– Astrophysics– Gravity
• Current State of affairs• What can the SKA do.
Radio Pulsars
Gravitational Waves
“Ripples in the fabric of space-time itself”
g = + h
h / t + 2 h = 4 T
G (g) = 8 T
Pulsar Timing
• Pulsar timing is the act of measuring the arrival times of the individual pulses
How does one detect G-waves using Radio pulsars?
Pulsar timing involves measuring the time-of arrival (TOA) of each individual pulse and then subtracting off the expected time-of-arrival given a physical model of the system.
R = TOA – TOAm
Timing residuals from PSR B1855+09
From Jenet, Lommen, Larson, & Wen, ApJ , May, 2004
Data from Kaspi et al. 1994
Period =5.36 msOrbital Period =12.32 days
The effect of G-waves on the Timing residuals
h = R Rrms 1 s h >= 1 s /N1/2
10-14
10-13
10-12
3 10-9
h
Frequency, Hz
3 10-8 3 10-7
10-15
10-16
3 10-103 10-11
Sensitivity of a Pulsar timing “Detector”
*3C 66B 1010 Msun BBH
@ a distance of 20 Mpc
109 Msun BBH@ a distance of 20 Mpc
SMBH Background
*OJ287
The Stochastic Background
hc(f) = A f
gw(f) = (2 2/3 H02) f2 hc(f)2
Super-massive Black Holes:
= -2/3A = 10-15 - 10-14 yrs-2/3
Characterized by its “Characterictic Strain” Spectrum:
•Jaffe & Backer (2002)•Wyithe & Lobe (2002)•Enoki, Inoue, Nagashima, Sugiyama (2004)
For Cosmic Strings:
= -7/6
A= 10-21 - 10-15 yrs-7/6
•Damour & Vilenkin (2005)
The Stochastic Background
The best limits on the background are due to pulsar timing.
For the case where gw(f) is assumed to be a constant (=-1):
Kaspi et al (1994) report gwh2 < 6 10-8 (95% confidence)McHugh et al. (1996) report gwh2 < 9.3 10-8
Frequentist Analysis using Monte-Carlo simulations Yield gwh2 < 1.2 10-7
The Stochastic BackgroundThe Parkes Pulsar Timing Array Project
Goal:Time 20 pulsars with 100 nano-second residual RMS over 5 years
Current StatusTiming 20 pulsars for 2 years, 5 currently have an RMS < 300 ns
Combining this data with the Kaspi et al data yields:
= -1 : A<4 10-15 yrs-1 gwh2 < 8.8 10-9
= -2/3 : A<6.5 10-15 yrs-2/3 gw(1/20 yrs)h2 < 3.0 10-9
= -7/6 : A<2.2 10-15 yrs-7/6 gw(1/20 yrs)h2 < 6.9 10-9
The Stochastic Background
With the SKA: 40 pulsars, 10 ns RMS, 10 years
= -1 : A<3.6 10-17 gwh2 < 6.8 10-13
= -2/3 : A<6.0 10-17 gw(1/10 yrs)h^2 < 4.0 10-13
= -7/6 : A<2.0 10-17 gw(1/10 yrs)h^2 < 2.1 10-13
The Stochastic BackgroundA Dream, or almost reality with SKA:40 pulsars, 1 ns RMS, 20 years
= -2/3 : A<1.0 10-18 gw(1/10 yrs)h^2 < 1.0 10-16
The expected background due to white dwarf binaries lies in the range of A = 10-18 - 10-17! (Phinney (2001))
•Individual 108 solar mass black hole binaries out to ~100 Mpc.•Individual 109 solar mass black hole binaries out to ~1 Gpc
The timing residuals for a stochastic background
This is the same for all pulsars.
This depends on the pulsar.
The induced residuals for different pulsars will be correlated.
The Expected Correlation Function
Assuming the G-wave background is isotropic:
The Expected Correlation Function
How to detect the Background
For a set of Np pulsars, calculate all the possible correlations:
How to detect the Background
How to detect the Background
How to detect the Background
Search for the presence of () in C():
How to detect the Background
The expected value of is given by:
In the absence of a correlation, will be Gaussianly distributed with:
How to detect the BackgroundThe significance of a measured correlation is given by:
Single Pulsar Limit(1 s, 7 years)
Expected Regime
For a background of SMBH binaries: hc = A f-2/3
20 pulsars.
Single Pulsar Limit(1 s, 7 years)
1 s, 1 year
Expected Regime
For a background of SMBH binaries: hc = A f-2/3
20 pulsars.
Single Pulsar Limit(1 s, 7 years)
1 s, 1 year(Current ability)
Expected Regime
.1 s5 years
For a background of SMBH binaries: hc = A f-2/3
20 pulsars.
Single Pulsar Limit(1 s, 7 years)
1 s, 1 year(Current ability)
Expected Regime
.1 s5 years
.1 s10 years
For a background of SMBH binaries: hc = A f-2/3
20 pulsars.
Single Pulsar Limit(1 s, 7 years)
1 s, 1 year(Current ability)
Expected Regime
.1 s5 years
.1 s10 years
SKA10 ns5 years40 pulsars
hc = A f-2/3
Detection SNR for a given level of the SMBH background Using 20 pulsars
Graviton Mass• Current solar system limits place mg < 4.4 10-22 eV
• 2 = k2 + (2 mg/h)2
• c = 1/ (4 months)
• Detecting 5 year period G-waves reduces the upper bound on the graviton mass by a factor of 15.
• By comparing E&M and G-wave measurements, LISA is expected to make a 3-5 times improvement using LMXRB’s and perhaps up to 10 times better using Helium Cataclismic Variables. (Cutler et al. 2002)
• Radio pulsars can directly detect gravitational waves– R = h/s , 100 ns (current), 10 ns (SKA)
• What can we learn?– Is GR correct?
• SKA will allow a high SNR measurement of the residual correlation function -> Test polarization properties of G-waves
• Detection implies best limit of Graviton Mass (15-30 x)
– The spectrum of the background set by the astrophysics of the source.
• For SMBHs : Rate, Mass, Distribution (Help LISA?)
• Current Limits– For SMBH, A<6.5 10-15 or gw(1/20 yrs)h2 < 3.0 10-9
• SKA Limits– For SMBH, A<6.0 10-17 or gw(1/10 yrs)h2 < 4.0 10-13
– Dreamland: A<1.0 10-18 or gw(1/10 yrs)h2 < 1.0 10-16
• Individual 108 solar mass black hole binaries out to ~100 Mpc.• Individual 109 solar mass black hole binaries out to ~1 Gpc