Transcript Gravitational Wave Detection Using Pulsar Timing Current

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
John Armstrong
JPL
USA
Teviet Creighton
Caltech
USA
George Hobbs
ATNF/CSIRO
Australia
KJ Lee
Peking U.
China
Shane L. Larson
Penn State
USA
Dick Manchester
ATNF/CSIRO
Australia
Andrea Lommen
Franklin & Marshall
USA
Linqing Wen
AEI
Germany
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”
gmn = hmn + hmn
Gm n (g) = 8 p Tm n
- 2 hmn /2 t + 2 hmn = 4p Tmn
Pulsar Timing
• Pulsar timing is the act of measuring the
arrival times of the individual pulses
How does one detect Gwaves 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 ms
Orbital Period =12.32 days
The effect of G-waves on the
Timing residuals
Sensitivity of a Pulsar timing
“Detector”
h=WR
Rrms  1 m s
h >= 1 ms W/N1/2
3C 66B
10-12
*
@ a distance of 20 Mpc
10-13
h
1010 Msun BBH
109 Msun BBH
@ a distance of 20 Mpc
10-14
10-15
OJ287
10-16
*
3  10-11 3  10-10 3  10-9
3  10-8
Frequency, Hz
3  10-7
The Stochastic Background
Characterized by its “Characterictic Strain” Spectrum:
hc(f) = A f
Wgw(f) = (2 p2/3 H02) f2 hc(f)2
Super-massive Black Holes:
 = -2/3
A = 10-15 - 10-14 yrs-2/3
•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 Wgw(f) is assumed to be a constant (=-1):
Kaspi et al (1994) report Wgwh2 < 6  10-8 (95% confidence)
McHugh et al. (1996) report Wgwh2 < 9.3  10-8
Frequentist Analysis using Monte-Carlo simulations Yield
Wgwh2 < 1.2  10-7
The Stochastic Background
The Parkes Pulsar Timing Array Project
Goal:
Time 20 pulsars with 100 nano-second residual RMS over 5 years
Current Status
Timing 20 pulsars for 2 years, 5 currently have an
RMS < 300 ns
Combining this data with the Kaspi et al data yields:
 = -1 :
 = -2/3 :
A<4  10-15 yrs-1
Wgwh2 < 8.8 10-9
2
A<6.5  10-15 yrs-2/3 Wgw(1/20 yrs)h < 3.0 10-9
 = -7/6 :
A<2.2 
10-15
yrs-7/6
2
Wgw(1/20 yrs)h < 6.9 10-9
The Stochastic Background
With the SKA: 40 pulsars, 10 ns RMS, 10 years
 = -1 :
 = -2/3 :
A<3.6  10-17
A<6.0  10-17
Wgwh2 < 6.8 10-13
Wgw(1/10 yrs)h^2 < 4.0 10-13
 = -7/6 :
A<2.0  10-17
Wgw(1/10 yrs)h^2 < 2.1 10-13
The Stochastic Background
A Dream, or almost reality with SKA:
40 pulsars, 1 ns RMS, 20 years
 = -2/3 :
A<1.0  10-18
Wgw(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 h(q) in C(q):
How to detect the Background
The expected value of r is given by:
In the absence of a correlation, r will be Gaussianly distributed
with:
How to detect the Background
The significance of a measured correlation is given by:
For a background of SMBH binaries: hc = A f-2/3
20 pulsars.
Expected Regime
Single Pulsar Limit
(1 ms, 7 years)
For a background of SMBH binaries: hc = A f-2/3
20 pulsars.
Expected Regime
Single Pulsar Limit
(1 ms, 7 years)
1 ms, 1 year
For a background of SMBH binaries: hc = A f-2/3
20 pulsars.
Expected Regime
Single Pulsar Limit
(1 ms, 7 years)
.1 m s
5 years
1 ms, 1 year
(Current ability)
For a background of SMBH binaries: hc = A f-2/3
20 pulsars.
Expected Regime
Single Pulsar Limit
(1 ms, 7 years)
.1 m s
10 years
.1 m s
5 years
1 ms, 1 year
(Current ability)
Detection SNR for a given level of the SMBH background
Using 20 pulsars
-2/3
hc = A f
SKA
10 ns
5 years
40 pulsars
Expected Regime
Single Pulsar Limit
(1 ms, 7 years)
.1 m s
10 years
.1 m s
5 years
1 ms, 1 year
(Current ability)
Graviton Mass
• Current solar system limits place mg < 4.4 10-22 eV
•
2 = k2 + (2 p mg/h)2
•
nc = 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/   ms , 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 Wgw(1/20 yrs)h2 < 3.0 10-9
• SKA Limits
– For SMBH, A<6.0  10-17 or Wgw(1/10 yrs)h2 < 4.0 10-13
– Dreamland: A<1.0  10-18 or Wgw(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