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