Gravitational wave detection using pulsar timing current status and future progress
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Gravitational Wave Detection Using Pulsar Timing Current Status and Future Progress. Fredrick A. Jenet Center for Gravitational Wave Astronomy University of Texas at Brownsville. Dick Manchester ATNF/CSIRO Australia. George Hobbs ATNF/CSIRO Australia. KJ Lee Peking U. China.

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Gravitational Wave Detection Using Pulsar Timing Current Status and Future Progress

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Gravitational Wave Detection Using Pulsar TimingCurrent Status and Future Progress

Fredrick A. Jenet

Center for Gravitational Wave Astronomy

University of Texas at Brownsville


Dick Manchester

ATNF/CSIRO

Australia

George Hobbs

ATNF/CSIRO

Australia

KJ Lee

Peking U.

China

Andrea Lommen

Franklin & Marshall

USA

Shane L. Larson

Penn State

USA

Linqing Wen

AEI

Germany

Collaborators

John Armstrong

JPL

USA

Teviet Creighton

Caltech

USA


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


- ¶2 hmn /¶2 t + 2 hmn = 4p Tmn

Gravitational Waves

“Ripples in the fabric of space-time itself”

gmn = hmn + hmn

Gmn(g) = 8 p Tmn


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 ms

Orbital Period =12.32 days


The effect of G-waves on the Timing residuals


1010 Msun BBH

10-12

OJ287

3C 66B

*

*

@ a distance of 20 Mpc

10-13

109 Msun BBH

@ a distance of 20 Mpc

h

10-14

SMBH Background

10-15

10-16

3  10-11

3  10-10

3  10-9

3  10-8

3  10-7

Frequency, Hz

Sensitivity of a Pulsar timing “Detector”

h = W R

Rrms 1 m s

h >= 1 ms W/N1/2


The Stochastic Background

Characterized by its “Characterictic Strain” Spectrum:

hc(f) = A f

gw(f) = (2 2/3 H02) f2 hc(f)2

Super-massive Black Holes:

 = -2/3

A = 10-15 - 10-14 yrs-2/3

For Cosmic Strings:

 = -7/6

A= 10-21 - 10-15 yrs-7/6

  • Jaffe & Backer (2002)

  • Wyithe & Lobe (2002)

  • Enoki, Inoue, Nagashima, Sugiyama (2004)

  • 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 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 : 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 Background

A 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 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.

Single Pulsar Limit

(1 ms, 7 years)

Expected Regime


For a background of SMBH binaries: hc = A f-2/3

20 pulsars.

Single Pulsar Limit

(1 ms, 7 years)

Expected Regime

1 ms, 1 year


For a background of SMBH binaries: hc = A f-2/3

20 pulsars.

Single Pulsar Limit

(1 ms, 7 years)

Expected Regime

1 ms, 1 year

(Current ability)

.1 m s

5 years


For a background of SMBH binaries: hc = A f-2/3

20 pulsars.

Single Pulsar Limit

(1 ms, 7 years)

Expected Regime

1 ms, 1 year

(Current ability)

.1  s

10 years

.1 m s

5 years


Single Pulsar Limit

(1 ms, 7 years)

Expected Regime

1 ms, 1 year

(Current ability)

Detection SNR for a given level of the SMBH background Using 20 pulsars

hc = A f-2/3

SKA

10 ns

5 years

40 pulsars

.1  s

10 years

.1 m s

5 years


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


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