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 timing current status and future progress

Gravitational Wave Detection Using Pulsar TimingCurrent Status and Future Progress

Fredrick A. Jenet

Center for Gravitational Wave Astronomy

University of Texas at Brownsville


Collaborators

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

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

Radio Pulsars


Gravitational waves

- ¶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

  • Pulsar timing is the act of measuring the arrival times of the individual pulses


How does one detect g waves using radio pulsars

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


Gravitational wave detection using pulsar timing current status and future progress

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

The effect of G-waves on the Timing residuals


Sensitivity of a pulsar timing detector

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

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 background1

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 background2

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 background3

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 background4

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

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

The Expected Correlation Function

Assuming the G-wave background is isotropic:


The expected correlation function1

The Expected Correlation Function


How to detect the background

How to detect the Background

For a set of Np pulsars, calculate all the possible correlations:


How to detect the background1

How to detect the Background


How to detect the background2

How to detect the Background


How to detect the background3

How to detect the Background

Search for the presence of h(q) in C(q):


How to detect the background4

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 background5

How to detect the Background

The significance of a measured correlation is given by:


Gravitational wave detection using pulsar timing current status and future progress

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

20 pulsars.

Single Pulsar Limit

(1 ms, 7 years)

Expected Regime


Gravitational wave detection using pulsar timing current status and future progress

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


Gravitational wave detection using pulsar timing current status and future progress

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


Gravitational wave detection using pulsar timing current status and future progress

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


Gravitational wave detection using pulsar timing current status and future progress

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

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)


Gravitational wave detection using pulsar timing current status and future progress

  • 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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