Fredrick A. Jenet Center for Gravitational Wave Astronomy

University of Texas at Brownsville

Pulsar timing and the properties of Gravitational Waves

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 2

Executive Summary of G-wave detection with Pulsar timing:

Number of gravitational wave sources detected by pulsar timing to date:

0

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 3

Collaborators Dick Manchester

ATNF/CSIRO Australia

George Hobbs ATNF/CSIRO

Australia

李柯伽

KJ Lee

CGWA/UTB

Joris Verbiest Swinburne Australia

文中略 Zhonglue Wen

Beijing Astronomical Observatory

Richard Price CGWA/UTB

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 4

Take home   Pulsar timing is sensitive to the nanoHz

regime of the gravitational wave spectrum.   If we get sensitive enough, we could see

supermassive black hole binaries out to large red shift.

  We can test general relativity by measuring the polarization properties of GWs.

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 5

Radio Pulsars

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 6

Gravitational Waves

“Ripples in the fabric of space-time itself”

gµν = ηµν + hµν

- ∂2 hµν /∂2 t + ∇2 hµν = -16πTµν

Rυν[αβ;δ](g)=0 Rα

µ α ν - gµνRα µ

αµ/2= -8 π Tµ ν

6/26/08 7 Frequency, Hz

h

10-16 10-8 10-4 102 10-25

10-20

10-15

10-10

10-5

LF VLF

ELF

The Big Picture of G-wave Detection

HF

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 8

Science in the Nano-Hz Gravitational Wave Band

  Binary Supermassive Black Hole formation and Evolution

  Equation of State of the Early Universe (Quintessence)

  Study of Cosmic Strings   Testing GR by measuring the polarization

properties of GWs.

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 9

How do we detect/limit GW using radio pulsars?

Consider small perturbations from a flat space-time:

The slight change in the rate at which pulsar pulses arrive at Earth is given by:

Pulsar timing observations measure the timing residuals:

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 10

The Basic Strategy for GW detection

  GWs will induce correlations between the timing residuals of different pulsars.

  Exactly what correlations one is looking for depends on the type of signal.

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 11

Detecting a single supermassive black hole binary

The amplitude of a gravitational wave strain produced by a SMBH binary is given by:

Now, include the effects of cosmology:

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 12

文中略 (Zhonglue Wen)

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 13

Individual Supermassive Black Hole Binaries

Probability of detecting individual sources:

20 Pulsars, 100 ns: < 2% 5 Pulsars, 10 ns: > 90%

(Preliminary results by 文中略 (Zhonglue Wen))

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 14

Gravitational Waves The whole mess together says that we have 2 possible polarizations states.

If we remove the last equations, we can have up to 6 possible states.

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 15

Polarization Properties of GWs   GR predicts only two

polarization modes.   A general metric theory

has 4 more.

(Eardly, Lee, Lightman ‘73)

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 16

The Stochastic Background (Definitions of various quantities)

The stochastic background is made up of a sum of a large number of plane gravitational waves. The power spectrum of h is given by Sh(f) and satisfies:

hc(f) is the ‘characteristic strain’ spectrum and is defined by the above equation.

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 17

The Stochastic Background

hc(f) = A fα

Ωgw(f) = (2 π2/3 H02) f2 hc(f)2

Characterized by its “Characteristic Strain” Spectrum:

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 18

Detecting a Stochastic Background of GWs

Pulse arrival time fluctuations from different pulsars will be correlated:

C(θij) = <RI Rj>

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 19

Testing GR with the stochastic background

  Different polarization modes will have different curves.

  The actual correlation curve will be a weighted sum of these curves.

(Lee, Jenet, Price, 2008)

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 20

How well will pulsar timing be able to measure the polarization properties of

GW?   Assume a background made up of GR +

another polarization class.

In order to have a hope of discriminating between different modes, one needs:

# pulsars Mode 40 Breathing 100 Longitudinal

500 Shear

6/26/08 Fredrick Jenet, Center for Gravitational Wave

Astronomy, UTB 21

Summary   Pulsar timing can be used to study gravitational waves in

the nanoHz region of the GW spectrum.   With current sensitivities, we can see SMBBHs with Mc =

1010 Msolar out to z=10.   With rms timing residuals at 10 ns, we can see all Mc=109 SMBBHS in

the universe.   We have analyzed the prospects of studying the polarization

properties of GWs in a stochastic background. We need at least 40 pulsars @ 100 ns to discriminate the breathing mode.   For more info, see Lee, Jenet, Price, ApJ 2008.