Nano-Hertz Gravitational Wave Detection Using Pulsars

Andrea N. LommenAssistant Professor of Physics and Astronomy

Head of Astronomy Program

Director of Grundy Observatory

Franklin and Marshall College

Lancaster, PA

Table of Contents

• NANO-Grav

• Illustrative Example of General Concept

• Limits on Stochastic Background

• What limit says about sources

• Measurements of Polarization

• Burst Detection

• Summary

Collaborators

• Rick Jenet, UT Brownsville • David Nice, Bryn Mawr College • Ingrid Stairs, U. British Columbia• Don Backer, UC Berkeley• Scott Ransom, NRAO• Paul Demorest, NRAO• Rob Ferdman, U. British Columbia,• Dick Manchester, ATNF• Bill Coles, UC San Diego• George Hobbs, ATNF• Joris Verbiest, ATNF and Swinburne

Introducing NANO-Grav

The North American Nano-Hertz Observatory of Gravitational Waves

(NANO-Grav)

Telescopes:

The Arecibo 300-m Telecope

The Green Bank 140-ft Telescope

The Allen Telescope Array?

The Green Bank 85-ft Telescope?

NANO-Grav MembersAndrea Lommen (chair), Franklin and Marshall College

Rick Jenet, UT Brownsville

Scott Ransom, Paul Demorest and Walter Brisken, NRAO

Ingrid Stairs, UBC

David Nice, Bryn Mawr College

Paulo Freire, NAIC Arecibo

Maura McLaughlin and Duncan Lorimer, West Virginia University

Joe Lazio, NRL

Don Backer, UC Berkeley

Zaven Arzoumanian, Goddard

Anne Archibald, McGill University

Ryan Shannon, Cornell University

Ryan Lynch, University of Virginia

The Arecibo Observatory

Illustrative Example of General Concept

From Kaspi, Taylor & Ryba 1994

Orbital Motion in the Radio Galaxy 3C 66B: Evidence for a Supermassive Black Hole Binary Hiroshi Sudou,1* Satoru Iguchi,2 Yasuhiro Murata,3 Yoshiaki Taniguchi1

Supermassive black hole binaries may exist in the centers of active galactic nuclei such as quasars and radio galaxies, and mergers between galaxies may result in the formation of supermassive binaries during the course of galactic evolution. Using the very-long-baseline interferometer, we imaged the radio galaxy 3C 66B at radio frequencies and found that the unresolved radio core of 3C 66B shows well-defined elliptical motions with a period of 1.05 ± 0.03 years, which provides a direct detection of a supermassive black hole binary.

Volume 300, Number 5623, Issue of 23 May 2003, pp. 1263-1265. Copyright © 2003 by The American Association for the Advancement of Science. All rights reserved.

From Jenet, Lommen, Larson, & Wen, ApJ 2004

From Jenet, Lommen, Larson, & Wen, ApJ 2004

Limit on Stochastic Background

20yrs of B1855+09

PSR J1713+0747 over 12 years

€

Ωgw ( f ) =2

3

π 2

H02f 2hc ( f )

2

fmin =1

dataspan

hc ( fmin )∝rms

dataspan

Ωgw ( f )∝rms2

dataspan4

From Jenet, Hobbs, van Straten, Manchester, Bailes, Verbiest, Edwards, Hotan, Sarkissian & Ord (2006)

Rough Limit

Monte Carlo simulation• First demonstrated by:

– Jenet et al (2006),

• Improved by:– Lommen, Verbiest, Hobbes, Coles (2008, in prep)

• Generate 10,000 versions of the simulated background

• Query the simulations for the upper limit (Allen & Romano 1999)

Monte Carlo simulation

• Generating a background:– 10000 GWs each with

• Amplitude randomly generated as member of a model spectrum (cosmic strings, relic GWs, SMBHs)

• Random polarization• Random phase• Random direction

– Do everything above 10000 times

– Measure its spectrum€

hc = Af

yr−1

⎛

⎝ ⎜

⎞

⎠ ⎟

α gw

What’s the appropriate question?

• Allen & Romano (1999):– What is the minimum value of A required to detect

the background 95% of the time? (Jenet et al 2006)

– What is the value of A that leads to the conclusion that the background is absent with 95% confidence? (Lommen, Verbiest, Hobbs, Coles 2008)

Limit on Energy Density of Gravitational Waves

€

Ωgw 1/20yr( )h2 = 2.1×10−9

-110 Mpc s km 100 -= hH

What limit says about sources

Figure courtesy of George Hobbs

Our upper limit is:•Equal to the predicted background using (one of) the calculations of Wyithe and Loeb (2003)

•Larger by a factor of about 5 than Jaffe and Backer (2003)

•Larger still than estimations by Enoki (2004)

Measurement of Polarization

The shape of the GW response

Thanks Bill Coles

(KJ Lee and Rick Jenet, 2008)

Detectability of a Waveform

• “Recall”

€

R(t) =1

21+ cosμ( ) r+ t( )cos 2ψ( ) + r× t( )sin 2ψ( )[ ]

r+,× t( ) = r+,×e − r+,×

p

r+,×e = h+,×

e τ( )0

t

∫ dτ

r+,×p = h+,×

p τ −d

c1− cosμ( )

⎡ ⎣ ⎢

⎤ ⎦ ⎥

0

t

∫ dτ

(Jenet, Lommen, Larson and Wen 2004)

Burst Detection

A burst being anything shorter than our observing timescale

Some Possible Sources of Burst Radiation

• Formation of SMBH (Thorne and Braginski ‘76)

• Close encounters of massive objects (Kocsis 06)

• Highly eccentric SMBH binaries (Enoki and Nagashima ‘06)

• Cosmic Strings (Hogan & Rees ‘84, Caldwell, Battye, and Shellard, ‘96, Damour and Vilenkin ‘05)

Detectability of a Waveform (continued)

So what matters is the integral of the waveform:

€

R = h τ( )0

t

∫ dτ

Sinusoidal source :

R = h0 cos ωτ( )0

t

∫ dτ =h0

ωsin ωt( ) = h0

P

2πsin ωt( )

or a Gaussian source :

R = h0e− τ −tc( ) /σ( )

2

0

t

∫ dτ = h0σ π

The shape of the GW response

Thanks Bill Coles

Detection algorithm: Weighted sum of residuals

So what can we detect?• 20 pulsars, 1 microsecond RMS, daily obs, we

would detect a 0.70 microsecond maximum response about 93% of the time. For a 2-week burst we calculate the corresponding characteristic strain:

Max response (us)

Characteristic strain (h)

Percent detected

0.7 3.3e-13 93

0.5 2.3e-13 40

0.3 1.4e-13 2

Scaling that last slide

• Statistic scales as number of pulsars so e.g. measurable strains halve if number of pulsars doubles

• Response scales as burst length, so measurable strains halve if burst length doubles

• If 20 pulsars have 100 ns RMS, divide left two columns by 10

Sensitivity to a 0.75 s 2-week burst, daily observing, 20 pulsars

Sensitivity to a 0.75 s 2-week burst, daily observing, 20 pulsars

Sensitivity to a 0.75 s 2-week burst, daily observing, 20 pulsars

Sensitivity to a 0.75 s 2-week burst, daily observing, 20 pulsars + 3 more

Summary

Summary and Prospects

• The new GW observatory: NANO-Grav • We have already ruled out significant

sources, both individually and in the stochastic background

• Pulsar timing is best way to measure polarization of GWs

• Burst detection offers interesting prospects for detection and directionality