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Pulsar Timing Arrays are using millisecondpulsars in the Galaxy to search for extragalacticGravitational waves from black-hole binaries.

millisecondpulsar

Earth

gravitationalwave

Gravitational waves

On gravitational-wave detection by Pulsar Timing Arrays

Pivture Credit: David Champion

Content:

1. Pulsar timing arrays

2. Data analysis techniques

3. Current upper limits on extragalactic gravitational waves

4. Future

Dance and merger of black holesCaltech+CornellDance and merger of black holes

credit: Caltech+Cornell

Data from Kaspi, Taylor, Ryba 1994

Res

idu

al(µ

s)

-10

10

0

Simulated residuals due to 3c66b Jenet et al. 2004

Res

idu

al(µ

s)-10

10

0

Pulsar GW sensitivityband

Periods: months to~10 yr

Sazhin 1978Detweiler 1979

Can already rule outBH binary candidates!

Gravitational waves: a (Gaussian, stochastic) background!

Phinney 01Jaffe & Backer 03Wyithe & Loeb 03Sesana et al. 07, 09

Click to edit Master text stylesSecond level

Third levelFourth level

Fifth level

amplitude spectralindex

General Relativity prediction:

Timing residuals correlated, both for single sources andstochastic background

Isotropic background:

Hellings & Downs 83Foster & Backer 90Jenet et al. 05

3 pulsar timing arrays:3 pulsar timing arrays:1. Parkes PTA

ATNF (Manchester, Hobbs,…)Swinburne (Bailes, van Straaten..)Texas (Jenet,…)San Diego (Coles,...)…

Currently the best

• timing residuals• upper limit on the GWB to be published

• Anne Archibald, McGill University• Zaven Arzoumanian, Goddard Space Flight Center• Don Backer, University of California, Berkeley• Adam Brazier, Cornell University• Jason Boyles, West Virginia University• Brian Burt, Franklin and Marshall College• Jim Cordes, Cornell University• Paul Demorest, National Radio Astronomy Observatory• Justin Ellis, West Virginia University• Rob Ferdman, CNRS, France• L. Samuel Finn, Center of Gravitational Physics at Penn State University• Paulo Freire, National Astronomy and Ionospheric Center• Alex Garcia, University of Texas, Brownsville• Marjorie Gonzalez, University of British Columbia• Rick Jenet, University of Texas, Brownsville, CGWA• Victoria Kaspi, McGill University• Joseph Lazio, Naval Research Laboratories• Andrea Lommen, Franklin and Marshall College• Duncan Lorimer, West Virginia University• Ryan Lynch, University of Virginia• Maura McLaughlin, West Virginia University• Jonathan Nelson, Oberlin College• David Nice, Bryn Mawr College• Nipuni Palliyaguru, West Virginia University• Delphine Perrodin, Franklin and Marshall College• Scott Ransom, National Radio Astronomy Observatory• Ryan Shannon, Cornell University• Xavi Siemens, University of Wisconsin• Ingrid Stairs, University of British Columbia• Dan Stinebring, Oberlin College• Kevin Stovall, University of Texas, Brownsville

• Anne Archibald, • Zaven Arzoumanian,• Don Backer, • Adam Brazier, • Jason Boyles,• Brian Burt, • Jim Cordes, • Paul Demorest, • Justin Ellis, • Rob Ferdman, • L. Samuel Finn, • Paulo Freire, • Alex Garcia,• et al…..

2. NanoGrav

3 pulsar timing arrays: 3. European PTA

3. • Jodrell Bank• Effelsberg• Westerbork• Nancay• Sardinia

Combine all the data: International Pulsar Timing Array.Future: Meerkat (South Africa), FAST (China), SKA

Data EPTA

Data Parkes

Our data analysis approach:Bayesian Inference

van Haasteren, L., McDonald, Lu 09van Haasteren, L., et al. (EPTA), 2012

Example problem: finding the white noise amplitude

(Frequentist) estimator:

Example problem: finding the white noise amplitude

Bayesian Theorist:

Likelyhood

Posterior

Evidence Prior

Example problem: finding the white noise amplitude

Bayesian Theorist:

Complication: white noise + jump

Complication: white noise + jump

Pulsar observer: fit for

Lazy Bayesian Theorist:

1. Find

2. Integrate over

Complication: white noise + jump

Pulsar observer: fit for

Lazy Bayesian Theorist:

1. Find

2. Integrate over

Complication: white noise + jump

ANALYTICAL!

Pulsar observer: fit for

Lazy Bayesian Theorist:

1. Find

2. Integrate over

Complication: white noise + jump

3. Get expression , insensitive to jumps!

Jump removal:

Real life: stochastic contribution

pulsarindices observing

runs

Correlation matrix

Real life: stochastic contribution

Correlation matrix

Gravitational-wavebackground Pulsar

noises

Red noise(power law)

Whitenoise

individualtiming-residualerror bars

Real life: deterministic contributions of unknown amplitude

binaryparametererrors

zero offsetsbetweenobservatoris

period error

period derivativeerror

positionerror

proper motionerror

GW backgroundtiming residuals(simulated)

Procedure EPTA 2011 limit

• Select 5 pulsars with no prominent red noise

• Some pulsars observed with more than 1 telescope. Noise model for each pulsar-telescope pair.

• Exhaustive list of deterministic contributions. Marginalize analytically.

• Marginalize via Markov Chain Monte Carlo over pulsar noise parameters.

EPTA, Nanograv upper limit.Parkes about to beat this van Haasteren, L., et al., 2011

(Sesana et al 2008)

Demorest at al. (2012)

This has been moving up (McWilliams, et al. 12, Sesana 12)

EPTA would-be detection van Haasteren, L., et al. 11

Conclusions

• Rapid PTA development around the world

• New limits, sensitivity improvements, and good prospects for the future.

Binary with spinBinary without spin

Eccentric inspiral

Circular inspiralScott Hughes, MIT

“Listening” to gravitational waves from black-hole mergers