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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