Gravitational Wave Detection and Data Analysis for Pulsar Timing Arrays

149 Pages·2014·3.21 MB·English

by  Rutger van Haasteren (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
Rutger van Haasteren
Gravitational Wave
Detection and Data
Analysis for Pulsar
Timing Arrays
Springer Theses
Recognizing Outstanding Ph.D. Research
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Rutger van Haasteren
Gravitational Wave
Detection and Data Analysis
for Pulsar Timing Arrays
Doctoral Thesis accepted by
the University of Leiden, The Netherlands
123
Author Supervisor
Dr. Rutgervan Haasteren Yuri Levin
Max PlanckInstituteforGravitational School ofPhysics
Physics(Albert EinsteinInstitute) Monash Center forAstrophysics
Hannover Clayton
Germany Australia
ISSN 2190-5053 ISSN 2190-5061 (electronic)
ISBN 978-3-642-39598-7 ISBN 978-3-642-39599-4 (eBook)
DOI 10.1007/978-3-642-39599-4
SpringerHeidelbergNewYorkDordrechtLondon
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Supervisor’s Foreword
Pulsars are among the most extraordinary objects in the universe. They are pro-
ducedinextremelyluminoussupernovaevents,duringwhichthecoreofamassive
starcollapsesintoaneutronstaraboutthesizeofamajorcityandmoredensethan
anatomicnucleus.Pulsarsareasub-classofneutronstarsthataredistinguishedby
bright,stronglycollimated,andcoherentradioemission.Asthepulsarspinsonits
axis, the lighthouse-like radio beams swing across the Galaxy to be observed at
Earth as a series of periodic pulses. Some pulsars possess phenomenal rotational
stability,whichisnotfarbelowthatofthebestatomicclocksonEarth.Thismakes
them unique instruments for experimental exploration of gravity. Relativistic
gravitationaleffectssuchasorbitalprecession,Shapirodelay,geodeticprecession,
and shrinking of the pulsar orbit due to the emission of gravitational waves have
beenmeasuredwithexquisiteprecisioninsystemswhereapulsarisamemberofa
tight binary, and have been found to be in excellent agreement with general
relativity.
The major current quest is to use pulsars for direct detection of long-period
(monthstoyears)gravitationalwaves,thatareexpectedtobeproducedbybinaries
of supermassive black holes at the centers of distant galaxies, as well as (more
speculatively)byoscillatingcosmicstringloops.Inordertoachievethis,scientists
carryoutlong-termtimingcampaignsofsets(alsoknownasarrays)ofparticularly
stablyrotatingmillisecondpulsars.Thedeviationsfromregularpulsearrivaltimes
(the so-called timing residuals) contain information about the dynamical space-
timedistortionsofthegalaxy;thegravitationalwavesleaveacorrelatedimprintin
the timing residuals that is different from all other known sources of timing
irregularities. Three major collaborations (the Pulsar Timing Arrays, or PTAs) of
radio astronomers and gravitational-wave theorists have formed around the world
during the last decade. The Australian-based Parkes PTA uses the data from the
Parkestelescope;theNorthAmericanNANOgravcollaborationutilizestheGreen
Bank Telescope and Arecibo, while the European PTA is fundamentally a multi-
telescope project that uses radio dishes at Nancay in France, Jodrell Bank in the
United Kingdom, Effelsberg in Germany, Westerbork in The Netherlands, and
Sardinia in Italy. The super-array, called the International PTA, has also been
formed and will utilize the timing residuals obtained by all of the PTAs to carry
out a joint search for gravitational waves.
v
vi Supervisor’sForeword
The thesis presented in this book deals with how one takes thousands of
seemingly random timing residuals that are measured by pulsar observers, and
extracts information about the presence and character of the gravitational waves
with months-to-years periods that are washing over our galaxy. During his Ph.D.
work at Leiden Observatory, Rutger van Haasteren developed from scratch a
sophisticatedmathematicalalgorithmthatdealswiththisissue,andthatiscurrently
in active use within the PTA community (van Haasteren et al. 2009, Chapter 2).
Moving beyond purely theoretical work, van Haasteren studied the observational
procedure in depth (which he learned partly during his first 2-month stay in Aus-
tralia), and, together with Gemma Jansen (then a postdoctoral fellow at Jodrell
Bank), led the joint effort offive teams of pulsar observers on the European con-
tinent,tocombinetheirEuropanPulsarTimingArray(EPTA)datasetsinorderto
searchforgravitationalwaves.Thisstudyhasplacedthemoststringentpublished
limittodate(March2013)ontheintensityofgravitationalwavesthatareproduced
bypairsofsupermassiveblackholesdancingaroundeachotherindistantgalaxies,
as well as those that may be produced by vibrating cosmic strings. The signature
EPTApaper(vanHaasterenetal.2011,Chapter3)developstheprocedureofhow
totreatthedatacombinedfrommultipleradiotelescopes,thatwilllikelyserveasa
templatefortheupcomingIPTAgravitationalwavesearches.Thealgorithmofvan
Haasterenetal.(2009)hasnowbeenimplementedandfurtherdevelopedbyseveral
groups around the world: Vallisneri and colleagues at JPL, Cornish at Montana
StateUniversity,Lentati,Taylor,Gair,andothersatCambridgeUniversity,andvan
Haasteren himself. Some elements of the algorithm (in particular its emphasis on
the time domain rather than the frequency-domain formalism) have been adopted
for the recentNANOGrav study by Demorest et al. (2012).
Apart from the gravitational-wave search, van Haasteren carried out two the-
oretical projects during his Ph.D.. In the first one, he showed that PTAs are
sensitivetotheChristodouloumemoryburstsfrommergersofsupermassiveblack
holes,andestimatedtheeventratethatwillbeseenbytheongoingandfuturePTA
experiments(van Haasterenand Levin 2010, Chapter 4;similar calculations were
independently and simultaneously carried out by two other groups). A significant
part of this chapter (Sect. 3) is devoted to the methodological question that goes
beyond a particular gravitational-wave source that was considered, of how to
incorporate the timing-model fitting into the search for gravitational waves pro-
ducedbyasinglesource.Inthesecondtheoreticalproject,vanHaastereninvented
a new computational procedure for evaluating the Bayesian evidence using Mar-
kov Chains (van Haasteren, Chapter 5).
For the work described in this book, Rutger van Haasteren has been awarded
with the Gravitational Waves International Committee (GWIC) thesis prize for
2011,thatisgivenannuallytothebestthesisongravitationalwavescienceamong
those defended during that year world-wide. van Haasterens award was the first
GWIC thesis prize given for the work on Pulsar Timing Arrays.
Clayton, Australia, March 17 2013 Yuri Levin
Acknowledgments
Beforedivinginthetechnicaldetailsofmyresearch, Iwouldliketofillthispage
with some words of gratitude toward people who have not directly contributed to
theresearchinthisthesis,butwhostillhavehadapositiveeffectontheresearchin
this thesis. One of the most important lessons I have learned during my Ph.D.
research is that I do not want to be a successful scientist if I cannot have a
successful and happy life next to it. As with everything in life, it is about the
balance. The balance between passionate research and a healthysocial life in this
case. For this lesson I have to thank everyone in my social circle. Additionally, a
rich social life does not just provide distractions, but also inspiration and good
ideas.
TheSterrewacht,whereIhavespentabigportionofmydailylifeforyears,is
home to numerous colleagues that have helped me in one way or the other to
produce the work you are now reading. All of you, thank you very much for
allowingmetoenjoymyselfthere!Thereare,however,afewpeoplethatIwould
like to mention by name. First my office mate Chael. Thanks for putting up with
meforyears,andforbeingthefirstinlinetotalkscienceto.Maarten,Ihopeyou
have come to appreciate me and my great sense of humor just as much as I have
cometolikeourdailylunchbreaks.Ann-Marie,thankyouformakingMelbourne
as awesome as it was. We’ll keep that up.
Ialsowanttothankmy‘‘cordialgenoten’’forthewonderfultimeIhavealways
had with them. Some of these guys I want to name specifically. Boot,you were a
wonderful flatmate, and I will always think of our time at the Wagenstraat with
fond memories. P, the number of years of my life that I have wasted hanging out
with you I have been able to reclaim quadratically in good times. What would I
havedonewithoutyou?Ralph,squashwasalwaysahighlightintheweek,andthe
conversations were always high quality. And of course I should also mention the
good times in or outside of the pub with the standard crew members Gijs, Vuijk,
IJs, and Jap.
AtMonash,thewholegangImetthere,youallmadeitaverypleasantplaceto
work.AndthanksforintroducingmetoalltheotherthingsthatmakeMelbournea
nice place to live. Amanda, thank you for your hospitality and the good times.
Remko, naturally I cannot forget you here. I will soon drop by for an old
fashionedevening.Caroline,eventhoughithasonlybeenoneyear,thankyoufor
your love and support. Lucy, thanks for the wonderful conversations and the
vii
viii Acknowledgments
inspiration. Sonja, my dear sister, although you were far away, I have always
enjoyed our skype sessions. And finally, mom and dad: words can never describe
what you have done for me. I love you. All of you.
March 1 2011 Rutger van Haasteren
References
vanHaasterenR.,LevinY.,McDonaldP.,LuT.,2009,MNRAS,395,1005
vanHaasterenR.,LevinY.,JanssenG.H.,LazaridisK.,KramerM.,StappersB.W.,DesvignesG.,
PurverM.B.,etal.,2011,MNRAS,414,3117
vanHaasterenR.,LevinY.,2010,MNRAS,401,2372
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 General Relativity and GR Tests. . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Black Hole Binaries: Sources for GW Emission. . . . . . . 5
1.2 Pulsars and Pulsar Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Pulsar Timing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 GR Tests with Pulsar Timing. . . . . . . . . . . . . . . . . . . . 8
1.3 Current GW Experiments, and PTAs. . . . . . . . . . . . . . . . . . . . 9
1.3.1 GW Detectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Pulsar Timing Arrays . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Bayesian PTA Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.1 Modelling the PTA Data . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.2 Markov Chain Monte Carlo . . . . . . . . . . . . . . . . . . . . . 16
1.5 Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 On Measuring the Gravitational-Wave Background Using
Pulsar Timing Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 The Theory of GW-Generated Timing Residuals. . . . . . . . . . . . 25
2.2.1 Timing Residual Correlation. . . . . . . . . . . . . . . . . . . . . 25
2.3 Bayesian Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.1 Basic Ideas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.2 Removal of Quadratic Spindown and Other
Systematic Signals of Known Functional Form. . . . . . . . 29
2.3.3 Low-Frequency Cut-Off. . . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Numerical Integration Techniques. . . . . . . . . . . . . . . . . . . . . . 33
2.4.1 Metropolis Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.2 Current MCMC Computational Cost. . . . . . . . . . . . . . . 34
2.4.3 Choosing a Suitable Prior Distribution. . . . . . . . . . . . . . 34
2.4.4 Generating Mock Data. . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5 Tests and Parameter Studies. . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.1 Single Dataset Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.2 Multiple Datasets, Same Input Parameters . . . . . . . . . . . 38
ix