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Introduction to Pulsar, Pulsar Timing, and measuring of Pulse Time-of-Arrivals
Kuo Liu Max-Planck-Institut für Radioastronomie, Bonn, Germany
Station de Radioastronomie de Nançay, Observatoire de Paris, France
IPTA 2017 Student Workshop, CIEP, Sèvres, France
26/06/2017
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We found a pulsar…
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Well…in fact…there are many of them!
Up to 22/06/2017, there are over 2600 pulsars that have been discovered “officially”.
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Pulsars
Credit:NRAO
Externally,pulsarsare: • Fast-rota7ngmagne7cdipoles;
• Emi=ngelectromagne7cwaveatradio
wavelength/X-ray/γ-ray…;
• Cosmic“lighthouses”;
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Pulsars
Credit:NRAO
Externally,pulsarsare: • Fast-rota7ngmagne7cdipoles;
• Emi=ngelectromagne7cwaveatradio
wavelength/X-ray/γ-ray…;
• Cosmic“lighthouses”;
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Pulsars
Externally,pulsarsare: • Fast-rota7ngmagne7cdipoles;
• Emi=ngelectromagne7cwaveatradio
wavelength/X-ray/γ-ray…;
• Cosmic“lighthouses”;
Credit:NRAO
Internally,pulsarsare: • Smallobjects,~20kmindiameter;
• Heavyobjects,~1solarmass;
• Mul7-layerstructure;
• Commonlybelievedtobeneutronstars;
Credit:B.Link
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Integrated pulse profile: pulsar’s fingerprint
• Pulsarproducesperiodicpulsa.onsignals->oXentooweaktodetect;
[Lorimer&Kramer2005]
• Fold/Integratedpulsarsignalswithrespecttoitsrota.onalperiod->increasesignal
qualityandformintegratedpulseprofile;
• Pulsarsaredis.nguishedbytheirintegratedpulseprofiles(notbytheirnames!)->all
pulsarshavetheiruniqueprofileshape,justlikehuman’sfingerprint!
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Integrated pulse profile: pulsar’s fingerprint
Credit:JBCA
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Integrated pulse profile vs single pulses
Credit:A.Lyne
• Integratedprofilesareseentobe
consistentfromdifferentobserva7ons
andingeneralstablein7me;
• Pulseemissionsfromeachindividual
rota7ons,i.e.,singlepulses,areseento
behighlyvariablefrompulsetopulse!
OMG! �
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Integrated pulse profile vs single pulses
Credit:A.Lyne
• Integratedprofilesareseentobe
consistentfromdifferentobserva7ons
andingeneralstablein7me;
• Pulseemissionsfromeachindividual
rota7ons,i.e.,singlepulses,areseento
behighlyvariablefrompulsetopulse!
• Varia7onofsinglepulsescanbeboth
stochas.candsystema.c(periodic
intensitymodula7on,driXingsub-pulse,
mode-changing,nulling,etc.);
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Pulsar signal and dispersion delay
Credit:A.Lyne
• Inbetweenthepulsarandtheearth,thereis
interstellarmedium(ISM),containingcold
plasmaofionizedfreeelectrons,etc.;
• Electromagne7cwavesinradiofrequency
propaga7ngthroughtheISMwillendurea
.medelay(smallergroupvelocity)depending
ontheirfrequencies.
• Thedifferencein7medelaybetweensignals
attwodifferentfrequenciesaregivenby:
wherethedispersionmeasure(DM)isdefinedbythecolumndensityoffreeelectrons
alongthelineofsight:
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P-Pdot diagram and classification
Canonical/slowpulsars
Magnetars
Recycled/millisecondpulsars(MSPs)
Newborn
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Formation and evolution of binary pulsar
Credit:D.Lorimer • Binarypulsarintheend:
1).Mildlyrecycledpulsars(P
>20ms)withheavy
companion(neutronstar);
2).Fullyrecycledpulsars(P<
20ms),i.e.,MSPs,with
lightcompanion(white
dwarf);
3).Pulsar-blackholepossible;
• Companionofbinary
pulsarsfoundsofar:white
dwarf,neutronstar,pulsar,
main-sequencestar,
planet;
Onlyblackholemissing!
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The first principle of timing experiment
Credit:D.Champion �
ISM �
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Time transformation in timing experiment
• Top-level.mingformula:
Pulsar proper time (at the centre of the
pulsar)
TOA at observatory time
(after clock correction to TT)
Transfer to solar-
system barycentre
Transfer to barycentre of
the pulsar (system)
Transfer to pulsar centre (if in a binary
system)
• Pulsephase/“counts”ofpulsesatpulsarproper7me:
Thefrac7onalpartofφ(t)isthe.mingresidual.
Pulsar is intrinsically a precise clock -> It is a clock ONLY WHEN we measure with respect to
its proper time!
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Time model
• Componentsof7metransforma7on:
[Edwardsetal.2006]
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To better understand the gravitational time dilation…
One hour on this planet is 7 years on
Earth…
Great!
I will do my PhD here.
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Timing residuals
Note: You may well have ambiguity of an integer number (i.e., lose coherency in pulse phase) if the initial values of the timing parameters are not good enough to keep
residuals within ± half a period;
• The7mingparametersarefioedbasedonalinearsingular-valuedecomposi7on,
weightedleast-squaresalgorithm,minimising:
• The7mingresidualsaresupposedtobeGaussian/whitenoisewhenthemodel&
modelparametersdescribethedataperfectly.
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Timing stabilities
Canonical Pulsars
[ Lyne et al. 2010 ]
Verbiest et al. 2009
Millisecond pulsars
[ Desgivnes et al. 2010 ]
[ Hartnett & Luiten 2011 ]
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Testing General Relativity with pulsar timing
Physics 1993
Hulse-TaylorPulsar �
[ Weisberg et al. 2010 ]
Thedouble-pulsarsystem �
[ Kramer et al. 2006 ]
The most constraining test of General Relativity (better than 99.95%) !
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Constraining alternative theory of gravity
• Dipolegravita7onalradia7onwhenasymmetryinmass
components(e.g.,NS-WD):
[ Freire et al. 2012 ]
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The gravitational wave astronomy
• Gravita7onalwavesare: a).Ripplesinthecurvatureofspace-7mepropaga7ngasawave;
b).PredictedbyGeneralRela7vityandalterna7vetheories;
c).IndirectevidencefoundfromtheHulse-Taylorpulsar’sorbitaldecay;
d).Directdetec7oncanbefrombothstochas7cbackground(GWB)and
singlesources(e.g.,supermassiveblackholepairs);
e).WindownowopenedbytheLIGOdetec.on!
• TheGWB:
a).Generatedfromtheearlyuniverse!
b).Originofmajorcomponent:s7llnotclear!
(largenumberofsupermassblackhole
binaries?Cosmicstrings?…?)
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Detecting gravitational wave with a pulsar timing array
• Apulsar7mingarray(PTA)gravita7onalwavedetector: a).ConsistofagroupofMSPswithhighprecision7ming,atdifferentskydirec7ons;
b).Lookforuniquespa.alcorrela.onsbetween7mingsignalspulsars;
c).Acomplementarydetector@NanoHertzgravita7onalwavesky;
d).Thecurrentorganisa7ons:
EuropeanPTA+ParkesPTA+Nanograv=Interna.onalPTA
[ Helling & Downs 1983 ] Credit:D.Champion �
[ Janssen et al. 2015 ]
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Gravitational wave experiments with PTA
• Detectgravita7onalwave/placeanupperlimitonGWBcan:
a).Constraincosmologicalmodelsofsupermassiveblackholepopula7on;
b).Constrainstringtensionofcosmicstringsandmodelsoftheearlyuniverse;
c).Measureproper7es(e.g.,polarisa7on,speed)ofgravita7onalwaveandtestGeneral
Rela7vity;
[ Shannon et al., 2013 ] [ Lentati et al., 2015 ]
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Processing pulsar data
to obtain pulse time-of-
arrival
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The pulsar timing signal chain
Calibra7on,RFIremoval,
folding
[ van Haasteren et al., 2011 ]
Dedispersion,detec7on,
onlinefolding
Telescope frontend
(receivers)
Pulsar backend (data
acquisition)
Data preprocessing
(PSRChive)
Timing analysis (Tempo / Tempo2 /
PINT /…)
Support staff
Hard/software engineer
Pulsar observers
Theorist / Data analyst
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Signal with polarisation
Credit: R. Karuppusamy
Credit: wikipidia
• PulsarEMsignalusuallyhassignificantpolarisa.ons
(specificorienta7onofoscilla7onduringpropaga7on);
• Thesignalcanbefullyrepresentedbysamplingindual
polarisa7ononeitherlinearorcircularbasis,andis
detectedintheformofstokesparameters(I,Q,U,V);
• Calibra7onneededtoobtaintheoriginalpolarizedsignal(correctforfeedrota7on&receiverimperfec7on):
P0
P1
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Radio interference
• Radiointerference(RFI)iscommoninobserva7onsofRadioAstronomy!
• Terrestrialar7ficialradiosignal,manypossibleorigins:satellite,plane,radiobroadcast,
wifi,cellphone,lightening,mircowave,…
• ”Mostcommon”feature:strong,narrowband,7me-variant,withzeroDM,appearin
mul7plebeams(ifany)simultaneously(near-field),…
Data needs to be cleaned to minimize systematics !!!
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Measuring TOA with template-matching
• ExpecteduncertaintyofTOAgiventhesignal-to-noise(S/N)ofdetec7onoftheintegratedprofile(averagedNpulses),whenonlyradiometernoise(whitenoise)is
ontopoftheprofile:
[ Downs & Reichley, 1983; Liu et al., 2011 ]
• Inprac7ce,TOAsaremeasuredbycross-correla7ngtheintegratedprofilewitha
templateprofile(normallyformedfromindependentobserva7ons),assumingthe
integratedprofileisdescribedbythetemplatevia:
• ThetemplateprofileneedstobeofhighS/N,ornoisefree(analy7c),oraWernoise-
removaltechnique.
Integrated profile
Baseline in data
Scaling factor
Template profile
Phase offset (TOA)
Noise component
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Frequency-domain fitting algorithm
• Thetemplate-matchingisnormallycarriedoutinthefrequency-domain,aXer
Discrete-Fourier-Transformofthedata:
• Themodelbecomes:
• Theparameters(b,τ)arethenobtainedbyminimisingthegoodness-of-fit:
• Theerrorsareobtainedfromstandarderrorpropaga7on(covariancematrix):
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Frequency-domain fitting algorithm
Credit:J.McKee
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Frequency-domain fitting algorithm
• Ifthetemplateprofileusedisnotperfect,
e.g.,ofadifferentshapefromthe
integratedprofileorofsignificantnoise,
theaccuracyoftheTOAwillbeaffected,
i.e.,lessthanexpectedfromtheory.
• InlowS/Nregion,theerrorscalesnon-linearlywithS/N,andthestandarderror
propaga7onintemplate-matching
underes7matetheuncertainty;
• Thereareotherapproaches(e.g.,theFDM
method)thatcanbeusedtoobtainamore
reliableerrores7mate.