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

Once upon a time…

Far far away…

In the Galaxy…

We found a pulsar…

Well…in fact…there are many of them!

Up to 22/06/2017, there are over 2600 pulsars that have been discovered “officially”.

What are pulsars?

Pulsars

Credit:NRAO

Externally,pulsarsare: • Fast-rota7ngmagne7cdipoles;

• Emi=ngelectromagne7cwaveatradio

wavelength/X-ray/γ-ray…;

• Cosmic“lighthouses”;

Pulsars

Credit:NRAO

Externally,pulsarsare: • Fast-rota7ngmagne7cdipoles;

• Emi=ngelectromagne7cwaveatradio

wavelength/X-ray/γ-ray…;

• Cosmic“lighthouses”;

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

Integrated pulse profile: pulsar’s fingerprint

• Pulsarproducesperiodicpulsa.onsignals->oXentooweaktodetect;

[Lorimer&Kramer2005]

• Fold/Integratedpulsarsignalswithrespecttoitsrota.onalperiod->increasesignal

qualityandformintegratedpulseprofile;

• Pulsarsaredis.nguishedbytheirintegratedpulseprofiles(notbytheirnames!)->all

pulsarshavetheiruniqueprofileshape,justlikehuman’sfingerprint!

Integrated pulse profile: pulsar’s fingerprint

Credit:JBCA

Integrated pulse profile vs single pulses

Credit:A.Lyne

• Integratedprofilesareseentobe

consistentfromdifferentobserva7ons

andingeneralstablein7me;

• Pulseemissionsfromeachindividual

rota7ons,i.e.,singlepulses,areseento

behighlyvariablefrompulsetopulse!

OMG! �

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.);

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:

P-Pdot diagram and classification

Canonical/slowpulsars

Magnetars

Recycled/millisecondpulsars(MSPs)

Newborn

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!

Pulsar timing

The first principle of timing experiment

Credit:D.Champion �

ISM �

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!

Time model

• Componentsof7metransforma7on:

[Edwardsetal.2006]

To better understand the gravitational time dilation…

One hour on this planet is 7 years on

Earth…

Great!

I will do my PhD here.

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.

Timing stabilities

Canonical Pulsars

[ Lyne et al. 2010 ]

Verbiest et al. 2009

Millisecond pulsars

[ Desgivnes et al. 2010 ]

[ Hartnett & Luiten 2011 ]

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%) !

Constraining alternative theory of gravity

• Dipolegravita7onalradia7onwhenasymmetryinmass

components(e.g.,NS-WD):

[ Freire et al. 2012 ]

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?…?)

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 ]

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 ]

Processing pulsar data

to obtain pulse time-of-

arrival

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

Signal with polarisation

Credit: R. Karuppusamy

Credit: wikipidia

• PulsarEMsignalusuallyhassignificantpolarisa.ons

(specificorienta7onofoscilla7onduringpropaga7on);

• Thesignalcanbefullyrepresentedbysamplingindual

polarisa7ononeitherlinearorcircularbasis,andis

detectedintheformofstokesparameters(I,Q,U,V);

• Calibra7onneededtoobtaintheoriginalpolarizedsignal(correctforfeedrota7on&receiverimperfec7on):

P0

P1

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 !!!

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

Frequency-domain fitting algorithm

• Thetemplate-matchingisnormallycarriedoutinthefrequency-domain,aXer

Discrete-Fourier-Transformofthedata:

• Themodelbecomes:

• Theparameters(b,τ)arethenobtainedbyminimisingthegoodness-of-fit:

• Theerrorsareobtainedfromstandarderrorpropaga7on(covariancematrix):

Frequency-domain fitting algorithm

Credit:J.McKee

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.