a few applications of model section on gw astrophysics · a few applications of model section on gw...

AfewapplicationsofmodelsectiononGWastrophysicsSalvatoreVitale

MITalsoreportingworkbyChrisVDB,WalterDP,T.Li,

MichalisA.

Theroughidea

• Givensomedataandtwo(ormore)alternativemodelsthatcouldexplainit,howtopickthe“best”model?

• UseBayesianmodelselection!– Advantages• Occam’srazorisbuiltin• Canalwaysupdateevidenceasmoredatagetsin

– Caveats• Canbecomputationallyexpensive• Yougetarelativeranking.I.e.whichofthemodelfitsbestthedata,w/oguaranteesthatanyofthemisactuallycorrect!

S.Vitale,Aug262016 2

Bayesianmodelselection

• GiventwomodelsAandBandGWdatad,buildoddsratio

• Ifmanydetectionsareavailableanddataisindependent


CumulativeBayesfactor

Evidence

• EachBayesfactoristheratiooftheevidenceforthedatagiveneachofthetwomodels


EvidenceformodelA,eventj

LALInference

• Theevidenceisthemarginalizedposteriorofthedatagiventhemodelandthemodel’sparameters

• IntheLVC,weveryoftenuseLALInference (Veitch+2014)tocalculatetheevidence– NestedsamplingorMCMC


LALInference

• Theevidenceisthemarginalizedposteriorofthedatagiventhemodelandthemodel’sparameters

• IntheLVC,weveryoftenuseLALInference (Veitch+2014)tocalculatetheevidence– NestedsamplingorMCMC


Likelihood Prior

TIGER

• GWhaveallowedusforthefirsttimetoaccessinadirectwaythedynamicalregimeofGR.– IsGRstillagooddescriptionofgravityatthoseenergies?

• TestInfrastructureforGEneral Relativity(Li+2011,Agathos+2013)• Theidea:– UsemodelsectiontoverifyifdetectedgravitationalwavesareconsistentwithwhatexpectedwithinGR

– Doesnotrequireknowledgeofalternativetheory– Testedforbinaryneutronstars(BNS)


TIGER– 2

• Oneofthetwomodelswetestis,ofcourse,GR• Howisthe“GRiswrong”modelimplemented?

• Inpost-Newtoniantheory,thephasecoefficientsareknownfunctionsofthetwocomponentmassesandspins

• Onecanleavethesecoeffs freetovaryfromtheirGRvalues


TIGER-3

• Introduceauxiliaryhypotheses– :thePNcoeffs 𝑖", 𝑖$, … , 𝑖& arepotentiallydifferentfromGR,whiletheothersarefixedattheirGRvalues

• ThemodifiedGR(modGR)canbethenwrittenasasumofmutuallyexclusivehypotheses

• Wewanttheodds


TIGER-4

• Sincetheauxmodelsweredefinedasmutex,thenumeratorisjustthesumoftheposteriorsoftheauxmodes.

• Finallyonehas

• Trivialtoextendtomorethanonesource


Theneedforabackground

• Ifourunderstandifthedatawereperfect,gettingalargeoddsinfavorofmodGR wouldbeenough

• Inpractice,whileweassumethenoiseisGaussian,itisreallynot

• RunTIGERon(simulated)GRsignalstobuildabackgroundofoddsratioinabsence ofdeviationsfromGR

• RUNTIGERon(simulated)modGR signalsandcheckhowtheoddscomparewiththebackground


Results

• Oddsdistributionforindividualsources


background

modGRsignals(10%addedtothe1.5PN)

FavorsmodGRFavorsGR

Results

• Cumulativeoddsdistributionforcatalogsof15sources


background

modGRsignals(10%addedtothe1.5PN)

FavorsmodGRFavorsGR

TIGER- caveats

• OddsinfavorofmodGR not necessarilyequivalentto“GRiswrong”

• Couldbethatwaveformmodelisinappropriatetostartwith• Somethingweirdwiththedataorcalibration• Unaccounted(GR)physics– E.g.non-linearNStides(Essick+2016)

• PriorsonGRparameters(?)• MostoftheseeffectsshowntobeundercontrolinAgathos+2013


Neutronstarequationofstate(EOS)

• Oneofthekeyopenquestionsinastrophysics,withpotentiallylargeimpactonnuclearphysics.

• Impossibletostudyinalab• Hardtostudywithelectromagneticradiation– NeedveryprecisemeasurementofNSradius– NICERlunchedsoon,butonly1suretarget

• (Atleastconceptually)SimplerwithGWs


Lineartides

• LineartideswillaffectthewaveformsinawaythatdependsontheEOS

• Lateinspiral,highPNorder(>6PN),highfrequencyeffect– Veryhardtomeasureforanyoneevent

• Modelselectionapproach(DelPozzo+,Agathos+2014)– AssumeallNShavesameEOS– IntroduceamodelforeachproposedEOS– RankthemodelsgivenNBNSdetectios


Method

• SimulateBNSsourceswithagivenEOS(e.g.MS1)• Consider3othermodels:PP(pointparticle),SQM3,H4• BuildcumulativeoddsofalternativeEOSvsMS1


Results

S.Vitale,Aug262016 18FavorsalternativeEOSFavorsMS1

Nospins

Results

S.Vitale,Aug262016 19FavorsalternativeEOSFavorsMS1

For80%ofthecatalogsthe(correct)MS1modelispreferredoverPP

Alternativemodelsrakedbyincreasinghardness

Nospins

Results

• Checkedeffectofpriormismatch


Injectionmassesfrompeakedgaussian(sigma=0.05M)whileusingflatprior([1,2]M)

Injectionspinsfrompeakedgaussian (sigma=0.02)whileusingflatprior([-0.1,0.1])

Non-lineartides

• Weinberg(XXX)suggestednon-lineartidescouldplayarole– Resonanceofchildrenmodescouldmaketheeffectenterthewaveformveryearly intheinspiral


Plothere

CBCformationchannels


Abinarymodelselectionapproach

• Assumeonlytwoformationchannelsexist– Commonenvelope(galacticfields)– Randomencounters(globularclusters)

• Willdistinguishthemusingthe(expected,hoped?)resultingspinsorientationdistributions:– Commonenvelope->spin~(anti)alignedwithL– Randomencounters->randomspindistribution


Implementation

• “Aligned”model:bothtiltanglessmallerthan10degs• “Non-Aligned”model:isotropictiltangles(excludingtheregionwherealignedistrue)

• Enforcedthroughdifferentpriorrangesintheevidencecalculation.

• Simulatesignalsfromeithertypeandbuildcumulativeoddsratio(Vitale+,2017)


Results


Favorsaligned

Favorsnon-aligned

NSBH

BBH

Caveats

• Canonlybuildcumulativeoddsifonebelievesonlyonechannelsispossible– Inrealitybothareprobablypossible

• Canmodifymethodtomeasuretheposteriorfractionofalignedsystems


Measuringthemixturefraction


Trueunderlyingfractionofalignedsources

NSBH

BBH

100NSBH200BBH

Caveats– Todos

• AssumedwhatIcalled"aligned”iswhattheuniversecallsaligned– shouldincludepossiblepriormismatch

• Canextendthemodelsothattheyalsotakeintoaccountmassratios,eccentricity,oranythingelsethatmightbeusefultodistinguish

• Canincludemorethan2models


BeyondCBCs

• ModelselectioncurrentlyusedinotherLIGOgroups

• Corecollapsesupernovae:inferexplosionmechanism(Gossan+2016)

• LookforextraGRpolarizations

• Asadetectionstatistic(Lynch+2015,Kanner+2016)


a few applications of model section on gw astrophysics · a few applications of model section on gw...

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