A few applications of model section on GW astrophysics

AfewapplicationsofmodelsectiononGW
astrophysics
SalvatoreVitale
MIT
alsoreportingworkbyChrisVDB,WalterDP,T.Li,
MichalisA.
Theroughidea
• Givensomedataandtwo(ormore)alternativemodelsthat
couldexplainit,howtopickthe“best”model?
• UseBayesianmodelselection!
– Advantages
• Occam’srazorisbuiltin
• Canalwaysupdateevidenceasmoredatagetsin
– Caveats
• Canbecomputationallyexpensive
• Yougetarelativeranking.I.e.whichofthemodelfitsbestthedata,w/o
guaranteesthatanyofthemisactuallycorrect!
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Bayesianmodelselection
• GiventwomodelsAandBandGWdatad,buildoddsratio
• Ifmanydetectionsareavailableanddataisindependent
Cumulative
Bayesfactor
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Evidence
• EachBayesfactoristheratiooftheevidenceforthedatagiven
eachofthetwomodels
Evidenceformodel
A,eventj
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LALInference
• Theevidenceisthemarginalizedposteriorofthedatagiven
themodelandthemodel’sparameters
• IntheLVC,weveryoftenuseLALInference (Veitch+2014)to
calculatetheevidence
– NestedsamplingorMCMC
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LALInference
• Theevidenceisthemarginalizedposteriorofthedatagiven
themodelandthemodel’sparameters
• IntheLVC,weveryoftenuseLALInference (Veitch+2014)to
calculatetheevidence
– NestedsamplingorMCMC
Likelihood
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Prior
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TIGER
• GWhaveallowedusforthefirsttimetoaccessinadirectwaythe
dynamicalregimeofGR.
– IsGRstillagooddescriptionofgravityatthoseenergies?
• TestInfrastructureforGEneral Relativity(Li+2011,Agathos+2013)
• Theidea:
– Usemodelsectiontoverifyifdetectedgravitationalwavesareconsistent
withwhatexpectedwithinGR
– Doesnotrequireknowledgeofalternativetheory
– Testedforbinaryneutronstars(BNS)
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TIGER– 2
• Oneofthetwomodelswetestis,ofcourse,GR
• Howisthe“GRiswrong”modelimplemented?
• Inpost-Newtoniantheory,thephasecoefficientsareknown
functionsofthetwocomponentmassesandspins
• Onecanleavethesecoeffs freetovaryfromtheirGRvalues
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TIGER-3
• Introduceauxiliaryhypotheses
–
:thePNcoeffs 𝑖" , 𝑖$ , … , 𝑖& arepotentiallydifferentfrom
GR,whiletheothersarefixedattheirGRvalues
• ThemodifiedGR(modGR)canbethenwrittenasasumof
mutuallyexclusivehypotheses
• Wewanttheodds
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TIGER-4
• Sincetheauxmodelsweredefinedasmutex,thenumeratoris
justthesumoftheposteriorsoftheauxmodes.
• Finallyonehas
• Trivialtoextendtomorethanonesource
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Theneedforabackground
• Ifourunderstandifthedatawereperfect,gettingalargeodds
infavorofmodGR wouldbeenough
• Inpractice,whileweassumethenoiseisGaussian,itisreally
not
• RunTIGERon(simulated)GRsignalstobuildabackgroundof
oddsratioinabsence ofdeviationsfromGR
• RUNTIGERon(simulated)modGR signalsandcheckhowthe
oddscomparewiththebackground
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Results
• Oddsdistributionforindividualsources
background
modGR
signals(10%
addedtothe
1.5PN)
FavorsGR
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FavorsmodGR
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Results
• Cumulativeoddsdistributionforcatalogsof15sources
background
modGR
signals(10%
addedtothe
1.5PN)
FavorsGR
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FavorsmodGR
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TIGER- caveats
• OddsinfavorofmodGR not necessarilyequivalentto“GRis
wrong”
• Couldbethatwaveformmodelisinappropriatetostartwith
• Somethingweirdwiththedataorcalibration
• Unaccounted(GR)physics
– E.g.non-linearNStides(Essick+2016)
• PriorsonGRparameters(?)
• MostoftheseeffectsshowntobeundercontrolinAgathos+2013
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Neutronstarequationofstate(EOS)
• Oneofthekeyopenquestionsinastrophysics,withpotentially
largeimpactonnuclearphysics.
• Impossibletostudyinalab
• Hardtostudywithelectromagneticradiation
– NeedveryprecisemeasurementofNSradius
– NICERlunchedsoon,butonly1suretarget
• (Atleastconceptually)SimplerwithGWs
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Lineartides
• Lineartideswillaffectthewaveformsinawaythatdependson
theEOS
• Lateinspiral,highPNorder(>6PN),highfrequencyeffect
– Veryhardtomeasureforanyoneevent
• Modelselectionapproach(DelPozzo+,Agathos+2014)
– AssumeallNShavesameEOS
– IntroduceamodelforeachproposedEOS
– RankthemodelsgivenNBNSdetectios
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Method
• SimulateBNSsourceswithagivenEOS(e.g.MS1)
• Consider3othermodels:PP(pointparticle),SQM3,H4
• BuildcumulativeoddsofalternativeEOSvsMS1
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Results
Nospins
FavorsMS1
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FavorsalternativeEOS
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Results
Nospins
For80%ofthe
catalogsthe
(correct)MS1
modelispreferred
overPP
Alternativemodels
rakedby
increasing
hardness
FavorsMS1
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FavorsalternativeEOS
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Results
• Checkedeffectofpriormismatch
Injectionmassesfrompeakedgaussian
(sigma=0.05M)whileusingflatprior([1,2]M)
Injectionspinsfrompeakedgaussian (sigma=0.02)
whileusingflatprior([-0.1,0.1])
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Non-lineartides
• Weinberg(XXX)suggestednon-lineartidescouldplayarole
– Resonanceofchildrenmodescouldmaketheeffectenterthe
waveformveryearly intheinspiral
Plothere
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CBCformationchannels
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Abinarymodelselectionapproach
• Assumeonlytwoformationchannelsexist
– Commonenvelope(galacticfields)
– Randomencounters(globularclusters)
• Willdistinguishthemusingthe(expected,hoped?)resulting
spinsorientationdistributions:
– Commonenvelope->spin~(anti)alignedwithL
– Randomencounters->randomspindistribution
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Implementation
• “Aligned”model:bothtiltanglessmallerthan10degs
• “Non-Aligned”model:isotropictiltangles(excludingtheregion
wherealignedistrue)
• Enforcedthroughdifferentpriorrangesintheevidence
calculation.
• Simulatesignalsfromeithertypeandbuildcumulativeodds
ratio(Vitale+,2017)
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Results
Favorsaligned
BBH
NSBH
Favorsnon-aligned
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Caveats
• Canonlybuildcumulativeoddsifonebelievesonlyone
channelsispossible
– Inrealitybothareprobablypossible
• Canmodifymethodtomeasuretheposteriorfractionof
alignedsystems
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Measuringthemixturefraction
100NSBH
200BBH
True
underlying
fractionof
aligned
sources
NSBH
BBH
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Caveats– Todos
• AssumedwhatIcalled"aligned”iswhattheuniversecalls
aligned– shouldincludepossiblepriormismatch
• Canextendthemodelsothattheyalsotakeintoaccountmass
ratios,eccentricity,oranythingelsethatmightbeusefulto
distinguish
• Canincludemorethan2models
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BeyondCBCs
• ModelselectioncurrentlyusedinotherLIGOgroups
• Corecollapsesupernovae:inferexplosionmechanism
(Gossan+2016)
• LookforextraGRpolarizations
• Asadetectionstatistic(Lynch+2015,Kanner+2016)
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