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! S.Vitale,Aug262016 2 Bayesianmodelselection • GiventwomodelsAandBandGWdatad,buildoddsratio • Ifmanydetectionsareavailableanddataisindependent Cumulative Bayesfactor S.Vitale,Aug262016 3 Evidence • EachBayesfactoristheratiooftheevidenceforthedatagiven eachofthetwomodels Evidenceformodel A,eventj S.Vitale,Aug262016 4 LALInference • Theevidenceisthemarginalizedposteriorofthedatagiven themodelandthemodel’sparameters • IntheLVC,weveryoftenuseLALInference (Veitch+2014)to calculatetheevidence – NestedsamplingorMCMC S.Vitale,Aug262016 5 LALInference • Theevidenceisthemarginalizedposteriorofthedatagiven themodelandthemodel’sparameters • IntheLVC,weveryoftenuseLALInference (Veitch+2014)to calculatetheevidence – NestedsamplingorMCMC Likelihood S.Vitale,Aug262016 Prior 6 TIGER • GWhaveallowedusforthefirsttimetoaccessinadirectwaythe dynamicalregimeofGR. – IsGRstillagooddescriptionofgravityatthoseenergies? • TestInfrastructureforGEneral Relativity(Li+2011,Agathos+2013) • Theidea: – Usemodelsectiontoverifyifdetectedgravitationalwavesareconsistent withwhatexpectedwithinGR – Doesnotrequireknowledgeofalternativetheory – Testedforbinaryneutronstars(BNS) S.Vitale,Aug262016 7 TIGER– 2 • Oneofthetwomodelswetestis,ofcourse,GR • Howisthe“GRiswrong”modelimplemented? • Inpost-Newtoniantheory,thephasecoefficientsareknown functionsofthetwocomponentmassesandspins • Onecanleavethesecoeffs freetovaryfromtheirGRvalues S.Vitale,Aug262016 8 TIGER-3 • Introduceauxiliaryhypotheses – :thePNcoeffs 𝑖" , 𝑖$ , … , 𝑖& arepotentiallydifferentfrom GR,whiletheothersarefixedattheirGRvalues • ThemodifiedGR(modGR)canbethenwrittenasasumof mutuallyexclusivehypotheses • Wewanttheodds S.Vitale,Aug262016 9 TIGER-4 • Sincetheauxmodelsweredefinedasmutex,thenumeratoris justthesumoftheposteriorsoftheauxmodes. • Finallyonehas • Trivialtoextendtomorethanonesource S.Vitale,Aug262016 10 Theneedforabackground • Ifourunderstandifthedatawereperfect,gettingalargeodds infavorofmodGR wouldbeenough • Inpractice,whileweassumethenoiseisGaussian,itisreally not • RunTIGERon(simulated)GRsignalstobuildabackgroundof oddsratioinabsence ofdeviationsfromGR • RUNTIGERon(simulated)modGR signalsandcheckhowthe oddscomparewiththebackground S.Vitale,Aug262016 11 Results • Oddsdistributionforindividualsources background modGR signals(10% addedtothe 1.5PN) FavorsGR S.Vitale,Aug262016 FavorsmodGR 12 Results • Cumulativeoddsdistributionforcatalogsof15sources background modGR signals(10% addedtothe 1.5PN) FavorsGR S.Vitale,Aug262016 FavorsmodGR 13 TIGER- caveats • OddsinfavorofmodGR not necessarilyequivalentto“GRis wrong” • Couldbethatwaveformmodelisinappropriatetostartwith • Somethingweirdwiththedataorcalibration • Unaccounted(GR)physics – E.g.non-linearNStides(Essick+2016) • PriorsonGRparameters(?) • MostoftheseeffectsshowntobeundercontrolinAgathos+2013 S.Vitale,Aug262016 14 Neutronstarequationofstate(EOS) • Oneofthekeyopenquestionsinastrophysics,withpotentially largeimpactonnuclearphysics. • Impossibletostudyinalab • Hardtostudywithelectromagneticradiation – NeedveryprecisemeasurementofNSradius – NICERlunchedsoon,butonly1suretarget • (Atleastconceptually)SimplerwithGWs S.Vitale,Aug262016 15 Lineartides • Lineartideswillaffectthewaveformsinawaythatdependson theEOS • Lateinspiral,highPNorder(>6PN),highfrequencyeffect – Veryhardtomeasureforanyoneevent • Modelselectionapproach(DelPozzo+,Agathos+2014) – AssumeallNShavesameEOS – IntroduceamodelforeachproposedEOS – RankthemodelsgivenNBNSdetectios S.Vitale,Aug262016 16 Method • SimulateBNSsourceswithagivenEOS(e.g.MS1) • Consider3othermodels:PP(pointparticle),SQM3,H4 • BuildcumulativeoddsofalternativeEOSvsMS1 S.Vitale,Aug262016 17 Results Nospins FavorsMS1 S.Vitale,Aug262016 FavorsalternativeEOS 18 Results Nospins For80%ofthe catalogsthe (correct)MS1 modelispreferred overPP Alternativemodels rakedby increasing hardness FavorsMS1 S.Vitale,Aug262016 FavorsalternativeEOS 19 Results • Checkedeffectofpriormismatch Injectionmassesfrompeakedgaussian (sigma=0.05M)whileusingflatprior([1,2]M) Injectionspinsfrompeakedgaussian (sigma=0.02) whileusingflatprior([-0.1,0.1]) S.Vitale,Aug262016 20 Non-lineartides • Weinberg(XXX)suggestednon-lineartidescouldplayarole – Resonanceofchildrenmodescouldmaketheeffectenterthe waveformveryearly intheinspiral Plothere S.Vitale,Aug262016 21 CBCformationchannels S.Vitale,Aug262016 22 Abinarymodelselectionapproach • Assumeonlytwoformationchannelsexist – Commonenvelope(galacticfields) – Randomencounters(globularclusters) • Willdistinguishthemusingthe(expected,hoped?)resulting spinsorientationdistributions: – Commonenvelope->spin~(anti)alignedwithL – Randomencounters->randomspindistribution S.Vitale,Aug262016 23 Implementation • “Aligned”model:bothtiltanglessmallerthan10degs • “Non-Aligned”model:isotropictiltangles(excludingtheregion wherealignedistrue) • Enforcedthroughdifferentpriorrangesintheevidence calculation. • Simulatesignalsfromeithertypeandbuildcumulativeodds ratio(Vitale+,2017) S.Vitale,Aug262016 24 Results Favorsaligned BBH NSBH Favorsnon-aligned S.Vitale,Aug262016 25 Caveats • Canonlybuildcumulativeoddsifonebelievesonlyone channelsispossible – Inrealitybothareprobablypossible • Canmodifymethodtomeasuretheposteriorfractionof alignedsystems S.Vitale,Aug262016 26 Measuringthemixturefraction 100NSBH 200BBH True underlying fractionof aligned sources NSBH BBH S.Vitale,Aug262016 27 Caveats– Todos • AssumedwhatIcalled"aligned”iswhattheuniversecalls aligned– shouldincludepossiblepriormismatch • Canextendthemodelsothattheyalsotakeintoaccountmass ratios,eccentricity,oranythingelsethatmightbeusefulto distinguish • Canincludemorethan2models S.Vitale,Aug262016 28 BeyondCBCs • ModelselectioncurrentlyusedinotherLIGOgroups • Corecollapsesupernovae:inferexplosionmechanism (Gossan+2016) • LookforextraGRpolarizations • Asadetectionstatistic(Lynch+2015,Kanner+2016) S.Vitale,Aug262016 29
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