a few applications of model section on gw astrophysics · a few applications of model section on gw...
TRANSCRIPT
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
S.Vitale,Aug262016 3
CumulativeBayesfactor
Evidence
• EachBayesfactoristheratiooftheevidenceforthedatagiveneachofthetwomodels
S.Vitale,Aug262016 4
EvidenceformodelA,eventj
LALInference
• Theevidenceisthemarginalizedposteriorofthedatagiventhemodelandthemodel’sparameters
• IntheLVC,weveryoftenuseLALInference (Veitch+2014)tocalculatetheevidence– NestedsamplingorMCMC
S.Vitale,Aug262016 5
LALInference
• Theevidenceisthemarginalizedposteriorofthedatagiventhemodelandthemodel’sparameters
• IntheLVC,weveryoftenuseLALInference (Veitch+2014)tocalculatetheevidence– NestedsamplingorMCMC
S.Vitale,Aug262016 6
Likelihood Prior
TIGER
• GWhaveallowedusforthefirsttimetoaccessinadirectwaythedynamicalregimeofGR.– IsGRstillagooddescriptionofgravityatthoseenergies?
• TestInfrastructureforGEneral Relativity(Li+2011,Agathos+2013)• Theidea:– UsemodelsectiontoverifyifdetectedgravitationalwavesareconsistentwithwhatexpectedwithinGR
– Doesnotrequireknowledgeofalternativetheory– Testedforbinaryneutronstars(BNS)
S.Vitale,Aug262016 7
TIGER– 2
• Oneofthetwomodelswetestis,ofcourse,GR• Howisthe“GRiswrong”modelimplemented?
• Inpost-Newtoniantheory,thephasecoefficientsareknownfunctionsofthetwocomponentmassesandspins
• Onecanleavethesecoeffs freetovaryfromtheirGRvalues
S.Vitale,Aug262016 8
TIGER-3
• Introduceauxiliaryhypotheses– :thePNcoeffs 𝑖", 𝑖$, … , 𝑖& arepotentiallydifferentfromGR,whiletheothersarefixedattheirGRvalues
• ThemodifiedGR(modGR)canbethenwrittenasasumofmutuallyexclusivehypotheses
• Wewanttheodds
S.Vitale,Aug262016 9
TIGER-4
• Sincetheauxmodelsweredefinedasmutex,thenumeratorisjustthesumoftheposteriorsoftheauxmodes.
• Finallyonehas
• Trivialtoextendtomorethanonesource
S.Vitale,Aug262016 10
Theneedforabackground
• Ifourunderstandifthedatawereperfect,gettingalargeoddsinfavorofmodGR wouldbeenough
• Inpractice,whileweassumethenoiseisGaussian,itisreallynot
• RunTIGERon(simulated)GRsignalstobuildabackgroundofoddsratioinabsence ofdeviationsfromGR
• RUNTIGERon(simulated)modGR signalsandcheckhowtheoddscomparewiththebackground
S.Vitale,Aug262016 11
Results
• Oddsdistributionforindividualsources
S.Vitale,Aug262016 12
background
modGRsignals(10%addedtothe1.5PN)
FavorsmodGRFavorsGR
Results
• Cumulativeoddsdistributionforcatalogsof15sources
S.Vitale,Aug262016 13
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
S.Vitale,Aug262016 14
Neutronstarequationofstate(EOS)
• Oneofthekeyopenquestionsinastrophysics,withpotentiallylargeimpactonnuclearphysics.
• Impossibletostudyinalab• Hardtostudywithelectromagneticradiation– NeedveryprecisemeasurementofNSradius– NICERlunchedsoon,butonly1suretarget
• (Atleastconceptually)SimplerwithGWs
S.Vitale,Aug262016 15
Lineartides
• LineartideswillaffectthewaveformsinawaythatdependsontheEOS
• 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
S.Vitale,Aug262016 18FavorsalternativeEOSFavorsMS1
Nospins
Results
S.Vitale,Aug262016 19FavorsalternativeEOSFavorsMS1
For80%ofthecatalogsthe(correct)MS1modelispreferredoverPP
Alternativemodelsrakedbyincreasinghardness
Nospins
Results
• Checkedeffectofpriormismatch
S.Vitale,Aug262016 20
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
S.Vitale,Aug262016 21
Plothere
CBCformationchannels
S.Vitale,Aug262016 22
Abinarymodelselectionapproach
• Assumeonlytwoformationchannelsexist– Commonenvelope(galacticfields)– Randomencounters(globularclusters)
• Willdistinguishthemusingthe(expected,hoped?)resultingspinsorientationdistributions:– Commonenvelope->spin~(anti)alignedwithL– Randomencounters->randomspindistribution
S.Vitale,Aug262016 23
Implementation
• “Aligned”model:bothtiltanglessmallerthan10degs• “Non-Aligned”model:isotropictiltangles(excludingtheregionwherealignedistrue)
• Enforcedthroughdifferentpriorrangesintheevidencecalculation.
• Simulatesignalsfromeithertypeandbuildcumulativeoddsratio(Vitale+,2017)
S.Vitale,Aug262016 24
Results
S.Vitale,Aug262016 25
Favorsaligned
Favorsnon-aligned
NSBH
BBH
Caveats
• Canonlybuildcumulativeoddsifonebelievesonlyonechannelsispossible– Inrealitybothareprobablypossible
• Canmodifymethodtomeasuretheposteriorfractionofalignedsystems
S.Vitale,Aug262016 26
Measuringthemixturefraction
S.Vitale,Aug262016 27
Trueunderlyingfractionofalignedsources
NSBH
BBH
100NSBH200BBH
Caveats– Todos
• AssumedwhatIcalled"aligned”iswhattheuniversecallsaligned– shouldincludepossiblepriormismatch
• Canextendthemodelsothattheyalsotakeintoaccountmassratios,eccentricity,oranythingelsethatmightbeusefultodistinguish
• Canincludemorethan2models
S.Vitale,Aug262016 28
BeyondCBCs
• ModelselectioncurrentlyusedinotherLIGOgroups
• Corecollapsesupernovae:inferexplosionmechanism(Gossan+2016)
• LookforextraGRpolarizations
• Asadetectionstatistic(Lynch+2015,Kanner+2016)
S.Vitale,Aug262016 29