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ComplexandABracCve:WriCngandPloGngScalarFieldDataEvolvinginaBlackHoleSpace-Cme

KadeYoung1;PeterDiener,PhD2,3;FrankLoffler,PhD2

1DepartmentofMathemaAcs,TrumanStateUniversity2CenterforComputaAon&Technology,LouisianaStateUniversity3DepartmentofPhysics&AstronomyLouisianaStateUniversity

KadeYoungTrumanStateUniversityEmail:hky3218@truman.edu

Contact References

PredictedbyEinstein’sGeneralTheoryofRelaAvity,gravitaAonalwavesarewrinklesinspace-Amecausedbymassive,high-energyevents.Thisresearch,asawhole,isaimedatsimulaAngthegravitaAonalwavesproducedbyanExtremeMassRaAoInspiralsystemofblackholes.WiththedetecAonofthesewavesbyLIGO,andtheupcominglaunchoftheLaserInterferometerSpaceAntenna(LISA)(seefigure1),thereisaneedtosimulatethegravitaAonalwavesproducedbyparAcularsystems.ThesesimulaAonswillhelpidenAfywavesduringfuturedetecAonefforts.ThisparAcularprojectworkedwiththedataoutputbythesimulaAonineffortstoreducethesizeofthedataandproducesignificantdataplots.

Abstract

WewereabletowriteafortranrouAne,usingthesamestructureastheoriginaloutputfortranscript,tooutputallofthedatafromthesimulaAonintoanHDF5file.OutpuqngintoHDF5is,infact,effecAveinreducingthesizeofthesimulaAon’sdata.Forexample,aCeraparAcularsimulaAon,theoutputdataintheASCIIfilestookabout50GBofdiskspacewhilethesamedataoutputintoanHDF5filetook4GB.ThissizeraAowillremainthesameforallsizesofsimulaAons.UsingthedatanowwrisenintoanHDF5fileandaPythonscript,wecreateplotsofallsignificantvalues,includingtheprocessionofthesmallblackhole(seefigure3).Currently,thePythoncodethatoutputstheplotsalsocreatesawebpageoverviewofallrelevantplotsforeachsimulaAon.Figures3and4areexamplesofplotsoutputtothewebpageoverview.

Background

WhyHDF5?ThissimulaAon’scodeoriginallyoutputthedatainaseriesofASCIIfiles.Whileuseful,theseASCIIfilestakeupalargeamountofdiskspace.Also,thesimulaAonoutputsdataintoamulAtudeofASCIIfilesdependingonparameters,soitissomeAmesdifficulttofindspecificdatathatisneeded.OutpuqngthedataintoanHDF5(HierarchicalDataFormat5)filecannotonlyreducethedisksizeofthedata,butcanalsomakethedataeasiertoworkwith.SinceallthedataisinoneHDF5file,itwillalsomakewriAngcodetoplotthedataeasierandmoreefficient.

PloGngThereisalsoaneedtoproducerelevantplotsofparAculardataoutputbythesimulaAon.Theseplotsinclude:•  AplotoftheorbitoftheparAclearoundthesupermassiveblackhole•  Aplotoftheself-forcedatafordifferentlmodes•  Plotsofthesystem’sangularmomentumandenergy

ProjectDescripCon

Movingforward,wewouldliketocleanuptheplotsproducedbyourcode,aswellasproduceanimaAonandmoviescriptstoshowhowthefieldevolvesoveranenAresimulaAon.OneofourcurrentvisualizaAoncodescanonlyworkwithcircularorbitsofthesmallblackhole,butwewilleventuallyneedittoworkwithotherorbitsaswell.

FutureWork

ExtremeMassRaCoInspiralExtremeMassRaAoInsiprals(orEMRIs),refertoatwo-bodysystemofasmallblackholeorneutronstarrotaAngaroundamuchlargerblackhole.ThisprojectissimulaAnganEMRIsystemofblackholes:asmallblackholeorbiAngasupermassiveblackhole.Becauseoftheextremedifferencesinmass,thesmallblackholecanbetreatedasapointmassandthesupermassiveblackholecanbetreatedasstaAonary.ThegravitaAonalwavesproducedbythissystemcarryawayenergyandcausethesmallerblackholetospiralinwardtowardthesupermassiveblackhole.

DecomposingintoSphericalHarmonicsSinceoursystemisinthesphericallysymetricSchwarzschildbackgroundmetric,itisworthwhiletodecomposeintosphericalharmonics.ThisgivesusdifferentlandmcombinaAonstocollectdatafrom.Whendecomposingintosphericalharmonics,theindividuall-mmodesdecoupleturningthe3+1Dproblemintoasetof1+1dproblemsthatareeasiertosolve.

Results

Figure1.AnimageoftheapprovedLISAmission,agravitaAonalwavedetecAonsystemthatissettolaunchin2030.ItissupposedtobeabletodetectgravitaAonalwavesfromEMRIsystems.[1]

Figure2.Anexampleofhowspace-AmeisshapedinanEMRIsystemwithasmallblackholespiralingintowardasupermassiveblackhole.ThesmallblackholeradiatesgravitaAonalwavesasitspiralsinward.[2] Figure3.Theplotoftheorbitofthesmall

blackholearoundthesupermassiveblackholelocatedattheorigin.NoAcethatthesmallblackholeactuallyrotatesaroundthesupermassiveblackholethreeAmesforonefullorbit.

AcknowledgementsThismaterialisbaseduponworksupportedbytheNaAonalScienceFoundaAonunderawardOCI-1560410withaddiAonalsupportfromtheCenterforComputaAon&TechnologyatLouisianaStateUniversity.

Figure4.AloglogplotofthegravitaAonalself-forceacrossdifferentlmodes.Theself-forcedecreasesastheinverseofl2,whichiswhatisexpected.

[1]ESA.EuropeanSpaceAgency.Retrievedfromhsp://sci.esa.int/lisa/46425-the-lisa-spacecraC-constellaAon/[2]ExtremeMassRaAoInspirals.Retrievedfromhsps://en.wikipedia.org/wiki/Extreme_mass_raAo_inspiral

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Chart1and2.ChartsdepicAngthedifferenceindiskspaceusageandrunAmefor6differentsimulaAons.SimulaAons1,2,and3outputonedimensionaldataevery100iteraAons,whilevaryingtheamountofzerodimensionaldataevery10,100,and1000iteraAonsrespecAvely.SimulaAons4,5,and6havethesamevariaAonofzerodimensionaloutput,butonedimensionaldataiswrisenevery1000iteraAons.NoAcethat,inallsimulaAons,usinganHDF5dataformatsignificantlyreducesdiskspace.Also,withtheexcepAonofsimulaAon4,therunAmeisalsosignificantlyreducedbyusingHDF5.