Dynamics of Fe-Ni Bubbles in Young Supernova Remnants

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

DYNAMICSOFFE-NIBUBBLESINYOUNGSUPERNOVAREMNANTS

JohnM.Blondin,KazimierzJ.Borkowski,andStephenP.Reynolds

DepartmentofPhysics,NorthCarolinaStateUniversity,Raleigh,NC27695

ABSTRACT

arXiv:astro-ph/0010285v1 14 Oct 2000Observationsofcore-collapsesupernovae(SNe)haverevealedthepresenceofexten-sivemixingofradioactivematerialinSNejecta.Themixingofradioactivematerial,mostlyfreshlysynthesizedNi,isnotcomplete,whichleadstoatwo-phaseSNejectastructure.Thelow-densityphaseconsistsofFebubbles,createdbytheenergyinputfromradioactiveCoandNi,surroundedbycompressedhigh-densitymetal-richejecta.Wereportonthetheoreticalinvestigationofsupernovaremnant(SNR)dynamicswiththetwo-phaseSNejecta.We rstpresent3-dimensionalhydrodynamicsimulationsofasingleFebubbleimmersedinanouterejectaenvelope,andcomparetheresultswithpreviousworkonshock-cloudinteractions.WethenconsiderrandomlydistributedFebubbleswithanaveragevolume llingfractionof1/2.We ndthatthepresenceofFebubblesleadstovigorousturbulenceandmixingofFewithotherheavyelementsandwiththeambientnormal-abundancegas.Theturbulentenergycanbeanorderofmagnitudelargerthaninthecaseofsmoothejecta.Asigni cantfractionoftheshockedejectaisfoundinnarrow lamentsandclumpsmovingwithradialvelocitieslargerthanthevelocityoftheforwardshock.Observationalconsequencesofthetwo-phaseejectaonSNRX-rayspectraandimagesarebrie ymentioned.Subjectheadings:hydrodynamics–instabilities–shockwaves–ISM:supernovarem-nants

1.INTRODUCTION

Thepresenceoflarge-scalemixingofejectaincore-collapsesupernovae(SNe)hasbeenwellestablishedonbothobservationalandtheoreticalgrounds.Theearly,unexpectedemergenceofX-raysandγ-raysshortlyaftertheexplosionofSN1987AprovideddramaticevidenceformixingofradioactiveNithroughouttheHecoreandH-richenvelope.ExtensivemixingofNiisalsorequiredtoexplainthelightcurveandspectralobservationsofSN1987A(seeMcCray1993forareviewofSN1987A).Fromstudiesoflightcurvesandspectraofnumerouscore-collapseSNe,itisnowknownthatsuchlarge-scalemixingisnearlyalwayspresent.AnotherlineofevidenceisprovidedbystudiesofmeteoriticgraphitegrainswhichcondensedinSNejecta(Travaglioetal.1999andreferencestherein).Suchgrainsapparentlycontainedradioactive,short-livedisotopessuchas44Tiatthetimeoftheirformation,whichimpliesextensivemixingoffreshly-synthesizedmaterialdeepinthe

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

SNejectawiththeC-richlayeratthebottomoftheHecore.Thisoverwhelmingobservationalevidenceformixingisconsistentwithourpresentunderstandingofthecollapseandexplosionofmassivestars.Theneutrino-drivenRayleigh-Taylorinstabilityjustoutsidetheproto-neutronstarleadstoconvectivemotions,strengtheningthepost-bounceshockandmaybeevenmakingtheexplosionpossibleinmanycases(e.g.,Mezzacappaetal.1998;Kifonidisetal.2000).FurthermixingoccurslaterduringtheSNexplosionbecauseofRayleigh-Taylorinstabilitiesgeneratedatinterfacesbetweenstellarlayerswithdi erentchemicalcomposition(e.g.,Fryxell,Arnett,&Mueller1991;Hachisuetal.1992;Kifonidisetal.2000).

Large-scaleturbulencegeneratedduringtheexplosionappearsnottobesu cienttomixSNejectacompletely,butonlymacroscopically.InCasA,opticalobservationsrevealedthepresenceofejectawithverydi erentchemicalabundances,suchasO-,S-,Ar-,andCa-richejectaknots,whichweremacroscopicallymixedduringtheSNexplosionasevidencedbythelackofspatialstrati cationexpectedintheabsenceofmixing(e.g.,Fesen&Gunderson1996).ThemostrecentIRandX-rayobservationsofCasAprovidefurtherevidenceforthismacroscopicbutnotmicroscopicmixing(Arendtetal.1999;Douvionetal.1999;Hughesetal.2000;Hwangetal.2000).SpectroscopicobservationsofnumerousSNealsocon rmthepresenceofclumpyejecta(Spyromilio1994).DetailedstudiesofSN1987Aleadtothesameconclusion.

InSN1987A,theinhomogeneitiestakeaparticularlyinterestingform:Fe-Nibubbles(Lietal.1993),inferredfromobservationsofFe,Co,andNilines.Ni-richejectaclumps,transportedoutwardsbyturbulentmotions,areheatedbytheirownradioactiveenergyinput,andexpandintheambientsubstrateofotherheavyelements,forminglow-densityFebubbles.TheSNstructureisthenexpectedtobelikeaSwisscheese,withFebubblesoccupyingasubstantial(～0.5)fractionoftheejectavolume(Lietal.1993;Basko1994).Thesebubblesshouldleadtovigorousturbulenceandmixinginyoungsupernovaremnants(SNRs)ingeneral.

MostofejectainyoungSNRscanbeseeninX-rays,wheremodernX-rayobservatoriessuchasChandraandXMM-Newtonhavebeguntoprovidehigh-qualityinformation.Interpretationoftheseobservationsmustbedoneintheframeworkofappropriatehydrodynamicalmodels.ButrealisticsimulationsforyoungSNRs,whichincludethepresenceofFebubblesinSNejecta,arelacking.Wereporthereonsuch3-dimensionalhydrodynamicalsimulations(preliminaryresultsbasedon2-DsimulationswerereportedbyBorkowskietal.2000).OurgoalistostudythebasichydrodynamicsoftheinteractionbyinvestigatingasingleFebubble,andtoexplorehowthepresenceofmultipleFebubbleschangestheglobaldynamicsofyoungSNRs.

2.HYDRODYNAMICSIMULATIONS

Weuseaparallelversion(implementedwithMessagePassingInterface)oftheVirginiaHy-drodynamics(VH-1)numericalcodetostudythecomplexdynamicsofSNRswithFebubbles.Thesimulationswerecomputedonasphericalgridof4003zonescoveringanangularspanof1.6stera-

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

dians.ThisresolutioniscomparabletothesimulationsbyChevalieratal.(1992)thatusedagridof2562.Ahigherresolutionsimulationwouldshowmoresmallscalemixing,butthelarge-scaledynamicsoftheproblemwouldnotchange(Chevalieretal.1992).Periodicboundaryconditionswereappliedinboththeθandφdirections.Thischoiceforθissomewhatunorthodox,butwewishedtoavoidthenumericalartifactsassociatedwiththecoordinatesingularityatθ=0,sowecenteredourgridabouttheequator(0.3π<θ<0.7π).Weexperimentedwithotherboundaryconditions(e.g.,re ectingorzerogradients),buttheyprovedunsatisfactoryforvariousreasons.Thenumericalgridwasexpandedtofollowtheforwardblastwavesotheevolutioncouldbetrackedformanyexpansiontimes.

Thesimulationswereinitializedwithaself-similardrivenwave(SSDW)solution(Chevalier1982)withanejectadensitypowerlawofn=9expandingintoeitherauniformambientdensity(anambientdensitypowerlawofs=0)orarelicstellarwind(anambientdensitypowerlawofs=2).Theradialboundaryconditionsweresettomatchthesepowerlaws.Thisself-similarstructurehasthefollowingcomponents:anouterblastwave,awavy(dynamicallyunstable)contactdiscontinu-itybetweentheshockedambientmediumandtheshockedSNejecta,andaninnerreverseshock.Fortheseparameters,theforwardshockdeceleratesaccordingtoRs∝t6/7(t6/9fors=0),andthereverseshockislocatedataradiusof0.785Rs(0.842Rsfors=0).Theinitialconditionsaresphericallysymmetric,sothenarrowshellofshockedejectastartso smoothbuteventuallyshowssignsofconvectiveinstability(Chevalieretal.1992).

3.DYNAMICSWITHASINGLEBUBBLE

HydrodynamicalsimulationsareshowninFigure1ofaSSDW(n=9,s=2)withasingleFebubbleinthesupersonicejecta.Thebubble,withafractionalradiusof0.4(theradiusofthebubbleis0.4timesthedistanceofthecenterofthebubblefromthecenteroftheSNexplosion),is100timeslessdensethantheambientSNejectaataradiuscorrespondingtothecenterofthebubble.Thepressureinsidethebubbleisequaltothepressureofthesurroundingejectainordertominimizemotions,buttheMachnumberofexpansionisstillrelativelyhighwithinthebubble.

TheinitialcontactbetweentheFebubbleandthereverseshockisillustratedinFigure1(left).Whentheouteredgeofthebubblereachesthereverseshock,thereverseshockacceleratesintothebubblebecauseofitslowdensity,whileararefactionwavepropagatesbackintotheshockedejecta.ThepressurebehindthereverseshockpropagatingthroughthebubbledropstomorethananorderofmagnitudesmallerthanthenominalpressurebetweentheforwardandreverseshocksinthesphericalSSDW.Thereisonlyamodestdropinpressure(comparedtothesphericalSSWD)intheshockedambientmediumaheadofthebubblebecausetheSNRexpansiontimescaleiscomparabletothesoundcrossingtimeacrossthebubble.Thehighpressureoftherelativelytenuousambientgasthendrivesdenseshockedejectadeepintothebubble’sinterior.ThissituationisRayleigh-Taylorunstable,whichleadstovigorousmixingofdenseshockedejectawiththelow-densityshockedFefromthebubbleandtheshockedambientgas.Thisenhancedmixingisevident

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

inthemiddle-leftframeofFigure1.Notethatalthoughthereverseshockismovinginwardsinthisexpandingframe,atnotimeinthesimulationisgasevermovingradiallyinwardsinthe xedframeofthe

explosion.

Fig.1.—DynamicalinteractionofanFebubblewithaSSDW.These2Dslicesthroughthecenterofthebubblearecoloredaccordingtogasdensity,withalogarithmicscalespanningarangeof

3.5ordersofmagnitude(yellow=high,blue=low).Theblacklinesmarkthesurfaceoftheforwardandreverseshocks.Thethinbluestripontherightofeachpanelmarkstheundisturbedambientgasbetweentheforwardshockandtheedgeofthenumericalgrid.Notetheslightdeviationoftheshockfromspherical.

Eventuallythereverseshockre ectso thebottomofthebubble(middle-rightpanelofFigure

1)andpropagatesbackthroughthelayerofmixedgaswithashockMachnumberof～1.5.Thereverseshockisalsotransmittedintothedenseejecta,reformingthethinlayerofshockedejectapresentintheinitialSSDW.ThebottomedgeofthebubbleisdrivenbackouttotheoriginalSSDWbythehighdensityoftheejecta,andintheprocesstheextendedlayerofmixedgasinsidethebubbleissweptupandcompressedintoathinlayer.

Theshockre ectedfromthebubble’sbottomeventuallyovertakestheblastwaveandthelayerofshockedejectaispushedbacktotheoriginalradiusofthereverseshock.Thismarksthetransitionbacktotheoriginalself-similarstage,andtheendofthetransientstageassociatedwiththebubble’spresence.

Whatislessapparent,butperhapsmostimportant,inthissimulationistheroleoftheobliqueshocksalongthebubblewallsingeneratingvorticity.Asthereverseshocktraversesthelow-densitybubble,itdrivesanobliqueshockintothewallofdenseejectasurroundingthebubble.Thisobliqueshockgeneratesvorticityatthebubble’sboundary,andthethinlayerofshockedejectaalongthebubble’swallquicklybecomesunstable.Thise ectismostpronouncedalongthesidesofthebubblewherethetransmittedshockisveryoblique.Bythetimethebubblehasbeencompletelyshocked,thisexcessvorticityhaspiledupinathickringwitharadiusslightlysmallerthantheoriginalFebubble,asshowninFigure2.Itisthistorusofhighvorticitywherethemostvigorous

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

Fig.2.—A2Dslicethroughthesinglebubblesimulation,showingthestrongvorticitygener-atedinatorusaroundthesideofthebubble.Thecolorcorrespondstovorticity(red=positive,blue=negative,white=0).Theslightlyobliqueforwardandre ectedreverseshocksshowupasthinlinesofredandblue.Thistimesliceisthesameasthemiddle-rightpanelinFigure1.

mixingoccurs.Thismixingcanleadtorelativelylargevelocities,withsomeshockedejectatravelingoutwards50%fasterthanthegasimmediatelybehindtheforwardshock.

Ahydrodynamicalproblemofaplaneshockinteractingwithalowdensityspherical(orcylin-drical)bubblehasbeenofinteresttothe uiddynamicscommunity.Experiments(e.g.,Haas&Sturtevant1987)andhydrodynamicalsimulations(e.g.,Quirk&Karni1996)revealedhowvortexlines(forcylindricalbubbles)andvortexrings(forsphericalbubbles)forminthisinteractionpro-cess,althoughacompleteunderstandingofthiscomplexinteraction(includingdetailsofmixingofbubble’smaterialwiththeambientmedium)isstilllacking.Althoughgeometryanddynam-icsinoursimulationsaremorecomplexthanintheseidealizedexperimentsandsimulations,theemergenceofvortexringsinoursimulationsisinqualitativeagreementwithresultsreportedintheliterature.WereferthereadertoarecentreviewbyZabusky(1999)forfurtherdetailsaboutgenerationofvorticityinshock-acceleratedinhomogeneous ows.

Thishydrodynamicalproblemofashockinteractingwithalowdensitybubblecanbecomparedwiththemoreoftenstudiedproblemofashockinteractingwithanoverdensecloud(e.g.,Kleinetal.1994;Xu&Stone1995;seealsoZabusky1999andreferencestherein).Inbothcasestheimportantlong-termresultoftheshockinteractionisthegenerationofvorticityandarapidmixingofthegasinsideandoutsidethebubble/cloud.ThisisdemonstratedinadramaticfashionbelowwhenweconsiderSNejectawithmultiplebubblesinsteadofasinglebubble.

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

4.DYNAMICSWITHMULTIPLEBUBBLES

AmorerealisticmodelofFebubblesinSNejectashouldincludemultiplebubblesoccupyingasubstantialfractionoftheejectavolume.Wehaveevolvedsuchmodelsforboths=0(Figure

3)ands=2(Figure4).Intheseexamples,bubbleswithafractionalradiusof0.2andwithauniformdensity100timessmallerthantheejectadensityaredistributedrandomlyintheejecta,withanaveragevolume llingfractionof～0.5.Wetrackedthe llingfractionbycomputingthefractionalareaoccupiedbybubblesataradiusof0.5Rs.Duetotheclusteringofbubblescreatedbytherandomnumbergenerator,the llingfractionwentashighas0.7andaslowas0.3,butaveragedreasonablycloseto

0.5.

Fig.3.—DynamicalinteractionofmultipleFebubbleswithaSSDWpropagatingthroughauniformambientmedium(s=0).These2Dslicesthroughthecenterofthesimulationshowthegasdensity(red=high,blue=low)alongwithpressurecontoursmarkingthelocationoftheforwardandreverseshocks.

Theoutershockwaveisrelativelyuna ectedbythepresenceoftheFebubblesinthesesimulations;theshapeoftheoutershockremainsrelativelysphericalandthedecelerationparameter(Vt/Rs)iswithinafewpercentoftheanalyticsolutionof6/7forasphericalSSDWwithn=9ands=2(6/9fors=0).ThetimeevolutionofthedecelerationparameterfrombothrunsisshowninFigure5.TheSSDWhasbeenevolvedmorethansixordersofmagnitudeinradius,requiring30,000timesteps,inordertoallowtheblastwavetoreachaquasiself-similarform(seethetime-dependenceofturbulentenergydensityinFigure9).

Incontrasttotheforwardshock,thepresenceofmultiplebubblesdramaticallyaltersthereverseshockandmakestheinteractionregionveryturbulentandinhomogeneous.Fromtheresultsofthesinglebubblesimulation,weexpectthepositionofthereverseshocktovaryrandomlyonascaleofordertheradiusofthebubbles.Thisvariationisillustratedinthe2Dslicesofthemultiple

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

Fig.4.—DynamicalinteractionofmultipleFebubbleswithaSSDWpropagatingthrougharelicwind(s=2).These2Dslicesthroughthecenterofthesimulationshowthegasdensity(red=high,blue=low)alongwithpressurecontoursmarkingthelocationoftheforwardandreverseshocks.Notetherelativelycommonprotrusionsthroughtheforwardshockdrivenbyclumpsofshockedejecta.1

0.9

deceleration0.80.70.6

0.5

0.4S = 0S = 21101001000

time100001000001e+06

Fig.5.—Timeevolutionofthedecelerationparameter(Vst/Rs)forthesimulationswithmultiplebubbles.ThestraightlinescorrespondtotheanalyticvaluesofthedecelerationparameterforthecorrespondingsphericallysymmetricSSDW.

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

bubblesimulationshowninFigures3and4.Thedeviationscaninfactbemuchlargerthanabubblediameterbecauseoftheoverlapofbubbleswhenthe llingfactorislarge.Inthes=2modelthereverseshockcameclosetotheinnerradialboundaryat0.5Rsatseveraltimesduringthesimulation.Inthes=0modelwewereforcedtoextendtheradialgridbeyond0.5Rsinordertokeepthereverseshockcontainedwithinthesimulationdomain.Inadditiontoastrongvariationintheradiusofthereverseshock,theaverageradiusofthereverseshockissigni cantlysmallerthanintheSSDWsolution.Theaveragewidthoftheinteractionregiongrowsby～50%duringthe rsthalfofthesimulations,fromtheanalyticvalueof0.21toanaveragevalueof0.31fors=2andfrom0.16to0.26fors=0.

Angle-averagedradialpro lesofdensity,turbulentenergy,velocity,andpressurefors=0(Fig.6)ands=2(Fig.7)quantitativelydemonstratehowthepresenceofFebubblesa ectstheSNRstructure.Densityandvelocitypro lesareremarkablysmoothwhencomparedwithanalyticandnumericalsolutionsforhomogeneousejecta.Aspatially-distinctshellofshockedejectavisibleinthesesolutionsisnolongerdiscernibleinsimulationswithbubbles.Thisnearlycompleteobliterationofradialstructureisnotsurprisinginviewoftheirregularshapeofthereverseshockjustdiscussed.Theincreaseinthewidthoftheinteractionregionmentionedaboveismostclearlydemonstratedbythebroadpressurepro les.Angle-averagedpressuresaregenerallylowerthanforhomogeneousejectabecauseofthepresenceofunshockedejectawithnegligiblepressurethroughouttheinteractionregion.Inthevicinityoftheblastwaveangle-averagedpressureisalsolowerbecauseofthepresenceoftheunshockedambientgaslocatedbetweentheblastwaveprotrusions.

Theirregularshapeofthereverseshockhasanimportante ectonthedynamicsoftheSNR.Ifaregionofinterbubbleejectaencountersarelativelyobliquereverseshock,itwillbedeceleratedlessthanitwouldinasphericallysymmetricSSDW.Thisdenseregionwouldthenpropagatethroughtheintershockregiontoproduceaprotrusionoftheforwardshock.Ine ect,thegeometryoftheinterbubbleejectaproducedsmalloverdenseregionsthatbehavedmorelikeclumpswithinlow-densityejectathanbubbleswithinhigh-densityejecta.Theregionsofinterbubbleejectathatappearedtohavethemoste rgerregionsofejectawithoutbubblesresultedinarelativelyplanarreverseshock,whilesmallerregionsofejectabetweenbubblesdidnotsigni cantlyperturbtheintershockregion.

However,eveninthemostfavorablescenario,regionsofdenseshockedejectatravelingthroughtheintershockregionwerequicklydisruptedby uidinstabilitiesandultimatelyhadaminimalimpactontheforwardshock.DenseclumpsbeingslowedbythemoretenuousshockedambientgasareRayleigh-Taylorunstable,whileshear owaroundtheclumpscreatesKelvin-Helmholtzinstability.Bothprocessesacttospreadouttheclumplaterallyandincreasethedrag.Theresultisthatanydenseclumpcreatingaprotrusionoftheforwardshockisalmostimmediatelyshearedapart,withtheremainingpiecesquicklyadvectedbackintotheintershockregion.Notethatthesesameprocessesareresponsibleforshapingtheshellofshockedejectainthecaseofspherically-symmetricejecta(Chevalieretal.1992).IntheabsenceofFebubbles,however,thedragwithin

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

density

turbulent energy

velocity

pressure2010.150.10.0501.20.80.400.80.60.4

0.2

00.60.70.8

radius0.911.1

Fig.6.—Angle-averagedradialpro lesfors=0,comparingthe3DFe-Nibubblesimulation(solid

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

400

density

turbulent energy

velocity

pressure2010.150.10.0500.80.400.80.60.4

0.2

00.60.70.8

radius0.911.1

Fig.7.—Angle-averagedradialpro lesfors=2,comparingthe3DFe-Nibubblesimulation(solid

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

theintershockregionpreventedtheshockedejectafromgettinganywhereclosetotheshock

front.Fig.8.—DeformationsoftheforwardshockduetoFebubblesintheSNejecta,fors=0(left)ands=2(right).

TheimpactoftheseejectaclumpsontheshapeoftheforwardshockisshowninFigure8.Themostpronounceddeformationsoftheforwardshockwererelativelysmallwavelength(lessthanabubbleradius)protrusionsdrivenbyclumpsofshockedejecta.Someoftheseprotrusionspushedtheforwardshockoutanextra15%,whilelongerwavelengthvariationsintheradiusoftheforwardshockwerelimitedtoonlyafewpercent.Angle-averagedpro les(Figs.6and7)showthat≤5%excursionsoftheblastwavearecommon.

Wang&Chevalier(2000)arrivedatsimilarconclusionsregardingclumpyejecta,namelythatevenextremelyoverdensecloudshaverelativelylittlee ectontheforwardshock.Theyused2Dsimulationstostudytheevolutionofasmall,densecloudplacedintheejectaofaTypeIaSNmodelinwhichthenominalejectaaredescribedbyanexponentialdensitypro le.Aslongassu cientspatialresolutionwasprovided,theiroverdenseclumpswere attenedoutandbrokenupby uidinstabilitiesbeforetheyreachedtheshockfront.In3Dandwithhighernumericalresolution,thisprocessshouldhappenevenfaster.

Thedynamicsinthesemultiple-bubblesimulationsappearmuchricherthanisolatedbubbles

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

0.2

turbulent energy density0.150.1bubble ejecta0.05

smooth ejecta

01101001000

time100001000001e+06

Fig.9.—Timeevolutionoftheturbulentenergydensitywithintheintershockregion,forthesimulationswithmultiplebubbles.Dashedlines:s=0.Solidlines:s=2.

orcloudsalone.Inthemultiplebubblesimulationsthepropagationofthereverseshockthroughbubblesandaroundinterbubbleregionsleadstoasubstantialamountofturbulenceintheintershockregion.Wetrackedtheturbulentenergydensityintheintershockregionbysummingupthetransverse(non-radial)kineticenergyineachzonebetweenthereverseandforwardshocks.Weadjustedthisvalueby3/2toaccountfortheradialcomponentoftheturbulent ow(i.e.,we

2～v2～v2).assumeallthreecomponentsoftheturbulent owhavecomparablemagnitude:vrφθ

Thisaveragewasthennormalizedbythekineticenergydensity owingthroughtheshockfront,ρoVs2.TheresultsareplottedasafunctionofradiusinFigures6and7,andasafunctionoftimeinFigure9.Incontrasttothecaseofhomogeneousejecta,theturbulentregionisnolongerrestrictedtotheshockedejectaandtheadjacentshockedambientgas.Theturbulenceextendsacrossthewholeinteractionregion,asimpliedbybroad,slowlyvaryingturbulentenergypro les.Theaverageturbulentenergydensitygrowsrelativelyslowly,buteventuallyreachesasigni cantfraction(>10%)oftheenergydensityassociatedwiththeforwardshock.

5.OBSERVATIONALCONSEQUENCES

5.1.GasTemperatureandVelocity

TheirregularshapeofthereverseshockhasimportantimplicationsregardingtheX-rayspec-trumproducedbytheseSNRmodels.Anydeviationfromasphericalshockwilldecreasetheshockvelocityandhencethepostshocktemperature.FromFigures3and4weseethatthiswillbemildly

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

importantfortheforwardshock,butcanbeexpectedtohavedramatice ectsforthereverseshock.Furthermore,asthereverseshockmovesbackwardthroughabubble(intheexpandingframe),theshockvelocitycanbehigherthaninthesphericalcase,resultinginhigherpostshocktemperatures(butwithsmallemissionmeasurebecauseofthelowdensity).

Toestimatethesee ectswithoutundertakingthecomplicatede ortofcalculatingX-rayspec-tra,wehavesummeduptheemissionmeasure(EM)foreachzoneinthesimulation,andplottedthisasafunctionoftemperatureandradialvelocity(scaledtothepostshocktemperatureandshockvelocity).(ThisisonlyaveryapproximateprocedureasweneglectedvariationsinthemeanmolecularweightbetweenFebubblesandtheambientejecta.FordetailedcomparisonswithX-rayobservationsonealsoneedstoconsiderelectrontemperaturewhichisgenerallylowerthanthemeangastemperaturediscussedhere.)

Theresultsforboththes=2ands=0multiplebubblesimulationsareshowninFigures10and11.SuperimposedontheseplotsarethecurvescorrespondingtoemissionfromsphericallysymmetricSSDWs.Inbothcasesthesecurvesarecomposedoftwopieces,onefortheshockedejectaandonefortheshockedambientgas.Shockedgasimmediatelybehindtheforwardshockislocatedatlog(T)=0andV=0.75.Forthes=2casethegastemperatureintheSSDWdecreaseswithincreasingdistancefromtheforwardshock,whiletheoppositeholdsfors=0.Shockedejectaimmediatelybehindthereverseshockarelocatedatlog(T)= 1.76andV=0.82anddecreaseintemperatureawayfromtheshockinthecaseofs=2.Fors=0,theshockedejectastarto atlog(T)= 0.75andV=0.95andincreaseintemperatureawayfromtheshock.Despitethesedi erencesinthesphericallysymmetricmodels,theemissionmapsfromthe3Dsimulationswithmultiplebubblesappearrelativelysimilar.InbothcasesX-rayemittinggasissigni cantlyspreadoutintemperature.Thisismostdramaticinthes=0case,forwhichthereisnocoolgasinthesphericalsolution.

ThereisalsoalargespreadintheradialvelocityoftheX-rayemittinggas,particularlyforthecaseofs=0.Inbothsimulationstheradialvelocityoftheshockedambientgasisspreadtolowervelocitiesasaresultofprotrusionsintheforwardshock,whiletheradialvelocityoftheshockedejectaisspreadtohighervelocities.Inthecaseofs=0,thebulkoftheX-rayemittingejectaistravelingfasterthantheforwardshock.

5.2.SNRMorphology

ToprovideaqualitativeestimateofhowFebubblesmighta ecttheobservedmorphologyofSNRs,wecreatedavolumerenderingoftheemissionmeasureofshockedgascomputedfromthelastframeinourmultiple-bubblesimulations.WhiletheactualemissionobservedfromaSNRwillalsodependonthelocaltemperature,abundance,andionization,theemissionmeasureprovidesasimple,convenientmeansforexploringtheX-raymorphologyimpliedbyagivenhydrodynamicalmodel.Assuch,theseimagesaremeantonlytoshowanoverallqualitativeagreementwiththe

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

Fig.10.—Amapoftheemissionmeasureasafunctionoftemperatureandradialvelocityforboththes=0ands=2simulations.Thetemperatureisscaledtothepostshocktemperature,andthevelocityisscaledtothevelocityoftheforwardshock.TheblacklinesmapouttheregionofemissionforthecorrespondingsphericalSSDW,withstarsattheirendsmarkingshocklocations.Notethatwhiletheanalyticsolutionsdi erconsiderablybetweens=0ands=2,theresultsofthe3DhydrodynamicsimulationswithFebubblesarequitesimilar.

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

1e+05

Emission Measure

Emission Measure1e+041e+031e+021e+011e+011e+00

1e-010.40.50.60.70.80.911.11.21.3-2.5-2-1.5-1-0.500.5

Radial VelocityLog (Mean Temperature)

Fig.11.—Theemissionmeasureasafunctionoftemperatureandradialvelocityforboththes=0(bottom)ands=2(top)simulations.Thetemperatureisscaledtothepostshocktemperature,andthevelocityisscaledtothevelocityoftheforwardshock.Thesolidlinescorrespondtothe3DsimulationwithFe-Nibubbles.Forcomparison,wealsoplottheemissionmeasurefromtheshockedejecta(dashedlines)andshockedambientmedium(dottedlines)inthecorresponding1Dself-similarsolutions.

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

observedX-raymorphologyofSNRslikeCasA.

TherenderedimagesshowninFigure12aredominatedbynarrow lamentsofshockedejecta.These lamentsarebarelyresolvedinournumericalsimulations,andtheyoccupyaverysmallfractionofthevolumeoftheSNR.Inthes=2model,90%oftheEMcomesfromlessthan2%ofthevolumeofshockedgas.These lamentsoftenshowupasringsorpartialringsrepresentingthecircumferenceofFebubblesastheypassthroughthereverseshock.Theseringsshowupmoreprominentlyinthes=0

simulation.

Fig.12.—Avolumerenderingofthegasdensityfromthemultiplebubblesimulations(s=0ontheleft,s=2ontheright),illustratingtheprominenceofthe lamentsofshockedejecta.ThisviewislookingdownontothesimulationsuchthattheSSDWispropagatingupoutofthepage.

6.SUMMARY

Ourprimaryconclusionisthatlarge-scaleinhomogeneitiesassociatedwiththepresenceofFebubblesinheavy-elementejectaleadtovigorousturbulenceandmixinginyoungSNRs.Theturbu-lentenergydensitymaybeincreasedbyanorderofmagnitudewhencomparedwithhomogeneousejecta.Thisturbulenceradicallychangesthespatialstructureoftheinteractionregionbetweentheblastwaveandthereverseshock.Whilethetime-averageddynamicsandthepropagationoftheforwardshockarewelldescribedbyaself-similarsolution(Chevalier1982;Chevalieretal.1992),thereverseshockgeometryandthestructureoftheshockedregionareverydi erentinthepresenceoftheFebubbles.Thereverseshockisnolongerapproximatelysphericallysymmetric,andjet-like ngersofejectacanevena ectthelocationoftheblastwave.Angle-averageddensitypro les

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

risesmoothlytowardtheremnant’sinterior,withnosignsforthepresenceofaspatiallydistinctshellofejecta.Pressureandtemperaturevariationsofordersofmagnitudearealsopresent,un-likethecaseofhomogeneousejectawhichcanbedescribedbywell-de neddensity,pressure,andtemperaturepro les.Suchlargevariationsshoulddramaticallyin uenceX-rayemission,whichdependsstronglyontemperatureanddensity.Inparticular,lowtemperature,denseejectaareparticularlye cientinproducingX-rayemission,andmaydominateX-rayspectra.Butthisemissionisgenerallyproducedbyejectawhichsu eredtheleastamountofdeceleration,sothattheirradialvelocitiesandpropermotionsmaybeevenhigherthanthatoftheblastwave.ThisexampledemonstratesthatstandardSSDWsolutionsshouldbeusedwithanextremecautionforyoungSNRswithinhomogeneousejecta.TheamountofturbulencegeneratedbythepresenceofFebubblesinSNRsmostlikelyvariesfromremnanttoremnantbecauseoflarge(～100)variationsintheradioactiveNiyieldsincore-collapseSNe.Inaddition,theamountofturbulencemightbelowerforthoseSNRswhichdidnothaveenoughtimetoentertheself-similarturbulentregime,becauseoflongtimescalesnecessarytoachieveit.ButunlessmixingofheavyelementsissomehowinhibitedduringaSNexplosion,itshouldbeclearthatone-dimensionalmodelsareclearlynotacceptableforremnantsofcore-collapseSNe,andthatmultidimensionalhydrodynamicalmodelingisessentialforunderstandingdynamicsofheavy-elementejectainsuchremnants.ItisalsopossiblethatNibubblescanbeformedinTypeIasupernovaexplosions(Wang&Chevalier2000),sothatourresultsmaybeapplicablethereaswell.

Weexpectthatsmall-scaleturbulencewillhaveastronge ectonthesynchrotronradiomor-phologyofayoungremnant.In2-DMHDsimulationsoftheSSDWphaseofayoungTypeIa(s=0)supernovaremnant,Jun&Norman(1996)foundthatturbulentenergyeventuallyrosetoabout0.6%ofthekineticenergyintheremnant,andthatrandommagneticenergyroseaswell,toalevelofabout0.3%oftheturbulentenergy.Therandommagnetic- eldenergydidnottrackthetotalturbulentenergyprecisely,butspatiallocationsofstrongturbulence(Kelvin-HelmholtzunstableedgesofRayleigh-Taylor ngers)werealsothelocationsofstrongmagnetic- eldampli- cation.Insynchrotronvisualizations,Jun&Norman(1996)alsofoundthatregionsofstrongmagnetic eldproducedstrongsynchrotronemission,buttheirsimulationusedarelativelysimpledescriptionofrelativistic-electronaccelerationandtransport.Weexpectthatmagnetic eldsinabubblesimulationwouldalsotracklocationsofturbulenceandvorticity,thatis,shouldindicatebubblewalls,andoughttobenoticeableinsynchrotronimages.Inaddition,thefarhigherlevelsofturbulentenergywe ndcomparedtosmoothejectamodelssuchasJunandNorman’sshouldresultinconsiderablyhighermagneticenergydensitiesandconsequenthighersynchrotronemissivities.However,hydrodynamicsimulationsincludingmagnetic- eldtrackingandparticleaccelerationandsubsequentevolutionwillbenecessarytomakemorede nitepredictions.

OurresultsareinqualitativeagreementwiththeobservedmorphologyofCasA,undoubtedlythebestexampleofayoungSNRwithampleevidenceforvigorousmixing.Oursimulationsareabletoreproduce lamentaryejectaemissionseeninChandraimages.TheraggedappearanceofCasA,includingits“jet”feature,mayalsobeaconsequenceofaninteractionofbubblyejectawith

Observations of core-collapse supernovae (SNe) have revealed the presence of extensive mixing of radioactive material in SN ejecta. The mixing of radioactive material, mostly freshly synthesized Ni, is not complete, which leads to a two-phase SN ejecta str

theambientmedium,andnotnecessarilytheresultofastronglyasymmetricexplosion.Itisalsotemptingtoidentifyitsringsofopticalknots(Reedetal.1995)withthemostdenseejectaclumpsattheboundariesofFebubbles.OurcurrentsimulationsarehowevernotsuitableforadetailedmodelingoftheCasAdynamicsbecauseoftheevidenceforthedynamicallyimportantshellofcircumstellarmatterinCasA(Chevalier&Liang1989).Thecircumstellarinteraction,studiedbyusthroughone-dimensionalhydrodynamicalsimulations(Borkowskietal.1996),mustbenowsimulatedin3-Dintheframeworkofbubblyejecta.AquantitativestudyofspatialmorphologyofCasA,coupledwithamoredetailedexaminationofspatialstructuresinhydrodynamicaldatasets,wouldalsobeuseful.

X-rayobservationsshouldprovideamostcompletetestofthetwo-phasemodel,becausetheyprobethebulkoftheshockedmaterial.WhilemodelingofX-rayemissionbasedonmultidimen-sionalcalculationsclearlydemandsaseparatee ort,webrie youtlinewhatmajore ectsareexpected.IfmostFeinitiallyresidesinlow-densityshockedbubbles,whileotherheavyelementsarelocatedinthedensephaseofSNejecta,thenFelinesshouldgenerallybemuchweakerthanlinesfromotherabundantheavyelements.FelinesindeedappeartobeweakerthanexpectedinCasA(Borkowskietal.1996;Vinketal.1996;Favataetal.1997)whencomparedwithstrongSi,S,Ar,andCalines,basedonnucleosyntheticyieldsofcore-collapseSNe.UnlikeintheopticalandIR,freshlysynthesizedFewasdetectedbyChandra(Hughesetal.2000;Hwangetal.2000),butitsspatialdistributionisdi erentthanthatofSi-andS-richejecta.ThismeansthatnotallFeresidedinlow-densitybubbles,eitherbecauseofmicroscopicmixingofFeatthebubbles’boundariesorbecauseradioactiveNiwasmixedtosu cientlyhighvelocitieswherethebubblegrowthwasinhibitedbyescapeofγ-raysfromNiclumps.QuantitativeanalysisofChandraCasAdata,coupledwithhydrodynamicalsimulationsandX-raymodeling,shouldprovideastringenttestofthetwo-phaseejectamodelwithFebubbles.

Asremnantsbecomeolder,turbulentmixingwillleadtoagradualstrengtheningofFelineswithrespecttootherheavyelements.EvenifFeismicroscopicallymixedwithotherelementsduringtheSNRevolution,itsionizationageshouldlagbehindthatofotherelements.Inthenextfewyears,acombinationofnewX-rayobservationsandsophisticatedhydrodynamicalandX-raymodelingshouldprovideuswithavastlybetterunderstandingofhowchemicalelementsareejectedinexplosionsofmassivestarsandhowtheyaredispersedintoambientinterstellarmedium.

WethankDickMcCrayfordiscussionsaboutFe-NibubblesinSN1987A.Thethree-dimensionalsimulationsreportedherewereperformedattheNorthCarolinaSupercomputingCenterusing100processorsofanIBMSP2.WethankNCSCandIBMfortheirgeneroussupportofcomputingresources.SupportforthisworkwasprovidedbyNASAundergrantNAG-7153.

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