198 9ApJ. . .346. .847C -1 5 (Lundqvist andFransson1988). SN1980Kwasfolloweddown evidence forpulsaractivity (Bandiera,Pacini,andSalvati dence forpulsaractivityinsupernovae hasbeenlacking.Radio (Bandiera, Pacini,andSalvati1984;Pacini1987;Michel, emission fromsupernovae,which hasbeentakenaspossible Kennel, andFowler1987).However, clearobservationalevi- vational effectsofapulsarnebulahavebeenemphasized assumed thattheyarerapidlyrotatingpulsarsandtheobser- M yrfor24s. putation wasroughlyequivalenttoamassaccretionrateof 14 nosity manyordersofmagnitudehigherthanthis.Theircom- photon luminosityattheEddingtonlimitandaneutrinolumi- considered indetail,theinitialconditionsformasswere a 1984), canbemodeledindetail bycircumstellarinteraction static power-lawdensitydistribution.Theseauthorsfound a While thephysicalprocessesclosetoneutronstarwere accretion ofupto10“Mmatterontoaneutron star. star. Zel’dovich,Ivanova,andNadezhin(1972)computed the enough todrivetheobjectovermasslimitforaneutron found thatthetotalaccretedmasswasconsiderable,probably pressure gradientdrivesmattertowardtheneutronstar.He (1971) emphasizedthatneutrinolossesinthevicinityof neutron stardecreasethepressureinthatregionso matter fromthesupernovatowardneutronstar.Colgate form insupernovae,therewerecalculationsofthefallback 0 0 The AstrophysicalJournal,346:847-859,1989November15 © 1989.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. More recentworkonneutronstarsinsupernovaehas Soon aftertherecognitionthatneutronstarsarelikelyto 12 38-1 _4 42-1 56 Subject headings:stars:accretion—neutronsupernovae accreting envelopeislargerthanthemagneticpressureofa10Gneutronstarfield. rotation duringthefallbackprocess.Throughoutearlyaccretionphases,pressureatbaseof so thatitsenergycanberadiatedawayinaboutayear.Thistimescalewouldlengthenedbyeffectsof reduce orevenreversetheinflowoutsideshockedenvelope.Theenvelopemassissmallatanage>0.5yr, nosity attheEddingtonlimitforaheavyelementgas,3.5x10ergss,isexpected.Thisluminositycan begin todiffuseoutfromtheshockedregion.Whileanenvelopeispresentaroundneutronstar,alumi- age of7months,theshockradiusreachesradiationtrappingininflowsothatcan by ashockwaveisreleasedneutrinolosses.Whentheaccretionratedropstoabout3x10Matan solutions inwhichgravitationalenergygeneratedbysubsonicinfallthroughanextendedenvelopebounded trapped intheflowandneutrinolossesareimportantclosetoneutronstarsurface.Wefindsteadystate the largeaccretionratesoccurringduringearlyphases(3x10"to310Myr),radiationis more smaller.ThetimescaleforthisaccretioninSN1987Aisafewhours.Atanageofabout10days, radiative diffusionbecomesimportantandthepressureforcesarenolongerabletolimitaccretion.For this phasemaybeabout0.1M;formorenormalTypeIIsupernovae,themassafactorof100or ginally boundgasfallsbackoraspressureforceslimittheaccretion.TheeffectofNiheatingonatimescale of daysistoreducetheaccretionrate.ForparametersrelevantSN1987A,totalmassfallbackduring peaks whenthereverseshockwavereachesneutronstarandsubsequentlysteeplydeclineseitherasmar- trate onfallbackafterareverseshockwavemakesitswaytothecenterofsupernova.Therate clusion. Fallbackduringthisearlyphasedependsontheunknownexplosionmechanism,sohereweconcen- explosion islikelytounbindsurroundingcorematerial,althoughearlyneutrinolossescouldaffectthiscon- 0 0 0 © American Astronomical Society • Provided by the NASA Astrophysics Data System Accretion ofmatterontoaremnantneutronstaratthecentersupernovaisinvestigated.Theinitial I. INTRODUCTION NEUTRON STARACCRETIONINASUPERNOVA Department ofAstronomy,UniversityVirginia Received 1989January20;acceptedMay22 Roger A.Chevalier ABSTRACT 847 46 39- 37_1 Colgate’s arguments,Michel (1988) estimatedthefallbackrate mass infall.Whilepressureforces playedanimportantrolein magnetic effectsmayberesponsible forturningaroundthe for aneutronstarandhesuggested thatneutrinoheatingand back couldincreasethetotal massovertheupperlimit phenomenon. Colgate(1988) reemphasized thepointthatfall- supernova, andtherehasbeen renewedinterestinthefallback study ofneutronstaraccretion,ifitdoestakeplacein this energy ofonlyabout8x10ergs. “injection” periods.A0.5speriodcorrespondstoarotational pulsar phase,itisplausiblethattheyarebornwiththeir (Narayan 1987;EmmeringandChevalier1989).Whileneutron many pulsarsare“injected”withperiodsof0.5sormore early times.Recentstudiesofpulsarstatisticshaveshown that stars couldbebornrapidlyrotatingandspindowninanon- cases isthattheneutronstarrelativelyslowlyrotatingfrom energy inputfromapulsar(Chevalier1987).TheHalumi- nosity inthiscaseisabout3x10ergss^ slower declineover4yr(Rupenetal1987),whichsuggests compatible withradioactiveenergyinput,SN1986Jshoweda complete wavelengthcoverage.WhileSN1980Kand steady luminositysourceinSN1987A,wherewehavemore yr (UomotoandKirshner1986)withoutshowinganyevidence of steadypulsarenergyinput.Stronglimitscannowbesetona to anHaluminosityof2x10ergssatagenearly 1987A showeddeclinesoveraperiodofalmost2yrthatare The proximityofSN1987Ashouldmakepossibleadetailed A possiblereasonfortheapparentlow-energyinputinmany 198 9ApJ. . .346. .847C w 6 5 where aand/?isdimensionlessconstant. because the samedimensionsasEandK.Thisispossibleifs =2 below itsequilibriumvalueso thatthereissomeinitialinfall. is thenadimensionlessconstant.Theinitialconditionsoutside For smallervaluesofathe neglectoftheinfallbecomes In anactualsituation,thecore pressuremaydropsomewhat pressure the explosionaretakentobehydrostaticequilibriumwith the GM, whereGisthegravitationalconstant,canbeexpressed in increasingly accurate. resulting shockwaveexpandsasapowerlawintime K givenbyp=Kr~,wherewisaconstant(Sedov1959).The explosion inapower-lawdensityprofilealreadydetermines effects ofacentralmassonanexplosion.Theproblem two parameters,theenergy£,andinitialdensityparameter case wheretheflowisself-similarinordertoestimate computations. Inasimplifiedtreatmenthere,weexamine explosion wouldinvolvenumericalworkincludingequationof Colgate (1971)hasalreadynotedthedifficultieswithnumerical over averylargerangeintemperature,density,andradius. state, radiativetransport,neutrinolosses,andhydrodynamics mathematical detailsmaywishtobeginwiththissection. Throughout thispaper,weuseastandardneutronstarmassof discussed in§IV.Effectssuchasrotation,neutronstarvelo- period in§III.Theaccretionofmatterontheneutronstaris imations aremadesothatsemianalyticmethodscanbeused. electron scatteringEddingtonlimit,whichis may formaroundtheneutronstar.Pinto,Woosley,and which alsosuggestsfuturework.Thereaderuninterestedin major conclusionsofthispaperaresummarizedin§VII, cities, andmagneticfieldsarebrieflytreatedin§V.InVI,we M =1.4M©andradiusr10cm. novae andmentionthepossibilityofacentralblackhole.The discuss therelevanceofresultstodifferentkindssuper- The explosionphaseistreatedin§IIandthelaterfallback the fallbackphenomenon,althoughanumberofapprox- mass (setto1.4M©),cisthespeedoflight,andkopacity. thetical pulsarwouldbesmotheredbyinfallforthefirst0.14yr on theassumptionofballisticmotion.Hefoundthatahypo- where Gisthegravitationalconstant,Mneutronstar and thatsubsequentlyadiskwithmassoforder10“M© Ensman (1988)notedtheplausibilityofalateluminosityat 848 ns A centralmass,M,canbeaddedtotheflowifparameter A fullcalculationoftheneutronstaraccretionduring Our purposehereistogiveamoredetaileddescriptionof ^Edd “' 4tüGMc © American Astronomical Society • Provided by the NASA Astrophysics Data System a K R= At s 3 = 3.5x10 II. THEEXPLOSIONPHASE a = r —~— GMK GMK 21 E 0.2 cmg 1/(5-s) 2 /(5-s) , t ergs s (2.1) (2.3) (2.2) CHEVALIER yi46)l3 2 2 1/3 are erroneous. tions ofCarrusetalarenotisentropic andwebelievethatthey at thecontactdiscontinuity where U=rj.They1.5solu- y =1.5thepostshockflowis expected tobeisentropic.Thisis perty appliestothecentral region oftheshockedflow.For true inoursolutionsandthepressure anddensityremainfinite entropy attheshockfront;wenotethatp/poct'~. For behavior canbeobtainedbyexaminingtheevolutionof the this point,p-►constantandp-+oo.Someinsightinto this radius atwhichthereisacontactdiscontinuitywithU=rj. At y =1.5and5/3forarangeofvalues^.Weagree with their resultsfory=5/3.Thesolutionsextendintoafinite solution tothedifferentialequationsisfound. time, butcanbedeterminedfromenergyconservationonce a y >1.5,theentropydropsto0atearlytimesandthat pro- For agivensituation,theconstantßisnotknownahead of (rj =1)are Taking C=KA,theboundaryconditionsatshockfront remains constantduringtheexplosionat where theprimeimpliesd/drj.Thecaseofinterestinthis shock expansionrate,theMachnumberofshock, section hasa=fands2,and~A(ßE/K).Forthestated where Cisaconstant,leadingtotheequations where visthevelocityandyadiabaticindex.Theself- similar variablesaretakentobe f Carrus etal(1951)havealreadysolvedthisproblemfor The fluidequationstobesolvedare [2(a —1)+(yl)as]Pa(Urj)P Ct as 2<,1>,s 1 =^’pQ(ri), v =aAf-'Uit]),pCa,4r‘~P(>7), a(U -r,)U'+(a-l)U+^F-^=0, 2 (u -f/)Q'+airsfi=o, (y -l)^+2’l)y^ -J- +v—y dp p dt drp 2 t;- (y +l)^_(2y^—y1) z T: +7rrH—j"=0> dv 1dpGM dt drpr dp dv2pv„ dt drr 2 e/# 2 (y -1MT+2 2 (y -hl)«^ 3 ya* dp , dt dr yo—p;— P(U-ri) _ Q^ Q' =0, Vol. 346 (2.12) (2.11) (2.10) (2.9) (2.8) (2.7) (2.6) (2.5) (2.4) 198 9ApJ. . .346. .847C _1 2 2 mass, pocrand-►constant atthecenter.Valuesofa,ßk, for thiscase.For0
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