Long GRBs from binary stars runaway, Wolf-Rayet progenitors

Wolf-Rayetprogenitors

M.Cantiello∗,S.-C.Yoon†,N.Langer∗andM.Livio∗∗

arXiv:0709.0829v1 [astro-ph] 6 Sep 2007AstronomicalInstitute,UtrechtUniversity,

Princetonplein5,3584CC,Utrecht,TheNetherlands

†

DepartmentofAstronomyandAstrophysics,UniversityofCalifornia,SantaCruz,CA950,USA

∗∗

SpaceTelescopeScienceInstitute,3700SanMartinDrive,Baltimore,MD21218Abstract.Thecollapsarmodelforlonggamma-rayburstsrequiresarapidlyrotatingWolf-Rayetstarasprogenitor.WetesttheideaofproducingrapidlyrotatingWolf-Rayetstarsinmassiveclosebinariesthroughmassaccretionandconsecutivequasi-chemicallyhomogeneousevolution—thelatterhadpreviouslybeenshowntoprovidecollapsarsbelowacertainmetallicitythresholdforsinglestars.Thebinarychannelpresentedheremayprovideameansformassivestarstoobtainthehighrotationratesrequiredtoevolvequasi-chemicallyhomogeneousandfulfillthecollapsarscenario.Moreover,itsuggeststhatapossiblylargefractionoflonggamma-rayburstsoccursinrunawaystars.

Keywords:Stars:binary–Stars:rotation–Stars:evolution–Stars:mass-loss–Supernovae:general–Gammarays:burstsPACS:97.

∗

INTRODUCTION

Longgamma-rayburstsarethoughttobeproducedbyasubsetofdyingmassiveandpossiblymetal-poorstars[1,2,3].Withinthecurrentlyfavoredcollapsarscenario[4],theburstisproducedbyarapidlyrotatingmassiveWolf-Rayet(WR)starwhosecorecollapsesintoablackhole[5].Whilesinglestarevolutionmodelswithoutinternalmagneticfieldscanproducesuchconfigurations[6,7],onlymodelsincludingmagneticfieldsarecapableofreproducingtheslowspinsofyoungGalacticneutronstars[8,9]andwhitedwarfs[10],duetothemagneticcore-envelopecouplingduringthegiantstage.

YoonandLanger[11],Yoonetal.[12]andWoosleyandHeger[13]recentlyshowedthatbelowacertainmetallicitythreshold,veryrapidlyrotatingsinglestarsavoidthemagneticbrakingofthecorethroughtheso-calledquasi-chemicallyhomogeneousevo-lution:rotationallyinducedmixingprocesseskeepthestarclosetochemicalhomogene-ity,andthusthegiantstageisavoidedaltogether.Whilethesemodelsaresuccessfulinproducingmodelswhichfulfillallconstraintsofthecollapsarmodel,theyrequireveryrapidinitialrotation.

Thequestionthusariseswhetherthequasi-chemicallyhomogeneousevolutionofmassivestarscanalsobeobtainedinmasstransferringmassivebinarysystems[14],sinceinsuchsystemsthemassgainercanbespun-uptoclosetocriticalrotation[see15,6],independentofitsinitialrotationrate.

FIGURE1.Leftpanel:evolutionarytrackofthemassgainerinour16M⊙+15M⊙earlyCaseBbinarymodel(5dinitialorbitalperiod)intheHRdiagram(solidline),fromthezeroagemainsequenceuptocorecarbonexhaustion.Themainevolutionaryphasesarelabeledbynumbers(seelegend).Thedashedlineshowstheevolutionarytrackofaveryrapidlyrotating(󰀁init/󰀁K=0.9)24M⊙singlestar.BothstarshaveSMCmetallicity,andundergoquasi-chemicallyhomogeneousevolution(seetext).Rightpanel:evolutionoftheinternalstructureofthemassgainerofthecomputed16M⊙+15M⊙earlyCaseBbinarysequence,asfunctionoftime,fromthezero-agemainsequencetocorecarbonexhaustion.Thetimeaxisislogarithmic,withthetimeofcorecollapseaszeropoint.Convectivelayersarehatched.Semiconvectivelayersaremarkedbydots(reddotsintheelectronicversion).Gray(blue)shadingindicatesnuclearenergygeneration(colorbartotherightofthefigure).Thetopmostsolidlinedenotesthesurfaceofthestar.

THEMODEL

Weusea1-Dhydrodynamicbinaryevolutioncodetosimulatetheevolutionofa16+15M⊙binarymodelwithaninitialorbitalperiodof5daysandSMCmetallicity(Z=0.004).Internaldifferentialrotation,rotationallyinducedmixingandmagneticfieldsarein-cludedinbothcomponents,aswellasnon-conservativemassandangularmomen-tumtransfer,andtidalspin-orbitcoupling.DetaileddescriptionofthecodeandoftheadoptedphysicscanbefoundinCantielloetal.[16]andreferencestherein.

WechoseanearlyCaseBsystemwithaninitialmassratioclosetoonefortworeasons.Firstly,theexpectedmasstransferefficiencyforthiscasewasabout60%(meaningthat60%ofthetransferedmattercanberetainedbythemassgainer),basedonthecalculationsbyWellstein[17],Langeretal.[18],andPetrovicetal.[15].Secondly,aCaseBratherthanCaseAsystemwaschosentoavoidsynchronizationafterthemajormasstransferphase.

RESULTS

Theevolutionofthebinarysystemproceededasfollows(cf.Table1).Theinitialrotationalvelocityofbothstarshasbeensetto230kms−1,butbothstarssynchronizewiththeorbitalrotationwithinabout1Myr,toequatorialrotationalvelocitiesofonlyabout50kms−1.Rotationallyinducedmixingbeforetheonsetofmasstransferisthusnegligible—incontrasttotypicalOstarsevolvinginisolation[19,20].Theinitially

TABLE1.Majorevolutionaryphasesofthecomputed16M⊙+15M⊙earlyCaseBbinarysequence.Thebinarycalculationendsaftercorecarbonexhaustionofthemassloser(theprimary),andthemassgainer(thesecondary)isthenevolvedasasinglestar.Weshowevolutionarytime,massesofbothstars,orbitalperiod,surfacerotationalvelocityofbothstars,surfaceandcoreheliummassfractionofthemassgainer,andorbitalvelocityofthemassgainer.Theabbreviationsfortheevolutionaryphasesare:ZAMS=zeroagemainsequence;ECHB=endcorehydrogenburning;ICB=ignitionofcarbonburning;ECCB=endcorecarbonburning.ThenumberedevolutionarystagescorrespondtothosegiveninFig.1,leftpanel.

Time

1ZAMS

9.

3endCaseB

11.3018.10

6ICBsecondary

18.56

–

12.83

–

–

258

0.000

0.996

–

3.71–

20.8616.76

42.7–

40–

767202

0.4570.996

0.4410.956

27–

15.92

14.94

5.1

96

85

0.879

0.248

198

M1

M2

P

󰀁rot,1

󰀁rot,2

Yc,2

Ys,2

󰀁orbit,2

stars.Thisconfirmsthatthescenarioofquasi-chemicallyhomogeneousevolutionmightnotberestrictedtosinglestars,butmayapplytotheaccretingcomponentofmassiveclosebinariesaswell.

Whileweprovideonlyoneexample,itseemslikelythatthisscenarioappliestomostmassiveclosebinarycomponentswhichaccreteorgainanappreciableamountofmass;thismayencompassCaseAbinariesandearlyCaseBbinaries[21,22,23].CaseAmergerarealsolikelycontributingtothisscenario.Whilethemergedobjectwillhavemoremassthantheinitiallymoremassivestarinthebinary,theproductwillbeextremelyrapidlyrotatingduetotheorbitalangularmomentum,asinthecaseofsomebluestragglers[24].

Binariesandthedistributionofrotationalvelocities

Thebestconstraintsofaronthedistributionofinitialrotationalvelocities(IRF)comesfromtherecentstudyofyoungOstarsintheSMC,mostlyfromtheclusterNGC346[25].AccordingtoYoonetal.[12],thethreemostrapidrotatorsfromthesampleof21Ostarswouldqualifyforthequasi-chemicallyhomogeneousevolutionscenario,andremarkably,allthreestarsarefoundtobehelium-enhanced.ThesimplestapproachtounderstandthosestarsistoassumethattheycorrespondtothetipoftheIRF.

However,thatdataofMokiemetal.[25]revealsanotherinterestingfeature:twoofthethethreementionedstarsarerunawaystars,withradialvelocitiesdeviatingby30...70kms−1fromtheaverageclusterradialvelocity.Whiledealingwithlownumberstatistics,thisinformationopensanotherpossibility:thatthemostrapidlyrotatingyoungOstarsintheSMCareproductsofbinaryevolution.AcloserexaminationoftheIRFderivedbyMokiemetal.[25]appearstosupportthisidea:Whilethethreerapidrotators

−1−1show󰀁sini>∼290kms,allotherstarshave󰀁sini<∼210kms.

Thefollowinghypothesisthereforeseemsconceivable:TheIRFofsingleOstarsintheSMCendsatabout210kms−1—tooearlytoallowquasi-chemicallyhomogeneousevolutionandcollapsarformation.However,massiveclosebinaryevolutionenhancestheIRFtowhatwemaycalltheapparentIRFasmeasuredbyMokiemetal.[25],whichleadstotheredshiftdependentGRBrateasworkedoutbyYoonetal.[12].AccordingtothebinarypopulationsynthesismodelofPodsiadlowskietal.[21],about10%ofallmassivebinariesmightleadtoaCaseAmergerorearlyCaseBmasstransfer,whichissufficienttopopulatetherapidlyrotatingpartoftheIRFofMokiemetal.Inthatcontext,therapidlyrotatingOstarinthesampleofMokiemetal.[25]whichdoesnotappearasrunawaystarcouldeitherhaveanundetectedhighpropermotion,oritcouldbetheresultofaCaseAmerger—wherenorunawayisproduced.

EffectsfromrunawayGRBs

TherunawaynatureofaGRBprogenitor,asobtainedinourexample,hasimportantobservationalconsequencesforboththepositionsofGRBs,andtheirafterglowprop-erties.Concerningtheafterglow,itisrelevantthatthemediumclosetoaWRstarhas

thedensityprofileofafree-streamingwind,andanalyticalandnumericalcalculationsbothsuggestthatthefreewindofasingleWRstartypicallyextendsovermanyparsec[26].However,fromtheanalysisofGRBafterglows,aconstantcircumstellarmediumdensityhasbeeninferredinmanycases[27,28,29,30].ApossibleexplanationhasbeenproposedbyvanMarleetal.[26],whosimulatedthecircumstellarmediumaroundamovingWRstar.AstheGRBjetaxisislikelyperpendiculartothespacevelocityvec-tor,thejetescapesthrougharegionofthebow-shockwherethewindterminationshockisveryclosetothestar.Therefore,thejetmayenteraconstantdensitymediumquicklyinthissituation.

ConcerningtheGRBpositions,sincethespinaxisofthestarsinaclosebinarysystemarelikelyorthogonaltotheorbitalplane,theobservationofaGRBproducedbytheproposedbinarychannelispossibleonlyifthebinaryorbitisseennearlyfaceon.ThenthedirectionofmotionoftherunawayGRBprogenitormustbeorthogonaltothelineofsight,allowingtheprogenitor,forthegivenspacevelocity,toobtainthemaximumpossibleapparentseparationfromitsformationregion.ThefindingofHammeretal.[31],thatthenearestthreelonggamma-rayburstsmaybeduetorunawaystarsisinremarkableagreementwithourscenario.Whilethecollapsarprogenitorinourbinarymodeltravelsonly200pcbeforeitdies,comparedtothe400...800pcdeducedbyHammeretal.[31],binaryevolutionresultinginhigherrunawayvelocitiesarecertainlypossible[15].ItremainstobeanalyzedwhethertherunawayscenarioiscompatiblewiththefindingthatlongGRBsaremoreconcentratedinthebrightestregionsoftheirhostgalaxiesthancorecollapsesupernovae[32].

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