Delay-time distribution of core-collapse supernovae with late events resulting from binary interaction

1.4 MB·

by  E. Zapartas

Astronomy&Astrophysicsmanuscriptno.zapartas_arxiv_submission_final (cid:13)cESO2017
January26,2017
Delay-time distribution of core-collapse supernovae with late
events resulting from binary interaction
E.Zapartas1,S.E.deMink1,R.G.Izzard2,S.-C.Yoon3,C.Badenes4,Y.Götberg1,A.deKoter1,5,C.J.Neijssel1,
M.Renzo1,A.Schootemeijer6,andT.S.Shrotriya6
1 AntonPannekoekInstituteforAstronomy,UniversityofAmsterdam,SciencePark904,1098XH,Amsterdam,TheNetherlands
e-mail:[e-mail], [e-mail]
2 InstituteofAstronomy,UniversityofCambridge,MadingleyRoad,CambridgeCB30HA,UK
3 AstronomyProgram,DepartmentofPhysicsandAstronomy,SeoulNationalUniversity,Seoul,151-747,Korea
4 DepartmentofPhysicsandAstronomy&PittsburghParticlePhysics,Astrophysics,andCosmologyCenter(PITT-PACC),Univer-
7 sityofPittsburgh,Pittsburgh,PA15260,USA
1 5 InstituteofAstronomy,KULeuven,Celestijnenlaan200D,B-3001Leuven,Belgium
0 6 Argelander-InstitutfürAstronomie,UniversitätBonn,AufdemHügel71,53121Bonn,Germany
2
AcceptedforpublicationinAstronomy&Astrophysics
n
a
J
ABSTRACT

4
2 Mostmassivestars,theprogenitorsofcore-collapsesupernovae,areinclosebinarysystemsandmayinteractwiththeircompanion
throughmasstransferormerging.Weundertakeapopulationsynthesisstudytocomputethedelay-timedistributionofcore-collapse

] supernovae,thatis,thesupernovarateversustimefollowingastarburst,takingintoaccountbinaryinteractions.Wetestthesystematic
E robustnessofourresultsbyrunningvarioussimulationstoaccountfortheuncertaintiesinourstandardassumptions.
H Wefindthatasignificantfraction,15+9%,ofcore-collapsesupernovaeare‘late’,thatis,theyoccur50-200Myrsafterbirth,when
−8
allmassivesinglestarshavealreadyexploded.Theselateeventsoriginatepredominantlyfrombinarysystemswithatleastone,or,
.
h inmostcases,withbothstarsinitiallybeingofintermediatemass(4−8M ).Themainevolutionarychannelsthatcontributeoften
(cid:12)
p involveeitherthemergingoftheinitiallymoremassiveprimarystarwithitscompanionortheengulfmentoftheremainingcoreofthe
- primarybytheexpandingsecondarythathasaccretedmassatanearlierevolutionarystage.Also,thetotalnumberofcore-collapse
o supernovaeincreasesby14+15%becauseofbinarityforthesameinitialstellarmass.
r −14
t The high rate implies that we should have already observed such late core-collapse supernovae, but have not recognized them as
s such.WearguethatφPerseiisalikelyprogenitorandthateccentricneutronstar–whitedwarfsystemsarelikelydescendants.Late
a
eventscanhelpexplainthediscrepancyinthedelay-timedistributionsderivedfromsupernovaremnantsintheMagellanicCloudsand
[
extragalactictypeIaevents,loweringthecontributionofpromptIaevents.Wediscusswaystotestthesepredictionsandspeculateon

1 theimplicationsforsupernovafeedbackinsimulationsofgalaxyevolution.
v
Keywords. supernovae:general–binaries:close–stars:massive–stars:evolution
2
3
0
71. Introduction exchange of mass and angular momentum through Roche-lobe
0 overflow, common envelope evolution, and merging of the two
.Core-collapse supernovae (ccSNe) are bright explosions that stars(Wellstein&Langer1999;deMinketal.2013;DeMarco
1
0mark the end of the lives of massive stars (e.g., Heger et al. &Izzard2016).Thisinteractioncandrasticallyaffectthefurther
2003;Smartt2009)andthebirthofneutronstarsorblackholes
7 evolution of both stars and thus the properties of their possible
1(e.g., Ertl et al. 2016). They play a crucial role as sources of supernovae.Pioneersinmodelingtheeffectson(samplesof)cc-
chemical enrichment (e.g., Arnett 1973; Woosley et al. 2002)
: SNeincludePodsiadlowskietal.(1992);DeDonder&Vanbev-
vand feedback, driving the evolution of their host galaxies (e.g.,
eren(2003b);Yoonetal.(2010);Eldridgeetal.(2008,2013).
XiHopkins et al. 2014). Their extreme brightness also allows us
tousethemasprobesofstar-forminggalaxiesouttoappreciable Ourunderstandingoftheendpointsofmassivestarsisradi-
r
aredshifts(e.g.,Strolgeretal.2015).Theseexplosionsareusually callybeingtransformedbytheriseof(automated)transientsur-
attributed to stars with birth masses larger than approximately veys, which enable the efficient detection of ccSNe and other
8M(cid:12) (Heger et al. 2003), although the exact value depends on transientsinlargenumbers.ExamplesaretheLickObservatory
model assumptions concerning core overshooting, stellar-wind Supernova Search (LOSS, Filippenko et al. 2001), the Palomar
mass-loss, and metallicity (e.g., Poelarends et al. 2008; Jones Transient Factory (PTF, Rau et al. 2009; Law et al. 2009), and
etal.2013;Takahashietal.2013;Dohertyetal.2015). its near-future upgrade, the Zwicky Transient Facility, the All-
Observing campaigns of young massive stars in our galaxy Sky Automated Survey for SuperNovae (ASAS-SN, Shappee
andtheMagellanicCloudsshowthataverylargefractionhave et al. 2014), Pan-STARRS (Kaiser et al. 2002), and eventually
oneormorecompanions,formingaclosebinarysystemwhere theLargeSynopticSurveyTelescope(LSST,Ivezicetal.2008).
severe interaction between the stars during their lives is un- The datasets provided by these facilities will be large, but may
avoidable (e.g., Kobulnicky & Fryer 2007; Mason et al. 2009; notnecessarilyprovideverydetailedinformationaboutindivid-
Sanaetal.2012;Chinietal.2012).Suchinteractioncanbethe ual events, since this typically requires more intensive follow
Articlenumber,page1of22
A&Aproofs:manuscriptno.zapartas_arxiv_submission_final
up, to obtain spectra, for example. The large potential of these 2006,2009)withupdatesdescribedindeMinketal.(2013)and
datasets will be the statistical constraints that they can provide, Schneider et al. (2015). The code employs rapid algorithms by
allowingfornewconstraintsontheoreticalmodelsforbothcom- Tout et al. (1997) and Hurley et al. (2000, 2002) based on ana-
monandrareevents.Fullyharvestingthesedatasetswillrequire lyticalfitstothedetailednon-rotatingsinglestellarmodelscom-
adaptationsfromthetheorysideandthuspredictionsofthesta- putedbyPolsetal.(1998).
tisticalpropertiesforlargesampleswillbeneeded. The code enables us to efficiently simulate the evolution of
Motivated by the technological and observational develop- singlestarsandbinarysystemsfromthezero-agemainsequence
ments,aswellastheinsightintothelargeimportanceofbinarity, until they leave behind compact remnants. This allows us to
wehavestartedasystematictheoreticalinvestigationaimingto make predictions for an entire population of massive stars by
quantify the impact of binarity on the statistical properties ex- spanningtheextensiveparameterspaceofinitialpropertiesthat
pected for large samples of ccSNe. This paper is the first in a determinetheirevolution.Italsoallowsustoexploretherobust-
seriesinwhichwedescribethemotivationandsetupofoursim- nessofourresultsagainstvariationsinourassumptions.
ulations (section 2). In two papers that were completed ahead In subsection 2.1, we discuss the initial conditions and in
ofthisone,theleadauthorsofthisteamdemonstratedtheearly subsection2.2,wediscussthephysicalassumptions.Fromnow
applicationofthesenewsimulationsagainstobservationsoftwo on when we mention “standard models” or “standard simula-
individualevents. tions”,werefertothesimulationswherewefollowedourmain
In Van Dyk et al. (2016), we compared these simulations assumptions in all the key parameters that we discuss below.
withnewdeepHubbleSpaceTelescopeobservationsofthesite Therearetwostandardmodelswithonesimulatingonlysingle
ofthenowfadedstripped-envelopetypeIcsupernovaSN1994I stars and the other including binaries (discussed also below in
in search of a surviving companion star. While no companion theparagraphforbinaryfraction).Asummaryofthekeyparam-
wasdetected,thedataprovidednewstrongupperbrightnesslim- eters, their values for our standard assumptions and the model
its, constraining the companion mass to less than 10M . This variationsthatweconsiderisprovidedinTable1.
(cid:12)
resultisconsistentwiththetheoreticalpredictionsofoursimu-
lations and allowed a subset of formation scenarios to be ruled
2.1. Initialconditions
out.InMarguttietal.(2016),weusedthesesimulationstointer-
pret the multi-wavelength observations of supernova SN2014C Initialdistributions –Weassumethatthedistributionoftheini-
whichoverthetimescaleofayearunderwentacompletemeta- tial mass, M , of primary stars (the initially most massive star
1
morphosis from an ordinary H-poor type Ib supernova into a inabinarysystem)andofsinglestarsfollowsaKroupa(2001)
strongly interacting, H-rich supernova of type IIn. These sim- initialmassfunction(IMF),
ulations helped us to estimate the possibility that the surround-
inghydrogenshelloriginatedfromapriorbinaryinteraction(as
dN
opposed to ejection resulting from instabilities during very late ∝ Mα(cid:48), (1)
burningphases,e.g., Quataertetal.2016). dM1 1
In this paper, we focus on the distribution of the expected
where,
delay time between formation of the progenitor star and its fi-

n(2a0l0e3xbp)l.oWsioeni,nvexestetingdaitneghtohwebwinoarkryoifnDteeraDctoionndearff&ectVsathnebedveelareyn- α(cid:48) = −−01..33 00..0018<< MM11//MM(cid:12)(cid:12) <<00..05,8, (2)
teixmpeecdteisdtrtiobubteio‘nlaotef’c,cthSaNteis.,AthseiygnoicficcuarnwtiftrhacdteiolanyotfimcceSsNloengareer  −2.α3 0.51<< MM1//MM(cid:12) <<11,00.
1 (cid:12)
thanapproximately50 Myr,whichisthemaximumdelaytime
expectedforsinglestars.Weshowthattheselateeventsoriginate In our standard models, we adopt α = −2.3. When assessing
fromprogenitorsinbinarysystemswithmostofthembeingof theuncertainties,weconsidervariationsinwhichα = −1.6and
intermediatemass.WediscusstheselateccSNeinsection3and −3.0 following the uncertainty given in Kroupa (2001) as well
describethevariousevolutionarychannelsthatproducethem. asonemodelinwhichα=−2.7(e.g.,Kroupaetal.1993).
Wefurtherdescribetheoutcomeofanextensivestudyofthe Fortheinitialmassratioq≡ M2/M1,whereM2istheinitial
robustnessofourresultsagainstvariationsinthemodelassump- massofthesecondarystar,wetake
tionsandwecomparewithearlierworkinsection5.Insection6,
dN
wediscuss(possible)observationalevidence.Wearguethatthe ∝qκ. (3)
wellknownbinaryφPerseiprovidesadirectprogenitorsystem dq
that is expected to result in a late ccSN and we discuss how
Weadoptauniformdistributioninourstandardsimulation,for
the observed eccentric neutron star – white dwarf systems may example,κ =0forq∈[0.1,1],consistentwithKiminki&Kob-
well provide the direct remnants. We then compare our results
ulnicky(2012)andSanaetal.(2012).Wealsoconsiderthevari-
directly with the inferred delay time measured from supernova ationsκ=−1and1.
remnants in the Magellanic Clouds, showing that they are con-
Fortheinitialorbitalperioddistribution,weassume
sistent with our predictions. We finish with a brief discussion
oganlapxoisessibblyesimhopwliicnagtiothnesdfoiffrefreeendcbeasckwiitnhstthaer-wfoirdmeliyngusreegdiosinnsgilne dlodgN P ∝(cid:0)log10P(cid:1)π. (4)
star predictions by the STARBURST99 simulations (Leitherer 10
etal.1999).Weendwithasummaryofourfindingsinsection7. Weadoptπ = 0,alsoknownasÖpik’slaw(1924),forsystems
withprimarymassesupto15M (Kobulnickyetal.2014;Moe&
(cid:12)
DiStefano2015).Toaccountforthestrongpreferenceofmore
2. Method
massive stars to reside in short period systems, we adopt π =
We use a binary population synthesis code, binary_c (ver- −0.55 when M > 15M as found by Sana et al. (2012). The
1 (cid:12)
sion2.0,SVNrevision4105),developedbyIzzardetal.(2004, rangeofinitialperiodsweconsiderislog (P/day)∈[0.15,3.5]
10
Articlenumber,page2of22
E.Zapartas,S.E.deMink,R.G.Izzard,S.-C.Yoon,C.Badenesetal.:Delay-timedistributionofcore-collapsesupernovae
asgivenbySanaetal.(2012).Whenassessingtheuncertainties, 106M . Forthis,weintegrate overthefullrange oftheIMFas
(cid:12)
weconsiderπ=−1and1overthefullmassrange. specified in Equation 2. For stars with masses above M , we
low
Fortheinitialspinperiodofthestars,wefollowHurleyetal. account for the mass contained in the companion star as speci-
(2000). Although this does not account for the full distribution fied in Equation 3. Effectively, we assume that low-mass stars,
(e.g., Huang et al. 2010; Dufton et al. 2013; Ramírez-Agudelo with M < M , do not have companions massive enough to
1 low
et al. 2013, 2015), this is sufficient for investigating the role of significantly contribute to the mass of the stellar population. In
binarityastheimpactoftheadoptedbirthspinisnegligiblecom- our standard assumptions we adopt M = 2M and we vary
low (cid:12)
paredtotheangularmomentumthestarlaterreceivesasaresult this parameter to 1 and 3M to check that this choice does not
(cid:12)
ofinteractionbytidesandmasstransfer(deMinketal.2013). havealargeinfluenceonourresults.
Althoughweaccountfortheeffectsofeccentricity,wechose
toadoptcircularorbitsatbirthtolimitthenumberofdimensions
that our grid of models spans. This is justified as most systems Metallicity –Weassumesolarmetallicityinourstandardpop-
circularize shortly before the onset of mass transfer by Roche- ulation, adopting a mass fraction of elements heavier than he-
lobe overflow as a result of tides (Portegies Zwart & Verbunt lium of Z = 0.014 (Asplund et al. 2009) because present day
1996; Hurley et al. 2002). However, with this approach, we do transientsurveysfocusonlargergalaxieswithmetallicitiesthat
not account for systems that are too wide to strongly interact are comparable to solar. We also consider low metallicities of
when circular, but where eccentricity implies periastron sepa- Z = 2 × 10−4 relevant for metal-poor progenitors of globular
rations small enough to trigger Roche-lobe overflow. We may clusters and populations formed at high redshift. We addition-
thereforeslightlyunderestimatetheimpactofbinaryinteraction. ally test Z = 0.004 and Z = 0.008, relevant to nearby dwarf
See, for example, the interacting systems arising from binaries galaxiessimilartotheSmallandLargeMagellanicClouds.We
withinitialorbitalperiodswellinexcessof103.5 daysdepicted furtherprovideresultsfortheformercanonicalsolarabundance
in Fig. 2 of de Mink & Belczynski (2015). We explore the un- ofZ =0.02(e.g.,Grevesseetal.1996)forcomparisonwithear-
certaintiesarisingfromthisassumptionindirectlywhenwevary lierstudiesandonesupersolarmetallicity,Z =0.03,relevantto
theinitialorbitalperioddistributionandthetotalbinaryfraction. thecentralregionsoflargegalaxies.
Binaryfraction –Inourtwostandardmodelsweeithersimulate 104
only single stars or we adopt a binary fraction of fbin = 0.7. Mmin,cc≃ 7.5 M¤ This work
Here,wedefineabinaryasasystemwithinitialmassratioq ∈ white dwarfs core-collapse MESA (αov=0.335)
MESA (no overshooting)
[0.1,1] and initial period log10(P/day) ∈ [0.15,3.5] based on r) 103 Schaller+92
Sanaetal.(2012)andconsistentwiththerangesadoptedabove. y
M
Weconsidervariationsof fbin =0.3and1.0. (
e
The binary fraction for intermediate-mass stars is less well m 102
constrained.Wethereforeconsideramodelvariationwherewe feti τmax,cc≃ 48 Myr
adopt a binary fraction that decreases with mass based on Moe Li
&DiStefano(2013).Theseauthorsprovidetheinferredfraction 101
of systems with a companion in very close orbit, P = 2 − 10
τ ≃ 3 Myr
days, and q > 0.1. They find that this fraction drops from 0.22 min,cc
forearlyB-typeto0.16forlateB-typestars.Informationonsys- 100
temswithorbitslongerthan10daysarenotavailablefromthis 1.2
sdteucdrye.asTehsestoewreasrdusltslamteayspeeicthtrearlitnydpiecsatoerththaattthtehebrienaisrysifmrapcltyiona Δ τ / τ 1.0
preferenceforsystemswithorbitalperiodslongerthan10days 0.8
inthesestars.Weusetheseresultstoconstructamass-dependent 2 4 6 10 20 40 60 100
binary fraction assuming that the binary companions of B-type
Initial mass (M )
stars still follow an (Öpik 1924) law over the full period range ¤
0.15 < log P < 3.5. We construct a mass-dependent binary
10 Fig.1. Thelifetimeτ(untilthewhitedwarfphaseorcorecollapse)as
fraction f (M) referring to the binary fraction for the full pe-
bin a function of initial mass for single stars adopted in this work (black
riodrange,suchthatthebinaryfractionforperiods P = 2−10 line) is compared with predictions that we obtained using the MESA
daysareasinMoe&DiStefano(2013).Thisresultsin stellar evolutionary code (Paxton et al. 2011) with and without over-
shooting(darkandlightbluedots)andwithGenevamodelsofSchaller
etal.(1992,blackdots).SinglestarswithmasseslessthanM end
 min,cc
fbin(M1)= 000...46741 156≤≤ MMM11///MMM(cid:12)(cid:12) <<615 ∼∼∼leOaat,relyBB, , tethoxeptiherecltilevidefesbtaiemstwweseheointfeτtdhmwein,amccrfoassnitdnasτntmedaaxld,eccaosf(tycmeclSlaoNswseivs(ehhaasdtsaherdedtroergueginoidonen)r,)gw.ochcciSocNhreerceaoferler-
1 (cid:12) lapse.Thebottompanelshowstherelativedifferenceinlifetimeswith
(5)
respecttothelifetimesusedinourwork(subsection2.2).
whichweadoptasoneofthemodelvariations.Wewanttostress
theimportanceoffurtherobservationalcampaignsaimedtocon-
strain the initial binary distributions and the binary fraction for
2.2. Physicalassumptions
thefullM ,qandperiodrange(e.g.,Moe&DiStefano2016).
1
Forafulldescriptionofthecode,werefertothereferencescited
Normalization –Whenquotingabsoluterates,weexpressour atthestartofthissection.Herewediscussthemainassumptions
results normalized by the total mass formed in stars in units of thatareofdirectrelevancetothisstudy.
Articlenumber,page3of22
A&Aproofs:manuscriptno.zapartas_arxiv_submission_final
Stellarlifetimes –Theevolutionarytracksandstellarlifetimes considerthevariationsη=3andη=0.33forallmass-lossrates
(until reaching the white dwarf phase or core collapse) of sin- simultaneously.
gle stars in our simulations originate from the grid of detailed
non-rotating stellar evolutionary models of Pols et al. (1998)
Tides – We account for the effect of tides on the stellar spins
computed with an updated version of the STARS code (Eggle-
andthestellarorbitsofstarsinbinarysystems(Zahn1977;Hur-
ton1971,1972;Polsetal.1995).Forstarsupto20M ,weuse
(cid:12) ley et al. 2002) and the transfer of angular momentum during
thefittingformulaeofHurleyetal.(2000)forthesemodels.At
masstransferviaanaccretiondiskorthedirectimpactoftheac-
highermass,weswitchtoalogarithmictabularinterpolationof
cretion stream onto the surface as described in de Mink et al.
thelifetimesbyPolsetal.(1998),andabove50M ,weextrapo-
(cid:12) (2013) following Ulrich & Burger (1976) and Packet (1981).
lateasdescribedinSchneideretal.(2015).
Weassumethatthestellarspinsarealignedwiththeorbit(Hut
Ourresultingmass-lifetimerelationisshowninFigure1.We 1981).
findgoodagreementwithsimulationswiththeevolutionarycode
MESA, version 7184 (Paxton et al. 2011, 2013, 2015) for non-
rotating stars when using our standard metallicity, Z = 0.014, Masstransfer –WhenastarfillsitsRochelobeandmasstrans-
and the Schwarzschild criterion for convection with a step- ferisstable,wecomputethemass-lossratefromthedonorstar
overshootingparameterα =0.335H ,whereH isthepressure byremovingasmuchmassasneededforthestartoremainin-
ov p p
scaleheight,ascalibratedbyBrottetal.(2011). sideitsRochelobe.Theresultingmasstransferratesarecapped
bythethermaltimescaleofthedonor.Wedefinethemasstrans-
The widely-used Geneva models of Schaller et al. (1992) ferefficiency,β,asthefractionofthemasslostbythedonorthat
predictlifetimesthatare10-15%shorter,ascanbeseeninFig-
isaccretedbythecompanion,
ure1.Thesearemodelsofnon-rotatingstarswithametallicity
Zass=um0i.n0g2.nOouorveMrsEhoSoAtinsigm,αuloavti=on0s.Ggiivveensitmheileavrildifeentcimefeosrwexhterna β≡ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)MM˙˙acc(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12). (6)
mixing processes beyond the convective core based on calibra- don
tionsoftheovershootingparameterαov (e.g.,Ribasetal.2000; If mass is transferred on a timescale that is much shorter than
Claret2007;Brottetal.2011),weconsiderthelifetimepredic- thethermaltimescaleoftheaccretingstarτ ,thestarwillbe
th,acc
tionsbyourmodelswithovershootingtobemorerealistic. drivenoutofthermalequilibriumandexpand(Neoetal.1977).
Althoughoursimulationsdonotfollowthisphaseindetail,itis
expected that the companion can only accrete a fraction of the
Stellarwinds –Weincludeupdatedmass-lossprescriptionsas transferredmaterialwhen|M˙ |(cid:29) M˙ ≡ M /τ ,where
don acc,th acc th,acc
described in de Mink et al. (2013), which include the recipes
M isthemassoftheaccretingstar.Inlinewiththisphysical
acc
of Vink et al. (2000). At luminosities in excess of 4000L , we
(cid:12) picture,welimitthemassaccretionrateto
switchtotheempiricalmass-lossratesofNieuwenhuijzen&de
Jager(1990)whentheseratesexceedthosebyVinketal.(2000).
(cid:32) (cid:33)
Toaccountfortheempiricalboundaryofstarsintheupperpart |M˙ |=min |M˙ |, f Macc , (7)
oftheHertzsprung-RusselldiagramasdescribedinHumphreys acc don τ
th,acc
&Davidson(1994),weaddafactorinthemasslossasdescribed
in Hurley et al. (2000) to simulate the enhanced mass loss of where f isanefficiencyparameterforwhichweadopt10inour
LuminousBlueVariables(LBV)thatarethoughttoresidenear standardsimulation(toreproducethemasstransferefficiencyof
thisboundary.Forstarsthatarestrippedfromtheirhydrogenen- Schneideretal.2015).Themasstransferefficiencyinthiscase,
velopes, we adopt the Wolf-Rayet (WR) mass-loss prescription whichwerefertoasβth,variesbetween0and1dependingonthe
by Hamann et al. (1995) and Hamann & Koesterke (1998) re- physicalpropertiesofthedonorandtheaccretor.Theefficiency
ducedbyafactorof10toaccountfortheeffectofwindclumping of mass transfer is poorly constrained (see, e.g., the discussion
(Yoon 2015). For post-main-sequence stars, Asymptotic Giant in de Mink et al. 2007). We therefore also explore the extreme
Branch(AGB)stars,andthermallypulsatingAGBstars,weuse casewherenoneofthetransferredmassisaccreted,β = 0,the
Kudritzki & Reimers (1978), Vassiliadis & Wood (1993), and caseofveryinefficientmassaccretion,β = 0.2,aswellasfully
Karakas et al. (2002) respectively, as described in Izzard et al. conservativemasstransfer,β=1.
(2009).
Our mass-loss prescriptions scale with metallicity as M˙ ∝ Angular momentum loss – Mass that is lost from the system
(Z/Z(cid:12))m where m = 0.69 in main-sequence stars (Vink et al. also takes away angular momentum. The specific angular mo-
2001; Mokiem et al. 2007). In post-main-sequence phases, we mentum h, carried away from the system during mass loss, is
adopt m = 0.5 (Kudritzki et al. 1989). In the WR phase, mass parametrizedby,
lossscaleswithmetallicityassumingapower-lawindexof0.86
(Vink&deKoter2005).IntheLBVphase,masslossisassumed
J
tobeinvariantformetallicity. h=γ orb , (8)
M +M
Themass-lossratebystellarwindsaswellaseruptiveevents acc don
isuncertain,inparticularforthelatephasesandthemostmas- whereJ isthetotalorbitalangularmomentum,M andM
orb acc don
sivestars(Smith2014).Inthemassrangewearemostinterested are the masses of the accretor and donor star respectively and
in,masslossduringthelatephasesonlyaffectsthestellarenve- γ is a free parameter. In our standard simulation, we assume
lope. It does not have a large impact on the core of the stars that mass lost from the system is emitted in a spherical wind
and thus on the remaining lifetimes, which are the main focus or bipolar outflow originating from the accreting star (van den
ofthiswork.Nevertheless,weexploretheimpactofchangesin Heuvel1994).Thus,thespecificangularmomentum,h,thatthe
themass-lossratebymultiplyingthemasslossbyanefficiency lostmasscarriesisequaltothespecificorbitalangularmomen-
factor,η,whichwesettounityinourstandardsimulations.We tumoftheaccretingstar,whichyieldsγ=γ ≡ M /M .
orb,acc don acc
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E.Zapartas,S.E.deMink,R.G.Izzard,S.-C.Yoon,C.Badenesetal.:Delay-timedistributionofcore-collapsesupernovae
Wealsoconsidertheextremelimitingcaseofnegligiblean- ing.Thisalgorithmusestwoparameters,µ =0.1,whichisthe
loss
gular momentum transported by the mass lost from the system fractionofthetotalmasslostfromthesystemduringthemerger,
duringmasstransfer(γ=0).Wefurtherconsiderthecasewhere andµ = 0.1,whichisthefractionoftheremainingenvelope
mix
mass is lost through the outer Lagrangian point, forming a cir- massthatismixedintotheconvectivecore.Thevaluesaboveare
cumbinarydisk.BasedonsimulationsbyArtymowicz&Lubow adoptedinourstandardsimulation.Wevaryµ between0and
loss
(1994),weconsiderthatthebinarysystemwillclearoutthein- 0.25andµ between0and1.
mix
nerportionofthediskbyresonancetorques.Weexplorethecase Weaccountfortherejuvenatingeffectofmixingoffreshhy-
thataninnerregionofsizermin =2aiscleared,whererministhe drogen into the central regions of accreting stars and mergers.
inner radius of the circumbinary disk and a the separation of Forthis,weusefitstotheeffectivemassoftheconvectivecore
the binary system. This is consistent with typical values found byGlebbeek&Pols(2008)asdescribedindeMinketal.(2013)
byArtymowicz&Lubow(1994).Wethusconsiderthecaseof andSchneideretal.(2015).
γ=γ ,
disk
(cid:114)
(M +M )2 r Minimum mass for core-collapse supernovae – We predict
γ ≡ acc don min. (9)
disk M M a the final fate of the stars in our simulation using our estimate
acc don
of the final metal core mass, that is, the mass of the core con-
sisting of elements heavier than helium, sometimes referred to
Contact and common envelope evolution –Todecidewhich ascarbonoxygen(CO)coremass.Weadoptaminimummetal
systemscomeintocontactorexperiencecommonenvelope(CE) core threshold of M = 1.37M for a collapse (Nomoto
min,metal (cid:12)
evolution, we consider a critical mass ratio, qcrit. In binary sys- 1984, 1987; Podsiadlowski et al. 2004; Takahashi et al. 2013).
temswithapost-main-sequencedonor,weassumethatsystems Inourstandardsimulations,thiscorrespondstoaminimumsin-
with Macc/Mdon <qcrit enteracommonenvelopephase.Wefol- glestarinitialmassof Mmin,cc = 7.53M(cid:12).Wealsoconsiderthe
lowtheprescriptionsofHurleyetal.(2002)forqcrit,exceptfor variationsMmin,metal =1.30and1.40M(cid:12)whenexploringthesen-
thecasewhenthedonorfillsitsRochelobewhileexperiencing sitivityofourresults.Insinglestars,thesevaluescorrespondto
hydrogenshellburningandcrossingtheHertzsprunggap(HG), aminimuminitialmassof M ≈ 7and8 M ,respectively,
where we use qcrit,HG = 0.4 (de Mink et al. 2013). We use the inourstandardmetallicity.Wmeind,coc notexplicitly(cid:12)distinguishbe-
samevalueforthenakedheliumstardonorsthatexperiencehe- tween electron capture and iron ccSN (e.g., Tauris et al. 2015).
liumshellburning(HeHG). Wealsodonotconsidertheaccretion-induced-collapseofwhite
Commonenvelopeevolutionmayeitherleadtotheremoval dwarfs.
oftheenvelopeor,iftheejectionisnotsuccessful,amerger.In
It is uncertain whether or not the collapse of the core leads
ourtreatmentofcommonenvelopeevolutionweusetheformal-
toasuccessfulsupernovaexplosioninallcasesandwhetheror
ism described in Tout et al. (1997) based on Webbink (1984),
notthisexplosionisabrightevent.Especiallyinmassivestars,
Livio & Soker (1988) and de Kool (1990). In this formalism,
the explosion may fail to eject the outer layers resulting in fall
twoparametersareintroduced,theefficiencyparameterofejec-
backofmaterial.Thispossiblyleadstofainterexplosions(e.g.,
tion,α ,andλ whichparametrizesthebindingenergyofthe
CE CE O’Connor & Ott 2011; Ugliano et al. 2012; Nadezhin 1980;
envelope(seeeq.73and69inHurleyetal.2002,respectively).
Lovegrove & Woosley 2013; Piro 2013), or even the simple
Inourstandardmodel,weassumethatα isunity(e.g.,Web-
CE disappearance of a star without any electromagnetic signature
bink 1984; Iben & Tutukov 1984; Hurley et al. 2002), but we
(e.g.,Kochaneketal.2008).Inourstandardsimulations,weas-
alsorunmodelswitharangeofvalues(0.1,0.2,0.5,2,5,10)to
sume that all core collapses result in an observable event. We
probe the large uncertainties associated with this phase of evo-
also run model variations in which we exclude all supernovae
lution. By varying the efficiency parameter, we also implicitly
from stars with metal cores more massive than a single star of
considertheeffectofuncertaintiesinthebindingenergyλCE as M = 35M and M = 20M wouldproduce,mimick-
αCEλCEappearsasaproductintheexpression.ValuesofαCE >1 ingm,axin,ccasimplifi(cid:12)edway,mthaxe,cceffectof‘(cid:12)failed’explosions.
accountforpossibleextraenergysourcesusedtounbindtheen-
velopeapartfromtheorbitalenergy(e.g.,DeMarcoetal.2011;
Ivanova&Nandez2016).Tocomputetheenvelopebindingen- Supernova kick – We account for the effect of sudden mass
ergyparameter,λCE,weusefitstodetailedmodels(Dewi&Tau- lossduringthesupernovaexplosionontheorbit(Blaauw1961;
ris2000,2001;Tauris&Dewi2001).Wealsoconsideramodel Boersma 1961; Hurley et al. 2002). In addition, at the onset of
variation where we adopt a constant value λCE = 0.5 (e.g., de the supernova, asymmetries in the explosion mechanism may
Kool1990).Foradiscussionofthelimitationsofthisformalism leadtoanatalkicktothecompactremnant.Weassumeanatal
werefertoIvanovaetal.(2013b). kickforthecompactobjectasinequation(A15)ofHurleyetal.
Insystemswithamain-sequencedonor,weadoptqcrit,MS = (2002),wheretheremnantreceivesakickinarandomdirection
0.65 to account for systems that come into contact during the andwithascalarvelocitydrawnfroma1-DMaxwelliandistri-
rapid thermal timescale mass transfer phase, which is consis- butioncharacterizedbya1-Drootmeansquareofσ=265km/s
tent with the detailed models by de Mink et al. (2007). Alter- (Hobbs et al. 2005). We also examine the effect of the extreme
natively,binarysystemsmaycomeintocontactbecauseoftheir caseswithnosupernovanatalkickattheremnant(σ )andwith
0
ownnucleartimescaleevolution.Inmain-sequencestars,weas- kicksstrongenoughtoalwaysdisruptabinarysystemafterthe
sumethatcontactleadstoamerger. explosion.
Mergers and rejuvenation – In case a merger occurs, we fol- 2.3. Simulationsetup
low Table 2 of Hurley et al. (2002) to determine the outcome.
Whentwomain-sequencestars(MS+MS)merge,wefollowthe Inourstandardassumptions,weevolve104singlestarsandmore
updated algorithm by de Mink et al. (2013, 2014), based on than3×106 binarysystemswithvaryingprimarymasses,mass
Glebbeeketal.(2013),toaccountformasslossandinternalmix- ratios, and orbital periods on a grid of 150 × 150 × 150 sys-
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Table1.Summaryofthekeyparametersadoptedinourstandardsimulationsandthevariationsthatweconsider.Seesection2foradescription
ofthesymbolsandfurtherassumptions.
Symbol Standardmodels(a) Modelvariations
Physicalassumptions
- masstransferefficiency β β 0,0.2,1
th
- angularmomentumloss γ γ 0,γ
orb,acc disk
- masslossduringmergeroftwoMSstars µ 0.1 0,0.25
loss
- mixingduringmergeroftwoMSstars µ 0.1 0,1
mix
- natalkickcompactremnant(kms−1) σ 265 σ ,∞
0
- commonenvelopeefficiency α 1 0.1,0.2,0.5,2,5,10
CE
- envelopebindingenergy λCE λDewi+00 0.5
- criticalmassratioforcontactforMSdonor q 0.65 0.25,0.8
crit,MS
- criticalmassratioforunstablemasstransferforHGdonor q 0.4 0,0.25,0.8,1
crit,HG
- stellar-windmass-lossefficiencyparameter η 1 0.33,3
- maximumsingle-starequivalentbirthmassforccSN(M ) M 100 20,35
(cid:12) max,cc
- minimummetalcoreforccSN(M ) M 1.37 1.3,1.4
(cid:12) min,metal
Initialconditions
- slopeinitialmassfunction α −2.3 -1.6,-2.7,-3.0
- slopeinitialmassratiodistribution κ 0 -1,1
- slopeofinitialperioddistr. π πOpik24,Sana+12 -1,1
- metallicity Z 0.014 0.0002,0.004,0.008,0.02,0.03
- binaryfraction(a) f 0.7,0.0(a) 0.3,1, f (M )
bin bin 1
- normalizationparameter(M ) M 2 1,3
(cid:12) low
Notes.(a)Thedifferencebetweenourtwostandardmodelsisthatinonewesimulateonlysinglestarsandintheotherweassumeabinaryfraction
of0.7.
tems. Test simulations indicate that these resolutions are suffi- Equivalentsinglestarinitialmass(M )
cient for the purpose of this work. The difference between our 70 35 20 15 10 8 6 4fl
1600
two standard models is that in one we take into account only single stars
singlestarsandintheotherweassumeabinaryfractionof0.7. 1400
We take primary masses spaced at equal logarithmic intervals
between M = 3 and 100M . The lower limit encompasses all 1200
1 (cid:12) 1
systemsinoursimulationswiththepotentialtoresultinacore- −
)
collapse event within a safe margin. We take mass ratios lin- Mfl1000
earlyspacedbetweenq=0.1and1andorbitalperiodsspacedat 6
equal logarithmic intervals between log P(d) = 0.15 and 3.5. 10 800
10 (
Weweigheachsystemaccordingtotheinitialdistributionfunc- e
N 600
tionsspecifiedinsubsection2.1.Whencomputingvariationsin S
c
theassumptions,wereducetheresolutionofthegridsineachdi- c 400
mensionbyafactoroftworesultinginapproximately4.2×105
systemsineachmodelvariation. 200
0
1 2 5 10 20 50 100 200 500 1000
3. Results Time after starburst (Myr)
The lifetime of a star is determined by the amount of nuclear Fig. 2. The delay-time distribution of core-collapse supernovae based
fuel available and the rate at which it burns this fuel. In single onoursinglestarmodels.Thediagramshowsthenumberofeventsper
stars, both of these properties are primarily a function of the logarithmic time bin for a starburst of 106M in our standard model.
(cid:12)
initial mass, as shown in Figure 1. The lifetime approximately Thetopaxisshowstheinitialmassofsinglestarswiththecorrespond-
scales with mass as τ(M) ≈ M−x. The relation is steeper for inglifetimegiveninthebottomaxis,computedwithbinary_c.Themost
intermediate-massstars(x ≈ 2.4near M = 5M )andflattensat massivestarsevolvemostrapidlyandendtheirlifeafterapproximately
(cid:12)
highermasses(x≈0.6nearM =50M ).Atthehighestmasses, 3Myr. There are no core-collapse events after approximately 48Myr
(cid:12)
when the least massive single star that can undergo core collapse ex-
thelifetimeconvergestoafinitevalueofapproximately3Myr.
plodes.
For stars in binary systems, the lifetime is no longer a simple
functionoftheirinitialmassalone,duetopossiblemasstransfer
ormerging.
Inthissection,wediscussthedistributionofstellarlifetimes
of single stars and binary systems that produce a core-collapse
supernova. The lifetime sets the time-delay between formation SNe.Wefirstdiscussthecaseofapopulationofsinglestarsin
ofthestarandthemomentitscorecollapses.Wethereforerefer subsection3.1,followedbythecaseofapopulationthatcontains
to this distribution as the delay-time distribution (DTD) of cc- arealisticfractionofbinarysystemsinsubsection3.2.
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E.Zapartas,S.E.deMink,R.G.Izzard,S.-C.Yoon,C.Badenesetal.:Delay-timedistributionofcore-collapsesupernovae
3.1. Delay-timedistributionofsinglestars The most striking feature that distinguishes the binary star
distribution from that of single stars is the prominent excess of
In a population of single stars formed in an instantaneous star- eventsbetween50and200Myr.Theseoccurafterthelastsingle
burstatτ=0,weexpectccSNebetweenτmin,cc ≈3Myr,corre- starexplodedatτmax,cc ≈48Myr.Werefertothemas“latecore-
spondingtothelifetimeofthemostmassivestarinoursimula- collapse supernovae” and discuss them in detail in section 4.
tion, and τmax,cc ≈ 48Myr, corresponding to the lifetime of the These late events account for 15.5+8.8% of the total number of
−8.3
leastmassivestarthatundergoescorecollapseinoursimulation, ccSNe. The main value quoted here corresponds to the relative
with Mmin,cc = 7.53M(cid:12) (Figure1).ThiscanbeseeninFigure2 contributionoflateeventswithrespecttoallcore-collapseevents
whereweshowtheDTDforsinglestarsfora106M(cid:12) starburst. asfoundinourstandardsimulation.Theerrorsreflectthemini-
The diagram shows the number of ccSNe per logarithmic time mumandmaximumwefindwhenconsideringmodelvariations,
bin. aswediscussinsection5.TheaboveratiooflateccSNetototal
The distribution rises steadily between τ and τ . ccSNewillbereferredtoas f fromnowon.
min,cc max,cc late
TheslopeofthedistributionisdictatedbytheslopeoftheIMF Theaveragedelaytimeforapopulationincludingarealistic
and the derivative of τ−1(M), the inverse of the lifetime-mass fraction of binaries is τ = 21.6Myr, around 20% longer than
av
relation. The IMF favors less massive stars that contribute in inoursinglestarsimulation.Themediantimedelayisτ =
50%,all
the later time bins. The flattening of the lifetime-mass relation 22.1Myr,nearly10%longerthaninoursingle-starsimulation.
for the highest masses leads to a relative pile-up of ccSNe in We observe a tail of very late events with delay times >
the early time bins. The net effect is a distribution that rises 300Myr.Theyareextremelyrareinourstandardsimulationac-
steadily, when expressed in the units chosen here, with a slope counting for less than 0.01% of all core-collapse events. How-
that is slightly steeper at early times, τ (cid:46) 5Myr. The average ever,insomeof thevariationsthatweconsider,wefind higher
delay time of the distribution is τ = 17.5Myr, the median is fractions of 0.03%. These very late events result from a vari-
av
τ =19.6Myr. ety of rare binary evolutionary paths. They typically originate
50%,all
The units and axes used here have the advantage that an fromsystemswithalow-masssecondary(<4M(cid:12))inaninitially
equalnumberofsystemsoccupyanequalareainthisdiagram, wide orbit (∼ 1000 days). The systems usually evolve through
which is useful as a visualization of the discussion in the para- multipleCEandmasstransferepisodes,eventuallyleadingtoa
graphsthatfollow.Forconvenience,wealsoshowtheevolution mergerofamassivewhitedwarf(theprimary)withaheliumstar
oftheccSNrate(thenumberofeventsperyearpermass)inAp- secondary.Someofthesemayresultinanaccretion-inducedcol-
pendixA.Therateforsinglestarspeaksaround5.1Myrinour lapse,buttodeterminethefateofthesemergersrequiresdetailed
simulation to a value of approximately 4.75×10−10 events per modelingbeyondthescopeofthiswork.
yrperM ,asshowninFigureA.1.
(cid:12)
3.3. Totalnumberofcore-collapsesupernovae
3.2. Delay-timedistributionincludingbinaries Accounting for binaries increases the number of ccSNe for
the same total stellar mass of a population. We find a rela-
The picture changes when we account for a realistic fraction tive increase of 14+15% when accounting for a realistic binary
of binary systems. Some intermediate-mass stars, with M < −14
population. The increase is due to the added contribution of
M , can accrete mass from their companions and become
min,cc intermediate-masssystems,whicharefavoredbytheIMF.How-
massive enough to experience the advanced nuclear burning
ever, the increase is limited by the fact that we normalize our
stages. As a result, they end their lives as supernovae leaving
simulationsbythetotalstellarmass;iftheaveragemassofsin-
neutron stars as remnants instead of becoming white dwarfs. gle stars is (cid:104)M(cid:105) then that of a binary systems is (cid:104)M + M (cid:105) =
Mintaossthaecccreentitoranlablsuornreinjugvreengaitoenssa,setffarebcteicvaeulysepfrroelsohnfguienlgisitmsilxifeed. (cid:104)M(cid:105) + 1/2(cid:104)M(cid:105)=3/2(cid:104)M(cid:105),assumingthatsingleandpri1mary2stars
follow the same IMF and taking into account that the typical
However,massaccretionalsoacceleratesaging.Makingthestar
mass ratio is q ≈ 0.5. Thus, in a population of the same total
moremassiveincreasesitsluminosityandthustherateatwhich
mass, the number of systems is lower when binary systems are
itburnsitsremainingfuel.Conversely,massstrippingcan,under included.Wefindthatthenetresultofboththeaboveeffectsis
certainconditions,preventamassivestarfromendingitslifeas
anincreaseinthenumberofccSNeinapopulationthatcontains
asupernova.Thisisonlytrueifmasslossoccursearlyinitsevo-
binarysystems.
lution,beforethestarhasafullydevelopedcore.Weinvestigate
ThetotalnumberN ofccSNeina106M stellarpopulation
howallthesebinaryevolutionprocessesinterplayandcompete (cid:12)
is less well constrained because of uncertainties in the normal-
inaffectingtheDTD.
izationofthemasscontainedinlow-massstars.Inourstandard
InFigure3weshowthedistributionofccSNeresultingfrom simulations, we find N = 1.14×104 for single stars and N =
a106M(cid:12)starbursteventinourstandardsimulationthataccounts 1.30×104 for a realistic binary fraction. Variations in the IMF
for binaries. The single star DTD is over-plotted for compari- slopealone(α=−3.0and−1.6)leadtoN =0.28−2.53×104,re-
son.Bothdistributionsareremarkablysimilaratearlytimes.The spectively,inthesingle-starpopulationandN =0.35−2.53×104
differencesbecomeevidentataround20Myr,wherethebinary in the simulation that includes binaries. All other model varia-
distributionpeaks.Ataround30-50Myr,thebinarydistribution tions considered in Table 2 lead to changes in the total number
shows a deficit with respect to the single star distribution. The ofeventsbylessthan25%.
deficitresultsfromclosesystemsinwhichtheprimarystarhasa
massjustabovebutcloseto M .Ifitisstrippedofitsenve-
min,cc
lope early in its evolution, that is, before the completion of hy- 4. Latecore-collapsesupernovaeandtheir
drogen burning, this can prevent its core from growing enough
progenitors
inmasstoreachtheadvancedburningstages.Thus,interaction
withacompanionpreventsthesestarsfromendingtheirlivesas Late ccSNe occurring around 50-200Myr after star formation
ccSNe. arenotpredictedinsinglestellarevolution.Theyareexclusively
Articlenumber,page7of22
A&Aproofs:manuscriptno.zapartas_arxiv_submission_final
Equivalent single star initial mass (M )
70 35 20 15 10 8 6 4 fl
1600
single stars
u
incl. binaries a
1400 t
1200
1
−
) 1000
fl
M
6
0 800
1
(
e
N
S 600
c
c
400
200
0
1 2 5 10 20 50 100 200 500 1000
Time after starburst (Myr)
Fig.3.Thedelay-timedistributionofcore-collapsesupernovaeforapopulationconsistingof70%binarysystems(greenhistogram)compared
tothedistributionforapopulationofonlysinglestars(blackdashedline).Itshowsthenumberofeventsperlogarithmictimebinforastarburst
of106M forourstandardmodels.Thetopaxisshowstheinitialmassofsinglestarswiththecorrespondinglifetimegiveninthebottomaxis,
(cid:12)
computedwithbinary_c.Themoststrikingdifferenceisthefractionof‘late’core-collapsesupernovae(f = 15.5+8.8%),afterthelastmassive
late −8.3
singlestarexplodesatτ ≈48 Myr.Theerrorsinthefractionaboveresultfromvariationsofourstandardassumptions.
max,cc
0.18 0.40 0.25 3.0 0.7
00..1146 00..3305 0.20 2.5 00..56
x) 00..1102 0.25 0.15 2.0 0.4
f( 00..0068 00..1250 0.10 11..05 0.3
00..0024 00..0150 0.05 0.5 00..12
0.00 0.00 0.00 0.0 0.0
6 8 10 12 14 16 18 20 4 6 8 10 2 4 6 8 0.2 0.4 0.6 0.8 1.0 0 1 2 3
M (M ) M (M ) M (M ) q logP (days)
tot 1 2
(cid:12) (cid:12) (cid:12)
Fig.4. Theprogenitorpropertiesof‘late’core-collapsesupernovaeforourstandardsimulationwithbinarystars.Thenormalizedhistograms
showthedistributionoftheinitialtotalmassM ,theinitialmassoftheprimary,M ,andsecondary,M ,theinitialmassratio,q≡ M /M ,and
tot 1 2 2 1
theinitialorbitalperiodPofbinarysystemsthatproduceatleastonecorecollapseafterthelastsinglestarhasexplodedataround48 Myr.
the product of interacting binaries and, as mentioned, they ac- tialmassoftheprimaryandsecondary,M andM respectively,
1 2
countfor f =15.5+8.8%ofallccSNe.Almostallsystemsthat the initial mass ratio, q ≡ M /M , and the initial orbitalperiod
late −8.3 2 1
leadtoalateeventhaveatleastoneintermediate-massstarwith log P.
10
M < M = 7.53M , the threshold mass for a single star
min,cc (cid:12) The distribution of initial total mass for the progenitor sys-
to undergo core collapse. Approximately three out of four late
temspeaksat9M (leftmostpanelofFigure4).Itextendsupto
eventsresultfromsystemsinwhichbothstarshaveinitialmasses (cid:12)
around15M ,thatis,approximately2M ,rapidlydeclining
below M .Bothstarsinthesesystemsweredestinedtoend (cid:12) min,cc
min,cc forhighermasses.Thedistributiondropsoffsteeplyformasses
theirlivesaswhitedwarfs,ifitwerenotfortheinteractionwith
lowerthanthepeakwithaminimumapproaching M .
their companion. This can be seen in Figure 4, where we show min,cc
the normalized distributions of the initial properties of the pro- The typical mass of the primary star is in the range 5–8M
(cid:12)
genitorsystems.Weprovidetheinitialtotalmass, M ,theini- (secondpanelofFigure4).Starsinthismassrangetakearound
tot
50-200Myrtoevolveoffthemainsequenceandstartinteracting.
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E.Zapartas,S.E.deMink,R.G.Izzard,S.-C.Yoon,C.Badenesetal.:Delay-timedistributionofcore-collapsesupernovae
quentmergerchannelsthatwedonotdiscussareresponsiblefor
Evolu6onary
 channels
 for
 “late”
 core-­‐collapse
 Supernovae

acombinedcontributionof16%ofthelateevents.
Forward
 mergers

  9%
  15%
  Figure5providesasummaryoftherelativeratescontributed
(24%)
  MS
  MS
  HG
  MS
  bythemainchannels.Whileoursimulationscannotreliablyfol-
low the details of the merger process and the interior structure
ofthenewlyformedstellarobject,wecanpredictrelativerates
Reverse
 mergers

  20%
  10%
  ofthedifferentchannelsandassestheevolutionarystatusatthe
(47%)

HG
  HG
  onsetofthemerger.Thisinformationcanguidefuturenumerical
HeStar
  COWD
  experiments.
11%
  6%
  Forward mergers – Inourstandardsimulations,wefindthat
HG
  AGB
  24% of the late ccSNe come from systems that experience a
ONeWD
  COWD
  merger in which the expansion of the primary star beyond its
Rochelobeinitiatesthemergerprocess.Wedistinguishthefol-
Other
 merger
 channels

  Non-­‐merger
 channels

  lowingcases.
combined
 (16%)
  combined
 (13%)

MS⇒MS: The merger between two main-sequence stars con-
tributes 9% of the late ccSNe in our standard simulations;
Fig. 5. The main channels for ‘late’ core-collapse supernovae in our they result from intermediate-mass primaries with initial
standard simulation and their relative contribution to the number of masses of 5–8M(cid:12) in tight binaries with initial orbital peri-
lateevents(onlyshowingthosethatcontribute>5%ofthenumberof odsthataretypicallyshorterthanapproximately3days.The
late ccSNe, i.e., >0.75% of the total number of ccSNe). For merger maincontributioncomesfromsystemswithinitialmassra-
channels, we indicate the evolutionary state of the primary and sec- tiosq<0.65.Insuchsystems,theinitialrapidphaseofmass
ondary star at the onset of merging. Arrows indicate the direction of transfer drives the accreting star out of thermal equilibrium
mass transfer preceding the merger, which can be forward (from pri-
causingittoswellup.Suchsystemscomeintocontactdur-
marytosecondary)orreverse(fromsecondarytoprimary).MS:main
ingtheinitialrapidmasstransferphase,denotedasCaseAR,
sequence,HG:Hertzsprunggap,COWDandONeWD:carbon-oxygen
withAreferringtothefactthatthedonorstarstillresideson
andoxygen-neon-magnesiumwhitedwarf,HeStar:nakedheliumstar,
themainsequenceandRreferringtotherapidmasstransfer
AGB:AsymptoticGiantBranch.
phaseintheclassificationbyKippenhahn&Weigert(1967)
andNelson&Eggleton(2001).Asecondcontributioncomes
from systems with initial mass ratios q ≈ 1 in periods of
Hence, it is mainly the relatively slow evolution of the primary
less than approximately 2 days, in which both stars evolve
that causes the eventual explosions in these systems to be late.
onasimilartimescale.Thestarscomeintocontactwhenthe
Asecondaryreasonforlongerdelaytimesisrejuvenationofthe
secondarystaralsofillsitsRochelobeduetoitsownevolu-
accretingstar(ormergerproduct).
tionaryexpansion.Thisoccursduringtheslownucleartime
The distribution of secondary masses ranges from approxi-
scalemasstransferphase(denotedasCaseAS).
mately 1 - 8 M and peaks near 4.5M , as can be seen in the
(cid:12) (cid:12) The primary has typically already completed over 80% of
thirdpanelofFigure4.Thereisapreferenceforsystemsthatini-
its main sequence evolution at the moment of coalescence.
tiallyhavemassratiosnearunity,asshowninthefourthpanel.
ThesecondaryisinasimilarevolutionaryphaseinCaseAS,
Mostprogenitorsystemsoriginatefromsystemswithinitialor-
whereasitisquiteunevolvedinCaseAR,havingonlycom-
bitalperiodslessthanapproximately30days,ascanbeseenin
pleted10–30%ofitsmain-sequenceevolution.InCaseAR
therightmostpanel.Systemswithinitialmassratiosnearunity
mergers,themoreevolvedprimarystaristhemoremassive
andorbitalperiodsbelow∼30daysgenerallyexperienceamore
component at the onset of the merger, at 5−8M , whereas
conservative first phase of mass transfer in our simulations (cf. (cid:12)
the secondary mass is 1−4M . In Case AS mergers, mass
Figure3ofSchneideretal.2015).Thismeansthatasignificant (cid:12)
transferleadstoareversalofthemassratio.Asaresult,the
fraction of the mass lost by the primary star is accreted by the
massoftheprimaryisapproximately2–4M attheonsetof
secondary and is thus retained in the system. This is necessary (cid:12)
merging and that of the secondary is 6–9M (see also Fig-
for an intermediate-mass binary system to produce a ccSN be- (cid:12)
ureB.1intheappendix).
cause in most cases neither of the stars is individually massive
In both cases, the stars come into a deep over-contact con-
enoughtoproduceacollapse.
figuration (Pols 1994; Wellstein et al. 2001; de Mink et al.
2007). In our simulations, contact results in merging of the
stars as this is the most likely outcome (see also discussion
4.1. Evolutionarychannels
by de Mink et al. 2014). The simulations of Gaburov et al.
Theevolutionarychannelsthatleadtolateeventsofteninvolve (2008) and Glebbeek et al. (2013) suggest that the merger
multiple phases of mass transfer. The majority of late events, productthatformswillinitiallybeapuffedupandredobject
87% in our standard simulation, result from binary channels in (Tylenda et al. 2011; Pejcha et al. 2016), but as it radiates
whichthetwostarscoalesce.Wedistinguishbetween‘forward’ awaytheexcessenergy,itwillrecoverathermalequilibrium
and ‘reverse’ mergers depending on whether it is the primary, structure. The core of the primary is thought to sink to the
thatis,theinitiallymoremassivestar,orthesecondarythatfills center of the new object with the core of the less evolved
itsRochelobeandinitiatesthemergerprocess,respectively.Be- secondarysettlingabove(Glebbeeketal.2013).Theroleof
low,weelaborateonthesemergerchannelsandafterwediscuss mixing and mass loss during this stage is highly uncertain.
the non-merger scenarios. We limit the discussion to channels Tofirstorder,thefurtherevolutionmaybeapproximatedby
thatcontributeatleast5%ofthelateevents(i.e.,morethanap- that of a rejuvenated (rotating) single star. It will continue
proximately0.75%ofthetotalcore-collapserate).Thelessfre- with the subsequent burning stages and, if massive enough,
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A&Aproofs:manuscriptno.zapartas_arxiv_submission_final
enditslifeasitscorecollapses.Whetherornottheabnormal Nomoto1984;Habets1986;Nomoto1987)andcanproduce
interiorchemicalprofileorenhancedbudgetofangularmo- ametalcoremassofatleastM .
min,metal
mentumleavessignificantimprintsonthefinalpre-explosion The typical progenitor system involves two intermediate-
structureandleadstoobservablesignaturesremainstobein- mass stars with similar initial masses (q>0.6) and an ini-
vestigated. tial period shorter than approximately 10 days. The typical
HG⇒MS: Forward mergers involving a post-main-sequence massofthenakedHeprimarystaratthemomentofmerging
primarystararedominatedbycaseswheretheprimarystar ranges from 0.4 to 1.3M , while the secondary star ranges
(cid:12)
iscrossingtheHertzsprunggap(HG).Theseso-calledCase from6to13M andhasdevelopedaHecoreof1.5to3M
(cid:12) (cid:12)
B mergers account for 15% of the late ccSNe. They orig- (seealsoFigureB.1intheappendix).
inate from systems with unequal masses (q < 0.4 in our
COWD⇐HG: Wefindthat10%oflateccSNeresultfromthe
standard simulations). The systems come into contact as a
mergerofamassiverecentlyformedCOwhitedwarf,being
resultoftheexpansionofthesecondaryinresponsetorapid
massaccretionand/or,forthemostextrememassratios,be- theremnantoftheprimary,whichisengulfedbyaHGsec-
ondarystar.ThetypicalmassoftheCOWDisapproximately
causemasstransferisunstable(seehoweverPavlovskiietal.
0.9M ,beingtheremnantofastarwithinitialmassaround
2016). This leads to a common envelope phase that may (cid:12)
5-8M ,althoughthereisasmallcontributionofprogenitors
lead to the ejection of (part of) the envelope while the or- (cid:12)
with masses of 9-12M that results in more massive white
bitshrinks.Iftheejectionfails,weareleftwithamergerof (cid:12)
dwarfs(seealsoFigureB.1intheappendix).Thefirstgroup
apartiallystrippedpost-main-sequenceprimarywithitsless
originatesfromwidesystemswithperiodsP>100daysex-
evolved main-sequence secondary. The typical mass of the
periencing almost non-conservative mass transfer. The sec-
primaryis6–7M attheonsetofthemerger.Atthisstage,it
(cid:12) ond group involves systems in tighter orbits, P (cid:46) 30 days,
hasaninertheliumcoreof1–1.4M .Thetypicalsecondary
(cid:12)
thatevolvedfairlyconservatively,allowingthesecondaryto
star has a mass of 1–3M in our standard simulations (see
(cid:12)
almostdoubleitsmass.
alsoFigureB.1intheappendix).
Simulations by Glebbeek et al. (2013) indicate that the he- Assessing the outcome of these mergers will require fu-
lium core of the original primary will sink to the center. turededicatedsimulations.Sabach&Soker(2014)havead-
Thesteepmeanmolecularweightgradientwilllikelyinhibit dressed the question of what is the result of these reverse
mixingbetweenthecoreandlayersabove.Afterthemerger common envelope channels involving a white dwarf. Here
product has radiated away the excess energy and restores we speculate on some of the possible outcomes. We expect
thermalequilibrium,ithasthestructureofagiantwithacore the white dwarf to spiral in and sink to the center of the
massthatisabnormalforitstotalmasscomparedtoaregu- merger product, where it will find itself surrounded by the
largiantcreatedthroughsingle-starevolution.Afractionof formerheliumcoreofthesecondary,thatis,by1–3M(cid:12)ofhe-
theseobjectsareexpectedtoappearasbluesupergiants.The lium.Thestructureofthestarisapost-core-helium-burning
heliumcoregrowsasaresultofshellhydrogenburningand, star,withanabnormalratioforthecoreandshellmass.Nu-
whenmassiveenough,continueswiththeadvancedburning clear burning will proceed in a hydrogen burning shell (if
stages. The final pre-explosion properties are uncertain but hydrogenisleftafterthespiralinphase)andaheliumburn-
someofthesemaygiveriseto1987-likeevents(e.g.,Podsi- ingshell.TheCOcorewillgrowduetoashesofthehelium
adlowskietal.1990);seealsoVanbeverenetal.(2013)and burningshell.Thismayleadtooff-centerignitionofcarbon.
Justhametal.(2014). Carbonignitionmayoccurinnon-degenerateconditionsand
lead to the formation of an ONeMg core, which may even-
tually collapse as a result of electron capture (e.g., Nomoto
Reverse mergers – Approximately half of the late ccSNe 1984).
(47%) in our standard simulation (equivalent to 7.5% of all cc-
Alternatively, if carbon ignition occurs under degenerate
SNe) originate from mergers following a reverse mass-transfer
conditions,itcould,inprinciple,leadtoeitheradeflagration,
phase from the initially less massive secondary back to the ini-
leavinganeutronstarremnant,oradetonationoftheentire
tially more massive primary. Nearly all these systems experi-
core,similartoatypeIathermonuclearexplosion(Nomoto
enced one or more semi-conservative phases of mass transfer
&Kondo1991).ThemaindifferencefromnormalIasuper-
from the primary to the secondary before, allowing the sec-
novae is that it would occur inside a hydrogen envelope. In
ondary to grow beyond the mass threshold M . The sec-
min,cc the case of the detonation of the core without leaving any
ondarywouldhaveexplodedasaccSNasaresultofthis.How-
remnant, it may be similar to the “type 1.5” supernova that
ever, as it evolves and expands, it encounters the stripped rem-
Iben&Renzini(1983)proposed,whichisthedetonationof
nant core of the primary, which is still in orbit, triggering a re-
theCOcoreofanAsymptoticGiantBranch(AGB)starthat
versemass-transferphase.Thedonorstarisnowtypicallyafew
reachesamassclosetotheChandrasekharlimit.Ithasbeen
timesmoremassivethantheremainingcoreoftheprimary,lead-
suggested that this can also be the final outcome of single
ing to common envelope. The secondary engulfs the primary.
intermediate-massstarsinverylowmetallicityenvironments
Theorbitshrinkswhilepartoftheenvelopeofthesecondaryis
(e.g.,Zijlstra2004;Lauetal.2008)wherethewindmassloss
ejected. If complete ejection is unsuccessful, the two stars will
islowenoughtoallowtheformationofsuchamassiveCO
coalesce.Wedistinguishdifferentcasesdependingontheevolu-
core.Asweshowhere,binaritymayallowsimilarstructures
tionarystageoftheprimaryandsecondary.
evenathighermetallicities.Thetheoretical“type1.5”super-
HeStar⇐HG: In our standard simulation, 20% of the late nova mechanism is suggested as a possible explanation for
events are produced by the merger of the naked helium theobservedclassofthermonuclearexplosionsthatshowin-
core of the initially more massive primary star and a post- teraction with circumstellar material, sometimes referred to
main-sequence secondary after a common envelope phase. asIa-CSMsupernovae(e.g.,SN2002ic,Hamuyetal.2003).
Thesearecaseswherethecombinedheliumcoremassafter A third possibility that we cannot exclude at present is that
the merger exceeds the single star threshold for ccSN (e.g., the effects of mass loss and possible dredge-up prevent the
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