TOAPPEARINTHEASTROPHYSICALJOURNAL PreprinttypesetusingLATEXstyleemulateapjv.10/09/06 YOUNGANDMASSIVEBINARYPROGENITORSOFTYPEIaSUPERNOVAE ANDTHEIRCIRCUMSTELLARMATTER IZUMIHACHISU DepartmentofEarthScienceandAstronomy,CollegeofArtsandSciences,UniversityofTokyo,Komaba3-8-1,Meguro-ku,Tokyo153-8902,Japan MARIKOKATO DepartmentofAstronomy,KeioUniversity,Hiyoshi4-1-1,Kouhoku-ku,Yokohama223-8521,Japan AND 8 KEN’ICHINOMOTO 0 DepartmentofAstronomy,UniversityofTokyo,Hongo7-3-1,Bunkyo-ku,Tokyo113-0033,andInstituteforthePhysicsandMathematicsoftheUniverse, 0 UniversityofTokyo,Kashiwa,Chiba277-8582,Japan 2 toappearintheAstrophysicalJournal n ABSTRACT a J WepresentnewevolutionarymodelsforTypeIasupernova(SNIa)progenitors,introducingmass-stripping 7 effect on a main-sequence (MS) or slightly evolved companion star by winds from a mass-accreting white 2 dwarf (WD). The mass-stripping attenuates the rate of mass transfer from the companion to the WD. As a result, quitea massive MScompanioncan avoidforminga commonenvelopeandincreasethe WD mass up ] totheSNIaexplosion. Includingthemass-strippingeffect,wefollowbinaryevolutionsofvariousWD+MS h systemsandobtaintheparameterregionintheinitialdonormass–orbitalperiodplanewhereSNe Iaoccur. p The newly obtained SN Ia region extends to donor masses of 6- 7 M , although its extension depends on - ⊙ o the efficiencyof mass-strippingeffect. The strippedmatter would mainly be distributed on the orbitalplane r andformverymassivecircumstellarmatter(CSM)aroundtheSNIaprogenitor. ItcanexplainmassiveCSM t s around SNe Ia/IIn(IIa) 2002ic and 2005gj as well as tenuous CSM around normal SN Ia 2006X. Our new a model suggests the presence of very young (.108 yr) populations of SNe Ia, being consistent with recent [ observationalindicationsofyoungpopulationSNeIa. 2 Subjectheadings:binaries: close—circumstellarmatter—stars: winds,outflows—supernovae: individual v (SN2002ic,SN2005gj,SN2006X) 9 1 3 1. INTRODUCTION 2002ic (Hamuyetal. 2003) and 2005gj (Alderlingetal. 0 2006; Prietoetal. 2007) (Type Ia/IIn or IIa (Dengetal. The nature of Type Ia supernova (SN Ia) progenitors has . 2004)), thermal X-rays from 2005ke (Immleretal. 2006), 0 not been clarified yet (e.g., Niemeyer&Hillebrandt 2004; 1 Nomotoetal. 2000),althoughithasbeencommonlyagreed andNaIDlinesin2006X(Patatetal. 2007a). The identification of SN 2002ic as an SN Ia has been 7 that the exploding star is a mass-accreting carbon-oxygen 0 white dwarf (C+O WD). For the exploding WD itself, the confirmed by the recent spectral comparison between SN : observed features of SNe Ia are better explained by the 2005gj and SNe Ia (Prietoetal. 2007), being against v the Type Ic suggestion by Benettietal. (2006). Sev- Xi Cmhoadnedlr(aes.egk.,hLarivmioass20m0o0d).elHthoawnetvheer,suthbe-Crehhaansdrbaeseenkhnaormcleaassr eral CSM interaction models suggested a 1- 2 M⊙ CSM (Chugaietal. 2004; Nomotoetal. 2005). The evolution- r observational indication as to how the WD mass gets close a ary origin of such a massive CSM has been explored by enough to the Chandrasekhar mass for carbon ignition; i.e., Livio&Reiss (2003)basedonacommonenvelopeevolution whether the WD accretes H/He-rich matter from its binary model, by Han&Podsiadlowski (2006) from the delayed companion [single degenerate (SD) scenario], or two C+O dynamical instability model of binary mass transfer, and by WDsmerge[doubledegenerate(DD)scenario]. Wood-Vasey&Sokoloski (2006) based on a recurrent nova Recently, the following two important findings have been modelwitharedgiantcompanion. reportedinrelationtotheSNIaprogenitors:(1)circumstellar FornormalSNe Ia, non-detectionofradio hasputthe up- matter (CSM) around the progenitors, and (2) a very young (.108yr)populationoftheprogenitors. per limit of mass loss rate as M˙/v10 .10- 8M⊙ yr- 1, where Circumstellar Matter: In the SD scenario, H/He-rich v10≡v/10kms- 1(Panagiaetal. 2006).However,theoptical CSM is expected to exist around SNe Ia as a result of observationsofSN2006XhavedetectedvariableNaIDlines mass transfer fromthe companionas well as the WD winds fromCSM,whoseexpansionvelocityandmasshavebeenes- (e.g.,Nomoto 1982;Hachisu,Kato,&Nomoto1999a).Thus timated to be v10 ∼ 10 and ∼10- 4 M⊙ (Patatetal. 2007a). searchingforH/He-richCSM is oneof thekeyobservations Patatetal. havesuggestedthattheCSMinSN2006Xorigi- toidentifythe progenitors(e.g.,Lundqvistetal. 2003). Re- natedfromthered-giantcompanionbecauseofrelativelylow centlydetectionsofsuchCSMhavebeenreportedforseveral velocities. Comparing the SN 2006X light curves with the SNeIa,i.e.,observationsofnarrowH-emissionlinesinSNe other normal SNe Ia light curves, Wangetal. (2007a) sug- gested that the obvious deviation, the decline rate is slow- Electronicaddress:[email protected] ing down in a later phase, can be explained by an interac- Electronicaddress:[email protected] tion between ejecta and CSM or a light echo of circumstel- Electronicaddress:[email protected] 2 Hachisuetal. lar/interstellarmatter(seealsoWangetal. 2007b). Inthepresentpaper,weshowthatthismass-strippingeffect YoungPopulation: AccordingtoMannuccietal. (2006), derives(1)formationsofcircumstellarmatter(CSM)around thepresentobservationaldataofSNeIaarebestmatchedbya SNeIaand(2)averyyoungpopulationofSNeIa. Wesum- bimodalpopulationoftheprogenitors,inwhichabout50per- marize our basic treatments of mass-stripping effect and bi- centofSNeIaexplodesoonaftertheirstellarbirthatthedelay nary evolutions in §2, and then show our numerical results timeoft ∼108yr,whiletheremaining50percenthavea and their relations to a very young population of SNe Ia in delay much wider distribution of the delaytimeof t ∼ 3 Gyr. §3. In§4wepresenttheoriginofCSMaroundSNeIabased delay Aubourgetal. (2007) recentlyreportedevidencefora short on our results and show a relation between the very young (lessthan70Myr)delaytimecomponentintheSNIapopu- populationofSNeIaandtheirmassiveCSM.Discussionand lation. Inthispaper,wedefinethetermdelaytimeastheage concludingremarksfollowin§§5and6. ofabinarysystemattheSNIaexplosion,inordertocompare our results with the earlier results (e.g., Greggio&Renzini 2. MASS-STRIPPINGEFFECTANDBINARYEVOLUTION 1983;Greggio 2005;Mannuccietal. 2006). Strong winds from a mass-accreting WD collide with the This kind of short delay times (tdelay .108 yr) of SNe Ia companionstar andstrip offitssurface. Thismass-stripping havebeen suggestedfromthe distributionofSNe Ia relative effect plays an important role in binary evolutions (e.g. tospiralarms(e.g.,Bartunovetal. 1994;dellaValle&Livio Hachisuetal. 1999a). Here we reformulateits treatmentin 1994). Recently,DiStefano&Kong (2003)reported,based ourbinaryevolutioncalculation. ontheChandradatafromfourexternalgalaxies:anelliptical galaxy (NGC 4967), two face-on spiral galaxies (M101 and 2.1. NewAspectsofBinaryEvolutions M83), andan interactinggalaxy(M51),thatin everygalaxy Firstwebrieflyintroduceanewbinaryevolutionaryprocess there are at least several hundred luminous supersoft X-ray sources(SSXSs)withaluminosityof&1037ergs- 1andthat, throughstages(a)-(d)below(alsoshowninFig.1a–d),where (c)and(d)arenewstagesintroducedbymass-stripping. in the spiral galaxies M101, M83, and M51, SSXSs appear (a) The more massive (primary) component of a binary tobeassociatedwiththespiralarms. Thelattermayindicate evolves to a red giant star (with a helium core) or an AGB thatSSXSsareyoungsystems,possiblyyoungerthan108yr, star(withaC+Ocore)andfillsitsRochelobe. Masstransfer and has some close relation to the youngpopulationof SNe fromtheprimarytothesecondarybeginsandacommonen- Ia. velopeisformed. Afterthefirstcommonenvelopeevolution, The SD scenario has ever not predicted such young pop- theseparationshrinksandtheprimarycomponentbecomesa ulations of t ∼ 108 yr, corresponding to, at least, the zero-age maidnel-asyequence (ZAMS) stars at mass 5- 6 M heliumstaroraC+OWD.TheheliumstarevolvestoaC+O ⊙ WDafteralargepartofheliumisexhaustedbycore-helium- (see, e.g.,Li&vandenHeuvel 1997;Hachisuetal. 1999b; burning.WeeventuallyhaveaclosepairofaC+OWDanda Langeretal. 2000; Han&Podsiadlowski 2004). In the main-sequence(MS)starasshowninFigure1a. present paper, we propose a scenario for such a young SN (b) After the secondary evolves to fill its Roche lobe, the Iapopulationbyintroducingmass-strippingeffectintobinary mass transfer to the WD begins. This mass transfer occurs evolutions. Mass-accreting WDs blow optically thick winds in a thermal timescale because the secondary mass is more when the mass transfer rate to the WD exceeds the critical rate of M˙ ∼1×10- 6M yr- 1 (Hachisuetal. 1996). The massivethantheWD.Themasstransferrateexceedsthecrit- cr ⊙ ical rate for the optically thick wind to blow from the WD WDwindcollideswiththesecondary’ssurfaceandstripsoff (Hachisuetal. 1996,1999a,b). matter.Whenthemass-strippingeffectisefficientenough,the (c) Optically thick winds from the WD collide with masstransferratetotheWDisattenuatedandthebinarycan the secondary surface and strips off its surface layer avoidthe formationof a commonenvelopeevenfora rather (Hachisu&Kato 2003a,b,c). Thismass-strippingattenuates massivesecondary. therateofmasstransferfromthesecondarytotheWD,thus The mass-stripping effect on a MS companion has been preventing the formation of a common envelope for a more first introduced by Hachisu&Kato (2003b,c), who ana- massive secondary in the case with than in the case without lyzed two quasi-periodic transient supersoft X-ray sources, RX J0513.9- 6951 and V Sge: RX J0513 shows a quasi- this effect. Thus the mass-stripping effect widens the donor periodicoscillation betweenopticalhigh(∼100- 120days) massrangeofSNIaprogenitors(seeFig. 3below). (d)Suchstripped-offmatterformsamassivecircumstellar and low (∼ 40 days) states with an amplitude of 1 mag torus on the orbital plane, which may be gradually expand- (Alcocketal. 1996). RX J0513is X-ray brightonlyduring ingwithanoutwardvelocityof∼10- 100kms- 1 (Fig. 1d), theopticallowstates(Reinschetal. 2000). Hachisu&Kato becausetheescapevelocityfromthesecondarysurfacetoL3 (2003b)proposedamodelthatthemasstransferismodulated point is v ∼[(φ - φ )GM/a]1/2 ∼100 km s- 1 (see be- bytheWDwindbecausetheWDwindcollideswiththecom- esc L3 MS low). Subsequentinteractionbetweenthefastwindfromthe panionandstripsoffitssurfaceandattenuatesthemasstrans- WDandtheveryslowlyexpandingcircumbinarytorusforms ferrate.Whenthemasstransferratedecreasesbelowthecrit- ˙ anhourglassstructure(Fig. 1c–d). ical rate M , the WD wind stops and supersoft X-ray turns cr on. Thiscorrespondstoan opticallowsate. Thenthemass- transferraterecoversbecauseofnoattenuationbyWDwinds 2.2. FormulationofMass-stripping andtheWDblowswindsagain. X-rayturnsoffandanopti- Faststrongwindscollidewiththecompanionasillustrated calhighstate resumesandthe binarystartsthe nextcycleof inFigure1. Thecompanion’ssurfacegasisshock-heatedand quasi-periodicoscillation. Suchaself-sustainedmodelnatu- ablatedinthewind.Weestimatetheshock-heatingbyassum- rallyexplainsmajorcharacteristicsofquasi-periodichighand ing that the velocity component normal to the companion’s low states and this success encouragesus to adopt the same surface is dissipated by the shock and the kinetic energy is ideaintheevolutionscenarioofsupersoftX-raysourcesand converted into the thermal energy of the surface layer. The SNIaprogenitors. heatedsurfacelayerexpandstobeablatedinthewind. ProgenitorsofTypeIaSupernovae 3 WD MS (a) mass winds stripping (b) torus torus (c) hot WD winds 1000 km/s line of expanding sight torus 10-100 km/s (d) FIG. 1.— Aschematic configuration ofabinary evolution including mass-stripping effect. (a)Herewestartapair ofaC+O WDandamoremassive main-sequence (MS)starwithaseparationofseveraltoafewtensofsolarradii. (b)WhenthesecondaryevolvestofillitsRochelobe, masstransferonto theWDbegins. Themasstransferrateexceedsacriticalrateforopticallythickwinds. StrongwindsblowfromtheWD.(c)ThehotwindfromtheWDhits thesecondaryandstripsoffitssurface. (d)Suchstripped-offmaterialformsamassivecircumstellar diskortorusanditgraduallyexpandswithanoutward velocityof∼10- 100kms- 1. TheinteractionbetweentheWDwindandthecircumstellartorusformsanhourglassstructure. TheWDmassincreasesupto MIa=1.38M⊙ andexplodesasanSNIa. WhenweobservetheSNIafromahighinclinationanglesuchasdenotedby“lineofsight,”circumstellarmatter (CSM)canbedetectedasabsorptionlineslikeinSN2006X. Toobtainthemassstrippingrate,weusethesameformula- effect of Roche lobe overflow from the L3 point. Then the tionproposedbyHachisu&Kato (2003b,c). We equatethe strippingrateisestimatedas strippingratetimesthegravitationalpotentialatthecompan- ˙ ˙ ionsurfacetothenetrateofenergydissipationbytheshock Mstrip=c1Mwind, (2) as: where GaM(φL3- φMS)·M˙strip= 12v2·ηeff·g(q)·M˙wind, (1) c1≡ φηeff-·gφ(q) (cid:18)2vG2aM(cid:19). (3) where M =M +M , M is the WD mass, M is the L3 MS WD MS WD MS main-sequencecompanionmass,aistheseparationofthebi- HereweassumethattheWDwindissphericallysymmetric. nary;φ andφ denotetheRochepotential(normalizedby IftheasphericityoftheWDwindisnotsolarge,havingalat- MS L3 GM/a)attheMSsurfaceandtheL3pointneartheMScom- itudinal(θ-angle)dependencylikeabroadanglejet,wehave panion,respectively;vistheWDwindvelocity,η istheef- a different form of g(q) and its value may be much smaller eff ficiencyofconversionfromkineticenergytothermalenergy than that for the spherically symmetric WD winds. We also bytheshock,g(q)isthegeometricalfactoroftheMSsurface assumeη =1inthepresentcalculation. Whenthewindve- eff hit by the wind includingthe inclination(obliqueshock) ef- locityisasfastas4,000kms- 1,wehavec ∼10asestimated 1 fectofthewindvelocityagainstthecompanion’ssurface(see byHachisu&Kato (2003b). Althoughthereisalargeambi- Hachisu,Kato,&Nomoto 1999a, for more details on g(q)), guityinthiskindofparameterizationasc ,Hachisu&Kato 1 andq≡M /M =M /M isthemassratio.Herewemod- (2003b,c) found the best fit models with c = 1.5- 10 for 2 1 MS WD 1 ified equation (21) of Hachisuetal. (1999a) to include the RXJ0513.9- 6953andc =7- 8forVSge. Wethusassume 1 4 Hachisuetal. FIG. 2.— SNIaevolutionsfortwotypicalcasesofWINDandCALM.(a)CaseWIND:startingfromMWD,0=1.0M⊙,M2,0=5.0M⊙,andP0=2.15days withc1=3,theWDreachestheSNIaexplosioninthewindphaseatt=6.57×105yr. TheWDmass(MWD),secondarymass(M2),masslossratefromthe secondary(M˙2),WDwindmasslossrate(M˙wind),radiusofthesecondary(R2),effectiveradiusoftheRochelobeforthesecondary(R∗2),andorbitalperiod (Porb)areplotted. Onlytheorbitalperiodismultipliedbyfourtoeasilyseeitschange. (b)CaseCALM:startingfromMWD,0=1.0M⊙,M2,0=5.0M⊙,and P0=6.79dayswithc1=3,theWDreachestheSNIaexplosionbutinanSSXSphasewithoutwindsatt=6.93×105yr.TheWDwindstopsatt=5.5×105yr. ˙ Evenafterthat,theWDlosesitsmassduetoweakheliumshellflashes(Kato&Hachisu 1999).HereMwindincludesanaveragemasslossratebyheliumshell flashesandthusdoesnotbecomezeroaftertheopticallythickwindofsteadyhydrogenshellburningstops. Valuesofthesecondaryradius(R2)andtheRoche loberadiusforthesecondary(R∗)aredividedbytwotosqueezethemintothefigure. 2 c =1, 3, and 10 to examine the dependence on the mass- matedas 1 stripping effect, because the essential ambiguity of our for- q 2 ℓ = . (5) mulationisincludedinthec1parameter. w (cid:18)1+q(cid:19) WhenwindsblowfromtheWD andstripoffthecompan- ion’s surface, the change of the separation, a˙, is calculated The ablated gas from the companionis assumed to have the from angularmomentumatthecompanion’ssurface.Thenwehave anumericalfactorof a˙ M˙ +M˙ M˙ M˙ J˙ = 1 2- 2 1- 2 2+2 h(q) a MM˙1++MM˙2 MM˙1 MM˙2 J ℓs= g(q), (6) = 1 2- 2 1- 2 2 whichwasgivenin Table1 of Hachisuetal. (1999a) andis M +M M M +21M1+2M2 ℓ1M˙ +2ℓ M˙ , (4) froatrhmerosremdaelltaciolsmopfaℓre.)d with ℓw. (See Hachisuetal. 1999a, w wind s strip s M M 1 2 (cid:0) (cid:1) 2.3. ModifiedMassTransferRate where M =M , M =M , ℓ and ℓ are the specific an- 1 WD 2 MS w s gular momenta of the WD wind and the stripped-offmatter, We have followed binary evolutions from the initial state respectively,inunitsofa2Ω withΩ beingtheorbitalan- of (M , M , P), i.e., (M , M , P ), where P is the orb orb 1,0 2,0 0 WD,0 MS,0 0 0 gular velocity. Since the WD wind is much faster than the initial orbital period. Here, the subscript naught(0) denotes orbitalmotion,thewindcannotgetangularmomentumfrom stage (a) in Figure 1, that is, before the mass transfer from theorbitaltorqueduringitsjourney,sothatthewindhasthe the secondary starts. The radius, R (M ,t), and luminosity, 2 2 same specific angular momentum as the WD, which is esti- L (M ,t), of stars which have slightly evolved off from the 2 2 ProgenitorsofTypeIaSupernovae 5 zero-agemain-sequence(ZAMS),arecalculatedusingthean- for- M˙ >M˙ . Othertreatmentsforbinaryevolutionarees- 2 cr alyticformgivenbyToutetal. (1997). sentiallythesameasthoseinHachisuetal. (1999b). The mass transfer proceeds on a thermal time scale when Figure 2 shows two typical evolutionary sequences that themassratioM /M exceeds0.79.Weapproximatethemass demonstrate the effects by the modified mass transfer rate, 2 1 ˙ transferrateas M ,inequation(7). 2 - M˙2= τM2 ·max(cid:18)ζRLζ- ζMS,1(cid:19), (7) P0(=a)2S.1ta5rtdinagysfrwoimthMc1W=D,03,=th1e.0WMD⊙,reMac2h,0es=th5e.0SMN⊙I,aaenxd- KH MS plosionin the wind phase(Case WIND) att =6.57×105 yr whereτ istheKelvin-Helmholtztimescalegivenby after the secondary fills its Roche lobe. The WD increases KH M 2 R L - 1 itsmass(MWD)uptoMIa=1.38M⊙ toexplodeasanSNIa. τKH≈3×107yr 2 2 · 2 (8) Thesecondarymass(M2)decreasesto2.01M⊙ attheexplo- (cid:18)M⊙(cid:19) (cid:18)R⊙ L⊙(cid:19) sion. Boththemassdecreasingrateofthesecondary(dashed ˙ (e.g.,Paczynski 1971),andζRL=dlogR∗/dlogMandζMS= linelabel˙edM2)andtheWDwindmasslossrate(dashedline labeled M ) are also decreasing rapidly especially in the dlogR /dlogM arethemass-radiusexponentsoftheinner wind criticalMRSochelobeandthemainsequencecomponent,respec- early phase of t .1×105 yr. This is because - M˙2 is large ˙ tively (e.g., Hjellming&Webbink 1987). The effective ra- andthemasstransferrate,M ,islargeduringthisphase, transfer dius of the inner critical Roche lobe, R∗, is calculated from andasaresult,boththeWDwindmasslossrate,M˙ ,and ˙ wind Eggleton’s(1983)empiricalformula,i.e., thestrippingrate,M ,arealsolarge.Shortlyafterthisearly strip phase,theRochelobe’smass-radiusexponent,ζ ,becomes R∗ 0.49q2/3 RL = f(q)≡ , (9) smallerthanthesecondary’smass-radiusexponent,ζMS,that a 0.6q2/3+ln(1+q1/3) is, ζ - ζ <0. This gives - M˙ =M /τ from equation RL MS 2 2 KH whereq=M /M . (7). Wekeepthismasstransferrateaslongasthesecondary When the2mas1s transfer rate to the WD exceeds a critical overfillstheRochelobe,i.e., R2>R∗2. InFigure2a, weplot value,whichisgivenby thesecondaryradius(theredline labeledR2) andthe Roche loberadiusforthesecondarycomponent(thebluelinelabeled M˙cr≈0.75×10- 6 MWD - 0.4 M⊙ yr- 1, (10) R∗2)toshowtheconditionofR2>R∗2 duringtheevolution. (cid:18) M⊙ (cid:19) (b) Starting from MWD,0 = 1.0 M⊙, M2,0 = 5.0 M⊙, and P =6.79dayswithc =3,theWDreachestheSNIaexplo- for the solar composition (hydrogen content of X =0.7 and 0 1 sionbutinaphaseofnowinds(CaseCALM)att=6.93×105 metallicity of Z =0.02), the WD blows a wind with a mass ˙ ˙ yrafterthesecondaryfillsitsRochelobe.Inthiscasetheevo- lossrateofM (<0). ThiscriticalrateofM isthesame wind cr lutionofthemasstransferrateisdifferentfromCaseWIND asthecritic˙alrateformass-accretingWDstoexpandtoagiant above.With- M˙2=M2/τKHforζRL<ζMSinequation(7),the slaiztieo,ni.oef.,M˙MRG).(TseheeNmoamssoltoossetfraol.m2th0e07W,Dforaltshoeorceccuernstdcuarlcinug- secondaryeventuallyunderfillstheRochelobe,i.e.,R2<R∗2. RG This can be seen in Figure 2b, where the line of R crosses thehydrogenshellflasheswhen- M˙2<M˙stable,whereM˙stable theline ofR∗ att ∼1×105 yr. Thisis becausethe2stripped 2 is the lowest rate for steady hydrogenburning and given by matter has rather low specific angular momentum (eq. [6]), equation sothatthebinaryseparationhardlyshrinksorevenincreases as seen from the temporal increase in the orbital period in M˙stable≈0.31×10- 6 MWD - 0.54 M⊙ yr- 1 (11) Figure 2b. In realistic binary evolutions, the mass transfer (cid:18) M⊙ (cid:19) is tuned in a way that the secondary radius is always equal n(Noommaostsoleotsasl.ass2o0c0i7a)te.dWwhiethnsMt˙esatadblye <hy-drMo˙g2e<nMs˙hcerl,l-wbeurhnainvge TtohethreefoRreoc-hMe˙ loibsedrraasdtiiucasllfyordethcreeasseecdonadftaerry,ti∼.e.1, ×R210=5Ry∗2r., 2 but have mass loss by helium shell flashes. This mass as shown in Figure 2b. Thus, the optically thick WD wind lossplaysomeroleinthebinaryevolution(Kato&Hachisu stopsatt=5.5×105yr. Insuchalowmasstransferphaseas 1999). Therefore, M˙wind is the summation of the optically M˙transfer∼1×10- 6M⊙ yr- 1, weakheliumshellflashesoccur thickwindmassloss,hydrogenshellflashes,andheliumshell and play an importantrole as a mass loss mechanism. This flashes. helium flash wind also strips off the secondarysurface, thus Wehavetherelation working as a stripping effect. We introduce mass-stripping M˙1+M˙2=M˙wind+M˙strip, (12) eVfefreyctsmbyaltlhbeusetfihneiltieumM˙ shelilnflFaisghuersei2nbto(aofuterrbwinianrdysesvtooplu)trieopn-. wind fromthe total mass conservation, thusdefining the net mass resentsthemasslossfromtheWDatheliumshellflashesand ˙ transferratetotheWDas M includestheensuingmass-strippingfromthesecondary. 2 M˙transfer≡M˙strip- M˙2=M˙1- M˙wind, (13) 3. YOUNGPOPULATIONTYPEIASUPERNOVAE wheresignsofM˙ >0,M˙ ≤0,M˙ <0,M˙ ≥0,and Based on the binary evolution scenario proposed by transfer strip 2 1 M˙ ≤0 should be noted. If M˙ is given, we have the net Hachisuetal. (1999a,b),wehavefollowedbinaryevolutions wind 2 startingfromstage(b)inFigure1,thatis,justwhenthecom- masstransferrateof panion evolves to fill its Roche lobe. The main difference M˙transfer=(cid:26)(c1M˙cr- -M˙M˙2)2/,(c1+1), ffoorr -- MM˙˙22>≤MM˙˙ccrr , (14) fsrtroimpptihnegperffeevciot.uOsuwrorreksuclittsedaraebsohvoewinsitnheFiingculruessio3n–1o0f.mass- Figure 3 shows the parameter regions that produce SNe whereweuseequations(2),(13),andarelationof Ia (SNIaregion) in the logP - M (the initial orbital pe- - M˙ =M˙ - M˙ , (15) riodandtheinitialsecondary0mass)2,p0lanefortheWD + MS wind transfer cr 6 Hachisuetal. FIG. 3.— TheinitialparameterregionsproducingSNeIaareplottedinthelogP0- M2,0 (orbitalperiod—donormass)planefortheWD+MSsystems withvariousmass-strippingfactors,c1. Thicksolid: c1=10. Mediumsolid: c1=3. Thinsolid: c1=1. Dotted: c1=0. The(red)hatchedregionindicatesa regionwithashortdelaytime(tdelay≤100Myr)forthecaseofc1=10.Theregionextendstothemoremassivedonorsforthelargerc1.TwosupersoftX-ray sources,RXJ0513.9- 6951(opencircle)andVSge(filledcircle),areplotted,massesofwhichareestimatedtobe2.7M⊙(Hachisu&Kato 2003b)and3.5M⊙ (Hachisu&Kato 2003c),orbitalperiodsofwhicharedeterminedtobe0.76days(Pakulletal. 1993)and0.51days(Herbigetal. 1965;Pattersonetal. 1998), respectively.ThepositionofVSgesuggeststhatc1>0. FIG.4.— DependenceoftheSNIaparameterregionontheinitialWDmass,MWD,0,foramass-strippingfactorofc1=3.Frominsidetooutside,MWD,0=0.7, 0.8,0.9,1.0(thicksolidline),and1.1M⊙.ThereisnoregionforMWD,0=0.6M⊙.The(red)sparsehatchedregionindicatesthedelaytimeoftdelay≤100Myr forMWD,0=1.1M⊙butthe(blue)densehatchedregionforMWD,0=0.7M⊙. TABLE1 THREETYPICALCASESOFSNIAEXPLOSION case wind Hburning CSM pre-SNhistory SNIa delaytime immediateradio/X-ray WIND wind steady massive:near WIND(VSgetype) IIa(02ic-like) young yes CALM nowind steady thin:far WIND→SSXS normalIa young no(∼10- 100yr) RN nowind flash verythin:manyshells WIND→SSXS→RN normalIa broad no(∼100–1000yr) orSSXS→RN ProgenitorsofTypeIaSupernovae 7 FIG.5.— TheparameterregionthatproducesSNeIaisplottedinthelogP- Md(orbitalperiod—donormass)planefortheWD+MSsystem.Hereweassume MWD,0=1.1M⊙ fortheinitialwhitedwarfmass. TheinitialWD+MSsysteminsidetheregionencircledbythe(red)thinsolidline(labeled“initial”)will increaseitswhitedwarfmassuptothecriticalmass(MIa=1.38M⊙)fortheSNIaexplosiontooccur.ThefinalstateoftheWD+MSsysteminthelogP- Md planejustbeforetheSNIaexplosionisencircledbythe(blue)thicksolidline(labeled“final”). ThefinalstateoftheWDjustbeforetheSNIaexplosionis specifiedbyoneofwind(opencircle),steadyH-burning(filledtriangle),orrecurrentnova(opensquare)phase. Anhatchedregionindicatesaregioninwhich theprogenitorexplodesinadelaytimeoftdelay≤100Myr.Dashedline:inadelaytimeof200Myr.Dottedline:inadelaytimeof400Myr.Currentlyknown positionsofthreerecurrentnovaeareindicatedbyastarmark(⋆)forUSco(e.g.,Schaefer&Ringwald, 1995;Hachisuetal. 2000a,b),andbyarrowsforthe othertworecurrentnovae,V394CrA(Schaefer 1990)andCIAql(Mennickent&Honeycutt 1995),ofunknowncompanionmasses.TheWDmassesofUSco andV394CrAwereestimatedtobe1.37M⊙(Hachisuetal. 2000a;Hachisu&Kato 2000)whilethatofCIAqlwas1.2M⊙(Hachisu&Kato 2003a). FIG.6.— ThefinalSNIaregionjustbeforeanSNIaexplosion.EachsymbolhasthesamemeaningasinFig.5.Theupperblacksolidlineandlowermagenta solidlinedenotelinesat- M˙2=M˙crand- M˙2=M˙stable,respectively,justattheSNIaexplosion,whereM˙2iscalculatedfromeq.(17)withR2andL2takenfrom asinglestarevolutiongivenbyToutetal. (1997).BoththelinesagreereasonablywiththebordersofWIND–CALMandCALM–RN,respectively. 8 Hachisuetal. FIG.7.— SameasFig.5,butforaninitialWDmassofMWD,0=1.0M⊙. FIG. 8.— SameasFig. 6,butforaninitialwhitedwarfmassofMWD,0=1.0M⊙.LargedifferenceintheborderofWIND–CALMcomesfromthefactthat thesecondaryconsiderablyoverfillstheRochelobe,i.e.,R2>R∗2,attheSNIaexplosionintheCaseWIND. system. Here the initial white dwarf mass is assumed to be massfromincreasing. (3) Theupperboundaryis limited by MWD,0 =1.0 M⊙. The white dwarfs within these SN Ia re- the formation of a common envelope. Here we assume that gions will increase their mass, MWD, up to the critical mass a common envelope is formed when M˙transfer &1×10- 4M⊙ (MTIah=e 1S.N38IaMr⊙eg)ifoonrtihnethSeNloIagePx0p- loMsi2o,0nptolanoecciusr.enclosed by yHra- c1hbiseucaeutsael.R11,p9h9&9b,af∼or1m0oRre⊙dfeotarislsu)c.h(4a)hTighherMi˙gtrhantsbfeoru(nsede- fourboundaries. (1)Theleftboundaryisgivenbythemass- arycorrespondstotheendofcentralhydrogenburningofthe radiusrelationforthezero-agemain-sequencestars. (2)The MScompanion: afterthat,itshrinksandunderfillsitsRoche lowerboundaryissetbystrongnovaexplosions,belowwhich lobe. M˙transfer .1×10- 7M⊙ yr- 1 andthe resultantnovaexplosion InFigure3,theSNIaregionsforthevariousmass-stripping ejects most of the accreted matter, thus preventing the WD factorc =10,3,and1areencircledbythethick,medium,and 1 ProgenitorsofTypeIaSupernovae 9 FIG.9.— SameasFig.5,butforaninitialwhitedwarfmassofMWD,0=0.9M⊙.ThereisnoCaseWIND(noopencircles). FIG.10.— SameasFig.6,butforaninitialwhitedwarfmassofMWD,0=0.9M⊙. thinsolidlines,respectively,andthenostrippingcase(c =0) caseofc &3. 1 1 bythedottedline. Thepositionofthe GalacticsupersoftX- SuchWD+MSsystemswithamassiveMSsecondarycon- raysourceVSgeisclearlyoutsidetheSNIaregionforc =0, sistofaveryyoungpopulationofSNeIa.Weshowtheregion 1 but inside the SN Ia region if c >0. For larger c , the SN of short delay times, t ≤100 Myr, by the red shadow in 1 1 delay IaregionextendstomoremassiveM ,becausethestronger Figures3,4,5,7,and9. Figure4showstheSNIaregionsfor 2,0 mass-strippingleadstothelowermasstransferrate,M˙transfer, different initial WD masses, MWD,0 =0.7, 0.8, 0.9, 1.0, and from the secondary to the WD (see eq.[14]), thus prevent- 1.1M⊙.Thered(sparse)andblue(dense)hatchedregionsin- ingtheformationofacommonenvelopeforlargerM2,0. As dicatethedelaytimeoftdelay≤100MyrforMWD,0=1.1M⊙ showninthisfigurequitemassivesecondariesproduceSNeIa and0.7M⊙,respectively. (e.g.,M2,0=7.5M⊙forc1=10)forthestrongmass-stripping We apply the present result to equation (1) of 10 Hachisuetal. Iben&Tutukov (1984),i.e., as well as the final state at the SN Ia explosion (encircled by the blue thick line and labeled “final”). Here we assume ν=0.2·∆q· Mu dM ·∆log a yr- 1, (16) c1=3andMWD,0=1.1,1.0,and0.9M⊙. Inthesefigures,we Z M2.5 distinguishthree finalstates justbeforetheSN Iaexplosion, Ml i.e., optically thick WD wind phase (WIND: open circles), where ∆q, ∆log a, M, and M are the appropriate ranges l u steadyhydrogenburningphasewithoutopticallythickwinds ofthemassratioandtheinitialseparation,andthelowerand fromWDs(CALM:filledtriangles),andrecurrentnova(RN) upperlimitsoftheprimarymassforSNIaexplosionsinsolar phase (RN: open squares). The characteristic properties for massunits,respectively.WethenestimatetheSNIabirthrate these three progenitorstages are summarizedin Table 1 and in our Galaxy as νWD+MS ∼0.004 yr- 1, which is consistent thecorrespondingbinaryparametersaretabulatedinTable2. withtheobservation(Cappellaroetal. 1999). Ontheotherhand,Hachisuetal. (1999a)proposedanother 4.1. CaseWIND channel to SNe Ia, the symbiotic channel, binary of which consists of a white dwarf and a red giant (WD + RG), and When the mass transfer rate from the secondary continu- estimateditsbirthratetobeνWD+RG∼0.002yr- 1. ously exceeds the critical rate of equation (10) until the fi- Assuming the initial distribution of binaries given by nalstage,theWDsexplodeduringthewindphase(Fig. 2a). equation (16) at the burst of star formation (single event), Therefore, we call this Case WIND. Case WIND is real- we estimate the delay time distribution of SNe Ia for the ized in the region of M2,0 & 3 M⊙ and P2,0 . 2 days for WD + MS systems in Figure 11. The number ratio of MWD,0=1.1M⊙and1.0M⊙(opencircle),butnoCaseWIND these young populations is calculated for 10 bins of delay existsforMWD,0≤0.9M⊙ asshowninFigures5,7,and9. time,(0.025,0.05),(0.05,0.1),(0.1,0.2),(0.2,0.4),(0.4,0.8), The stripped-off matter from the companion can easily (0.8,1.6), (1.6,3.2), (3.2,6.4), (6.4,12.8), and (12.8,25.6) amountto∆Mstrip∼1- 2M⊙andevenreach3- 4M⊙asseen Gyr. The number ratio with t ≤ 100 Myr and t ≤ fromthedonormassdifference∆M betweenthe“initial”and delay delay 2 200 Myr are about 50% and 80%, respectively, of the to- the“final”inFigures5, 7, and9. Moreprecisely,∆M con- 2 tal SNe Ia coming from the WD + MS system, which is sistsofthreeparts,thestripped-offmass∆M ,theaccreted strip consistent with the recent observational suggestions (e.g., massbytheWD∆M ,andthemassejectedbytheWDwind 1 Mannuccietal. 2006;Aubourgetal. 2007). ∆M ,i.e.,M˙ =M˙ +M˙ - M˙ fromequation(12).This wind 2 strip wind 1 Shortdelaytimes(tdelay.108yr)ofsomeSNeIahavebeen canbeapproximatedasM˙2≈M˙strip+M˙wind=(1+1/c1)M˙strip= suggested from the distribution of SNe Ia relative to spiral 4/3M˙ becauseM˙ ≪- M˙ ,sothat∆M ≈3/4∆M for arms(e.g.,Bartunovetal. 1994; dellaValle&Livio 1994). strip 1 2 strip 2 c =3. Petrosianetal. (2005)reportedthatabout30–40%ofSNeIa 1 Thestripped-offmaterialformsCSMveryneartheSN Ia. areassociatedwithspiralarmsintheirsamples,beingconsist- We expectthatstripped-offmatterdid notgoaway fromthe ingwith ourresults. Mannuccietal. (2006) have suggested system because the velocity of stripped-off matter may not that the delay time distribution function of SNe Ia has a bi- exceed the escape velocity of the binary system. Then the modality,oneforyoungpopulation(t ∼100Myr)andthe delay SNIaundergoescircumstellarinteractionasobservedinType otherwithabroaddistributionover∼3Gyr. Ourdelaytime Ia/IIn(orIIa)SNe2002icand2005gj. distributionfunctionhasapeakaroundt ≤100Myrfrom delay Alderlingetal. (2006) suggested that the host galaxy of theWD+MSsystemsandabroaddistributionfromtheWD SN2005gjhadaburstofstarformation200±70Myrago. If +RGsystems(Hachisuetal. 1999a)asshowninFigure12. the progenitorof SN 2005gjwas born at that time, its delay time is consistent with our Case WIND as shown in Figure 4. FINALSTAGEOFBINARYEVOLUTIONANDCIRCUMSTELLAR MATTER 11. ThefinalstateoftheWDdependsmainlyonthemasstrans- ˙ 4.2. CaseCALM ferrateM fromthedonorstartotheWDattheSNIaex- transfer plosion(Nomoto 1982;Hachisuetal. 1999a;Nomotoetal. When the mass transfer rate from the secondary is below 2007). As shown in Figure2, M˙ dropsquicklyin the early thecriticalrateforopticallythickwindsbutabovethelowest 2 ˙ ˙ ˙ stage and then slows down to almost a constant value. At rateofsteadyhydrogenburning,i.e.,M <M <M , stable transfer cr least,intheearlyphase,themasstransferproceedsonather- the WDs undergosteady H-burningatthe time of SN Ia ex- mal time scale, represented by the second term of equation plosion (filled triangles in Figs. 5–10). We call this Case (7),whenthemassratioM /M exceeds0.79.Soweapprox- CALMbecausenoopticallythickwindsoccur. TheWDsare 2 1 imatethemasstransferrateas observedassupersoftX-raysources(SSXSs)untiltheSNIa - M˙ ≈ M2 ∼3×10- 8M yr- 1 R2 · L2 M2 - 1 ebxepenlosdiiosnp.ersTehdetostoripfapredto-obffemdeatteecritaeldfiomrmmsedCiaStMelybauftteitrhthaes 2 ⊙ τKH (cid:18)R⊙ L⊙(cid:19)(cid:18)M⊙(cid:19) SNIaexplosion. (17) The CALM case is realized in the regionof M2,0 &3 M⊙ By applying the approximate M2- L2 relation of L2 ∝M2m, andP2,0&2daysforMWD,0=1.1M⊙and1.0M⊙ inFigures where m ∼ 4 for the 1.5- 3 M⊙ zero-age main-sequence 5, 7, and 9, where M˙ in the early phase is much larger (ZAMS)starsorm∼3.5forthe3- 7M⊙ ZAMSstars, thanthatofP .2dtraanyssfe,rbecauseinequations(7)and(17), 2,0 - M˙ ∝R Mm- 1. (18) R2andL2 aremuchlargerthanthoseforP2,0.2days. Then 2 2 2 ˙ M is much larger, thus much more mass had been lost Thus- M˙ decreaseasM decreases. intrtahnesfeerarlier phase. As a result, the wind phase finishes at 2 2 Figures5–10showtheSNIaregionsinthelogP- M (or- anearliertimeevenforthesameinitialmassM asseenin d 2,0 bital period — donor mass) plane for the initial WD + MS Figures2aand2b.Therefore,attheSNIaexplosion,nowind system (encircled by the red thin line and labeled “initial”) occurs.