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Mon.Not.R.Astron.Soc.000,1–9(2008) Printed22January2009 (MNLATEXstylefilev2.2) Helium star donor channel for the progenitors of type Ia supernovae 9 B. Wang1,2 ⋆, X. Meng3, X. Chen1 and Z. Han 1 0 0 1 National Astronomical Observatories/Yunnan Observatory, the Chinese Academy of Sciences, Kunming 650011, China 2 2 Graduate School of the Chinese Academy of Sciences, Beijing100049, China 3 Department of Physics and Chemistry, Henan Polytechnic University,Jiaozuo 454003, China n a J 22January2009 2 2 ABSTRACT ] R Type Ia supernovae (SNe Ia) play an important role in astrophysics,especially in the S studyofcosmicevolution.Thereareseveralprogenitormodels forSNe Iaproposedin . thepastyears.Inthispaper,wehavecarriedoutadetailedstudyoftheHestardonor h channel,inwhichacarbon-oxygenwhitedwarf(COWD)accretesmaterialfromaHe p main sequence star or a He subgiantto increase its mass to the Chandrasekharmass. - o EmployingEggleton’sstellar evolutioncode with anoptically thick wind assumption, r and adopting the prescription of Kato & Hachisu (2004) for the mass accumulation t s efficiency of the He-shell flashes onto the WDs, we performed binary evolution calcu- a lations for about 2600 close WD binary systems. According to these calculations, we [ mapped out the initial parameters for SNe Ia in the orbital period–secondary mass 1 (logPi−M2i) plane for various WD masses from this channel. The study shows that v the He star donor channel is noteworthy for producing SNe Ia (i.e. ∼1.2×10−3yr−1 6 in the Galaxy), and that the progenitors from this channel may appear as supersoft 9 X-ray sources. Importantly, this channel can explain SNe Ia with short delay times 4 (.108yr), which is consistent with recent observational implications of young popu- 3 lations of SN Ia progenitors. . 1 Key words: binaries: close – stars: evolution – white dwarfs – supernovae: general 0 9 0 : v i 1 INTRODUCTION withtheearlytimespectraofmostSNeIa,whilethatofthe X sub-Ch mass model has difficulty in matching observations TypeIaSupernovae(SNeIa)areexcellentcosmological dis- r (Höflich&Khokhlov1996).ACOWDcanincreaseitsmass a tance indicators dueto their high luminosities and remark- to the Ch mass through a single degenerate (SD) scenario, able uniformity. They have been applied successfully in de- wheretheCOWDaccretesH/He-richmaterialfromanon- termining cosmological parameters (e.g. Ω and Λ; Riess et degenerate companion star (Whelan & Iben 1973; Nomoto al. 1998; Perlmutter et al. 1999). It is widely believed that etal. 1984), orthrougha doubledegenerate (DD)scenario, SNeIaarethermonuclearexplosionsofcarbon-oxygenwhite where another CO WD mergers with it and the total mass dwarfs (CO WDs) accreting matter from their companions ofthetwoCOWDsislargerthantheChmasslimit(Iben& (see a review of Nomoto et al. 1997). However, several key Tutukov1984;Webbink1984).Theoretically,itissuggested issues related to thenature of their progenitor systems and that the DD scenario likely leads to an accretion-induced the physics of the explosion mechanisms are still not well collapse rather than a SN Ia (Nomoto & Iben 1985; Saio & understood (Hillebrandt & Niemeyer 2000; Röpke & Hille- Nomoto 1985; Timmes et al. 1994). brandt 2005; Wang et al. 2008; Podsiadlowski et al. 2008), whichmayraisedoubtsaboutthedistancecalibrationbeing For the SD Ch scenario, the companion is probably a purelyempiricalandonthebasisoftheSNIasampleofthe MSstaroraslightlyevolvedsubgiantstar(WD+MSchan- low red-shift Universe. nel),oraredgiantstar(WD+RGchannel)(Hachisuetal. At present, two SN Ia explosion models are discussed 1996, 1999a, 1999b; Li & van den Heuvel 1997; Langer et frequently, that is, Chandrasekhar (Ch) mass model and al.2000;Han&Podsiadlowski 2004, 2006; Chen&Li2007; sub-Chandrasekhar (sub-Ch) mass model. The synthetic Meng et al. 2008; Han 2008). Meanwhile, a CO WD may spectra of the Ch mass model are in excellent agreement also accrete material from a He star companion to increase its mass to the Ch mass, which is known as the He star donor channel in this paper. The study of Iben & Tutukov ⋆ E-mail:[email protected] (1994) showed that WD + He star systems can be formed 2 B. Wang, X. Meng, X. Chen and Z. Han via binary evolutions. Yoon & Langer (2003) have carried where G, c, MWD and M2 are the gravitational constant, out the evolution of a CO WD + He star system with a vacuum speed of light, the mass of the accreting WD and 1.0M CO WD anda 1.6M Hestar in a 0.124 day orbit. themass of thecompanion Hestar, respectively. ⊙ ⊙ In this binary, the WD accretes He from the He star and Instead of solving stellar structure equations of a WD, grows in mass to the Ch mass. It is believed that WD + weuseanopticallythickwindmodel(Kato&Hachisu1994; Hestarsystemsaregenerally originated from intermediate- Hachisu et al. 1996) and adopt the prescription of Kato & mass binary systems. Thus, this channel may explain SNe Hachisu(2004)(KH04)forthemassaccumulationefficiency Iawithshortdelaytimes(Mannuccietal.2006;Aubourget of He-shell flashes onto the WD. If the mass transfer rate, al. 2008). At present, however, there are no comprehensive |M˙2|,isaboveacriticalrate,M˙cr,weassumethatHeburns investigations on this channel. steadilyonthesurfaceoftheWDandthattheHe-richmat- The existence of WD + He star systems is supported terisconvertedintoCandOatarateM˙cr.Theunprocessed bysomeobservations.Forexample,KPD1930+2752issug- matterislostfromthesystem,presumablyintheformofan gested tobesuchasystem (Maxtedetal.2000; Geieretal. opticallythickwindatamasslossrateM˙wind =|M˙2|−M˙cr. 2007). Anotherexampleisfrom thediscovery of aHenova, The critical mass transfer rate is V455Pup(Ashok& Banerjee 2003; Kato&Hachisu 2003). Recently, Kato et al. (2008) presented a free-free emission M˙cr =7.2×10−6(MWD/M⊙−0.6)M⊙yr−1, (2) dominated light curvemodel of V445 Pup,based on an optically thickwind theory(Kato&Hachisu1994; Hachisuet based on WD models computed with constant mass accre- al. 1996). Thelight curvefittingin theirstudyshowed that tion rates (Nomoto 1982). the mass of the WD is lager than 1.35M , and half of the accreted matter remains on the WD, lea⊙ding to the mass Followingassumptionsareadoptedwhen|M˙2|issmaller increase of the WD. Thus, V445 Pup is suggested to be a than M˙cr. (1) If |M˙2| is less than M˙cr but higher than strong candidate of SNIa progenitor (Katoet al. 2008). theminimum accretion rateof stableHe-shellburning,M˙st (KH04),itisassumedthattheHe-shellburningisstableand ThepurposeofthispaperistostudytheHestardonor channelfor SN Iaprogenitors comprehensively and system- that there is no mass loss. (2) If |M˙2| is less than M˙st but higher than the minimum accretion rate of weak He-shell ically,andthentodeterminethevalidparameterspacesfor SNe Ia, which can be used in binary population synthesis flashes, M˙low = 4.0×10−8M⊙yr−1 (Woosley et al. 1986), He-shellflashesoccurandapartoftheenvelopemassisas- (BPS)studies.InSection2,wedescribethenumericalcode sumedtobeblownofffromthesurfaceoftheWD.Themass for thebinary evolution calculations and the grid of the bi- growthrateofWDsinthiscaseislinearlyinterpolatedfrom nary models. The binary evolutionary results is shown in agridcomputedbyKH04,whereawiderangeofWDmass Section 3. In Section 4, we estimate SN Ia birthrate of this and accretion rate were calculated in the He-shell flashes. channel. Finally, a discussion is given in Section 5, and a summary in Section 6. (3) If |M˙2| is lower than M˙low, the He-shell flashes will be so strong that nomass can beaccumulated onto theWD. We define the mass growth rate of the CO WD, M˙CO, as 2 BINARY EVOLUTION CALCULATIONS In WD + He star systems, the He star fills its Roche lobe M˙CO =ηHe|M˙2|, (3) at HeMS or Hesubgiant stage, and then themass transfer begins. The He star transfers some of its material onto the where ηHe is the mass accumulation efficiency for He-shell surfaceoftheWD,whichincreasesthemassoftheWDasa burning.Accordingtotheassumptions above,thevaluesof consequence.IftheWDgrowsto1.378M ,weassumethat ⊙ ηHe are: the WD explodes as a SN Ia. Here we use Eggleton’s stellar evolution code (Eggleton 1971, 1972, 1973) to calculate the binary evolutions of WD + He star systems. The code |MM˙˙c2r| , |M˙2|>M˙cr, htharsebeedeencaudpedsa(tHedanweitthalt.h1e99la4t;ePstolisnpetutalp.h1y9s9i5c,s1o9v9e8r)t.hReolcahset ηHe= 1ηH′e ,, MM˙˙cstr>>||MM˙˙22||>>MM˙˙lsotw,, (4) lobe overflow (RLOF) is treated within the code described 0 , |M˙2|<M˙low. by Han et al. (2000). We set the ratio of mixing length to  localpressurescaleheight,α=l/Hp,tobe2.0.Theopacity Weincorporate theprescriptions aboveintoEggleton’s tablesare compiled byChen &Tout (2007) from Iglesias & stellar evolution code and follow the binary evolutions of Rogers(1996)andAlexander&Ferguson(1994).Inourcal- WD + He star systems. The mass lost from these systems culations,theHestarmodelsarecomposedofHeabundance isassumedtotakeawayspecificorbitalangularmomentum Y = 0.98 and metallicity Z = 0.02, and all calculations for of the accreting WD. We have calculated about 2600 WD the He stars are carried out without enhanced mixing (i.e. + Hestar systems, and obtained a large, densemodel grid. the overshooting parameter, δov, is taken to be zero; see Theinitialmassofthedonorstars,Mi,rangesfrom0.85M 2 ⊙ Dewi et al. 2002). In addition, orbital angular momentum to 3.1M ; the initial mass of the CO WDs, Mi , is from ⊙ WD loss duetogravitational waveradiation (GWR) is included 0.865M to1.20M ;theinitialorbitalperiodofthebinary ⊙ ⊙ byadoptingastandardformulapresentedbyLandau&Lif- systems, Pi, changes from the minimum value, at which a shitz (1971), He zero-age MS (He ZAMS) star would fill its Roche lobe, d lnJGR =−32G3 MWDM2(MWD+M2), (1) teond∼o3f1t6hedaHyesr,twzshperruentghgeaHp.e star fills its Roche lobe at the dt 5c5 a4 Progenitors of SNe Ia 3 Figure 1. A representative case of binary evolution calculations, in which the binary system is in the weak He-shell flashes phase at the moment of the SN explosion. In panel (a), the solid, dashed and dash-dotted curves show M˙2, M˙CO and MWD varing with time, respectively.Inpanel(b),theevolutionarytrackofthedonorstarisshownasasolidcurveandtheevolutionoforbitalperiodisshown as adash-dotted curve. Dotted vertical lines inboth panels and asterisks inpanel (b) indicate the position where the WD is expected to explode as aSN Ia. The initialbinaryparameters and the parameters at the moment of the SN Ia explosion arealsogiven in these twopanels. Figure 2.SimilartoFig.1,butthebinarysystemisinthestableHe-shellburningphaseatthemomentoftheSNexplosion. Figure 3.SimilartoFig.1,butthebinarysystem isintheopticallythickwindphaseatthemomentoftheSNexplosion. 4 B. Wang, X. Meng, X. Chen and Z. Han Figure4.SimilartoFig.1,butthiscasediffersfromthethreeabove.BeforetheSNexplosion,thebinarysystemexperiencestwomass transferphases. 3 BINARY EVOLUTION RESULTS when the CO WD reaches 1.378M . The binary param- ⊙ 3.1 Typical binary evolution calculations leotger(sPSaNt/dMaWy)D==−11.1.327986.M⊙ are M2SN = 1.0070M⊙ and In Figs 1-4, we present three representative cases in our bi- (iii)Case3(seeFig.3):Thebinarysystemisintheop- naryevolutioncalculationsaccordingtotheconditionofthe ticallythickwindphaseatthemomentoftheSNexplosion. binary system at the moment of SN explosion, and display Thebinaryinthiscaseis(M2i,MWi D,log(Pi/day))=(1.80, onespecialcaseforproducingSNeIa.Inpanels(a)ofthese 1.10, -0.60). Since the initial mass of the WD is more mas- figures, we show theM˙2, M˙CO and MWD varing with time, sive than that of the other two cases above, the WD may andthepanels(b)aretheevolutionarytracksoftheHestars grow in mass to the Ch mass more easily, that is, it is still in the Hertzsprung-Russell diagrams, where the evolutions in the optically thick wind phase when MWD = 1.378M⊙, of the orbital periods are also shown. at which M2SN =1.2047M⊙ and log(PSN/day)=−0.6232. (i)Case1(seeFig.1):Thebinarysystemisintheweak (iv)Case4(seeFig.4):Thiscasediffersfromthethree He-shell flash phase at the moment of the SN explosion. above. Before the SN explosion, the binary system experi- The binary shown in this case is (Mi, Mi , log(Pi/day)) ences two mass transfer phases. The binary in this case is 2 WD = (1.35, 0.9, -1.20), where M2i, MWi D and Pi are the initial (M2i, MWi D, log(Pi/day)) = (1.25, 1.10, -1.30). Due to the mass of the He star and of the CO WD in solar masses, shortinitialorbitalperiodofthesystem,angularmomentum and the initial orbital period in days, respectively. In this lossinducedbyGWRleadstheHestartofillitsRochelobe case, the He star fills its Roche lobe after the exhaustion before the exhaustion of central He, resulting in Case BA of central He (it now contains a CO core), and this results mass transfer. The mass transfer continuestoproceed until in Case BB mass transfer 1. The mass transfer rate |M˙2| themassdonorstartstoshrinkbelowitsRochelobe,termi- exceeds M˙cr soon after the onset of RLOF, leading to a natingthemasstransferphase.AfterithasexhaustedHein wind phase, where a part of the transferred mass is blown its core, the He star expands and fills its Roche lobe again off in an optically thick wind, and the left is accumulated when it evolves to the subgiant stage, leading to Case BB ontotheWD.Afterabout5×104yr,|M˙2|dropsbelowM˙cr evolution.Thefollowingevolutionofthissystemissimilarto but still higher than M˙st. Thus, the optically thick wind Case 1.WhentheaccretingWDgrows totheCh mass, the stops and the He-shell burning is stable. With the continu- binaryisintheHe-shellflashphase,andthebinaryparam- ous decreasing of |M˙2|, the system enters into a weak He- eters are M2SN =0.6983M⊙ and log(PSN/day)=−1.1848. shell flash phase after about 5 ×104yr. The WD always grows in mass until it explodes as a SN Ia in the weak He- 3.2 Initial parameters for SN Ia progenitors shell flash phase. At theSN explosion moment,themass of the donor star is M2SN = 0.8030M⊙ and the orbital period Figs5-7showthefinaloutcomesofabout2600binaryevolu- log(PSN/day)=−1.1940. tioncalculationsintheinitialorbitalperiod–secondarymass (ii) Case 2 (see Fig. 2): The binary system is in the (logPi−Mi) plane, where the filled symbols are for those 2 stable He-shell burning phase at the moment of the SN ex- resulting in SN Ia explosions. The different cases described plosion.Thebinaryinthiscaseis(M2i,MWi D,log(Pi/day)) in Section 3.1 are plotted with different symbols, that is, = (1.40, 1.00, -1.10). The binary evolves in a similar way thefilled squares, circles and triangles denote that the WD to that of Case 1, but it is in stable He-shell burning stage explodesintheopticallythickwindphase,inthestableHe- shell burning phase and in the weak He-shell flash phase, respectively. Some WD + He star systems fail to produce 1 We distinguishcase BB (Roche lobe overflow occurs after He- SNe Ia because of He nova explosions (which prevents the coreburningbutbeforecarbonignition)fromcaseBA(inwhich WD growing in mass; the crosses in these figures) or dy- mass transfer is initiated during He-core burning) (see Dewi et namically unstable mass transfer (resulting in a common al.2002). envelope; open circles in these figures). Note that, the left Progenitors of SNe Ia 5 Figure5.Finaloutcomesofthebinaryevolutioncalculationsintheinitialorbitalperiod–secondarymass(logPi,Mi)planeoftheCO 2 WD + He star system for initial WD mass of 1.2M⊙. The filled symbols are for those resulting inSN Ia explosions, that is, the filled squares, circles and triangles denote that the WD explodes inthe optically thick windphase, inthe stable He-shellburning phase and in the weak He-shell flash phase, respectively (see Cases 1-3 in Section 3.1). Crosses indicate systems that may experience He novae, preventingtheWDfromreaching1.378M⊙,andopencirclesarethoseunderdynamicallyunstablemasstransfer. Figure 6.SimilartoFig.5,butforinitialWDmassof1.1M⊙. boundaries of the initial logPi−Mi plane in these figures of the contours in these figures (Figs 5-6 and panel c of 2 are determined by the minimum value of logPi, at which Fig. 7) areset bythecondition thatRLOFstartswhen the theHe ZAMS star would fill its Rochelobe. secondary is on the He ZAMS 2, while systems beyond the The contours of initial parameters for producing SNe Ia are also presented in these figures. The left boundaries 2 Notethat,theupperpartsoftheleftboundariesareconstrained 6 B. Wang, X. Meng, X. Chen and Z. Han Figure 7.SimilartoFig.5,butforinitialWDmassesof0.865,0.9and1.0M⊙. 1.2M ), where Pr and Mr are the orbital period and the ⊙ 2 mass of the He companion star at the onset of RLOF, respectively. Note that, the enclosed region almost vanishes forMi =0.865M ,whichisthenassumedtobethemin- WD ⊙ imum WD mass for producing SNe Ia from this channel. If the parameters of a CO WD + He star system at the onset of RLOF are located in the contours, a SN Ia is then assumed to be produced. Thus, these contours can be ex- pediently used in BPS studies. One can send a request to [email protected] for the data points of these contours and theinterpolation FORTRANcode for these contours. Note,thecontoursforSNeIabetweenFigs5-7andFig. 8 have some differences, that is, Figs 5-7 are for initial pa- rameterswhileFig.8forthoseattheonsetofRLOF.GWR may change the orbital period during this time, especially for binaries with short orbital periods (i.e. less than 1 day Figure 8. Regions in orbital period–secondary mass plane in this paper). For example, the left boundary of the con- (logPr, M2r) for WD binaries (at the onset of the RLOF stage) tour for MWi D = 1.2M⊙ in Fig. 8 has shorter periods than thatproduce SNeIaforinitialWDmassesof0.865,0.90,1.0,1.1 thatinFigs 5-7,becauseangularmomentumloss viaGWR and1.2M⊙.TheregionalmostvanishesforMWi D=0.865M⊙. is more in short period binary systems than that in long period systems. rightboundaryexperiencemasstransferataveryhighrate due to the rapid expansion of the He stars in the subgiant 4 BIRTHRATE OF SNE IA stage and they lose too much mass via the optically thick wind, preventing the WDs increasing their masses to the Adopting a prescription similar to that of Hachisu et al. Ch mass. The upper boundaries are also set mainly by a (1999b) and based on Fig. 8 of this paper, we can roughly highmasstransferratebutowingtoalargemassratio.The estimate Galactic SN Ia birthrate from the He star donor lowerboundariesareconstrainedbythefactsthatthemass channel by using equation (1) of Iben & Tutukov (1984), transfer rate M˙2 should be high enough to ensure that the i.e. WD can grow in mass, and that the donor is sufficiently massive so that enough mass can be transferred onto the ν =0.2∆q MB dM ∆logAyr−1, (5) WD to reach theCh mass. Z M2.5 MA There is a time delay (up to about 106yr) from the where∆q, ∆logA,MA and MB are theappropriate ranges formation of most WD + He star systems to the onset of of the initial mass ratio and the initial separation and the RLOFs, and this time delay varies with component masses lower and upper limits of the primary mass for producing and initial orbital periods. Fig. 8 shows thecontours at the SNe Ia in solar masses, respectively. We give the details of onsetofRLOFforproducingSNeIainthelogPr−Mrplane 2 thecalculations in thefollowing. forvariousWDmasses(i.e.Mi =0.865,0.90,1.0,1.1and WD ToestimatethebirthrateofSNeIa,wedividetheinitial WD mass of Mi into three intervals, i.e. 0.9 −1.0M , WD ⊙ mainlybyahighmasstransferratebecauseoforbitdecayinduced 1.0−1.1M⊙,and1.1−1.2M⊙ (seealsoHachisuetal.1999b). byGWRandlargemassratio,whichleadstomuchofthemasses We ignore the range of MWi D = 0.865−0.9M⊙, since its lostfromthesystemsinawayoftheopticallythickwind. birthrate is too small to contribute to the SN Ia birthrate Progenitors of SNe Ia 7 WD may be above the standard Ch mass (i.e. the super- Table1.ThebirthratesofSNeIafordifferentWDmassintervals. Ch mass model; Uenishi et al. 2003; Yoon & Langer 2005). MWi D ∆logA MA MB ∆q νWD However, in this paper we mainly focus on the Ch mass (M⊙) (M⊙) (M⊙) (10−3yr−1) explosions of theaccreting WDs. Yoon & Langer (2003) (YL03) only considered a case 0.9−1.0 1.0×2/3 5.60 6.63 0.02 0.03 BB evolution of a CO WD + He star system which could 1.0−1.1 1.8×2/3 6.63 7.58 0.18 0.31 produce a SN Ia. In this paper, we systematically studed 1.1−1.2 3.7×2/3 7.58 8.48 0.34 0.82 theHestardonorchannelfortheprogenitorsofSNeIa(in- cludingcaseBAandcaseBBbinaryevolution)andshowed the contours of SNe Ia for various initial WD masses. The binary studied in YL03 is located in the contours of this as seen in Fig. 8. We use equation (11) of Yungelson et al. paper. However, there are some differences between our as- (1995)toestimateMA andMB,i.e.thefinalcoremass(CO sumptions and theirs in mass accumulation efficiency. This WD mass) versustheZAMS mass relation, ismainlybecausethattheeffectofwindmasslossinYL03’s 2.5 calculationistakenintoaccountbasedanempiricalformula logMWD =−0.22+0.36 log Mi , (6) ofWolf-Rayetstarmassloss,whileweusedanopticallythick M⊙ (cid:18) M⊙(cid:19) windmodel(Kato&Hachisu1994;Hachisuetal.1996)and where MWD and Mi are the mass of the final CO WD and adoptedtheprescriptionofKH04forthemassaccumulation oftheZAMSinsolar masses, respectively.Inaddition,sim- efficiency of theHe-shell flashes onto theWDs. ilartoHachisuetal.(1999b),wealsouseanapproximation The estimated birthrate of this channel is ∼ 1.2 × relation to obtain ∆logA, i.e. 10−3yr−1, which is comparable tothat of WD+ MS channel (this is considered as an important channel to SNe Ia; 2 ∆logA≈ ∆logPr, (7) Han&Podsiadlowski2004).Thus,theHestardonorchannel 3 shouldnotbeignoredwhenwestudytheprogenitorsofSNe where ∆logPr is taken from the SN Ia region in Fig. 8 Ia,andthischannelmayincreasethecontributionofSDCh and the factor of 2/3 comes from the conversion between scenario to SN Ia birthrate in theory. Note, the estimated the period and the separation. Take WD mass interval of birthratemaybehigherthan thatin areal condition, since 1.1−1.2M⊙ as an example, we find that SN Ia explosions thelongorbitperiod(i.e.&1dayinFig.8)systemsconsid- occurfortherangesofM1,i =7.58−8.48M⊙,MHe,i =0.95− ered to produce SNe Ia in equation (1) of Iben & Tutukov 3.0M⊙ and ∆logA = 3.7×2/3, where M1,i is the initial (1984) may not contribute to SNe Ia. Moreover, Umeda et massoftheprimaryatZAMS,andMHe,i istheinitialmass al. (1999) concluded that the upperlimit mass of CO cores of the He star. Using Eggleton’s stellar evolution code, we born in binaries is about 1.07M . If this value is adopted ⊙ canobtaintheinitialZAMSmassMi=5.60M⊙forthefinal as the upper limit of the CO WD, the birthrate of SNe Ia He-core mass of 0.95M⊙ (i.e. He star mass). Considering from this channel will decrease to be ∼ 0.2×10−3yr−1 in theinitialmassofthesecondaryatZAMSisnotmorethan theGalaxy. thatoftheprimaryatZAMS,weconstraintherangeofM2,i Someprecursory studies(Iben& Tutukov1994; YL03) from 5.60M⊙ to M1,i, where M2,i is the initial mass of the suggested that WD + He star systems may appear as su- secondary at ZAMS. Thus, we obtain νWD,1.1−1.2 ∼0.82× persoft X-ray sources (SSSs) before SN Ia explosions. The 10−3yr−1 by substituting ∆logA = 3.7×2/3, ∆q = 1− initial orbital periods of WD + He star systems producing (5.60/8.48)=0.34,MA =7.58andMB =8.48intoequation SNe Ia for this channel range from ∼ 1h to ∼ 200days, (5). The SN Ia birthrates for different WD mass intervals which may explain SSSs with various orbital periods. we are summarized in Table 1. Note, for different initial WD can estimate the X-ray luminosity of a WD + He star sys- masses, the birthrate tendency of this channel is different tem by LX ∼ ǫHe|M˙2|, where ǫHe = 6×1017ergg−1 is the from that of WD + MS channel, that is, massive WDs for energy generation rate owing to He burning. A WD + He producing SNe Ia have a high birthrate for the WD + He starsystem hasluminosity around1037−1038ergs−1 when star channel.This isbecause that massive WDseasily have He burning is stable on the surface of the WD, consistent massive He stars as theircompanions. with that of observed from SSSs (LX =1036−1038ergs−1; Finally, the sum of SN Ia birthrates for three intervals Kahabka&vandenHeuvel1997).Note,strongHeIIλ4686 (0.9−1.0M⊙,1.0−1.1M⊙,and1.1−1.2M⊙)givesν ∼1.2× lines are prominent in the luminous SSSs (see Kahabka & 10−3yr−1 in the Galaxy, which is lower than that inferred van den Heuvel 1997). Thus, we emphasize that SN Ia pro- observationally (i.e. 3−4×10−3 yr−1; van den Bergh & genitors in the He star donor channel may appear as SSSs Tammann 1991; Cappellaro & Turatto 1997). during the stable He-shell burning phase without winds 3. By multiplying the birthrate, ∼ 1.2×10−3yr−1, with an average duration of the SSS phase, ∼ several times 105yr, we estimate the current number of this type of progenitors 5 DISCUSSION as SSSsin theGalaxy to befrom a few to several hundred. Inourwork,wehavenotconsideredtheinfluenceofrotation However,we donot observesuch numberof WD + Hestar on the He accreting WDs. The calculations of Yoon et al. systemsinSSSphase.ThismayattributetotheGalacticin- (2004) showed that, if rotation is taken into account, He burningismuchlessviolentthanthatwithoutrotating.This maysignificantlyincreasetheaccretionefficiency(ηHeinthis 3 Massive wind may absorb soft X-rays, which then cannot be paper). Meanwhile, themaximum stable mass of a rotating detectable (Hachisuetal.1999b;Kato&Hachisu2003). 8 B. Wang, X. Meng, X. Chen and Z. Han terstellarabsorptionofSSSs(DiStefano&Rappaport1994; of SN explosion, which might be verified byfutureobserva- Hachisu et al. 2008a). Moreover, Di Stefano & Rappaport tions. (1994) also suggested that circumstellar matter may play a role in the obscuration of X-rays (see also Hachisu et al. 2008a). ACKNOWLEDGMENTS Generally,aCOWD+Hestarsystemisproducedfrom an intermediate-mass binary, which can be found in stellar We thank an anonymous referee for his/her valuable com- populationswithrelativelyrecentstarformation.Themini- ments which help to improve the paper. Bo Wang thanks mumHestarmassforproducingSNeIafromthischannelis Prof.M.KatoofKeioUniversityforhelpfuldiscussions.Bo 0.95M⊙,withwhichwecanroughlyestimatethemaximum Wangalsothanksprof.Ph.PodsiadlowskiofOxfordUniver- delay time of this channel. The initial ZAMS mass Mi = sityforhelpfuldiscussionsduringhisvisittoNAOC/YNAO 5.6M⊙ can produce He star mass of 0.95M⊙ (see Sect. 4). in April 2008. This work is supported bytheNational Nat- TheMSlifetimeisabout81Myrforastarof5.6M⊙(Eggle- ural Science Foundation of China (Grant Nos. 10433030, ton 2006). Moreover, we should consider the MS lifetime of 10521001, 2007CB815406 and 10603013) and the Foun- He stars, since the He stars in long orbital period systems dation of the Chinese Academy of Sciences (Grant No. experience RLOF after the exhaustion of central He. The 06YQ011001). MS lifetime of 0.95M He star is about 18Myr. Thus, the ⊙ maximumdelaytimeofthischannelisabout108yr,i.e.the He star donor channel can explain SNe Ia with short delay REFERENCES times(.108yr;Mannuccietal.2006;Aubourgetal.2008). Note, Hachisu et al. (2008a) investigated new evolutionary AlexanderD. R., Ferguson J. W., 1994, ApJ,437, 879 modelsforSNIaprogenitors,introducingthemass-stripping Ashok N. 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