Evolving to Type Ia Supernovae with Short Delay Times
aa r X i v : . [ a s t r o - ph . S R ] J un Draft version November 19, 2018
Preprint typeset using L A TEX style emulateapj v. 03/07/07
EVOLVING TO TYPE IA SUPERNOVAE WITH SHORT DELAY TIMES
Bo Wang,
Xuefei Chen, Xiangcun Meng, and Zhanwen Han Draft version November 19, 2018
ABSTRACTThe single-degenerate model is currently a favourable progenitor model for Type Ia supernovae (SNeIa). Recent investigations on the WD + He star channel of the single-degenerate model imply thatthis channel is noteworthy for producing SNe Ia. In this paper we studied SN Ia birthrates and delaytimes of this channel via a detailed binary population synthesis approach. We found that the GalacticSN Ia birthrate from the WD + He star channel is ∼ . × − yr − according to our standardmodel, and that this channel can explain SNe Ia with short delay times ( ∼ . × − . × yr).Meanwhile, these WD + He star systems may be related to the young supersoft X-ray sources priorto SN Ia explosions. Subject headings: binaries: close — stars: evolution — supernovae: general — white dwarfs INTRODUCTION
Type Ia supernovae (SNe Ia) play an important role inastrophysics, especially in the study of cosmic evolution.They have been applied successfully in determining cos-mological parameters (e.g., Ω and Λ; Riess et al. 1998;Perlmutter et al. 1999). It is widely accepted that SNeIa are thermonuclear explosions of carbon-oxygen (CO)white dwarfs (WDs) accreting matter from their com-panions (for a review see Nomoto et al. 1997). However,there is still no agreement on the nature of their progeni-tors (Hillebrandt & Niemeyer 2000; R¨opke & Hillebrandt2005; Wang et al. 2008; Podsiadlowski et al. 2008),and this may raise doubts about the distance calibrationwhich is purely empirical and based on the SN Ia sampleof the low red-shift Universe.At present, various progenitor models of SNe Ia canbe examined by comparing the distribution of the delaytime (between the star formation and SN Ia explosion)expected from a progenitor channel with that of obser-vations (e.g., Chen & Li 2007; Xu & Li 2009; L¨u et al.2009; Mannucci 2009; Schawinski 2009). Recently, thereare three important observational results for SNe Ia, i.e.,the strong enhancement of the SN Ia birthrate in radio-loud early-type galaxies, the strong dependence of theSN Ia birthrate on the colors of the host galaxies, andthe evolution of the SN Ia birthrate with redshift (DellaValle et al. 2005; Mannucci et al. 2005, 2006, 2008). Therelation between SN Ia birthrate and radio power impli-cates the information on the time-scales of the order of10 yr, which corresponds to the radio activity lifetime;the strong dependence of the local birthrate on the col-ors of the host galaxies is related to the time-scales ofthe order of the galaxy color evolution (i.e., 0 . − National Astronomical Observatories/Yunnan Observatory,the Chinese Academy of Sciences, Kunming 650011, China;[email protected], [email protected] Graduate University of Chinese Academy of Sciences, Beijing100049, China Department of Physics and Chemistry, Henan Polytechnic Uni-versity, Jiaozuo 454003, China be best matched by a bimodal delay time distribution, inwhich about half of the SNe Ia explode soon after star-burst, with a delay time less than ∼ yr, while thoseremaining have a much wider distribution, which can bewell described by an exponential function with a decaytime of about 3 Gyr (see also Mannucci 2008). Note thatScannapieco & Bildsten (2005) explored the two compo-nents of SN Ia birthrates and found that a young SN Iapopulation may be helpful to explain the Fe content ofthe intracluster medium in galaxy clusters. Moreover,by investigating the star formation history of 257 SN Iahost galaxies, Aubourg et al. (2008) recently found ev-idence of a short-lived population of SN Ia progenitorswith lifetimes of less than 180 Myr.Over the last decades, two competing progenitor mod-els of SNe Ia were discussed frequently, i.e., the single-degenerate (SD) and double-degenerate (DD) models. Ofthese two progenitor models, the SD model (Whelan &Iben 1973; Nomoto et al. 1984; Fedorova et al. 2004; Han2008; Meng et al. 2009) is widely accepted at present.It is suggested that the DD model, which involves themerger of two CO WDs (Iben & Tutukov 1984; Webbink1984; Han 1998), likely leads to an accretion-induced col-lapse rather than a SN Ia (Nomoto & Iben 1985; Saio &Nomoto 1985; Timmes et al. 1994). For the SD model,the companion is probably a MS star or a slightly evolvedsubgiant star (WD + MS channel), or a red-giant star(WD + RG channel). However, these two SD channelsdid not predict such young SN Ia populations (Hachisuet al. 1996, 1999a, 1999b; Li & van den Heuvel 1997;Langer 2000; Han & Podsiadlowski 2004, 2006). Wang et al. (2009) recently studied a WD + He starchannel for the SD model to produce SNe Ia. In thestudy they carried out detailed binary evolution calcula-tions of this channel for about 2600 close WD binarieswith metallicity Z = 0 .
02, in which a CO WD accretesmaterial from a He MS star or a He subgiant to increaseits mass to the Chandrasekhar-mass limit. The study Note that Hachisu et al. (2008) investigated new evolutionarymodels for SN Ia progenitors, introducing the mass-stripping effecton a MS or slightly evolved companion star by winds from a mass-accreting WD. The model can explain the presence of very young( . yr) populations of SN Ia progenitors, but the model dependson the efficiency of the mass-stripping effect. WANG et al.showed the SN Ia production regions in the (log P i , M i2 )plane (see Fig. 8 of Wang et al. 2009), where P i and M i2 are the orbital period and the mass of the He compan-ion star at the onset of the Roche lobe overflow (RLOF),respectively, and indicated that this channel is notewor-thy for producing SNe Ia. Because the WD + He starsystems are from intermediate mass binary systems, thischannel is likely to explain SNe Ia with short delay times.However, SN Ia birthrates and delay times through thischannel are not well known from a viewpoint of the bi-nary population synthesis (BPS).The purpose of this paper is to study SN Ia birthratesfor the WD + He star channel and to explore possibleSN Ia progenitor systems with short delay times from thischannel. In Section 2, we describe the BPS approach forthe WD + He star channel. The simulation results of theBPS approach is shown in Section 3. Finally, discussionand conclusion are given in Section 4. BINARY POPULATION SYNTHESIS
In order to investigate SN Ia birthrates and delay timesfor the WD + He star channel, we have performed a se-ries of Monte Carlo simulations in the BPS study. Ineach simulation, by using the Hurley’s rapid binary evo-lution code (Hurley et al. 2000, 2002), we have followedthe evolution of 4 × sample binaries from the star for-mation to the formation of the WD + He star systemsaccording to three evolutionary channels (Sect. 2.2). Weassumed that, if the parameters of a CO WD + He starsystem at the onset of the RLOF are located in the SNIa production regions in the (log P i , M i2 ) plane (Fig. 8 ofWang et al. 2009), a SN Ia is produced. Hereafter, weuse the term primordial to represent the binaries beforethe formation of WD + He star systems. Common Envelope in Binary Evolution
When the primordial primary (massive star) in a bi-nary system fills its Roche lobe, the primordial mass ratio(primary to secondary) is crucial for the mass transfer. Ifit is larger than a critical mass ratio, q c , the mass trans-fer may be dynamically unstable and a common envelope(CE) forms (Paczy´nski 1976). The mass ratio q c varieswith the evolutionary state of the primordial primary atthe onset of RLOF (Hjellming & Webbink 1987; Web-bink 1988; Han et al. 2002; Podsiadlowski et al. 2002).In this study we adopt q c = 4.0 when the primary is inthe MS stage or Hertzsprung gap. This value is sup-ported by detailed binary evolution studies (Han et al.2000; Chen & Han 2002, 2003). If the primordial pri-mary is on the first giant branch (FGB) or asymptoticgiant branch (AGB) stage, we use q c = [1 . − x + 2( M Pc1 M P1 ) ] / . , (1)where M P1 is the mass of the primordial primary, M Pc1 is the core mass of the primordial primary, and x =d ln R P1 / d ln M p1 is the mass-radius exponent of the pri-mordial primary and varies with composition. If the massdonor stars (primaries) are naked He giants, q c = 0.748based on equation (1) (see Hurley et al. 2002 for details).When a CE forms, the embedded in the CE is a ‘new’binary consisting of the dense core of the primordial pri-mary and the primordial secondary. Owing to frictional drag within the envelope, the orbit of the ‘new’ binarydecays and a large part of the orbital energy released inthe spiral-in process is injected into the envelope (Livio& Soker 1988). The CE ejection is still an open problem.Here, we use the standard energy equations (Webbink1984) to calculate the output of the CE phase. The CEis ejected if α ce (cid:18) GM fdon M acc a f − GM idon M acc a i (cid:19) = GM idon M env λR don , (2)where λ is a structure parameter that depends on theevolutionary stage of the donor, M don is the mass of thedonor, M acc is the mass of the accretor, a is the orbitalseparation, M env is the mass of the donor’s envelope, R don is the radius of the donor, and the indices i andf denote the initial and final values, respectively. Theright side of the equation represents the binding energyof the CE, the left side shows the difference between thefinal and initial orbital energy, and α ce is the CE ejec-tion efficiency, i.e., the fraction of the released orbitalenergy used to eject the CE. For this prescription of theCE ejection, there are two highly uncertain parameters(i.e., λ and α ce ). We usually set λ to be 0.5 to constrain α ce (de Kool 1990), although an exact calculation shouldtake into account the issue that λ depends on the stellarstructure. In principle, we expect 0 < α ce ≤
1, but we of-ten find that α ce exceeds 1 for the purpose of explainingobserved binaries. This may indicate that other energysources may also contribute to the ejection of the enve-lope, e.g., the internal energy of the envelope (Han et al.1994, 1995; Podsiadlowski et al. 2003; Webbink 2008).As in previous studies, we combine α ce and λ into onefree parameter α ce λ , and set it to be 0.5 and 1.5 (e.g.,L¨u et al. 2006). Evolutionary Channels to WD + He Star Systems
According to the evolutionary phase of the primordialprimary at the beginning of the first RLOF, there arethree channels which can produce CO WD + He starsystems and then produce SNe Ia.(1)
He star channel.
The primordial primary first fillsits Roche lobe when it is in the subgiant or RG stage(Case B mass transfer defined by Kippenhahn & Weigert1967). At the end of the RLOF, the primary becomesa He star and continues to evolve. After the exhaus-tion of central He, the He star which now contains a COcore may fill its Roche lobe again due to expansion ofthe He star itself, and transfer its remaining He-rich en-velope to the MS companion star, eventually leading tothe formation of a CO WD + MS system. After that,the MS companion star continues to evolve and fills itsRoche lobe in the subgiant or RG stage. A CE is possi-bly formed quickly because of dynamically unstable masstransfer. If the CE can be ejected, a close CO WD +He star system is then produced. The CO WD + Hestar system continues to evolve, and the He star mayfill its Roche lobe again (due to orbit decay induced bythe gravitational wave radiation or the expansion of theHe star itself), and transfer some material onto the sur-face of the CO WD. The accreted He may be convertedinto C and O via He-shell burning, and the CO WD in-creases in mass and explodes as a SN Ia when its massreaches the Chandrasekhar mass limit. For this channel,VOLVING TO SNe Ia WITH SHORT DELAY TIMES 3SN Ia explosions occur for the ranges M , i ∼ . − . M ⊙ , M , i ∼ . − . M ⊙ and P i ∼ −
40 days, where M , i , M , i and P i are the initial mass of the primary and thesecondary at ZAMS, and the initial orbital period of abinary system.(2) EAGB channel.
If the primordial primary is on theearly AGB (EAGB, i.e., He is exhausted in the center ofthe star while thermal pulses have not yet started), aCE will be formed because of dynamically unstable masstransfer. After the CE is ejected, the orbit decays andthe primordial primary becomes a He RG. The He RGmay fill its Roche lobe and start mass transfer, whichis likely stable and leaves a CO WD + MS system. Thefollowing evolution of the CO WD + MS system is similarto that in the
He star channel above, and may form aCO WD + He star system and finally produce a SN Ia.For this channel, SN Ia explosions occur for the ranges M , i ∼ . − . M ⊙ , M , i ∼ . − . M ⊙ and P i ∼ − TPAGB channel.
The primordial primary fills itsRoche lobe at the thermal pulsing AGB (TPAGB) stage,and the companion star evolves to a He-core burningstage. A CE is easily formed owing to dynamically un-stable mass transfer during the RLOF. After the CE ejec-tion, the primordial primary becomes a CO WD, then aCO WD + He star system is produced. The followingevolution of the CO WD + He star system is similar tothat in two channels above, i.e., a SN Ia may be pro-duced finally. For this channel, SN Ia explosions occurfor the ranges M , i ∼ . − . M ⊙ , M , i ∼ . − . M ⊙ and P i & Basic Parameters for Monte Carlo Simulations
In the BPS study, the Monte Carlo simulation requiresas input the initial mass function (IMF) of the primary,the mass-ratio distribution, the distribution of initial or-bital separations, the eccentricity distribution of binaryorbit and the star formation rate (SFR).(1) The IMF of Miller & Scalo (1979, MS79) is adopted.The primordial primary is generated according to theformula of Eggleton et al. (1989) M p1 = 0 . X (1 − X ) . + 0 . − X ) . , (3)where X is a random number uniformly distributed in therange [0, 1] and M p1 is the mass of the primordial primary,which ranges from 0.1 M ⊙ to 100 M ⊙ . The studies of theIMF by Kroupa et al. (1993) and Zoccali et al. (2000)support this IMF. As an alternative IMF we also considerthe IMF of Scalo (1986, S86) M p1 = 0 . (cid:18) X − X (cid:19) . , (4)where the meanings of X and M p1 are similar to that ofequation (3).(2) The initial mass-ratio distribution of the binaries, q ′ , is quite uncertain for binary evolution. For simplicity,we take a constant mass-ratio distribution (Mazeh et al.1992; Goldberg & Mazeh 1994): n ( q ′ ) = 1 , < q ′ ≤ , (5)where q ′ = M p2 /M p1 . This constant mass-ratio distribu-tion is supported by the study of Shatsky & Tokovinin (2002). As alternatives we also consider a rising massratio distribution n ( q ′ ) = 2 q ′ , ≤ q ′ ≤ , (6)and the case where both binary components are chosenrandomly and independently from the same IMF (uncor-related).(3) We assume that all stars are members of binarysystems and that the distribution of separations is con-stant in log a for wide binaries, where a is separation andfalls off smoothly at small separation: a · n ( a ) = (cid:26) α sep ( a/a ) m , a ≤ a ,α sep , a < a < a , (7)where α sep ≈ . a = 10 R ⊙ , a = 5 . × R ⊙ =0 .
13 pc and m ≈ .
2. This distribution implies that thenumbers of wide binary systems per logarithmic intervalare equal, and that about 50 percent of stellar systemshave orbital periods less than 100 yr (Han et al. 1995).(4) A circular orbit is assumed for all binaries. Theorbits of semidetached binaries are generally circularizedby the tidal force on a timescale which is much smallerthan the nuclear timescale. Moreover, a binary is ex-pected to become circularized during the RLOF. As analternative, we also consider a uniform eccentricity dis-tribution in the range [0, 1].(5) We simply assume a constant SFR over the last15 Gyr or, alternatively, as a delta function, i.e., a singlestarburst. In the case of a constant SFR, we assume thata binary calibrated with its primary more massive than0 . M ⊙ is formed annually (see Iben & Tutukov 1984;Han et al. 1995; Hurley et al. 2002). From this calibra-tion, we can get SFR = 5 M ⊙ yr − (see also Willems &Kolb 2004). For the case of a single starburst, we assumea burst producing 10 M ⊙ in stars. In fact, the SFR ina galaxy is neither a constant nor a delta function overthe last 15 Gyr. A galaxy may have a complicated starformation history. We only choose these two extremesfor a simplicity. A constant SFR is similar to the sit-uation of our Galaxy (Yungelson & Livio 1998; Han &Podsiadlowski 2004), while a delta function to the situa-tion of elliptical galaxies or globular clusters. Under theassumption of the SFR as a delta function, one can ob-tain the delay time of SNe Ia from a progenitor channel,and then to compare with that of observations (e.g., Han& Podsiadlowski 2004). THE RESULTS OF BINARY POPULATION SYNTHESIS
Birthrates of SNe Ia
We performed six sets of simulations (see Table 1) withmetallicity Z = 0 .
02 to systematically investigate Galac-tic birthrates of SNe Ia for the WD + He star channel,where set 1 is our standard model with the best choice ofmodel parameters (e.g., Han et al. 2002, 2003, 2007). Wevary the model parameters in the other sets to examinetheir influences on the final results.In Figure 1, we show Galactic birthrates of SNe Iafor the WD + He star channel by adopting Z = 0 . M ⊙ yr − . The simulation for our stan-dard model (set 1) gives Galactic SN Ia birthrate of ∼ . × − yr − , which is lower than that inferredobservationally (i.e., 3 − × − yr − ; van den Bergh& Tammann 1991; Cappellaro & Turatto 1997). This WANG et al. TABLE 1Galactic birthrates of SNe Ia for different simulationsets, where set 1 is our standard model. α ce λ = CEejection parameter; n ( q ′ ) = initial mass ratiodistribution; IMF = initial mass function; ecc =eccentricity distribution of binary orbit; ν = Galacticbirthrates of SNe Ia. Set α ce λ n ( q ′ ) IMF ecc ν (10 − yr − )1 0 . . . . . . . . . . . . Fig. 1.—
The evolution of Galactic birthrates of SNe Ia for aconstant star formation rate ( Z = 0 .
02, SFR = 5 M ⊙ yr − ). Thekey to the line-styles representing different sets is given in the upperleft corner. The results of sets 2 and 3 almost coincide with thatof set 1. implies that the WD + He star channel is only a sub-class of SN Ia production, and there may be some otherchannels or mechanisms also contributing to SNe Ia,e.g., WD + MS channel, WD + RG channel or double-degenerate channel (see Meng et al. 2009 for details).Especially, as mentioned by Han & Podsiadlowski (2004),the WD + MS channel can give a Galactic birthrate of ∼ . − . × − yr − , and is considered to be an im-portant channel to produce SNe Ia.According to the results of the six sets of Monte Carlosimulations, we find that the BPS is sensitive to uncer-tainties in some input parameters, in particular the mass-ratio distribution. If we adopt a mass-ratio distributionfor un-correlated component masses (set 6), the birthratewill decrease to be ∼ × − yr − , as most of the donorsin the WD + He star channel are not very massive whichhas the consequence that WDs cannot accrete enoughmass to reach the Chandrasekhar-mass limit.The SN Ia birthrate in galaxies is the convolution ofthe distribution of the delay times (DDT) with the starformation history (SFH) (e.g., Greggio et al. 2008): ν ( t ) = Z t SF R ( t − t ′ ) DDT ( t ′ ) dt ′ , (8)where the SF R is the star formation rate, and t ′ is thedelay times of SNe Ia. Due to a constant SFR adoptedin this paper, the SN Ia birthrate ν ( t ) is only related to Fig. 2.—
Similar to Fig. 1, but for a single starburst with a totalmass of 10 M ⊙ . The result of set 3 almost coincides with that ofset 2. the DDT , which can be expressed by
DDT ( t ) = , t < t ,DDT ′ ( t ) , t ≤ t ≤ t , , t > t , (9)where t and t are the minimum and maximum delaytimes of SNe Ia, respectively, and the DDT ′ is the dis-tribution of the delay times between t and t . When t is larger than the t , the equation (8) can be written as ν ( t ) = SFR Z t t DDT ′ ( t ′ ) dt ′ = constant . (10)Therefore, the SN Ia birthrates shown in figure 1 seemsto be so completely flat after the first rise.Figure 2 displays the evolution of SN Ia birthrates fora single starburst with a total mass of 10 M ⊙ . Inthe figure we see that SN Ia explosions occur between ∼ . × yr and ∼ . × yr after the starburst,which can explain SNe Ia with short delay times (Scan-napieco & Bildsten 2005; Mannucci et al. 2006; Aubourget al. 2008). The minimum delay time in the figure ismainly decided by the MS lifetime of a 8 M ⊙ star (it isalso the maximum mass for the progenitors of CO WDs).Moreover, after the primordial binary system evolves toa WD + He star system, the MS lifetime of the He com-panion star also contributes to the minimum time, butthe time is short, e.g., the MS lifetime of a 1 M ⊙ He staris only about 15 Myr (Eggleton 2006).
Distribution of Initial Parameters of WD + HeStar Systems for SNe Ia
Observationally, some WD + He star systems are pos-sible SN Ia progenitors (Wang et al. 2009). Furtherinvestigations are necessary for final confirmation of this(from both observations and theories). In this section,we will present some properties of initial WD + He starsystems for SNe Ia according to our BPS approach, whichmay help to search for potential SN Ia progenitors.Figure 3 shows the distribution of the initial orbitalperiods of the WD + He star systems that ultimatelyproduce SNe Ia with different α ce λ . The simulation usesa metallicity Z = 0 .
02 and a constant initial mass-ratiodistribution. The figure displays a result of the currentepoch for a constant SFR. In the figure we can see thatVOLVING TO SNe Ia WITH SHORT DELAY TIMES 5 -1.6 -1.2 -0.8 -0.4 0.00.000.050.100.15 P e r c en t log ( P i /day ) Fig. 3.—
The distribution of the initial orbital periods of theWD + He star systems which can ultimately produce SNe Ia fordifferent α ce λ . The simulation uses a metallicity Z = 0 .
02 and aconstant initial mass-ratio distribution. The solid and the dottedhistograms represent the cases with α ce λ = 0 . α ce λ =1 . P e r c en t M WD (M ) Fig. 4.—
Similar to Fig. 3, but for the distribution of the initialmasses of the CO WDs. there are obviously two peaks for each case. The leftpeak in these two cases results from the
He star channel .Many of the SNe Ia in the right peak are also from the
He star channel , while others from the
EAGB channel and the
TPAGB channel (see Sect. 2.2). The
He starchannel has an important contribution to the formationof SNe Ia. This figure also shows that a high value of α ce λ leads to wider WD binaries, since a high value of α ce λ is easier to eject the CE in the binary evolution.Figure 4 represents the distribution of the initialmasses of the CO WDs. In the figure, a low value of α ce λ tends to have larger WD masses on average. The He star channel in Sect. 2.2, which allows stable RLOFto produce massive WDs (rather lead to dynamical masstransfer and a CE phase), is useful to understand thistrend. According to our BPS simulations, we find that a P e r c en t M He (M ) Fig. 5.—
Similar to Fig. 3, but for the distribution of the initialmasses of the He donor stars. low value of α ce λ will produce more SNe Ia through the He star channel than other two channels, and then pro-duce more massive WDs on average. Figure 5 displaysthe distribution of the initial masses of the He donorstars. A low value of α ce λ in the figure tends to havelarger He star masses on average. This is also related tothe stable RLOF, which leads to more massive compan-ion star resulting in the final larger He-core mass (He starmass). Moreover, a massive He donor star in the WD +He star channel will evolve more quickly and hence pro-duce a SN at an earlier time.When the WDs in Figure 4 increase their masses to theChandrasekhar-mass limit, they will explode as SNe Ia.Meanwhile, the He donor stars in Figure 5, which affordmaterial to the WDs though the RLOF, will loss a signif-icant amount of masses. We find that the He stars havemasses ∼ . − . M ⊙ at the moment of SN explosions.Marietta et al. (2000) presented several high-resolutiontwo-dimensional numerical simulations of the impacts ofSN Ia explosions with companions. The impact makesthe companion in the WD + MS channel lose a mass of0 . − . M ⊙ , but the impact in the WD + He starchannel is still unknown. The companion in the WD +He star channel may lose more masses than that of theWD + MS channel. This is because the orbit separationat the moment of SN explosion from this channel is sig-nificantly less than that of the WD + MS channel, whichmay result in a much stronger impact to the companion.The surviving companion star from the WD + He starchannel could be verified by future observations. DISCUSSION AND CONCLUSION
Wang et al. (2009), based on equation (1) of Iben &Tutukov (1984), estimated the potential SN Ia birthratethrough the WD + He star channel to be ∼ . × − yr − in the Galaxy. The birthrate from Wang etal. (2009) is higher than that in this paper, this is due tothe fact that the long orbit period (i.e., & . M ⊙ . If this value is adopted as theupper limit of the CO WD, the birthrate of SNe Ia fromthis channel will decrease to be ∼ . × − yr − in theGalaxy according to our standard model.In this paper we assume that all stars are in binariesand about 50 percent of stellar systems have orbital pe-riods less than 100 yr. In fact, it is known not to be thecase, and the binary fractions may depend on metallicity,environment, spectral type, etc. If we adopt 40 percent ofstellar systems have orbital periods below 100 yr by ad-justing the parameters in equation (7), we estimate thatthe birthrate of SNe Ia from this channel will decrease tobe ∼ . × − yr − for our standard model.SNe Ia from the WD + He star channel usually havemassive CO WDs as their progenitors. Some previousstudies showed that a massive CO WD leads to a lowerC/O ratio in the Chandrasekhar-mass WD, and thus alower amount of Ni synthesized in the thermonuclearexplosion, which results in a lower luminosity of SNeIa (Umeda et al. 1999b; Nomoto et al. 1999, 2003).However, brighter SNe Ia more frequently occur in ac-tive star formation galaxies (Hamuy et al. 1995, 1996),in which the young stellar population implies that theseSNe Ia have short delay times (see also Aubourg et al.2008), i.e., the CO WD + He star channel might pro-duce brighter SNe Ia. Therefore, it is difficult to explainSN Ia diversity by using the C/O ratio. Note that 3Dsimulations about SN Ia explosions by R¨opke & Hille-brandt (2004) also indicated that different C/O ratioshave a negligible effect on the amount of Ni produced.To understand the diversity of SN Ia explosions, the for-mation of brighter SNe Ia should be explored in futureinvestigations.It is suggested that the WD + He star systems mayappear as supersoft X-ray sources (SSSs) prior to SN Iaexplosions (Iben & Tutukov 1994; Yoon & Langer 2003;Wang et al. 2009). Recently, Di Stefano & Kong (2003)used a set of conservative criteria, applicable to
Chandra data, to identify luminous SSSs in four external galaxies(an elliptical galaxy, NGC 4967; two face-on spiral galax-ies, M101 and M83; and an interacting galaxy, M51).They found that in every galaxy there are at least severalhundred luminous SSSs with a luminosity of 10 erg s − ,and that in spiral galaxies M101, M83 and M51, the SSSsappear to be associated with spiral arms. This may indi-cate that some SSSs are young systems, possibly youngerthan 10 yr. Note that a WD + He star system has X-rayluminosity around 10 − erg s − when He burningis stable on the surface of the WD (Wang et al. 2009).Meanwhile, the distribution of SNe Ia with short delaytimes associated with galactic spiral arms (Bartunov etal. 1994; Della Valle & Livio 1994). Therefore, we em-phasize that these WD + He star systems may be relatedto the young SSSs prior to SN Ia explosions.The most important conclusion of this study is that theWD + He star channel can explain SNe Ia with short de-lay times ( ∼ . × − . × yr), which is consistentwith recent observational implications of young popula-tions of some SN Ia progenitors (Scannapieco & Bild-sten 2005; Mannucci et al. 2006; Aubourg et al. 2008).The young population of SNe Ia may have an effect onmodels of galactic chemical evolution, since they wouldreturn large amounts of iron to the interstellar mediummuch earlier than previously thought. It may also havean impact on cosmology, as they are used as cosmologicaldistance indicators.We thank an anonymous referee for his/her valuablecomments that helped to improve the paper. BW thanksDr. Richard Pokorny for improving the English languageof the original manuscript. This work is supported by theNational Natural Science Foundation of China (GrantNos. 10521001, 2007CB815406 and 10603013), the Foun-dation of the Chinese Academy of Sciences (Grant No.06YQ011001) and the Yunnan Natural Science Founda-tion (Grant No. 08YJ041001). REFERENCESAubourg, E., Tojeiro, R., Jimenez, R., Heavens, A. F., Strauss, M.A., & Spergel, D. N. 2008, A&A, 492, 631Bartunov, O. S., Tsvetkov, D. Yu., & Filimonova, I. V. 1994, PASP,106, 1276Cappellaro, E., & Turatto, M. 1997, in Thermonuclear Supernovae,ed. P. Ruiz-Lapuente, R. Cannal, & J. Isern (Dordrecht: Kluwer),77Chen, X., & Han, Z. 2002, MNRAS, 335, 948Chen, X., & Han, Z. 2003, MNRAS, 341, 662Chen, W.-C., & Li, X.-D. 2007, ApJ, 658, L51de Kool, M. 1990, ApJ, 358, 189Della Valle, M., & Livio, M. 1994, ApJ, 423, L31Della Valle, M., Panagia, N., Padovani, P., Cappellaro, E.,Mannucci, F., & Turatto, M. 2005, ApJ, 629, 750Di Stefano, R., & Kong, A. K. H. 2003, ApJ, 592, 884Eggleton, P. P., Tout, C. A., & Fitechett, M. J. 1989, ApJ, 347,998Eggleton, P. P. 2006, Evolutionary Processes in Binary andMultiple Stars. Cambridge Univ. Press, CambridgeFedorova, A. V., Tutukov, A. V., & Yungelson, L. R. 2004, Astron.Lett., 30, 73Goldberg, D., & Mazeh, T. 1994, A&A, 282, 801Greggio, L., Renzini, A., & Daddi, E. 2008, MNRAS, 388, 829Hachisu, I., Kato, M., & Nomoto, K. 1996, ApJ, 470, L97Hachisu, I., Kato, M., Nomoto, K., & Umeda, H. 1999a, ApJ, 519,314Hachisu, I., Kato, M., & Nomoto, K. 1999b, ApJ, 522, 487Hachisu, I., Kato, M., & Nomoto, K. 2008, ApJ, 679, 1390 Hamuy, M., Phillips, M. M., Maza, J., Suntzeff, N. B., Schommer,R. A., & Aviles, R. 1995, AJ, 109, 1Hamuy, M., Phillips, M. M., Suntzeff, N. B., Schommer, R. A.,Maza, J., & Aviles, R. 1996, AJ, 112, 2391Han, Z., Podsiadlowski, Ph., & Eggleton, P. P. 1994, MNRAS, 270,121Han, Z., Podsiadlowski, Ph., & Eggleton, P. P. 1995, MNRAS, 272,800Han, Z. 1998, MNRAS, 296, 1019Han, Z., Tout, C. A., & Eggleton, P. P. 2000, MNRAS, 319, 215Han, Z., Podsiadlowski, Ph., Maxted, P. F. L., Marsh, T. R., &Ivanova, N. 2002, MNRAS, 336, 449Han, Z., Podsiadlowski, Ph., Maxted, P. F. L., & Marsh, T. R.2003, MNRAS, 341, 669Han, Z., & Podsiadlowski, Ph. 2004, MNRAS, 350, 1301Han, Z., & Podsiadlowski, Ph. 2006, MNRAS, 368, 1095Han, Z., Podsiadlowski, Ph., & Lynas-Gray, A. E. 2007, MNRAS,380, 1098Han, Z. 2008, ApJ, 677, L109Hjellming, M. S., & Webbink, R. F. 1987, ApJ, 318, 794Hillebrandt, W., & Niemeyer, J. C. 2000, ARA&A, 38, 191Hurley, J. R., Pols, O. R., & Tout, C. A. 2000, MNRAS, 315, 543Hurley, J. R., Tout, C. A., & Pols, O. R. 2002, MNRAS, 329, 897Iben, I., & Tutukov, A. V. 1984, ApJS, 54, 335Iben, I., & Tutukov, A. V. 1994, ApJ, 431, 264Kippenhahn, R., & Weigert, A. 1967, ZA, 65, 251Kroupa, P., Tout, C. A., & Gilmore, G. 1993, MNRAS, 262, 545