THE BIRTH RATE OF SNe Ia FROM HYBRID CONe WHITE DWARFS

As very good cosmological distance indicators, Type Ia supernovae (SNe Ia) have been successfully used for determining basic cosmological parameters; this has led to the discovery of an accelerating expansion of the universe (Riess et al. 1998; Perlmutter et al. 1999). However, the exact nature of SNe Ia is still not clear, especially concerning their progenitor systems (Hillebrandt & Niemeyer 2000; Leibundgut 2000); indeed, the identification of their progenitors is important for several astrophysical fields (Wang & Han 2012). For the past four decades, two basic scenarios for the progenitor of SNe Ia have been in competition. In the single-degenerate (SD) model, a carbon–oxygen white dwarf (CO WD) grows in mass via accretion from a non-degenerate companion (Whelan & Iben 1973; Nomoto et al. 1984), while in the double-degenerate scenario, two WDs merge after losing orbital angular momentum by gravitational wave radiation (Iben & Tutukov 1984; Webbink 1984). At present, there is some observational and/or theoretical support for both basic scenarios, but there are also counter arguments (e.g., Maoz et al. 2014; Ruiz-Lapuente 2014).

The discovery of circumstellar material from the SN Ia progenitor system has provided significant evidence in support of the SD scenario (Patat et al. 2007; Sternberg et al. 2011; Dilday et al. 2012), but a major shortcoming of the model is that present estimates of their birth rate appear to be somewhat lower than the observationally inferred rate (Han & Podsiadlowski 2004; Meng & Yang 2010; also see Hachisu et al. 1999b; Yungelson & Livio 2000; Ruiter et al. 2009; Mennekens et al. 2010; Claeys et al. 2014). One reason for the low birth rate is that it is difficult to increase the WD mass to reach the Chandrasekhar limit (Branch et al. 1995; Howell 2011; Maoz & Mannucci 2012; Maoz et al. 2014). Recently, following the discovery of Denissenkov et al. (2013), Chen et al. (2014) found that considering the uncertainty of the C-burning rate (CBR) and the treatment of convective boundaries, hybrid CONe WDs with carbon-rich cores may instead form from pure ONe WDs even for stars with initial masses larger than 7.0 M_☉. In their most extreme case (for a CBR efficiency factor of 0.1), the hybrid WD could be as large as 1.30 M_☉. It is relatively easy for such WDs to accrete enough mass to reach the Chandrasekhar limit, i.e., the discovery by Chen et al. (2014) could increase the fraction of stars that form WDs capable of igniting carbon in a thermonuclear runaway and contribute to the birth rate of SNe Ia. Chen et al. (2014) did not estimate the birth rate of SNe Ia from hybrid CONe WDs. The purpose of this paper is to provide such estimates using binary population synthesis (BPS) based on the results in Chen et al. (2014).

In Section 2, we describe our method and present the results of our calculations in Section 3. In Section 4, we conclude with a short discussion of the implications.

To estimate the birth rate of SNe Ia from hybrid CONe WDs, we do not perform new binary evolution calculations but instead use previously published ones. Based on the optically thick wind model (Hachisu et al. 1996), Meng et al. (2009) previously obtained a dense model grid leading to SNe Ia with different metallicities and initial WD masses. In their calculations, they only considered the case of main sequence or sub-giant companions (WD+MS). Here, we also only consider the WD+MS case since the contribution to the total SNe Ia from WD binaries with red-giant (RG) companions is quite uncertain (e.g., Yungelson et al. 1995; Hachisu et al. 1999a; Han & Podsiadlowski 2004). Using the results of Meng et al. (2009), we simply extrapolate the WD mass by a linear assumption to obtain the parameter space leading to SNe Ia for $M_{\rm WD}^{\rm i}=1.30$ M_☉. Figure 1 shows the contours leading to SNe Ia for different initial WD masses.

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To obtain the birth rate of hybrid CONe WDs, we carried out a series of detailed Monte Carlo simulations with the rapid binary evolution code developed by Hurley et al. (2000, 2002). We assumed that if a WD is less massive than the most massive hybrid shown in Figure 5 of Chen et al. (2014) and is not a CO WD, it is a hybrid CONe WD. If a binary system in the simulations evolves to the CONe WD+MS stage and the system is located in the (log Pⁱ – $M_{\rm 2}^{\rm i}$) plane for a SN Ia at the onset of Roche-lobe overflow (RLOF), we assume that carbon may be ignited in the center of the WD regardless of how massive the CO core is in the hybrid WD, resulting in a SN Ia. We follow the evolution of 10⁸ sample binaries. This evolutionary channel is described in more detail in Meng et al. (2009). As in Meng et al. (2009), we adopted the following input for the simulations: (1) a single starburst (where 10¹¹ M_☉ of stars are formed at the same instant of time) or a constant star formation rate (SFR) over the last 15 Gyr. (2) The initial mass function (IMF) of Miller & Scalo (1979). (3) A constant mass-ratio distribution is taken to be constant. (4) The distribution of separations in log a for wide binaries, where a is the orbital separation. (5) Circular orbit for all binaries. (6) The common-envelope (CE) ejection efficiency α_CE, which denotes the fraction of the released orbital energy used to eject the CE, is set to 0.5, 0.75, 1.0, or 3.0. (See Meng et al. (2009) for details.) In this paper, we do not test the effect of other inputs to produce the binary samples on the final results such as different IMF, since they may not change the basic conclusion significantly (see also Wang et al. 2013).

The birth rate of SNe Ia for a single starburst from our BPS simulations is presented in Figure 2. It shows that most supernovae occur between 0.1 and 1 Gyr after a starburst, even though some SNe Ia can be as young as 30 Myr. The contribution of these extremely young SNe Ia decreases with decreasing α_CE. These extremely young SNe Ia come from the He star channel, as defined in Meng et al. (2009), where the first mass-transfer phase in the primordial binary occurs when the original primary crosses the Hertzprung gap or is on the RG branch. In this case, mass transfer leads to the formation of a CE, and the primary becomes a He star after its ejection. The helium star fills its Roche lobe again after central helium is exhausted (so-called case BB mass transfer). Since the mass donor is much less massive than before, the second phase of RLOF is dynamically stable, resulting in a close WD+MS system where the companion is helium-rich. In this binary channel, even a star as massive as 8–10 M_☉ can avoid the fate of a core-collapse supernova and form a WD. However, this channel is different from the one described in Chen et al. (2014), and it is still unclear whether or not the WD from such channel is a hybrid CONe WD. Irrespectively, SNe Ia from this channel are rare (see also Figure 3).

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Figure 2 also shows that a low α_CE leads to a higher birth rate (see also Figure 3) since, for a low α_CE, the primordial system needs to release more orbital energy to eject the CE to form a WD+MS system; this produces WD+MS systems that tend to have shorter orbital periods that more easily fulfill the condition for SNe Ia. At the same time, increasingly more systems that could otherwise pass through the He star channel merge with decreasing α_CE; this results in a decrease of the number of SNe Ia from this channel. Figure 2 also shows that the birth rate decreases with the CBR factor, but the difference between a CBR factor of 0.1 and 1 is not significant as the very massive WDs are rare.

Figure 3 shows the Galactic birth rates of SNe Ia for a constant SFR (SFR = 5.0 M_☉ yr⁻¹) from hybrid CONe WD. The Galactic birth rate is around 0.26–2.4 × 10⁻⁴ yr⁻¹, depending on α_CE and the CRB factor. This is much lower than the inferred overall SN Ia rate from observations (3–4 × 10⁻³ yr⁻¹, van den Bergh & Tammann 1991; Cappellaro & Turatto 1997). Hence, these can only contribute between 0.65% and 8% of the total SN Ia rate. Again, the Galactic birth rate increases in line with an decreasing CBR factor and α_CE.

Figure 4 shows the mass distribution of the initial masses of the hybrid CONe WDs. Most of the WDs are initially more massive than 1.05 M_☉ (the upper limit for CO WDs in Figure 5 of Chen et al. (2014) for a CBR factor of 1, see also Meng et al. 2008); i.e., irrespective of the correct value of α_CE, most SNe Ia come from the channel described by Chen et al. (2014), and the contribution from the He star channel is only minor. There is a relatively small difference of distribution between CBR factors of 0.1 and 1, as well as the birth rate as shown in Figures 2 and 3.

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4.1. Uncertainties

4.2. The Effect of the CBR Factor

4.3. Properties of SNe Ia from Hybrid CONe WDs

4.4. A Possible Progenitor for 2002cx-like Supernova?

We are grateful to the anonymous referee for constructive comments. This work was partly supported by NSFC (11273012, 11033008) and the Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences.