Double CO WD Systems from the WD+He Subgiant Channel and Type Ia Supernovae

Open Astron. 2017; 26: 195–198

Research Article

Dongdong Liu*, Bo Wang, and Chengyuan Wu Double CO WD systems from the WD+He subgiant channel and type Ia supernovae

https://doi.org/10.1515/astro-2017-0436 Received Sep 28, 2017; accepted Oct 26, 2017

Abstract: Recent studies suggested that at least some of the observed SNe Ia originate from the double-degenerate model, which involves the merging of double carbon-oxygen white dwarfs (CO WDs). However, the delay time distributions predicted by previous theoretical studies are inconsistent with the observed SNe Ia at the early epoches of < 1 Gyr and old epoches of > 8 Gyr. Previous studies suggested that the CO WD+He subgiant channel has a significant contribution to the formation of massive double CO WDs, the merging of which may produce SNe Ia. In the present work, we added this channel into the double-degenerate model to investigate its influence on the delay time distributions of SNe Ia. We found that the delay time distributions would match better with the observed SNe Ia when the CO WD+He subgiant channel is included in the double-degenerate model.

Keywords: binaries: close – stars: evolution – supernovae: general 1 Introduction the Chandrasekhar mass limit, an SN Ia explosion will occur. In the DD model, a double WD system loses its orbital angular momentum driven by gravitational wave radia- Type Ia supernovae (SNe Ia), which belong to the most lution. Thus, the two WDs would get closer and closer, and minous phenomena in the Universe, are used as a tool to eventually they may merge and produce an SN Ia explo- probe the mystery of the Universe. It has been generally sion. However, some recent observations seem to slightly suggested that SNe Ia stem from massive carbon-oxygen favor the DD model, e.g. the missing H and He lines in white dwarfs (CO WDs) in close binaries. At present, the the nebular of most SNe Ia, no surviving companion that key issues are the uncertainty of the companion type and has been conclusive identified, the lack of radio emission, the exploding mechanism. Up to now, there are two most the discovery of super-luminous SNe Ia, the consistency of popular models dominating the landscape of SN Ia pro- theory and observation for the birthrates, and delay time genitor scenarios, i.e. the single-degenerate (SD) model distribution of SNe Ia. Here, the delay time of an SN Ia is de- and the double-degenerate (DD) model (for details see fined as the time interval from the formation of the primor- Podsiadlowski et al. 2008; Wang & Han 2012; Maoz et al. dial binary to the production of SN Ia explosion. However, 2014). the delay time distributions predicted by previous theoret- In the SD model, the primary WD could accrete H-rich ical studies are still inconsistent with the observations for matter from a main-sequence star (i.e., WD+MS channel) delay times < 1 Gyr and > 8 Gyr (e.g. Yungelson & Kuranov or a red-giant star (i.e., WD+RG channel), or accrete He- 2017). rich material from a He star or a He subgiant (i.e. WD+He Liu et al. (2016) found that the WD+He subgiant chan- star channel). As soon as the primary WD grows its mass to nel is a dominant pathway for the formation of massive DD systems (see also Ruiter et al. (2013)). In this channel, the

Corresponding Author: Dongdong Liu: Key Laboratory for the primary WD grows in mass by accreting matter from a He Structure and Evolution of Celestial Objects, Yunnan Observatories, subgiant and eventually forms a double WD system. In the CAS, Kunming 650216, China; University of Chinese Academy of Sci- present work, we added the WD+He subgiant channel into ences, Beijing 100049, China; Center for Astronomical Mega-Science, the DD model, and found that the delay time distributions CAS, Beijing 100012, China; Email: [email protected] of SNe Ia will match better with that from the observations. Bo Wang, Chengyuan Wu: Key Laboratory for the Structure and Evolution of Celestial Objects, Yunnan Observatories, CAS, Kunming 650216, China; University of Chinese Academy of Sciences, Beijing 100049, China; Center for Astronomical Mega-Science, CAS, Beijing 100012, China

Open Access. © 2017 D. Liu et al., published by De Gruyter Open. This work is licensed under the Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 License 196 Ë D. Liu et al., Double CO WD systems from the WD+He subgiant channel

Figure 1. Parameter space of WD+He star systems for the formation Figure 2. Delay time distributions of SNe Ia based on the DD model. of SNe Ia based on the DD model. From Liu et al. (2017). The solid, dashed and dash-dotted lines present the cases with

αCEλ = 0.5, 1.0 and 1.5, respectively. The thick curves represent the delay time distributions of SNe Ia from the WD+He subgiant chan- 2 Parameter space nel, and the thin ones show that from all channels. Points with error bars represent the observational date of elliptical galaxies from the Subaru/XMM−Newton Deep Survey (the open circles; Totani et al. In order to investigate the mass-transfer process from the 2008), galaxy clusters at the redshifts from Z = 0 to Z = 1.45 He subgiant onto the primary WD in detail, we perform (the filled triangles; Maoz et al. 2010), a galaxy sample from SDSS a large set of full stellar evolution computations with the (the filled squares; Maoz et al. 2012), and an SN Ia sample from Eggleton stellar evolution code (Eggleton 1973). As soon the Cluster Lensing And Supernova survey with Hubble (the open square; Graur & Maoz 2013). as the He star evolves to the subgiant stage, it may fill its Roche-lobe and transfer He-rich matter onto the primary WD. The Roche-lobe overflow and mass accumulation pro- which is marked as a square with error bar in this figure. cesses are calculated similar to that in Liu et al. (2016). As We speculate that KPD 1930+2752 will evolve to form a dou- soon as the envelope of the He star is exhausted, a double WD and then produce an SN Ia via the WD+He subgiant ble WD system is formed. The two WDs gradually approach channel of the DD model. each other and eventually merge because of the loss of orbital angular momentum by gravitational wave radiation. In this work, we assume that an SN Ia explosion occurs as 3 Binary population synthesis soon as the total mass of the WD merger is higher than the Chandrasekhar limit (adopted to be 1.378 M⊙). By employing the Hurley rapid binary evolution code (Hur- Figure 1 shows the parameter space of WD+He star sys- ley et al. 2002), we conducted a series of binary popu- tems which can produce double WDs and then form SNe Ia lation synthesis computations. In each of of our simula- in the log Pi − Mi plane. The initial WD mass Mi ranges 2 WD tion, we evolved 1 × 107 binaries from their zero age main- from 0.5 to 1.2 M⊙ for different contours. For this grid, sequence to the formation of WD+He star systems. If the the upper boundaries are determined by the condition that formed WD+He star system can be located into the param- He stars should evolve to be CO WDs but not ONe WDs eter space presented in Figure 3, we assumed that an SN Ia (range I). Binaries beyond the right boundaries have de- explosion would occur. The properties of the double WDs lay times larger than the Hubble timescale for the forma- are calculated by interpolations in the three dimension tion of WD mergers (range II). The lower boundaries are grids presented in Figure 1. In order to investigate the delay set by the criterion that the total mass of the formed dou- time distributions of SNe Ia, we simply adopted a delta- ble WDs should be larger than the Chandrasekhar limit 10 function star formation rate, i.e. a star burst of 10 M⊙ (range III). For the binaries beyond the left boundaries, SN in stars. We employed the standard energy prescription Ia explosions will occur via the double detonation model described in Webbink (1984) to investigate the output of (the lower part, range IV), or the He stars will fill their common envelope (CE) evolutions, in which the CE ejec- Roche-lobe at the He ZAMS (the upper part, range V). KPD tion parameter α λ is set to be 0.5, 1.0 and 1.5 for com- 1930+2752 is a WD+sdB star system (e.g. Geier et al. 2007), CE D. Liu et al., Double CO WD systems from the WD+He subgiant channel Ë 197

MWD2/MWD1 is the mass ratio of the less massive WD to the massive WD, and Mtotal = MWD1 + MWD2. The mass ratio of double WDs that are potentially producing SNe Ia are mainly located in the range of 0.6-0.8, while the total masses have a wide distribution ranging from 1.378 to 2.4 M⊙. This distribution is divided into two parts: the mass ratio increases with the total mass in the massive part, while the mass ratio decreases with the total mass in the less-massive part. Double WDs in the less-massive part may evolve from the WD+He subgiant channel or the CE ejection channel, whereas all of the massive part originate from the WD+He subgiant channel. Since the double WDs originating from WD+He subgiant channel are Figure 3. Density distribution of the masses of double WDs that can both surrounded by He-rich atmospheres, which should q M merge and form SNe Ia in the mass ratio−total mass ( − total) be double DB/DO WD systems. Thus, it is predictable that plane. double WDs in the massive part might always be double DB/DO WD systems. The filled squares with error bars parison. In addition to the WD+He star channel, there ex- represent the double degenerate core of a planetary neb- ist some other channels for producing massive double WD ula Henize 2-428 and the double WDs originating from systems and forming SNe Ia (named as the CE ejection KPD 1930+2752, respectively (Geier et al. 2007; Santander- channel), which are also considered in our calculations. García et al. 2015). We speculate that both Henize 2-428 Figure 2 shows SN Ia delay time distributions from the and KPD 1930+2752 would produce SNe Ia through the DD merging of double WDs from different formation channels. model in the future. Here, the thick lines represent the delay time distributions of SNe Ia from the WD+He subgiant channel, whereas the thin lines show that from all channels. From this figure, 4 Summary we can see that the delay times of SNe Ia are from about 110 Myr to the Hubble time based on the WD+He subgiant In this study, we conducted a large number of binary evo- channel, and range from about 70 Myr to the Hubble time lution computations for WD+He star sytems, and obtained based on all channels. The delay time distributions of SNe the parameter space for producing SNe Ia through the DD Ia from all channels are roughly proportional to t−1 and the model. We then followed a series of binary population syn- birthrates are comparable with that in the observed ellip- thesis simulations for the DD model from the WD+He sub- tical galaxies (or galaxy clusters). Without considering the giant channel and all channels. According to our simula- WD+He subgiant channel, Yungelson & Kuranov (2017) tions, we found that the delay times of SNe Ia range from found that the delay time distributions of SNe Ia are in- ∼ 110 Myr to the Hubble time for WD+He subgiant chan- consistent with the observations in the epoches of < 1 Gyr nel of the DD model, and from ∼ 70 Myr to the Hubble time and > 8 Gyr. We found that SN Ia delay time distributions for all channels of the DD model. The delay time distribu- from our simulations can roughly reproduce the observed tions of SNe Ia fit better with that from the observations results when the WD+He subgiant channel is considered. when the WD+He subgiant channel is considered, even for It is hard to reproduce the delay time distributions of SNe SNe Ia in the epoches of < 1 Gyr and > 8 Gyr in which Ia from observations when the CE ejection parameter α λ CE previous studies are inconsistent with observations. The is adopted to be 0.5. Thus, a larger CE ejection parameter mass ratio of double WDs potentially producing SNe Ia are α λ is required if the DD model indeed contributes to most CE mainly in the range of 0.6-0.8, and the total masses have a of SNe Ia. wide distribution ranging from the Chandrasekhar mass The outcomes of WD mergers are still not fully iden- limit to 2.4 M⊙. Note that double WDs originating from tified. The mass ratio and total mass of WD mergers have WD+He subgiant channel should be double DB/DO WD a great influence on their outcomese.g. ( Sato et al. 2016; systems, which may be very important for the formation Pakmor et al. 2010). Figure 3 shows the density distribu- of SNe Ia for the DD model. Thus, we hope more double tion of the masses of WD mergers that can produce SNe DB/DO WD systems can be identified in the observations. Ia via the DD model in the q − Mtotal plane, where q = 198 Ë D. Liu et al., Double CO WD systems from the WD+He subgiant channel

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