A&A 622, A35 (2019) Astronomy https://doi.org/10.1051/0004-6361/201833010 & c ESO 2019 Astrophysics The progenitors of type-Ia supernovae in semidetached binaries with red giant donors D. Liu1,2,3,4 , B. Wang1,2,3,4 , H. Ge1,2,3,4 , X. Chen1,2,3,4 , and Z. Han1,2,3,4 1 Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216, PR China e-mail: [email protected], [email protected] 2 Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming 650216, PR China 3 University of Chinese Academy of Sciences, Beijing 100049, PR China 4 Center for Astronomical Mega-Science, Chinese Academy of Sciences, Beijing 100012, PR China Received 13 March 2018 / Accepted 25 November 2018 ABSTRACT Context. The companions of the exploding carbon-oxygen white dwarfs (CO WDs) that produce type-Ia supernovae (SNe Ia) have still not been conclusively identified. A red-giant (RG) star can fill this role as the mass donor of the exploding WD − this channel for producing SNe Ia has been named the symbiotic channel. However, previous studies on this channel have given a relatively low rate of SNe Ia. Aims. We aim to systematically investigate the parameter space, Galactic rates, and delay time distributions of SNe Ia arising from the symbiotic channel under a revised mass-transfer prescription. Methods. We adopted an integrated mass-transfer prescription to calculate the mass-transfer process from a RG star onto the WD. In this prescription, the mass-transfer rate varies with the local material states. First, we obtain the parameter space that leads to SNe Ia by evolving a large number of semidetached WD+RG systems with the Eggleton stellar-evolution code. Second, we investigate the Galactic rates and delay-time distributions of SNe Ia using a binary population synthesis method. Results. The parameter space of WD+RG systems that can produce SNe Ia is enlarged significantly judging by our calculations. This channel could produce SNe Ia with intermediate and old ages, contributing up to 5% of all SNe Ia in the Galaxy. Our model increases the SN Ia rate from this channel by a factor of five. We suggest that the symbiotic systems RS Oph and T CrB are strong candidates for the progenitors of SNe Ia. Key words. binaries: close – stars: evolution – supernovae: general – white dwarfs 1. Introduction hole model, and so on (for recent reviews see Wang 2018; Soker 2018; Livio & Mazzali 2018). Type-Ia supernovae (SNe Ia) are good distance indicators in cos- In the single-degenerate model, the primary WDs can accrete mology. They revealed the accelerating expansion of the uni- H-rich matter from RG stars and form SNe Ia when they grow verse and led to the discovery of dark energy (e.g., Howell 2011; close to MCh in terms of mass. This formation channel is known Meng et al. 2015). It is generally believed that SNe Ia result from as the symbiotic channel (e.g., Whelan & Iben 1973; Kenyon the thermonuclear explosions of carbon-oxygen white dwarfs 1986; Kenyon et al. 1993; Munari & Renzini 1992; Hachisu et al. (CO WDs) in binaries (e.g., Hoyel & Fowler 1960; Nomoto et al. 1996; Li & van den Heuvel 1997; Yungelson & Livio 1998; King 1984). However, the identity of the mass donor for the exploding et al. 2003; Lü et al. 2006, 2009; Chen et al. 2011). Although the CO WD is still not fully confirmed (e.g., Podsiadlowski et al. actual number of symbiotic stars in the Galaxy is still unknown 2008; Wang & Han 2012; Maoz et al. 2014; Ruiz-Lapuente (e.g., Mikołajewska 2012; Rodríguez-Flores et al. 2014), many 2014). The mass donor could be a main sequence (MS) star, a symbiotic systems have been observed (e.g., Belczynski´ et al. red giant (RG) star, or a helium (He) star in the single-degenerate 2000; Miszalski & Mikołajewska 2014; Li et al. 2015). In these (SD) model, in which the CO WD that accretes H-/He-rich mat- systems, the symbiotic novae T CrB and RS Oph are possi- ter may produce an SN Ia when its mass approaches the Chan- ble progenitor candidates for SNe Ia (Kraft 1958; Brandi et al. drasekhar limit (MCh; e.g., Whelan & Iben 1973; Nomoto et al. 2009). Patat et al.(2007) detected Na I absorption lines with low 1984; Li & van den Heuvel 1997; Langer et al. 2000; Han & expansion velocities in SN 2006X, and speculated that the com- Podsiadlowski 2004; Chen & Li 2007; Wang et al. 2009). The panion of the exploding WD may be an early RG star, although mass donor may also be another CO WD in the double- Chugai(2008) argued that the absorption lines detected in SN degenerate (DD) model, in which the merger of the double 2006X cannot be formed in the RG wind. Voss & Nelemans WDs may produce SNe Ia (e.g., Iben & Tutukov 1984; Webbink (2008) suggested that the progenitor of SN 2007on may be a 1984; Han 1998; Nelemans et al. 2001; Toonen et al. 2012). In WD+RG system after studying the pre-explosion X-ray images addition, some other progenitor models have been proposed to at the same position. In addition, the surviving companions of explain the observed diversity of SNe Ia, such as for example the SNe Ia from the symbiotic channel may be related to the forma- double-detonation model, the core-degenerate model, the colli- tion of single low-mass He WDs in observations (e.g., Justham sional WD model, the single star model, the WDs near black et al. 2009; Wang & Han 2010). Article published by EDP Sciences A35, page 1 of8 A&A 622, A35 (2019) However, previous studies argued that the rate of SNe Ia investigate the semidetached symbiotic channel for producing from the symbiotic channel is relatively low (e.g., Li & van den SNe Ia. In Sect.2, we show the methods for detailed binary evo- Heuvel 1997; Yungelson & Livio 1998; Han & Podsiadlowski lution computations and the corresponding results. The method 2004). These studies usually adopted a surface boundary condi- for and results of synthesizing a binary population are provided tion to calculate the process of Roche-lobe overflow (RLOF), as in Sect.3. We present a discussion in Sect.4 and finally a sum- follows: mary in Sect.5. 2 !33 ˙ 6 rstar 7 M2 = −Cmax 60; − 1 7 ; (1) 2. Detailed binary evolution computations 4 rlobe 5 2.1. Methods where M˙ 2 is the mass-transfer rate, rstar is the radius of the lobe- We use the Eggleton stellar evolution code (Eggleton 1973) to filling star, rlobe is the radius of its Roche lobe and C is a con- stant (see Han et al. 2000). The constant C is usually set to follow the binary evolution of semidetached WD+RG systems. −1 be 1000 M yr . According to this prescription, the exceeding The typical Pop I composition is adopted for the initial MS mod- mass of the donor star would be transferred onto the accretor els with H fraction X = 0:7, He fraction Y = 0:28; and metallic- immediately as soon as the donor star exceeds its Roche-lobe, ity Z = 0:02. In this work, we do not calculate the structure of the WD and consider it as a point mass. When the WD grows in since (rstar=rlobe − 1) is always less than 0.001 once Eq. (1) is used. In this case, the mass-transfer rate in WD+RG systems is mass to MCh (set to be 1:378 M ), an SN Ia explosion is assumed usually relatively high, resulting in two cases that prevent the for- to occur. In this work, we adopted the integrated mass-transfer mation of SNe Ia: (1) A common envelope (CE) may be formed prescription presented in the Appendix of Ge et al.(2010) to if the mass-transfer is dynamically unstable (e.g., Ivanova et al. calculate the RLOF in semidetached WD+RG systems (see also 2013). The binary is likely to merge after the formation of a CE, Kolb & Ritter 1990). The mass-transfer rate which prevents the formation of SNe Ia. If the CE can be ejected, 3 Z φs 2πRL 1=2 2 Γ+1 1=2 the binary may evolve into a CO WD+He WD system or a CO M˙ 2 = − f (q) Γ ( ) 2(Γ−1) (ρP) dφ, (2) WD+He-burning star system (e.g., Han et al. 2000). The CO GM2 φL Γ + 1 WD+He-burning star system may evolve to double CO WDs and then produce SNe Ia via the DD model (Ruiter et al. 2013; Liu where RL is the effective Roche-lobe radius, G is the gravita- et al. 2016, 2018). (2) The stellar wind driven by the WD radia- tional constant, M2 is the donor mass, Γ is the adiabatic index, ρ tion may blow away too much accreted matter from the surface is the local gas density, and P is the local gas pressure. The inte- gration is from the Roche-lobe potential energy (φL) to the stellar of the WD, preventing the WD from growing in mass to MCh. The local gas density and sound velocity in the region around surface potential energy (φs). The potential energy is written as the inner Lagrange point L1 of a RG star are significantly dφ = GM R−2 dR; (3) lower than those of a MS star. Furthermore, hydrodynamic esti- 2 mates of the dimensionless parameter C are of the order of in which R is the donor radius.