The envelope mass of red giant donors in type Ia supernova progenitors

Context. The single degenerate model is the most widely accepted progenitor model of type Ia supernovae (SNe Ia), in which a carbon-oxygen white dwarf (CO WD) accretes hydrogen-rich material from a main sequence or a slightly evolved star (WD +MS) or from a red giant star (WD + RG), to increase its mass and explodes when approaching the Chandrasekhar mass. The explosion ejecta may impact the envelope of and strip off some hydrogen-rich material from the companion. The stripped-off hydrogen-rich material may manifest itself by means of a hydrogen line in the nebular spectra of SNe Ia. However, no hydrogen line is detected in the nebular spectra. Aims. We compute the remaining amounts of hydrogen in red giant donors to see whether the conflict between theory and observations can be overcome. Methods. By considering the mass-stripping effect from an optically thick wind and the effect of thermally unstable disk, we systematically carried out binary evolution calculation for WD + MS and WD + RG systems. Results. Here, we focus on the evolution of WD + RG systems. We found that some donor stars at the time of the supernova explosion contain little hydrogen-rich material on top of the helium core (as low as 0.017 $M_{\odot}$), which is smaller than the upper limit to the amount derived from observations of material stripped-off by explosion ejecta. Thus, no hydrogen line is expected in the nebular spectra of these SN Ia. We also derive the distributions of the envelope mass and the core mass of the companions from WD + RG channel at the moment of a supernova explosion by adopting a binary population synthesis approach. We rarely find a RG companion with a very low-mass envelope. Furthermore, our models imply that the remnant of the WD + RG channel emerging after the supernova explosion is a single low-mass white dwarf (0.15–0.30 $M_{\odot}$). Conclusions. The absence of a hydrogen line in nebular spectra of SNe Ia provides support to the proposal that the WD + RG system is the progenitor of SNe Ia