The single-degenerate channel for the progenitors of Type Ia supernovae

We have carried out a detailed study of one of the most favoured evolutionary channels for the production of Type Ia supernova (SN Ia) progenitors, the single-degenerate channel (CO + MS), where a carbon/oxygen (CO) white dwarf (WD) accretes matter from an unevolved or slightly evolved non-degenerate star until it reaches the Chandrasekhar mass limit. Employing Eggleton's stellar evolution code and adopting the prescription of Hachisu et al. for the accretion efficiency, we performed binary stellar evolution calculations for about 2300 close WD binary systems and mapped out the initial parameters in the orbital period-secondary mass (P-M₂) plane (for a range of WD masses) which lead to a successful Type Ia supernova. We obtained accurate, analytical fitting formulae to describe this parameter range which can be used for binary population synthesis (BPS) studies. The contours in the P-M₂ plane differ from those obtained by Hachisu et al. for low-mass CO WDs, which are more common than massive CO WDs. We confirm that WDs with a mass as low as 0.67 M_solar can accrete efficiently and reach the Chandrasekhar limit. We have implemented these results in a BPS study to obtain the birth rates for SNe Ia and the evolution of birth rates with time of SNe Ia for both a constant star formation rate and a single starburst. The birth rates are lower than (but comparable to) those inferred observationally.