The evolution of main sequence star + white dwarf binary systems towards Type~Ia supernovae

Close binaries consisting of a main sequence star and a white dwarf are considered as candidates for Type~Ia supernova progenitors. We present selfconsistent calculations of the time dependence of the structure of the main sequence star, the mass transfer rate, and the orbit by means of a binary stellar evolution program. In contrast to results based on simple estimates of the mass transfer rate in systems of the considered type, our results allow for the possibility that even systems with rather small initial white dwarf masses (~ 0.7 M_sun) may produce Type Ia supernovae. We present results for two different metallicities, Z=0.02 and Z=0.001. We find that for systems with the lower metallicity, the mass transfer rates are on average five times larger than in comparable system at solar metallicity. This leads to a systematic shift of the supernova Ia progenitor population. Firstly, while for Z=0.02 donor star initial masses in supernova progenitor systems are restricted to the range 1.6...2.3 M_sun, they are in the interval 1.4...1.8 M_sun at low Z. Secondly, the initial white dwarf masses need, on average, to be larger by 0.2 M_sun at low Z in order to obtain a Chandrasekhar mass white dwarf. This metallicity dependences may be responsible for a drop of the Type Ia supernova rate for low metallicity, and may introduce a Z-dependence in the properties of supernovae. We also estimate the X-ray luminosities of the computed systems, and investigate their donor star and orbital properties.