The evolution of main sequence star plus white dwarf binary systems towards type Ia supernovae

Close binaries consisting of a main sequence st ar and a white dwarf are co nsidered as candidates for Type Ia supernova progenitors. We present selfco nsistent calculations of the time dependence of the structure of the main s equence star, the mass transfer rate, and the orbit by means of a binary st ellar evolution program. We obtain, for the first time, a complete picture of the time evolution of the mass transfer rate in such systems. We find a long switch-on phase of the mass transfer, about 10(6) yr, during which nov a outbursts should persist in all systems. Furthermore, we find that the wh ite dwarfs can reach the Chandrasekhar mass only during the decline phase o f the mass transfer, which may have consequences for the critical accretion rate for stationary nuclear burning on the white dwarf surface. In contras t 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 sy stems with rather small initial white dwarf masses (similar to 0.7 Mo) may produce Type Ia supernovae, which then might originate from very rapidly ro tating white dwarfs. We present results for two different metallicities, Z = 0.02 and Z = 0.001. We fmd that for systems with the lower metallicity, the mass transfer rate s are on average five times larger than in comparable system at solar metal licity. This leads to a systematic shift of the supernova Ia progenitor pop ulation. Firstly while for Z = 0.02 - for our choice of white dwarf wind ma ss loss and mass accumulation rate - donor star initial masses in supernova progenitor systems are restricted to the range 1.6 M-....2.3 M-., they are in the interval 1.4 M-....1.8 M-. at low Z. Secondly, the initial white dw arf masses need, on average, to be larger by 0,2 M-. at low Z in order to o btain a Chandrasekhar mass white dwarf. This metallicity dependences have v ery little effect on the progenitor life times, but 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 which stem from close main sequence star + white dwarf systems. We estimate the X-ray luninosities of the computed systems, and investigate their donor star and orbital properties. We find the donor stars to be und erluminous by up to one order of magnitude, and more compact than normal ma in sequence stars. In general, our systems correspond well to observed clos e binary supersoft X-ray sources. We further derive the chemical and kinema tical properties of the stellar remnants of our systems after the explosion of the white dwarf, which may serve as a test of the viability of the cons idered Type Ia supernova scenario.