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We discuss the evolution of white dwarf containing binaries, in particular such systems consisting of a white dwarf and a main sequence star which have the potential to produce a Type Ia supernova. After investigating current problems in connecting observations of supersoft X-ray sources with such systems, we consider two major problems which theoretical models encounter to produce Chandrasekhar-mass white dwarfs: the helium shell burning instability and the white dwarf spin-up. We conclude by suggesting that the formation of Chandrasekhar-mass white dwarfs may be easier when these two problem are considered simultaneously.
We present models for the complete life and death of a 60 Msolar star evolving in a close binary system, from the main-sequence phase to the formation of a compact remnant and fallback of supernova debris. After core hydrogen exhaustion, the star expands, loses most of its envelope by Roche lobe overflow, and becomes a Wolf-Rayet star. We study its post-mass transfer evolution as a function of the Wolf-Rayet wind mass-loss rate (which is currently not well constrained and will probably vary with the initial metallicity of the star). Varying this mass-loss rate by a factor of 6 leads to stellar masses at collapse that range from 3.1 up to 10.7 Msolar. Because of different carbon abundances left by core helium burning and nonmonotonic effects of the late shell-burning stages as function of the stellar mass, we find that, although the iron core masses at collapse are generally larger for stars with larger final masses, they do not depend monotonically on the final stellar mass or even the C/O core mass. We then compute the evolution of all models through collapse and bounce. The results range from strong supernova explosions (Ekin>1051ergs) for the lower final masses to the direct collapse of the star into a black hole for the largest final mass. Correspondingly, the final remnant masses, which were computed by following the supernova evolution and fallback of material for a timescale of about one year, are between 1.2 and 10 Msolar. We discuss the remaining uncertainties of this result and outline the consequences of our results for the understanding of the progenitor evolution of X-ray binaries and gamma-ray burst models.