No abstract

In contrast to the mass spectrum of single white dwarfs which has a single narrow peak at ~0.6 M⊙, the observed mass spectrum of white dwarfs of cataclysmic binaries (CB's) shows a rather uniform distribution of the masses in the range ~0.3 M⊙, to ~1.3 M⊙. The formation of CB's with white dwarfs of less than about 0.8 M⊙ can be understood as the result of a binary evolution according to low mass Case B or Case C with a subsequent spiraling-in in a common envelope. On the other hand the formation of massive white dwarfs of M ≲ 1 M⊙, can be explained as the result of a massive Case B mass transfer yielding a helium star which subsequently undergoes a second Case B mass transfer (so called Case BB evolution). The ultimate product of such an evolution is either a CO-white dwarf with a mass up to the Chandrasekhar limit or a neutron star. The formation of CB's via Case BB evolution requires the binary to undergo at least one, most probably two separate phases of spiraling-in in a common envelope.

Following Schatzman and Maeder (1981) we compute the evolution of the sun with partial mixing by hydrodynamic instabilities. Instead of simply assuming a turbulent diffusion coefficient which is a constant multiple of the viscosity, we incorporate some of the properties of hydrodynamic instabilities. This puts limits on the amount of diffusion that can be obtained, and makes it dependent on time and position in the star.