Theoretical studies of accretion of matter onto white dwarfs and the single degenerate scenario for supernovae of Type Ia

We review our current knowledge about the thermonuclear processing that occurs during the evolution of accretion onto white dwarfs (WDs) both with and without the mixing of core with accreted material. We present a brief summary of the single degenerate scenario for the progenitors of Type Ia supernovae in which it is assumed that a low mass carbon-oxygen white dwarf is growing in mass as a result of accretion from a secondary star in a close binary system. The growth in mass requires that more material remain on a white dwarf after a thermonuclear runaway than is ejected by the explosion. Recent hydrodynamic simulations of accretion of solar material onto white dwarfs without mixing always produce a thermonuclear runaway and "steady burning" does not occur. For a broad range in WD mass (0.4 M_ȯ to 1.35 M_ȯ), the maximum ejected material occurs for the 1.25M_ȯ sequences and then decreases as the white dwarf mass decreases. Therefore, the white dwarfs are growing in mass as a consequence of the accretion of solar material, and as long as there is no mixing of accreted material with core material. In contrast, a thermonuclear runaway in the accreted hydrogen-rich layers on the low luminosity WDs in close binary systems where mixing of core matter with accreted material has occurred is the outburst mechanism for classical (CN), recurrent, and symbiotic novae. The differences in characteristics of these systems is likely the WD mass and mass accretion rate. The high levels of enrichment of CN ejecta in elements ranging from carbon to sulphur confirm that there is dredge-up of matter from the core of the WD and enable them to contribute to the chemical enrichment of the interstellar medium. Therefore, studies of classical novae can lead to an improved understanding of Galactic nucleosynthesis, some sources of pre-solar grains, and the Extragalactic distance scale. The characteristics of the outburst depend on the white dwarf mass, luminosity, mass accretion rate, and the chemical composition of both the accreting material and WD material. The properties of the outburst also depends on when, how, and if the accreted layers are mixed with the WD core and the mixing mechanism is still unknown.