Theoretical Studies of Accretion of Matter onto White Dwarfs and the   Single Degenerate Scenario for Supernovae of Type Ia
  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. 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 Solar masses to 1.35 Solar Masses), the maximum ejected material occurs for the 1.25 Solar Mass 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, 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 sulfur 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 CNe 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. 
S. Starrfield, C. Iliadis, F. X. Timmes, W. R. Hix, W. D. Arnett, C.   Meakin, W. M. Sparks
astro-ph.SR