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Cataclysmic Variables (CVs) are close binary star systems with one component a white dwarf (WD) and the other a larger cooler star that fills its Roche Lobe. The cooler star is losing mass through the inner Lagrangian point of the binary and some unknown fraction of this material is accreted by the WD. One consequence of the WDs accreting material, is the possibility that they are growing in mass and will eventually reach the Chandrasekhar Limit. This evolution could result in a Supernova Ia (SN Ia) explosion and is designated the Single Degenerate Progenitor (SD) scenario. This paper is concerned with the SD scenario for SN Ia progenitors. One problem with the single degenerate scenario is that it is generally assumed that the accreting material mixes with WD core material at some time during the accretion phase of evolution and, since the typical WD has a carbon-oxygen CO core, the mixing results in large amounts of carbon and oxygen being brought up into the accreted layers. The presence of enriched carbon causes enhanced nuclear fusion and a Classical Nova explosion. Both observations and theoretical studies of these explosions imply that more mass is ejected than is accreted. Thus, the WD in a Classical Nova system is losing mass and cannot be a SN Ia progenitor. However, the composition in the nuclear burning region is important and, in new calculations reported here, the consequences to the WD of mixing of accreted material with core material have been investigated so that the material involved in the explosion has only a Solar composition. WDs with a large range in initial masses and mass accretion rates have been evolved. I find that once sufficient material has been accreted, nuclear burning occurs in all evolutionary sequences and continues until a thermonuclear runaway (TNR) occurs and the WD either ejects a small amount of material or its radius grows to about 1012 cm and the evolution is ended. In all cases where mass ejection occurs, the mass of the ejecta is far less than the mass of the accreted material. Therefore, all the WDs are growing in mass. It is also found that the accretion time to explosion can be sufficiently short for a 1.0M WD that recurrent novae can occur on a low mass WD. This mass is lower than typically assumed for the WDs in recurrent nova systems. Finally, the predicted surface temperatures when the WD is near the peak of the explosion imply that only the most massive WDs will be significant X-ray emitters at this time.


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