The Fate of a WD Accreting H-Rich Material at High Rates
  We study C/O white dwarfs with masses of 1.0 to 1.4 Msun accreting solar-composition material at very high accretion rates. We address the secular changes in the WDs, and in particular, the question whether accretion and the thermonuclear runaways result is net accretion or erosion. The present calculation is unique in that it follows a large number of cycles, thus revealing the secular evolution of the WD system.   We find that counter to previous studies, accretion does not give rise to steady state burning. Instead, it produces cyclic thermonuclear runaways of two types. During most of the evolution, many small cycles of hydrogen ignition and burning build a helium layer over the surface of the white dwarf. This He layer gradually thickens and progressively becomes more degenerate. Once a sufficient amount of He has accumulated, several very large helium burning flashes take place and expel the accreted envelope, leaving no net mass accumulation.   The results imply that such a system will not undergo an accretion induced collapse, nor will it lead to a SN Type Ia, unless a major new physical process is found. 
Irit Idan, Nir J. Shaviv, Giora Shaviv
astro-ph.SR