Thermally Stable Nuclear Burning on Accreting White Dwarfs

One of the challenges to increasing the mass of a white dwarf through accretion is the tendency for the accumulating hydrogen to ignite unstably and potentially trigger mass loss. It has been known for many years that there is a narrow range of accretion rates for which the hydrogen can burn stably, allowing for the white dwarf mass to increase as a pure helium layer accumulates. We first review the physics of stable burning, providing a clear explanation for why radiation pressure stabilization leads to a narrow range of accretion rates for stable burning near the Eddington limit, confirming the recent work of Nomoto and collaborators. We also explore the possibility of stabilization due to a high luminosity from beneath the burning layer. We then examine the impact of the β-decay-limited ``hot'' CNO cycle on the stability of burning. Although this plays a significant role for accreting neutron stars, we find that for accreting white dwarfs, it can only increase the range of stably burning accretion rates for metallicities <0.01 Z_solar.