White dwarfs experience a thermal renaissance when they receive mass from a
stellar companion in a binary. For accretion rates < 10^-8 Msun/yr, the freshly
accumulated hydrogen/helium envelope ignites in a thermally unstable manner
that results in a classical novae (CN) outburst and ejection of material. We
have undertaken a theoretical study of the impact of the accumulating envelope
on the thermal state of the underlying white dwarf (WD). This has allowed us to
find the equilibrium WD core temperatures (T_c), the classical nova ignition
masses (M_ign) and the thermal luminosities for WDs accreting at rates of
10^-11 - 10^-8 Msun/yr. These accretion rates are most appropriate to WDs in
cataclysmic variables (CVs) of P_orb <~ 7 hr, many of which accrete
sporadically as dwarf novae. We have included ^3He in the accreted material at
levels appropriate for CVs and find that it significantly modifies the CN
ignition mass. We compare our results with several others from the CN
literature and find that the inclusion of ^3He leads to lower M_ign for
>~ 10^-10 Msun/yr, and that for below this the particular author's
assumption concerning T_c, which we calculate consistently, is a determining
factor. Initial comparisons of our CN ignition masses with measured ejected
masses find reasonable agreement and point to ejection of material comparable
to that accreted.Comment: 14 pages, 11 figures; uses emulateapj; accepted by the Astrophysical
Journal; revised for clarity, added short discussion of diffusio