Accretion onto a 1.4 M_⊙ white dwarf: classical nova, recurrent nova, or supernova?

We have computed successive outbursts on a carbon-oxygen 1.4 M_⊙ white dwarf, accreting hydrogen-rich material at rates of 10^-10 to 10^-6 M_⊙ yr^-1. Mass accretion, diffusion, nuclear burning - using a network of 36 isotopes - and hydrodynamic mass loss are included in these calculations. We find the outburst characteristics to vary considerably with the accretion rate. For the highest accretion rate, the outbursts diminish in strength and should eventually lead to steady burning; no mass is ejected and hence such a scenario should result in a Type I supernova explosion. For an accretion rate of 10^-7 M_⊙ yr^-1, the eruptions occur at intervals of almost a year and some mass is ejected, but still less than the mass accreted prior to outburst. An accretion rate of 10^-8 M_⊙ yr^-1 results in outbursts typical of recurrent novae: the recurrence time is less than 20 yr, velocities are ∼1500 km s^-1, and the ejected mass - larger than the accreted mass - is ∼2 × 10^-7 M_⊙; it is significantly enriched in helium, but also to a lesser extent, in CNO elements. The lowest accretion rates considered lead to outbursts characteristic of very fast novae, with decline times of a few days, velocities up to 3000 km s^-1, amplitudes up to 14 mag and ejected masses of ∼10^-6 M_⊙, moderately enriched in CNO. We conclude that accretion onto a very massive white dwarf may lead, depending on the accretion rate, either to recurrent novae, to very fast classical novae, or to mass accumulation that may eventually lead to a supernova. We emphasize that, in all cases, several outbursts should be calculated in order to obtain the correct composition and mass of the ejected material.