Nuclear-dominated accretion and subluminous supernovae from the merger of a white dwarf with a neutron star or black hole

We construct one dimensional steady-state models of accretion disks produced by the tidal disruption of a white dwarf (WD) by a neutron star (NS) or stellar mass black hole (BH). At radii r <~ 1e8.5-1e9 cm the midplane density and temperature are sufficiently high to burn the initial white dwarf material into increasingly heavier elements (e.g. Mg, Si, S, Ca, Fe, and Ni) at sequentially smaller radii. When the energy released by nuclear reactions is comparable to that released gravitationally, we term the disk a nuclear-dominated accretion flow (NuDAF). At small radii <~1e7 cm Fe photo-disintegrates into He and then free nuclei, and cooling by neutrinos may be efficient. At the high accretion rates of relevance ~ 0.1-1e-4 Msun/s, most of the disk is radiatively inefficient and prone to outflows powered by viscous dissipation and nuclear burning. Outflow properties are calculated by requiring that material in the midplane be marginally bound (Bernoulli constant <~ 0), due (in part) to cooling by matter escaping the disk. For reasonable assumptions regarding the properties of disk winds, we show that a significant fraction >50-80 per cent of the total WD mass is unbound. The ejecta composition is predominantly O, C, Si, Mg, Ne, Fe, and S [He, C, Si, S, Ar, and Fe], in the case of C-O [He] WDs, respectively, along with a small quantity ~1e-3-1e-2 Msun of radioactive Ni56 and, potentially, a trace amount of H. We use our results to evaluate possible EM counterparts of WD-NS/BH mergers, including optical transients powered by the radioactive decay of Ni56 and radio transients powered by the interaction of the ejecta with the interstellar medium. We address whether recently discovered subluminous Type I supernovae result from WD-NS/BH mergers. Our results also have implications for accretion following the core collapse of massive stars in collapsar models for gamma-ray bursts.