On the brightness distribution of Type Ia supernovae from violent white dwarf mergers

We investigate the brightness distribution expected for thermonuclear explosions that might result from the ignition of a detonation during the violent merger of white dwarf (WD) binaries. Violent WD mergers are a subclass of the canonical double degenerate scenario where two carbon-oxygen (CO) WDs merge when the larger WD fills its Roche lobe. Determining their brightness distribution is critical for evaluating whether such an explosion model could be responsible for a significant fraction of the observed population of Type Ia supernovae (SNe Ia). We argue that the brightness of an explosion realized via the violent merger model is mainly determined by the mass of Ni-56 produced in the detonation of the primary COWD. To quantify this link, we use a set of sub-Chandrasekhar mass WD detonation models to derive a relationship between primary WD mass (m(WD)) and expected peak bolometric brightness (M-bol). We use this m(WD)-M-bol relationship to convert the masses of merging primary WDs from binary population models to a predicted distribution of explosion brightness. We also investigate the sensitivity of our results to assumptions about the conditions required to realize a detonation during violent mergers of WDs. We find a striking similarity between the shape of our theoretical peak-magnitude distribution and that observed for SNe Ia: our model produces a M-bol distribution that roughly covers the range and matches the shape of the one observed for SNe Ia. However, this agreement hinges on a particular phase of mass accretion during binary evolution: the primary WD gains similar to 0.15-0.35M(circle dot) from a slightly evolved helium star companion. In our standard binary evolution model, such an accretion phase is predicted to occur for about 43 per cent of all binary systems that ultimately give rise to binary CO WD mergers. We also find that with high probability, violent WD mergers involving the most massive primaries (>= 1.3M(circle dot), which should produce bright SNe) have delay times <= 500 Myr.