Despite their unique astrophysical relevance, the outcome of white dwarf binary mergers has so far only been studied for a very restricted number of systems. Here we present the results of a survey with more than two hundred simulations systematically scanning the white dwarf binary parameter space. We consider white dwarf masses ranging from 0.2 to 1.2 $M_odot$ and account for their different chemical compositions. We find excellent agreement with the orbital evolution predicted by mass transfer stability analysis. Much of our effort in this paper is dedicated to determining which binary systems are prone to a thermonuclear explosion just prior to merger or at surface contact. We find that a large fraction of He-accreting binary systems explode: all dynamically unstable systems with accretor masses below 1.1 $M_odot$ and donor masses above $sim$ 0.4 $M_odot$ are found to trigger a helium detonation at surface contact. A substantial fraction of these systems could explode at earlier times via detonations induced by instabilities in the accretion stream, as we have demonstrated in our previous work. We do not find definitive evidence for an explosion prior to merger or at surface contact in any of the studied double carbon-oxygen systems. Although we cannot exclude their occurrence if some helium is present, the available parameter space for a successful detonation in a white dwarf binary of pure carbon-oxygen composition is small. We demonstrate that a wide variety of dynamically unstable systems are viable type Ia candidates. The next decade thus holds enormous promise for the study of these events, in particular with the advent of wide-field synoptic surveys allowing a detailed characterization of their explosive properties.
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