The runaway velocity of the white dwarf companion in the double detonation scenario of supernovae

We consider the finite velocity of the ejecta of a type Ia supernova (SN Ia) in the double detonation (DDet) scenario with a white dwarf (WD) mass-donor companion, and find that the runaway velocity of the surviving (mass donor) WD is lower than its pre-explosion orbital velocity by about 8-11%. This implies that the fastest runaway WDs in the Galaxy, if come from the DDet scenario, require even more massive WDs than what a simple calculation that neglects the finite ejecta velocity gives. This extreme set of initial conditions makes such binaries less common. We also tentatively find that the inner ejecta deviates from spherical symmetry, but not to the degree that we can use observations to make any claim. Our findings support the claim that the DDet scenario leads mostly to peculiar SNe Ia but not to normal SNe Ia.