Masses of White Dwarf Binary Companions to Type Ia Supernovae Measured from Runaway Velocities

The recently proposed "dynamically driven double-degenerate double-detonation" (D6) scenario posits that Type Ia supernovae (SNe) may occur during dynamically unstable mass transfer between two white dwarfs (WDs) in a binary. This scenario predicts that the donor WD may then survive the explosion and be released as a hypervelocity runaway, opening up the exciting possibility of identifying remnant stars from D6 SNe and using them to study the physics of detonations that produce Type Ia SNe. Three candidate D6 runaway objects have been identified in Gaia data. The observable runaway velocity of these remnant objects represents their orbital speed at the time of SN detonation. The orbital dynamics and Roche lobe geometry required in the D6 scenario place specific constraints on the radius and mass of the donor WD that becomes the hypervelocity runaway. In this letter, we calculate the radii required for D6 donor WDs as a function of the runaway velocity. Using mass-radius relations for WDs, we then constrain the masses of the donor stars as well. With measured velocities for each of the three D6 candidate objects based on Gaia EDR3, this work provides a new probe of the masses and mass ratios in WD binary systems that produce SN detonations and hypervelocity runaways.