A systematic survey for hypervelocity runaways from thermonuclear supernovae

The explosion of a white dwarf (WD) in a close binary can launch a surviving runaway star at velocities of $\gtrsim 1000\, \rm km\,s^{-1}$. Such runaways provide a direct probe of thermonuclear supernovae (SNe) in double-degenerate binaries. Several candidate runaways are known, but their evolutionary states and the demographics of the broader population are uncertain. To enable robust population inference, we carry out a systematic survey for hypervelocity runaways with a simple selection function, selecting candidates based on large Gaia-inferred tangential velocities and blue colors. We classify 100% of the resulting 92 candidates using a combination of spectroscopic follow-up and archival data. The search yields ten suspected D$^6$ stars and three LP 40-365 stars. Three D$^6$ stars are new discoveries, including two hot ($T_{\rm eff} > 50,000$ K) objects and one cool ($T_{\rm eff}\approx 7,000$ K) object. We forward-model our survey under several proposed D$^6$ star evolutionary models, coupling each to a Galactic model and the survey selection function. No single model reproduces the observed diversity of D$^6$ stars, which likely reflects a range of remnant masses, ages, and heating mechanisms. Models in which runaway companions are heated by SN shocks alone are too faint and short-lived to explain most of the observed sample, while fully reheated models are too luminous and long-lived. Models with intermediate heating, as occurs in some simulations of violent mergers and partially disrupted remnants, best match the observed magnitude, distance, and kinematic-age distributions. The inferred D$^6$ star birth rate is model dependent, but the models that best match the observed population require rates of only a few percent of the Galactic SN Ia rate, perhaps implying that most SNe Ia result from WD binaries in which both components explode.