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 ≳ 1000 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 D6 stars and three LP 40-365 stars. Three D6 stars are new discoveries, including two hot (Teff ≳ 50,000 K) objects and one cool (Teff ≈ 7,000 K) object. We forward-model our survey under several proposed D6 star evolutionary models, coupling each to a Galactic model and the survey selection function. No single model reproduces the observed diversity of D6 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 D6 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. If most SNe Ia do produce surviving runaways, these must be fainter or shorter-lived than the currently known runaways. 9 Maynooth Academic Publishing application/pdf