Abstract Astrometry from the Gaia mission has revealed a large population of white dwarf (WD) + main sequence (MS) binaries with periods of 100–1000 days. These systems have separations intermediate to predictions from standard binary evolution scenarios, challenging models of binary interaction and mass transfer. Because the selection function of Gaia astrometric catalogs is complex, the underlying population demographics of WD+MS binaries remain imperfectly understood. We present a forward-model of the AU-scale WD+MS binary population probed by Gaia that begins with a realistic binary population and incorporates a full model of Gaia mock observations and astrometric model fitting, as well as cuts employed in producing the Gaia astrometric catalog and selecting WD+MS binary candidates. We model the formation of AU-scale WD+MS binaries as the result of interaction when the WD progenitor is an AGB star. We test several models for the binaries’ formation, including stable mass transfer with theoretically predicted stability criteria and two different formalisms for common envelope evolution. None of these models succeed in reproducing the observed component mass distributions or the absolute number of WD+MS binaries. The data are best reproduced by a model in which post-AGB binaries remain wide only if the accretor-to-donor mass ratio exceeds ∼0.4. Our model allows us to constrain the intrinsic population demographics of intermediate-separation WD+MS binaries. The inferred period distribution is close to flat, with d N / d P orb ∝ P orb 0.12 , while the WD mass distribution is sharply peaked at 0.6 M ⊙ . The model implies that ∼0.4% of solar-type stars have WD companions with periods of 100–1000 days.
Yamaguchi et al. (Wed,) studied this question.