A Global View of Post-interaction White Dwarf-main Sequence Binaries

Abstract Common-envelope evolution (CEE) is among the most uncertain phases in binary evolution. To empirically constrain CEE, we construct a uniformly selected sample of eclipsing post–common-envelope binaries (PCEBs). Starting from an unresolved white dwarf–main-sequence (WDMS) candidate sample within 200 pc selected from the Gaia color-magnitude diagram, we identify 39 detached eclipsing WDMS binaries using Zwicky Transient Facility light curves. The binaries contain cool M dwarfs orbiting warm white dwarfs with orbital periods ( P orb ) of 0.1–2 days. The sample’s simple selection function allows us to model observational incompleteness and infer intrinsic properties of the PCEB population. We find an orbital-period distribution consistent with being log-uniform over 0.1–2 days, contrary to recent reports of a bimodal distribution. The intrinsic companion-mass distribution peaks around 0.25 M ⊙ and declines steeply toward larger masses. The estimated local space density is 7.2 × 10 −5 pc −3 , corresponding to a Galaxy-wide birth rate of 0.01 yr −1 . Combining our results with recent Gaia-based constraints on wider WDMS binaries, we construct an empirical period distribution of post-interaction WDMS binaries spanning 0.1–1000 days. The emerging period distribution is roughly log-flat ( d N / d log P orb ∝ P orb 0 ) at P orb < 2 days and log-increasing ( d N / d log P orb ∝ P orb 1 ) at P orb = 100–1000 days. The 10–100 days regime is poorly constrained by existing surveys, but a few nearby systems suggest that it is also well-populated. Short-period PCEBs ( P orb ≲ 2 days) with M dwarf companions are roughly 2–3 times more common than wide ( P orb = 100–1000 days) WDMS binaries with FGK companions, which likely formed through stable mass transfer. These results provide direct observational constraints on CEE and an empirical benchmark for binary-population models.