Beyond what's observed: hierarchical inference of Gaia astrometric compact-object binaries

Astrometry from the Gaia mission has revealed a large and homogeneous population of binaries containing compact objects, including more than 3000 white dwarf--main sequence (WDMS) binaries with orbital periods of P orb about100 -- 1000 d. Most of these binaries likely underwent mass transfer from asymptotic giant branch donors, but their evolutionary histories remain uncertain. We develop a hierarchical Bayesian inference model to constrain the intrinsic properties of the Gaia WDMS binary population while accounting for measurement uncertainties and the survey selection function. We infer the distributions of orbital period, component masses, and eccentricity, as well as the total space density. We find that the intrinsic orbital-period distribution follows a declining power law, p(P orb) proportional to P orb-0.445 plus or minus0.048, and the WD mass distribution is sharply peaked near 0.6,M, with only 1% of systems hosting WDs more massive than 0.8,M. The inferred MS-star mass distribution is relatively flat down to 0.3,M, which is unexpected if the population is dominated by products of stable mass transfer with a fixed critical mass ratio. The eccentricity distribution peaks at a nonzero value, e=0.046 plus or minus0.001, suggesting incomplete circularization or eccentricity excitation. We infer a midplane space density of 3 times10 4, kpc-3 for WDMS binaries in the parameter space probed by Gaia DR3. These properties provide empirical benchmarks for future work to constrain binary evolution models. We also apply the framework to Gaia black hole and neutron star binaries, inferring that 30+66-20 and 614+203-149 such systems exist within 2 kpc, respectively. This framework will enable detailed population-level constraints on a wide range of systems identified from the much larger catalog of astrometric orbits expected from Gaia DR4.