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

Gaia astrometry has revealed a large, homogeneous population of compact-object binaries, including more than 3,000 white dwarf–main sequence (WDMS) binaries with orbital periods of P_orb ~ 100–1000 d. Most of these systems likely underwent mass transfer from asymptotic giant branch donors, but their evolutionary histories remain uncertain.

The authors 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. The framework infers distributions of orbital period, component masses, and eccentricity, as well as the total space density.

The intrinsic orbital-period distribution follows a declining power law, p(P_orb) ∝ P_orb^{-0.445±0.048}. The white dwarf mass distribution is sharply peaked near 0.6 M_sun, with only ~1% of systems hosting white dwarfs more massive than 0.8 M_sun. The inferred main-sequence-star mass distribution is relatively flat down to ~0.3 M_sun, 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±0.001, suggesting incomplete circularization or eccentricity excitation. The authors infer a midplane space density of ~3×10^4 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.

The framework is also applied to Gaia black hole and neutron star binaries, inferring that 30^{+66}_{-20} and 614^{+203}_{-149} such systems exist within 2 kpc, respectively. It 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.