Realistic predictions for Gaia black hole discoveries: comparison of isolated binary and dynamical formation models

TL;DR

This study compares isolated binary and dynamical formation models for Gaia-detected black hole binaries, revealing significant differences in predicted detection rates and orbital period distributions, and forecasts about 30 detections in Gaia DR4.

Contribution

It applies a realistic Gaia astrometric detection model to compare formation channels, highlighting discrepancies in predictions and refining expectations for future Gaia data releases.

Findings

The isolated binary evolution model underpredicts Gaia BH detections.

The dynamical formation model overpredicts Gaia BH detections by a factor of ~8.

Predicted Gaia DR4 will detect about 30 BH binaries, constituting ~0.1% of Milky Way BHs with luminous companions.

Abstract

Astrometry from Gaia has enabled discovery of three dormant black holes (BHs) in au-scale binaries. Numerous models have been proposed to explain their formation, including several that have forecasted Gaia detections. However, previous works have used simplified detectability metrics that do not capture key elements of the Gaia astrometric orbit selection function. We apply a realistic forward-model of Gaia astrometric orbit catalogs to BH binary populations generated through (a) isolated binary evolution (IBE) and (b) dynamical formation in star clusters. For both formation channels, we analyze binary populations in a simulated Milky Way-like galaxy with a realistic metallicity-dependent star formation history and 3D dust map. We generate epoch astrometry for each binary from the Gaia scanning law and fit it with the cascade of astrometric models used in Gaia DR3. The IBE model of Chawla et al. (2022) predicts that no BH binaries should have been detected in DR3 and thus significantly underpredicts the formation rate of Gaia BHs. In contrast, the dynamical model of Di Carlo et al. (2024) overpredicts the number of BHs receiving DR3 orbital solutions by a factor of $\sim$8. The two models predict very different orbital period distributions, with the IBE model predicting only binaries that avoided common envelope evolution and have $P_{\text{orb}} \gtrsim 2,000$ d to be detectable, and the dynamical formation model predicting a period distribution that is roughly log-uniform. Adopting the dynamical channel as a fiducial model and rescaling by a factor of 1/8 to match DR3, we predict that $\sim$30 BH binaries will be detected in Gaia DR4, representing $\sim0.1\%$ of Milky Way BHs with luminous companions in au-scale orbits.