Binarity at LOw Metallicity (BLOeM): Bayesian inference of natal kicks from inert black hole binaries

Context. The emerging population of inert black hole binaries (BHBs) provides a unique opportunity to constrain black hole (BH) formation physics. These systems are composed of a stellar-mass BH in a wide orbit around a nondegenerate star with no observed X-ray emission. Inert BHBs allow narrow constraints to be inferred on the natal kick and mass loss during BH-forming core-collapse events. Aims. In anticipation of the upcoming BLOeM survey, we aim to provide tight constraints on BH natal kicks by exploiting the full parameter space obtained from combined spectroscopic and astrometric data to characterize the orbits of inert BHBs. Multi-epoch spectroscopy from the BLOeM project will provide measurements of periods, eccentricities, and radial velocities for inert BHBs in the SMC, which complements Gaia astrometric observations of proper motions. Methods. We present a Bayesian parameter estimation framework to infer natal kicks and mass loss during core-collapse from inert BHBs. The framework accounts for all available observables, including the systemic velocity and its orientation relative to the orbital plane. The framework further allows for circumstances when some of the observables are unavailable, such as for the distant BLOeM sources, which preclude resolved orbits. This method was implemented using a publicly available open source package, SIDEKICKS.JL. Results. With our new framework, we are able to distinguish between BH formation channels, even in the absence of a resolved orbit. In cases when the pre-explosion orbit can be assumed to be circular, we precisely recover the parameters of the core-collapse, highlighting the importance of understanding the eccentricity landscape of pre-explosion binaries, both theoretically and observationally. Treating the near-circular, inert BHB VFTS 243 as a representative of the anticipated BLOeM systems, we constrained the natal kick to ≲27 km s⁻¹ and the mass loss to ≲2.9 M_⊙ within a 90% credible interval.