Binarity at LOw Metallicity (BLOeM)

Bayesian inference of natal kicks from inert black hole binaries

¹ Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
² Leuven Gravity Institute, KU Leuven, Celestijnenlaan 200D, Box 2415 3001 Leuven, Belgium
³ Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, B-9000 Gent, Belgium
⁴ Max-Planck-Institute for Astrophysics, Karl-Schwarzschild-Strasse 1, 85748 Garching, Germany
⁵ Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
⁶ ESO – European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garchingbei München, Germany
⁷ Department of Astrophysics and Planetary Science, Villanova University, 800 E Lancaster Ave., Villanvona, PA 19085, USA
⁸ Department of Astronomy and Physics, Saint Mary’s University, 923 Robie Street, Halifax B3H 3C3, Canada
⁹ Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
¹⁰ Royal Observatory of Belgium, Department of Astronomy and Astrophysics, Avenue Circulaire/Ringlaan 3, B-1180 Brussels, Belgium
¹¹ Centro de Astrobiologia (CAB), CSIC-INTA, Carretera de Ajalvir km 4, 28850 Torrejón de Ardoz, Madrid, Spain
¹² University of Arizona, Department of Astronomy & Steward Observatory, 933 N. Cherry Ave., Tucson, AZ 85721, USA
¹³ Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut, Mönchhofstr. 12-14, 69120 Heidelberg, Germany
¹⁴ The School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
¹⁵ Center for Computational Astrophysics, Flatiron Institute, New York NY 10010, USA
¹⁶ Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA

^⋆ Corresponding author: reinhold.willcox@kuleuven.be

Received: 23 April 2025
Accepted: 23 June 2025

Abstract

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.