Relativistic Common-envelope Dynamics of a Stellar-mass Black Hole II: Kerr Black Hole

Abstract: The common envelope phase plays a critical role in binary system evolution. In this study, we investigate the mass and momentum accretion rates during the interaction between a stellar mass black hole and the envelope of a red supergiant using simplified two dimensional simulations. We explore various Mach numbers and density gradients, finding that our simulations align with previous Bondi Hoyle Lyttleton accretion analyses. We observe the formation of a shock cone in the downstream flow, bow shocks in specific configurations, and subsonic regions within shocked flows. The shock cone is dragged when significant pressure gradients are present in the common envelope, with additional dragging near the black hole for highly rotating cases. We provide analytical fits for mass and momentum accretion rates, as well as bremsstrahlung luminosity, as functions of black hole spin, density gradients, and Mach number, offering first insights into general relativistic hydrodynamics modelling of the secular evolution of the common envelope phase.