Common-envelope Dynamics of a Stellar-mass Black Hole: General Relativistic Simulations

With the goal of providing more accurate and realistic estimates of the secular behavior of the mass accretion and drag rates in the common-envelope scenario encountered when a black hole or a neutron star moves in the stellar envelope of a red supergiant star, we have carried out the first general relativistic simulations of the accretion flow onto a nonrotating black hole moving supersonically in a medium with regular but different density gradients. The simulations reveal that the supersonic motion always rapidly reaches a stationary state and produces a shock cone in the downstream part of the flow. In the absence of density gradients we recover the phenomenology already observed in the well-known Bondi-Hoyle-Lyttleton accretion problem, with super-Eddington mass accretion rate and a shock cone whose axis is stably aligned with the direction of motion. However, as the density gradient is made stronger, the accretion rate also increases and the shock cone is progressively and stably dragged toward the direction of motion. With sufficiently large gradients, the shock-cone axis can become orthogonal to the direction, or even move in the upstream region of the flow in the case of the largest density gradient. Together with the phenomenological aspects of the accretion flow, we have also quantified the rates of accretion of mass and momentum onto the black hole. Simple analytic expressions have been found for the rates of accretion of mass, momentum, drag force, and bremsstrahlung luminosity, all of which have been employed in the astrophysical modeling of the secular evolution of a binary system experiencing a common-envelope evolution. We have also compared our results with those of previous studies in Newtonian gravity, finding similar phenomenology and rates for motion in a uniform medium. However, differences develop for nonzero density gradients, with the general relativistic rates increasing almost exponentially with the density gradients, while the opposite is true for the Newtonian rates. Finally, the evidence that mass accretion rates well above the Eddington limit can be achieved in the presence of nonuniform media increases the chances of observing this process also in binary systems of stellar-mass black holes.