Relativistic wind accretion on to a Schwarzschild black hole

Abstract

We present a novel analytic model of relativistic wind accretion on to a Schwarzschild black hole. This model constitutes a general relativistic extension of the classical model of wind accretion by Bondi, Hoyle, and Lyttleton (BHL). As in BHL, this model is based on the assumptions of steady state, axisymmetry, and ballistic motion. Analytic expressions are provided for the wind streamlines while simple numerical schemes are presented for calculating the corresponding accretion rate and density field. The resulting accretion rate is greater in the relativistic model when compared to the Newtonian BHL one. Indeed, it is two times greater for asymptotic wind speeds $v_\infty \ge 0.4\,\mathrm{c}$ and more than an order of magnitude greater for $v_\infty \ge 0.8\,\mathrm{c}$. We have compared this full relativistic model versus numerical simulations performed with the free GNU Public Licensed hydrodynamics code AZTEKAS and found a good agreement for the streamlines in the upstream region of the flow and also, to within 10 per cent, for the corresponding accretion rates.