Black holes in radiation-dominated gas: an analogue of the Bondi accretion problem

Black holes, unlike other compact objects, are able to accrete matter more rapidly than their Eddington rate, |M_ E=L_ E/c²|⁠. Nevertheless, at such a high |M|⁠, radiation will probably be emitted by the in-falling gas in copious enough quantities to have a profound influence on the flow. To aid in understanding the nature of this influence, we study the steady flow, on to a stationary Schwarzschild black hole, of a uniform, non-relativistic gas in which radiation pressure swamps thermal pressure at infinity, and in which Thomson scattering provides the only radiation–gas couple. Asymptotic radiation pressure p∞ and matter density ρ∞ determine an asymptotic sound speed c∞, from which one can derive an accretion rate |M_ B| corresponding to the adiabatic flow of a |γ=4/3| gas. The actual accretion rate depends on the optical depth τB of a column of unperturbed gas spanning the Bondi radius, |rB=GM/c²_∞|⁠. If |τB>(√2/3)(c/c_∞)|⁠, then the flow is adiabatic, and |M= M_ B|⁠. For a somewhat smaller τB, diffusion is efficient enough for the radiation to leak out of the gas as it moves towards the trans-sonic point. As a result, the sound speed decreases inwards in the subsonic region, while the density must increase steeply to maintain pressure balance. |M| may then exceed |M_ B| by a factor of up to |(√2/3)(c/τ_ B c_∞)|⁠, although this effect can be limited by thermal pressure. Finally, for small enough τB the diffusion approximation breaks down, and radiation drag limits an otherwise thermally-determined |M|⁠. Our boundary conditions occur within super-massive |(M/M₁0²)| stars, and in the pre- and post-recombination universe. If a super-massive star of |M/M₅×10⁵| happens to have a small |(MBH1 M₎| black hole passing through it on a bound orbit, it will capture and be swallowed by the hole, before it has a chance to ignite its nuclear fuel and blow itself apart. In any milieu where both small black holes and super-massive stars are likely to form (e.g. a dense star cluster), this may provide a natural mechanism for forming black holes in the mass range |10²-10⁵M_|⁠.