Bondi-Hoyle accretion in a turbulent medium

The Bondi-Hoyle formula gives the approximate accretion rate onto a point particle accreting from a uniform medium. However, in many situations accretion onto point particles occurs from media that are turbulent rather than uniform. In this paper we give an approximate solution to the problem of a point particle accreting from an ambient medium of supersonically turbulent gas. Accretion in such media is bimodal, at some points resembling classical Bondi-Hoyle flow, and in other cases being closer to the vorticity-dominated accretion flows recently studied by Krumholz, McKee, & Klein. Based on this observation, we develop a theoretical prediction for the accretion rate and confirm that our predictions are highly consistent with the results of numerical simulations. The distribution of accretion rates is lognormal, and the mean accretion rate in supersonically turbulent gas can be substantially enhanced above the value that would be predicted by a naive application of the Bondi-Hoyle formula. However, it can also be suppressed by the vorticity, just as Krumholz, McKee, & Klein found for non-supersonic vorticity-dominated flows. Magnetic fields, which we have not included in these models, may further inhibit accretion. Our results have significant implications for a number of astrophysical problems, ranging from star formation to the black holes in galactic centers. In particular, there are likely to be significant errors in results that assume that accretion from turbulent media occurs at the unmodified Bondi-Hoyle rate or that are based on simulations that do not resolve the Bondi-Hoyle radius of accreting objects.