Nearly collisionless spherical accretion

Abstract
A fluid-like gas accretes much more efficiently than a collisionless gas. The ability of an accreting gas to behave like a fluid depends on the relationship of the mean free path of a gas particle at $$r\rightarrow\infty\enspace(\lambda_\infty)$$, to the typical length scales associated with the star–gas system. We examine this relationship in detail by generalizing the model of Danby & Camm to cases where λ is finite. For constant collision cross-section we find evidence for a rapid changeover from collisionless to fluid-like accretion flows when λ drops below a certain value, but for hard Coulomb collisions, the transition is more gradual, and is sensitive to the adiabatic index of the gas at $$r\rightarrow\infty$$. To these results must be added the effects of the substantial cusp of bound particles, which always develops in a system with arbitrarily small but non-zero cross-section. The density run in such a cusp depends on the collision properties of the particles, but it is always steeper than the ‘zero flow’ solution described by Bahcall & Wolf. ‘Loss-cone’ accretion from the cusp may in some cases exceed the accretion rate predicted from our generalization of Danby & Camm's theory. Our result may apply to the accretion of grains and the dynamics of stellar cusps around massive black holes, as well as providing a cautionary tale for those who accept the fluidity of all accreting plasmas as gospel truth.

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