Subsonic accretion and dynamical friction for a black hole moving through a self-interacting scalar dark matter cloud
Alexis Boudon, Philippe Brax, Patrick Valageas
Abstract
We investigate the flow around a black hole moving through a cloud of self-interacting scalar dark matter. We focus on the large scalar mass limit, with quartic self-interactions, and on the subsonic regime. We show how the scalar field behaves as a perfect gas of adiabatic index ${\ensuremath{\gamma}}_{\mathrm{ad}}=2$ at large radii while the accretion rate is governed by the relativistic regime close to the Schwarzschild radius. We obtain analytical results thanks to large-radius expansions, which are also related to the small-scale relativistic accretion rate. We find that the accretion rate is greater than for collisionless particles, by a factor $c/{c}_{s}\ensuremath{\gg}1$, but smaller than for a perfect gas, by a factor ${c}_{s}/c\ensuremath{\ll}1$, where ${c}_{s}$ is the speed of sound. The dynamical friction is smaller than for a perfect gas, by the same factor ${c}_{s}/c\ensuremath{\ll}1$, and also smaller than Chandrasekhar's result for collisionless particles, by a factor ${c}_{s}/(cC)$, where $C$ is the Coulomb logarithm. It is also smaller than for fuzzy dark matter, by a factor ${v}_{0}/c\ensuremath{\ll}1$.