Dynamical friction of a massive black hole in a turbulent gaseous medium

Abstract

The orbital decay of massive black holes in galaxies in the aftermath of mergers is at the heart of whether massive black holes successfully pair and merge, leading to emission of low-frequency gravitational waves. The role of dynamical friction sourced from the gas distribution has been uncertain because many analytical and numerical studies have either focussed on a homogeneous medium or have not reached resolutions below the scales relevant to the problem, namely the Bondi-Hoyle-Lyttleton radius. We performed numerical simulations of a massive black hole moving in a turbulent medium in order to study dynamical friction from turbulent gas. We find that the black hole slows down to the sound speed, rather than the turbulent speed, and that the orbital decay is well captured if the Bondi-Hoyle-Lyttleton radius is resolved with at least five resolution elements. We find that the larger the turbulent eddies, the larger the scatter in dynamical friction magnitude, because of the stochastic nature of the problem, and also because of the larger over- and under-densities encountered by the black hole along its trajectory. Compared to the classic solution in a homogeneous medium, the magnitude of the force depends more weakly on the Mach number, and dynamical friction is overall more efficient for high Mach numbers, but less efficient towards and at the transonic regime.