Dynamical Friction in a Gas: The Subsonic Case

TL;DR

This paper analytically investigates the subsonic dynamical friction force on a gravitating object in an isothermal gas, deriving a new expression applicable in various astrophysical contexts.

Contribution

It provides the first analytical derivation of the steady-state dynamical friction force in the subsonic regime, extending previous hypersonic results.

Findings

Friction force equals mass accretion rate times velocity (Mdot*V).

Object speed decreases as the inverse square of its mass.

Derived an analytic formula for Mdot as a function of velocity.

Abstract

We study the force of dynamical friction acting on a gravitating point mass that travels through an extended, isothermal gas. This force is well established in the hypersonic limit, but remains less understood in the subsonic regime. Using perturbation theory, we analyze the changes in gas velocity and density far from the mass. We show analytically that the steady-state friction force is Mdot*V, where Mdot is the mass accretion rate onto an object moving at speed V. It follows that the speed of an object experiencing no other forces declines as the inverse square of its mass. Using a modified version of the classic Bondi-Hoyle interpolation formula for Mdot as a function of V, we derive an analytic expression for the friction force. This expression also holds when mass accretion is thwarted, e.g. by a wind, as long as the wind-cloud interaction is sufficiently confined spatially. Our result should find application in a number of astrophysical settings, such as the motion of galaxies through intracluster gas.