On dynamical friction in a gaseous medium with a boundary

TL;DR

This paper analytically investigates how a boundary in a gaseous medium affects dynamical friction, revealing significant modifications such as velocity limits, possible reversal of friction, and additional orthogonal forces, challenging standard estimates.

Contribution

It provides a novel analytical study of boundary effects on dynamical friction, showing significant deviations from classical formulas and implications for numerical simulations.

Findings

Perturbers are pushed away from the boundary and reach a terminal velocity near Mach 0.37.

Dynamical friction can be reversed for Mach numbers less than 0.37.

Additional orthogonal friction is much stronger than standard friction along the motion.

Abstract

Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. We study the effects of the presence of a boundary on dynamical friction by studying analytically the interaction of perturber with uniform rectilinear motion in a uniform homogeneous medium with a reflecting planar boundary. Wake reflection at a medium's boundary may occur at the edges of truncated disks perturbed by planetary or stellar companions as well as in numerical simulations of planet-disk interaction with no-outflow boundary conditions. In this paper, we show that the presence of the boundary modifies the behaviour of dynamical friction significantly. We find that perturbers are invariably pushed away from the boundary and reach a terminal subsonic velocity near Mach 0.37 regardless of initial velocity. Dynamical friction may even be reversed for Mach numbers less than 0.37 thereby accelerating instead of decelerating the perturber. Perturbers moving parallel to the boundary feel additional friction orthogonal to the direction of motion that is much stronger than the standard friction along the direction of motion. These results indicate that the common use of the standard Chandrasekhar formula as a short hand estimate of dynamical friction may be inadequate as observed in various numerical simulations.