Dynamical Friction on extended perturbers

TL;DR

This paper derives a modified Chandrasekhar dynamical friction law using wave-mechanical methods, accounting for different density profiles of perturbers, and confirms the convergence of the Coulomb logarithm at small scales.

Contribution

It introduces a wave-mechanical approach to dynamical friction, incorporating various density profiles and showing the shape of the perturber influences the Coulomb logarithm.

Findings

The shape of the perturber affects the Coulomb logarithm.

The Coulomb logarithm converges at small impact parameters.

Wave-mechanical treatment recovers classical dynamical friction law.

Abstract

Following a wave-mechanical treatment we calculate the drag force exerted by an infinite homogeneous background of stars on a perturber as this makes its way through the system. We recover Chandrasekhar's classical dynamical friction (DF) law with a modified Coulomb logarithm. We take into account a range of models that encompasses all plausible density distributions for satellite galaxies by considering the DF exerted on a Plummer sphere and a perturber having a Hernquist profile. It is shown that the shape of the perturber affects only the exact form of the Coulomb logarithm. The latter converges on small scales, because encounters of the test and field stars with impact parameters less than the size of the massive perturber become inefficient. We confirm this way earlier results based on the impulse approximation of small angle scatterings.