Chandrasekhar's Dynamical Friction and non-extensive statistics

TL;DR

This paper extends Chandrasekhar's classical dynamical friction theory by incorporating non-extensive statistics, providing a generalized analytical formula that accounts for long-range interactions and better explains observed large timescales in astrophysical systems.

Contribution

It introduces a non-extensive kinetic theory approach to derive a generalized dynamical friction formula, relaxing the Maxwellian assumption and explaining large timescales in galactic dynamics.

Findings

Derived an analytical formula for dynamical friction using non-extensive statistics.

Recovered classical results in the limit of q=1.

Applied the model to globular cluster dynamics, explaining large timescales.

Abstract

The motion of a point like object of mass $M$ passing through the background potential of massive collisionless particles ($m << M$) suffers a steady deceleration named dynamical friction. In his classical work, Chandrasekhar assumed a Maxwellian velocity distribution in the halo and neglected the self gravity of the wake induced by the gravitational focusing of the mass $M$. In this paper, by relaxing the validity of the Maxwellian distribution due to the presence of long range forces, we derive an analytical formula for the dynamical friction in the context of the $q$-nonextensive kinetic theory. In the extensive limiting case ($q = 1$), the classical Gaussian Chandrasekhar result is recovered. As an application, the dynamical friction timescale for Globular Clusters spiraling to the galactic center is explicitly obtained. Our results suggest that the problem concerning the large timescale as derived by numerical $N$-body simulations or semi-analytical models can be understood as a departure from the standard extensive Maxwellian regime as measured by the Tsallis nonextensive $q$-parameter.