Nonextensive Effects on Chandrasekhar's Dynamical Friction

TL;DR

This paper derives a generalized formula for Chandrasekhar's dynamical friction using nonextensive kinetic theory, explaining discrepancies in timescales observed in simulations and models.

Contribution

It introduces a nonextensive approach to dynamical friction, extending Chandrasekhar's classical results to account for long-range interactions and non-Maxwellian velocity distributions.

Findings

Derived an analytical formula for nonextensive dynamical friction.

Reproduces classical results in the extensive limit (q=1).

Explains large timescales in simulations as deviations from Maxwellian behavior.

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 dynamic 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 dynamic 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 dynamic 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.