Chandrasekhar's Dynamical Friction and non-extensive statistics

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.

arXiv comment16pp 5 figs, revised and extended version of arXiv:1202.1873 . Accepted for publication by JCAP

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• Nonextensive Kinetic Theory and H-Theorem in General Relativity
• Transport Equation for Small Systems and Nonadditive Entropy
• Relativistic dynamical friction in stellar systems