Chandrasekhar's dynamical friction and non-extensive statistics

Abstract

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.

Nonextensive kinetic theory and H-theorem in general relativity

“…It was found that the large timescale of globular clusters spiraling to the center of the Milky Way, as obtained from N-body simulations, can be interpreted as a departure from the extensive Gaussian result in agreement with Tsallis power-law approach [13].…”

Emergence of a stellar cusp by a dark matter cusp in a low-mass compact ultrafaint dwarf galaxy

“…These phenomena are inconsistent with predictions by the simplified Chandrasekhar formula. Various physical mechanisms of the deviation from the analytic formula have been proposed: orbital resonance between a massive and field particles (Inoue 2011;Zelnikov & Kuskov 2016), coherent velocity field among particles (Read et al 2006), a non-Maxwellian velocity distribution (Silva et al 2016;Petts et al 2015;Just et al 2011), decrease of low-velocity particles (Antonini & Merritt 2012;Petts et al 2016;Dosopoulou & Antonini 2016) and inhomogeneity of background density and a variable Λ (Just & Peñarrubia 2005).…”

Growth of Supermassive Black Hole Seeds in ETG Star-forming Progenitors: Multiple Merging of Stellar Compact Remnants via Gaseous Dynamical Friction and Gravitational-wave Emission

“…(e.g., Rephaeli & Salpeter 1980;Lacey & Cole 1993;Silva 2016) 5 ; other authors commonly assume r max = v t that for a straight motion (or equivalently highly eccentric orbits) would correspond to the length of the wake behind the perturber (e.g., Ostriker 1999;Tagawa et al 2016), or a direct proportionality r max = 2 r to the orbital radius r for perturbers in nearly circular and supersonic motion (Kim & Kim 2007).…”