Relativistic dynamical friction in stellar systems

¹ Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via Campi 213/A, 41125 Modena, Italy
e-mail: caterina.chiari@unimore.it
² CNR – ISC, Via Madonna del piano 10, 50019 Sesto Fiorentino, Italy
e-mail: pierfrancesco.dicintio@cnr.it
³ INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy
⁴ INFN – Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy

Received: 28 November 2022
Accepted: 18 July 2023

Abstract

Aims. We extend the classical formulation of the dynamical friction effect on a test star by Chandrasekhar to the case of relativistic velocities and velocity distributions, also accounting for post-Newtonian corrections to the gravitational force.

Methods. The original kinetic framework was revised and used to construct a special-relativistic dynamical friction formula where the relative velocity changes in subsequent encounters are added up with Lorentz transformation, and the velocity distribution of the field stars accounts for relativistic velocities. Furthermore, a simple expression is obtained for systems where the post-Newtonian correction on the gravitational forces become relevant even at non-relativistic particle velocities. Finally, using a linearized Lagrangian we derived another expression for the dynamical friction expression in a more compact form than previously used.

Results. Comparing our formulation with the classical one, we observe that a given test particle undergoes a slightly stronger drag when moving through a distribution of field stars with relativistic velocity distribution. Vice versa, a purely classical treatment of a system where post-Newtonian (PN) corrections should be included, overestimates the effect of dynamical friction at low test particle velocity, regardless of the form of velocity distribution. Finally, a first-order PN dynamical friction covariant formulation is weaker its classical counterpart at small velocities, but much higher for large velocities over a broad range of mass ratios.