A disturbance in the force

How force fluctuations hinder dynamical friction and induce core stalling

¹ Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 17, 50022 Sesto Fiorentino (FI), Italy
² INFN – Sezione di Firenze, via G. Sansone 1, 50022 Sesto Fiorentino (FI), Italy
³ INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
⁴ Laboratoire J.-A. Dieudonné, UMR 6621, Université Côte d’Azur, Parc Valrose, 06108 Nice Cedex 02, France
⁵ Departamento de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense Madrid, 28040 Madrid, Spain

^⋆ Corresponding authors: pierfrancesco.dicintio@cnr.it; bruno.marcos@univ-cotedazur.fr

Received: 7 May 2025
Accepted: 15 July 2025

Abstract

Context. Dynamical friction is an important phenomenon in stellar dynamics (and plasma physics) resulting in the slowing down of a massive test particle upon many two-body scatters with background particles. Chandrasekhar’s original formulation, developed for idealized infinite and homogeneous systems, has been found to be sufficiently accurate even in models of finite extent and radially dependent density profiles. However, in some cases N-body simulations have evidenced a breakdown of Chandrasekhar’s formalism. In particular, in the case of cored stellar systems, the analytical predictions underestimate the rate of in-fall of the test particle. Moreover, the orbital decay appears to stop at a critical radius where in principle the effect of dynamical friction should still be non-negligible.

Aims. Several explanations for such discrepancy have been proposed so far. In spite of this, it remains unclear whether the origin is a finite N effect or an effect arising from the resonance (or near-resonance) of the orbits of the test and field particles, which is independent of N, such as dynamical buoyancy. Here we aim to shed some light on this issue with tailored numerical experiments.

Methods. We performed ad hoc simulations of a massive tracer initially placed on a low-eccentricity orbit in spherical equilibrium models with increasing resolution. We used an N-body code for which the self-consistent interaction among the background particles can be substituted with the effect of the static smooth potential of the system’s continuum limit, so that the higher-order contributions to the dynamical friction arising from the formation of a wake can be neglected if needed.

Results. We find that, contrary to what has been reported in previous literature, a suppression of dynamical friction happens in both cuspy and cored models. When neglecting the interaction among field particles, we observe in both cases a clear N^−1/2 scaling of the radius at which dynamical friction ceases to be effective. This hints at a granularity-induced origin of the so-called core-stalling of the massive tracer in cored models.