A disturbance in the force. How force fluctuations hinder dynamical friction and induce core stalling

Dynamical friction is an important phenomena in stellar dynamics resulting in the slowing down of a 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 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. 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 of the orbits of the test and field particles, which is independent on $N$, such as dynamical buoyancy. Here we aim at shedding some light on this issue with tailored numerical experiments. We perform ad hoc simulations of a massive tracer initially placed on a low eccentricity orbit in spherical equilibrium models with increasing resolution. We use an $N-$body code where 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. We find that, contrary to what reported in the 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 towards a granularity-induced origin of the so-called core-stalling of the massive tracer in cored models.