Effect of Chaotic Orbits on Dynamical Friction

Abstract

When a body moves through a medium of smaller particles, it suffers a deceleration due to dynamical friction (Chandrasekhar 1943). Dynamical friction is inversely proportional to the relaxation time, which can be defined as the time needed for the orbits to experiment an energy exchange of the order of their initial energies, as a result of the perturbations produced by stellar encounters. Chaotic orbits, present in non-integrable systems, have exponential sensitivity to perturbations, a feature that makes them to relax in a time much shorter than regular ones, which suggests that dynamical friction would increase in the presence of chaotic orbits (Pfenniger 1986). We present preliminary results of numerical experiments used to check this idea, investigating the orbital decay, caused by dynamical friction, of a rigid satellite which moves within a larger stellar system (a galaxy) whose potential is non-integrable. Triaxial models with similar density distributions but different percentages of chaotic orbits are considered. This last quantity depends on the central concentration of the models. If the potential corresponds to triaxial mass models with smooth cores, the regular orbits have shapes that can be identified with one of the four families of regular orbits in Stäckel potentials (box and three types of tubes). Chaotic orbits behave very much like regular orbits for hundreds of oscillations at least. In this case, the galaxy is represented by the triaxial generalization of the γ-models with γ = 0 (Merritt & Fridman 1996). However, the situation is very different in triaxial models with divergent central densities (cusps) or black holes, a feature that is in agreement with the observations. While the tube orbits are not strongly affected by central divergencies, the boxlike orbits are often rendered chaotic (Gerhard & Binney 1985). The rimescale in which the chaos manifests itself in the orbital motion is short compared to a Hubble time. In this models, the compact object is taken as a Plummer sphere.