Substructure in Dark Halos: Orbital Eccentricities and Dynamical Friction

We examine the distributions of eccentricities of orbits within mass distributions like those we see for galaxies and clusters. A comprehensive understanding of these orbital properties is essential to calculate the rates of physical processes relevant to the formation and evolution of galaxies and clusters. We derive the orbital eccentricity distributions for a number of spherical potentials. These distributions depend strongly on the velocity anisotropy, but only slightly on the shape of the potential. We also present high resolution N-body simulations of the orbital decay of satellite systems on eccentric orbits in an isothermal halo. The dynamical friction timescales are found to decrease with increasing orbital eccentricity, but the dependence is weaker than previously suggested. The orbital eccentricity stays remarkably constant throughout the decay; although the eccentricity decreases near pericenter, it increases again near apocenter, such that there is no net circularization. Finally, we discuss a number of applications. We find that the distribution of orbital eccentricities of the globular clusters in the Milky Way is consistent with a close to isotropic velocity distribution. The limited data on the galactic system of satellites, however, appears to be different and warrants further investigation as a clue to the formation and evolution of our Milky Way and its halo substructure.