Substructure in Dark Halos: Orbital Eccentricities and Dynamical Friction

Abstract

The virialized regions of galaxies and clusters contain signiÐcant amounts of substructure ; clusters have hundreds to thousands of galaxies, and satellite systems and globular clusters orbit the halos of individual galaxies. These orbits can decay owing to dynamical friction. Depending on their orbits and their masses, the substructures either merge, are disrupted, or survive to the present day. We examine the distributions of eccentricities of orbits within mass distributions similar to 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. The eccentricity distributions in the case of an isotropic distribution function are strongly skewed toward high eccentricities, with a median value of typically D0.6, corresponding to an apocenter-to-pericenter ratio of 4.0. We also present high-resolution N-body simulations of the orbital decay of satellite systems on eccentric orbits in an isother-mal halo. The dynamical friction timescales are found to decrease with increasing orbital eccentricity because of the dominating deceleration at the orbitÏs pericenter. 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. We brieÑy discuss several applications for our derived distributions of orbital eccentricities and the resulting decay rates from dynamical friction. We compare the theoretical eccentricity distributions to those of globular clusters and galactic satellites for which all six phase-space coordinates (and therewith their orbits) have been determined. We Ðnd that the globular clusters are consistent with a close-to-isotropic velocity distribution, and they show large orbital eccentricities because of this (not in spite of this, as has been previously asserted). In addition, we Ðnd that the limited data on the Galactic system of satellites appears to be di †erent and warrants further investigation as a clue to the formation and evolution of our Milky Way and its halo substructure.