A Realistic Model for Spatial and Mass Distributions of Dark Halo Substructures: An Analytic Approach

We construct a realistic model for the dark halo substructures, and derive analytically their spatial, mass, and velocity distributions. Basically, our model is a modification of the Press-Schechter theory to account for the dominant dynamical processes that mark the evolution of dark halo substructures such as the tidal stripping and dynamical friction. Our analytic model successfully reproduces all the well known behaviors of the substructure distributions that have been found in recent numerical simulations: the weak dependence of the mass distributions on the host halo mass; the anti-bias of the spatial distribution relative to the dark matter particle components; the nearly power-law shapes of the mass and velocity distributions. We compare our analytic results with recent high-resolution N-body simulation data and find that they are in excellent agreement with each other.