Dark Matter Halos: The Dynamical Basis of Effective Empirical Models
  We investigate the dynamical basis of the classic empirical models
(specifically, Sersic-Einasto and generalized NFW) that are widely used to
describe the distributions of collisionless matter in galaxies. We submit that
such a basis is provided by our \alpha-profiles, shown to constitute solutions
of the Jeans dynamical equilibrium with physical boundary conditions. We show
how to set the parameters of the empirical in terms of the dynamical models; we
find the empirical models, and specifically Sersic-Einasto, to constitute a
simple and close approximation to the dynamical models. Finally, we discuss how
these provide an useful baseline for assessing the impact of the small-scale
dynamics that may modulate the density slope in the central galaxy regions.
