Abstract
We investigate the dynamical basis of the classic empirical models (specifically, Sérsic-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 ourα-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 Sérsic-Einasto, to constitute a simple and close approximation to the dynamical models. Finally, we discuss how these provide a useful baseline for assessing the impact of the small-scale dynamics that may modulate the density slope in the central galaxy regions.
Highlights
The classic Sersic [1] models met a wide and lasting success as empirical representations of the projected (2-dimensional) light distributions in spheroidal galaxies
We investigate the dynamical basis of the classic empirical models (Sersic-Einasto and generalized NFW) that are widely used to describe the distributions of collisionless matter in galaxies
We have discussed the dynamical basis of the Sersic-Einasto empirical models, in terms of well-behaved solutions of the Jeans equation with physical boundary conditions comprising: a finite central energy density, a closely self-similar body, and a finite overall mass
Summary
The classic Sersic [1] models met a wide and lasting success as empirical representations of the projected (2-dimensional) light distributions in spheroidal galaxies (for a review, see Kormendy et al [2]). Recent extensive N-body simulations (e.g., [4,5,6,7,8]) indicate that the Sersic and Einasto functional forms provide good patterns to represent the sphericallyaveraged mass distributions in dark matter (DM) halos ranging from galaxies to galaxy clusters. These hold at levels comparable to, or even better than the popular NFW formula [9].
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