Analytical galactic models with mild stellar cusps

TL;DR

This paper introduces a new family of spherical analytical models for galaxies with mild stellar cusps, providing explicit formulas for distribution functions and velocity dispersions, facilitating comparison across different cusp profiles.

Contribution

It presents a novel analytical model family for galactic centers with mild cusps, including isotropic and anisotropic cases, with unified hypergeometric series solutions.

Findings

Analytical formulas for distribution functions and velocity dispersions.

Unified representation for different cusp profiles.

Facilitates comparison of galactic core properties.

Abstract

In the past two decades, it has been established by high-resolution observations of early-type galaxies that their nuclear surface brightness and corresponding stellar mass densities are characterized by cusps. In this paper, we present a new spherical analytical model family describing mild cuspy centres. We study isotropic and anisotropic models of Osipkov-Merritt type. It is shown that the associated distribution functions and intrinsic velocity dispersions can be represented analytically in a unified way in terms of hypergeometric series, allowing thus a straightforward comparison of these important global quantities for galaxies having underlying mass densities which may differ significantly in their degree of central cuspiness or radial falloff.