Equilibrium models of radially anisotropic spherical stellar systems with softened central potentials

TL;DR

This paper introduces a new class of equilibrium spherical stellar system models with radially anisotropic velocities and softened central potentials, addressing singularity issues in previous models and aiding stability analysis.

Contribution

It presents a novel two-parametric family of models with finite central density and potential, improving upon generalized polytropes for studying stability.

Findings

Models have finite density and potential at the center.

Comparison with other models shows improved physical realism.

Facilitates better analysis of radial orbit instability.

Abstract

We study a new class of equilibrium two-parametric distribution functions of spherical stellar systems with radially anisotropic velocity distribution of stars. The models are less singular counterparts of the so called generalized polytropes, widely used in works on equilibrium and stability of gravitating systems in the past. The offered models, unlike the generalized polytropes, have finite density and potential in the center. The absence of the singularity is necessary for proper consideration of the radial orbit instability, which is the most important instability in spherical stellar systems. Comparison of the main observed parameters (potential, density, anisotropy) predicted by the present models and other popular equilibrium models is provided.