Anisotropic Models for Globular Clusters, Galactic Bulges and Dark Halos

TL;DR

This paper develops a family of anisotropic, self-gravitating spherical models in the post-Newtonian framework, useful for describing galaxies and dark matter halos with cuspy density profiles and analyzing their stability.

Contribution

It introduces analytically derived, anisotropic models in post-Newtonian gravity that generalize known profiles like Plummer and Hernquist, bridging polytropic and isothermal behaviors.

Findings

Models exhibit cuspy density profiles suitable for galaxies and dark matter halos.

The models interpolate between polytropic spheres and isothermal cores.

Thermodynamic analysis suggests these models are stable.

Abstract

Spherical systems with polytropic equations of state are of great interest in astrophysics. They are widely used to describe neutron stars, red giants, white dwarfs, brown dwarfs, main sequence stars, galactic halos, and globular clusters of diverse sizes. In this paper we construct analytically a family of self-gravitating spherical models in the post-Newtonian approximation of general relativity. These models present interesting cusps in their density profiles which are appropriate for the modeling of galaxies and dark matter halos. The systems described here are anisotropic in the sense that their equiprobability surfaces in velocity space are nonspherical, leading to an overabundance of radial or circular orbits, depending on the parameters of the model under consideration. Among the family of models, we find the post-Newtonian generalization of the Plummer and Hernquist models. A close inspection of their equation of state reveals that these solutions interpolate smoothly between a polytropic sphere in the asymptotic region and an inner core that resembles an isothermal sphere. Finally, we study the thermodynamics of these models and argue for their stability.