Multilayer spherical stellar cluster with uniform density

TL;DR

This paper explores new analytic solutions for the equilibrium states of multilayer spherical stellar clusters with uniform density, including cases with hollow centers and multiple layers with different distribution functions.

Contribution

It introduces novel analytic solutions for multilayer spherical stellar clusters with uniform density, including hollow centers and varying distribution functions.

Findings

Derived solutions for hollow spherical clusters.

Established equilibrium conditions for multilayer configurations.

Provided mathematical models for different distribution functions.

Abstract

Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions are obtained for a uniform sphere with a hollow spherical volume and central mass inside the sphere. Solutions are also obtained for an arbitrary number of spherical layers with the same density, but with different equilibrium distribution functions.