Self-graviting Gas Spheres in Equilibrium State

TL;DR

This paper analyzes equilibrium states of stars modeled as self-gravitating gas spheres, deriving exact pressure and density distributions for various density profiles using a simplified analytic approach.

Contribution

It introduces a simplified analytic model for star equilibrium states and derives exact solutions for different density distributions, enhancing understanding of stellar structure.

Findings

Exact mass and pressure distributions obtained

Central pressure expressions derived

Multiple density profiles analyzed

Abstract

In the paper we discuss equilibrium states of stars, using a simplified analytic model. A star is considered as self-graviting body of gas. We use a condition for the equilibrium state of the body in the form of a differential equation, which relates the pressure distribution and mass density in the body. The density distributions of constant, potential, gaussian, and exponential forms are discussed. Exact expressions for the distribution of mass and pressure along the radial direction, and the central pressure were obtained.