Axisymmetric, Rotating and Stratified Star

TL;DR

This paper derives simplified equations for modeling the shape of rotating, stratified stars governed by Euler-Poisson equations, providing approximate solutions for their structure and gravitational fields.

Contribution

It reduces complex six-equation models to two equations in cylindrical and spherical coordinates, enabling analytical approximation of star shapes.

Findings

Derived expressions for pressure in stratified rotating stars.

Obtained approximate solutions for star shape and gravitational field.

Provided analytical tools for modeling rotating, stratified stellar structures.

Abstract

The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric stars under the additional assumption that it is composed of incompressible stratified fluid. The original system of six nonlinear equations is reduced to two equations, one for the mass density and the other for gravitational field. This reduction is carried out separately in cylindrical and spherical coordinates. As a "byproduct" we derive also expressions for the pressure. The resulting equations are then solved approximately and these analytic solutions are used then to determine the shape of the rotating star.