Computing N-dimensional polytrope via power series

Abstract

Polytropic equations (Lane–Emden [LE] equations) are valuable because they offer a simple explanation for a star’s interior structure, interstellar matter, molecular clouds, and even spiral arms that can be calculated and used to estimate various physical parameters. Many analytical and numerical methods are used to solve the polytropic LE equation. The series expansion method played an essential role in many areas of science and has found application in many branches of physical science. This work uses the series expansion method to examine N-dimensional polytropes (i.e., slab, cylinder, and sphere). To solve LE-type equations, a computational method based on accelerated series expansion (ASE) is applied. We calculate several models for the N-dimensional polytropes. The numerical results show good agreement between the ASE and numerical and analytical models of the N-dimensional polytropes.

Keywords

• equation of state
• n-dimensional polytrope
• series solution
• physical characteristic
• stellar structure