Monte Carlo Simulation of Lane-Emden Type Equations Arising in Astrophysics

TL;DR

This paper introduces a Monte Carlo computational technique to solve Lane-Emden equations in astrophysics, demonstrating good agreement with existing models across multiple equations related to stellar structures.

Contribution

The paper presents a novel Monte Carlo method for solving Lane-Emden equations, expanding computational tools for astrophysical models of stellar phenomena.

Findings

Good agreement between Monte Carlo and existing models

Successful computation of multiple Lane-Emden equations

Applicable to various astrophysical scenarios

Abstract

Monte Carlo (MC) method played an essential role in many areas of human activity and has found application in many branches of physical science. This paper proposes a computational technique based on MC algorithms to solve Lane-Emden (LE) type equations. We analyze four LE equations arising in astrophysics: the positive and negative indices of the polytropic gas spheres, the isothermal gas sphere, and the white dwarf equation. We calculated eleven models (i.e., eleven LE equations) of the positive index polytropes, nine for the negative index polytrope, the isothermal gas sphere, and the white dwarf equation. Comparing the MC and numerical/analytical models gives good agreement for the four LE equations under study.