Computing Polytropic and Isothermal Models Using Monte Carlo Method

Polytropic and isothermal gas spheres are crucial in the theory of stellar structure and evolution, galaxy cluster modeling, thermodynamics, and various other physics, chemistry, and engineering disciplines. Based on two Monte Carlo algorithms (MC₁ and MC₂), we introduce a numerical approach for solving Lane-Emden (LE) equations of the polytropic and isothermal gas spheres. We found that the MC₁ and MC₂ models agree with each other and also with numerical and analytical models. We tested the compatibility between the MC and the numerical polytropic models by calculating the mass-radius relation and the pressure profile for the polytrope with n=3.