ANN AND ANALYTICAL SOLUTIONS TO RELATIVISTIC ISOTHERMAL GAS SPHERES

Abstract

Relativistic isothermal gas spheres are a powerful tool to model many astronomical objects, like compact stars and clusters of galaxies. In the present paper, we introduce an artificial neural network (ANN) algorithm and Taylor series to model the relativistic gas spheres using Tolman-Oppenheimer-Volkoff differential equations (TOV). Comparing the analytical solutions with the numerical ones revealed good agreement with maximum relative errors of 10−3. The ANN algorithm implements a three-layer feed-forward neural network built using a back-propagation learning technique that is based on the gradient descent rule. We analyzed the massradius relations and the density profiles of the relativistic isothermal gas spheres against different relativistic parameters and compared the ANN solutions with the analytical ones. The comparison between the two solutions reflects the efficiency of using the ANN to solve TOV equations.