The Stability Analysis of Coupled Differential Equations in Stellar Structure

Abstract

Astrophysical and Mathematical Models usually describes the evolutionary processes of life cycle of stellar structure. The process of star formation undergoes various stages during its life cycle. In human time scale it is not possible to observe whole of the evolution of stellar structure. From the birth of star to the death of star, different complex cosmological phenomenon occurs in the galactic region. In general theory of astrophysics stars are assumed to be static and spherical in nature. This nature results from hydrostatic and thermostatic equilibrium. Self-gravitating forces makes the star to collapse gradually and intermittently. At the same time thermal nature of chemical composition inside the star develops the pressure and hinders the sudden collapse. As a result, there is change in physical quantities like temperature, density, mass, radius, luminosity opacity and many more structural behaviours of star. These quantities are taken as variable in differential equation which are evolved in due process of star evolution. During the evolution of star, hydrostatic equilibrium and thermal equilibrium remains the major areas of study, therefore emphasis is laid on the stability of stellar structure with main focus on the hydrostatic and thermal equilibrium.