Effects of Eccentric Orbits And Asynchronous on the Equillibrium Structures of Rotationally and Tidally Distorted Polytropic Models of Stars

Abstract

In astrophysics it has great importance to study the problems of equilibrium structures of stars distorted by rotational and tidal effects. So, The aim of the present thesis is to study the effects of eccentric orbits and asynchronous on the equilibrium structure of distorted stars.This types of problem helps in better understanding to inner structure and stability of binary system. \vspace{0.5cm}\\ It is quite a complex problem to determine the equilibrium structure of distorted stellar models analytically. Therefore, researchers tried to solve such problems by approximations. In one of those attempts, Mohan, Saxena and Aggarwal used Kippenhahn and Thomas averaging technique together with the results of Kopal on Roche Equipotential, to determine the effects of rotational and tidal distortion on the equilibrium structure of binary stars. However, the problems of determining the equilibrium structures of eccentric orbits and asynchronous on the rotationally and tidally distorted polytropic models of stars have not been satisfactory tackled so far.In the present thesis an attempt has been made to study the effects of eccentric orbits and asynchronous on the equilibrium structures of rotationally and tidally distorted polytropic models of stars.

This thesis consists of three chapters. Chapter one is introductory in nature where we discussed the astrophysical importance of studying the equilibrium structure of rotationally and tidally distorted stellar models. Chapter two deals with the concept of Roche equipotential of distorted stars which accounts for the effects of eccentric orbits and asynchronous rotation of the binary system. Along with the results of Roche equipotential, the explicit expressions for distortional parameters u, v, w, $f_{P}$ and $f_{T}$ are obtained by using Kippenhahn and Thomas averaging technique. In this chapter we also discussed about how to find the equilibrium structure of rotationally and tidally distorted stellar models in presence of eccentric orbits and asynchronous rotation.

The methodology discussed in chapter-II is next used in chapter-III to determine the equilibrium structure of rotationally and tidally distorted polytropic models of stars. Computation is carried out to determine the structure as well as various parameters like volume and surface area of the rotationally and tidally distorted polytropic models with various values of degree of non synchronous parameter F. Conclusion is based on study has finally been discussed.