Equilibrium Structure of Non-Synchronously Rotating and Tidally Distorted Binary Stars

Abstract

The problem of determining the structure of equilibrium structures of stars distorted by rotation tidal forces has a great importance in astrophysics. Such a problems will help in better understanding the nature of inner structure of rotating stars and stars in binary/ or multiple systems. Thus, there is need for in depth investigation the equilibrium structure of gaseous sphere. Analytic study of determining the equilibrium structure of rotationally and tidally distorted stellar models is quite complex. Therefore, investigation attempted to solve such a problems in some approximate way. In one such attempt Mohan, Saxsena and Agarwal (62,63) used kippenhahn and Thomas averaging technique together with the results of Kopal(32) on Roche equipotential, to determine the effects of rotation and tidal forces on the equilibrium structures of eccentric binaries. They also implemented this approach in the case of the polytropic models of the stars as well as certain realistic main sequence stars. Several authors such as Lal(40), Sharma(84), Saini(80), Pathenia(72) used this method to study some astrophysical problems. However, the problems of determining the equilibrium structures of non-synchronously rotating binary is not satisfactory tacked so far. The thesis consists of three chapters. Chapter one deals with the importance of studying equilibrium structure of rotating and tidally distorted gaseous spheres. In the present thesis an attempt has been made to modify the Roche equipotential that takes into account for non-synchronous rotation and eccentric orbits. Using average technique of Kippenhahn and Thomas(28) is conjunction with results of modified Roche equipotential. Kippenhahn and Thomas(28) averaging technique is also discussed briefly in this chapter. This chapter ends with the brief survey of literature available on this subject and summary of the work presented in the succeeding chapter. In chapter II, we firstly discuss the approach of Sepinsky et al.(2007) for determining the Roche equipotential, which takes into account the motion of mass elements in non-synchronous, eccentric binary and planetary system. The results of such a roche equipotential are next used in conjunctions with Kippenhahn and Thomas averaging technique to develop analytic expressions representing equilibrium structure of non-synchronously rotating and tidally distorted stellar models. The equilibrium structures equations marginally deviates from the equilibrium structure equations earlier discussed by Mohan, Saxena and Agarwal (62,63) for non-synchronously rotation. The methodology developed in chapter – II has next been used in chapter-III to determine the equilibrium structure of rotationally and tidally distorted polytropic models. Certain results of physical parameter have been computed for various polytropic indices 1.5, 3.0 and 4.0. Conclusion based on the present study has finally been discussed.