Equilibrium Structures of the Rotating Stars and Stars in Binary Systems

Abstract

In this dissertation, we have studied the equilibrium structures of rotating stars and stars in binary systems (rotationally and/or tidally distorted stars) that are distorted by both rotational and tidal forces. While studying the equilibrium structures of primary component of synchronous binaries, Kopal (1972) obtained a series expression for computing the radius of the Roche equipotential surfaces by retaining terms up to in r0. This series expression was then used in his work to find the series expressions for computing volume of Roche Equipotential Surfaces. Mohan and Saxena (1983) extended this analysis to study rotating stars, synchronous and non synchronous binaries and used the series expressions for radius, volume, surface area and other parameters by retaining terms up to in r0. Now as these series solutions of radius, volume and surface area of the Roche equipotential surfaces are the only approximate analytical solutions available in literature that is why they are of great significance. However, the numerical results obtained from these series expressions are not very accurate. Keeping these factors in view, in the present work we have used the series expressions of the radius of Roche equipotential surfaces as given by Pathania and Medupe (2012) in which terms up to in r0 has been retained and has used it subsequently to obtain the series expressions for volume, surface area and various other parameters by retaining terms up to in r0. The objective of the present work is to check the variations in the numerical results on expanding the series expressions further. Thesis consists of 3 chapters. Chapter I is introductory in nature. In this chapter, brief literature survey, Roche equipotential and methodology of Mohan and Saxena (1983) to study the equilibrium structures of rotationally and/or tidally distorted (from here after we will call rotationally and/or for tidally distorted stars as RTD stars) stars has been discussed. In chapter II, we have used the extended series expression of radius of the Roche Equipotential surfaces as given by Pathania and Medupe (2012) to obtain extended series expressions for volume, surface area and other parameters. The methodology of Mohan and Saxena (1983) along with the results of Kopal (1972) has been used to obtain these series expressions. In chapter III we have used these extended series expressions to find the equilibrium structures of RTD polytropic models of stars. The numerical results so obtained have been compared with the results of Mohan and Saxena (1983). Finally conclusions based on the present study has also been drawn in this chapter.