Algorithmic Approach to Study Equilibrium Structure of Rotationally and Tidally Distorted Stellar Models

Abstract

In the present thesis, we have proposed a algorithmic approach for Mohan,Saxena and Aggarwal method to determine the effect of rotation and tidal distortion in the equilibrium structure of polytropic models of stars. Although efforts have been made to develop analytic expression in series form whose closed form solutions have not possible. Even these series solutions do not provide any analytic expression which could provide some result of practical significance. It may, therefore, be of interest to see if instead of developing detailed series expansion of distortional parameters r,u,v,w,f, etc. required in determining the equilibrium structure and periods of oscillations of rotationally and tidally distorted stars. In fact, this does not seem to be difficult proposition in view of the availability of fast computing machines. Thus, there is need of developing an efficient computational method which directly evaluates these distortional parameters without using their explicit expressions in the form of series available in the literature.. The thesis consists of three chapters. Chapter-I is introductory in nature. We briefly discuss the astrophysical significance of the problem of determining the equilibrium structures of rotationally and tidally distorted stellar models. A brief survey of the literature available on this subject and summary of the work presented in succeeding chapters of this thesis also appears in this chapter. In Chapter-II we first present suitable Gauss quadrature formula for evaluating double integral having singularity at the end of the intervals and how it has been used to evaluate double integral appearing in most of the mathematical expressions for distortional and structural parameters of rotationally and tidally distorted stellar models. An algorithm to use Mohan, Saxena and Agarwal (62,63) approach has been formalized in this chapter to determine the effects of rotation and tidal forces on the equilibrium structure without using the explicit expressions for the distortional parameters available in the literature. The algorithm developed in Chapter-II has next been used in Chapter-III to determine the equilibrium structure of rotationally and tidally distorted polytropic models of stars. The equilibrium structure and other physical parameters of various rotationally and tidally distorted polytropic models with polytropic indices 1.5, 3.0 and 4.0 have been computed. The results thus obtained have been compared with the results earlier obtained by Mohan and Saxena (57,58) for the same models using the explicit expressions for the distortional parameters . Certain conclusions based on this study have also been drawn. The astrophysical importance of the present work as well as the limitation of the scope of the present work is finally discussed in this chapter.