Equilibrium Structure of Rotationally, Tidally and Magnetically Distorted Polytropic Models of Stars

Abstract

The current thesis takes into account the problems of investigating the collective effects of rotational, tidal and magnetic distortions up on the equilibrium structure of a binary star system. This study has practical significance in the branch of astrophysics which requires to comprehend the challenges regarding the stability of a binary star system and its corresponding variations arising because of tidally and magnetically distorted non-synchronously rotating stars along with the stars in binary and multiple system. In theoretical models, most of the observed stars are essentially considered as self-gravitating spheres of gases in both hydrostatic and thermal equilibrium. Theoretical analysis of these kinds of problems which deal with the investigation of the equilibrium structure of stars, have been thoroughly carried out to comprehend the intriguing environment of the inner stellar structure. Some of such gaseous spheres are observed to be single while many are found in clusters. The single stars rotate about their own axis of rotation. Stars with a single companion are termed as binary stars while those with multiple companions are termed as multiple star. Such types of stars rotate about their own axis besides revolving around each other. If we take into account the equilibrium model of a distinct isolated star, which does not rotate, as a gaseous sphere, then the corresponding model describing the equilibrium structures of rotating stars would be rotationally distorted star. Likewise the equilibrium model of the stars present in the form of a cluster would be tidally distorted gaseous sphere provided it does not rotate but in the presence of rotation, the model would be a rotationally and tidally distorted gaseous sphere. Complex analytical studies have been discussed in literature to reveal the equilibrium structure of rotationally and tidally distorted stars. Generally, magnetic forces have been neglected while obtaining Roche equipotential surface of stars because its impact was presumed to be very minute in comparison with centrifugal and gravitational forces. However, magnetic field is also one of the factors causing the asphericity in stars. These stellar magnetic fields are considered to enact a vital role in controlling and thus affecting the stability of a star or a system of stars. By taking into account the major significance of magnetic distortion, on the structure of a star or a system of stars, an effort in this direction has been made in the present work to theoretically (and computationally) inspect significant aspects of magnetic distortion acting upon the equilibrium assemblies of asynchronously rotationally and tidally distorted gaseous spheres, that furthermore requires examinations as an attempt to gain deeper understanding of stellar structure.Although many efforts have been made to develop analytical expressions in the form of series, but to retrieve closed form solutions from these has not been possible. It is also observed that no significant practical result can be extracted from these analytical solutions. It thus seems encouraging to bring into picture the detailed series expansion of the distortion parameters rψ , u, v, w, fp and ft etc. which are required essentially in establishing the equilibrium structure of rotationally , tidally and magnetically distorted stars. In today’s era it seems to be an excellent proposition by keeping in view of the availability of fast computing machines. Hence arises the need to develop an efficient and reliable computational method which could directly evaluate these distortion parameters without depending on their explicit expression in the form of series. The thesis consist of 3 chapters. First chapter is introductory in nature. It comprises of brief discussion on the astrophysical importance of the equilibrium structures of rotationally, tidally and magnetically distorted binary stellar models. It also comprises of a brief inspection of the literature on this explicit topic. Chapter two aligns with the brief description about the binary stars and Roche equipotential surfaces. It describes in detail the effect of inclusion of magnetic forces upon the mass transfer that takes place in a binary system and how it causes stellar mass reduction. It provides us an insight into the methodology employed by Kippenhahn and Thomas to understand the stellar environment in more depth and breadth. Phenomenon of magnetic braking has been discussed to emphasise on the significance of inclusion of magnetic distortion on the stellar grounds, which were not considered to an appreciable extent to be included in the past stellar studies. The chapter concludes with the introduction to the equipotential surfaces of the polytropic model of rotationally, tidally and magnetically distorted binary stars. Chapter three is the final chapter of my thesis. It involves the numerical computation, the methods and approach employed to obtain the stellar parameters. Certain conclusions based upon the present study have been extracted. The chapter concludes on the final note on the discussion of the importance of the present work along with the limitations observed in our approach, and finally the future scope of our present work in astrophysics.