Roche Coordinates for Rotationally and Magnetically Distorted Binary Stars

Abstract

Apart from gravitational and centrifugal forces, magnetic field also plays an important role while studying the equilibrium structures and also period of oscillations of rotating stars as well as stars in binary system. A new system of co-ordinates was introduced by Kopal[19] which is known as Roche system of co-ordinates and he also emphasized that how this system of co-ordinates can be used to study the problems of vibrations of rotationally and tidally distorted stellar models. Mohan and Singh [24], Singh [18], Singh and Gupta [19], have discussed the system of Roche co-ordinates for certain types of distorted stars. However after the formulation of equipotential surfaces of rotationally, tidally and magnetically distorted stars the Roche coordinates for these stars have not been taken into account. So the present thesis is an attempt to develop expressions for Roche coordinates and related parameters for Roche equipotential surfaces for stars distorted by rotation and magnetic field. Chapter wise summary of work done in this thesis is as follows: Chapter 1 is just introductory in nature. We study the significance in terms of astronomy of deducing the equilibrium structure of tidally, rotationally and magnetically deformed binary Stars. Then there is a brief literature review. Then we proceed by introducing some mathematical methods. And at last we define in detail a system of Roche equipotential including the effects of magnetic field. vii In chapter 2 we will discuss in detail a system of binary star and two types of mass transfer in such systems. Further we will proceed to study effects of magnetic fields on the mass transmission and reduction along with generations of poloidal and toroidal magnetic fields. Next we will explain the concept of magnetic braking and how it affects the binary system. At last we will compile our chapter by evaluating the effect of magnetic field on the shapes of the binary system. Chapter 3 is the final chapter that comprises an introduction to curvilinear coordinate system which has been included to explain the basis of Roche Coordinates. Finally we will derive expressions of Roche coordinates for modified roche equipotential surface for rotationally and/or magnetically distorted system of stars and their metric coefficients.