System of Roche Coordinates of Rotationally and Tidally Distorted Stars in Presence of Coriolis Force

Abstract

Besides the gravitational and centrifugal forces, coriolis force also plays an important role while studying the equilibrium structures and the periods of oscillations of rotating stars and stars in binary system. Kopal (6) introduced a new system of co-ordinates called Roche- coordinates and imphasized how this system of co-ordinates could be used to study the prob- lems of vibrations of rotationally and tidally distorted stellar models. Some of his co-workers (Kitamura(33), Ali(34)) also investigated some mathematical properties of the system of Roche Coordinates. Since then several authors such as Mohan and Singh (36), Singh(35), Singh and Gupta(37), Kumar(38) etc. have extensively discussed the system of Roche coor- dinates of equipotential surfaces and applied these methodologies to analyse the vibrations of certain types of distorted stars. The expressions for Roche-coordinates of distorted stellar models developed by them only incorporate the effect of gravitational and centrifugal forces. However, the contribution of coriolis force on the Roche coordinates has not been taken into account while formulating Roche equipotential surface. Pathania (11) modified the expression for Roche equipotentials of rotationally and tidally distorted stellar models by taking into account of coriolis force. He has studied the equi- librium structure and periods of oscillations of rotationally and tidally distorted stars under the influence of gravitational, centrifugal and coriolis forces. But, he has not discussed at all about its Roche coordinates and its related properties . In the present thesis an attempt has been made to develop expressions for the Roche-coordinates and related parameters for Roche equipotential surfaces of stars distorted by rotation and tidal forces earlier discussed by Pathania (11). Chapter wise summary of the work presented in the subsequent chapters of this thesis is as follows: First chapter is introductory in nautre. A brief literature available on this topic is discussed in this chapter. Introduction of general curvilinear coordinate system as well as Roche coordintes have also been briefly discussed in this chapter. In chapter 2, we have obtained the explicit expressions of Roche-coordinates for Roche equipotential surfaces of rotationally and tidally distorted stellar models in which effect of coriolis force has been taken into account in addition to gravitational and centrifugal force. We have also discussed in this chapter how the Roche coordinates of earlier authors can be obtained as a special case who have not considered the effect of force. Chapter 3 deals with the formulation of metric coefficients h1, h2 and h3 which are asso- ciated with the Roche coordinates ξ, η and ζ developed in chapter 2. Certain conclusions based on the present study have finally been drawn in this chapter.