OSCILLATIONS OF ROTATIONALLY AND TIDALLY DISTORTED GASEOUS SPHERES

Abstract

The present thesis deals with the problems of small oscillations of rotationally and tidally distorted gaseous spheres. Oscillations of rotationally and tidally distorted gaseous spheres have importance in Astrophysics. Observations have shown that there are many stars which are rotating about their axes. The theoretical models of such rotating stars can be considered to be rotationally distorted gaseous spheres. Also many stars have been observed to exist in binary pairs. These stellar pairs are observed to be rotating about their axes as well as revolving about the common centre of gravity of the system. Because of the gravitational pull of the companion and because of the effect of rotation, the stellar models of stars in such systems get distorted by the tidal and rotational effects. Some of the rotating stars as well as stars in binary pairs have been observed to exhibit light variations which are supposed to be due to their small oscillations. In order to understand the observed phenomena of such variable stars as well as to understand the problems of the stability of rotating stars and stars in binary systems it is necessary to investigate the theoretical problem of small oscillations of rotationally and tidally distorted gaseous spheres. An attempt has been made in the present thesis to study these problems to some extent. 11 The whole thesis comprises of eight chapters . The first chapter is introductory in nature. Besides stressing the astrophysical importance of the problems of small oscillations of rotationally and tidally distorted gaseous spheres, a brief review of the work done in literature in this direction has been presented in this chapter. A brief summary of the work done in succeeding chapters also appears in this chapter. Chapter two of the thesis is devoted to the analytical study of the system of Roche coordinates. In chapters third and fourth the problems of small oscillations of rotationally distorted gaseous spheres undergoing solid body rotation and differential rotation have respectively been presented. Chapters fifth and sixth deal with the tidally distorted gaseous spheres taking respectively first and second order effects of tidal distortion into consideration. Chapter seven is devoted to the study of the combined effect of rotational and tidal forces on the problem of small of oscillations of such spheres. The numerical results from chapter third to chapter seven have been tabulated in each chapter. Chapter eight discusses these results and gives the conclusions drawn from them. The contents of chapter III and V were presented in the form of two papers in Annual Scientific Meetings of Astronomical Society of India and National Academy of Sciences, Allahabad, held in Nov.1976 at Nainital and Ill • Feb. 1977 at Delhi University respectively. The contents of these two chapters have also been accepted for publication in the form of two papers in the International Journal of Astrophysics and Space Science, published by D.Reidel publishing company,Holland. The first of these is being published in Vol.54 part 2 (April 1978) and the second in Vol.56 part 1 (June 1978). The contents of chapter VI have been recently submitted for publication to the same Journal. The contents of chapter IV have been accepted for publication in the Journal of National Academy of Sciences, Allahabad. The contents of chapter VII will be submitted for publication shortly.