A Study of Anharmonic Pulsation of Rotationally and Tidally Distorted Stars

Abstract

The present thesis deals with the study of investigating the effects of rotation and tidal distortions on the shapes of the radial velocity curves of the pulsating variable stars. Such a study has practical relevance in astrophysics where it is expected to help in better understanding the problems of the shapes of the radial velocity curves of the rotating stars as well as stars in the binary and multiple systems. A lot of work has been done on the problem of determining the equilibrium structures, periods of pulsation of pulsating variable stars and their light curves. However, the concept of anharmonic pulsations has not yet fully explored to understand the observed shape of the radial velocity curves. Most of the studies have included only the fundamental and first two higher modes of oscillations in the equation of anharmonic pulsation expecting that inclusion of higher modes will not substantially change the shape of the radial velocity curve. However, Mohan [42] has found that when higher modes are included in the case of a massive star in helium burning phase the shape of the radial velocity curve gets radically changed. But, after this study no systematic works have been done to check whether this was an isolated phenomenon, specific to that model or it is a general trend. It is well known that in a pulsating star alongwith the radial modes, the nonradial modes of oscillations are also likely to be excited. However, no attempt has been made so far to see how the inclusion of nonradial modes of oscillations in the equation of anharmonic pulsation will affect the shape of the radial velocity curves. Many of the pulsating variable stars are known to be rotating stars as well as stars in binary systems. Extensive study has been done on the problem of determining the effect of rotation and tidal distortion on the periods of oscillations of stellar models. However, the effect of rotation and tidal distortion on the radial velocity curve of such stars has not been investigated in detail. So it will be worthwhile to see how the rotation and tidal effects will affect the shapes of radial velocity curves of certain stellar models. The following objectives have been accomplished in this study: 1. To investigate the effect of inclusion of higher modes of radial oscillations in the equation of anharmonic pulsation and hence to analyze its corresponding effect on the shapes of radial velocity curves of certain theoretical models of stars, representing different types of pulsating variable stars. 2. To study the effect of inclusion of nonradial modes of oscillation in the equation of anharmonic pulsations and hence to analyze the corresponding effect on the shape of radial velocity curve of certain nonradial pulsating stellar models. 3. To determine the effects of rotation and tidal distortions on the shapes of radial velocity curves of certain radial and nonradial stellar models. In the present thesis we have used the anharmonic theory of pulsating stars as proposed by Rosseland [61] and methodology of Prasad [58] to study the anharmonic pulsation of pulsating variable stars. The Mohan and saxena ([44], [45]) approach has been used to incorporate the effects of rotation and tidal distortions in our study. So, in the present work we have considered the possibility of further using Mohan and Saxena ([44], [45]) approach to determine the effects of rotation and tidal distortions on the shapes of radial velocity curves of the radial and non-radial oscillations of the polytropic models of pulsating variable stars using the technique of Rosseland [61] and Prasad [58].