Small adiabatic barotropic non-radial modes of oscillations of differentially rotating stars

Abstract

In this paper the approach of Mohan and Saxena (for instance see : C. Mohan and R. M. Saxena; Effect of rotation and tidal distortion on the periods of small adiabatic oscillations of the polytropic models, Astrophys. & Space Sci., 85, 1983 ) using the averaging technique of Kippenhahn and Thomas (for instance see : R. Kippenhahn and H. C. Thomas, A simple method for the solution of the stellar structure equations including rotation and tidal forces : Stellar Rotation, 1970) in conjunction with Kopal's method (The Roche models and its applications to close binary system) of evaluating various parameters on a Roche- equipotential has been used for computing the eigenfrequencies of small adiabatic barotropic nonradial modes of oscillations of differentially rotating (DR) polytropic stars. It is assumed that stellar models are rotating according to the law of differential rotation ω=∑i=13aie−bis2. Here ω is the angular velocity of rotation of a fluid element situated at distance s from the axis of rotation. ai and bi are some numerical constants. This method utilizes Kippenhahn and Thomas approach and the concepts of Roche-equipotential to incorporated with the effects of differential rotation.