Effects of differential rotation on the eigenfrequencies of small adiabatic barotropic modes of oscillations of polytropic models of stars

Abstract

Mohan et al (1992 Astrophys. Space. Sci. 193 69) (1998 Indian J. Pure Appl. Math. 29 199) investigated the problem of equilibrium structures and periods of small adiabatic oscillations of differentially rotating stellar models using a law of differential rotation of the type ω2 = b0 + b1s2 + b2s4 (here ω is a nondimensional measure of the angular velocity of rotation of a fluid element at a distance s from the axis of rotation and b′s are suitably chosen constant parameters). This law of differential rotation assumes cylindrical symmetry for the rotating fluid elements. In the present paper, we have extended their study and used a more general law of differential rotation of the type ω2 = b0 + b1s2 + b2s4 + b3z2 + b4z4 + b5z2s2 in which the angular velocity of rotation of a fluid element is assumed to depend both on its distance s from the axis of rotation and on its distance z from the plane through the center of the star perpendicular to the axis of rotation. The main objective of this study has been to investigate whether the dependence of angular velocity of rotation on the parameter z in addition to the parameter s substantially alters the behavior of the eigenfrequencies of small adiabatic barotropic modes of oscillations of differentially rotating stars or not.