Oscillations of differentially rotating and tidally distorted gaseous spheres : Effect of non-uniform density

The original Strum-Liouville type of equation is tuned suitably to study the pulsational properties of gaseous spheres of non-uniform densities from centre to surface, which are non-rotating, have solid body rotation or are differentially rotating as well as those which are varying by tidal effects. The eign-frequencies of radial oscillations have been computed numerically for certain polytropic stellar models of non-uniform densities. In order to analyse the effect of non-radial modes of oscillations, the linearised system of differential equations that govern non-radial modes of oscillations, have also been developed and solved for certain polytropic models. It has been observed that with the exception of purely radial oscillations, which are unstable only when gamma < 4/3 (gamma is the ratio of molar specific heats), there also exist non-radial modes of oscillations. It is necessary to consider radial as well as non-radial nodes of oscillations in order to ascertain the stabilities of the existence of any assumed model.