Abstract
Eigen-frequencies (EF) of non–radial modes (NRM) of pulsations of differentially rotating (D R) and tidally distorted (T D) stellar models by considering the effect of mass variation (MV) on its equi-potentials surfaces inside a star. The method utilizes an averaging proposal of Kippenhahn and Thomas (K and T) with conjunction of the concept of Roche-equipotential. The study accolades and corrects earlier studies of non-radial (NR) pulsations of DR and TD stellar structures of different natures such as radial and non-radial oscillations, X-ray, gamma ray and other electromagnetic disturbances. The reflection of the work comes from the requirements of the inclusion of non-uniform densities that yield Lane-Emden equation to have reliable results up to second order disturbances.
Highlights
Observations have shown that pulsars are suffered by different types of mechanical perversions, such as differential rotation, vibrations, non-uniform densities inside, along their lifetime in order to reproduce X ray, gamma-ray, different types of waves and other electromagnetic perturbations Glendenning (2012)
The analysis of oscillations spectrum provides an unrivaled method for probing the stellar structure because the frequencies of these pulsations depends upon the sound speed inside the star, which in turn depends on the density, temperature, gas motion and other properties of stellar interior
The results based on this study show that the assortment patterns of NR modes of pulsations of the gaseous spheres having mass variation, are similar to the assortment pattern of NR pulsations of same models having constant densities
Summary
Observations have shown that pulsars are suffered by different types of mechanical perversions, such as differential rotation, vibrations, non-uniform densities inside, along their lifetime in order to reproduce X ray, gamma-ray, different types of waves and other electromagnetic perturbations Glendenning (2012). Analytic study of the problem of determining the equilibrium structures, periods of pulsations and stability of rotationally and tidally (RT) distorted stellar models is quite complex. It will become more complex, if the rotation is differential. Most of the authors such as, Mohan et al (1991) formulated EF of NRM of pulsations of rotationally and tidally (R and T) distorted stellar models. It was applied initially only to polytropic equation of state, and some years later to more realistic pulsars Several authors such as Yojisoki (1986), Chandrasekhar and Ferrari (1991) have made significant contributions to the studies of the problems of NR pulsations of stars. Notation Non dimensional eigenfunctions Pressure and density on equi-potentials surfaces Total potential (EF of pulsations) AQN(azimuthal quantum number) gravitational constant density at centre
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