Dynamic equilibrium and oscillations of stars with uneven mass of particles of the medium

Abstract

Background. The study examines a model of the structure and evolution of stars in dynamic equilibrium, supplemented by a new analysis of the zonal flow velocity, new elements for describing the evolution of the heat flow, and the introduction of unequal particle mass. The purpose of the work is to describe a modified model of the structure of stars under conditions of dynamic equilibrium and their oscillations, in which the problem with the peculiarity of the zonal flow on the rotation axis is eliminated. The model is also generalized by introducing into it the coefficient of particle massiveness. Materials and methods. To derive and analyze the equations of dynamic equilibrium of stars, the method of hydrodynamic markers or Lagrangian variables is used, supplemented by a new interpretation of the gravitational field parameters using marker fields. To describe the thermal properties of the medium, the assumption of quasi-adiabatic processes in stars is used. Results. In this work, generalized equations for the structure and evolution of stars in dynamic equilibrium are obtained as a general type of equilibrium. The model considers the zonal flow, which describes the differential rotation of stars, the separate influence of thermal processes on the zonal flow and the distribution of temperature and density in the star, as well as the inhomogeneous distribution of particle mass, which is associated with the inhomogeneous distribution of the nuclei of chemical elements inside stars. Within the framework of the model, general relations are obtained for the distribution of the local angular velocity of the zonal flow. General factors influencing the behavior of the light curve of stars under dynamic equilibrium conditions have been identified. Period-luminosity diagrams were obtained in analytical form. The obtained relationships make it possible to refine the model of 11-year solar oscillations constructed in [1]. Conclusions. The proposed model can be used as a basic model for describing pulsating stars of various types.

Keywords

• dynamic equilibrium
• stellar structure
• nonlinear oscillations of stars
• differential rotation
• light curves
• period-luminosity diagrams