Steady low-frequency oscillations in electromagnetic polytropic star. 1. Differential rotation of the Sun

A. A. Bobnev

Abstract
The steady-state (quasi-stationary) solutions for an electromagnetic star in the approximation of an ideally conducting perfect polytropic gas are divided into 4 types. Types 3 and 4 are studied in detail, where the j-component of the strength of a magnetic field are of the same order of magnitude as its polhodal components. In case of the low-frequency steady state oscillations the processes within the internal layers of a star can be described by means of the quasi-stationary solutions, which are non-uniformly applicable along the radius of a star; the region of nonuniformity (low-frequency boundary layer) is localised in the proximity of the surface of a star. A more general problem of the low-frequency boundary layer is stated as well as some solutions of the problem are devised, where the angular velocity of rotation is of the same order of magnitude as the frequency of oscillations. The cases are considered, where the angular velocity is much higher than the frequency of oscillations. In order to solve the problem of nonuniqueness two principles are proposed: the principle of a minimum of the surface electromagnetic energy over the period of oscillations and the principle of a minimum of the volumetric kinetic energy. The influence of characteristics of the differential rotation as well as of other quantities upon the parameters of the problem are established. Temporal and spatial symmetry of properties of solutions are observed which exhibit general differences within internal regions, as well as at the surface of a star; the accuracy of symmetry of solutions is determined as a function of a small parameter. It is noted that the frequency of oscillations of nonelectromagnetic quantities exceeds that of electromagnetic quantities by a factor of 2. Figs 14, Refs 11.