No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Е А Михайлов ,Daniela Boneva,M V Pashentseva

doi:10.3390/data6010004

Abstract

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

Highlights

Magnetic fields play an important role for different astrophysical objects and have a large influence on various physical processes
If we are speaking about the accretion discs surrounding neutron stars, black holes and white dwarfs, the magnetic field can describe the transition of the angular momentum between different parts of the disc [4]
We show the stability of the solution for concrete cases connected with the accretion discs

Summary

Introduction

Magnetic fields play an important role for different astrophysical objects and have a large influence on various physical processes. The first one is connected with the so-called Zeeman effect It describes the splitting of the spectral lines, which is based on the influence of the magnetic field on the atoms in the cosmic medium. If the wave passes through the magnetized medium, the rotation angle is proportional to the value of the magnetic field, squared wavelength and the electron density It is the basic method of studying the magnetic fields in the galaxies [8] and other celestial objects. One of the most important results have been obtained by the CHANG-ES project, which give the calculations of the magnetic field based on the Faraday rotation data for 13 galaxies [9]. We discuss the magnetic fields in other astrophysical objects, such as the galaxies which have quite similar shape of the disc

Basic Equations of the No-z Approximation

Stable Solutions of the Equations

Stability for the Kepler Rotation Curve

Conclusions