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

Evgeny Mikhailov, Daniela Boneva and Maria Pashentseva
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Evgeny Mikhailov: Faculty of Physics, M.V. Lomonosov Moscow State University, Leninskie Gori 1-2, 119991 Moscow, Russia
Daniela Boneva: Space Research and Technology Institute, Bulgarian Academy of Sciences, Acad. Georgy Bonchev St., bl. 1, 1113 Sofia, Bulgaria
Maria Pashentseva: Faculty of Physics, M.V. Lomonosov Moscow State University, Leninskie Gori 1-2, 119991 Moscow, Russia

Data, 2021, vol. 6, issue 1, 1-11

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.

Keywords: dynamo; no- z approximation; stability; discs (search for similar items in EconPapers)
JEL-codes: C8 C80 C81 C82 C83 (search for similar items in EconPapers)
Date: 2021
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