Evolution of the Total Magnetic and Kinetic Energy in the Convective Zone of a Star

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Abstract

Qualitative estimates of the dynamics of the stellar convective zone as a whole are useful either when observation - data on a star are scares or as a preliminary step before constructing a more complex model that requires complicated computations. In this work, we present a qualitative model that describes the evolution of the mean square values of the velocity and magnetic field in the convective zone of a Sun-like star. The stability of possible equilibrium values of the mean squares of velocity and magnetic field is investigated. Solutions of the model equations are obtained for different values of buoyancy and the ratio of the convection and magnetic field timescales. It is shown that the following scenarios are possible: 1) the magnetic field increases starting from an arbitrary small initial value; 2) the magnetic field vanishes being initially finite; 3) the velocity and magnetic-field behavior in the vicinity of the stationary values and far from them can differ significantly. The amplification/decay of the mean-square magnetic field does not depend on the initial conditions, but is determined solely by the parameters of the stellar convective zone. The parameters of the Sun’s convective zone correspond to a boundary case between scenarios 1 and 2, and their small changes can lead to different outcomes.

About the authors

R. A. Kislov

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation

Email: kr-rk@bk.ru
Troitsk, Moscow, Russia

S. V. Starchenko

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation

Email: sstarchenko@mail.ru
Troitsk, Moscow, Russia

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