Magnetic fields of low-mass main sequences stars: Nonlinear dynamo theory and mean-field numerical simulations

Abstract

Our theoretical and numerical analysis have suggested that for low-mass main sequences stars (of the spectral classes from M5 to G0) rotating much faster than the Sun, the generated large-scale magnetic field is caused by the mean-field ${\alpha }^2\Omega$ dynamo, whereby the ${\alpha }^2$ dynamo is modified by a weak differential rotation. Even for a weak differential rotation, the behaviour of the magnetic activity is changed drastically from aperiodic regime to non-linear oscillations and appearance of a chaotic behaviour with increase of the differential rotation. Periods of the magnetic cycles decrease with increase of the differential rotation, and they vary from tens to thousand years. This long-term behaviour of the magnetic cycles may be related to the characteristic time of the evolution of the magnetic helicity density of the small-scale field. The performed analysis is based on the mean-field simulations (MFS) of the ${\alpha }^2\Omega$ and ${\alpha }^2$ dynamos and a developed non-linear theory of ${\alpha }^2$ dynamo. The applied MFS model was calibrated using turbulent parameters typical for the solar convective zone.

arXiv comment14 pages, final version

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