A new simple dynamo model for stellar activity cycle

TL;DR

This paper introduces a simplified dynamo model for stellar activity cycles that incorporates turbulent cross helicity, offering new insights into magnetic field reversals and stellar magnetic activity through coupled evolution equations.

Contribution

The model uniquely includes the cross-helicity effect as a key dynamo ingredient and solves its evolution alongside magnetic fields, differing from traditional alpha-Omega models.

Findings

Eigenvalue analysis produces a butterfly diagram consistent with observations.

The model shows cross helicity oscillation as a driver of magnetic field reversals.

Results suggest cross helicity reversal causes magnetic activity cycles.

Abstract

A new simple dynamo model for stellar activity cycle is proposed. By considering an inhomogeneous mean flow effect on turbulence, it is shown that turbulent cross helicity (velocity--magnetic-field correlation) should enter the expression of turbulent electromotive force as the coupling coefficient for the mean absolute vorticity. The inclusion of the cross-helicity effect makes the present model different from the current $\alpha$--$\Omega$-type models mainly in two points. First, in addition to the usual $\alpha$ (helicity effect) and $\beta$ (turbulent magnetic diffusivity), we consider the $\gamma$ coefficient (cross-helicity effect) as a key ingredient of the dynamo process. Second, unlike the $\alpha$ and $\beta$ coefficients, which are often treated as an adjustable parameter in the current studies, the spatiotemporal evolution of $\gamma$ coefficient is solved simultaneously with the mean magnetic-field equations. The basic scenario is as follows: In the presence of turbulent cross helicity, the toroidal field is induced by the toroidal rotation in mediation by the turbulent cross helicity. The $\alpha$ effect generates the poloidal field from the toroidal one. This poloidal field produces a turbulent cross helicity whose sign is opposite to the original one. Then a cycle of reversal completes. Eigenvalue analyses of the simplest possible present model give a butterfly diagram, which confirms the above scenario as well as the equator-ward migrations, the phase relationship between the cross helicity and magnetic fields, etc. These results suggest that the oscillation of the turbulent cross helicity is a key for the activity cycle. The reversal of the turbulent cross helicity is not the result of the magnetic-field reversal, but the cause of the latter. This new model is expected to open up the possibility of the mean-field or turbulence closure dynamo approaches.