Rotational threshold in global numerical dynamo simulations

TL;DR

This study investigates how magnetic field strength in global numerical dynamo models depends on rotation rate, revealing a threshold (Rossby number 0.1) where dynamo efficiency saturates, which may explain observed stellar activity patterns.

Contribution

It identifies a rotational threshold affecting dynamo efficiency in numerical models, linking magnetic field strength to rotation and providing insights into stellar magnetic activity.

Findings

Dynamo efficiency increases with rotation up to a Rossby number of 0.1.

Above Rossby number 0.1, field strength shows no systematic dependence on rotation.

The efficiency gain is related to the rotational dependence of the mean electromotive force.

Abstract

Magnetic field observations of low-mass stars reveal an increase of magnetic activity with increasing rotation rate. The so-called activity-rotation relation is usually attributed to changes in the underlying dynamo processes generating the magnetic field. We examine the dependence of the field strength on rotation in global numerical dynamo models and interpret our results on the basis of energy considerations. In agreement with the scaling law proposed by Christensen & Aubert (2006), the field strength in our simulations is set by the fraction of the available power used for the magnetic field generation. This is controlled by the dynamo efficiency calculated as the ratio of Ohmic to total dissipation in our models. The dynamo efficiency grows strongly with increasing rotation rate at a Rossby number of 0.1 until it reaches its upper bound of one and becomes independent of rotation. This gain in efficiency is related to the strong rotational dependence of the mean electromotive force in this parameter regime. For multipolar models at Rossby numbers clearly larger than 0.1, on the other hand, we do not find a systematic dependence of the field strength on rotation. Whether the enhancement of the dynamo efficiency found in our dipolar models explains the observed activity-rotation relation needs to be further assessed.