Do non-dipolar magnetic fields contribute to spin-down torques?

TL;DR

This study investigates whether non-dipolar magnetic field components significantly influence the spin-down torques of low-mass stars, finding that dipolar fields generally dominate unless mass-loss rates are high, with some evidence of non-dipolar contributions at large Rossby numbers.

Contribution

It introduces a method to determine when non-dipolar magnetic modes contribute to stellar spin-down based on mass-loss rates and magnetic field geometry.

Findings

Most stars' mass-loss rates are below the critical threshold, so dipolar fields suffice for spin-down calculations.

Some stars at large Rossby numbers show potential non-dipolar contributions.

The critical mass-loss rate depends on the magnetic field geometry.

Abstract

Main sequence low-mass stars are known to spin-down as a consequence of their magnetised stellar winds. However, estimating the precise rate of this spin-down is an open problem. The mass-loss rate, angular momentum-loss rate and the magnetic field properties of low-mass stars are fundamentally linked making this a challenging task. Of particular interest is the stellar magnetic field geometry. In this work, we consider whether non-dipolar field modes contribute significantly to the spin-down of low-mass stars. We do this using a sample of stars that have all been previously mapped with Zeeman-Doppler imaging. For a given star, as long as its mass-loss rate is below some critical mass-loss rate, only the dipolar fields contribute to its spin-down torque. However, if it has a larger mass-loss rate, higher order modes need to be considered. For each star, we calculate this critical mass-loss rate, which is a simple function of the field geometry. Additionally, we use two methods of estimating mass-loss rates for our sample of stars. In the majority of cases, we find that the estimated mass-loss rates do not exceed the critical mass-loss rate and hence, the dipolar magnetic field alone is sufficient to determine the spin-down torque. However, we find some evidence that, at large Rossby numbers, non-dipolar modes may start to contribute.