The effect of magnetic topology on thermally-driven winds: towards a general formulation of the braking law

TL;DR

This study develops a unified formulation for stellar wind torque that accounts for various magnetic topologies, including dipolar, quadrupolar, and octupolar, by relating it to the open magnetic flux, improving understanding of stellar spin-down mechanisms.

Contribution

The paper introduces a universal torque law for stellar winds applicable to multiple magnetic topologies, validated through extensive simulations and observational data.

Findings

A single torque law fits all tested magnetic topologies.

The torque correlates with the open magnetic flux in the wind.

The formulation applies to realistic stellar magnetic configurations.

Abstract

Stellar winds are thought to be the main process responsible for the spin down of main-sequence stars. The extraction of angular momentum by a magnetized wind has been studied for decades, leading to several formulations for the resulting torque. However, previous studies generally consider simple dipole or split monopole stellar magnetic topologies. Here we consider in addition to a dipolar stellar magnetic field, both quadrupolar and octupolar configurations, while also varying the rotation rate and the magnetic field strength. 60 simulations made with a 2.5D, cylindrical and axisymmetric set-up and computed with the PLUTO code were used to find torque formulations for each topology. We further succeed to give a unique law that fits the data for every topology by formulating the torque in terms of the amount of open magnetic flux in the wind. We also show that our formulation can be applied to even more realistic magnetic topologies, with examples of the Sun in its minimum and maximum phase as observed at the Wilcox Solar Observatory, and of a young K-star (TYC-0486- 4943-1) whose topology has been obtained by Zeeman-Doppler Imaging (ZDI).