The influence of the magnetic topology on the braking of sun-like stars

TL;DR

This study investigates how different magnetic topologies of sun-like stars influence stellar wind braking, providing a universal torque law based on open magnetic flux applicable to various magnetic configurations.

Contribution

It introduces a new torque formulation that accounts for quadrupolar and octupolar magnetic fields, extending previous models limited to dipolar topologies.

Findings

Developed a universal torque law based on open magnetic flux.

Validated the law with simulations of different magnetic topologies.

Applied the law to real stellar magnetic data from the Sun and a young K-star.

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). Ideas about how to compute the open flux from ZDI Maps are discussed.