The Effect of Combined Magnetic Geometries on Thermally Driven Winds I: Interaction of Dipolar and Quadrupolar Fields

Abstract

Cool stars with outer convective envelopes are observed to have magnetic fields with a variety of geometries, which on large scales are dominated by a combination of the lowest order fi elds such as the dipole, quadrupole and octupole modes. Magnetised stellar wind outflows are primarily responsible for the loss of angular momentum from these objects during the main sequence. Previous works have shown the reduced effectiveness of the stellar wind braking mechanism with increasingly complex, but singular, magnetic field geometries. In this paper, we quantify the impact of mixed dipolar and quadrupolar fi elds on the spin-down torque using 50 MHD simulations with mixed field, along with 10 of each pure geometries. The simulated winds include a wide range of magnetic fi eld strength and reside in the slow-rotator regime. We fi nd that the stellar wind braking torque from our combined geometry cases are well described by a broken power law behaviour, where the torque scaling with fi eld strength can be predicted by the dipole component alone or the quadrupolar scaling utilising the total field strength. The simulation results can be scaled and apply to all main-sequence cool stars. For Solar parameters, the lowest order component of the fi eld (dipole in this paper) is the most signi ficant in determining the angular momentum loss.