2017ApJ...845...46F

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 fields such as the dipole, quadrupole, and octupole modes. Magnetized 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 fields on the spin-down torque using 50 MHD simulations with mixed fields, along with 10 each of the pure geometries. The simulated winds include a wide range of magnetic field strength and reside in the slow-rotator regime. We find that the stellar wind braking torque from our combined geometry cases is well described by a broken power-law behavior, where the torque scaling with field strength can be predicted by the dipole component alone or the quadrupolar scaling utilizing 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 field (dipole in this paper) is the most significant in determining the angular momentum loss.