  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).

Solar and Stellar Astrophysics