The missing magnetic morphology term in stellar rotation evolution (Research Note)

Aims. This study examines the relationship between magnetic field complexity and mass and angular momentum losses. Observations of open clusters have revealed a bimodal distribution of the rotation periods of solar-like stars that has proven difficult to explain under the existing rubric of magnetic braking. Recent studies suggest that magnetic complexity can play an important role in controlling stellar spin-down rates. However, magnetic morphology is still neglected in most rotation evolution models due to the difficulty of properly accounting for its effects on wind driving and angular momentum loss. Methods. Using state-of-the-art magnetohydrodynamical magnetized wind simulations we study the effect that different distributions of the magnetic flux at different levels of geometrical complexity have on mass and angular momentum loss rates. Results. Angular momentum loss rates depend strongly on the level of complexity of the field but are independent of the way this complexity is distributed. We deduce the analytical terms representing the magnetic field morphology dependence of mass and angular momentum loss rates. We also define a parameter that best represents complexity for real stars. As a test, we use these analytical methods to estimate mass and angular momentum loss rates for 8 stars with observed magnetograms and compare them to the simulated results. Conclusions. Magnetic field complexity provides a natural physical basis for stellar rotation evolution models requiring a rapid transition between weak and strong spin-down modes.