How supercritical are stellar dynamos, or why do old main-sequence dwarfs not obey gyrochronology?

Asteroseismological determinations of stellar ages have shown that old main-sequence dwarfs do not obey gyrochronology. Their rotation is slow compared to young stars but faster than gyrochronology predicts. This can be explained by the presence of a maximum rotation period beyond which the large-scale dynamo switches off and stops providing global magnetic fields necessary for stellar spindown. Assuming this explanation, the excess of stellar dynamo parameters over their marginal values can be estimated for given spectral type and rotation rate. The estimation gives the dynamo number for the Sun about 10% above its critical value. The corresponding dynamo model provides - though with some further tuning - reasonable results for the Sun. Following the same approach, the differential rotation and marginal dynamo modes are computed for stars between 0.7 and 1.2 solar masses. With increasing stellar mass, the differential rotation and the ratio of toroidal-to-poloidal field are predicted to increase while the field topology changes from dipolar to mixed quadrupolar-dipolar parity.