Cycle period, differential rotation, and meridional flow for early M dwarf stars

Recent observations suggest the existence of two characteristic cycle times for early-type M stars dependent on the rotation period. They are of order one year for the fast rotators ($P_{\rm rot}<1$ day) and of order 4 years for the slower rotators. Additionally, the equator-to-pole differences of the rotation rates with $\delta\Omega$ up to 0.03 rad d$^{-1}$ are known from Kepler data for the fast-rotating stars. These values are well-reproduced by the theory of large-scale flows in rotating convection zones on the basis of the $\Lambda$ effect. The resulting amplitudes $u^{\rm m}$ of the bottom value of the meridional circulation allows the calculation of the travel time from pole to equator at the base of the convection zone of early-type M stars. These travel times strongly increase with rotation period and they always exceed the observed cycle periods. Therefore, the operation of an advection-dominated dynamo in early M dwarfs, where the travel time must always be shorter than the cycle period, is not confirmed by our model nor the data.