The recent discovery of an Earth-like exoplanet around Proxima Centauri has shined a spot light on slowly rotating fully convective M-stars. When such stars rotate rapidly (period $lesssim 20$ days), they are known to generate very high levels of activity that is powered by a magnetic field much stronger than the solar magnetic field. Recent theoretical efforts are beginning to understand the dynamo process that generates such strong magnetic fields. However, the observational and theoretical landscape remains relatively uncharted for fully convective M-stars that rotate slowly. Here we present an anelastic dynamo simulation designed to mimic some of the physical characteristics of Proxima Centauri, a representative case for slowly rotating fully convective M-stars. The rotating convection spontaneously generates differential rotation in the convection zone which drives coherent magnetic cycles where the axisymmetric magnetic field repeatedly changes polarity at all latitudes as time progress. The typical length of the `activity cycle in the simulation is about nine years, in good agreement with the recently proposed activity cycle length of about seven years for Proxima Centauri. Comparing our results with earlier work, we hypothesis that the dynamo mechanism undergoes a fundamental change in nature as fully convective stars spin down with age.
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