Anharmonic and standing dynamo waves: theory and observation of stellar magnetic activity

The familiar decadal cycle of solar activity is one expression of interannual variability of surface magnetism observed in stars on or near the lower main sequence. From studies of time-series of Ca II H and K emission fluxes that go back more than 35 yr and have been accumulated for such stars at the Mount Wilson Observatory by the HK Project, we define a quantitative measure, called anharmonicity, of the cyclic component of interannual magnetic variability. Anharmonicity provides a connection between observed variations in magnetic activity and the two-dimensional description of a Parker dynamo model. We explore the parameter space of the Parker dynamo model and find an excellent counterpart in the records of several of the lowest-mass (late K-type to early M-type) active stars in the HK Project sample to the solutions containing highly anharmonic, standing dynamo waves. We interpret anharmonicity apparent in the records as resulting from non-propagating or standing dynamo waves, which operate in a regime that is substantially supercriticial. There, for the majority of a cycle, or pulse of decadal-to-interdecadal variability, the large-scale magnetic fields are generated and maintained by winding of field by differential rotation rather than by the joint action of differential rotation and helical convection. Among the less active stars (the Sun is considered such a star in the HK Project sample) we find a correspondence between anharmonicity and Parker dynamo model solutions that include simple harmonic, migratory and/or intermediate-type dynamo wave patterns over a broad range of dynamo parameters.