Asymptotic dynamos in late-type stars

Abstract

The behaviour of a simple thin-shell α‐� dynamo model is considered in the asymptotic regime, characterized by dynamo numbers much larger than the critical ones, in order to derive scaling relationships connecting the properties of dynamo waves with global stellar parameters. The proposed approach is applied to stellar models of subgiant and giant stars from K0IV to K1III spectral types in the Hertzsprung‐Russell diagram, to predict some characteristics of activity cycles in very active stars. We found that the strength of the dynamo action in such stars is higher than in the Sun. Therefore, larger magnetic field energy and larger spot filling factors are expected, in agreement with observations. The periods of stellar cycles are also estimated and compared with observations. The characteristic times of migration of the star-spot belts relative to the cycle period, namely the Hale number, together with the ratio of toroidal to poloidal dynamo magnetic fields are estimated. From our simplified analysis we can only derive general trends, but cannot perform a direct comparison with the observed properties of particular active stars. These general trends indicate that the cycle periods have a large spread for stars with low rotation rates (∼1‐5 times the solar one), while they tend to be saturated for stars with high rotation rates (∼5‐15 times solar), for which the periods range from 10 to 20 yr. For such stars, Hale numbers range from 1.5 to approximately 4 (the Hale number for the Sun is approximately 1.1), denoting the possible existence of cycles with different periodicities present simultaneously, the ratio of toroidal to poloidal dynamo fields tends to become smaller for increasing rotation rates, indicating a transition from the α‐� to the α 2 ‐� type of dynamo. Moreover, the magnetic field filling factors tend to become larger for faster rotation rates, though the effect of the convection zone depth should not be neglected. Our results show a reasonable agreement with available observations of a sample of active stars we have considered.