On the Formation of Polar Spots in Sun-like Stars

We simulate the photospheric magnetic field on very active cool stars using a flux injection and surface distribution model with strictly solar parameters, including an 11 yr sunspot cycle and associated butterfly pattern. The only free parameter is the magnitude of the cycle. We demonstrate that the combination of supergranulation-driven dispersal and meridional advection of the field on a very active Sun-like star leads to a strong polar cap field. The polar caps contain so much flux that in comparable environments on the Sun convection is suppressed; it appears inevitable that this leads to the formation of (clusters of) starspots within large unipolar areas that form at high latitudes. The model exhibits a peak total flux in the polar cap regions that is roughly proportional to the cycle amplitude for active regions, 𝒜0, whereas the total absolute flux covering the stellar surface has a significantly weaker than linear dependence on 𝒜0. We find, for example, that for a star with a rotation period of P ~ 6 days, the total absolute flux on the star is ~10 times that characteristic of the active Sun, while the peak polar cap flux is stronger by a factor of ~30. Within the polar caps of such active stars, flux concentrations coagulate to form relatively large clusters. The tendency for larger flux concentrations to disperse more slowly causes the polar cap flux to be concentrated in a more restricted latitude range with increasing activity; the corresponding longitudinally averaged flux density in the polar caps of the simulated star with P ~ 6 days reaches ~300-500 Mx cm-2. The polar cap field in these simulations displays a ring of one polarity at high latitudes around a polar patch of the opposite polarity during much of the spot cycle. This bipolar pattern forms a persistent flux reservoir, so that the cycle modulation of the polar cap flux of an active star is relatively weak, consistent with observations of polar cap spot coverage on active cool stars. Based on these model results, we propose that polar spots are consistent with a dynamo like that of the Sun for a sufficiently enhanced emergence frequency of active regions.