Investigating the variation of latitudinal stellar spot rotation and its relation to the real stellar surface rotation

Aims. In this work the latitude-dependent stellar spot rotation is investigated based on dynamo models, and with similar analysis techniques as for real observations. The resulting surface differential rotation patterns are compared to the known input rotation law used in the calculation of the dynamo model. Methods. Snapshots of the dynamo simulations are used to measure the surface differential rotation. The maps of the magnetic pressure at the surface are treated similarly to the temperature maps obtained using Doppler imaging techniques, and a series of snapshots from the dynamo models are cross-correlated to obtain the shift of the magnetic patterns at each latitude and time point. These shifts are used to study the surface rotation pattern over a wide latitude range at different epochs during the activity cycle, and are compared to the known input rotation law. Results. Two different rotation laws are investigated, one solar-type law and one with axis-distance-dependent rotation. Three different dynamo calculations are carried out based on the axis-distance-dependent law: one with a large-scale dynamo field only, one with an additional strong small-scale field and one with a weaker small-scale field. The surface differential rotation patterns obtained from the snapshots of all four dynamo calculations show variability over the activity cycle. Clear evolution and variation in the measured surface rotation patterns is seen, but in the models using only the large-scale dynamo field the measured rotation patterns are only at times similar to the input rotation law. This is because the spot motion is mainly determined by the geometric properties of the large-scale dynamo field. In the models with an additional small-scale magnetic field the surface differential rotation measured from the model follows the input rotation law well. Conclusions. Here, the surface differential rotation patterns are investigated in detail based on dynamo calculations for the first time. The results imply that the stellar spots caused by the large-scale dynamo field are not necessarily tracing the stellar differential rotation, whereas the spots formed from small-scale fields trace the surface flow patterns well. One may wonder whether the large spots observed in active stars could be caused by small-scale fields. Therefore, it is still unclear if the true stellar surface rotation can be recovered using measurements of large starspots, which are currently the only observable feature