The rotation of photospheric magnetic fields: A random walk transport model

In an earlier study of solar differential rotation, we showed that the transport of magnetic flux across latitudes acts to establish quasi-stationary patterns, therby accounting for the observed rigid rotation of the large-scale photospheric field. In that paper, the effect of supergranular convection was represented by a continuum diffusion, limiting the applicability of the calculations to large spatial scales. Here we extend the model to scales comparable to that of the supergranulation itself by replacing the diffusive transport with a discrete random walk process. Rotation curves are derived by cross-correlating the simulated photospheric field maps for a variety of time lags and spatial resolutions. When the lag between maps is relatively short less than or approximately = 15 days), the midlatitude correlation functions show two distinct components: a broad feature associated with the large-scale unipolar patterns and a narrow feature originating from small magnetic structures encompossing from one to several supergranular cells. By fitting the broad component we obtain the rigid rotation profile of the patterns, whereas by fitting the narrow component, we recover the differential rate of the photospheric plasma itself. For time lags of 1 month or greater, only the broad feature associated with the long-lived patterns remains clearly identifiable in the simulations.