Kinematic models of supergranular diffusion on the Sun

We develop kinematic models of diffusion generated by supergranulation at the solar surface. These models use current observations for the size, horizontal velocity, and lifetime of supergranules. Because there is no observational description of the appearance and disappearance of supergranules, we investigate models using several plausible evolution processes, including the effect of different lifetime distribution functions for the cells. The results are quite insensitive to the methods chosen to replace old supergranules, the distribution of cell lifetimes, and even the cell lifetime itself, for mean lifetimes between 15 to 30 hr. Calculated diffusion coefficients range between 500 and 700 sq km/s, in agreement with the best fit diffusion coefficients used by Sheeley and his collaborators to model the large-scale distribution of magnetic fields over the solar surface. However, our models do not explain the field distribution in plage, and they predict that virtually all the strong field in quiet Sun exists in relatively isolated clumps. We suggest possible mechanisms for the creation of plage and the bright network seen in quiet Sun.