Dispersal of magnetic flux in the quiet solar photosphere

We study the random walk of magnetic flux concentrations on two sequences of high-resolution magnetograms, observed with the Michelson Doppler Imager on board SOHO. The flux contained in the concentrations ranges from \Phi\ = 10(18) Mr to \Phi\ = 10(19) Mr, with an average of \Phi\ = 2.5 x 10(18) Mr. Larger concentrations tend to move slower and live longer than smaller ones. On short timescales, the observed mean-square displacements are consistent with a random walk, characterized by a diffusion coefficient D(t < 10 ks)= 70 - 90 km(2) s(-1). On longer timescales, the diffusion coefficient increases to D(t > 30 ks)= 200-250 km(2) s(-1), approaching the measurements for a five-day set of Big Bear magnetograms, D similar or equal to 250 km(2) s(-1). The transition between the low and large diffusion coefficients is explained with a model and simulations of the motions of test particles, subject to random displacements on both the granular and supergranular scales, simultaneously. In this model, the supergranular flow acts as a negligible drift on short timescale, but dominates the granular diffusion on longer timescales. We also investigate the possibility that concentrations are temporarily confined, as if they were caught in supergranular vertices, that form short-lived, relatively stable environments. The best agreement of model and data is found for step lengths of 0.5 and 8.5 Mm, associated evolution times of 14 minutes and 24 hr, and a cofinement time of no more than a few hours. On our longest timescale, D-Sim(t > 10(5)) --> 285 km(2) s(-1), which is the sum of the small- and large-scale diffusion coefficients. Models of random walk diffusion on the solar surface require a larger value: D-Wang = 600 +/- 200 km(2) s(-1). One possible explanation for the difference is a bias in our measurements to the longest lived, and therefore slower concentrations in our data sets. Another possibility is the presence of an additional, much larger diffusive scale.