Turbulent Diffusion in the Photosphere as Derived from Photospheric Bright Point Motion

On the basis of observations of solar granulation obtained with the New Solar Telescope (NST) of Big Bear Solar Observatory, we explored proper motion of bright points (BPs) in a quiet sun area, a coronal hole, and an active region plage. We automatically detected and traced bright points (BPs) and derived their mean-squared displacements as a function of time (starting from the appearance of each BP) for all available time intervals. In all three magnetic environments, we found the presence of a super-diffusion regime, which is the most pronounced inside the time interval of 10-300 seconds. Super-diffusion, measured via the spectral index, $gamma$, which is the slope of the mean-squared displacement spectrum, increases from the plage area ($gamma=1.48$) to the quiet sun area ($gamma=1.53$) to the coronal hole ($gamma=1.67$). We also found that the coefficient of turbulent diffusion changes in direct proportion to both temporal and spatial scales. For the minimum spatial scale (22 km) and minimum time scale (10 sec), it is 22 and 19 km$^{2}$ s$^{-1}$ for the coronal hole and the quiet sun area, respectively, whereas for the plage area it is about 12 km$^{2}$ s$^{-1}$ for the minimum time scale of 15 seconds. We applied our BP tracking code to 3D MHD model data of solar convection (Stein et al. 2007) and found the super-diffusion with $gamma=1.45$. An expression for the turbulent diffusion coefficient as a function of scales and $gamma$ is obtained.