1. Valentina Abramenko 1, Vasyl Yurchyshyn 1, Philip R. Goode 1, Vincenzo Carbone 2, Robert Stein 3 1 - Big Bear Solar Observatory of NJIT, USA; 2 – Univ. della Calabria, Italy; 3 – Michigan State Univ, USA Super-Diffusivity in the Quiet Sun as Derived from Observed and Model Data NST Bright Points for a QS on August 3, 2010HMI magnetograms for a QS on August 3, 2010 Summary we find the presence of a super-diffusion regime. The obtained spectra are in a very good agreement with model data. On the basis of HMI magnetograms and observations of solar granulation obtained with the New Solar Telescope (NST) of Big Bear Solar Observatory, we explore proper motions of magnetic elements and bright points (BPs) in a quiet sun area. We derived their mean-squared displacements as a function of time (i.e., we determined how far every element was moved during a fixed interval τ, and then we averaged obtained squared displacements for a given τ). From both data sets, we find the presence of a super-diffusion regime. We measure super-diffusion via the spectral index, γ, which is the slope of the mean-squared displacement spectrum. We find that γ=1.5 for the 10s- 10min time interval, and it decreases to 1.2 for the 13- 300min interval. The obtained spectra are in a very good agreement with model data. We applied our tracking code to 3D MHD model data of solar convection (Stein et al. 2007) and found super-diffusion with γ=1.50 inside the 1-12 min interval. We also found that the coefficient of turbulent diffusion changes in direct proportion to both temporal and spatial scales. The regime of super-diffusion ensures a decrease of diffusivity with decreasing scales, thus creating favorable conditions for turbulent dynamo operation. Fig. 1 - An 8-hour data set of 45s HMI magnetograms recorded on August 3, 2010 (9 – 19 UT) was utilized here. A disk center area of 385x265 arcsec was selected to track magnetic elements of the flux density exceeding 30 G, an area exceeding 4 pixels and detected at least in 3 consecutive magnetograms. Total 17312 elements were tracked, and their displacements were derived to calculate the displacement spectrum (red dots in Figure 5). Fig.2 – A 2-hour data set of solar granulation observations in the TiO (705 nm) spectral line with the NST was used. A fragment of 28x26 arcsec of the same solar area as shown in Fig.1, was studied for the time period from 17 to 19 UT. Left - trajectories of BPs detected in the first image (background) of the data set ans existed longer than 3 timesteps(30 s). Right - trajectories of all tracked BPs lived longer than 30 s. MHD-model data Fig. 3 – Three fragments of simulated solar granulation images from a 3D MHD solar magneto-convection code (Stein et al. 2007). BPs in intergranular lanes are visible. Trajectories of BPs Fig. 4 – Typical trajectories of BPs. The time intervals between adjacent measurements (circles) is Δt=10 sec. Blue circles mark the start point of the trajectory. Displacements were determined as distances between the start point and the position on the trajectory in 1Δt, 2 Δt, 3Δt, etc. Fig. 5 – The mean-squared displacement spectra as a function of time. For a Brownian motions, the slope of this spectrum is equal to unity: γ=1. For sub-diffusion, γ 1. Previously (see, e.g., Cadavid et al. 1999) the sub-diffusion in the photosphere was reported. For sub-diffusion, the diffusivity grows with decreasing scale (see orange dot line in Fig.6). Main result is here! Fig. 6 – Diffusion coefficients as a function of spatial scale (left) and of temporal scale (right). Solid lines mark the results obtained in this study, whereas others refer to previously published studies.