Migration of Ca II H bright points in the internetwork

The migration of magnetic bright point-like features (MBP) in the lower solar atmosphere reflects the dispersal of magnetic flux as well as the horizontal flows of the atmospheric layer they are embedded in. We analyse trajectories of the proper motion of intrinsically magnetic, isolated internetwork Ca II H MBPs (mean lifetime 461 +- 9 s) to obtain their diffusivity behaviour. We use seeing-free high spatial and temporal resolution image sequences of quiet-Sun, disc-centre observations obtained in the Ca II H 3968 Å passband of the Sunrise Filter Imager (SuFI) onboard the Sunrise balloon-borne solar observatory. Small MBPs in the internetwork are automatically tracked. The trajectory of each MBP is then calculated and described by a diffusion index (γ) and a diffusion coefficient (D). We further explore the distribution of the diffusion indices with the help of a Monte Carlo simulation. We find γ = 1.69 +- 0.08 and D = 257 +- 32 km^2/s averaged over all MBPs. Trajectories of most MBPs are classified as super-diffusive, i.e., γ > 1, with the determined γ being to our knowledge the largest obtained so far. A direct correlation between D and time-scale (τ) determined from trajectories of all MBPs is also obtained. We discuss a simple scenario to explain the diffusivity of the observed, relatively short-lived MBPs while they migrate within a small area in a supergranule (i.e., an internetwork area). We show that the scatter in the γ values obtained for individual MBPs is due to their limited lifetimes. The super-diffusive MBPs can be well-described as random walkers (due to granular evolution and intergranular turbu- lence) superposed on a large systematic (background) velocity, caused by granular, mesogranular and supergranular flows.