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The migration of magnetic bright point-like features (MBP) in the lower solaratmosphere reflects the dispersal of magnetic flux as well as the horizontalflows of the atmospheric layer they are embedded in. We analyse trajectories ofthe proper motion of intrinsically magnetic, isolated internetwork Ca II H MBPs(mean lifetime 461 +- 9 s) to obtain their diffusivity behaviour. We useseeing-free high spatial and temporal resolution image sequences of quiet-Sun,disc-centre observations obtained in the Ca II H 3968 {\AA} passband of theSunrise Filter Imager (SuFI) onboard the Sunrise balloon-borne solarobservatory. Small MBPs in the internetwork are automatically tracked. Thetrajectory of each MBP is then calculated and described by a diffusion index({\gamma}) and a diffusion coefficient (D). We further explore the distributionof the diffusion indices with the help of a Monte Carlo simulation. We find{\gamma} = 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., {\gamma} >1, with the determined {\gamma} being to our knowledge the largest obtained sofar. A direct correlation between D and time-scale ({\tau}) determined fromtrajectories of all MBPs is also obtained. We discuss a simple scenario toexplain the diffusivity of the observed, relatively short-lived MBPs while theymigrate within a small area in a supergranule (i.e., an internetwork area). Weshow that the scatter in the {\gamma} values obtained for individual MBPs isdue to their limited lifetimes. The super-diffusive MBPs can be well-describedas random walkers (due to granular evolution and intergranular turbu- lence)superposed on a large systematic (background) velocity, caused by granular,mesogranular and supergranular flows.

Migration of Ca II H bright points in the internetwork