Detection of flux emergence, splitting, merging, and cancellation in quiet Sun

We investigate the frequency of magnetic activities, namely flux emergence, splitting, merging, and cancellation, through an automatic detection in order to understand the generation of the power-law distribution of magnetic flux reported by Parnell et al. (2009). The quiet Sun magnetograms observed in the Na I line by Hinode/ SOT is used in this study. Investigated patches range from 10^{17}Mx to 10^{19}Mx. Emergence and cancellation are much less frequent than merging and splitting. The time scale for splitting is found to be ~33 minutes and is independent of the flux contained in the splitting patch. Moreover magnetic patches split into any flux contents with an equal probability. It is shown that such a fragmentation process leads to a distribution with a power-law index -2. Merging has a very weak dependence on flux content only with a power-law index -0.33. These results suggest that 1) magnetic patches are fragmented by splitting, merging, and tiny cancellation; 2) flux is removed from the photosphere through tiny cancellations after these fragmentations.