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We investigate the frequency of magnetic activities, namely flux emergence,splitting, merging, and cancellation, through an automatic detection in orderto understand the generation of the power-law distribution of magnetic fluxreported by Parnell et al. (2009). The quiet Sun magnetograms observed in theNa I line by Hinode/ SOT is used in this study. Investigated patches range from10^{17}Mx to 10^{19}Mx. Emergence and cancellation are much less frequent thanmerging and splitting. The time scale for splitting is found to be ~33 minutesand is independent of the flux contained in the splitting patch. Moreovermagnetic patches split into any flux contents with an equal probability. It isshown that such a fragmentation process leads to a distribution with apower-law index -2. Merging has a very weak dependence on flux content onlywith a power-law index -0.33. These results suggest that 1) magnetic patchesare fragmented by splitting, merging, and tiny cancellation; 2) flux is removedfrom the photosphere through tiny cancellations after these fragmentations.

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