Coronal heating by nanoflares and the variability of the occurrence frequency in solar flares

It has been proposed that flares in the solar corona may well be a result of an internal self-organized critical (SOC) process in active regions. We have developed a cellular automaton SOC model that simulates flaring activity extending over an active subflaring background. In the resulting frequency distributions we obtain two distinct power laws. That of the weaker events is shorter and much steeper (power law with index similar or equal to-3.26) than that of the intermediate and large events (power law with index similar or equal to-1.73). The flatter power law is in close agreement with observations of flares. Weaker events are responsible for similar or equal to 90% of the total magnetic energy released, indicating a possible connection of nanoflares with coronal heating. Moreover, certain mechanisms cause the variability of the resulting indices and may provide answers to the problem of the variability of flares' occurrence frequency during the solar cycle.