Factors That Determine the Power-law Index of an Energy Distribution of Solar Flares

Abstract

Abstract The power-law index of an occurrence frequency distribution of flares as a function of energy is one of the most important indicators to evaluate the contribution of small-scale flares to coronal heating. For a few decades, many studies tried to derive the power-law index using various instruments and methods. However, these results are various and the cause of this uncertainty is unknown due to the variety of observation conditions. Therefore, we investigated the dependence of the index on the solar activity, coronal features, released energy range, and active region properties such as magnetic flux, twist, and size. Our findings are (1) annual power-law index derived from time series of total solar irradiance (Sun-as-a-star observation analysis) has a negative correlation with sunspot number; (2) power-law index in active region is smaller than that of the quiet Sun and coronal holes; (3) power-law index is almost constant in the energy range of 1025 ≲ E ≲ 1030 erg; and (4) active regions that have more magnetic free energy density, unsigned magnetic flux, and shear angle tend to have smaller power-law indices. Based on the results and energy-scaling law of Petschek-type reconnection, we suggest that the power-law index of sunspot-scale events is smaller than that of granule-scale events. Moreover, we indicated that sunspot-scale events follow CSHKP flare model whereas granule-scale events follow Parker’s nanoflare model.