A Study of variability in the frequency distributions of the superflares of g-type stars observed by the Kepler mission

The energy and time profiles of 4944 superflares from 77 G-type stars with well-defined light curve periodicities from the Kepler measurements have been analyzed in detail. The total value of the power-law index of the flare frequency distribution as a function of energy (dN/dE E ^-γ) between 5 × 10³⁴ and 10³⁶ erg is on average γ = 2.04 ± 0.17, which is in agreement with previous results. The γ values of eight stars with frequent flaring activity vary between 1.59 ± 0.06 and 2.11 ± 0.19, suggesting a possible diversity of energy release effects. In general, stars with shorter rotation periods tend to have larger γ values. There is an indication that the flare energy is saturated at about 2 × 10³⁷ erg. For a few large superflares of this energy range, it is found that their temporal behaviors could be characterized by a transition from single impulsive flares to long-duration flares composed of several flares.