Figure 2: Histograms of the activity distribution of solar-like stars.

(main-sequence stars with effective temperatures between 5,100 and 6,000 K) in black compared with those of these stars that show superflares in their Kepler light-curve in the analysis of Shibayama et al.¹⁶ in red. The blue shaded region marks the range of the S index of the Sun between solar cycle minima and maxima³⁴. The two distributions are different at a 6σ level, clearly showing that the superflare stars generally have higher activity levels than average solar-like stars. The green curve shows the distribution of superflare stars with total energies larger than 2·10³⁴ erg in the analysis of Shibayama et al.¹⁶ It is seen that this distribution is shifted to even higher activity levels. The error bars are based on the number of stars in each bin, assuming Poisson statistics. The uncertainties on the measured S indicies are smaller than 0.03 (see Supplementary Fig. 2 for details). The error bars in the figure represent a single standard deviation.