Statistical properties of superflares on solar-type stars based on the Kepler 1-min cadence data

We searched for superflares on solar-type stars using the Kepler short-cadence (1-min sampling) data in order to detect superflares with short duration. We found 187 superflares on 23 solar-type stars whose bolometric energy ranges from the order of $10^{32}$ erg to $10^{36}$ erg. Using these new data combined with the results from the data with 30-min sampling, we found the occurrence frequency ($dN/dE$) of superflares as a function of flare energy ($E$) shows the power-law distribution ($dN/dE \propto E ^{-\alpha}$) with $\alpha=1.5$ for $10^{33}<E<10^{36}$ erg. The upper limit of energy released by superflares is basically comparable to a fraction of the magnetic energy stored near starspots which is estimated from the amplitude of brightness variations. We also found that the duration of superflares ($\tau$) increases with the flare energy ($E$) as $\tau \propto E^{0.39\pm 0.03}$. This can be explained if we assume the time-scale of flares is determined by the Alfv$\acute{\rm e}$n time.