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 10³² erg to 10³⁶ 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 ~ E ^-α) with α=1.5 for 10³³ < E < 10³⁶ 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 (τ) increases with the flare energy (E) as τ ~ E ^0.39+/-0.03. This can be explained if we assume the time-scale of flares is determined by the Alfvén time.