SUPERFLARES ON SOLAR-TYPE STARS OBSERVED WITH KEPLER II. PHOTOMETRIC VARIABILITY OF SUPERFLARE-GENERATING STARS: A SIGNATURE OF STELLAR ROTATION AND STARSPOTS

We performed simple spot-model calculations for quasi-periodic brightness variations of solar-type stars showing superflares using Kepler photometric data. Most of the superflare stars show quasi-periodic brightness modulations with a typical period of one to a few tens of days. Our results indicate that these brightness variations can be explained by the rotation of a star with fairly large starspots. Using the results of the period analysis, we investigated the relation between the energy and frequency of superflares and the rotation period. Stars with relatively slower rotation rates can still produce flares that are as energetic as those of more rapidly rotating stars although the average flare frequency is lower for more slowly rotating stars. We found that the energy of superflares is related to the total coverage of the starspot. The correlation between the spot coverage and the flare energy in superflares is similar to that in solar flares. These results suggest that the energy of superflares can be explained by the magnetic energy stored around the starspots.