  We performed simple spot-model calculations for quasi-periodic brightness
variations of solar-type stars showing superflares, by using Kepler photometric
data. Most of superflare stars show quasi-periodic brightness modulations with
the typical period of one to a few tens of days. Our results indicate that
these brightness variations of superflare stars can be explained by the
rotation of the star with fairly large starspots. Using the result 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 are related to the
total coverage of starspots. 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 starspots.

Solar and Stellar Astrophysics