Statistical Properties of Superflares on Solar-type Stars: Results Using All of the Kepler Primary Mission Data

Abstract

We report the latest statistical analyses of superflares on solar-type (G-type main-sequence; effective temperature is 5100 - 6000 K) stars using all of the $Kepler$ primary mission data, and $Gaia$-DR2 (Data Release 2) catalog. We updated the flare detection method from our previous studies by using high-pass filter to remove rotational variations caused by starspots. We also examined the sample biases on the frequency of superflares, taking into account gyrochronology and flare detection completeness. The sample size of solar-type stars and Sun-like stars (effective temperature is 5600 - 6000 K and rotation period is over 20 days in solar-type stars) are $\sim$4 and $\sim$12 times, respectively, compared with Notsu et al. (2019, ApJ, 876, 58). As a result, we found 2341 superflares on 265 solar-type stars, and 26 superflares on 15 Sun-like stars: the former increased from 527 to 2341 and the latter from 3 to 26 events compared with our previous study. This enabled us to have a more well-established view on the statistical properties of superflares. The observed upper limit of the flare energy decreases as the rotation period increases in solar-type stars. The frequency of superflares decreases as the stellar rotation period increases. The maximum energy we found on Sun-like stars is $4 \times 10^{34}$ erg. Our analysis of Sun-like stars suggest that the Sun can cause superflares with energies of $\sim 7 \times 10^{33}$ erg ($\sim$X700-class flares) and $\sim 1 \times 10^{34}$ erg ($\sim$X1000-class flares) once every $\sim$3,000 years and $\sim$6,000 years, respectively.