Statistical Studies of Solar White-Light Flares and Comparisons with Superflares on Solar-type Stars

Recently, many superflares on solar-type stars have been discovered as white-light flares (WLFs). The statistical study found a correlation between their energies ($E$) and durations ($tau$): $tau propto E^{0.39}$ (Maehara et al. 2017 $EP& S$, 67, 59), similar to those of solar hard/soft X-ray flares: $tau propto E^{0.2-0.33}$. This indicates a universal mechanism of energy release on solar and stellar flares, i.e., magnetic reconnection. We here carried out a statistical research on 50 solar WLFs observed with textit{SDO}/HMI and examined the correlation between the energies and durations. As a result, the $E$--$tau$ relation on solar WLFs ($tau propto E^{0.38}$) is quite similar to that on stellar superflares ($tau propto E^{0.39}$). However, the durations of stellar superflares are one order of magnitude shorter than those expected from solar WLFs. We present the following two interpretations for the discrepancy. (1) In solar flares, the cooling timescale of WLFs may be longer than the reconnection one, and the decay time of solar WLFs can be elongated by the cooling effect. (2) The distribution can be understood by applying a scaling law ($tau propto E^{1/3}B^{-5/3}$) derived from the magnetic reconnection theory. In this case, the observed superflares are expected to have 2-4 times stronger magnetic field strength than solar flares.