Statistical Study of Solar White-light Flares and Comparison with Superflares on Solar-type Stars

Recently, many superflares on solar-type stars were discovered as white-light flares (WLFs). A correlation between the energies (E) and durations (t) of superflares is derived as \(t\propto E^{0.39}\), and this can be theoretically explained by magnetic reconnection (\(t\propto E^{1/3}\)). In this study, we carried out a statistical research on 50 solar WLFs with SDO/HMI to examine the t-E relation. As a result, the t-E relation on solar WLFs (\(t\propto E^{0.38}\)) is quite similar stellar superflares, but the durations of stellar superflares are much shorter than those extrapolated from solar WLFs. We present the following two interpretations; (1) in solar flares, the cooling timescale of WL emission may be longer than the reconnection one, and the decay time can be determined by the cooling timescale; (2) the distribution can be understood by applying a scaling law \(t\propto E^{1/3}B^{-5/3}\) derived from the magnetic reconnection theory.