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 proportional to E-0.39, similar to those of solar hard/soft X-ray flares, tau proportional to E0.2-0.33. This indicates a universal mechanism of energy release on solar and stellar flares, i.e., magnetic reconnection. We here carried out statistical research on 50 solar WLFs observed with Solar Dynamics Observatory/HMI and examined the correlation between the energies and durations. As a result, the E-tau relation on solar WLFs (tau proportional to E-0.38) is quite similar to that on stellar superflares (tau proportional to 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 proportional to (EB-5/3)-B-1/3) derived from the magnetic reconnection theory. In the latter case, the observed superflares are expected to have 2-4 times stronger magnetic field strength than solar flares.