2019ApJ...873...97L

From an analysis of the long cadence light curves of M and K dwarfs obtained by the K2 observations, 3589 flares on 548 M dwarfs and 1647 flares on 343 K dwarfs have been identified. We compared the M and K dwarfs' flares with the G dwarfs' flares reported by Shibayama et al. The later type stars' flare occurrence frequencies are higher than those of the earlier type stars, but the earlier type stars produce more powerful flares than those of the later type stars. For the stars of all spectral types, the flare activities, including the flare energy, peak amplitude, and percentage of magnetic activity, increase with faster rotation of stars. The longer the flare duration is, the more energy the flare releases, but an upper limit exists. The saturation energy of M, K, and G dwarfs are derived to be about 1 x 10³⁵ erg, 4 x 10³⁵ erg and 1 x 10³⁶ erg, respectively, in the present study. We estimated the power-law indices of the flare frequency distributions of three spectral type stars. They are 1.82 ± 0.02 (M dwarfs) and 1.86 ± 0.02 (K dwarfs) in comparison to the 2.01 ± 0.03 for the G dwarfs found by Shibayama et al. For stars with P_rot <= 10 days, they are 1.78 ± 0.02 (M dwarfs), 1.82 ± 0.03 (K dwarfs), and 2.09 ± 0.04 (G dwarfs). The power-law indices of flare frequency distributions of the fast-rotating M- and K-type stars are nearly the same. This indicates that the flare or magnetic mechanisms of different types of low-mass stars may be similar in some sense.