LAMOST M stars stellar and flare parameters

This may be the result of the different cadences for the three data sets. The highest regions of the flare energies of Kepler, K2 and TESS are 32-32.5, 32-32.5 and 31-31.5 erg in Log format, respectively. A linear relationship between flare duration and energy emerges from our analysis.

The ratio of flare duration to total observational time is approximately 0.2%-0.3% for the Kepler, K2 and TESS surveys. The occurrence rate of a star with a flare event increases from the M0 to M4 subtypes. We also determined the spatial distribution of the flare rate of M stars in the Milky Way.

It seems that the flare rate decreases as the vertical height increases. The power index of the flare energies is in the region of 1.53-2.32, which is similar to previous result for solar type star (2.0). Further, we examined the relationship between the flare amplitude and chromospheric intensity.

The flare activity increases rapidly with the increase in the H{alpha} EW at the lower values (less approximately 2{AA}) and it increases slowly at the higher values.