Properties of Flare Events on M Stars from LAMOST Spectral Survey Based on Kepler and TESS Light Curves

A catalog of M stars has been published from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope data release 7 (LAMOST DR7). We cross-matched the LAMOST M catalog with Kepler, Kepler 2 (K2) and Transiting Exoplanet Survey Satellite (TESS) surveys. We obtained the light curves from the Kepler and TESS surveys. We detected 20,047 flare events from 4053 M stars and calculated their durations, amplitudes, and energies. We analyzed the distribution of the flare durations and energies. The distributions of flare duration for Kepler, K2 and TESS peak are at 3-3.5 hr, 4-6 hr and 1-1.5 hr, respectively. 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 angstrom) and it increases slowly at the higher values.