Stellar activity sample of active M dwarfs

Furthermore, the correlation between flare amplitude and duration and cumulative flare energy frequency distributions was investigated to probe the underlying mechanisms driving magnetic activity in flaring M dwarfs. We find that the flare occurrence rate displays a flat distribution across spectral types M0-M4 (T_eff_~3200K) and declines for later types. Faster rotators with P_rot_<1day exhibit a higher flare occurrence rate and flare activity.

M dwarfs with a higher flare occurrence rate tend to exhibit lower flare amplitudes, indicating that frequent flares in these M dwarfs are generally less energetic. Within the mass range of 0.15-0.76M_{sun}_, the median of L_{Halpha_/L_bol_ in evenly divided mass bins of ~0.1M_{sun}_ varies by a factor of ~2.5, while {Delta}EW decreases by 92% across the sample. We derive power-law indexes of the cumulative flare frequency distribution for M dwarf subgroups, indicating a decreasing trend from M0 to M5 dwarfs with a value of alpha from 1.68 to 1.95, respectively.

We characterized the stellar activity in M dwarfs through chromospheric indicators like H{alpha} emission, star-spot coverage, flare occurrence rates, flare energies, and flare duration. Our results suggest a stellar activity transition near M4, with stronger H{alpha} emission linked to higher flare occurrence. Rapid rotators (P_rot_<1day) exhibit significantly higher flare occurrence rate, supporting the idea that strong magnetic dynamos in fast-rotating M dwarfs sustain frequent flaring activity.

Our analysis confirms that highly active stars dissipate magnetic energy through numerous low-energy flares rather than fewer high-energy events. We also show that chromospheric activity and flare activity follow a power-law relationship.