The MUSCLES Treasury Survey. V. FUV Flares on Active and Inactive M Dwarfs

M dwarf stars are known for their vigorous flaring. This flaring could impact the climate of orbiting planets, making it important to characterize M dwarf flares at the short wavelengths that drive atmospheric chemistry and escape. We conducted a far-ultraviolet flare survey of 6 M dwarfs from the recent MUSCLES (Measurements of the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems) observations, as well as 4 highly-active M dwarfs with archival data. When comparing absolute flare energies, we found the active-M-star flares to be about 10$\times$ more energetic than inactive-M-star flares. However, when flare energies were normalized by the star's quiescent flux, the active and inactive samples exhibited identical flare distributions, with a power-law index of -$0.76^{+0.1}_{-0.09}$ (cumulative distribution). The rate and distribution of flares are such that they could dominate the FUV energy budget of M dwarfs, assuming the same distribution holds to flares as energetic as those cataloged by Kepler and ground-based surveys. We used the observed events to create an idealized model flare with realistic spectral and temporal energy budgets to be used in photochemical simulations of exoplanet atmospheres. Applied to our own simulation of direct photolysis by photons alone (no particles), we find the most energetic observed flares have little effect on an Earth-like atmosphere, photolyzing $\sim$0.01% of the total O$_3$ column. The observations were too limited temporally (73 h cumulative exposure) to catch rare, highly energetic flares. Those that the power-law fit predicts occur monthly would photolyze $\sim$1% of the O$_3$ column and those it predicts occur yearly would photolyze the full O$_3$ column. Whether such energetic flares occur at the rate predicted is an open question.