Why M-dwarf flares have a limited impact on the atmospheric evaporation of sub-Neptunes and Earth-sized planets

The habitable zones (HZs) of M-type stars are prime targets for exoplanet searches. These stars also exhibit significant magnetic flaring activity, particularly during their first billion years, which can potentially accelerate the evaporation of the hydrogen-helium envelopes of close-in planets. We employed the time-dependent photoionization hydrodynamics code <ns0:monospace>ATES</ns0:monospace> to investigate the impact of flares on atmospheric escape, focusing on an Earth-sized and a sub-Neptune-sized planet orbiting an early M-type star at distances of 0.01, 0.1, and 0.18-0.36 AU - i.e., around the inner and outer edges of the HZ. Stellar flaring was modeled as a 1-gigayear-long high-activity phase followed by a 4-gigayear-long low-activity phase, each characterized by an appropriate flare frequency distribution. We find that flares have a modest impact on the cumulative atmospheric mass loss - less than a factor of 2 - with the greatest absolute increase occurring when the planets are at their closest separation. However, the relative increase in mass loss between flaring and non-flaring cases is greater at larger orbital separations. This trend arises because as stellar irradiation fluctuates between quiescent levels and peak flares, the proportion of time that a planet spends in the energy-limited versus recombination-limited mass-loss regimes depends on its orbital separation. Additionally, we demonstrate the existence of a characteristic flare energy, between the minimum and maximum values, that maximizes the fractional contribution to flare-driven mass loss. Our results indicate that the flaring activity of M dwarfs does not significantly affect the atmospheric retention of close-in planets, including those within the HZ. The potential occurrence of rare super-flares, which current observational campaigns may be biased against, does not alter our conclusions.