Extending TESS flare frequency distributions with CHEOPS: Power-law versus lognormal

Abstract

Stellar flares are intense bursts of radiation caused by magnetic reconnection on active stars. They are especially frequent on M dwarfs, where they can significantly influence the habitability of orbiting planets. Flare frequency distributions (FFDs) are typically modelled as power laws. However, recent studies challenge this assumption and propose alternatives such as lognormal laws that imply different flare generation mechanisms and planetary impacts. This study investigates which statistical distribution best describes flare occurrences on M dwarfs, considering both equivalent duration (ED), directly measured from light-curve photometry, and bolometric energy, relevant for physical interpretation and habitability. We analysed 110 M dwarfs observed with TESS and CHEOPS, detecting 5620 flares. We decomposed complex events, corrected for detection biases in recovery rate and energy estimation, and scaled the FFDs to construct a combined distribution spanning six orders of magnitude in bolometric energy. We find that ED-based FFDs follow a power law, reflecting intrinsic photometric flare occurrence. However, bolometric-energy-based FFDs deviate from a pure power law. They are better described by a lognormal distribution, although the best fit is a truncated power law with a break at $1.8 \times 10^{35}$ erg. Using right-tail-stabilised Kolmogorov-Smirnov and exceedance tests, we attribute this deviation to limited sampling of the most energetic events. Our results show that the low-energy flattening, previously interpreted as lognormal behaviour, arises from observational biases and can be corrected through flare injection-recovery and combining observations with different sensitivities. Current instruments cannot reliably sample flares above $10^{35}$ erg, the most relevant for exoplanetary atmospheres. The upcoming PLATO mission will be able to investigate both regimes.