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

¹ Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
² Institut d’Estudis Espacials de Catalunya (IEEC), 08860 Castelldefels (Barcelona), Spain
³ Departament d’Enginyeria Electrònica i Biomèdica, Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, IEEC-UB, Martí i Franquès 1, 08028 Barcelona, Spain

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 16 October 2025
Accepted: 11 March 2026

Abstract

Context. Stellar flares are intense bursts of radiation caused by magnetic reconnection events 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 alternative distributions such as lognormal laws that imply different flare generation mechanisms and levels of planetary impact.

Aims. This study investigates which statistical distribution best describes flare occurrences on M dwarfs, considering both equivalent duration (ED), the quantity directly measured from light-curve photometry, and bolometric energy, which is relevant for physical interpretation and habitability assessment.

Methods. We analysed 110 M dwarfs observed with TESS and CHEOPS, detecting 5620 flares. We decomposed complex flare events, corrected for detection biases in the recovery rate and energy estimation, and scaled the FFDs from both missions to construct a combined distribution covering six orders of magnitude in bolometric energy.

Results. We find that ED-based FFDs closely follow a power-law distribution, reflecting the intrinsic photometric flare occurrence. However, bolometric-energy-based FFDs deviate significantly from a pure power law. They are better described by a lognormal distribution, although the best fit is achieved with a truncated power law, exhibiting a break at 1.8 × 10³⁵ erg. Using right-tail-stabilised Kolmogorov–Smirnov and exceedance tests, we attribute this deviation to limited sampling of the most energetic events.

Conclusions. Our results show that the low-energy flattening, previously interpreted as evidence of lognormal behaviour, arises from observational biases and can be corrected through flare injection-recovery and the combination of observations from instruments with different sensitivities. We also find that current instruments are unable to reliably sample flares above 10³⁵ erg, which are the most relevant for exoplanetary atmospheric effects. The upcoming PLATO mission will be able to investigate both regimes.