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Extending TESS Flare Frequency Distributions with CHEOPS: power-law or lognormal?

Julien Poyatos, Octavi Fors, José Maria Gómez Cama

TL;DR

This study investigates the statistical form of flare frequency distributions (FFDs) for M dwarfs by combining TESS and CHEOPS data to extend the energy coverage from equivalent duration (ED) to bolometric energy. It shows that ED-based FFDs follow a power law, while bolometric-energy FFDs deviate from a pure power law and are better described by a lognormal or truncated power law with a break near $E \ 10^{33}$ erg, after correcting for detection biases and decomposing complex flares. The truncation implies a change in flare generation physics between regular flares and superflares and affects estimates of cumulative planetary atmospheric impacts, though a high-energy drop above $E \ 10^{35}$ erg remains unresolved. The study demonstrates the importance of cross-mission data, injection–recovery corrections, and flare decomposition for reliable FFDs and discusses implications for exoplanet habitability and future missions like PLATO.

Abstract

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 strongly influence planetary habitability. Flare frequency distributions (FFDs) are usually modeled as power laws, but recent studies have proposed alternatives such as lognormal distributions, implying different flare mechanisms and planetary impacts. This work investigates which statistical distribution best describes flare occurrences on M dwarfs, considering both equivalent duration (ED), the quantity directly measured from photometry, and bolometric energy, which is more relevant for habitability assesments. We analyzed 110 M dwarfs observed with TESS and CHEOPS, detecting 5,620 flares. Complex events were decomposed, detection biases corrected, and FFDs from both missions scaled to build a combined distribution spanning nearly 10 orders of magnitude in bolometric energy. ED-based FFDs follow a power law, reflecting intrinsic photometric flare occurrence. However, bolometric energy-based FFDs deviate from a pure power law, being better described by a lognormal distribution or, more accurately, by a truncated power law with a break near $10^{33}$ erg, the typical superflare threshold. This truncation suggests a change in flare-generation physics between regular flares and superflares, with implications for the cumulative impact on exoplanetary atmospheres. The apparent low-energy flattening previously attributed to lognormal behavior arises from observational biases, while the drop in flare frequency above $10^{35}$ erg remains unexplained, possibly reflecting an intrinsic cutoff or current observational limits. The upcoming PLATO mission will be well suited to probe both regimes.

Extending TESS Flare Frequency Distributions with CHEOPS: power-law or lognormal?

TL;DR

This study investigates the statistical form of flare frequency distributions (FFDs) for M dwarfs by combining TESS and CHEOPS data to extend the energy coverage from equivalent duration (ED) to bolometric energy. It shows that ED-based FFDs follow a power law, while bolometric-energy FFDs deviate from a pure power law and are better described by a lognormal or truncated power law with a break near erg, after correcting for detection biases and decomposing complex flares. The truncation implies a change in flare generation physics between regular flares and superflares and affects estimates of cumulative planetary atmospheric impacts, though a high-energy drop above erg remains unresolved. The study demonstrates the importance of cross-mission data, injection–recovery corrections, and flare decomposition for reliable FFDs and discusses implications for exoplanet habitability and future missions like PLATO.

Abstract

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 strongly influence planetary habitability. Flare frequency distributions (FFDs) are usually modeled as power laws, but recent studies have proposed alternatives such as lognormal distributions, implying different flare mechanisms and planetary impacts. This work investigates which statistical distribution best describes flare occurrences on M dwarfs, considering both equivalent duration (ED), the quantity directly measured from photometry, and bolometric energy, which is more relevant for habitability assesments. We analyzed 110 M dwarfs observed with TESS and CHEOPS, detecting 5,620 flares. Complex events were decomposed, detection biases corrected, and FFDs from both missions scaled to build a combined distribution spanning nearly 10 orders of magnitude in bolometric energy. ED-based FFDs follow a power law, reflecting intrinsic photometric flare occurrence. However, bolometric energy-based FFDs deviate from a pure power law, being better described by a lognormal distribution or, more accurately, by a truncated power law with a break near erg, the typical superflare threshold. This truncation suggests a change in flare-generation physics between regular flares and superflares, with implications for the cumulative impact on exoplanetary atmospheres. The apparent low-energy flattening previously attributed to lognormal behavior arises from observational biases, while the drop in flare frequency above erg remains unexplained, possibly reflecting an intrinsic cutoff or current observational limits. The upcoming PLATO mission will be well suited to probe both regimes.
Paper Structure (12 sections, 4 equations, 14 figures, 1 table)

This paper contains 12 sections, 4 equations, 14 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Target selection
  4. Light curve detrending
  5. Flare detection and decomposition
  6. Energy and recovery probability correction
  7. FFD construction and fit
  8. Results
  9. Discussion
  10. Conclusion
  11. Target table
  12. Additional complex flare decompositions

Figures (14)

  • Figure 1: Flow diagram of the analysis procedure used in this study. Left bubbles describe the main steps, while right squares provide additional details.
  • Figure 2: Parameters of the stellar sample. Panels from top to bottom show histograms of Gaia $G$-band magnitude, $T_{eff}$, log(V sin i), radius, distance, rotation period, and spectral type.
  • Figure 3: Response function of CHEOPS (green) and TESS (red), shown together with a 10,000 K flare blackbody spectrum (black).
  • Figure 4: Coordinates of the target stars overlaid on the CHEOPS sky coverage map, with a minimum observing duration of 39 minutes per orbit, corresponding to $\sim$40% efficiency. Circle colours show the number of TESS sectors covering each target. Background shading indicates total CHEOPS observing time in days per year, with black contours marking 20, 40, 60, and 80 days.
  • Figure 5: Example TESS light curve of the M5V star GJ 65. The top panel shows the detrended light curve (blue points) from sector 30, with the raw light curve in the background (grey points). The middle panel presents a one-week zoom of a selected portion, while the bottom panel provides 4 close-ups of individual flares. Grey boxes mark the sections shown in the zooms. In the bottom panels, the fitted flare components are plotted as solid coloured lines.
  • ...and 9 more figures