Molecular hydrogen controls the temperatures of flares on TRAPPIST-1

TL;DR

The paper addresses why flares on the ultracool dwarf TRAPPIST-1 reach much lower temperatures ($ oughly$3000–4000 K) than solar flares, despite comparable flare energies ($E > 10^{30}$ erg). Using chemical-equilibrium calculations with the MPS-ATLAS code to track $H_2$/$H$ abundances and isobaric heat capacities, the authors identify the $H_2$ dissociation thermostat as a robust thermodynamic regulator that absorbs flare energy and prevents substantial heating in TRAPPIST-1's dense atmosphere. They contrast this with solar-like stars, where hydrogen ionization acts as the thermostat, capping temperatures near $9\times 10^3$ K, and show the mechanism’s effectiveness depends on atmospheric pressure and $H_2$ abundance. The findings imply a simple, physically motivated constraint for future radiative-hydrodynamic and magnetohydrodynamic flare simulations and have broad implications for interpreting exoplanet atmospheres around active, cool stars and the associated energy budgets of stellar flares.

Abstract

Early JWST observations of TRAPPIST-1 have revealed an unexpected puzzle: energetic white-light flares ($\rm{E} > 10^{30}$ erg) reach temperatures of only ${\sim}$3500--4000\,K, nearly three times cooler than typical solar flares, which peak around 9000--10000\,K. Here we explain this difference by identifying the physical mechanism that regulates flare temperatures on late M-dwarfs. The key factor is that in the cool, dense atmosphere of TRAPPIST-1, magnetic heating is strongly moderated by the dissociation of molecular hydrogen (H$_2$) into atomic hydrogen. This "H$_2$ dissociation thermostat" acts as an efficient energy sink, preventing flare regions from heating above ${\sim}4000$\,K. Our chemical equilibrium and heat capacity calculations show that this effect depends sensitively on stellar atmospheric pressure and the local abundance of H$_2$. In hotter stars, from early M dwarfs to solar-type stars, the scarcity of molecular hydrogen renders this mechanism ineffective; instead, atomic hydrogen ionization limits flare temperatures near ${\sim}$9000\,K.

Figures (6)

• Figure 1: Illustration of flare heating in three types of stars. The dashed line marks the stellar surface; blue areas show the quiet atmosphere, and red areas show regions heated during a white-light flare. Vertical arrows indicate the radiative output, with length proportional to intensity. In solar-like stars (left), heating is regulated by hydrogen ionization, which limits temperatures of white-light flares to $\sim 9000$ K. In late M dwarfs like TRAPPIST-1 (middle), molecular hydrogen dissociation acts as a thermostat, capping temperatures of white-light flares near $\sim 3500-4000$ K. In early M dwarfs (right), insufficient concentration of $\rm H_2$ means the dissociation thermostat is ineffective, allowing higher white-light flare temperatures.
• Figure 2: Molecular hydrogen dissociation and atomic hydrogen ionization thermostats in stellar atmospheres. Left panel: Relative concentrations of molecular, atomic, and ionized hydrogen, normalized to the total concentration of heavy particles (i.e., all particles except electrons), shown as functions of temperature. The concentration of molecular hydrogen is multiplied by two to account for the fact that each molecule consists of two hydrogen atoms. The horizontal blue line indicates the condition where hydrogen exists entirely in a single stage, either molecular, neutral, or ionized. Right panel: isobaric heat capacity. The calculations are performed for solar elemental composition and pressure, $\sim 0.1$ bar, typical for the solar surface. The key message of the figure is that both dissociation and ionization occur over a very narrow temperature range, resulting in two distinct peaks in heat capacity — the $\rm H_2$ and H thermostats.
• Figure 3: Hydrogen thermostats at different pressure values. Shown are heat capacities computed for solar elemental composition and pressure values of 1 mbar (typical for the solar temperature minimum region), 0.1 bar (typical for the solar surface), and 5 bar (typical for TRAPPIST-1 optical surface, see Fig. \ref{['fig:TP_structure']}). The key message of the figure is that the thermostat temperatures depend on pressure, and therefore vary with the type of star and the height in the stellar atmosphere from which the white-light flare emission originates.
• Figure 4: The $\rm H_2$ energy reservoir. Energy required to isobarically heat a mass of gas equivalent to 0.45% of TRAPPIST-1’s atmosphere (typical of strong flares, see text for details) from 2000 K. The two dashed horizontal lines indicate bolometric energies of the two strongest TRAPPIST-1 flares analyzed by Howard2023. The figure demonstrates that the dissociation energy stored in $\rm H_2$ is sufficient to account for the flare’s total bolometric emission.
• Figure 5: The $\rm \bf H_2$ thermostat disappears for hotter stars. The heat capacity (per particle) as a function of stellar effective temperature. The key takeaway from the figure is that the $\rm H_2$ thermostat weakens with increasing stellar effective temperature and essentially vanishes in early M- and late K-dwarfs.