Molecular hydrogen controls the temperatures of flares on TRAPPIST-1
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.