Can rocky planets around red dwarf stars keep atmospheres?
In plain words
Red dwarfs are the most common stars and the easiest around which to study small planets, but they emit intense ultraviolet light and flares that may strip planetary atmospheres. Whether their rocky planets keep any air is unknown.
Precise statement
For rocky planets in and near the habitable zones of M dwarfs (e.g., TRAPPIST-1 e, f, g), determine whether secondary atmospheres with surface pressure $\ge 10^{5}\,\mathrm{dyn}/\mathrm{cm}^{2}$ ($0.1\,\mathrm{bar}$) survive XUV-driven escape, flares and stellar winds over Gyr. The answer is yes or no for a defined class of planets, from thermal emission and transmission measurements.
What would settle it
JWST secondary-eclipse and phase-curve measurements of dayside temperatures for a sample of rocky M-dwarf planets spanning instellation and escape velocity.
Status in the literature
JWST 15 micron eclipse photometry in 2023 disfavors thick CO2 atmospheres on TRAPPIST-1 b and c.