Recent James Webb Space Telescope observations of cool, rocky exoplanets reveal a probable lack of thick atmospheres, suggesting the prevalent escape of the “secondary” atmospheres formed after losing primordial hydrogen. Yet, simulations indicate that the hydrodynamic escape of secondary atmospheres, composed of nitrogen and carbon dioxide, requires intense fluxes of ionizing radiation (X-ray and extreme ultraviolet (XUV)) to overcome the effects of high molecular weight and efficient line cooling. This transonic outflow of hot, ionized metals (not hydrogen) presents a novel astrophysical regime ripe for exploration. We introduce an analytic framework to determine which planets retain or lose their atmospheres, positioning them on either side of the cosmic shoreline. We model the radial structure of escaping atmospheres as polytropic expansions—power-law relationships between density and temperature driven by local XUV heating. Our approach diagnoses line cooling with a three-level atom model and incorporates how ion–electron interactions reduce the mean molecular weight. Crucially, hydrodynamic escape onsets for a threshold XUV flux depend upon the atmosphere’s gravitational binding. The ensuing escape rates either scale linearly with XUV flux when weakly ionized (energy limited) or are controlled by a collisional–radiative thermostat when strongly ionized. Thus, airlessness is determined by whether the XUV flux surpasses the critical threshold during the star’s active periods, accounting for expendable primordial hydrogen and revival by volcanism. We explore atmospheric escape from the young Sun Mars and Earth, LHS 1140 b and c, and TRAPPIST-1 b. Our modeling characterizes the bottleneck of atmospheric loss on the occurrence of observable Earth-like habitats and offers analytic tools for future studies.
5101 Astronomical Sciences
,51 Physical Sciences
