The 3D Cosmic Shoreline for Nurturing Planetary Atmospheres

Abstract: Various cosmic shorelines" have been proposed to delineate which planets have atmospheres. The fates of individual planet atmospheres may be set by a complex sea of growth and loss processes, driven by unmeasurable environmental factors or unknown historical events. Yet, defining population-level boundaries helps illuminate which processes matter and identify high-priority targets for future atmospheric searches. Here, we provide a statistical framework for inferring the position, shape, and fuzziness of an instellation-based cosmic shoreline, defined in the three-dimensional space of planet escape velocity, planet bolometric flux received, and host star luminosity; explicitly including luminosity partially circumvents the need to estimate host stars' historical X-ray and extreme ultraviolet fluences. Using Solar System and exoplanet atmospheric constraints, under the restrictive assumption that one planar boundary applies across a wide parameter space, we find the critical flux threshold for atmospheres scales with escape velocity with a power-law index of $p=6.08^{+0.69}_{-0.48}$, steeper than the canonical literature slope of $p=4$, and scales with stellar luminosity with a power-law index of $q=1.25^{+0.31}_{-0.22}$, steep enough to disfavor atmospheres on Earth-sized planets out to the habitable zone for stars less luminous than $\log_{10} (L_\star/L_\odot) = -2.22 \pm 0.21$ (roughly spectral type M4.5V). If we relax the assumption that one power law must stretch from the hottest exoplanets to the coolest Solar System worlds, the narrower question ofWhich warm planets have thick CO$_2$ secondary atmospheres?" is still poorly constrained by data but should improve significantly with planned JWST observations.