The Cosmic Shoreline Revisited: A Metric for Atmospheric Retention Informed by Hydrodynamic Escape

Abstract

The "cosmic shoreline," a semi-empirical relation that separates airless worlds from worlds with atmospheres as proposed by K. J. Zahnle & D. C. Catling, is now guiding large-scale JWST surveys aimed at detecting rocky exoplanet atmospheres. We expand upon this framework by revisiting the shoreline using existing hydrodynamic escape models applied to Earth-like, Venus-like, and steam atmospheres for rocky exoplanets, and we estimate energy-limited escape rates for CH4 atmospheres. We determine the critical instellation required for atmospheric retention by calculating time-integrated atmospheric mass loss. Our analysis introduces a new metric for target selection in the Rocky Worlds Director's Discretionary Time and refines expectations for rocky planet atmosphere searches. Exploring initial volatile inventory ranging from 0.01% to 1% of planetary mass, we find that its variation prevents the definition of a unique clear-cut shoreline, though nonlinear escape physics can reduce this sensitivity to initial conditions. Additionally, uncertain distributions of high-energy stellar evolution and planet age further blur the critical instellations for atmospheric retention, yielding broad shorelines. Hydrodynamic escape models find atmospheric retention is markedly more favorable for higher-mass planets orbiting higher-mass stars, with carbon-rich atmospheres remaining plausible for 55 Cancri e despite its extreme instellation. We caution that our estimates are sensitive to processes with poorly understood dynamics, such as atomic line cooling. Finally, we illustrate how density measurements can be used to statistically test the existence of the cosmic shorelines, emphasizing the need for more precise mass and radius measurements.