Smaller Than Earth Habitability Model (STEHM): The Lower Size Limit for Atmosphere Retention in the Habitable Zone

Abstract: With recent advances in exoplanet observational techniques enabling the discovery of increasingly smaller planets, a crucial question emerges in the search for habitable planets: how small can a planet be and still maintain an atmosphere? We present results from the Smaller Than Earth Habitability Model (STEHM) which examines how small a planet can be and still maintain a long-term (multi-gigayear) atmosphere for planets from 1.0$R_\oplus$ down to 0.5$R_\oplus$. The model is based on a stagnant lid planet orbiting within the habitable zone of a sun-like star. Our model demonstrates that planets $\geq$0.8$R_\oplus$ can maintain their atmospheres under our Earth-like default conditions for a solar analog star, while smaller planets lose their atmospheres. Variations from the default Earth-like values cause mostly minor variations to the planet size boundary results, with some changes allowing $\geq$0.7$R_\oplus$ planets to maintain their atmosphere. Initial carbon inventory emerges as the most influential parameter for atmospheric retention, though orders of magnitude difference to Earth values are required to make a significant difference to longevity of atmospheric retention. Planets with substantial initial carbon content, large amounts of heat producing elements, cool initial mantle temperatures and low core radius fractions show the best atmospheric retention capabilities. Our results indicate that atmospheric retention on small planets depends strongly on their formation conditions and early evolution, providing important constraints for future observations of rocky exoplanets and their potential habitability.