Physically motivated analytic model of energy efficiency for extreme-ultraviolet-driven atmospheric escape of close-in exoplanets

¹ Faculty of Physics, University of Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany
² Department of Physics, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
³ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, 20133 Milano, Italy

^★ Corresponding author; hiroto.mitani@uni-due.de

Received: 25 October 2024
Accepted: 11 February 2025

Abstract

Extreme-ultraviolet (EUV) driven atmospheric escape is a key process in the atmospheric evolution of close-in exoplanets. In many evolutionary models, an energy-limited mass-loss rate with a constant efficiency (typically ∼10%) is assumed for calculating the mass-loss rate. However, hydrodynamic simulations have demonstrated that this efficiency depends on various stellar and planetary parameters. Comprehending the underlying physics of the efficiency is essential for understanding planetary atmospheric evolution and recent observations of the upper atmosphere of close-in exoplanets. We introduce relevant temperatures and timescales derived from physical principles to elucidate the mass-loss process. Our analytical mass-loss model is based on phenomenology and consistent across a range of planetary parameters. We compared our mass-loss efficiency with that of radiation hydrodynamic simulations, finding that our model can predict efficiency in both energy-limited and recombination-limited regimes. We further applied our model to exoplanets observed with hydrogen absorption (Lyα and Hα). Our findings suggest that Lyα absorption is detectable in planets subjected to intermediate EUV flux; under these conditions, the escaping outflow is insufficient in low-EUV environments, while the photoionization timescale remains short in high EUV ranges. Conversely, Hα absorption is detectable under high-EUV-flux conditions, facilitated by the intense Lyα flux exciting hydrogen atoms. According to our model, the non-detection of neutral hydrogen can be explained by a low mass-loss rate and is not necessarily due to stellar wind confinement or the absence of a hydrogen-dominated atmosphere in many cases. This model can help identify future observational targets and explicates the unusual absorption detection/non-detection patterns observed in recent studies.