Analytical modeling of helium absorption signals of isothermal atmospheric escape

Atmospheric escape driven by extreme ultraviolet radiation is a critical process shaping the evolution of close-in exoplanets. Recent observations have detected helium triplet absorption in numerous close-in exoplanets (>20), highlighting the importance of understanding upper atmospheric thermo-chemical structure. While super-solar metallicity has been observed in the atmospheres of some close-in exoplanets, the impact of metal species on both atmospheric escape dynamics and observed absorption features remains poorly understood. In this study, we derived a simplified yet accurate formula for calculating the equivalent width of helium absorption in the limit of an isothermal temperature for the upper atmosphere. Our results demonstrate that planets with lower temperatures (metal-rich atmospheres) exhibit lower mass-loss rates, though the equivalent width of helium triplet absorption remains largely independent of atmospheric temperature (metallicity) because the low temperatures in these atmospheres enhance the fraction of helium in its triplet state. Additionally, we present a hydrodynamic model based on radiation-hydrodynamic simulations that incorporates the effects of metal cooling. Our analytical model can predict the helium triplet equivalent width of the atmosphere in simulations. The analytical model provides a comprehensive framework for understanding how metal cooling in the upper atmosphere influences the thermo-chemical structure and observable helium features of close-in exoplanetary atmospheres, offering valuable insights for interpreting current and future observational data.