A Multispecies Atmospheric Escape Model with Excited Hydrogen and Helium: Application to HD209458b

Atmospheric escape shapes exoplanet evolution and star-planet interactions, with He I 10830 Å absorption serving as a key tracer of mass loss in hot gas giants. However, transit depths vary significantly across observed systems for reasons that remain poorly understood. HD209458b, the archetypal hot-Jupiter, exhibits relatively weak He I 10830 Å and Hα absorption, which has been interpreted as evidence for a high H/He ratio (98/2), possibly due to diffusive separation. To investigate this possibility and other processes that control these transit depths, we reassess excitation and de-excitation rates for metastable helium and explore the impact of diffusion processes, stellar activity, and tidal forces on the upper atmosphere and transit depths using a model framework spanning the whole atmosphere. Our model reproduces the observed He I transit depth and Hα upper limit, showing strong diffusive separation. We match the observations assuming a photoelectron efficiency of 20%-40%, depending on the composition of the atmosphere, corresponding to mass-loss rates of 1.9-3 × 10¹⁰ g s⁻¹. We find that the He I 10830 Å transit depth is sensitive to both stellar activity and diffusion processes, while Hα is largely unaffected due to its strong dependence on Lyα excitation. These differences may help explain the system-to-system scatter seen in population-level studies of the He I line. While He I data alone may not tightly constrain mass-loss rates or temperatures, they do confirm atmospheric escape and help narrow the viable parameter space when interpreted with physically motivated models. Simultaneous observations of He I, Hα, and stellar activity indicators provide powerful constraints on upper atmosphere dynamics and composition, even in the absence of full transmission spectra.