Modelling helium in exoplanet atmospheres. A revised network with photoelectron-driven processes

The He I line at 1.08 $\mu$m is a valuable tracer of atmospheric escape in exoplanet atmospheres. We expand past networks used to predict the absorbing He(2$^3S$) by including, firstly, processes that involve H$_2$ and some molecular ions and, secondly, the interaction of photoelectrons with the atmosphere. We survey the literature on the chemical-collisional-radiative processes that govern the production-loss of He(2$^3S$). We simulate the atmospheric outflow from the Neptune-sized GJ 436 b by coupling a hydrodynamic model that solves the bulk properties of the gas and a Monte Carlo model that tracks the energy degradation of the photoelectrons. We identify Penning ionization of H as a key He(2$^3S$) loss process at GJ 436 b and update its rate coefficient to a value consistent with the most recent available cross sections. The update affects notably the predicted strength of the He I line. For GJ 436 b, photoelectron-driven processes (mainly ionization and excitation) modify the He(2$^3S$) population in layers too deep to affect the in-transit spectrum. The situation might be different for other atmospheres though. The spectral energy distribution of GJ 436 has a strong effect on the predicted in-transit signal. The published non-detections of the He I line for GJ 436 b are reasonably consistent with our model predictions for a solar-metallicity atmosphere when the model adopts a recently proposed spectral energy distribution. The interpretation of the He I line at 1.08 $\mu$m is model-dependent. Our revised network provides a general framework to extract more robust conclusions from measurements of this line, especially in atmospheres where H$_2$ remains abundant to high altitudes. We will explore additional, previously-ignored processes in future work.