The effects of stellar activity cycles on planetary atmospheric escape and the He  <scp>i</scp> 1083 nm transit signature

ABSTRACT The ${\rm He\, {\small I}}$ 1083 nm transit signature is commonly used in tracing escaping planetary atmospheres. However, it can be affected by stellar activity, complicating detections and interpretations of atmospheric escape. We model how stellar activity cycles affect the atmospheric escape and ${\rm He\, {\small I}}$ 1083 nm signatures of four types of highly irradiated exoplanets, at 0.025 and 0.05 au, during minimum and maximum cycle phases. We consider two stars, exhibiting different cycle behaviours: the Sun and the more active star $\iota$ Hor, for which we reconstruct its spectral energy distributions at minimum and maximum phases using X-ray observations and photospheric models. We show that over a modulated activity cycle, the release of extreme ultraviolet photons, responsible for atmospheric escape, varies substantially more than that of mid-ultraviolet (UV) photons, capable of photoionizing He i ($2^3$S). This leads to consistently stronger helium signatures during maximum phases. We show that planets at the largest orbit are more affected by cycles, showing larger variations in escape rates and absorptions between minimum and maximum. We also confirm the counter-intuitive behaviour that, despite the fall-off in escape rate with orbital distance, the ${\rm He\, {\small I}}$ 1083 nm absorption is not significantly weaker at further orbits, even strengthening with orbital distance for some $\iota$ Hor planets. We partially explain this behaviour with the lower mid-UV fluxes at more distant orbits, leading to less He i ($2^3$S) photoionizations. Finally, we propose that stellar cycles could explain some of the conflicting ${\rm He\, {\small I}}$ 1083 nm observations of the same planet, with detections more likely during a phase of activity maximum.