The GAPS programme at TNG: LXIII. Photo-evaporating puzzle: Exploring the enigmatic nature of TOI-5398 b's atmospheric signal

Context. Atmospheric characterisation plays a key role in the study of exoplanetary systems, giving hints about the current and past conditions of the planets. The information retrieved from the analysis of pivotal lines such as the Hα and He I triplet allow us to constrain the evolutionary path of the planets due to atmospheric photo-evaporation. After focussing for many years on ultra-hot Jupiters, atmospheric characterisation is slowly moving towards smaller and colder planets, which are harder to study due to the difficulties in extracting the planetary signal and which require more precise analysis. Aims. We aim to characterise the atmosphere of TOI-5398 b (P ~ 10.59 days), the outer warm Saturn orbiting a young (~650 Myr) G-type star that also hosts the small inner planet TOI-5398 c (P ~ 4.77 days). Both planets are suitable for atmospheric probing due to the closeness to their host star, which results in strong photo-evaporation processes, especially the larger outer one with an estimated transmission spectroscopy metric of 288 (higher than those of several well-known hot Jupiters). Methods. We investigated the atmosphere of planet b, analysing the data collected during a transit with HARPS-N and GIANO-B high-resolution spectrographs, employing both cross-correlation and single-line analysis to study the presence of atomic species. Incidentally, we recorded the simultaneous transit of planet c, and hence we also focussed on discerning the origin of the signal. We expect planet b to be the cause of the detected signal, since, according to existing evaporation models, it is currently expected to lose more mass than planet c. Results. We detected the presence of Hα and He I triplets, two markers of the photo-evaporation processes predicted for the system, retrieving a height in the atmosphere of 2.33 Rp and 1.65 Rp, respectively. We confirmed these predictions by employing the models computed with the ATES software, which predict a He I absorption arising from planet b comparable with the observed one. Moreover, the ATES models suggested an He/H ratio of 1/99 to match our observations. The investigation of atomic species led to the detection of an Na I doublet via single-line analysis, while the cross-correlation did not return a detection for any of the atomic species investigated.