The GAPS Programme at TNG. XLIX. TOI-5398, the Youngest Compact Multi-Planet System Composed of an Inner Sub-Neptune and an Outer Warm Saturn

Context. Short-period giant planets (P less than or similar to 10 days, M-p >0.1 M-J) are frequently found to be solitary compared to other classes of exo-planets. Small inner companions to giant planets with P less than or similar to 15 days are known only in five compact systems: WASP-47, Kepler-730, WASP-132, TOI-1130, and TOI-2000. Here, we report the confirmation of TOI-5398, the youngest known compact multi-planet system composed of a hot sub-Neptune (TOI-5398 c, P-c = 4.77271 days) orbiting interior to a short-period Saturn (TOI-5398 b, P-b = 10.590547 days) planet, both transiting around a 650 +/- 150 Myr G-type star. Aims. As part of the Global Architecture of Planetary Systems (GAPS) Young Object project, we confirmed and characterised this compact system, measuring the radius and mass of both planets, thus constraining their bulk composition. Methods. Using multi-dimensional Gaussian processes, we simultaneously modelled stellar activity and planetary signals from the Transiting Exoplanet Survey Satellite (TESS) Sector 48 light curve and our High Accuracy Radial velocity Planet Searcher (HARPS-N) radial velocity (RV) time series. We confirmed the planetary nature of both planets, TOI-5398 b and TOI-5398 c, and obtained a precise estimation of their stellar parameters. Results. Through the use of astrometric, photometric, and spectroscopic observations, our findings indicate that TOI-5398 is a young, active G dwarf star (650 +/- 150 Myr) with a rotational period of P-rot = 7.34 days. The transit photometry and RV measurements enabled us to measure both the radius and mass of planets b, R-b = 10.30 +/- 0.40 R-circle plus, M-b = 58.7 +/- 5.7 M-circle plus, and c, R-c = 3.52 +/- 0.19 R-circle plus, M-c = 11.8 +/- 4.8 M-circle plus. TESS observed TOI-5398 during sector 48 and no further observations are planned in the current Extended Mission, making our ground-based light curves crucial for improvement of the ephemeris. With a transmission spectroscopy metric (TSM) value of around 300, TOI-5398 b is the most amenable warm giant (10 < P < 100 days) for JWST atmospheric characterisation.