The GAPS Programme at TNG XLII. A characterisation study of the multi-planet system around the 400 Myr-old star HD63433 (TOI-1726)

Context. The GAPS collaboration is carrying out a spectroscopic and photometric follow-up of a sample of young stars with planets (age less than or similar to 600 Myr) to characterise planetary systems at the early stages of their evolution.Aims. For more than 2 yr, we monitored with the HARPS-N spectrograph the 400 Myr-old star HD63433, which hosts two close-in (orbital periods P-b similar to 7.1 and P-c similar to 20.5 days) sub-Neptunes detected by the TESS space telescope, and it was announced in 2020. Using radial velocities and additional TESS photometry, we aim to provide the first measurement of their masses, improve the measure of their size and orbital parameters, and study the evolution of the atmospheric mass-loss rate due to photoevaporation.Methods. We tested state-of-the-art analysis techniques and different models to mitigate the dominant signals due to stellar activity that are detected in the radial velocity time series. We used a hydro-based analytical description of the atmospheric mass-loss rate, coupled with a core-envelope model and stellar evolutionary tracks, to study the past and future evolution of the planetary masses and radii.Results. We derived new measurements of the planetary orbital periods and radii (P-b = 7.10794 +/- 0.000009 days, r(b) = 2.02(-0.05)(+0.06) R-circle plus; P-c = 20.54379 +/- 0.00002 days, r(c) = 2.44 +/- 0.07 R-circle plus), and determined mass upper limits (m(b) less than or similar to 11 M-circle plus; m(c) less than or similar to 31 M-circle plus; 95% confidence level), with evidence at a 2.1-2.7 sigma significance level that HD63433 c might be a dense mini-Neptune with a Neptune-like mass. For a grid of test masses below our derived dynamical upper limits, we found that HD63433 b has very likely lost any gaseous H-He envelope, supporting HST-based observations that are indicative of there being no ongoing atmospheric will keep evaporating over the next similar to 5 Gyr if its current mass is m(c) less than or similar to 15 M-circle plus, while it should be hydrodynamically stable for higher masses.