The GAPS Programme at TNG XLII. A characterisation study of the multi-planet system around the 400 Myr-old star HD 63433 (TOI-1726)

For more than two years, we monitored with the HARPS-N spectrograph the 400 Myr-old star HD\,63433, which hosts two close-in (orbital periods $P_b\sim7.1$ and $P_c\sim20.5$ 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. 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. We derived new measurements of the planetary orbital periods and radii ($P_b=7.10794\pm0.000009$ d, $r_b=2.02^{+0.06}_{-0.05}$ $R_{\oplus}$; $P_c=20.54379\pm0.00002$ d, $r_c=2.44\pm0.07$ $R_{\oplus}$), and determined mass upper limits ($m_b\lesssim$11 $M_{\oplus}$; $m_c\lesssim$31 $M_{\oplus}$; 95$\%$ confidence level), with evidence at a 2.1--2.7$\sigma$ significance level that HD\,63433\,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 HD\,63433\,b has very likely lost any gaseous H-He envelope, supporting HST-based observations that are indicative of there being no ongoing atmospheric evaporation. HD\,63433\,c will keep evaporating over the next $\sim$5 Gyr if its current mass is $m_c\lesssim$15 $M_{\oplus}$, while it should be hydrodynamically stable for higher masses.