Constraining stellar rotation and planetary atmospheric evolution of a dozen systems hosting sub-Neptunes and super-Earths

Context. Planetary atmospheric evolution modelling is a prime tool for understanding the observed exoplanet population and constraining formation and migration mechanisms, but it can also be used to study the evolution of the activity level of planet hosts. Aims. We constrain the planetary atmospheric mass fraction at the time of the dispersal of the protoplanetary disk and the evolution of the stellar rotation rate for a dozen multi-planet systems that host sub-Neptunes and/or super-Earths. Methods. We employ a custom-developed PYTHON code that we have dubbed PASTA (Planetary Atmospheres and Stellar RoTation RAtes), which runs within a Bayesian framework to model the atmospheric evolution of exoplanets. The code combines MESA stellar evolutionary tracks, a model describing planetary structures, a model relating stellar rotation and activity level, and a model predicting planetary atmospheric mass-loss rates based on the results of hydrodynamic simulations. Results. Through a Markov chain Monte Carlo scheme, we retrieved the posterior probability density functions of all considered parameters. For ages older than about 2 Gyr, we find a median spin-down (i.e. P(t) proportional to t(y)) of (y) over bar = 0.38(-0.27)(+0.38), indicating a rotation decay slightly slower than classical literature values (approximate to 0.5), though still within 1 sigma. At younger ages, we find a median spin-down (i.e. P(t) proportional to t(x)) of (x) over bar = 0.261(-0.1)(9)(+0.42), which is below what is observed in young open clusters, though within lo . Furthermore, we find that the x probability distribution we derived is skewed towards lower spin-down rates. However, these two results are likely due to a selection bias as the systems suitable to be analysed by PASTA contain at least one planet with a hydrogen-dominated atmosphere, implying that the host star has more likely evolved as a slow rotator. We further look for correlations between the initial atmospheric mass fraction of the considered planets and system parameters (i.e. semi-major axis, stellar mass, and planetary mass) that would constrain planetary atmospheric accretion models, but without finding any. Conclusions. PASTA has the potential to provide constraints to planetary atmospheric accretion models, particularly when considering warm sub-Neptunes that are less susceptible to mass loss compared to hotter and/or lower-mass planets. The TESS, CHEOPS, and PLATO missions are going to be instrumental in identifying and precisely measuring systems amenable to PASTA'S analysis and can thus potentially constrain planet formation and stellar evolution.