Close-in sub-Neptunes reveal the past rotation history of their host stars: atmospheric evolution of planets in the HD3167 and K2-32 planetary systems

Planet atmospheric escape induced by high-energy stellar irradiation is a key phenomenon shaping the structure and evolution of planetary atmospheres. Therefore, the present-day properties of a planetary atmosphere are intimately connected with the amount of stellar flux received by a planet during its lifetime, thus with the evolutionary path of its host star. Using a recently developed analytic approximation based on hydrodynamic simulations for atmospheric escape rates, we track within a Bayesian framework the evolution of a planet as a function of stellar flux evolution history, constrained by the measured planetary radius, with the other system parameters as priors. We find that the ideal objects for this type of study are close-in sub-Neptune-like planets, as they are highly affected by atmospheric escape, and yet retain a significant fraction of their primordial hydrogen-dominated atmospheres. Furthermore, we apply this analysis to the HD3167 and K2-32 planetary systems. For HD3167, we find that the most probable irradiation level at 150 Myr was between 40 and 130 times solar, corresponding to a rotation period of 1.78^{+2.69}_{-1.23} days. For K2-32, we find a surprisingly low irradiation level ranging between half and four times solar at 150 Myr. Finally, we show that for multi-planet systems, our framework enables one to constrain poorly known properties of individual planets.