Close-in Sub-Neptunes Reveal the Past Rotation History of Their Host Stars: Atmospheric Evolution of Planets in the HD 3167 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. 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 HD 3167 and K2-32 planetary systems. For HD 3167, we find that the most probable irradiation level at 150 Myr was between 40 and 130 times solar, corresponding to a rotation period of 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.