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Planet atmospheric escape induced by high-energy stellar irradiation is a keyphenomenon shaping the structure and evolution of planetary atmospheres.Therefore, the present-day properties of a planetary atmosphere are intimatelyconnected with the amount of stellar flux received by a planet during itslifetime, thus with the evolutionary path of its host star. Using a recentlydeveloped analytic approximation based on hydrodynamic simulations foratmospheric escape rates, we track within a Bayesian framework the evolution ofa planet as a function of stellar flux evolution history, constrained by themeasured planetary radius, with the other system parameters as priors. We findthat the ideal objects for this type of study are close-in sub-Neptune-likeplanets, as they are highly affected by atmospheric escape, and yet retain asignificant 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 wasbetween 40 and 130 times solar, corresponding to a rotation period of1.78^{+2.69}_{-1.23} days. For K2-32, we find a surprisingly low irradiationlevel ranging between half and four times solar at 150 Myr. Finally, we showthat for multi-planet systems, our framework enables one to constrain poorlyknown properties of individual planets.

astrophysical journal/the astrophysical journal

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