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

Abstract

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 hydrogendominated 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.

The Kepler-11 system: evolution of the stellar high-energy emission and initial planetary atmospheric mass fractions

“…The modelling framework we used for the analysis of the Kepler-11 system was developed and thoroughly described in Kubyshkina et al (2019), but with a few improvements that we detail here. The modelling approach combines three main ingredients that are necessary to study the evolution of a planetary atmosphere: a model of the stellar flux evolutionary track, a model that relates planetary parameters and atmospheric mass, and a model for computing atmospheric escape rates.…”

“…In our previous works we modelled the planetary atmospheric evolution (Kubyshkina et al 2018a(Kubyshkina et al , 2019 and considered an initial planetary radius (and therefore f at,0 ) corresponding to a value of the restricted Jeans escape parameter Λ equal to 5, where Λ is the Jeans escape parameter at the position of the planetary radius and for a temperature equal to T eq , for a hydrogen-dominated atmosphere (Jeans 1925;Fossati et al 2017). As we showed in Kubyshkina et al (2019), this approximation does not influence the result for the majority of planets, but some of the planets in the Kepler-11 system (d, e, and likely g) are an exception. We therefore further set the initial atmospheric mass fraction of all planets as a free parameter here.…”

“…Within the framework of our model, the ideal objects to study are close-in planets of sub-Neptune to Neptune masses because they are highly affected by atmospheric escape, but still retain a significant fraction of their primordial hydrogen-dominated atmospheres. Kubyshkina et al (2019) tested the framework for a wide range of system parameters and then applied it to the HD 3167 and K2-32 planetary systems, each containing one planet with the appropriate characteristics for our analysis. However, the tests carried out and presented in that work indicated that the constraint on the evolution of the stellar XUV flux may improve significantly if the analysis is carried out simultaneously considering multiple planets in the same system.…”

“…We present here the results obtained from simultaneously modelling the atmospheric evolution of all Kepler-11 planets considering the more recent parameters given by Bedell et al (2017). We also describe here a few upgrades to the modelling framework described by Kubyshkina et al (2019). We give constraints on the evolution of the XUV emission of the host star and on the initial atmospheric mass fractions of the Kepler-11 planets.…”

“…This paper is organised as follows. Section 2 gives a brief description of the modelling framework and of its upgrades with respect to what is described in Kubyshkina et al (2019). Sections 3 and 4 present the results and their discussion, and Section 5 draws the conclusions of this work.…”