Irradiation-driven escape of primordial planetary atmospheres

Abstract

Making use of the publicly available 1D photoionization hydrodynamics code ATES we set out to investigate the combined effects of specific planetary gravitational potential energy (ϕp ≡ GMp/Rp) and stellar X-ray and extreme ultraviolet (XUV) irradiation (FXUV) on the evaporation efficiency (η) of moderately-to-highly irradiated gaseous planets, from sub-Neptunes through hot Jupiters. We show that the (known) existence of a threshold potential above which energy-limited thermal escape (i.e., η ≃ 1) is unattainable can be inferred analytically, by means of a balance between the ion binding energy and the volume-averaged mean excess energy. For log ϕp ≳ log ϕpthr ≈ [12.9 − 13.2] (in cgs units), most of the energy absorption occurs within a region where the average kinetic energy acquired by the ions through photo-electron collisions is insufficient for escape. This causes the evaporation efficiency to plummet with increasing ϕp, by up to 4 orders of magnitude below the energy-limited value. Whether or not planets with ϕp ≲ ϕpthr exhibit energy-limited outflows is primarily regulated by the stellar irradiation level. Specifically, for low-gravity planets, above FXUVthr ≃ 104–5 erg cm−2 s−1, Lyα losses overtake adiabatic and advective cooling and the evaporation efficiency of low-gravity planets drops below the energy-limited approximation, albeit remaining largely independent of ϕp. Further, we show that whereas η increases as FXUV increases for planets above ϕpthr, the opposite is true for low-gravity planets (i.e., for sub-Neptunes). This behavior can be understood by examining the relative fractional contributions of advective and radiative losses as a function of atmospheric temperature. This novel framework enables a reliable, physically motivated prediction of the expected evaporation efficiency for a given planetary system; an analytical approximation of the best-fitting η is given in the appendix.

Constraining planetary mass-loss rates by simulating Parker wind profiles with Cloudy

“…For lower gravity gaseous planets, expansion cooling always dominates over radiative cooling, resulting in generally cooler temperatures that decrease with altitude. A similar difference between the dominant cooling process in planets with high and low gravitational potential was identified by Salz et al (2016) and Caldiroli et al (2022).…”

“…An example of a solution to this problem was provided by Murray-Clay et al (2009), under the assumption that hydrogen photo-ionization and Lyman-α emission are the main contributors to Γ and Λ, respectively. Recently, Caldiroli et al (2022) presented a more advanced solution that includes additional contributors such as heating by helium ionization and cooling by bremsstrahlung and recombination. Isothermal Parker wind profiles simplify the problem by ignoring Eq.…”

“…A main difficulty for such analyses lies in finding the value of η and how it depends on planetary parameters. Many works have addressed this problem through different avenues (Owen & Jackson 2012;Shematovich et al 2014;Owen & Alvarez 2016;Caldiroli et al 2022). Although this manuscript is not a systematic investigation into the value of η, we still find it illustrative to plug the mass-loss rates we constrained for our sample of six planets into Eq.…”

“…Inspired by Fig. 5 of Caldiroli et al (2022), in Fig. 6 we show K Ṁ versus F XUV /ρ p of our sample together with various estimates from the literature, where the choice of axes ensures η is read off easily.…”

The influence of host star activity evolution on the population of super-Earths and mini-Neptunes

“…Murray-Clay et al 2009a;Salz et al 2016). Recent calculations using a hydrodynamics code for exoplanetary atmospheres and explicitly solving the photoionozation equilibrium give a more detailed view on the relation between high-energy heating and radiative cooling of individual modelled exoplanets (Caldiroli et al 2021(Caldiroli et al , 2022.…”