Planetary evolution with atmospheric photoevaporation

Abstract

Context. Observations by the Kepler satellite have revealed a gap between larger sub-Neptunes and smaller super-Earths that atmospheric escape models had predicted as an evaporation valley prior to discovery. Aims. We seek to contrast results from a simple X-ray and extreme-ultraviolet (XUV)-driven energy-limited escape model against those from a direct hydrodynamic model. The latter calculates the thermospheric temperature structure self-consistently, including cooling effects such as thermal conduction. Besides XUV-driven escape, it also includes the boil-off escape regime where the escape is driven by the atmospheric thermal energy and low planetary gravity, catalysed by stellar continuum irradiation. We coupled these two escape models to an internal structure model and followed the planets’ temporal evolution. Methods. To examine the population-wide imprint of the two escape models and to compare it to observations, we first employed a rectangular grid, tracking the evolution of planets as a function of core mass and orbital period over gigayear timescales. We then studied the slope of the valley also for initial conditions derived from the observed Kepler planet population. Results. For the rectangular grid, we find that the power-law slope of the valley with respect to orbital period is −0.18 and −0.11 in the energy-limited and hydrodynamic model, respectively. For the initial conditions derived from the Kepler planets, the results are similar (−0.16 and −0.10). While the slope found with the energy-limited model is steeper than observed, the one of the hydrodynamic model is in excellent agreement with observations. The reason for the shallower slope is caused by the two regimes in which the energy-limited approximation fails. The first one are low-mass planets at low-to-intermediate stellar irradiation. For them, boil-off dominates mass loss. However, boil-off is absent in the energy-limited model, and thus it underestimates escape relative to the hydrodynamic model. The second one are massive compact planets at high XUV irradiation. For them, the energy-limited approximation overestimates escape relative to the hydrodynamic model because of cooling by thermal conduction, which is neglected in the energy-limited model. Conclusions. The two effects act together in concert to yield, in the hydrodynamic model, a shallower slope of the valley that agrees very well with observations. We conclude that a hydrodynamic escape model that includes boil-off and a more realistic treatment of cooling mechanisms can reproduce one of the most important constraints for escape models, the valley slope.

Exomoon Phase Curves: Toroidal Exosphere Simulations of Exo‐Ios Orbiting 8 Exoplanets in Alkali Spectroscopy

“…The planetary mass-loss rate Ṁp depends on the stellar XUV flux at the orbital distance of the exoplanet, which we compute according to the host star's spectral type from Lammer, H. et al (2009). The precise XUV flux at a system is a subject of ongoing theoretical work on photoevaporation on a population of exoplanets (Affolter, L. et al, 2023;Mordasini, 2020). According to this calculation the exomoons orbit inside the Alfvén spheres even for heating efficiencies up to 30%, such that the plasma is driven into a rigid corotation with the planet at a ☽ < R mag similar to the case of Io in the Solar System (see Table 3).…”

“…(2009). The precise XUV flux at a system is a subject of ongoing theoretical work on photoevaporation on a population of exoplanets (Affolter, L. et al., 2023; Mordasini, 2020). According to this calculation the exomoons orbit inside the Alfvén spheres even for heating efficiencies up to 30%, such that the plasma is driven into a rigid corotation with the planet at $${a}_{{\rightmoon}}< {R}_{\text{mag}}$$ similar to the case of Io in the Solar System (see Table 3).…”

Evaporation of Close-in Sub-Neptunes by Cooling White Dwarfs

“…Along with core-powered mass loss (Ginzburg et al 2018;Gupta & Schlichting 2019), photoionization-driven atmospheric escape is thought to play a significant role in shaping the observed properties of the Kepler planet population (Fulton et al 2017), likely contributing to carving the observed radius valley by stripping sub-Neptune-sized planets of their primordial envelopes and turning them into rocky cores (e.g., Owen & Wu 2013Rogers & Owen 2021;Affolter et al 2023;Owen & Schlichting 2024).…”