[Paper Review] Planetary evolution with atmospheric photoevaporation

C. Mordasini|arXiv (Cornell University)|Feb 6, 2020

Astro and Planetary SciencePhysics and Astronomy135 references114 citations

TL;DR

This paper analytically and numerically investigates the origin of the 'evaporation valley'—a bimodal distribution in exoplanet radii separating super-Earths from sub-Neptunes—by modeling atmospheric photoevaporation of close-in low-mass planets. It derives that the valley's lower boundary, defined by the largest stripped core radius Rbare, scales weakly with stellar XUV luminosity (LXUV^0.135) and core mass, explaining why the valley is clearly visible across diverse models despite varying initial H/He masses.

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.

Motivation & Objective

• To analytically derive the locus of the evaporation valley in the radius-orbital distance plane.
• To understand how the valley's position depends on planetary core mass, initial H/He envelope mass, and stellar XUV luminosity.
• To constrain planet formation models by linking observed valley morphology to physical processes like photoevaporation.

Proposed method

• Conducts numerical simulations of atmospheric escape for close-in low-mass planets with varying core mass, orbital separation, and initial H/He mass.
• Uses energy-limited photoevaporation theory with an efficiency factor ε to model mass loss.
• Develops an analytical model based on the condition that complete evaporation occurs when the integral of absorbed XUV irradiation exceeds the envelope binding energy.
• Employs the ANEOS equation of state to model planetary interior structure and thermodynamics.
• Performs parameter studies across grids of core mass, orbital distance, and atmospheric composition.
• Derives the scaling of Rbare with orbital period P as P^−0.18, assuming constant ε and Mc ∝ Rpc^c.

Experimental results

Research questions

• RQ1 How does the lower boundary of the evaporation valley (Rbare) depend on stellar XUV luminosity?
• RQ2 What is the dependence of Rbare on the initial H/HE mass of the planet?
• RQ3 Why is the evaporation valley so clearly visible in observations despite varying initial conditions?
• RQ4 How does the efficiency factor ε of energy-limited evaporation affect the valley's morphology?
• RQ5 What constraints does the observed valley place on planetary core composition and formation models?

Key findings

• Rbare at a given orbital distance depends only weakly on the initial H/He mass, scaling as L_XUV^0.135.
• The dependence of Rbare on stellar XUV luminosity is weak but sufficient to explain the valley's existence and non-empty nature.
• Rbare scales with orbital period as P^−0.18 for constant ε, consistent with observed trends.
• For a 10-day orbital period and Earth-like composition, Rbare ≈ 1.7 R⊕, increasing linearly with ice mass fraction.
• The analytical model explains numerical results by equating the time-integrated XUV energy absorbed to the gravitational binding energy of the envelope.
• The weak dependence on initial H/He mass implies the valley does not strongly constrain gas accretion during planet formation.