[论文解读] Planetary evolution with atmospheric photoevaporation

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

Astro and Planetary Science参考文献 135被引用 114

一句话总结

本文通过建模近距离低质量系外行星的大气光致蒸发，对'蒸发谷'——即分隔超级-Earth与亚-Neptune的系外行星半径双峰分布——的起源进行了理论和数值研究。推导表明，该谷底的下边界（即最大剥离核心半径 Rbare）与恒星XUV辐射 luminosity（LXUV^0.135）及核心质量的依赖关系微弱，解释了为何在不同模型下该谷仍能清晰可见，尽管初始H/He质量存在差异。

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.

研究动机与目标

• 在半径-轨道距离平面上，理论推导蒸发谷的轨迹。
• 理解谷的位置如何依赖于行星核心质量、初始H/He包层质量及恒星XUV辐射 luminosity。
• 通过将观测到的谷形态与光致蒸发等物理过程关联，约束行星形成模型。

提出的方法

• 对具有不同核心质量、轨道分离度和初始H/He质量的近距离低质量系外行星进行大气逃逸的数值模拟。
• 采用能量限制光致蒸发理论，并引入效率因子 ε 来模拟质量损失。
• 基于完全蒸发发生的条件（吸收的XUV辐射积分超过包层的结合能）发展理论模型。
• 使用 ANEOS 方程态模型描述行星内部结构与热力学性质。
• 在核心质量、轨道距离和大气成分的参数网格上进行参数研究。
• 在假设 ε 恒定且 Mc ∝ Rpc^c 的前提下，推导 Rbare 与轨道周期 P 的关系为 P^−0.18。

实验结果

研究问题

• RQ1 在给定轨道距离下，蒸发谷下边界（Rbare）如何依赖于恒星XUV辐射 luminosity？
• RQ2 Rbare 对行星初始H/He质量的依赖关系如何？
• RQ3 为何在观测中该蒸发谷即使在初始条件各异的情况下仍如此清晰可见？
• RQ4 能量限制蒸发的效率因子 ε 如何影响谷的形态？
• RQ5 观测到的谷对行星核心成分和形成模型有何约束？

主要发现

• 在给定轨道距离下，Rbare 对初始H/He质量的依赖关系极弱，其标度关系为 L_XUV^0.135。
• Rbare 对恒星XUV辐射 luminosity 的依赖关系虽弱，但足以解释谷的存在及其非空性。
• 在 ε 恒定条件下，Rbare 随轨道周期 P 的变化关系为 P^−0.18，与观测趋势一致。
• 对于10天轨道周期且具有类地成分的行星，Rbare ≈ 1.7 R⊕，并随冰质分数线性增加。
• 理论模型通过将时间积分吸收的XUV能量与包层引力结合能相等来解释数值结果。
• 对初始H/He质量的微弱依赖关系意味着该谷对行星形成期间气体吸积过程的约束力有限。