[论文解读] Thermal evolution of Uranus and Neptune II -- Deep thermal boundary layer

Ludwig Scheibe, Nadine Nettelmann+1 more|arXiv (Cornell University)|May 4, 2021

Astro and Planetary Science参考文献 55被引用 30

一句话总结

本研究探讨了海王星和天王星深部内部热导性边界层（TBL）对其热演化及观测光度的影响。利用先进的状态方程和从头算热导率数据，作者表明，即使仅几公里厚的TBL，也能显著减缓冷却过程。要使天王星的观测光度保持黯淡，其必须长期处于与太阳辐射热平衡的状态；对于海王星，若TBL厚度超过15公里或热导率增强，则可解释其高于绝热模型的光度。

ABSTRACT

Thermal evolution models suggest that the luminosities of both Uranus and Neptune are inconsistent with the classical assumption of an adiabatic interior. Such models commonly predict Uranus to be brighter and, recently, Neptune to be fainter than observed. In this work, we investigate the influence of a thermally conductive boundary layer on the evolution of Uranus- and Neptune-like planets. This thermal boundary layer (TBL) is assumed to be located deep in the planet, and be caused by a steep compositional gradient between a H-He-dominated outer envelope and an ice-rich inner envelope. We investigate the effect of TBL thickness, thermal conductivity, and the time of TBL formation on the planet's cooling behaviour. The calculations were performed with our recently developed tool based on the Henyey method for stellar evolution. We make use of state-of-the-art equations of state for hydrogen, helium, and water, as well as of thermal conductivity data for water calculated via ab initio methods. We find that even a thin conductive layer of a few kilometres has a significant influence on the planetary cooling. In our models, Uranus' measured luminosity can only be reproduced if the planet has been near equilibrium with the solar incident flux for an extended time. For Neptune, we find a range of solutions with a near constant effective temperature at layer thicknesses of 15 km or larger, similar to Uranus. In addition, we find solutions for thin TBLs of few km and strongly enhanced thermal conductivity. A $\sim$ 1$~$Gyr later onset of the TBL reduces the present $\Delta T$ by an order of magnitude to only several 100 K. Our models suggest that a TBL can significantly influence the present planetary luminosity in both directions, making it appear either brighter or fainter than the adiabatic case.

研究动机与目标

• 探究深层热边界层（TBL）对天王星和海王星热演化的影响。
• 确定TBL厚度、热导率及形成时间对行星冷却与光度的影响。
• 调和观测光度与经典绝热演化模型之间的差异。
• 评估TBL是否能解释为何天王星比绝热模型预测的更黯淡，而海王星更明亮。
• 评估组分梯度与热导率在塑造冰巨星热历史中的作用。

提出的方法

• 使用基于Henyey方法的OTTER恒星演化代码模拟行星热演化。
• 应用H、He和H2O的最先进状态方程以计算热力学性质。
• 整合通过密度泛函理论（DFT-MD）计算的水的从头算热导率数据。
• 假设三层次内部结构：岩石核心、富含冰的包层，以及以H/He为主的外层包层。
• 改变TBL厚度（从几公里到15公里）、热导率（最高达水的100倍）及形成时间（从形成时刻到约10亿年之后）。
• 在球对称条件下求解能量与动量守恒方程，将自转视为微扰。

实验结果

研究问题

• RQ1 热导性边界层（TBL）如何影响天王星和海王星的冷却速率？
• RQ2 TBL能否解释天王星尽管年龄极高，却仍保持低观测光度的现象？
• RQ3 TBL能否解释海王星相比绝热模型表现出的异常高光度？
• RQ4 需要何种TBL厚度与热导率才能重现观测到的有效温度？
• RQ5 TBL形成时间如何影响行星当前的热状态？

主要发现

• 只有当行星长期处于与太阳辐射热平衡状态时，才能重现天王星的观测光度，这要求TBL足够厚以捕获其大部分原始热量。
• 对于海王星，若TBL厚度达到15公里或更厚，则光度演化呈现平台状，导致有效温度接近恒定，与天王星相似。
• 薄TBL（几公里厚）且热导率显著增强（λ/λH2O ≈ 100）的解可解释海王星高于绝热模型的光度，提示可能存在双扩散对流或分层对流状态。
• 若TBL在形成约10亿年后开始形成，可使当前温度差（∆T）降低一个数量级，仅剩数百开尔文。
• TBL可使行星在外观上比绝热模型更亮或更暗，具体取决于其厚度与热导率，从而同时解释天王星的黯淡与海王星的明亮。
• TBL可能通过加速外层包层冷却，促进水-氢相分离，从而有助于冰巨星中沉积过程的进行。