巨行星演化的半解析代理模型：利用局域热力学、Softplus渐近线与B样条测光绕过常微分方程求解器

中文摘要 AI 辅助

背景：演化模型将巨行星和褐矮星的可观测光度、温度与颜色转化为质量和年龄。生成其冷却轨道通常需要结合预计算的大气网格，用常微分方程（ODE）求解器对内部能量随时间积分，该过程在云凝结、电子简并发生等尖锐转变处会出现数值刚性，且在贝叶斯反演中稳定性差。目标：我们旨在直接从离散大气网格生成连续冷却轨道和测光光变曲线，无需ODE求解器。方法：我们将网格映射到对数热力学空间，在固定行星参数下通过高斯加权回归提取局域代理模型；用有界分段Softplus函数拟合熵和冷却率与内部温度的关系，以捕捉结构和冷却率转变；在同一温度轴上拟合半径；用固定节点三次B样条表示波段测光；通过对这些解析函数数值积分得到年龄，从每次拟合的残差散射传播不确定性。结果：代理模型CoolTrack重现了电子简并转变以及色-量图中L型到T型光谱型的转变，与太阳系基准吻合，在标准台式CPU上毫秒级即可完成完整演化轨道的计算。结论：通过消除正向建模瓶颈，CoolTrack适合直接用于贝叶斯反演管道，可联合推断行星的年龄、质量、形成熵及其大气属性。

英文摘要

Context. Evolutionary models translate the observable luminosity, temperature, and colours of giant planets and brown dwarfs into mass and age. Generating their cooling tracks normally requires integrating the internal energy over time with an ordinary differential equation (ODE) solver coupled to pre-computed atmospheric grids, which becomes numerically stiff at sharp transitions such as cloud condensation and the onset of electron degeneracy, and is fragile inside Bayesian retrievals. Aims. We aim to generate continuous cooling tracks and photometric light curves directly from discrete atmospheric grids, without an ODE solver. Methods. We mapped the grids into a logarithmic thermodynamic space and extracted localised surrogate models with Gaussian-weighted regressions at fixed planetary parameters. We fitted the entropy and cooling rate against the internal temperature using bounded piecewise softplus functions to capture structural and cooling-rate transitions; the radius was fitted on the same temperature axis; and band photometry was represented with fixed-knot cubic B-splines. The age followed from numerical integration of these analytic functions, and uncertainties were propagated from the residual scatter of each fit. Results. The surrogate, CoolTrack, reproduces the transition into electron degeneracy and the L-to-T spectral-type transition in the colour-magnitude diagram, converges on Solar System benchmarks, and evaluates a full evolutionary track in milliseconds on a standard desktop CPU. Conclusions. By removing the forward-modelling bottleneck, CoolTrack is suitable for direct use in Bayesian retrieval pipelines, where the age, mass, and formation entropy of a planet can be inferred jointly with its atmospheric properties.

发表机构

• LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台，PSL大学，索邦大学，巴黎西岱大学，塞吉-蓬图瓦兹大学，法国国家科学研究中心）
• Space Telescope Science Institute（太空望远镜科学研究所）
• Department of Physics & Astronomy, University of Exeter（埃克塞特大学物理与天文学系）
• Observatoire de la Côte d’Azur, Université Côte d’Azur（蔚蓝海岸天文台，蔚蓝海岸大学）

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