基于物理信息神经网络从TESS单次凌星数据获取轨道周期与平衡温度
Orbital Periods and Equilibrium Temperatures from Single TESS Transits with a Physics-Informed Neural Network
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中文总结 AI 辅助
针对TESS单次凌星无法测量长周期行星轨道周期的问题，本文提出物理信息神经网络对未观测几何边缘化，结合开普勒定律从凌星持续时间恢复周期，精度优于Box Least Squares，可用于确定行星平衡温度与宜居带位置。
中文摘要 AI 辅助
轨道周期长于TESS一个观测扇区的行星仅会产生一次凌星，而任何周期图方法都无法测量其周期：仅单次凌星时，所有长于观测基线的试周期都能同等拟合数据。本文表明这并非灵敏度限制，而是结构性限制——对16颗已确认的单次凌星行星，Box Least Squares算法返回的功率谱在95%的搜索网格上数值恒定，将网格从27天扩大到200天，中位数误差变化为-0.0个百分点。轨道周期可通过开普勒第三定律和凌星几何从凌星持续时间直接恢复，无需搜索网格。对15颗目标的直接反演低估了周期，中位数符号误差为-69%，因为假设中心凌星会返回与观测持续时间一致的最短周期。本文训练了一个用于对未观测几何进行边缘化处理的神经网络，消除了这种偏差，相对于Box Least Squares的79.5%，其中位数绝对误差达到40.5%，16颗目标中有14颗的真实周期落在1-sigma区间内。对于NGTS-38 b，其180.5天的周期比其TESS扇区最长连续跨度长10倍，对未观测几何的边缘化处理恢复的后验中位数为190.7天，真实周期处于第47.8百分位，而Box Least Squares得到的结果为18.5天。由于平衡温度与P^(-1/3)成比例，由此产生的8.8倍周期区间压缩为2.1倍温度区间：T_eq=445 K，68%区间为272-562 K，足以通过单次观测确定该行星相对于宜居带的位置。
英文摘要
Planets with orbital periods longer than a TESS sector produce a single transit, and no periodogram method can measure their period: with one transit, every trial period longer than the observing baseline fits the data identically. We show this is not a sensitivity limit but a structural one -- across 16 confirmed single-transit planets, Box Least Squares returns a power spectrum that is numerically constant over 95% of its search grid, and widening that grid from 27 to 200 days changes the median error by -0.0 percentage points. Orbital period can instead be recovered from transit duration through Kepler's third law and transit geometry, requiring no search grid. A direct inversion of these equations underestimates the period in 14 of 15 targets with a median signed error of -69%, because assuming a central transit returns the shortest period consistent with an observed duration. A neural network trained to marginalise over the unobserved geometry removes this bias, reaching a median absolute error of 40.5% against Box Least Squares' 79.5%, with the true period inside the 1-sigma interval for 14 of 16 targets. For NGTS-38 b, whose 180.5 d period lies ten times beyond the longest contiguous span of its TESS sector, marginalising over the unobserved geometry recovers a posterior median of 190.7 d with the true period at the 47.8th percentile, against 18.5 d from Box Least Squares. Because equilibrium temperature scales as P^(-1/3), the resulting factor-8.8 period interval compresses to a factor-2.1 temperature interval: T_eq = 445 K with a 68% interval of 272-562 K, sufficient to place the planet relative to the habitable zone from a single observation.
