AI 中文总结
本研究提出正则化高斯过程似然框架，在539颗恒星的基准测试中使成功恢复自转周期的比例平均提高7%，可提升恒星活动建模中高斯过程超参数的物理可解释性。
AI 中文摘要
高斯过程（Gaussian Processes, GPs）被广泛用于建模光度巡天中的恒星变异性，但统计上成功的拟合并不保证推断出的超参数对应物理上有意义的恒星属性。这对年轻、活跃的恒星尤为重要，它们的TESS光变曲线包含演化的星斑、谐波和非正弦变异性。我们以恒星自转为案例，研究准周期高斯过程的周期超参数何时可被解释为物理自转周期。我们引入一种正则化高斯过程似然，该似然会对边际似然中的协方差复杂度项进行加权，减少无约束模型收敛到偏好但误导性解的倾向。我们在IC2602、杜鹃-时钟座星协、双鱼座-波江座和GroupX中的539颗恒星上测试该框架，这些恒星具有独立报告且经人工核验的自转周期。该基准以最少的人工干预评估高斯过程超参数的可解释性和自动周期恢复能力。我们在多个正则化强度λ下比较正则化与非正则化模型，使用文献一致性、扇区级诊断和TESS扇区间的一致性作为评估指标。与标准高斯过程似然相比，正则化使成功恢复自转周期的比例平均提高7%，还通常降低了扇区间周期的中位数绝对分数偏差，表明改进不仅限于灾难性失败，还可缓解较小的系统误差。正则化对非正弦或演化调制尤其有益，因为无约束高斯过程可能会恢复谐波或虚假时标。这些结果表明，似然正则化和跨扇区一致性是评估基于高斯过程的自转周期是否可靠的实用诊断方法。
英文摘要
Gaussian Processes (GPs) are widely used to model stellar variability in photometric surveys, but a statistically successful fit does not guarantee that the inferred hyperparameters correspond to physically meaningful stellar properties. This is especially important for young, active stars, whose TESS light curves contain evolving spots, harmonics, and non-sinusoidal variability. We use stellar rotation as a case study to examine when the period hyperparameter of a quasi-periodic GP can be interpreted as a physical rotation period. We introduce a regularized GP likelihood that reweights the covariance-complexity term in the marginal likelihood, reducing the tendency of unconstrained models to converge toward preferred but misleading solutions. We test this framework on 539 stars in IC2602, the Tucana-Horologium Association, Pisces-Eridanus, and GroupX, with independently reported and manually vetted rotation periods. This benchmark evaluates GP hyperparameter interpretability and automated period recovery with minimal human intervention. We compare regularized and unregularized models across several regularization strengths, λ, using literature agreement, sector-level diagnostics, and consistency across TESS sectors. Relative to the standard GP likelihood, regularization improves successful rotation-period recovery by an average of 7%. It also generally reduces the median absolute fractional deviation of periods across sectors, showing that the improvement is not limited to catastrophic failures but also mitigates smaller systematic errors. Regularization is particularly beneficial for non-sinusoidal or evolving modulation, where unconstrained GPs may recover harmonics or spurious timescales. These results show that likelihood regularization and cross-sector consistency are practical diagnostics for assessing when GP-based rotation periods are robust.
Comments(23 pages, 12 figures, 5 tables)
