标题： 瑞利判据：天文学周期图的分辨率极限 显示英文标题

标题： The Rayleigh Criterion: Resolution Limits of Astronomical Periodograms

摘要： 瑞利准则确定了周期图的分辨率极限，即分辨两个正弦波所需的最小频率间隔。 忽视瑞利准则可能导致对长周期信号的错误解释，或错误地认为两个紧密相邻的周期图峰值代表两种不同的物理过程。 我们展示了如何应用瑞利准则可以帮助观察者避免由于观测时间不均匀或观测时间基线不足而导致的误报检测。 我们提出了三个合成数据集来说明： (1) 由于观测时间不均匀导致的单个振荡的分裂 Lomb-Scargle 周期图峰值可能被误认为是两个振荡，如果忽略瑞利准则的话；(2) 对周期图的频率网格进行过采样并不能提高分辨率；(3) 分辨两个紧密相邻振荡所需的观测时间基线。 我们使用瑞利准则重新审视了来自四个已发表数据集中的行星、恒星活动和差分自转的检测结果。 我们表明，行星 55~Cnc~d 和活动周期之间的频率间隔太小，仅凭已发表的径向速度（RVs）无法区分这两种现象。 同样，围绕 HD~99492 运行的争议性的 4970 天行星无法从零频率中进行统计分离。 我们确定，三次多项式比正弦模型更能解释巴纳德星的长期 RV 变化。 最后，我们对{\it 开普勒}观测的两颗活跃恒星的重新分析显示，之前归因于差分自转的信号可以用具有单一准周期性的高斯过程进行建模。 这项工作展示了在构建时域模型时瑞利准则的重要性。 显示英文摘要

摘要： The Rayleigh criterion determines the resolution limit of a periodogram, which is the minimum frequency separation required to barely resolve two sinusoids. Failing to consider the Rayleigh criterion may result in incorrect interpretations of long-period signals or spurious claims that two closely spaced periodogram peaks represent two distinct physical processes. We demonstrate how applying the Rayleigh criterion can help observers avoid false positive detections caused by uneven observing cadence or insufficient observing time baseline. We present three synthetic datasets that illustrate (1) a single oscillation with a split Lomb-Scargle periodogram peak resulting from uneven observing cadence can be mistaken for two oscillations if the Rayleigh criterion is neglected, (2) oversampling a periodogram's frequency grid does not improve resolution, and (3) observing time baseline requirements for resolving two closely spaced oscillations. We use the Rayleigh criterion to revisit detections of planets, stellar activity, and differential rotation from four published datasets. We show that the frequency separation between planet 55~Cnc~d and the activity cycle is too small to distinguish the two phenomena based on published radial velocities (RVs) alone. Likewise, the contested 4970-day planet orbiting HD~99492 cannot be statistically separated from zero frequency. We determine that a cubic polynomial better explains the long-term RV variability of Barnard's star than a sinusoid model. Finally, our re-analysis of {\it Kepler} observations of two active stars shows that the signals previously attributed to differential rotation can be modeled by a Gaussian process with a single quasiperiodicity. This work demonstrates the importance of the Rayleigh criterion when constructing a time-domain model.