利用傅里叶级数从噪声光变曲线中提取周期性Transit信号
Extracting Periodic Transit Signals from Noisy Light Curves using Fourier Series
摘要：
我们提出了一个简单而强大的方法，用于从噪声光变曲线中提取与已知过境行星相关的过境信号。假设行星的轨道周期是已知的，并且信号是周期性的，我们说明了系统噪声可以在傅立叶空间中在所有频率下被去除，通过仅使用具有等于整数个轨道周期的宽度的固定时间帧内的数据。这导致了对整个渡越信号的重构，其平均而言是无偏的，尽管在分析中没有使用噪声或渡越信号本身的先验知识。因此，该方法具有明显的优势，标准的相位折叠，通常需要外部输入，如附近的恒星或噪声模型，以消除系统的组件。此外，我们可以同时提取完整的轨道过境信号（$360$度），并且可以在短短几秒钟内分析\emph{Kepler}之类的数据。我们说明了我们的方法的性能，将其应用到一个数据集组成的光变曲线从\emph{Kepler}与假注入信号模拟行星环。对于提取周期性过境信号，我们提出的方法通常是最佳和最小偏差的估计，因此可以引导对第一次检测的方式，例如，行星环和特洛伊系外小行星
英文摘要：
We present a simple and powerful method for extracting transit signals associated with a known transiting planet from noisy light curves. Assuming the orbital period of the planet is known and the signal is periodic, we illustrate that systematic noise can be removed in Fourier space at all frequencies, by only using data within a fixed time frame with a width equal to an integer number of orbital periods. This results in a reconstruction of the full transit signal which on average is unbiased, despite that no prior knowledge of either the noise or the transit signal itself is used in the analysis. The method has therefore clear advantages over standard phase folding, which normally requires external input such as nearby stars or noise models for removing systematic components. In addition, we can extract the full orbital transit signal ($360$ degrees) simultaneously, and \emph{Kepler} like data can be analyzed in just a few seconds. We illustrate the performance of our method by applying it to a dataset composed of light curves from \emph{Kepler} with a fake injected signal emulating a planet with rings. For extracting periodic transit signals, our presented method is in general the optimal and least biased estimator and could therefore lead the way toward the first detections of, e.g., planet rings and exo-trojan asteroids.
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