关于余谱的统计性质
On the Statistical Properties of Cospectra
摘要：
近年来，交叉光谱作为表征天文源随波长变化的一种手段，受到了相当大的关注。虽然已经写了很多关于时间和相位滞后的统计数据，但直到最近，共谱才被理解为减轻天文探测器中依赖于时间频率的仪器效应的手段，以及表征不同时间尺度上两个波长范围内的相干变化的方法。在本文中，我们奠定了统计基础的共谱，从最简单的情况下检测周期性信号的存在下，白噪声。这种情况特别适用于在受仪器效应严重影响的探测器中探测微弱的X射线天体，包括NuSTAR，Astrosat和IXPE。我们发现，统计分布的单一和平均cospectromets有很大的不同，从标准周期图。虽然一个单一的cospectrum严格遵循拉普拉斯分布，平均cospectrum近似高斯分布只有超过30个平均段，取决于试验的数量。我们提供了一个指导性的例子，准周期振荡NuSTAR和应用标准的周期图统计导致低估的尾部概率周期检测。我们还展示了应用这些分布的NuSTAR观测的X射线脉冲星武仙座X-1。
英文摘要：
In recent years, the cross spectrum has received considerable attention as a means of characterising the variability of astronomical sources as a function of wavelength. While much has been written about the statistics of time and phase lags, the cospectrum has only recently been understood as means of mitigating instrumental effects dependent on temporal frequency in astronomical detectors, as well as a method of characterizing the coherent variability in two wavelength ranges on different time scales. In this paper, we lay out the statistical foundations of the cospectrum, starting with the simplest case of detecting a periodic signal in the presence of white noise. This case is especially relevant for detecting faint X-ray pulsars in detectors heavily affected by instrumental effects, including NuSTAR, Astrosat and IXPE. We show that the statistical distributions of both single and averaged cospectra differ considerably from those for standard periodograms. While a single cospectrum follows a Laplace distribution exactly, averaged cospectra are approximated by a Gaussian distribution only for more than ~30 averaged segments, dependent on the number of trials. We provide an instructive example of a quasi-periodic oscillation in NuSTAR and show that applying standard periodogram statistics leads to underestimated tail probabilities for period detection. We also demonstrate the application of these distributions to a NuSTAR observation of the X-ray pulsar Hercules X-1.
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