活动星系核光变曲线互相关的概率分布与零假设检验
On the Probability Distribution and Null-hypothesis Testing of Cross-correlation for Light Curves in Active Galactic Nuclei
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中文总结 AI 辅助
本文利用随机时间序列理论，提出基于自相关函数解析估计方差的正态近似方法，实现对活动星系核光变曲线互相关显著性的快速零假设检验，并应用于反响映射数据。
中文摘要 AI 辅助
互相关在多波长通量变异性研究中至关重要，尤其是在活动星系核（AGNs）的 reverberation mapping（反响映射）分析中，其中插值互相关函数被广泛用于测量光变曲线之间的时间延迟。虽然时间延迟的不确定性可以通过通量随机化和随机子集选择方法来估计，但文献中仍缺乏评估互相关显著性的适当框架。在此，我们尝试通过利用随机时间序列理论中一个公认的性质来填补这一空白，即独立随机光变曲线的互相关系数的概率分布渐近地趋近于正态分布。其方差可以利用光变曲线的自相关函数进行解析估计。我们采用蒙特卡洛模拟来验证这一性质对于不规则采样、红噪声活动星系核光变曲线的适用性，然后提出一种快速程序来对活动星系核光变曲线的互相关进行零假设检验。我们还展示了该方法在活动星系核反响映射数据中的示例应用。该程序需要预先确定光变曲线的自相关函数，这可以通过模型拟合获得。当光变曲线持续时间与典型变化时标相当时，关于无偏恢复自相关函数的长期问题仍未解决，值得未来进一步研究。
英文摘要
Cross-correlation is crucial in studies of multiwavelength flux variability in active galactic nuclei (AGNs), especially for reverberation mapping analysis, where interpolated cross-correlation function is widely used to measure time lags between light curves. While time-lag uncertainties can be estimated via the flux randomization and random subset selection method, an appropriate framework for assessing cross-correlation significance remains lacking in the literature. Here we attempt to fill this gap by leveraging the well-established property from stochastic time series theory, namely that the probability distribution of cross-correlation coefficients for independent stochastic light curves asymptotically approaches a normal distribution. Its variance can be analytically estimated using the auto-correlation functions of the light curves. We employ Monte Carlo simulations to validate this property for irregularly sampled, red-noise AGN light curves, and then propose a fast procedure to perform null-hypothesis testing for the cross-correlation of AGN light curves. We also present exemplary applications to AGN reverberation mapping data. This procedure requires prior determination of the auto-correlation functions of light curves, which can be obtained via model fitting. The long-standing issue regarding unbiasedly recovering the auto-correlation function remains unresolved when light-curve duration is comparable to the typical variation timescale, warranting further future investigation.
发表机构
- State Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所粒子天体物理国家重点实验室）
- School of Astronomy and Space Sciences, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
- National Astronomical Observatory of China（中国科学院国家天文台）
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