发表机构
School of Astronomy and Space Science, Nanjing University; Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education; Purple Mountain Observatory, Chinese Academy of Sciences; Institute of Space Weather, School of Atmospheric Physics, Nanjing University of Information Science and Technology; Guangxi Key Laboratory for Relativistic Astrophysics, School of Physical Science and Technology, Guangxi University; State Key Laboratory of Radio Astronomy and Technology, NAOC, Chinese Academy of Sciences（南京大学天文与空间科学学院; 教育部现代天文与天体物理重点实验室（南京大学）; 中国科学院紫金山天文台; 南京信息工程大学大气物理学院太空天气研究所; 广西大学物理科学与技术学院相对论天体物理广西壮族自治区重点实验室; 中国科学院国家天文台射电天文与技术国家重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非均匀采样使标准相关函数失效的问题，本文提出NUACF/NUCCF方法，通过时间间隔权重和错位惩罚计算相关函数，并用蒙特卡洛模拟提供误差估计，在模拟和真实数据中均优于传统方法，适用于时域巡天及FRB等新兴现象。
AI 中文摘要
非均匀采样是天体物理时域分析中一个长期存在的挑战，它使标准的自相关函数和互相关函数失效，迫使研究者采用插值或分箱等临时方法，这些方法会引入未量化的偏差，并且缺乏严格的误差估计。本文提出了一种新的方法，用于计算不规则采样时间序列的非均匀自相关函数（NUACF）和非均匀互相关函数（NUCCF）。该方法不依赖插值，而是通过引入时间间隔权重和错位惩罚来自然地评估相关函数。蒙特卡洛模拟为显著性评估提供了置信带，并为时间延迟提供了完整的误差预算，该误差预算同时考虑了流量不确定性和采样不规则性（这一点至关重要，但现有方法通常缺失）。通过大量模拟，我们证明了该方法在各种条件下均优于传统方法，从严格周期性的变化到复杂的重复性变化模式（例如，间歇性但非周期性的变化）。其有效性通过多个真实天体物理数据集得到了验证，包括揭示恒星光变曲线中的重复性变化、测量活动星系核Fairall 9中多波段盘反响的时间延迟，以及为引力透镜类星体HE 0435-1223的时间延迟提供模型无关的验证。该方法为非均匀采样这一普遍问题提供了严格且通用的解决方案，使其成为大规模时域巡天数据分析的有用工具。该框架还直接适用于新兴的时域现象，如快速射电暴（FRBs），例如，能够研究持续射电源光度与重复FRB活动之间的相关性，或FRB发射本身的多参数变化曲线之间的相关性。
英文摘要
Nonuniform sampling presents a long-standing challenge in astrophysical time-domain analysis, invalidating the standard autocorrelation and cross-correlation functions and forcing researchers to adopt ad-hoc methods like interpolation or binning, which introduce unquantified biases and lack rigorous error estimation. Here we introduce a new method for calculating the nonuniform autocorrelation function (NUACF) and nonuniform cross-correlation function (NUCCF) for irregularly sampled time series. Instead of relying on interpolation, it naturally evaluates the correlation function by incorporating time-interval weights and misalignment penalties. Monte Carlo simulations provide confidence bands for significance assessment and a complete error budget for the time delays that accounts for both flux uncertainties and sampling irregularity (essential but generally absent from existing methods). Through extensive simulations, we demonstrate our method outperforms traditional methods across various conditions, from strictly periodic to complex repeating variability patterns (e.g., intermittent but aperiodic). Its effectiveness is demonstrated via various real astrophysical data sets, revealing repetitive variability in stellar light curves, measuring time delays for multi-band disc reverberation in the AGN Fairall 9, and providing model-independent validation of time delays for the gravitationally lensed quasar HE 0435-1223. The method provides a rigorous and general solution to the ubiquitous problem of nonuniform sampling, positioning it as a useful tool for large-scale time-domain survey data analysis. The framework is also directly applicable to emerging time-domain phenomena such as fast radio bursts (FRBs), enabling, e.g., the study of correlations between persistent radio source luminosity and repeating FRB activity, or among the multi-parameter variability curves of FRB emission itself.
Comments41 pages, 19 figures, 2 figure sets
