AI 中文总结
本文提出一种生成具有任意功率谱、相干函数和相位滞后轮廓的时间序列对的算法，可用于X射线天文学中测试多洛伦兹拟合技术，经双洛伦兹模型验证，生成数据与输入模型吻合良好。
AI 中文摘要
互谱方法已成为研究X射线双星和活动星系核中吸积物理的关键手段，相干性和相位滞后测量可约束物理模型，揭示仅从功率谱中无法观测到的变率成分。近期多洛伦兹拟合技术通过联合分析功率谱与互谱，发现了新的准周期特征，但测试这些方法需要具有真实统计特性的合成数据。本文提出一种算法，用于生成具有任意功率谱、相干函数和相位滞后轮廓的时间序列对。该方法将相关时间序列分解为相干和不相干分量，其中相干部分通过对参考序列应用复传递函数构建，以此扩展现有方法。本文推导了传递函数和归一化条件，以在实现指定互谱特性的同时保留目标谱形；还得到了相干性和相位滞后估计量方差的近似解析表达式，并构建了关联这些量与基础功率及互谱的近似协方差矩阵。在对功率谱与互谱进行联合模型拟合时，似然计算必须纳入这些相关性。本文将该方法应用于具有分量相关相位滞后的双洛伦兹模型，证明在四个数量级的频率范围内，输入模型与生成的功率谱、相干函数及相位滞后轮廓吻合良好。
英文摘要
Cross-spectral methods have become essential for studying accretion physics in X-ray binaries and active galactic nuclei, where coherence and phase lag measurements constrain physical models and reveal variability components invisible in power spectra alone. Recent multi-Lorentzian fitting techniques have uncovered new quasi-periodic features through joint analysis of power spectra and cross-spectra, but testing these methods requires synthetic data with realistic statistical properties. We present an algorithm for generating pairs of time series with arbitrary power spectra, coherence functions, and phase lag profiles. The method extends existing methods by decomposing the dependent time series into coherent and incoherent components, where the coherent part is constructed through a complex transfer function applied to a reference series. We derive the transfer function and normalization required to preserve target spectral shapes while achieving specified cross-spectral properties. We obtain approximate analytic expressions for the variance of coherence and phase lag estimators and construct the approximate covariance matrix relating these quantities to the underlying power and cross-spectra. When fitting models jointly to power and cross-spectra, these correlations must be incorporated into the likelihood. We apply the method to a two-Lorentzian model with component-specific phase lags and demonstrate close agreement between input models and generated power spectra, coherence function, and phase lag profile across four decades in frequency.
Comments10 + 5 pages, 4 figures. Accepted to RAS Techniques and Instruments
