发表机构
Columbia University; Barnard College, Columbia University（哥伦比亚大学; 哥伦比亚大学巴纳德学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究人员首次将Koopman算子理论与EDMD应用于X射线光变曲线，成功表征X射线双星的非线性动力学，实现提前数天至数周的流量预测，为天体物理计时提供新方法。
AI 中文摘要
致密天体双星的X射线变异性编码了冕-喷流相互作用和吸积盘不稳定性的非线性动力学。标准计时技术能很好地表征周期性和准周期性变异性，但无法对潜在的非线性动力学进行建模，也无法预测其演化。我们首次将Koopman算子理论及其数据驱动近似方法——扩展动态模式分解（EDMD）应用于X射线光变曲线。Koopman理论将非线性演化表示为无限维线性算子$\boldsymbol{\textit{K}}$，其特征分解将复杂系统分解为独立演化的线性模式。我们推导得出，每个Koopman本征函数都会在功率谱中贡献一个洛伦兹峰，为准周期性振荡提供了动力学解释：过程噪声会阻尼模式并展宽其峰。在混沌杜芬振子模拟以及对X射线双星4U 1705-44进行的约30年RXTE ASM和MAXI监测中，变化最慢的本征函数将相空间划分为低流量和高流量状态，在光变曲线中可见转变的数天至数周前就会改变符号。迭代$\boldsymbol{\textit{K}}$还能产生数天至数周尺度的流量预测。该框架的优势在于其对线性和非线性系统的普适性、通过携带明确动力学意义的分解模式实现的内在可解释性，以及通过将学习到的动力学向前传播实现的预测能力。这些结果确立了Koopman算子理论作为天体物理计时的新前沿，并有助于推进用于科学发现和理解的可解释机器学习。
英文摘要
X-ray variability in compact-object binaries encodes the nonlinear dynamics of corona-jet interactions and accretion disk instabilities. Standard timing techniques characterize periodic and quasi-periodic variability well, but do not model underlying nonlinear dynamics or forecast their evolution. We apply Koopman operator theory and a data-driven approximation, extended dynamic mode decomposition (EDMD), to X-ray light curves for the first time. Koopman theory represents nonlinear evolution as an infinite-dimensional linear operator $\mathcal{K}$, whose eigendecomposition separates a complex system into independently evolving linear modes. We derive that each Koopman eigenfunction contributes a Lorentzian peak to the power spectrum, giving quasi-periodic oscillations a dynamical interpretation in which process noise damps modes and broadens their peaks. In both chaotic Duffing oscillator simulations and $\sim$30 yr of RXTE ASM and MAXI monitoring of the X-ray binary 4U 1705-44, the slowest-varying eigenfunction partitions state space into low- and high-flux regimes, changing sign days to weeks before transitions become visible in the light curve. Iterating $\mathcal{K}$ additionally yields flux forecasts on days-to-weeks horizons. The strengths of this framework are its generality across linear and nonlinear systems, its intrinsic interpretability through decomposed modes carrying explicit dynamical meaning, and its predictive power from propagating learned dynamics forward. These results establish Koopman operator theory as a new frontier of astrophysical timing and help advance interpretable machine learning for scientific discovery and understanding.
Comments31 pages, 16 figures, to be published in the Astrophysics Journal Supplement Series (ApJS)
