标题： 多周期性、调制和翻转在变星光曲线中的研究 I. 载波拟合方法 显示英文标题

标题： Multiperiodicity, modulations and flip-flops in variable star light curves I. Carrier fit method

摘要： 变星的光变曲线通常使用简单的三角函数模型进行描述，这些模型假设模型参数随时间保持不变。 然而，这一假设常常被违反，因此具有随时间缓慢变化成分的时间序列模型具有重要意义。 在本文中，我们引入了一类数据分析和可视化方法，这些方法可以应用于变星研究的许多不同情境，例如有黑子的恒星、表现出Blazhko效应的变星以及快速旋转体的自转减慢。 所提出的方法属于探索性方法，在使用更传统的手段进行更深入的数据分析和解释时，可以提供重要帮助。我们的方法基于输入时间序列的简单分解，包括一个快速的“计时”周期性和平滑的调制曲线。 快速频率，称为载波频率，可以从早期观测中获得（例如在光度数据的情况下，周期可以从独立测量的径向速度获得），通过一些简单的物理原理进行假定（如吸积盘中的开普勒旋转定律），或从数据中作为某种平均频率进行估计。 平滑的调制曲线由三角多项式或样条曲线描述。 数据逼近过程基于实现简单或约束最小二乘拟合类型算法的标准计算包。 显示英文摘要

摘要： The light curves of variable stars are commonly described using simple trigonometric models, that make use of the assumption that the model parameters are constant in time. This assumption, however, is often violated, and consequently, time series models with components that vary slowly in time are of great interest. In this paper we introduce a class of data analysis and visualization methods which can be applied in many different contexts of variable star research, for example spotted stars, variables showing the Blazhko effect, and the spin-down of rapid rotators. The methods proposed are of explorative type, and can be of significant aid when performing a more thorough data analysis and interpretation with a more conventional method.Our methods are based on a straightforward decomposition of the input time series into a fast "clocking" periodicity and smooth modulating curves. The fast frequency, referred to as the carrier frequency, can be obtained from earlier observations (for instance in the case of photometric data the period can be obtained from independently measured radial velocities), postulated using some simple physical principles (Keplerian rotation laws in accretion disks), or estimated from the data as a certain mean frequency. The smooth modulating curves are described by trigonometric polynomials or splines. The data approximation procedures are based on standard computational packages implementing simple or constrained least-squares fit-type algorithms.