非线性耦合振子模型化如何解释Blazhko效应、层同步、模式选择、极限环和不稳定带的红限
How the nonlinear coupled oscillators modelization explains the Blazhko effect, the synchronisation of layers, the mode selection, the limit cycle, and the red limit of the instability strip
摘要：
上下文天琴座RR型恒星的Blazhko效应是一个世纪之谜。存在着几十种理论，但没有一种能够完全重现与这种调制现象相关的观测事实。现有的理论都依赖于通常的恒星连续模型化。目标。我们提出了一个新的范例，这不仅将解释Blazhko效应，但在同一时间，将给我们提供替代解释的红色极限的不稳定带，层的同步，模式选择和存在的极限环径向脉动星。方法.我们把RR型Lyrant型脉动星描述为一个耦合的非线性振子系统。考虑空间离散的恒星，假设球对称，我们开发的运动方程和能量的径向和绝热的情况下，到第三阶。然后，我们包括作为弛豫振荡器的电离区域的影响，包括同步理论的元素。结果这种离散的方法使我们能够利用现有的结果在耦合非线性振子领域。例如，同步性的研究导致解释的模式选择，层同步，极限环和红色限制的不稳定带。但是，最重要的是，与费米-帕斯塔-乌拉姆（FPU）实验的类比使我们能够理解Blazhko效应。由孤子引起的不同模式之间的能量转移不仅给出了光变曲线调制的合理理论，而且还解释了旁瓣的不对称性。
英文摘要：
Context. The Blazhko effect, in RR Lyrae type stars, is a century old mystery. Dozens of theory exists, but none have been able to entirely reproduce the observational facts associated to this modulation phenomenon. Existing theory all rely on the usual continuous modelization of the star. Aims. We present a new paradigm which will not only explain the Blazhko effect, but at the same time, will give us alternative explanations to the red limit of the instability strip, the synchronization of layers, the mode selection and the existence of a limit cycle for radially pulsating stars. Methods. We describe the RR Lyrae type pulsating stars as a system of coupled nonlinear oscillators. Considering a spatial discretisation of the star, supposing a spherical symmetry, we develop the equation of motion and energy up to the third order in the radial and adiabatic case. Then, we include the influence of the ionization region as a relaxation oscillator by including elements from synchronisation theory. Results. This discrete approach allows us to exploit existing results in the coupled nonlinear oscillator field. For instance, the study of synchronicity leads to an explanation of the mode selection, the layers synchronisation, the limit cycle and the red limit of the instability strip. But, most of all, the analogy with the Fermi-Pasta-Ulam (FPU) experiment enables us to understand the Blazhko effect. The transfer of energy between different modes, as induced by solitons, not only gives a plausible theory for lightcurve modulation, but also explains the asymmetry of sidelobes.
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