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arXiv 1102.0157astro-ph.SR
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RR Lyrant流体动力学模型的倍周期分岔和高阶共振

Period doubling bifurcation and high-order resonances in RR Lyrae hydrodynamical models

Z. Kolláth, L. Molnár, R. Szabó

摘要:

我们首次在RR Lyrics模型中研究了动力系统中的一个著名现象--倍周期。这些研究为最近用开普勒太空望远镜发现的Blazhko RR型天琴座星的倍周期提供了理论背景。由于倍周期到目前为止只在Blazhko调制的恒星中观察到,该现象也有助于理解调制。利用佛罗里达-布达佩斯湍流对流流体动力学代码,我们确定了辐射和对流模型中的现象。倍周期级联也跟进到一个八期的解决方案,确认极限环的不稳定确实是潜在的现象。通过计算Floquet稳定性根,研究了这一现象发生的可能原因。构造了一个二维诊断图来显示基模和不同泛音之间的各种共振。结合这两种工具,我们证实了倍周期不稳定性是由9阶泛音和基模之间的9:2共振引起的。由于泛音是一种奇怪的模式,因此,由高阶模式的共振引起的极限环失稳是可能的。共振被发现是足够强,足以转移的泛音周期高达百分之十。我们的研究表明,一个更复杂的相互作用的径向(大概是非径向)模式可能会发生在RR天琴座恒星,可能有连接的Blazhko效应以及。

英文摘要:

We investigated period doubling, a well-known phenomenon in dynamical systems, for the first time in RR Lyrae models. These studies provide theoretical background for the recent discovery of period doubling in some Blazhko RR Lyrae stars with the Kepler space telescope. Since period doubling was observed only in Blazhko-modulated stars so far, the phenomenon can help in the understanding of the modulation as well. Utilising the Florida-Budapest turbulent convective hydrodynamical code, we identified the phenomenon in radiative and convective models as well. A period-doubling cascade was also followed up to an eight-period solution confirming that the destabilisation of the limit cycle is indeed the underlying phenomenon. Floquet stability roots were calculated to investigate the possible causes and occurrences of the phenomenon. A two-dimensional diagnostic diagram was constructed to display the various resonances between the fundamental mode and the different overtones. Combining the two tools, we confirmed that the period-doubling instability is caused by a 9:2 resonance between the 9th overtone and the fundamental mode. Destabilisation of the limit cycle by a resonance of a high-order mode is possible because the overtone is a strange mode. The resonance is found to be sufficiently strong enough to shift the period of overtone with up to 10 percent. Our investigations suggest that a more complex interplay of radial (and presumably non-radial) modes could happen in RR Lyrae stars that might have connections with the Blazhko effect as well.

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