In the oscillation spectra of giant stars, nonradial modes may be seen to undergo avoided crossings, which produce a characteristic "mode bumping" of the otherwise uniform asymptotic p- and g-mode patterns in their respective echelle diagrams. Avoided crossings evolve very quickly relative to typical observational errors, and are therefore extremely useful in determining precise ages of stars, particularly in subgiants. This phenomenon is caused by coupling between modes in the p- and g-mode cavities that are near resonance with each other. Most theoretical analyses of the coupling between these mode cavities rely on the JWKB approach, which is strictly speaking inapplicable for the low-order g-modes observed in subgiants, or the low-order p-modes seen in very evolved red giants. We present both a nonasymptotic prescription for isolating the two mode cavities, as well as a perturbative (and also nonasymptotic) description of the coupling between them, which we show to hold good for the low-order g- and p-modes in these physical situations. Finally, we discuss how these results may be applied to modelling subgiant stars and determining their global properties from oscillation frequencies. We also make our code for all of these computations publicly available.

中文翻译：

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混合模式的隔离和耦合的半解析表达式

在巨星的振荡光谱中，可以看到非径向模式避免了交叉，这在它们各自的阶梯图中产生了原本均匀的渐近 p 和 g 模式模式的特征“模式碰撞”。相对于典型的观测误差，避免的交叉演化非常快，因此在确定恒星的精确年龄方面非常有用，特别是在亚巨星中。这种现象是由彼此接近共振的 p 和 g 模式腔中的模式之间的耦合引起的。大多数对这些模式腔之间耦合的理论分析依赖于 JWKB 方法，严格来说，这不适用于在亚巨星中观察到的低阶 g 模式，或在非常进化的红巨星中观察到的低阶 p 模式。我们提出了隔离两个模式腔的非渐近处方，以及它们之间耦合的微扰（也是非渐近）描述，我们证明这对这些物理中的低阶 g 和 p 模式有效情况。最后，我们讨论如何将这些结果应用于模拟次巨星并根据振荡频率确定它们的全局特性。我们还公开了所有这些计算的代码。