标题： 解决一颗恒星地震学的灾难：主序之外的重力波相位函数的结构诊断 显示英文标题

标题： Resolving an Asteroseismic Catastrophe: Structural Diagnostics from p-mode Phase Functions off the Main Sequence

摘要： 在主序星上，径向与四极p模式之间的振声小频率分离$\delta\nu_{02}$通常被解释为内部结构的直接诊断工具。这种解释基于一个著名的积分估计器，该估计器将$\delta\nu_{02}$与径向平均声速梯度联系起来。然而，当应用于红巨星的结构模型时，这个估计器会灾难性地失效：因此，它们的小分离必须以不同的方式来解释。我们推导出一个单一表达式，它在应用于主序星模型时会退化为经典的估计器，但在非常演化的红巨星模型的小分离方面又能重现定性特征。这个表达式表明，红巨星的小分离主要与其全局地震特性呈$\delta\nu_{02} \propto \Delta\nu^2/\nu_\mathrm{max}$的比例关系，而不是对其内部结构有任何敏感性。从主序到红巨星阶段过渡期间偏离这一渐近行为的现象最近已在K2任务数据的开普勒星团Christensen-Dalsgaard（C-D）图中报道。详细研究这些现象后，我们证明了当对流包层边界通过恒星中心的一个特定声学距离——大约是一个波长的三分之一（$\nu_\mathrm{max}$）时，就会发生这种情况，此时径向模式对边界的位移变得最为敏感。在$\epsilon_p$和C-D（或$r_{02}$）图中相应特征的形状可能有助于约束对流边界混合性质的研究，特别是在对流包层下方欠冲区域的情境下。 显示英文摘要

摘要： On the main sequence, the asteroseismic small frequency separation $\delta\nu_{02}$ between radial and quadrupole p-modes is customarily interpreted to be a direct diagnostic of internal structure. Such an interpretation is based on a well-known integral estimator relating $\delta\nu_{02}$ to a radially-averaged sound-speed gradient. However, this estimator fails, catastrophically, when evaluated on structural models of red giants: their small separations must therefore be interpreted differently. We derive a single expression which both reduces to the classical estimator when applied to main-sequence stellar models, yet reproduces the qualitative features of the small separation for stellar models of very evolved red giants. This expression indicates that the small separations of red giants scale primarily with their global seismic properties as $\delta\nu_{02} \propto \Delta\nu^2/\nu_\mathrm{max}$, rather than being in any way sensitive to their internal structure. Departures from this asymptotic behaviour, during the transition from the main-sequence to red giant regimes, have been recently reported in open-cluster Christensen-Dalsgaard (C-D) diagrams from K2 mission data. Investigating them in detail, we demonstrate that they occur when the convective envelope boundary passes a specific acoustic distance -- roughly a third of a wavelength at $\nu_\mathrm{max}$ -- from the centre of the star, at which point radial modes become maximally sensitive to the position of the boundary. The shape of the corresponding features on $\epsilon_p$ and C-D (or $r_{02}$) diagrams may be useful in constraining the nature of convective boundary mixing, in the context of undershooting beneath a convective envelope.