标题： 氦燃烧芯混合处理的模型--II.来自星团恒星计数的限制 显示英文标题

标题： The treatment of mixing in core helium burning models -- II. Constraints from cluster star counts

摘要： 核心氦燃烧期间对流边界处理问题是恒星演化计算中的一个基本问题。在论文 I 中，我们展示了这些恒星的新星震观测表明它们要么具有非常大的对流核，要么具有被困住重力波的半对流/部分混合区。我们通过从 48 个银河球状星团最近的 HST 光度测量中推断 AGB 和 HB 的相对寿命来探测这种混合，即 $R_2$ 的观测比值。我们的 $R_2$ 新确定结果比以前的研究更加自洽，而我们的整体 $R_2 = 0.117 \pm 0.005$ 计算现在是最具统计学鲁棒性的。我们还确定了 HB 和 AGB 团块之间的光度差为 $\Delta \log{L}_\text{HB}^\text{AGB} = 0.455 \pm 0.012$。我们的结果与早期发现一致，标准模型预测的 $R_2$ 比观测值低。我们证明了模型中不确定性主要来源是对流混合的处理方式以及由此数值处理可能产生的随机效应。我们从观测中推导出的光度概率密度函数在 AGB 团块附近有一个尖锐的峰值。这构成了对核心呼吸脉冲的一个强有力的反对新论据，因为后者会扩大峰值的预测宽度。我们得出结论，能够匹配星震学的两种混合方案也可以匹配球状星团观测，但前提是：(i) 在具有半对流/部分混合区的模型中避免核心呼吸脉冲；或者 (ii) 具有大对流核的模型在随后的早期 AGB '重力核'对流中具有特定深度的混合。 显示英文摘要

摘要： The treatment of convective boundaries during core helium burning is a fundamental problem in stellar evolution calculations. In Paper~I we showed that new asteroseismic observations of these stars imply they have either very large convective cores or semiconvection/partially mixed zones that trap g-modes. We probe this mixing by inferring the relative lifetimes of asymptotic giant branch (AGB) and horizontal branch (HB) from $R_2$, the observed ratio of these stars in recent HST photometry of 48 Galactic globular clusters. Our new determinations of $R_2$ are more self-consistent than those of previous studies and our overall calculation of $R_2 = 0.117 \pm 0.005$ is the most statistically robust now available. We also establish that the luminosity difference between the HB and the AGB clump is $\Delta \log{L}_\text{HB}^\text{AGB} = 0.455 \pm 0.012$. Our results accord with earlier findings that standard models predict a lower $R_2$ than is observed. We demonstrate that the dominant sources of uncertainty in models are the prescription for mixing and the stochastic effects that can result from its numerical treatment. The luminosity probability density functions that we derive from observations feature a sharp peak near the AGB clump. This constitutes a strong new argument against core breathing pulses, which broaden the predicted width of the peak. We conclude that the two mixing schemes that can match the asteroseismology are capable of matching globular cluster observations, but only if (i) core breathing pulses are avoided in models with a semiconvection/partially mixed zone, or (ii) that models with large convective cores have a particular depth of mixing beneath the Schwarzschild boundary during subsequent early-AGB `gravonuclear' convection.