关于在恒星演化计算中正确使用Schwarzschild和Ledoux判据
On the proper use of the Schwarzschild and Ledoux criteria in stellar evolution computations
摘要：
由CoRoT和$\textit{Kepler}$等空间飞行任务开启的详细的星震分析时代突出了对没有数值误差的恒星模型的需要，以便能够诊断在标准恒星建模中哪些物理方面被忽略或处理不当。我们在这里解决的重要问题，固定对流区边界的局部混合长度理论的框架。首先，我们表明，唯一正确的方法来定位对流区边界是找到，在每个迭代步骤，通过插值或外推点$\textit{within the convective zone}$，质量的辐射光度等于总的。然后我们讨论了边界条件的两个误用以及它们对恒星模拟和恒星演化的影响。第一种是在对流边界的$\textit{radiative}$侧应用对流不稳定的中性条件。第二种误用边界条件的方法来自于通过寻找可能的\textit{discontinuous}函数的符号变化来固定对流边界的过程。我们发现，这些误用可能会导致对流核心的大小与以下演变阶段的重要后果完全错误的估计。我们指出了在每个对流区边界使用双网格点的优点。本文讨论了对流壳层的特殊问题，并给出了有关超调的一些注记。
英文摘要：
The era of detailed asteroseismic analyses opened by space missions such as CoRoT and $\textit{Kepler}$ has highlighted the need for stellar models devoid of numerical inaccuracies, in order to be able to diagnose which physical aspects are being ignored or poorly treated in standard stellar modeling. We tackle here the important problem of fixing convective zones boundaries in the frame of the local mixing length theory. First we show that the only correct way to locate a convective zone boundary is to find, at each iteration step, through interpolations or extrapolations from points $\textit{within the convective zone}$, the mass where the radiative luminosity is equal to the total one. We then discuss two misuses of the boundary condition and the way they affect stellar modeling and stellar evolution. The first one consists in applying the neutrality condition for convective instability on the $\textit{radiative}$ side of the convective boundary. The second way of misusing the boundary condition comes from the process of fixing the convective boundary through the search for a change of sign of a possibly \textit{discontinuous} function. We show that these misuses can lead to completely wrong estimates of convective core sizes with important consequences for the following evolutionary phases. We point out the advantages of using a double mesh point at each convective zone boundaries. The specific problem of a convective shell is discussed and some remarks concerning overshooting are given.
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