用不同的振荡程序计算给定恒星模型的g-、f-和p-模的相互比较
Inter-comparison of the g-, f- and p-modes calculated using different oscillation codes for a given stellar model
摘要：
为了使天文地震学成为探索恒星内部的有力工具，不同的数值代码应该对相同的输入物理给出相同的振荡频率。这项工作致力于测试，比较，并在必要时，优化用于计算本征频率的地震代码，最后与观测结果进行比较。本研究中使用了该领域九个研究小组的振荡代码。所有代码都采用了相同的物理原理，以隔离任何可能差异的非物理依赖性。使用了两种具有不同网格的平衡模型，2172和4042网格点，后者包括对流核心外的对流的显式建模。比较这两个模型的结果说明了网格点的数量和它们在模型的特别关键的部分中的分布的影响，例如对流核心外部的陡峭的成分梯度。一个全面的研究发现不同的代码的频率差异，以及。这些差异主要是由于使用了不同的数值积分方案。使用二阶积分方案加上Richardson外推法提供了与四阶积分方案类似的结果。平衡模型中Brunt-Vaisala频率的适当数值描述对于某些模式也是至关重要的。这项研究的一个意外结果是，在实验确定的范围内，频率差对振荡代码中引力常量（G）值的不一致使用的高度敏感性，这些值不同于用于计算平衡模型的值。
英文摘要：
In order to make astroseismology a powerful tool to explore stellar interiors, different numerical codes should give the same oscillation frequencies for the same input physics. This work is devoted to test, compare and, if needed, optimize the seismic codes used to calculate the eigenfrequencies to be finally compared with observations. The oscillation codes of nine research groups in the field have been used in this study. The same physics has been imposed for all the codes in order to isolate the non-physical dependence of any possible difference. Two equilibrium models with different grids, 2172 and 4042 mesh points, have been used, and the latter model includes an explicit modelling of semiconvection just outside the convective core. Comparing the results for these two models illustrates the effect of the number of mesh points and their distribution in particularly critical parts of the model, such as the steep composition gradient outside the convective core. A comprehensive study of the frequency differences found for the different codes is given as well. These differences are mainly due to the use of different numerical integration schemes. The use of a second-order integration scheme plus a Richardson extrapolation provides similar results to a fourth-order integration scheme. The proper numerical description of the Brunt-Vaisala frequency in the equilibrium model is also critical for some modes. An unexpected result of this study is the high sensitivity of the frequency differences to the inconsistent use of values of the gravitational constant (G) in the oscillation codes, within the range of the experimentally determined ones, which differ from the value used to compute the equilibrium model.
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