Abstract

In view of the absence of a satisfactory solution to the globular cluster (GC) classification problem, we have searched for a physical parameter that admits of the GC classification and finding empirical dependences on observed physical characteristics. For this purpose, we have considered a model of the apparent density in GCs with three free parameters. Using the widely known simplex method of minimizing the square of the difference between the observed and theoretical densities, we have found the corresponding free parameters for 26 GCs. As observational data we have taken mostly the density profiles constructed by Miocchi et al. (2013) based on a combination of Hubble Space Telescope and ground-based data. One of the free parameters of our model characterizes the concentration of stars toward the GC center. We have found a number of empirical dependences of this parameter on the main physical characteristics of GCs. The derived empirical formulas can be used in determining these characteristics for other GCs via the concentration and vice versa.

中文翻译：

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到全局聚类分类问题。计算 26 个星团的恒星浓度

摘要

鉴于球状星团 (GC) 分类问题缺乏令人满意的解决方案，我们已经搜索了一个物理参数，该参数允许 GC 分类并找到对观察到的物理特性的经验依赖性。为此，我们考虑了具有三个自由参数的 GC 表观密度模型。使用广为人知的单纯形方法来最小化观察到的密度和理论密度之间的差异的平方，我们已经找到了 26 个 GC 的相应自由参数。作为观测数据，我们主要采用 Miocchi 等人构建的密度剖面。(2013) 基于哈勃太空望远镜和地面数据的组合。我们模型的自由参数之一表征了恒星向 GC 中心的浓度。我们已经发现该参数对 GC 主要物理特性的许多经验依赖性。导出的经验公式可用于通过浓度确定其他 GC 的这些特征，反之亦然。