标题： 星团形成理论的观测限制——I. 质量-半径关系 显示英文标题

标题： Observational constraints on star cluster formation theory - I. The mass-radius relation

摘要： 恒星主要以群体形式形成，通常被称为星团或恒星集团。 观测到的恒星群体展现出广泛的质量、大小和其他属性的分布，因此常常假设这种多样性中没有潜在的结构。 在这里我们表明，假设存在无结构的大量星团或恒星集团类型可能是误导性的。 目前关于星团的数据汇编显示了星团质量、大小、年龄、最大恒星质量等之间的相关性。 在这篇第一篇论文中，我们更仔细地研究了星团质量和半径之间的相关性。 我们使用文献数据来探索太阳邻域中的星团和分子核心属性的关系。 我们发现，对于太阳邻域中的嵌入式星团，星团质量和半质量半径之间存在明确的相关性，形式为 $M_c = C R_c^{\gamma}$，其中 γ = 1.7 ± 0.2。 这一相关性适用于红外K波段数据以及X射线源，并且对于包含数百颗恒星到由数万颗恒星组成的星团都成立。 由于样本数量少，难以验证包含<30颗恒星的星团的相关性。 密集的气体团块是嵌入式星团的前身。 我们发现密集、大质量气体团块的质量-大小关系与嵌入式恒星星团具有相似的斜率。 这可能表明从气体到恒星质量的直接转换：然而，很难将星团（恒星）的尺寸测量值与气体轮廓的尺寸测量值联系起来。 考虑到从团块质量到星团质量的多种途径，我们得出太阳邻域中嵌入式星团的平均恒星形成效率为18%{+9.3}{-5.7} 。 推导出的质量-半径关系为聚团恒星形成的理论提供了限制条件。 分析模型和聚团恒星形成的模拟必须重现这个关系才能被认为是现实的（摘要）。 显示英文摘要

摘要： Stars form predominantly in groups usually denoted as clusters or associations. The observed stellar groups display a broad spectrum of masses, sizes and other properties, so it is often assumed that there is no underlying structure in this diversity. Here we show that the assumption of an unstructured multitude of cluster or association types might be misleading. Current data compilations of clusters show correlations between cluster mass, size, age, maximum stellar mass etc. In this first paper we take a closer look at the correlation of cluster mass and radius. We use literature data to explore relations in cluster and molecular core properties in the solar neighborhood. We show that for embedded clusters in the solar neighborhood there exists a clear correlation between cluster mass and half-mass radius of the form $M_c = C R_c^{\gamma}$ with gamma = 1.7 +/-0.2. This correlation holds for infra red K band data as well as X-ray sources and for clusters containing a hundred stars up to those consisting of a few tens of thousands of stars. The correlation is difficult to verify for clusters containing <30 stars due to low-number statistics. Dense clumps of gas are the progenitors of the embedded clusters. We find a similar slope for the mass-size relation of dense, massive clumps as for the embedded star clusters. This might point at a direct translation from gas to stellar mass: however, it is difficult to relate size measurements for clusters (stars) to those for gas profiles. Taking into account multiple paths for clump mass into cluster mass, we obtain an average star-formation efficiency of 18%{+9.3}{-5.7} for the embedded clusters in the solar neighborhood. The derived mass-radius relation gives constraints for the theory of clustered star formation. Analytical models and simulations of clustered star formation have to reproduce this relation in order to be realistic (abridged)