低至中等马赫数下的引力坍缩：恒星形成效率与大质量天体质量占比的关系
Gravitational collapse at low to moderate Mach numbers: The relationship between star formation efficiency and the fraction of mass in the massive object
AI总结：
本研究分析不同环境下大质量天体形成的引力坍缩模拟，探究恒星形成效率与大质量天体质量占比的关联，发现碰撞参数结合恒星形成效率可有效预测最大质量天体的质量占比。
摘要：
通过引力坍缩形成大质量天体的过程，既与解释第一代超大质量黑洞的起源相关，也涉及大质量恒星形成的研究背景。本文分析了不同研究团队在多种环境下开展的大质量天体形成模拟，研究场景涵盖超大质量黑洞、第三代恒星（即原初恒星）以及现今大质量恒星的形成过程。我们重点关注小位力参数区间，即初始动能与引力能的比值较低、马赫数处于低至中等水平，且反馈作用尚未充分发挥的阶段。我们使用无量纲参数对比不同条件下的坍缩结果，核心参数包括恒星形成效率ε_*、最大质量天体质量占总恒星质量的比例f_*，以及最大质量天体质量占总质量的比例f_{\rm tot}随总质量的变化关系。研究发现，在本文分析的所有模拟中，f_{\rm tot}均随ε_*的增大而升高，不过增长的陡峭程度取决于所处环境。f_*与ε_*之间的关系则更为复杂，且强烈依赖于模拟初始阶段存在的原恒星数量。我们提出，以系统尺度与典型碰撞长度的比值估算得到的碰撞参数，可大致表征碰撞过程是否会发挥重要作用。我们使用斯皮尔曼（Spearman）系数分析了这些无量纲量之间的统计相关性，并通过机器学习分析证实，结合ε_*与碰撞参数的粗略估算，可对f_*做出良好预测。这一结果表明，一旦知晓给定环境下的最大恒星形成效率，就能对最大质量天体的质量做出较好的估算。
英文摘要：
The formation of massive objects via gravitational collapse is relevant both for explaining the origin of the first supermassive black holes and in the context of massive star formation. Here, we analyze simulations of the formation of massive objects pursued by different groups and in various environments, concerning the formation of supermassive black holes, primordial stars, as well as present-day massive stars. We focus particularly on the regime of small virial parameters, i.e., low ratios of the initial kinetic to gravitational energy, low to moderate Mach numbers, and the phase before feedback is very efficient. We compare the outcomes of collapse under different conditions using dimensionless parameters, particularly the star formation efficiency ε_*, the fraction f_* of mass in the most massive object relative to the total stellar mass, and the fraction f_{\rm tot} of mass of the most massive object as a function of the total mass. We find that in all simulations analyzed here, f_{\rm tot} increases as a function of ε_*, although the steepness of the increase depends on the environment. The relation between f_* and ε_* is found to be more complex and also strongly depends on the number of protostars present at the beginning of the simulations. We show that a collision parameter, estimated as the ratio of the system size divided by the typical collision length, allows us to approximately characterize whether collisions will be important. We analyze the statistical correlation between the dimensionless quantities using the Spearman coefficient and confirm via a machine learning analysis that good predictions of f_* can be obtained from ε_* together with a rough estimate of the collision parameter. This suggests that a good estimate of the mass of the most massive object can be obtained once the maximum efficiency for a given environment is known.
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