基于 excursion set 理论的最概然外密度分布
The Most Probable Outer Density Profile from Excursion Set Theory
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中文总结 AI 辅助
该研究放宽 excursion set 理论的简化假设，重新推导外密度分布众数，发现其解析分布与数值双分布吻合，但与 N-body 模拟分布偏离，表明该解析分布仅可作为少参数有效描述。
中文摘要 AI 辅助
星系团周围回转半径的测量可用于打破当前物质与暗能量能量密度测量之间的简并性。Korkidis 与 Pavlidou 指出，回转半径与 N-body 模拟中外密度分布和 excursion set 理论预测的解析分布的首次偏离点重合。然而，他们的解析分布依赖于大量简化假设，每个假设都可能引入系统误差。我们评估这些假设对解析分布形状及其与模拟外密度分布对应关系的影响。我们放宽关键简化假设，重新推导 excursion set 理论中外密度分布的众数，随后在一系列质量和成团参数范围内数值求解双分布（DD），并将数值众数估计与重新推导的解析分布进行比较。我们发现，我们的解析分布与数值实现的 DD 之间吻合度极佳，但我们的解析分布与 N-body 模拟分布存在偏离，且随着我们逐步放宽假设，这种偏离会增大。我们将这种不匹配归因于解析方法与基于模拟的方法所使用的窗函数不同，二者分别产生马尔可夫型和相关密度轨迹。我们得出结论，Korkidis 与 Pavlidou 提出的解析分布仅应作为最概然外密度分布的少参数有效描述，其参数需根据宇宙学模拟结果拟合。
英文摘要
Measurements of the turnaround radius around galaxy clusters can be used to break the degeneracy between measurements of the present day energy density of matter and dark energy. Korkidis & Pavlidou showed that the turnaround radius coincides with the first point of deviation between outer density profiles in N-body simulations and the analytic profile predicted by excursion set theory. However, their analytic profile relied on a number of simplifying assumptions, which may each introduce systematic error. We evaluate the effect of these assumptions on the shape of the analytic profile and its correspondence with simulated outer density profiles. We relax the key simplifying assumptions and re-derive the mode of the outer density profile from excursion set theory. We then numerically resolve the double distribution (DD) across a range of masses and clustering parameters, and compare the numerical mode estimate to the re-derived analytic profile. We find excellent agreement between our analytic profile and the numerically-realized DD. However, our analytic profiles diverge from N-body profiles, and this divergence grows as we relax successive assumptions. We relate this mismatch to the differing window functions used in the analytic and simulation-based approaches, which respectively yield Markovian and correlated density trajectories. We conclude that the analytic profile proposed by Korkidis & Pavlidou should only be used as a few-parameter effective description of the most-probable outer density profile, with parameters fitted to results of cosmological simulations.
