发表机构
University of California, Los Angeles; Scuola Normale Superiore; University of Tsukuba; The University of Tokyo; Institute for Cosmic Ray Research, The University of Tokyo; University of Catania; National Astronomical Observatory of Japan, National Institutes of Natural Sciences; SOKENDAI (The Graduate University for Advanced Studies); Kavli Institute for the Physics and Mathematics of the Universe (WPI)（加州大学洛杉矶分校; 比萨高等师范学院; 筑波大学; 东京大学; 东京大学宇宙射线研究所; 卡塔尼亚大学; 日本国立天文台，国立自然科学研究院; 综合研究大学院大学; 宇宙物质与物理学 Kavli 研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入持续同调的Betti-0曲线作为新汇总统计量，约束LAE成团性以推断再电离中性氢占比，性能优于或媲美传统统计量，联合约束可提升精度约2倍。
AI 中文摘要
莱曼-α发射体（LAEs）的空间成团性是约束再电离过程最有前景的可观测量之一。在本工作中，我们引入持续同调——拓扑数据分析中的一种常用工具，并特别采用Betti-0曲线作为汇总统计量来表征LAEs的成团性。我们通过量化它们利用Fisher信息约束再电离期间全球中性氢占比$x_{\rm HI}$的能力，将Betti-0曲线与角相关函数（ACF）和空洞概率函数（VPF）的性能进行比较。我们使用21cmFAST对LAEs观测进行前向建模，将$\mathrm{Ly}\alpha$发射作为后处理步骤纳入，并考虑宇宙方差不确定性。我们将分析聚焦于SILVERRUSH巡天在$z=5.7$和6.6红移处的星表框架内，发现Betti-0曲线的表现与ACF和VPF相当或更优。我们还发现这些统计量对不同物理尺度最为敏感，因此探测互补信息，进而同时约束所有三个统计量可将约束精度比单独使用ACF提高约2倍，在$x_{\rm HI}=0.05$、$z=5.7$处预测最小不确定度为$\sigma_{\rm min} \sim 0.03$，在$x_{\rm HI}=0.20$、$z=6.6$处为$\sigma_{\rm min} \sim 0.07$。我们的结果表明，Betti-0曲线是利用LAE成团性约束再电离的一种有前景的汇总统计量，并激励在其他宽场巡天（如南希·格雷斯·罗曼太空望远镜所实现的巡天）中进一步探索持续同调用于相同目的。
英文摘要
The spatial clustering of Lyman-$α$ emitters (LAEs) is one of the most promising observables for constraining reionization. In this work, we introduce persistent homology, a popular tool in topological data analysis, and specifically the Betti-0 curve as a summary statistic to characterize the clustering of LAEs. We compare the performance of the Betti-0 curve against the angular correlation function (ACF) and void probability function (VPF) by quantifying their ability to constrain the global neutral fraction $x_{\rm HI}$ during reionization using the Fisher information. We forward model observations of LAEs using 21cmFAST by including $\mathrm{Ly}α$ emission as a post-processing step and account for cosmic variance uncertainties. We focus our analysis within the framework of the SILVERRUSH. catalog at $z=5.7$ and 6.6, and find that the Betti-0 curve performs as well as or better than the ACF and VPF. We also find that the statistics are most sensitive to different physical scales and thus probe complementary information, and as a consequence that simultaneously constraining all three statistics improves constraints by a factor of $\sim 2$ compared with the ACF alone, with predicted minimum uncertainties of $σ_{\rm min} \sim$ 0.03 and 0.07 at $x_{\rm HI} = 0.05$ and $z=5.7$ and $x_{\rm HI} = 0.20$ and $z=6.6$, respectively. Our results show that the Betti-0 curve is a promising summary statistic to constrain reionization using LAE clustering and motivate further exploration of persistent homology for the same purpose in other wide-field surveys such as those made possible by the Nancy Grace Roman Telescope.
Comments29 pages, 10 figures; updated formatting for submission to JCAP
