Constraining reionization with persistent homology: a novel summary statistic for wide-field Lyman-α emitter observations
Abstract
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 xHI during reionization using the Fisher information. We forward model observations of LAEs using 21cmFAST by including Lyα 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 ∼ 2 compared with the ACF alone, with predicted minimum uncertainties of σmin ∼ 0.03 and 0.07 at xHI = 0.05 and z=5.7 and xHI = 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.
Related
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- Impact of Residual Gain Errors on the Detectability of Ionized Bubbles during Reionization with SKA 21-cm observations
- Prospects for Near-Far Constraints on Reionization from Simulated LSST Observations of Milky Way Dwarf Galaxies and Stellar Streams
BibTeX
@misc{wyatt2026constraining,
title = {{Constraining reionization with persistent homology: a novel summary statistic for wide-field Lyman-$α$ emitter observations}},
author = {Michael M. Wyatt and Nikolaos Triantafyllou and Steven R. Furlanetto and Hiroya Umeda and Samuel Gagnon-Hartman and Andrei Mesinger and Masami Ouchi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.36092},
eprint = {2609.36092},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36092},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constraining reionization with persistent homology: a novel summary statistic for wide-field Lyman-α emitter observations
AU - Michael M. Wyatt
AU - Nikolaos Triantafyllou
AU - Steven R. Furlanetto
AU - Hiroya Umeda
AU - Samuel Gagnon-Hartman
AU - Andrei Mesinger
AU - Masami Ouchi
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.36092
UR - https://arxiv.org/abs/2609.36092
AB - 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_HI during reionization using the Fisher information. We forward model observations of LAEs using 21cmFAST by including Lyα 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 ∼ 2 compared with the ACF alone, with predicted minimum uncertainties of σ_min ∼ 0.03 and 0.07 at x_HI = 0.05 and z=5.7 and x_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.
ER -