Stacking 21-cm Maps around Lyman-$α$ Emitters during Reionization: Prospects for a Cross-correlation Detection with the Hydrogen Epoch of Reionization Array

TL;DR

The paper investigates the feasibility of detecting a cross-correlation between 21-cm maps and Lyman-α emitters (LAEs) during the Epoch of Reionization by stacking 21-cm image cubes around spectroscopically confirmed LAEs. It develops a realistic, linear, foreground-filtered mapping pipeline (direct optimal mapping + DPSS delay filtering) and ties the stacked signal to the global neutral fraction via a THESAN-based signal template that accounts for LAE selection and IGM transmission. The study forecasts detection prospects with the Hydrogen Epoch of Reionization Array (HERA): around 50–100 LAEs can begin to constrain reionization, while hundreds to about a thousand LAEs may yield a detection depending on redshift precision and $ar{x}_ ext{HI}$; non-detections can place meaningful upper limits on $ar{x}_ ext{HI}$. This work lays groundwork for joint analyses of 21-cm data with Euclid/Roman high-redshift galaxy surveys and highlights practical considerations for foreground treatment and signal modeling in 21-cm cross-correlation science.

Abstract

Observations of the redshifted 21-cm line during the Epoch of Reionization will open a new window to probe the intergalactic medium during the formation of the first stars, galaxies, and black holes. A particularly promising route to an initial detection is to cross-correlate tomographic 21-cm maps with spectroscopically confirmed Lyman-$α$ emitters (LAEs). High-redshift LAEs preferentially reside in ionized bubbles that are strongly anticorrelated with the surrounding neutral regions traced by 21-cm observations. In this work, we study the prospect of detecting such a cross-correlation signal by stacking 21-cm image cubes around LAEs using a current-generation 21-cm instrument -- the Hydrogen Epoch of Reionization Array (HERA). Our forecast adopts a realistic mapping pipeline to generate foreground-free 21-cm image cubes. The statistical properties of these images, arising from the complex instrumental response, are carefully accounted for. We further introduce a physically motivated signal template calibrated on the THESAN radiation-hydrodynamic simulations, which connects the cross-correlation amplitude to the global neutral fraction. Our results show that a sample of ~50 spectroscopically confirmed LAEs is sufficient to begin constraining the reionization history. These results represent an important preparatory step toward joint analyses of 21-cm experiments with upcoming wide-area, high-redshift galaxy surveys from Euclid and the Nancy Grace Roman Space Telescope.

Figures (6)

• Figure 1: $\textit{Top}$: Effective observing time (see Eq. \ref{['eq:t_eff']}) for a transit array under different time-average weighting scheme. This shows how the signal-to-noise ratio for a point source changes (measured in terms of $\sqrt{t_\mathrm{eff}}$) as a function of observed time $t_\mathrm{obs}$. Here, we assume the source transits across zenith at $t_\mathrm{obs}=0$. Bottom: Averaged noise level when stacking two lines of sight from different separation. If two lines of sight are completely independent, the noise level should decrease by a factor of $\sqrt{2}$. Instrumental response makes pixels that lie within the array's synthesis beam particularly correlated with each other. This is well characterized by the diffraction limit scale $1.22\,\lambda_\mathrm{obs} / b_\mathrm{max}$. In this plot, the observed wavelength $\lambda_\mathrm{obs}\approx 1.67\,\mathrm{meter}$ which traces 21-cm lines at $z\sim7$, and the longest baseline length is at $b_\mathrm{max}\approx265\,\mathrm{meter}$.
• Figure 2: $\textit{Top}$: Frequency-frequency correlations in image space due to foreground filtering. Here, each baseline is filtered to the delay of $|\boldsymbol{\mathbf{b}}|/c$. Bottom: Correlation in image space (solid black line) versus those in visibility space for various baselines (dashed lines). Here, we are showing correlation between the frequency channel at around $179.9$ MHz (which traces 21-cm lines at $z\sim7$) with its neighboring channels.
• Figure 3: Left: Snapshot of 21-cm brightness temperature from thesan at redshift 7 with LAEs marked in white stars. We draw 21-cm spectra along the line of sight from each LAE to form a template for the stacked 21-cm signal. Right: Stacked 21-cm spectra around LAEs that are intrinsically bright (left) and can be observed by a fiducial ground-based spectroscopy survey (right). Different curves mimic a different reionization history which predicts a different global neutral fraction at redshift $z\sim 7$.
• Figure 4: Layout of the 320 core antennas of HERA used in this forecast. The 172 antennas marked in green have been taking data since 2022 and are used as a baseline configuration to investigate the prospect of cross-correlation with existing HERA data.
• Figure 5: Stacked 21-cm brightness temperature signal as observed by HERA assuming different neutral fraction $\bar{x}_\mathrm{HI}$ at $z\sim7$. Different lines correspond to different redshift uncertainties for the LAEs. These signals have gone through the foreground filtering procedure as described in Sec. \ref{['subsec:foreground_filter']} and \ref{['appendix:fg_filter']}.