TORRCH: Tomographic reconstruction of the reionization of cosmic hydrogen with Ly$α$ emitters and non-Ly$α$-selected galaxies

TL;DR

This work develops TORRCH, a galaxy-based tomographic framework that reconstructs the reionization ionization field $x_{ m HI}(oldsymbol{r})$ from 3D LAE and NLSG distributions. It trains a deterministic 3D U-Net with a voxel-wise heteroscedastic head on radiative-transfer–post-processed hydrodynamic simulations to map tracer fields to $x_{ m HI}$, achieving accurate large-scale morphology and preserving key statistics such as the one-point PDF, projected power spectrum, and galaxy–IGM cross-correlation. The method demonstrates robustness to tracer completeness and redshift uncertainties, and generalizes across ionization conditions, making it suitable for current and near-future LAE surveys and for joint analyses with 21-cm data as part of a multi-tracer reionization approach. Overall, this approach provides a practical path to field-level tomographic constraints on reionization topology, advancing beyond global fractions to spatially resolved insights into bubble sizes, topology, and galaxy–IGM coupling.

Abstract

Tomographic reconstruction of reionization is a long-sought goal. It would move the field beyond global summary statistics, such as the volume-averaged ionised fraction, to direct, field-level constraints on the ionization topology. With this in mind, we present TORRCH (TOmographic Reconstruction of the Reionization of Cosmic Hydrogen), a deep-learning framework that reconstructs the neutral-hydrogen fraction field during the epoch of reionization from the spatial distributions of Ly$α$ emitters (LAEs) and non-Ly$α$-selected galaxies (NLSGs) at luminosity limits comparable to current surveys. Using hydrodynamical simulations post-processed with radiative transfer, we train a deterministic 3D U-Net on mock surveys spanning diverse reionization scenarios and predict the neutral-fraction field. We find that TORRCH recovers the large-scale ionization morphology from synthetic data comparable to current surveys with high fidelity, and reproduces both the one-point distribution and the 2D power spectrum of projected neutral fractions. The predicted galaxy-IGM cross-correlation is also captured well, including the expected small-scale anti-correlation and its decline towards zero at large separations. Reconstruction quality depends on tracer completeness, with deep joint LAE+NLSG samples yielding the most accurate morphology, while LAE-only selections retain bubble-scale topology but with reduced fidelity. Robustness tests show that the method is stable to variations in ionization conditions between training and test data, and to realistic redshift uncertainties. Our results suggest that galaxy-based tomography can potentially deliver reliable reionization maps across realistic survey redshift windows.

Figures (16)

• Figure 1: Schematic architecture of the 3D U-Net used for tomographic reconstruction in this work. The network takes as input the three-dimensional distribution of Ly$\alpha$ emitters (LAEs) and non-Ly$\alpha$ selected galaxies (NLSGs) in a $80 \,h^{-1}\mathrm{cMpc} \times 80 \,h^{-1}\mathrm{cMpc} \times 30 \,h^{-1}\mathrm{cMpc}$ subvolume, which is processed through a hierarchy of 3D convolutional and residual blocks in the encoder (left). Each stage applies convolutional filters with kernel size $7\times 7\times 7$ and increases the feature dimensionality, beginning from 8 channels in the first layer to 64 in the final layer. Skip connections link encoder outputs to their corresponding decoder layers (right), enabling the recovery of fine-scale spatial structure otherwise lost during deep feature extraction. The decoder mirrors the encoder with a sequence of channel-reducing 3D convolutions and residual blocks, reconstructing the three-dimensional ionization field in a $80 \,h^{-1}\mathrm{cMpc} \times 80 \,h^{-1}\mathrm{cMpc} \times 30 \,h^{-1}\mathrm{cMpc}$ subvolume from the learned hierarchical representation. Kernel sizes ($7\times 7\times 7$ for the first 3 layers and $3\times 3\times 3$ for the final layer) and feature channel counts (shown above each block) indicate the effective receptive field and representation capacity at every stage. This U-Net formulation, without a latent compression step, focuses purely on deterministic reconstruction and preserves maximal spatial information throughout the network.
• Figure 2: Comparison of reconstructed neutral hydrogen fraction fields ($x_{\mathrm{HI}}$) projected along the redshift axis over $30~h^{-1}\mathrm{cMpc}$ and true-predicted relations for the Early reionization model at $z=7.14$. Each row corresponds to a different survey configuration: Deep, Shallow, and LAE-only (see Table \ref{['tab:survey_configs']}). For each case, the left three panels show the spatial distribution of LAEs and NLSGs, the true ionization map, and the reconstructed map. The rightmost panels display the voxel-wise comparison between true and reconstructed $x_{\mathrm{HI}}$, showing the median relation and 68% confidence intervals for both the unsmoothed ($L_{\mathrm{smooth}}=0$; grey) and smoothed ($L_{\mathrm{smooth}}=7~h^{-1}\,\mathrm{cMpc}$; magenta) fields. Smoothing reduces small-scale fluctuations and improves the correlation with the true field, while the overall trends remain consistent across survey configurations.
• Figure 3: Comparison of reconstructed neutral hydrogen fraction fields ($x_{\mathrm{HI}}$) projected along the redshift axis over $30~h^{-1}\mathrm{cMpc}$ and true–predicted relations for the Oligarchic reionization model at $z=7.14$. Each row corresponds to a different survey configuration: Deep, Shallow, and LAE-only (see Table \ref{['tab:survey_configs']}). For each case, the left three panels show the spatial distribution of LAEs and NLSGs, the true ionization map, and the reconstructed map. The rightmost panels display the voxel-wise comparison between true and reconstructed $x_{\mathrm{HI}}$, showing the median relation and $68\%$ confidence intervals for both the unsmoothed ($L_{\mathrm{smooth}}=0$; grey) and smoothed ($L_{\mathrm{smooth}}=7~h^{-1}\,\mathrm{cMpc}$; magenta) fields.
• Figure 4: Pearson correlation coefficient between the true and reconstructed three-dimensional $x_{\mathrm{HI}}$ field as a function of Gaussian smoothing scale for different reionization models at $z=7.14$. Each panel corresponds to one reionization scenario (Extremely Early, Early, Oligarchic, and Fiducial). Markers with $1\sigma$ error bars indicate the inter-slice variation in correlation for the three survey configurations: Deep, Shallow, and LAE-only (see Table \ref{['tab:survey_configs']}). A horizontal dashed line at $r=0.5$ marks the approximate threshold above which the reconstruction begins to recover meaningful large-scale structure. Overall, the correlation strength increases with smoothing scale, with the Early and Extremely Early models exhibiting systematically higher fidelity than the Oligarchic and Fiducial models.
• Figure 5: Probability distribution functions (PDFs) of the projected (over $30~h^{-1}\mathrm{cMpc}$ in the redshift direction) neutral hydrogen fraction, $x_{\mathrm{HI}}$, reconstructed under four reionization scenarios at $z=7.14$: Extremely Early, Early, Oligarchic, and Fiducial, after Gaussian smoothing with $L_{\mathrm{smooth}}=7~h^{-1}\,\mathrm{cMpc}$. In each panel, the Fiducial model is shown as a common reference via the purple shaded band, enabling a direct comparison between alternative reionization histories and the same baseline. The solid black curve and grey band indicate the mean and 68% confidence interval of the true $x_{\mathrm{HI}}$ distribution for the model shown in each panel. Colored symbols with error bars show reconstructed PDFs for the three survey configurations: Deep (blue), Shallow (orange) and LAE-only (green) (see Table \ref{['tab:survey_configs']}). The inset panel summarises the mean neutral fraction $\langle x_{\mathrm{HI}}\rangle$ for each case, shown as thick horizontal error bars representing the 68% confidence intervals.