Constraining Reionization Morphology and Source Properties with 21cm-Galaxy Cross-Correlation Surveys

TL;DR

The paper tackles constraining reionization morphology and source properties using 21cm-Galaxy cross-correlations. It combines forward-modeling of cross-power spectra with likelihood-free SBI (EoRFlow) to infer $x_ ext{HI}(z)$, $\big\langle 1+\delta_ ext{HI} \big\rangle(z)$, and ionizing-source parameters ($f_ ext{esc}$, $f_*$). Key findings show cross-power provides complementary information that tightens global reionization constraints and enables constraints on source properties that auto-power alone cannot; survey design—especially redshift precision—and foreground-removal capabilities critically determine the achievable information gains. The approach demonstrates a scalable pathway to maximize the scientific return of future SKA-Low and high-redshift galaxy surveys, with implications for observational planning and data-analysis strategies.

Abstract

Cross-correlations between 21cm observations and galaxy surveys provide a powerful probe of reionization by reducing foreground sensitivity while linking ionization morphology to galaxies. We quantify the constraining power of 21cm-Galaxy cross-power spectra for inferring neutral hydrogen fraction $x_\mathrm{HI}(z)$ and mean overdensity $\langle 1+δ_\mathrm{HI} \rangle(z)$, exploring dependence on field of view, redshift precision $σ_z$, and minimum halo mass $M_\mathrm{h,min}$. We employ our simulation-based inference framework EoRFlow for likelihood-free parameter estimation. Mock observations include thermal noise for 100h SKA-Low with foreground avoidance and realistic galaxy survey effects. For a fiducial survey ($\mathrm{FOV}=100\,\mathrm{deg}^2$, $σ_z=0.001$, $M_\mathrm{h,min}=10^{11}\mathrm{M}_\odot$), cross-power spectra yield unbiased constraints with posterior volumes (PV) of $\sim$10% relative to priors. Cross-power measurements reduce PV by 20-30% versus 21cm auto-power alone. With foreground avoidance, spectroscopic redshift precision is essential; photometric redshifts render cross-correlations uninformative. Notably, cross-power spectra constrain ionizing source properties, the escape fraction $f_\mathrm{esc}$ and star formation efficiency $f_*$, which remain degenerate in auto-power (PV $>$60%). Tight constraints require either deep surveys detecting faint galaxies ($M_\mathrm{h,min} \sim 10^{10}\mathrm{M}_\odot$) with moderate foregrounds, or conservative mass limits with optimistic foreground removal (PV $<$15%). 21cm-Galaxy cross-correlations enhance morphology constraints beyond auto-power while enabling previously inaccessible source property constraints. Realizing full potential requires precise redshifts and either faint galaxy detection limits or improved 21cm foreground cleaning.

Figures (8)

• Figure 1: 21cm-Galaxy cross-power spectrum at $z=7.6$ ($x_{\mathrm{HI}}=0.75$) for the fiducial survey configuration explored in the inference analysis in Section \ref{['sec: EoR timeline']} (${\mathrm{FOV}}=100 {\mathrm{deg}}^2$, $\sigma_z=0.001$, $M_{\mathrm{ h,min}}=10^{11} M_\odot$). The blue line shows the physical signal, the shaded blue region indicates the $1\sigma$ uncertainty, and orange points represent the mock observation including instrumental noise. Three distinct regimes characterize the cross-power spectrum. The first region corresponds to the 21cm foreground wedge where large-scale modes are contaminated by bright foreground emission, resulting in poor SNR. We are omitting the signal here based on our foreground avoidance strategy. The second region is signal dominated and provides access to the ionization morphology. It exhibits strong anti-correlation at intermediate scales ($k\sim0.25$-$0.75 h {\mathrm{Mpc}}^{-1}$) where galaxies predominantly occupy ionized bubbles while the 21cm signal traces neutral hydrogen in the IGM. At $k\sim0.75 h {\mathrm{Mpc}}^{-1}$, the zero crossing corresponds to the characteristic scale of ionized regions. On scales smaller than the typical size of ionized bubbles, both the galaxy distribution and neutral hydrogen density respond to the same underlying matter fluctuations, resulting in positive correlation. The third region shows the shot-noise dominated regime at small scales ($k>1.0 h {\mathrm{Mpc}}^{-1}$) owing to the discrete nature of galaxy datasets.
• Figure 2: Marginalized posteriors for the neutral fraction $x_\mathrm{HI}(z)$ and the mean density in neutral regions $\langle 1+\delta_\mathrm{HI} \rangle (z)$ for a selection of redshift slices and a randomly chosen set of parameters ($\log_{10} f_{*,10}=0.04$, $\log_{10} f_{\mathrm{esc}, 10}=0.05$, $\alpha_*=0.44$ and $\alpha_\mathrm{esc}=-0.60$) assuming moderate 21cm foreground avoidance. Shadings indicate the 68% and 95% confidence intervals. Blue, dotted contours show the posteriors derived from 21cm-Galaxy cross-power spectra, while orange, solid lines represent the results when combining both cross and auto-power spectra. The grey, dashed contours denote the model trained on 21cm auto-power spectra only and true parameter values are indicated by black dots.
• Figure 3: Informativeness measured by the normalized posterior volume on the neutral fraction $x_\mathrm{HI}(z)$ and the mean density in neutral regions $\langle 1+\delta_\mathrm{HI} \rangle (z)$ as a function of redshift assuming moderate 21cm foreground avoidance as well as our fiducial galaxy survey (100 deg$^2$, $\sigma_z = 0.001$, $M_{\mathrm{h,min}} = 10^{11}$ M$_\odot$). The errors are obtained from bootstrapping.
• Figure 4: Posterior volume (averaged over neutral fraction, density, redshifts, and test observations) as a function of galaxy survey parameters assuming moderate 21cm foreground avoidance. Each panel shows results for a different minimum detectable halo mass threshold. The color scale ranges from white (posterior volume near zero, highly constraining) to dark purple (posterior volume near unity, uninformative), with numerical values annotated in each cell. Left panel ($M_\mathrm{h,min} = 10^{10}$ M$_\odot$), center panel ($10^{10.5}$ M$_\odot$), right panel ($10^{11}$ M$_\odot$). The FOV increases from top to bottom, and redshift precision improves from right to left.
• Figure 5: Fractional mutual information gain from including 21cm-Galaxy cross-power spectrum measurements in addition to 21cm auto-power, as a function of redshift and wave-number. Upper panel: neutral fraction $x_\mathrm{HI}(z)$. Lower panel: mean density contrast $\langle 1+\delta_\mathrm{HI} \rangle(z)$. The color scale indicates the ratio $I(\theta; \mathrm{cross}_{z,k} | \mathrm{auto}_{z,k}) / I(\theta; \mathrm{auto}_{z,k})$, quantifying the relative additional information provided by cross-correlations. Purple regions indicate high information gain (cross-power provides substantial additional constraints), while white regions show minimal gain (auto-power is sufficient). The cross-power provides significant information across most scales and redshifts, with 78% of bins showing fractional gains exceeding 100%. The information gain increases with redshift and peaks at small scales $k \sim 1-2$ Mpc$^{-1}$, reflecting the evolving correlation between ionization morphology and galaxy clustering during reionization.