Reionization Bubbles from Real-Space Cross Correlations of Line Intensity Maps

Abstract

We propose a new way to reconstruct the ionized-bubble size distribution during the Epoch of Reionization (EoR) through the real-space cross-correlation of 21-cm and star-forming line-intensity maps. Understanding the evolution and timing of the EoR is crucial for both astrophysics and cosmology, and a wealth of information on the first sources can be extracted from the study of ionized bubbles. Nevertheless, directly mapping bubbles is challenging due to the high redshifts involved, possible selection biases, and foregrounds in 21-cm maps. Here, we exploit the real-space cross-correlation $ξ_{21,ν}$ between 21-cm and line-intensity mapping (LIM) signals to reconstruct the evolution of bubble sizes during reionization. For the first time, we show that $ξ_{21,ν}(r)$ departs from a saturation level for each separation $r$ when bubbles of size $r$ begin to form, providing a handle for the onset of bubbles of each radius. Moreover, we demonstrate that $ξ_{21,ν}$ evolves from positive to negative as the EoR progresses, reaching a minimum (i.e. maximum anti-correlation) when bubbles of radius $r$ reach peak abundance. We show that these results are robust to changes in the astrophysical model as well as the timing/topology of reionization. This real-space observable complements usual Fourier-space estimators by capturing the localized nature of bubbles, offering new insights into the sources driving cosmic reionization.

Figures (8)

• Figure 1: Maps of the 21-cm signal $T_{21}$ (top) and [OIII] intensity (bottom) at $z=7.5$ (corresponding to a volume ionized fraction $\overline{x_{\text{HII}}}^{\rm{V}}=0.29$). The colored contours locate ionized bubbles of effective radius $R_{\rm{b}} \sim 15$ cMpc, and clearly highlight the anti-correlation between the 21-cm and LIM signals at this scale.
• Figure 2: Real-space cross-correlation coefficient $\rho_{\rm{21cm,}\nu}$ (top) at different separations $r$ (in colors) and bubble size distributions $dn/dR_{\rm{b}}$ (bottom) for different bubble sizes $R_{\rm{b}}$ (in colors, where bubbles need not be spherical, so radius is to be understood as $R_{\rm{b}}\sim V_{\rm{b}}^{1/3}$). For reference, the black dashed-dotted line in the top panel shows the Pearson coefficient Libanore:2025gte, which is the zero-separation cross-correlation function. The vertical lines represent the redshift at which 0.1% of the cosmic volume is occupied by bubbles of each radius (i.e., $V_{\rm{b}}R_{\rm{b}} dn/dR_{\rm{b}}\gtrsim10^{-3}$), which coincide with the point where $\rho_{\rm{21cm,}\nu}\lesssim 0.9$, illustrating that $\rho_{\rm{21cm,}\nu}$ can pinpoint the timing at which the first bubbles of a given size appear. Moreover, the colored dots show the peak of the BSD at each size $R_{\rm{b}}$, which are traced by the minimum of $\rho_{\rm{21cm,}\nu}$ for each $r$, so the cross-correlation is minimal when the BSD peaks. The shaded colored regions represent the scatter between our set of 10 simulations, and reionization is over at $z\sim 5.8$, as indicated by the gray band.
• Figure 3: Fourier-space cross-correlation coefficient $\tilde{\rho}_{\rm{21cm,}\nu}$ at different wavenumbers $k=2\pi/r$ (in colors). As in Fig. \ref{['fig:xi_BSD']}, the vertical lines represent the redshift at which $V_{\rm{b}}R_{\rm{b}} dn/dR_{\rm{b}}(R_{\rm{b}})=10^{-3}$ and the colored dots correspond to the redshifts at which the BSD peaks. This figure shows how the sharp decline of correlations at different separations seen in Fig. \ref{['fig:xi_BSD']} is erased in Fourier space, due to mode mixing.
• Figure 4: We test that our results hold when varying the timing and topology of reionization through changes in the escape fraction amplitude $f_{\rm{esc}}^{(0)}$ (in blue), its power law index $\alpha_{\rm{esc}}$ (in yellow), and the X-ray luminosity $L_{\rm{X,SFR}}$ (in red). We show the volume fraction of ionized hydrogen $\overline{x_{\text{HII}}}^{\rm{V}}$ (top), real-space cross-correlation coefficient $\rho_{\rm{21cm,}\nu}$ (middle), and BSDs (bottom). In all cases (except disfavored low $L_{\rm{X,SFR}}\lesssim 39.5$HERA:2023, red-dashed) we find a strong correlation between the departure of $\rho_{\rm{21cm,}\nu}(r=11$cMpc) from unity (middle panel) and the onset of the first 11-cMpc bubbles (bottom). Likewise, the BSD peaks where $\rho_{\rm{21cm,}\nu}$ reaches its minimum.
• Figure 5: Real-space cross-correlation coefficient $\rho_{\rm{21cm,}\nu}$ (top, vs separation $r$) and bubble size distributions (bottom, vs size $R_b$), both shown at different redshifts $z$ (in colors). The solid and dotted lines show the two sets of simulations, the first one with $(dx,L_{\text{box}}) = (1 \text{ cMpc},250 \text{ cMpc})$ and the second one with $(dx,L_{\text{box}}) = (2 \text{ cMpc},500 \text{ cMpc})$.