The effect of photon re-scattering due to cosmic reionization on 21-cm images and power spectra

Abstract

The 21-cm signal from neutral hydrogen serves as a critical tool for unraveling the astrophysical processes that shaped cosmic dawn and the epoch of reionization. We explore the usually overlooked impact of re-scattering of 21-cm photons during and after reionization, similarly to cosmic microwave background photons. This scattering affects the observed brightness temperature by mixing the original signal with light scattered into the line of sight from other regions, effectively at the mean 21-cm brightness temperature. This gives a small but significant effect. We show that it attenuates the fluctuations in a 21-cm image by $4-7\%$, while reducing the 21-cm power spectrum by a scale-independent $7-13\%$ during cosmic dawn and reionization. Incorporating this correction is vital for precisely comparing theoretical predictions with observations from experiments such as NenuFAR, LOFAR, and HERA, and the upcoming Square Kilometre Array.

Figures (5)

• Figure 1: Left panel: Cumulative optical depth ($\tau$) to the CMB as a function of $z$ for our "Standard" and "High $\tau$" case. Here The solid curves represent the total integrated optical depth from $z=0$ to $z$ for the two cases considered: the "Standard" case (blue) yielding $\tau = 0.0542$ at $z=30$, and the "High $\tau$" case (orange) yielding $\tau = 0.0674$. The corresponding dotted curves illustrate the residual contribution to the total $\tau$ from redshifts greater than $z$, emphasizing the dominance of high-$z$ contributions in both scenarios. Right panel: Ionized hydrogen fraction ($1 -x_{\rm{HI}}$) as a function of $z$ for the "Standard" and "High $\tau$" cases.
• Figure 2: Global signal as a function of $z$ for our "Standard" and "High $\tau$" cases. Also shown is $T_{21}=0$ (dashed black line).
• Figure 3: 21-cm slices at $z=16$ without (left panel ) or with (middle panel ) the $\tau$ correction for the "Standard" model. As appropriate for observations with an interferometer, each slice is shown relative to the mean intensity (global signal) at that redshift which is -103.9 mK. Right panel: The difference between the two slices (With $\tau$ minus Without $\tau$). Note that the pixels in these maps (as in our simulations) are 3 Mpc on a side.
• Figure 4: 21-cm power spectrum as a function of $z$ at $k=0.1$ Mpc$^{-1}$, without or with the $\tau$ correction. Left panel: "Standard" model. Right panel: "High $\tau$" model. Dashed curves show the power spectrum without the $\tau$ correction while solid gray curved give the absolute difference between the $\tau$ corrected and uncorrected cases, revealing differences of $\sim 10\%$ throughout reionization and cosmic dawn.
• Figure 5: Relative difference (in percent) as a function of $z$, for the "Standard" (blue curves) and "High $\tau$" (orange curves) cases. The dashed curves represent the imaging factor $(1-e^{-\tau})$, which quantifies the suppression of the mean 21 cm brightness temperature. The solid curves represent the power spectrum factor $(1-e^{-2\tau})$, which quantifies the suppression of the 21-cm power spectrum. Here we calculate the relative differences directly from the calculated $\tau$. These factors increase with $z$, reaching up to $\sim 10.3\%$ for the "Standard" case and $\sim 12.6\%$ for the "High $\tau$" case.