The Effect of Large Optical Depths on the Non-Gaussian 21-cm signal from Cosmic Dawn

TL;DR

This study investigates how large HI 21-cm optical depths during Cosmic Dawn modify the non-Gaussian features of the 21-cm signal. By comparing exact and approximate δTb calculations that include higher-order terms in $τ$ (up to $τ^3$) against GRIZZLY-based radiative-transfer simulations across a range of X-ray heating efficiencies and halo-hosting masses, the authors quantify impacts on skewness and the bispectrum, as well as the power spectrum. They find that large $τ$ suppresses the two-point statistics but enhances non-Gaussian signals, with skewness and bispectrum changes reaching hundreds of percent in some models, especially at early CD when heating is weak. The key conclusion is that retaining higher-order terms in the $τ$ expansion is essential to accurately model non-Gaussian features of the CD 21-cm signal, although the simpler approximation can suffice in later stages when $τ$ is small.

Abstract

During the Cosmic Dawn (CD), the HI 21-cm optical depth ($τ$ ) in the intergalactic medium can become significantly large. Consequently, the second and higher-order terms of $τ$ appearing in the Taylor expansion of the HI 21-cm differential brightness temperature ($δT_{\rm b}$ ) become important. This introduces additional non-Gaussianity into the signal. We study the impact of large $τ$ on statistical quantities of HI 21-cm signal using a suite of standard numerical simulations that vary X-ray heating efficiency and the minimum halo mass required to host radiation sources. We find that the higher order terms suppress statistical quantities such as skewness, power-spectrum and bispectrum. However, the effect is found to be particularly strong on the non-Gaussian signal. We find that the change in skewness can reach several hundred percent in low X-ray heating scenarios, whereas for moderate and high X-ray heating models changes are around $\sim40\%$ and $60\%$, respectively, for $M_{\rm h,min}=10^{9}\, {\rm M}_{\odot}$. This change is around $\sim 75\%$, $25\%$ and $20\%$ for low, moderate and high X-ray heating models, respectively, for $M_{\rm h,min}=10^{10}\, {\rm M}_{\odot}$. The change in bispectrum in both the halo cutoff mass scenarios ranges from $\sim 10\%$ to $\sim 300\%$ for low X-ray heating model. However, for moderate and high X-ray heating models the change remains between $\sim 10\%$ to $\sim 200\%$ for both equilateral and squeezed limit triangle configuration. Finally, we find that up to third orders of $τ$ need to be retained to accurately model $δT_{\rm b}$, especially for capturing the non-Gaussian features in the HI 21-cm signal.

Figures (8)

• Figure 1: Redshift evolution of the mean HI 21-cm optical depth and the differential brightness temperatures. The upper and lower panels show the redshift evolution of mean H i 21-cm optical depth, $\tau$, and the global 21-cm differential brightness temperature $\overline{\delta T_{\rm b}}(z)$, respectively. In the lower panel, the evolution of both approximated (solid curve) and exact $\overline{\delta T_{\rm b}}(z)$ (dashed curve) is shown.
• Figure 2: Probability distribution function (PDF) of H i 21-cm optical depth ($\tau$) for models with $f_{\rm x}=0.1$, $M_{\rm h,min}=10^9$${\rm M}_{\odot}$ (top left); $f_{\rm x}=0.1$, $M_{\rm h,min}=10^{10}$${\rm M}_{\odot}$ (top right) and $f_{\rm x}=46.4$, $M_{\rm h,min}=10^{10}$${\rm M}_{\odot}$ (bottom left), at redshift $z=12.3$. The bottom right panel shows the cumulative distribution function (CDF) of $\tau$ for all three scenarios.
• Figure 3: Probability distribution function (PDF) of simulated $\delta T_{\rm b}$ for models with $f_{\rm x}=0.1$, $M_{\rm h,min}=10^9$${\rm M}_{\odot}$; $f_{\rm x}=0.1$, $M_{\rm h,min}=10^{10}$${\rm M}_{\odot}$ and $f_{\rm x}=46.4$, $M_{\rm h,min}=10^{10}$${\rm M}_{\odot}$, at redshift $z=12.3$.
• Figure 4: Redshift evolution of skewness for the approximated and exact $\delta T_{\rm b}$ (left panels) and the percentage change (right panels) for all the CD scenarios. In the left panel the blue solid and red dashed lines represent the skewness for the approximated and exact $\delta T_{\rm b}$ respectively.
• Figure 5: Redshift evolution of the spherically averaged dimensionless bispectrum for approximated and exact $\delta T_{\rm b}$, along with the percentage change between them, at the scale $k_1=0.16\, {\rm Mpc}^{-1}$. In the left panel, the blue solid and dashed lines represent bispectrum of approximated and exact $\delta T_{\rm b}$, respectively, for $M_{\rm h,min} = 10^9 {\rm M}_{\odot}$ while, the red solid and dashed lines represent the same for $M_{\rm h,min} = 10^{10} {\rm M}_{\odot}$. In the right panel, the blue and red solid lines represent the percentage difference between the approximated and exact $\delta T_{\rm b}$ for the models with $M_{\rm h,min} = 10^9\ {\rm M}_{\odot}$ and $M_{\rm h,min} = 10^{10}\ {\rm M}_{\odot}$, respectively.