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

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 (δTb ) 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 the changes are around ∼40% and ∼60%, respectively, for Mh, min = 109 M⊙. This change is around ∼75%, 25% and 20% for low, moderate and high X-ray heating models, respectively, for Mh, min = 1010 M⊙. The change in bispectrum in both the halo cutoff mass scenarios ranges from ∼10% to ∼300% for low X-ray heating model. However, for moderate and high X-ray heating models the change remains between ∼10% to ∼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 δTb, especially for capturing the non-Gaussian features in the H i 21-cm signal.