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

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.