Testing common approximations to predict the 21-cm signal at the epoch of reionization and cosmic dawn

Predicting the 21-cm signal from the epoch of reionization and cosmic dawn is a complex and challenging task. Various simplifying assumptions have been applied over the last decades to make the modeling more affordable. In this paper, we investigate the validity of several such assumptions, using a simulation suite consisting of three different astrophysical source models that agree with the current constraints on the reionization history and the UV luminosity function. We first show that the common assumption of a saturated spin temperature may lead to significant errors in the 21-cm clustering signal over the full reionization period. The same is true for the assumption of a neutral universe during the cosmic dawn which may lead to significant deviation from the correct signal during the heating and the Lyman-$\alpha$ coupling period. Another popular simplifying assumption consists of predicting the global differential brightness temperature ($d{T}_b$) based on the average quantities of the reionization fraction, gas temperature, and Lyman-$\alpha$ coupling. We show that such an approach leads to a 10 percent deeper absorption signal compared to the results obtained by averaging the final $d{T}_b$-map. Finally, we investigate the simplifying method of breaking the 21-cm clustering signal into different auto and cross components that are then solved assuming linearity. We show that even though the individual fields have a variance well below unity, they often cannot be treated perturbatively as the perturbations are strongly non-Gaussian. As a consequence, predictions based on the perturbative solution of individual auto and cross power spectra may lead to strongly biased results, even if higher-order terms are taken into account.