An effective model for the cosmic-dawn 21-cm signal

The 21-cm signal holds the key to understanding the first structure formation during cosmic dawn. Theoretical progress over the last decade has focused on simulations of this signal, given the non-linear and non-local relation between initial conditions and observables (21 cm or reionization maps). Here, instead, we propose an effective and fully analytical model for the 21-cm signal during cosmic dawn. We take advantage of the exponential-like behaviour of the local star-formation rate density (SFRD) against densities at early times to analytically find its correlation functions including non-linearities. The SFRD acts as the building block to obtain the statistics of radiative fields (X-ray and Lyman a fluxes), and therefore the 21-cm signal. We implement this model as the public PYTHON package Zeus21. This code can fully predict the 21-cm global signal and power spectrum in similar to 1 s, with negligible memory requirements. When comparing against state-of-the-art semi-numerical simulations from 21CMFAST we find agreement to similar to 10 per cent precision in both the 21-cm global signal and power spectra, after accounting for a (previously missed) underestimation of adiabatic fluctuations in 21CMFAST. Zeus21 is modular, allowing the user to vary the astrophysical model for the first galaxies, and interfaces with the cosmological code CLASS , which enables searches for beyond standard-model cosmology in 21-cm data. This represents a step towards bringing 21-cm to the era of precision cosmology.