ECHO21: a tool for modelling global 21-cm signal from dark ages to reionization

We introduce a Python package called ECHO21 for modelling the global 21-cm signal from the dark ages through cosmic dawn to the end of reionization. Leveraging its analytical framework, ECHO21 generates a single model in $\mathcal{O}(1),$s, allowing a large number of signals to be generated efficiently by distributing models across multiple cores. Thus, it is ideal for performing astrophysical or cosmological inference from a given 21-cm dataset. We offer six astrophysical parameters that control the Lyman-$α$ (Ly$α$) emissivity, X-ray emissivity, emissivity of ionizing photons, and star formation rate. Beyond its efficiency some of the attractive and novel features in ECHO21 relative to previously published codes are inclusion of Ly$α$ heating, ability to vary the standard cosmological parameters as easily as the astrophysical parameters, and different models of star formation rate density (physically-motivated, a semi-empirical, and an empirically-motivated). With a number of 21-cm experiments soon to provide cosmic dawn 21-cm data, ECHO21 is a flexible and extensible new open-source package for making quick but sufficiently realistic astrophysical inferences. We make our code publicly available.

💡 Research Summary

The manuscript presents ECHO21, a new open‑source Python package designed to compute the global (sky‑averaged) 21‑cm brightness temperature from the dark ages through cosmic dawn to the end of reionization. The authors emphasize speed: a single model spanning redshifts 0 ≤ z ≤ 1500 can be generated in O(1) seconds on a single CPU core, and the code is trivially parallelizable across multiple cores, making it well suited for large‑scale Bayesian inference (MCMC, nested sampling, or machine‑learning emulators).

Physical framework
ECHO21 adopts a two‑zone intergalactic medium (IGM) description, separating bulk neutral gas from ionized H II regions. The globally averaged ionized fraction is (\bar{x}_i = Q + (1-Q)x_e), where (Q) is the H II volume filling factor and (x_e) the electron fraction in the bulk. The observable 21‑cm brightness temperature is given by the standard expression \