[Paper Review] An Effective Model for the Cosmic-Dawn 21-cm Signal

Julián B. Muñoz|arXiv (Cornell University)|Feb 16, 2023

Radio Astronomy Observations and Technology4 citations

TL;DR

This paper presents Zeus21, a fully analytic, open-source Python package that models the cosmic-dawn 21-cm signal using a lognormal approximation for the star-formation rate density (SFRD), enabling fast and precise computation of the global signal and power spectrum in ~1 second. The model captures nonlinear and nonlocal effects via exponential SFRD dependence on density, achieving ~10% agreement with 21CMFAST simulations after correcting for adiabatic fluctuation underestimation.

ABSTRACT

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 nonlinear and nonlocal relation between initial conditions and observables (21-cm or reionization maps). Here, instead, we propose an {\it effective} and fully analytic model for the 21-cm signal during cosmic dawn. We take advantage of the exponential-like behavior of the local star-formation rate density (SFRD) against densities at early times to analytically find its correlation functions including nonlinearities. The SFRD acts as the building block to obtain the statistics of radiative fields (X-ray and Lyman-$α$ 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 $\sim 1$ s, with negligible memory requirements. When comparing against state-of-the-art semi-numerical simulations from 21CMFAST we find agreement to $\sim10\%$ 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.

Motivation & Objective

• To develop a fast, fully analytic model for the 21-cm signal during cosmic dawn that captures nonlinear and nonlocal physics without relying on costly simulations.
• To address the computational bottleneck of simulating the 21-cm signal across vast parameter spaces during the early universe.
• To provide a modular, open-source tool that enables efficient exploration of astrophysical and beyond-Standard-Model cosmological models.
• To improve precision in 21-cm data analysis by identifying and correcting previously missed effects in existing simulation codes like 21CMFAST.
• To enable rapid inference and forecasting for upcoming 21-cm experiments by integrating with cosmological codes like CLASS.

Proposed method

• Model the star-formation rate density (SFRD) as a lognormal variable due to its exponential dependence on overdensity at high redshift, derived from the effective bias γR.
• Use analytic correlation functions of lognormal variables to compute the statistics of radiative fields (X-ray and Lyman-α fluxes) and thus the 21-cm signal.
• Construct the 21-cm signal as a sum of SFRDs over different smoothing radii R, enabling nonlocal and nonlinear effects to be captured analytically.
• Implement the model in the open-source Zeus21 Python package, which computes the global signal and power spectrum in ~1 second with minimal memory.
• Integrate with the cosmological code CLASS to allow self-consistent inclusion of non-cold dark matter and other beyond-Standard-Model physics.
• Validate the model against 21CMFAST simulations, identifying and correcting a previously missed underestimation of adiabatic fluctuations in the standard code.

Experimental results

Research questions

• RQ1 How can the nonlinear and nonlocal relationship between initial conditions and the 21-cm signal during cosmic dawn be modeled analytically with high precision?
• RQ2 What is the impact of SFRD's exponential dependence on density on the statistical properties of the 21-cm signal and its power spectrum?
• RQ3 To what extent can a fully analytic model match the accuracy of semi-numerical simulations like 21CMFAST, and where do discrepancies arise?
• RQ4 How can the model be made modular and extensible to test new astrophysical and cosmological physics, including non-cold dark matter and arbitrary source SEDs?
• RQ5 Can the model identify and correct for systematic errors in existing simulation pipelines, such as the underestimation of adiabatic fluctuations in 21CMFAST?

Key findings

• The Zeus21 model computes the 21-cm global signal and power spectrum in approximately 1 second with negligible memory usage, enabling rapid parameter space exploration.
• The model achieves ~10% agreement with 21CMFAST simulations for both the global signal and power spectrum after correcting for a previously missed underestimation of adiabatic fluctuations in 21CMFAST.
• The SFRD is modeled as a lognormal variable due to its exponential dependence on density, enabling analytic computation of correlation functions and nonlinear effects.
• The model successfully identifies and corrects for a systematic error in 21CMFAST related to adiabatic cooling, improving consistency with theoretical expectations.
• Zeus21 is modular and interfaces with CLASS, allowing direct implementation of non-cold dark matter models, millicharged particles, and arbitrary X-ray/UV spectral energy distributions (SEDs).
• The model enables efficient joint analysis of 21-cm data with CMB and large-scale structure data through its integration with cosmological codes.