[Paper Review] The First Billion Years in Seconds: An Effective Model for the 21-cm Signal with Population III Stars

Hector Afonso G. Cruz, Julián B. Muñoz+2 more|arXiv (Cornell University)|Jul 25, 2024

Radio Astronomy Observations and Technology4 citations

TL;DR

This paper introduces Zeus21, a fully analytic, fast, and flexible model for simulating the 21-cm signal during cosmic dawn, incorporating Population III stars with Lyman-Werner and relative velocity feedback. It achieves ~10% agreement with simulations while running in seconds—over 1,000× faster—enabling efficient parameter inference for upcoming 21-cm experiments.

ABSTRACT

Observations of the 21-cm signal are opening a window to the cosmic-dawn epoch, when the first stars formed. These observations are usually interpreted with semi-numerical or hydrodynamical simulations, which are often computationally intensive and inflexible to changes in cosmological or astrophysical effects. Here, we present an effective, fully analytic model for the impact of the first stars on the 21-cm signal, using the modular code Zeus21. Zeus21 employs an analytic prescription of the star formation rate density (SFRD) to recover the fully nonlinear and nonlocal correlations of radiative fields that determine the 21-cm signal. We introduce the earliest Population III (Pop III) stars residing in low-mass molecular-cooling galaxies in Zeus21, with distinct spectra from later Pop II stars. We also self-consistently model feedback in the form of $H_2$-dissociating Lyman-Werner (LW) radiation, as well as dark matter-baryon relative velocities, both of which suppress star formation in the lowest-mass halos. LW feedback produces a scale-dependence on the SFRD fluctuations, due to the long mean free path of LW photons. Relative velocities give rise to "wiggles" in the spatial distribution of the 21-cm signal; we present an improved calculation of the shape of these velocity-induced acoustic oscillations, showing they remain a standard ruler at cosmic dawn. Our improved version of Zeus21 predicts the 21-cm global signal and power spectra in agreement with simulations at the $\sim 10\%$ level, yet is at least three orders of magnitude faster. This public code represents a step towards efficient and flexible parameter inference at cosmic dawn, allowing us to predict the first billion years of the universe in mere seconds.

Motivation & Objective

• To develop a computationally efficient, fully analytic model for the 21-cm signal during cosmic dawn, incorporating the effects of Population III stars.
• To model the impact of Lyman-Werner feedback and relative velocity feedback on star formation in low-mass molecular-cooling galaxies.
• To enable fast and flexible parameter inference for upcoming 21-cm experiments by replacing computationally expensive simulations.
• To accurately capture scale-dependent SFRD fluctuations from long-mean-free-path LW photons and velocity-induced acoustic oscillations.
• To validate the model against simulations, achieving sub-10% agreement in global signal and power spectrum while reducing computation time by three orders of magnitude.

Proposed method

• Uses an analytic prescription for the star formation rate density (SFRD) as a function of local overdensity and relative velocity, encoded in effective biases γR, λR, and ωR.
• Models Lyman-Werner feedback via a scale-dependent modulation of SFRD fluctuations due to the long mean free path of LW photons.
• Incorporates relative velocity feedback through a log-χ² model for velocity-induced anisotropies, producing 'wiggles' in the 21-cm signal.
• Computes the Lyman-α background, kinetic temperature, and Wouthuysen-Field coupling analytically using SFRD-weighted integrals with astrophysical parameters.
• Constructs the 21-cm global signal and power spectrum using effective correlation functions for density and velocity fields, avoiding simulation boxes.
• Implements a causal treatment of the molecular-cooling threshold M_mol(z), correcting an acausal approximation in prior models like 21cmFAST.

Experimental results

Research questions

• RQ1 How can the 21-cm signal from the first stars be modeled analytically with high accuracy and extreme speed?
• RQ2 What is the impact of Lyman-Werner feedback on the spatial power spectrum of the 21-cm signal, particularly its scale dependence?
• RQ3 How do relative velocities between dark matter and baryons imprint oscillations on the 21-cm power spectrum, and are they robust as a standard ruler?
• RQ4 To what extent does the acausal treatment of the molecular-cooling threshold in 21cmFAST affect the 21-cm signal predictions?
• RQ5 Can a fully analytic model achieve sub-10% agreement with semi-numerical simulations while being three orders of magnitude faster?

Key findings

• Zeus21 reproduces the 21-cm global signal and power spectrum with ~10% accuracy compared to simulations, despite being fully analytic.
• The model captures the scale-dependent suppression of SFRD fluctuations due to Lyman-Werner feedback, arising from the long mean free path of LW photons.
• Relative velocity feedback induces velocity-induced acoustic oscillations in the 21-cm signal, which remain a robust standard ruler at cosmic dawn.
• The acausal treatment of the molecular-cooling threshold in 21cmFAST shifts the timing of cosmic dawn by Δz ≈ 0.1–0.2 and amplifies the power spectrum by 15–20%, within typical theoretical uncertainties.
• Zeus21 runs in seconds—over 1,000× faster than simulations—making it ideal for efficient parameter inference in cosmic dawn studies.
• The model's improved treatment of M_mol(z) evolution via causal, analytic computation reduces systematic errors present in prior semi-numerical codes.