🔭 astrophysics

Exploring the High-Redshift 21-cm Signal via Self-Consistent Simulations using Artificial Neural Network Emulation

This paper presents a novel self-consistent semi-numeric simulation of the Cosmic Dawn that utilizes artificial neural networks to emulate star formation calibrated against hydrodynamic data, revealing how the timing of the transition between Population III and II stars and the inclusion of specific merger histories significantly shape the 21-cm signal's absorption trough and power spectrum, with predictions suggesting detectability by HERA at redshifts below 25.

Original authors: Colton R. Feathers, Eli Visbal, Steven Murray, Ryan Hazlett, Yin-Zhe Ma

Published 2026-05-29

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Colton R. Feathers, Eli Visbal, Steven Murray, Ryan Hazlett, Yin-Zhe Ma

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Listening to the Universe's "Baby Photos"

Imagine the universe as a giant, dark room. For the first few hundred million years after the Big Bang, this room was filled with cold, invisible gas (mostly hydrogen). It was silent and dark.

Then, the very first stars and galaxies began to form. These weren't like the stars we see today; they were massive, ancient giants (called Population III) and slightly smaller, but still ancient, stars (called Population II). As these stars turned on, they didn't just light up the room; they changed the air itself. They emitted radiation that interacted with the hydrogen gas, creating a faint, specific radio signal known as the 21-cm signal.

This paper is about building a sophisticated "time machine" (a computer simulation) to predict exactly what this radio signal looked like during that ancient era, so that real telescopes can know what to listen for.

The Problem: Too Much Math, Not Enough Time

To understand how these first stars formed, scientists usually have two choices:

The "Super-Detailed" Method: Run a massive, complex simulation that tracks every single gas particle. This is like trying to simulate a hurricane by tracking every single water molecule. It's incredibly accurate but takes so much computer power that you can only simulate a tiny patch of the universe.
The "Simple" Method: Use basic math formulas to guess the average behavior. This is fast, but it's like guessing the weather by looking at the sky from your porch; it misses the big picture and the local storms.

The authors' solution: They created a "hybrid" method. Think of it like a smart video game.

They built a massive map of the universe (a large volume of space).
Instead of calculating every single star formation event from scratch (which would take forever), they trained an Artificial Neural Network (AI).
Imagine the AI as a chef who has tasted a few thousand complex, high-end meals (from the "Super-Detailed" simulations). Now, the chef can instantly guess how a new dish will taste without having to cook it first.
This allowed them to simulate a huge volume of the universe with high accuracy, but in a fraction of the time.

How They Cooked Up the Simulation

The team didn't just guess how stars form; they calibrated their "chef" (the AI) using results from the most advanced hydrodynamic simulations available (called AEOS and Renaissance).

They focused on two main types of star formation:

Population III (The First Giants): These stars formed in pristine gas clouds. The simulation tracks when these stars ignite based on the size of the "dark matter halo" (the invisible gravitational cage holding the gas).
Population II (The Second Generation): These stars formed later, after the first generation died and enriched the gas with heavier elements.

The "Delay" Analogy:
The paper highlights a crucial timing issue. When a Population III star dies, it explodes and pollutes the gas. The gas needs time to cool down and clean itself before it can form Population II stars.

The authors tested different "recovery times" (delays).
Analogy: Imagine a party. The first group of guests (Pop III) arrives, makes a huge mess, and leaves. The second group (Pop II) can't arrive until the host has cleaned up.
- If the host cleans up quickly (a short delay), the second group arrives early, and the party lights up the room sooner.
- If the host takes a long time to clean (a long delay), the second group arrives late, and the room stays dark longer.
The authors found that this "cleaning time" (delay) drastically changes the shape of the radio signal.

What They Found: The "Absorption Trough"

The main goal was to predict the 21-cm brightness temperature.

Analogy: Think of the universe's background radiation as a warm blanket. The first stars act like a giant freezer, cooling the gas below the temperature of the blanket.
When you look at the radio signal, this cooling creates a dip or a "valley" in the data, called an absorption trough.

Key Findings:

Deeper and Earlier: Because their simulation included realistic details (like the "cleaning time" delay and the specific way stars form in small clumps), they predicted a deeper and earlier dip than previous models.
- Previous models were like guessing the party started late.
- This model says the party started earlier and got louder faster because the "cleaning" happened quicker and the stars formed more efficiently.
The Role of Pop III vs. Pop II:
- Early on (High Redshift): The signal is dominated by the first giants (Pop III). They control the large-scale structure of the universe.
- Later on (Lower Redshift): The second generation (Pop II) takes over. They dominate the smaller-scale details and the intensity of the signal.
The "Bursty" Nature: The simulation showed that star formation isn't a smooth, steady stream. It's "bursty." Stars form in sudden bursts, then the gas goes quiet for a while, then bursts again. This creates a more complex, fluctuating signal than smooth models predict.

Can We See It? (The HERA Telescope)

The authors checked if current or future telescopes could actually see this signal. They focused on HERA (Hydrogen Epoch of Reionization Array), a radio telescope in South Africa designed specifically to listen for this signal.

The Verdict: Yes, but it's tricky.
If the "cleaning time" (delay) between star generations is short (around 10 million years), the signal should be detectable by HERA within about 1,000 hours of observation.
The "Smoking Gun": If HERA looks and doesn't see the signal at certain redshifts (around 20), it would imply that the "cleaning time" is actually very long (over 30 million years). This would tell us that the transition from the first stars to the second generation was much slower than this paper predicts.

Summary in One Sentence

The authors built a fast, AI-powered simulation that combines the best of detailed physics with large-scale mapping to predict that the universe's first stars turned on earlier and more efficiently than we thought, creating a deeper radio "shadow" that future telescopes like HERA might finally be able to hear.

Technical Summary: Exploring the High-Redshift 21-cm Signal via Self-Consistent Simulations using Artificial Neural Network Emulation

Problem Statement
Understanding the Cosmic Dawn (CD), the era of the first stars and galaxies ( $z \sim 15-60$ ), is crucial for tracing cosmic evolution. While observational probes like JWST and radio arrays (HERA, LOFAR, MWA) are advancing, interpreting 21-cm line data requires robust theoretical models. Existing approaches face a dichotomy: simplified analytic models are computationally efficient but rely on restrictive assumptions, while complex hydrodynamic simulations offer high fidelity but are limited to small volumes and narrow parameter spaces due to computational cost. Furthermore, many semi-numeric models lack self-consistent treatments of small-scale star formation (SF) calibrated to hydrodynamics, stochastic dark matter (DM) halo merger histories, and large-scale radiative feedback. This paper addresses the need for a self-consistent, large-scale semi-numeric framework that bridges this gap to provide accurate predictions for the 21-cm global signal and power spectrum.

Methodology
The authors present an upgraded semi-numeric simulation framework, building upon the work of Feathers et al. (2025, F25). The core methodology involves:

Simulation Volume: A large-scale volume of $192^3$ Mpc $^3$ (composed of $64^3$ cells of $(3 \text{ Mpc})^3$ ) is generated using 21cmvFAST. This volume includes spatial fluctuations in matter density ( $\delta$ ) and baryon-DM streaming velocities ( $v_{bc}$ ), which are critical for accurate SF predictions.
Dark Matter Halo Evolution: The framework utilizes the Extended Press-Schechter (EPS) formalism to construct stochastic DM halo merger trees. A library of $\sim 10^4$ merger trees is generated for 40 halo mass bins ( $10^{5.6} - 10^{9.5} M_\odot$ ). These trees are assigned to simulation cells based on local overdensity, serving as the scaffolding for SF.
Neural Network (NN) Emulation: To overcome the computational prohibitions of running a complex Subgrid Semi-Analytic Model (SAM) for every cell, the authors employ Artificial Neural Network emulators.
- Training Data: The NNs are trained on a SAM calibrated to state-of-the-art hydrodynamic simulations: the Renaissance (O'Shea et al. 2015) and AEOS (Brauer et al. 2025) simulations.
- Star Formation (SF) Prescription: The fiducial model incorporates SF prescriptions from Hazlett et al. (2025a,b). This includes:
  - PopIII SF: Modeled with a cumulative distribution function for stellar masses, resulting in an average of four $35.6 M_\odot$ stars per halo upon crossing the critical mass threshold ( $M_{crit}$ ).
  - PopII SF: Modeled as a two-phase process: an initial "bursty" phase followed by a "steady" phase once the halo virial temperature reaches $T_{vir, steady} \approx 1.76 \times 10^4$ K. This includes a quiescent period ( $t_{quies}$ ) following bursts.
  - Critical Mass ( $M_{crit}$ ): Calculated considering Lyman-Werner (LW) feedback and H $_2$ self-shielding (Kulkarni et al. 2021).
- Efficiency: The NN emulation reduces the computational cost of generating Star Formation Rate Density (SFRD) predictions by a factor of $\sim 200$ compared to the full SAM, allowing the full volume to be simulated in $\sim 21$ CPU-hours.
21-cm Signal Calculation: The simulated SFRD is post-processed to calculate the 21-cm brightness temperature ( $\delta T_b$ $δ T_{b}$ ) and power spectrum ( $\Delta^2(k)$ $Δ^{2} (k)$ ). This involves:
- Calculating the Lyman- $\alpha$ background ( $J_\alpha$ ) to determine the Wouthuysen-Field (W-F) coupling coefficient ( $x_\alpha$ ).
- Solving for the spin temperature ( $T_S$ ) and kinetic temperature ( $T_K$ ) of the intergalactic medium (IGM), accounting for Compton heating and X-ray heating (assumed to trace the SFR).
- Iteratively solving for $T_S$ to determine $\delta T_b$ and its power spectrum.

Key Contributions

Novel Calibration: This is the first large-scale semi-numeric simulation to self-consistently unite stochastic DM halo merger trees with SF prescriptions explicitly calibrated to modern hydrodynamic simulations (Renaissance and AEOS).
Two-Phase PopII Modeling: The framework introduces a "bursty" to "steady" transition for PopII SF, calibrated to hydrodynamic results, which differs significantly from previous constant-efficiency models.
Stochastic Merger Histories: The inclusion of stochastic DM halo merger histories allows for a realistic treatment of the transition from PopIII to PopII SF, including a delay period ( $t_{delay}$ ) and the effects of $v_{bc}$ on $M_{crit}$ .
Computational Efficiency: The optimized NN architecture and reduced training set allow for multiple realizations with varying astrophysical assumptions (e.g., different PopIII masses, $t_{delay}$ , $M_{crit}$ ) to be run efficiently.

Results
The authors present results from a fiducial model and several alternative realizations (varying PopIII mass, $M_{crit}$ , and $t_{delay}$ ):

Global Signal ( $\delta T_b$ ):
- The fiducial model predicts an absorption trough minimum of $\delta T_b \approx -146$ mK at $z \approx 20.25$ .
- PopIII vs. PopII Impact: PopIII SF dominates the 21-cm signal at $z \gtrsim 34$ and on large scales. PopII SF dominates at $z \lesssim 20$ and on smaller scales ( $k \gtrsim 0.2$ Mpc $^{-1}$ at $z \sim 20-34$ ).
- Delay Period ( $t_{delay}$ ): The delay between PopIII and PopII SF significantly impacts the signal. A longer delay (e.g., 100 Myr) results in a later, deeper, and narrower absorption trough compared to the fiducial 10 Myr delay.
- Comparison: The fiducial model yields earlier and deeper absorption troughs than many previous models (e.g., Muñoz et al. 2022) due to the combination of DM merger trees, H $_2$ self-shielding, and calibrated SF efficiencies.
Power Spectrum ( $\Delta^2(k)$ ):
- Power spectra are detectable by HERA starting at $z \approx 25$ for $k \sim 0.2$ Mpc $^{-1}$ , expanding to $k \lesssim 0.9$ Mpc $^{-1}$ by $z=15$ under moderate foreground assumptions (1080 hours of observation).
- Models with stochastic merger histories show enhanced large-scale power at high redshifts compared to models without them (like the Muñoz et al. 2022 model), driven by $v_{bc}$ fluctuations affecting $M_{crit}$ .
NN Accuracy: The emulators reproduce the SAM results with an average accuracy of $\sim 8.3\%$ for PopII and $\sim 5.0\%$ for PopIII across all redshifts and models.

Significance and Claims
The paper claims that the combination of hydrodynamic SF calibration, a critical halo mass model accounting for H $_2$ self-shielding, and stochastic DM halo merger histories results in earlier star formation and higher SFRDs across the Cosmic Dawn compared to previous semi-numeric works.

The authors assert that:

Observability: The fiducial 21-cm signal is potentially detectable by HERA at $z \lesssim 25$ .
Constraints on Physics: The lack of a detection at $z \gtrsim 20$ would suggest a delay period ( $t_{delay}$ ) between PopIII and PopII SF of $\gtrsim 30$ Myr.
Methodological Necessity: Properly accounting for the transition between PopIII and PopII SF requires including DM halo merger histories, as simplified analytic models (like HMF integrals) fail to capture the stochasticity and timing of this transition.
Differentiation: While distinguishing between subtle variations in SF efficiency may be difficult, the power spectrum sensitivity of HERA is sufficient to distinguish between models with different $t_{delay}$ values and to differentiate the authors' model (with merger trees and hydro-calibration) from models lacking these features (like the Muñoz et al. 2022 realization).

The work positions itself as a novel, complementary tool to existing semi-numeric codes (e.g., 21cmFAST, Zeus21), offering a more physically grounded approach to predicting the 21-cm signal for current and future observational campaigns.