🔭 astrophysics

How X-rays heat the IGM in different 21-cm simulation codes: a comparison between Licorice and Beorn

This study compares the 3D radiative transfer code Licorice with the 1D code Beorn to demonstrate that while they agree on global X-ray heating properties, their differing treatments of temperature distribution lead to a ~30% discrepancy in the 21-cm power spectrum, causing significant biases ( $\gtrsim 1\sigma$ ) in inferred astrophysical parameters.

Original authors: Romain Meriot, Jonathan R. Pritchard, Timothée Schaeffer

Published 2026-08-17

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CC BY 4.0

Original authors: Romain Meriot, Jonathan R. Pritchard, Timothée Schaeffer

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

Imagine the universe as a giant, invisible ocean of gas, mostly made of hydrogen, stretching out in every direction. For the first few hundred million years after the Big Bang, this ocean was dark, cold, and silent. Then, the first stars and galaxies ignited like lighthouses in the fog. Their intense radiation began to heat up the gas and rip electrons away from atoms, a process called "reionization." Astronomers are desperate to see this era unfold because it holds the secrets to how our universe grew up. To do this, they are building a massive radio telescope called the Square Kilometre Array (SKA), which acts like a giant ear listening for a faint whisper: the "21-cm signal." This signal is a specific radio wave emitted by neutral hydrogen, and its strength changes depending on how hot the gas is. If the gas is cold, the signal looks different than if it is warm. By measuring this signal, scientists hope to map the history of the universe's heating.

However, there is a catch. The universe is too vast and complex to watch directly in real-time; we have to build computer models to simulate what happened billions of years ago. These simulations are like digital time machines. But just like any time machine, they are only as good as the rules they follow. Some simulations are incredibly detailed, tracking every single particle of gas and every ray of light, but they take supercomputers weeks to run. Others are faster and use shortcuts, making them easier to use but potentially less accurate. The big question is: do these shortcuts work well enough to trust the results? If two different simulation codes tell us different stories about how hot the gas got, which one should we believe? This is the puzzle that a new study by Romain Meriot and his team sets out to solve.

The team decided to put two very different "time machines" head-to-head to see how they handle the heating of the cosmic gas by X-rays. On one side, they had Licorice, a high-definition, 3D simulation that acts like a full-motion video game, calculating how gas moves and how light travels through it in three dimensions. On the other side, they had Beorn, a faster, simpler code that uses a "one-dimensional" approach. Think of Licorice as a master chef cooking a complex stew, stirring every ingredient individually, while Beorn is like a microwave that heats the whole meal based on an average recipe. The researchers wanted to see if the microwave could produce a meal that tasted just as good as the chef's stew, specifically regarding how the X-rays from the first stars warmed up the hydrogen gas.

To make a fair fight, the scientists didn't just let the two codes run with their own random settings. Instead, they took the "ingredients" (the stars and their light output) from the detailed Licorice simulation and fed them into Beorn. This ensured that both codes were trying to cook the exact same universe, just using different methods. They then compared the results: the temperature of the gas, the brightness of the 21-cm signal, and the statistical patterns of how that signal fluctuates across the sky.

The results were a mix of good news and a warning. When they looked at the big picture—the average temperature of the gas and the overall strength of the signal—the two codes agreed very well. It was as if the microwave and the chef both managed to get the stew to the right average temperature. However, when the scientists looked closer at the details, the differences started to show. The distribution of heat wasn't the same. In the detailed 3D simulation, the heat was patchy, with some spots being much hotter and others cooler, creating a complex texture. In the faster 1D simulation, the heat was smoother and more uniform.

These small differences in the "texture" of the heat turned out to be surprisingly important. When the team calculated the "power spectrum"—a fancy way of measuring how much the signal fluctuates at different scales—they found a discrepancy of about 30% between the two codes. To put that in perspective, if you were trying to guess the recipe of a cake based on a single bite, a 30% difference in the taste would mean you'd guess the wrong ingredients entirely.

The researchers then dug deeper to find out why the codes disagreed. They discovered that the shortcuts used in the faster code were the culprit. Specifically, the 1D code assumed that the density of the gas was the same everywhere (like assuming the ocean is perfectly flat) and used a simplified formula for how much heat the X-rays actually deposited. In reality, the gas is clumpy, and the heating depends on exactly where the gas is. When the team forced the detailed 3D code to use these same simplified shortcuts, the results drifted closer to the 1D code, confirming that these approximations were the source of the error.

Finally, the team asked the ultimate question: "If we use these different simulations to analyze data from the future SKA telescope, will we get the wrong answers?" They simulated a scenario where the telescope would observe for 100 hours. They found that the differences between the codes would lead to a significant bias in the estimated properties of the first stars. In statistical terms, the error was large enough to be greater than 1 sigma (a measure of confidence), and for some parameters, it was even higher. This means that if astronomers used the faster, simpler code to interpret real data, they might confidently conclude that the first stars were different than they actually were.

The study concludes that while the faster codes are useful and get the "average" story right, they are not yet precise enough for the era of the SKA. The 30% difference in the power spectrum and the resulting bias in the data suggest that we cannot simply trust the shortcuts when we are trying to measure the universe with extreme precision. The authors suggest that while the codes are similar enough for current, less sensitive telescopes, a lot of work is needed to refine the faster codes or develop new ways to correct their errors before the SKA starts listening. It's a reminder that in the quest to understand the dawn of the universe, the devil is truly in the details.

Technical Summary: How X-rays heat the IGM in different 21-cm simulation codes: a comparison between Licorice and Beorn

Problem Statement
The interpretation of the 21-cm signal from neutral hydrogen during the Cosmic Dawn and Epoch of Reionization relies heavily on Bayesian inference pipelines fed by simulation codes. While 3D radiative transfer (RT) codes (e.g., Licorice) offer high physical fidelity, they are computationally expensive, prompting the development of faster, approximate codes (e.g., 1D RT codes like Beorn, or semi-numerical codes like 21cmFAST). A critical gap in the literature is the lack of rigorous comparison regarding how these different codes model X-ray heating of the Intergalactic Medium (IGM). Previous comparisons often focused on ionization fields or assumed saturated spin temperatures, neglecting the specific discrepancies in thermal evolution. As the Square Kilometre Array (SKA) approaches, understanding the variance introduced by these approximations is essential to avoid biased astrophysical parameter inference.

Methodology
The authors perform a controlled comparison between Licorice, a hydro-radiative 3D RT code coupling Smoothed Particle Hydrodynamics (SPH) with Monte Carlo ray-tracing, and Beorn, a 1D RT code that "paints" pre-computed temperature profiles around sources.

To ensure a fair comparison, the authors developed a pipeline to transfer source populations from Licorice to Beorn:

Source Extraction: They extracted 3D cubes of UV luminosity from Licorice simulations (running from $z=100$ to $z=8$ ).
Luminosity Histories: Since Beorn requires halo accretion histories but Licorice tracks particles without explicit halo catalogs, the authors tracked non-zero pixels in the luminosity cubes backward in time. They constructed luminosity histories for these "sources," sorting them into luminosity bins ( $N=1000$ ) based on their final luminosity at the lowest redshift.
Profile Painting: Beorn used these binned histories to compute 1D temperature profiles, which were then painted onto the 3D grid at the locations of the corresponding Licorice sources.
Experimental Setup: The authors ran two sets of experiments:
- Realistic: Using the native physics of both codes (Licorice uses local density and variable heating efficiency $f_{heat}$ ; Beorn uses global average density and global $f_{heat}$ ).
- Idealised: Introducing specific approximations into Licorice to mimic Beorn's physics (e.g., forcing Licorice to use mean density for optical depth and a constant $f_{heat}$ ).
Inference Impact: They utilized the Loreli II emulator (an emulator of Licorice power spectra) within an MCMC pipeline to translate differences in 21-cm power spectra into biases in posterior distributions of astrophysical parameters ( $f_X$ , $\tau_{SF}$ , $M_{min}$ ), assuming SKA noise levels corresponding to 100 hours of observation.

Key Results

Global Agreement: The total X-ray luminosity fields, mean temperatures, and global 21-cm signals show good agreement between the two setups (differences $\lesssim 10\%$ in mean temperature).
Field Discrepancies: Despite global agreement, the spatial distribution of temperature and the 21-cm signal differs significantly. Beorn produces narrower temperature distributions with fewer extreme values compared to Licorice. Topological analysis (Betti numbers) confirms that the heating morphology differs, with Licorice showing more small-scale fluctuations.
Power Spectrum Differences: The 21-cm power spectra exhibit discrepancies of approximately 20–30% in the realistic case and ~11% in the idealised case. These differences are most pronounced at high redshifts ( $z \sim 11-12$ ) where heating drives the signal evolution.
Source of Error: The authors isolate that common approximations in 1D codes—specifically the use of a homogeneous density field for optical depth calculations and a global average heating efficiency ( $f_{heat}$ )—individually produce differences of the same magnitude as the full code comparison.
Inference Bias: When these power spectrum differences are fed into the MCMC pipeline, they result in significant biases in the recovered astrophysical parameters. The authors observe typical biases of $\gtrsim 1\sigma$ (and up to several $\sigma$ for $f_X$ ) between the posteriors derived from the 3D (Licorice) and 1D (Beorn) models.

Significance and Claims
The paper claims that while 1D and 3D codes may agree on global quantities, their treatment of X-ray heating leads to structural differences in the IGM temperature field that are significant enough to bias astrophysical inference.

Model Error vs. Noise: The authors highlight that the bias introduced by using different simulation codes (model error) can exceed the bias introduced by using different inference methods on a single code.
SKA Readiness: While the codes may be sufficiently similar for current SKA pathfinders, the observed $\sim 20-30\%$ power spectrum discrepancy and the resulting $\gtrsim 1\sigma$ parameter biases suggest that significant work is needed to align these codes before the SKA era, where systematics-free data will demand higher precision.
Modesty: The authors do not claim one code is definitively "correct" over the other, noting that both rely on uncertain modeling choices. They conclude that achieving sub-noise level agreement between codes is difficult, but an agreement of $\sim 20\%$ in power spectra is a reasonable benchmark given the complexity of the problem. They explicitly state that generalizing these results to other codes (e.g., 21cmFAST, Grizzly) requires further dedicated comparisons.

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