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The Three Hundred Project: validating $H_0$ inference from mock X-ray and millimetre analyses of galaxy clusters

Using a sample of 100 to 1000 galaxy clusters from The Three Hundred hydrodynamical simulations, this study demonstrates that joint X-ray and millimetre observations, when corrected for morphological and dynamical systematics, can constrain the Hubble constant ( $H_0$ ) with a precision of 1.5% to 4% and a systematic uncertainty of approximately 0.6–0.8 km s⁻¹ Mpc⁻¹.

Original authors: F. De Luca, H. Bourdin, P. Mazzotta, E. Rasia, A. Kozmanyan, W. Cui, M. De Petris, D. de Andres, G. Yepes

Published 2026-07-10

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Original authors: F. De Luca, H. Bourdin, P. Mazzotta, E. Rasia, A. Kozmanyan, W. Cui, M. De Petris, D. de Andres, G. Yepes

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 is a giant, invisible ocean made of hot gas, and floating in it are massive islands called galaxy clusters. Astronomers want to measure how fast the universe is expanding right now (a number called $H_0$ ), and they think these floating islands are perfect rulers to do the job. But there's a catch: the gas inside these islands isn't a smooth, perfect balloon. It's lumpy, wobbly, and sometimes getting hit by other islands.

When astronomers try to measure the size of these gas balloons using two different tools—one that sees X-rays and another that sees millimeter waves—they often get slightly different answers. It's like trying to guess the size of a squishy, shape-shifting jellyfish by looking at it from the side and then from the top; if you assume the jellyfish is a perfect sphere, your math will be a little off. This "off-ness" is called a bias, and it messes up the measurement of the universe's expansion.

The Big Discovery: The "Jellyfish" Has a Pattern
In this study, a team of scientists used a super-powerful computer simulation called "The Three Hundred Project" to create 324 fake galaxy clusters. They didn't just make them up; they simulated the physics of gas, stars, and gravity to see how these clusters actually behave.

They found that the "off-ness" (the bias) isn't random chaos. It follows a pattern! Just like a real jellyfish, the more "relaxed" and calm a cluster is, the closer its shape is to a perfect sphere, and the smaller the error. But if a cluster is "disturbed" (wobbly, crashing into things, or full of lumps), the error gets bigger and more unpredictable.

The authors discovered that they could predict this error based on how "relaxed" or "disturbed" a cluster looks. They built a mathematical map (using something called Gaussian Processes) that says, "If a cluster looks like this, expect an error of that size."

The Test: Does the Map Work?
To see if this map could actually save the day, the team ran a massive test. They pretended to be astronomers looking at a fake universe where they already knew the true answer for the expansion rate ( $H_0$ ). They then tried to measure it using their new "error map" to correct their data.

The result? It worked perfectly.

No Bias: When they used their new method, they didn't get a wrong answer. They found the true value of $H_0$ without any systematic error.
Precision: With a sample of 100 clusters, they could pin down the expansion rate with about 4% precision. With 1,000 clusters, they could get it down to 1.5% precision.
The Limit: However, even with thousands of clusters, there is a tiny "floor" to how perfect the measurement can get. The paper suggests that no matter how many clusters you add, there will always be a tiny bit of uncertainty left over, about 0.6–0.8 km s⁻¹Mpc⁻¹, due to the complex physics of the gas itself.

What They Ruled Out
The paper explicitly argues against the idea that you can just ignore the shape of these clusters or treat them all the same. You can't just say, "Oh, it's a sphere," and move on. The study shows that if you don't account for whether a cluster is "relaxed" or "disturbed," your measurement of the universe's expansion will be biased. They also showed that simply looking at the total mass or temperature of the cluster doesn't help predict the error; it's specifically the shape and dynamical state (how calm or chaotic it is) that matters.

How Sure Are They?
It is important to remember that these results come from simulations. The scientists didn't look at real telescopes for this specific test; they looked at a computer model of the universe.

They simulated the data to prove their method works.
They suggest that this method could be applied to real data from telescopes like XMM-Newton and Planck.
They found that in their simulated world, the method is unbiased and well-calibrated.

The paper concludes that this "simulation-informed" approach is a promising way to fix the messy math of galaxy clusters. By teaching the computer to recognize the "jellyfish shapes" of the universe, we might finally get a super-accurate ruler to measure how fast our cosmic ocean is expanding. But until they test this on real, physical light from the sky, it remains a very strong, very promising simulation.

Technical Summary: The Three Hundred Project: validating H0 inference from mock X-ray and millimetre analyses of galaxy clusters

Problem Statement
Measurements of thermodynamical quantities in galaxy clusters, specifically when derived from joint X-ray and millimetre (Sunyaev-Zel'dovich, SZ) observations, are subject to systematic biases arising from simplified modelling assumptions. These assumptions typically include hydrostatic equilibrium, spherical symmetry, and the absence of gas clumps. Such simplifications lead to discrepancies between temperature profiles inferred from X-ray spectroscopy and those derived from joint X-ray and SZ imaging. These discrepancies, quantified by a bias factor $B$ , limit the precision of cosmological parameter inference, particularly the Hubble constant ( $H_0$ ), when using galaxy clusters as standard rulers. Previous work (Kozmanyan et al. 2019, hereafter K19) utilized hydrodynamical simulations to model the distribution of $B$ and incorporate it as an informative prior in Bayesian analyses, but this was limited to smaller samples and did not fully account for the continuous dependence of $B$ on cluster dynamical and morphological states.

Methodology
This study extends the K19 framework using a larger synthetic sample of 324 galaxy clusters from "The Three Hundred" (The300) hydrodynamical simulations, specifically the gadget-x run. The analysis proceeds through the following steps:

Mock Data Generation: The authors generated mock X-ray and SZ observables for the clusters by projecting particle data along three orthogonal lines of sight, resulting in a sample of 972 objects. They computed projected emission measures, spectroscopic-like temperatures ( $T_{sl}$ ), and Compton- $y$ parameters.
Bias Characterization: The bias factor $B$ was derived by comparing the spectroscopic-like temperature inferred from the joint X-ray/SZ reconstruction ( $T_{SZ,X}$ ) against the direct spectroscopic-like temperature ( $T_{sl}$ ) from the simulation. In the simulation context, where the true cosmology and physics are known, $B \equiv \eta_T = T_{sl} / T_{SZ,X}$ .
Dynamical and Morphological Classification: Clusters were classified into relaxed, hybrid, and disturbed categories based on dynamical indicators (sub-halo mass fraction and center-of-mass offset) and morphological indicators (concentration, centroid shift, power ratios).
Informative Prior Modelling: Two strategies were developed to model the distribution of $B$ $B$ as an informative prior for cosmological inference:
- 3DS Model: A trichotomous class-conditional model where $B$ follows a distinct log-normal distribution for each dynamical class (relaxed, hybrid, disturbed).
- Gaussian Process (GP) Models: Two regression approaches were implemented to model the continuous dependence of $B$ $B$ on the morphological indicator $M_X$ $M_{X}$ :
  - GPkernel: A pragmatic approach using a kernel structure to approximate heteroscedasticity (input-dependent variance).
  - GPhetero: A fully probabilistic heteroscedastic model using PyMC to jointly infer the mean and intrinsic scatter of $\ln B$ as a function of $M_X$ .
Cosmological Pipeline Validation: A Bayesian pipeline was constructed to infer $H_0$ , $\Omega_m$ , and helium abundance ( $Y$ ) from mock $\eta_T$ catalogues. The pipeline marginalizes over the nuisance parameters representing the cluster structure bias ( $B$ ) using the derived priors. The validation involved testing for unbiasedness, variance scaling with sample size, and posterior calibration using simulation-based calibration techniques.

Key Results

Distribution of $B$ : The distribution of $B$ is positively skewed and leptokurtic. While a single log-normal distribution fits the full sample, a class-conditional model (3DS) provides a significantly better fit (lower BIC). Relaxed systems cluster near $B \approx 1$ with low scatter, while disturbed systems exhibit higher values and larger dispersion.
Correlations: $B$ shows weak correlations with dynamical ( $\chi$ ) and morphological ( $M_X$ ) indicators but no significant correlation with cluster mass or temperature. The scatter in $B$ increases systematically from relaxed to disturbed systems.
Cosmological Inference:
- The Bayesian pipeline, when informed by the simulation-derived priors (either 3DS or GP models), yields unbiased estimates of $H_0$ in mock tests.
- The method is primarily sensitive to $H_0$ . Constraints on $\Omega_m$ and $Y$ remain prior-dominated due to degeneracies and the intrinsic sensitivity of the probe ( $\eta_T \propto D_A^{-1/2}$ ).
- Precision: For a sample of 100 clusters, the precision on $H_0$ is approximately 4%. For 1000 clusters, this improves to 1.5%.
- Systematic Floor: The uncertainty scaling follows $\sigma^2(N) = \sigma_0^2/N + \sigma_s^2$ . The statistical component ( $\sigma_0 \approx 26.6$ km s $^{-1}$ Mpc $^{-1}$ ) dominates for small samples, while a systematic floor of $\sigma_s \approx 0.6–0.8$ km s $^{-1}$ Mpc $^{-1}$ limits the precision for large samples ( $N \gtrsim 1200$ ).
- Calibration: Posterior calibration tests confirm that the inferred posteriors are well-calibrated, with coverage rates of $\sim70\%$ at 68% confidence and $\sim95\%$ at 95% confidence, consistent with uniform rank statistics.

Significance and Claims
The paper claims to validate a methodology for using joint X-ray and millimetre observations of galaxy clusters to constrain the Hubble constant ( $H_0$ ) with high precision. By leveraging hydrodynamical simulations (The300) to characterize the systematic bias $B$ arising from cluster morphology and dynamics, the authors demonstrate that these biases can be statistically modeled and incorporated as informative priors in a Bayesian framework.

The authors assert that this approach allows for the use of larger, less relaxed cluster samples (beyond the traditional "relaxed" subsamples) while maintaining unbiased cosmological constraints. The work highlights that the structural term driving discrepancies between X-ray and SZ thermodynamic reconstructions can be robustly characterized via simulations. Consequently, this method supports the future application of joint X-ray and SZ cluster datasets to place tight constraints on $H_0$ , with the ultimate precision limited not by statistical noise in large samples, but by residual systematic uncertainties of approximately 0.6–0.8 km s $^{-1}$ Mpc $^{-1}$ . The authors remain modest regarding the transferability to real data, noting that future work must address additional systematics related to observational data quality and the specific physics implementations of the hydrodynamical simulations.

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