ERGO-ML and how to directly infer the multi-temperature nature of intra-cluster gas: simulation-based inference with TNG-Cluster

Though galaxy clusters are virialized and mostly in thermodynamic equilibrium, their internal gas thermodynamics are complex. The hot gas is multiphase and spatially inhomogeneous. The new analysis still awaits peer review, but it already lays out the central claim clearly.

The significance lies in cosmology operates at the edge of what current instruments can measure, where systematic errors and model assumptions are never trivial. Small discrepancies between independent measurements have historically pointed toward missing physics rather than simple calibration errors, and the ongoing tension in the Hubble constant is a live example of how a persistent disagreement between methods can reshape the theoretical landscape. Each new dataset that approaches this territory with independent systematics adds real information to a problem that has resisted easy resolution for more than a decade. Though galaxy clusters are virialized and mostly in thermodynamic equilibrium, their internal gas thermodynamics are complex. The exact state of the gas contains important information about the internal physics governing clusters, however, measuring the multiphase distribution of the X-ray emitting gas.

In this work (part of the ERGO-ML series), we present a direct inference method of the multiphase temperature distribution of the gas in the intra-cluster medium (ICM), applicable. It works using different spectral resolutions (XRISM-like and Chandra-like) and realistic photon noise.

Our method is an application of simulation-based inference. We train a neural-network on X-ray spectra in the range 0.1-10 keV, generated for $\approx 10^5$ sightlines of massive clusters ($M_{\rm 200c} = 10^{14.2-15.

On top of that it gives accurate measures of the fraction of sub- and super-virial gas. Our method is capable of extracting the cooler gas phase even if the flux contribution is 3 orders of magnitude below that of the virial gas phase.

The relevance goes beyond one dataset because even small shifts in measured parameters can matter when the field is testing the limits of the standard cosmological model. The Lambda-CDM framework describes the observable universe with remarkable economy, but its success rests on two components, dark matter and dark energy, whose physical nature remains entirely unknown. Any credible measurement that tightens or loosens the constraints on those components moves the entire theoretical enterprise forward, regardless of whether the immediate result looks dramatic on its own terms.

We then show that we can accurately recover the spatial distribution of multi-phase gas both in relaxed and merging systems. This opens the way to studies of the multiphase nature of the ICM and the violent physics of feedback, accretion and merging.

Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether the effect survives when independent surveys, different calibration strategies and tighter control of systematic uncertainties enter the picture. Programmes such as Euclid, DESI and the Rubin Observatory will deliver datasets over the next several years that cover the same parameter space with largely independent methods. If the current signal persists through those tests, its theoretical implications will become impossible to set aside. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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