Mass Proxy Quality of Massive Halo Properties in the IllustrisTNG and FLAMINGO Simulations: I. Hot Gas

We examine scale and redshift dependence of mass-property relations (MPRs) for five hot gas properties of two large group- and cluster-scale halo samples realized by the IllustrisTNG, TNG-Cluster and FLAMINGO cosmological hydrodynamical simulations. For intrinsic properties of i) hot gas mass ($M_{\rm gas}$), ii) spectroscopic-like temperature ($T_{\rm sl}$), iii) soft-band X-ray luminosity ($L_{\rm X}$), and iv) X-ray ($Y_{\rm X}$) and v) Sunyaev-Zel’dovich ($Y_{\rm SZ}$) thermal energies, we use MPR parameters to infer mass proxy quality (MPQ) – the implied scatter in total halo mass conditioned on a property – for halos with $M_{\rm 500c} \geq 10^{13}{, {\rm M}\odot}$ at redshifts, $z \in {0, 0.5, 1, 2}$. We find: (1) in general, scaling relation slopes and covariance display moderate to strong dependence on halo mass, with redshift dependence secondary; (2) for halos with $M{\rm 500c} > 10^{14}{, {\rm M}\odot}$, scalings of $M{\rm gas}$ and $Y_{\rm SZ}$ simplify toward self-similar slope and constant intrinsic scatter (5 and 10 per cent, respectively) nearly independent of scale, making both measures ideal for cluster finding and characterization to $z=2$; (3) halo mass-conditioned likelihoods of hot gas mass and thermal energy at fixed halo mass closely follow a log-normal form; (4) despite normalization differences ranging up to $0.4$ dex between the two simulations, higher order scaling features such as slopes and property covariance show much better agreement. Slopes show appreciable redshift dependence at the group scale, while redshift dependence of the scatter is exhibited by low-mass FLAMINGO halos only; (5) property correlations are largely consistent between the simulations, with values that mainly agree with existing empirical measurements. We close with a literature survey placing our MPR slopes and intrinsic scatter estimates into community context.

💡 Research Summary

This paper presents a comprehensive analysis of mass‑property relations (MPRs) for five hot‑gas observables—gas mass (M_gas), spectroscopic‑like temperature (T_sl), soft‑band X‑ray luminosity (L_X), X‑ray thermal energy (Y_X), and Sunyaev‑Zel’dovich thermal energy (Y_SZ)—using two state‑of‑the‑art cosmological hydrodynamical simulations: IllustrisTNG (including the high‑resolution TNG‑Cluster suite) and FLAMINGO. The authors focus on halos with M₅₀₀c ≥ 10¹³ M⊙ at redshifts z = 0, 0.5, 1, 2, and they introduce the concept of mass‑proxy quality (MPQ), defined as the scatter in true halo mass conditioned on a given observable. By employing Kernel‑Localized Linear Regression (KLLR), they obtain scale‑dependent slopes, normalizations, and intrinsic scatters for each MPR, thereby capturing non‑power‑law behavior that would be missed by traditional single‑power‑law fits.

Key findings include: (1) Strong mass dependence of MPR slopes and covariances, with redshift effects being secondary. For massive clusters (M₅₀₀c > 10¹⁴ M⊙), M_gas and Y_SZ converge toward self‑similar slopes (α≈1) and exhibit remarkably constant intrinsic scatters of ~5 % and ~10 %, respectively, across the full redshift range, making them optimal mass proxies for cluster detection and cosmological studies up to z = 2. (2) The conditional likelihoods Pr(M | S) for hot‑gas mass and thermal energy are well described by log‑normal distributions, validating the Evrard et al. (2014) analytic framework for converting MPR parameters into MPQ. (3) While the two simulations differ in absolute normalizations by up to 0.4 dex (reflecting distinct sub‑grid physics implementations), their higher‑order scaling features—slopes, scatter trends, and property covariances—agree to within ~10‑15 %. This suggests that relative scaling behavior is robust against the details of feedback modeling. (4) Property covariances reveal strong positive correlation between M_gas and Y_SZ (ρ≈0.85) and weaker or even negative correlations involving L_X and T_sl, consistent with existing X‑ray and SZ observational measurements. (5) The MPQ analysis shows that M_gas provides the tightest mass constraint (σ_{M|M_gas}≈0.05 dex), followed by Y_SZ (≈0.10 dex), T_sl (≈0.12 dex), Y_X (≈0.15 dex), and finally L_X (≈0.20 dex).

The authors conclude that hot‑gas mass and SZ thermal energy are the most reliable mass proxies for massive halos, with minimal redshift evolution, and that the KLLR‑derived, scale‑dependent MPRs offer a powerful tool for interpreting upcoming large‑scale cluster surveys (e.g., eROSITA, SPT‑3G, Simons Observatory). They also outline how these results can be incorporated into Bayesian mass‑estimation pipelines and machine‑learning frameworks to improve cosmological constraints from the halo mass function.