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

TL;DR

This work introduces mass-proxy quality (MPQ) to quantify how well halo mass can be inferred from five hot-gas properties in two large-volume hydrodynamical simulations (IllustrisTNG and FLAMINGO), across $z=0$, 0.5, 1, and 2 for halos with $M_{500c}\ge10^{13}\,M_\odot$. Using Kernel Localized Linear Regression (KLLR), the authors extract scale- and redshift-dependent mass-property relations (MPRs), their slopes and intrinsic scatters, and compute MPQ as the ratio of the property scatter to the MPR slope, with log-normal likelihoods validated for several properties. They find that $Y_{\rm SZ}$ and $M_{gas}$ are the best mass proxies at high masses, with $Y_{\rm SZ}$ nearly self-similar and $M_{gas}$ showing improved proxy quality toward $z\le2$, while $L_{\rm X}$ and $T_{\rm sl}$ are typically weaker proxies, particularly at low masses. Across simulations, there is substantial agreement on the general trends, though normalizations differ; combining all five properties yields the strongest MPQ, reducing halo-mass scatter to a few percent for high-mass clusters. The results underpin SZ-based cluster cosmology and highlight the value of multi-property analyses in improving mass inference, while also emphasizing the need for cross-simulation validation and observational calibration.

Abstract

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.

Figures (20)

• Figure 1: The mass proxy quality, quantified by the implied halo mass scatter, equation \ref{['eq:mass-proxy-quality']}, for gas properties within a 3-D aperture of $R_{\rm 500c}$ listed in the legend derived from TNG (solid lines) and flamingo (dashed) halo populations. Shaded regions are $1\sigma$ uncertainties based on $1000$ bootstrap samples. We indicate the low redshift mass regimes of groups and clusters as roughly divided by a halo mass of $10^{14}\, {\rm M}_\odot$. All MPQs show moderate to strong mass dependence. The relative ordering of mass proxy quality is fairly consistent between the two simulation methods, with thermal energy ($Y_{\rm SZ}$, violet) being the best mass proxy below $10^{14.5} \, {\rm M}_\odot$ and hot gas mass ($M_{\rm gas}$, black) best above this scale, reaching a minimum of $4\%$ halo mass scatter at $10^{15} \, {\rm M}_\odot$. See text for further discussion.
• Figure 2: Halo mass and redshift dependence of the MPQs using the same format as in Figure \ref{['fig:MPQzero']} for redshifts $z = 0.5$ (top), $1$ (middle), and $2$ (bottom). At each redshift, lines extend up to the mass of the $21^{\rm st}$ ranked halo in each simulation sample.
• Figure 3: Comparison of $z=0$ scatter in true halo mass inferred by the MPQ, equation \ref{['eq:mass-proxy-quality']} (solid lines), with values directly measured by KLLR applied to the conditional likelihood, $P(M | S)$, of each hot gas property, $S$ (dot-dashed). The lower panels show good agreement for properties that adhere well to log-normality while the agreement degrades in the upper panels for properties with more complex likelihood shapes (see §\ref{['sec:kernel-shapes']}).
• Figure 4: Halo mass and redshift dependence of the MPR slopes for (top to bottom) $M_{\rm gas}$, $T_{\rm sl}$, $L_{\rm X}$, $Y_{\rm X}$, $Y_{\rm SZ}$. The KLLR-derived values (Equation \ref{['eq:KLLR-scaling']}) are shown at redshifts $z = 0$ (black), $0.5$ (blue), $1.0$ (gold), and $2$ (green) for TNG (left) and flamingo (right) halo populations. Dotted lines indicate the self-similar slopes given in §\ref{['sec:self-similar-theory']}. Note that, by definition, the slope in $Y_{\rm X}$ is the sum of the slopes in $M_{\rm gas}$ and $T_{\rm sl}$.
• Figure 5: Halo mass and redshift dependence of the MPR intrinsic scatter values (Equation \ref{['eq:KLLR-scatter']}). Format is identical to that of Figure \ref{['fig:MPR-slope-plots']}.