The temperature and metallicity distributions of the ICM: insights with TNG-Cluster for XRISM-like observations

TL;DR

By combining TNG-Cluster cosmological zoom-in simulations with end-to-end XRISM/Resolve-like mocks, this work quantifies how well common spectral-emission models recover the ICM's central temperature distribution and Fe abundance. It shows that intrinsic central temperatures and metallicities are broad and multi-faceted, and that neither Normal nor Log-Normal forms fully capture the temperature distributions predicted by TNG-Cluster; emission-weighted temperatures are reliably recovered, while mass-weighted central temperatures are biased low by about $1.19$ keV on average, with a notable halo-mass dependence. All models systematically underestimate the central Fe abundance by about 0.12 Solar (22%), and projection effects along the line of sight further bias metallicity estimates for the full column, highlighting the crucial role of deprojection in interpreting high-resolution spectra. The results argue for using temperature-distribution spectral models and for deprojecting observations to obtain robust ICM properties, offering practical guidance for XRISM analyses and future high-resolution X-ray missions.

Abstract

The new era of high-resolution X-ray spectroscopy will significantly improve our understanding of the intra-cluster medium (ICM) by providing precise constraints on its underlying physical properties. However, spectral fitting requires reasonable assumptions on the thermal and chemical distributions of the gas. We use the output of TNG-Cluster, the newest addition to the IllustrisTNG suite of cosmological magnetohydrodynamical simulations, to provide theoretical expectations for the multi-phase nature of the ICM across hundreds of z=$ clusters (M$_{500c} = 10^{14.0-15.3}~M_\odot$) based upon a realistic model for galaxy formation and evolution. We create and analyse, in an observer-like manner, end-to-end XRISM/Resolve mock observations towards cluster centres. We then systematically compare the intrinsic temperature and Fe abundance of the simulated gas with the inferred ones from spectral fitting via a variety of commonly used spectral-emission models. Our analysis suggests that models with a distribution of temperatures, better describe the broad thermal distributions of the ICM, as predicted by TNG-Cluster, but still incur biases in the inferred temperature of 0.5-2 keV (16th-84th percentiles). However, all spectral-emission models systematically underestimate the Fe abundance of the central ICM by 0.12 Solar (22 per cent), almost an order of magnitude higher than the abundance errors reported in the literature, primarily due to projection effects. Selecting only strong cool core clusters leads to minor improvements on inference quality, removing the majority of outliers but maintaining similar overall biases and cluster-to-cluster scatter.

Figures (16)

• Figure 1: Illustration of the end-to-end XRISM/Resolve mocking procedure of simulated clusters from the TNG-Cluster suite. On the top left, we present the intrinsic X-ray luminosity of a randomly-selected cluster from TNG-Cluster, highlighting the FoV of XRISM/Resolve, pointing at the centre of the cluster. Following the process described in Section \ref{['sec:mock_proc']}, we generate a mock event file as if it was observed by XRISM/Resolve, presented in the top right corner. The mock spectrum extracted from the event file and a zoom-in on the Fe-K lines are presented in the bottom row. This process showcases our ability in generating high-quality mock spectra from our cosmologically-simulated clusters as if they were observed by XRISM/Resolve.
• Figure 2: Distributions of the gas temperature (top) and Fe abundance (bottom) for the central ICM of TNG-Cluster halos at z=0. For both cases, each thin solid curve represents the mass-weighted Kernel Density Estimation (KDE) of all the gas cells inside the central 33.5 kpc (1.5' at the redshift of Perseus, to approximate XRISM FoV) of a given simulated cluster, colour coded based on the M$_{\rm{500c}}$ halo mass. The thicker dashed curves indicate the running averages per halo mass bin, as indicated. TNG-Cluster (based on the IllustrisTNG model) predicts extended i.e. broad thermal and Fe abundance distributions for the ICM at the centre of clusters, with a singular peak, but with large variations from cluster to cluster, even for clusters with similar halo masses.
• Figure 3: What is the best functional form to describe the temperature distribution of the central ICM of TNG-Cluster? The dashed curves represent the geometric mean of the mass-weighted gas in the 3D clusters' centres (top, as in \ref{['fig:gas_prop']}) and of the emission-weighted gas for a central pointing with a XRISM-like FoV (bottom), binned with respect to M$_{500\mathrm{c}}$ halo mass. More specifically, we plot the Probability Mass Functions (PMFs) normalized by the mass (top) and the Emission Measure (bottom; see Eq. \ref{['eq:EM']}) of the gas in each bin. The solid curves represent the results of fitting the temperature distribution of each individual cluster with a Normal (left) and Log-Normal (right) functional form, then deriving the geometric mean across all cluster fits in each halo mass bin. We quote the median $\chi^2$ of the fits for our entire cluster sample, as well as its 16$^{\rm th}$ and 84$^{\rm th}$ percentile ranges. Residuals between the simulated and fitted temperature distributions of each studied cluster are provided in \ref{['fig:residuals']}. Our analysis indicates that both functional forms may introduce systematic biases for the the description of the temperature distributions predicted by TNG-Cluster. Namely, the Normal distribution tends to overestimate the amount of cooler gas present in the ICM, while the Log-Normal distribution remains insensitive to the lower-temperature tails. The reported $\chi^2$ values would suggest that either model lacks the ability to fully capture the complexity of the simulations thermal distributions but both do a good job at describing the bulk of the ICM mass around the virial temperature peaks.
• Figure 4: Best-fit parameters of the Log-Normal distribution adopted to describe the ICM temperature of clusters' centres from TNG-Cluster. We present the central temperature and standard deviation of the best-fit Log-Normal distributions for every TNG-Cluster halo at $z=0$, colour coded by its M$_{\rm{500c}}$ halo mass. The average distributions for each mass bin are shown in \ref{['fig:gas_prop']} and \ref{['fig:gas_prop_fit']}. While there is an obvious correlation between the best-fit central temperature and the halo mass, no such strong correlation exists for the standard deviation: how broad the temperature distribution is does not depend on total mass and can vary by an order of magnitude depending on the individual systems.
• Figure 5: Observational inferences of the ICM temperature at the centre of clusters. In the left panels, we compare the temperature inferred by analysing the X-ray spectra from XRISM/Resolve-like observations by adopting a variety of spectral-emission models (different colours) to the true mean temperature of the input temperature distribution, i.e. of systems simulated in TNG-Cluster. In particular, as ground truth, we first consider the mass-weighted gas in the 3D clusters’ centres (top) and then the emission-weighted gas for a central pointing with a XRISM-like FoV (bottom). One marker represents one simulated cluster, in a random projection. Filled and empty symbols represent accepted and rejected best fits, respectively (as defined in Section \ref{['sec:accept']}). In the right panels, we indicate the inference offset (or inference error) as a function of each cluster's M$_\text{500c}$ halo mass. Solid lines and shaded regions represent the running average and 1$\sigma$ standard deviation of the difference in bins of log$_{10}$(M$_{500\text{c}}$/M$_\odot$)=0.25, accounting only for the accepted fits. In all panels, the black dashed line represents unity, i.e. perfect accuracy of the model inference. Our results indicate that all models, are capable of correctly inferring the emission-weighted mean temperature of the gas in the targeted FoV, i.e. accounting for all gas on the line of sight. However, no model returns a best-fit ICM temperature value that is representative of the mass-weighted temperature of the central ICM gas to better than $1-2$ keV on average.