Characterizing hydrostatic mass bias with Mock-X

TL;DR

Mock-X establishes a framework to generate synthetic, multiwavelength cluster images from cosmological simulations and to analyze them with observational pipelines. Applying this to IllustrisTNG, BAHAMAS, and MACSIS, the study finds a mass-independent hydrostatic bias of $b\approx0.11$–$0.15$ when using simulation-derived profiles, and a mass-dependent bias up to $b\approx0.3$ when using X-ray spectroscopic temperatures, driven by multi-temperature gas and the density-squared weighting of X-ray emission. The results align with current observations and show projection has little impact on bias, while the scatter remains sizable and partially controlled by cluster sphericity and relaxation state. Overall, the work demonstrates that temperature structure is a key factor in bias, with implications for the interpretation of upcoming large cluster surveys and the calibration of observable-mass relations.

Abstract

Surveys in the next decade will deliver large samples of galaxy clusters that transform our understanding of their formation. Cluster astrophysics and cosmology studies will become systematics limited with samples of this magnitude. With known properties, hydrodynamical simulations of clusters provide a vital resource for investigating potential systematics. However, this is only realized if we compare simulations to observations in the correct way. Here we introduce the \textsc{Mock-X} analysis framework, a multiwavelength tool that generates synthetic images from cosmological simulations and derives halo properties via observational methods. We detail our methods for generating optical, Compton-$y$ and X-ray images. Outlining our synthetic X-ray image analysis method, we demonstrate the capabilities of the framework by exploring hydrostatic mass bias for the IllustrisTNG, BAHAMAS and MACSIS simulations. Using simulation derived profiles we find an approximately constant bias $b\approx0.13$ with cluster mass, independent of hydrodynamical method or subgrid physics. However, the hydrostatic bias derived from synthetic observations is mass-dependent, increasing to $b=0.3$ for the most massive clusters. This result is driven by a single temperature fit to a spectrum produced by gas with a wide temperature distribution in quasi-pressure equilibrium. The spectroscopic temperature and mass estimate are biased low by cooler gas dominating the emission, due to its quadratic density dependence. The bias and the scatter in estimated mass remain independent of the numerical method and subgrid physics. Our results are consistent with current observations and future surveys will contain sufficient samples of massive clusters to confirm the mass dependence of the hydrostatic bias.

Figures (9)

• Figure 1: Mock-X schematic from the IllustrisTNG $300^{3}\,\mathrm{Mpc}^{3}$ volume. Top left: Gas density slice of $1\,\mathrm{Mpc}$ width through the simulation volume centred on the most massive cluster at $z=0.1$. The red square denotes the $3\,r_{\mathrm{500,sim}}$ square field-of-view used for synthetic image generation. Top right: Synthetic optical image of the cluster showing the bolometric luminosity of the star particles. Middle right: Synthetic Compton-$y$ image for a NIKA2-like facility. Bottom row: Synthetic X-ray images for a Chandra-like telescope projected along the shortest axis ($C$, left), longest axis ($A$, middle) and the $x$ axis (right) of the simulation volume. The dashed blue line in the synthetic image panels denotes $r_{\mathrm{500,sim}}$.
• Figure 2: Synthetic X-ray images of a cluster in the TNG300 level 1 volume at $z=1$ for facilities like those currently available and planned. We demonstrate the expected images from Chandra (top left), XXM (top middle), eRosita (top right), Athena (bottom left), AXIS (bottom middle) and Lynx (bottom right) like instruments. The blue circle denotes $r_{\mathrm{500,sim}}$. We note the chosen cluster is below the expected detection threshold of eRosita at this redshift, with $7$ total photons predicted within $r_{\mathrm{500,sim}}$ for an exposure of $100\,\mathrm{ksec}$. The power of future facilities is demonstrated by the significant increase in photons collected at larger radii.
• Figure 3: The median hydrostatic mass estimate to true mass $(M_{\mathrm{500,sim}})$ ratio as a function of true mass at $z=0.1$ for estimates derived from simulation (left) and synthetic X-ray image (right) profiles. We plot simulated samples from BAHAMAS (dark blue), MACSIS (light blue), TNG300 level 1 (dark green), level 2 (medium green), and level 3 (light green). The shaded area denotes the $1\sigma$ scatter and the dashed lines denote the median ratio where the number of clusters in a bin of width $\Delta\log_{10}(M_{\mathrm{500,sim}}\,/\,\mathrm{M}_{\astrosun})=0.1$ is less than 10. The hydrostatic bias is relatively independent of true mass for profiles derived directly from the simulation but is clearly mass-dependent for synthetic X-ray profiles.
• Figure 4: The median hydrostatic mass derived from X-ray images to true mass ratio as a function of true mass at $z=0.1$ against a collection of observed biases. The simulation lines styles are the same as Fig. \ref{['fig:Mbias']}. The collection of observational points compare hydrostatic mass estimates to weak lensing derived mass estimates and are taken from Weighing the Giants (WtG) vonderLinden2014, CCCP Hoekstra2015, CS82-ACT Battaglia2016, LoCuSS Smith2016, CLASH PennaLima2017, PSZ2LenS Sereno2017, HSC-Planck Medezinski2018 and HSC-ACT Miyatake2019. We find excellent agreement in the magnitude of hydrostatic bias between the simulated and observed samples. Additionally, the sample variance of the observations is well matched to the scatter of the simulated sample.
• Figure 5: The median X-ray derived hydrostatic mass to true mass ratio as a function of true mass at $z=0.1$, split by simulation and projection axis. For TNG300 levels 3 (top left), 2 (top middle), 1 (top right), BAHAMAS (bottom left) and MACSIS (bottom middle) we plot the median ratio along axes $x$ (grey), $y$ (green), $z$ (blue), $A$ (orange), $B$ (red) and $C$ (purple). The dashed lines denote the median ratio where the number of clusters in a bin of width $\Delta\log_{10}(M_{\mathrm{500,sim}}\,/\,\mathrm{M}_{\astrosun})=0.1$ is less than 10 and the shaded regions denote the $1\sigma$ scatter in the ratio. In the bottom right panel, we compare projections along the longest $(A)$ and shortest $(C)$ axes of the cluster and find minor differences in the median ratio that are significantly smaller than the scatter in any given sample.