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Register a new userCharacterizing hydrostatic mass bias with Mock-X
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David J. Barnes
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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 $bapprox0.13$ 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.
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Clusters of galaxies are useful tools to constrain cosmological parameters, only if their masses can be correctly inferred from observations. In particular, X-ray and Sunyaev-Zeldovich (SZ) effect observations can be used to derive masses within the framework of the hydrostatic equilibrium. Therefore, it is crucial to have a good control of the possible mass biases that can be introduced when this hypothesis is not valid. In this work, we analyzed a set of 260 synthetic clusters from the MUSIC simulation project, at redshifts $0 leq z leq 0.82$. We estimate the hydrostatic mass of the MUSIC clusters from X-ray only (temperature and density) and from X-ray and SZ (density and pressure). Then, we compare them with the true 3D dynamical mass. The biases are of the order of 20%. We find that using the temperature instead of the pressure leads to a smaller bias, although the two values are compatible within 1$sigma$. Non-thermal contributions to the total pressure support, arising from bulk motion and turbulence of the gas, are also computed and show that they are sufficient to account for this bias. We also present a study of the correlation between the mass bias and the dynamical state of the clusters. A clear correlation is shown between the relaxation state of the clusters and the bias factor. We applied the same analysis on a subsample of 32 objects, already selected for supporting the NIKA2 SZ Large Program.
Accurate and precise measurements of masses of galaxy clusters are key to derive robust constraints on cosmological parameters. Rising evidence from observations, however, confirms that X-ray masses, obtained under the assumption of hydrostatic equilibrium, might be underestimated, as previously predicted by cosmological simulations. We analyse more than 300 simulated massive clusters, from `The Three Hundred Project, and investigate the connection between mass bias and several diagnostics extracted from synthetic X-ray images of these simulated clusters. We find that the azimuthal scatter measured in 12 sectors of the X-ray flux maps is a statistically significant indication of the presence of an intrinsic (i.e. 3D) clumpy gas distribution. We verify that a robust correction to the hydrostatic mass bias can be inferred when estimates of the gas inhomogeneity from X-ray maps (such as the azimuthal scatter or the gas ellipticity) are combined with the asymptotic external slope of the gas density or pressure profiles, which can be respectively derived from X-ray and millimetric (Sunyaev-Zeldovich effect) observations. We also obtain that mass measurements based on either gas density and temperature or gas density and pressure result in similar distributions of the mass bias. In both cases, we provide corrections that help reduce both the dispersion and skewness of the mass bias distribution. These are effective even when irregular clusters are included leading to interesting implications for the modelling and correction of hydrostatic mass bias in cosmological analyses of current and future X-ray and SZ cluster surveys.
We present the reconstruction of hydrostatic mass profiles in 13 X-ray luminous galaxy clusters that have been mapped in their X-ray and SZ signal out to $R_{200}$ for the XMM-Newton Cluster Outskirts Project (X-COP). Using profiles of the gas temperature, density and pressure that have been spatially resolved out to (median value) 0.9 $R_{500}$, 1.8 $R_{500}$, and 2.3 $R_{500}$, respectively, we are able to recover the hydrostatic gravitating mass profile with several methods and using different mass models. The hydrostatic masses are recovered with a relative (statistical) median error of 3% at $R_{500}$ and 6% at $R_{200}$. By using several different methods to solve the equation of the hydrostatic equilibrium, we evaluate some of the systematic uncertainties to be of the order of 5% at both $R_{500}$ and $R_{200}$. A Navarro-Frenk-White profile provides the best-fit in nine cases out of 13, with the remaining four cases that do not show a statistically significant tension with it. The distribution of the mass concentration follows the correlations with the total mass predicted from numerical simulations with a scatter of 0.18 dex, with an intrinsic scatter on the hydrostatic masses of 0.15 dex. We compare them with the estimates of the total gravitational mass obtained through X-ray scaling relations applied to $Y_X$, gas fraction and $Y_{SZ}$, and from weak lensing and galaxy dynamics techniques, and measure a substantial agreement with the results from scaling laws, from WL at both $R_{500}$ and $R_{200}$ (with differences below 15%), from cluster velocity dispersions, but a significant tension with the caustic masses that tend to underestimate the hydrostatic masses by 40% at $R_{200}$. We also compare these measurements with predictions from alternative models to the Cold Dark Matter, like the Emergent Gravity and MOND scenarios.
This article is the second in a series in which we perform an extensive comparison of various galaxy-based cluster mass estimation techniques that utilise the positions, velocities and colours of galaxies. Our aim is to quantify the scatter, systematic bias and completeness of cluster masses derived from a diverse set of 25 galaxy-based methods using two contrasting mock galaxy catalogues based on a sophisticated halo occupation model and a semi-analytic model. Analysing 968 clusters, we find a wide range in the RMS errors in log M200c delivered by the different methods (0.18 to 1.08 dex, i.e., a factor of ~1.5 to 12), with abundance matching and richness methods providing the best results, irrespective of the input model assumptions. In addition, certain methods produce a significant number of catastrophic cases where the mass is under- or over-estimated by a factor greater than 10. Given the steeply falling high-mass end of the cluster mass function, we recommend that richness or abundance matching-based methods are used in conjunction with these methods as a sanity check for studies selecting high mass clusters. We see a stronger correlation of the recovered to input number of galaxies for both catalogues in comparison with the group/cluster mass, however, this does not guarantee that the correct member galaxies are being selected. We do not observe significantly higher scatter for either mock galaxy catalogues. Our results have implications for cosmological analyses that utilise the masses, richnesses, or abundances of clusters, which have different uncertainties when different methods are used.
The mass of galaxy clusters can be inferred from the temperature of their X-ray emitting gas, $T_{mathrm{X}}$. Their masses may be underestimated if it is assumed that the gas is in hydrostatic equilibrium, by an amount $b^{mathrm{hyd}}sim(20pm10)$ % suggested by simulations. We have previously found consistency between a sample of observed textit{Chandra} X-ray masses and independent weak lensing measurements. Unfortunately, uncertainties in the instrumental calibration of {em Chandra} and {em XMM-Newton} observatories mean that they measure different temperatures for the same gas. In this paper, we translate that relative instrumental bias into mass bias, and infer that textit{XMM-Newton} masses of $sim 10^{14},mbox{M}_{odot}$ ($> 5cdot 10^{14} mbox{M}_{odot}$) clusters are unbiased ($sim 35$ % lower) compared to WL masses. For massive clusters, textit{Chandra}s calibration may thus be more accurate. The opposite appears to be true at the low mass end. We observe the mass bias to increase with cluster mass, but presence of Eddington bias precludes firm conclusions at this stage. Nevertheless, the systematic textit{Chandra} -- textit{XMM-Newton} difference is important because {em Planck}s detections of massive clusters via the Sunyaev-Zeldovich (SZ) effect are calibrated via {em XMM-Newton} observations. The number of detected SZ clusters are inconsistent with {em Planck}s cosmological measurements of the primary Cosmic Microwave Background (CMB). Given the textit{Planck} cluster masses, if an (unlikely) uncorrected $sim 20$ % calibration bias existed, this tension would be eased, but not resolved.
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