In hierarchical clustering, galaxy clusters accrete mass through the aggregation of smaller systems. Thus, the velocity field of the infall regions of clusters contains significant random motion superimposed on radial infall. Because the purely spherical infall model does not predict the amplitude of the velocity field correctly, methods estimating the cosmological density parameter Omega_0 based on this model yield unreliable biased results. In fact, the amplitude of the velocity field depends on local dynamics and only very weakly on the global properties of the universe. We use N-body simulations of flat and open universes to show that the amplitude of the velocity field of the infall regions of dark matter halos is a direct measure of the escape velocity within these regions. We can use this amplitude to estimate the mass of dark matter halos within a few megaparsecs from the halo center. In this region dynamical equilibrium assumptions do not hold. The method yields a mass estimate with better than 30% accuracy. If galaxies trace the velocity field of the infall regions of clusters reliably, this method provides a straightforward way to estimate the amount of mass surrounding rich galaxy clusters from redshift data alone.

Infall Regions of Galaxy Clusters

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.

Exploring the hydrostatic mass bias in MUSIC clusters: application to the NIKA2 mock sample

We study the connection between morphology and dynamical state of simulated clusters in $z\in[0,1.031]$ from THE THREE HUNDRED Project cluster sample. We evaluate the dynamical state using a combination of dynamical parameters -- $\chi$ from theoretical measures and compare the results with other two relaxation criteria that come from observation measures: the morphology in mock X-ray and Sunyaev-Zeldovich (SZ) effect images of galaxy clusters -- the $M$ indicator which is a combination of seven morphological parameters, and the offsets $\Delta$ between the peaks or centroids of X-ray and SZ maps and the Brightest Central Galaxy (BCG) position estimated from optical maps. We study the efficiency of morphological indicators and the correlations with the dynamical state of the combined $M$ and dynamical $\chi$ parameters, that have the advantage of proving and collecting different aspects of the cluster structures than single parameters. An evolution with the redshift of the dynamical state is present, but the populations of the dynamical state classes differ when different radii are used. The main source of contamination in relaxed fraction inferred from morphological parameters is constituted by hybrid clusters. $M$ combined parameter describes with the same efficiency the morphology in X-ray and SZ maps, with a correlation coefficient of $\rho=0.81$. A moderately strong correlation between $M$ and $\chi$ is present, with a coefficient of $\rho=-0.66$. The offset parameters based on centroids are more sensitive to dynamical state than peaks positions offsets. The correlation with $\chi$ for centroids is of the same order of $M$, with $\rho=-(0.63$-$0.67)$ if SZ or X-ray centroids are respectively used.

The Three Hundred project: dynamical state of galaxy clusters and morphology from multiwavelength synthetic maps

Galaxy groups are more than an intermediate scale between clusters and halos hosting individual galaxies, they are crucial laboratories capable of testing a range of astrophysics from how galaxies form and evolve to large scale structure (LSS) statistics for cosmology. Cosmological hydrodynamic simulations of groups on various scales offer an unparalleled testing ground for astrophysical theories. Widely used cosmological simulations with ~(100 Mpc)^3 volumes contain statistical samples of groups that provide important tests of galaxy evolution influenced by environmental processes. Larger volumes capable of reproducing LSS while following the redistribution of baryons by cooling and feedback are essential tools necessary to constrain cosmological parameters. Higher resolution simulations can currently model satellite interactions, the processing of cool (T~10^4 K) multi-phase gas, and non-thermal physics including turbulence, magnetic fields, and cosmic ray transport. We review simulation results regarding the gas and stellar contents of groups, cooling flows and the relation to the central galaxy, the formation and processing of multi-phase gas, satellite interactions with the intragroup medium, and the impact of groups for cosmological parameter estimation. Cosmological simulations provide evolutionarily consistent predictions of these observationally difficult-to-define objects, and have untapped potential to accurately model their gaseous, stellar, and dark matter distributions.

Simulating Groups and the IntraGroup Medium: The Surprisingly Complex and Rich Middle Ground Between Clusters and Galaxies.

The knowledge of the dynamical state of galaxy clusters allows to alleviate systematics when observational data from these objects are applied in cosmological studies. Evidence of correlation between the state and the morphology of the clusters is well studied. The morphology can be inferred by images of the surface brightness in the X-ray band and of the thermal component of the Sunyaev-Zel'dovich (tSZ) effect in the millimetre range. For this purpose, we apply, for the first time, the Zernike polynomial decomposition, a common analytic approach mostly used in adaptive optics to recover aberrated radiation wavefronts at the telescopes pupil plane. With this novel way we expect to correctly infer the morphology of clusters and so possibly, their dynamical state. To verify the reliability of this new approach we use more than 300 synthetic clusters selected in THE THREE HUNDRED project at different redshifts ranging from 0 up to 1.03. Mock maps of the tSZ, quantified with the Compton parameter, $y$-maps, are modelled with Zernike polynomials inside $R_{500}$, the cluster reference radius. We verify that it is possible to discriminate the morphology of each cluster by estimating the contribution of the different polynomials to the fit of the map. The results of this new method are correlated with those of a previous analysis made on the same catalogue, using two parameters that combine either morphological or dynamical-state probes. We underline that instrumental angular resolution of the maps has an impact mainly when we extend this approach to high-redshift clusters.

The Three Hundred Project: quest of clusters of galaxies morphology and dynamical state through Zernike polynomials

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.

Characterizing hydrostatic mass bias with MOCK-X

Characterizing hydrostatic mass bias with Mock-X

Dynamically relaxed galaxy clusters have long played a role in galaxy cluster studies because it is thought their properties can be reconstructed more precisely and with less systematics. As relaxed clusters are desirable, there exist a plethora of criteria for classifying a galaxy cluster as relaxed. In this work, we examine $9$ commonly used observational and theoretical morphological metrics extracted from $54,000$ Mock-X synthetic X-ray images of galaxy clusters taken from the IllustrisTNG, BAHAMAS and MACSIS simulation suites. We find that the simulated criteria distributions are in reasonable agreement with the observed distributions. Many criteria distributions evolve as a function of redshift, cluster mass, numerical resolution and subgrid physics, limiting the effectiveness of a single relaxation threshold value. All criteria are positively correlated with each other, however, the strength of the correlation is sensitive to redshift, mass and numerical choices. Driven by the intrinsic scatter inherent to all morphological metrics and the arbitrary nature of relaxation threshold values, we find the consistency of relaxed subsets defined by the different metrics to be relatively poor. Therefore, the use of relaxed cluster subsets introduces significant selection effects that are non-trivial to resolve.

Kaili Cao

Papers

Characterizing hydrostatic mass bias with MOCK-X

Characterizing hydrostatic mass bias with Mock-X

Studying galaxy cluster morphological metrics with mock-X

Studying galaxy cluster morphological metrics with Mock-X