The SRG/eROSITA all-sky survey: The morphologies of clusters of galaxies: II. The intrinsic distributions of morphological parameters

TL;DR

This study infers the intrinsic distributions and evolution of key cluster morphology parameters from the eRASS1 all-sky survey by jointly modelling morphology with a detailed selection function in a Bayesian framework. The authors implement a forward-modeling approach with scaling relations tying morphological parameters to X-ray luminosity and redshift, allowing the scatter to evolve and comparing peak- versus fit-centred measures. They find that concentration and scaled central density increase with luminosity and decrease with redshift, while fixed-aperture concentrations show milder trends, and ellipticity/slosh show little or no evolution; several inner-density and cuspiness parameters require non-Gaussian, interpolated, or skewed distributions. Comparisons with SZ-selected samples suggest eRASS1 clusters are more centrally peaked, though interpretation is complicated by potential selection biases and measurement differences. Overall, the work demonstrates a robust path to unveiling the true morphology distribution of clusters and sets the stage for exploiting larger eROSITA samples in the near future.

Abstract

X-ray selected surveys of clusters of galaxies have been reported to contain more regular cool core clusters compared to samples selected using the Sunyaev-Zel'dovich (SZ) effect. Morphology population studies on X-ray selected clusters will be biased without taking into account selection, as cool cores are more easily detected at low redshifts, but can be mistaken for point sources at high redshift. eROSITA, aboard SRG, found over 12000 optically-identified clusters in its first survey, eRASS1. Taking account of the selection function obtained from simulations, we obtain using a Bayesian framework the intrinsic distribution of morphological parameters, including the concentration, central density, cuspiness, ellipticity and slosh. We construct scaling relations for the parameters as a function of redshift (z) and luminosity (LX), and study their distribution within z or LX bins. We find that the concentration in a scaled aperture evolves positively with LX, similarly to the central scaled density, and negatively with z. When using a fixed aperture, its evolution with LX is lower, but also dependent on the choice of cluster centre. The mean ellipticity does not significantly evolve with z or LX. eRASS1 clusters show indications of higher concentrations compared to SZ-selected objects, even after taking account the selection; this suggests that if our X-ray selection model is correct SZ-selected clusters may also suffer from morphological selection effects. We compare different parameter distribution models in bins of z and LX. The distribution of concentration and ellipticity is generally consistent with a normal one, but other parameters such as the central density and cuspiness strongly favour more complex distributions. However, modelling of all clusters as a single population generally prefers non-normal distributions. [abridged]

Figures (10)

• Figure 1: Clusters with $>50$ counts plotted on PDFs combining the maximum likelihood scaling relation, selection function and mass function. Shown are the clusters in four redshift bins, plotting the concentration, $c_{500}$ (left), and scaled density, $n_{\mathrm{s},0}$ (right). The images show the average maximum likelihood scaling relation combined with the selection function and mass function for the clusters in the redshift ranges, with the solid contour lines at difference levels of $-2$, $-4$, $-6$, $-8$ and $-10$ from the maximum. The dashed contour lines show the average selection function, at levels of 0.05, 0.2, 0.4, 0.6, 0.8 and 0.95.
• Figure 2: Evolution of mean and width for several parameters. (Left) The confidence contours for the evolution of $\mu$, with the results using the cluster fit positions as solid lines and the peak-centred cluster results as dashed lines. (Right) The confidence contours of the evolution of $\sigma$. The contours contain 39.3, 67.5, 86.4 and 95% of the MCMC samples. See Appendix \ref{['appen:scaling']} for corner plots of the other parameters.
• Figure 3: Comparison of model distributions in bins of redshift and luminosity. Shown is the difference in Bayesian evidence (the Bayes factor) between each model and the model with the largest Bayesian evidence, where the models with the largest evidence are plotted at lower values and the best model has a value of $1$. Shown are typical thresholds for Bayes factors from KassRaftery95.
• Figure 4: Comparison of different distribution models for the whole sample. (Left panel) Model comparison, as in Fig. \ref{['fig:evidence']}, for each parameter, assuming that the clusters have a single distribution. Models with larger evidence have lower values. (Right panels) The PDFs of each parameter, for each of the model types, coloured as in the left panel. The shaded regions contain 68.27% of samples.
• Figure 5: Comparison of eRASS1 probability densities compared to SPT and Planck selected samples. The distribution of the parameters for the Chandra-SPT sample is plotted as a histogram, with the median value indicated by a dashed line. The Planck values are for ESZ clusters from Lovisari17. The model distribution for the eRASS1 clusters in the high luminosity bin is plotted ($\log L_X=44.3-45.6$, fitted using interpolated model). For those parameters where we fitted a scaling relation (Appendix \ref{['appen:scaling']}), we computed matched PDFs given the redshift and luminosities of the SPT and Planck samples. Also plotted are the distributions of parameter values for the bright 300 count cluster eRASS1 subset.