# Towards a characterization of X-ray galaxy clusters for cosmology

## TL;DR

This paper investigates galaxy cluster X-ray surface brightness profiles, comparing traditional models with a novel wavelet-based approach, to improve understanding of cluster morphologies and selection effects for cosmological studies.

## Contribution

It introduces a wavelet decomposition method for modeling cluster SB profiles, highlighting biases in traditional $eta$-models and analyzing correlations with cluster properties.

## Key findings

- Single $eta$-models cause a ~3% bias in outer SB measurements.
- Fixing $eta$ to 2/3 increases residuals to over 40%.
- No systematic core-type differences in outskirts profiles.

## Abstract

In the framework of the hierarchical model the intra-cluster medium properties of galaxy clusters are tightly linked to structure formation, which makes X-ray surveys well suited for cosmological studies. To constrain cosmological parameters accurately by use of galaxy clusters in X-ray surveys, a better understanding of selection effects related to the detection method is needed. We aim at a better understanding of galaxy cluster morphologies to include corrections between the different core types and covariances with X-ray luminosities in selection functions. We stress the morphological deviations between a newly described surface brightness (SB) profile characterization and a commonly used single $\beta$-model. We investigate a novel approach to describe SB profiles, where the excess cool-core emission in the galaxy cluster centres is modelled using wavelet decomposition. Morphological parameters and the residuals are compared to classical single $\beta$-models. Using single $\beta$-models to describe the ensemble of overall SB profiles leads on average to a non-zero bias ($0.032 \pm 0.003$) in the outer part of the clusters, i.e. a $\sim 3\%$ systematic difference in the SB at large radii. In addition $\beta$-models show a general trend towards underestimating the flux in the outskirts for smaller core radii. Fixing the $\beta$ parameter to $2/3$ doubles the bias and increases the residuals from a single $\beta$-model up to more than $40\%$. Modelling the core region in the fitting procedure reduces the impact of these two effects significantly. We find a positive scaling between shape parameters and temperature, as well as a negative correlation ($\sim-0.4$) between extent and luminosity. Our non-parametric analysis of the self-similar scaled emission measure profiles indicates no systematic core-type differences of median profiles in the galaxy clusters outskirts.