# The XXL Survey: XXXVIII. Scatters and correlations of X-ray proxies in the bright XXL cluster sample

## TL;DR

This study measures the intrinsic scatter and correlations among X-ray properties of galaxy clusters, revealing that gas mass is the least scattered proxy and that properties are positively correlated, consistent with self-similar evolution.

## Contribution

It introduces a self-consistent method to measure the scatter covariance matrix of X-ray cluster properties without external calibration or mass knowledge.

## Key findings

- Gas mass has the lowest intrinsic scatter (~8%).
- Temperature is less scattered (~20%) but has larger measurement uncertainties.
- X-ray properties are positively correlated, influenced by dynamical state and merger history.

## Abstract

Context. Scaling relations between cluster properties embody the formation and evolution of cosmic structure. Intrinsic scatters and correlations between X-ray properties are determined from merger history, baryonic processes, and dynamical state. Aims. We look for an unbiased measurement of the scatter covariance matrix between the three main X-ray observable quantities attainable in large X-ray surveys -- temperature, luminosity, and gas mass. This also gives us the cluster property with the lowest conditional intrinsic scatter at fixed mass. Methods. Intrinsic scatters and correlations can be measured under the assumption that the observable properties of the intra-cluster medium hosted in clusters are log-normally distributed around power-law scaling relations. The proposed method is self-consistent, based on minimal assumptions, and requires neither the external calibration by weak lensing, dynamical, or hydrostatic masses nor the knowledge of the mass completeness. Results. We analyzed the 100 brightest clusters detected in the XXL Survey and their X-ray properties measured within a fixed radius of 300 kpc. The gas mass is the less scattered proxy (~8%). The temperature (~20%) is intrinsically less scattered than the luminosity (~30%) but it is measured with a larger observational uncertainty. We found some evidence that gas mass, temperature and luminosity are positively correlated. Time-evolutions are in agreement with the self-similar scenario, but the luminosity-temperature and the gas mass-temperature relations are steeper. Conclusions. Positive correlations between X-ray properties can be determined by the dynamical state and the merger history of the halos. The slopes of the scaling relations are affected by radiative processes.