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We present a detailed study of cool-core systems in a sample of four galaxyclusters (RXCJ1504.1-0248, A3112, A4059, and A478) using archival X-ray datafrom the Chandra X-ray Observatory. Cool cores are frequently observed at thecenters of galaxy clusters and are considered to be formed by radiative coolingof the intracluster medium (ICM). Cool cores are characterized by a significantdrop in the ICM temperature toward the cluster center. We extract and analyzeX-ray spectra of the ICM to measure the radial profiles of the ICMthermodynamic properties including temperature, density, pressure, entropy, andradiative cooling time. We define the cool-core radius as the turnover radiusin the ICM temperature profile and investigate the relation between thecool-core radius and the properties of the host galaxy clusters. In our sample,we observe that the radiative cooling time of the ICM at the cool-core radiusexceeds 10\,Gyr, with RXCJ1504.1-0248 exhibiting a radiative cooling time of$32^{+5}_{-11}$\,Gyr at its cool-core radius. These results indicate that notonly radiative cooling but also additional mechanisms such as gas sloshing mayplay an important role in determining the size of cool cores. Additionally, wefind that the best-fit relation between the cool-core radius and the clustermass ($M_{500}$) is consistent with a linear relation. Our findings suggestthat cool cores are linked to the evolution of their host galaxy clusters.

The relation between the cool-core radius and the host galaxy clusters: thermodynamic properties and cluster mass