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

We present a detailed study of cool-core systems in a sample of four galaxy clusters (RXCJ1504.1-0248, A3112, A4059, and A478) using archival X-ray data from the Chandra X-ray Observatory. Cool cores are frequently observed at the centers of galaxy clusters and are considered to be formed by radiative cooling of the intracluster medium (ICM). Cool cores are characterized by a significant drop in the ICM temperature toward the cluster center. We extract and analyze X-ray spectra of the ICM to measure the radial profiles of the ICM thermodynamic properties including temperature, density, pressure, entropy, and radiative cooling time. We define the cool-core radius as the turnover radius in the ICM temperature profile and investigate the relation between the cool-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 radius exceeds 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 not only radiative cooling but also additional mechanisms such as gas sloshing may play an important role in determining the size of cool cores. Additionally, we find that the best-fit relation between the cool-core radius and the cluster mass ($M_{500}$) is consistent with a linear relation. Our findings suggest that cool cores are linked to the evolution of their host galaxy clusters.