We explore the scaling relation between the flux of the Sunyaev-Zeldovich (SZ) effect and the total mass of galaxy clusters using already reduced Chandra X-ray data present in the ACCEPT (Archive of Chandra Cluster Entropy Profile Tables) catalogue. The analysis is conducted over a sample of 226 objects, examining the relatively small scale corresponding to a cluster overdensity equal to 2500 times the critical density of the background universe, at which the total masses have been calculated exploiting the hydrostatic equilibrium hypothesis. Core entropy (K0) is strongly correlated with the central cooling time, and is therefore used to identify cooling-core (CC) objects in our sample. Our results confirm the self-similarity of the scaling relation between the integrated Comptonization parameter (Y) and the cluster mass, for both CC and NCC (non-cooling-core) clusters. The consistency of our calibration with recent ones has been checked, with further support for Y as a good mass proxy. We also investigate the robustness of the constant gas fraction assumption, for fixed overdensity, and of the Yx proxy (Kravstov et al. 2007) considering CC and NCC clusters, again sorted on K0 from our sample. We extend our study to implement a K0-proxy, obtained by combining SZ and X-ray observables, which is proposed to provide a CC indicator for higher redshift objects. Finally, we suggest that an SZ-only CC indicator could benefit from the employment of deprojected Comptonization radial profiles.
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