The Fraction of cool-core clusters in X-ray versus SZ samples using Chandra observations

We derive and compare the fractions of cool-core clusters in the Planck Early Sunyaev-Zel’dovich sample of 164 clusters with z≤slant 0.35 and in a flux-limited X-ray sample of 100 clusters with z≤slant 0.30, using Chandra observations. We use four metrics to identify cool-core clusters: (1) the concentration parameter, which is the ratio of the integrated emissivity profile within 0.15 r 500 to that within r 500; (2) the ratio of the integrated emissivity profile within 40 kpc to that within 400 kpc; (3) the cuspiness of the gas density profile, which is the negative of the logarithmic derivative of the gas density with respect to the radius, measured at 0.04 r 500; and (4) the central gas density, measured at 0.01 r 500. We find that the sample of X-ray-selected clusters, as characterized by each of these metrics, contains a significantly larger fraction of cool-core clusters compared to the sample of SZ-selected clusters (44% ± 7% versus 28% ± 4% using the concentration parameter in the 0.15-1.0 r 500 range, 61% ± 8% versus 36% ± 5% using the concentration parameter in the 40-400 kpc range, 64% ± 8% versus 38% ± 5% using the cuspiness, and 53% ± 7% versus 39 ± 5% using the central gas density). Qualitatively, cool-core clusters are more X-ray luminous at fixed mass. Hence, our X-ray, flux-limited sample, compared to the approximately mass-limited SZ sample, is overrepresented with cool-core clusters. We describe a simple quantitative model that uses the excess luminosity of cool-core clusters compared to non-cool-core clusters at fixed mass to successfully predict the observed fraction of cool-core clusters in X-ray-selected samples.