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Description
We derive and compare the fractions of cool-core clusters in the Planck Early Sunyaev-Zel'dovich sample of 164 clusters with z<=0.35 and in a flux- limited X-ray sample of 100 clusters with z<=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 40kpc to that within 400kpc; (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.
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