Cosmology and Astrophysics from Relaxed Galaxy Clusters V: Consistency with Cold Dark Matter Structure Formation

This is the fifth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Our sample comprises 40 clusters identified as being dynamically relaxed and hot in Papers I and II of this series. Here we use constraints on cluster mass profiles from X-ray data to test some of the basic predictions of cosmological structure formation in the Cold Dark Matter (CDM) paradigm. We present constraints on the concentration--mass relation for massive clusters, finding a power-law mass dependence with a slope of $\kappa_m=-0.16\pm0.07$, in agreement with CDM predictions. For this relaxed sample, the relation is consistent with a constant as a function of redshift (power-law slope with $1+z$ of $\kappa_\zeta=-0.17\pm0.26$), with an intrinsic scatter of $\sigma_{\ln c}=0.16\pm0.03$. We investigate the shape of cluster mass profiles over the radial range probed by the data (typically $\sim50$kpc--1Mpc), and test for departures from the simple Navarro, Frenk & White (NFW) form, for which the logarithmic slope of the density profile tends to $-1$ at small radii. Specifically, we consider as alternatives the generalized NFW (GNFW) and Einasto parametrizations. For the GNFW model, we find an average value of (minus) the logarithmic inner slope of $\beta=1.02\pm0.08$, with an intrinsic scatter of $\sigma_\beta=0.22\pm0.07$, while in the Einasto case we constrain the average shape parameter to be $\alpha=0.29\pm0.04$ with an intrinsic scatter of $\sigma_\alpha=0.12\pm0.04$. Our results are thus consistent with the simple NFW model on average, but we clearly detect the presence of intrinsic, cluster-to-cluster scatter about the average.