Linking a universal gas density profile to the core-excised X-ray luminosity in galaxy clusters up to z ∼ 1.1

We investigate the regularity of galaxy cluster gas density profiles and the link to the relation between core-excised luminosity, L_Xc, and mass from the Y_X proxy, M_YX, for 93 objects selected through their Sunyaev-Zeldovich effect (SZE) signal. The sample spans a mass range of M₅₀₀ = [0.5−20]×10¹⁴ M_⊙, and lies at redshifts 0.05 < z < 1.13. To investigate differences in X-ray and SZE selection, we compare to the local X-ray-selected REXCESS sample. Using XMM-Newton observations, we derive an average intra-cluster medium (ICM) density profile for the SZE-selected systems and determine its scaling with mass and redshift. This average profile exhibits an evolution that is slightly stronger than self-similar (α_z = 2.09 ± 0.02), and a significant dependence on mass (α_M = 0.22 ± 0.01). Deviations from this average scaling with radius, which we quantify, indicate different evolution for the core regions as compared to the bulk. We measure the radial variation of the intrinsic scatter in scaled density profiles, finding a minimum of ∼20% at R ∼ [0.5−0.7] R₅₀₀ and a value of ∼40% at R₅₀₀; moreover, the scatter evolves slightly with redshift. The average profile of the SZE-selected systems adequately describes the X-ray-selected systems and their intrinsic scatter at low redshift, except in the very central regions. We examine the evolution of the scaled core properties over time, which are positively skewed at later times, suggesting an increased incidence of centrally peaked objects at lower redshifts. The relation between core-excised luminosity, L_Xc, and mass is extremely tight, with a measured logarithmic intrinsic scatter of σ_lnLXc|MYx ∼ 0.13. Using extensive simulations, we investigate the impact of selection effects, intrinsic scatter, and covariance between quantities on this relation. The slope is insensitive to selection and intrinsic scatter between quantities; however, the scatter is very dependent on the covariance between L_Xc and Y_X. Accounting for our use of the Y_X proxy to determine the mass, for observationally motivated values of covariance we estimate an upper limit to the logarithmic intrinsic scatter with respect to the true mass of σ_lnLXc|M ∼ 0.22. We explicitly illustrate the connection between the scatter in density profiles and that in the L_Xc − M relation. Our results are consistent with the overall conclusion that the ICM bulk evolves approximately self-similarly, with the core regions evolving separately. They indicate a systematic variation of the gas content with mass. They also suggest that the core-excised X-ray luminosity, L_Xc, has a tight and well-understood relation to the underlying mass.