The universal galaxy cluster pressure profile from a representative sample of nearby systems (REXCESS) and the YSZ - M500 relation

We investigate the regularity of cluster pressure profiles with REXCESS, a representative sample of 33 local (z < 0.2) clusters drawn from the REFLEX catalogue and observed with XMM-Newton. The sample spans a mass range of 10¹⁴ M_⊙ < M₅₀₀ < 10¹⁵ M_⊙, where M₅₀₀ is the mass corresponding to a density contrast of 500. We derive an average profile from observations scaled by mass and redshift according to the standard self-similar model, and find that the dispersion about the mean is remarkably low, at less than 30 per cent beyond 0.2 R₅₀₀, but increases towards the center. Deviations about the mean are related to both the mass and the thermo-dynamical state of the cluster. Morphologically disturbed systems have systematically shallower profiles while cooling core systems are more concentrated. The scaled profiles exhibit a residual mass dependence with a slope of ~0.12, consistent with that expected from the empirically-derived slope of the M₅₀₀ - Y_X relation; however, the departure from standard scaling decreases with radius and is consistent with zero at R₅₀₀. The scatter in the core and departure from self-similar mass scaling is smaller compared to that of the entropy profiles, showing that the pressure is the quantity least affected by dynamical history and non-gravitational physics. Comparison with scaled data from several state of the art numerical simulations shows good agreement outside the core. Combining the observational data in the radial range [0.03-1] R₅₀₀ with simulation data in the radial range [1-4] R₅₀₀, we derive a robust measure of the universal pressure profile, that, in an analytical form, defines the physical pressure profile of clusters as a function of mass and redshift up to the cluster "boundary". Using this profile and direct spherical integration of the observed pressure profiles, we estimate the integrated Compton parameter Y and investigate its scaling with M₅₀₀ and L_X, the soft band X-ray luminosity. We consider both the spherically integrated quantity, Y_sph(R), proportional to the gas thermal energy, and the cylindrically integrated quantity, Y_cyl(R)=Y_SZ D_A², which is directly related to the Sunyaev-Zel'dovich (SZ) effect signal. From the low scatter of the observed Y_sph(R₅₀₀) - Y_X relation we show that variations in pressure profile shape do not introduce extra scatter into the Y_sph(R₅₀₀) - M₅₀₀ relation as compared to that from the Y_X - M₅₀₀ relation. The Y_sph(R₅₀₀) - M₅₀₀ and Y_sph(R₅₀₀) - L_X relations derived from the data are in excellent agreement with those expected from the universal profile. This profile is used to derive the expected Y_SZ - M₅₀₀ and Y_SZ - L_X relations for any aperture.