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

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(abridged) We investigate the regularity of cluster pressure profiles with REXCESS, a representative sample of 33 local clusters observed with XMM-Newton. The sample spans a mass range of 10¹4 Mₛun <M₅00<10¹5 Mₛun. We derive an average profile from observations scaled by mass and z according to the standard self-similar model, and find that the dispersion about the mean is remarkably low beyond 0.2R₅00, but increases towards the centre. Deviations about the mean are related to both the mass and the thermo-dynamical state of the cluster. Unrelaxed systems have systematically shallower profiles while cooling core systems are more concentrated. The scaled profiles exhibit a residual mass dependence with a slope of about 0.12; 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 several state of the art numerical simulations shows good agreement outside the core. Combining the observational data below R₅00 with simulation data above, we derive the universal pressure profile, that, in an analytical form, defines the physical pressure profile of clusters as a function of mass and z up to the cluster 'boundary'. Using this profile and the observed pressure profiles, we investigate the scaling properties of the integrated Compton parameter Y, considering both the spherically integrated quantity and the cylindrically integrated quantity, directly related to the Sunyaev-Zel'dovich (SZ) effect signal. We further derive the expected YₛZ-M₅00 and YₛZ-Lₓ relations for any aperture.