The universal galaxy cluster pressure profile from a representative sample of nearby systems (REXCESS) and the<i>Y</i>_SZ–<i>M</i>₅₀₀relation

Abstract

We investigate the regularity of cluster pressure profiles with REXCESS, a representative sample of 33 local (<i>z<i/> < 0.2) clusters drawn from the REFLEX catalogue and observed with <i>XMM-Newton<i/>. The sample spans a mass range of 10<sup>14<sup/> < <i>M<i/><sub>500<sub/> < 10<sup>15<sup/> , where <i>M<i/><sub>500<sub/> 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 <i>R<i/><sub>500<sub/>, 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 <i>M<i/><sub>500<sub/> – <i>Y<i/><sub>X<sub/> relation; however, the departure from standard scaling decreases with radius and is consistent with zero at <i>R<i/><sub>500<sub/>. 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] <i>R<i/><sub>500<sub/> with simulation data in the radial range [1–4] <i>R<i/><sub>500<sub/>, 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 <i>Y<i/> and investigate its scaling with <i>M<i/><sub>500<sub/> and <i>L<i/><sub>X<sub/>, the soft band X-ray luminosity. We consider both the spherically integrated quantity, <i>Y<i/><sub>sph<sub/>(<i>R<i/>), proportional to the gas thermal energy, and the cylindrically integrated quantity, <i>Y<i/><sub>cyl<sub/>(<i>R<i/>)=<i>Y<i/><sub>SZ<sub/> <i>D<i/><sub>A<sub/><sup>2<sup/>, which is directly related to the Sunyaev-Zel'dovich (SZ) effect signal. From the low scatter of the observed <i>Y<i/><sub>sph<sub/>(<i>R<i/><sub>500<sub/>) – <i>Y<i/><sub>X<sub/> relation we show that variations in pressure profile shape do not introduce extra scatter into the <i>Y<i/><sub>sph<sub/>(<i>R<i/><sub>500<sub/>) – <i>M<i/><sub>500<sub/> relation as compared to that from the <i>Y<i/><sub>X<sub/> – <i>M<i/><sub>500<sub/> relation. The <i>Y<i/><sub>sph<sub/>(<i>R<i/><sub>500<sub/>) – <i>M<i/><sub>500<sub/> and <i>Y<i/><sub>sph<sub/>(<i>R<i/><sub>500<sub/>) – <i>L<i/><sub>X<sub/> relations derived from the data are in excellent agreement with those expected from the universal profile. This profile is used to derive the expected <i>Y<i/><sub>SZ<sub/> – <i>M<i/><sub>500<sub/> and <i>Y<i/><sub>SZ<sub/> – <i>L<i/><sub>X<sub/> relations for any aperture.