The physics inside the scaling relations for X-ray galaxy clusters: gas clumpiness, gas mass fraction and slope of the pressure profile

Abstract

In galaxy clusters, the relations between observables in X-ray and millimetre wave bands and the total mass have normalizations, slopes and redshift evolutions that are simple to estimate in a self-similar scenario. We study these scaling relations and show that they can be efficiently expressed, in a more coherent picture, by fixing the normalizations and slopes to the self-similar predictions, and advocating, as responsible of the observed deviations, only three physical mass-dependent quantities: the gas clumpiness C, the gas mass fraction fg and the logarithmic slope of the thermal pressure profile βP. We use samples of the observed gas masses, temperature, luminosities and Compton parameters in local clusters to constrain normalization and mass dependence of these three physical quantities, and measure C0.5fg = 0.110( ± 0.002 ± 0.002)(EzM/5 × 1014 M⊙)0.198( ± 0.025 ± 0.04) and βP = −dln P/dln r = 3.14( ± 0.04 ± 0.02)(EzM/5 × 1014 M⊙)0.071( ± 0.012 ± 0.004), where both a statistical and systematic error (the latter mainly due to the cross-calibration uncertainties affecting the Chandra and XMM–Newton results used in the present analysis) are quoted. The degeneracy between C and fg is broken by using the estimates of the Compton parameters. Together with the self-similar predictions, these estimates on C, fg and βP define an intercorrelated internally consistent set of scaling relations that reproduces the mass estimates with the lowest residuals.