Galaxy cluster thermodynamic profiles beyond self-similarity

Galaxy cluster formation is, to first order, a self-similar and scale-free process of gravitational collapse. However, the thermodynamic properties of the intracluster medium often deviate from self-similar predictions. We investigate these deviations using a sample of 92 galaxy clusters selected through their Sunyaev-Zeldovich effect signal, spanning a mass range of M_ 500c = 0.5-20 10^ 14 M _⊙, and with redshifts 0.08 < z < 1.13. Adopting a flexible framework that allows for radial variations in both redshift and mass scaling, we characterise the behaviour of scaled density, temperature, pressure, and entropy profiles, while simultaneously constraining their intrinsic scatter. When scaled according to the critical density of the Universe, we detect significant radial deviations from self-similar expectations in both redshift and mass scalings in all profiles. These deviations are strongest in the core regions, where baryonic processes dominate, but remain measurable out to large radii (∼ R_ 500c ), indicating that even cluster outer regions are not fully described by purely gravitational evolution. We investigate the impact of an offset, a mass-dependence, and increased scatter between the mass proxy and the true mass on the radial mass scaling, finding that while its shape remains stable, its normalisation depends on the latter two effects. The pressure is the only thermodynamic quantity that exhibits approximately self-similar behaviour: outside the core it evolves self-similarly, with no dependence on mass at the 2σ level. In contrast, the entropy exhibits the strongest deviations from self-similarity as a function of radius. For all profiles, the intrinsic scatter peaks in the central regions and reaches a minimum at intermediate radii (łesssim 20 % at ∼ 0.2--0.8 500c ), making this range optimal to reduce scatter in scaling relations. We conclude that the thermodynamic distributions exhibit non-self similar, mass-dependent scaling extending well beyond the core regime, likely shaped by the interplay between baryonic processes and ongoing accretion across all radii.