As the end products of the hierarchical process of cosmic structure formation, galaxy clusters present some predictable properties, like those mostly driven by gravity, and some others, more affected by astrophysical dissipative processes, that can be recovered from observations and that show remarkable universal behaviour once rescaled by halo mass and redshift. However, a consistent picture that links these universal radial profiles and the integrated values of the thermodynamical quantities of the intracluster medium, also quantifying the deviations from the standard self-similar gravity-driven scenario, has to be demonstrated. In this work, we use a semi-analytic model based on a universal pressure profile in hydrostatic equilibrium within a cold dark matter halo with a defined relation between mass and concentration to reconstruct the scaling laws between the X-ray properties of galaxy clusters. We also quantify any deviation from the self-similar predictions in terms of temperature dependence of a few physical quantities such as the gas mass fraction, the relation between spectroscopic temperature and its global value, and, if present, the hydrostatic mass bias. This model allows to reconstruct both the observed profiles and the scaling laws between integrated quantities. We use the Planck-selected ESZ sample to calibrate the predicted scaling laws between gas mass, temperature, luminosity and total mass. Our universal model reproduces well the observed thermodynamic properties and provides a way to interpret the observed deviations from the standard self-similar behaviour. By combining these results with the constraints on the observed $Y_{SZ}-T$ relation, we show how we can quantify the level of gas clumping affecting the studied sample, estimate the clumping-free gas mass fraction, and suggest the average level of hydrostatic bias present.
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