i(cm)z, a semi-analytic model for the thermodynamic properties in galaxy clusters: Calibrations with mass and redshift, and implication for the hydrostatic bias

In the self-similar scenario for galaxy cluster formation and evolution, thermodynamic properties of X-ray emitting plasma can be predicted in their dependencies on halo mass redshift only. However, several departures from this simple have been observed. We show how our semi-analytic model $i(cm)z$, which modifies predictions through two temperature-dependent quantities, gas fraction $f_g=f_0 T^{f_1} E_z^{f_z}$ temperature variation $f_T=t_0 T^{t_1} E_z^{t_z}$, calibrated to incorporate dependencies. used a published set 17 scaling relations constrain parameters model. were subsequently able make as slope any observed relation within few percent central value about one $\sigma$ nominal error. Contextually, evolution these laws was also determined, with $1.5 \sigma$ 10 observational constraints. Relying calibration, we evaluated consistency radial profiles some datasets. For sample high-quality data (X-COP), further parameter model, hydrostatic bias $b$. By calibrating determined that (i) slopes dependence are $f_1=0.403 (\pm0.009)$ $t_1=0.144 (\pm0.017)$; (ii) upon $E_z$ constrained $f_z=-0.004 (\pm 0.023)$ $t_z=0.349 0.059)$. These values permit estimate directly normalizations given quantity $Q_{\Delta}$ changes function (or temperature) form $Q_{\Delta} \sim M^{a_M} E_z^{a_z} T^{a_T} E_z^{a_{Tz}}$, very good agreement current