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

Abstract

Context. In the self-similar scenario for galaxy cluster formation and evolution, the thermodynamic properties of the X-ray emitting plasma can be predicted in their dependencies on the halo mass and redshift only. However, several departures from this simple self-similar scenario have been observed. Aims. We show how our semi-analytic model i(cm)z, which modifies the self-similar predictions through two temperature-dependent quantities, the gas mass fraction fg = f0Tf1Ezfz and the temperature variation fT = t0Tt1Eztz, can be calibrated to incorporate the mass and redshift dependencies. Methods. We used a published set of 17 scaling relations to constrain the parameters of the model. We were subsequently able to make predictions as to the slope of any observed scaling relation within a few percent of the central value and about one σ of the nominal error. Contextually, the evolution of these scaling laws was also determined, with predictions within 1.5σ and within 10 percent of the observational constraints. Relying on this calibration, we have also evaluated the consistency of the predictions on the radial profiles with some observational datasets. For a sample of high-quality data (X-COP), we were able to constrain a further parameter of the model, the hydrostatic bias b. Results. By calibrating the model versus a large set of X-ray scaling laws, we have determined that (i) the slopes of the temperature dependence are f1 = 0.403 (±0.009) and t1 = 0.144 (±0.017); and that (ii) the dependence upon Ez are constrained to be fz = −0.004 (±0.023) and tz = 0.349 (±0.059). These values, which are inserted in the scaling laws that propagate the mass and redshift dependence to the integrated quantities, permit one to estimate directly how the normalizations of a given quantity QΔ changes as a function of the mass (or temperature) and redshift halo in the form QΔ ∼ MaMEzaz ∼ TaT EzaTz, which is in very good agreement with the current observational constraints. When applied to the best spatially resolved data, we obtained estimates of the hydrostatic bias b that are lower than, but still comparable with, the results obtained by other, more standard, means. We conclude that the calibrated semi-analytic model i(cm)z is able to make valuable predictions on the slope and redshift evolution of the X-ray scaling laws, and on the expected radial behavior of the thermodynamic quantities, including any possible hydrostatic bias.