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

S. Ettori, L. Lovisari, D. Eckert

Submitted on 6 November 2022, last revised on 18 November 2022


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. 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. 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. By calibrating the model, 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 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 QΔMaMEzazTaTEzaTz, in very good agreement with the current observational constraints.


Comment: 15 pages; A&A in press. Updated to match the published version

Subject: Astrophysics - Cosmology and Nongalactic Astrophysics


Differences between the predicted and observed values of the slope (filled circle) and the redshift dependence (cross) of the listed scaling relations. (Top panel) Deviations in terms of $\sigma = (O-M) / \epsilon_O$, where $O$ is the estimate constrained from the observations with error $\epsilon_O$ and $M$ is the predicted value; (bottom panel) systematic deviation $\delta = (O-M) / M$. Shaded regions represent $[-3, +3] \, \sigma$ and $[-0.3, +0.3] \, \delta$ in the top and bottom panel, respectively. Labels indicate the following: luminosity, either bolometric ($L_{\rm b}$) or in bands (0.5-2 keV, $L_{05}$; 0.1-2.4 keV, $L_{01}$); total ($M$) and gas ($M_{\rm g}$) mass; and temperature $T$ and X-ray $Y_x = M_{\rm g} \, T$.