2014A&A...566A..42C

The origin of radio halos in galaxy clusters is still unknown and is the subject of a vibrant debate from both observational and theoretical points of view. In particular, the amount and the nature of nonthermal plasma and of the magnetic field energy density in clusters hosting radio halos is still unclear. The aim of this paper is to derive an estimate of the pressure ratio X=P_non–th/P_th between the nonthermal and thermal plasma in radio halo clusters that have combined radio, X-ray and Sunyaev-Zel'dovich (SZ) effect observations. From the simultaneous P_1.4-L_X and P_1,4-Y_SZ correlations for a sample of clusters observed with Planck, we derive a correlation between Y_SZ and L_X that we use to derive a value for X. This is possible since the Compton parameter Y_SZ is proportional to the total plasma pressure in the cluster, which we characterize as the sum of the thermal and nonthermal pressure, while the X-ray luminosity L_X is proportional only to the thermal pressure of the intracluster plasma. Our results indicate that the average (best-fit) value of the pressure ratio in a self-similar cluster formation model is X=0.55±0.05 in the case of an isothermal β-model with β=2/3 and a core radius r_c=0.3. R₅₀₀, holding on average for the cluster sample. We also show that the theoretical prediction for the Y_SZ-L_X correlation in this model has a slope that is steeper than the best-fit value for the available data. The agreement with the data can be recovered if the pressure ratio X decreases with increasing X-ray luminosity as L_X^–0.96. We conclude that the available data on radio halo clusters indicate a substantial amount of nonthermal pressure in cluster atmospheres whose value must decrease with increasing X-ray luminosity or increasing cluster mass (temperature). This is in agreement with the idea that nonthermal pressure is related to nonthermal sources of cosmic rays that live in cluster cores and inject nonthermal plasma in the cluster atmospheres, which is subsequently diluted by the intracluster medium acquired during cluster collapse, and has relevant impact for further studies of high-energy phenomena in galaxy clusters.