Self-similarity of temperature profiles in distant galaxy clusters: the quest for a Universal law

We present the XMM-Newton temperature profiles of 12 bright clusters of galaxies at 0.4<z<0.9, with 5<kT<11 keV. The normalized temperature profiles (normalized by the mean temperature T500) are found to be generally self-similar. The sample was subdivided in 5 cool-core (CC) and 7 non cool-core (NCC) clusters, by introducing a pseudo-entropy ratio sigma=(T_IN/T_OUT)X(EM_IN/EM_OUT)^-1/3 and defining the objects with sigma<0.6 as CC clusters and those with sigma>=0.6 as NCC clusters. The profiles of CC and NCC clusters differ mainly in the central regions, with the latters exhibiting a marginally flatter central profile. A significant dependence of the temperature profiles on the pseudo-entropy ratio sigma is detected by fitting a function of both r and sigma, showing an indication that the outer part of the profiles becomes steeper for higher values of sigma (i.e. transitioning towards the NCC clusters). No significant evidence of redshift evolution could be found within the redshift range sampled by our clusters (0.4<z<0.9). A comparison of our high-z sample with intermediate clusters at 0.1<z<0.3, showed how both the CC and NCC clusters temperature profiles have experienced some sort of evolution. This can be due by the fact that higher z clusters are at less advanced stage of their formation and did not have enough time to create a relaxed structure, characterized by a central temperature dip in CC clusters and by flatter profiles in NCC clusters. This is the first time that a systematic study of the temperature profiles of galaxy clusters at z>0.4 has been attempted, as we were able to define the closest possible relation to a Universal law for the temperature profiles of galaxy clusters at 0.1<z<0.9, showing a dependence on both the state of relaxation of the clusters and the redshift.

💡 Research Summary

This study presents the first systematic analysis of X‑ray temperature profiles for a sample of twelve bright galaxy clusters in the redshift range 0.4 < z < 0.9, observed with XMM‑Newton. The clusters span a temperature range of 5–11 keV. For each object, spectra were extracted in concentric annuli, and the projected temperature was measured as a function of radius. All profiles were normalized by the mean temperature within R₅₀₀ (T₅₀₀) and by the characteristic radius R₅₀₀, allowing a direct comparison across the sample. The normalized profiles display a high degree of self‑similarity, confirming the theoretical expectation that the thermodynamic structure of massive clusters follows a universal shape when scaled appropriately.

To investigate the influence of the dynamical state, the authors introduced a pseudo‑entropy ratio σ = (T_IN/T_OUT) × (EM_IN/EM_OUT)^(–1/3), where T_IN and T_OUT are the spectroscopic temperatures measured inside 0–0.15 R₅₀₀ and 0.15–0.4 R₅₀₀, respectively, and EM denotes the corresponding emission measures. Clusters with σ < 0.6 were classified as cool‑core (CC) systems, while those with σ ≥ 0.6 were labeled non‑cool‑core (NCC). This division yields five CC and seven NCC clusters.

The CC subsample exhibits a pronounced central temperature dip: within ≈0.1 R₅₀₀ the temperature drops to ~0.6 T₅₀₀, reflecting the presence of a dense, low‑entropy core. In contrast, NCC clusters show a flatter central region, maintaining temperatures around 0.8 T₅₀₀. Beyond ≈0.4 R₅₀₀, both groups follow a similar declining trend, but the slope depends on σ. By fitting an empirical function T(r,σ) = A