XMM-Newton observations of three poor clusters: Similarity in dark matter and entropy profiles down to low mass

We present an analysis of the mass and entropy profiles of three poor galaxy clusters (A1991, A2717 and MKW9) observed with XMM-Newton. The clusters have very similar temperatures (kT = 2.65, 2.53 and 2.58 keV), and similar redshifts (0.04 < z < 0.06). We trace the surface brightness, temperature, entropy and integrated mass profiles with excellent precision up to ∼500 h −1 70 kpc (A1991 and A2717) and ∼350 h −1 70 kpc (MKW9). This corresponds to 0.5(0.35) r200 ,w herer200 is the radius corresponding to a density contrast of 200 with respect to the critical density at the cluster redshifts. None of the surface brightness profiles is well fitted with a single β-model. Double isothermal β-models provide reasonable fits, and in all cases the value of the external β parameter is consistent with the value found for richer clusters. The temperature profiles have central dips but are approximately flat at the exterior, up to the detection limit. The integrated mass profiles are very similar in physical units and are reasonably well fitted with the NFW mass model with concentration parameters in the range c200 = 4− 6a nd M200 = 1.2−1.6 × 10 14 h −1 70 M� . A King model is inconsistent with these mass data. The entropy profiles are very similar at large scale, but there is some scatter in the very central region (r < 50 kpc). However, none of the clusters has an isentropic core. We then discuss the structural and scaling properties of cluster mass and entropy profiles, including similar quality XMM-Newton data on the slightly cooler cluster A1983 (kT = 2.2 keV), and on the massive cluster A1413 (kT = 6. 5k eV). We find that the mass profiles scaled in units of M200 and r200 nearly coincide, with <20 per cent dispersion in the radial range (0.05−0.5) r200, where we could compare the profiles without excessive extrapolation. We provide a quantitative test of mass profile shapes by combining the concentration parameters of these poor clusters with other values of similar precision from the literature, and comparing with the c200 − M200 relation derived from numerical simulations for a ΛCDM cosmology. The data are fully consistent with the predictions, taking into account the measurement errors and expected intrinsic scatter, in the mass range M200 = (1.2 × 10 14 − 1.9 × 10 15 ) h −1 70 M� . This excellent agreement with theoretical predictions - a quasi universal cusped mass profile with concentration parameters as expected - shows that the physics of the dark matter collapse is basically understood. Scaling the entropy profiles using the self-similar relation S ∝ T , we find a typical scatter of ∼30 per cent in scaled entropy in the radial range (0.05−0.5) r200. The dispersion is reduced (∼22 per cent) if we use the empirical relation S ∝ T 0.65 . The scatter is nearly constant with radius, indicating a genuine similarity in entropy profile shape. The averaged scaled pro- file is well fi tted by ap ower law for 0.05 < r/r200 < 0.5, with a slope slightly lower than expected from pure shock heating (α = 0.94 ± 0.14), and a normalisation at 0.1 r200 consistent with previous ROSAT/ASCA studies. These precise XMM ob- servations confirm that the entropy profiles of clusters are self-similar down to low mass (kT ∼ 2 keV), but that the entropy temperature relation is shallower than in the purely gravitational model. This self-similarity of shape is a strong constraint, allowing us to rule out simple pre-heating models. The gas history thus probably depends not only on gravitational processes, but also on the interplay between cooling and various galaxy feedback mechanisms.