Structure and scaling of the entropy in nearby galaxy clusters

Using XMM-Newton observations, we investigate the scaling and structural properties of the ICM entropy in a sample of 10 nearby (z < 0.2) relaxed galaxy clusters in the temperature range 2-9 keV. We derive the local entropy-temperature (S –T ) relation at R = 0.1, 0.2, 0.3 and 0.5R200. The logarithmic slope of the relation is the same within the 1σ error at all scaled radii. However, the intrinsic dispersion about the best fitting relation is significantly higher at 0.1R200. The slope is 0.64 ± 0.11 at 0.3 R200, in excellent agreement with previous work. We also investigate the entropy-mass relation at density contrasts δ = 5000, 2500 and 1000. We find a shallower slope than that expected in simple self-similar models, which is in agreement with the observed empirically-determined entropy-temperature and mass-temperature scaling. The dispersion is smaller than for the S –T relation. Once scaled appropriately, the entropy profiles appear similar beyond ∼ 0.1R200, with an intrinsic dispersion of ∼ 15 per cent and a shape consistent with gravitational heating (S (r)∝ ∼ r1.1). However, the scatter in scaled entropy profiles increases with smaller scaled radius, to more than 60 per cent at R . 0.05R200. Our results are in qualitative agreement with models which boost entropy production at the accretion shock. However, localised entropy modification may be needed to explain the dispersion in the inner regions.