We present a Chandra study of 38 X-ray luminous clusters of galaxies in the ROSAT Brightest Cluster Sample (BCS) that lie at z~0.15-0.4. We find that the majority of clusters at moderate redshift generally have smooth, relaxed morphologies with some evidence for mild substructure perhaps indicative of recent minor merger activity. Using spatially-resolved spectral analyses, cool cores appear to still be common at these redshifts. At a radius of 50 kpc, we find that at least 55 per cent of the clusters in our sample exhibit signs of mild cooling [t(cool)<10 Gyr], while in the central bin at least 34 per cent demonstrate signs of strong cooling [t(cool)<2 Gyr]. These percentages are nearly identical to those found for luminous, low-redshift clusters of galaxies, suggesting little evolution in cluster cores since z~0.4 and that heating and cooling mechanisms may already have stabilised by this epoch. Comparing the central cooling times to central Halpha emission in BCS clusters, we find a strong correspondence between the detection of Halpha and central cooling time. (Abridged)
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