The X-ray properties of a relaxed cluster of galaxies are determined primarily by its gravitational potential well and the entropy distribution of its intracluster gas .
That entropy distribution reflects both the accretion history of the cluster and the feedback processes which limit the condensation of intracluster gas .
Here we present Chandra observations of the core entropy profiles of nine classic “ cooling-flow ” clusters that appear relaxed and contain intracluster gas with a cooling time less than a Hubble time .
We show that those entropy profiles are remarkably similar , despite the fact that the clusters range over a factor of three in temperature .
They typically have an entropy level of \approx 130 { keV cm ^ { 2 } } at 100 kpc that declines to a plateau \sim 10 { keV cm ^ { 2 } } at \lesssim 10 kpc .
Between these radii , the entropy profiles are \propto r ^ { \alpha } with \alpha \approx 1.0 - 1.3 .
The non-zero central entropy levels in these clusters correspond to a cooling time \sim 10 ^ { 8 } { yr } , suggesting that episodic heating on this timescale maintains the central entropy profile in a quasi-steady state .