Entropy profiles in the cores of cooling flow clusters of galaxies

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 that limit the condensation of intracluster gas. Here we present Chandra observations of the core entropy profiles of nine classic cooling flow'' clusters that appear relatively relaxed ( at least outside the central 10 - 20 kpc) 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 3 in temperature. They typically have an entropy level of approximate to 130 keV cm(2) at 100 kpc that declines to a plateau similar to 10 keV cm(2) at less than or similar to 10 kpc. Between these radii, the entropy profiles are proportional to r(alpha) with alpha approximate to 1.0-1.3. The nonzero central entropy levels in these clusters correspond to a cooling time similar to 10(8) yr, suggesting that episodic heating on this timescale maintains the central entropy profile in a quasi - steady state. We show in an appendix that although disturbances and bubbles are visible in the central regions of these clusters, these phenomena do not strongly bias our entropy estimates.