The Effects of Radiative Cooling on the Entropy Distribution of Intracluster Gas

High resolution X-ray observations indicate that the entropy profiles in the central regions of some massive cooling flow clusters are well approximated by powerlaws. McCarthy and coworkers recently accounted for this trend with an analytic model that includes the detailed effects of radiative cooling. Interestingly, these authors found that cooling (and subsequent inflow of the gas) naturally establishes approximate steady-state powerlaw entropy profiles in the cores of clusters. However, the origin of this behavior and its dependence on initial conditions have yet to be elucidated. In the present study, we explain this trend in the context of the self-similar cooling wave model developed previously by Bertschinger (1989). It is shown that the logarithmic slope of the entropy profile in the cores of relaxed cooling flow clusters is given by a simple analytic function that depends only on the logarithmic slopes of the local gravitational potential and the cooling function. We discuss a number of potentially interesting uses of the above result, including: (1) a way of measuring the shapes of gravitational potentials of cooling flow clusters (which may, for example, be compared with the results of the standard hydrostatic equilibrium method); (2) a simple method for constructing realistic analytic cluster models that include the effects of radiative cooling; and (3) a test of the reliability of cooling routines implemented in analytic models and hydrodynamic simulations.