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Astrophysical Coronae: Lessons from Modeling of the Intracluster Medium

Coronae exist in most astrophysical objects: stars, accretion disks, and individual galaxies and clusters of galaxies. Coronae in these varied systems have some common properties: 1) hydrostatic equilibrium in background gravity is a good assumption; 2) they are optically thin, i.e., photons escape as soon as they are born; 3) they have cooling times shorter than their ages, and thus require heating for sustenance. Generally the coronal heating mechanisms are quite complex but the structure of the corona is tightly constrained by the interplay of cooling, {\em global} heating, and background gravity. We briefly summarize the results from our studies of the intracluster medium (the cluster corona) and draw inferences which should apply to most astrophysical coronae.