beta-model and cooling flows in X-ray clusters of galaxies

The spatial emission from the core of cooling flow clusters of galaxies is inadequately described by a beta-model(Cavaliere and Fusco-Femiano 1976). Spectrally, the central region of these clusters are well approximated with a two-temperature model, where the inner temperature represents the multiphase status of the core and the outer temperature is a measure of the ambient gas temperature.Following this observational evidence, I extend the use of the beta-model to a two-phase gas emission, where the two components coexist within a boundary radius r_cool and the ambient gas alone fills the volume shell at radius above r_cool. This simple model still provides an analytic expression for the total surface brightness profile. Based upon a physically meaningful model for the X-ray emission, this formula can be used (i) to improve significantly the modeling of the surface brightness profile of cooling flow clusters of galaxies when compared to the standard beta-model results, (ii) to constrain properly the physical characteristics of the intracluster plasma in the outskirts, like, e.g., the ambient gas temperature.