β ‐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 β ‐model. Spectrally, the central region of these clusters is 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 β ‐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 a radius above r cool . This simple model still provides an analytic expression for the total surface brightness profile (Note in the first term the different sign with respect to the standard β ‐model.) Based upon a physically meaningful model for the X‐ray emission, this formula can be used (i) to improve significantly the modelling of the surface brightness profile of cooling flow clusters of galaxies when compared to the standard β ‐model results, (ii) to constrain properly the physical characteristics of the intracluster plasma in the outskirts, like, e.g., the ambient gas temperature.