A phenomenological model of galaxy clusters

We present a simple model to describe the dark matter density, the gas density and the gas temperature profiles of galaxy clusters. Analytical expressions for these quantities are given in terms of only five free parameters with a clear physical meaning: the mass M of the dark matter halo (or the characteristic temperature T₀), the characteristic scale radius a, the cooling radius in units of a (0 < α < 1), the central temperature in units of T₀ (0 < t < 1) and the asymptotic baryon fraction in units of the cosmic value (f ~ 1). It is shown that our model is able to reproduce the three-dimensional density and temperature profiles inferred from X-ray observations of real clusters within a 20 per cent accuracy over most of the radial range. Some possible applications are briefly discussed.