A Simple and Accurate Model for Intracluster Gas

Starting with the well-known NFW dark matter halo distribution, we construct a simple polytropic model for the intracluster medium that is in good agreement with high-resolution numerical hydrodynamic simulations, apply this model to a very large scale concordance dark matter simulation, and compare the resulting global properties with recent observations of X-ray clusters, including the mass-temperature and luminosity-temperature relations. We make allowances for a nonnegligible surface pressure, removal of low-entropy (short cooling time) gas, energy injection due to feedback, and a relativistic (nonthermal) pressure component. A polytropic index n = 5 (Γ = 1.2) provides a good approximation to the internal gas structure of massive clusters (except in the very central regions where cooling becomes important) and allows one to recover the observed M₅₀₀-T, L_X-T, and T/n ∝ T^0.65 relations. Using these concepts and generalizing this method so that it can be applied to fully three-dimensional N-body simulations, one can predict the global X-ray and SZE trends for any specified cosmological model. We find a good fit to observations when assuming that 12% of the initial baryonic mass condenses into stars, that the fraction of rest mass of this condensed component transferred back to the remaining gas (feedback) is 3.9 × 10^-5, and that the fraction of total pressure from a nonthermal component is near 10%.