Universal gas density and temperature profile

We present an analytic approach to predict gas density and temperature profiles in dark matter haloes. We assume that the gas density profile traces the dark matter profile in outer parts of the haloes, as suggested by a number of hydrodynamic simulations. Under this assumption the hydrostatic equilibrium uniquely fixes the two free parameters in the model, the mass– temperature normalization and the polytropic index, that determine the temperature profile. This enables us to predict a universal gas profile from any universal dark matter profile. Our results show that gas tracing dark matter in the outer parts of the cluster is inconsistent with gas being isothermal and requires temperature to slowly decrease there, in agreement with observations. We compare our predictions for X-ray surface brightness profiles of the haloes and the mass–temperature relation with observations and find that they are generally in a good agreement. We compare the universal profile to the β profile and find that, although the β profile gives a reasonable fit to our predicted profiles, the deviations from it can explain many of the observed trends once the observational selection effects are taken into account. Our model predicts that the mass–temperature relation does not follow the self-similar relation because of the mass dependent halo concentration. We also predict surface brightness profiles of the Sunyaev–Zel’dovich (SZ) effect and find that fitted to the β-profile the core radii and β inferred from the SZ effect are systematically larger than those from the X-ray measurements.