Department of Astrophysical Sciences, Princeton University,
Princeton, NJ 08544, USA
2. Astronomical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan
3. Department of Physics, Princeton University, Princeton, NJ 08544, USA
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 density profile in outer parts of the haloes, as suggested by many 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 haloes is inconsistent with gas being isothermal; on the contrary, it requires temperature to decrease slowly with radius, in agreement with observations. We compare our predictions for X-ray surface brightness profiles of the haloes and the mass-temperature relation with observations. We find that they are generally in a good agreement. We compare the universal profile with the beta profile and find that, although the beta profile gives a reasonable fit to our predicted profiles, the deviation from it can explain many of the observed trends, once we take into account the observational selection effects. 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. We find that fitted to the beta profile the core radii and beta inferred from the SZ effect are systematically larger than those from the X-ray measurement.