A dynamical model for the distribution of dark matter and gas in galaxy clusters
Using high-resolution non-radiative hydrodynamic simulations of galaxy clusters we obtain simple analytic formulae for DM and gas distribution in the spherical approximation. We derive fits for the DM density, velocity dispersion and velocity anisotropy. We use these models to test the dynamical equilibrium hypothesis through the Jeans equation: we find that this is satisfied to good accuracy. This result show that our fits constitute a self-consistent dynamical model. We then extend our analysis to the gas, studying its density, temperature and velocity structure, with no further hypothesis on the dynamical status or state equation. Gas and DM show self-similar density profiles down to 0.06 R_vir, while at smaller radii the gas produces a central core. Gas temperatures are almost isothermal out to 0.2 R_vir, then steeply decrease reaching at R_vir a value a factor of 2 lower. We find that the gas is not at rest inside R_vir: velocity dispersions are increasing functions of the radius, motions are isotropic to slightly tangential, and contribute to the total pressure support. We test our model using a generalization of the hydrostatic equilibrium equation, where the gas motion is properly taken into account. We find that our fits provide an accurate description of the system: the gas is in equilibrium and is a good tracer the overall cluster potential if all terms are taken into account, while simpler assumptions, as the beta-model, cause systematic mass underestimates. We also find that, if gas velocities are neglected, then a simple isothermal model fares better at large radii than a non-isothermal one. (abridged)