A dynamical model for the distribution of dark matter and gas in galaxy clusters

Abstract

Using the results of an extended set of high-resolution non-radiative hydrodynamic simulations of galaxy clusters, we obtain simple analytic formulae for the dark matter and hot gas distribution, in the spherical approximation. Starting from the dark matter phase-space radial density distribution, we derive fits for the dark matter 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 by our simulated clusters inside their virial radii. This result also shows that our fits constitute a self-consistent dynamical model for these systems. We then extend our analysis to the hot gas component, obtaining analytic fits for the gas density, temperature and velocity structure, with no further hypothesis on the gas dynamical status or state equation. Gas and dark matter show similar density profiles down to ≈0.06Rv (with Rv the virial radius), while at smaller radii the gas flattens, producing a central core. Gas temperatures are almost isothermal out to roughly 0.2 Rv, then steeply decrease, reaching at the virial radius a value almost a factor of 2 lower. We find that the gas is not at rest inside Rv: velocity dispersions are increasing functions of the radius, motions are isotropic to slightly tangential, and contribute non-negligibly to the total pressure support. We test this model using a generalization of the hydrostatic equilibrium equation, where the gas motion is properly taken into account. Again we find that the fits provide an accurate description of the system: the hot gas is in equilibrium and is a good tracer of the overall cluster potential if all terms (density, temperature and velocity) are taken into account, while simpler assumptions cause systematic mass underestimates. In particular, we find that using the so-called β-model underestimates the true cluster mass by up to 50 per cent at large radii. We also find that, if gas velocities are neglected, then a simple isothermal model fares better at large radii than a non-isothermal one. The shape of the gas density profile at small radii is at least partially explained by the gas expansion caused by energy transfer from dark matter during the collapse. In fact, when gas bulk energy is also considered, gas and dark matter are in energy equipartition in the final system at radii r > 0.1Rv, while at smaller radii the gas is hotter than the dark matter. This energy imbalance is also probably the reason of the further global halo compression compared with a pure collisionless collapse, which we point out by comparing the dark matter and total density profiles of our hydro-simulated clusters with a set of identical – but pure N-body – ones. The compression has the effect of raising the mean concentration by an amount of roughly 10 per cent.