Turbulent Mixing in Clusters of Galaxies

We present a spherically-symmetric, steady-state model of galaxy clusters inwhich radiative cooling from the hot gas is balanced by heat transport throughturbulent mixing. We assume that the gas is in hydrostatic equilibrium, anddescribe the turbulent heat diffusion by means of a mixing length prescriptionwith a dimensionless parameter alpha_mix. Models with alpha_mix ~ 0.01-0.03yield reasonably good fits to the observed density and temperature profiles ofcooling core clusters. Making the strong simplification that alpha_mix istime-independent and that it is roughly the same in all clusters, the modelreproduces remarkably well the observed scalings of X-ray luminosity, gas massfraction and entropy with temperature. The break in the scaling relations at kT\~ 1-2 keV is explained by the break in the cooling function at around thistemperature, and the entropy floor observed in galaxy groups is reproducednaturally.Comment: Accepted for publication in ApJ