Turbulent Mixing in Clusters of Galaxies

We present a spherically-symmetric, steady-state model of galaxy clusters in which radiative cooling from the hot gas is balanced by heat transport through turbulent mixing. We assume that the gas is in hydrostatic equilibrium, and describe the turbulent heat diffusion by means of a mixing length prescription with a dimensionless parameter alpha_mix. Models with alpha_mix ~ 0.01-0.03 yield reasonably good fits to the observed density and temperature profiles of cooling core clusters. Making the strong simplification that alpha_mix is time-independent and that it is roughly the same in all clusters, the model reproduces remarkably well the observed scalings of X-ray luminosity, gas mass fraction 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 this temperature, and the entropy floor observed in galaxy groups is reproduced naturally.