Probability densities for different quantities. Lateral slices from ten snapshots are used to calculate a probability distribution function at each radial point. The ten snapshots are taken after the numerical relaxation of the initial conditions and are all 1τ_dyn apart. Different columns represent models with different boundary luminosities, increasing the luminosity from left to right. The different rows represent, from top to bottom: the density-weighted radial velocity, the magnitude of the tangential velocity , the gas density, the effective Eddington parameter, and the ratio of κ^line over κ^OPAL. The color maps in the top three rows are scaled differently to those of the bottom two rows for visibility reasons. This is because the probability distribution functions of the top three quantities are typically thinner and higher peaked. The probability density functions are normalized such that the integral over the variable shown on the y-axis gives unity at each radius.