Mean values of the turbulent velocity dispersion vs. halo mass (top) and mean thermal energy (bottom) for halos at redshift z = 1 (left) and z = 0 (right). As indicated in the legend, both volume- and mass-weighted averages are computed for cells within the virial radius or cells with density and temperature above the specified thresholds. While the thick solid lines in the top plots (σ_turb vs. M) are sliding medians as Fig. 9, the lower plots (σ_turb vs. e) show power-law fits with slope α.