Fraction of clusters with radio halos with ν_s  ≥  1000 MHz (black, upper, solid lines) as a function of the cluster mass in the redshift range 0−0.1 (left panel) and 0.4−0.5 (right panel). The fractions of clusters with radio halos with ν_s in different frequency ranges are also shown: 1000 < ν_s < 1400 MHz (red lines), 1400 < ν_s < 2000 MHz (blue lines), 2000 < ν_s < 4000 MHz (magenta lines), and ν > 4000 MHz (green lines).