Distributions of radio spectral index between 140 and 50 MHz, only for ≥1σ_rms detectable pixels in radio maps of the run E at four different epochs. The solid lines give the distribution of distribution of spectra for the electron evolution model including shocks and turbulent re-acceleration, the dashed lines are for the electron model only including shock re-acceleration and loss terms, and the dotted lines are for the electron model only including radiative losses and adiabatic changes after the injection by jets.