Expanding trends for β_exp obtained from the simulations. Top left panel: (blue solid points) obtained from the best fit for the radio-γ response for the ten simulations with β_exp ranging [0.001, 0.3]. The dashed line represents the best fit with the first equation of Eq. (25). Top right panel: same as in the top left panel, but for the case of . The dashed line corresponds to the best fit with the second equation of Eq. (25). Bottom right panel: same as in the top left panel, but for . The dashed line corresponds to the best fit with the third equation of Eq. (25). Bottom left panel: strong correlation between the fit model-to-data ratios and the cooling ratios in Fig. 9.