Production rate of secondary particles from hadronic processes. Left: relative comparison of the production rate of γ-rays in the case of no helium and zero metallicity in the Kafexhiu et al. (2014) and the Kelner et al. (2006) parameterization, using the Pythia8 parameterization from Kafexhiu et al. (2014) as a reference. For Kelner et al. (2006), we also show the low- and high-energy (δ-approximation) limits as dashed lines, which were combined to compute the rate over the total energy range. Middle: effect of including helium and metals in the model. This was done with Pythia8 using the Kafexhiu et al. (2014) parameterization. Right: comparison of the production rate for γ-rays, electrons, positrons, and neutrinos, computed for a radius r = 100 kpc. We also include the power-law function proportional to E^−2.4 for comparison because it corresponds to the injected CRp distribution.