Method used to measure the spectrum slope. The central SMBH (•) particle and the SNe (⋆) injected CRs with an initial spectrum of slope α₀. While propagating along the magnetic field lines, the slope of this spectrum can exhibit some modifications due to the energy dependence of the diffusion coefficient, and to a fraction of the CRs escaping the disk. The slope of the spectrum in the solar neighborhood α_S(t) (later simply denoted α) is then measured as a function of time for both the SNe and the CS populations by comparing the relative amounts of energy contained in each energy bin, averaged over all solar neighborhood gas cells.