Radial distribution of protons with certain kinetic energies. Left panel: flux of 10 MeV protons as a function of radial distance r under different assumptions of medium density (black lines for n = 1 cm⁻³, and red linesfor n = 100 cm⁻³) and diffusioncoefficient (solid lines for χ = 1.0, dashed lines for χ = 0.1, dotted lines for χ = 0.01). Right panel: flux of protons with different kinetic energies E_p as a functionof radial distance r, assuming n = 1 cm⁻³, and χ = 1. For comparison, two radial profiles 1∕r (dashed grayline) and 1∕r³ (dotted gray line) are also shown. In both panels, we assume s = 2.0 and Q∕d² = 1 × 10³⁸ erg s⁻¹ kpc⁻².