γ-ray emissivity ofthe secondary electrons and positrons and parent protons at different epochs characterised by the parameter n × T (in unit cm⁻³ s): 10¹³ (black curve), 10¹⁴ (red curve), 10¹⁵ (blue curve).different n × T value. The distribution of the parent protons is assumed saturated with an injection power-law spectrum in momentum with indices Γ = 2 (left panel) and Γ = 2.85 (right panel). The proton density is normalised such that the energy density above 1 GeV is 1 eV cm⁻³. The gas number density is n = 1 cm⁻³.