Proton emissivity calculated from Eq. (17), considering a broken power-law luminosity function (Eq. (19)) with γ₂ = 2.5. Panel a: Different positioning of ℒ_*; the low luminosity index is γ₁ = 0.5. Panel b: Different low-luminosity behavior; the positioning of the break is fixed at ℒ_* = 10⁴⁴ erg/s. Panel c: Different choices of ℒ_low; the position of the break is ℒ_* = 10⁴⁴ erg/s and the slope is γ₁ = 0.5.