Cosmic-ray intensity at Earth. Panel a: Different positioning of ℒ_*, with γ₁ = 0.5. Panel b: Different slope, with the positioning of the break fixed at ℒ_* = 10⁴⁴ erg/s. Panel c: Different choices of ℒ_low, with ℒ_* = 10⁴⁴ erg/s and γ₁ = 0.5. γ₂ = 2.5 in all the cases. The all-particle spectrum (Abreu et al. 2021; Aab et al. 2020) measured by Auger and the proton fraction (Aab et al. 2014a,b, 2016) inferred through the EPOS-LHC hadronic interaction model (Pierog et al. 2015) are shown with black squares and red circles, respectively. As a comparison, the same result is shown for an injection Q_src(E)∝E⁻² (dashed black).