Proton number-spectra at later times. Solid lines represent the total spectra, and dashed and dotted lines indicate the forward shock upstream and the downstream spectra, respectively. The grey vertical lines at 200 GeV and 30 GeV denote the escape energies at 11 000 years and 30 000 years, respectively. The arrows point out the energy bands with spectral indices of 2.2 and 2.6.