Gamma-ray spectrum of IC 443. The Fermi data are shown in red, MAGIC in blue and VERITAS in green dots with errors. Our fit is shown by the solid red line. The distribution of the parental protons is shown by the red line in Fig. 8. The emission and the particle spectra are calculated with the scales tm = 60 days and pm = 9.5 × 103mpc as well as the values of dx = 100 days and βx = 0.8; the last two parameters determine the fit of the γ-ray spectrum above 20 GeV. The emission spectrum for the same case but with the steady injection is shown by the green dashed line. The green dotted lines represent the spectra with the artificial injection terms which are the same as Qt but zero before day 100 (the rightmost line), before day 1517 (middle line) and before day 8014 (the leftmost line). The γ-ray spectrum is calculated following the recipe of Aharonian & Atoyan (2000) with the cross-section for the pion production from Kelner et al. (2006); such an approach is very accurate for γ-rays with energies below a few TeV (Kelner et al. 2006).
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