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The acceleration times of the highest-energy particles which emit gamma-raysin young and middle-age SNRs are comparable with SNR age. If the number ofparticles starting acceleration was varying during early times after thesupernova explosion then this variation should be reflected in the shape of thegamma-ray spectrum. We use the solution of the non-stationary equation forparticle acceleration in order to analyze this effect. As a test case, we applyour method to describe gamma-rays from IC443. As a proxy of the IC443 parentsupernova we consider SN1987A. First, we infer the time dependence of injectionefficiency from evolution of the radio spectral index in SN1987A. Then, we usethe inferred injection behavior to fit the gamma-ray spectrum of IC443. We showthat the break in the proton spectrum needed to explain the gamma-ray emissionis a natural consequence of the early variation of the cosmic ray injection,and that the very-high energy gamma-rays originate from particles which beganacceleration during the first months after the supernova explosion. We concludethat the shape of the gamma-ray spectrum observed today in SNRs criticallydepends on the time variation of the cosmic ray injection process in theimmediate post explosion phases. With the same model, we estimate also thepossibility in the future to detect gamma-rays from SN 1987A.

Linking gamma-ray spectra of supernova remnants to the cosmic ray injection properties in the aftermath of supernovae