Evolution of High-energy Particle Distribution in Supernova Remnants

The spectra fits to a sample of 34 supernova remnants (Zeng et al., 2019) are updated. $\gamma$-ray spectra of 20 supernova remnants (SNRs) with a soft TeV spectrum are further analyzed. We found that 17 of them can be fitted in the hadronic scenario with a single power-law ion distribution with an index of $\sim$ 2.6, which is significantly softer than the ion distribution inferred from $\gamma$-ray observations of star-burst galaxies. If Galactic cosmic rays are mostly produced by SNRs, this result suggests that SNRs in star-burst galaxies may never reach the phase with a soft $\gamma$-ray spectra or escape of high-energy particles from SNRs before they reach this phase with a soft $\gamma$-ray spectrum dominates the contribution of SNRs to Galactic cosmic rays.