Observational constraints on the maximum energies of accelerated particles in supernova remnants

Supernova remnants (SNRs) are thought to be the most plausible sources of Galactic cosmic rays. One of the principal questions is whether they are accelerating particles up to the maximum energy of Galactic cosmic rays ($\sim$PeV). In this paper, we summarize our recent studies on gamma-ray-emitting SNRs. We first evaluated the reliability of SNR age estimates to quantitatively discuss time dependence of their acceleration parameters. Then we systematically modeled their gamma-ray spectra to constrain the acceleration parameters. The current maximum energy estimates were found to be well below PeV for most sources. The basic time dependence of the maximum energy assuming the Sedov evolution ($\approx t^{-0.8\pm0.2}$) cannot be explained with the simplest acceleration condition (Bohm limit) and requires shock-ISM (interstellar medium) interaction. The inferred maximum energies during lifetime averaged over the sample can be expressed as $\lesssim 20$ TeV ($t_{{\rm M}}/\text{1 kyr})^{-0.8}$ with $t_{\rm M}$ being the age at the maximum, which reaches $\sim$PeV only if $t_{\rm M} \lesssim 10$ yr. The maximum energies during lifetime are suggested to have a variety of 1-2 orders of magnitude from object to object on the other hand. This variety will reflect the dependence on environments.