Population study of Galactic supernova remnants at very high $gamma$-ray energies with H.E.S.S.

Shell-type supernova remnants (SNRs) are considered prime candidates for the acceleration of Galactic cosmic rays (CRs) up to the knee of the CR spectrum at $mathrm{E} approx mathrm{3}times mathrm{10}^mathrm{15}$ eV. Our Milky Way galaxy hosts more than 350 SNRs discovered at radio wavelengths and at high energies, of which 220 fall into the H.E.S.S. Galactic Plane Survey (HGPS) region. Of those, only 50 SNRs are coincident with a H.E.S.S source and in 8 cases the very high-energy (VHE) emission is firmly identified as an SNR. The H.E.S.S. GPS provides us with a legacy for SNR population study in VHE $gamma$-rays and we use this rich data set to extract VHE flux upper limits from all undetected SNRs. Overall, the derived flux upper limits are not in contradiction with the canonical CR paradigm. Assuming this paradigm holds true, we can constrain typical ambient density values around shell-type SNRs to $nleq 7~textrm{cm}^textrm{-3}$ and electron-to-proton energy fractions above 10~TeV to $epsilon_textrm{ep} leq 5times 10^{-3}$. Furthermore, comparisons of VHE with radio luminosities in non-interacting SNRs reveal a behaviour that is in agreement with the theory of magnetic field amplification at shell-type SNRs.