Hadronic versus leptonic origin of gamma-ray emission from supernova remnants

GeV and TeV emission from the forward shocks of supernova remnants (SNRs) indicates that they are capable particle accelerators, making them promising sources of Galactic cosmic rays (CRs). However, it remains uncertain whether this $\gamma$-ray emission arises primarily from the decay of neutral pions produced by very high energy hadrons, or from inverse-Compton and/or bremsstrahlung emission from relativistic leptons. By applying a semi-analytic approach to non-linear diffusive shock acceleration (NLDSA) and calculating the particle and photon spectra produced in different astrophysical environments, we parametrize the relative strength of hadronic and leptonic emission. We show that, even if CR acceleration is likely to occur in all SNRs, the observed photon spectra may instead primarily reflect the environment surrounding the SNR, specifically the ambient density and radiation field. We find that the most hadronic-appearing spectra are young and found in environments of high density but low radiation energy density. This study aims to guide the interpretation of current $\gamma$-ray observations and single out the best targets of future campaigns.