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Abstract 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 thisγ-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, and calculating the particle and photon spectra produced in different environments, we parameterize 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 primarily reflect the environment surrounding the SNR: the emission is expected to look hadronic unless the ambient density is particularly low (with proton number density ≲0.1 cm⁻³) or the photon background is enhanced with respect to average Galactic values (with radiation energy densityu_rad≳ 10 eV cm⁻³). We introduce a hadronicity parameter to characterize how hadronic or leptonic we expect a source to look based on its environment, which can be used to guide the interpretation of currentγ-ray observations and the detection of high-energy neutrinos from SNRs. 

SpECTRE is an open-source code for multi-scale, multi-physics problems in astrophysics and gravitational physics. In the future, we hope that it can be applied to problems across discipline boundaries in fluid dynamics, geoscience, plasma physics, nuclear physics, and engineering. It runs at petascale and is designed for future exascale computers. SpECTRE is being developed in support of our collaborative Simulating eXtreme Spacetimes (SXS) research program into the multi-messenger astrophysics of neutron star mergers, core-collapse supernovae, and gamma-ray bursts.