2022MNRAS.511.5915F

HESS J1804-216 is one of the brightest yet most mysterious TeV γ-ray sources discovered to date. Previous arc-minute scale studies of the interstellar medium (ISM) surrounding this TeV γ-ray source revealed HESS J1804-216 is likely powered by a mature supernova remnant (SNR) or pulsar, hence its origin remains uncertain. In this paper, we focus on the diffusive escape of cosmic ray protons from potential SNR accelerators. These cosmic rays interact with the ISM to produce TeV γ-rays. We utilize the isotropic diffusion equation solution for particles escaping from a shell, to model the energy-dependent escape and propagation of protons into the ISM. This work is the first attempt at modelling the spatial morphology of γ-rays towards HESS J1804-216, using arc-minute ISM observations from both Mopra and the Southern Galactic Plane Survey. The spectral and spatial distributions of γ-rays for the two nearby potential SNR counterparts, SNR G8.7-0.1 and the progenitor SNR of PSR J1803-2137, are presented here. We vary the diffusion parameters and particle spectrum and use a grid search approach to find the best combination of model parameters. We conclude that moderately slow diffusion is required for both candidates. The most promising candidate to be powering the TeV γ-rays from HESS J1804-216 in a hadronic scenario is the progenitor SNR of PSR J1803-2137.