Constraining leptonic and hadronic gamma-ray emission from HESS J1825-137 and its environment

We present a broadband spectral analysis of the $\gamma$-ray emission from the pulsar wind nebula HESS~J1825$-$137, combining observations from Fermi Large Area Telescope ($\mathit{\text{Fermi}}$-LAT), High Energy Stereoscopic System (H.E.S.S.), High-Altitude Water Cherenkov Observatory (HAWC), and Very Energetic Radiation Imaging Telescope Array System (VERITAS) across the $\sim 0.1$~GeV–$160$~TeV energy range. The spectral energy distribution is modelled under purely leptonic, purely hadronic, and lepto-hadronic scenarios using the $\text{textsc}Naima$ radiative modeling framework with Markov Chain Monte Carlo parameter estimation. Model comparison via the Bayesian Information Criterion reveals that the baseline GeV–TeV data favour a purely leptonic interpretation, while the inclusion of simulated Cherenkov Telescope Array Observatory (CTAO) observations or Large High Altitude Air Shower Observatory (LHAASO) ultra-high-energy (UHE; $E_{\gamma }\ge 100\mathrm{T}\mathrm{e}\mathrm{V}$) measurements shifts the preference toward models incorporating a hadronic component ($\mathrm{\Delta }\mathrm{B}\mathrm{I}\mathrm{C}=-28.87$ and $-7.89$, respectively). The inferred electron energy budget for the baseline GeV–TeV dataset, $W_e=4.25\times {10}^{48}$~erg, is consistent with previous estimates reported in the literature. The proton energy budget, $W_p\approx 2.5\times {10}^{48}$~erg, is energetically compatible with $pp$ interactions in the dense molecular environment adjacent to the nebula. These results demonstrate that precise spectral measurements above $\sim 10$~TeV, where Klein–Nishina suppression of inverse Compton emission creates a window for hadronic processes, are essential to establish the dominant emission mechanism in this source.