A 3D diffusive and advective model of electron transport applied to the pulsar wind nebula HESS J1825 - 137

HESS J1825 - 137 is one of the most powerful and luminous TeV gamma-ray pulsar wind nebulae, making it an excellent laboratory to study particle transportation around pulsars. We present a model of the (diffusive and advective) transport and radiative losses of electrons from the pulsar PSR J1826 - 1334 powering HESS J1825 - 137 using interstellar medium gas (ISM) data, soft photon fields, and a spatially varying magnetic field. We find that for the characteristic age of $21\, \mathrm{k}\mathrm{yr}$, PSR J1826 - 1334 is unable to meet the energy requirements to match the observed X-ray and gamma-ray emission. An older age of $40\, \mathrm{k}\mathrm{yr}$, together with an electron conversion efficiency of 0.14 and advective flow of v = 0.002c, can reproduce the observed multiwavelength emission towards HESS J1825 - 137. A turbulent ISM with magnetic field of $B=20 \,{\rm to}\, 60 \,\mathrm{\mu }{\rm G}$ to the north of HESS J1825 - 137 (as suggested by ISM observations) is required to prevent significant gamma-ray contamination towards the northern $\mathrm{T}\mathrm{e\mathrm{V}}$ source HESS J1826 - 130.