On the nature of the energy-dependent morphology of the composite multi-TeV gamma-ray source HESS J1702-420

HESS J1702-420 is a multi-TeV gamma-ray source with an unusual energy-dependent morphology. The recent H.E.S.S. observations suggest that the emission is well described by a combination of point-like HESS J1702-420A (dominating at highest energies, $\gtrsim$ 30 TeV ) and diffuse ($\sim$ 0.3${}^{\circ }$) HESS J1702-420B (dominating below $\lesssim$ 5TeV) sources with very hard ($\mathrm{\Gamma }\sim 1.5$) and soft ($\mathrm{\Gamma }$ ~2.6) power-law spectra, respectively. Here we propose a model which postulates that the proton accelerator is located at the position of HESS J1702-420A and is embedded into a dense molecular cloud that coincides with HESS J1702-420B. In the proposed model, the VHE radiation of HESS J1702-420 is explained by the pion-decay emission from the continuously injected relativistic protons propagating through a dense cloud. The energy-dependent morphology is defined by the diffusive nature of the low-energy protons propagation, transiting sharply to (quasi) ballistic propagation at higher energies. Adopting strong energy dependence of the diffusion coefficient, $D\propto E^{\beta }$ with $\beta \ge 1$, we argue that HESS J1702-420 as the system of two gamma-ray sources is the result of the propagation effect. Protons injected by a single accelerator at the rate $Q_0\simeq {10}^{38}(n_0\mathrm{/}100\mathrm{c}{\mathrm{m}}^{-3}{)}^{-1}(\mathrm{d}\mathrm{/}0.25\mathrm{k}\mathrm{p}\mathrm{c}{)}^{-1}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{/}\mathrm{s}$ can reasonably reproduce the morphology and fluxes of two gamma-ray components.