Pursuing the origin of the gamma rays in RX J1713.7$-$3946 quantifying the hadronic and leptonic components

We analyzed the TeV gamma-ray image of a supernova remnant RX J1713.7$-$3946 (RX J1713) through a comparison with the interstellar medium (ISM) and the non-thermal X-rays. The gamma-ray datasets at two energy bands of $>$2 TeV and $>$250-300 GeV were obtained with H.E.S.S. (H.E.S.S. Collaboration 2018; Aharonian et al. 2007) and utilized in the analysis. We employed a new methodology which assumes that the gamma-ray counts are expressed by a linear combination of two terms; one is proportional to the ISM column density and the other proportional to the X-ray count. We then assume these represent the hadronic and leptonic components, respectively. By fitting the expression to the data pixels, we find that the gamma-ray counts are well represented by a flat plane in a 3D space of the gamma-ray counts, the ISM column density and the X-ray counts. The results using the latest H.E.S.S. data at 4.8 arcmin resolution show that the hadronic and leptonic components occupy $(67\pm8)$% and $(33\pm8)$% of the total gamma rays, respectively, where the two components have been quantified for the first time. The hadronic component is greater than the leptonic component, which reflects the massive ISM of $\sim$10$^4$ $M_{\odot}$ associated with the SNR, lending support for the acceleration of the cosmic-ray protons. There is a marginal hint that the gamma rays are suppressed at high gamma-ray counts which may be ascribed to the second order effects including the shock-cloud interaction and the penetration-depth effect.