The role of the diffusive protons in the gamma-ray emission of supernova remnant RX J1713.7$-$3946 --- a two-zone model

Abstract

RX~J1713.7$-$3946 is a prototype in the $γ$-ray-bright supernova remnants (SNRs) and is in continuing debates on its hadronic versus leptonic origin of the $γ$-ray emission. We explore the role played by the diffusive relativistic protons that escape from the SNR shock wave in the $γ$-ray emission, apart from the high-energy particles' emission from the inside of the SNR. In the scenario that the SNR shock propagates in a clumpy molecular cavity, we consider that the$γ$-ray emission from the inside of the SNR may arise either from the inverse Compton scattering or from the interaction between the trapped energetic protons and the shocked clumps. The dominant origin between them depends on the electron-to-proton number ratio. The diffusive protons that escaped from the shock wave during the expansion history can provide an outer hadronic $γ$-ray component by bombarding the surrounding dense matter. The broadband spectrum can be well explained by this two-zone model, in which the $γ$-ray emission from the inside governs the TeV band, while the outer emission component substantially contributes to the GeV $γ$-rays. The two-zone model can also explain the TeV $γ$-ray radial brightness profile that significantly stretches beyond the nonthermal X-ray-emitting region. In the calculation, we present a simplified algorithm for Li & Chen's (2010) "accumulative diffusion" model for escaping protons and apply the Markov Chain Monte Carlo method to constrain the physical parameters.