Modeling the Saddle-like GeV-TeV Spectrum of HESS J1809-193: $\gamma$-Rays Arising from Reverse-Shocked Pulsar Wind Nebula?

Abstract

Evolution of pulsar wind nebulae (PWNe) could be expected to leave imprints in $\gamma$-rays. We suggest that intriguing GeV-TeV spectral energy distribution (SED) of HESS J1809$-$193 and Fermi-LAT source J1810.3$-$1925e is very likely to be the $\gamma$-ray signature of PWN J1809$-$193 in light of the scenario that the PWN was struck by the reverse shock of the parent supernova remnant. Based on evolutionary theory of PWNe, we consider that, when the PWN was disrupted during collision by the reverse shock, some very high-energy electrons escaped impulsively. The remaining electrons stayed in the relic PWN, which was displaced from the pulsar. The very high-energy part of the remaining electrons were depleted by the strong magnetic field that was enhanced by the reverse shock compression in the reverberation stage, leaving the other part of them generating GeV emission. The particles injected from the pulsar after the disruption enter the relic PWN through the newly formed tunnel called the cocoon. The $\gamma$-ray emission from the escaped electrons can account for the TeV spectrum of component A of HESS J1809$-$193 or the TeV halo, while the electrons remaining after disruption can account for the GeV spectrum of J1810.3$-$1925e. Thus, combination of contributions from these two populations of electrons naturally reproduces the saddle-like SED of HESS J1809$-$193 and J1810.3$-$1925e from 5 GeV to 30 TeV, together with the spectral hardening around 100 GeV. We also show that the post-disruption injection of electrons can explain the spectrum of the relatively faint $\gamma$-ray emission of component B of HESS J1809$-$193.