Discerning the $\gamma$-ray emitting region in the flat spectrum radio quasars

A model-dependent method is proposed to determine the location of the $\gamma$-ray emitting region for a given flat spectrum radio quasar (FSRQ). In the model, the extra-relativistic electrons are injected at the base of the jet and non-thermal photons are produced by both synchrotron radiation and inverse-Comtpon (IC) scattering in the energy dissipation region. The target photons dominating inverse-Comtpon scattering originate from both synchrotron photons and external ambient photon fields, and the energy density of external radiation field is a function of the distance between the position of dissipation region and a central super-massive black hole, and their spectra are seen in the comoving frame. Moreover, the energy dissipation region could be determined by the model parameter through reproducing the $\gamma$-ray spectra. Such a model is applied to reproduce the quasi-simultaneous multi-wavelength observed data for 36 FSRQs. In order to define the width of the broad-line region shell and dusty molecular torus shell, a simple numerical constraint is used to determine the outer boundary of the broad-line region and dusty molecular torus. Our results show that 1) the $\gamma$-ray emitting regions are located at the range from 0.1 pc to 10 pc; 2) the $\gamma$-ray emitting regions are located outside the broad-line regions and within the dusty molecular tori; and 3) the $\gamma$-ray emitting region are located closer to the dusty molecular torus ranges than the broad-line regions. Therefore, it may concluded that a direct evidence for the \emph{far site} scenario could be obtained on the basis of the model results.