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We consider the active galactic nuclei (AGN) consisting of a super massive non-rotating black hole and a standard accretion disk. We calculate the optical depth of the high energy gamma-rays which results from the thermal radiation of the accretion disk. The calculation of the optical depth is based on the $\alpha$-disk model proposed by Shakura and Sunyaev (1972). We find that the choice of value of $\alpha$, mass of the black hole and the accretion rate can significantly affect the optical depth. Furthermore, photons with energies larger than 0.1GeV cannot escape from this thermal radiation field for a wide range of parameters if the emission region is closed to the black hole. Therefore, the time variability of the EGRET data cannot be interpreted as the position of the emission region. We conclude that the optical depth of the thermal radiation puts strong constrant on the position of the emission region.
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