External Compton Scattering in Blazar Jets and the Location of the Gamma-Ray Emitting Region

I study the location of the $\gamma$-ray emission in blazar jets by creating a Compton-scattering approximation valid for all anisotropic radiation fields in the Thomson through Klein-Nishina regimes, which is highly accurate and can speed up numerical calculations by up to a factor $\sim10$. I apply this approximation to synchrotron self-Compton, and external Compton-scattering of photons from the accretion disk, broad-line region (BLR), and dust torus. I use a stratified BLR model and include detailed Compton-scattering calculations of a spherical and flattened BLR. I create two dust torus models, one where the torus is an annulus, and one where it is an extended disk. I present detailed calculations of the photoabsorption optical depth using my detailed BLR and dust torus models, including the full angle dependence. I apply these calculations to the emission from a relativistically moving blob traveling through these radiation fields. The ratio of $\gamma$-ray to optical flux produces a predictable pattern that could help locate the $\gamma$-ray emission region. I show that the bright flare from 3C 454.3 in 2010 November detected by the Fermi Large Area Telescope is unlikely to originate from a single blob inside the BLR since it moves outside the BLR in a time shorter than the flare duration, although emission by multiple blobs inside the BLR is possible; and $\gamma$-rays are unlikely to originate from outside the BLR from scattering of photons from an extended dust torus, since then the cooling timescale would be too long to explain the observed short variability.