External Compton Radiation from Rapid Nonthermal Flares in Blazars
  In this paper we extend our approach to modeling multifrequency emission variability from blazars to include external-radiation Compton (ERC) emission and electron energy losses from inverse Compton scattering of seed photons originating outside the jet. We consider seed-photon emission from a dusty molecular torus and the broad line region (BLR) surrounding the central engine. We establish constraints on the properties of the molecular torus and BLR under which synchrotron self-Compton (SSC) emission dominates such that the results obtained in our previous paper are applicable. The focus of this study is on relative time delays between the light curves observed at different frequencies. For definiteness, we consider emission resulting from a collision between relativistic shocks, but the results apply more generally to conditions involving acceleration of relativistic electrons and/or magnetic field amplification at any type of front. Unlike SSC emission, ERC flares involving a constant field of seed photons are not delayed by light travel time of the seed photons. The main cause of delays is from radiative energy losses, which result in frequency stratification behind the front and quench the flare first at the highest frequencies, progressing to lower frequencies as time advances. However, if the spectrum of electrons injected at the shock front is characterized by a relatively high value of the minimum energy (a Lorentz factor $\gamma_{min}\sim100$ is sufficient), the ERC flare in the X-ray band can be delayed and may even peak after the injection has ceased. This effect is strongly frequency dependent, with a longer lag at lower frequencies and an X-ray spectral index that changes rapidly from positive (inverted spectrum) to steep values. 
Andrei Sokolov and Alan P. Marscher