Electron Acceleration In Blazars: Application to the 3C 279 Flare on 2013 December 20

The broadband spectrum from the 2013 December 20 $\gamma$-ray flare from 3C~279 is analyzed with our previously-developed one-zone blazar jet model. We are able to reproduce two SEDs, a quiescent and flaring state, the latter of which had an unusual SED, with hard $\gamma$-ray spectrum, high Compton dominance, and short duration. Our model suggests that there is insufficient energy for a comparable X-ray flare to have occurred simultaneously, which is an important constraint given the lack of X-ray data. We show that first- and second-order Fermi acceleration are sufficient to explain the flare, and that magnetic reconnection is not needed. The model includes particle acceleration, escape, and adiabatic and radiative energy losses, including the full Compton cross-section, and emission from the synchrotron, synchrotron self-Compton, and external Compton processes. We provide a simple analytic approximation to the electron distribution solution to the transport equation that may be useful for simplified modeling in the future.