Energetic Constraints on a Rapid Gamma-Ray Flare in PKS 1222+216
  We study theoretical implications of a rapid Very-High-Energy (VHE) flare
detected by MAGIC in the Flat-Spectrum Radio Quasar PKS 1222+216. The minimum
distance from the jet origin at which this flare could be produced is 0.5 pc. A
moderate Doppler factor of the VHE source, D_{VHE} ~ 20, is allowed by all
opacity constraints. The concurrent High-Energy (HE) emission observed by Fermi
provides estimates of the total jet power and the jet magnetic field strength.
Energetic constraints for the VHE flare are extremely tight: for an isotropic
particle distribution they require a huge co-moving energy density in the
emitting region and a very efficient radiative process. We disfavor hadronic
processes due to their low radiative efficiency, as well as the synchrotron
scenario recently proposed for the case of HE flares in the Crab Nebula, since
the parameters needed to overcome the radiative losses are quite extreme. The
VHE emission can be explained by the Synchrotron Self-Compton (SSC) mechanism
for D_{VHE} ~ 20 or by the External Radiation Compton (ERC) mechanism involving
the infrared radiation of the dusty torus for D_{VHE} ~ 50. After discussing
several alternative scenarios, we propose that the extreme energy density
constraint can be satisfied when the emission comes from highly anisotropic
short-lived bunches of particles formed by the kinetic beaming mechanism in
magnetic reconnection sites. By focusing the emitting particles into very
narrow beams, this mechanism allows one to relax the causality constraint on
the source size, decreasing the required energy density by 4 orders of
magnitude.
