Model for the High-Energy Emission from Blazars

Approximate formulae for the instantaneous scattered radiation spectra are derived in the Thomson and Klein-Nishina regimes, assuming that the relativistic electrons are described by an isotropic angular and power-law energy distribution in the outflowing fluid frame. The soft photon source is assumed to be axially symmetric. We find that the Thomson-limit luminosity enhancement in the direction that the scattered radiation is most intense varies as Γ6 for photons entering from the side and as Γ² for photons entering directly from behind, where Γ is the bulk Lorentz factor of the outflowing plasma cloud. Energy loss and flow are treated in a model where energetic electrons are instantaneously injected with a power-law energy distribution at some height above a point or disk photon source, and instantaneous and time-average spectra are calculated. We also treat the electron energy-loss rate and scattered photon spectra from photon fields that are isotropic in the stationary frame. We calculate broad-band spectra for the case where soft photons are produced by a cool blackbody outer disk extending to the innermost stable orbit of a Schwarzschild black hole, and fit these results to observations of high-energy radiation from 3C 279, 3C 273, and Mrk 421. The observed spectral softening in the regime between hard X-ray and >100 MeV gamma-ray energies is attributed to the transition from an uncooled to a cooling electron distribution, yielding a break of 0.5 units in the scattered photon spectra index.