The Beaming Pattern and Spectrum of Radiation from Inverse Compton Scattering in Blazars

Abstract

By including Klein-Nishina effects, we generalize previous calculations of the beaming pattern of photons produced by inverse Compton scattering. For an isotropic distribution of soft photons upscattered by nonthermal electrons with a power-law density distribution n(γ) ∝ γ-p, embedded in a plasma moving with relativistic bulk speed, we show that the observed radiation intensity is proportional to D3+p, where D is the Doppler boosting factor. This agrees with previous computations performed in the Thomson limit, where the observed spectral index is α = (p - 1)/2 and the beaming pattern is D4+2α. Independent of D, Klein-Nishina effects limit the location of the peak energy peakmec2 of the observed spectral energy distribution such that peak ≲ 1/0, where 0 is the energy of the seed photons in units of mec2. Assuming that the seed photons originate in the broad-line region, we demonstrate that the GeV emission of blazars is significantly modified by Klein-Nishina effects, the spectrum being softer than that calculated in the Thomson limit. We further show that the change in the spectral index of the inverse Compton emission across peak can exceed the value of 0.5 predicted by computations performed in the Thomson limit. The model spectra agree with OSSE and COMPTEL limits on this break without invoking the effects of differential absorption at the edge of a gamma-ray photosphere.