Synchrotron and inverse-Compton emissions from pairs formed in GRB afterglows (Analytical Treatment)

Abstract

We calculate the synchrotron and inverse-Compton emissions from pairs formed in gamma-ray burst (GRB) afterglows from high-energy photons (above 100 MeV), assuming a power-law photon spectrum C ν∝ν-2and considering only the pairs generated from primary high-energy photons. The essential properties of these pairs (number, minimal energy, cooling energy, distribution with energy) and of their emission (peak flux, spectral breaks, spectral slope) are set by the observables GeV fluence Φ(t) = Ft and spectrum, and by the Lorentz factor, Γ, and magnetic field, B, of the source of high-energy photons, at observer time, t. Optical and X-ray pseudo light curves, F ν(Γ), are calculated for the given B; proper synchrotron self-Compton light curves are calculated by setting the dynamics Γ(t) of the high-energy photon source to be that of a decelerating, relativistic shock. It is found that the emission from pairs can accommodate the flux and decays of the optical flashes measured during the prompt (GRB) phase, but it decays faster than the X-ray plateaus observed during the delayed (afterglow) phase. The brightest pair optical emission is obtained for 100 < Γ < 500, and depends mostly on the GeV fluence, being independent of the source redshift. Emission from pairs formed during the GRB phase offers an alternate explanation to reverse-shock optical flashes. These two models may be distinguished based on their corresponding flux decay index-spectral slope relations, different correlations with the Large Area Telescope fluence, or through modeling of the afterglow multiwavelength data.