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Synchrotron and inverse-Compton emissions from pairs formed in GRB afterglows (analytical treatment)

We calculate the synchrotron and inverse-Compton emissions from pairs formed in GRB afterglows from high-energy photons (above 100 MeV), assuming a power-law photon spectrum C_nu ~ nu^{-2} and 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 Phi (t) = Ft and spectrum, and by the Lorentz factor Gamma and magnetic field B of the source of high-energy photons, at observer-time t. Optical and X-ray pseudo--light-curves F_nu (Gamma) are calculated for given B; proper synchrotron self-Compton light-curves are calculated by setting the dynamics Gamma(t) of the high-energy photons 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 and of the faster-decaying X-ray plateaus observed during the delayed (afterglow) phase. The brightest pair optical emission is obtained for 100 < Gamma < 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 LAT fluence, or through modeling of the afterglow multiwavelength data.