Left panels: time-evolving observer frame photon spectrum without absorption on extragalactic background light (top panel) and electron distribution (bottom panel) from the forward shock together with an additional photon injection term that roughly represents prompt GRB emission. The electron distributions are plotted as a function of the dimensionless electron momentum p (Eq. (1)) instead of γ (note that p → γ for γ ≫ 1). The number of electrons per unit dimensionless momentum is N(p) ≡ dn/dp. The parameters of the forward shock emission are E₀ = 1.4 × 10⁵⁵ erg, n₀ = 3 × 10^-2 cm^-3, ϵ_e = 0.2, ϵ_B = 10^-6, Γ₀ = 800 and s = 2.4. The injected photons are distributed according to a Band function, with the parameters α = −0.61, β = −3.8 and E_pk = 730 keV (as defined in Eq. (24)). The Band function cuts off at E = 1 GeV and the injection lasts for t = 22 s, after which the photon luminosity decreases exponentially with time. The GRB takes place at z = 1.8. The black long-dashed lines show the photon and electron distributions at t = 0.1 s without pair production, and the solid magenta line in the bottom left panel represents the positron distribution at t = 0.1 s. Right panels: the evolution of the observer frame photon spectrum (top panel) and electron distribution (bottom panel) without photon injection. The forward shock parameters are same as in the simulation presented in the left panels.