Afterglow spectra of the fiducial example at different observation times. A constant pressure profile is adopted for the shocked blast region. Equation (1) is used to calculate the cooling history of electron energies. The curvature effect is also fully taken into account. The following parameters are adopted: L _ej(τ) = L ₀ = 10 ⁵² erg s ⁻¹, τ _b = 5 s, E _b = 5 × 10 ⁵² erg, n ₁ = 1cm ⁻³, Γ _ej = 300, z = 1, p = 2.3, and _e = 0.1. Top left: the slow cooling case with _B = 0.001. Bottom left: spectral index β evolution as a function of observer time t _obs for the slow cooling case, which shows a very slow transition of ν _c crossing. Top right: the fast cooling case with _B = 0.1. Bottom right: β evolution for the fast cooling case.