Effect of a decaying magnetic field on the synchrotron spectrum: Realistic case including inverse Compton scatterings. The normalised synchrotron spectrum νu_ν/u_e as well as the photon index are plotted as a function of the normalised frequency $\nu \prime /\nu {\prime }_{\mathrm{m}}$ for a constant magnetic field (black) or a decaying magnetic field on a timescale of $t{\prime }_{\mathrm{B}}/t{\prime }_{\mathrm{dyn}}={10}^{-1}$ (red) and 10⁻² (blue). The calculation includes adiabatic cooling, synchrotron radiation, and inverse Compton scatterings but does not take into account synchrotron self-absorption and pair production. Each panel corresponds to a different value of the parameter w_m, which measures the importance of Klein-Nishina effects, from 10⁻² (Thomson regime) to 10⁴ (strong Klein-Nishina regime). The spectra are plotted for Y_Th = 10⁻¹, 1, 10, 10², 10³, and 10⁴, which corresponds to an increasing efficiency of scatterings (see text). We assumed everywhere an electron slope p = 2.5 and a magnetic field B′₀ in the acceleration site corresponding to Γ_c/Γ_m = 1/300.