The effect of adiabatic cooling on the fast cooling synchrotron spectrum in presence of inverse Compton scatterings. The normalized synchrotron spectrum defined by is plotted as a function of the normalized frequency ν/ν_m, as well as the corresponding photon index dlnu_ν/dlnν − 1. All spectra in thick solid line are computed numerically using a detailed radiative code including synchrotron radiation, inverse Compton scatterings and adiabatic cooling (see text). Spectra in thin dotted line are computed without inverse Compton scatterings. All other processes (synchrotron self-absorption, γγ annihilation) are neglected. Each panel corresponds to a different set of parameters indicated in the top-left corner. In each panel, spectra are plotted for increasing ratios Γ_c/Γ_m = 0.01, 0.1, 1 and 10. As in Fig. 2, the maximum Lorentz factor of electrons is computed with a fixed ratio Γ_max/Γ_min = 10⁴. Spectra in dashed lines are radiatively inefficient (slow cooling regime). The table inserted in each panel lists the values of the radiative efficiency f_rad of the electrons.