C. Light Curves for the early radiative phase
If the electrons' energy is large (namely if e is not far from unity), then early on during the first few hours of the afterglow there will be a radiative phase in which a significant fraction of the kinetic energy is lost via the radiative processes. One can generalize the BM solution to this radiative stage (see Cohen et al.  and Section VIIA). The essence of the radiative phase is that in this case the energy varies as E , where (R / L)-3. Note that L is calculated in terms of M and the initial energy of the explosion, E0, via M = E0 / 0 c2, where 0 is the initial Lorentz factor of the ejecta:
The transition time from the radiative to the adiabatic phase takes place when the radiation losses become negligible. This happens at:
Following Sari et al.  one can use the above expressions to express the different typical frequencies and fluxes as:
Like in the adiabatic case this can be translated to the times of passage of the break frequencies at a given observed frequency:
Unlike the adiabatic case, here c must be below m. Otherwise the bulk of the electrons do not cool and the system won't be radiative. Indeed at trad (given by Eq. 94 above) c = m.