**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.
[58]
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, *E*_{0}, via *M* = *E*_{0} /
_{0}
*c*^{2}, where
_{0} is
the initial Lorentz factor of the ejecta:

(93) |

The transition time from the radiative to the adiabatic phase takes place when the radiation losses become negligible. This happens at:

(94) |

Following Sari et al. [376] one can use the above expressions to express the different typical frequencies and fluxes as:

(95) |

Like in the adiabatic case this can be translated to the times of passage of the break frequencies at a given observed frequency:

(96) |

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 *t*_{rad} (given by Eq. 94
above) _{c} =
_{m}.