  Observations of gamma-ray burst (GRB) afterglows have long provided the most
detailed information about the origin of this spectacular phenomena. The model
that is most commonly used to extract physical properties of the event from the
observations is the relativistic fireball model, where ejected material moving
at relativistic speeds creates a shock wave when it interacts with the
surrounding medium. Electrons are accelerated in the shock wave, generating the
observed synchrotron emission through interactions with the magnetic field in
the downstream medium. It is usually assumed that the accelerated electrons
follow a simple power-law distribution in energy between specific energy
boundaries and that no electron exists outside these boundaries. This work
explores the consequences of adding a low-energy power-law segment to the
electron distribution whose energy contributes insignificantly to the total
energy budget of the distribution. The low-energy electrons have a significant
impact on the radio emission, providing synchrotron absorption and emission at
these long wavelengths. Shorter wavelengths are affected through the
normalization of the distribution. The new model is used to analyze the light
curves of GRB 990510 and the resulting parameters compared to a model without
the extra electrons. The quality of the fit and the best fit parameters are
significantly affected by the additional model component. The new component is
in one case found to strongly affect the X-ray light curves showing how changes
to the model at radio frequencies can affect light curves at other frequencies
through changes in best fit model parameters.
