Afterglow Properties
Shortly after inference of ultra-relativistic ejecta in GRBs, it was realized that GRBs should also give rise to longer-lived, panchromatic emission that we call the "afterglow" \cite{Meszaros_1993}. While the "prompt" gamma-ray emission arises from some process internal to the ejecta, the expanding blastwave will eventually accelerate electrons in the circumburst medium, which will then emit broadband synchrotron radiation. Confirmation of this prediction of X-ray, optical, and radio afterglows in 1997 following GRBs stands as one of the preeminent accomplishments of modern theoretical astrophysics.
The broadband spectrum resulting from this afterglow emission can be described in terms of three characteristic frequencies \cite{Sari1998}, shown for the "slow cooling" regime in Figure 6. For expansion into a constant density medium, these frequencies can be calculated as: