Exercise 2: For typical short-duration GRB afterglow parameters, calculate the locations of the various break frequencies and the flux at X-ray (4e17 Hz), optical (4e14 Hz), and radio (4e9 Hz) wavelengths at a time of 12 hours after the burst.  How do these sensitivities compare to various telescopes?

While the first afterglow of long-duration GRBs were discovered in 1997, it was not until nearly a decade later that the first afterglows of short GRBs were identified.  Both the energy scale and density scale of the circumburst medium are significantly lower for short-duration GRBs, which make their afterglows significantly more challenging to detect.  The first short-duration GRB with a long-wavelength counterpart was GRB050509B (Figure 7), where the X-ray afterglow (a mere 11 photons) was identified by the X-ray Telescope on the Neil Gehrels Swift Observatory \cite{Gehrels_2005}.  Shortly thereafter, the first optical (GRB050709) and radio (GRB050724) afterglows were discovered.  Immediately the population of host galaxies was starkly different from the heavily star-forming galaxies that dominate the long-duration GRB population (see below).