We predict the rate at which gamma-ray burst (GRB) afterglows should be detected in supernova (SN) searches as a function of limiting flux. Although GRB afterglows are rarer than supernovae (SNs), they are detectable at greater distances because of their higher intrinsic luminosity. Assuming that GRBs trace the cosmic star formation history and that every GRB gives rise to a bright afterglow, we find that the average detection rate of SNs and afterglows should be comparable at limiting magnitudes brighter than K = 18. The actual rate of afterglows is expected to be somewhat lower since only a fraction of all gamma-ray-selected GRBs were observed to have associated afterglows. Hence, current and future SN searches can place strong constraints on the afterglow appearance fraction of GRB sources.
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