The local energy production rates of GRB photons and of UHECRs

In a recent analysis it was found that the local (z=0) rate at which gamma-ray bursts (GRBs) produce energy in 1 MeV photons, Q_GRB(z=0), is 300 times lower than the local energy production rate in ultra-high energy cosmic-rays. This may appear to be in contradiction with earlier results, according to which Q_GRB(z=0) is similar to the local energy production rate in

10^{19} eV cosmic-rays, Q_{10EeV}(z=0). This short (1 page) note identifies the origin of the apparent discrepancy and shows that Q_GRB(z=0) \sim Q_{10EeV}(z=0) holds.