Effects of the energy error distribution of fluorescence telescopes on the UHECR energy spectrum

The measurement of the ultra high energy cosmic ray (UHECR) spectrum is strongly affected by uncertainties on the reconstructed energy. The determination of the presence or absence of the GZK cutoff and its position in the energy spectrum depends not only on high statistics but also on the shape of the energy error distribution. Here, we determine the energy error distribution for fluorescence telescopes, based on a Monte Carlo simulation. The HiRes and Auger fluorescence telescopes are simulated in detail. We analyze the UHECR spectrum convolved with this energy error distribution. We compare this spectrum with one convolved with a lognormal error distribution as well as with a Gaussian error distribution. We show that the energy error distribution for fluorescence detectors cannot be represented by these known distributions. We conclude that the convolved energy spectrum will be smeared but not enough to affect the GZK cutoff detection. This conclusion stands for both HiRes and Auger fluorescence telescopes. This result differs from the effect of the energy error distribution obtained with ground detectors and reinforces the importance of the fluorescence energy measurement. We also investigate the effect of possible fluorescence yield measurement errors in the energy spectrum.