Low Statistics of EHECRs

Abstract

The nature of the unknown sources of ultra-high energy cosmic rays can be revealed through the detection of the GZK feature in the cosmic ray spectrum. The only two experiments that have probed this energy range, AGASA and HiRes, have apparently conflicting results. HiRes measured a flux consistent with the GZK feature while AGASA reported a larger than expected flux of so-called Super-GZK particles. Here we emphasize that neither experiment has gathered the statistics necessary for making a definitive measurement of the GZK cutoff. The photo-pion production responsible for the GZK feature is stochastic for energies around the cutoff leading to large fluctuations of the spectrum for low statistics measurements. We show that the results from AGASA and HiRes results are within about $ 2 σ$ of one another by simulating 400 spectra for a range of input spectral indices normalized to the number of events above $10^{19}$ eV for each experiment. If a 15% systematic correction in energy is applied to both experiments, the agreement between the experiments improves considerably and the best fit input spectral index becomes $\sim 2.6$ for both data sets. Our results clearly show the need for much larger experiments such as Auger and EUSO, that can increase the number of detected events by 2 orders of magnitude. Only large statistics experiments can finally prove or disprove the existence of the GZK feature in the cosmic ray spectrum.