On the influence of statistics on the determination of the mean value of the depth of shower maximum for ultra high energy cosmic ray showers

Abstract

The chemical composition of ultra high energy cosmic rays is still uncertain. The latest results obtained by the Pierre Auger Observatory and the HiRes collaboration, concerning the measurement of the mean value and the fluctuations of the atmospheric depth at which the showers reach the maximum development, X max, are inconsistent. From comparison with air shower simulations it can be seen that, while the Auger data may be interpreted as a gradual transition to heavy nuclei for energies larger than 2-3 × 10 18eV, the HiRes data are consistent with a composition dominated by protons. In Wilk and Wlodarczyk (2011 J. Phys. G: Nucl. Part. Phys. 38 085201), it is suggested that a possible explanation for the observed deviation of the mean value of X max from the proton expectation, observed by Auger, could originate in a statistical bias arising from the approximated exponential shape of the X max distribution, combined with the decrease of the number of events as a function of primary energy. In this paper, we consider a better description of the X max distribution and show that the possible bias in the Auger data is at least one order of magnitude smaller than the one obtained when assuming an exponential distribution. Therefore, we conclude that the deviation of the Auger data from the proton expectation is unlikely to be explained by such statistical effect. © 2012 IOP Publishing Ltd.