The Use of the Signal at an Optimal Distance from the Shower Core as a Surrogate for Shower Size

Abstract

When analysing data from air-shower arrays, it has become common practice to use the signal at a considerable distance from the shower axis ($r_\text{opt}$) as a surrogate for the size of the shower. This signal, $S(r_\text{opt}$), can then be related to the primary energy in a variety of ways. After a brief review of the reasons behind the introduction of $r_\text{opt}$ laid out in a seminal paper by Hillas in 1969, it will be shown that $r_\text{opt}$, is a more effective tool when detectors are laid out on a triangular grid than when detectors are deployed on a square grid. This result may have implications for explaining the differences between the flux observed by the Auger and Telescope collaborations above 10\,EeV and should be kept in mind when designing new shower arrays.