The non-linearity between <ln A> and <Xmax> induced by the acceptance of fluorescence telescopes

TL;DR

This paper investigates how the finite field-of-view and atmospheric attenuation of fluorescence telescopes introduce non-linearity in the relationship between the average depth of shower maximum and the logarithm of primary cosmic-ray mass, affecting data interpretation.

Contribution

It demonstrates that detector acceptance effects cause a non-linear relation between <Xmax> and <ln A>, which varies with each telescope setup, complicating cosmic-ray composition analysis.

Findings

Acceptance effects induce non-linearity in <Xmax>-<ln A> relation.

The non-linearity is specific to each detector configuration.

Implications for comparing cosmic-ray data across experiments.

Abstract

The measurement of the average depth of the shower maximum is the most commonly used observable for the possible inference of the primary cosmic-ray mass composition. Currently, different experimental Collaborations process and present their data not in the same way, leading to problems in the comparability and interpretation of the results. Whereas <Xmax> is expected to be proportional to <ln A> in ideal conditions, we demonstrate that the finite field-of-view of fluorescence telescopes plus the attenuation in the atmosphere can introduce a non-linearity into this relation, which is specific for each particular detector setup.