Explaining the characteristics of lateral shower age of cosmic ray extensive air showers

Abstract

A simple analytical argument is proposed for a possible explanation of the characteristics of the lateral shower age (s) of proton (p)/nuclei-initiated showers. The argument states that the lateral density distribution (LDD) of electrons of a p-initiated shower is due to the superposition of several electromagnetic (EM) sub-showers developed at a very early stage in the atmosphere from the decay of neutral pions ( $$\pi ^{0}$$ s). Thanks to the superposition property of the electron LDD in a p shower, a plausible analytical parametrisation has been worked out by giving a well represented lateral density function for the electron LDDs of p- and $$\pi ^{0}$$ -initiated showers. Based on cosmic ray extensive air shower simulations, we have validated how the various characteristics of s can be understood in the context of the proposed argument. The s parameter of a p shower and its correlations with the shower ages of electron- and $$\pi ^{0}$$ -initiated showers support the idea that the result of superposition of several EM sub-showers initiated by $$\pi ^{0}$$ s with varied energies at a very early stage might produce the LDD of electrons of a p shower. It is also noticed with the simulated data that the present conjecture works well relating to the notion of the local shower age parameter.