On the Estimation of the Depth of Maximum of Extensive Air Showers Using the Steepness Parameter of the Lateral Distribution of Cherenkov Radiation

TL;DR

This paper presents a method to estimate the maximum depth of extensive air showers using Cherenkov radiation data, achieving about 9 g/cm^2 accuracy, and explores estimating the primary particle's mass from the same data.

Contribution

The paper introduces a quadratic model linking the Cherenkov light distribution steepness parameter to the shower maximum depth and an exponential relation to estimate the primary particle's mass.

Findings

Average difference in $X_{max}$ estimation is about 9 g/cm^2.

Mass estimation of primary particles has an average error less than 0.5 atomic mass units.

Model tested on simulated data shows promising accuracy.

Abstract

Using Monte Carlo simulation of extensive air showers, we showed that the maximum depth of showers, $X_{max}$ can be estimated using $P=Q(100)/Q(200)$, the ratio of Cherenkov photon densities at 100 and 200 meters from the shower core, which is known as the steepness parameter of the lateral distribution of Cherenkov radiation on the ground. A simple quadratic model has been fitted to a set of data from simulated extensive air showers, relating the steepness parameter and the shower maximum depth. Then the model has been tested on another set of simulated showers. The average difference between the actual maximum depth of the simulated showers and the maximum depth obtained from the lateral distribution of Cherenkov light is about 9 $g/cm^2$. In addition, possibility of a more direct estimation of the mass of the initial particle from $P$ has been investigated. An exponential relation between these two quantities has been fitted. Applying the model to another set of showers, we found that the average difference between the estimated and the actual mass of primary particles is less than 0.5 atomic mass unit.