Abstract
The atmospheric depth of the air shower maximum X max is an observable commonly used for the determination of the nuclear mass composition of ultra-high energy cosmic rays.Direct measurements of X max are performed using observations of the longitudinal shower development with fluorescence telescopes.At the same time, several methods have been proposed for an indirect estimation of X max from the characteristics of the shower particles registered with surface detector arrays.In this paper, we present a deep neural network (DNN) for the estimation of X max. The reconstruction relies on the signals induced by shower particles in the ground based water-Cherenkov detectors of the Pierre Auger Observatory.The network architecture features recurrent long short-term memory layers to process the temporal structure of signals and hexagonal convolutions to exploit the symmetry of the surface detector array.We evaluate the performance of the network using air showers simulated with three different hadronic interaction models. Thereafter, we account for long-term detector effects and calibrate the reconstructed X max using fluorescence measurements. Finally, we show that the event-by-event resolution in the reconstruction of the shower maximum improves with increasing shower energy and reaches less than 25 g/cm2 at energies above 2 × 1019 eV.
Highlights
When changing the hadronic interaction model for the evaluation of the network, we find that only the absolute bias in the Xmax reconstruction changes
A high statistics measurement of the first moment Xmax and the second moment σ(Xmax) using the deep neural network reconstruction of the water-Cherenkov detectors (WCDs)-signal traces has a great potential to provide new insights into the cosmic-ray composition at the highest energies
Summary
The measured air shower footprint consists of a characteristic pattern of several triggered WCDs arranged in a hexagonal grid (see figure 1(a)). An example of a simulated signal trace is shown in figure 1(b). The raw information for each triggered station consists of three signal time traces, the station position and the time of the first shower particles arriving at the station. For successful adjustment of the network parameters, careful preparations of the data sets from simulation campaigns used for the optimization process are crucial. The parameters can be set more if the numerical values of the input variables do not vary considerably. Both the amplitudes and the time values of the WCD-signal traces are re-scaled prior to their input into the network. We specify the data sets from simulation campaigns, and data with information from the FD used to validate the Xmax reconstruction of the deep neural network
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