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Deep-Learning based Reconstruction of the Shower Maximum $X_{mathrm{max}}$ using the Water-Cherenkov Detectors of the Pierre Auger Observatory

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 Added by Jonas Glombitza
 Publication date 2021
  fields Physics
and research's language is English




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The atmospheric depth of the air shower maximum $X_{mathrm{max}}$ is an observable commonly used for the determination of the nuclear mass composition of ultra-high energy cosmic rays. Direct measurements of $X_{mathrm{max}}$ 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 $X_{mathrm{max}}$ 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 $X_{mathrm{max}}$. 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 $X_{mathrm{max}}$ 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 $25~mathrm{g/cm^{2}}$ at energies above $2times 10^{19}~mathrm{eV}$.



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Cosmic rays arriving at Earth collide with the upper parts of the atmosphere, thereby inducing extensive air showers. When secondary particles from the cascade arrive at the ground, they are measured by surface detector arrays. We describe the methods applied to the measurements of the surface detector of the Pierre Auger Observatory to reconstruct events with zenith angles less than $60^circ$ using the timing and signal information recorded using the water-Cherenkov detector stations. In addition, we assess the accuracy of these methods in reconstructing the arrival directions of the primary cosmic ray particles and the sizes of the induced showers.
The Auger Surface Detector consists of a large array of water Cherenkov detector tanks each with a volume of 12,000 liters, for the detection of high energy cosmic rays. The accuracy in the measurement of the integrated signal amplitude of the detector unit has been studied using experimental air shower data. It can be described as a Poisson-like term with a normalization constant that depends on the zenith angle of the primary cosmic ray. This dependence reflects the increasing contribution to the signal of the muonic component of the shower, both due to the increasing muon/electromagnetic (e+- and gamma) ratio and muon track length with zenith angle.
Muons decaying in the water volume of a Cherenkov detector of the Pierre Auger Observatory provide a useful calibration point at low energy. Using the digitized waveform continuously recorded by the electronics of each tank, we have devised a simple method to extract the charge spectrum of the Michel electrons, whose typical signal is about 1/8 of a crossing vertical muon. This procedure, moreover, allows continuous monitoring of the detector operation and of its water level. We have checked the procedure with high statistics on a test tank at the Observatory base and applied with success on the whole array.
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