Search for small-scale arrival direction correlations driven by transformer-based cosmic-ray-mass estimators at the Pierre Auger Observatory

RWTH Publications (RWTH Aachen)

Abstract

In the search for sources of ultra-high-energy cosmic rays, deflections in cosmic magnetic fields pose a particular challenge. Information regarding the mass and therefore charge of the particles play a crucial role, as they, together with the energy, enable data selections that reduce the degree of deflection and thus potentially increase overdensities in source directions. As the particles interact with the atmosphere, extended air showers are formed, whose properties such as the atmospheric depth $X_\mathrm{max}$ and the muon content $R_\mu$ provide estimators of the particle mass. In this work, a deep Transformer neural network is developed to reconstruct $X_\mathrm{max}$ and $R_\mu$ from air shower measurements at the Pierre Auger Observatory. To analyze the measurements from multiple stations of the surface detector, an efficient Performer is employed to characterize the temporal evolution of the photomultiplier traces of individual Water Cherenkov Detectors (WCDs), followed by a Vision Transformer that takes the spatial distribution of the stations into account. The future-proof architecture also allows for the consideration and complementary processing of additional detectors, such as the scintillator (SSD) of the AugerPrime upgrade. Simulations are used to train and evaluate the network. The performance and working principle of the architecture are investigated both for the case of measurements with only WCDs, as well as the combination of WCD and SSD, with the latter providing an estimate of the potential improvement by the SSD. The network is applied to WCD measurements of the Pierre Auger Observatory to obtain a dataset that includes mass estimators. Based on physical considerations, selections are designed that select events as a function of energy, $X_\mathrm{max}$ and the combination of $X_\mathrm{max}$ and $R_\mu$, with the goal of isolating datapoints with reduced deflections in magnetic fields. The exact properties of the selections are optimized on simulations to maximize overdensities in autocorrelations at small angular scales. The analysis strategy is based on the combination of a selection of light particles with a selection of a narrow band in $X_\mathrm{max}$. Despite this pre-selection, no overdensities in autocorrelations are found in the application to data, with a combined significance of $0.78\sigma$. A comparison with simulations enables the determination of a lower limit for the density of ultra-high-energy cosmic-ray sources. Under the assumption of a homogeneous source distribution and using the JF12 magnetic field model, a lower limit of $\rho_\mathrm{lim}^{95} = 5.3^{+0.9}_{-1.1}\cdot10^{-4}\,\mathrm{Mpc}^{-3}$ is found at $95\,\%$ confidence level, compatible with previous results.

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