Deep-learning based reconstruction of the shower maximum X$_{max}$ using the water-Cherenkov detectors of the Pierre Auger Observatory
A. Aab, P. Abreu, M. Aglietta, Justin M. Albury, I. Allekotte, A. Almela, Jaime Álvarez-Muñiz, Rafael Alves Batista, Gioacchino Alex Anastasi, Luis A. Anchordoqui, Belén Andrada, S. Andringa, C. Aramo, Paulo Ricardo Araújo Ferreira, Juan Carlos Arteaga Velázquez, H. Asorey, P. Assis, G. Ávila, Alina Mihaela Badescu, Alena Bakalová, A. Balaceanu, Felicia Barbato, Ricardo Jorge Barreira Luz, K.H. Becker, Jose A. Bellido, Corinne Bérat, M. E. Bertaina, X. Bertou, Peter L. Biermann, Teresa Bister, Jonathan Biteau, Jiří Blažek, C. Bleve, Boháčová, M., Denise Boncioli, C. Bonifazi, Luan Bonneau Arbeletche, Nataliia Borodai, Ana Martina Botti, J. Brack, T. Bretz, P. Gabriel Brichetto Orchera, F. L. Briechle, P. Buchholz, A. Bueno, S. Buitink, Mario Buscemi, K. S. Caballero‐Mora, Lorenzo Caccianiga, Fabrizia Canfora, Ioana Caracas, J. M. Carceller, R. Caruso, A. Castellina, Fernando Catalani, G. Cataldi, Lorenzo Cazon, M. Cerda, J. A. Chinellato, K. Choi, J. Chudoba, L. Chytka, R. W. Clay, Agustín Cobos Cerutti, Roberta Colalillo, Alan Coleman, M. R. Coluccia, R. Conceição, Antonio Condorelli, Giovanni Consolati, F. Contreras, Fabio Convenga, Diego Correia dos Santos, C. E. Covault, S. Dasso, K. Daumiller, B. R. Dawson, J.A. Day, R. M. de Almeida, Joaquín de Jesús, S. J. de Jong, G. De Mauro, De Mello Neto, J.R.T., I. De Mitri, Jaime de Oliveira, Danelise de Oliveira Franco, De Palma, F., De Souza, V., Emanuele De Vito, M. del Río, O. Deligny, Armando di Matteo, C. Dobrigkeit, J. C. D’Olivo, R. C. dos Anjos, M. T. Dova, Jan Ebr, R. Engel, Italo Epicoco, M. Erdmann
Abstract
The atmospheric depth of the air shower maximum Xmax is an observable commonly used for the determination of the nuclear mass composition of ultra-high energy cosmic rays. Direct measurements of Xmax 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 Xmax 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 Xmax. 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 Xmax 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.