Deep-learning based reconstruction of the shower maximum X max using the water-Cherenkov detectors of the Pierre Auger Observatory

Author:

Aab A.,Abreu P.,Aglietta M.,Albury J.M.,Allekotte I.,Almela A.,Alvarez-Muñiz J.,Alves Batista R.,Anastasi G.A.,Anchordoqui L.,Andrada B.,Andringa S.,Aramo C.,Araújo Ferreira P.R.,Arteaga Velázquez J.C.,Asorey H.,Assis P.,Avila G.,Badescu A.M.,Bakalova A.,Balaceanu A.,Barbato F.,Barreira Luz R.J.,Becker K.H.,Bellido J.A.,Berat C.,Bertaina M.E.,Bertou X.,Biermann P.L.,Bister T.,Biteau J.,Blazek J.,Bleve C.,Boháčová M.,Boncioli D.,Bonifazi C.,Bonneau Arbeletche L.,Borodai N.,Botti A.M.,Brack J.,Bretz T.,Brichetto Orchera P.G.,Briechle F.L.,Buchholz P.,Bueno A.,Buitink S.,Buscemi M.,Caballero-Mora K.S.,Caccianiga L.,Canfora F.,Caracas I.,Carceller J.M.,Caruso R.,Castellina A.,Catalani F.,Cataldi G.,Cazon L.,Cerda M.,Chinellato J.A.,Choi K.,Chudoba J.,Chytka L.,Clay R.W.,Cobos Cerutti A.C.,Colalillo R.,Coleman A.,Coluccia M.R.,Conceição R.,Condorelli A.,Consolati G.,Contreras F.,Convenga F.,Correia dos Santos D.,Covault C.E.,Dasso S.,Daumiller K.,Dawson B.R.,Day J.A.,de Almeida R.M.,de Jesús J.,de Jong S.J.,De Mauro G.,de Mello Neto J.R.T.,De Mitri I.,de Oliveira J.,de Oliveira Franco D.,de Palma F.,de Souza V.,De Vito E.,del Río M.,Deligny O.,Di Matteo A.,Dobrigkeit C.,D'Olivo J.C.,dos Anjos R.C.,Dova M.T.,Ebr J.,Engel R.,Epicoco I.,Erdmann M.,Escobar C.O.,Etchegoyen A.,Falcke H.,Farmer J.,Farrar G.,Fauth A.C.,Fazzini N.,Feldbusch F.,Fenu F.,Fick B.,Figueira J.M.,Filipčič A.,Fodran T.,Freire M.M.,Fujii T.,Fuster A.,Galea C.,Galelli C.,García B.,Garcia Vegas A.L.,Gemmeke H.,Gesualdi F.,Gherghel-Lascu A.,Ghia P.L.,Giaccari U.,Giammarchi M.,Giller M.,Glombitza J.,Gobbi F.,Gollan F.,Golup G.,Gómez Berisso M.,Gómez Vitale P.F.,Gongora J.P.,González J.M.,González N.,Goos I.,Góra D.,Gorgi A.,Gottowik M.,Grubb T.D.,Guarino F.,Guedes G.P.,Guido E.,Hahn S.,Hamal P.,Hampel M.R.,Hansen P.,Harari D.,Harvey V.M.,Haungs A.,Hebbeker T.,Heck D.,Hill G.C.,Hojvat C.,Hörandel J.R.,Horvath P.,Hrabovský M.,Huege T.,Hulsman J.,Insolia A.,Isar P.G.,Janecek P.,Johnsen J.A.,Jurysek J.,Kääpä A.,Kampert K.H.,Keilhauer B.,Kemp J.,Klages H.O.,Kleifges M.,Kleinfeller J.,Köpke M.,Kunka N.,Lago B.L.,Lang R.G.,Langner N.,Leigui de Oliveira M.A.,Lenok V.,Letessier-Selvon A.,Lhenry-Yvon I.,Lo Presti D.,Lopes L.,López R.,Lu L.,Luce Q.,Lucero A.,Lundquist J.P.,Machado Payeras A.,Mancarella G.,Mandat D.,Manning B.C.,Manshanden J.,Mantsch P.,Marafico S.,Mariazzi A.G.,Mariş I.C.,Marsella G.,Martello D.,Martinez H.,Martínez Bravo O.,Mastrodicasa M.,Mathes H.J.,Matthews J.,Matthiae G.,Mayotte E.,Mazur P.O.,Medina-Tanco G.,Melo D.,Menshikov A.,Merenda K.-D.,Michal S.,Micheletti M.I.,Miramonti L.,Mollerach S.,Montanet F.,Morello C.,Mostafá M.,Müller A.L.,Muller M.A.,Mulrey K.,Mussa R.,Muzio M.,Namasaka W.M.,Nasr-Esfahani A.,Nellen L.,Niculescu-Oglinzanu M.,Niechciol M.,Nitz D.,Nosek D.,Novotny V.,Nožka L.,Nucita A.,Núñez L.A.,Palatka M.,Pallotta J.,Papenbreer P.,Parente G.,Parra A.,Pech M.,Pedreira F.,Pȩkala J.,Pelayo R.,Peña-Rodriguez J.,Pereira Martins E.E.,Perez Armand J.,Pérez Bertolli C.,Perlin M.,Perrone L.,Petrera S.,Pierog T.,Pimenta M.,Pirronello V.,Platino M.,Pont B.,Pothast M.,Privitera P.,Prouza M.,Puyleart A.,Querchfeld S.,Rautenberg J.,Ravignani D.,Reininghaus M.,Ridky J.,Riehn F.,Risse M.,Rizi V.,Rodrigues de Carvalho W.,Rodriguez Rojo J.,Roncoroni M.J.,Roth M.,Roulet E.,Rovero A.C.,Ruehl P.,Saffi S.J.,Saftoiu A.,Salamida F.,Salazar H.,Salina G.,Sanabria Gomez J.D.,Sánchez F.,Santos E.M.,Santos E.,Sarazin F.,Sarmento R.,Sarmiento-Cano C.,Sato R.,Savina P.,Schäfer C.M.,Scherini V.,Schieler H.,Schimassek M.,Schimp M.,Schlüter F.,Schmidt D.,Scholten O.,Schovánek P.,Schröder F.G.,Schröder S.,Schulte J.,Sciutto S.J.,Scornavacche M.,Segreto A.,Sehgal S.,Shellard R.C.,Sigl G.,Silli G.,Sima O.,Šmída R.,Sommers P.,Soriano J.F.,Souchard J.,Squartini R.,Stadelmaier M.,Stanca D.,Stanič S.,Stasielak J.,Stassi P.,Streich A.,Suárez-Durán M.,Sudholz T.,Suomijärvi T.,Supanitsky A.D.,Šupík J.,Szadkowski Z.,Taboada A.,Tapia A.,Taricco C.,Timmermans C.,Tkachenko O.,Tobiska P.,Todero Peixoto C.J.,Tomé B.,Travaini A.,Travnicek P.,Trimarelli C.,Trini M.,Tueros M.,Ulrich R.,Unger M.,Vaclavek L.,Vacula M.,Valdés Galicia J.F.,Valore L.,Varela E.,Varma K.C. V.,Vásquez-Ramírez A.,Veberič D.,Ventura C.,Vergara Quispe I.D.,Verzi V.,Vicha J.,Vink J.,Vorobiov S.,Wahlberg H.,Watanabe C.,Watson A.A.,Weber M.,Weindl A.,Wiencke L.,Wilczyński H.,Winchen T.,Wirtz M.,Wittkowski D.,Wundheiler B.,Yushkov A.,Zapparrata O.,Zas E.,Zavrtanik D.,Zavrtanik M.,Zehrer L.,Zepeda A.

Abstract

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.

Publisher

IOP Publishing

Subject

Mathematical Physics,Instrumentation

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