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Depth of maximum of air-shower profiles above $10^{17.7} eV$ measured with the fluorescence detector of the Pierre Auger Observatory

A. Abdul Halim¹³, P. Abreu⁶⁷, M. Aglietta^50,49, M. Ahmed³¹, I. Allekotte¹, K. Almeida Cheminant^75,74, R. Aloisio^42,43, J. Alvarez-Muñiz⁷³, A. Ambrosone^42,43 et al. (Pierre Auger Collaboration)

A. Ambrosone^42,43, J. Ammerman Yebra⁷³, L. Anchordoqui⁷⁹, B. Andrada⁷, L. Andrade Dourado^42,43, L. Apollonio^55,46, C. Aramo⁴⁷, E. Arnone^59,49, J. C. Arteaga Velázquez⁶³, P. Assis⁶⁷, G. Avila¹¹, E. Avocone^53,43, A. Bakalova²⁹, Y. Balibrea¹¹, A. Baluta⁷⁰, F. Barbato^42,43, A. Bartz Mocellin⁷⁸, J. P. Behler¹⁰, J. A. Bellido¹³, C. Berat^h, M. E. Bertaina^59,49, M. Bianciotto³⁹, P. L. Biermann^a, V. Binet⁵, K. Bismark^35,7, T. Bister^74,75, J. Biteau^33,j, J. Blazek²⁹, J. Blümer³⁷, M. Boháčová²⁹, D. Boncioli^53,43, C. Bonifazi^16,8, N. Borodai⁶⁵, J. Brack^f, P. G. Brichetto Orquera^7,37, A. Bueno⁷², S. Buitink¹⁵, A. Bwembya^74,75, T. R. Caba Pineda³⁷, K. S. Caballero-Mora⁶², S. Cabana-Freire⁷³, L. Caccianiga^55,46, J. Caraça-Valente⁷⁸, R. Caruso^54,44, A. Castellina^50,49, F. Catalani¹⁸, G. Cataldi⁴⁵, L. Cazon⁷³, M. Cerda¹⁰, B. Čermáková³⁷, A. Cermenati^42,43, K. Cerny³⁰, J. A. Chinellato²¹, J. Chudoba²⁹, L. Chytka³⁰, R. W. Clay¹³, A. C. Cobos Cerutti⁶, R. Colalillo^56,47, R. Conceição⁶⁷, G. Consolati^46,51, M. Conte^52,45, F. Convenga^42,43, D. Correia dos Santos²⁵, P. J. Costa⁶⁷, C. E. Covault⁷⁷, M. Cristinziani⁴¹, C. S. Cruz Sanchez³, S. Dasso^4,2, K. Daumiller³⁷, B. R. Dawson¹³, R. M. de Almeida²⁵, E.-T. de Boone⁴¹, B. de Errico²⁵, J. de Jesús⁷³, S. J. de Jong^74,75, J. R. T. de Mello Neto²⁵, I. De Mitri^42,43, D. de Oliveira Franco⁴⁰, F. de Palma^52,45, V. de Souza¹⁹, E. De Vito^52,45, A. Del Popolo^54,44, O. Deligny³¹, N. Denner²⁹, K. Denner Syrokvas²⁸, L. Deval⁴⁹, A. di Matteo⁴⁹, C. Dobrigkeit²¹, J. C. D’Olivo⁶⁴, L. M. Domingues Mendes^16,67, T. Dominguez¹, Y. Dominguez Ballesteros²⁷, Q. Dorosti⁴¹, R. C. dos Anjos²⁴, J. Ebr²⁹, F. Ellwanger³⁷, R. Engel^35,37, I. Epicoco^52,45, M. Erdmann³⁸, A. Etchegoyen^7,12, C. Evoli^42,43, H. Falcke^74,76,75, G. Farrar⁸¹, A. C. Fauth²¹, T. Fehler⁴¹, F. Feldbusch³⁶, A. Fernandes⁶⁷, M. Fernández Alonso¹⁴, B. Fick⁸⁰, J. M. Figueira⁷, P. Filip^35,7, A. Filipčič^71,70, T. Fitoussi³⁷, B. Flaggs⁸³, A. Franco⁴⁵, M. Freitas⁶⁷, T. Fujii^82,i, A. Fuster^7,12, C. Galea⁷⁴, B. García⁶, C. Gaudu³⁴, P. L. Ghia³¹, U. Giaccari⁴⁵, M. Giammarco^53,43, C. Glaser³⁹, F. Gobbi¹⁰, F. Gollan⁷, G. Golup¹, P. F. Gómez Vitale¹¹, J. P. Gongora¹¹, N. González⁷, D. Góra⁶⁵, A. Gorgi^50,49, M. Gottowik³⁷, F. Guarino^56,47, G. P. Guedes²², Y. C. Guerra¹⁰, L. Gülzow³⁷, S. Hahn³⁵, P. Hamal²⁹, M. R. Hampel⁷, P. Hansen³, V. M. Harvey¹³, A. Haungs³⁷, M. Havelka²⁹, T. Hebbeker³⁸, C. Hojvat^d, J. R. Hörandel^74,75, P. Horvath³⁰, M. Hrabovský³⁰, T. Huege^37,15, A. Insolia^54,44, P. G. Isar⁶⁹, M. Ismaiel^74,75, P. Janecek²⁹, V. Jilek²⁹, K.-H. Kampert³⁴, B. Keilhauer³⁷, V. V. Kizakke Covilakam^7,37, H. O. Klages³⁷, M. Kleifges³⁶, A. Klingel²⁹, J. Köhler³⁷, F. Krieger³⁸, M. Kubatova²⁹, N. Kunka³⁶, B. L. Lago¹⁷, N. Langner³⁸, N. Leal⁷, M. A. Leigui de Oliveira²³, Y. Lema-Capeans⁷³, A. Letessier-Selvon³², I. Lhenry-Yvon³¹, L. Lopes⁶⁷, J. P. Lundquist⁷⁰, M. Mallamaci^57,44, S. Mancuso^50,49, D. Mandat²⁹, P. Mantsch^d, A. G. Mariazzi³, C. Marinelli^42,43, I. C. Mariş¹⁴, G. Marsella^57,44, D. Martello^52,45, S. Martinelli^37,7, O. Martínez Bravo⁶⁰, A. Martínez-Mendez²⁷, M. A. Martins²⁹, H.-J. Mathes³⁷, J. Matthews^g, G. Matthiae^58,48, E. Mayotte⁷⁸, S. Mayotte⁷⁸, P. O. Mazur^d, G. Medina-Tanco⁶⁴, J. Meinert³⁴, D. Melo⁷, A. Menshikov³⁶, C. Merx³⁷, S. Michal²⁹, M. I. Micheletti⁵, L. Miramonti^55,46, M. Mogarkar⁶⁵, S. Mollerach¹, F. Montanet^h, L. Morejon³⁴, K. Mulrey^74,75, R. Mussa⁴⁹, W. M. Namasaka³⁴, S. Negi²⁹, L. Nellen⁶⁴, K. Nguyen⁸⁰, G. Nicora⁹, M. Niechciol⁴¹, D. Nitz⁸⁰, D. Nosek²⁸, A. Novikov⁸³, V. Novotny²⁸, L. Nožka³⁰, A. Nucita^52,45, L. A. Núñez²⁷, S. E. Nuza⁴, J. Ochoa^7,37, M. Olegario¹⁹, C. Oliveira²⁰, L. Östman²⁹, M. Palatka²⁹, J. Pallotta⁹, G. Parente⁷³, T. Paulsen³⁴, J. Pawlowsky³⁴, M. Pech²⁹, J. Pȩkala⁶⁵, R. Pelayo⁶¹, V. Pelgrims¹⁴, C. Pérez Bertolli⁷³, L. Perrone^52,45, S. Petrera^42,43, T. Pierog³⁷, M. Pimenta⁶⁷, M. Platino⁷, B. Pont⁷⁴, M. Pourmohammad Shahvar^57,44, P. Privitera⁸², C. Priyadarshi⁶⁵, M. Prouza²⁹, K. Pytel⁶⁶, S. Querchfeld³⁴, J. Rautenberg³⁴, D. Ravignani⁷, J. V. Reginatto Akim²¹, M. Z. Rennó²¹, A. Reuzki³⁸, J. Ridky²⁹, F. Riehn³⁹, M. Risse⁴¹, V. Rizi^53,43, B. Rocha Moldes⁷³, E. Rodriguez^7,37, G. Rodriguez Fernandez⁴⁸, J. Rodriguez Rojo¹¹, S. Rossoni⁴⁰, M. Roth³⁷, E. Roulet¹, A. C. Rovero⁴, A. Saftoiu⁶⁸, M. Saharan⁷⁴, F. Salamida^53,43, H. Salazar⁶⁰, G. Salina⁴⁸, P. Sampathkumar³⁷, N. San Martin⁷⁸, J. D. Sanabria Gomez²⁷, F. Sánchez⁷, F. M. Sánchez Rodriguez⁷³, E. Santos²⁹, F. Sarazin⁷⁸, R. Sarmento⁶⁷, R. Sato¹¹, P. Savina^42,43, V. Scherini^52,45, H. Schieler³⁷, M. Schimp³⁴, D. Schmidt³⁷, O. Scholten^15,b, H. Schoorlemmer^74,75, P. Schovánek²⁹, F. G. Schröder^83,37, J. Schulte³⁸, T. Schulz²⁹, S. J. Sciutto³, M. Scornavacche⁷, A. Sedoski⁷, S. Sehgal³⁴, S. U. Shivashankara⁷⁰, G. Sigl⁴⁰, K. Simkova^15,14, F. Simon³⁶, R. Šmída⁸², S. Soares Sippert²⁵, P. Sommers^e, S. Stanič⁷⁰, J. Stasielak⁶⁵, P. Stassi^h, S. Strähnz³⁵, M. Straub³⁸, T. Suomijärvi³³, A. D. Supanitsky⁷, Z. Svozilikova²⁹, Z. Szadkowski⁶⁶, F. Tairli¹³, A. Tapia²⁶, C. Taricco^59,49, C. Timmermans^75,74, O. Tkachenko²⁹, P. Tobiska²⁹, C. J. Todero Peixoto¹⁸, B. Tomé⁶⁷, A. Travaini¹⁰, P. Travnicek²⁹, C. Trimarelli^42,43, M. Tueros³, M. Unger ³⁷, R. Uzeiroska-Geyik³⁴, L. Vaclavek³⁰, M. Vacula³⁰, I. Vaiman^42,43, J. F. Valdés Galicia⁶⁴, L. Valore^56,47, P. van Dillen^74,75, E. Varela⁶⁰, V. Vašíčková³⁴, A. Vásquez-Ramírez²⁷, D. Veberič³⁷, I. D. Vergara Quispe³, S. Verpoest⁸³, V. Verzi⁴⁸, J. Vicha²⁹, S. Vorobiov⁷⁰, J. B. Vuta²⁹, C. Watanabe²⁵, A. A. Watson^c, A. Weindl³⁷, M. Weitz³⁴, L. Wiencke⁷⁸, H. Wilczyński⁶⁵, B. Wundheiler⁷, B. Yue³⁴, A. Yushkov²⁹, E. Zas⁷³, D. Zavrtanik^70,71, and M. Zavrtanik^71,70 (Pierre Auger Collaboration)

¹Centro Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina
²Departamento de Física and Departamento de Ciencias de la Atmósfera y los Océanos, FCEyN, Universidad de Buenos Aires and CONICET, Buenos Aires, Argentina
³IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina
⁴Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA), Buenos Aires, Argentina
⁵Instituto de Física de Rosario (IFIR)—CONICET/U. N. R. and Facultad de Ciencias Bioquímicas y Farmacéuticas U.N.R., Rosario, Argentina
⁶Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), and Universidad Tecnológica Nacional—Facultad Regional Mendoza (CONICET/CNEA), Mendoza, Argentina
⁷Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
⁸International Center of Advanced Studies and Instituto de Ciencias Físicas, ECyT-UNSAM and CONICET, Campus Miguelete—San Martín, Buenos Aires, Argentina
⁹Laboratorio Atmósfera—Departamento de Investigaciones en Láseres y sus Aplicaciones—UNIDEF (CITEDEF-CONICET), Argentina
¹⁰Observatorio Pierre Auger, Malargüe, Argentina
¹¹Observatorio Pierre Auger and Comisión Nacional de Energía Atómica, Malargüe, Argentina
¹²Universidad Tecnológica Nacional—Facultad Regional Buenos Aires, Buenos Aires, Argentina
¹³Adelaide University, Adelaide, S.A., Australia
¹⁴Université Libre de Bruxelles (ULB), Brussels, Belgium
¹⁵Vrije Universiteit Brussels, Brussels, Belgium
¹⁶Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil
¹⁷Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Petropolis, Brazil
¹⁸Universidade de São Paulo, Escola de Engenharia de Lorena, Lorena, SP, Brazil
¹⁹Universidade de São Paulo, Instituto de Física de São Carlos, São Carlos, SP, Brazil
²⁰Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazil
²¹Universidade Estadual de Campinas (UNICAMP), IFGW, Campinas, SP, Brazil
²²Universidade Estadual de Feira de Santana, Feira de Santana, Brazil
²³Universidade Federal do ABC, Santo André, SP, Brazil
²⁴Universidade Federal do Paraná, Setor Palotina, Palotina, Brazil
²⁵Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro, RJ, Brazil
²⁶Universidad de Medellín, Medellín, Colombia
²⁷Universidad Industrial de Santander, Bucaramanga, Colombia
²⁸Charles University, Faculty of Mathematics and Physics, Institute of Particle and Nuclear Physics, Prague, Czech Republic
²⁹Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
³⁰Palacky University, Olomouc, Czech Republic
³¹CNRS/IN2P3, IJCLab, Université Paris-Saclay, Orsay, France
³²Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Sorbonne Université, Université de Paris, CNRS-IN2P3, Paris, France
³³Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
³⁴Bergische Universität Wuppertal, Department of Physics, Wuppertal, Germany
³⁵Karlsruhe Institute of Technology (KIT), Institute for Experimental Particle Physics, Karlsruhe, Germany
³⁶Karlsruhe Institute of Technology (KIT), Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany
³⁷Karlsruhe Institute of Technology (KIT), Institute for Astroparticle Physics, Karlsruhe, Germany
³⁸RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
³⁹TU Dortmund University, Department of Physics, Dortmund, Germany
⁴⁰Universität Hamburg, II. Institut für Theoretische Physik, Hamburg, Germany
⁴¹Universität Siegen, Department Physik—Experimentelle Teilchenphysik, Siegen, Germany
⁴²Gran Sasso Science Institute, L’Aquila, Italy
⁴³INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italy
⁴⁴INFN, Sezione di Catania, Catania, Italy
⁴⁵INFN, Sezione di Lecce, Lecce, Italy
⁴⁶INFN, Sezione di Milano, Milano, Italy
⁴⁷INFN, Sezione di Napoli, Napoli, Italy
⁴⁸INFN, Sezione di Roma “Tor Vergata”, Roma, Italy
⁴⁹INFN, Sezione di Torino, Torino, Italy
⁵⁰Osservatorio Astrofisico di Torino (INAF), Torino, Italy
⁵¹Politecnico di Milano, Dipartimento di Scienze e Tecnologie Aerospaziali, Milano, Italy
⁵²Università del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”, Lecce, Italy
⁵³Università dell’Aquila, Dipartimento di Scienze Fisiche e Chimiche, L’Aquila, Italy
⁵⁴Università di Catania, Dipartimento di Fisica e Astronomia “Ettore Majorana“, Catania, Italy
⁵⁵Università di Milano, Dipartimento di Fisica, Milano, Italy
⁵⁶Università di Napoli “Federico II”, Dipartimento di Fisica “Ettore Pancini”, Napoli, Italy
⁵⁷Università di Palermo, Dipartimento di Fisica e Chimica ”E. Segrè”, Palermo, Italy
⁵⁸Università di Roma “Tor Vergata”, Dipartimento di Fisica, Roma, Italy
⁵⁹Università Torino, Dipartimento di Fisica, Torino, Italy
⁶⁰Benemérita Universidad Autónoma de Puebla, Puebla, México
⁶¹Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas del Instituto Politécnico Nacional (UPIITA-IPN), México, D.F., México
⁶²Universidad Autónoma de Chiapas, Tuxtla Gutiérrez, Chiapas, México
⁶³Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, México
⁶⁴Universidad Nacional Autónoma de México, México, D.F., México
⁶⁵Institute of Nuclear Physics PAN, Krakow, Poland
⁶⁶University of Łódź, Faculty of High-Energy Astrophysics,Łódź, Poland
⁶⁷Laboratório de Instrumentação e Física Experimental de Partículas—LIP and Instituto Superior Técnico—IST, Universidade de Lisboa—UL, Lisboa, Portugal
⁶⁸“Horia Hulubei” National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania
⁶⁹Institute of Space Science, Bucharest-Magurele, Romania
⁷⁰Center for Astrophysics and Cosmology (CAC), University of Nova Gorica, Nova Gorica, Slovenia
⁷¹Experimental Particle Physics Department, J. Stefan Institute, Ljubljana, Slovenia
⁷²Universidad de Granada and C.A.F.P.E., Granada, Spain
⁷³Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago de Compostela, Spain
⁷⁴IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands
⁷⁵Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science Park, Amsterdam, The Netherlands
⁷⁶Stichting Astronomisch Onderzoek in Nederland (ASTRON), Dwingeloo, The Netherlands
⁷⁷Case Western Reserve University, Cleveland, Ohio, USA
⁷⁸Colorado School of Mines, Golden, Colorado, USA
⁷⁹Department of Physics and Astronomy, Lehman College, City University of New York, Bronx, New York, USA
⁸⁰Michigan Technological University, Houghton, Michigan, USA
⁸¹New York University, New York, New York, USA
⁸²University of Chicago, Enrico Fermi Institute, Chicago, Illinois, USA
⁸³University of Delaware, Department of Physics and Astronomy, Bartol Research Institute, Newark, Delaware, USA

^aMax-Planck-Institut für Radioastronomie, Bonn, Germany.
^balso at Kapteyn Institute, University of Groningen, Groningen, The Netherlands.
^cSchool of Physics and Astronomy, University of Leeds, Leeds, United Kingdom.
^dFermi National Accelerator Laboratory, Fermilab, Batavia, Illinois, USA (Affiliation for identification purposes only).
^ePennsylvania State University, University Park, Pennsylvania , USA.
^fColorado State University, Fort Collins, Colorado, USA.
^gLouisiana State University, Baton Rouge, Louisiana, USA.
^hUniversité Grenoble Alpes, CNRS, Grenoble Institute of Engineering, LPSC-IN2P3, Grenoble, France.
ⁱnow at Graduate School of Science, Osaka Metropolitan University, Osaka, Japan.
^jInstitut universitaire de France (IUF), France.

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Phys. Rev. D 114, 043016 – Published 10 August, 2026

DOI: https://doi.org/10.1103/n616-15v5

Abstract

We present measurements of the depth of shower maximum, $X_{\max}$ , for cosmic-ray-induced extensive air showers recorded by the fluorescence detector of the Pierre Auger Observatory over 17 years. The dataset covers primary energies from $10^{17.7} eV$ to beyond $10^{19.6} eV$ . With improved event reconstruction and an exposure 2.4 times larger than in our previous analysis, this work confirms and refines our conclusions on the mass composition at ultrahigh energies. The energy evolution of the mean $X_{\max}$ exhibits a pronounced break at a cosmic-ray energy of about $10^{18.4} eV$ , providing direct, model-independent evidence for a change in the evolution of the mass composition. Independently, the observed decrease of the $X_{\max}$ fluctuations with energy indicates a transition toward a heavier and less diverse primary mass composition. No statistically significant declination dependence of the $X_{\max}$ distributions is observed within the exposure of the Observatory, consistent with an isotropic mass composition at the sensitivity of this analysis. The mean and standard deviation of the $X_{\max}$ distributions, interpreted with air-shower simulations, yield the energy dependence of the average and variance of the logarithmic mass of cosmic rays arriving at Earth. Furthermore, energy-dependent fractional abundances of four representative primary-mass groups (p, He, CNO, Fe) are obtained by fitting the observed $X_{\max}$ distributions in each energy bin with a weighted sum of elemental templates. These results provide strong evidence against a long-standing assumption that ultrahigh-energy cosmic rays are predominantly protons: above $\sim 10^{18.4} eV$ , the average cosmic-ray mass increases, accompanied by a steadily decreasing diversity in the elemental composition.

Physics Subject Headings (PhySH)

Cosmic ray composition & spectra

Article Text

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Phys. Rev. D 114, 043016– Published 10 August, 2026

Vol. 114, Iss. 4 — 15 August 2026

Received 14 May 2026
Accepted 9 July 2026

DOI: https://doi.org/10.1103/n616-15v5

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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Depth of maximum of air-shower profiles above $10^{17.7} eV$ measured with the fluorescence detector of the Pierre Auger Observatory

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Depth of maximum of air-shower profiles above 1017.7 eV measured with the fluorescence detector of the Pierre Auger Observatory

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Depth of maximum of air-shower profiles above $10^{17.7} eV$ measured with the fluorescence detector of the Pierre Auger Observatory