Update on testing of air-shower modelling using combined data of the Pierre Auger Observatory and phenomenological consequences
The combined data of Fluorescence and Surface Detectors of the Pierre Auger Observatory has recently provided the strongest constraints on the validity of predictions from current models of hadronic interactions. The unmodified predictions of these models on the depth of shower maximum (Xmax) and the hadronic part of the ground signal are unable to accurately describe the measured data at a level of more than 5$\sigma$ in the energy range 3-10 EeV. This inconsistency has been shown to originate not only from the predicted amount of muons at the ground level, but also from the predicted scale of Xmax, which must be adjusted to better match the observed data. The resulting deeper Xmax scales of the models imply a heavier mass composition to be interpreted from the Xmax measurements. We show the results of the test with an updated data set of the Pierre Auger Observatory, studying also the energy evolution of the fitted modification parameters and new versions of the models of hadronic interactions. Additionally, we discuss the phenomenological consequences of the deeper Xmax scale of models on the interpretation of the features of the energy spectrum and the muon problem in air-shower modelling.
Authors
- Belén Andrada
- Zbigniew Szadkowski (ORCID: https://orcid.org/0000-0002-2690-9912)
- Bruno L. Lago (ORCID: https://orcid.org/0000-0001-9672-0499)
- Marvin Gottowik (ORCID: https://orcid.org/0000-0001-7436-389X)
- Carla Taricco (ORCID: https://orcid.org/0000-0002-0129-5539)
- Giovanni Consolati (ORCID: https://orcid.org/0000-0003-3614-245X)
- Juan Manuel Gonzalez (ORCID: https://orcid.org/0000-0001-9193-0921)
- S. Petrera (ORCID: https://orcid.org/0000-0002-6029-1255)
- T. Pierog (ORCID: https://orcid.org/0000-0002-7472-8710)
- G. Sigl (ORCID: https://orcid.org/0000-0002-4396-645X)
- Mateo Fernandez
- T. Huege (ORCID: https://orcid.org/0000-0002-2783-4772)
- Marta Bianciotto (ORCID: https://orcid.org/0000-0002-9599-3214)
- Nicolas Leal
- Carmina Pérez Bertolli (ORCID: https://orcid.org/0000-0002-9790-5732)
- Carlo Salvattore Cruz Sanchez (ORCID: https://orcid.org/0009-0002-6173-0974)
- Frank Schröder (ORCID: https://orcid.org/0000-0001-8495-7210)
- Gustavo Medina‐Tanco (ORCID: https://orcid.org/0000-0002-3202-319X)
- A. C. Fauth (ORCID: https://orcid.org/0000-0001-7239-0288)
- Enrico Arnone (ORCID: https://orcid.org/0000-0001-6740-5051)
- Enrique Varela (ORCID: https://orcid.org/0000-0003-0715-7513)
- O. Schölten (ORCID: https://orcid.org/0000-0003-3649-1254)
- K. Nguyen (ORCID: https://orcid.org/0000-0001-5839-9569)
- Olena Tkachenko (ORCID: https://orcid.org/0000-0001-6393-7851)
- Lorenzo Cazon (ORCID: https://orcid.org/0000-0001-6748-8395)
- Lukáš Vaclavek (ORCID: https://orcid.org/0000-0002-0910-3415)
- B. R. Dawson (ORCID: https://orcid.org/0000-0002-4271-3055)
- A. Haungs (ORCID: https://orcid.org/0000-0002-9638-7574)
- Harm Schoorlemmer (ORCID: https://orcid.org/0000-0002-8999-9249)
- Dalibor Nosek (ORCID: https://orcid.org/0000-0001-6219-200X)
- G. Parente (ORCID: https://orcid.org/0000-0003-2847-0461)
- Paula Gina Isar (ORCID: https://orcid.org/0000-0002-1241-584X)
- Janning Meinert (ORCID: https://orcid.org/0000-0001-7582-3456)
- Emanuele De Vito (ORCID: https://orcid.org/0000-0003-2045-7588)
- Adila Abdul Halim (ORCID: https://orcid.org/0000-0003-1218-1737)
- Gonzalo Rodriguez Fernandez (ORCID: https://orcid.org/0000-0002-4683-230X)
- Jiří Blažek (ORCID: https://orcid.org/0000-0002-5870-8947)
- Therese Paulsen
- Adriel Bartz Mocellin
- Berenika Čermáková
- S. J. de Jong (ORCID: https://orcid.org/0000-0002-3120-3367)
- Armando di Matteo (ORCID: https://orcid.org/0000-0002-8260-1867)
- Andres Travaini (ORCID: https://orcid.org/0000-0001-7875-2147)
- Alexey Yushkov (ORCID: https://orcid.org/0000-0001-5107-9116)
- K. Daumiller (ORCID: https://orcid.org/0000-0002-0527-4823)
- A. Insolia (ORCID: https://orcid.org/0000-0002-9040-1566)
- Darko Veberič (ORCID: https://orcid.org/0000-0003-2683-1526)
- María Isabel Micheletti (ORCID: https://orcid.org/0000-0002-1063-9938)
- A. Segreto (ORCID: https://orcid.org/0000-0001-7341-6603)
- L. Nellen (ORCID: https://orcid.org/0000-0003-1059-8731)
- Felicia Barbato (ORCID: https://orcid.org/0000-0003-0751-6731)
- Thomas Fitoussi (ORCID: https://orcid.org/0000-0001-9473-9356)
- Katarína Simkova (ORCID: https://orcid.org/0000-0003-2363-9846)
- R. Caruso (ORCID: https://orcid.org/0000-0003-1622-8731)
- I. Allekotte (ORCID: https://orcid.org/0000-0002-9624-3044)
- F. Sarazin (ORCID: https://orcid.org/0000-0001-5614-1986)
- Luis A. Núñez
- Chaitanya Priyadarshi (ORCID: https://orcid.org/0000-0002-9160-9617)
- Fernando Gollan (ORCID: https://orcid.org/0000-0002-0495-2768)
- M. Cristinziani (ORCID: https://orcid.org/0000-0003-3893-9171)
- E. Zas (ORCID: https://orcid.org/0000-0002-4430-8117)
- Clara Keiko Oliveira Watanabe
- Roberta Colalillo (ORCID: https://orcid.org/0000-0002-4179-9352)
- M. Hrabovský (ORCID: https://orcid.org/0000-0003-4223-7316)
- L. Miramonti (ORCID: https://orcid.org/0000-0002-2808-5363)
- F. Simon (ORCID: https://orcid.org/0000-0002-5978-0289)
- F. Salamida (ORCID: https://orcid.org/0000-0002-9306-8447)
- P. Trávnı́ček (ORCID: https://orcid.org/0000-0002-1655-9584)
- Benjamin Flaggs (ORCID: https://orcid.org/0000-0002-5549-1869)
- Michael Unger
- P. Hamal (ORCID: https://orcid.org/0000-0003-3139-7234)
- G.P. Guedes (ORCID: https://orcid.org/0000-0002-9160-4832)
- A. D. Supanitsky (ORCID: https://orcid.org/0000-0002-6942-6216)
- Pedro J. Costa
- Maximilian Straub
- R. Mussa (ORCID: https://orcid.org/0000-0002-0294-9071)
- Camilla Petrucci
- Steffen Hahn (ORCID: https://orcid.org/0000-0001-5040-3666)
- Federico Maria Mariani
- Fiona H. Ellwanger
- A. Castellina (ORCID: https://orcid.org/0000-0002-0045-2467)
- J. Vícha (ORCID: https://orcid.org/0000-0002-7945-3605)
- Jaime Álvarez-Muñiz (ORCID: https://orcid.org/0000-0002-2367-0803)
- Denise Boncioli (ORCID: https://orcid.org/0000-0003-1186-9353)
- L. Chytka (ORCID: https://orcid.org/0000-0001-5741-259X)
- Martin Vacula (ORCID: https://orcid.org/0000-0003-4844-3962)
- Miguel A. Martins (ORCID: https://orcid.org/0000-0002-7294-6204)
- F. Guarino (ORCID: https://orcid.org/0000-0003-1427-9885)
- M. Erdmann (ORCID: https://orcid.org/0000-0002-1653-1303)
- Jarosław Stasielak (ORCID: https://orcid.org/0000-0002-9284-7000)
- Shima Ujjani Shivashankara
- A. Letessier‐Selvon (ORCID: https://orcid.org/0000-0002-2044-3103)
- C. E. Covault (ORCID: https://orcid.org/0000-0001-5405-5371)
- Alex Tapia (ORCID: https://orcid.org/0000-0003-0585-7161)
- P. Abreu (ORCID: https://orcid.org/0000-0002-9973-7314)
- Tobias Schulz (ORCID: https://orcid.org/0000-0002-4208-2599)
- L. Nožka
- M. Palatka (ORCID: https://orcid.org/0000-0003-2061-6059)
- I. De Mitri (ORCID: https://orcid.org/0000-0002-8665-1730)
- K. S. Caballero‐Mora (ORCID: https://orcid.org/0000-0002-4042-3855)
- Antonio Franco (ORCID: https://orcid.org/0000-0001-7707-4241)
- Roberto Aloisio (ORCID: https://orcid.org/0000-0003-0161-5923)
- Bjarni Pont (ORCID: https://orcid.org/0000-0002-2578-5364)
- Simone Rossoni
- S. Buitink (ORCID: https://orcid.org/0000-0002-6177-497X)
- Juan Ammerman Yebra (ORCID: https://orcid.org/0000-0002-2059-6206)
- Edivaldo Moura Santos (ORCID: https://orcid.org/0000-0002-2818-8813)
- Violet M. Harvey (ORCID: https://orcid.org/0000-0002-6764-4789)
- Achille Nucita (ORCID: https://orcid.org/0000-0002-7926-3481)
- Hermann-Josef Mathes (ORCID: https://orcid.org/0000-0002-0680-040X)
- P. Mantsch (ORCID: https://orcid.org/0000-0002-8382-7745)
- Rukije Uzeiroska
- Nicolás Martín González (ORCID: https://orcid.org/0000-0001-6566-2222)
- Silvia Mollerach (ORCID: https://orcid.org/0000-0002-9339-5317)
- Toshihiro Fujii (ORCID: https://orcid.org/0000-0003-2401-504X)
- Nicolas San Martin
- Zuzana Svozilikova (ORCID: https://orcid.org/0000-0001-5210-0781)
- М. Бертаина (ORCID: https://orcid.org/0000-0003-1069-1397)
- Maximilian Stadelmaier (ORCID: https://orcid.org/0000-0002-7943-6012)
- P. Assis (ORCID: https://orcid.org/0000-0001-7765-3606)
- F. Montanet (ORCID: https://orcid.org/0000-0001-9787-596X)
- Mohit Saharan
- T. Hebbeker (ORCID: https://orcid.org/0000-0002-9736-266X)
- M. Mallamaci (ORCID: https://orcid.org/0000-0003-4068-0496)
- Alena Bakalová (ORCID: https://orcid.org/0000-0003-1001-4484)
- Peter L. Biermann (ORCID: https://orcid.org/0000-0003-3948-6143)
- Jan Ebr (ORCID: https://orcid.org/0000-0001-8807-6162)
- Anthony Bwembya (ORCID: https://orcid.org/0000-0002-6995-5978)
- J. A. Chinellato (ORCID: https://orcid.org/0000-0002-1236-0789)
- S. Andringa (ORCID: https://orcid.org/0000-0002-6397-9207)
- Luis A. Anchordoqui (ORCID: https://orcid.org/0000-0003-1463-7136)
- Jorge Caraça-Valente
- Krzysztof Pytel (ORCID: https://orcid.org/0000-0002-2937-7886)
- R. Conceição (ORCID: https://orcid.org/0000-0003-4945-5340)
- C. Bonifazi (ORCID: https://orcid.org/0000-0002-3087-3609)
- Shefali Negi (ORCID: https://orcid.org/0000-0003-0891-0829)
- Jon Paul Lundquist (ORCID: https://orcid.org/0000-0002-4245-5092)
- Peter Mazur
- Jan Pękala (ORCID: https://orcid.org/0000-0002-1062-5595)
- Edyvânia Emily Pereira Martins (ORCID: https://orcid.org/0000-0002-1167-8314)
- Fridtjof Feldbusch
- Josina Schulte (ORCID: https://orcid.org/0000-0002-5822-2445)
- S. Vorobiov (ORCID: https://orcid.org/0000-0001-8679-3424)
- Alexander Novikov (ORCID: https://orcid.org/0000-0002-1086-7252)
- Varada Varma Kizakke Covilakam
- Emanuele Avocone (ORCID: https://orcid.org/0000-0003-3757-2718)
- J. Biteau (ORCID: https://orcid.org/0000-0002-4202-8939)
- H. Wilczyński (ORCID: https://orcid.org/0000-0003-2652-9685)
- Antonio Ambrosone (ORCID: https://orcid.org/0000-0002-9942-1029)
- Pranav Sampathkumar
- M. Aglietta (ORCID: https://orcid.org/0000-0001-8354-5388)
- Patricia María Hansen
- A. Gorgi (ORCID: https://orcid.org/0000-0002-8085-2304)
- F. de Palma (ORCID: https://orcid.org/0000-0001-5898-2834)
- V. de Souza (ORCID: https://orcid.org/0000-0003-0865-233X)
- Esteban Roulet (ORCID: https://orcid.org/0000-0003-1478-9260)
- S. Dasso (ORCID: https://orcid.org/0000-0002-7680-4721)
- Leo Östman
- Fabio Convenga (ORCID: https://orcid.org/0000-0002-2841-1034)
- J. Matthews (ORCID: https://orcid.org/0000-0002-1832-4420)
- Fernando Catalani (ORCID: https://orcid.org/0000-0001-9332-1476)
- Adrian Sedoski (ORCID: https://orcid.org/0000-0002-4253-3361)
- Radomir Šmída (ORCID: https://orcid.org/0000-0003-0122-1123)
- Eva Santos (ORCID: https://orcid.org/0000-0002-0474-8863)
- Joaquín de Jesús (ORCID: https://orcid.org/0000-0002-4741-1769)
- Milton Freitas
- Niklas Langner (ORCID: https://orcid.org/0000-0001-7443-3042)
- Jose A. Bellido (ORCID: https://orcid.org/0000-0002-0833-9194)
- Kathrin Bismark (ORCID: https://orcid.org/0000-0001-8637-7041)
- Adrián Rovero (ORCID: https://orcid.org/0000-0001-6979-5604)
- D. Góra (ORCID: https://orcid.org/0000-0002-4853-5974)
- J. Řídký (ORCID: https://orcid.org/0000-0001-6697-1393)
- B. Keilhauer (ORCID: https://orcid.org/0000-0003-4494-1155)
- G. Golup (ORCID: https://orcid.org/0000-0001-9471-8811)
- Stef Verpoest (ORCID: https://orcid.org/0000-0002-3031-3206)
- Katharine Mulrey (ORCID: https://orcid.org/0000-0001-8026-8020)
- Mario Buscemi (ORCID: https://orcid.org/0000-0003-2123-5434)
- Wilson M. Namasaka
- Vincent Pelgrims (ORCID: https://orcid.org/0000-0002-5053-3847)
- Chloé Gaudu (ORCID: https://orcid.org/0000-0002-2803-4873)
- Yago Lema-Capeans
- Carmen Merx
- Mohsen Pourmohammad Shahvar
- Lukas Gülzow (ORCID: https://orcid.org/0009-0001-0620-3525)
- Nikolas Denner
- Sergio Cabana-Freire (ORCID: https://orcid.org/0000-0002-4042-3855)
- Alessandro Cermenati
- Simon Strähnz
- Beatriz de Errico (ORCID: https://orcid.org/0009-0002-4212-0708)
- João Vítor Reginatto Akim (ORCID: https://orcid.org/0000-0001-8179-9747)
- Fedor Tairli
- Alex Reuzki
- Tim Fehler
- Eric William Mayotte (ORCID: https://orcid.org/0000-0003-2618-9166)
- J. Chudoba (ORCID: https://orcid.org/0000-0002-6425-2579)
- Paolo Privitera (ORCID: https://orcid.org/0000-0002-0623-9261)
- Markus Roth (ORCID: https://orcid.org/0000-0002-9041-1414)
- A. De Roeck (ORCID: https://orcid.org/0000-0002-3234-6634)
- Brian Wundheiler (ORCID: https://orcid.org/0000-0003-3121-7037)
- Jacco Vink (ORCID: https://orcid.org/0000-0002-0816-9949)
- Gioacchino Alex Anastasi (ORCID: https://orcid.org/0000-0003-0824-5283)
- Indira D. Vergara Quispe (ORCID: https://orcid.org/0000-0001-8377-5933)
- José Ochoa (ORCID: https://orcid.org/0009-0001-1395-4159)
- Marko Zavrtanik (ORCID: https://orcid.org/0000-0001-5606-6912)
- K.‐H. Kampert (ORCID: https://orcid.org/0000-0002-2805-0195)
- Jose Sanabria Gomez (ORCID: https://orcid.org/0000-0002-4217-3212)
- B. Garćıa (ORCID: https://orcid.org/0000-0003-0919-2734)
- Marcus Niechciol (ORCID: https://orcid.org/0000-0001-6823-8056)
- Leonel Morejón (ORCID: https://orcid.org/0000-0003-1494-2624)
- J. Brack (ORCID: https://orcid.org/0000-0003-4096-2063)
- Igor Vaiman (ORCID: https://orcid.org/0000-0002-8255-3631)
- Ralph Engel
- Giorgio Matthiae
- Juan Carlos D'Olivo
- Juan Pallotta
- Andrej Filipčič
- Alberto Etchegoyen
- Humberto Ibarguen Salazar
- Rita Cassia dos Anjos
- Jörg R. Hörandel
- Analisa Mariazzi
- Andreas Weindl
- Sergio J Sciutto
- Luca Deval
- Stanislav Michal
- Johannes Blümer
- Jelena Köhler
- Antonino Del Popolo
- Manuel Platino
- Julian Rautenberg
- Danilo Zavrtanik
- Jaime de Oliveira
- Isabelle Lhenry-Yvon
- Carlos Hojvat
- Qader Dorosti (ORCID: https://orcid.org/0000-0001-9711-0609)
- Italo Epicoco
- Bernardo Tomé
- Sara Martinelli
- Felix Riehn
- Charles Timmermans
- Paul Filip
- Antonio Bueno
- Carlos J. Todero Peixoto (ORCID: https://orcid.org/0000-0003-3669-8212)
- Alejandro Almela
- Gabriela Nicora
- Luan Bonneau Arbeletche (ORCID: https://orcid.org/0000-0002-3087-3609)
- Carmelo Evoli
- Michael Prouza
- Adriana Vásquez-Ramírez
- Mariano Gómez Berisso
- Roger W Clay
- Margita Kubátová
- Melanie Weitz (ORCID: https://orcid.org/0009-0001-9010-9610)
- A. A. Watson
- Primo F. Gómez Vitale
- Rogerio M. de Almeida
- Corinne Berat
- Glennys R. Farrar
- Martina Boháčová
- David Schmidt
- R. Sarmento (ORCID: https://orcid.org/0000-0002-5018-5467)
- Pavel Horváth (ORCID: https://orcid.org/0000-0002-6710-5339)
- G. Marsella (ORCID: https://orcid.org/0000-0002-3152-8874)
- Nataliia Borodai (ORCID: https://orcid.org/0000-0003-1864-937X)
- Cristina Galea
- Kévin Almeida Cheminant (ORCID: https://orcid.org/0000-0001-6352-5339)
- Miroslav Pech
- Martin Schimassek (ORCID: https://orcid.org/0000-0003-4295-7719)
- Jose F. Valdés Galicia
- H. Schieler (ORCID: https://orcid.org/0000-0002-2637-4778)
- Petr Tobiska (ORCID: https://orcid.org/0000-0003-4017-2475)
- Lawrence Wiencke
- Jorge Rubén Rodriguez Rojo
- Daniele Martello
- Florian Lukas Briechle
- Marcelo Augusto Leigui de Oliveira
- Marcos Cerda
- Vincenzo Rizi
- Valerio Verzi
- Michael Schimp
- Laura Valore
- Tiina Suomijärvi
- Mário Pimenta
- Piera Luisa Ghia
- P. Gabriel Brichetto Orchera
- Gaetano Salina
- Markus Risse
- Ruben Squartini
- Agustín Cobos Cerutti
- Petr Janecek
- Diego Correia dos Santos
- Dave Nitz
- Brian Fick
- Hans Klages
- Alan Fuster
- Vladimír Novotný
- Lorenzo Perrone
- Virginia Binet
- Olivier Deligny
- Marina Scornavacche
- Alexander Menshikov
- Dusan Mandat
- C. Dobrigkeit
- Juan Carlos Arteaga Velázquez
- Ioana Codrina Maris
- Ricardo Sato
- Cainã Oliveira
- Max Büsken
- A. Săftoiu (ORCID: https://orcid.org/0000-0002-7903-6510)
- L. Lopes (ORCID: https://orcid.org/0000-0001-8571-0033)
- Patrick Stassi (ORCID: https://orcid.org/0000-0001-5584-8410)
- Abha Khakurdikar (ORCID: https://orcid.org/0000-0002-4857-5255)
- Sonja Mayotte (ORCID: https://orcid.org/0000-0001-8957-8033)
- F. Sánchez (ORCID: https://orcid.org/0000-0002-6861-6261)
- Rodrigo Pelayo
- Fabian Gobbi
- Baobiao Yue
- Lorenzo Apollonio (ORCID: https://orcid.org/0009-0008-5625-5893)
- Carla Aramo
- Teresa Bister
- Srijan Sehgal
- Joao dos Anjos
- Diego Melo
- Pierpaolo Savina
- Shayoni Panja
- Vlastimil Jílek (ORCID: https://orcid.org/0000-0001-5774-7285)
- Matías Rolf Hampel
- Veronika Vašíčková
- Paul Sommers
- Alexandra Fernandes (ORCID: https://orcid.org/0000-0002-9187-4007)
- Ugo GIACCARI
- Norbert Kunka
- Viviana Scherini
- Luiz Augusto Pereira
- Heino Falcke
- Matteo Conte
- Ezequiel Rodríguez
- Jannis Pawlowsky
- Danelise de Oliveira Franco
- Juan Manuel Figueira
- Federico Campuzano
- Luis Miguel Domingues Mendes
- Frederik Krieger
- Gael Flores Avila (ORCID: https://orcid.org/0000-0001-8375-6492)
- Sven Querchfeld
- Matthias Kleifges
- Samo Stanič
- Gabriella Cataldi
- Luciana Andrade Dourado
- Petr Schovánek (ORCID: https://orcid.org/0000-0002-5344-7645)
- Tomáš Fodran (ORCID: https://orcid.org/0009-0000-9529-0853)
- Matias Jorge Tueros (ORCID: https://orcid.org/0000-0003-1570-1419)
- D. Ravignani (ORCID: https://orcid.org/0000-0001-7410-8522)
- Megha Mogarkar
- Jhansi Bhavani Vuta
- Eric-Teunis de Boone
- Mohamed Ismaiel
- Karolina Syrokvas
- Matteo Tambone
- Pim van Dillen
Publication Details
- Published
- 2025-09-24
- DOI
- https://doi.org/10.22323/1.501.0431
- Primary Topic
- Precipitation Measurement and Analysis
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Strong
- European Commission
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Ministerstvo Školství, Mládeže a Tělovýchovy
- Grantová Agentura České Republiky
- Fonds De La Recherche Scientifique - FNRS
- Consejo Nacional de Investigaciones Científicas y Técnicas
- Fonds Wetenschappelijk Onderzoek
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
- Centre National de la Recherche Scientifique
- Financiadora de Estudos e Projetos
- Ministério da Ciência, Tecnologia, Inovações e Comunicações
- Vlaamse regering
- Agencia Nacional de Promoción Científica y Tecnológica
- Institut National de Physique Nucléaire et de Physique des Particules