Calculation of rescaling factors and nuclear multiplication of muons in extensive air showers

Recent results obtained from leading cosmic ray experiments indicate that simulations using LHC-tuned hadronic interaction models underestimate the number of muons in extensive air showers compared to experimental data. This is the so-called muon deficit problem. Determination of the muon component in the air shower is crucial for inferring the mass of the primary particle, which is a key ingredient in the efforts to pinpoint the sources of ultra-high energy cosmic rays.In this paper, we present a new method to derive the muon signal in detectors, which uses the difference between the total reconstructed (data) and simulated signals is roughly independent of the zenith angle, but depends on the mass of the primary cosmic ray. Such a method offers an opportunity not only to test/calibrate the hadronic interaction models, but also to derive the $\beta$ exponent, which describes an increase of the number of muons in a shower as a function of the energy and mass of the primary cosmic ray. Detailed simulations show a dependence of the $\beta$ exponent on hadronic interaction properties, thus the determination of this parameter is important for understanding the muon deficit problem. We validate the method by using Monte Carlo simulations for the EPOS-LHC and QGSJetII-04 hadronic interaction models, and showing that this method allows us to recover the ratio of the muon signal between EPOS-LHC and QGSJetII-04 and the average $\beta$ exponent for the studied system, within less than a few percent. This is a consequence of the good recovery of the muon signal for each primary included in the analysis.Comment: This work corresponds to the presentation at the ICNFP 2022 at Kolymbari, Crete, in September 2022. The proceedings will be published in Physica Scripta. arXiv admin note: text overlap with arXiv:2108.0752

The muon deficit problem: a new method to calculate the muon rescaling factors and the Heitler-Matthews β exponent

Simulations of extensive air showers using current hadronic interaction models predict too small numbers of muons compared to events observed in the air-shower experiments, which is known as the muon-deficit problem. In this work, we present a new method to calculate the factor by which the muon signal obtained via Monte-Carlo simulations must be rescaled to match the data, as well as the exponent from the Heitler-Matthews model which governs the number of muons found in an extensive air shower as a function of the mass and the energy of the primary cosmic ray. This method uses the so-called variable (difference between the total reconstructed and the simulated signals), which is connected to the muon signal and is roughly independent of the zenith angle, but depends on the mass of the primary cosmic ray. Using a mock dataset built from QGSJetII-04, we show that such a method allows us to reproduce the average muon signal from this dataset using Monte-Carlo events generated with the EPOS-LHC hadronic model, with accuracy better than 6%. As a consequence of the good recovery of the muon signal for each primary included in the analysis, also the exponent can be obtained with accuracy of less than 1% for the studied system. Detailed simulations show a dependence of the exponent on hadronic interaction properties, thus the determination of this parameter is important for understanding the muon deficit problem

The muon deficit problem: a new method to calculate the muon rescaling factors and the Heitler-Matthews beta exponent

Simulations of extensive air showers using current hadronic interaction models predict too small numbers of muons compared to events observed in the air-shower experiments, which is known as the muon-deficit problem. In this work, we present a new method to calculate the factor by which the muon signal obtained via Monte-Carlo simulations must be rescaled to match the data, as well as the beta exponent from the Heitler-Matthews model which governs the number of muons found in an extensive air shower as a function of the mass and the energy of the primary cosmic ray. This method uses the so-called z variable (difference between the total reconstructed and the simulated signals), which is connected to the muon signal and is roughly independent of the zenith angle, but depends on the mass of the primary cosmic ray. Using a mock dataset built from QGSJetII-04, we show that such a method allows us to reproduce the average muon signal from this dataset using Monte-Carlo events generated with the EPOS-LHC hadronic model, with accuracy better than 6%. As a consequence of the good recovery of the muon signal for each primary included in the analysis, also the beta exponent can be obtained with accuracy of less than 1% for the studied system. Detailed simulations show a dependence of the beta exponent on hadronic interaction properties, thus the determination of this parameter is important for understanding the muon deficit problem.Comment: 8 pages, 5 figures, 2 tables, accepted for publication in the proceedings of the 27th European Cosmic Ray Symposiu

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary file