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The number of muons in an air shower is a strong indicator of the mass of the primary particle and increases with a small power of the cosmic ray mass by the $\beta$-exponent, $N_{\mu} \sim A^{(1-\beta)}$. This behaviour can be explained in terms of the Heitler-Matthews model of hadronic air showers. In this paper, we present a method for calculating $\beta$ from the Heitler-Matthews model. The method has been successfully verified with a series of simulated events observed by the Pierre Auger Observatory at $10^{19}$ eV. To follow real measurements of the mass composition at this energy, the generated sample consists of a certain fraction of events produced with p, He, N and Fe primary energies. Since hadronic interactions at the highest energies can differ from those observed at energies reached by terrestrial accelerators, we generate a mock data set with $\beta =0.92$ (the canonical value) and $\beta =0.96$ (a more exotic scenario). The method can be applied to measured events to determine the muon signal for each primary particle as well as the muon scaling factor and the $\beta$-exponent. Determining the $\beta$-exponent can effectively constrain the parameters that govern hadronic interactions and help solve the so-called muon problem, where hadronic interaction models predict too few muons relative to observed events. In this paper, we lay the foundation for the future analysis of measured data from the Pierre Auger Observatory with a simulation study., Comment: Proccedings of 38th International Cosmic Ray Conference (ICRC2023)

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 Symposium

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:2108.07527

The Cosmic Ray Extremely Distributed Observatory (CREDO) is a newly formed, global collaboration dedicated to observing and studying cosmic rays (CR) and cosmic ray ensembles (CRE): groups of a minimum of two CR with a common primary interaction vertex or the same parent particle. The CREDO program embraces testing known CR and CRE scenarios, and preparing to observe unexpected physics, it is also suitable for multi-messenger and multi-mission applications. Perfectly matched to CREDO capabilities, CRE could be formed both within classical models (e.g. as products of photon-photon interactions), and exotic scenarios (e.g. as results of decay of Super Heavy Dark Matter particles). Their fronts might be significantly extended in space and time, and they might include cosmic rays of energies spanning the whole cosmic ray energy spectrum, with a footprint composed of at least two extensive air showers with correlated arrival directions and arrival times. Since CRE are mostly expected to be spread over large areas and, because of the expected wide energy range of the contributing particles, CRE detection might only be feasible when using available cosmic ray infrastructure collectively, i.e. as a globally extended network of detectors. Thus, with this review article, the CREDO Collaboration invites the astroparticle physics community to actively join or to contribute to the research dedicated to CRE, and in particular to share any cosmic ray data useful for the specific CRE detection strategies., Comment: 59 pages, 23 figures

The Cosmic-Ray Extremely Distributed Observatory (CREDO) is a project created a few years ago in the Institute of Nuclear Physics PAS in Krak\'ow and dedicated is to global studies of extremely extended cosmic-ray phenomena. The main reason for creating such a project was that the cosmic-ray ensembles (CRE) are beyond the capabilities of existing detectors and observatories. Until now, cosmic ray studies, even in major observatories, have been limited to the recording and analysis of individual air showers therefore ensembles of cosmic-rays, which may spread over a significant fraction of the Earth were neither recorded nor analyzed. In this paper the status and perspectives of the CREDO project are presented., Comment: 8 pages, 5 figures

We study the feasibility of detecting preshower initiated by ultra-high energy photons using Monte-Carlo simulations of nearly horizontal air showers for the example of the La Palma site of the Cherenkov Telescope Array. We investigate the efficiency of multivariate analysis in correctly identifying preshower events initiated by 40 EeV photons and cosmic-ray dominated background simulated in the energy range 10 TeV -- 10 EeV. The effective areas for such kind of events are also investigated and event rate predictions related to different ultra-high energy photons production models are presented. While the expected number of preshowers from diffuse emission of UHE photon for 30 hours of observation is estimated around $3.3\times10^{-5}$ based on the upper limits put by the Pierre Auger Observatory, this value is at the level of $2.7\times10^{-4}$ ($5.7\times 10^{-5}$) when considering the upper limits of the Pierre Auger Observatory (Telescope Array) on UHE photon point sources. However, UHE photon emission may undergo possible "boosting" due to gamma-ray burst, increasing the expected number of preshower events up to 0.17 and yielding a minimum required flux of $\sim 0.2$ $\mathrm{km^{-2}yr^{-1}}$ to obtain one preshower event, which is about a factor 10 higher than upper limits put by the Pierre Auger Observatory and Telescope Array (0.034 and 0.019 $\mathrm{km^{-2}yr^{-1}}$, respectively)., Comment: 16 pages, 16 figures, 4 tables

The search for Cosmic-Ray Ensembles (CRE), groups of correlated cosmic rays that might be distributed over very large areas, even of the size of the planet, requires a globally spread and dense network of detectors, as proposed by the Cosmic-Ray Extremely Distributed Observatory (CREDO) Collaboration. This proposal motivates an effort towards exploring the potential of using even very much diversified detection technologies within one system, with detection units located even in hard-to-reach places, where, nevertheless, the sensors could work independently - without human intervention. For these reasons we have developed a dedicated communication solution enabling the connection of many different types of detectors, in a range of environments. The proposed data transmission system uses radio waves as an information carrier on the 169MHz frequency band in a contrast to the typical commercially used frequencies in a IoT systems (868MHz). The connectivity within the system is based on the star topology, which ensures the least energy consumption. The solution is now being prepared to being implemented using the prototype detection system based on the CosmicWatch open hardware design: a portable, pocket size, and economy particle detector using the scintillation technique. Our prototype detector is equipped with a dedicated software that integrates it with the already operational CREDO server system., Comment: ICRC2019

Ultra-high energy photons constitute one of the most important pieces of the astroparticle physics problems. Their observation may provide new insight on several phenomena such as supermassive particle annihilation or the GZK effect. Because of the absence of any significant photon identification by a leading experiments such as the Pierre Auger Observatory, we consider a screening phenomenon called preshower effect which could efficiently affect ultra-high energy photon propagation. This effect is a consequence of photon interactions with the geomagnetic field and results in large electromagnetic cascade of particles several thousands kilometers above the atmosphere. This collection of particles, called cosmic-ray ensembles (CRE), may reach the atmosphere and produce the well-known air showers. In this paper we propose to use gamma-ray telescopes to look for air showers induced by CRE. Possible sources of ultra-high energy photons include the GZK effect and Super Heavy Dark Matter particles. Simulations involving the preshower effect and detectors response are performed and properties of these peculiar air showers are investigated. The use of boosted decision trees to obtain the best cosmic-ray ensemble/hadron separation, the aperture and event rate predictions for a few models of photon production are also presented., Comment: 8 pages, 3 figures, International Cosmic Ray Conference 2019

Propagation of ultra-high energy photons in the galactic and intergalactic space gives rise to cascades comprising thousands of photons. Using Monte Carlo simulations, we investigate the development of such cascades in the solar magnetosphere, and find that the photons in the cascades are distributed over hundreds of kilometers as they arrive at the top of the Earth's atmosphere. We also perform similar study for cascades starting as far as 10 Mpc away from us using relevant magnetic field models. A few photons correlated in time are expected to arrive at the Earth from the latter type of cascade. We present our simulation results and discuss the prospects for detection of these cascades with the Cosmic-Ray Extremely Distributed Observatory.

The Cosmic-Ray Extremely Distributed Observatory (CREDO) is a project dedicated to global studies of extremely extended cosmic-ray phenomena, the cosmic-ray ensembles (CRE), beyond the capabilities of existing detectors and observatories. Up to date cosmic-ray research has been focused on detecting single air showers, while the search for ensembles of cosmic-rays, which may spread over a significant fraction of the Earth, is a scientific terra incognita. The key idea of CREDO is to combine existing cosmic-ray detectors (large professional arrays, educational instruments, individual detectors, such as smartphones, etc.) into a worldwide network, thus enabling a global analysis. The second goal of CREDO involves a large number of participants (citizen science!), assuring the geographical spread of the detectors and managing manpower necessary to deal with vast amount of data to search for evidence for cosmic-ray ensembles. In this paper the status and perspectives of the project are presented., Comment: Proceedings of 36th International Cosmic Ray Conference - ICRC2019 - July 24th - August 1st, 2019 Madison, WI, U.S.A