The bulk of air showers initiated by very high energy cosmic rays exhibits a longitudinal development in depth with a single well-defined shower maximum. However, a small fraction of showers has a profile that differs considerably from this average behaviour. In extreme cases, such anomalous longitudinal profiles can even have two distinct shower maxima. We discuss the properties of the primary interactions that lead to such profiles. Simulations are used to estimate the rate of anomalous profiles in dependence of primary energy, mass, and characteristic features of hadronic multiparticle production at very high energies.
Equations for the center of gravity of the shower originated by high energy proton in the atmosphere are written and, within certain simplifications, solved for the case of logarithmically decreasing interaction length of hadrons in the air. Obtained expression provides transparent view of the way in which hadronic interaction characteristics determine the longitudinal shower development.
The description of high-energy hadronic interactions plays an important role in the (astrophysical) interpretation of air shower data. The parameter space important for the development of air showers (energy and kinematical range) extends well beyond todays accelerator capabilities. Therefore, accurate measurements of air showers are used to constrain modern models to describe high-energy hadronic interactions. The results obtained are complementary to information gained at accelerators and add to our understanding of high-energy hadronic interactions.
The Cherenkov radio pulse emitted by hadronic showers in ice is calculated for showers of energies in the EeV range. This is obtained with three dimensional simulations of both shower development and the coherent radio pulse emitted as the excess charge develops in the shower. A Monte Carlo, ZHAireS, has been developed for this purpose combining the high energy hadronic interaction capabilities of AIRES, and the dense media propagation capabilities of TIERRAS, with the precise low energy tracking and specific algorithms developed to calculate the radio emission in ZHS. A thinning technique is …
We report on a study about some characteristics of muon production during the development of extended air showers initiated by ultra-high-energy cosmic rays. Using simulations with the recent new version of the AIRES air shower simulation system, we analyze and discuss on the observed discrepancies between experimental measurements and simulated data.
We study the dependence of extensive air shower development on the first hadronic interactions at ultra-high energies occurring in the startup phase of the air shower cascade. The interpretation of standard air shower observables depends on the characteristics of these interactions. Thus, it is currently difficult to draw firm conclusions for example on the primary cosmic ray mass composition from the analysis of air shower data. On the other hand, a known primary mass composition would allow us to study hadronic interactions at center of mass energies well above the range that is accessible t…
Predictions of the hadronic interaction model EPOS~1.61 as implemented in the air shower simulation program CORSIKA are compared to observations with the KASCADE experiment. The investigations reveal that the predictions of EPOS are not compatible with KASCADE measurements. The discrepancies seen are most likely due to use of a set of inelastic hadronic cross sections that are too high.
We introduce a simple branching model for the development of hadronic showers in the Earth's atmosphere. Based on this model, we show how the size of the pionic component followed by muons can be estimated. Several aspects of the subsequent muonic component are also discussed. We focus on the energy evolution of the muon production depth. We also estimate the impact of the primary particle mass on the size of the hadronic component. Even though a precise calculation of the development of air showers must be left to complex Monte Carlo simulations, the proposed model can reveal qualitative insi…
The aim of this report of the Working Group on Hadronic Interactions and Air Shower Simulation is to give an overview of the status of the field, emphasizing open questions and a comparison of relevant results of the different experiments. It is shown that an approximate overall understanding of extensive air showers and the corresponding hadronic interactions has been reached. The simulations provide a qualitative description of the bulk of the air shower observables. Discrepancies are however found when the correlation between measurements of the longitudinal shower profile are compared to t…
We describe the analysis of longitudinal air shower profiles as measured by the fluorescence detectors of the Pierre Auger Observatory and present the measurement of the depth of maximum of extensive air showers, Xmax, with energies >10^18 eV. The measured energy evolution of the average of Xmax and its fluctuations are compared to air shower simulations for different primary particles.
With the aim to describe the longitudinal development of Cherenkov dominated showers we investigate the energy deposit and the number of charged particles in air showers induced by energetic cosmic rays. Based on the Monte Carlo simulations, discrepancies between different estimates of calorimetric energies are documented. We focus on the energy deposit profiles of air showers deducible from the fluorescence and Cherenkov light generated along CONEX and CORSIKA cascades.
The Heitler-Matthews model for hadronic air showers will be extended to all the generations of electromagnetic subshowers in the hadronic cascade. The analysis is outlined in detail for showers initiated by primary protons. For showers initiated by iron primaries the part of the analysis is given for as far as it differs from the analysis for a primary proton. Predictions for shower sizes and the depth of maximum shower size are compared with results of Monte Carlo simulations. The depth of maximum as it follows from the extrapolation of the Heitler-Matthews model restricted to the first gener…
Hadronic interaction models at cosmic ray (CR) energies are inherently uncertain due to the lack of a fundamental theoretical description of soft hadronic and nuclear interactions and the large extrapolation required from collider energies to the range of the most energetic cosmic rays observed ($>10^{20}$ eV). Model uncertainties are evaluated within the QGSJET-II model, by varying some of the crucial parameters in the limits allowed by collider data, and between QGSJET-II and other models commonly used in air shower simulations. The crucial parameters relate to hard processes, string fragmen…
The paper presents data on the muon component with a threshold \(\varepsilon_{thr} \geq\) 1 GeV. Air showers were registered at the Yakutsk array during almost 50 years of continuous air shower observations. The characteristics of muons are compared with calculations of QGSjetII-04 and EPOS LHC models for a proton and an iron nucleus. There is a muon deficit in the models, at energies greater than 5 EeV. To make an agreement between experimental data and simulations on muons, further tuning of the models is required.
The aim of the Pierre Auger Observatory is the investigation of the nature of cosmic ray particles at ultra-high energies. It can simultaneously observe the longitudinal air shower development in the atmosphere as well as particle densities on the ground. While there are no dedicated muon detectors, techniques have been developed to estimate the number of muons, $N_μ$, produced by air showers. Both, the longitudinal development, in particular the depth of the shower maximum, $X_{\rm max}$, and the muon content of air showers are highly sensitive to hadronic interactions at ultra-high energies.…
Cosmic rays provide an unique approach to study hadronic interactions at high energies in the kinematic forward direction. The KASCADE air shower experiment was the first to conduct quantitative tests of hadronic interactions with air shower data. A brief overview is given on results from KASCADE and its extension KASCADE-Grande with respect to investigations of hadronic interactions and the properties of cosmic rays.
Extensive Air Showers are complex macroscopic objects initiated by single ultra-high energy particles. They are the result of millions of high energy reactions in the atmosphere and can be described as the superposition of hadronic and electromagnetic cascades. The hadronic cascade is the air shower backbone, and it is mainly made of pions. Decays of neutral pions initiate electromagnetic cascades, while the decays of charged pions produce muons which leave the hadronic core and travel many kilometers almost unaffected. Muons are smoking guns of the hadronic cascade: the energy, transverse mom…
In this article, I will review how observations performed with extensive air showers are being used to probe hadronic interactions at high energy. I will briefly overview the new studies exploring the connection between the dynamics of air showers and multiparticle production, and how this knowledge can be translated into constraints on high energy hadronic models. I will also overview direct measurements, complementary to, and beyond the reach of, accelerator experiments.
Studies of the nature of cosmic ray particles at the highest energies are based on the measurement of extensive air showers. Most cosmic ray properties can therefore only be obtained from the interpretation of air shower data and are thus depending on predictions of hadronic interaction models at ultra-high energies. We discuss different scenarios of model extrapolations from accelerator data to air shower energies and investigate their impact on the corresponding air shower predictions. To explore the effect of different extrapolations by hadronic interaction models we developed an ad hoc mod…
We present the first results of the application of the recently found universality of behavior of muon signal to electromagnetic (EM) signal ratio with respect to the vertical depth of showers maximum for mass composition and hadronic interaction studies. Making use of the fact that for zenith angles above 45 degrees the dependence of the ratio on the vertical depth of shower maximum is very similar for QGSJET II and EPOS 1.99 we show that this provides the possibility to estimate muon shower content in almost interaction model independent way. To evaluate the excess of signal in the data in r…
The concept of Universal Shower Profile is used to characterize the average behavior of high energy cosmic rays. The shape variables contain important information about composition. They are independent of the primary cross-section by construction, but affected by other hadronic parameters, like multiplicity. The two variables give access to the average nuclear mass of the sample and their compatibility serves as a test of hadronic models.
Characteristics of the high energy families (bundle of high energy e, gamma) and hadrons in the air-showers detected in the hybrid experiment together with emulsion chamber and AS-array at Mt.Chacaltaya are studied in detail by comparing with those of CORSIKA simulations using interaction models of QGSJET and EPOS. Because the atmospheric families and hadron component have more direct information of the nuclear interaction, correlations between atmospheric families and burst (hadron component of air-showers) accompanied to air-showers are more sensitive to the mechanism of the the cosmic-ray i…
In the sub-TeV regime, the most widely used hadronic interaction models disagree significantly in their predictions of particle spectra from cosmic ray induced air showers. We investigate the nature and impact of model uncertainties, focussing on air shower primaries with energies around the transition between high and low energy hadronic interaction models, where the dissimilarities are largest and which constitute the bulk of the interactions in air showers.
An alternative parametrization of the particle shower longitudinal profile is presented. The accuracy of the obtained shower profile description is about 2-3% for the 0-1500 g/cm^2 atmosphere slant depths and primary H, He,... Fe nuclei in the 1 PeV-10 EeV energy range. It is shown that the shape of shower profile depends only on the nucleon energy, whereas the maximum shower size also depends on the energy of the parental nucleus. Results are based on the CORSIKA simulated shower profiles and are presented in comparison with the Gaisser-Hillas parametrization.
We present a summary of recent tests and measurements of hadronic interaction properties with air showers. This report has a special focus on muon density measurements. Several experiments reported deviations between simulated and recorded muon densities in extensive air showers, while others reported no discrepancies. We combine data from eight leading air shower experiments to cover shower energies from PeV to tens of EeV. Data are combined using the z-scale, a unified reference scale based on simulated air showers. Energy-scales of experiments are cross-calibrated. Above 10 PeV, we find a m…
Muons serve as the best probes of the physics of hadronic interactions in the upper atmosphere because of their simple physics. All the properties of detected muons, such as their energy and angle of incidence, are governed by the properties of their parent hadrons. The angular distribution of the detected muons is a result of a superposition of multiple effects, and is governed by a number of parameters, such as the cutoff rigidity (magnetic field), atmospheric attenuation, interaction cross sections, production height, multiplicity and pseudorapidity. Since particle interactions are handled …
In the sub-TeV regime, the most widely used hadronic interaction models disagree significant lying their predictions for post-first interaction and ground-level particle spectra from cosmic ray induced air showers. These differences generate an important source of systematic uncertainty in their experimental use. We investigate the nature and impact of model uncertainties through a simultaneous analysis of ground level particles and first interaction scenarios. We focus on air shower primaries with energies close to the transition between high and low energy hadronic interaction models, where …
Longitudinal Development Analysis of Extensive Air Showers Using CORSIKA Simulations
Ministry of Agriculture, Directorate of Animal ResourceDepartment of Protection of Genetic Resource（农业部动物资源局遗传资源保护处）；Mustansiriyah University, College of Science（穆斯塔纳西尔大学理学院）
In this paper we review air shower data related to the mass composition of cosmic rays above 10$^{15}$ eV. After explaining the basic relations between air shower observables and the primary mass and energy of cosmic rays, we present different approaches and results of composition studies with surface detectors. Furthermore, we discuss measurements of the longitudinal development of air showers from non-imaging Cherenkov detectors and fluorescence telescopes. The interpretation of these experimental results in terms of primary mass is highly susceptible to the theoretical uncertainties of hadr…
The characteristics of extensive air showers are sensitive to the details of hadronic interactions at energies and in kinematic regions beyond those tested by human-made accelerators. Uncertainties on extrapolations of the hadronic interaction models in these regions hamper the interpretation of the ultra high energy cosmic ray data in terms of primary mass composition. We report on how the Pierre Auger Observatory is able to constrain the hadronic interaction models by measuring the muon content and muon production depth of air showers and also by measuring the proton-air cross section for pa…
In extensive air shower experiments, the number of muons crossing a detector at a given position, as well as their arrival time, arrival direction, and energy, are determined by a more fundamental 3-dimensional distribution linked to the hadronic core of the shower. Muons are produced high up in the atmosphere after the decay of mesons in the hadronic cascade. The distributions of production depth, energy, and transverse momentum of muons are enough to fully predict the muon component of air showers in any particular observational condition. By using air-shower simulations with the state-of-th…
We present a method to reconstruct the longitudinal profile of electrons in showers using Cherenkov telescopes. We show how the Cherenkov light collected by an array of telescopes can be transformed into the number of electrons as a function of atmospheric depth. This method is validated using air shower and simplified telescope simulations. The reconstruction of the depth in which the shower has the maximum number of electrons ($\mathrm{X_{max}}$) opens the possibility of cosmic ray composition studies with Cherenkov telescopes in the energy range from 10 to 100 TeV. A resolution of less than…
KASCADE-Grande is dedicated for investigations of cosmic-ray air showers in the primary energy range from 10 PeV to 1 EeV. The multi-detector system allows us to reconstruct charged particles, electron and muon numbers for individual air showers with high accuracies. Based on the shower size ($N_{ch}$) spectra of the charged particle component, the all-particle energy spectrum of cosmic rays is reconstructed, where attenuation effects in the atmosphere are corrected by applying the constant intensity cut method. The energy calibration is performed by using CORSIKA simulations with high-energy …
Extensive air showers initiated by ultra-high energy cosmic rays are sensitive to the details of hadronic interactions models, so we present the main results obtained using the data of the Pierre Auger Observatory. The depth at which the maximum of the electromagnetic development takes place is the most sensitive parameter to infer the nature of the cosmic rays. However, the hadronic models cannot describe consistently the maximum and the muon measurements at energies higher than those reached at the LHC.
The Pierre Auger Observatory is the largest facility in the world to study ultra-high-energy cosmic rays. It has a hybrid detection technique that combines the observation of the longitudinal development of extensive air showers and the measurement of their particles at the ground. This capability has opened the possibility to probe hadronic interactions taking place at energies well beyond those accessible by human-made accelerators. In this report, we present a selection of the latest results on hadronic interactions with measurements from the Pierre Auger Observatory. These data span over t…
The energy spectrum of muons at ground level in air showers are studied and a new observable is proposed to constrain hadronic interaction models used in air shower simulations. An asymmetric Gaussian function is proposed to describe the muon ground energy spectrum and its parameters are studied regarding primary particle, energy and hadronic interaction models. Based on two realistic measurements of the muon density at a given distance from the shower axis, a new observable (\rmu) is defined. Considering realistic values of detector resolutions and number of measured events, it is also shown …
The simulation analysis of the Extensive Air Showers (EAS) was executed by exploring the longitudinal development employing the AIRES system (version 19.04.00) for several hadronic interaction models (SIBYLL, QGSJET, and EPOS) for high energies. The simulation was performed for different high energies (10^17, 10^18, and 10^19) eV and two dissimilar primary particles, proton as well iron nuclei, with several zenith angles values (0^o, 10^o, and 30^o). The shower size of longitudinal development was parameterized using the sigmoidal function (Boltzmann model) and gave a new four parameters as fu…
Anomalous Air Showers and What They Reveal About Hadronic Interactions and Cosmic-ray Masses
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of Manchester（曼彻斯特大学）；Vrije Universiteit Brussel（布鲁塞尔自由大学）；Radboud University Nijmegen（奈梅亨拉德堡德大学）；Curtin University（科廷大学）；University of Groningen（格罗宁根大学）；Netherlands Institute for Radio Astronomy（荷兰射电天文研究所）；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；Nikhef（尼赫夫国家粒子物理研究所）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Khalifa University（哈利法大学）；Can Tho University（芹苳大学）；Nanjing University（南京大学）；Xidian University（西安电子科技大学）；University of Science and Technology of China（中国科学技术大学）
The predictions of hadronic interaction models for cosmic-ray induced air showers contain inherent uncertainties due to limitations of available accelerator data and theoretical understanding in the required energy and rapidity regime. Differences between models are typically evaluated in the range appropriate for cosmic-ray air shower arrays ($10^{15}$-$10^{20}$ eV). However, accurate modelling of charged cosmic-ray measurements with ground based gamma-ray observatories is becoming more and more important. We assess the model predictions on the gross behaviour of measurable air shower paramet…
A hybrid experiment has been started by ASγ collaboration at Tibet, China, since May 2009, that consists of a burst-detector-grid (YAC, Yangbajing Air shower Core array) and the Tibet air-shower array (Tibet-III). The first step of YAC, called YAC-I, contains 16 detector units and observes high energy electromagnetic particles in air-shower cores within several meters from the shower axis, and Tibet-III array measures the total energy and the arrival direction of air showers. YAC-I is used to check hadronic interaction models currently used for air-shower simulations such as QGSJET, SIBYLL, EP…
In gamma-ray astronomy through Imaging Atmospheric Cherenkov Telescopes (IACT), the atmosphere is used as a calorimeter. Incident gamma-rays in the GeV-TeV energy range are observed through the electromagnetic showers they produce in the atmosphere and the Cherenkov light emitted by them. We aim to obtain a parameterisation of the longitudinal profiles of electromagnetic showers in the atmosphere. The longitudinal Cherenkov emission profiles of these showers can be used for the reconstruction of the parameters of the gamma-photon as well gamma-hadron discrimination. Obtaining an accurate param…
Extensive air showers are complex objects, resulting of billions of particle reactions initiated by single cosmic ray at ultra-high-energy. Their characteristics are sensitive both to the mass of the primary cosmic ray and to the details of hadronic interactions. Many of the interactions that determine the shower features occur in kinematic regions and at energies beyond those tested by human-made accelerators. We will report on the measurement of the proton-air cross section for particle production at a center-of-mass energy per nucleon of 39 TeV and 56 TeV. We will also show comparisons of p…
The hybrid design of the Pierre Auger Observatory allows for the measurement of a number of properties of extensive air showers initiated by ultra-high energy cosmic rays. By comparing these measurements to predictions from air shower simulations, it is possible to both infer the cosmic ray's mass composition and test hadronic interactions beyond the energies reached by accelerators. In this paper, we will present a compilation of results of air shower measurements by Pierre Auger Observatory which are sensitive to the properties of hadronic interactions and can be used to constrain the hadron…
We present a new version of the hadron interaction event generator Sibyll. While the core ideas of the model have been preserved, the new version handles the production of baryon pairs and leading particles in a new way. In addition, production of charmed hadrons is included. Updates to the model are informed by high-precision measurements of the total and inelastic cross sections with the forward detectors at the LHC that constrain the extrapolation to ultra-high energy. Minimum-bias measurements of particle spectra and multiplicities support the tuning of fragmentation parameters. This paper…
We observe a correlation between the slope of radio lateral distributions, and the mean muon pseudorapidity of 59 individual cosmic-ray-air-shower events. The radio lateral distributions are measured with LOPES, a digital radio interferometer co-located with the multi-detector-air-shower array KASCADE-Grande, which includes a muon-tracking detector. The result proves experimentally that radio measurements are sensitive to the longitudinal development of cosmic-ray air-showers. This is one of the main prerequisites for using radio arrays for ultra-high-energy particle physics and astrophysics.
The average profiles of cosmic ray shower development as a function of atmospheric depth are measured for the first time with the Fluorescence Detectors at the Pierre Auger Observatory. The profile shapes are well reproduced by the Gaisser-Hillas parametrization at the 1% level in a 500 g/cm2 interval around the shower maximum, for cosmic rays with log(E/eV) > 17.8. The results are quantified with two shape parameters, measured as a function of energy. The average profiles carry information on the primary cosmic ray and its high energy hadronic interactions. The shape parameters predicted by t…
