The muonic and electromagnetic components of air showers are sensitive to the mass of the primary cosmic particle. The sizes of the components can be measured with particle detectors on ground, and the electromagnetic component in addition indirectly via its radio emission in the atmosphere. The electromagnetic particles do not reach the ground for very inclined showers. On the contrary, the atmosphere is transparent for the radio emission and its footprint on ground increases with the zenith angle. Therefore, the radio technique offers a reliable detection over the full range of zenith angles, and in particular for inclined showers. In this work, the mass sensitivity of a combination of the radio emission with the muons is investigated in a case study for the site of the Pierre Auger Observatory using CORSIKA Monte Carlo simulations of showers in the EeV energy range. It is shown, that the radio-muon combination features superior mass separation power in particular for inclined showers, when compared to established mass observables such as a combination of muons and electrons or the shower maximum Xmax. Accurate measurements of the energy-dependent mass composition of ultra-high energy cosmic rays are essential to understand their still unknown origin. Thus, the combination of muon and radio detectors can enhance the scientific performance of future air-shower arrays and offers a promising upgrade option for existing arrays.
The mass composition of ultra-high energy cosmic rays can be studied from the distributions of the depth of shower maximum and/or the muon shower size. Here, we study the dependence of the mean muon shower size on the depth of shower maximum in detail. Air showers induced by protons and iron nuclei were simulated with two models of hadronic interactions already tuned with LHC data (run I-II). The generated air showers were combined to obtain various types of mass composition of the primary beam. We investigated the shape of the functional dependence of the mean muon shower size on the depth of…
I discuss the conversion of muon counts in air showers, which are observable by experiments, into mean logarithmic mass, an important variable to express the mass composition of cosmic rays. Stochastic fluctuations in the shower development and statistical fluctuations from muon sampling can subtly bias the conversion. A central theme is that the mean of the logarithm of the muon number is not identical to the logarithm of the mean. It is discussed how that affects the conversion in practice. Simple analytical formulas to quantify and correct such biases are presented, which are applicable to …
The paper present correlation of radio signal with air shower parameters: shower energy E0 and depth of maximum Xmax. It is shown that from radio emission measurements of air showers one can obtain individual showers parameters and mass composition of cosmic rays. We also derived generalized formula for calculating energy of the air showers.
IceTop, the surface component of the IceCube detector, has been used to measure the energy spectrum of cosmic ray primaries in the range between 1.58 PeV and 1.26 EeV. It can also be used to study the low energy muons in air showers by looking at large distances (> 300m) from the shower axis. We will show the muon lateral distribution function at large lateral distances as measured with IceTop and discuss the implications of this measurement. We also discuss the prospects for low energy muon studies with IceTop.
The pattern of the radio emission of air showers is finely sampled with the Low-Frequency ARray (LOFAR). A set of 382 measured air showers is used to test a fast, analytic parameterization of the distribution of pulse powers. Using this parameterization we are able to reconstruct the shower axis and give estimators for the energy of the air shower as well as the distance to the shower maximum.
AERA, the Auger Engineering Radio Array, located at the Pierre Auger Observatory in Malargüe, Argentina measures the radio emission of extensive air showers in the 30-80 MHz frequency range and is optimized for the detection of air showers up to 60$^{\circ}$ zenith angle. In this contribution the motivation, the status, and first results of the analysis of horizontal air showers with AERA will be presented.
We introduce a new Monte Carlo template-based reconstruction method for air shower arrays, with a focus on shower core and energy reconstruction of $γ$-ray induced air showers. The algorithm fits an observed lateral amplitude distribution of an extensive air shower against an expected probability distribution using a likelihood approach. A full Monte Carlo air shower simulation in combination with the detector simulation is used to generate the expected probability distributions. The goodness of fit can be used to discriminate between $γ$-ray and hadron induced air showers. As an example, we a…
Measuring radio emission from air showers provides excellent opportunities to directly measure all air shower properties, including the shower development. To exploit this in large-scale experiments, a simple and analytic parameterization of the distribution of the radio signal at ground level is needed. Data taken with the Low-Frequency Array (LOFAR) show a complex two-dimensional pattern of pulse powers, which is sensitive to the shower geometry. Earlier parameterizations of the lateral signal distribution have proven insufficient to describe these data. In this article, we present a paramet…
The High Altitude Water Cherenkov (HAWC) gamma-ray observatory is a ground-based air shower array designed to detect Cherenkov light produced in water by secondary particles from atmospheric air showers. In order to improve the sensitivity at the highest energies, especially for the shower cores falling outside the main array, 345 smaller Water Cherenkov Detectors (WCDs) were installed around the main array, the outrigger array. This extension increased the instrumented area of HAWC by a factor of four. With the increased size of the array, and the ability to detect shower particles further aw…
The paper aims to explore the asymmetry of the muon content of non-vertical and very high energy Monte Carlo showers due to the influence of Earth's geomagnetic field. Simulations have shown that the geomagnetic field modifies the trajectories of muons in a shower producing a polar asymmetry in the density/number of positive and negative muons in the shower front plane. The asymmetry is quantified by a transverse separation between the positive and negative muons barycentric positions through opposite quadrants across the shower core. The dependence of this transverse muon barycenter separatio…
High-energy cosmic rays impinging onto the atmosphere of the Earth initiate extensive air showers. With the LOFAR radio telescope and the Auger Engineering Radio Array (AERA) at the Pierre Auger Observatory radio emission from air showers is detected. Recent results are presented from both experiments. The measured properties of the radio emission are described. The measurements are used to derive the properties of high-energy cosmic rays: their arrival direction, energy, and particle type (mass).
The Auger Engineering Radio Array (AERA), at the Pierre Auger Observatory in Argentina, measures the radio emission of extensive air showers in the 30-80 MHz frequency range. AERA consists of more than 150 antenna stations distributed over 17 km$^2$. Together with the Auger surface detector, the fluorescence detector and the under-ground muon detector (AMIGA), AERA is able to measure cosmic rays with energies above 10$^{17}$ eV in a hybrid detection mode. AERA is optimized for the detection of air showers up to 60$^{\circ}$ zenith angle, however, using the reconstruction of horizontal air show…
Reflection of radio waves off the short-lived plasma produced by the high-energy shower particles in the air is simulated, considering various radar setups and shower geometries. We show that the plasma produced by air showers has to be treated always as underdense. Therefore, we use the Thomson cross-section for scattering of radio waves corrected for molecular quenching and we sum coherently contributions of the reflected radio wave over the volume of the plasma disk to obtain the time evolution of the signal arriving at the receiver antenna. The received power and the spectral power density…
In this paper we explore the possibility to complement the cosmic ray physics program of the IceCube observatory with an extended surface array of radio antennas. The combination of air-shower sampling on the surface and muon calorimetry underground offers significant scientifc potential: the neutrino sensitivity above the horizon can be enhanced by vetoing air-showers on the ground, photon-induced air-showers can be identifed by their small muon component and the coincident measurement of the particle density on the surface and the muon component gives useful information on the composition of…
We describe a method for restoring information lost during statistical thinning in extensive air shower simulations. By converting weighted particles from thinned simulations to swarms of particles with similar characteristics, we obtain a result that is essentially identical to the thinned shower, and which is very similar to non-thinned simulations of showers. We call this method dethinning. Using non-thinned showers on a large scale is impossible because of unrealistic CPU time requirements, but with thinned showers that have been dethinned, it is possible to carry out large-scale simulatio…
Imaging the radio-wave emission from extensive air showers
Radboud University Nijmegen（奈梅亨拉德堡德大学）；Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF)（荷兰核与高能物理国家研究所）；Max-Planck-Institute for Nuclear Physics（马克斯·普朗克核物理研究所）
We present two new aspects of Extensive Air Shower (EAS) development universality allowing to make accurate estimation of muon and electromagnetic (EM) shower contents in two independent ways. In the first case, to get muon (or EM) signal in water Cherenkov detectors it is enough to know the vertical depth of shower maximum and the total signal. In the second case, the EM signal can be calculated from the primary particle energy and the zenith angle. In both cases the parameterizations of muon and EM signals are almost independent on primary particle nature, energy and zenith angle.
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.
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.
The spatial distribution of Cherenkov radiation from cascade showers generated by muons in water has been measured with Cherenkov water calorimeter (CWC) NEVOD. This result allowed to improve the techniques of treating cascade showers with unknown axes by means of CWC response analysis. The techniques of selecting the events with high energy cascade showers and reconstructing their parameters are discussed. Preliminary results of measurements of the spectrum of cascade showers in the energy range 100 GeV - 20 TeV generated by cosmic ray muons at large zenith angles and their comparison with ex…
It is shown, that highly accurate estimation of muon shower content can be performed on the basis of knowledge of only vertical depth of shower maximum and total signal in ground detector. The estimate is almost independent on primary energy and particle type and on zenith angle. The study is performed for 21500 showers, generated with CORSIKA~6.204 from spectrum $E^{-1}$ in the energy range $\log10(E)$ [eV]=18.5--20 and uniformly in $\cos^2θ$ in zenith angle interval $θ=0^\circ-65^\circ$ for QGSJET II/Fluka interaction models.
Over the last two decades, various experiments have measured muon densities in extensive air showers over several orders of magnitude in primary energy. While some experiments observed differences in the muon densities between simulated and experimentally measured air showers, others reported no discrepancies. We will present an update of the meta-analysis of muon measurements from nine air shower experiments, covering shower energies between a few PeV and tens of EeV and muon threshold energies from a few 100 MeV to about 10 GeV. In order to compare measurements from different experiments, th…
The number of muons in extensive air showers predicted using LHC-tuned hadronic interaction models, such as EPOS-LHC and QGSJetII-04, is smaller than observed in showers recorded by leading cosmic ray experiments. In this paper, we present a new method to derive muon rescaling factors by analyzing reconstructions of simulated showers. The z-variable used (difference of initially simulated and reconstructed total signal in detectors) is connected to the muon signal and is roughly independent of the zenith angle but depends on the mass of primary cosmic ray. The performance of the method is test…
IceTop, the surface array of IceCube, measures air showers from cosmic rays within the energy range of 1 PeV to a few EeV and a zenith angle range of up to $\approx$ 36$^\circ$. This detector array can also measure air showers arriving at larger zenith angles at energies above 20 PeV. Air showers from lighter primaries arriving at the array will produce fewer muons when compared to heavier cosmic-ray primaries. A discrimination of these muons from the electromagnetic component in the shower can therefore allow a measurement of the primary mass. A study to discriminate muons using Monte-Carlo a…
The Sydney University Giant Air-shower Recorder (SUGAR) measured the muon component of extensive air showers with a unique array of muon detectors. The SUGAR data allow us to reconstruct the empirical dependence of muon density on the distance from the axis of the shower, the lateral distribution function (LDF). We compare the shape of this function with the predictions of hadronic-interaction models, QGSJET-II-04 and EPOS-LHC, in the energy range 10^17.6 - 10^18.6 eV. We find a difference between the observed data and the simulation: the observed muon density falls faster with the increased c…
The IceCube Neutrino Observatory at the South Pole can provide unique tests of muon production models in extensive air showers by measuring both the low-energy (GeV) and high-energy (TeV) muon components. We present here a measurement of the TeV muon content in near-vertical air showers detected with IceTop in coincidence with IceCube. The primary cosmic-ray energy is estimated from the dominant electromagnetic component of the air shower observed at the surface. The high-energy muon content of the shower is studied based on the energy losses measured in the deep detector. Using a neural netwo…
We demonstrate that the shower-to-shower fluctuations of the muon content of extensive air showers correlate with the fluctuations of a variable of the first interaction of Ultra High Energy Cosmic Rays, which is computed from the fraction of energy carried by the hadrons that sustain the hadronic cascade. The influence of subsequent stages of the shower development is found to play a sub-dominant role. As a consequence, the shower-to-shower distribution of the muon content is a direct probe of the hadron energy spectrum of interactions beyond 100 TeV center of mass energies.
Neutrino air showers can be formed in any part of the atmosphere passing a long was in the matter due to its physical properties. In general, air showers produced by neutrinos are highly inclined and formed near the ground level, i.e. young showers. Therefore, one should expect a large number of peaks in the signal of such air showers [1, 2, 3]. The goal of our work is to search for air shower candidates produced by neutrino. For this purposes, we analyzed large amount of data from scintillation detectors with different area and energy thresholds [1, 2]. Preliminary analysis of Yakutsk array d…
Some discrepancies have been reported between observed and simulated muon content of extensive air showers: the number of observed muons exceeded the expectations in HiRes-MIA, Yakutsk and Pierre Auger Observatory data. Here, we analyze the data of the Moscow State University Extensive Air Shower (EAS-MSU) array on E_mu>~10 GeV muons in showers caused by ~(10^17-10^18) eV primary particles and demonstrate that they agree with simulations (QGSJET-II-04 hadronic interaction model) once the primary composition inferred from the surface-detector data is assumed.
By using the integral method in the muon propagation through water, we calculate the range fluctuation of high and ultra high energy muons. Many authors divide all radiative processes into two parts, namely, the continuous part and radiative part in their Monte Carlo simulation in order to consider the fluctuation in the both ranges and energies of the muons, while we treat all stochastic processes as exactly as possible, without the introduction of the continuous parts in all stochastic processes. The validity of our Monte Carlo method is checked by the corresponding analytical method which i…
In this article we identify the key elements that govern the propagation of muons from the production in extensive air showers to ground. We describe a model based on simple assumptions that propagates the muons starting from the few relevant distributions at production. We compare the results to the ground distributions given by a full air shower Monte Carlo. This study is motivated by the need of modeling the muon component in extensive air showers with the goal of experimentally reconstructing their distributions at production, which act as a footprint of the hadronic cascade.
Several methods developed within the Pierre Auger Collaboration for the estimation of the muonic component of the Extensive Air Showers observed in the surface Cherenkov detectors are described. The results derived from the data show a deficit of muons predicted by the current hadronic interactions models at ultra-high energies.
We present a meta-analysis of recent muon density measurements made by eight air shower experiments which cover shower energies ranging from PeV to tens of EeV regarding the muon puzzle in extensive air showers. Some experimental analyses reported deviations between recorded and simulated muon densities in extensive air showers, and others reported no discrepancies. Comparisons between experiments were made using a universal reference scale based on the relative difference to simulated proton and iron initiated air showers. We have applied a cross-calibration of energy scales between experimen…
Using the simulation code SELFAS2, we present predictions of the radio signal emitted by extensive air showers (EAS) during their development in the atmosphere. The radio emission in the MHz range coming from air showers is the superposition of two mechanisms: the variation of the transverse current due to the systematic opposite drift of electrons and positrons in the Earth's magnetic field and the variation of the charge excess due to the electrons in excess in the shower front. In this paper, we stress particularly the effect of the realistic air refractive index on the radio signal predict…
The surface detector array of the Pierre Auger Observatory provides information about the longitudinal development of the muonic component of extensive air showers. Using the timing information from the flash analog-to-digital converter traces of surface detectors far from the shower core, it is possible to reconstruct a muon production depth distribution. We characterize the goodness of this reconstruction for zenith angles around 60 deg. and different energies of the primary particle. From these distributions we define X(mu)max as the depth along the shower axis where the production of muons…
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…
Atmospheric scattering of light emitted by an air shower not only attenuates direct fluorescence light from the shower, but also contributes to the observed shower light. So far only direct and singly-scattered Cherenkov photons have been taken into account in routine analyses of the observed optical image of air showers. In this paper a Monte Carlo method of evaluating the contribution of multiply scattered light to the optical air shower image is presented, as well as results of simulations and a parameterization of scattered light contribution to measured shower signal.
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.
Inspired by recent astrophysical observations of leptonic excesses measured by satellite experiments, we consider the impact of some general models of the dark sector on the muon production in extensive air showers. We present a compact approximative expression for the bremsstrahlung of a massive photon from an electron and use it within Monte Carlo simulations to estimate the amount of weakly interacting photon-like massive particles that could be produced in an extensive air shower. We find that the resulting muon production is by many orders of magnitude below the average muon count in a sh…
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…
Recently, several experiments reported a muon deficit in air shower simulations with respect to the data. This problem can be studied using an estimator that quantifies the relative muon content of the data with respect to those of proton and iron Monte Carlo air shower simulations. We analyze two estimators. The first one, based on the logarithm of the mean of the muon content, is built from experimental considerations. It is ideal for comparing results from different experiments as it is independent of the detector resolution. The second estimator is based on the mean of the logarithm of the…
The physics of radio emission from cosmic-ray induced air showers is shortly summarized. It will be shown that the radio signal at different distances from the shower axis provides complementary information on the longitudinal shower evolution, in particular the early part, and on the distribution of the electrons in the shower core. This complements the information obtained from surface, fluorescence, and muon detectors and is very useful in getting a comprehensive picture of an air shower.
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 origin and nature of ultra high energy cosmic rays remains being a mystery. However, great progress has been made in recent years due to the observations performed by the Pierre Auger Observatory and Telescope Array. In particular, it is believed that the composition information of the cosmic rays as a function of the energy can play a fundamental role for the understanding of their origin. The best indicators for primary mass composition are the muon content of extensive air shower and the atmospheric depth of the shower maximum. In this work we consider a maximum likelihood method to per…
We present the first hybrid measurement of the average muon number in air showers at ultra-high energies, initiated by cosmic rays with zenith angles between $62^\circ$ and $80^\circ$. The measurement is based on 174 hybrid events recorded simultaneously with the Surface Detector array and the Fluorescence Detector of the Pierre Auger Observatory. The muon number for each shower is derived by scaling a simulated reference profile of the lateral muon density distribution at the ground until it fits the data. A $10^{19}$~eV shower with a zenith angle of $67^\circ$, which arrives at the Surface D…
A new promising development in astroparticle physics is to measure the radio emission from extensive air showers. The particles in the cascade emit synchrotron radiation (30 - 90 MHz) which is detected with arrays of dipole antennas. Recent experimental efforts are discussed.
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…
In this paper we analyze the energy evolution of the muon content of air showers between $10^{18.4}$ and $10^{19.6}$ eV to be able to determine the most likely mass composition scenario from future number of muons measurements. The energy and primary mass evolution of the number of muons is studied based on the Heitler-Matthews model and Monte Carlo simulation of the air shower. A simple model to describe the evolution of the first and second moments of number of muons distributions is proposed and validated. An analysis approach based on the comparison between this model's predictions and dat…
The ratio of the number of muons with a threshold of 1 GeV and charged particles at a distance of 600 m from the axis is analyzed. Air showers with energies above 5 EeV and zenith angles with less than 60 degrees are considered. Comparison of experimental data with calculations by the QGSJETII-04 model for various primary nuclei, including a gamma ray, showed that the mass composition of cosmic rays up to energies of $\sim$ 10 EeV mainly consists of protons and helium nuclei, with a small number of heavy nuclei. Data include air showers with a very low muon content, which are assumed to be pro…
Measurements of the muon content of extensive air showers at the highest energies show discrepancies compared to simulations as large as the differences between proton and iron. This so-called muon puzzle is commonly attributed to a lack of understanding of the hadronic interactions in the shower development. Furthermore, measurements of the fluctuations of muon numbers suggest that the discrepancy is likely a cumulative effect of interactions of all energies in the cascade. A feature of the air shower simulation code CORSIKA 8 allows us to access all previous generations of final-state muons …
Using a large set of simulated extensive air showers, we investigate universality features of electron and positron distributions in very-high-energy cosmic-ray air showers. Most particle distributions depend only on the depth of the shower maximum and the number of particles in the cascade at this depth. We provide multi-dimensional parameterizations for the electron-positron distributions in terms of particle energy, vertical and horizontal momentum angle, lateral distance, and time distribution of the shower front. These parameterizations can be used to obtain realistic electron-positron di…
The Sydney University Giant Air-shower Recorder (SUGAR) measured the energy spectrum of ultra-high-energy cosmic rays reconstructed from muon-detector readings, while the Pierre Auger Observatory, looking at the same Southern sky, uses the calorimetric fluorescence method for the same purpose. Comparison of their two spectra allows us to reconstruct the empirical dependence of the number of muons in the shower on the primary energy for energies between $10^{17}$ and $10^{18.5}$ eV. We compare this dependence with the predictions of hadronic interaction models \mbox{QGSJET-II-04} and \mbox{EPOS…
At ground level, the azimuthal distribution of muons in inclined Extensive Air Showers (EAS) is asymmetric, mainly due to geometric effects. Several EAS observables sensitive to the primary particle mass, are constructed after mapping the density of secondary particles from the ground plane to the shower plane (perpendicular to the shower axis). A simple orthogonal projection of the muon coordinates onto this plane distorts the azimuthal symmetry in the shower plane. Using CORSIKA simulations, we correct for this distortion by projecting each muon onto the normal plane following its incoming d…
