Correlated features of arrival time and angle-of-incidence distributions of EAS muons

Various features and correlations of the arrival time and angle-of- incidence distributions of muons of extensive air showers (EAS) are studied by analyses based on Monte-Carlo simulations of the EAS development by using the air shower simulation code CORSIKA. Trends and dependencies of the temporal dispersion of the EAS muon component on shower size and distance from the shower core are displayed by the distribution of the arrival time and angle of incidence of the first muon, of the mean and median of the single shower distribution. Special attention is called to multi-correlations in observations at different radial distances from the shower core. These ‘radial’ correlations provide additional information for the discrimination of different EAS primaries, while the correlation of muon arrival time and angle-of-incidence is shown to improve the mass separation only insignificantly. This feature does not basically change, when arrival times and angles of incidence are displayed by transformed quantities like ‘muon production heights’.     

Distortions of experimental muon arrival time distributions of extensive air showers by the observation conditions

Event-by-event measured arrival time distributions of extensive air shower (EAS) muons are affected and distorted by various interrelated effects which originate from the time resolution of the timing detectors, from fluctuations of the reference time and the number (multiplicity) of detected muons spanning the arrival time distribution of the individual EAS events. The origin of these effects is discussed, and different correction procedures, which involve detailed simulations, are proposed and illustrated. The discussed distortions are relevant for relatively small observation distances (R_μ<200 m) from the EAS core. Their significance decreases with increasing observation distance and increasing primary energies. Local arrival time distributions which refer to the observed arrival time of the first local muon prove to be less sensitive to the mass of the primary. This feature points to the necessity of arrival time measurements with additional information on the curvature of the EAS disk.     

Simulation of extensive air showers at ultra-high energy using the CORSIKA Monte Carlo code

Extensive simulations have been carried out with CORSIKA version 5.62 to investigate the general properties of giant cosmic air shower in the energy range 1–100 EeV. The comparison between protons, heavy nuclei and γ initiated showers exhibits unexpected and interesting features. The apparent muon electron ratio at great distances (1.5 km from axis) tends to be comparable at ultra-high energy in both photon-induced cascades and hadronic cascades (compensation between the enhancement versus energy of photo-production cross-section and of the decrease of both pair production cross-section and the bremsstrahlung cross-section, with Landau–Pomeranchuk–Migdal effect); for proton and nuclei primaries, a correlation with lateral electron profile suggests a new energy estimator, in complement to electrons size or density at 600 m, suitable for the determination of the total primary energy spectrum. Another tendency is the local contrast in the abundance of positive and negative muons (with a possible ellipticity in the lateral muon distribution) induced by the geomagnetic field, especially visible for some azimuthal and zenith angles. These distortions are more intense for heavy primaries; they can be exploited on the most favorable horizontal axis or areas, for the discrimination between nuclei and protons.     

Muon density measurements with the KASCADE central detector

Frequency distributions of local muon densities in high-energy extensive air showers (EAS) are presented as signature of the primary cosmic ray energy spectrum in the knee region. Together with the gross shower variables like shower core position, angle of incidence, and the shower sizes, the KASCADE experiment is able to measure local muon densities for two different muon energy thresholds. The spectra have been reconstructed for various core distances, as well as for particular subsamples, classified on the basis of the shower size ratio N_μ/N_e. The measured density spectra of the total sample exhibit clear kinks reflecting the knee of the primary energy spectrum. While relatively sharp changes of the slopes are observed in the spectrum of EAS with small values of the shower size ratio, no such feature is detected at EAS of large N_μ/N_e ratio in the energy range of 1–10 PeV. Comparing the spectra for various thresholds and core distances with detailed Monte Carlo simulations the validity of EAS simulations is discussed.     

Underground water Cherenkov muon detector array with the Tibet air shower array for gamma-ray astronomy in the 100 TeV region

We propose to build a large water-Cherenkov-type muon-detector array (Tibet MD array) around the 37 000 m² Tibet air shower array (Tibet AS array) already constructed at 4300 m above sea level in Tibet, China. Each muon detector is a waterproof concrete pool, 6 m wide × 6 m long × 1.5 m deep in size, equipped with a 20 inch-in-diameter PMT. The Tibet MD array consists of 240 muon detectors set up 2.5 m underground. Its total effective area will be 8640 m² for muon detection. The Tibet MD array will significantly improve gamma-ray sensitivity of the Tibet AS array in the 100 TeV region (10–1000 TeV) by means of gamma/hadron separation based on counting the number of muons accompanying an air shower. The Tibet AS+MD array will have the sensitivity to gamma rays in the 100 TeV region by an order of magnitude better than any other previous existing detectors in the world. The Tibet ASγ Collaboration.     

A non-parametric approach to infer the energy spectrum and the mass composition of cosmic rays

The experiment KASCADE observes simultaneously the electron–photon, muon, and hadron components of high-energy extensive air showers (EAS). The analysis of EAS observables for an estimate of energy and mass of the primary particle invokes extensive Monte Carlo simulations of the EAS development for preparing reference patterns. The present studies utilize the air shower simulation code corsika with the hadronic interaction models VENUS, QGSJet and Sibyll, including simulations of the detector response and efficiency. By applying non-parametric techniques the measured data have been analyzed in an event-by-event mode and the mass and energy of the EAS inducing particles are reconstructed. Special emphasis is given to methodical limitations and the dependence of the results on the hadronic interaction model used. The results obtained from KASCADE data reproduce the knee in the primary spectrum, but reveal a strong model dependence. Owing to the systematic uncertainties introduced by the hadronic interaction models no strong change of chemical composition can be claimed in the energy range around the knee.     

Monte-Carlo simulations of atmospheric muon production: Implication of the past martian environment

In order to evaluate the obliquity-driven atmospheric-density path length effect on nuclide production rate on Mars, we performed a Monte-Carlo simulation to produce the number of secondary particles such as muons, neutrons and protons in the martian atmosphere and to simulate that production of ¹⁰Be and ³⁶Cl in the martian regolith by muons and neutrons depends on how much atmosphere had been present for the past 10 million years. The vertical profile of the present martian atmosphere to generate secondary particles has been determined based on the data provided by the Viking missions. For other thickness profiles, we scaled Linsley's atmospheric model. Atmospheric shower has been generated with the SIBYLL 2.1 for high-energy hadronic interactions and EHSA for low energy photonuclear interactions. With increasing atmospheric thickness, more primary interactions occur in the atmosphere. Consequently the proton flux is reduced and the secondary cosmic ray flux, such as muons or energetic neutrons increases at surface. The result indicates that the muon production is more sensitive to obliquity-driven atmospheric variations than proton reduction. A thicker atmosphere would result in enhanced nuclide production at a place deeper than 5 m below the surface and the nuclides present in detectable concentrations. Application to the polar deposit is described.     

Seasonal dependences of geomagnetic variations in the polar region in connection with large-amplitude annual Z-variation at the geomagnetic pole

A noticeable depression of the vertical component Z of the geomagnetic field is observed in the polar cap in summer. From the statistical analysis of the equivalent overhead current patterns for daily geomagnetic variations in the summer and winter polar regions for three different conditions of IMF (interplanetary magnetic field), it was concluded that the annual variation of geomagnetic Z in the vicinity of the geomagnetic pole is attributed to the relative spatial shift of the twin-vortex current patterns over the polar cap from summer to winter. In winterthe clockwise current vortex in the dawn sector extends almost over the entire polar cap (except for the periods when the B_z component of IMF has a large positive value), and this will result in the positive variation of the Z-value at the geomagnetic pole. In summer the counter-clockwise current vortex in the dusk sector always extends over the whole polar cap even when B_z of IMF is positiveso that the variation of Z becomes negative. The persistent existence of current vortex in the dawn sector is important for the further study of magnetospheric convection when B_z is positive.     

Time structure of the extensive air shower front

The GREX/COVER_PLASTEX experiment has measured the temporal and spatial fine structure of the EAS disc at sea level in a new and original way, using resistive plate counter detectors for direct measurements of the arrival time of each particle crossing the detector. Data were taken at EAS core distances up to 100 m for shower size N > 10⁵ (PeV energy range). Arrival times of shower particles were measured with nanosecond accuracy. More than 450000 air shower events have been included in this analysis.     

On the extension of the sensitive area of an extensive air shower surface array

A large distance between true and reconstructed core locations of an extensive air shower (EAS) may result in great systematic mis-estimation of EAS parameters. The reconstruction of those EASs whose core locations are outside the boundary of a surface array (outside EAS (OEAS)) results in a large distance of the reconstructed core location from the true one, especially when the true core is far outside the array. Although it may not be mentioned, the rejection of OEASs is a necessary and important step in the reconstruction procedure of an EAS. In this paper, an existing technique is optimized for the rejection of OEASs. The simultaneous use of this technique and a recently developed approach for reconstructing the core location of an EAS can significantly increase the sensitive area of a surface array.     

The center of lateral iso-density contours for inclined cosmic air showers

The horizontal lateral density of a cosmic air shower with a non-zero zenith angle is asymmetric. The asymmetry consist of a stretching of the iso-density contours to ellipses and to a shift of the center of the elliptic contours with respect to the core of the shower. The shift is caused by atmospheric attenuation. The modeling of the attenuation results in an equation for the shift as a function of zenith angle and the size of the iso-density contours. A more accurate equation is obtained by investigating the shift in lateral densities of simulated showers. It is shown how the shift can be incorporated in an elliptic lateral density function. A linear approximation for the shift allows for an analytical solution for the shifted elliptic density. Its predictions for the polar variations of the density are compared with data of simulated showers.     

A three-dimensional code for muon propagation through the rock: MUSIC

We present a new three-dimensional Monte-Carlo code MUSIC (MUon SImulation Code) for muon propagation through the rock. All processes of muon interaction with matter with high energy loss (including the knock-on electron production) are treated as stochastic processes. The angular deviation and lateral displacement of muons due to multiple scattering, as well as bremsstrahlung, pair production and inelastic scattering are taken into account. The code has been applied to obtain the energy distribution and angular and lateral deviations of single muons at different depths underground. The muon multiplicity distributions obtained with MUSIC and CORSIKA (Extensive Air Shower simulation code) are also presented. We discuss the systematic uncertainties of the results due to different muon bremsstrahlung cross-sections.     

Identify signatures of underground muons from atmospheric charm: Simulation study

Muons from the “prompt” decays of charmed mesons in cosmic ray air showers start to show abundance on the atmospheric muon spectrum from few tens of TeV. Study of these prompt muons have broader interest in particle and astroparticle physics. The measurement of prompt muon in air showers is challenging because of their low production rate and the large amount of conventional muons produced in company with them. This paper describes the simulation study of a method that identifies prompt muon signatures based on the pattern of stochastic energy losses by muon bundles in deep under ice. The systematics associated with different hadronic interaction models and cosmic ray primary composition assumptions were estimated. Using IceCube as an example, we briefly discussed the challenge of using this method in experimental data analysis.     

Comparison of the performance of various light enclosures for extensive air shower experiments

We have carried out a series of measurements with twenty-one light enclosures of different geometry and inside finishes to compare their performance for use in extensive air shower experiments. It is found that for light enclosures with white inside finish there is an inherent induced uncertainty in time measurement, in addition to the uncertainty arising from the uncertain transit location of the shower particle in a large area scintillator. Both of these uncertainties which can not be improved with better electronics limit the angular resolution of EAS arrays.     

Preparation of enriched cosmic ray mass groups with KASCADE

The KASCADE experiment measures a high number of EAS observables with a large degree of sampling of the electron–photon, muon, and hadron components. It provides accurate data for an event-by-event analysis of the primary cosmic ray flux in the energy range around the knee. The possibility of selecting samples of enriched proton and iron induced extensive air showers by applying the statistical techniques of multivariate analyses is scrutinized using detailed Monte Carlo simulations of three different primaries. The purity and efficiency of the proton and iron classification probability is investigated. After obtaining enriched samples from the measured data by application of the procedures the reconstructed number of hadrons, hadronic energy and other parameters are investigated in the primary energy range 10¹⁵–10¹⁶ eV. By comparing these shower parameters for purified proton and iron events, respectively, with simulated distributions an attempt is made to check the validity of strong interaction models at high energies.     

Characterization of the atmospheric muon flux in IceCube

Muons produced in atmospheric cosmic ray showers account for the by far dominant part of the event yield in large-volume underground particle detectors. The IceCube detector, with an instrumented volume of about a cubic kilometer, has the potential to conduct unique investigations on atmospheric muons by exploiting the large collection area and the possibility to track particles over a long distance. Through detailed reconstruction of energy deposition along the tracks, the characteristics of muon bundles can be quantified, and individual particles of exceptionally high energy identified. The data can then be used to constrain the cosmic ray primary flux and the contribution to atmospheric lepton fluxes from prompt decays of short-lived hadrons.In this paper, techniques for the extraction of physical measurements from atmospheric muon events are described and first results are presented. The multiplicity spectrum of TeV muons in cosmic ray air showers for primaries in the energy range from the knee to the ankle is derived and found to be consistent with recent results from surface detectors. The single muon energy spectrum is determined up to PeV energies and shows a clear indication for the emergence of a distinct spectral component from prompt decays of short-lived hadrons. The magnitude of the prompt flux, which should include a substantial contribution from light vector meson di-muon decays, is consistent with current theoretical predictions.The variety of measurements and high event statistics can also be exploited for the evaluation of systematic effects. In the course of this study, internal inconsistencies in the zenith angle distribution of events were found which indicate the presence of an unexplained effect outside the currently applied range of detector systematics. The underlying cause could be related to the hadronic interaction models used to describe muon production in air showers.     

Time structure of individual extensive air showers

Extensive air showers detected by the GREX array have been sampled by means of highly segmented 8 m² bakelite RPC in the GREX/COVER_PLASTEX experiment. Delay distributions of particles with respect to the first arriving particle in the EAS front at PeV energies have been analysed for individual events in the core distance range of 0–100 m. It is shown that both mean arrival time and EAS front thickness in individual showers fluctuate strongly and cannot be a good measure of the distance from the EAS axis in a 0–100 m core distance interval.

Individual distributions have been compared with integrated inclusive distributions measured in the same experiment. Results indicate that the width of the individual distribution is systematically less than that of the inclusive distribution. It means that the bulk of particles in individual showers arrive as a relatively compact group delayed by different time intervals from the first arriving particle. Such fluctuations of the arrival time for most of the shower particles may be the consequence of large fluctuations in the shower longitudinal development.

Comparison with CORSIKA Monte Carlo simulations confirmed the difference between the mean width of inclusive and individual arrival time distribution. It revealed also the presence in the experiment of the excessive train of delayed particles near the shower core. This train is obviously due to the non-relativistic low energy hadrons most abundant in the shower core region.     

A Study of the Effect of Geomagnetic Field on Extensive Air Showers with Small Arrays

We have studied Extensive Air Showers (EAS) with two small arraysof 1 m² scintillation detectors inTehran, 1200 m above sea level.The distribution of air showersin zenith and azimuth angles has been studied and a cosⁿΘdistribution with n = 7.2±0.2 was obtained for zenith angledistribution. An asymmetry has been observed in the azimuthaldistribution of EAS of cosmic rays because of magnetic field ofthe Earth. Amplitudes of the first and the second harmonics ofobserved distribution depend on zenith angle as A _I ≈ (0.02 + 0.35 sin²Θ)±0.02, and A _II ≈ (0.03 + 0.42 sin⁴Θ)±0.03. Meanwhile, the uncertainties arising from the instrument, transit location of shower particles in the scintillator and fluctuations in the shower front have been calculated.