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.     

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.     

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’.     

Time resolved spectroscopy of cosmic-ray muons induced background

The appropriate selection of a coincidence time interval in low-background experiments that are based on the rejection of anticoincidence background events is very important for reducing the influence of cosmic-ray muons on acquired spectral data, especially on certain energy regions of the obtained spectra. In an experiment that was performed by the coincidence system of an HPGe detector and a plastic detector in a surface laboratory, where the cosmic-ray muon flux is much higher than it would be in the conditions found deep underground (thus, better statistics in the acquired data are provided), the time resolution of the detected events is explored. We found that the prompt and delayed coincidence events between a plastic veto detector and a Ge detector can be sharply divided for approximately 100 ns in two groups. In addition, the bremsstrahlung and annihilation events can be time-resolved from the (n, n′) events, although all of these events belong to the group of delayed events. We also detected substantially delayed annihilation events, which are caused by the decays of stopped positive muons.     

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.     

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.     

Neutrino-induced and atmospheric single-muon fluxes measured over five decades of intensity by LVD at Gran Sasso Laboratory

We report data taken by the LVD Experiment during a live-time period of 11 556 h. We have measured the muon intensity at slant depths of standard rock from about 3000 hg/cm² to about 20 000 hg/cm². This is an exclusive study, namely our data include only events containing single muons. This interval of slant depth extends into the region where the dominant source of underground muons seen by LVD is the interaction of atmospheric neutrinos with the rock surrounding LVD. The interesting result is that this flux is independent of slant depth beyond a slant depth of about 14 000 hg/cm² of standard rock. Due to the unique topology of the Gran Sasso Laboratory the muons beyond about 14 000 hg/cm² of standard rock are at a zenithal angle near 90°. Hence we have, for this fixed angle, a muon flux which is independent of slant depth. This is direct evidence that this flux is due to atmospheric neutrinos interacting in the rock surrounding LVD. The value of this flux near 90° is (8.3 ± 2.6) × 10⁻¹³ cm⁻² s⁻¹ sr⁻¹, which is the first reported measurement at a zenithal angle near 90° and for slant depths between 14 000 and 20 000 hg/cm². Our data cover over five decades of vertical intensity, and can be fit with just three parameters over the full range of our experiment. This is the first time a single experiment reports the parameters of a fit made to the vertical intensity over such a large range of standard rock slant depth. The results are compared with a Monte Carlo simulation which has as one of the two free parameters γ_πκ, the power index of the differential energy spectrum of the pions and kaons in the atmosphere. This comparison yields a value of 2.75 ± 0.03 for γ_πκ, where the error includes the systematic uncertainties. Our data are compared to other measurements made in our slant depth interval. We also report the value of the muon flux in Gran Sasso at θ = 90° as a function of the azimuthal angle.     

Comparison of measured and simulated lateral distributions for electrons and muons with KASCADE

Lateral distributions for electrons and muons in extensive air showers measured with the array of the KASCADE experiment are compared to results of simulations based on the high-energy hadronic interaction models QGSJet and SIBYLL. It is shown, that the muon distributions are well described by both models. Deviations are found for the electromagnetic component, where both models predict a steeper lateral shape than observed in the data. For both models the observed lateral shapes of the electron component indicate a transition from a light to a more heavy composition of the cosmic ray spectrum above the knee.     

A proposed method for measurement of cosmic-ray mass composition based on geomagnetic spectroscopy

The effect of the geomagnetic Lorentz force on the muon component of extensive air shower (EAS) has been studied in a Monte Carlo generated simulated data sample. This geomagnetic field affects the paths of muons in an EAS, causing a local contrast or polar asymmetry in the abundance of positive and negative muons about the shower axis. The asymmetry can be approximately expressed as a function of transverse separation between the positive and negative muons barycentric positions in the EAS through opposite quadrants across the shower core in the shower front plane. In the present study, it is found that the transverse muon barycenter separation and its maximum value obtained from the polar variation of the parameter are higher for iron primaries than protons for highly inclined showers. Hence, in principle, these parameters can be exploited to the measurement of primary cosmic-ray mass composition. Possibility of practical realization of the proposed method in a real experiment is briefly discussed.     

Comparison of AGASA data with CORSIKA simulation

An interpretation of Akeno giant air shower array (AGASA) data by comparing the experimental results with the simulated ones by cosmic ray simulation for KASCADE (CORSIKA) has been made. General features of the electromagnetic component and low energy muons observed by AGASA can be well reproduced by CORSIKA. The form of the lateral distribution of charged particles agrees well with the experimental one between a few hundred metres and 2000 m from the core, irrespective of the hadronic interaction model studied and the primary composition (proton or iron). It does not depend on the primary energy between 10^17.5 and 10²⁰ eV as the experiment shows. If we evaluate the particle density measured by scintillators of 5 cm thickness at 600 m from the core S₀(600), suffix 0 denotes the vertically incident shower) by taking into account the similar conditions as in the experiment, the conversion relation from S₀(600) to the primary energy is expressed as E (eV)=2.15×10¹⁷S₀(600)^1.015 within 10% uncertainty among the models and composition used, which suggests the present AGASA conversion factor is the lower limit. Although the form of the muon lateral distribution fits well to the experiment within 1000 m from the core, the absolute values change with hadronic interaction model and primary composition. The slope of the ρ_μ(600) (muon density above 1 GeV at 600 m from the core) vs. S₀(600) relation in experiment is flatter than that in simulation of any hadronic model and primary composition. As the experimental slope is constant from 10¹⁵ to 10¹⁹ eV, we need to study this relation in a wide primary energy range to infer the rate of change of chemical composition with energy.     

Stokes imaging of AM Her systems using 3D inhomogeneous models – I. Description of the code and an application to V834 Cen

Polars (or AM Her systems) are cataclysmic variables without a disc due to the strong magnetic field of the white dwarf. Most of their emission comes from the region where the accretion column impacts the white dwarf and cools through cyclotron and bremsstrahlung processes. We present a new code, cyclops , to model the optical emission from these systems including the four Stokes parameters. It considers a three-dimensional region with the electronic density and temperature varying following a shock-like profile and a dipolar magnetic field. The radiative transfer is solved in steps considering the solution with non-null input radiation. The footprint of the column in the white dwarf surface is determined by the threading region in the equatorial plane, i.e. the region from where the flow follows the magnetic lines. The extinction caused by the Thomson scattering above the emitting region is optionally included. The search for the model parameters that best fit an observational data set is carried out using a hybrid approach: a genetic algorithm is used to seek for the regions of the parameter space having the best models and then an amoeba code refines the search. An example of the application to multi-wavelength data of V834 Cen is presented. The fit found is consistent with previous parameter estimates and is able to reproduce the features of V834 data in three wavebands.     

Production of neutrinos and secondary electrons in cosmic sources

We study the individual contribution to secondary lepton production in hadronic interactions of cosmic rays (CRs) including resonances and heavier secondaries. For this purpose we use the same methodology discussed earlier [C.-Y. Huang, S.-E. Park, M. Pohl, C.D. Daniels, Astropart. Phys. 27 (2007) 429], namely the Monte-Carlo particle collision code DPMJET3.04 to determine the multiplicity spectra of various secondary particles with leptons as the final decay states, that result from inelastic collisions of cosmic-ray protons and Helium nuclei with the interstellar medium of standard composition. By combining the simulation results with parametric models for secondary particle (with resonances included) for incident cosmic-ray energies below a few GeV, where DPMJET appears unreliable, we thus derive production matrices for all stable secondary particles in cosmic-ray interactions with energies up to about 10 PeV.

We apply the production matrices to calculate the radio synchrotron radiation of secondary electrons in a young shell-type SNR, RX J1713.7-3946, which is a measure of the age, the spectral index of hadronic cosmic rays, and most importantly the magnetic field strength. We find that the multi-mG fields recently invoked to explain the X-ray flux variations are unlikely to extend over a large fraction of the radio-emitting region, otherwise the spectrum of hadronic cosmic rays in the energy window 0.1–100 GeV must be unusually hard.

We also use the production matrices to calculate the muon event rate in an IceCube-like detector that are induced by muon neutrinos from high-energy γ-ray sources such as RX J1713.7-3946, Vela Jr. and MGRO J2019+37. At muon energies of a few TeV, or in other word, about 10 TeV neutrino energy, an accumulation of data over about 5–10 years would allow testing the hadronic origin of TeV γ-rays.     

Prompt muon production in cosmic rays

Results of calculations of fluxes of prompt muons reaching the sea level are given for muon energies up to 10⁷ GeV. The calculations are made in the frame of an empirical model and are based on the up-to-date data from experiments in cosmic rays, at accelerators, and on the most recent theoretical achievements on charm production in nucleon–air nucleus interactions.     

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.     

The effect of wave generation on HXR bremsstrahlung spectra from flare thick-target beams

Fast electrons in the solar atmosphere are detected by their hard X-ray bremsstrahlung and by type III radio bursts caused by ‘bump-on-tail’ plasma wave generation. This paper investigates empirically the effect of wave generation on the HXR spectrum. Purely collisional propagation of an electron beam generates a bump in the distribution function, due to stopping of low-velocity electrons. The consequent positive gradient means there is a possibility of wave generation, production of type III radio bursts, and energy redistribution of the electron beam. We have represented this relaxation parametrically and calculated the global bremsstrahlung HXR emission spectrum. We show that for a range of relaxed forms, with different local electron spectral shapes, the bremsstrahlung spectrum integrated over the whole target is identical in shape to the purely collisionally evolved beam. Our results show that spatially integrated HXR spectral measurements would be unable to distinguish between the presence or absence of relaxation effects. Only spatially resolved hard X-ray spectra, such as anticipated from the HESSI mission, will be able to remove this ambiguity in HXR diagnostics of beam relaxation.     

Neutrino-Astronomy with the Macro Experiment at Gran Sasso

The MACRO experiment at Gran Sasso is collecting muons since February 1989. These muons are induced by charged current interactions of atmospheric and, possibly, astrophysical muon neutrinos below the apparatus. A search has been made for discrete astrophysical sources of VHE and UHE neutrinos using the upward going muons direction information. Given the large area and the long period of data taking MACRO is, at the moment, able to set very competitive upper limits to the flux of neutrinos from most of the sources considered in the search. This revised version was published online in July 2006 with corrections to the Cover Date.     

Flux predictions of high-energy neutrinos from pulsars

Young, rapidly rotating neutron stars could accelerate ions from their surfaces to energies of ∼1 PeV. If protons reach such energies, they will produce pions (with low probability) through resonant scattering with X-rays from the stellar surface. The pions subsequently decay to produce muon neutrinos. Here, we calculate the energy spectrum of muon neutrinos, and estimate the event rates at Earth. The spectrum consists of a sharp rise at ∼50 TeV, corresponding to the onset of the resonance, above which the flux drops with neutrino energy as  ε⁻²_ν  up to an upper energy cut-off that is determined by either kinematics or the maximum energy to which protons are accelerated. We estimate event rates as high as 10–100 km⁻² yr⁻¹ from some candidates, a flux that would be easily detected by IceCube. Lack of detection would allow constraints on the energetics of the poorly understood pulsar magnetosphere.     

Electron, muon, and hadron lateral distributions measured in air showers by the KASCADE experiment

Measurements of electron, muon and hadron lateral distributions of extensive air showers as recorded in the Karlsruhe shower core and array detector experiment are presented. The data cover the energy range from 5×10¹⁴ eV up to almost 10¹⁷ eV and extend from the inner core region to distances of 200 m. The electron and muon distributions are corrected for mutual contaminations by taking into account the detector properties in the experiment. All distributions are well described by NKG functions. The scale radii describing the electron and hadron data best are 30 and 10 m, respectively. We discuss the correlation between the scale radii and the ‘age' parameter as well as their dependence on shower size, zenith angle, and particle energy threshold.     

Cosmic rays and other nonsense in astronomical CCD imagers

Cosmic-ray muons make recognizable straight tracks in the new-generation CCD's with thick sensitive regions. Wandering tracks (‘worms’), which we identify with multiply-scattered low-energy electrons, are readily recognized as different from the muon tracks. These appear to be mostly recoils from Compton-scattered gamma rays, although worms are also produced directly by beta emitters in dewar windows and field lenses. The gamma rays are mostly byproducts of ⁴⁰K decay and the U and Th decay chains. Trace amounts of these elements are nearly always present in concrete and other materials. The direct betas can be eliminated and the Compton recoils can be reduced significantly by the judicious choice of materials and shielding. The cosmic-ray muon rate is irreducible. Our conclusions are supported by tests at the Lawrence Berkeley National Laboratory low-level counting facilities in Berkeley and 180 m underground at Oroville, California. This revised version was published online in July 2006 with corrections to the Cover Date.