An extended Heitler–Matthews model for the full hadronic cascade in cosmic air showers

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 generation of electromagnetic subshowers is too small with respect to Monte Carlo predictions. It is shown that the inclusion of all the generations of electromagnetic subshowers leads to smaller predictions for the depth of maximum and to smaller predictions for the elongation rate. The discrepancy between discrete model predictions and Monte Carlo predictions for the depth of maximum can therefore not be explained from the number of generations that is taken into consideration. An alternative explanation will be proposed.     

Changes of the cosmic-ray mass composition in the 10–10 eV energy range

Data taken with ten Cosmic Ray Tracking (CRT) detectors and the HEGRA air-shower array on La Palma, Canary Islands, have been analysed to investigate changes of the cosmic ay mass composition at the ‘knee’ of the cosmic-ray flux spectrum near 10¹⁵ eV energy. The analysis is based on the angular distributions of particles in air showers. HEGRA data provided the shower size, direction, and core position and CRT data the particle track information. It is shown that the angular distribution of muons in air showers is sensitive to the composition over a wide range of shower sizes and, thus, primary cosmic-ray energies with little systematic uncertainties. Results can be easily expressed in terms of ln A of primary cosmic rays. In the lower part of the energy range covered, we have considerable overlap with direct composition measurements by the JACEE collaboration and find compatible results in the observed rise of ln A. Above about 10¹⁵ eV energy we find no or at most a slow further rise of ln A. Simple cosmic-ray composition models are presented which are fully consistent with our results as well as the JACEE flux and composition measurements and the flux measurements of the Tibet ASγ collaboration. Minimal three-parameter composition models defined by the same power-law slope of all elements below the knee and a common change in slope at a fixed rigidity are inconsistent with these data.     

Measurement of the cosmic ray composition at the knee with the SPASE-2/AMANDA-B10 detectors

The mass composition of high-energy cosmic rays at energies above 10¹⁵ eV can provide crucial information for the understanding of their origin. Air showers were measured simultaneously with the SPASE-2 air shower array and the AMANDA-B10 Cherenkov telescope at the South Pole. This combination has the advantage to sample almost all high-energy shower muons and is thus a new approach to the determination of the cosmic ray composition. The change in the cosmic ray mass composition was measured versus existing data from direct measurements at low energies. Our data show an increase of the mean log atomic mass lnA by about 0.8 between 500 TeV and 5 PeV. This trend of an increasing mass through the “knee” region is robust against a variety of systematic effects.     

Determination of the proton-to-helium ratio in cosmic rays at ultra-high energies from the tail of the Xmax distribution

We present a method to determine the proton-to-helium ratio in cosmic rays at ultra-high energies. It makes use of the exponential slope, Λ, of the tail of the X_max distribution measured by an air shower experiment. The method is quite robust with respect to uncertainties from modeling hadronic interactions and to systematic errors on X_max and energy, and to the possible presence of primary nuclei heavier than helium. Obtaining the proton-to-helium ratio with air shower experiments would be a remarkable achievement.To quantify the applicability of a particular mass-sensitive variable for mass composition analysis despite hadronic uncertainties we introduce as a metric the ‘analysis indicator’ and find an improved performance of the Λ method compared to other variables currently used in the literature. The fraction of events in the tail of the X_max distribution can provide additional information on the presence of nuclei heavier than helium in the primary beam.     

超高能宇宙线大气簇射平均纵向发展曲线的测量（英文）

利用HiRes宇宙线实验的观测数据,通过扣除测量信号中的切仑科夫光成份,测量了广延大气簇射的纵向发展曲线。把所有的纵向发展曲线归一并且平均,获得平均纵向发展曲线。根据所得曲线,检验了3个簇射模型,它们都能较好地描述纵向发展曲线。如果利用高斯函数来描述簇射的纵向发展曲线,发现纵向发展曲线的宽度（σ）与簇射发展最大的深度有一定的关联,而且该参量从1017eV到1020 eV能量范围内几乎保持不变。另外还对平均纵向发展曲线的不确定性进行了讨论。     

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.     

The role of planetary formation and evolution in shaping the composition of exoplanetary atmospheres

Over the last twenty years, the search for extrasolar planets has revealed the rich diversity of outcomes from the formation and evolution of planetary systems. In order to fully understand how these extrasolar planets came to be, however, the orbital and physical data we possess are not enough, and they need to be complemented with information about the composition of the exoplanets. Ground-based and space-based observations provided the first data on the atmospheric composition of a few extrasolar planets, but a larger and more detailed sample is required before we can fully take advantage of it. The primary goal of a dedicated space mission like the Exoplanet Characterization Observatory (EChO) proposal is to fill this gap and to expand the limited data we possess by performing a systematic survey of extrasolar planets. The full exploitation of the data that space-based and ground-based facilities will provide in the near future, however, requires knowledge about the sources and sinks of the chemical species and molecules that will be observed. Luckily, the study of the past history of the Solar System provides several indications about the effects of processes like migration, late accretion and secular impacts, and on the time they occur in the life of planetary systems. In this work we will review what is already known about the factors influencing the composition of planetary atmospheres, focusing on the case of gaseous giant planets, and what instead still need to be investigated.     

Application of CORSIKA Simulation Code to Study Lateral and Longitudinal Distribution of Fluorescence Light in Cosmic Ray Extensive Air Showers

In this paper, we used CORSIKA code to understand the characteristics of cosmic ray induced showers at extremely high energy as a function of energy, detector distance to shower axis, number, and density of secondary charged particles and the nature particle producing the shower. Based on the standard properties of the atmosphere, lateral and longitudinal development of the shower for photons and electrons has been investigated. Fluorescent light has been collected by the detector for protons, helium, oxygen, silicon, calcium and iron primary cosmic rays in different energies. So we have obtained a number of electrons per unit area, distance to the shower axis, shape function of particles density, percentage of fluorescent light, lateral distribution of energy dissipated in the atmosphere and visual field angle of detector as well as size of the shower image. We have also shown that location of highest percentage of fluorescence light is directly proportional to atomic number of elements. Also we have shown when the distance from shower axis increases and the shape function of particles density decreases severely. At the first stages of development, shower axis distance from detector is high and visual field angle is small; then with shower moving toward the Earth, angle increases. Overall, in higher energies, the fluorescent light method has more efficiency. The paper provides standard calibration lines for high energy showers which can be used to determine the nature of the particles.     

Prospects for radio detection of ultra-high energy cosmic rays and neutrinos

The origin and nature of the highest energy cosmic ray events is currently the subject of intense investigation by giant air shower arrays and fluorescent detectors. These particles reach energies well beyond what can be achieved in ground-based particle accelerators and hence they are fundamental probes for particle physics as well as astrophysics. One of the main topics today focuses on the high energy end of the spectrum and the potential for the production of high-energy neutrinos. Above about 10²⁰ eV cosmic rays from extragalactic sources are expected to be severely attenuated by pion photoproduction interactions with photons of the cosmic microwave background. Investigating the shape of the cosmic ray spectrum near this predicted cut-off will be very important. In addition, a significant high-energy neutrino background is naturally expected as part of the pion decay chain which also contains much information.Because of the scarcity of these high-energy particles, larger and larger ground-based detectors have been built. The new generation of digital radio telescopes may play an important role in this, if properly designed. Radio detection of cosmic ray showers has a long history but was abandoned in the 1970s. Recent experimental developments together with sophisticated air shower simulations incorporating radio emission give a clearer understanding of the relationship between the air shower parameters and the radio signal, and have led to resurgence in its use. Observations of air showers by the SKA could, because of its large collecting area, contribute significantly to measuring the cosmic ray spectrum at the highest energies. Because of the large surface area of the moon, and the expected excellent angular resolution of the SKA, using the SKA to detect radio Cherenkov emission from neutrino-induced cascades in lunar regolith will be potentially the most important technique for investigating cosmic ray origin at energies above the photoproduction cut-off.     

The shape of the radio wavefront of extensive air showers as measured with LOFAR

Extensive air showers, induced by high energy cosmic rays impinging on the Earth’s atmosphere, produce radio emission that is measured with the LOFAR radio telescope. As the emission comes from a finite distance of a few kilometers, the incident wavefront is non-planar. A spherical, conical or hyperbolic shape of the wavefront has been proposed, but measurements of individual air showers have been inconclusive so far. For a selected high-quality sample of 161 measured extensive air showers, we have reconstructed the wavefront by measuring pulse arrival times to sub-nanosecond precision in 200 to 350 individual antennas. For each measured air shower, we have fitted a conical, spherical, and hyperboloid shape to the arrival times. The fit quality and a likelihood analysis show that a hyperboloid is the best parameterization. Using a non-planar wavefront shape gives an improved angular resolution, when reconstructing the shower arrival direction. Furthermore, a dependence of the wavefront shape on the shower geometry can be seen. This suggests that it will be possible to use a wavefront shape analysis to get an additional handle on the atmospheric depth of the shower maximum, which is sensitive to the mass of the primary particle.     

The cosmic ray primary composition between 10 and 10 eV from Extensive Air Showers electromagnetic and TeV muon data

The cosmic ray primary composition in the energy range between 10¹⁵ and 10¹⁶ eV, i.e., around the “knee” of the primary spectrum, has been studied through the combined measurements of the EAS-TOP air shower array (2005 m a.s.l., 10⁵ m² collecting area) and the MACRO underground detector (963 m a.s.l., 3100 m w.e. of minimum rock overburden, 920 m² effective area) at the National Gran Sasso Laboratories. The used observables are the air shower size (N_e) measured by EAS-TOP and the muon number (N_μ) recorded by MACRO. The two detectors are separated on average by 1200 m of rock, and located at a respective zenith angle of about 30°. The energy threshold at the surface for muons reaching the MACRO depth is approximately 1.3 TeV. Such muons are produced in the early stages of the shower development and in a kinematic region quite different from the one relevant for the usual N_μ−N_e studies. The measurement leads to a primary composition becoming heavier at the knee of the primary spectrum, the knee itself resulting from the steepening of the spectrum of a primary light component (p, He) of Δγ=0.7±0.4 at E₀4×10¹⁵ eV. The result confirms the ones reported from the observation of the low energy muons at the surface (typically in the GeV energy range), showing that the conclusions do not depend on the production region kinematics. Thus, the hadronic interaction model used (CORSIKA/QGSJET) provides consistent composition results from data related to secondaries produced in a rapidity region exceeding the central one. Such an evolution of the composition in the knee region supports the “standard” galactic acceleration/propagation models that imply rigidity dependent breaks of the different components, and therefore breaks occurring at lower energies in the spectra of the light nuclei.     

Measurements of attenuation and absorption lengths with the KASCADE experiment

The attenuation of the electron shower size beyond the shower maximum is studied with the KASCADE extensive air shower (EAS) experiment in the primary energy range of about 10¹⁴–10¹⁶ eV. Attenuation and absorption lengths are determined by applying different approaches, including the method of constant intensity, the decrease of the flux of EASs with increasing zenith angle, and its variation with ground pressure. We observe a significant dependence of the results on the applied method. The determined values of the attenuation length ranges from 175 to 196 g/cm² and of the absorption length from 100 to 120 g/cm². The origin of these differences is discussed emphasizing the influence of intrinsic shower fluctuations.     

Auroral ion velocity distributions using a relaxation model

For application to the auroral ionosphere we have calculated ion velocity distributions for a weakly-ionized plasma subjected to crossed electric and magnetic fields. By replacing the Boltzmann collision integral with a simple relaxation model, we have been able to obtain an exact solution to Boltzmann's equation. This solution has the advantage over a series expansion in that all the higher order velocity moments are inherent in it. The exact solution is particularly advantageous when studying large departures of the distribution from its Maxwellian form because these departures are caused by the higher velocity moments. In general, however, a simple relaxation model can only be used to obtain qualitative information on the distribution function. Consequently, we can determine when the higher order velocity moments affect the ion velocity distribution and the nature of their effect, but we cannot obtain accurate quantitative results. The higher velocity moments have their greatest effect on the distribution function above about 120 km, where the ion-neutral collision frequency is less than the ion cyclotron frequency. As the magnitude of the electric field increases, these higher moments act to decrease the number of ions at the peak of the distribution function. Peak densities are reduced by a few per cent for perpendicular electric fields of about 20 mV m^?1.     

Simulations of a giant hybrid air shower detector

We have used Monte Carlo simulations to investigate the capabilities of a giant air shower observatory designed to detect showers initiated by cosmic rays with energies exceeding 10¹⁹ eV. The observatory is to consist of an array of detectors that will characterise the air shower at ground level, and optical detectors to measure the fluorescence light emitted by the shower in the atmosphere. Using these detectors together in a ‘hybrid’ configuration, we find that precise geometrical reconstruction of the shower axis is possible, leading to excellent resolution in energy. The technique is also shown to provide very good reconstruction below 10¹⁹ eV, at energies where the ground array is not fully efficient.     

Comparison of simulated longitudinal profiles of hadronic air showers with MASS2 balloon data

The KASKADE and CORSIKA air shower generators are compared to the data collected by MASS2 balloon experiment in 1991. The test of longitudinal profile for proton, helium and muon flux production provide good constraints on these air shower generators. KASKADE and CORSIKA especially with the new simulator UrQMD for low energies are found to fit these data well. This study is limited to a comparison of longitudinal profiles and therefore does not provide constraints on the overall shower development.     

The Lateral Trigger Probability function for the Ultra-High Energy Cosmic Ray showers detected by the Pierre Auger Observatory

In this paper we introduce the concept of Lateral Trigger Probability (LTP) function, i.e., the probability for an Extensive Air Shower (EAS) to trigger an individual detector of a ground based array as a function of distance to the shower axis, taking into account energy, mass and direction of the primary cosmic ray. We apply this concept to the surface array of the Pierre Auger Observatory consisting of a 1.5 km spaced grid of about 1600 water Cherenkov stations. Using Monte Carlo simulations of ultra-high energy showers the LTP functions are derived for energies in the range between 10¹⁷ and 10¹⁹ eV and zenith angles up to 65°. A parametrization combining a step function with an exponential is found to reproduce them very well in the considered range of energies and zenith angles. The LTP functions can also be obtained from data using events simultaneously observed by the fluorescence and the surface detector of the Pierre Auger Observatory (hybrid events). We validate the Monte Carlo results showing how LTP functions from data are in good agreement with simulations.     

Enhancing the relative Fe-to-proton abundance in ultra-high-energy cosmic rays

We study a generic class of models for ultra-high energy cosmic ray (UHECR) phenomenology, in which the sources accelerate protons and nuclei with a power-law spectrum having the same index, but with different values for the maximum proton energies, distributed according to a power-law. We show that, for energies sufficiently lower than the maximum proton energy, such models are equivalent to single-type source models, with a larger effective power law index and a heavier composition at the source. We calculate the resulting enhancement of the abundance of nuclei, and find typical values of a factor 2-10 for Fe nuclei. At the highest energies, the heavy nuclei enhancement ratios become larger, and the granularity of the sources must also be taken into account. We conclude that the effect of a distribution of maximum energies among sources must be considered in order to understand both the energy spectrum and the composition of UHECRs, as measured on Earth.     

Reanalysis of GU miniarray data using CORSIKA

The GU miniarray is a ultra high energy cosmic ray (UHECR) detector consisting of eight plastic scintillators of carpet area 2 m², each viewed by fast PMTs. It is used to detect Giant EAS by the method of time spread measurement of secondary particles produced in the atmosphere. The energies of the air showers have been reestimated using CORSIKA program. As in the original analysis the Cosmic Ray energy was determined via its relation to the ground level parameter N_s, the shower size. This relation was obtained previously through a best fit relation in agreement with QGS model and Yakutsk data. In this work we use CORSIKA code with QGSJET model of high energy hadronic interactions to simulate miniarray data leading to a modified relation between primary energy and shower size. A revised energy spectrum is reported for 10¹⁷–10¹⁹ eV primary energy.     

Cascades in the Earth’s magnetosphere initiated by photons with the parameters of the highest energy AGASA events

We investigate the cascading effects of extremely high energy (EHE) photons in the Earth’s magnetosphere assuming that these photons arrive with the parameters of the highest energy AGASA events (energies, arrival directions). For the location of the AGASA Observatory, we determine the directions in the sky from which photons can cascade with a high (low) probability. In the case of the primary photons with the parameters of the events with the energies >10²⁰ eV, we compute the average cascade spectra of secondary photons entering the Earth’s atmosphere, and estimate their fluctuations around these average values by selecting the events with the largest and smallest number of secondary cascade photons. It is shown that most photons with the parameters of the highest energy AGASA events should initiate cascades in the Earth’s magnetosphere with a high probability even though they tend to arrive from directions in the sky for which the perpendicular component of the magnetic field is weaker. On the other hand, if these events are caused by the photons with lower energies, then the fluctuations in their shower development in the magnetosphere and the atmosphere should be higher than in the case of photons with the energies estimated by the AGASA experiment.     

Mass composition sensitivity of combined arrays of water cherenkov and scintillation detectors in the EeV range

We consider an array of scintillation detectors combined with an array of water Cherenkov detectors designed to simultaneously measure the cosmic-ray primary mass composition and energy spectrum at energies around 1EeV. In this work we investigate the sensitivity to primary mass composition of such combined arrays. The water Cherenkov detectors are arranged in a triangular grid with fixed 750m spacing and the configuration of the scintillation detectors is changed to study the impact of different configurations on the sensitivity to mass composition. We show that the performance for composition determination can be compared favorably to that of fluorescence measurements after the difference in duty cycles is considered.