An alternative parametrization of the particle shower longitudinal profile is presented. The accuracy of the obtained shower profile description is about 2-3% for the 0-1500 g/cm^2 atmosphere slant depths and primary H, He,... Fe nuclei in the 1 PeV-10 EeV energy range. It is shown that the shape of shower profile depends only on the nucleon energy, whereas the maximum shower size also depends on the energy of the parental nucleus. Results are based on the CORSIKA simulated shower profiles and are presented in comparison with the Gaisser-Hillas parametrization.
Cosmic rays impacting on the atmosphere cause particle-showers. Several descriptions exist for the evolution of the shower size along the atmospheric depth. The well known functions for shower profiles, Greisen, Gaisser-Hillas and `Gaussian in Age', are intimately connected in that they all are approximate solutions of versions of the Rossi and Greisen diffusion equations. The mathematical connection will be demonstrated by means of two simple models for the longitudinal electromagnetic shower profile. Both models can be regarded either as a generalization of the Heitler model or as a simplifi…
The bulk of air showers initiated by very high energy cosmic rays exhibits a longitudinal development in depth with a single well-defined shower maximum. However, a small fraction of showers has a profile that differs considerably from this average behaviour. In extreme cases, such anomalous longitudinal profiles can even have two distinct shower maxima. We discuss the properties of the primary interactions that lead to such profiles. Simulations are used to estimate the rate of anomalous profiles in dependence of primary energy, mass, and characteristic features of hadronic multiparticle prod…
We describe the analysis of longitudinal air shower profiles as measured by the fluorescence detectors of the Pierre Auger Observatory and present the measurement of the depth of maximum of extensive air showers, Xmax, with energies >10^18 eV. The measured energy evolution of the average of Xmax and its fluctuations are compared to air shower simulations for different primary particles.
With the aim to describe the longitudinal development of Cherenkov dominated showers we investigate the energy deposit and the number of charged particles in air showers induced by energetic cosmic rays. Based on the Monte Carlo simulations, discrepancies between different estimates of calorimetric energies are documented. We focus on the energy deposit profiles of air showers deducible from the fluorescence and Cherenkov light generated along CONEX and CORSIKA cascades.
Average universal shower profile reconstruction using radio interferometry
Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela（加利西亚高能物理研究所，圣地亚哥-德孔波斯特拉大学）；Faculty of Physics, University of Warsaw（华沙大学物理学院）；Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高级技术学院物理系）；LIP - Laboratório de Instrumentação e Física Experimental de Partículas（粒子仪器与实验物理实验室）
We present a method to reconstruct the longitudinal profile of electrons in showers using Cherenkov telescopes. We show how the Cherenkov light collected by an array of telescopes can be transformed into the number of electrons as a function of atmospheric depth. This method is validated using air shower and simplified telescope simulations. The reconstruction of the depth in which the shower has the maximum number of electrons ($\mathrm{X_{max}}$) opens the possibility of cosmic ray composition studies with Cherenkov telescopes in the energy range from 10 to 100 TeV. A resolution of less than…
A simulation study of the energy released by extensive air showers in the form of MHz radiation is performed using the CoREAS simulation code. We develop an efficient method to extract this radiation energy from air-shower simulations. We determine the longitudinal profile of the radiation energy release and compare it to the longitudinal profile of the energy deposit by the electromagnetic component of the air shower. We find that the radiation energy corrected for the geometric dependence of the geomagnetic emission scales quadratically with the energy in the electromagnetic component of the…
The simulation analysis of the Extensive Air Showers (EAS) was executed by exploring the longitudinal development employing the AIRES system (version 19.04.00) for several hadronic interaction models (SIBYLL, QGSJET, and EPOS) for high energies. The simulation was performed for different high energies (10^17, 10^18, and 10^19) eV and two dissimilar primary particles, proton as well iron nuclei, with several zenith angles values (0^o, 10^o, and 30^o). The shower size of longitudinal development was parameterized using the sigmoidal function (Boltzmann model) and gave a new four parameters as fu…
In gamma-ray astronomy through Imaging Atmospheric Cherenkov Telescopes (IACT), the atmosphere is used as a calorimeter. Incident gamma-rays in the GeV-TeV energy range are observed through the electromagnetic showers they produce in the atmosphere and the Cherenkov light emitted by them. We aim to obtain a parameterisation of the longitudinal profiles of electromagnetic showers in the atmosphere. The longitudinal Cherenkov emission profiles of these showers can be used for the reconstruction of the parameters of the gamma-photon as well gamma-hadron discrimination. Obtaining an accurate param…
We observe a correlation between the slope of radio lateral distributions, and the mean muon pseudorapidity of 59 individual cosmic-ray-air-shower events. The radio lateral distributions are measured with LOPES, a digital radio interferometer co-located with the multi-detector-air-shower array KASCADE-Grande, which includes a muon-tracking detector. The result proves experimentally that radio measurements are sensitive to the longitudinal development of cosmic-ray air-showers. This is one of the main prerequisites for using radio arrays for ultra-high-energy particle physics and astrophysics.
The average profiles of cosmic ray shower development as a function of atmospheric depth are measured for the first time with the Fluorescence Detectors at the Pierre Auger Observatory. The profile shapes are well reproduced by the Gaisser-Hillas parametrization at the 1% level in a 500 g/cm2 interval around the shower maximum, for cosmic rays with log(E/eV) > 17.8. The results are quantified with two shape parameters, measured as a function of energy. The average profiles carry information on the primary cosmic ray and its high energy hadronic interactions. The shape parameters predicted by t…
Longitudinal Development Analysis of Extensive Air Showers Using CORSIKA Simulations
Ministry of Agriculture, Directorate of Animal ResourceDepartment of Protection of Genetic Resource（农业部动物资源局遗传资源保护处）；Mustansiriyah University, College of Science（穆斯塔纳西尔大学理学院）
We explore the possibilities of measuring the longitudinal profile of individual air showers beyond $X_{\rm max}$ when using very dense radio arrays such as SKA. The low-frequency part of the Square Kilometre Array, to be built in Australia, features an enormous antenna density of about $50,000$ antennas in the inner core region of radius 500 m, with a frequency band from 50 to 350 MHz. From CoREAS simulations, a SKA-Low antenna model plus noise contributions, and adapted LOFAR analysis scripts, we obtain a resolution in the shower maximum $X_{\rm max}$ and energy that is considerably better t…
The radio intensity and polarization footprint of a cosmic-ray induced extensive air shower is determined by the time-dependent structure of the current distribution residing in the plasma cloud at the shower front. In turn, the time dependence of the integrated charge-current distribution in the plasma cloud, the longitudinal shower structure, is determined by interesting physics which one would like to extract such as the location and multiplicity of the primary cosmic-ray collision or the values of electric fields in the atmosphere during thunderstorms. To extract the structure of a shower …
Equations for the center of gravity of the shower originated by high energy proton in the atmosphere are written and, within certain simplifications, solved for the case of logarithmically decreasing interaction length of hadrons in the air. Obtained expression provides transparent view of the way in which hadronic interaction characteristics determine the longitudinal shower development.
A simulation study of the energy released by extensive air showers in the form of MHz radiation is performed using the CoREAS simulation code. We develop an efficient method to extract this radiation energy from air-shower simulations. We determine the longitudinal profile of the radiation energy release and compare it to the longitudinal profile of the energy deposit by the electromagnetic component of the air shower. We find that the radiation energy corrected for the geometric dependence of the geomagnetic emission scales quadratically with the energy in the electromagnetic component of the…
A large area (128 m^2) Muon Tracking Detector (MTD), located within the KASCADE experiment, has been built with the aim to identify muons (E_mu > 0.8 GeV) and their directions in extensive air showers by track measurements under more than 18 r.l. shielding. The orientation of the muon track with respect to the shower axis is expressed in terms of the radial- and tangential angles. By means of triangulation the muon production height H_mu is determined. By means of H_mu, a transition from light to heavy cosmic ray primary particle with increasing shower energy Eo from 1-10 PeV is observed. Muon…
The aim of the Pierre Auger Observatory is the investigation of the nature of cosmic ray particles at ultra-high energies. It can simultaneously observe the longitudinal air shower development in the atmosphere as well as particle densities on the ground. While there are no dedicated muon detectors, techniques have been developed to estimate the number of muons, $N_μ$, produced by air showers. Both, the longitudinal development, in particular the depth of the shower maximum, $X_{\rm max}$, and the muon content of air showers are highly sensitive to hadronic interactions at ultra-high energies.…
The electromagnetic and the muonic longitudinal profile at production enclosure important information about the primary particle and the hadronic interactions that rule the shower development. In fact, these two profiles provide two different insights of the shower: the electromagnetic component gives a measurement of the energy and the strength of the neutral pion channel; while the muonic profile, being intimately related with the charged mesons decays, can be used as a direct probe for the high energy hadronic interactions. In this work we explore the interplay between the electromagnetic a…
Anomalous Air Showers and What They Reveal About Hadronic Interactions and Cosmic-ray Masses
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of Manchester（曼彻斯特大学）；Vrije Universiteit Brussel（布鲁塞尔自由大学）；Radboud University Nijmegen（奈梅亨拉德堡德大学）；Curtin University（科廷大学）；University of Groningen（格罗宁根大学）；Netherlands Institute for Radio Astronomy（荷兰射电天文研究所）；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；Nikhef（尼赫夫国家粒子物理研究所）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Khalifa University（哈利法大学）；Can Tho University（芹苳大学）；Nanjing University（南京大学）；Xidian University（西安电子科技大学）；University of Science and Technology of China（中国科学技术大学）
We describe the measurement of the depth of maximum, Xmax, of the longitudinal development of air showers induced by cosmic rays. Almost four thousand events above 10^18 eV observed by the fluorescence detector of the Pierre Auger Observatory in coincidence with at least one surface detector station are selected for the analysis. The average shower maximum was found to evolve with energy at a rate of (106 +35/-21) g/cm^2/decade below 10^(18.24 +/- 0.05) eV and (24 +/- 3) g/cm^2/decade above this energy. The measured shower-to-shower fluctuations decrease from about 55 to 26 g/cm^2. The interpr…
The production of very high energy muons inside an extensive air shower is observable at $ν$ telescopes and sensitive to the composition of the primary cosmic ray. Here we discuss five different sources of these muons: pion and kaon decays; charmed hadron decays; rare decays of unflavored mesons; photon conversion into a muon pair; and photon conversion into a $J/ψ$ vector meson decaying into muons. We solve the cascade equations for a $10^{10.5}$ GeV proton primary and find that unflavored mesons and gamma conversions are the two main sources of $E\ge 10^{8.5}$ GeV muons, while charm decays d…
Calibrating the absolute energy scale of air showers initiated by ultra-high energy cosmic rays is an important experimental issue. Currently, the corresponding systematic uncertainty amounts to 14-21% using the fluorescence technique. Here we describe a new, independent method which can be applied if ultra-high energy photons are observed. While such photon-initiated showers have not yet been identified, the capabilities of present and future cosmic-ray detectors may allow their discovery. The method makes use of the geomagnetic conversion of UHE photons (preshower effect), which significantl…
Cosmic rays with energy exceeding ~ 10^{18} eV are referred to as ultra-high energy cosmic rays (UHECRs). Monte Carlo codes for extensive air shower (EAS) simulate the development of EASs initiated by UHECRs in the Earth's atmosphere. Experiments to detect UHECRs utilize EAS simulations to estimate their energy, arrival direction, and composition. In this paper, we compare EAS simulations with two different codes, CORSIKA and COSMOS, presenting quantities including the longitudinal distribution of particles, depth of shower maximum, kinetic energy distribution of particle at the ground, and en…
To search for ultra-high-energy photons in primary cosmic rays, air shower observables are needed that allow a good separation between primary photons and primary hadrons. We present a new observable, $F_γ$, which can be extracted from ground-array data in hybrid events, where simultaneous measurements of the longitudinal and the lateral shower profile are performed. The observable is based on a template fit to the lateral distribution measured by the ground array with the template taking into account the complementary information from the measurement of the longitudinal profile, i.e. the prim…
The understanding of the basic properties of the ultra - high energy extensive air showers is strongly dependent on the description of the hadronic interactions in a energy range beyond that probed by the LHC. One of the uncertainties present in the modeling of the air showers is the treatment of diffractive interactions, which are dominated by non - perturbative physics and usually described by phenomenological models. These interactions are expect to affect the development of the air showers, since they provide a way of transporting substantial amounts of energy deep in the atmosphere, modif…
We describe a method of reconstructing air showers induced by cosmic rays using deep learning techniques. We simulate an observatory consisting of ground-based particle detectors with fixed locations on a regular grid. The detector's responses to traversing shower particles are signal amplitudes as a function of time, which provide information on transverse and longitudinal shower properties. In order to take advantage of convolutional network techniques specialized in local pattern recognition, we convert all information to the image-like grid of the detectors. In this way, multiple features,…
The Pierre Auger Observatory is the largest extensive air shower detector. Based on a hybrid system, this experiment measures the longitudinal shower development and the particles at the ground. This detection system allows the extraction of the p-air cross-section at energies much higher than the ones accessible by current colliders. It is also possible to test hadronic interaction models using correlations between different air shower observables, like the depth of shower maximum and the muon number at the ground and their fluctuations. Thanks to the low energy extension of the Pierre Auger …
We show that combining the published Pierre Auger Observatory measurements of the longitudinal_and_ lateral properties of UHE atmospheric showers, points to an unforeseen change in the nature of particle interactions at ultrahigh energy. A "toy model" of UHE proton-air interactions is presented which provides the first fully consistent description of air shower observations. It demonstrates that the observed energy dependence of the depth-of-shower-maximum distribution may not indicate a transition to a heavier composition, as commonly assumed. While fundamentally phenomenological, the model i…
An in-depth characterization of coherent radio Cherenkov pulses from particle showers in dense dielectric media, referred to as the Askaryan effect, is presented. The time-domain calculation developed in this article is based on a form factor to account for the lateral dimensions of the shower. It is computationally efficient and able to reproduce the results of detailed particle shower simulations with high fidelity in most regions of practical interest including Fresnel effects due to the longitudinal development of the shower. In addition, an intuitive interpretation of the characteristics …
Novel methods to reconstruct the slant depth of the maximum of the longitudinal profile (\Xmax) of high-energy showers initiated by gamma-rays as well as their energy ($E_0$) are presented. The methods were developed for gamma rays with energies ranging from a few hundred GeV to $\sim 10$ TeV. An estimator of \Xmax is obtained, event-by-event, from its correlation with the distribution of the arrival time of the particles at the ground, or the signal at the ground for lower energies. An estimator of $E_0$ is obtained, event-by-event, using a parametrization that has as inputs the total measure…
We report on studies of the composition of ultra high energy cosmic rays with the Pierre Auger Observatory. The detection of longitudinal air shower profiles with the fluorescence detector is described and the measurement of the average shower maximum as a function of energy is presented. Furthermore, mass sensitive parameters that can be obtained from the observatory's surface detector data are discussed.
The simulation of the extensive air showers was performed by investigating the longitudinal development parameters (N and Xmax) by using AIRES system version 19.04.0. The simulation was performed at the energy range (10^18-10^20 eV) for different primary particles (such as primary proton and iron nuclei) and different zenith angles. The longitudinal development curves of EAS are fitted using Gaussian function that gave a new parameters for different primary particles and different zenith angles at the energy range (10^18-10^20 eV).
LOPES was the radio extension of the KASCADE-Grande particle-detector array consisting of up to 30 antennas measuring the radio emission of cosmic-ray air showers between 40 and 80 MHz with an energy threshold of around 100 PeV. Even with the external trigger by the particle detectors, the separation of the air-shower signal from the radio background was difficult in the noisy environment of the Karlsruhe Institute of Technology. For the typical event this was only possible because of the digital, interferometric beamforming technique pioneered by LOPES for cosmic-ray detection. Using this tec…
Improved statistics and mass-composition-sensitive observation are required to clarify the origin of ultra-high energy cosmic rays (UHECRs). Inevitably in the future, the UHECR observatories will have to be expanded due to the small flux; however, the upgrade will be expensive with the detectors currently in use. Hence, we are developing a new fluorescence detector for UHECR observation. The proposed fluorescence detector, called cosmic ray air fluorescence Fresnel-lens telescope (CRAFFT), has an extremely simple structure and can observe the longitudinal development of an air shower. Furtherm…
The field of ultra-high energy cosmic rays made a lot of progresses last years with large area experiments such as the Pierre Auger Observatory, HiRes and the Telescope Array. A suppression of the cosmic ray flux at energies above $5.5x10^{19}$ eV is observed at a very high level of significance but the origin of this cut-off is not established: it can be due to the Greisen-Zatsepin-Kuzmin suppression but it can also reflect the upper limit of particle acceleration in astrophysical objects. The key characteristics to be measured on cosmic rays is their composition. Upper limits are set above $…
At the Pierre Auger Observatory and the Telescope Array, the measurements of depths of maximum of air-shower profiles, $X_\mathrm{max}$, are performed using direct observations of the longitudinal development of showers with the help of the fluorescence telescopes. Though the same detection technique is used at both installations, the straightforward comparison of the characteristics of the measured $X_\mathrm{max}$ distributions is not possible due to the different approaches to the analysis of the recorded events. In this work, the Auger-Telescope Array composition working group presents a t…
Currently new radio detection techniques are being explored to detect astrophysical neutrinos beyond the PeV scale interacting in polar ice. Due to the long attenuation length of radio waves in a medium, it can be expected that such instruments will also be sensitive to the radio emission of cosmic ray air showers. Furthermore, cosmic ray air showers hitting a high-altitude layer of ice will initiate an in-ice particle cascade, also leading to radio emission. We present the first results of detailed simulations of the in-ice continuation of these cosmic-ray-induced particle cascades, using a c…
The Pierre Auger Observatory infers the chemical composition of ultra-high-energy cosmic rays through two independent detection techniques. The Fluorescence Detector (FD) measures the longitudinal profile of high energy air showers and can determine the depth of the shower maximum $X_{max}$, which is sensitive to the chemical composition of the primary cosmic rays. Additionally, measurements by the Surface Detector (SD) provide independent experimental observables based on the muonic shower component to analyze the chemical composition. We present the results for the $X_{max}$ distributions an…
