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 16 $\mathrm{g/cm^{2}}$ in the $\mathrm{X_{max}}$ reconstruction is obtained.
The angular distribution of Cherenkov light in an air shower is closely linked to that of the shower electrons and positrons. As charged particles in extensive air showers are deflected by the magnetic field of the Earth, a deformation of the angular distribution of the Cherenkov light, that would be approximately symmetric about the shower axis if no magnetic field were present, is expected. In this work we study the variation of the Cherenkov light distribution as a function of the azimuth angle in the plane perpendicular to shower axis. It is found that the asymmetry induced by the geomagne…
The Cherenkov light produced in air showers largely contributes to the signal observed in ground-based gamma-ray and cosmic-ray observatories. Yet, no description of this phenomenon is available covering both regions of small and large angles to the shower axis. To fill this gap, a parametrization of the angular distribution of Cherenkov photons is performed in terms of a physically-motivated parametric function. Model parameters are constrained using simulated gamma-ray and proton showers with energies in the TeV to EeV region. As a result, a new parametrization is obtained that improves the …
A wide field-of-view Cherenkov telescope has been working in the surroundings of the Yakutsk array experiment since 2012. Its main function is to measure the waveform of the Cherenkov radiation signal induced by extensive air showers of cosmic rays. Analysis of the dataset collected by telescope is intended for the reconstruction of the parameters of the development of the shower in addition to the main shower characteristics measured by the rest of the array detectors. In this paper, the observed duration of the Cherenkov radiation signal as a function of the shower core distance is used to e…
Using Monte Carlo simulation of extensive air showers, we showed that the maximum depth of showers, $X_{max}$ can be estimated using $P=Q(100)/Q(200)$, the ratio of Cherenkov photon densities at 100 and 200 meters from the shower core, which is known as the steepness parameter of the lateral distribution of Cherenkov radiation on the ground. A simple quadratic model has been fitted to a set of data from simulated extensive air showers, relating the steepness parameter and the shower maximum depth. Then the model has been tested on another set of simulated showers. The average difference betwee…
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 describe a method of observation for PeV--EeV tau neutrinos using Cherenkov light from the air showers of decayed taus produced by tau neutrino interactions in the Earth. Aiming for the realization of neutrino astronomy utilizing the Earth-skimming tau neutrino detection technique, highly precise determination of arrival direction is key due to the following issues: (1) Clear identification of neutrinos by identifying those vertices originating within the Earth's surface; (2) Identification of very high energy neutrino sources. The Ashra detector uses newly developed light collectors which …
The proposed SCORE detector consists of a large array of light collecting modules designed to sample the Cherenkov light front of extensive air showers in order to detect high energy gamma-rays. A large spacing of the detector stations makes it possible to cover a huge area with a reasonable effort, thus achieving a good sensitivity up to energies of about a few 10 PeV. In this paper the event reconstruction algorithm for SCORE is presented and used to obtain the anticipated performance of the detector in terms of angular resolution, energy resolution, shower depth resolution and gamma / hadro…
We have estimated the reflected component of Cherenkov radiation, which arises in developing of an extensive air shower with primary energy of 10^20 eV over the ocean surface. It has been shown that, under conditions of the TUS experiment, a flash of the reflected Cherenkov photons at the end of the fluorescence track can be identified in showers with zenith angles up to 20 degrees.
We study the azimuthal distributions of Cherenkov photons in Extensive Air Showers (EASs) initiated by $γ$-ray, proton and iron primaries of different energies incident at various zenith angles over a high altitude observation level. The azimuthal distributions of electrons and positrons along with their asymmetric behaviour have also been studied here to understand the feature of azimuthal distributions of Cherenkov photons in EASs. The main motivation behind this study is to see whether the azimuthal distribution of Cherenkov photons can provide any means to distinguish the $γ$-ray initiated…
The development of a 3-dimensional simulation for Cherenkov photon emissions in Extensive Air Showers (EAS) is reported in this paper. CORSIKA is the most widely used Monte-Carlo generator for the description of EAS, but it is not recommended to calculate Cherenkov light emissions for EAS at ultra high energies due to the enormous amount of data storage and running time required. The presented BinTheSky is a framework to simulate the Cherenkov light emissions using the spatial information produced by Monte-Carlo generators. The light is emitted in the shower, propagated and attenuated to the g…
Future experiments based on the observation of Earth's atmosphere from sub-orbital and orbital altitudes plan to include optical Cherenkov cameras to observe extensive air showers produced by high-energy cosmic radiation via its interaction with both the Earth and its atmosphere. As discussed elsewhere, particularly relevant is the case of upward-moving showers initiated by astrophysical neutrinos skimming and interacting in the Earth. The Cherenkov cameras, by looking above Earth's limb, can also detect cosmic rays with energies starting from less than a PeV up to the highest energies (tens o…
The energy spectrum of cosmic rays in the range 10^15 eV to 6*10^19 eV has been studied using the air Cherenkov light detectors of the Yakutsk array. The total flux of photons produced by relativistic electrons (including positrons as well, hereafter) of extensive air showers in the atmosphere is used as the energy estimator of the primary particle initiating a shower. The resultant differential flux of cosmic rays exhibits, in accordance with previous measurements, a knee and ankle features at energies 3*10^15 and ~10^19 eV, respectively. A comparison of observational data with simulations is…
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.
Stereoscopic arrays of Imaging Atmospheric Cherenkov Telescopes allow to reconstruct gamma-ray-induced showers in 3 dimensions, which offers several advantages: direct access to the shower parameters in space and straightforward calorimetric measurement of the incident energy. In addition, correlations between the different images of the same shower are taken into account. An analysis method based on a simple 3D-model of electromagnetic showers was recently implemented in the framework of the H.E.S.S. experiment. In the present article, the method is completed by an additional quality criterio…
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.
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…
We consider a ground array of scintillation and water Cherenkov detectors with the purpose of determining the muon content of air showers. The different response characteristics of these two types of detectors to the components of the air shower provide a way to infer their relative contributions. We use a detailed simulation to estimate the impact of parameters, such as scintillation detector size, in the determination of the size of the muon component.
The reconstruction of cosmic-ray-induced extensive air showers with a non-imaging Cherenkov detector array requires knowledge of the Cherenkov yield of any given air shower for a given set of shower parameters. Although air showers develop in a stochastic cascade, certain characteristics of the particles in the shower have been shown to come from universal probability distributions, a property known as shower universality. Both the energy and the angular distributions of charged particles within a shower have been parameterized. One can use these distributions to calculate the Cherenkov photon…
The simulation of Cherenkov photon's lateral density and arrival time distributions in Extensive Air Showers (EASs) was performed with the CORSIKA code in the energy range: 100 GeV to 100 TeV. On the basis of this simulation we obtained a set of approximating functions for the primary $γ$-ray photons, protons and iron nuclei incident at zenith angles from 0$^\circ$ to 40$^\circ$ over different altitudes of observation. Such a parameterisation is important for the primary particle identification, for the reconstruction of the shower observables and hence for a more efficient disentanglement of …
Cosmic-ray observatories necessarily rely on Monte Carlo simulations for their design, calibration and analysis of their data. Detailed simulations are very demanding computationally. We present a python-based package called ShowerModel to model cosmic-ray showers, their light production and their detection by an array of telescopes. It is based on parameterizations of both Cherenkov and fluorescence emission in cosmic-ray induced air showers. The package permits the modelling of fluorescence telescopes, imaging air Cherenkov telescopes, wide-angle Cherenkov detectors or any hybrid design. Sho…
We present a sophisticated likelihood reconstruction algorithm for shower-image analysis of imaging Cherenkov telescopes. The reconstruction algorithm is based on the comparison of the camera pixel amplitudes with the predictions from a Monte Carlo based model. Shower parameters are determined by a maximisation of a likelihood function. Maximisation of the likelihood as a function of shower fit parameters is performed using a numerical non-linear optimisation technique. A related reconstruction technique has already been developed by the CAT and the H.E.S.S. experiments, and provides a more pr…
We have investigated some features of the density and arrival time distributions of Cherenkov photons in extensive air showers using the CORSIKA simulation package. The main thrust of this study is to see the effect of hadronic interaction models on the production pattern of Cherenkov photons with respect to distance from the shower core. Such studies are very important in ground based $γ$-ray astronomy for an effective rejection of huge cosmic ray background, where the atmospheric Cherenkov technique is being used extensively within the energy range of some hundred GeV to few TeV. We have fou…
Since its commissioning in autumn 2012, Tunka-Rex, the radio extension of the air-Cherenkov detector Tunka-133, performed three years of air shower measurements. Currently the detector consists of 44 antennas connected to air-Cherenkov and scintillator detectors, respectively, placed in the Tunka valley, Siberia. Triggered by these detectors, Tunka-Rex measures the radio signal up to EeV-scale air-showers. This configuration provides a unique possibility for cross-calibration between air-Cherenkov, radio and particle techniques. We present reconstruction methods for the energy and the shower m…
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.
Radio detection of cosmic-ray-induced air showers has come to a flight the last decade. Along with the experimental efforts, several theoretical models were developed. The main radio-emission mechanisms are established to be the geomagnetic emission due to deflection of electrons and positrons in Earth's magnetic field and the charge-excess emission due to a net electron excess in the air shower front. It was only recently shown that Cherenkov effects play an important role in the radio emission from air showers. In this article we show the importance of these effects to extract quantitatively…
The Cherenkov radio pulse emitted by hadronic showers in ice is calculated for showers of energies in the EeV range. This is obtained with three dimensional simulations of both shower development and the coherent radio pulse emitted as the excess charge develops in the shower. A Monte Carlo, ZHAireS, has been developed for this purpose combining the high energy hadronic interaction capabilities of AIRES, and the dense media propagation capabilities of TIERRAS, with the precise low energy tracking and specific algorithms developed to calculate the radio emission in ZHS. A thinning technique is …
Cherenkov telescopes have the capability of detecting high energy tau neutrinos in the energy range of 1--1000 PeV by searching for very inclined showers. If a tau lepton, produced by a tau neutrino, escapes from the Earth or a mountain, it will decay and initiate a shower in the air which can be detected by an air shower fluorescence or Cherenkov telescope. In this paper, we present detailed Monte Carlo simulations of corresponding event rates for the VERITAS and two proposed Cherenkov Telescope Array sites: Meteor Crater and Yavapai Ranch, which use representative AGN neutrino flux models an…
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…
The presence of muons in air-showers initiated by cosmic ray protons and nuclei is well established as a powerful tool to separate such showers from those initiated by gamma rays. However, so far this approach has been fully exploited only for ground level particle detecting arrays. We explore the feasibility of using Cherenkov light from muons as a background rejection tool for imaging atmospheric Cherenkov telescope arrays at the highest energies. We adopt an analytical model of the Cherenkov light from individual muons to allow rapid simulation of a large number of showers in a hybrid mode.…
Singular Templates of Imaging Cherenkov Shower distribution (STOICS): A background estimation method for Very-High-Energy $γ$-ray observations
Department of Physics and Astronomy, Barnard College, Columbia University（哥伦比亚大学巴纳德学院物理与天文系）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学、巴黎西岱大学、法国原子能和替代能源委员会、法国国家科学研究中心、天体物理学与信息数学研究所）；Department of Physics, University of Maryland（马里兰大学物理系）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）
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 Simulation of Cherenkov light lateral distribution function (LDF) from particles of Extensive Air Showers (EAS) with ultra high energy cosmic rays (E>=10^16 eV) was simulated for primary protons by the computer code CORSIKA. The parameterization, that constructed on the basis of this simulation have allowed us to reconstruct the events, that is, to reconstruct the type and energy of the particle that generated EAS from signal amplitudes of Cherenkov light registered with the Tunka-25 facility. The extrapolation of the Cherenkov light LDF approximation at the energy range (10^16-2.10^18 eV)…
The presence of muons in air-showers initiated by cosmic ray protons and nuclei is well established as a powerful tool to separate such showers from those initiated by gamma-rays. However, so far this approach has been fully exploited only for ground level particle detecting arrays. In this contribution, we explore the feasibility of using Cherenkov light from muons as a background rejection tool for imaging atmospheric Cherenkov telescope arrays at the highest energies. We adopt an analytical model of the Cherenkov light from individual muons to allow rapid simulation of a large number of sho…
Very energetic cosmic rays entering the atmosphere of the Earth will create a plasma cloud moving with almost the speed of light. The magnetic field of the Earth induces an electric current in this cloud which is responsible for the emission of coherent electromagnetic radiation. We propose to search for a new effect: due to the index of refraction of air this radiation is collimated in a Cherenkov cone. To express the difference from usual Cherenkov radiation, i.e. the emission from a fast moving electric charge, we call this magnetically-induced Cherenkov radiation. We indicate its signature…
We present a macroscopic calculation of coherent electro-magnetic radiation from air showers initiated by ultra-high energy cosmic rays, based on currents obtained from three-dimensional Monte Carlo simulations of air showers in a realistic geo-magnetic field. We discuss the importance of a correct treatment of the index of refraction in air, given by the law of Gladstone and Dale, which affects the pulses enormously for certain configurations, compared to a simplified treatment using a constant index. We predict in particular a geomagnetic Cherenkov radiation, which provides strong signals at…
The electric field of the Cherenkov radio pulse produced by a single charged particle track in a dielectric medium is derived from first principles. An algorithm is developed to obtain the pulse in the time domain for numerical calculations. The algorithm is implemented in a Monte Carlo simulation of electromagnetic showers in dense media (specifically designed for coherent radio emission applications) as might be induced by interactions of ultra-high energy neutrinos. The coherent Cherenkov radio emission produced by such showers is obtained simultaneously both in the time and frequency domai…
The simulation of the Cherenkov light lateral distribution function (LDF) in Extensive Air Showers (EAS) was perfomed with the CORSIKA code in the energy range 10^13-10^16 eV for configuration of the Tunka-25 EAS array. On the basis of this simulation we obtained sets of approximating functions for primary protons, iron nuclei and gamma-quanta for zenith angles Theta<=20. The comparison of the calculated Cherenkov light LDF with that measured with the Tunka-25 array has shown an opportunity of primary particle identification and definition of its energy around the "knee".
The radio approach for detecting the ultra-high energy cosmic neutrinos has become a mature field. The Cherenkov signals in radio detection are originated from the charge excess of particle showers due to Askaryan effect. The conventional way of calculating the Cherenkov pulses by making Fraunhofer approximation fails when the sizes of the elongated showers become comparable with the detection distances. We present a calculation method of Cherenkov pulses based on the finite-difference time-domain (FDTD) method, and attain a satisfying effeciency via the GPU- acceleration. Our method provides …
The SPHERE-2 balloon-borne detector designed for extensive air shower (EAS) observations using EAS optical Vavilov-Cherenkov radiation (``Cherenkov light''), reflected from the snow-covered surface of Lake Baikal is described. We briefly discuss the concept behind the reflected Cherenkov light method, characterize the conditions at the experimental site and overview the construction of the tethered balloon used to lift the SPHERE-2 telescope above the surface. This paper is mainly dedicated to a detailed technical description of the detector, including its optical system, sensitive elements, e…
The radio approach for detecting the ultra-high energy cosmic neutrinos has become a mature field. The Cherenkov pulse in radio detection originates from the charge excess of particle showers due to Askaryan effect. The conventional way of calculating the Cherenkov pulse by making far- field approximation fails when the size of elongated showers become comparable with detection distance. We investigate the Cherenkov pulse in near-field by a numerical code based on the finite- difference time-domain (FDTD) method. Our study shows that the near-field radiation exhibits very different behaviors f…
We present a detailed modeling and computation methodology to determine the optical Cherenkov signals produced by upward-moving extensive air showers (EASs) induced by $τ$-leptons and muons, sourced from the interaction of high-energy astrophysical neutrinos interacting in the Earth. Following and extending the physics modeling and Cherenkov signal simulations performed in arxiv:1902.11287, this scheme encompasses a new, state-of-the-art computation of the muon neutrino propagation inside the Earth and the contribution to the $τ$-lepton muon decay channel. The modeling takes into account all p…
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…
Cosmic-ray muons and especially their secondaries break apart nuclei ("spallation") and produce fast neutrons and beta-decay isotopes, which are backgrounds for low-energy experiments. In Super-Kamiokande, these beta decays are the dominant background in 6--18 MeV, relevant for solar neutrinos and the diffuse supernova neutrino background. In a previous paper, we showed that these spallation isotopes are produced primarily in showers, instead of in isolation. This explains an empirical spatial correlation between a peak in the muon Cherenkov light profile and the spallation decay, which Super-…
The validity of our Monte Carlo simulation procedure ({\it the integral method}) had been verified by the corresponding analytical procedure of which is quite independent of our method methodologically. Also, the results obtained by our procedure are compared with those obtained by the different Monte Carlo simulation procedure ({\it the differential method}) which have been exclusively utilized by the different authors and the agreement between them are found to be well. By utilizing our Monte Carlo procedures, the validity of which is guaranteed in two different procedures, we investigate no…
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.
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…
We perform a new, detailed calculation of the flux and energy spectrum of Earth-emerging $τ$-leptons generated from the interactions of tau neutrinos and antineutrinos in the Earth. A layered model of the Earth is used to describe the variable density profile of the Earth. Different assumptions regarding the neutrino charged- and neutral-current cross sections as well as the $τ$-lepton energy loss models are used to quantify the systematic uncertainty from these on the results. A baseline simulation is then used to generate the optical Cherenkov signal from upward-moving extensive air showers …
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…
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.
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.
