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 domains. A consistency check performed by Fourier-transforming the pulse in time and comparing it to the frequency spectrum obtained directly in the simulations yields, as expected, fully consistent results. The reversal of the time structure inside the Cherenkov cone and the signs of the corresponding pulses are addressed in detail. The results, besides testing algorithms used for reference calculations in the frequency domain, shed new light into the properties of the radio pulse in the time domain. The shape of the pulse in the time domain is directly related to the depth development of the excess charge in the shower and its width to the observation angle with respect to the Cherenkov direction. This information can be of great practical importance for interpreting actual data.
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.
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.
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.
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 …
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 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 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 …
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 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…
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 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…
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 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…
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…
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…
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.
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".
We present computing results of the Cherenkov light propagation in air and water from extensive air showers developing over the ocean. Limits on zenith angles of the showers, at which the registration of flashes of reflected Cherenkov photons by the satellite-based detector TUS is possible, are analyzed with consideration for waves on the ocean surface.
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…
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…
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 …
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…
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…
Ground-based Imaging Cherenkov Telescope Arrays observe the Cherenkov radiation emitted in extended atmospheric showers generated by cosmic gamma rays in the TeV regime. The rate of these events is normally overwhelmed by 2-3 orders of magnitude more abundant cosmic rays induced showers. A large fraction of these 'background' events is vetoed at the online trigger level, but a substantial fraction still goes through data acquisition system and is saved for the offline reconstruction. What kind of information those events carry, normally rejected in the analysis? Is there the possibility that a…
The validity of our Monte Carlo simulation procedure (the time sequential procedure) had been verified by the corresponding analytical procedure which is independent of our method methodologically. Also, the results obtained by our procedure are compared with those obtained by the different Monte Carlo simulation procedure (the v_{cut} procedure) which has been exclusively utilized by different authors and the agreement between ours and theirs are found to be good. By utilizing our Monte Carlo procedure, the validity of which is guaranteed in two different procedures, we investigate not only t…
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 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 …
Here the results of calculations of pulses in Cherenkov light detectors for the Yakutsk array are presented. As long as the Vavilov-Cherenkov light is used to calibrate signals in scintillation detectors at the Yakutsk array it is vital for these measurements to be precise. The validity of measurements of the signal Q(400) used as the estimation parameter at the Yakutsk array has been confirmed. Our calculations show that the width of time pulses increases from nearly 50 ns at a distance of 100 m from the shower axis up to 700 ns at 1000 m.
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 …
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…
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…
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-…
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…
We present predictions for the radio pulses emitted by extensive air showers using ZHAireS, an AIRES-based Monte Carlo code that takes into account the full complexity of ultra-high energy cosmic-ray induced shower development in the atmosphere, and allows the calculation of the electric field in both the time and frequency domains. We do not presuppose any emission mechanism, but our results are compatible with a superposition of geomagnetic and charge excess radio emission effects. We investigate the polarization of the electric field as well as the effects of the refractive index n and show…
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）
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…
Cosmic rays and air showers at ultra-high energy are unique tools to test the validity of Lorentz invariance. A brief overview is given on such tests focusing on isotropic, non-birefringent Lorentz violation (LV) in the photon sector. Based on the apparent absence of vacuum Cherenkov radiation and photon decay, the LV parameter $κ$ is bound to $-0.6 \cdot 10^{-20} < κ< 6 \cdot 10^{-20}$ (98\% CL). We report an updated limit from cosmic-ray photon observations and preliminary results on testing vacuum Cherenkov radiation in air showers.
The main interest of the present work is in analyzing the lateral distribution function (LDF) of Cherenkov radiation from particles that produced in Extensive Air Showers (EAS). The simulation of Cherenkov radiation LDF is fulfilled by utilizing the CORSIKA program at 1 PeV of the primary energy around the knee region for many primaries for vertical showers for Tunka-133 array conditions. Depending on the numerical simulation results of Cherenkov light LDF, sets of parameterized polynomial functions are resetted for several particles as a function of primary particle type. The comparison betwe…
Measuring radio emission from air showers offers a novel way to determine properties of the primary cosmic rays such as their mass and energy. Theory predicts that relativistic time compression effects lead to a ring of amplified emission which starts to dominate the emission pattern for frequencies above ~100 MHz. In this article we present the first detailed measurements of this structure. Ring structures in the radio emission of air showers are measured with the LOFAR radio telescope in the frequency range of 110 - 190 MHz. These data are well described by CoREAS simulations. They clearly c…
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…
Cosmic gamma-ray photons incident on the upper atmosphere create air showers that move to the Earth's surface with superluminal speed, relative to the air. Even though many of these air showers remain superluminal all along their trajectories, the shower's velocity component toward a single Imaging Atmospheric Cherenkov Telescope (IACT) may drop from superluminal to subluminal. When this happens, an IACT that is able to resolve the air shower both in time and angle should be able to document an unusual optical effect known as relativistic image doubling (RID). The logic of RID is that the show…
The HAWC observatory reconstructs atmospheric showers induced by very high-energy primary cosmic- or gamma-rays. Cosmic-rays with hadronic nature are several orders of magnitude more frequent than primary gammas and therefore it is necessary to perform the best gamma-hadron discrimination for each event to be able to survey the gamma-ray sky. Single vertical muons cause very characteristic signals in the 300 HAWC detectors. Particularly, those events that produce signals in the four PMTs of a tank corresponding to muons traversing the tank in the central region. In such cases exist the correla…
Cherenkov telescopes could have the capability of detecting high energy tau neutrinos by searching for very inclined showers. If a tau lepton, produced by a tau neutrino, escapes from the Earth crust, it will decay and initiate an air shower which can be detected by a fluorescence/Cherenkov telescope. Here we present a detailed Monte Carlo simulation of event rates induced by tau neutrinos in the energy range from 1 PeV to 1 EeV. Topographic conditions are taken into account for a set of example locations. As expected, we find a neutrino sensitivity which depends on the shape of the energy spe…
