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 made in the knee and ankle regions in order to choose the models of galactic and extragalactic components of cosmic rays which describe better the energy spectrum measured.
The paper presents short technical description of Yakutsk Radio Array and some preliminary results obtained from measurements of radio emission at 32 MHz frequency induced by air shower particles with energy ε$\geq$1$\cdot$10$^{19}$ eV. The data obtained at Yakutsk array in 1987-1989 (first set of measurements) and 2009-2014 (new set of measurements). For the first time, at Yakutsk array radio emission from air shower with energy > 10$^{19}$ eV was registered including the shower with highest energy ever registered at Yakutsk array with energy $\sim$2$\cdot$10$^{20}$ eV.
Cherenkov light lateral distribution function (CLLDF) in Extensive Air Showers (EAS) for different primary particles (e-, n , p, F, K and Fe) was simulated using CORSIKA code for conditions and configurations of Yakutsk EAS array with the fixed primary energy 3 PeV around the knee region at different zenith angles. Basing on the results of CLLDF numerical simulation, sets of approximated functions are reconstructed for different primary particles as a function of the zenith angle. A comparison of the parameterized CLLDF with that simulated with Yakutsk EAS array is verified. The parameterized …
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…
The Yakutsk Extensive Air Shower Array has been continuously operating for more than 50 years (since 1970) and up until recently it has been one of world's largest ground-based instruments aimed at studying the properties of cosmic rays in the ultra-high energy domain. In this report we discuss results recently obtained at the array - on cosmic rays energy spectrum, mass composition and directional anisotropy - and how they fit into the world data. Special attention is paid to the measurements of muonic component of extensive air showers. Theoretical results of particle acceleration at shocks …
The Yakutsk array dataset in the energy interval $(10^{17},10^{19})$ eV is revisited in order to interpret the zenith angle distribution of an extensive air shower event rate of ultra-high energy cosmic rays. The close relation of the distribution to the attenuation of the main measurable parameter of showers, $S_{600}$, is examined. Measured and expected distributions are used to analyze the arrival directions of cosmic rays on an equatorial map including the energy range below $10^{18}$ eV, which was previously avoided due to the reduced trigger efficiency of the array in the range. While th…
In this research, the simulation of lateral distribution function (LDF) of Cherenkov radiation was performed using CORSIKA software for two hadronic models QGSJET and GHEISHA. This simulation was performed for several elementary particles such as protons, iron nuclei, electrons and gamma quanta, in the range of energies 1-20 PeV for three zenith angles 0, 20 and 30 degrees. A parameterization of Cherenkov light LDF was performed for that simulated curves using Lorentzian function. The comparison between the obtained results for LDF of Cherenkov light with that measured with Yakutsk EAS array g…
We present of measurements of radio emission from EAS at the frequency 32 MHz performed in 2008-2012. Showers were selected by zenith and azimuth directions, sampled by energy. A mean lateral distribution function was fitted to the data each interval. The paper presents unied approximation formula for all three energy intervals of lateral distribution, using connection between equation (1) and (2) coefficients with energy and geomagnetic angle. Here we analyze the connection between the shape of lateral distribution and the depth of the maximum shower development Xmax too.
Lateral distribution of muons in extensive air showers registered at the Yakutsk array was investigated. The analysis covers two periods of observation: before 2018 and after 2020, when the revision of muon detectors with 1-GeV threshold was complete. Measured values of muon density are compared to computational results obtained within the framework of two hadron interaction models. Within the energy domain above $10^{18}$ eV the best agreement is observed for proton composition primary cosmic rays.
Characteristics of the muon component in EAS are analyzed together with their fluctuations. The aim of this analysis -- a comparison of experimental data with computational results obtained within frameworks of various hadron interaction models for protons and iron nuclei and an estimation of cosmic ray mass composition in the ultra-high energy region.
In this paper, we present results obtained from the measurements of radio emission at frequency of 32 MHz with energy more than 10$^{19}$ eV. Generalized formula that describe lateral distribution and depends on main characteristic of the air showers: energy E$_0$ and depth of maximum X$_{max}$ was derived. The formula has a good agreement with data at average and large distances from shower axis. Employing the ratio of radio emission amplitude at distances 175 m and 725 m we determined the depth of maximum X$_{max}$ for air shower with energy 3.7$\cdot$10$^{19}$ eV, which in our case is equal…
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.
Arrival directions of ultrahigh energy extensive air showers (EAS) by world arrays data are analyzed. It is shown that arrival directions of ultrahigh energy EAS by Yakutsk and P. Auger data are some correlated with pulsars of Local Arm Orion of Galaxy. It is found large amplitude of first harmony of Fourier row by data Yakutsk array. The problem of cosmic rays origin is discussed.
This paper presents the set of measurements of ultra-high energy air shower radio emission at frequency 32 MHz in period of 2008-2012. The showers are selected by geomagnetic and azimuth angles and then by the energy in three intervals: 3*10^16 3*10^17 eV, 3*10^17 6*10^17 eV and 6*10^17 5*10^18 eV. In each energy interval average lateral distribution function using mathematically averaged data from antennas with different directions are plotted. In the paper, using experimental data the dependence of radio signal averaged amplitude from geomagnetic angle, the shower axis distance and the energ…
Responses of surface and underground scintillation detectors of Yakutsk array are calculated for showers initiated by primary particles with energy E0>=1.0E17 eV within the frameworks of QGSJet01 QGSIIJet-II-04, SIBYLL-2.1 and EPOS-LHC hadron interaction models. A new estimation of E0 is obtained with the use of various methods. The resulting energy is lower compared to the obtained with earlier method by factor ~1.33.
The paper presents the results of the longitudinal development of extensive air showers (X$_{max}$) of ultra-high energies and mass composition of cosmic rays. The measurements of X$_{max}$ are based on data from observations of the Cherenkov radiation at the Yakutsk array for the period 1974-2014. The cascade curves of individual showers and the depth of maximum X$_{max}$ were reconstructed over the energy range 10$^{16}$-5.7$\cdot$10$^{19}$ eV. It is shown that the displacement rate of the parameter dX$_{max}$ / dE in the atmosphere is nonlinear and depends on the energy. Such a feature indi…
Comparing the signals measured by the surface and underground scintillator detectors of the Yakutsk Extensive Air Shower Array, we place upper limits on the integral flux and the fraction of primary cosmic-ray photons with energies E > 10^18 eV, E > 2*10^18 eV and E > 4*10^18 eV. The large collected statistics of the showers measured by large-area muon detectors provides a sensitivity to photon fractions < 10^-2, thus achieving precision previously unreachable at ultra-high energies.
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 …
From the data on Cherenkov light from EASs collected over the period of more than 15 years, the spectrum of cosmic rays was obtained in the energy range 1.0E15-1.0E18 eV. This spectrum has two features: at ~3.0E15 eV (first knee) and at ~1.0E17 eV (second knee). The first knee is characterized by the indexes γ_1=2.7+/-0.03 and γ_2 = 3.12+/-0.03 and the second knee - by γ_1 = 2.92+/-0.03 and γ_2=3.24+/-0.04. In the second case the difference amounts to Δγ_23=0.32{\pm}0.03{\pm}0.05 which is less than the case of the first knee Δγ_12=0.42+/-0.03+/-0.05 (here dual errors represent statistics and s…
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…
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 …
This paper presents the results of searches for anisotropy in arrival directions of ultra-high energy cosmic rays detected with the Yakutsk Array during the 1974--2008 observational period together with available data from other giant extensive air shower arrays working at present. A method of analysis based on a comparison of the minimal width of distributions in equatorial coordinates is applied. As a result, a hypothesis of isotropy in arrival directions is rejected at the $99.5\%$ significance level. The observed decrease in the minimal width of distribution can be explained by the presenc…
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 discuss the lateral distribution of charged particles in extensive air showers with energy above $10^{17}$ eV measured by surface scintillation detectors of Yakutsk EAS array. The analysis covers the data obtained during the period from 1977 to 2013. Experimental values are compared to theoretical predictions obtained with the use of CORSIKA code within frameworks of different hadron interaction models. The best agreement between theory and experiment is observed for QGSJet01 and QGSJet-II-04 models. A change in the cosmic ray mass composition towards proton is observed in the energy range …
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 lateral distribution of muons with ~1.0x\sec(θ) GeV in extensive air showers within ~10^{17}-10^{19} eV energy region obtained during different observational periods from November 1987 to June 2013 has been analyzed. Experimental data have been compared to predictions of various hadron interaction models. The best agreement is observed with QGSJETII-04. Until 1996, the mass composition of cosmic rays with energy below 2x10^{18} eV was significantly lighter than in later periods.
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 lateral distribution of muons with threshold energy e ~ 1*sec(theta) GeV have been studied in showers with energy E>=10^17 eV. The data considered in the analysis have been collected from November 2011 to June 2013. Experimental values are compared to predictions obtained with the use of CORSIKA code within the framework of various hadron interaction models. The best agreement between experiment and theory is observed for QGSJETII-04 model. At E~10^17 eV it complies to a mixed cosmic ray composition with the mean atomic number <lnA>~3.0+/-0.5. At E>= 4*10^17 eV the composition varies aroun…
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…
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…
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…
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…
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 …
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.
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…
Results obtained from an analysis of the energy spectrum of cosmic rays with energies in the region of $E_0 \ge 10^{17}$ eV over the period of continuous observations from 1974 to 2017 are presented. A refined expression for estimating the primary-particle energy is used for individual events. This expression is derived from calculations aimed at determining the responses of the ground-based and underground scintillation detectors of the Yakutsk array for studying extensive air showers (EAS) and performed within the QGSJET01, QGSJET-II-04, SIBYLL-2.1, and EPOS-LHC models by employing the CORSI…
The energies of the most energetic extensive air showers observed at the Yakutsk array have been estimated with help of the all detectors readings instead of using of the standard procedure with a parameter s(600). The energy of the most energetic extensive air shower observed at the Yakutsk array happened to be 200, 200, 180 and 165 EeV with the values of the Xi**2 function per one degree of freedom 0.9, 1., 0.9 and 1.1 for the primary protons and helium, oxygen and iron nuclei accordingly.
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…
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.
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…
Several energy spectra of cosmic rays with energies E_0 \geq 10^17 eV measured at the Yakutsk EAS, AGASA, Haverah Park, HiRes, Auger, and SUGAR arrays are considered. It is shown that the fairly good mutual agreement of the spectrum shapes can be achieved if the energy of each spectrum is multiplied by a factor K specific for each spectrum. These factors exhibit a pronounced dependence on the latitude of the above-mentioned arrays.
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…
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 arrival directions of ultrahigh energy extensive air showers (EAS) by Yakutsk, AGASA, P. Auger array data are analyzed. For the first time, the maps of equal exposition of celestial sphere for the distribution of particles by AGASA and P. Auger arrays data have been constructed. The large-scale anisotropy of cosmic particles at E>4.1019 eV by Yakutsk, AGASA and P. Auger array data has been detected. The problem of cosmic particle origin is discussed.
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.…
