A parameterization for the radio emission of air showers as predicted by CoREAS simulations and applied to LOFAR measurements

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 parameterization derived from air-shower simulations. We are able to fit the two-dimensional distribution with a double Gaussian, requiring five fit parameters. All parameters show strong correlations with air shower properties, such as the energy of the shower, the arrival direction, and the shower maximum. We successfully apply the parameterization to data taken with LOFAR and discuss implications for air shower experiments.     

Time structure of individual extensive air showers

Extensive air showers detected by the GREX array have been sampled by means of highly segmented 8 m² bakelite RPC in the GREX/COVER_PLASTEX experiment. Delay distributions of particles with respect to the first arriving particle in the EAS front at PeV energies have been analysed for individual events in the core distance range of 0–100 m. It is shown that both mean arrival time and EAS front thickness in individual showers fluctuate strongly and cannot be a good measure of the distance from the EAS axis in a 0–100 m core distance interval.

Individual distributions have been compared with integrated inclusive distributions measured in the same experiment. Results indicate that the width of the individual distribution is systematically less than that of the inclusive distribution. It means that the bulk of particles in individual showers arrive as a relatively compact group delayed by different time intervals from the first arriving particle. Such fluctuations of the arrival time for most of the shower particles may be the consequence of large fluctuations in the shower longitudinal development.

Comparison with CORSIKA Monte Carlo simulations confirmed the difference between the mean width of inclusive and individual arrival time distribution. It revealed also the presence in the experiment of the excessive train of delayed particles near the shower core. This train is obviously due to the non-relativistic low energy hadrons most abundant in the shower core region.     

Monte Carlo simulations of radio pulses in atmospheric showers using ZHAireS

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 and 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 shower geometry on the radio pulses. We show that geometry, coupled to the relativistic effects that appear when using a realistic refractive index n > 1, play a prominent role on the radio emission of air showers.     

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

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

Coherent Cherenkov radio pulses from hadronic showers up to EeV energies

The Cherenkov radio pulse emitted by hadronic showers of energies in the EeV range in ice is calculated for the first time using full 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 implemented to allow the simulation of radio pulses induced by showers up to 10 EeV in ice. The code is validated comparing the results for electromagnetic and hadronic showers to those obtained with GEANT4 and ZHS codes. The contribution to the pulse of other shower particles in addition to electrons and positrons, mainly protons, pions and muons, is found to be below 3% for 10 PeV and above proton induced showers. The characteristics of hadronic showers and the corresponding Cherenkov frequency spectra are compared with those from purely electromagnetic showers. The dependence of the spectra on shower energy and high-energy hadronic model is addressed and parameterizations for the radio emission in hadronic showers in ice are given for practical applications.     

Correlated features of arrival time and angle-of-incidence distributions of EAS muons

Various features and correlations of the arrival time and angle-of- incidence distributions of muons of extensive air showers (EAS) are studied by analyses based on Monte-Carlo simulations of the EAS development by using the air shower simulation code CORSIKA. Trends and dependencies of the temporal dispersion of the EAS muon component on shower size and distance from the shower core are displayed by the distribution of the arrival time and angle of incidence of the first muon, of the mean and median of the single shower distribution. Special attention is called to multi-correlations in observations at different radial distances from the shower core. These ‘radial’ correlations provide additional information for the discrimination of different EAS primaries, while the correlation of muon arrival time and angle-of-incidence is shown to improve the mass separation only insignificantly. This feature does not basically change, when arrival times and angles of incidence are displayed by transformed quantities like ‘muon production heights’.     

The air shower maximum probed by Cherenkov effects from radio emission

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 position of the shower maximum from the radio signal, which is a sensitive measure for the mass of the initial cosmic ray. We also show that the relative magnitude of the charge-excess and geomagnetic emission changes considerably at small observer distances where Cherenkov effects apply.     

Coherent synchrotron emission from cosmic ray air showers

Coherent synchrotron emission by particles moving along semi-infinite tracks is discussed, with a specific application to radio emission from air showers induced by high-energy cosmic rays. It is shown that in general, radiation from a particle moving along a semi-infinite orbit consists of usual synchrotron emission and modified impulsive bremsstrahlung. The latter component is due to the instantaneous onset of the curved trajectory of the emitting particle at its creation. Inclusion of the bremsstrahlung leads to broadening of the radiation pattern and a slower decay of the spectrum at the cut-off frequency than the conventional synchrotron emission. Possible implications of these features for air shower radio emission are discussed.     

A southern hemisphere survey of meteor shower radiants and associated stream orbits using single station radar observations

The 33.2 MHz interferometric meteor radars located at Davis Station, Antarctica and Darwin, Australia typically detect around 15 000 specular underdense meteor echoes every day. While the angle of arrival of the scattered radio wave can be inferred using phase differences between receive antennae, the direction of individual meteors is not known beyond a plane of ambiguity perpendicular to the angle of arrival. Using the great circle mapping technique with a Jones & Jones type weighting function, 37 meteor shower systems were detected in data collected at both locations over 2006–2007, including nine undocumented showers. The orbital elements of the parent debris streams were then calculated for the 31 showers where sufficiently precise measurements were available.     

Simulations of reflected radio signals from cosmic ray induced air showers

We present the calculation of coherent radio pulses emitted by extensive air showers induced by ultra-high energy cosmic rays accounting for reflection on the Earth’s surface. Results have been obtained with a simulation program that calculates the contributions from shower particles after reflection at a surface plane. The properties of the radiation are discussed in detail emphasizing the effects of reflection. The shape of the frequency spectrum is shown to be closely related to the angle of the observer with respect to shower axis, becoming hardest in the Cherenkov direction. The intensity of the flux at a fixed observation angle is shown to scale with the square of the primary particle energy to very good accuracy indicating the coherent aspect of the emission. The simulation methods of this paper provide the foundations for energy reconstruction of experiments looking at the Earth from balloons and satellites. They can also be used in dedicated studies of existing and future experimental proposals.     

Measurement of the cosmic-ray energy spectrum above 1016 eV with the LOFAR Radboud Air Shower Array

The energy reconstruction of extensive air showers measured with the LOFAR Radboud Air Shower Array (LORA) is presented in detail. LORA is a particle detector array located in the center of the LOFAR radio telescope in the Netherlands. The aim of this work is to provide an accurate and independent energy measurement for the air showers measured through their radio signal with the LOFAR antennas. The energy reconstruction is performed using a parameterized relation between the measured shower size and the cosmic-ray energy obtained from air shower simulations. In order to illustrate the capabilities of LORA, the all-particle cosmic-ray energy spectrum has been reconstructed, assuming that cosmic rays are composed only of protons or iron nuclei in the energy range between ∼2 × 10¹⁶ and 2 × 10¹⁸ eV. The results are compatible with literature values and a changing mass composition in the transition region from a Galactic to an extragalactic origin of cosmic rays.     

Numerical simulation of radio signal from extended air showers

The burst of radio emission by an extensive air shower provides a promising alternative for detecting ultra-high energy cosmic rays. We have developed an independent numerical program to simulate these radio signals. Our code is based on a microscopic treatment, with both the geosynchrotron radiation and charge included.Here we give the first presentation of our basic program and its results. When the time-domain signals for different polarizations are computed, we find that the pulses take on a bipolar pattern and the spectrum is suppressed towards the lower frequencies. We investigate how showers at different heights in the atmosphere contribute to the total signal, and examine the signal strength and distribution at sites with different elevations. We also study the signal from showers with different inclination angles and azimuth directions. In all these cases we find the charge excess effect is important.     

Coherent radio emission from cosmic ray air-showers in the turbulent atmosphere

Coherent electromagnetic erenkov radiation is produced by cosmic ray air showers passing through the atmosphere. This radiation is detected by radio telescopes. We demonstrate here that the effect of random spatial fluctuations in the refractive index of air, about a mean exceeding unity, causes the airshower to emit not only the spontaneous coherent radio emission described elsewhere by Kahn and Lerche, but also an induced radiation field which can exceed the spontaneous field in certain frequency bands. Further the conditions for emission of the coherent radio erenkov radiation are altered by the presence of the refractive index fluctuations. And the Earth's magnetic field gives rise to the dominant term in the far-field radiation, be it spontaneous or induced, since it causes a systematic separation of electrons and positrons in the shower which, for parameters currently acceptable for air showers, is the major factor in determining the far-field radiation pattern. Also we suggest that the coherent 500 Mc/sec radiation seen from occasional showers is probably a reflection of an atmospheric correlation length of order 15 cm at the time the shower passes through the atmosphere.     

Interpretation of the time structure of the EAS disc measured by the GREX/COVER_PLASTEX experiment

Simulation results for the time structure of the extensive air shower disc are presented and compared with data from the GREX/COVER_PLASTEX experiment. The distribution of the arrival times at various distances from the shower core and the contributions from the secondary particles to the shape of the distribution are described. The main parameters of the distribution, the mean time of arrival τ and the standard deviation σ, reflect the shower disc profile and thickness. The dependence of the shower profile and thickness on the energy and mass of the primary particle initiating the shower as well as on its inclination angle is discussed. The influence of the experimental conditions on the disc profile and thickness measured by the GREX/COVER_PLASTEX experiment is analysed and a parametrization of the average profile and thickness is given.     

Stereoscopic observations of gamma rays at the Whipple observatory

Observations of photons at E ≥ 550 GeV from the Crab Nebula are presented and used to assess the potential of multi-telescope systems for γ-ray astronomy.

The Whipple observatory 10 m and 8 m imaging atmospheric erenkov telescopes have been used to provide a stereoscopic view of air showers to make a more complete measurement of air shower parameters. Here we present a measurement of the spread in the arrival direction of primary γ-rays originating from a point source. The data show that the shower arrival direction can be reconstructed with an accuracy of σ = 0.°14.     

Cherenkov τ shower earth-skimming method for PeV–EeV ντ observation with Ashra

We describe a method of observation for PeV–EeV τ neutrinos using Cherenkov light from the air showers of decayed τs produced by τ neutrino interactions in the Earth. Aiming for the realization of neutrino astronomy utilizing the Earth-skimming τ 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 and (2) identification of very high energy neutrino sources. The Ashra detector uses newly developed light collectors which realize both a 42°-diameter field-of-view and arcminute resolution. Therefore, it has superior angular resolution for imaging Cherenkov air showers. In this paper, we estimate the sensitivity of and cosmic-ray background resulting from application of the Ashra-1 Cherenkov τ shower observation method. Both data from a commissioning run and a long-term observation (with fully equipped trigger system and one light collector) are presented. Our estimates are based on a detailed Monte Carlo simulation which describes all relevant shower processes from neutrino interaction to Cherenkov photon detection produced by τ air showers. In addition, the potential to determine the arrival direction of Cherenkov showers is evaluated by using the maximum likelihood method. We conclude that the Ashra-1 detector is a unique probe into detection of very high energy neutrinos and their accelerators.     

Chaos in cosmic ray air showers

Unexpected chaotic features are found in time series of arrival time intervals of successive air showers with (E > 3 × 10¹⁴ eV). Over 99 % of air shower arrival time intervals obey the Poisson distribution law representing stochastic behaviors, but occasionally there are air showers showing real chaotic behaviors as distinguished from both random and colored noises. With two systems of the Kinki university installations, we found 13 cases showing chaotic time series in 3.36 yr with the system-1 and the 1.37 yr with the system-2. Five out of 10 chaotic air showers of the Kinki installation are detected during the same time zone also by the Osaka City university installation which is at 115 km distance from the Kinki one. In a remarkable example of September 19, 1991, the correlation dimension was observed to have dropped from about 4 to the minimum of 1.3 and recovered smoothly in about 38 h. The chaos structure in this case is detected in nearly the same time zone at the Ohya station of the Institute for Cosmic Ray Research, University of Tokyo, which is separated from the Kinki one by 460 km. Formation of chaos structure due to energetic cosmic ray dust particles is suggested. Progress of cosmic ray physics may be expected with the study of air showers marked with chaos.     

Time structure of the extensive air shower front

The GREX/COVER_PLASTEX experiment has measured the temporal and spatial fine structure of the EAS disc at sea level in a new and original way, using resistive plate counter detectors for direct measurements of the arrival time of each particle crossing the detector. Data were taken at EAS core distances up to 100 m for shower size N > 10⁵ (PeV energy range). Arrival times of shower particles were measured with nanosecond accuracy. More than 450000 air shower events have been included in this analysis.