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Register a new userThe shape of the radio wavefront of extensive air showers as measured with LOFAR
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Extensive air showers, induced by high energy cosmic rays impinging on the Earths atmosphere, produce radio emission that is measured with the LOFAR radio telescope. As the emission comes from a finite distance of a few kilometers, the incident wavefront is non-planar. A spherical, conical or hyperbolic shape of the wavefront has been proposed, but measurements of individual air showers have been inconclusive so far. For a selected high-quality sample of 161 measured extensive air showers, we have reconstructed the wavefront by measuring pulse arrival times to sub-nanosecond precision in 200 to 350 individual antennas. For each measured air shower, we have fitted a conical, spherical, and hyperboloid shape to the arrival times. The fit quality and a likelihood analysis show that a hyperboloid is the best parametrization. Using a non-planar wavefront shape gives an improved angular resolution, when reconstructing the shower arrival direction. Furthermore, a dependence of the wavefront shape on the shower geometry can be seen. This suggests that it will be possible to use a wavefront shape analysis to get an additional handle on the atmospheric depth of the shower maximum, which is sensitive to the mass of the primary particle.
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We present LOFAR measurements of radio emission from extensive air showers. We find that this emission is strongly polarized, with a median degree of polarization of nearly $99%$, and that the angle between the polarization direction of the electric field and the Lorentz force acting on the particles, depends on the observer location in the shower plane. This can be understood as a superposition of the radially polarized charge-excess emission mechanism, first proposed by Askaryan and the geomagnetic emission mechanism proposed by Kahn and Lerche. We calculate the relative strengths of both contributions, as quantified by the charge-excess fraction, for $163$ individual air showers. We find that the measured charge-excess fraction is higher for air showers arriving from closer to the zenith. Furthermore, the measured charge-excess fraction also increases with increasing observer distance from the air shower symmetry axis. The measured values range from $(3.3pm 1.0)%$ for very inclined air showers at $25, mathrm{m}$ to $(20.3pm 1.3)%$ for almost vertical showers at $225, mathrm{m}$. Both dependencies are in qualitative agreement with theoretical predictions.
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.
The antenna array LOPES is set up at the location of the KASCADE-Grande extensive air shower experiment in Karlsruhe, Germany and aims to measure and investigate radio pulses from Extensive Air Showers. The coincident measurements allow us to reconstruct the electric field strength at observation level in dependence of general EAS parameters. In the present work, the lateral distribution of the radio signal in air showers is studied in detail. It is found that the lateral distributions of the electric field strengths in individual EAS can be described by an exponential function. For about 20% of the events a flattening towards the shower axis is observed, preferentially for showers with large inclination angle. The estimated scale parameters R0 describing the slope of the lateral profiles range between 100 and 200 m. No evidence for a direct correlation of R0 with shower parameters like azimuth angle, geomagnetic angle, or primary energy can be found. This indicates that the lateral profile is an intrinsic property of the radio emission during the shower development which makes the radio detection technique suitable for large scale applications.
For the interpretation of measurements of radio emission from extensive air showers, an important systematic uncertainty arises from natural variations of the atmospheric refractive index $n$. At a given altitude, the refractivity $N=10^6, (n-1)$ can have relative variations on the order of $10 %$ depending on temperature, humidity, and air pressure. Typical corrections to be applied to $N$ are about $4%$. Using CoREAS simulations of radio emission from air showers, we have evaluated the effect of varying $N$ on measurements of the depth of shower maximum $X_{rm max}$. For an observation band of 30 to 80 MHz, a difference of $4 %$ in refractivity gives rise to a systematic error in the inferred $X_{rm max}$ between 3.5 and 11 $mathrm{g/cm^2}$, for proton showers with zenith angles ranging from 15 to 50 degrees. At higher frequencies, from 120 to 250 MHz, the offset ranges from 10 to 22 $mathrm{g/cm^2}$. These offsets were found to be proportional to the geometric distance to $X_{rm max}$. We have compared the results to a simple model based on the Cherenkov angle. For the 120 to 250 MHz band, the model is in qualitative agreement with the simulations. In typical circumstances, we find a slight decrease in $X_{rm max}$ compared to the default refractivity treatment in CoREAS. While this is within commonly treated systematic uncertainties, accounting for it explicitly improves the accuracy of $X_{rm max}$ measurements.
CoREAS is a Monte Carlo simulation code for the calculation of radio emission from extensive air showers. It is based on the endpoint formalism for radiation from moving charges implemented directly in CORSIKA. Consequently, the full complexity of the air-shower physics is taken into account without the need for approximations or assumptions on the emission mechanism. We present results of simulations for an unthinned shower performed with CoREAS for both MHz and GHz frequencies. At MHz frequencies, the simulations predict the well-known mixture of geomagnetic and charge excess radiation. At GHz frequencies, the emission is strongly influenced by Cherenkov effects arising from the varying refractive index in the atmosphere. In addition, a qualitative difference in the symmetry of the GHz radiation pattern is observed when compared to the ones at lower frequencies. We also discuss the strong increase in the ground area subtended by the radio emission when going from near-vertical to very inclined geometries, making very inclined air showers the most promising ones for cosmic ray radio detection.
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