Radio Measurements of the Depth of Air-Shower Maximum at the Pierre Auger Observatory

Abstract

The Auger Engineering Radio Array (AERA), part of the Pierre Auger Observatory, is currently the largest array of radio antenna stations deployed for the detection of cosmic rays, spanning an area of $17$ km$^2$ with 153 radio stations. It detects the radio emission of extensive air showers produced by cosmic rays in the $30-80$ MHz band. Here, we report the AERA measurements of the depth of the shower maximum ($X_\text{max}$), a probe for mass composition, at cosmic-ray energies between $10^{17.5}$ to $10^{18.8}$ eV, which show agreement with earlier measurements with the fluorescence technique at the Pierre Auger Observatory. We show advancements in the method for radio $X_\text{max}$ reconstruction by comparison to dedicated sets of CORSIKA/CoREAS air-shower simulations, including steps of reconstruction-bias identification and correction, which is of particular importance for irregular or sparse radio arrays. Using the largest set of radio air-shower measurements to date, we show the radio $X_\text{max}$ resolution as a function of energy, reaching a resolution better than $15$ g cm$^{-2}$ at the highest energies, demonstrating that radio $X_\text{max}$ measurements are competitive with the established high-precision fluorescence technique. In addition, we developed a procedure for performing an extensive data-driven study of systematic uncertainties, including the effects of acceptance bias, reconstruction bias, and the investigation of possible residual biases. These results have been cross-checked with air showers measured independently with both the radio and fluorescence techniques, a setup unique to the Pierre Auger Observatory.

Figures (18)

• Figure 1: Example of a footprint of the radio emission on the ground for a simulated air shower with an energy of $8.2\cdot10^{17}$ eV, a zenith angle of $50.2^\circ$, and a depth of the shower maximum of $749$ g cm$^{-2}$. The strength of the emission is evaluated at simulated antenna positions (markers) and interpolated in between for visibility (background). The footprint has been projected into the shower plane, i.e., tilted into the plane perpendicular to the shower axis $\vec{v}$ and rotated to project the magnetic field $\vec{B}$ along the x-axis.
• Figure 2: Schematic view of three air showers that started at different heights in the atmosphere, and their radio emission footprints on the ground. It illustrates that the depth of the shower maximum affects the radio emission footprint both in width and general shape. The asymmetry is a consequence of how the geomagnetic and charge excess radio emission mechanisms interfere during the shower development. This figure has been previously published in ref:geoceldf.
• Figure 3: Layout of the AERA stations (triangles), marked with whether they are externally- or self-triggered. Also shown is part of the SD array of water-Cherenkov detectors (circles) and the field of view (FOV) of one of the FD telescope sites located near AERA. The FD contains $6$ regular telescope bays (light green) and in addition $3$ bays (dark green) looking at higher elevations. Scale and orientation of the layout are indicated with markers.
• Figure 4: Distributions of shower energy (left), and the azimuth and zenith angles of the shower arrival direction (center and right, respectively) for the pre-selection of $2153$ high-quality AERA showers (blue), the showers for which $X_\text{max}$ was reconstructed successfully with our method (gray), and the sample of showers after acceptance and reconstruction cuts are applied (green). The cosmic-ray energy spectrum as measured by Auger SD ref:Infill_Efficiency_v2 (gray dashed line) is scaled to the energy distribution of AERA to illustrate the level of completeness of the AERA event set at the higher energies.
• Figure 5: Parabola fit (dashed black line) to the reduced chi-squared values between a measured shower and each of the simulated showers for this event (blue and red markers) [see Eq. (\ref{['eq:XmaxRecChiSquared']})] as a function of the true MC $X_\text{max}$ values for each simulation. The minimum of the parabola (green line) is an estimator for the $X_\text{max}$ value of the measured shower. This measured shower has an energy of $8.2\cdot10^{17}$ eV, a zenith angle of $50.2^\circ$, and reconstructed $X_\text{max}=763\pm19$ g cm$^{-2}$. It has been chosen as a representative shower falling in the middle of the AERA energy range (Fig. \ref{['fig:Datasel']}, left), being close to the most common zenith angle (Fig. \ref{['fig:Datasel']}, right), and having a typical $X_\text{max}$ resolution (Fig. \ref{['fig:Resolution']}).