Performance of the RF Detectors of the Astroneu Array

Abstract

Since 2014, the university campus of Hellenic Open University (HOU) has hosted the Astroneu array, which is dedicated to the detection of extensive air showers (EAS) induced by high-energy cosmic rays (CR). The Astroneu array incorporates 9 large particle scintillation detectors and 6 antennas sensitive to the radio frequency (RF) range 1–200 MHz. The detectors are adjusted in three autonomous stations operating in an environment with a strong electromagnetic background. As shown by previous studies, EAS radio detection in such environments is possible using innovative noise rejection methods, as well as advanced analysis techniques. In this work, we present the analysis of the collected radio data corresponding to an operational period of approximately four years. We present the performance of the Astroneu radio array in reconstructing the EAS axis direction using different RF detector geometrical layouts and a technique for the estimation of the shower core by comparing simulation and experimental data. Moreover, we measure the relative amplitudes of the two mechanisms that give rise to RF emission (the Askaryan effect and geomagnetic emission) and show that they are in good agreement with previous studies as well as with the simulation predictions.

1. Introduction

Cosmic rays (CR) is the common term used to describe all radiation formed by relativistic charge particles1 originating from outer space and colliding with the Earth’s atmosphere. At low energies (up to ${10}^5$ GeV), the flux of cosmic rays is mostly of a solar origin and large enough to make their direct detection possible by detectors of relatively small surface areas deployed outside the atmosphere (in balloons or satellites). At energies beyond the knee (>${10}^6$ GeV), the galactic and extra-galactic CR components are characterized by low particle fluxes, and the direct detection of CR is not practical. Instead, at these energies, the study of CR properties is realistic through the analysis of the particle showers induced in the atmosphere.

When a high-energy CR reaches the atmosphere, after passing through a certain amount of matter, it eventually collides with an air nucleus, and a cascade of secondary particles, the so-called extensive air shower (EAS), is formed. Apart from the particle component of the EAS, during its evolution in the atmosphere, a significant amount of electromagnetic radiation is emitted both in the optical (fluorescence and Cherenkov light) as well as in the radio frequency (RF) parts of the spectrum. Consequently, the most traditional ways to detect EAS are the particle detector arrays (i.e., scintillators or water Cherenkov tanks) deployed on the ground, as well as optical telescopes that record the atmospheric Cherenkov and fluorescence light emissions. However, in the last 22 years, considerable progress has been made concerning the RF detection of EAS (see [1,2] for an extensive review). EAS radio detection appears to be quite competitive with traditional methods for the reconstruction of the primary particle’s main parameters (arrival direction, energy and composition), and furthermore, it is characterized by low-cost detectors as well as minor dependence on the atmospheric conditions.

There are two fundamental physical processes related to the production of the RF electric field by CR air showers. The dominant one is emission correlated with the geomagnetic field, first introduced by Kahn and Lerche [3]. The Earth’s magnetic field (${\overrightarrow{B}}_{\mathrm{E}}$) exerts a Lorentz force on the electrons and positrons of the shower which accelerates them in a direction perpendicular to the EAS axis. As the shower develops, the time variation of the number of electrons and positrons results in RF emissions. Moreover, the generated electric field is polarized in the direction of the Lorentz force (${\overrightarrow{n}}_{\mathrm{sh}}\times {\overrightarrow{B}}_{\mathrm{E}}$), where the propagation direction of the secondary particles can be identified with the direction of the EAS axis ${\overrightarrow{n}}_{\mathrm{sh}}$. In addition to the geomagnetic mechanism, a subdominant contribution to the emitted electric field originates from the negative charge excess in the EAS front as described by Askaryan [4]. The number of electrons in the EAS front appears to be increased relative to the number of positrons due to the ionization of the air molecules caused by secondary shower particles and positron annihilation. In the atmospheric depth where the EAS reaches its maximum number of secondary particles ($X_{\max }$), an electron excess of 15–25% is estimated to appear. The time dependence of this excess in the shower front produces RF emissions, with the field vector oriented radially to the EAS axis. The measured electric field on the ground is the superposition of these two contributions and depends strongly on the observer’s location with respect to the shower axis.

The Astroneu array [5] is a hybrid EAS detection array deployed at the Hellenic Open University (HOU) campus near the city of Patras in Greece. The array is composed of three autonomous stations, each one equipped with both particle and RF detectors for hybrid EAS detection. The particle detectors are large scintillator counters (hereafter noted as scintillator detector modules (SDMs)) which were designed and constructed in the physics laboratory of HOU [6], while the RF detectors are dipole antennas produced by the CODALEMA collaboration [7]. Since the area around the stations suffers from intense electromagnetic activity, previous studies [8] have shown that the radio signal from EAS can be successfully detected by imposing an appropriate noise shedding formula. Additionally, studies on the RF signal features were implemented by correlating data from both RF and SDM detectors as well as with Monte Carlo (MC) simulations [9]. In these studies, the EAS axis direction was reconstructed using either the RF pulse arrival times or using the pulse power spectrum and innovative signal processing methods [10].

In this work, we present analysis for the full RF dataset collected for a period of approximately 4 years (2017–2021). The RF system’s efficiency in reconstructing the EAS axis direction is evaluated for different geometrical layouts (positions) of the RF detectors. In addition, by determining the polarization of the transmitted electric field, the contribution rate of each mechanism (charge excess and geomagnetic field) to the measured RF signal is calculated. In Section 2, the station’s architecture is briefly reported, while in Section 3, the data sample and the simulation procedure are presented. Section 4 describes the analysis related to the estimation of the EAS axis direction using different RF antenna geometrical layouts, and the results are compared with the direction obtained from the SDM measurements as well as the simulation predictions. In Section 5, a new method for EAS core reconstruction is presented based on the comparison between RF data and electric field simulations, while in Section 6, the relative strength of the two dominant mechanisms in the measured RF signal amplitude is measured and quantified using the charge excess-to-geomagnetic ratio (C${}_{\mathrm{GRT}}$). Furthermore, the dependencies of this ratio on the zenith and azimuth angles as well as the distance from the shower core are investigated. Finally, in Section 7, the concluding remarks and discussion are given.

2. The Astroneu Array

The Astroneu array [5,6] is a hybrid EAS detection array operating inside the HOU campus. The locations of the stations and their relative distances are depicted in Figure 1. During the first phase of operation (2014–2017), Astroneu was composed of three autonomous stations (station A, station B and station C), each one consisting of three large SDMs and one RF detector (antenna). In the second operation period (2017–2022), three more RF detectors were installed at station A, as shown on the left side of Figure 2. The other two stations (B and C) were not changed. In station A, the positions of the four RF antennas were chosen in such a way that by combining three of them, triangles of different kinds (equilateral or amblygonal) and dimensions were formed. This offered the opportunity to study the performance of different geometrical layouts when only antennas were used to reconstruct the direction of the EAS axis (i.e., using the timing of the three RF signals and the positions of the three antennas).

The SDMs are made of two layers of plastic scintillation tiles each covering an area of approximately 1 m${}^2$ (80 tiles per layer). The generated light by the scintillator is driven through wavelength shifting fibers (WLS) to a photomultiplier tube (PMT) and transformed into a voltage signal. The three SDM PMT pulses are received by a Quarknet board [11] which measures the crossing time of the pulses’ waveforms with a predetermined amplitude threshold (which is set to 9.7 mV) with an accuracy of 1.25 ns. The instant of the first crossing is GPS tagged and defines the pulse arrival time, while the period of time that the waveform remains above the threshold (time over threshold (ToT)) is used for the estimation of the pulse size. A detailed schematic representation of the connections between the Quarknet board and the SDMs of station A is shown in Figure 2 (right).

The RF detector is an antenna with two orthogonal bow-tie-shaped dipoles connected to a low-noise amplifier (LNA) mounted on top of the central support pole, as shown in Figure 2 (right). These types of antennas were constructed, calibrated and first used in the CODALEMA experiment [7,12]. Their design has been fixed in order to be broadband (1–200 MHz), isotropic and sensitive to weak electromagnetic signals (such as those emitted from EAS). The RF system is equipped with a dedicated electronics and data acquisition (DAQ) system, providing the opportunity for both self- and external trigger operation. In the Astroneu array, we use the latter option, where the external trigger is provided by the Quarknet board upon reception of three SDM signals that exceed the voltage threshold of 9.7 mV. By receiving such a trigger, the last 2560 sampled data (corresponding to a 2560 ns record) from both antenna’s polarizations (in the EW and NS directions) are digitized and stored. The GPS card of the RF system provides appropriate timestamps for the registered events. The correlation of the data recorded by the SDMs and the RF system is carried out offline by making use of the corresponding GPS time tags. Following the same methodology, data from different stations of the telescope are combined.

3. Data Sample and Simulations

3.1. Data Sample: RF Event Selection

In this work, the data sample was collected by the Astroneu array’s station A (3SDM-4RF) over a period of 4 years (2017–2021), corresponding to an operating time of approximately 25,500 h. The initial sample was composed of 480,000 EAS events detected and reconstructed by the 3 SDMs of the station with an energy threshold of 10 TeV. As expected, for energies below 10${}^4$ TeV, the RF signals from EAS are very weak and therefore undetectable, especially in areas with high levels of electromagnetic interference (coming mainly from man-made and stationary sources). Therefore the vast majority of these events, as expected, contained no detectable RF signal.

For the 4 × 480,000 recorded RF waveforms (from the 4 RF detectors of station A), the offline RF event selection algorithm was deployed (see [8,9,10] for analytic description). The event selection algorithm for the RF data is a procedure consisting of two steps: the filtering process and the noise rejection algorithm. The filtering process, which uses a Tukey window filter and a Fast Fourier transform (FFT), rejects waveform frequencies outside the region of 30–80 MHz. (Below 30 MHz, the ionospheric noise is enhanced, while above 80 MHz, parasitic signals from the radio FM band are expected.) Since the RF signals emitted by EAS are characterized by an intense peak located in a short time interval (transient) of approximately 30 ns, the filtered waveforms are checked for transients within the “signal window” of the 2560 ns buffer. The “signal window” is the time window inside the 2560 ns buffer where the signal waveform should appear (according to the trigger signal), and ot is defined to be between 1000 ns and 1500 ns. Waveforms with mean powers (in the “signal window”) six times greater than the mean power of the noise were retained for the next analysis stage. Of course, transients from parasitic sources were also expected, especially in an area with a powerful electromagnetic background. Therefore, the second stage of the event selection algorithm was applied with the aim of rejecting these parasitic transients.

The two waveforms (EW and NS polarizations) are digitized with a sampling rate of 1 GHz. For each waveform, 2560 voltage values are stored in the array ($V\left(i\right),i=1,\dots ,2560$). The first subroutine of the noise rejection algorithm checks the values of the rise time ($R_{\mathrm{t}}$) of the RF signal, defined as the time interval between two fixed values of the normalized cumulative function $C\left(i\right)$2 of the signal. An update version of this subroutine was used in this work, compared with the one reported in [8,9], where $R_{\mathrm{t}}$ was calculated to be between 25% and 65% of the cumulative function ($R_{\mathrm{t}}=C(65\%)-C(25\%)$) and events with $R_{\mathrm{t}}>$ 20 ns were rejected. This improved the noise rejection efficiency without significant loss of data, as concluded from simulation samples. The second stage of the noise rejection algorithm involves the estimation of the degree of polarization (d.o.p. 3) of the RF transient. In contrast to parasitic signals, the pulse emitted during EAS development is expected to be linearly polarized. The threshold value for the d.o.p. was set to 0.85 (i.e., events with $d.o.p.<0.85$ were rejected).

The above criteria resulted in a final RF data sample of 460 events with signals in all four antennas of the station.

3.2. RF Simulation Package

The simulation package is a four-step process. The first step involves the generation of high-energy EAS (10${}^{17}$–2 × 10${}^{18}$ eV) using the MC simulation package CORSIKA [13]. The QGSJET-II-04 [14] and GEISHA [15] packages are applied for high- and low-energy hadronic interactions, respectively, while the EGS4 Code [16] is used for the electromagnetic interactions. In producing very high-energy EAS, the distributions of the primary particle, direction and spectral index are used according to recent measurements described in [17,18,19]. Finally, the EAS core position is uniformly distributed in a radius of 400 m around the center of the station. The MC sample size at this stage consists of approximately 100,000 events.

The second step in the simulation procedure involves the generation of the electric field produced by EAS, where the RF simulation code SELFAS [20] is used (particularly the updated version, SELFAS3). Since SELFAS calculates the electric field values only, the third step is the convolution of the electric field with the impulse response4 of the RF system (antenna + LNA). In the next stage, the simulated voltage signal is distorted by adding electromagnetic noise, as measured in the area around the station for a period of one year. In the final stage, the event selection algorithm is imposed as described in Section 3.1. The simulation sample after the described procedure was reduced to 30,500 events, which was used for the rest of the analysis. In Figure 3 (left), the EW waveform of an event reconstructed by an antenna of station A is shown (black line). In the same plot, the EW waveform is also shown (before and after the addition of noise) for a simulated event with almost the same direction and shower core as the real event5. The corresponding power spectra of these waveforms are depicted in Figure 3 (right). In both cases, the agreement was satisfactory.

4. The Effect of the RF Antennas’ Geometrical Layout on the EAS Direction Resolution

The estimation of the EAS axis arrival direction (the zenith $\theta$ and azimuth $\varphi$ angles) was implemented by using the arrival times of the RF signals, as well as the detector positions. The selected conventions were to define east at $\varphi =0^{\circ }$ and north at $\varphi ={90}^{\circ }$. For the reasons detailed in [12], the arrival time $t_{\det ,k}$ in the $k$th RF detector was defined as the time of the maximum of the RF signal’s envelope6. In first approximation, the EAS axis direction ($\theta$, $\varphi$) was estimated by assuming a plane wavefront for the RF pulse, and a plane fit was implemented by minimizing the quantity

$${\chi }^2=\sum _{\mathrm{k}=1}^N=\frac{{\left(c(t_{\det ,k}-t_0)-(A·x_{\mathrm{k}}+B·y_{\mathrm{k}})\right)}^2}{{\sigma }_{\mathrm{k}}^2},$$

(1)

where N is the number of considered RF detectors, (${\mathit{x}}_{\mathrm{k}}$, ${\mathit{y}}_{\mathrm{k}}$) are the position coordinates of the $k$th detector and $t_0$ is the arrival time at the origin of the coordinate system (0, 0). The quantity ${\sigma }_{\mathrm{k}}$ corresponds to the resolution in estimating the time in the $k$th detector as calculated in [9], varying from 8.4 to 8.9 ns for the 4 RF detectors of station A. The zenith and azimuth angles of the EAS axis were determined using the equations

$$\theta =arcsin\left(\sqrt{A^2+B^2}\right),\varphi =arctan\left(\frac{B}{A}\right).$$

(2)

In the first stage of the present analysis, the EAS axis direction was reconstructed using timing data from the four RF detectors only, as well as timing data from only the three SDM detectors. The results were cross-correlated with the predictions of the MC simulations. Figure 4 shows the zenith (left) and the azimuth angle (right) distributions as reconstructed from the RF system (red squares), as well as the corresponding distributions using the SDM (blue circles) system. The histogram corresponds to the MC predictions. Moreover, Figure 5 shows the differences in the zenith ($\Delta \theta ={\theta }_{\mathrm{SDM}}-{\theta }_{\mathrm{RF}}$, left) and azimuth angles ($\Delta \varphi ={\varphi }_{\mathrm{SDM}}-{\varphi }_{\mathrm{RF}}$, right) as derived from the reconstructions based on the RF and SDM data (blue points) compared with the simulations (histogram). Both distributions were well-fitted (red line), with Gaussian functions of ${\sigma }_{\Delta \theta }={3.06}^{\circ }\pm {0.43}^{\circ }$ and ${\sigma }_{\Delta \varphi }={6.78}^{\circ }\pm {0.86}^{\circ }$ for the zenith and azimuth angle differences, respectively.

In the next stage of analysis, in order to correlate the effect of the station geometry to the resolution of the EAS axis reconstruction, four combinations of three RF detectors were used. As indicated in Figure 6 (right), two of the four RF antenna combinations formed an approximately isosceles triangle (456, 146), while the remaining two formed an amblygonal triangle (145, 156). Between formations 456 and 146, the former exhibited greater distances separating the detectors. Likewise, the 145 triangle formed by the antennas had a larger diameter compared with the 156 triangle formed by the antennas. The resolution of the described geometries in reconstructing the EAS axis direction was initially calculated for the simulation sample where the true direction was known (as used in the simulation’s input file). In Figure 6 (left), the distributions of the difference between the true and estimated (using the RF simulations sample) zenith (${\theta }_{\mathrm{true}}-{\theta }_{\mathrm{RF}}$) and azimuth angles (${\varphi }_{\mathrm{true}}-{\varphi }_{\mathrm{RF}}$) are presented. All distributions were fitted to Gaussian functions, while the fitting results are shown in

Table 1. The results from fitting the Gaussian functions to the difference (${\theta }_{\mathrm{true}}-{\theta }_{\mathrm{RF}}$), (${\varphi }_{\mathrm{true}}-{\varphi }_{\mathrm{RF}}$) distributions for the considered RF detector formations.

RF-Detectors	456	146	145	156
${\mu }_{({\theta }_{\mathrm{true}}-{\theta }_{\mathrm{RF}}){(}^{\circ })}$	$-0.01\pm 0.55$	$-0.02\pm 0.47$	$-0.01\pm 0.41$	$-0.04\pm 0.59$
${\sigma }_{({\theta }_{\mathrm{true}}-{\theta }_{\mathrm{RF}}){(}^{\circ })}$	$2.70\pm 0.34$	$2.94\pm 0.37$	$3.12\pm 0.41$	$3.30\pm 0.39$
${\mu }_{({\varphi }_{\mathrm{true}}-{\varphi }_{\mathrm{RF}}){(}^{\circ })}$	$0.05\pm 0.53$	$-0.01\pm 0.44$	$0.03\pm 0.61$	$0.00\pm 0.61$
${\sigma }_{({\varphi }_{\mathrm{true}}-{\varphi }_{\mathrm{RF}}){(}^{\circ })}$	$4.96\pm 0.64$	$5.16\pm 0.58$	$5.60\pm 0.59$	$5.98\pm 0.55$

.

It is evident from the aforementioned results that among formations of the same shape, increasing the distance between the detectors increased the accuracy of EAS axis direction reconstruction. Furthermore, as the shape of the triangle was converted from obtuse to (approximately) equilateral, the resolution in reconstructing the axis direction was improved. The next step of the analysis involved the correlation of the EAS axis directions, as derived from measurements using the considered RF antenna formations and as extracted from the SDM data independently. In Figure 7, the distribution of the difference between the reconstructed zenith (left) and azimuth (right) angle using the SDM data and the RF data from the different antenna formations (histogram) are shown, while the red line corresponds to the fitted Gaussian function. The corresponding fitting results are represented in

Table 2. Gaussian fitting results for the difference (${\theta }_{\mathrm{SDM}}-{\theta }_{\mathrm{RF}}$), (${\varphi }_{\mathrm{SDM}}-{\varphi }_{\mathrm{RF}}$) distributions for the considered RF detector formations.

RF-Detectors	456	146	145	156
${\mu }_{({\theta }_{\mathrm{SDM}}-{\theta }_{\mathrm{RF}}){(}^{\circ })}$	$0.13\pm 0.53$	$0.10\pm 0.67$	$0.21\pm 0.61$	$-0.14\pm 0.69$
${\sigma }_{({\theta }_{\mathrm{SDM}}-{\theta }_{\mathrm{RF}}){(}^{\circ })}$	$3.64\pm 0.84$	$3.74\pm 0.87$	$4.02\pm 0.91$	$4.30\pm 0.89$
${\mu }_{({\varphi }_{\mathrm{SDM}}-{\varphi }_{\mathrm{RF}}){(}^{\circ })}$	$-0.059\pm 0.53$	$-0.23\pm 0.54$	$0.15\pm 0.60$	$-0.57\pm 0.81$
${\sigma }_{({\varphi }_{\mathrm{SDM}}-{\varphi }_{\mathrm{RF}}){(}^{\circ })}$	$6.77\pm 0.94$	$6.89\pm 0.88$	$7.30\pm 0.89$	$7.74\pm 0.95$

. In all formations, the sigmas of the distributions were consistent with the individual resolutions of the SDM system7 and the corresponding RF formation (Table 1), which means that the sigmas were equal to the square root of the quadratic sum of the individual resolutions achieved by the two systems.

5. EAS Core Reconstruction

The term “shower core” is commonly used for the intersection point of the EAS axis with the ground level. In this study, we present a new method of estimating the EAS core by correlating the electric field map as measured on the ground with the expected field values estimated using MC simulations. For each event identified as being of a cosmic origin, a set of 60 simulations was prepared with the specifications described in Section 3.2. In these MC events, the electric field at ground level was calculated at 220 points spread in a radius of approximately 250 m around the center of station A, as depicted in Figure 8. These positions were chosen with the criterion that the electric field could also be calculated at the intermediate points using linear interpolation. For the production of the simulations, the primary direction (zenith and azimuth angles) was fixed to the reconstructed direction using the RF data, while the primary energy was set arbitrarily to 10${}^{18}$ eV 8. The core position was placed at the center of station A, and for the primary particle, we used protons (p) and iron nuclei (Fe), since these were expected to be the main CR candidates at ultra-high energies. Out of 60 simulations, 40 corresponded to protons primarily, and 20 corresponded to iron nuclei, enclosing a sensible number of $X_{\max }$ values in accordance with the fluctuations that appeared between EAS of the same energy9.

By averaging the simulated electric fields of these 60 showers, the map of the electric field on the ground was obtained when the shower core $(x_{\mathrm{cr}},y_{\mathrm{cr}})$ was located at the center of station A (i.e., $(x_{\mathrm{cr}},y_{\mathrm{cr}})=(0,0)$). By moving the field map within a circular disk of a radius of 200 m10 around the center of the station, a new field map could be obtained for a different $(x_{\mathrm{cr}},y_{\mathrm{cr}})$ position. In order to estimate the shower core position from the RF data, a fitting procedure was employed where the measurements of the four antennas $V_{\det }(x_{\mathrm{k}},y_{\mathrm{k}}),k=1,\dots ,4$ were compared with a large number11 of fields maps, with each one corresponding to different shower core positions $(x_{\mathrm{cr}},y_{\mathrm{cr}})$. Then, the estimation of the shower core position from the data was obtained by searching the minimum value of the quantity

$${\chi }^2(x_{\mathrm{cr}},y_{\mathrm{cr}})=\sum _{\mathrm{k}=1}^4=1^4{\left(V_{\det }^k-V_{\mathrm{sim}}^k(x_{\mathrm{cr}},y_{\mathrm{cr}})\right)}^2/{\sigma }_{\mathrm{k}}^2,$$

(3)

where $V_{\det }^k$ is the measured pulse height of the kth RF antenna and $V_{\mathrm{sim}}^k(x_{\mathrm{cr}},y_{\mathrm{cr}})$ is the expected pulse height at the position of the kth RF antenna according to the field map with a shower core at $(x_{\mathrm{cr}},y_{\mathrm{cr}})$. Since the energy of the primary particle in the MC sample was fixed to ${10}^{18}\mathrm{eV}$, and taking into account that the electric field, and consequently the RF signal, was proportional to the primary energy, a scaling factor a was applied to $V_{\mathrm{sim}}^k(x_{\mathrm{cr}},y_{\mathrm{cr}})$. The scaling factor a was estimated to be $a=(1/4)·{\sum }_1^4\left(V_{\det }^k/V_{\mathrm{sim}}^k(x_{\mathrm{cr}},y_{\mathrm{cr}})\right)$ (i.e., the mean value of the scale factors between the four RF antennas). In this way, we eliminated the effect of the shower energy on the strength of the shower signal and retained only the effect of the attenuation of the signal due to the distance to the shower axis. In future studies, this scaling factor can be incorporated into the ${\chi }^2$ fitting procedure in order to estimate the energy of the shower. The term ${\sigma }_{\mathrm{k}}$ corresponds to the background RF interference as measured in the RF detector positions, while the EAS core position ($X_{\mathrm{cr}}$, $Y_{\mathrm{cr}}$) corresponds to the values $(x_{\mathrm{cr}},y_{\mathrm{cr}})$ that minimize the ${\chi }^2$ value of Equation (3).

The described method for the EAS core estimation was tested using the simulation sample (which consisted of 30,500 events, as described in Section 3.2), where the true core position was known. In order to reduce significantly the required computational time12, only events with true core positions located within a radius of 200 m around the center of station A were selected. (These corresponded to 20,500 events.) For each event, the core position was estimated (using the described method) and compared with the true one. The left plot of Figure 9 represents the distribution of the difference between the true $X_{\mathrm{cr}}^{\mathrm{true}}$ and estimated $X_{\mathrm{cr}}^{\mathrm{estim}}$ coordinate of the core position, while the corresponding distribution for the Y coordinate is shown in the middle plot of Figure 9. A Gaussian fit was imposed on both distributions, with the resulting mean value being close to zero and standard deviation being approximately 20 m for both coordinates. Subsequently, the method was applied to the collected RF data for the full sample of 460 events. Again, only events whose core positions were at distances less than or equal to 200 m from the center of station A were selected. The right plot of Figure 9 shows the distribution of these EAS core distances for the RF data (denoted by red points) in comparison with the simulation prediction (histogram). As no other method for determining the core position was available, the efficiency of the method was further tested by calculating the charge excess-to-geomagnetic ratio (as presented in Section 6 / below), which strongly depends on the core position.

6. Charge Excess-to-Geomagnetic Ratio

As already mentioned in Section 1, the directions of the electric field vectors associated with the two main mechanisms (geomagnetic and charge excess) of the RF emission are different. The electric field (${\overrightarrow{E}}_G$) related to the geomagnetic mechanism is in the direction ${\widehat{n}}_s\times {\widehat{n}}_B$ (${\widehat{n}}_s$ and ${\widehat{n}}_B$ are the unit vectors in the directions of the EAS axis and the geomagnetic field, respectively), while the charge excess component (${\overrightarrow{E}}_C$) is directed from the point of observation toward the EAS axis. The measured EW and NS components of the EAS RF transient ($E_{\mathrm{EW}}$ and $E_{\mathrm{NS}}$, respectively) can be expressed in terms of the projections of the two contributions in the ground plane ($E_{\mathrm{G}}^{\mathrm{pr}}$ and $E_{\mathrm{C}}^{\mathrm{pr}}$) according to the formula

$$E_{\mathrm{EW}}=E_{\mathrm{G}}^{\mathrm{pr}}cos{\psi }_{\mathrm{G}}+E_{\mathrm{C}}^{\mathrm{pr}}cos{\psi }_{\mathrm{C}},E_{\mathrm{NS}}=E_{\mathrm{G}}^{\mathrm{pr}}sin{\psi }_{\mathrm{G}}+E_{\mathrm{C}}^{\mathrm{pr}}sin{\psi }_{\mathrm{C}},$$

(4)

where ${\psi }_{\mathrm{G}}$ and ${\psi }_{\mathrm{C}}$ are the angles formed between the EW direction and the projected geomagnetic ($E_{\mathrm{G}}^{\mathrm{pr}}$) and charge excess ($E_{\mathrm{C}}^{\mathrm{pr}}$) electric fields, respectively, as depicted in Figure A1. The $sin{\psi }_{\mathrm{G}}$ and $cos{\psi }_{\mathrm{G}}$ can be expressed in terms of the EAS axis ($\theta$, $\varphi$) and the geomagnetic field (${\theta }_{\mathrm{B}}$, ${\varphi }_{\mathrm{B}}$) directions, while the $sin{\psi }_{\mathrm{C}}$ and $cos{\psi }_{\mathrm{C}}$ can be expressed in terms of the core ($X_{\mathrm{cr}}$, $Y_{\mathrm{cr}}$) and the RF detector (x${}_{\mathrm{k}}$, y${}_k$) coordinates, as discussed in Appendix A.

The contribution of each mechanism to the measured EAS RF signal can be quantified by the charge-excess-to-geomagnetic ratio (${\mathrm{C}}_{\mathrm{GRT}}$), defined by the relation

$${\mathrm{C}}_{\mathrm{GRT}}=\frac{E_{\mathrm{C}}^{\mathrm{pr}}}{\frac{E_{\mathrm{G}}^{\mathrm{pr}}}{sin \alpha }}=\frac{E_{\mathrm{C}}^{\mathrm{pr}}}{E_{\mathrm{G}}^{\mathrm{pr}}}·sin\alpha ,$$

(5)

where $\alpha$ (geomagnetic angle) represents the angle between the EAS axis (${\widehat{n}}_s$) and the geomagnetic field direction (${\widehat{n}}_B$). Since the geomagnetic component is proportional to $sin\alpha$, the term $E_{\mathrm{G}}^{\mathrm{pr}}/sin\alpha$ expresses the relative strength of the mechanism, excluding ${\mathrm{C}}_{\mathrm{GRT}}$ large values due to small geomagnetic angles13. The polarization angle (${\varphi }_p$)14 of the RF signal can be also expressed in terms of ${\mathrm{C}}_{\mathrm{GRT}}$, as derived by combining Equations (4) and (5).

$$tan{\varphi }_p=\frac{sin{\psi }_{\mathrm{G}}+{\mathrm{C}}_{\mathrm{GRT}}{\left(sin\alpha sin{\psi }_{\mathrm{C}}\right)}^{-1}}{cos{\psi }_{\mathrm{G}}+{\mathrm{C}}_{\mathrm{GRT}}{\left(sin\alpha cos{\psi }_{\mathrm{C}}\right)}^{-1}}.$$

(6)

On the other hand, using the recorded EW and NS waveforms, the polarization angle ${\varphi }_p$ can be estimated from the data:

$$tan{\varphi }_p=\frac{E_{\mathrm{NS}}}{E_{\mathrm{EW}}}.$$

(7)

Consequently, ${\mathrm{C}}_{\mathrm{GRT}}$ can be estimated by these two expressions of the polarization angle, assuming that the direction of the shower as well as the shower core are known. As demonstrated in simulation studies [22], ${\mathrm{C}}_{\mathrm{GRT}}$ depends strongly on the opening angle from the point of the EAS maximum ($X_{\max }$) to the point of observation. In particular, ${\mathrm{C}}_{\mathrm{GRT}}$ is expected to increase as the observation angle increases. Large opening angles correspond to large distances from the EAS core for an almost vertical EAS axis. For an inclined EAS axis, the point of the EAS maximum is further away from the observation point (related to a vertical one), which means that the same distance from the EAS core corresponds to a smaller opening angle and consequently to a smaller ${\mathrm{C}}_{\mathrm{GRT}}$ value. We can therefore conclude that the ${\mathrm{C}}_{\mathrm{GRT}}$ value increases with increasing distance from the EAS core and decreases with an increasing EAS zenith angle. These dependences for ${\mathrm{C}}_{\mathrm{GRT}}$ were studied in the present work, using both the experimental RF data as well as the simulation sample.

Figure 10 (left) shows the C${}_{\mathrm{GRT}}$ variation for increasing distances from the shower core ($d_{\mathrm{cr}}$), considering four different bins for the zenith angle (from 0${}^{\circ }$ to 60${}^{\circ }$). The results from the RF data are represented with red points. The black curve corresponds to the simulation sample. Similarly, Figure 10 (right) represents the C${}_{\mathrm{GRT}}$ variation for increasing EAS axis zenith angles ($\theta$), considering four different distance ranges (from 0 m to 200 m). RF data are presented with red points, while the black curve corresponds to the simulation sample. In all cases, the C${}_{\mathrm{GRT}}$ values were in agreement with those expected from the simulations and verified in previous studies [23,24]. A synopsis of the estimated C${}_{\mathrm{GRT}}$ values is shown in

Table 3. The summary of the estimated C${}_{\mathrm{GRT}}$ values for different EAS zenith angles and distances from EAS core position.

	$\mathit{d}\in [0,50]$ m	$\mathit{d}\in (50,100]$ m	$\mathit{d}\in (100,150]$ m	$\mathit{d}\in (150,200]$ m
$\theta \in [0,{15}^{\circ }]$	8.10%	13.15%	17.14%	19.23%
$\theta \in (15,{30}^{\circ }]$	6.96%	10.76%	12.50%	14.92%
$\theta \in (30,{45}^{\circ }]$	5.16%	7.08%	8.74%	10.76%
$\theta \in (45,{60}^{\circ }]$	4.13%	6.56%	8.62%	10.45%

.

Figure 10 (bottom) shows the distribution of the C${}_{\mathrm{GRT}}$ values as reconstructed from simulations (black histogram) and data (red points). The two distributions are in good agreement. Since the values of C${}_{\mathrm{GRT}}$ were highly dependent on the EAS core position, the apparent agreement of the C${}_{\mathrm{GRT}}$ values presented in this study compared with previous ones and simulations is strong evidence that the EAS core reconstruction method is efficient.

7. Conclusions

The Astroneu array is a small-scale hybrid array operating in a strong electromagnetic noise environment. In this paper, we exploited further the RF signals captured by the array after proper filtering and noise rejection. For this purpose, data from various RF antennas as well as large simulation samples were analyzed. The arrival times of the RF signals were used to estimate the EAS axis direction, and it was found that the RF system measurements were in very good agreement with the particle detector measurements as well as with the simulation predictions. It was also shown that the reconstructed EAS direction resolution (around 3 degrees for the zenith angle and 5.5 degrees for the azimuth angle) improved for equilateral geometrical layouts and larger distances between the detectors, a feature that is also known for particle detectors. A new method for the reconstruction of the EAS core using the expected field map of the electric field and the detailed response of the RF antennas was also presented. The reconstruction resolution was found to be approximately 20 m in both the x and y directions for showers within an area of a 200 m radius around station A of the Astroneu array. The estimated shower core position was also used for the measurement of the relative strength between the two main mechanisms of radio emission by high-energy showers (i.e., the charge excess-to-geomagnetic ratio ${\mathrm{C}}_{\mathrm{GRT}}$). The estimated ${\mathrm{C}}_{\mathrm{GRT}}$ values varied from 3% for large zenith angles and small core distances to up to 24% for roughly vertical showers at large distances (>150 m). These measurements are in very good agreement with the expectations as well as other experimental measurements. In the planned Astroneu array extension (with more RF and SDM detectors), the ${\mathrm{C}}_{\mathrm{GRT}}$ measurements will be used supplementarily with the existing noise rejection algorithms, aiming for the development of a self-trigger operation mode. Finally, since the charge excess mechanism is the main contribution to RF emission in dense media, the analysis of ${\mathrm{C}}_{\mathrm{GRT}}$ can also be used as a powerful tool for distinguishing EAS propagating on different media.