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Status of the radio technique for cosmic-ray induced air showers
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Nuclear and Particle Physics Proceedings 279–281 (2016) 190–197 www.elsevier.com/locate/nppp
Status of the radio technique for cosmic-ray induced air showers Frank G. Schr¨oder Institut f¨ur Kernphysik, Karlsruhe Institute of Technology (KIT), Germany
Abstract Radio measurements yield calorimetric information on the electromagnetic shower component around the clock. However, until recently it was not clear whether radio measurements can compete in accuracy with established nighttime techniques like air-Cherenkov or air-fluorescence detection. Due to recent progress in the radio technique as well as in the understanding of the emission mechanisms, the performance of current radio experiments has significantly improved. Above 100 PeV, digital, state-of-the-art antenna arrays achieve a reconstruction accuracy for the energy similar to that of other techniques, and can provide an independent measurement of the absolute energy scale. Furthermore, radio measurements are sensitive to the mass composition of the primary particles: First, the position of the shower maximum can be reconstructed from the radio signal. Second, in combination with muon detectors the measurement of the electromagnetic component provides complementary information on the primary mass. Since the radio footprint is huge for inclined showers, and the radio signal does not suffer absorption in the atmosphere, future radio arrays either focus on inclined showers at the highest energy, or on ultra-high precision measurements with extremely dense arrays. This proceeding reviews the current status of radio experiments and simulations as well as future plans. Keywords: cosmic ray, air shower, radio
1. Introduction Measurements of cosmic-ray air showers are motivated typically by two different classes of scientific goals: first, a better understanding of the particle physics relevant for the first interaction of the primary particle and the development of the particle cascade; second, a better understanding of the astrophysics relevant for the sources and propagation of the primary cosmic rays. For both goals, the properties of the primary particles have to be known as accurately as possible, i.e., reconstructed from air-shower measurements. Different techniques for air-shower detection have different strengths and weaknesses (cf. Refs. [1, 2]). Particle detectors at ground can only measure one stage of the shower development and suffer from statistical uncertainties, since for economic reasons detectors in air-shower arrays cover only a small fraction of the total area. A different category of techniques provides http://dx.doi.org/10.1016/j.nuclphysbps.2016.10.027 2405-6014/© 2016 Published by Elsevier B.V.
an integral, calorimetric measurement of the full air shower, namely air-fluorescence, air-Cherenkov, and radio detection. However, these techniques are only sensitive to the electromagnetic shower component, not to the hadronic or muonic components. Moreover, air-fluorescence and air-Cherenkov techniques are restricted to dark, clear nights. Modern experiments usually combine both classes of techniques in hybrid detectors, to maximize the total accuracy for the type and energy of the primary cosmic-ray particles. Within the calorimetric techniques, only radio detection has the principal advantage of being available around the clock. Thus, radio detectors would be the ideal supplement for particle detector arrays. Still, in the past, the radio technique suffered from technical difficulties and problems in the understanding of the radio emission by air showers. Recently, these problems have been solved to a large extent, and current radio experi-
F.G. Schröder / Nuclear and Particle Physics Proceedings 279–281 (2016) 190–197
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Figure 1: Power of the radio emission over the distance to the shower axis simulated in different frequency bands (from Ref. [3]).
ments start to become competitive with the established air-Cherenkov and air-fluorescence techniques. 2. Radio emission from air showers Like air-fluorescence and air-Cherenkov emission, the radio signal is also generated by charged particles in the shower, mainly by the electrons and positrons. While air-fluorescence light is emitted isotropically by nitrogen molecules excited by the air-shower particles, air-Cherenkov light and radio signal are emitted by the air-shower particles themselves. Since the air-shower particles are highly relativistic, their emission is not isotropic but strongly beamed in the direction of the shower axis with an opening angle on the order of 2◦ . Since the shower front has a typical thickness on the order of meters, the emission is generally coherent at wavelengths of that order or larger. Thereby the exact coherence conditions depend on the observer position, since the refractive index of air causes the radio waves to propagate slightly slower or faster than the particles, depending on altitude [4, 5]. Therefore, at the Cherenkov angle the emission from all shower stages arrives simultaneously, and is coherent for wavelengths as short as centimeters [3]. Consequently, radio emission can be observed in a wide distance range at frequencies of several 10 MHz, and only at the Cherenkov angle also at much higher frequencies up to a few GHz (see figure 1). The Cherenkov angle corresponds to a distance to the shower axis on the order of 100 m for vertical showers at typical observation altitudes. This is why the lateral distribution features
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Figure 2: Two emission mechanisms are experimentally confirmed: The geomagnetic deflection of electrons and positrons causes linearly polarized radio emission (left), the time-variation of the charge excess in the shower front causes radially polarized radio emission, known as Askaryan effect (right). In case of a vertical shower, the v x B axis corresponds to the east-west axis, and the v x v x B axis corresponds to the north-south axis [8].
a kind of bump in this distance range, where the exact bump position depends on the observation altitude and the position of the shower maximum [6, 7]. Two different mechanisms have been confirmed experimentally to contribute significantly to the total emission (see figure 2), which makes the observed radio signals more complicated compared to all the other techniques relying on a single mechanism. The stronger of the two effects is the geomagnetic deflection of the electrons and positrons inducing a time-varying transverse current [9, 10]. This basically converts the shower front into a kind of simple Hertz dipole. The amplitude of the geomagnetic emission is proportional to the Lorentz forces and, thus, to sin α (with α being the geomagnetic angle between the shower axis and the geomagnetic field). The geomagnetic emission is linearly polarized like the emission by a dipole orthogonal to the shower axis and the geomagnetic field. The second mechanism is the Askaryan effect [11]: the shower front accumulates a time-varying net charge due to electrons kicked out from air atoms, and due to annihilation of positrons in the shower. This timevarying net charge causes radially polarized emission. The Askaryan effect dominates in dense media (and sometimes is confused with Cherenkov radiation), but is less strong in air, typically an order of magnitude weaker than the geomagnetic effect [12, 13, 14, 15]. Nevertheless, the relative strength depends strongly on
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the location of the observer relative to the shower axis and on the direction of the shower axis relative to the geomagnetic field. Hence, the Askaryan effect cannot be neglected in the interpretation of radio measurements. Further emission mechanisms, like molecular bremsstrahlung, have been suggested, but neither experimentally confirmed [7], nor is there any obvious deficit in the theoretical picture: the combination of the geomagnetic and Askaryan emission seems to fully explain experimental results within current measurement accuracies of about 20 % for the electric-field strength [16, 17, 18]. However, at lower frequencies of a few MHz further emission processes are under investigation, in particular radio emission produced by the termination of the shower entering the ground [19]. An accurate theoretical prediction of the radio signal requires simulations of the air-shower cascade and its radio emission. Several codes have been developed in the last years, like CoREAS [20], ZHAireS [21], SELFAS [22] or EVA [23]. Their latest versions generally give consistent results, with only small differences not yet completely explained [24]. So far only CoREAS has been compared in detailed studies with high statistics against measurements and found to be compatible (see figure 3) [17, 18]. Predictions of other codes have been compared with CoREAS and cross-checked for individual events [24, 16]. Consequently, simulation codes are and can confidently be applied for the interpretation of measurements - at least at the current level of accuracy, which in many aspects already is at a level competitive with other detection techniques. 3. Experiments Stimulated by theoretical predictions [11, 9], and first experimental detection [26], a series of analog radio experiments detected air showers in the 1960’s [27]. They discovered all general properties of the radio emission, but were not able to compete with other detection techniques for air showers. This started to change only in the 2000’s with the first digital antenna arrays dedicated to air-shower measurements, in particular LOPES [28], the radio extension of KASCADE-Grande [29] in Karlsruhe, Germany, and CODALEMA [30] close to Nanc¸ay, France. After this revival, a second generation of digital arrays is now operating, e.g., the Auger Engineering Radio Array (AERA) [31], which is the radio extension of the Pierre Auger Observatory in Argentina [32], LOFAR in the Netherlands [33], and the Tunka Radio Extension (Tunka-Rex) in Siberia [18] (see figure 4).
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Figure 3: Comparison of the amplitude at 100 m distance to the shower axis between LOPES measurements and CoREAS simulations for proton primaries using the direction and energy reconstructed by the co-located KASCADE-Grande experiment as initial parameters (from Ref. [17]).
Moreover, there are many related activities, like airshower observation at higher frequencies with ANITA [34] or CROME [7], or experiments aiming for neutrino initiated showers in ice. Motivated by historic measurements [35], also some modern research and development is done at lower frequencies of a few MHz, e.g., by the EXTASIS project at the CODALEMA site. Although all air-shower arrays use different layouts and antenna types, they converged in several aspects to a common design. The typical frequency band used is 30 − 80 MHz which provides a good balance between the signal strength and background, in particular the external background due to Galactic noise, which rises towards lower frequencies. Some experiments extend the range towards higher frequencies, which is more expensive and requires sufficient dynamic range to avoid saturation by FM radio present almost everywhere in the world. Moreover, all modern experiments digitally sample the recorded radio signal and store it for later offline analysis, often done with dedicated software frameworks [36]. Modern experiments generally feature two perpendicular antennas per station for polarization measurement. With additional information on the arrival direction the electric-field vector at each station can be reconstructed and analyzed. With only few exceptions all radio arrays feature hybrid detection of the same air showers in radio and secondary particles: Some radio
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Figure 4: Location of selected radio experiments for air-shower detection on a world map of the geomagnetic field strength [25, 8].
arrays are built as an extension of existing air-shower arrays, while other radio arrays were equipped with a simple particle detector array. This approach enables external triggering or, in case of self-triggering, later cross-check [37]. This cross-check is necessary, since current self-trigger strategies still suffer from low purity due to external background pulses, e.g., from human activities. Furthermore, the information of particle and radio detection can be combined during analyses to improve the total accuracy for the reconstructed air-shower parameters. Other differences between experiments regard the location, the antenna type, and the array geometry. From the geomagnetic field alone, the ideal location would be in Siberia, close to the Tunka-Rex experiment. Nevertheless, the variation in magnetic field strength is modest over the globe: Thus, usually other issues, like infrastructure or existing cosmic-ray experiments, decide on the location of radio arrays. The choice of different antenna types is driven by cost as well as optimization for threshold or systematic measurement uncertainties [38]. As for the location, the maximum effect on the threshold is on the order of a factor of 2. The density of an antenna array has a larger impact on the possible science of an experiment: Dense ar-
rays like LOFAR or the planned Square Kilometer Array (SKA) [39] provide very detailed measurements and a high accuracy for shower parameters. Sparse arrays, like AERA, CODALEMA, or Tunka-Rex, cover large areas at moderate costs aiming at higher energies and/or inclined showers with huge footprints. The threshold in antenna spacing between sparse and dense is on the order of 100 − 200 m, because roughly at this distance to the shower axis the exponential fall-off of the radio lateral distribution starts [40]. This means that the typical event at denser arrays features hundreds of antennas with signal, while at sparser arrays the typical event just features a few (often only 3 to 5) antennas with signal.
4. Reconstruction of shower parameters
There are many science goals of radio arrays, e.g., thunderstorm physics [41, 42] or particle physics related to air showers. For cosmic-ray science, the accurate reconstruction of air-shower parameters is of main relevance, in particular the arrival direction, the energy, and the position of the shower maximum, which provides a statistical estimator for the type of the primary particle.
F.G. Schröder / Nuclear and Particle Physics Proceedings 279–281 (2016) 190–197
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Figure 5: Deviation between the arrival direction reconstructed by the LOPES radio array and the KASCADE particle-detector array. The angular resolution of the radio array depends slightly on the assumed shape for the radio wavefront, and is better than the mean deviation. Thus, when using a hyperbolic wavefront the accuracy for the shower direction is at least 0.6◦ (from Ref. [43]).
4.1. Direction Since charged cosmic particles are deflected by magnetic fields, they do not arrive at Earth from the direction of their source. Thus, a direction resolution of a few degrees is sufficient for most cosmic-ray analyses, and only for photon and neutrino searches a higher resolution will be of advantage. A resolution on the order of 2◦ is easily provided by plane-wave triangulation as long as at least three antennas at different locations recorded the air-shower signal. By interferometric analyses, and by assuming a more realistic, hyperbolic wavefront even sub-degree resolutions have been experimentally demonstrated [43, 44] (see figure 5): LOPES digitally combines several antennas during offline analysis to a cross-correlation beam, which decreases the detection threshold, and increases the reconstruction accuracy - at least for the shower direction. 4.2. Energy The total radiation energy in the radio signal is an accurate measure for the energy content of the electromagnetic component, which depends mostly on the energy of the primary particle, and only to a few percent on its mass. Due to the coherent nature of the emission, the radiation energy is roughly proportional to the energy of the electromagnetic component squared (after correction for the angle between the shower axis and the geomagnetic field). Recently, this has been experimentally confirmed by AERA in a comparison of the radiation energy in the measured radio signal with the shower energy reconstructed by the surface-detector array (see figure 6). The resulting precision for the energy
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of the primary particle as reconstructed by AERA is about 17 %, with an uncertainty on the absolute scale of better than 20 % [46, 45]. Similarly accurate energy reconstructions have been demonstrated by other experiments, e.g., LOPES [47], Tunka-Rex [48], and others. Instead of using the total radiation energy as measure, these other experiments use the radio amplitude at a typical distance to the shower axis, which is on the order of 100 m. At this distance the amplitude depends least on the position of the shower maximum, which affects the slope of the lateral distribution. In the future, more detailed comparisons of both methods have to be done, e.g., studying systematic uncertainties over large zenith angle ranges. Nevertheless, with either method already now the radio reconstruction of the primary energy has equal accuracy compared to established methods, like air-Cherenkov, air-fluorescence detection. 4.3. Shower maximum The mass-composition of the primary cosmic rays is the most important goal of air-shower measurements, since its interpretation can confirm or constrain scenarios for the cosmic-ray origin. Radio measurements can contribute in two ways: First, the energy content of the electromagnetic cascade is a mass-sensitive parameter when combined with the number of muons. Second, the statistical distribution of the atmospheric depths of
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Figure 7: Distance to the shower maximum (in units of atmospheric depth) reconstructed by Tunka-Rex radio measurements and coincident Tunka-133 air-Cherenkov measurements (from Ref. [49]).
the shower maximum can be translated into a statistical distribution of the masses of primary particles. While the first method still needs an experimental proof-ofprinciple, for the second method this has been delivered. There are at least three different ways to reconstruct the position of the shower maximum using radio measurements, of which one already is experimentally confirmed. LOPES found evidence that the slope of the lateral distribution of the radio signal is sensitive to the longitudinal shower development measured by a muontracking detector [50]: the closer the shower maximum to the detector, the steeper the slope. Recently, a direct comparison of the distance to the shower maximum reconstructed from Tunka-Rex radio measurements and Tunka-133 air-Cherenkov measurements gave an independent confirmation (see figure 7) [48]. The derived precision for the Tunka-Rex measurement is about 40 g/cm2 , which is about twice the value achieved by fluorescence detectors [32]. Using a much denser array, and a more computing-intensive method LOFAR achieved an accuracy of 20 g/cm2 [51]. This is similar to the fluorescence method, but the radio measurements are possible around the clock. The method used by LOFAR relies on top-down simulations exploiting not only the lateral slope, but implicitly all features of the lateral distribution including its width. Future tests have to show whether this different method or the significantly larger number of antennas is the main reason for the improvement in accuracy compared to the economic and sparse Tunka-Rex array.
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Moreover, other methods for the reconstruction of the shower maximum have been suggested and studied with simulations: In particular the steepness of the hyperbolic radio wavefront depends on the distance to the shower maximum [43]. Since the wavefront can be reconstructed by arrival time measurements, this would be an independent access to the lateral distribution relying on amplitude measurements. Finally, the frequency spectrum depends on the position of the shower maximum as well as on the position of the antenna relative to the shower axis [52]. Thus, if the shower geometry is measured accurately by an independent detector, this would enable the reconstruction of the masscomposition using a single antenna in addition to a particle detector array. Nevertheless, for both methods, wavefront and frequency spectrum, the accuracy achievable under realistic measurement uncertainties still has to be demonstrated in practice. 5. Next steps For the further development and improvement of the radio technique several steps are planned. To obtain even more accurate energy measurements, further progress in the antenna calibration [17, 38, 53], and detailed comparisons of different simulation programs would be helpful. To increase the accuracy for the shower maximum, the methods using the frequency spectrum and the wavefront have to be further developed and experimentally tested. Since the wavefront method needs accurate arrival-time measurements, it will benefit from further progress in time calibration of radio arrays [54, 55]. Nevertheless, the currently achieved accuracy for energy and shower maximum might already be sufficient for competitive cosmic-ray analyses. The combination of radio and muon measurements might bring a major step forward in the total accuracy for the energy and mass composition, since both feature complementary information. Such a combination is under test at the Pierre Auger Observatory [31] and at the Tunka cosmic-ray facility [56]. This will be promising also for inclined showers, which at ground consist almost only of muons. Still the radio emission can be measured. Due to the distant shower maximum, the radio footprint extents over several kilometers for inclined showers, making sparse arrays feasible. The next-generation project GRAND plans to exploit this by placing about 100, 000 antennas on an area of 200, 000 km2 , which would make it by far the largest array in the world [57]. Its main target will be inclined
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neutrino-induced showers, but also for cosmic-ray induced air showers it would significantly exceed the exposure of current arrays, like the Pierre Auger Observatory. Complementary to GRAND, SKA will consist of a similar number of antennas, but on a much smaller area on the order of one square kilometer. This ultradense antenna layout will provide the most detailed radio measurements of air showers, enabling an unprecedented step forward in accuracy [39]. 6. Conclusion The radio technique for cosmic-ray air showers evolved significantly in the last few years on several levels. The technique became mature, and scalable concepts for antenna arrays have been developed and practically demonstrated. At the same time, the theoretical understanding improved significantly. Currently, the accuracy of simulation programs for the radio emission seems to be on the same level as the improved calibration accuracy of experiments, namely better than 20 % for the amplitude of the electric field. Although the dream of huge, stand-alone radio arrays delivering cosmic-ray science at cheapest cost has not yet been fulfilled, the radio technique is close to contributing to cosmic-ray science. Especially the combination of radio and particle detectors seems promising: As externally triggered extensions, radio arrays indeed are economic and available around the clock. Moreover, equal accuracy for shower parameters as for other detection techniques has been experimentally demonstrated: better than 1◦ angular resolution, better than 20 % accuracy for the energy of the primary particle (with a scale uncertainty also smaller than 20 %), and between 20 and 40 g/cm2 for the atmospheric depth of the shower maximum, depending on the array density and reconstruction method. This means that radio measurements can complement particle measurements by providing additional information on the shower maximum and the energy of the electromagnetic component. Consequently, radio-particle hybrid detection has the potential to boost the accuracy for the energy dependence of the cosmic-ray composition. This is needed to distinguish between different scenarios for the yet unknown origin of the highest-energy cosmic rays. References [1] J. Bl¨umer, R. Engel, J. R. H¨orandel, Cosmic rays from the knee to the highest energies, Progress in Particle and Nuclear Physics 63 (2009) 293–338.
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Nuclear and Particle Physics Proceedings 279–281 (2016) 190–197 www.elsevier.com/locate/nppp
Status of the radio technique for cosmic-ray induced air showers Frank G. Schr¨oder Institut f¨ur Kernphysik, Karlsruhe Institute of Technology (KIT), Germany
Abstract Radio measurements yield calorimetric information on the electromagnetic shower component around the clock. However, until recently it was not clear whether radio measurements can compete in accuracy with established nighttime techniques like air-Cherenkov or air-fluorescence detection. Due to recent progress in the radio technique as well as in the understanding of the emission mechanisms, the performance of current radio experiments has significantly improved. Above 100 PeV, digital, state-of-the-art antenna arrays achieve a reconstruction accuracy for the energy similar to that of other techniques, and can provide an independent measurement of the absolute energy scale. Furthermore, radio measurements are sensitive to the mass composition of the primary particles: First, the position of the shower maximum can be reconstructed from the radio signal. Second, in combination with muon detectors the measurement of the electromagnetic component provides complementary information on the primary mass. Since the radio footprint is huge for inclined showers, and the radio signal does not suffer absorption in the atmosphere, future radio arrays either focus on inclined showers at the highest energy, or on ultra-high precision measurements with extremely dense arrays. This proceeding reviews the current status of radio experiments and simulations as well as future plans. Keywords: cosmic ray, air shower, radio
1. Introduction Measurements of cosmic-ray air showers are motivated typically by two different classes of scientific goals: first, a better understanding of the particle physics relevant for the first interaction of the primary particle and the development of the particle cascade; second, a better understanding of the astrophysics relevant for the sources and propagation of the primary cosmic rays. For both goals, the properties of the primary particles have to be known as accurately as possible, i.e., reconstructed from air-shower measurements. Different techniques for air-shower detection have different strengths and weaknesses (cf. Refs. [1, 2]). Particle detectors at ground can only measure one stage of the shower development and suffer from statistical uncertainties, since for economic reasons detectors in air-shower arrays cover only a small fraction of the total area. A different category of techniques provides http://dx.doi.org/10.1016/j.nuclphysbps.2016.10.027 2405-6014/© 2016 Published by Elsevier B.V.
an integral, calorimetric measurement of the full air shower, namely air-fluorescence, air-Cherenkov, and radio detection. However, these techniques are only sensitive to the electromagnetic shower component, not to the hadronic or muonic components. Moreover, air-fluorescence and air-Cherenkov techniques are restricted to dark, clear nights. Modern experiments usually combine both classes of techniques in hybrid detectors, to maximize the total accuracy for the type and energy of the primary cosmic-ray particles. Within the calorimetric techniques, only radio detection has the principal advantage of being available around the clock. Thus, radio detectors would be the ideal supplement for particle detector arrays. Still, in the past, the radio technique suffered from technical difficulties and problems in the understanding of the radio emission by air showers. Recently, these problems have been solved to a large extent, and current radio experi-
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ments start to become competitive with the established air-Cherenkov and air-fluorescence techniques. 2. Radio emission from air showers Like air-fluorescence and air-Cherenkov emission, the radio signal is also generated by charged particles in the shower, mainly by the electrons and positrons. While air-fluorescence light is emitted isotropically by nitrogen molecules excited by the air-shower particles, air-Cherenkov light and radio signal are emitted by the air-shower particles themselves. Since the air-shower particles are highly relativistic, their emission is not isotropic but strongly beamed in the direction of the shower axis with an opening angle on the order of 2◦ . Since the shower front has a typical thickness on the order of meters, the emission is generally coherent at wavelengths of that order or larger. Thereby the exact coherence conditions depend on the observer position, since the refractive index of air causes the radio waves to propagate slightly slower or faster than the particles, depending on altitude [4, 5]. Therefore, at the Cherenkov angle the emission from all shower stages arrives simultaneously, and is coherent for wavelengths as short as centimeters [3]. Consequently, radio emission can be observed in a wide distance range at frequencies of several 10 MHz, and only at the Cherenkov angle also at much higher frequencies up to a few GHz (see figure 1). The Cherenkov angle corresponds to a distance to the shower axis on the order of 100 m for vertical showers at typical observation altitudes. This is why the lateral distribution features
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Figure 2: Two emission mechanisms are experimentally confirmed: The geomagnetic deflection of electrons and positrons causes linearly polarized radio emission (left), the time-variation of the charge excess in the shower front causes radially polarized radio emission, known as Askaryan effect (right). In case of a vertical shower, the v x B axis corresponds to the east-west axis, and the v x v x B axis corresponds to the north-south axis [8].
a kind of bump in this distance range, where the exact bump position depends on the observation altitude and the position of the shower maximum [6, 7]. Two different mechanisms have been confirmed experimentally to contribute significantly to the total emission (see figure 2), which makes the observed radio signals more complicated compared to all the other techniques relying on a single mechanism. The stronger of the two effects is the geomagnetic deflection of the electrons and positrons inducing a time-varying transverse current [9, 10]. This basically converts the shower front into a kind of simple Hertz dipole. The amplitude of the geomagnetic emission is proportional to the Lorentz forces and, thus, to sin α (with α being the geomagnetic angle between the shower axis and the geomagnetic field). The geomagnetic emission is linearly polarized like the emission by a dipole orthogonal to the shower axis and the geomagnetic field. The second mechanism is the Askaryan effect [11]: the shower front accumulates a time-varying net charge due to electrons kicked out from air atoms, and due to annihilation of positrons in the shower. This timevarying net charge causes radially polarized emission. The Askaryan effect dominates in dense media (and sometimes is confused with Cherenkov radiation), but is less strong in air, typically an order of magnitude weaker than the geomagnetic effect [12, 13, 14, 15]. Nevertheless, the relative strength depends strongly on
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the location of the observer relative to the shower axis and on the direction of the shower axis relative to the geomagnetic field. Hence, the Askaryan effect cannot be neglected in the interpretation of radio measurements. Further emission mechanisms, like molecular bremsstrahlung, have been suggested, but neither experimentally confirmed [7], nor is there any obvious deficit in the theoretical picture: the combination of the geomagnetic and Askaryan emission seems to fully explain experimental results within current measurement accuracies of about 20 % for the electric-field strength [16, 17, 18]. However, at lower frequencies of a few MHz further emission processes are under investigation, in particular radio emission produced by the termination of the shower entering the ground [19]. An accurate theoretical prediction of the radio signal requires simulations of the air-shower cascade and its radio emission. Several codes have been developed in the last years, like CoREAS [20], ZHAireS [21], SELFAS [22] or EVA [23]. Their latest versions generally give consistent results, with only small differences not yet completely explained [24]. So far only CoREAS has been compared in detailed studies with high statistics against measurements and found to be compatible (see figure 3) [17, 18]. Predictions of other codes have been compared with CoREAS and cross-checked for individual events [24, 16]. Consequently, simulation codes are and can confidently be applied for the interpretation of measurements - at least at the current level of accuracy, which in many aspects already is at a level competitive with other detection techniques. 3. Experiments Stimulated by theoretical predictions [11, 9], and first experimental detection [26], a series of analog radio experiments detected air showers in the 1960’s [27]. They discovered all general properties of the radio emission, but were not able to compete with other detection techniques for air showers. This started to change only in the 2000’s with the first digital antenna arrays dedicated to air-shower measurements, in particular LOPES [28], the radio extension of KASCADE-Grande [29] in Karlsruhe, Germany, and CODALEMA [30] close to Nanc¸ay, France. After this revival, a second generation of digital arrays is now operating, e.g., the Auger Engineering Radio Array (AERA) [31], which is the radio extension of the Pierre Auger Observatory in Argentina [32], LOFAR in the Netherlands [33], and the Tunka Radio Extension (Tunka-Rex) in Siberia [18] (see figure 4).
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Figure 3: Comparison of the amplitude at 100 m distance to the shower axis between LOPES measurements and CoREAS simulations for proton primaries using the direction and energy reconstructed by the co-located KASCADE-Grande experiment as initial parameters (from Ref. [17]).
Moreover, there are many related activities, like airshower observation at higher frequencies with ANITA [34] or CROME [7], or experiments aiming for neutrino initiated showers in ice. Motivated by historic measurements [35], also some modern research and development is done at lower frequencies of a few MHz, e.g., by the EXTASIS project at the CODALEMA site. Although all air-shower arrays use different layouts and antenna types, they converged in several aspects to a common design. The typical frequency band used is 30 − 80 MHz which provides a good balance between the signal strength and background, in particular the external background due to Galactic noise, which rises towards lower frequencies. Some experiments extend the range towards higher frequencies, which is more expensive and requires sufficient dynamic range to avoid saturation by FM radio present almost everywhere in the world. Moreover, all modern experiments digitally sample the recorded radio signal and store it for later offline analysis, often done with dedicated software frameworks [36]. Modern experiments generally feature two perpendicular antennas per station for polarization measurement. With additional information on the arrival direction the electric-field vector at each station can be reconstructed and analyzed. With only few exceptions all radio arrays feature hybrid detection of the same air showers in radio and secondary particles: Some radio
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Figure 4: Location of selected radio experiments for air-shower detection on a world map of the geomagnetic field strength [25, 8].
arrays are built as an extension of existing air-shower arrays, while other radio arrays were equipped with a simple particle detector array. This approach enables external triggering or, in case of self-triggering, later cross-check [37]. This cross-check is necessary, since current self-trigger strategies still suffer from low purity due to external background pulses, e.g., from human activities. Furthermore, the information of particle and radio detection can be combined during analyses to improve the total accuracy for the reconstructed air-shower parameters. Other differences between experiments regard the location, the antenna type, and the array geometry. From the geomagnetic field alone, the ideal location would be in Siberia, close to the Tunka-Rex experiment. Nevertheless, the variation in magnetic field strength is modest over the globe: Thus, usually other issues, like infrastructure or existing cosmic-ray experiments, decide on the location of radio arrays. The choice of different antenna types is driven by cost as well as optimization for threshold or systematic measurement uncertainties [38]. As for the location, the maximum effect on the threshold is on the order of a factor of 2. The density of an antenna array has a larger impact on the possible science of an experiment: Dense ar-
rays like LOFAR or the planned Square Kilometer Array (SKA) [39] provide very detailed measurements and a high accuracy for shower parameters. Sparse arrays, like AERA, CODALEMA, or Tunka-Rex, cover large areas at moderate costs aiming at higher energies and/or inclined showers with huge footprints. The threshold in antenna spacing between sparse and dense is on the order of 100 − 200 m, because roughly at this distance to the shower axis the exponential fall-off of the radio lateral distribution starts [40]. This means that the typical event at denser arrays features hundreds of antennas with signal, while at sparser arrays the typical event just features a few (often only 3 to 5) antennas with signal.
4. Reconstruction of shower parameters
There are many science goals of radio arrays, e.g., thunderstorm physics [41, 42] or particle physics related to air showers. For cosmic-ray science, the accurate reconstruction of air-shower parameters is of main relevance, in particular the arrival direction, the energy, and the position of the shower maximum, which provides a statistical estimator for the type of the primary particle.
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Figure 5: Deviation between the arrival direction reconstructed by the LOPES radio array and the KASCADE particle-detector array. The angular resolution of the radio array depends slightly on the assumed shape for the radio wavefront, and is better than the mean deviation. Thus, when using a hyperbolic wavefront the accuracy for the shower direction is at least 0.6◦ (from Ref. [43]).
4.1. Direction Since charged cosmic particles are deflected by magnetic fields, they do not arrive at Earth from the direction of their source. Thus, a direction resolution of a few degrees is sufficient for most cosmic-ray analyses, and only for photon and neutrino searches a higher resolution will be of advantage. A resolution on the order of 2◦ is easily provided by plane-wave triangulation as long as at least three antennas at different locations recorded the air-shower signal. By interferometric analyses, and by assuming a more realistic, hyperbolic wavefront even sub-degree resolutions have been experimentally demonstrated [43, 44] (see figure 5): LOPES digitally combines several antennas during offline analysis to a cross-correlation beam, which decreases the detection threshold, and increases the reconstruction accuracy - at least for the shower direction. 4.2. Energy The total radiation energy in the radio signal is an accurate measure for the energy content of the electromagnetic component, which depends mostly on the energy of the primary particle, and only to a few percent on its mass. Due to the coherent nature of the emission, the radiation energy is roughly proportional to the energy of the electromagnetic component squared (after correction for the angle between the shower axis and the geomagnetic field). Recently, this has been experimentally confirmed by AERA in a comparison of the radiation energy in the measured radio signal with the shower energy reconstructed by the surface-detector array (see figure 6). The resulting precision for the energy
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of the primary particle as reconstructed by AERA is about 17 %, with an uncertainty on the absolute scale of better than 20 % [46, 45]. Similarly accurate energy reconstructions have been demonstrated by other experiments, e.g., LOPES [47], Tunka-Rex [48], and others. Instead of using the total radiation energy as measure, these other experiments use the radio amplitude at a typical distance to the shower axis, which is on the order of 100 m. At this distance the amplitude depends least on the position of the shower maximum, which affects the slope of the lateral distribution. In the future, more detailed comparisons of both methods have to be done, e.g., studying systematic uncertainties over large zenith angle ranges. Nevertheless, with either method already now the radio reconstruction of the primary energy has equal accuracy compared to established methods, like air-Cherenkov, air-fluorescence detection. 4.3. Shower maximum The mass-composition of the primary cosmic rays is the most important goal of air-shower measurements, since its interpretation can confirm or constrain scenarios for the cosmic-ray origin. Radio measurements can contribute in two ways: First, the energy content of the electromagnetic cascade is a mass-sensitive parameter when combined with the number of muons. Second, the statistical distribution of the atmospheric depths of
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Figure 7: Distance to the shower maximum (in units of atmospheric depth) reconstructed by Tunka-Rex radio measurements and coincident Tunka-133 air-Cherenkov measurements (from Ref. [49]).
the shower maximum can be translated into a statistical distribution of the masses of primary particles. While the first method still needs an experimental proof-ofprinciple, for the second method this has been delivered. There are at least three different ways to reconstruct the position of the shower maximum using radio measurements, of which one already is experimentally confirmed. LOPES found evidence that the slope of the lateral distribution of the radio signal is sensitive to the longitudinal shower development measured by a muontracking detector [50]: the closer the shower maximum to the detector, the steeper the slope. Recently, a direct comparison of the distance to the shower maximum reconstructed from Tunka-Rex radio measurements and Tunka-133 air-Cherenkov measurements gave an independent confirmation (see figure 7) [48]. The derived precision for the Tunka-Rex measurement is about 40 g/cm2 , which is about twice the value achieved by fluorescence detectors [32]. Using a much denser array, and a more computing-intensive method LOFAR achieved an accuracy of 20 g/cm2 [51]. This is similar to the fluorescence method, but the radio measurements are possible around the clock. The method used by LOFAR relies on top-down simulations exploiting not only the lateral slope, but implicitly all features of the lateral distribution including its width. Future tests have to show whether this different method or the significantly larger number of antennas is the main reason for the improvement in accuracy compared to the economic and sparse Tunka-Rex array.
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Moreover, other methods for the reconstruction of the shower maximum have been suggested and studied with simulations: In particular the steepness of the hyperbolic radio wavefront depends on the distance to the shower maximum [43]. Since the wavefront can be reconstructed by arrival time measurements, this would be an independent access to the lateral distribution relying on amplitude measurements. Finally, the frequency spectrum depends on the position of the shower maximum as well as on the position of the antenna relative to the shower axis [52]. Thus, if the shower geometry is measured accurately by an independent detector, this would enable the reconstruction of the masscomposition using a single antenna in addition to a particle detector array. Nevertheless, for both methods, wavefront and frequency spectrum, the accuracy achievable under realistic measurement uncertainties still has to be demonstrated in practice. 5. Next steps For the further development and improvement of the radio technique several steps are planned. To obtain even more accurate energy measurements, further progress in the antenna calibration [17, 38, 53], and detailed comparisons of different simulation programs would be helpful. To increase the accuracy for the shower maximum, the methods using the frequency spectrum and the wavefront have to be further developed and experimentally tested. Since the wavefront method needs accurate arrival-time measurements, it will benefit from further progress in time calibration of radio arrays [54, 55]. Nevertheless, the currently achieved accuracy for energy and shower maximum might already be sufficient for competitive cosmic-ray analyses. The combination of radio and muon measurements might bring a major step forward in the total accuracy for the energy and mass composition, since both feature complementary information. Such a combination is under test at the Pierre Auger Observatory [31] and at the Tunka cosmic-ray facility [56]. This will be promising also for inclined showers, which at ground consist almost only of muons. Still the radio emission can be measured. Due to the distant shower maximum, the radio footprint extents over several kilometers for inclined showers, making sparse arrays feasible. The next-generation project GRAND plans to exploit this by placing about 100, 000 antennas on an area of 200, 000 km2 , which would make it by far the largest array in the world [57]. Its main target will be inclined
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neutrino-induced showers, but also for cosmic-ray induced air showers it would significantly exceed the exposure of current arrays, like the Pierre Auger Observatory. Complementary to GRAND, SKA will consist of a similar number of antennas, but on a much smaller area on the order of one square kilometer. This ultradense antenna layout will provide the most detailed radio measurements of air showers, enabling an unprecedented step forward in accuracy [39]. 6. Conclusion The radio technique for cosmic-ray air showers evolved significantly in the last few years on several levels. The technique became mature, and scalable concepts for antenna arrays have been developed and practically demonstrated. At the same time, the theoretical understanding improved significantly. Currently, the accuracy of simulation programs for the radio emission seems to be on the same level as the improved calibration accuracy of experiments, namely better than 20 % for the amplitude of the electric field. Although the dream of huge, stand-alone radio arrays delivering cosmic-ray science at cheapest cost has not yet been fulfilled, the radio technique is close to contributing to cosmic-ray science. Especially the combination of radio and particle detectors seems promising: As externally triggered extensions, radio arrays indeed are economic and available around the clock. Moreover, equal accuracy for shower parameters as for other detection techniques has been experimentally demonstrated: better than 1◦ angular resolution, better than 20 % accuracy for the energy of the primary particle (with a scale uncertainty also smaller than 20 %), and between 20 and 40 g/cm2 for the atmospheric depth of the shower maximum, depending on the array density and reconstruction method. This means that radio measurements can complement particle measurements by providing additional information on the shower maximum and the energy of the electromagnetic component. Consequently, radio-particle hybrid detection has the potential to boost the accuracy for the energy dependence of the cosmic-ray composition. This is needed to distinguish between different scenarios for the yet unknown origin of the highest-energy cosmic rays. References [1] J. Bl¨umer, R. Engel, J. R. H¨orandel, Cosmic rays from the knee to the highest energies, Progress in Particle and Nuclear Physics 63 (2009) 293–338.
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