Shower Maximum Research Articles

Testing Model Predictions of Depth of Air-Shower Maximum and Signals in Surface Detectors using Hybrid Data of the Pierre Auger Observatory

We present a method for testing the predictions of hadronic interaction models and improving their consistency with observed two-dimensional distributions of the depth of shower maximum, X max, and signal at the ground level as a function of zenith angle. The method relies on the assumption that the mass composition is the same at all zenith angles, while the atmospheric shower development and attenuation depend on composition in a correlated way. In the present work, for each of the three leading LHC-tuned hadronic interaction models, we allow a global shift ∆ X max of the predicted shower maximum, which is the same for every mass and energy, and a rescaling R Had of the hadronic component at the ground level which is constant with the zenith angle. We apply the analysis to 2297 events reconstructed with both the fluorescence and surface detectors of the Pierre Auger Observatory with energies 1018.5−19.0 eV and zenith angles below 60°. Given the modeling assumptions made in this analysis, the best fit reaches its optimum value when shifting the X max predictions of hadronic interaction models to deeper values and increasing the hadronic signal. This change in the predicted X max scale alleviates the previously identified model deficit in the hadronic signal (commonly called the muon puzzle) but does not fully remove it. Because of the size of the adjustments ∆ X max and R Had and the large number of events in the sample, the statistical significance of need for these adjustments is large, greater than 5σstat, even for the combination of the systematic experimental shifts within 1σsys that are the most favorable for the models.

The depth of the shower maximum of air showers measured with AERA

The Auger Engineering Radio Array (AERA), as part of the Pierre Auger Observatory, is an array of radio antennas probing the nature of ultra-high energy cosmic rays at energies around the transition from Galactic to extra-galactic origin. It measures the MHz radio emission of extensive air showers produced by cosmic rays hitting our atmosphere. The elemental composition of cosmic rays is a crucial piece of information in determining what the sources of cosmic rays are and how cosmic rays are accelerated. This composition can be obtained from the mass-sensitive parameterXmax, the depth of the shower maximum. We reconstructXmaxwith a likelihood analysis, by comparing the measured radio footprint on the ground to an ensemble of footprints from Monte-Carlo CORSIKA/CoREAS air shower simulations. We compare ourXmaxreconstruction with fluorescenceXmaxmeasurements on a per-event basis, a setup unique to the Pierre Auger Observatory, and show the methods to be fully compatible. Furthermore, we extensively validate our reconstruction by identifying and correcting for systematic uncertainties. We determine the resolution of our method as a function of energy and reach a precision better than 15 g cm−2at the highest energies. With a bias-free set of around 600 showers, we find a light to light-mixed composition at energies between 1017.5to 1018.8eV, also in agreement with the Auger fluorescence measurements.

Probing Lorentz violation at ultra-high energies using air showers

In air showers initiated by ultra-high-energy cosmic rays in the Earth’s atmosphere, even the secondary particles created in the start-up phase are produced at energies far above those accessible by other means. These high-energy particles can be used to search for New Physics, such as a violation of Lorentz invariance. We focus on isotropic, nonbirefringent Lorentz violation in the photon sector and consider the two cases κ < 0 and κ > 0 (i.e., the velocity of photons is larger/smaller than the maximum attainable velocity of standard Dirac fermions). In both cases, processes that are forbidden in the standard, Lorentz-invariant theory (κ = 0) become allowed, in particular photon decay in the case κ < 0 and vacuum-Cherenkov radiation for κ > 0. Implementing these processes into air-shower simulations, we found that the development of an air shower at the highest energies can be significantly impacted, specifically the average atmospheric depth of the shower maximum X max and its shower-to-shower fluctuations σ(X max). Comparing these simulations to actual measurements, we were able to obtain much stricter bounds on this specific type of LV in the case κ < 0 than possible with previous methods. We discuss these limits and, in addition, present first results for the case κ > 0.

The Snowmass UHECR White Paper on Ultra-High-Energy Cosmic Rays

This proceeding summarizes the talk given at the opening of the UHECR 2022 conference in L’Aquila on the whitepaper ‘Ultra-High-Energy Cosmic Rays: The Intersection of the Cosmic and Energy Frontiers’ [Astroparticle Physics 149 (2023) 102819 - arXiv:2205.05845] that has been prepared for the Snowmass survey in the USA. The whitepaper provides an overview of recent progress and open questions regarding the particle physics and astrophysics related to ultra-high-energy cosmic rays (UHECR) and outlines the connections between the particle and astrophysics aspects of cosmic rays. It also discusses what instrumentation is needed to address the major scientific questions in ultra-high-energy cosmic-ray physics. While the upgraded Pierre Auger Observatory and Telescope Array will remain the workhorses at the highest energies in the current decade, new experiments with significantly higher exposure are needed in the coming decade. Ground arrays featuring simultaneous detection of the position of the shower maximum and the size of the muonic component will enable particle astronomy by measuring the rigidity of individual events. They should be complemented by other detectors maximizing the total exposure. This can be achieved by a few next-generation experiments using the latest developments in detection and analysis techniques: GRAND as a ground-based radio array, and POEMMA as a space-borne stereo fluorescence telescope will feature complementary approaches to provide maximum exposure; IceCube-Gen2 with its surface array, and GCOS aim at increased statistics with high accuracy for particle physics and rigidity-based galactic and extra-galactic astrophysics. While designed to discover the astrophysical cosmic-ray sources at the highest energies, the same experiments also contribute to particle physics, e.g., by studying the muon puzzle in cosmic-ray air showers, and by their discovery potential for exciting new physics, such as certain Dark Matter candidates. With the full whitepaper available as a reference, this proceeding will briefly present the science cases of the experiments, highlighting their individual strengths and outlining how they complement each other.

Measurements of Cosmic Ray Mass Composition with the IceCube Neutrino Observatory

The IceCube Neutrino Observatory is a multi-component detector at the South Pole. Besides studying high-energy neutrinos, it is capable of measuring high-energy cosmic rays from PeV to EeV. This energy region is thought to cover the transition from galactic to extragalactic sources of cosmic rays. The observatory consists of the deep in-ice IceCube array, which measures the high-energy (≥500 GeV) muonic component, and the IceTop surface array, which is sensitive to the electromagnetic and low-energy muonic part of an air shower. The primary energy and the mass composition can be measured simultaneously by applying statistical methods including modern machine-learning techniques to reconstruct cosmic ray air showers. In this contribution, we will discuss recent improvements to the reconstruction techniques, the mass composition sensitivity, and an outlook on future improved measurements with the full surface scintillator/radio array to mitigate snow accumulation and measure the air shower maximum Xmax using imaging air-Cherenkov telescopes IceAct.

Model-independent Evidence for an Increase in the Mean Mass of Cosmic Rays above 3 EeV

Measurements of the Elongation Rate of the depth of shower maximum above 1 EeV are reviewed. There is evidence, from four independent estimates of this rate, made in the two hemispheres using three different techniques, for a decrease in the Elongation Rate above ~3 EeV, as first discovered by the Pierre Auger Collaboration over 15 year ago. Unless there is a dramatic change in the hadronic physics above this energy, the mean mass of the primary cosmic rays must increase as a function of energy, well into the decade beyond 10 EeV. To estimate the mass, the use of hadronic models is required, the accuracy of which remains uncertain. However, the possibility of a dramatic change in the hadronic physics appears unlikely, and would be inconsistent with data from the Auger Collaboration on the mass composition in the range 3 to 10 EeV, and on the anisotropy of arrival directions above 8 EeV. Both of these conclusions are insensitive to uncertainties in the shower models. Some remarks are made about the belief, still firmly held by some, that the highest-energy cosmic rays are dominantly protons.

Testing the Compatibility of the Depth of the Shower Maximum Measurements performed at Telescope Array and the Pierre Auger Observatory

The Telescope Array and the Pierre Auger Observatory estimate the composition of ultra-high-energy cosmic rays by observing the distribution of depths of air-shower maxima, X max. Both experiments directly observe the longitudinal development of air showers using fluorescence telescopes with surface particle detectors used in conjunction to provide precision in determining air-shower geometry. The two experiments differ in the details of the analysis of events, so a direct comparison of X max distributions is not possible. The Auger – Telescope Array Composition Working Group presents their results from a technique to compare X max measurements from Auger with those of Telescope Array. In particular, the compatibility of the first two moments of the X max distributions of Auger with the data from the Black Rock Mesa and Long Ridge detectors of the Telescope Array is tested for energies above 1018.2 eV. Quantitative comparisons are obtained using air-shower simulations of four representative species made using the Sibyll 2.3d high-energy interaction model. These are weighted to fit the fractional composition seen in Auger data and reconstructed using the Telescope Array detector response and analysis methods.

Update on the indication of a mass-dependent anisotropy above 1018.7 eV in the hybrid data of the Pierre Auger Observatory

We test for an anisotropy in the mass of arriving cosmic-ray primaries associated with the galactic plane. The sensitivity to primary mass is obtained through the depth of shower maximum, X max, extracted from hybrid events measured over a 14-year period at the Pierre Auger Observatory. The sky is split into distinct on-and off-plane regions using the galactic latitude of each arriving cosmic ray to form two distributions of X max, which are compared using an Anderson-Darling 2-samples test. A scan over roughly half of the data is used to select a lower threshold energy of 1018.7 eV and a galactic latitude splitting at |b| = 30°, which are set as a prescription for the remaining data. With these thresholds, the distribution of X max from the on-plane region is found to have a 9.1±1.6−2.2+2.1g/cm2 shallower mean and a 5.9±2.1−2.5+3.5g/cm2 narrower width than that of the off-plane region and is observed in all telescope sites independently. These di↵erences indicate that the mean mass of primary particles arriving from the on-plane region is greater than that of those from the off-plane region. Monte Carlo studies yield a 5.9 ×10−6 random chance probability for the result in the independent data, lowering to a 6.0 × 10−7 post-penalization random chance probability when the scanned data is included. Accounting for systematic uncertainties leads to an indication for anisotropy in mass composition above 1018.7 eV with a 3.3 σ-significance. Furthermore, the result has been newly tested using additional FD data recovered from the selection process. This test independently disfavors the on-and off-plane regions being uniform in composition at the 2.2 σ-level, which is in good agreement with the expected sensitivity of the dataset used for this test.

Sensitivity of the combined fit of energy spectrum, shower depth distributions, and arrival directions at the Pierre Auger Observatory

The Pierre Auger Observatory measures several characteristics of ultra-high-energy cosmic rays (UHECRs), most importantly the energy spectrum, the distribution of maximum shower depths and the arrival directions. We use all three observables for a combined fit, in which parameters of possible UHECR sources can be constrained. The astrophy sical model used in the fit consists of homogeneo usly distributed background sources as well as an adaptable contribution from a nearby source population . For this, the catalogs of starburst galaxies and active galactic nuclei are used which show an indication for a correlation with the UHECR arrival directions . The signal fraction, as well as the size of a rigidity-dependent magn etic field blurring, are part of the fit parameters, along with the parameters describing the source emission. Tn this work, we present an astro-physical simulation containing an energy-dependent contribution from starburst galaxies, which simultaneously describes the energy spectrum, shower depth distributions, and arrival directions measured by the Pierre Auger Observatory. On this simulation, the discrimination power of the method regarding the differentiation of source catalogs is demonstrated, and the expected statistical significance of the result is investigated.

Observational Constraints on Cosmic-Ray Escape from Ultrahigh-energy Accelerators

Interactions of ultra-high energy cosmic rays (UHECRs) accelerated in specific astrophysical environments have been shown to shape the energy production rate of nuclei differently from that of the secondary neutrons escaping from the confinement zone. Here, we aim at testing a generic scenario of in-source interactions through phenomenological modeling of the flux and composition of UHECRs. We fit a model in which nucleons and nuclei follow different particle energy distributions to the all-particle energy spectrum and proton spectrum below the ankle energy and distributions of maximum shower depths above this energy, as inferred at the Pierre Auger Observatory. We obtain that the data can be reproduced using a spatial distribution of sources that follows the density of extragalactic matter on both local and large scales, providing hence a realistic set of constraints for the emission mechanisms in cosmic accelerators, for their energetics, and for the abundances of elements at escape from their environments. While the quasi monoelemental increase of the cosmic-ray mass number observed on Earth from ≃2 EeV up to the highest energies calls for nuclei accelerated with a hard spectral index, the inferred flux of protons down to ≃0.6 EeV is shown to require for this population a spectral index significantly softer than that generally obtained up to now. We demonstrate that modeling UHECR data across the ankle substantiates the conjecture of in-source interactions in a robust statistical framework, although pushing the mechanism to the extreme.

Particle Physics with the Pierre Auger Observatory

The Pierre Auger Observatory is the largest extensive air shower detector. Based on a hybrid system, this experiment measures the longitudinal shower development and the particles at the ground. This detection system allows the extraction of the p-air cross-section at energies much higher than the ones accessible by current colliders. It is also possible to test hadronic interaction models using correlations between different air shower observables, like the depth of shower maximum and the muon number at the ground and their fluctuations. Thanks to the low energy extension of the Pierre Auger Observatory, the muon deficit in air shower simulations can be addressed over almost three decades at the highest energies.

Simulation study of the relative Askaryan fraction at the south pole

We use coreas simulations to study the ratio of geomagnetic and Askaryan radio emission from cosmic-ray air showers at the location of the south pole. The fraction of Askaryan emission relative to the total emission is determined by the polarization of the radio signal at the time of its peak amplitude. We find that the relative Askaryan fraction has a radial dependence increasing with the distance from the shower axis---with a plateau around the Cherenkov ring. We further find that the Askaryan fraction depends on shower parameters like the zenith angle and the distance to the shower maximum. While these dependencies are in agreement with earlier studies, they have not yet been utilized to determine the depth of the shower maximum, ${X}_{\mathrm{max}}$, based on the Askaryan fraction. Fitting these dependencies with a polynomial model, we arrive at an alternative method to reconstruct ${X}_{\mathrm{max}}$ using a measurement of the Askaryan fraction and shower geometry as input. Depending on the measurement uncertainties of the Askaryan fraction, this method provides a measurement of ${X}_{\mathrm{max}}$ with a resolution similar to other methods of reconstructing ${X}_{\mathrm{max}}$ from radio observables. Although existing template methods give superior resolution, they are more computationally intensive. Consequently, the use of polarization to extract the Askaryan fraction of the radio signal should be considered as an additional input observable in future generations of template-fitting reconstruction and other multivariate approaches for measuring ${X}_{\mathrm{max}}$.

The Unreasonable Effectiveness of the Air-Fluorescence Technique in Determining the EAS Shower Maximum

We review all existing air-fluorescence measurements of the elongation rate of extensive air showers (slope of mean EAS shower maximum Xmax vs. log of shower energy E) above 1017 eV. We find remarkable agreement for all current and historic experiments over a 30 yr period for the energy range from 1017 to 3 × 1018 eV. The mean elongation rate in this energy interval is near 80 g/cm2/decade. Above this energy, experiments in the Northern hemisphere are in good agreement with an average elongation rate of 48 ± 10 g/cm2/decade while Southern hemisphere experiments have a flatter elongation rate of 26 ± 2 g/cm2/decade. We point out that, given the agreement at lower energies, possible systematic reasons for this difference are unlikely. Given this, the world elongation rate data alone may indicate a composition difference of UHECR in the Northern and Southern hemisphere and thus a diversity of UHECR sources in the Northern and Southern sky.

Measuring temporal characteristics of the Cherenkov radiation signal from extensive air showers of cosmic rays with a wide field-of-view telescope addendum to the Yakutsk array

A wide field-of-view Cherenkov telescope has been working in the surroundings of the Yakutsk array experiment since 2012. Its main function is to measure the waveform of the optical Cherenkov radiation signal induced by extensive air showers of cosmic rays. Analysis of the dataset collected by the telescope in the vicinity of ${10}^{17}\text{ }\text{ }\mathrm{eV}$ is intended for the reconstruction of the parameters of the development of the showers in addition to the main shower characteristics measured by the rest of the array detectors. In this paper, the observed duration of the Cherenkov radiation signal as a function of the shower core distance is used to estimate the depth of the shower maximum in a different way based on the results of model simulations. The results are in general agreement with those of other works.

Development of an MCP-Based Timing Layer for the LHCb ECAL Upgrade-2

The increase in instantaneous luminosity during the high-luminosity phase of the LHC represents a significant challenge for future detectors. A strategy to cope with high-pileup conditions is to add a fourth dimension to the measurements of the hits, by exploiting the time separation of the various proton–proton primary collisions. According to LHCb simulation studies, resolutions of about 10–20 picoseconds, at least an order of magnitude shorter than the average time span between primary interactions, would be greatly beneficial for the physics reach of the experiment. Microchannel plate (MCP) photomultipliers are compact devices capable of measuring the arrival time of charged particles with the required resolution. The technology of large-area picosecond photodetectors (LAPPDs) is under investigation to implement a timing layer that can be placed within a sampling calorimeter module with the purpose of measuring the arrival time of electromagnetic showers. LAPPD performances, using a Gen-I tile with a delay-line anode and a Gen-II with a capacitively coupled anode, have been measured thoroughly both with laser (wavelength of 405 nm and pulse width of 27.5 ps FWHM) and high-energy electron (1–5.8 GeV) beams. Time resolutions of the order of 30 ps for single photoelectrons and 15 ps for electromagnetic showers initiated by 5-GeV electrons, as measured at the shower maximum, are obtained.

Radio interferometry applied to the observation of cosmic-ray induced extensive air showers

We developed a radio interferometric technique for the observation of extensive air showers initiated by cosmic particles. In this proof-of-principle study we show that properties of extensive air showers can be derived with high accuracy in a straightforward manner. When time synchronisation below sim 1 ns between different receivers can be achieved, direction reconstruction resolution of < 0.2^circ and resolution on the depth of shower maximum of <10 g/cm^2 are obtained over the full parameter range studied, with even higher accuracy for inclined incoming directions. In addition, by applying the developed method to dense arrays of radio antennas, the energy threshold for the radio detection of extensive air showers can be significantly lowered. The proposed method can be incorporated in operational and future cosmic particle observatories and with its high accuracy it has the potential to play a crucial role in unravelling the composition of the ultra-high-energy cosmic-particle flux.

Photon decay in ultrahigh-energy air showers: Stringent bound on Lorentz violation

In extensive air showers induced by ultra-high-energy (UHE) cosmic rays, secondary photons are expected to be produced at energies far above those accessible by other means. It has been shown that the decay of such photons, as possible in certain theories allowing Lorentz violation, can lead to significant changes of the shower development. Based on observations of the average depth of the shower maximum $\left<X_\text{max}\right>$, a stringent bound on Lorentz violation has been placed in a previous work. Here we include the shower-to-shower fluctuations $\sigma(X_\text{max})$ as an additional observable. The combined comparison of $\left<X_\text{max}\right>$ and $\sigma(X_\text{max})$ to shower observations allows a much stricter test of the possible decay of UHE photons, improving the previous bound by a factor of 50.

Deep-learning based reconstruction of the shower maximum X max using the water-Cherenkov detectors of the Pierre Auger Observatory

The atmospheric depth of the air shower maximum X max is an observable commonly used for the determination of the nuclear mass composition of ultra-high energy cosmic rays.Direct measurements of X max are performed using observations of the longitudinal shower development with fluorescence telescopes.At the same time, several methods have been proposed for an indirect estimation of X max from the characteristics of the shower particles registered with surface detector arrays.In this paper, we present a deep neural network (DNN) for the estimation of X max. The reconstruction relies on the signals induced by shower particles in the ground based water-Cherenkov detectors of the Pierre Auger Observatory.The network architecture features recurrent long short-term memory layers to process the temporal structure of signals and hexagonal convolutions to exploit the symmetry of the surface detector array.We evaluate the performance of the network using air showers simulated with three different hadronic interaction models. Thereafter, we account for long-term detector effects and calibrate the reconstructed X max using fluorescence measurements. Finally, we show that the event-by-event resolution in the reconstruction of the shower maximum improves with increasing shower energy and reaches less than 25 g/cm2 at energies above 2 × 1019 eV.

Expected performance of air-shower measurements with the radio-interferometric technique

Interferometric measurements with arrays of radio antennas are a powerful and widely used technique in astronomy. Recently, this technique has been revisited for the reconstruction of extensive air showers []. This “radio-interferometric technique” exploits the coherence in the radio emission emitted by billions of secondary shower particles to reconstruct the shower parameters, in particular the shower axis and depth of the shower maximum X max. The accuracy previously demonstrated on simulations with an idealized detector is very promising. The prospect of an accurate X max measurement for inclined air showers combined with measurements of the electromagnetic energy (also with radio antennas) and the muonic shower content (via ground particle detectors) is very intriguing as it would provide a high sensitivity to the mass of cosmic rays, key information to study their origin. In this article we evaluate the potential of interferometric X max measurements using (simulated) inclined air showers with sparse antenna arrays under realistic conditions. To determine prerequisites for the application of the radio-interferometric technique with various antenna arrays, the influence of inaccuracies in the time synchronisation between antennas and its inter-dependency with the antenna density is investigated in detail. We find a strong correlation between the antenna multiplicity (per event) and the maximum acceptable time jitter, i.e., inaccuracy in the time synchronisation. For data recorded with a time synchronisation accurate to within 1 ns in the commonly used frequency band of 30 MHz to 80 MHz, an antenna multiplicity of >50 is needed to achieve an X max resolution of g cm−2. For data recorded with 2 ns accuracy, already ≳ 200 antennas are needed to achieve this X max resolution. Furthermore, we find no advantage reconstructing X max from data simulated at higher observation frequencies, i.e., up to several hundred MHz. Finally, we provide a generalisation of our results from very inclined air showers to vertical geometries.

On the estimation of the depth of maximum of extensive air showers using the steepness parameter of the lateral distribution of Cherenkov radiation

Using Monte Carlo simulation of extensive air showers, we showed that the maximum depth of showers, Xmax can be estimated using P=Q(100)∕Q(200), the ratio of Cherenkov photon densities at 100 and 200 meters from the shower core, which is known as the steepness parameter of the lateral distribution of Cherenkov radiation on the ground. A simple quadratic model has been fitted to a set of data from simulated extensive air showers, relating the steepness parameter and the shower maximum depth. Then the model has been tested on another set of simulated showers. The average difference between the actual maximum depth of the simulated showers and the maximum depth obtained from the lateral distribution of Cherenkov light is about 9 g/cm2. In addition, possibility of a more direct estimation of the mass of the initial particle from P has been investigated. An exponential relation between these two quantities has been fitted. Applying the model to another set of showers, we found that the average difference between the estimated and the actual mass of primary particles is less than 0.5 atomic mass unit.