The measurements by the Pierre Auger Observatory of the energy spectrum and mass composition of cosmic rays can be interpreted assuming the presence of two extragalactic source populations, one dominating the flux at energies above a few EeV and the other below. To fit the data ignoring magnetic field effects, the high-energy population needs to accelerate a mixture of nuclei with very hard spectra, at odds with the approximate $E^{-2}$ shape expected from diffusive shock acceleration. The presence of turbulent extragalactic magnetic fields in the region between the closest sources and the Earth can significantly modify the observed CR spectrum with respect to that emitted by the sources, reducing the flux of low-rigidity particles that reach the Earth. We here take into account this magnetic horizon effect in the combined fit of the spectrum and shower depth distributions, exploring the possibility that a spectrum for the high-energy population sources with a shape closer to $E^{-2}$ be able to explain the observations. We find that a large inter-source separation $d_{\rm s}$ and a large magnetic field RMS amplitude within the Local Supercluster region, such that $B_{\rm rms}\simeq 100\,{\rm nG}\,(40\,{\rm Mpc}/d_{\rm s})\sqrt{25\,{\rm kpc}/L_{\rm coh}}$, are needed to interpret the data within this scenario, where $L_{\rm coh}$ is the magnetic field coherence length.

Cosmogenic neutrinos are expected to originate in the extragalactic propagation of ultra-high-energy cosmic rays (UHECRs), as a result of their interactions with background photons. Due to these reactions, the visible Universe in UHECRs is more limited than in neutrinos, which instead could reach us without interacting after traveling cosmological distances. In this contribution, we exploit a multimessenger approach by computing the expected energy spectrum and mass composition of UHECRs at Earth corresponding to combinations of spectral parameters and mass composition at their sources, as well as parameters related to the UHECR source distribution, and by determining, at the same time, the associated cosmogenic neutrino fluxes. By comparing the expected UHECR observables to the energy spectrum and mass composition measured at the Pierre Auger Observatory above $10^{17.8}$ eV and the expected neutrino fluxes to the most updated neutrino limits, we show the dependence of the neutrino fluxes on the characteristics of the the properties of the potential sources of UHECRs, such as their cosmological evolution and maximum redshift. In addition, the fraction of protons compatible with the data is also investigated in terms of expected neutrino fluxes.

The Pierre Auger Observatory uses fluorescence telescopes in conjunction with ground level particle detectors to measure high-energy cosmic rays and reconstruct, with greater precision, their arrival direction, their energy and the depth of shower maximum. The depth of shower maximum is important to infer cosmic ray mass composition. The fluorescence detector is capable of directly measuring the longitudinal shower development, which is used to reconstruct the cosmic ray energy and the atmospheric depth of shower maximum. However, given the limited field of view of the fluorescence detector, the shower profile is not always fully contained within the detector observation volume. Therefore, considerations need to be taken in order to reconstruct some events. In this contribution we will describe the method that the Pierre Auger Collaboration uses to reconstruct the longitudinal profiles of showers and present the details of its performance, namely its resolution and systematic uncertainties.

The Pierre Auger Observatory uses 27 large-aperture wide-angle Schmidt telescopes to measure the longitudinal profile of air showers using the air-fluorescence technique. Up to the year 2013, the absolute calibration of the telescopes was performed by mounting a uniform large-diameter light source on each of the telescopes and illuminating the entire aperture with a known photon flux. Due to the high amount of work and person-power required, this procedure was only carried out roughly once every three years, and a relative calibration was performed every night to track short-term changes. Since 2013, only the relative calibration has been performed. In this paper, we present a novel tool for the absolute end-to-end calibration of the fluorescence detectors, the XY-Scanner. The XY-Scanner uses a portable integrating sphere as a light source, which has been absolutely calibrated. This light source is installed onto a motorized rail system and moved across the aperture of each telescope. We mimic the illumination of the entire aperture by flashing the light source at ∼ 1700 positions evenly distributed across the telescope aperture. For the absolute calibration of the light source, we built a dedicated setup that uses a NIST-calibrated photodiode to measure the average photon flux and a PMT to track the pulse-to-pulse stability. We present the laboratory setups used to study the characteristics of the employed light sources and discuss the inter-calibration between selected telescopes.

ELVES are being studied since 2013 with the twenty-four FD Telescopes of the Pierre Auger Observatory, in the province of Mendoza (Argentina), the world’s largest facility for the study of ultra-high energy cosmic rays. This study exploits a dedicated trigger and extended readout. Since December 2020, this trigger has been extended to the three High Elevation Auger Telescopes (HEAT), which observe the night sky at elevation angles between 30 and 60 degrees, allowing a study of ELVES from closer lightning. The high time resolution of the Auger telescopes allows us to upgrade reconstruction algorithms and to do detailed studies on multiple ELVES. The origin of multiple elves can be studied by analyzing the time difference and the amplitude ratio between flashes and comparing them with the properties of radio signals detected by the ENTLN lightning network since 2018. A fraction of multi-ELVES can also be interpreted as halos following ELVES. Halos are disc shaped light transients emitted at 70-80 km altitudes, appearing at the center of the ELVES rings, due to the rearrangement of electric charges at the base of ionosphere after a strong lightning event.

Exploring physics at energies beyond the reach of human-built accelerators by studying cosmic rays requires an accurate reconstruction of their energy. At the highest energies, cosmic rays are indirectly measured by observing a shower of secondary particles produced by their interaction in the atmosphere. At the Pierre Auger Observatory, the energy of the primary particle is either reconstructed from measurements of the emitted fluorescence light, produced when secondary particles travel through the atmosphere, or shower particles detected with the surface detector at the ground. The surface detector comprises a triangular grid of water-Cherenkov detectors that measure the shower footprint at the ground level. With deep learning, large simulation data sets can be used to train neural networks for reconstruction purposes. In this work, we present an application of a neural network to estimate the energy of the primary particle from the surface detector data by exploiting the time structure of the particle footprint. When evaluating the precision of the method on air shower simulations, we find the potential to significantly reduce the composition bias compared to methods based on fitting the lateral signal distribution. Furthermore, we investigate possible biases arising from systematic differences between simulations and data.

A new radio interferometric technique was recently developed that takes into account time lags caused by the three-dimensional dependency of the refractive index in the atmosphere. It enables us to track the extensive air shower while it propagates through the atmosphere. Using this technique, properties of the air shower can be estimated, like the depth of maximum and the axis of propagation. In order to apply this method, strict constraints on the time-synchronisation between radio antennas in an array must be satisfied. In this contribution, we show that the Auger Engineering Radio Array can meet these timing criteria by operating a time reference beacon. We will show how this enables us to reconstruct air shower properties using the radio interferometric technique.

The distribution of aerosols in the atmosphere above cosmic ray fluorescence detectors must be well characterised in order to precisely recover extensive air shower properties such as the calorimetric energy, $E$, and depth of shower maximum, $X_\mathrm{max}$. The Pierre Auger Observatory uses two centrally located laser facilities to measure the vertical aerosol optical depth profile (VAOD) every hour. It is assumed that the night with the clearest atmosphere each year is effectively aerosol free and that it is an appropriate reference to set the absolute scale of VAOD throughout that year. We review the successes of this method and its associated sources of systematic uncertainty, then present a new cross-check of measured VAOD using air shower events observed in stereo mode. Special attention is paid to quantifying the uncertainties on this result. As the technique is only sensitive to VAOD bias at a fixed altitude, we combine it with a study of aerosol profiles independently measured using a less-sensitive Raman lidar system. This allows us to derive a complete model of the upper limit on the possible bias in the average measured VAOD, which we attribute primarily to an uncertainty on whether the annual reference nights are completely aerosol free. We formulate a correction for this bias and apply it retroactively to all VAOD measurements, then repeat the analysis of the complete air shower dataset and discuss the small but significant effect of this new correction on $E$ and $X_\mathrm{max}$. This correction is now fully integrated into the Auger analysis chain.

The determination of the energy spectrum features with low systematic uncertainty is crucial for interpreting the nature of cosmic rays. In this study, we conducted a measurement of the energy spectrum at the Pierre Auger Observatory using a surface detector with a calorimetric energy scale indirectly set by a fluorescence detector. The surface detector consists of an array of water-Cherenkov detectors that extends over 3000 km 2 with 1500 m spacing. Additionally, two nested arrays of the same kind with 750 m and 433 m spacing were utilized to lower the energy threshold of the measurements. This contribution presents, for the first time, the spectrum measured with the 433 m array, which reduces the energy threshold down to 63 PeV, nearly half the energy at which we previously published a steepening using the 750 m array. Our measurements include a characterization of the spectral features of the flux steepening around 230 PeV, known as the second-knee. The study benefits from a nearly 100% duty cycle and geometrical exposure. Notably, this is the first simultaneous measurement of the second knee energy and spectral indexes before and after the break, using a surface detector with an energy scale predominantly independent of air shower simulations and assumptions regarding hadronic interaction models.

We present a new analysis for estimating the depth of the maximum of air-shower profiles, $X_\mathrm{max}$, to investigate the evolution of the ultra-high-energy cosmic ray mass composition from 3 to 100 EeV. We use a recently developed deep-learning-based technique for the reconstruction of $X_\mathrm{max}$ from the data of the surface detector of the Pierre Auger Observatory. To avoid systematic uncertainties arising from hadronic interaction models in the simulation of surface detector data, we calibrate the new reconstruction technique with observations of the fluorescence detector. Using the novel analysis, we have a 10-fold increase of statistics at $E>5$ EeV with respect to fluorescence detector data. We are able, for the first time, to study the evolution of the mean and standard deviation of the $X_\mathrm{max}$ distributions up to 100 EeV. We find an excellent agreement with fluorescence observations and confirm the increase of the mean logarithmic mass and a decrease of the $X_\mathrm{max}$ fluctuations with energy. The $X_\mathrm{max}$ measurement at the highest --- so far inaccessible --- energies is consistent with a pure mass composition and a mean logarithmic mass of around $\sim3$ (estimated using the Sibyll 2.3d and the EPOS-LHC hadronic interaction models). Furthermore, with the increase in statistics, we find indications for a structure beyond a constant elongation rate in the evolution of $X_\mathrm{max}$.

The detection of ultra-high-energy cosmic rays by means of giant detector arrays is often limited by the saturation of the recorded signals near the impact point of the shower core at the ground, where the particle density dramatically increases. The saturation affects in particular the highest energy events, worsening the systematic uncertainties in the reconstruction of the shower characteristics. The upgrade of the Pierre Auger Observatory, called AugerPrime, includes the installation of an 1-inch Small PhotoMultiplier Tube (SPMT) inside each water-Cherenkov station (WCD) of the surface detector array. The SPMT allows an unambiguous measurement of signals down to about 250m from the shower core, thus reducing the number of events featuring a saturated station to a negligible level. In addition, a 3.8m$^2$ plastic scintillator (Scintillator Surface Detector, SSD) is installed on top of each WCD. The SSD is designed to match the WCD (with SPMT) dynamic range, providing a complementary measurement of the shower components up to the highest energies. In this work, the design and performances of the upgraded AugerPrime surface-detector stations in the extended dynamic range are described, highlighting the accuracy of the measurements. A first analysis employing the unsaturated signals in the event reconstruction is also presented.

The Auger Engineering Radio Array (AERA) is currently the largest facility to measure radio emissions from extensive air showers. Located at the Pierre Auger Observatory in Argentina, it comprises 153 autonomous radio-detector stations, covering an area of 17 km$^2$, and measures radio waves in the frequency range from 30 to 80 MHz. For the correct interpretation of data collected by AERA stations, the detector response has to be carefully calibrated. In the past, this was done by measuring the analogue chain in the laboratory, in addition to simulating and measuring the directional response of the antenna. In this work, we perform an absolute calibration by using the radio emission from the Galaxy. A model of the full radio sky is propagated through the system response, including the antenna, filters and amplifiers, and compared to the average spectra recorded by the stations. The method to determine the calibration constants, as the results, for each antenna will be presented. The behavior of the calibration constants is studied as a function of time from 2014 to 2020. There is no relevant ageing effect over a timescale of 10 years, showing that radio detectors could help to monitor possible ageing effects of other detector systems during long-term operations, stressing their importance in determining an absolute energy scale.

After more than 15 years of successful operation, the Pierre Auger Observatory is currently undergoing a major upgrade called AugerPrime. The aim is to study the mass composition of ultra-high-energy cosmic rays. Part of the upgrade program consists in installing a Short Aperiodic Loaded Loop Antenna (SALLA) atop each of the 1660 water-Cherenkov detectors. To obtain an absolute calibration for the SALLA, the frequency and directionally dependent antenna response (or vector effective length) must be known. The characteristics of the SALLA depend on various parameters, most prominent is the considered frequency of reception and the antenna geometry. Moreover, the interaction with the structure elements and the presence of the ground has an impact. The measurement of the characteristics of the SALLA is a complex experimental effort. In this view, investigation by numerical antenna simulations provides an important and useful tool. In this contribution, we describe the method used to calculate the vector equivalent length of the SALLA with an advanced and widely used software for antenna simulations like the Numerical Electromagnetics Code (NEC).

The surface detector (SD) of the Pierre Auger Observatory, consisting of 1660 water-Cherenkov detectors (WCDs), covers 3000 km$^2$ in the Argentinian pampa. Thanks to the high efficiency of WCDs in detecting gamma rays, it represents a unique instrument for studying downward Terrestrial Gamma-ray Flashes (TGFs) over a large area. Peculiar events, likely related to downward TGFs, were detected at the Auger Observatory. Their experimental signature and time evolution are very different from those of a shower produced by an ultrahigh-energy cosmic ray. They happen in coincidence with low thunderclouds and lightning, and their large deposited energy at the ground is compatible with that of a standard downward TGF with the source a few kilometers above the ground. A new trigger algorithm to increase the TGF-like event statistics was installed in the whole array. The study of the performance of the new trigger system during the lightning season is ongoing and will provide a handle to develop improved algorithms to implement in the Auger upgraded electronic boards. The available data sample, even if small, can give important clues about the TGF production models, in particular, the shape of WCD signals. Moreover, the SD allows us to observe more than one point in the TGF beam, providing information on the emission angle.

The Fluorescence Detector (FD) of the Pierre Auger Observatory has a large exposure to search for upward-going showers. Constraints have been recently obtained by using 14 years of FD data searching for upward-going showers in the zenith angle range $[110^\circ, 180^\circ]$. In this work, we translate these bounds to upper limits of a possible flux of ultra high energy tau-leptons escaping from the Earth into the atmosphere. Such a mechanism could explain the observation of "anomalous pulses" made by ANITA, that indicated the existence of upward-going air showers with energies above $10^{17}$ eV. As tau neutrinos would be absorbed within the Earth at the deduced angles and energies, a flux of upward-going taus could only be resulted from an unknown type of ultra high energy Beyond Standard Model particle penetrating the Earth with little attenuation, and then creating tau-leptons through interactions within a maximum depth of about 50 km before exiting. We test classes of such models in a generic way and determine upper flux limits of ultra high energy BSM particles as a function of their unknown cross section with matter.

To understand the physics of cosmic rays at the highest energies, it is mandatory to have an accurate knowledge of their mass composition. Since the mass of the primary particles cannot be measured directly, we have to rely on the analysis of mass-sensitive observables to gain insights into this composition. A promising observable for this purpose is the number of muons at the ground relative to that of an air shower induced by a proton primary of the same energy and inclination angle, commonly referred to as the relative muon number $R_\mathrm{µ}$. Due to the complexity of shower footprints, the extraction of $R_\mathrm{µ}$ from measurements is a challenging task and intractable to solve using analytic approaches. We, therefore, reconstruct $R_\mathrm{µ}$ by exploiting the spatial and temporal information of the signals induced by shower particles using neural networks. Using this data-driven approach permits us to tackle this task without the need of modeling the underlying physics and, simultaneously, gives us insights into the feasibility of such an approach. In this contribution, we summarize the progress of the deep-learning-based approach to estimate $R_{\mathrm{µ}}$ using simulated surface detector data of the Pierre Auger Observatory. Instead of using single architecture, we present different network designs verifying that they reach similar results. Moreover, we demonstrate the potential for estimating $R_\mathrm{µ}$ using the scintillator surface detector of the AugerPrime upgrade.

The AugerPrime upgrade of the Pierre Auger Observatory converts the existing surface detector, consisting of an array of 1660 water-Cherenkov detectors (WCDs), into a multi-hybrid instrument. This upgrade required improved surface detector electronics and acquisition software to accommodate the new detection channels corresponding to the scintillator surface detectors, radio detector antennas, and the underground muon detectors as well as the additional, small area photomultiplier in the WCDs. In this work, we present an overview of the data acquisition software, both at the level of individual detector stations and the central data acquisition system. We highlight the modifications performed to handle the new multi-hybrid data of AugerPrime and cope with surface detector stations with different hardware configurations operating simultaneously in the array during the transition phase.

The number of muons produced in extensive air showers is a reliable proxy for the amount of hadron production that occurs during the shower development. It is, therefore, an important observable in the context of identifying the mass composition of ultrahigh-energy cosmic rays. Beyond LHC energies, however, hadronic multiparticle production as it occurs in air showers from ultrahigh-energy cosmic rays, is poorly understood, and currently there is little to no way to directly test it experimentally. In simulations, current models of hadronic interactions are unable to produce the average number of muons that is measured by multiple air-shower experiments. In this work, we estimate the number of muons in vertical hybrid events detected by both the fluorescence and surface detectors of the Pierre Auger Observatory above a primary energy of 3 EeV. To reconstruct the signal, we use a model of the water-Cherenkov detector responses that is based on air-shower universality. We take into account the effect of the longitudinal shower development on the lateral distribution of the signal at the ground, as well as the primary energy estimated from the calorimetric energy deposition of the air shower. In this way, we are able to estimate the amount of muons created in vertical showers, relative to expectations from simulated showers using modern hadronic interaction models.

After seventeen years of operation, the first phase of measurements at the Pierre Auger Observatory finished and the process of upgrading it began. In this work, we present distributions of the depth of air-shower maximum, $X_\text{max}$, using profiles measured with the fluorescence detector of the Pierre Auger Observatory. The analysis is based on the Phase I data collected from 01 December 2004 to 31 December 2021. The $X_\text{max}$ measurements take advantage of an improved evaluation of the vertical aerosol optical depth and reconstruction of the shower profiles. We present the energy dependence of the mean and standard deviation of the $X_\text{max}$ distributions above $10^{17.8}$ eV. Both $X_\text{max}$ moments are corrected for detector effects and interpreted in terms of the mean logarithmic mass and variance of the masses by comparing them to the predictions of post-LHC hadronic interaction models. We corroborate our earlier findings regarding the change of the elongation rate of the mean $X_\text{max}$ at $10^{18.3}$ eV with higher significance. We also confirm, with four more years of data compared to the last results presented in 2019, that around the ankle in the cosmic rays spectrum, the proton component gradually disappears and that intermediate mass nuclei dominate the composition at ultra-high energies.

The origin of ultra-high-energy cosmic rays (UHECRs), particles from outer space with energies~$E \geq 1\;$EeV, is still unknown, though the near-isotropy of their arrival direction distribution excludes a dominant Galactic contribution, and interactions with background photons prevent them from travelling cosmologically large distances. This suggests that their sources must be searched for in nearby galaxy groups and clusters. Deflections by intergalactic and Galactic magnetic fields are expected to hinder such searches but not preclude them altogether. So far, the only anisotropy detected with statistical significance $\geq 5\sigma$ is a modulation in right ascension in the data from the Pierre Auger Observatory at~$E \geq 8\;$EeV interpretable as a 7% dipole moment. Various hints for higher-energy, smaller-scale anisotropies have been reported. UHECR arrival direction data from both the Pierre Auger Observatory and the Telescope Array experiment have been searched for anisotropies by a working group with members from both collaborations; combining the two datasets requires a cross-calibration procedure due to the different systematic uncertainties on energy measurements but allows us to perform analyses that are less model-dependent than what can be done with partial sky coverage. We report a significant dipole pointing away from the Galactic Center and a ${\sim}4.6\sigma$ anisotropy found when comparing the directions of UHECRs with a catalog of starburst galaxies.