Sources Of Ultra-high Energy Cosmic Rays Research Articles

What can be learnt from UHECR anisotropies observations

Context. Various signals of anisotropy of the ultra-high-energy cosmic rays (UHECRs) have recently been reported, whether at large angular scales, with a dipole modulation in right ascension observed in the data of the Pierre Auger observatory (Auger), as discussed in the first paper accompanying the present one, or at intermediate angular scales, with flux excesses identified in specific directions by Auger and the Telescope Array (TA) Collaborations. Aims. We investigated the implications of the current data regarding these intermediate scale anisotropies, and examined to what extent they can be used to shed light on the origin of UHECRs, and constrain the astrophysical and/or physical parameters of the viable source scenarios. We also investigated what could be learnt from the study of the evolution of the various UHECR anisotropy signals, and discussed the expected benefit of an increased exposure of the UHECR sky using future observatories. Methods. We simulated realistic UHECR sky maps for a wide range of astrophysical scenarios satisfying the current observational constraints, with the assumption that the UHECR source distribution follows that of the galaxies in the Universe, also implementing possible biases towards specific classes of sources. In each case, several scenarios were explored with different UHECR source compositions and spectra, a range of source densities and different models of the Galactic magnetic field. We also implemented the Auger sky coverage, and explored various levels of statistics. For each scenario, we produced 300 independent datasets on which we applied similar analyses as those recently used by the Auger Collaboration, searching for flux excesses through either blind or targeted searches and quantifying correlations with predefined source catalogues through a likelihood analysis. Results. We find the following. First, with reasonable choices of the parameters, the investigated astrophysical scenarios can easily account for the significance of the anisotropies reported by Auger, even with large source densities. Second, the direction in which the maximum flux excess is found in the Auger data differs from the region where it is found in most of our simulated datasets, although an angular distance as large as that between the Auger direction and the direction expected from the simulated models at infinite statistics, of the order of ∼20°, occurs in ∼25% of the cases. Third, for datasets simulated with the same underlying astrophysical scenario, and thus the same actual UHECR sources, the significance with which the isotropy hypothesis is rejected through the Auger likelihood analysis can be largest either when ‘all galaxies’ or when only ‘starburst’ galaxies are used to model the signal, depending on which model is used to model the Galactic magnetic field and the resulting deflections. Fourth, the study of the energy evolution of the anisotropy patterns can be very instructive and provide new astrophysical insight about the origin of the UHECRs. Fifth, the direction in which the most significant flux excess is found in the Auger dataset above 8 EeV appears to essentially disappear in the dataset above 32 EeV, and, conversely, the maximum excess at high energy has a much reduced significance in the lower energy dataset. Sixth, both of these appear to be very uncommon in the simulated datasets, which could point to a failure of some generic assumption in the investigated astrophysical scenarios, such as the dominance of one type of source with essentially the same composition and spectrum in the observed UHECR flux above the ankle. Seventh, given the currently observed level of anisotropy signals, a meaningful measurement of their energy evolution, say from 10 EeV to the highest energies, will require a significant increase in statistics and a new generation of UHECR observatories.

A Novel Model for the MeV Emission Line in GRB 221009A

Gamma-ray bursts (GRBs) have long been considered potential sources of ultrahigh-energy cosmic rays (UHECRs; with energy ≳1018 eV). In this work, we propose a novel model generating MeV emission lines in GRBs, which can constrain the properties of heavy nuclei that potentially exist in GRB jets. Specifically, we find that relativistic hydrogen-like high-atomic-number ions originating from the β decay of unstable nuclei and/or the recombination entrained in the GRB jet can generate narrow MeV emission lines through the de-excitation of excited electrons. This model can successfully explain the MeV emission line observed in the most luminous GRB ever recorded, GRB 221009A, with suitable parameters including a Lorentz factor γ ∼ 820–1700 and a total mass of heavy nuclei M tot ∼ 1023–1026 g. Especially, the emission line broadening can be reasonably attributed to both the expansion of the jet shell and the thermal motion of nuclei, naturally resulting in a narrow width (σ line/E line ≲ 0.2) consistent with the observation. Furthermore, we predict that different GRBs can exhibit lines in different bands with various evolving behaviors, which might be confirmed with further observations. Finally, our model provides indirect evidence that GRBs may be one of the sources of UHECRs.

Modified Temperature–Redshift Relation and Ultra-high-energy Cosmic Ray Propagation

We reexamine the interactions of ultra-high-energy cosmic rays (UHECRs) with photons from the cosmic microwave background (CMB) under a changed, locally nonlinear temperature–redshift relation T(z). This changed temperature–redshift relation has recently been suggested by the postulate of subjecting thermalized and isotropic photon gases such as the CMB to an SU(2) rather than a U(1) gauge group. This modification of ΛCDM is called SU(2)CMB, and some cosmological parameters obtained by SU(2)CMB seem to be in better agreement with local measurements of the same quantities, in particular H 0 and S8. In this work, we apply the reduced CMB photon density under SU(2)CMB to the propagation of UHECRs. This leads to a higher UHECR flux just below the ankle in the cosmic ray spectrum and slightly more cosmogenic neutrinos under otherwise equal conditions for emission and propagation. Most prominently, the proton flux is significantly increased below the ankle (5 × 1018 eV) for hard injection spectra and without considering the effects of magnetic fields. The reduction in CMB photon density also favors a decreased cosmic ray source evolution than the best fit using ΛCDM. In consequence, it seems that SU(2)CMB favors sources that evolve like the star formation rate, such as starburst galaxies and gamma-ray bursts, over active galactic nuclei as origins of UHECRs. We conclude that the question about the nature of primary sources of UHECRs is directly affected by the assumed temperature–redshift relation of the CMB.

Ultra-high-energy Cosmic-Ray Sources Can Be Gamma-Ray Dim

Ultra-high-energy cosmic rays (UHECRs), accelerated hadrons that can exceed energies of 1020 eV, are the highest-energy particles ever observed. While the sources producing UHECRs are still unknown, the Pierre Auger Observatory has detected a large-scale dipole anisotropy in the arrival directions of cosmic rays above 8 EeV. In this work, we explore whether resolved gamma-ray sources can reproduce the Auger dipole. We use various Fermi Large Area Telescope catalogs as sources of cosmic rays in CRPropa simulations. We find that in all cases, the simulated dipole has an amplitude significantly larger than that measured by Auger, even when considering large extragalactic magnetic field strengths and optimistic source weighting schemes. Our result implies that the resolved gamma-ray sources are insufficient to account for the population of sources producing the highest-energy cosmic rays, and there must exist a population of UHECR sources that lack gamma-ray emission or are unresolved by the current-generation gamma-ray telescopes.

Constraints on UHECR Sources and Extragalactic Magnetic Fields from Directional Anisotropies

A dipole anisotropy in ultra–high-energy cosmic ray (UHECR) arrival directions, of extragalactic origin, is now firmly established at energies E > 8 EeV. Furthermore, the UHECR angular power spectrum shows no power at smaller angular scales than the dipole, apart from hints of possible individual hot or warm spots for energy thresholds ≳40 EeV. Here we exploit the magnitude of the dipole and the limits on smaller-scale anisotropies to place constraints on two quantities: the extragalactic magnetic field (EGMF) and the number density of UHECR sources or the volumetric event rate if UHECR sources are transient. We also vary the bias between the extragalactic matter and the UHECR source densities, reflecting whether UHECR sources are preferentially found in over- or underdense regions, and find that little or no bias is favored. We follow Ding et al. (2021) in using the CosmicFlows-2 density distribution of the local universe as our baseline distribution of UHECR sources, but we improve and extend that work by employing an accurate and self-consistent treatment of interactions and energy losses during propagation. Deflections in the Galactic magnetic field are treated using either the full JF12 magnetic field model, with both random and coherent components, or just the coherent part, to bracket the impact of the GMF on the dipole anisotropy. This large-scale structure model gives good agreement with both the direction and magnitude of the measured dipole anisotropy and forms the basis for simulations of discrete sources and the inclusion of EGMF effects.

Muon measurements at the Pierre Auger Observatory

The Pierre Auger Observatory is the world’s largest detector for observation of ultra-high-energy cosmic rays (UHECRs) (above the energy of 10^{17}1017 eV). It consists of a Fluorescence Detector (FD) and an array of particle detectors known as the Surface Detector (SD). Observations of extensive air showers by the Observatory can be used to probe hadronic interactions at high energy, in a kinematic and energy region inaccessible to experiments at man-made accelerators and to measure the muon component of the shower. Air showers induced by different primaries have different muon contents. With increasing mass of the primary cosmic ray particle, it is expected that the muon content in the corresponding air showers should also increase. Therefore, the determination of the muon component in the air shower is crucial to infer the mass of the primary particle. This is a key ingredient in the searches conducted to pinpoint the sources of UHECRs. Recent results obtained from the Pierre Auger Observatory and other experiments indicate that all the shower simulations underestimate the number of muons in the showers compared to the data. This is the so-called muon deficit. In this paper we briefly review the muon measurements, and present in more detail recent results on fluctuations in the muon number. These results provide new insights into the origin of the muon deficit in air shower simulations and constrain the models of hadronic interactions at ultrahigh energies. With the current design of the surface detectors it is also difficult to reliably separate the contributions of muons to the SD signal from the contributions of photons, electrons, and positrons. Therefore, we also present a new method to extract the muon component of the signal time traces recorded by each SD station using recurrent neural networks. The combination of such algorithms, with the future data collected by the upgraded Pierre Auger Observatory, will be a major step forward, as we are likely to achieve an unprecedented resolution in mass estimation on an event-by-event basis.

A nearby source of ultra-high energy cosmic rays

Recently the Telescope Array collaboration reported an observation of cosmic ray event with very high energy 244 EeV (2.44 × 1020 eV). Importantly, the event is hard to correlate with the matter distribution in the local Universe, even after taking into account deflections in magnetic fields. This implies that the event is likely a nucleus with a large charge. An attenuation length of the nucleus of such a high energy in intergalactic space is quite small, therefore its source should be relatively close to our Galaxy. Using these arguments we derive a new upper bound on a distance to the closest ultra-high energy cosmic ray (UHECR) source and a lower bound on the UHECR source number density in general. The distance to the closest source should not exceed 5 Mpc at 95% C.L. and the 95% C.L. lower-bound on the sources number density is ρ > 1.0 × 10-4 Mpc-3. The number density of UHECR sources emitting heavy nuclei is constrained for the first time.

Binary Coalescences as Sources of Ultrahigh-Energy Cosmic Rays.

Binary coalescences are known sources of gravitational waves (GWs) and they encompass combinations of black holes (BHs) and neutron stars (NSs). Here we show that when BHs are embedded in magnetic fields (B's) larger than approximately 10^{10} G, charged particles colliding around their event horizons can easily have center-of-mass energies in the range of ultrahigh energies (≳10^{18} eV) and become more likely to escape. Such B-embedding and high-energy particles can take place in BH-NS binaries, or even in BH-BH binaries with one of the BHs being charged (with charge-to-mass ratios as small as 10^{-5}, which do not change GW waveforms) and having a residual accretion disk. Ultrahigh center-of-mass energies for particle collisions arise for basically any rotation parameter of the BH when B≳10^{10} G, meaning that it should be a common aspect in binaries, especially in BH-NS ones given the natural presence of a B onto the BH and charged particles due to the magnetosphere of the NS. We estimate that the number of ultrahigh center-of-mass collisions ranges from a few up to millions before the merger of binary compact systems. Thus, binary coalescences may also be efficient sources of ultrahigh energy cosmic rays (UHECRs) and constraints to NS/BH parameters would be possible if UHECRs are detected along with GWs.

A relook at the GZK neutrino-photon connection: impact of extra-galactic radio background & UHECR properties

Ultra-high energy cosmic rays (UHECRs) beyond the Greisen-Zatsepin-Kuzmin (GZK) cut-off provide us with a unique opportunity to understand the universe at extreme energies. Secondary GZK photons and GZK neutrinos associated with the same interaction are indeed interconnected and render access to multi-messenger analysis of UHECRs. The GZK photon flux is heavily attenuated due to the interaction with Cosmic Microwave Background (CMB) and the Extra-galactic Radio Background (ERB). The present estimate of the ERB comprising of several model uncertainties together with the ARCADE2 radio results in large propagation uncertainties in the GZK photon flux. On the other hand, the weakly interacting GZK neutrino flux is unaffected by these propagation effects. In this work, we make an updated estimate of the GZK photon and GZK neutrino fluxes considering a wide variation of both the production and propagation properties of the UHECR like, the spectral index, the cut-off energy of the primary spectrum, the distribution of sources and the uncertainties in the ERB estimation. We explore the detection prospects of the GZK fluxes with various present and upcoming UHECR and UHE neutrino detectors such as Auger, TA, GRAND, ANITA, ARA, IceCube and IceCube-Gen2. The predicted fluxes are found to be beyond the reach of the current detectors. In future, proposed IceCube-Gen2, Auger upgrade and GRAND experiments will have the sensitivity to the predicted GZK photon and GZK neutrino fluxes. Such detection can put constraints on the UHECR source properties and the propagation effects due to the ERB. We also propose an indirect limit on the GZK photon flux using the neutrino-photon connection for any future detection of GZK neutrinos by the IceCube-Gen2 detector. We find this limit to be consistent with our GZK flux predictions.

Reconstructing Galactic magnetic fields from local measurements for backtracking ultra-high-energy cosmic rays

Context. Ultra-high-energy cosmic rays (UHECRs) are highly energetic charged particles with energies exceeding 1018 eV. These energies are far greater than those achieved in Earth-bound accelerators, and identifying their sources and production mechanism can shed light on many open questions in both astrophysics and high-energy physics. However, due to the presence of the Galactic magnetic field (GMF) they are deflected, and hence the location of their true source on the plane of the sky (PoS) is concealed. The identification of UHECR sources is an open question, excacerbated by the large uncertainties in our current understanding of the three-dimensional structure of the GMF. This difficulty arises from the fact that currently all GMF observations are integrated along the line of sight (LoS). However, thanks to upcoming stellar optopolarimetric surveys as well as Gaia data on stellar parallaxes, we expect that local measurements of the GMF in the near future will become available. Aims. Given such a set of (sparse) local GMF measurements, the question is how to optimally use them in backtracking UHECRs through the Galaxy. In this paper, we evaluate the reconstruction of the GMF, in a limited region of the Galaxy, through Bayesian inference, using principles of information field theory. Methods. We employed methods of Bayesian statistical inference in order to estimate the posterior distribution of the GMF configuration within a certain region of the Galaxy from a set of sparse simulated local measurements. Given the energy, charge, and arrival direction of a UHECR, we could backtrack it through GMF configurations drawn from the posterior, and hence calculate the probability distribution of the true arrival directions on the PoS, by solving the equations of motion in each case. Results. We show that, for a weakly turbulent GMF, it is possible to correct for its effect on the observed arrival direction of UHECRs to within ~3°. For completely turbulent fields, we show that our procedure can still be used to significantly improve our knowledge on the true arrival direction of UHECRs.

Diffusive shock acceleration at EeV and associated multimessenger flux from ultra-fast outflows driven by active galactic nuclei

ABSTRACT Active galactic nuclei (AGN) can launch and sustain powerful winds featuring mildly relativistic velocity and wide opening angle. Such winds, known as ultra-fast outflows (UFOs), can develop a bubble structure characterized by a forward shock expanding in the host galaxy and a wind termination shock separating the fast, cool wind from the hot shocked wind. In this work, we explore whether diffusive shock acceleration can take place efficiently at the wind termination shock of UFOs. We calculate the spectrum of accelerated particles and find that protons can be energized up to the EeV range promoting UFOs to promising candidates for accelerating ultra-high energy cosmic rays (UHECRs). We also compute the associated gamma-ray and neutrino fluxes and compare them with available data in the literature. We observe that high-energy (HE) neutrinos are efficiently produced up to hundreds of PeV while the associated gamma rays could be efficiently absorbed beyond a few tens of GeV by the optical-ultraviolet AGN photon field. By assuming a typical source density of non-jetted AGN, we expect that UFOs could play a dominant role as diffuse sources of UHECRs and HE neutrinos. We finally apply our model to the recently observed NGC1068 and we find out that under specific parametric conditions an obscured UFO could provide a sizeable contribution to the observed gamma-ray flux while only contributing up to ∼10 per cent to the associated neutrino flux.

Feasibility of Correlated Extensive Air Shower Detection with a Distributed Cosmic-Ray Network

We explore the sensitivity offered by a global network of cosmic-ray detectors to a novel, unobserved phenomenon: widely separated simultaneous extended air showers. Existing localized observatories work independently to observe individual showers, offering insight into the source and nature of ultrahigh-energy cosmic rays. However no current observatory is large enough to provide sensitivity to anticipated processes such as the Gerasimova–Zatsepin effect or potential new physics that generate simultaneous air showers separated by hundreds to thousands of kilometers. A global network of consumer electronics (the Cosmic Rays Found In Smartphones (CRAYFIS) experiment), may provide a novel opportunity for observation of such phenomena. Two user scenarios are explored. In the first, with maximal user adoption, we find that statistically significant discoveries of spatially separated but coincident showers are possible within a couple years. In the second, more practical adoption model with 106 active devices, we find a worldwide CRAYFIS to be sensitive to novel “burst” phenomena where many simultaneous extensive air showers (EAS) occur at once.

Differences between the Pierre Auger Observatory and Telescope Array Spectra: Systematic Effects or Indication of a Local Source of Ultra-high-energy Cosmic Rays?

The Pierre Auger Observatory (PAO) and Telescope Array (TA) collaborations report significant differences in the observed energy spectra of ultra-high-energy cosmic rays (UHECRs) above 30 EeV. In this work we present a joint fit of TA and PAO data using the rigidity-dependent maximum energy model, including a full marginalization over all relevant parameters. We test two possible scenarios to explain these differences. One is that they are due to complex energy-dependent experimental systematics; the other is the presence of a local astrophysical source in the Northern Hemisphere, which is only visible by the TA experiment. We show that the astrophysical and systematic scenarios improve the explanation of the data equally well, compared to the scenario where both experiments observe the same UHECR flux from a cosmological source distribution and have energy-independent systematics. We test different mass compositions emitted from the local source and conclude that the data are best described by a source lying at a distance below 26 Mpc that emits cosmic rays dominated by the silicon mass group. We also discuss possible source candidates and the possible role of the putative local UHECR source in the observed TA anisotropy and in the differences in TA spectral data from different decl. bands.

Nuclear and electromagnetic cascades induced by ultra-high-energy cosmic rays in radio galaxies: implications for Centaurus A

ABSTRACT Very high energy (VHE) γ-rays ($\gtrsim\!\! 0.1\rm ~TeV$) and neutrinos are crucial for identifying accelerators of ultra-high-energy cosmic rays (UHECRs), but this is challenging especially for UHECR nuclei. In this work, we develop a numerical code to solve the transport equation for UHECRs and their secondaries, where both nuclear and electromagnetic cascades are taken into account self-consistently, considering steady UHECR accelerators such as radio galaxies. In particular, we focus on Centaurus A, which has been proposed as one of the most promising UHECR sources in the local Universe. Motivated by observations of extended VHE γ-ray emission from its kiloparsec-scale jet by the High Energy Stereoscopic System (H.E.S.S.), we study interactions between UHECRs accelerated in the large-scale jet and various target photon fields including blazar-like beamed core emission, and present a quantitative study on VHE γ-ray signatures of UHECR nuclei, including the photodisintegration and Bethe–Heitler pair production processes. We show that VHE γ-rays from UHECR nuclei could be detected by the ground-based γ-ray telescopes given that the dominant composition of UHECRs consists of intermediate-mass (such as oxygen) nuclei.

Effects of the Galactic Magnetic Field on the UHECR Correlation Studies with Starburst Galaxies

We estimate the biases caused by the coherent deflection of cosmic rays due to the Galactic magnetic field (GMF) in maximum likelihood analyses for searches of ultrahigh-energy cosmic-ray sources in the literature. We simulate mock event data sets with a set of assumptions for the starburst galaxy source model, coherent deflection by a GMF model, and mixed-mass composition. We then conduct a maximum likelihood analysis without accounting for the GMF in the same manner as previous studies. We find that the anisotropic fraction f ani is estimated to be systematically lower than the true value. We estimate the true parameters that are compatible with the best-fit parameters that were reported, and find that except for a narrow region with a large anisotropic fraction and a small separation angular scale, a wide parameter space is still compatible with the experimental results. We also develop a maximum likelihood method that takes the GMF model into account and confirm in Monte Carlo simulations that we can estimate the true parameters within a 1σ contour under the ideal condition that we know the event-by-event mass and the GMF.

Evaluations of uncertainties in simulations of propagation of ultrahigh-energy cosmic-ray nuclei derived from microscopic nuclear models

Photodisintegration is a main energy loss process for ultrahigh-energy cosmic-ray (UHECR) nuclei in intergalactic space. Therefore, it is crucial to understand systematic uncertainty in photodisintegration when simulating the propagation of UHECR nuclei. In this work, we calculated the cross sections using the random phase approximation (RPA) of density functional theory (DFT), a microscopic nuclear model. We calculated the E1 strength of 29 nuclei using three different density functionals. We obtained the cross sections of photonuclear reactions, including photodisintegration, with the E1 strength. Then, we implemented the cross sections in the cosmic-ray propagation code CRPropa. We found that assuming certain astrophysical parameter values, the difference between UHECR energy spectrum predictions using the RPA calculation and the default photodisintegration model in CRPropa can be more than the statistical uncertainty of the spectrum. We also found that the differences between the RPA calculations and CRPropa default in certain astrophysical parameters obtained by a combined fit of UHECR energy spectrum and composition data assuming a phenomenological model of UHECR sources can be more than the uncertainty of the data.

Effects of large-scale magnetic fields on the observed composition of ultrahigh-energy cosmic rays

Ultra high-energy (UHE) cosmic rays (CRs) from distant sources interact with intergalactic radiation fields, leading to their spallation and attenuation. They are also deflected in intergalactic magnetic fields (IGMFs), particularly those associated with Mpc-scale structures. These deflections extend the propagation times of CR particles, forming a magnetic horizon for each CR species. The cumulative cooling and interactions of a CR ensemble also modifies their spectral shape and composition observed on Earth. We construct a transport formulation to calculate the observed UHE CR spectral composition for 4 classes of source population. The effects on CR propagation brought about by IGMFs are modeled as scattering processes during transport, by centers associated with cosmic filaments. Our calculations demonstrate that IGMFs can have a marked effect on observed UHE CRs, and that source population models are degenerate with IGMF properties. Interpretation of observations, including the endorsement or rejection of any particular source classes, thus needs careful consideration of the structural properties and evolution of IGMFs. Future observations providing tighter constraints on IGMF properties will significantly improve confidence in assessing UHE CR sources and their intrinsic CR production properties.

Using the “least-deflected” subsamples of ultra-high energy cosmic rays to constrain source population(s)

Context. The source population(s) of ultra-high energy cosmic rays (UHECRs) with energies of ≥57 × 1018 eV (57 EeV) are still unknown and continue to be a subject of debate. The published arrival directions and energies of 303 UHECRs from the Pierre Auger Observatory and Telescope Array enable correlations with astronomical sources. However, deflections of UHECRs in the Galactic Magnetic Field (GMF) can be considerable, especially for heavy UHECR compositions. Aims. We aim to constrain the source(s) of UHECRs by focusing on the subset of UHECRs that experience minimal deflections by the Galactic magnetic field (GMF). Methods. We used Monte Carlo simulations of UHECR trajectories in a total of eight posited GMF models (and six UHECR compositions from H to Fe) to identify two subsamples of about 40 UHECRs. The H compositions of these subsamples suffer deflections of less than a few degrees in one (or most) of the GMFs. Both the total UHECR sample and the “least-deflected” (vs. the remaining “more-deflected”) subsamples of UHECRs were cross-correlated with catalogs of astronomical sources (at D ≲ 100 Mpc) and neutrino arrival directions. Results. For H compositions, the full sample of UHECRs is most closely correlated with Cen A, nearby (< 75 Mpc) radiogalaxies, and optically selected active galactic nuclei (AGNs); the least-deflected sub sample shows a most consistent correlation with nearby (D ≲ 25 Mpc) galaxies, although some GMF models show a preference for the IceCube muon-neutrino arrival detections. For oxygen compositions, the out-of-galaxy arrival directions of least-deflected UHECRs fall on the extragalactic plane (and thus close to nearby galaxies) in many GMFs. For Fe compositions, the out-of-galaxy UHECR arrival directions typically originate in a region ∼30 deg offset from Cen A, except in the case of the JF12 model; this offset can be decreased by re-scaling (by ∼50%) the magnitudes of the dipole and disk fields of the relevant GMFs.

Impact of the finite life-time of UHECR sources

The observational data on ultrahigh energy cosmic rays (UHECR), in particular their mass composition, show strong indications for extremely hard spectra of individual mass groups of CR nuclei at Earth. In this work, we show that such hard spectra can be the result of the finite life-time of UHECR sources, if a few individual sources dominate the UHECR flux at the highest energies. In this case, time delays induced by deflections in the turbulent extragalactic magnetic field as well as from the diffusive or advective escape from the source environment can suppress low-energy CRs, leading to a steepening of the observed spectrum. Considering radio galaxies as the main source of UHECRs, we discuss the necessary conditions that few individual sources dominate over the total contribution from the bulk of sources that have been active in the past. We provide two proof-of-principle scenarios showing that for a turbulent extragalactic magnetic field with a strength B and a coherence length l coh, the life-time of a source at a distance d src should satisfy t act ∼ (B/1 nG)2 (d src/10 Mpc)2 (l coh/1 Mpc) Myr to obtain the necessary hardening of the CR spectrum at Earth.

The science of ultra-high energy cosmic rays after more than 15 years of operation of the Pierre Auger Observatory

The Pierre Auger Observatory has been detecting ultra-high energy cosmic rays (UHECRs) for more than fifteen years. An essential feature of the Observatory is its hybrid design: cosmic rays above 100 PeV are detected through the observation of the associated air showers with different and complementary techniques, from surface detector arrays and fluorescence telescopes to radio antennas. The analyses of the multi-detector data have enabled high-statistics and high-precision studies of the energy spectrum, mass composition and distribution of arrival directions of UHECRs. The resulting picture is summarized in this contribution. While no discrete source of UHECRs has been identified so far, the extragalactic origin of the particles has been recently determined from the arrival directions above 8 EeV, and the ring is closing around nearby astrophysical sites at higher energies. Also, the established upper limits on fluxes of UHE neutrinos and photons have implications on dark matter and cosmological aspects that are also presented in this contribution.