Arrival Directions Of Cosmic Rays Research Articles

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.

Modeling of TeV Galactic Cosmic-ray Anisotropy based on Intensity Mapping in an MHD Model Heliosphere

Cosmic rays do not arrive at the Earth uniformly. Recent experiments have consistently observed small anisotropies with amplitudes of ∼0.2% in the arrival directions of cosmic rays at TeV energies. We perform the modeling of the cosmic-ray anisotropy at TeV energies using the intensity-mapping method based on Liouville’s theorem. This work indicates unrealistically small-scale ansiotropies with <∼10° angular scales in the distribution of the cosmic-ray relative intensity at the outer boundary of the heliosphere. We would possibly need to resolve an issue that the experimental data covers ten years while the Magnetohydrodynamics (MHD) model heliosphere used in this work is only a single snapshot at a certain moment. Performing the intensity-mapping for multiple snapshots of the MHD model heliosphere and taking the average of the results would improve the results of this work.

Revisiting the implications of Liouville's theorem to the anisotropy of cosmic rays

We present a solution to Liouville's equation for an ensemble of charged particles propagating in magnetic fields. The solution is presented using an expansion in spherical harmonics of the phase space density, allowing a direct interpretation of the distribution of arrival directions of cosmic rays. The results are found for chosen conditions of variability and source distributions. We show there are two conditions for an initially isotropic flux of particles to remain isotropic while traveling through a magnetic field: isotropy and homogeneity of the sources. In case isotropically-distributed sources inject particles continuously in time, a transient magnetic induced dipole will appear. This dipole will vanish if the system reaches a steady-state. The formalism is used to analyze the data measured by the Pierre Auger Observatory, contributing to the understanding of the dependence of the dipole amplitude with energy and predicting the energy in which the quadrupole signal should be measured.

Constraining models for the origin of ultra-high-energy cosmic rays with a novel combined analysis of arrival directions, spectrum, and composition data measured at the Pierre Auger Observatory

The combined fit of the measured energy spectrum and shower maximum depth distributions of ultra-high-energy cosmic rays is known to constrain the parameters of astrophysical models with homogeneous source distributions. Studies of the distribution of the cosmic-ray arrival directions show a better agreement with models in which a fraction of the flux is non-isotropic and associated with the nearby radio galaxy Centaurus A or with catalogs such as that of starburst galaxies. Here, we present a novel combination of both analyses by a simultaneous fit of arrival directions, energy spectrum, and composition data measured at the Pierre Auger Observatory. The model takes into account a rigidity-dependent magnetic field blurring and an energy-dependent evolution of the catalog contribution shaped by interactions during propagation. We find that a model containing a flux contribution from the starburst galaxy catalog of around 20% at 40 EeV with a magnetic field blurring of around 20° for a rigidity of 10 EV provides a fair simultaneous description of all three observables. The starburst galaxy model is favored with a significance of 4.5σ (considering experimental systematic effects) compared to a reference model with only homogeneously distributed background sources. By investigating a scenario with Centaurus A as a single source in combination with the homogeneous background, we confirm that this region of the sky provides the dominant contribution to the observed anisotropy signal. Models containing a catalog of jetted active galactic nuclei whose flux scales with the γ-ray emission are, however, disfavored as they cannot adequately describe the measured arrival directions.

UHECR anisotropy and extragalactic magnetic fields with the Telescope Array

We study the energy-dependent distribution of ultra-high energy cosmic ray arrival directions with respect to luminous matter in the local Universe. We use a specially designed test statistic (TS) that is robust to uncertainties of the galactic magnetic field. We generate realistic mock UHECR sets assuming various injected compositions, and different strengths of the extragalactic magnetic field (EGMF). Applying the TS to both mock sets and the Telescope Array Surface Detector data we constrain, for a given EGMF strength, the UHECR injected mass composition at energies above 10 EeV. At highest energies, higher than 100 EeV, only heavy composition — iron or at least silicon — is compatible with the data, irrespective of the EGMF strength. We then compare the obtained results with the direct Telescope Array fluorescence measurements of the UHECR mass composition. Requiring that the TA composition measurements are compatible with the arrival direction distribution allows us to constrain the parameters of the EGMF. It appears that light composition, measured by TA at around 10 EeV, is compatible with the arrival directions if the EGMF has strength of order 1 nG.

Large-scale anisotropies of extragalactic cosmic rays below the ankle

We study the anisotropies on large angular scales which can be present in the flux of cosmic rays reaching the Earth from a population of extragalactic sources, focusing on the energy range between the second knee and the ankle. In this energy range the particles are significantly affected by the Galactic magnetic field, which then plays a relevant role in shaping the expected anisotropies. The Galactic magnetic field deflects the cosmic-ray trajectories and thus modifies the anisotropies present outside the halo of the Galaxy, in particular the dipolar one associated with the translational motion of the observer (Compton-Getting effect). Also, due to the Galactic rotation, in the reference frame of an observer at Earth there is an electric component of the Galactic field that produces a small change in the particles' momentum. This acceleration depends on the cosmic-ray arrival direction and it hence induces anisotropies in the flux observed in a given energy range. We analyse the expected amplitude and phase of the resulting dipolar component of the flux and discuss the possibility to explain via these effects the change in the phase of the right-ascension distribution which is observed at energies around 1 EeV.

Arrival Directions of Cosmic Rays above 32 EeV from Phase One of the Pierre Auger Observatory

A promising energy range to look for angular correlations between cosmic rays of extragalactic origin and their sources is at the highest energies, above a few tens of EeV (1 EeV ≡ 1018 eV). Despite the flux of these particles being extremely low, the area of ∼3000 km2 covered at the Pierre Auger Observatory, and the 17 yr data-taking period of the Phase 1 of its operations, have enabled us to measure the arrival directions of more than 2600 ultra-high-energy cosmic rays above 32 EeV. We publish this data set, the largest available at such energies from an integrated exposure of 122,000 km2 sr yr, and search it for anisotropies over the 3.4π steradians covered with the Observatory. Evidence for a deviation in excess of isotropy at intermediate angular scales, with ∼15° Gaussian spread or ∼25° top-hat radius, is obtained at the 4σ significance level for cosmic-ray energies above ∼40 EeV.

Towards extracting cosmic magnetic field structures from cosmic-ray arrival directions

We present a novel method to search for structures of coherently aligned patterns in ultra-high energy cosmic-ray arrival directions simultaneously across the entire sky. This method can be used to obtain information on the Galactic magnetic field, in particular the integrated component perpendicular to the line of sight, from cosmic-ray data only. Using a likelihood-ratio approach, neighboring cosmic rays are related by rotatable, elliptically shaped density distributions and the significance of their alignment with respect to circular distributions is evaluated. In this way, a vector field tangential to the celestial sphere is fitted which approximates the local deflections in cosmic magnetic fields if significant deflection structures are detected. The sensitivity of the method is evaluated on the basis of astrophysical simulations of the ultra-high energy cosmic-ray sky, where a discriminative power between isotropic and signal-induced scenarios is found.

Anisotropies in the arrival directions of ultra-high-energy cosmic rays measured at the Pierre Auger Observatory

The search for anisotropies in the arrival directions of cosmic rays of the highest energies is essential in the ongoing effort to identify their sources. After more than 15 years of operation, the exposure of the Pierre Auger Observatory exceeds 100,000 km2 sr yr and several important scientific findings regarding anisotropy studies on various angular scales have been reported. In the large-scale regime, a dipolar modulation above an energy threshold of 8 EeV was discovered with a significance exceeding the 5σ confidence level. The dipole exhibits an amplitude of and its maximum points 125° away from the Galactic center, thus providing observational evidence for an extragalactic origin of the highest-energy cosmic rays. The analysis of the equatorial component was extended to lower energies down to 0.03 EeV where the dipole phase changes towards the Galactic center. At the highest energies, searches for small- and intermediate-scale anisotropies were performed. A model-independent search for overdensities as well as a correlation study with the direction of the nearby radio galaxy Centaurus A was conducted. Additionally, comparisons to four catalogs of candidate sources were performed using a maximum likelihood analysis. The comparison of the cosmic-ray arrival directions to a sample of starburst galaxies results in the highest post-trial significance, which lately surpassed the 4.5σ confidence level above 38 EeV. This review provides an overview of the Pierre Auger Collaboration’s most important findings concerning anisotropy in the arrival directions of ultra-high-energy cosmic rays.

The TeV Cosmic-Ray Bump: A Message from the Epsilon Indi or Epsilon Eridani Star?

A recently observed bump in the cosmic-ray (CR) spectrum from 0.3 to 30 TV is likely caused by a stellar bow shock that reaccelerates preexisting CRs, which further propagate to the Sun along the magnetic field lines. Along their way, these particles generate an Iroshnikov-Kraichnan (I-K) turbulence that controls their propagation and sustains the bump. Ad hoc fitting of the bump shape requires six adjustable parameters. Our model requires none, merely depending on three physical unknowns that we constrain using the fit. These are the shock Mach number, M, its size, l ⊥, and the distance to it, ζ obs. Altogether, they define the bump rigidity R 0. With M ≈ 1.5-1.6 and R 0 ≈ 4.4 TV, the model fits the data with ≈0.08% accuracy. The fit critically requires the I-K spectrum predicted by the model and rules out the alternatives. These attributes of the fit make an accidental agreement highly unlikely. In turn, the R 0 and M derived from the fit impose the distance-size relation on the shock: . For sufficiently large bow shocks, l ⊥ = 10-3-10-2 pc, we find the distance of ζ obs = 3-10 pc. Three promising stars in this range are the Scholz's Star at 6.8 pc, Epsilon Indi at 3.6 pc, and Epsilon Eridani at 3.2 pc. Based on their current positions and velocities, we propose that Epsilon Indi and Epsilon Eridani can produce the observed spectral bump. Moreover, Epsilon Eridani's position is only ~6°.7 off of the magnetic field direction in the solar neighborhood, which also changes the CR arrival direction distribution. Given the proximity of these stars, the bump appearance may change in a relatively short time.

Identification of patterns in cosmic-ray arrival directions using dynamic graph convolutional neural networks

We present a new approach for the identification of ultra-high energy cosmic rays from sources using dynamic graph convolutional neural networks. These networks are designed to handle sparsely arranged objects and to exploit their short- and long-range correlations. Our method searches for patterns in the arrival directions of cosmic rays, which are expected to result from coherent deflections in cosmic magnetic fields. The network discriminates astrophysical scenarios with source signatures from those with only isotropically distributed cosmic rays and allows for the identification of cosmic rays that belong to a deflection pattern. We use simulated astrophysical scenarios where the source density is the only free parameter to show how density limits can be derived. We apply this method to a public data set from the AGASA Observatory.

Large- and Medium-scale Anisotropies in the Arrival Directions of Cosmic Rays Observed with KASCADE-Grande

Abstract We search for anisotropies in the arrival directions of cosmic rays (CRs) observed by the KASCADE-Grande air shower experiment. The analysis is based on public data of about 23.7 million events with reconstructed primary energies above 1 PeV. We apply a novel maximum-likelihood reconstruction method for the CR anisotropy that compensates for spurious anisotropies induced by local detector effects. We find no evidence for a large-scale dipole anisotropy in the data, consistent with official results based on the conventional east–west derivative method. On the other hand, a subset of CRs with a median energy of 33 PeV shows strong evidence for a medium-scale feature with an angular diameter of 40°. After accounting for the look-elsewhere effect, the post-trial significance of this medium-scale feature is at the level of 4σ.

Cosmic ray small-scale anisotropies in quasi-linear theory

The distribution of arrival directions of cosmic rays is remarkably isotropic, which is a consequence of their repeated scattering in magnetic fields. Yet, high-statistics observatories like IceCube and HAWC have revealed the presence of small-scale structures at levels of 1 part in 10,000 at hundreds of TeV, which are not expected in typical diffusion models of cosmic rays. We follow up on the suggestion that these small-scale anisotropies are a result of cosmic ray streaming in a particular realisation of the turbulent magnetic field within a few scattering lengths in our local Galactic neighbourhood. So far, this hypothesis has been investigated mostly numerically, by tracking test particles through turbulent magnetic fields. For the first time, we present an analytical computation that through a perturbative approach allows predicting the angular power spectrum of cosmic ray arrival directions for a given model of turbulence. We illustrate this method for a simple, isotropic turbulence model and we find remarkable agreement with the results of numerical studies.

All-sky Measurement of the Anisotropy of Cosmic Rays at 10 TeV and Mapping of the Local Interstellar Magnetic Field

Abstract We present the first full-sky analysis of the cosmic ray arrival direction distribution with data collected by the High-Altitude Water Cherenkov and IceCube observatories in the northern and southern hemispheres at the same median primary particle energy of 10 TeV. The combined sky map and angular power spectrum largely eliminate biases that result from partial sky coverage and present a key to probe into the propagation properties of TeV cosmic rays through our local interstellar medium and the interaction between the interstellar and heliospheric magnetic fields. From the map, we determine the horizontal dipole components of the anisotropy δ 0h = 9.16 × 10−4 and δ 6h = 7.25 × 10−4 (±0.04 × 10−4). In addition, we infer the direction (229.°2 ± 3.°5 R.A., 11.°4 ± 3.°0 decl.) of the interstellar magnetic field from the boundary between large-scale excess and deficit regions from which we estimate the missing corresponding vertical dipole component of the large-scale anisotropy to be .

Search for Large-scale Anisotropy in the Arrival Direction of Cosmic Rays with KASCADE-Grande

Abstract We present the results of the search for large-scale anisotropies in the arrival directions of cosmic rays performed with the KASCADE-Grande experiment at energies higher than eV. To eliminate spurious anisotropies due to atmospheric or instrumental effects we apply the east–west method. We show, using the solar time distribution of the number of counts, that this technique allow us to remove correctly the count variations not associated to real anisotropies. By applying the east–west method we obtain the distribution of number of counts in intervals of 20 minutes of sidereal time. This distribution is then analyzed by searching for a dipole component; the significance of the amplitude of the first harmonic is 3.5σ, therefore, we derive its upper limit. The phase of the first harmonic is determined with an error of a few hours and is in agreement with the measurements obtained in the 1014 &lt; E &lt; 2 × 1015 eV energy range by the EAS-TOP, IceCube, and IceTop experiments. This supports the hypothesis of a change of the phase of the first harmonic at energies greater than ∼2 × 1014 eV.

Recent results from the Pierre Auger Observatory

In this paper some recent results from the Pierre Auger Collaboration are presented. These are the measurement of the energy spectrum of cosmic rays over a wide range of energies (1017.5 to above 1020 eV), studies of the cosmic-ray mass composition with the fluorescence and surface detector of the Observatory, the observation of a large-scale anisotropy in the arrival direction of cosmic rays above 8 × 1018 eV and indications of anisotropy at intermediate angular scales above 4 × 1019 eV. The astrophysical implications of the spectrum and composition results are also discussed. Finally the progress of the upgrade of the Observatory, AugerPrime is presented.

Investigating an angular correlation between nearby starburst galaxies and UHECRs with the Telescope Array experiment

The arrival directions of cosmic rays detected by the Pierre Auger Observatory (Auger) with energies above 39 EeV were recently reported to correlate with the positions of 23 nearby starburst galaxies (SBGs): in their best-fit model, 9.7% of the cosmic-ray flux originates from these objects and undergoes angular diffusion on a 12.9o scale. On the other hand, some of the SBGs on their list, including the brightest one (M82), are at northern declinations outside the Auger field of view. Data from detectors in the northern hemisphere would be needed to look for cosmic-ray excesses near these objects. In this work, we tested the Auger best-fit model against data collected by the Telescope Array (TA) in a 9-year period, without trying to re-optimize the model parameters for our dataset in order not to introduce statistical penalties. The resulting test statistic (double loglikelihood ratio) was – 1.00, corresponding to 1.1σ significance among isotropically generated random datasets, and to – 1.4σ significance among ones generated assuming the Auger best-fit model. In other words, our data is still insufficient to conclusively rule out either hypothesis. The ongoing fourfold expansion of TA will collect northern hemisphere data with much more statistics, improving our ability to discriminate between different flux models.

Physics Potential of a Radio Surface Array at the South Pole

A surface array of radio antennas will enhance the performance of the IceTop array and enable new, complementary science goals. First, the accuracy for cosmic-ray air showers will be increased since the radio array provides a calorimetric measurement of the electromagnetic component and is sensitive to the position of the shower maximum. This enhanced accuracy can be used to better measure the mass composition, to search for possible mass-dependent anisotropies in the arrival directions of cosmic rays, and for more thorough tests of hadronic interaction models. Second, the sensitivity of the radio array to inclined showers will increase the sky coverage for cosmic-ray measurements. Third, the radio array can be used to search for PeV photons from the Galactic Center. Since IceTop is planned to be enhanced by a scintillator array in the near future, a radio extension sharing the same infrastructure can be installed with minimal additional effort and excellent scientific prospects. The combination of ice-Cherenkov, scintillation, and radio detectors at IceCube will provide unprecedented accuracy for the study of highenergy Galactic cosmic rays.

Anisotropies of ultra-high energy cosmic rays dominated by a single source in the presence of deflections

This work presents a scenario of ultra-high energy cosmic ray source distribution where a nearby source is solely responsible for the anisotropies in arrival directions of cosmic rays while the rest of the sources contribute only isotropically. An analytical approach focused on large-scale anisotropies, which are influenced by deflections in a Kolmogorov-type turbulent magnetic field, is employed to provide more general results. When the recent Pierre Auger Observatory angular power spectrum above 8 EeV is used the restricted model gives, under the assumption of the small angle approximation, a solution where the RMS deflection with respect to the line of sight is αrms = (50-10+11)̂, while the relative flux from the single source η=0.03 ± 0.01. Furthermore, the solution can be translated into constraints on the source distance, luminosity, and extra-galactic magnetic field strength. For Centaurus A and the Virgo cluster the required relation between the coherence length and the RMS magnetic field strength is obtained: a coherence length of ∼ 100 kpc would imply the RMS field strength around 1 nG for iron dominated and above 10 nG for proton dominated composition. We also performed trajectory simulations with our publicly available code CRPropa to show that our analytical model can serve as a good approximation as long as the deflections in cosmic magnetic fields can be described as a random walk. The simulations showed that generally structured fields tend to suppress large-scale anisotropies, especially the dipole, compared to anisotropies at smaller scales described by higher multipoles.