Distribution Of Arrival Directions Research Articles

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.

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.

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.

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.

MultI-messenger probe of Cosmic Ray Origins: MICRO project

We present the milestones achieved by the MICRO (MultI-messenger probe of Cosmic Ray Origins) project. This multi-institute project consists of a study of bursting astrophysical sources as candidate sources for ultra-high-energy cosmic rays (UHECRs). We aim at identifying source classes that correlate best with existing observational data (arrival direction distribution, energy spectrum and primary mass composition) and to constrain the origin of UHECRs on the basis of the largest datasets acquired to this day. The study of the secondary fluxes of neutrinos and gamma rays will provide a powerful test of the most suitable astrophysical scenarios. For these achievements, a public software enabling a joint fit of both composition and flux data as a function of energy and direction is being developed. In addition, a modelling of transient sources is foreseen, including the treatment of hadronic interactions within the sources, which represents a novelty for UHECR simulation codes. This contribution will highlight the first results of the project and detail upcoming software releases, which will benefit the astroparticle community at large.

2022 report from the Auger-TA working group on UHECR arrival directions

After over 60 years, the powerful engines that accelerate ultra-high-energy cosmic rays (UHECRs) to the formidable energies at which we observe them from Earth remain mysterious. Assuming standard physics, we expect UHECR sources to lie within the local Universe (up to a few hundred Mpc). The distribution of matter in the local Universe is anisotropic, and we expect this anisotropy to be imprinted on the distribution of UHECR arrival directions. Even though intervening intergalactic and Galactic magnetic fields deflect charged UHECRs and can distort these anisotropies, some amount of information on the distribution of the sources is preserved. In this proceedings contribution, we present the results of the joint Pierre Auger Observatory and Telescope Array searches for (a) the largest-scale anisotropies (the harmonic dipole and quadrupole) and (b) correlations with a sample of nearby starburst galaxies and the 2MRS catalogue tracing stellar mass within 250 Mpc. This analysis updates our previous results with the most recent available data, notably with the addition of 3 years of new Telescope Array data. The main finding is a correlation between the arrival directions of 12.1%−3.1%+4.5% of UHECRs detected with E ≥ 38 EeV by Auger or with E ≳ 49 EeV by TA and the positions of nearby starburst galaxies on a 15.1°−3.0°+4.6° angular scale, with a 4.7σ post-trial significance, up from 4.2σ obtained in our previous study.

Updates on the Hotspot and the Perseus-Pisces supercluster Excess Observed by the Telescope Array Experiment

The Telescope Array (TA) experiment, the largest observatory studying ultra-high energy cosmic rays in the northern hemisphere, has reported evidence for two medium-scale anisotropies. The first, known as the TA hotspot, is an excess in the arrival direction distribution for events with energies greater than 5.7 × 1019 eV. More recently, an additional excess of events with energies greater than 1019.4 eV appearing in the direction of the Perseus-Pisces supercluster has been named the PPSC excess. In this presentation, we will update the status of the TA hotspot and the PPSC excess results using the most recent data measured by the TA surface detector array.

Galactic Contribution to the High-energy Neutrino Flux Found in Track-like IceCube Events

Astrophysical sources of neutrinos detected by large-scale neutrino telescopes remain uncertain. While there exist statistically significant observational indications that a part of the neutrino flux is produced by blazars, numerous theoretical studies suggest also the presence of potential Galactic point sources. Some of them have been observed in gamma rays above 100 TeV. Moreover, cosmic-ray interactions in the Galactic disk guarantee a diffuse neutrino flux. However, these Galactic neutrinos have not been unambiguously detected so far. Here we examine whether such a Galactic component is present among the observed neutrinos of the highest energies. We analyze public track-like IceCube events with estimated neutrino energies above 200 TeV. We examine the distribution of arrival directions of these neutrinos in the Galactic latitude b with the help of a simple unbinned, nonparametric test statistics, the median ∣b∣ over the sample. This distribution deviates from that implied by the null hypothesis of the neutrino flux isotropy, and is shifted toward lower ∣b∣ with the p-value of 4 × 10−5, corresponding to the statistical significance of 4.1σ. There exists a significant component of the high-energy neutrino flux of Galactic origin, matching well the multimessenger expectations from Tibet-ASγ observations of diffuse Galactic gamma rays at hundreds of TeV. Together with the previously established extragalactic associations, the Galactic component we report here implies that the neutrino sky is rich and is composed of contributions from various classes of sources.

Ultra-High energy cosmic rays

An overview of the status of the knowledge in the field of ultra-high energy cosmic rays is presented. The latest results on the spectrum, arrival direction distribution and composition measurements are summarized and some implications for the understanding of the cosmic ray origin and their propagation are discussed.

Surface detectors of the TAx4 experiment

Telescope Array (TA) is the largest ultrahigh energy cosmic-ray (UHECR) observatory in the Northern Hemisphere. It explores the origin of UHECRs by measuring their energy spectrum, arrival-direction distribution, and mass composition using a surface detector (SD) array covering approximately 700 km2 and fluorescence detector (FD) stations. TA has found evidence for a cluster of cosmic rays with energies greater than 57 EeV. In order to confirm this evidence with more data, it is necessary to increase the data collection rate. We have begun building an expansion of TA that we call TAx4. In this paper, we explain the motivation, design, technical features, and expected performance of the TAx4 SD. We also present TAx4’s current status and examples of the data that have already been collected.

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.

Ultrahigh-energy cosmic rays dipole and beyond

Recent data from the Pierre Auger Observatory has revealed the presence of a large-scale dipole in the arrival direction distribution of ultra-high energy cosmic rays (UHECR). In this work, we build up an understanding of the diffusive origin of such a dipolar behavior as well as its dependency on energy and astrophysical source assumptions such as extragalactic magnetic field strength and cosmic ray composition. We present a novel analytical approach for calculating the angular distribution of CR coming from a single source and discuss the regimes in which the steady-state dipole result is expected. We also present a semianalytical method for calculating the evolution with energy of the resultant dipole for an ensemble of sources. We show that a local source allows for a strong growth of the dipole with energy over a large energy range. The possibility of a transition from a dipolar to non-dipolar regime at the highest energies and its implications for the source density, magnetic field intensity, and cosmic ray composition are discussed.

Results of ultra-high-energy cosmic rays from the Telescope Array

The Telescope Array (TA) is the largest ultra-high-energy cosmic ray (UHECR) observatory in the northern hemisphere. It consists of 507 surface scintillator detectors covering approximately 700 km2, and three fluorescence telescope sites overlooking the surface array. The aim of the TA is to explore the origin and nature of UHECR by measuring the energy spectrum and the distribution of arrival directions and mass composition of UHECR. Here, the recent results obtained by the TA are reported. Additionally, two extensions are presented: an extension of the observation area (TAx4) for detecting the highest-energy cosmic rays and the TA Low-Energy extension (TALE) exploring the transition from galactic to extragalactic cosmic rays.

Performance and science reach of the Probe of Extreme Multimessenger Astrophysics for ultrahigh-energy particles

The Probe Of Extreme Multi-Messenger Astrophysics (POEMMA) is a potential NASA Astrophysics Probe-class mission designed to observe ultra-high energy cosmic rays (UHECRs) and cosmic neutrinos from space. POEMMA will monitor colossal volumes of the Earth's atmosphere to detect extensive air showers (EASs) produced by extremely energetic cosmic messengers: UHECRs above 20 EeV over the full sky and cosmic neutrinos above 20 PeV. We focus most of this study on the impact of POEMMA for UHECR science by simulating the detector response and mission performance for EAS from UHECRs. We show that POEMMA will provide a significant increase in the statistics of observed UHECRs at the highest energies over the entire sky. POEMMA will be the first UHECR fluorescence detector deployed in space that will provide high-quality stereoscopic observations of the longitudinal development of air showers. Therefore, it will be able to provide event-by-event estimates of the calorimetric energy and nuclear mass of UHECRs. The particle physics in the interactions limits the interpretation of the shower maximum on an event by event basis. In contrast, the calorimetric energy measurement is significantly less sensitive to the different possible final states in the early interactions. We study the prospects to discover the origin and nature of UHECRs using expectations for measurements of the energy spectrum, the distribution of arrival direction, and the atmospheric column depth at which the EAS longitudinal development reaches maximum. We also explore supplementary science capabilities of POEMMA through its sensitivity to particle interactions at extreme energies and its ability to detect ultra-high energy neutrinos and photons produced by top-down models including cosmic strings and super-heavy dark matter particle decay in the halo of the Milky Way.

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.

Deflections of UHECRs in the Galactic magnetic field

We report results of the first comprehensive, high resolution study of the deflections of UHECRs using a realistic model of the Galactic magnetic field and extending to sufficiently low rigidities, R ≡ E/Z ⩾ 1018V, to describe Fe in the UHE energy range above ∼55 EeV, or the mixed composition reported by the Pierre Auger Collaboration at the energy of the observed dipole anisotropy. We use the Jansson-Farrar (JF12) model, which has both a large scale coherent and a structured random component, and determine deflections for fifteen rigidities from 1018.0 to 1020.0 V, for two different coherence length choices for the random component, Lcoh = 30 pc and 100 pc. We also check the sensitivity of UHECR deflections to the particular realization of the random field, for 3 rigidity values. For each rigidity and field model studied, the UHECR arrival direction distribution is determined for an arbitrary source direction, by inverting the trajectories of > 5×107 isotropically-distributed anti-CRs of the given rigidity, which we backtrack using the code CRT. We present skyplots and tables characterizing the arrival directions, for representative 1o sources. Except at high rigidity, the pattern of multiple images is very complex and depends strongly on the coherence length and source direction. For almost all sources, average deflections grow rapidly as the rigidity falls below 10 EV and deflections commonly are greater than 90̂. Magnification and demagnification can be strong at almost all rigidities, and varies significantly with source direction. Much of the extragalactic celestial sphere, behind and south of the Galactic Center, cannot be seen in UHECRs below 10 EV. One empirical regularity is that the average deflection of UHECRs from a given source, while growing with decreasing rigidity and depending on source direction and Lcoh, is about twice as large as the RMS angular spread about the mean arrival direction (centroid), independently of source direction, rigidity or Lcoh, albeit with outliers. The pattern of deflections obtained with the coherent field alone can be significantly different than with the complete field model, even as regards the position of the centroid, for some source directions and rigidities. Multiple images, sometimes very widely separated, are common for small coherence length, especially for low rigidity.

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 .

Latest Cosmic Ray Results from IceTop and IceCube

The IceCube Neutrino Observatory at the geographic South Pole, with its surface array IceTop, detects three different components of extensive air showers: the total signal at the surface, low energy muons on the periphery of the showers, and high energy muons in the deep In Ice array of IceCube. These measurements enable determination of the energy spectrum and composition of cosmic rays from PeV to EeV energies, the anisotropy in the distribution of cosmic ray arrival directions, the muon density of cosmic ray air showers, and the PeV gamma-ray flux. Furthermore, IceTop can be used as a veto for the neutrino measurements. The latest results from these IceTop analyses will be presented along with future plans.

Ultrahigh-energy cosmic ray composition from the distribution of arrival directions

The sources of ultrahigh-energy cosmic rays (UHECRs) have been difficult to catch. It was recently pointed out that while sources of UHECR protons exhibit anisotropy patterns that become denser and compressed with rising energy, nucleus-emitting-sources give rise to a cepa stratis (onion-like) structure with layers that become more distant from the source position with rising energy. The peculiar shape of the hot spots from nucleus-accelerators is steered by the competition between energy loss during propagation and deflection on the Galactic magnetic field (GMF). Here, we run a full-blown simulation study to accurately characterize the deflections of UHECR nuclei in the GMF. We show that while the cepa stratis structure provides a global description of anisotropy patterns produced by UHECR nuclei en route to Earth, the hot spots are elongated depending on their location in the sky due to the regular structure of the GMF. We demonstrate that with a high-statistics sample at the high-energy-end of the spectrum, like the one to be collected by NASA's POEMMA mission, the energy dependence of the hot-spot contours could become a useful observable to identify the nuclear composition of UHECRs. This new method to determine the nature of the particle species is complementary to those using observables of extensive air showers, and therefore is unaffected by the large systematic uncertainties of hadronic interaction models.