Within the classical convection--diffusion approximation, we show that the angular distribution of cosmic rays (CRs) in a highly turbulent flow may exhibit significant small-scale anisotropies. The CR intensity angular power spectrum $ C_\ell $ is then a direct reflection of interstellar turbulence, from which one expects $ C_\ell\propto\ell^{-γ-1} $ for $ \ell\gg 1 $, where $ γ$ is the power-law turbulence spectral index. Observations by IceCube and HAWC at TeV energies can be explained approximately with the Kolmogorov law $ γ=5/3 $ with a convection velocity dispersion of 20 km/s on the scale of 10 pc.
The arrival directions of multi-TeV cosmic rays show significant anisotropies at small angular scales. It has been argued that this small scale structure is reflecting the local, turbulent magnetic field in the presence of a global dipole anisotropy in cosmic rays as determined by diffusion. This effect is analogous to weak gravitational lensing of temperature fluctuations of the cosmic microwave background. We show that the non-trivial power spectrum in this setup can be related to the properties of relative diffusion and we study the convergence of the angular power spectrum to a steady-stat…
We obtain the dipolar anisotropies in the arrival directions of ultra-high energy cosmic rays diffusing from nearby extragalactic sources. We discuss both the energy regime of spatial diffusion and the quasi-rectilinear one leading to just angular diffusion at higher energies. We obtain analytic results for the anisotropies from a single source which are validated using two different numerical simulations. For a scenario with a few sources in the local supercluster (with the closest source at a typical distance of few to tens of Mpc), we discuss the possible transition between the case in whic…
The spectral hardenings of cosmic ray nuclei above $\sim 200$ GV followed by softenings around 10 TV, the knee of the all-particle spectrum around PeV energies, as well as the pattern change of the amplitude and phase of the large-scale anisotropies around 100 TeV indicate the complexities of the origin and transportation of Galactic cosmic rays. It has been shown that nearby source(s) are most likely to be the cause of such spectral features of both the spectra and the anisotropies. In this work, we study the anisotropy features of different mass composition (or mass groups) of cosmic rays in…
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 mo…
The origin of Galactic cosmic rays (GCRs) remains a mystery after more than one century of their discovery. The diffusive propagation of charged particles in the turbulent Galactic magnetic field makes us unable to trace back to their acceleration sites. Nevertheless, nearby GCR source(s) may leave imprints on the locally measured energy spectra and the anisotropies of the arrival direction. In this work we propose a simple but natural description of the GCR production and propagation, within a two-zone disk-halo diffusion scenario together with a nearby source, to understand the up-to-date pr…
The large scale pattern in the arrival directions of extragalactic cosmic rays that reach the Earth is different from that of the flux arriving to the halo of the Galaxy as a result of the propagation through the galactic magnetic field. Two different effects are relevant in this process: deflections of trajectories and (de)acceleration by the electric field component due to the galactic rotation. The deflection of the cosmic ray trajectories makes the flux intensity arriving to the halo from some direction to appear reaching the Earth from another direction. This applies to any intrinsic anis…
Detailed simulations of the arrival directions of ultra-high energy cosmic rays are performed under the assumption of strong and structured extragalactic magnetic field (EGMF) models. Particles leaving Centaurus A, Virgo A, and Fornax A are propagated to Earth, and the simulated anisotropic signal is compared to the dipole and hotspots published by the Pierre Auger and Telescope Array Collaborations. The dominance of the EGMF structure on the arrival directions of events generated in local sources is shown. The absence of events from the Virgo A direction is related to the strong deviation cau…
The arrival directions of Galactic cosmic rays (CRs) are highly isotropic. This is expected from the presence of turbulent magnetic fields in our Galactic environment that repeatedly scatter charged CRs during propagation. However, various CR observatories have identified weak anisotropies of various angular sizes and with relative intensities of up to a level of 1 part in 1,000. Whereas large-scale anisotropies are generally predicted by standard diffusion models, the appearance of small-scale anisotropies down to an angular size of 10 degrees is surprising. In this review, we summarise the c…
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, …
The arrival directions of multi-TeV cosmic rays show significant anisotropies at small angular scales. It has been argued that this small-scale structure can naturally arise from cosmic ray scattering in local turbulent magnetic fields that distort a global dipole anisotropy set by diffusion. We study this effect in terms of the power spectrum of cosmic ray arrival directions and show that the strength of small-scale anisotropies is related to properties of relative diffusion. We provide a formalism for how these power spectra can be inferred from simulations and motivate a simple analytic ext…
Cosmic ray anisotropy has been observed in a wide energy range and at different angular scales by a variety of experiments over the past decade. However, no comprehensive or satisfactory explanation has been put forth to date. The arrival distribution of cosmic rays at Earth is the convolution of the distribution of their sources and of the effects of geometry and properties of the magnetic field through which particles propagate. It is generally believed that the anisotropy topology at the largest angular scale is adiabatically shaped by diffusion in the structured interstellar magnetic field…
The propagation of cosmic rays (CRs) in turbulent interstellar magnetic fields is typically described as a spatial diffusion process. This formalism predicts only a small deviation from an isotropic CR distribution in the form of a dipole in the direction of the CR density gradient or relative background flow. We show that the existence of a global CR dipole moment necessarily generates a spectrum of higher multipole moments in the local CR distribution. These "anomalous" anisotropies are a direct consequence of Liouville's theorem in the presence of a local turbulent magnetic field. We show t…
IceCube detects more than 100,000 neutrinos per year in the GeV- to PeV-energy range. Among those, we have isolated a flux of high-energy cosmic neutrinos. I will discuss the instrument, the analysis of the data, the significance of the discovery of cosmic neutrinos, and the recent multi-messenger observation of a flaring TeV blazar in coincidence with the IceCube neutrino alert IC170922.
Important observational results have been recently reported on the angular distributions of cosmic rays at all energies, calling into question the perception of cosmic rays a decade ago. These results together with their in-progress interpretations are summarised in this review paper, covering both large-scale and small-scale anisotropies from TeV energies to the highest ones. While the magnetic field in the Galaxy has long been considered as an external data imprinting a quasi-random walk to particles and thus shaping the angular distributions of Galactic cosmic rays through the induced avera…
Searches for large-scale anisotropies in the distribution of arrival directions of cosmic rays detected above $\simeq 10 $PeV at the Pierre Auger Observatory are presented. Although no significant deviation from isotropy is revealed at present, some of the measurements suggest that future data will provide hints for large-scale anisotropies over a wide energy range. Those anisotropies would have amplitudes which are too small to be significantly observed within the current statistics. Assuming that the cosmic ray anisotropy is dominated by dipole and quadrupole moments in the EeV-energy range,…
These lectures review some of the techniques used to analyze the arrival direction distribution of Cosmic Rays, and some relevant results on the field.
The images of ultrahigh-energy cosmic ray sources get distorted, in an energy dependent way, by the effects of Galactic and extragalactic magnetic fields. These deflections can also affect the observed cosmic ray spectrum, specially when the sources are transient. We study scenarios in which one or a few nearby extragalactic sources, such as CenA or M81/M82, provide the dominant contribution to the cosmic ray flux above the ankle of the spectrum. We discuss the effects of the angular dispersion induced by the turbulent extragalactic magnetic fields, and the coherent deflections caused by the r…
We study the spectrum and anisotropies of ultrahigh energy cosmic ray transient sources, accounting for the effects of their propagation through the turbulent extragalactic magnetic fields. We consider either bursting sources or sources emitting since a given initial time. We analyse in detail the transition between the diffusive and the quasi-rectilinear regimes, describing some new features that could be present
We search for anisotropies in the arrival directions of cosmic rays 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 cosmic ray 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 cosmic r…
The recent results of the Pierre Auger Observatory on the possible correlation of Ultra High Energy Cosmic Rays events and several nearby discrete sources could be the starting point of a new era with charged particles astronomy. In this paper we introduce a simple model to determine the effects of any local distribution of sources on the expected flux. We consider two populations of sources: faraway sources uniformly distributed and local point sources. We study the effects on the expected flux of the local distribution of sources, referring also to the set of astrophysical objects whose corr…
Important observational results have been recently reported on the angular distributions of cosmic rays (CRs) at all energies, calling into question the perception of CRs a decade ago. These results together with their in-progress interpretations are summarized in this short overview paper, following the contribution presented at the XXV European Cosmic Ray Symposium.
We analyze the distribution of arrival directions of ultra-high energy cosmic rays recorded at the Pierre Auger Observatory in 10 years of operation. The data set, about three times larger than that used in earlier studies, includes arrival directions with zenith angles up to $80^\circ$, thus covering from $-90^\circ$ to $+45^\circ$ in declination. After updating the fraction of events correlating with the active galactic nuclei (AGNs) in the Véron-Cetty and Véron catalog, we subject the arrival directions of the data with energies in excess of 40 EeV to different tests for anisotropy. We sear…
The arrival directions of TeV-PeV cosmic rays are remarkably uniform due to the isotropization of their directions by scattering on turbulent magnetic fields. Small anisotropies can exist in standard diffusion models, however, only on the largest angular scales. Yet, high-statistics observatories like IceCube and HAWC have found significant deviations from isotropy down to small angular scales. Here, we explain the formation of small-scale anisotropies by considering pairs of cosmic rays that get correlated by their transport through the same realisation of the turbulent magnetic field. We arg…
The Pierre Auger Observatory has recently reported the detection of a dipole anisotropy in the arrival directions of cosmic rays above 8 EeV with a post-trial significance of more than 5.2$σ$. This observation has profound consequences for the distribution and composition of candidate sources of cosmic rays above the ankle (3-5 EeV). In this paper we search for the presence of anisotropies on all angular scales in public Auger data. The analysis follows a likelihood-based reconstruction method that automatically accounts for variations in the observatory's angular acceptance and background rat…
In the standard picture of cosmic ray transport the propagation of charged cosmic rays through turbulent magnetic fields is described as a random walk with cosmic rays scattering on magnetic field turbulence. This is in good agreement with the highly isotropic cosmic ray arrival directions as this diffusion process effectively isotropizes the cosmic ray distribution. High-statistics observatories like IceCube and HAWC have however observed significant deviations from isotropy down to very small angular scales. This is in strong tension with this standard picture of cosmic ray propagation. Whil…
Efficient acceleration of cosmic rays (via the mechanism of diffusive shock acceleration) requires turbulent, amplified magnetic fields in the shock's upstream region. We present results of multidimensional particle-in-cell simulations aimed at observing the magnetic field amplification that is expected to arise from the cosmic-ray current ahead of the shock, and the impact on the properties of the upstream interstellar medium. We find that the initial structure and peak strength of the amplified field is somewhat sensitive to the choice of parameters, but that the field growth saturates in a …
Several experiments (e.g., Milagro and IceCube) have reported the presence in the sky of regions with significant excess in the arrival direction distributions of Galactic cosmic rays in the TeV to PeV energy range. Here we study the possibility that these hotspots are a manifestation of the peculiar nature of these cosmic rays, and of the presence of molecular clouds near the sources. We propose that stable quark matter lumps or so-called "strangelets" can be emitted in the course of the transition of a neutron star to a more compact astrophysical object. A fraction of these massive particles…
In the energy range from ~ 10^12 eV to ~ 10^15 eV, the Galactic cosmic ray flux has anisotropies both on large scales, with an amplitude of the order of 0.1%, and on scales between ~ 10 and ~ 30 degrees, with amplitudes smaller by a factor of a few. With a diffusion coefficient inferred from Galactic cosmic ray chemical abundances, the diffusion approximation predicts a dipolar anisotropy of comparable size, but does not explain the smaller scale anisotropies. We demonstrate here that energy dependent smaller scale anisotropies naturally arise from the local concrete realization of the turbule…
Important informations on the origin and the propagation mechanisms of cosmic rays may be provided by the measurement of the anisotropies of their arrival direction. In this paper the observation of anisotropy regions at different angular scales is reported. In particular, the observation of a possible anisotropy on scales between $\sim10^{\circ}$ and $\sim30^{\circ}$ may be a key-detection for speculations on the presence of unknown features of the magnetic fields the charged cosmic rays propagate through, as well as to potential contributions of nearby sources to the total flux of cosmic ray…
We obtain the dipolar anisotropies in the arrival directions of ultra-high energy cosmic ray nuclei diffusing from nearby extragalactic sources. We consider mixed-composition scenarios in which different cosmic ray nuclei are accelerated up to the same maximum rigidity, so that $E<ZE_\text{max}^p$, with $Z$ the atomic number and $E_\text{max}^p$ the maximum proton energy. We adopt $E_\text{max}^p\simeq 6$ EeV so as to account for an increasingly heavier composition above the ankle. We obtain the anisotropies through Monte Carlo simulations that implement the cosmic ray diffusion in extragalact…
UHECRs have attracted a lot of attention due to their challengingly high energies and their potential value to constrain physical processes and astrophysical parameters in the most energetic sources of the universe. Current detectors have failed to detect significant anisotropies which had been expected to allow source identification. Some indications about the UHECR composition, which may become heavier at the highest energies, has even put into question the possibility that such a goal could be achieved soon. We investigate the potential value of a new-generation detector, with 10 times larg…
There is a growing set of observational data demonstrating that cosmic rays exhibit small-scale anisotropies (5-30 deg) with amplitude deviations lying between 0.01-0.1 percent that of the average cosmic ray flux. A broad range of models have been proposed to explain these anisotropies ranging from finite-scale magnetic field structures to dark matter annihilation. The standard diffusion transport methods used in cosmic ray propagation do not capture the transport physics in a medium with finite-scale or coherent magnetic field structures. Here, we present a Monte Carlo transport method, apply…
The joint analysis of anisotropy signals and chemical composition of ultra-high energy cosmic rays offers strong potential for shedding light on the sources of these particles. Following up on an earlier idea, this paper studies the anisotropies produced by protons of energy >E/Z, assuming that anisotropies at energy >E have been produced by nuclei of charge Z, which share the same magnetic rigidity. We calculate the number of secondary protons produced through photodisintegration of the primary heavy nuclei. Making the extreme assumption that the source does not inject any proton, we find tha…
Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall present the nonlinear results for cosmic ray transport, in particular, the cross field transport of CRs and demonstrate that the concept of cosmic ray subdiffusion in general does not apply and the perpendicular motion is well described by normal diffusion with M_A^4 dependence.…
Turbulence in the weakly collisional intracluster medium of galaxies (ICM) is able to generate strong thermal velocity anisotropies in the ions (with respect to the local magnetic field direction), if the magnetic moment of the particles is conserved in the absence of Coulomb collisions. In this scenario, the anisotropic pressure magnetohydrodynamic (AMHD) turbulence shows a very different statistical behaviour from the standard MHD one and is unable to amplify seed magnetic fields, in disagreement with previous cosmological MHD simulations which are successful to explain the observed magnetic…
The arrival directions of Galactic cosmic rays exhibit anisotropies up to the level of one per-mille over various angular scales. Recent observations of TeV-PeV cosmic rays show that the dipole anisotropy has a strong energy dependence with a phase-flip around 100 TeV. We argue that this behavior can be well understood by the combination of various effects: the anisotropic diffusion of cosmic rays, the presence of nearby sources, the Compton-Getting effect from our relative motion and the reconstruction bias of ground-based observatories.
We obtain the angular distribution of the cosmic rays reaching an observer from an individual source and after propagation through a turbulent magnetic field, for different ratios between the source distance and the diffusion length. We study both the high-energy quasi-rectilinear regime as well as the transition towards the diffusive regime at lower energies where the deflections become large. We consider the impact of energy losses, showing that they tend to enhance the anisotropy of the source at a given energy. We also discuss lensing effects, in particular those that could result from the…
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 neig…
How and where cosmic rays are produced, and how they diffuse through various turbulent media, represent fundamental problems in astrophysics with far reaching implications, both in terms of our theoretical understanding of high-energy processes in the Milky Way and beyond, and the successful interpretation of space-based and ground based GeV and TeV observations. For example, recent and ongoing detections, e.g., by Fermi (in space) and HESS (in Namibia), of $γ$-rays produced in regions of dense molecular gas hold important clues for both processes. In this paper, we carry out a comprehensive n…
The arrival directions of ultra-high-energy cosmic rays appear to be approximately isotropically distributed over the whole sky, but the last-generation UHECR detector arrays, the Pierre Auger Observatory (Auger) and the Telescope Array (TA), have detected thousands of events, allowing us to study small deviations from isotropy. So far, Auger has detected a large-scale anisotropy consistent with a $\sim 6.5\%$ dipole moment in the distribution of cosmic rays with $E > 8$~EeV, and both collaborations have reported indications for smaller-scale anisotropies at higher energies. On the other hand,…
Constraining the behavior of cosmic ray data observed at Earth requires a precise understanding of how the cosmic rays propagate in the interstellar medium. The interstellar medium is not homogeneous; although turbulent magnetic fields dominate over large scales, small coherent regions of magnetic field exist on scales relevant to particle propagation in the nearby Galaxy. Guided propagation through a coherent field is significantly different from random particle diffusion and could be the explanation of spatial anisotropies in the observed cosmic rays. We present a Monte Carlo code to propaga…
External cosmic rays impinging upon circumstellar disks associated with young stellar objects provide an important source of ionization, and as such, play an important role in disk evolution and planet formation. However, these incoming cosmic rays are affected by a variety of physical processes internal to stellar/disk systems, including modulation by turbulent magnetic fields. Globally, these fields naturally provide both a funneling effect, where cosmic rays from larger volumes are focused into the disk region, and a magnetic mirroring effect, where cosmic rays are repelled due to the incre…
A model is introduced, in which the irregularity spectrum of the Galactic magnetic field beyond the dissipation length scale is first a Kolmogorov spectrum $k^{-5/3}$ at small scales $λ\, = \, 2 π/k$ with $k$ the wave-number, then a saturation spectrum $k^{-1}$, and finally a shock-dominated spectrum $k^{-2}$ mostly in the halo/wind outside the Cosmic Ray disk. In an isotropic approximation such a model is consistent with the Interstellar Medium (ISM) data. With this model we discuss the Galactic Cosmic Ray (GCR) spectrum, as well as the extragalactic Ultra High Energy Cosmic Rays (UHECRs), th…
Huge astrospheres or stellar wind bubbles influence the propagation of cosmic rays at energies up to the TeV range and can act as small-scale sinks decreasing the cosmic ray flux. We model such a sink (in 2D) by a sphere of radius 10\,pc embedded within a sphere of a radius of 1\,kpc. The cosmic ray flux is calculated by means of backward stochastic differential equations from an observer, which is located at $r_{0}$, to the outer boundary. It turns out that such small-scale sinks can influence the cosmic ray flux at the observer's location by a few permille (i.e\ a few 0.1\%), which is in the…
We investigate the diffusion of cosmic rays (CR) close to their sources. Propagating individual CRs in purely isotropic turbulent magnetic fields with maximal scale of spatial variations Lmax, we find that CRs diffuse anisotropically at distances r <~ Lmax from their sources. As a result, the CR densities around the sources are strongly irregular and show filamentary structures. We determine the transition time t* to standard diffusion as t* ~ 10^4 yr (Lmax/150 pc)^b (E/PeV)^(-g) (Brms/4 muG)^g, with b ~ 2 and g = 0.25-0.5 for a turbulent field with Kolmogorov power spectrum. We calculate the …
Cosmic rays (CRs) may be used to infer properties of intervening cosmic magnetic fields. Conversely, understanding the effects of magnetic fields on the propagation of high-energy CRs is crucial to elucidate their origin. In the present work we investigate the role of intracluster magnetic fields on the propagation of CRs with energies between $10^{16}$ and $10^{18.5}$ eV. We look for possible signatures of a transition in the CR propagation regime, from diffusive to ballistic. Finally, we discuss the consequences of the confinement of high-energy CRs in clusters and superclusters for the prod…
The wealth of data collected in the last few years thanks to the Pierre Auger Observatory and recently to the Telescope Array made the problem of the origin of ultra high energy cosmic rays a genuinely experimental/observational one. The apparently contradictory results provided by these experiments in terms of spectrum, chemical composition and anisotropies do not allow to reach any final conclusions as yet. Here I will discuss some of the theoretical challenges imposed by these data: in particular I will discuss some issues related to the transition from Galactic to extragalactic cosmic rays…
Radio galaxies are promising candidates as the sources of ultrahigh energy cosmic rays (UHECRs). In this work, we examine if the stringent constraints imposed by the dipole and quadropole anisotropies as well as the UHECR spectrum and composition allow that radio galaxies are the dominant extragalactic cosmic ray sources. In order to calculate the UHECR flux emitted by individual radio galaxies, we constrain their properties using information from the radio-CR correlation and a dynamical evolution model. In addition to the UHECR flux from individual, local sources, we include the diffuse flux …
The energy spectra and anisotropies are very important probes of the origin of cosmic rays. Recent measurements show that complicated but very interesting structures exist, at similar energies, in both the spectra and energy-dependent anisotropies, indicating a common origin of these structures. Particularly interesting phenomenon is that there is a reversal of the phase of the dipole anisotropies, which challenges a theoretical modeling. In this work, for the first time, we identify that there might be an additional phase reversal at $\sim 100$ GeV energies of the dipole anisotropies as indic…
A thorough search for large scale anisotropies in the distribution of arrival directions of cosmic rays detected above $10^{18}$ eV at the Pierre Auger Observatory is presented. This search is performed as a function of both declination and right ascension in several energy ranges above $10^{18}$ eV, and reported in terms of dipolar and quadrupolar coefficients. Within the systematic uncertainties, no significant deviation from isotropy is revealed. Assuming that any cosmic ray anisotropy is dominated by dipole and quadrupole moments in this energy range, upper limits on their amplitudes are d…
Since astrophysical neutrinos are produced in the interactions of cosmic rays, identifying the origin of cosmic rays using directional correlations with neutrinos is one of the most interesting possibilities of the field. For that purpose, especially the Ultra-High Energy Cosmic Rays (UHECRs) are promising, as they are deflected less by extragalactic and Galactic magnetic fields than cosmic rays at lower energies. However, photo-hadronic interactions of the UHECRs limit their horizon, while neutrinos do not interact over cosmological distances. We study the possibility to search for anisotropi…
