Techniques to study cosmic ray anisotropies

Small-scale anisotropies of cosmic rays from relative diffusion

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…

Anisotropies of different mass compositions of cosmic rays

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…

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 mo…

Anisotropies of ultra-high energy cosmic rays diffusing from extragalactic sources

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…

Search for Cosmic-Ray Electron and Positron Anisotropies with Seven Years of Fermi Large Area Telescope Data

The Large Area Telescope on board the Fermi Gamma-ray Space Telescope has collected the largest ever sample of high-energy cosmic-ray electron and positron events since the beginning of its operation. Potential anisotropies in the arrival directions of cosmic-ray electrons or positrons could be a signature of the presence of nearby sources. We use almost seven years of data with energies above 42 GeV processed with the Pass~8 reconstruction. The present data sample can probe dipole anisotropies down to a level of $10^{-3}$. We take into account systematic effects that could mimic true anisotro…

Understanding the phase reversals of Galactic cosmic ray anisotropies

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…

Cosmic ray transport and anisotropies

We show that the large-scale cosmic ray anisotropy at ~10 TeV can be explained by a modified Compton-Getting effect in the magnetized flow field of old supernova remnants. This approach suggests an optimum energy scale for detecting the anisotropy. Two key assumptions are that propagation is based on turbulence following a Kolmogorov law and that cosmic ray interactions are dominated by transport through stellar winds of the exploding stars. A prediction is that the amplitude is smaller at lower energies due to incomplete sampling of the velocity field and also smaller at larger energies due t…

Searches for Cosmic-Ray Electron Anisotropies with the Fermi Large Area Telescope

The Large Area Telescope on board the \textit{Fermi} satellite (\textit{Fermi}-LAT) detected more than 1.6 million cosmic-ray electrons/positrons with energies above 60 GeV during its first year of operation. The arrival directions of these events were searched for anisotropies of angular scale extending from $\sim$ 10 $^\circ$ up to 90$^\circ$, and of minimum energy extending from 60 GeV up to 480 GeV. Two independent techniques were used to search for anisotropies, both resulting in null results. Upper limits on the degree of the anisotropy were set that depended on the analyzed energy range…

Cosmic ray transport and anisotropies to high energies

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…

Cosmic Ray Small Scale Anisotropies in Slab Turbulence

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…

Effects of the galactic magnetic field upon large scale anisotropies of extragalactic Cosmic Rays

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…

Indication of nearby source signatures of cosmic rays from energy spectra and anisotropies

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…

Measurements and implications of cosmic ray anisotropies from TeV to trans-EeV energies

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…

湍流引起的宇宙线小尺度各向异性

Small-Scale Anisotropies of Cosmic Rays from Turbulent Flow

本文在经典对流-扩散框架下证明宇宙线角功率谱直接反映星际湍流，并用柯尔莫哥洛夫谱指数和对流速度弥散近似解释了 IceCube 与 HAWC 在 TeV 能段观测到的小尺度各向异性。

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, …

Strangelets and the TeV-PeV cosmic-ray anisotropies

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…

Anisotropies of ultrahigh-energy cosmic rays in a scenario with nearby sources

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…

Small-Scale Anisotropies of Cosmic Rays from Relative Diffusion

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…

The Anisotropies and Origins of Ultrahigh Energy Cosmic Rays

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.

Magnetic fields and cosmic ray anisotropies at TeV energies

Several cosmic-ray observatories have provided a high accuracy map of the sky at TeV--PeV energies. The data reveals an O(0.1%) deficit from north galactic directions that peaks at 10 TeV and then evolves with the energy, together with other anisotropies at smaller angular scales. Using Boltzmann's equation we derive expressions for the cosmic-ray flux that fit most of these features. The anisotropies depend on the local interstellar magnetic field B_{IS}, on the average galactic field B_{R} in our vicinity, and on the distribution of dominant cosmic-ray sources. We show that the initial dipol…

Origin of Small-Scale Anisotropies in Galactic Cosmic Rays

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…

Magnetically Induced Anisotropies in the Arrival Directions of Ultra-high-energy Cosmic Rays from Nearby Radio Galaxies

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…

Comic ray flux anisotropies caused by astrospheres

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…

Sensitivity of orbiting JEM-EUSO to large-scale cosmic-ray anisotropies

The two main advantages of space-based observation of extreme-energy ($\gtrsim 10^{19}$~eV) cosmic-rays (EECRs) over ground-based observatories are the increased field of view, and the all-sky coverage with nearly uniform systematics of an orbiting observatory. The former guarantees increased statistics, whereas the latter enables a partitioning of the sky into spherical harmonics. We have begun an investigation, using the spherical harmonic technique, of the reach of \J\ into potential anisotropies in the extreme-energy cosmic-ray sky-map. The technique is explained here, and simulations are …

Large-Scale Distribution of Arrival Directions of Cosmic Rays Detected at the Pierre Auger Observatory Above $10~$PeV

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,…

Anisotropies in the cosmic radiation observed with ARGO-YBJ

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…

No longer ballistic, not yet diffusive--the formation of cosmic ray small-scale anisotropies

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…

Detecting ultra-high energy cosmic ray anisotropies through cross-correlations

We propose an observable for ultra-high energy cosmic ray (UHECR) physics: the harmonic-space cross-correlation power spectrum between the arrival directions of UHECRs and the large-scale cosmic structure mapped by galaxies. This cross-correlation has not yet been considered in the literature, and it permits a direct theoretical modelling of the main astrophysical components. We describe the expected form of the cross-correlation and show how, if the distribution of UHECR sources trace the large-scale cosmic structure, it could be easier to detect with current data than the UHECR auto-correlat…

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 neig…

Large- and Medium-Scale Anisotropies in the Arrival Directions of Cosmic Rays observed with KASCADE-Grande

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…

Explaining TeV Cosmic-Ray Anisotropies with Non-Diffusive Cosmic-Ray Propagation

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…

Searching for All-Scale Anisotropies in the Arrival Directions of Cosmic Rays above the Ankle

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…

Ultra High Energy Cosmic Rays: Anisotropies and Spectrum

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…

Sensitivity of full-sky experiments to large scale cosmic ray anisotropies

The two main advantages of space-based observation of extreme energy ($\gtrsim5\times10^{19}$ eV) cosmic rays (EECRs) over ground based observatories are the increased field of view and the full-sky coverage with nearly uniform systematics across the entire sky. The former guarantees increased statistics, whereas the latter enables a clean partitioning of the sky into spherical harmonics. The discovery of anisotropies would help to identify the long sought origin of EECRs. We begin an investigation of the reach of a full-sky space-based experiment such as EUSO to detect anisotropies in the ext…

On the upper limits for dipole anisotropies in cosmic-ray positrons

The excess of cosmic-ray positrons in the energy range from 10 GeV to few hundred GeV reported by PAMELA and AMS experiments is not consistent with a pure secondary origin and requires the introduction of a source term. The presence of anisotropies in the positron arrival directions would be a distinctive signature of their origin. Current measurements are consistent with isotropy and limits to a dipole anisotropy have been established. In this note, we review the mathematical basis of this analysis and provide a general bound to the dipole upper limits achievable from a given sample of events…

A New Maximum-Likelihood Technique for Reconstructing Cosmic-Ray Anisotropy at All Angular Scales

The arrival directions of TeV-PeV cosmic rays show weak but significant anisotropies with relative intensities at the level of one per mille. Due to the smallness of the anisotropies, quantitative studies require careful disentanglement of detector effects from the observation. We discuss an iterative maximum-likelihood reconstruction that simultaneously fits cosmic ray anisotropies and detector acceptance. The method does not rely on detector simulations and provides an optimal anisotropy reconstruction for ground-based cosmic ray observatories located in the middle latitudes. It is particula…

Anomalous Anisotropies of Cosmic Rays from Turbulent Magnetic Fields

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…

在 Pierre Auger 天文台测量的超高能宇宙线大尺度各向异性

Large-scale anisotropies of ultra-high-energy cosmic rays measured at the Pierre Auger Observatory

本文综述 Pierre Auger 天文台对超高能宇宙线大尺度各向异性的测量，并基于19年数据讨论8 EeV以上显著偶极信号及其河外起源指示。

银河宇宙射线的谱和各向异性：磁暴实验室

Spectrum and anisotropies of Galactic cosmic rays: a laboratory for magnetic fields

通过研究银河宇宙射线的谱和各向异性，揭示磁暴结构的未知领域，并为未来研究提供新视角。

Anisotropies in Non-Thermal Distortions of Cosmic Light from Photon-Axion Conversion

Ultralight axions which couple sufficiently strongly to photons can leave imprints on the sky at diverse frequencies by mixing with cosmic light in the presence of background magnetic fields. We explore such direction dependent grey-body distortions of the CMB spectrum, enhanced by resonant conditions in the IGM plasma. We also find that if such axions are produced in the early universe and represent a subdominant dark radiation component today, they could convert into X-rays in supervoids, and brighten them at X-ray frequencies.

On the Energy Dependence of Galactic Cosmic Ray Anisotropies in the Very Local Interstellar Medium

We report on the energy dependence of galactic cosmic rays (GCRs) in the very local interstellar medium (VLISM) as measured by the Low Energy Charged Particle (LECP) instrument on the Voyager 1 (V1) spacecraft. The LECP instrument includes a dual-ended solid state detector particle telescope mechanically scanning through 360 deg across eight equally-spaced angular sectors. As reported previously, LECP measurements showed a dramatic increase in GCR intensities for all sectors of the >=211 MeV count rate (CH31) at the V1 heliopause (HP) crossing in 2012, however, since then the count rate data h…

Anisotropies in the diffuse gamma-ray background measured by the Fermi-LAT

The contribution of unresolved sources to the diffuse gamma-ray background could produce anisotropies in this emission on small angular scales. Recent studies have considered the angular power spectrum and other anisotropy metrics as tools for identifying contributions to diffuse emission from unresolved source classes, such as extragalactic and Galactic dark matter as well as various astrophysical gamma-ray source populations. We present preliminary results of an anisotropy analysis of the diffuse emission measured by the Fermi-LAT.