Distribution Of Cosmic-ray Sources Research Articles

Cosmic Ray Anisotropy and Spectra as Probes for Nearby Sources

Cosmic ray (CR) spectra and anisotropy are closely related to the distribution of CR sources, making them valuable probes for studying nearby sources. There are 12 nearby sources located within 1 kpc of the solar system, and which ones are the optimal candidates? In this work, we have selected the Geminga, Monogem, Vela, Loop I, and Cygnus SNR sources as the focus of our research, aiming to identify the optimal candidate by investigating their contribution to the energy spectra and anisotropy using the Spatially Dependent Propagation (SDP) model. Additionally, the anisotropic diffusion effect of the local regular magnetic field (LRMF) on CR particles is also considered in the SDP model. Our previous work only provided 1D anisotropy along the right ascension; this current work will further present 2D anisotropy maps along the right ascension and declination. When the injection power of different nearby sources is roughly equal, the results show that the Geminga, Momogem, and Loop I SNR sources contribute significantly to the nuclear energy spectra. Under the isotropic diffusion without considering the LRMF, the 2D anisotropy maps indicate that the phase points to the nearby source below 100 TeV. We further adjust the injection power of the Monogem SNR source in accordance with the spin-down energy of the Geminga and Monogem pulsars, and find that the contribution of the corrected Monogem SNR can be disregarded. Because the Loop I SNR source is located in the direction of the Galactic Center (GC), it cannot contribute to the excess of CRs in the anti-GC direction. Under anisotorpic diffusion with the consideration of the LRMF, the 2D anisotropy maps show that only the Geminga SNR can match the anisotropy measurement, while the other sources cannot. Finally, we conclude that the Geminga SNR source is the optimal nearby source.

Galactic cosmic ray propagation models using Picard

We will give an overview of recent developments in numerical modelling of CR transport in our Galaxy with the PICARD code. Corresponding numerical models aim at reproducing CR spectra and also diffuse gamma-ray emission from the Galaxy by solving the cosmic-ray transport problem in a three-dimensional model of the Galaxy. We address the impact of different transport physics processes on the flux and distribution of diffuse Galactic gamma rays: we investigate CR transport using different cosmic-ray source distribution models ranging from smooth source distributions to localised sources related to high-energy gamma-ray observations. Additionally, we consider anisotropic cosmic-ray diffusion in an improved Galactic magnetic field model. The choice of changing the different transport parameters is most readily visible in the inverse-Compton channel, which shows features not present in commonly-used axisymmetric transport models.

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.

High-energy Gamma Rays from the Milky Way: Three-dimensional Spatial Models for the Cosmic-Ray and Radiation Field Densities in the Interstellar Medium.

High-energy γ-rays of interstellar origin are produced by the interaction of cosmic-ray (CR) particles with the diffuse gas and radiation fields in the Galaxy. The main features of this emission are well understood and are reproduced by existing CR propagation models employing 2D galactocentric cylindrically symmetrical geometry. However, the high-quality data from instruments like the Fermi Large Area Telescope reveal significant deviations from the model predictions on few to tens of degrees scales, indicating the need to include the details of the Galactic spiral structure and thus requiring 3D spatial modeling. In this paper, the high-energy interstellar emissions from the Galaxy are calculated using the new release of the GALPROP code employing 3D spatial models for the CR source and interstellar radiation field (ISRF) densities. Three models for the spatial distribution of CR sources are used that are differentiated by their relative proportion of input luminosity attributed to the smooth disk or spiral arms. Two ISRF models are developed based on stellar and dust spatial density distributions taken from the literature that reproduce local near- to far-infrared observations. The interstellar emission models that include arms and bulges for the CR source and ISRF densities provide plausible physical interpretations for features found in the residual maps from high-energy γ-ray data analysis. The 3D models for CR and ISRF densities provide a more realistic basis that can be used for the interpretation of the nonthermal interstellar emissions from the Galaxy.

The Fermi Galactic Center GeV Excess and Implications for Dark Matter

Abstract The region around the Galactic Center (GC) is now well established to be brighter at energies of a few GeV than what is expected from conventional models of diffuse gamma-ray emission and catalogs of known gamma-ray sources. We study the GeV excess using 6.5 yr of data from the Fermi Large Area Telescope. We characterize the uncertainty of the GC excess spectrum and morphology due to uncertainties in cosmic-ray source distributions and propagation, uncertainties in the distribution of interstellar gas in the Milky Way, and uncertainties due to a potential contribution from the Fermi bubbles. We also evaluate uncertainties in the excess properties due to resolved point sources of gamma rays. The GC is of particular interest, as it would be expected to have the brightest signal from annihilation of weakly interacting massive dark matter (DM) particles. However, control regions along the Galactic plane, where a DM signal is not expected, show excesses of similar amplitude relative to the local background. Based on the magnitude of the systematic uncertainties, we conservatively report upper limits for the annihilation cross-section as a function of particle mass and annihilation channel.

Galactic cosmic ray propagation models using Picard

I will give an overview on the numerical approach for the solution of the Galactic cosmic-ray propagation problem used within the recently introduced code Picard. The code solves the transport equation for each cosmic-ray species resulting in a prediction of the cosmic ray flux everywhere in the Galaxy. Picard is a prominent example for the current transition from two-dimensional azimuthally symmetric models of Galactic cosmic-ray transport to those that allow higher degrees of realism. In Picard this is achieved by use of contemporary numerical solvers that allow efficient computation of very high resolution models. I will address the new physics that can be incorporated in such three-dimensional models, e.g. example problems like the transition from axisymmetric cosmic-ray source distributions to spiral-arm cosmic-ray source distributions, including consequences for the various observables related to cosmic rays.

Characteristics of the energy spectra of cosmic rays and a single source model

As the accuracy of measuring the energy spectra of different nuclei in the primary cosmic ray flux and their ratios grows, more evidence appears for the nonpower character of these spectra at energies below the knee at 3–4 PeV. Irregularities in the spectra are the natural consequence of the nonuniformity of the cosmic ray source distributions: their types, ages and distances to the Earth; the nonuniformity of the interstellar medium; and the different densities, temperatures, and natures of magnetic fields. In particular, the flattening of the proton and helium energy spectra, the growth of the fraction of positrons in the total flux of positrons and electrons, and the constancy of the ratio of antiprotons to protons at sub-PeV energies could be due to the contribution from nearby and young sources emitting harder energy spectra of particles. It is shown that the recent measurements of the ratio of the boron and carbon nuclei performed in the AMS-02 experiment could also indicate that there is a contribution from a single comparatively young and nearby source.

Reconciling the diffuse Galactic γ-ray and the cosmic ray spectra

Most of the diffuse Galactic GeV gamma-ray emission is produced via collisions of cosmic ray (CR) protons with ISM protons. As such the observed spectra of the gamma-rays and the CRs should be strongly linked. Recent observations of Fermi-LAT exhibit a hardening of the gamma-ray spectrum at around a hundred GeV, between the Sagittarius and Carina tangents, and a further hardening at a few degrees above and below the Galactic plane. However, standard CR propagation models that assume a time independent source distribution and a location independent diffusion cannot give rise to a spatially dependent CR (and hence gamma-ray) spectral slopes. Here we consider a dynamic spiral arm model in which the distribution of CR sources is concentrated in the (dynamic) spiral arms, and we study the effects of this model on the $\pi^0$-decay produced gamma-ray spectra. Within this model, near the Galactic arms the observed gamma-ray spectral slope is not trivially related to the CR injection spectrum and energy dependence of the diffusion coefficient. We find unique signatures that agree with the Fermi-LAT observations. This model also provides a physical explanation for the difference between the local CR spectral slope and the CR slope inferred from the average gamma-ray spectrum.

Cosmic-Ray Injection from Star-Forming Regions.

At present, all physical models of diffuse Galactic γ-ray emission assume that the distribution of cosmic-ray sources traces the observed populations of either OB stars, pulsars, or supernova remnants. However, since H_{2}-rich regions host significant star formation and numerous supernova remnants, the morphology of observed H_{2} gas (as traced by CO line surveys) should also provide a physically motivated, high-resolution tracer for cosmic-ray injection. We assess the impact of utilizing H_{2} as a tracer for cosmic-ray injection on models of diffuse Galactic γ-ray emission. We employ state-of-the-art 3D particle diffusion and gas density models, along with a physical model for the star-formation rate based on global Schmidt laws. Allowing a fraction, f_{H_{2}}, of cosmic-ray sources to trace the observed H_{2} density, we find that a theoretically well-motivated value f_{H_{2}}∼0.20-0.25 (i)provides a significantly better global fit to the diffuse Galactic γ-ray sky and (ii)highly suppresses the intensity of the residual γ-ray emission from the Galactic center region. Specifically, in models utilizing our best global fit values of f_{H_{2}}∼0.20-0.25, the spectrum of the galactic center γ-ray excess is drastically affected, and the morphology of the excess becomes inconsistent with predictions for dark matter annihilation.

On the radial distribution of Galactic cosmic rays

Abstract The spectrum and morphology of the diffuse Galactic γ-ray emission carries valuable information on cosmic ray (CR) propagation. Recent results obtained by analyzing Fermi-LAT data accumulated over 7 yr of observation show a substantial variation of the CR spectrum as a function of the distance from the Galactic Centre. The spatial distribution of the CR density in the outer Galaxy appears to be weakly dependent upon the galactocentric distance, as found in previous studies as well, while the density in the central region of the Galaxy was found to exceed the value measured in the outer Galaxy. At the same time, Fermi-LAT data suggest a gradual spectral softening while moving outwards from the centre of the Galaxy to its outskirts. These findings represent a challenge for standard calculations of CR propagation based on assuming a uniform diffusion coefficient within the Galactic volume. Here, we present a model of non-linear CR propagation in which transport is due to particle scattering and advection off self-generated turbulence. We find that for a realistic distribution of CR sources following the spatial distribution of supernova remnants and the space dependence of the magnetic field on galactocentric distance, both the spatial profile of CR density and the spectral softening can easily be accounted for.

IMPRINT OF A 2 MILLION YEAR OLD SOURCE ON THE COSMIC-RAY ANISOTROPY

We study numerically the anisotropy of the cosmic ray (CR) flux emitted by a single source calculating the trajectories of individual CRs. We show that the contribution of a single source to the observed anisotropy is instead determined solely by the fraction the source contributes to the total CR intensity, its age and its distance,and does not depend on the CR energy at late times. Therefore the observation of a constant dipole anisotropy indicates that a single source dominates the CR flux in the corresponding energy range. A natural explanation for the plateau between 2--20 TeV observed in the CR anisotropy is thus the presence of a single, nearby source. For the source age of 2 Myr, as suggested by the explanation of the antiproton and positron data from PAMELA and AMS-02 through a local source [arXiv:astro-ph/1504.06472], we determine the source distance as $\sim 200$ pc. Combined with the contribution of the global CR sea calculated in the escape model, we can explain qualitatively the data for the dipole anisotropy. Our results suggest that the assumption of a smooth CR source distribution should be abandoned between 200 GeV and 1 PeV.

Neutrinos from extra-large Hadron Collider in the Milky Way

Neutrino telescope IceCube has recently discovered astrophysical neutrinos with energies in the TeV–PeV range. We use the data of Fermi γ-ray telescope to demonstrate that the neutrino signal has significant contribution from the Milky Way Galaxy. Matching the γ-ray and neutrino spectra we find that TeV–PeV Galactic cosmic rays form a powerlaw spectrum with the slope p ≃ 2.45. This spectral slope is consistent with the average cosmic ray spectrum in the disks of the Milky Way and Large Magellanic Cloud galaxies. It is also consistent with the theoretical model of cosmic ray injection by diffusive shock acceleration followed by escape through the Galactic magnetic field with Kolmogorov turbulence. The locally observed TeV–PeV cosmic ray proton spectrum is softer than the average Galactic cosmic ray spectrum. This could be readily explained by variability of injection of cosmic rays in the local interstellar medium over the past 107 year and discreetness of the cosmic ray source distribution.

Propagation in 3D spiral-arm cosmic-ray source distribution models and secondary particle production using Picard

We study the impact of possible spiral-arm distributions of Galactic cosmic-ray sources on the flux of various cosmic-ray nuclei throughout our Galaxy. We investigate model cosmic-ray spectra at the nominal position of the sun and at different positions within the Galaxy. The modelling is performed using the recently introduced numerical cosmic ray propagation code Picard. Assuming non-axisymmetric cosmic-ray source distributions yields new insights on the behaviour of primary versus secondary nuclei.We find that primary cosmic rays are more strongly confined to the vicinity of the sources, while the distribution of secondary cosmic rays is much more homogeneous compared to the primaries. This leads to stronger spatial variation in secondary to primary ratios when compared to axisymmetric source distribution models. A good fit to the cosmic-ray data at Earth can be accomplished in different spiral-arm models, although leading to decisively different spatial distributions of the cosmic-ray flux. These lead to different cosmic ray anisotropies, where even reproducing the data becomes possible. Consequently, we advocate directions to seek best fit propagation parameters that take into account the higher complexity introduced by the spiral-arm structure on the cosmic-ray distribution. We specifically investigate whether the flux at Earth is representative for a large fraction of the Galaxy. The variance among possible spiral-arm models allows us to quantify the spatial variation of the cosmic-ray flux within the Galaxy in presence of non-axisymmetric source distributions.

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 dipole anisotropy along B_{IS} can be modulated by changes in the global cosmic ray wind, and that a variation in the dipole direction would imply a given radius of coherence for B_{IS}. We also show that small and medium-scale anisotropies may appear when the full-sky anisotropy finds a turbulence acting as a magnetic lens.

TeV Cosmic Ray Anisotropy and the Heliospheric Magnetic Field

Abstract. Cosmic rays are observed to possess a small non uniform distribution in arrival direction. Such anisotropy appears to have a roughly consistent topology between tens of GeV and hundreds of TeV, with a smooth energy dependency on phase and amplitude. Above a few hundreds of TeV a sudden change in the topology of the anisotropy is observed. The distribution of cosmic ray sources in the Milky Way is expected to inject anisotropy on the cosmic ray flux. The nearest and most recent sources, in particular, are expected to contribute more significantly than others. Moreover the interstellar medium is expected to have different characteristics throughout the Galaxy, with different turbulent properties and injection scales. Propagation effects in the interstellar magnetic field can shape the cosmic ray particle distribution as well. In particular, in the 1–10 TeV energy range, they have a gyroradius comparable to the size of the Heliosphere, assuming a typical interstellar magnetic field strength of 3 μG. Therefore they are expected to be strongly affected by the Heliosphere in a manner ordered by the direction of the local interstellar magnetic field and of the heliotail. In this paper we discuss on the possibility that TeV cosmic rays arrival distribution might be significantly redistributed as they propagate through the Heliosphere.

Spiral arms as cosmic ray source distributions

The Milky Way is a spiral galaxy with (or without) a bar-like central structure. There is evidence that the distribution of suspected cosmic ray sources, such as supernova remnants, are associated with the spiral arm structure of galaxies. It is yet not clearly understood what effect such a cosmic ray source distribution has on the particle transport in our Galaxy. We investigate and measure how the propagation of Galactic cosmic rays is affected by a cosmic ray source distribution associated with spiral arm structures.We use the PICARD code to perform high-resolution 3D simulations of electrons and protons in galactic propagation scenarios that include four-arm and two-arm logarithmic spiral cosmic ray source distributions with and without a central bar structure as well as the spiral arm configuration of the NE2001 model for the distribution of free electrons in the Milky Way. Results of these simulation are compared to an axisymmetric radial source distribution. Also, effects on the cosmic ray flux and spectra due to different positions of the Earth relative to the spiral structure are studied.We find that high energy electrons are strongly confined to their sources and the obtained spectra largely depend on the Earth’s position relative to the spiral arms. Similar finding have been obtained for low energy protons and electrons albeit at smaller magnitude. We find that even fractional contributions of a spiral arm component to the total cosmic ray source distribution influences the spectra on the Earth. This is apparent when compared to an axisymmetric radial source distribution as well as with respect to the Earth’s position relative to the spiral arm structure. We demonstrate that the presence of a Galactic bar manifests itself as an overall excess of low energy electrons at the Earth.Using a spiral arm geometry as a cosmic ray source distributions offers a genuine new quality of modeling and is used to explain features in cosmic ray spectra at the Earth that are else-wise attributed to other propagation effects. We show that realistic cosmic ray propagation scenarios have to acknowledge non-axisymmetric source distributions.

UNDERSTANDING TeV-BAND COSMIC-RAY ANISOTROPY

We investigate the temporal and spectral correlations between flux and anisotropy fluctuations of TeV-band cosmic rays in the light of recent data taken with IceCube. We find that for a conventional distribution of cosmic-ray sources the dipole anisotropy is higher than observed, even if source discreteness is taken into account. Moreover, even for a shallow distribution of galactic cosmic-ray sources and a reacceleration model, fluctuations arising from source discreteness provide a probability only of the order of 10% that the cosmic-ray anisotropy limits of the recent IceCube analysis are met. This probability estimate is nearly independent of the exact choice of source rate, but generous for a large halo size. The location of the intensity maximum far from the Galactic Center is naturally reproduced.

A method for constraining cosmic magnetic field models using ultra-high energy cosmic rays: The Field Scan Method

The Galactic magnetic field, locally observed to be on the order of a few μG, is sufficiently strong to induce deflections in the arrival directions of ultra-high energy cosmic rays. We present a method that establishes measures of self-consistency for hypothesis sets comprised of cosmic magnetic field models and ultra-high energy cosmic ray composition and source distributions. The method uses two independent procedures to compare the backtracked velocity vectors outside the magnetic field model to the distribution of backtracked velocity directions of many isotropic observations with the same primary energies. This allows for an estimate of the statistical consistency between the observed data and simulated isotropic observations. Inconsistency with the isotropic expectation of source correlation in both procedures is interpreted as the hypothesis set providing a self-consistent description of GMF and UHECR properties for the cosmic ray observations.

FERMI-LAT OBSERVATIONS OF THE DIFFUSE γ-RAY EMISSION: IMPLICATIONS FOR COSMIC RAYS AND THE INTERSTELLAR MEDIUM

The gamma-ray sky >100 MeV is dominated by the diffuse emissions from interactions of cosmic rays with the interstellar gas and radiation fields of the Milky Way. Observations of these diffuse emissions provide a tool to study cosmic-ray origin and propagation, and the interstellar medium. We present measurements from the first 21 months of the Fermi-LAT mission and compare with models of the diffuse gamma-ray emission generated using the GALPROP code. The models are fitted to cosmic-ray data and incorporate astrophysical input for the distribution of cosmic-ray sources, interstellar gas and radiation fields. To assess uncertainties associated with the astrophysical input, a grid of models is created by varying within observational limits the distribution of cosmic-ray sources, the size of the cosmic-ray confinement volume (halo), and the distribution of interstellar gas. An all-sky maximum-likelihood fit is used to determine the Xco-factor, the ratio between integrated CO-line intensity and molecular hydrogen column density, the fluxes and spectra of the gamma-ray point sources from the first Fermi-LAT catalogue, and the intensity and spectrum of the isotropic background including residual cosmic rays that were misclassified as gamma rays, all of which have some dependency on the assumed diffuse emission model. The models are compared on the basis of their maximum likelihood ratios as well as spectra, longitude, and latitude profiles. We also provide residual maps for the data following subtraction of the diffuse emission models. The models are consistent with the data at high and intermediate latitudes but under-predict the data in the inner Galaxy for energies above a few GeV. Possible explanations for this discrepancy are discussed, including the contribution by undetected point source populations and spectral variations of cosmic rays throughout the Galaxy. [Abridged]

Pinpointing cosmic ray propagation with the AMS-02 experiment

The Alpha Magnetic Spectrometer (AMS-02), which is scheduled to be deployed onboard the International Space Station later this year, will be capable of measuring the composition and spectra of GeV-TeV cosmic rays with unprecedented precision. In this paper, we study how the projected measurements from AMS-02 of stable secondary-to-primary and unstable ratios (such as boron-to-carbon and beryllium-10-to-beryllium-9) can constrain the models used to describe the propagation of cosmic rays throughout the Milky Way. We find that within the context of fairly simple propagation models, all of the model parameters can be determined with high precision from the projected AMS-02 data. Such measurements are less constraining in more complex scenarios, however, which allow for departures from a power-law form for the diffusion coefficient, for example, or for inhomogeneity or stochasticity in the distribution and chemical abundances of cosmic ray sources.