Propagation Of Galactic Cosmic Rays Research Articles

Measurement of the radial diffusion coefficient of galactic cosmic rays near the Earth by the GRAPES-3 experiment

The flux of galactic cosmic rays (GCRs) is isotropic in the interstellar space. However, in the heliosphere, the ram pressure of outward-moving solar wind convects the GCRs away from the Sun, thereby producing a density gradient in the radial direction. The diffusion of GCRs due to this gradient and scattering with the irregularities in the interplanetary magnetic field (IMF) induce variations in their flux that can be observed near the Earth. A framework for the diffusion-convection mechanism of GCR propagation developed by Parker and collaborators [Phys. Rev. 110, 1445 (1958); Planet. Space Sci. 13, 9 (1965); Astrophys. J. 772, 46 (2013); Space Sci. Rev. 78, 401 (1996); Astrophys. J. 234, 746 (1979); Astrophys. J. 361, 162 (1990); Space Sci. Rev. 176, 299 (2013)] offers a good description of this phenomenon. One of the outcomes of this framework is an anticorrelation of the variation in solar wind velocity (${\mathrm{V}}_{\mathrm{SW}}$) and the GCR flux. A second outcome of this gradient in the presence of IMF is the movement of GCRs perpendicular to the ecliptic plane called ``Swinson flow.'' Therefore, (i) the correlated variations of ${\mathrm{V}}_{\mathrm{SW}}$ and GCR flux and (ii) the GCR radial density gradient obtained from Swinson flow can each be used to independently measure the radial diffusion coefficient of GCRs in the inner heliosphere. In an earlier work [Phys. Rev. D 91, 121303(R) (2015)], the GCR flux was shown to be anticorrelated with ${\mathrm{V}}_{\mathrm{SW}}$ at $(\ensuremath{-}1.33\ifmmode\pm\else\textpm\fi{}0.07)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}%(\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}{)}^{\ensuremath{-}1}$. This anticorrelation yields a radial diffusion coefficient $\ensuremath{\kappa}=0.97\ifmmode\times\else\texttimes\fi{}{10}^{19}\text{ }\text{ }{\mathrm{m}}^{2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ at 1 AU. In another work [Astropart. Phys. 62, 21 (2015)], the measurement of Swinson flow was used to obtain a GCR radial density gradient of $0.65\text{ }\text{ }{\mathrm{A}\mathrm{U}}^{\ensuremath{-}1}$ at a median rigidity of 77 GV. Here, we report a measurement of radial diffusion coefficient $\ensuremath{\kappa}=1.04\ifmmode\times\else\texttimes\fi{}{10}^{19}\text{ }\text{ }{\mathrm{m}}^{2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ at 1 AU from the above-mentioned density gradient, for a mean ${\mathrm{V}}_{\mathrm{SW}}$ of $450\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. Thus, these two distinct approaches essentially yielded similar values of the radial diffusion coefficient $\ensuremath{\kappa}={10}^{19}\text{ }\text{ }{\mathrm{m}}^{2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ at 1 AU, characterizing the diffusion of GCRs at 77 GV. From this value of $\ensuremath{\kappa}$, the mean free path length for parallel diffusion ${\ensuremath{\lambda}}_{\ensuremath{\parallel}}$ was estimated to be 1.2 AU at 77 GV, consistent with earlier reports [Rev. Geophys. Space Phys. 20, 335 (1982); Astrophys. J. 420, 294 (1994); Astrophys. J. 604, 861 (2004)].

Effects of self-generated turbulence on Galactic Cosmic Ray propagation and associated diffuse γ-ray emission

Recent results obtained by analyzing diffuse γ-ray emission detected by Fermi-LAT show a substantial variation of the CR spectrum as a function of the distance from the Galactic Center. For energies up to tens of GeV, the CR proton density in the outer Galaxy appears to be weakly dependent upon the galactocentric distance 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 outward from the center 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 will show 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.

Proton Fluxes Measured by the PAMELA Experiment from the Minimum to the Maximum Solar Activity for Solar Cycle 24

Abstract Precise measurements of the time-dependent intensity of the low-energy (<50 GeV) galactic cosmic rays (GCRs) are fundamental to test and improve the models that describe their propagation inside the heliosphere. In particular, data spanning different solar activity periods, i.e., from minimum to maximum, are needed to achieve comprehensive understanding of such physical phenomena. The minimum phase between solar cycles 23 and 24 was peculiarly long, extending up to the beginning of 2010 and followed by the maximum phase, reached during early 2014. In this Letter, we present proton differential spectra measured from 2010 January to 2014 February by the PAMELA experiment. For the first time the GCR proton intensity was studied over a wide energy range (0.08–50 GeV) by a single apparatus from a minimum to a maximum period of solar activity. The large statistics allowed the time variation to be investigated on a nearly monthly basis. Data were compared and interpreted in the context of a state-of-the-art three-dimensional model describing the GCRs propagation through the heliosphere.

Simulation of the Galactic Cosmic Ray Shadow of the Sun**Supported by the National Natural Science Foundation of China under Grant No 11675187, the Specialized Research Fund for State Key Laboratories, and the CAS-TWAS President Fellowship Programme.

The cosmic-ray particles of TeV-regime, outside the solar system are blocked in their way to the Earth, a deficit of particles is observed corresponding to the location of the Sun known as the Sun shadow. The center of the Sun shadow is shifted from its nominal position due to the presence of magnetic fields in interplanetary space, and this shift is used indirectly as a probe to study the solar magnetic field that is difficult to measure otherwise. A detailed Monte Carlo simulation of galactic cosmic-ray propagation in the Earth–Sun system is carried out to disentangle the cumulative effects of solar, interplanetary and geomagnetic fields. The shadowing effects and the displacements results of the Sun shadow in different solar activities are reproduced and discussed.

The pinching method for Galactic cosmic ray positrons: Implications in the light of precision measurements

Context. Two years ago, the Ams-02 collaboration released the most precise measurement of the cosmic ray positron flux. In the conventional approach, in which positrons are considered as purely secondary particles, the theoretical predictions fall way below the data above 10 GeV. One suggested explanation for this anomaly is the annihilation of dark matter particles, the so-called weakly interactive massive particles (WIMPs), into standard model particles. Most analyses have focused on the high-energy part of the positron spectrum, where the anomaly lies, disregarding the complicated GeV low-energy region where Galactic cosmic ray transport is more difficult to model and solar modulation comes into play. Aims. Given the high quality of the latest measurements by Ams-02, it is now possible to systematically re-examine the positron anomaly over the entire energy range, this time taking into account transport processes so far neglected, such as Galactic convection or diffusive re-acceleration. These might impact somewhat on the high-energy positron flux so that a complete and systematic estimate of the secondary component must be performed and compared to the Ams-02 measurements. The flux yielded by WIMPs also needs to be re-calculated more accurately to explore how dark matter might source the positron excess. Methods. We devise a new semi-analytical method to take into account transport processes thus far neglected, but important below a few GeV. It is essentially based on the pinching of inverse Compton and synchrotron energy losses from the magnetic halo, where they take place, inside the Galactic disc. The corresponding energy loss rate is artificially enhanced by the so-called pinching factor, which needs to be calculated at each energy. We have checked that this approach reproduces the results of the Green function method at the per mille level. This new tool is fast and allows one to carry out extensive scans over the cosmic ray propagation parameters. Results. We derive the positron flux from sub-GeV to TeV energies for both gas spallation and dark matter annihilation. We carry out a scan over the cosmic ray propagation parameters, which we strongly constrain by requiring that the secondary component does not overshoot the Ams-02 measurements. We find that only models with large diffusion coefficients are selected by this test. We then add to the secondary component the positron flux yielded by dark matter annihilation. We carry out a scan over WIMP mass to fit the annihilation cross-section and branching ratios, successively exploring the cases of a typical beyond-the-standard-model WIMP and an annihilation through light mediators. In the former case, the best fit yields a p-value of 0.4% for a WIMP mass of 264 GeV, a value that does not allow to reproduce the highest energy data points. If we require the mass to be larger than 500 GeV, the best-fit χ2 per degree of freedom always exceeds a value of 3. The case of light mediators is even worse, with a best-fit χ2 per degree of freedom always larger than 15. Conclusions. We explicitly show that the cosmic ray positron flux is a powerful and independent probe of Galactic cosmic ray propagation. It should be used as a complementary observable to other tracers such as the boron-to-carbon ratio. This analysis shows also that the pure dark matter interpretation of the positron excess is strongly disfavoured. This conclusion is based solely on the positron data, and no other observation, such as the antiproton flux or the CMB anisotropies, needs to be invoked.

Simulation of the GCR spectrum in the Mars curiosity rover's RAD detector using MCNP6

The paper presents results from MCNP6 simulations of galactic cosmic ray (GCR) propagation down through the Martian atmosphere to the surface and comparison with RAD measurements made there. This effort is part of a collaborative modeling workshop for space radiation hosted by Southwest Research Institute (SwRI). All modeling teams were tasked with simulating the galactic cosmic ray (GCR) spectrum through the Martian atmosphere and the Radiation Assessment Detector (RAD) on-board the Curiosity rover. The detector had two separate particle acceptance angles, 4π and 30 ° off zenith. All ions with Z = 1 through Z = 28 were tracked in both scenarios while some additional secondary particles were only tracked in the 4π cases. The MCNP6 4π absorbed dose rate was 307.3 ± 1.3 µGy/day while RAD measured 233 µGy/day. Using the ICRP-60 dose equivalent conversion factors built into MCNP6, the simulated 4π dose equivalent rate was found to be 473.1 ± 2.4 µSv/day while RAD reported 710 µSv/day.

The HelMod Monte Carlo Model for the Propagation of Cosmic Rays in Heliosphere

AbstractThe heliospheric modulation model HelMod solves the transport-equation for Galactic Cosmic Ray propagation through the heliosphere down to Earth. It is based on a 2-D Monte Carlo approach that includes a general description of the symmetric and antisymmetric parts of the diffusion tensor, thus properly treating the particle drift effects as well as convection within the solar wind and adiabatic energy loss. The model was tuned in order to fit 1) the data observed outside the ecliptic plane at several distances from the Earth and 2) the spectra observed near the Earth for both, high and low solar activity periods. Great importance was given to description of polar regions of the heliosphere. We present the flux for protons, antiprotons and helium nuclei computed for solar cycle 23-24 in comparison with experimental observations and prediction for the full solar cycle 24.

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.

A Hitch-hiker’s Guide to Stochastic Differential Equations

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via “toy models”. Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.

Propagation of galactic cosmic rays in the outer heliosphere

The propagation of galactic cosmic rays in heliospheric magnetic fields is studied. An approximate solution to the cosmic ray transport equation has been derived on the basis of a method that takes into account the small value of anisotropy of particle angular distribution. The spatial and energy distributions of the cosmic ray intensity and anisotropy have been investigated, and estimates of cosmic ray energy flux have been carried out.

The propagation of galactic cosmic rays in the outer heliosphere

The propagation of galactic cosmic rays in the outer heliosphere

Northern Sky Galactic Cosmic Ray Anisotropy between 10 and 1000 TeV with the Tibet Air Shower Array

Abstract We report on the analysis of the 10–1000 TeV large-scale sidereal anisotropy of Galactic cosmic rays (GCRs) with the data collected by the Tibet Air Shower Array from 1995 October to 2010 February. In this analysis, we improve the energy estimate and extend the decl. range down to −30°. We find that the anisotropy maps above 100 TeV are distinct from that at a multi-TeV band. The so-called tail-in and loss-cone features identified at low energies get less significant, and a new component appears at ∼100 TeV. The spatial distribution of the GCR intensity with an excess (7.2σ pre-trial, 5.2σ post-trial) and a deficit (−5.8σ pre-trial) are observed in the 300 TeV anisotropy map, in close agreement with IceCube’s results at 400 TeV. Combining the Tibet results in the northern sky with IceCube’s results in the southern sky, we establish a full-sky picture of the anisotropy in hundreds of TeV band. We further find that the amplitude of the first order anisotropy increases sharply above ∼100 TeV, indicating a new component of the anisotropy. All these results may shed new light on understanding the origin and propagation of GCRs.

Galactic cosmic-ray propagation in the light of AMS-02: Analysis of protons, helium, and antiprotons

We present novel constraints on cosmic-ray propagation in the Galaxy using the recent precise measurements of proton and helium spectra from AMS-02, together with preliminary AMS-02 data on the antiproton over proton ratio. To explore efficiently the large (up to eleven-dimensional) parameter space we employ the nested-sampling algorithm as implemented in the \textsc{MultiNest} package, interfaced with the \textsc{Galprop} code to compute the model-predicted spectra. We use VOYAGER proton and helium data, sampling the local inter-stellar spectra, to constrain the solar modulation potential. We find that the turbulence of the Galactic magnetic field is well constrained, i.e., $\delta=0.30^{+0.03}_{-0.02}(stat)^{+0.10}_{-0.04}(sys)$, with uncertainties dominated by systematic effects. Systematic uncertainties are determined checking the robustness of the results to the minimum rigidity cut used to fit the data (from 1 GV to 5 GV), to the propagation scenario (convection vs no-convection), and to the uncertainties in the knowledge of the antiproton production cross section. Convection and reaccelaration are found to be degenerate and not well-constrained singularly when using data above 5 GV. Using data above 1 GV reacceleration is required, $v_{\rm A}=25\pm2$km/s, although this value might be significantly affected by the low energy systematic uncertainty in the solar modulation. In a forthcoming companion paper, we investigate the constraints imposed by AMS-02 measurements on lithium, boron, and carbon.

GALACTIC COSMIC-RAY INTENSITY MODULATION BY COROTATING INTERACTION REGION STREAM INTERFACES AT 1 au

ABSTRACT We present a new model that couples galactic cosmic-ray (GCR) propagation with magnetic turbulence transport and the MHD background evolution in the heliosphere. The model is applied to the problem of the formation of corotating interaction regions (CIRs) during the last solar minimum from the period between 2007 and 2009. The numerical model simultaneously calculates the large-scale supersonic solar wind properties and its small-scale turbulent content from 0.3 au to the termination shock. Cosmic rays are then transported through the background, and thus computed, with diffusion coefficients derived from the solar wind turbulent properties, using a stochastic Parker approach. Our results demonstrate that GCR variations depend on the ratio of diffusion coefficients in the fast and slow solar winds. Stream interfaces inside the CIRs always lead to depressions of the GCR intensity. On the other hand, heliospheric current sheet (HCS) crossings do not appreciably affect GCR intensities in the model, which is consistent with the two observations under quiet solar wind conditions. Therefore, variations in diffusion coefficients associated with CIR stream interfaces are more important for GCR propagation than the drift effects of the HCS during a negative solar minimum.

The TeV-scale cosmic ray proton and helium spectra: Contributions from the local sources

Recent measurements of cosmic ray proton and helium spectra show a hardening above a few hundreds of GeV. This excess is hard to understand in the framework of the conventional models of galactic cosmic ray production and propagation. Here, we propose to explain this anomaly by the presence of local sources. Cosmic ray propagation is described as a diffusion process taking place inside a two-zone magnetic halo. We calculate the proton and helium fluxes at the Earth between 50 GeV and 100 TeV. Improving over a similar analysis, we consistently derive these fluxes by taking into account both local and remote sources for which a unique injection rate is assumed. We find cosmic ray propagation parameters for which the proton and helium spectra remarkably agree with the PAMELA and CREAM measurements over four decades in energy.

Future Extensive Air Shower arrays: From Gamma-Ray Astronomy to Cosmic Rays

Despite large progresses in building new detectors and in the analysis techniques, the key questions concerning the origin, acceleration and propagation of Galactic Cosmic Rays are still open. A number of new EAS arrays is in progress. The most ambitious and sensitive project between them is LHAASO, a new generation multi-component experiment to be installed at very high altitude in China (Daocheng, Sichuan province, 4400 m a.s.l.). The experiment will face the open problems through a combined study of photon- and charged particle-induced extensive air showers in the wide energy range 10$^{11}$ - 10$^{18}$ eV. In this paper the status of the experiment will be summarized, the science program presented and the outlook discussed in comparison with leading new projects.

Cosmic ray heliospheric transport study with neutron monitor data

AbstractDetermining transport coefficients for galactic cosmic ray (GCR) propagation in the turbulent interplanetary magnetic field (IMF) poses a fundamental challenge in modeling cosmic ray modulation processes. GCR scattering in the solar wind involves wave‐particle interaction, the waves being Alfven waves which propagate along the ambient field (B). Empirical values at 1 AU are determined for the components of the diffusion tensor for GCR propagation in the heliosphere using neutron monitor (NM) data. At high rigidities, particle density gradients and mean free paths at 1 AU in B can only be computed from the solar diurnal anisotropy (SDA) represented by a vector A (components Ar, Aϕ, and Aθ) in a heliospherical polar coordinate system. Long‐term changes in SDA components of NMs (with long track record and the median rigidity of response Rm ~ 20 GV) are used to compute yearly values of the transport coefficients for 1963–2013. We confirm the previously reported result that the product of the parallel (to B) mean free path (λ||) and radial density gradient (Gr) computed from NM data exhibits a weak Schwabe cycle (11y) but strong Hale magnetic cycle (22y) dependence. Its value is most depressed in solar activity minima for positive (p) polarity intervals (solar magnetic field in the Northern Hemisphere points outward from the Sun) when GCRs drift from the polar regions toward the helioequatorial plane and out along the heliospheric current sheet (HCS), setting up a symmetric gradient Gθs pointing away from HCS. Gr drives all SDA components and λ|| Gr contributes to the diffusive component (Ad) of the ecliptic plane anisotropy (A). GCR transport is commonly discussed in terms of an isotropic hard sphere scattering (also known as billiard‐ball scattering) in the solar wind plasma. We use it with a flat HCS model and the Ahluwalia‐Dorman master equations to compute the coefficients α (=λ⊥/λ∥) and ωτ (a measure of turbulence in the solar wind) and transport parameters λ||, λ⊥, Gr, Gθs, and an asymmetric gradient Gθa normal to the ecliptic plane. We study their dependence on rigidity (R), p/n intervals, sunspot numbers (SSNs), and solar wind parameters at 1 AU. λ|| exhibits a strong 22y dependence but Gr does not, explaining solar polarity dependence of λ|| Gr. The computed Gr values are an order of magnitude greater than those reported by our colleagues making an ad hoc assumption that α is low (0.01). At high rigidities, the drift contribution at 1 AU is small and unsteady. A new methodology is outlined to compute yearly GCR north‐south anisotropy (Aθ) from the data for a single detector sorted for p/n intervals. We show that Gθa is the main contributor to Aθ in the steady state, and Gθa is shown not correlated with the north‐south excess SSNs.

Studying the distribution and the origin of Galactic cosmic rays by meter wavelength radio observation

The origin, propagation and distribution of Galactic cosmic rays is one of the important fields of cosmic ray study even after more than 100 years since its discovery. Although great progress has been made, It is still far from the final answer. In recent years, joint observations of radio, optical, X-ray and γ -ray play an important role in understanding the Galactic cosmic rays. These observations provide a lot of evidences supporting that Galactic cosmic rays are mainly accelerated in the shock of supernova remnant through the mechanism of diffusive shock acceleration. Our knowledge about the distribu-tion and composition of Galactic cosmic rays is also improved by analyzing the high sensitivity diffuse γ -ray data of Fermi . Meterwave radio observation may promote the studies of Galactic cosmic rays distribution, propagation (absorption obser-vation of HII and planetary nebulae, high sensitivity and resolution meter wavelength sky survey) and origin (observation of supernova remnants shock region, scintillation and scattering observation of extragalactic point sources and pulsars, searching the lower energy counterparts of TeV γ -ray sources).

TIME DEPENDENCE OF THEe−FLUX MEASURED BYPAMELADURING THE 2006 JULY–2009 DECEMBER SOLAR MINIMUM

Precision measurements of the electron component in the cosmic radiation provide important information about the origin and propagation of cosmic rays in the Galaxy not accessible from the study of the cosmic-ray nuclear components due to their differing diffusion and energy-loss processes. However, when measured near Earth, the effects of propagation and modulation of galactic cosmic rays in the heliosphere, particularly significant for energies up to at least 30 GeV, must be properly taken into account. In this paper the electron (e^-) spectra measured by PAMELA down to 70 MeV from July 2006 to December 2009 over six-months time intervals are presented. Fluxes are compared with a state-of-the-art three-dimensional model of solar modulation that reproduces the observations remarkably well.

Galactic Propagation of Cosmic Rays from Individual Supernova Remnants

It is widely believed that supernova remnants are the best candidate sources for the observed cosmic ray flux up to the knee, i.e. up to ∼PeV energies. Indeed, the gamma-ray spectra of some supernova remnants can be well explained by assuming the decay of neutral pions which are created in hadronic interactions. Therefore, fitting the corresponding gamma spectra allows us to derive the spectra of cosmic rays at the source which are locally injected into our Galaxy. Using these spectra as a starting point, we propagate the cosmic rays through the Galaxy using the publicly available GALPROP code. Here, we will present first results on the contribution of those SNRs to the total cosmic ray flux and discuss implications.