Cosmic Ray Propagation Models Research Articles

Beryllium Radioactive Isotopes as a Probe to Measure the Residence Time of Cosmic Rays in the Galaxy and Halo Thickness: A “Data-Driven” Approach

Cosmic rays are a powerful tool for the investigation of the structure of the magnetic fields in the Galactic halo and the properties of the inter-stellar medium. Two parameters of the cosmic ray propagation models, the Galactic halo (half) thickness, H, and the diffusion coefficient, D, are loosely constrained by current cosmic ray flux measurements; in particular, a large degeneracy exists, with only H/D being well measured. The 10Be/9Be isotopic flux ratio (thanks to the 2 My lifetime of 10Be) can be used as a radioactive clock providing the measurement of cosmic ray residence time in a galaxy. This is an important probe with which to solve the H/D degeneracy. Past measurements of 10Be/9Be isotopic flux ratios in cosmic rays are scarce, and were limited to low energy and affected by large uncertainties. Here a new technique to measure 10Be/9Be isotopic flux ratio, with a data-driven approach in magnetic spectrometers is presented. As an example, by applying the method to beryllium events published via PAMELA experiment, it is now possible to determine the important 10Be/9Be measurement while avoiding the prohibitive uncertainties coming from Monte Carlo simulations. It is shown how the accuracy of PAMELA data strengthens the experimental indication for the relativistic time dilation of 10Be decay in cosmic rays; this should improve the knowledge of the H parameter.

Origin of Galactic Sub-PeV Diffuse Gamma-Ray Emission: Constraints from High-energy Neutrino Observations

Abstract Very recently, diffuse gamma-rays with 0.1 PeV < E γ < 1 PeV have been discovered from the Galactic disk by the Tibet air shower array and muon detector array (Tibet AS+MD array). While the measured sub-PeV flux may be compatible with the hadronic origin in the conventional Galactic cosmic-ray propagation model, we find that it is in possible tension with the nondetection of Galactic neutrino emissions by the IceCube neutrino telescope. We further find that the presence of an extra cosmic-ray component of relatively hard spectrum, which is probably related to the Cygnus Cocoon region and other PeV cosmic-ray sources in the Galactic disk, would alleviate the tension. This scenario implies the existence of an extreme accelerator of either protons or electrons beyond PeV in the Cygnus region, and predicts the continuation of the gamma-ray spectrum of Cygnus Cocoon up to 1 PeV with a possible hardening beyond ∼30–100 TeV.

Data driven approach for the measurement of Be10/Be9 in cosmic rays with magnetic spectrometers

Cosmic rays (CRs) are a powerful tool for the investigation of the structure of the magnetic fields in the galactic halo and the properties of the interstellar medium. Two parameters of the CR propagation model---the galactic halo (half-)thickness $H$ and the diffusion coefficient $D$---are loosely constrained by current CR flux measurements; in particular, a large degeneracy exists being only $H/D$ well measured. The $^{10}\mathrm{Be}/^{9}\mathrm{Be}$ isotopic flux ratio (thanks to the 2 My lifetime of $^{10}\mathrm{Be}$) can be used as a radioactive clock, providing the measurement of CR residence time in the galaxy. This is an important tool for solving the $H/D$ degeneracy. Past measurements of the $^{10}\mathrm{Be}/^{9}\mathrm{Be}$ isotopic flux ratio in CRs are scarce, limited to low energy, and affected by large uncertainties. Here, a new technique to measure the $^{10}\mathrm{Be}/^{9}\mathrm{Be}$ isotopic flux ratio with a data-driven approach in magnetic spectrometers is presented. The analysis with the data driven approach of beryllium events collected by the PAMELA experiment is shown as an example. It is possible to measure the $^{10}\mathrm{Be}/^{9}\mathrm{Be}$ flux ratio avoiding the uncertainties related to the Monte Carlo simulation.

Measurements of the time-dependent cosmic-ray Sun shadow with seven years of IceCube data: Comparison with the Solar cycle and magnetic field models

Observations of the time-dependent cosmic-ray Sun shadow have been proven as a valuable diagnostic for the assessment of solar magnetic field models. In this paper, seven years of IceCube data are compared to solar activity and solar magnetic field models. A quantitative comparison of solar magnetic field models with IceCube data on the event rate level is performed for the first time. Additionally, a first energy-dependent analysis is presented and compared to recent predictions. We use seven years of IceCube data for the moon and the Sun and compare them to simulations on data rate level. The simulations are performed for the geometrical shadow hypothesis for the moon and the Sun and for a cosmic-ray propagation model governed by the solar magnetic field for the case of the Sun. We find that a linearly decreasing relationship between Sun shadow strength and solar activity is preferred over a constant relationship at the 6.4σ level. We test two commonly used models of the coronal magnetic field, both combined with a Parker spiral, by modeling cosmic-ray propagation in the solar magnetic field. Both models predict a weakening of the shadow in times of high solar activity as it is also visible in the data. We find tensions with the data on the order of 3σ for both models, assuming only statistical uncertainties. The magnetic field model CSSS fits the data slightly better than the PFSS model. This is generally consistent with what is found previously by the Tibet AS−γ Experiment; a deviation of the data from the two models is, however, not significant at this point. Regarding the energy dependence of the Sun shadow, we find indications that the shadowing effect increases with energy during times of high solar activity, in agreement with theoretical predictions.7 MoreReceived 26 June 2020Accepted 11 December 2020DOI:https://doi.org/10.1103/PhysRevD.103.042005© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCosmic ray propagationMagnetic field generation & plasma dynamoSpace & astrophysical plasmaWave-wave, wave-particle interactionsPropertiesInterplanetary magnetic fieldTechniquesCherenkov detectorsCosmic ray & astroparticle detectorsCosmic rays & astroparticlesNeutrino detectorsTest-particle methodsGravitation, Cosmology & AstrophysicsPlasma PhysicsParticles & Fields

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.

Time Dependence of the Flux of Helium Nuclei in Cosmic Rays Measured by the PAMELA Experiment between 2006 July and 2009 December

Abstract Precise time-dependent measurements of the Z = 2 component in the cosmic radiation provide crucial information about the propagation of charged particles through the heliosphere. The PAMELA experiment, with its long flight duration (2006 June 15–2016 January 23) and the low energy threshold (80 MeV/n) is an ideal detector for cosmic-ray solar modulation studies. In this paper, the helium nuclei spectra measured by the PAMELA instrument from 2006 July to 2009 December over a Carrington rotation time basis are presented. A state-of-the-art three-dimensional model for cosmic-ray propagation inside the heliosphere was used to interpret the time-dependent measured fluxes. Proton-to-helium flux ratio time profiles at various rigidities are also presented in order to study any features that could result from the different masses and local interstellar spectra shapes.

Two Numerical Methods for the 3D Anisotropic Propagation of Galactic Cosmic Rays

Abstract Conventional cosmic-ray propagation models usually assume an isotropic diffusion coefficient to account for the random deflection of cosmic rays by the turbulent interstellar magnetic field. Such models very successfully explain many observational phenomena related to the propagation of Galactic cosmic rays, such as broken power-law energy spectra, secondary-to-primary ratios, etc. However, the isotropic diffusion presupposition is facing severe challenges from recent observations. In particular, such observations on the large-scale anisotropy of TeV cosmic rays show that the dipole direction differs from the prediction of the conventional model. One possible reason is that the large-scale regular magnetic field, which leads to an anisotropic diffusion of cosmic rays, has not been included in the model provided by the public numerical packages. In this work, we propose two numerical schemes to solve the three-dimensional anisotropic transport equation: the pseudo-source method and Hundsdorfer–Verwer scheme. Both methods are verified by reproducing the measured B/C and proton spectrum and the radial variation of spectral index expected by former 2D simulation. As a demonstration of the prediction capability, dipole anisotropy is also calculated by a toy simulation with a rough magnetic field.

Deciphering the Local Interstellar Spectra of Secondary Nuclei with the Galprop/Helmod Framework and a Hint for Primary Lithium in Cosmic Rays.

Local interstellar spectra (LIS) of secondary cosmic-ray (CR) nuclei, lithium, beryllium, boron, and partially secondary nitrogen, are derived in the rigidity range from 10 MV to ~200 TV using the most recent experimental results combined with state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. The lithium spectrum appears somewhat flatter at high energies compared to other secondary species, which may imply a primary lithium component. Two propagation packages, GALPROP and HelMod, are combined to provide a single framework that is run to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. An iterative maximum-likelihood method is developed that uses GALPROP-predicted LIS as input to HelMod, which provides the modulated spectra for specific time periods of the selected experiments for the model-data comparison. The proposed LIS accommodates the low-energy interstellar spectra measured by Voyager 1, the High Energy Astrophysics Observatory-3 (HEAO-3), and the Cosmic Ray Isotope Spectrometer on board of the Advanced Composition Explorer (ACE/CRIS), as well as the high-energy observations by the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA), Alpha Magnetic Spectrometer-02 (AMS-02), and earlier experiments that are made deep in the heliosphere. The interstellar and heliospheric propagation parameters derived in this study are consistent with our earlier results for propagation of CR protons, helium, carbon, oxygen, antiprotons, and electrons.

Usine: Semi-analytical models for Galactic cosmic-ray propagation

I present the first public releases (v3.4 and v3.5) of the usine code for cosmic-ray propagation in the Galaxy (https://lpsc.in2p3.fr/usine). It contains several semi-analytical propagation models previously used in the literature (leaky-box model, 2-zone 1D and 2D diffusion models) for the calculation of nuclei (Z=1−30), anti-protons, and anti-deuterons. For minimisations, the geometry, transport, and source parameters of all models can be enabled as free parameters, whereas nuisance parameters are enabled on solar modulation levels, cross sections (inelastic and production), and systematics of the CR data. With a single ASCII initialisation file to configure runs, its many displays, and the speed associated to semi-analytical approaches, usine should be a useful tool for beginners, but also for experts to perform statistical analyses of high-precision cosmic-ray data. Program summaryProgram Title:usine.Program Files doi:http://dx.doi.org/10.17632/66dvnt642g.1Licensing provisions: GPLv3Programming language: C++External routines/libraries:root cern.Nature of problem: Semi-analytical models for GCR transport.Solution method: Partial derivatives on spatial coordinates solved analytically, partial derivatives on energy coordinates solved numerically (finite difference).Restrictions: Electronic capture decay not fully implemented.

Prospects of detecting dark matter through cosmic-ray antihelium with the antiproton constraints

Cosmic-ray (CR) antihelium is an important observable for dark matter (DM) indirect searches due to extremely low secondary backgrounds towards low energies. In a given DM model, the predicted CR antihelium flux is expected to be strongly correlated with that of CR antiprotons. In this work, we use the AMS-02 p̄/p data to constrain the DM annihilation cross section, and the ALICE data on the 3H̄ē and T̄ productions to determine the parameters in the coalescence model for anti-nucleus formation. The hadronic cross sections are estimated using Monte-Carlo event generators including EPOS-LHC and DPMJET. Based on these constraints, we make predictions for the maximal antihelium flux for typical DM annihilation final states, and perform a detailed analysis on the uncertainties due to the DM density profiles and CR propagation models. We find that the results are highly insensitive to both of them, but still significantly depend on the hadronization models in event generators. The prospects of detecting antihelium for the AMS-02 experiment is discussed. We show that with very optimistic assumptions, CR 3H̄ē is within the reach of the AMS-02 experiment. The 3H̄ē events which can be detected by AMS-02 are likely to have kinetic energy T ≳ 30 GeV, which is consistent with the preliminary AMS-02 search results. The events which can be observed by AMS-02 are likely to arise dominantly from secondary backgrounds rather than DM interactions.

Scrutinizing the evidence for dark matter in cosmic-ray antiprotons

Global fits of primary and secondary cosmic-ray (CR) fluxes measured by AMS-02 have great potential to study CR propagation models and search for exotic sources of antimatter such as annihilating dark matter (DM). Previous studies of AMS-02 antiprotons revealed a possible hint for a DM signal which, however, could be affected by systematic uncertainties. To test the robustness of such a DM signal, in this work we systematically study two important sources of uncertainties: the antiproton production cross sections needed to calculate the source spectra of secondary antiprotons and the potential correlations in the experimental data, so far not provided by the AMS-02 Collaboration. To investigate the impact of cross-section uncertainties we perform global fits of CR spectra including a covariance matrix determined from nuclear cross-section measurements. As an alternative approach, we perform a joint fit to both the CR and cross-section data. The two methods agree and show that cross-section uncertainties have a small effect on the CR fits and on the significance of a potential DM signal, which we find to be at the level of $3\sigma$. Correlations in the data can have a much larger impact. To illustrate this effect, we determine possible benchmark models for the correlations in a data-driven method. The inclusion of correlations strongly improves the constraints on the propagation model and, furthermore, enhances the significance of the DM signal up to above $5\sigma$. Our analysis demonstrates the importance of providing the covariance of the experimental data, which is needed to fully exploit their potential.

Galactic cosmic ray hydrogen spectra and radial gradients in the inner heliosphere measured by the HELIOS Experiment 6

Context. The HELIOS solar observation probes provide unique data regarding their orbit and operation time. One of the onboard instruments, the Experiment 6 (E6), is capable of measuring ions from 4 to several hundred MeV nucleon−1. Aims. In this paper we aim to demonstrate the relevance of the E6 data for the calculation of galactic cosmic ray (GCR), anomalous cosmic ray (ACR), and solar energetic particle (SEP) fluxes for different distances from the sun and time periods. Methods. Several corrections have been applied to the raw data: determination of the Quenching factor of the scintillator, correction of the temperature dependent electronics, degradation of the scintillator as well as the effects on the edge of semi-conductor detectors. Results. Fluxes measured by the E6 are in accordance with the force field solution for the GCR and match models of the anomalous cosmic ray propagation. GCR radial gradients in the inner heliosphere show a different behaviour than in the outer heliosphere.

Reverse direct detection: Cosmic ray scattering with light dark matter

Sub-GeV dark matter candidates are of increasing interest, because long-favored candidates such as GeV-scale WIMPs have not been detected. For low-mass dark matter, model-independent constraints are weak or nonexistent. We show that for such candidates, because the number density is high, cosmic ray propagation can be affected by elastic scattering with dark matter. We call this type of search `reverse direct detection,' because dark matter is the target and Standard Model particles are the beam. Using a simple propagation model for galactic cosmic rays, we calculate how dark matter affects cosmic ray spectra at Earth, and set new limits on the dark matter-proton and dark matter-electron cross sections. For protons, our limit is competitive with cosmological constraints, but is independent. For electrons, our limit covers masses not yet probed, and improves on cosmological constraints by one to two orders of magnitude. We comment on how future work can significantly improve the sensitivity of cosmic-ray probes of dark matter interactions.

CHANG-ES XII

Context. Low-frequency radio continuum studies of star-forming edge-on galaxies can help to further understand how cosmic-ray electrons (CRe) propagate through the interstellar medium into the halo and how this is affected by energy losses and magnetic fields. Aims. Observations with the Very Large Array (VLA) from Continuum Haloes in Nearby Galaxies – an EVLA Survey (CHANG-ES) are combined with those with the LOw Frequency ARray (LOFAR) from the LOFAR Two-metre Sky Survey (LoTSS ) to identify the prevailing mode of cosmic-ray transport in the edge-on spiral galaxy NGC 3556. Methods. We mapped the radio spectral index, magnetic field strength, and orientation using VLA 1.5 and 6 GHz and LOFAR 144 MHz data, and we fit 1D cosmic-ray propagation models to these maps using SPINNAKER (Spectral Index Numerical Analysis of K(c)osmic-ray electron radio emission) and its interactive wrapper SPINTERACTIVE. Results. We find that the spectral index in the galactic midplane is, as expected for young CRe, α ≈ −0.7 and steepens towards the halo of the galaxy as a consequence of spectral ageing. The intensity scale heights are about 1.4 and 1.9 kpc for the thin disc, and 3.3 and 5.9 kpc for the thick disc at 1.5 GHz and 144 MHz, respectively. While pure diffusion cannot explain our data, advection can, particularly if we assume a linearly accelerating wind. Our best-fitting model has an initial speed of 123 km s−1 in the galactic midplane and reaches the escape velocity at heights between 5 kpc and 15 kpc above the disc, depending on the assumed dark matter halo of the galaxy. This galactic wind scenario is corroborated by the existence of vertical filaments seen both in the radio continuum and in H α in the disc-halo interface and of a large-scale reservoir of hot, X-ray emitting gas in the halo. Conclusions. Radio haloes show the existence of galactic winds, possibly driven by cosmic rays, in typical star-forming spiral galaxies.

Positron flux and γ-ray emission from Geminga pulsar and pulsar wind nebula

Nearby pulsars have been suggested as sources of $\sim$TeV $e^+/e^-$ Cosmic Ray (CR) excess on Earth. The High-Altitude Water Cherenkov Observatory (HAWC) detected extended TeV emission regions in the direction of two nearby middle-aged pulsars, Geminga and PSR B0656+14. By modeling the TeV emission as inverse Compton emission from electron-positron pairs diffusing in the interstellar medium (ISM), the HAWC collaboration derives a diffusion coefficient much smaller than the standard value in the vicinity of the two pulsars, which make them unlikely the origin of the positron excess. We propose that the observed $\gamma$-ray emission originate from the relic pulsar wind nebula. A two zone diffusion model with a slow diffusion in the nebula and a fast diffusion in the ISM can explain the HAWC surface brightness profile and the positron excess simultaneously. Inefficient diffusion in the $\gamma$-ray emission region surrounding a middle-aged pulsar maybe a common phenomenon that can be tested by future observation. The implied diffusion coefficient in the ISM is smaller than the one suggested by the standard CR propagation model, but it is fully consistent with the predictions of the spiral arm model.

Revisit cosmic ray propagation by using 1H, 2H, 3He and 4He

The secondary-to-primary ratios are unique tools to investigate cosmic ray propagation mechanisms. In this work, we use the latest data of deuteron-to-helium 4 ratio and helium 3-to-helium 4 ratio measured by PAMELA combined with other Z≤2 primary fluxes measured by PAMELA and Voyager-1, to constrain the cosmic ray acceleration and propagation models. The analysis is performed by interfacing statistical tools with the GALPROP propagation package. To better fit both the modulated and unmodulated low energy cosmic ray data, we find that a time-, charge- and rigidity-dependent solar modulation model is better than the force-field approximation. Among all the studied cosmic ray propagation models, the diffusion–reacceleration–convection model is strongly supported by the derived Bayesian evidence. The robustness of the estimated diffusion slope δ is cross-checked by another low-mass secondary-to-primary ratio, i.e. the antiproton-to-proton ratio. It is shown that the diffusion–reacceleration–convection model can reconcile well with the high energy antiproton-to-proton ratio. This indicates that the estimated value of δ is reliable. The well constraint δ from the “best” model is found to be close to 1/3, inferring a Kolmogorov-type interstellar magnetic turbulence.

Gamma-Ray Emission from Molecular Clouds Generated by Penetrating Cosmic Rays

Abstract We analyze the processes governing cosmic-ray (CR) penetration into molecular clouds and the resulting generation of gamma-ray emission. The density of CRs inside a cloud is depleted at lower energies due to the self-excited MHD turbulence. The depletion depends on the effective gas column density (“size”) of the cloud. We consider two different environments where the depletion effect is expected to be observed. For the central molecular zone, the expected range of CR energy depletion is E ≲ 10 GeV, leading to the depletion of gamma-ray flux below E γ ≈ 2 GeV. This effect can be important for the interpretation of the GeV gamma-ray excess in the Galactic Center, which has been revealed from the standard model of CR propagation (assuming the CR spectrum inside a cloud to be equal to the interstellar spectrum). Furthermore, recent observations of some local molecular clouds suggest the depletion of the gamma-ray emission, indicating possible self-modulation of the penetrating low-energy CRs.

Lower Limits on the Nucleosynthesis of 44Ti and 60Fe in the Dynamic Spiral-arm Cosmic-Ray Propagation Model

We have previously focused on studying the electron-capture isotopes within the dynamic spiral-arms model and empirically derived the energy dependence of the electron attachment rate using the observation of $^{49}$Ti/$^{49}$V and $^{51}$V/$^{51}$Cr ratios in cosmic rays (Benyamin et al. 2017). We have also shown how this relation recovers the energy dependence seen in the lab measurements (Letaw et al. 1985). In this work we use this relation to construct the $^{44}$Ca/$^{44}$Ti ratio and place a lower limit on the amount of $^{44}$Ti that is required to be nucleosynthesized at the source. The results also imply that the acceleration process of the radioisotopes cannot be much longer than a century time scale (or else the required nucleosynthesized amount has to be correspondingly larger). We also provide a similar lower limit on the source $^{60}$Fe by comparing to the recently observed $^{60}$Fe/$^{56}$Fe (Binns et al. 2016).

Deciphering the Local Interstellar Spectra of Primary Cosmic-Ray Species with helmod.

Local interstellar spectra (LIS) of primary cosmic ray (CR) nuclei, such as helium, oxygen, and mostly primary carbon are derived for the rigidity range from 10 MV to ~200 TV using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. Two propagation packages, GALPROP and helmod, are combined into a single framework that is used to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. The developed iterative maximum-likelihood method uses GALPROP-predicted LIS as input to helmod, which provides the modulated spectra for specific time periods of the selected experiments for model-data comparison. The interstellar and heliospheric propagation parameters derived in this study are consistent with our prior analyses using the same methodology for propagation of CR protons, helium, antiprotons, and electrons. The resulting LIS accommodate a variety of measurements made in the local interstellar space (Voyager 1) and deep inside the heliosphere at low (ACE/CRIS, HEAO-3) and high energies (PAMELA, AMS-02).

Propagating Cosmic Rays with exact Solution of Fokker-Planck Equation

Shortfalls in cosmic ray (CR) propagation models obscure the CR sources and acceleration mechanisms. This problem became particularly obvious after the Fermi, Pamela, and AMS-02 have discovered the electron/positron and p/He spectral anomalies. Most of the CR models use diffusive propagation that is inaccurate for weakly scattered energetic particles. So, some parts of the spectra affected by the heliospheric modulation, for example, cannot be interpreted. I discuss and adopt an exact solution of the Fokker-Planck equation [M. A. Malkov, Exact solution of the Fokker-Planck equation for isotropic scattering arXiv:1610.01584, doi:https://doi.org/10.1103/PhysRevD.95.023007(2017)], which gives a complete description of a ballistic, diffusive and transdiffusive (intermediate between the first two) propagation regimes. I derive a simplified version of an exact Fokker-Planck propagator that can easily be employed in place of the Gaussian propagator, currently used in major Solar modulation and other CR transport models.