Cosmic Ray Propagation Models Research Articles

The Three-dimensional Spatial Distribution of Interstellar Gas in the Milky Way: Implications for Cosmic Rays and High-energy Gamma-ray Emissions.

Direct measurements of cosmic ray (CR) species combined with observations of their associated γ-ray emissions can be used to constrain models of CR propagation, trace the structure of the Galaxy, and search for signatures of new physics. The spatial density distribution of interstellar gas is a vital element for all these studies. So far, models have employed the 2D cylindrically symmetric geometry, but their accuracy is well behind that of the available data. In this paper, 3D spatial density models for neutral and molecular hydrogen are constructed based on empirical model fitting to gas line-survey data. The developed density models incorporate spiral arms and account for the warping of the disk, and the increasing gas scale height with radial distance from the Galactic center. They are employed together with the GALPROP CR propagation code to investigate how the new 3D gas models affect calculations of CR propagation and high-energy γ-ray intensity maps. The calculations reveal non-trivial features that are directly related to the new gas models. The best-fit values for propagation model parameters employing 3D gas models are presented and they differ significantly from those derived with the 2D gas density models that have been widely used. The combination of 3D CR and gas density models provide a more realistic basis for the interpretation of non-thermal emissions from the Galaxy.

HelMod in the Works: From Direct Observations to the Local Interstellar Spectrum of Cosmic-Ray Electrons.

The local interstellar spectrum (LIS) of cosmic-ray (CR) electrons for the energy range 1 MeV to 1 TeV is derived 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 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 model-data comparison. The optimized HelMod parameters are then used to adjust GALPROP parameters to predict a refined LIS with the procedure repeated subject to a convergence criterion. The parameter optimization uses an extensive data set of proton spectra from 1997 to 2015. The proposed CR electron LIS accommodates both the low-energy interstellar spectra measured by Voyager 1 as well as the high-energy observations by PAMELA and AMS-02 that are made deep in the heliosphere; it also accounts for Ulysses counting rate features measured out of the ecliptic plane. The interstellar and heliospheric propagation parameters derived in this study agree well with our earlier results for CR protons, helium nuclei, and anti-protons propagation and LIS obtained in the same framework.

On propagators of nonlocal relativistic diffusion of galactic cosmic rays

This report discusses a new model of cosmic ray propagation in the Galaxy. In contrast to the known models based on the principles of Brownian motion, the proposed model agrees with the relativistic principle of speed limitation and takes into account the large-scale turbulence of the interstellar medium, justifying introduction of fractional differential operators.

Electron-capture Isotopes Could Constrain Cosmic-Ray Propagation Models

Abstract Electron capture (EC) isotopes are known to provide constraints on the low-energy behavior of cosmic rays (CRs), such as reacceleration. Here, we study the EC isotopes within the framework of the dynamic spiral-arms CR propagation model in which most of the CR sources reside in the galactic spiral arms. The model was previously used to explain the B/C and sub-Fe/Fe ratios. We show that the known inconsistency between the 49Ti/49V and 51V/51Cr ratios remains also in the spiral-arms model. On the other hand, unlike the general wisdom that says the isotope ratios depend primarily on reacceleration, we find here that the ratio also depends on the halo size (Z h) and, in spiral-arms models, also on the time since the last spiral-arm passage ( ). Namely, EC isotopes can, in principle, provide interesting constraints on the diffusion geometry. However, with the present uncertainties in the lab measurements of both the electron attachment rate and the fragmentation cross sections, no meaningful constraint can be placed.

Robustness of dark matter constraints and interplay with collider searches for New Physics

We study the implications of dark matter searches, together with collider constraints, on the phenomenological MSSM with neutralino dark matter and focus on the consequences of the related uncertainties in some detail. We consider, inter alia, the latest results from AMS-02, Fermi-LAT and XENON1T. In particular, we examine the impact of the choice of the dark matter halo profile, as well as the propagation model for cosmic rays, for dark matter indirect detection and show that the constraints on the MSSM differ by one to two orders of magnitude depending on the astrophysical hypotheses. On the other hand, our limited knowledge of the local relic density in the vicinity of the Earth and the velocity of Earth in the dark matter halo leads to a factor 3 in the exclusion limits obtained by direct detection experiments. We identified the astrophysical models leading to the most conservative and the most stringent constraints and for each case studied the complementarities with the latest LHC measurements and limits from Higgs, SUSY and monojet searches. We show that combining all data from dark matter searches and colliders, a large fraction of our supersymmetric sample could be probed. Whereas the direct detection constraints are rather robust under the astrophysical assumptions, the uncertainties related to indirect detection can have an important impact on the number of the excluded points.

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.

Theoretical Interpretation of Pass 8 Fermi-LAT e+ + e− Data

Abstract The flux of positrons and electrons (e + + e −) has been measured by the Fermi Large Area Telescope (LAT) in the energy range between 7 GeV and 2 TeV. We discuss a number of interpretations of Pass 8 Fermi-LAT e + + e − spectrum, combining electron and positron emission from supernova remnants (SNRs) and pulsar wind nebulae (PWNe), or produced by the collision of cosmic rays (CRs) with the interstellar medium. We find that the Fermi-LAT spectrum is compatible with the sum of electrons from a smooth SNR population, positrons from cataloged PWNe, and a secondary component. If we include in our analysis constraints from the AMS-02 positron spectrum, we obtain a slightly worse fit to the e + + e − Fermi-LAT spectrum, depending on the propagation model. As an additional scenario, we replace the smooth SNR component within 0.7 kpc with the individual sources found in Green’s catalog of Galactic SNRs. We find that separate consideration of far and near sources helps to reproduce the e + + e − Fermi-LAT spectrum. However, we show that the fit degrades when the radio constraints on the positron emission from Vela SNR (which is the main contributor at high energies) are taken into account. We find that a break in the power-law injection spectrum at about 100 GeV can also reproduce the measured e + + e − spectrum and, among the CR propagation models that we consider, no reasonable break of the power-law dependence of the diffusion coefficient can modify the electron flux enough to reproduce the observed shape.

Possible evidence for the stochastic acceleration of secondary antiprotons by supernova remnants

The antiproton-to-proton ratio in the cosmic-ray spectrum is a sensitive probe of new physics. Using recent measurements of the cosmic-ray antiproton and proton fluxes in the energy range of 1-1000 GeV, we study the contribution to the $\bar{p}/p$ ratio from secondary antiprotons that are produced and subsequently accelerated within individual supernova remnants. We consider several well-motivated models for cosmic-ray propagation in the interstellar medium and marginalize our results over the uncertainties related to the antiproton production cross section and the time-, charge-, and energy-dependent effects of solar modulation. We find that the increase in the $\bar{p}/p$ ratio observed at rigidities above $\sim$ 100 GV cannot be accounted for within the context of conventional cosmic-ray propagation models, but is consistent with scenarios in which cosmic-ray antiprotons are produced and subsequently accelerated by shocks within a given supernova remnant. In light of this, the acceleration of secondary cosmic rays in supernova remnants is predicted to substantially contribute to the cosmic-ray positron spectrum, accounting for a significant fraction of the observed positron excess.

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.

Diffusion of cosmic rays in a model with interstellar turbulence damping due to interaction with energetic particles

A self-consistent model of galactic cosmic ray transport is considered. The resonance wave–particle interaction in this model causes a cascade of magnetosonic waves to decay in the interstellar medium. The calculated coefficient of diffusion of cosmic rays in the Galaxy has a characteristic minimum at an energy of several GeV/nucleon, which agrees with the empirical diffusion model of cosmic ray propagation.

Influence of the finiteness of particle velocity on the energy spectrum of cosmic rays in an anomalous diffusion model with Lévy flights

An estimate of the influence the finiteness of particle velocity has on the results of a fractional differential (anomalous) model of cosmic ray propagation in the Galaxy with Levy flights developed by the authors is considered. The results from Monte Carlo simulations of particle diffusion in random walk models with finite and infinite velocities are presented. It is shown that considering particle velocity finiteness has almost no effect on the cosmic ray energy spectrum obtained for E > 1 GeV in the anomalous diffusion model with Levy flights for nearby young sources.

Nonlocal relativistic diffusion (NoRD) model of cosmic ray propagation

The problem of physical interpretation of the nonlocal relativistic diffusion (NoRD model) for cosmic ray transport in the Galaxy is discussed. The model accounts for the turbulent character of the interstellar medium and the relativistic principle of the speed limitation. Involving fractional calculus and non-Gaussian Lévy statistics yields numerical results compatible with observation data. A special attention is paid to the knee problem. The relativistic speed limit requirement steepens theoretical background spectrum at certain energies, and the position of the break, its sharpness and slopes of asymptotes depend on Dα(E) and α.

Power requirements for cosmic ray propagation models involving diffusive reacceleration; estimates and implications for the damping of interstellar turbulence

We make quantitative estimates of the power supplied to the Galactic cosmic ray population by second-order Fermi acceleration in the interstellar medium, or as it is usually termed in cosmic ray propagation studies, diffusive reacceleration. Using recent results on the local interstellar spectrum from the Voyager missions we show that for parameter values, in particular the Alfv\'en speed, typically used in propagation codes such as Galprop to fit the B/C ratio, the power contributed by diffusive reacceleration is significant and can be of order 50\% of the total Galactic cosmic ray power. The implications for the damping of interstellar turbulence are briefly considered.

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.

On the contribution of a hard galactic plane component to the excesses of secondary particles**Supported by the Ministry of Science and Technology of China, Natural Sciences Foundation of China (11135010).

The standard model of cosmic ray propagation has been very successful in explaining all kinds of galactic cosmic ray spectra. However, high precision measurement have recently revealed an appreciable discrepancy between data and model expectations, from spectrum observations of γ-rays, e+/e− and probably the B/C ratio starting from ∼10 GeV energy. In this work, we propose that a hard galactic plane component, supplied by the fresh cosmic ray sources and detained by local magnetic fields, can contribute additional secondary particles interacting with local materials. By properly choosing the intensity and spectral index of the harder component up to multi-TeV energy, a two-component γ-ray spectrum is obtained and agrees very well with the observation. Simultaneously, the expected neutrino numbers from the galactic plane could contribute ∼60% of IceCube observed neutrino number below a few hundreds of TeV under our model. In addition to these studies, we find that the same pp-collision process responsible for the excess gamma ray emission could account for a significant amount of the positron excess, but a more detailed mechanism is needed for a full agreement. It is expected that the excesses in the and B/C ratio will show up when energy is above ∼10 GeV. We look forward this model being tested in the near future by new observations from AMS02, IceCube, ASγ, HAWC and future experiments such as LHASSO, HiSCORE and CTA.

Expectations for high energy diffuse galactic neutrinos for different cosmic ray distributions

The interaction of cosmic rays with the gas contained in our Galaxy is a guaranteed source of diffuse high energy neutrinos. We provide expectations for this component by considering different assumptions for the cosmic ray distribution in the Galaxy which are intended to cover the large uncertainty in cosmic ray propagation models. We calculate the angular dependence of the diffuse galactic neutrino flux and the corresponding rate of High Energy Starting Events in IceCube by including the effect of detector angular resolution. Moreover we discuss the possibility to discriminate the galactic component from an isotropic astrophysical flux. We show that a statistically significant excess of events from the galactic plane in present IceCube data would disfavour models in which the cosmic ray density is uniform, thus bringing relevant information on the cosmic ray radial distribution.

THE B/C AND SUB-IRON/IRON COSMIC RAY RATIOS—FURTHER EVIDENCE IN FAVOR OF THE SPIRAL-ARM DIFFUSION MODEL

ABSTRACT The boron to carbon (B/C) and sub-Fe/Fe ratios provide an important clue on cosmic ray (CR) propagation within the Galaxy. These ratios estimate the grammage that the CRs traverse as they propagate from their sources to Earth. Attempts to explain these ratios within the standard CR propagation models require ad hoc modifications and even with those these models necessitate inconsistent grammages to explain both ratios. As an alternative, physically motivated model, we have proposed that CRs originate preferably within the galactic spiral arms. CR propagation from dynamic spiral arms has important imprints on various secondary to primary ratios, such as the B/C ratio and the positron fraction. We use our spiral-arm diffusion model with the spallation network extended up to nickel to calculate the sub-Fe/Fe ratio. We show that without any additional parameters the spiral-arm model consistently explains both ratios with the same grammage, providing further evidence in favor of this model.

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.

Limits on dark matter from AMS-02 antiproton and positron fraction data

We derive limits on the dark matter annihilation cross section and lifetime using measurements of the AMS-02 antiproton ratio and positron fraction data. In deriving the limits, we consider the scenario of secondary particles accelerated in supernova remnants (SNRs) which has been argued to be able to reasonably account for the AMS-02 high energy positron/antiproton fraction data. We parameterize the contribution of secondary particles accelerated in SNRs and then fit the observational data within the conventional cosmic ray propagation model by adopting the GALPROP code. We use the likelihood ratio test to determine the 95$\%$ confidence level upper limits of the possible dark matter (DM) contribution to the antiproton/positron fractions measured by AMS-02. Our limits are stronger than that set by the Fermi-LAT gamma-ray Pass 8 data of the dwarf spheroidal satellite galaxies. We also show that the solar modulation (cosmic ray propagation) parameters can play a non-negligible role in modifying the constraints on the dark matter annihilation cross section and lifetime for $m_\chi<100$ GeV ($m_\chi>100$ GeV), where $m_\chi$ is the rest mass of the dark matter particles. Using this results, we also put limits on the effective field theory of dark matter.

Gamma-ray and neutrino diffuse emissions of the Galaxy above the TeV

Conventional cosmic ray propagation models face problems reproducing the diffuse 7-ray spectrum measured by Fermi-LAT over the entire sky. Those models also fail to smoothly connect Fermi-LAT results with data above the TeV as those taken by Milagro in the inner Galactic plane. In this contribution we show that a representative model adopting a spatial dependent rigidity scaling of the diffusion coefficient can reproduce all those experimental results without spoiling the consistency with local cosmic-ray measurements. We use the same model to compute the diffuse neutrino emission of the Galaxy and compare it with IceCube and ANTARES results.