Propagation of Cosmic Rays: Nuclear Physicsin Cosmic-Ray Studies

Igor V. Moskalenko∗†, Andrew W. Strong∗∗ and Stepan G. Mashnik‡

∗NASA/Goddard Space Flight Center, Code 661, Greenbelt, MD 20771†Joint Center for Astrophysics/University of Maryland, Baltimore County, Baltimore, MD 21250∗∗Max-Planck-Institut für extraterrestrische Physik, Postfach 1603, D-85740 Garching, Germany

‡Los Alamos National Laboratory, Los Alamos, NM 87544

Abstract. The nuclei fraction in cosmic rays (CR) far exceeds the fraction of other CR species, such as antiprotons, electrons,and positrons. Thus the majority of information obtained from CR studies is based on interpretation of isotopic abundancesusing CR propagation models where the nuclear data and isotopic production cross sections inp- andα-induced reactions arethe key elements. This paper presents an introduction to theastrophysics of CR and diffuseγ-rays and discusses some of thepuzzles that have emerged recently due to more precise data and improved propagation models. Merging with cosmology andparticle physics, astrophysics of CR has become a very dynamic field with a large potential of breakthrough and discoveriesin the near future. Exploiting the data collected by the CR experiments to the fullest requires accurate nuclear cross sections.

INTRODUCTION

The origin of CR have been intriguing scientists since1912 when V. Hess carried out his famous balloon flightto measure the ionization rate in the upper atmosphere.The energy density of relativistic particles (CR) is∼1eV cm−3 and is comparable to that of the interstellarradiation and magnetic fields, and turbulent motions ofthe interstellar gas. This makes CR one of the essentialfactors determining the dynamics and processes in theinterstellar medium (ISM). The observations of the SmallMagellanic Cloud [1] by the EGRET (Energetic GammaRay Experiment Telescope) on board of the ComptonGamma Ray Observatory (CGRO) have shown that theCR are a Galactic andnota “metagalactic” phenomenon.Observations of the Large Magellanic Cloud [2], in turn,have shown thatγ-ray flux is consistent with CR havinga density comparable to that in our Galaxy.

Major cosmic accelerators are supernova remnants(SNRs), with a fraction of CR coming from pulsars, com-pact objects in close binary systems, and stellar winds.Observations of X-ray andγ-ray emission from these ob-jects reveal the presence of energetic electrons thus tes-tifying to efficient acceleration [3]. The total power ofGalactic CR sources needed to sustain the observed CRdensity is estimated at 5×1040 erg s−1 which implies therelease of energy in the form of CR of∼5×1049 erg persupernova (SN) if the SN rate is∼ 3 per century.

Propagation in the ISM changes the initial composi-tion and spectra of CR species (Fig. 1). The destruction

of primary nuclei via spallation gives rise to secondarynuclei and isotopes which are rare in nature, antiprotons,and pions (π±, π0) that decay producing secondarye±’sandγ-rays. CR are “stored” in the Galaxy for tens of mil-lions years before escaping into the intergalactic space.

Although much progress has been made since the di-rect measurements in space have become possible, thedetailed information refers only to the environment nearto the sun. The CR source composition and CR propa-gation history are imprinted in their isotopic abundanceswhile diffuseγ-rays and synchrotron emission from dif-ferent directions carry clues to the proton and electronspectra in distant locations. These are the only pieces ofthe universal puzzle that we have and exploiting them re-quires extensive modeling.

FIGURE 1. Basic processes in the ISM.

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FIGURE 2. Spectrum (E2×Flux) of diffuseγ-rays from the

inner Galaxy as measured by the EGRET. Curves indicate in-dividual components:π0-decay (NN), electron bremsstrahlung(EB), inverse Compton (IC), and isotropic diffuse emission(ID). Adapted from [4].

INDICATIONS OF NEW PHENOMENA?

The puzzling excess in the EGRET data above 1 GeV(Fig. 2) relative to that expected [4, 5] has shown up inall models that are tuned to be consistent with local nu-cleon and electron spectra [6, 7]. The excess has shownup in all directions, not only in the Galactic plane. Anapparent discrepancy between the radial gradient in thediffuse Galacticγ-ray emissivity and the distribution ofCR sources (SNRs) has worsened the problem [6].

Positron fractione+/(all leptons) in CR as measuredby HEAT [8] also exhibits an excess above∼8 GeV(Fig. 3) compared to predictions of the diffusion modelfor secondary production [9].

Secondary antiprotons are produced in the same in-teractions of CR particles with interstellar gas ase+’sand diffuseγ-rays. Recent ¯p data with larger statistics[12] triggered a series of calculations of the secondary ¯pflux in CR. The diffusive reacceleration models have cer-tain advantages compared to other propagation models:they naturally reproduce secondary/primary nuclei ratiosin CR, have only three free parameters, and agree betterwith K-capture parent/daughter nuclei ratio. The detailedanalysis shows, however, that the reacceleration modelsunderproduce ¯p’s by a factor of∼2 at 2 GeV [13] (Fig. 4)because matching the B/C ratio at all energies requires

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FIGURE 3. Positrons/(all leptons) ratio in CR compared tocalculations in a leaky-box model [10] (solid) and GALPROPdiffusion model [9] (dashes). Adapted from [11].

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FIGURE 4. Spectrum of secondary antiprotons in CR ascalculated in reacceleration (solid lines) and optimized (dots)models. The upper curves – interstellar, lower curves – modu-lated (Φ = 550 MV) to compare with data. Adapted from [7].

the diffusion coefficient to be too large.If these excesses are not a simple artefact, they may be

telling us about processes in the ISM, in the Local Bub-ble, or signaling exotic physics (e.g., WIMP annihilation,primordial black hole evaporation), but also may indicatea flaw in the current models.

COSMIC RAYS AND DIFFUSE γ-RAYS

The modeling of CR diffusion in the Galaxy includes thesolution of the transport equation with a given sourcedistribution and boundary conditions (free escape intothe intergalactic space) for all CR species. The transportequation describes diffusion and energy losses and mayalso include [14] the convection by a hypothetical Galac-tic wind, distributed acceleration in the ISM due to theFermi second-order mechanism (reaccleration), and non-linear wave-particle interactions.

The study of transport of the CR nuclear componentrequires the consideration of nuclear spallation, radioac-tive decay, and ionization energy losses. Calculation ofisotopic abundances involves hundreds of secondary nu-clei produced in CR interactions with interstellar gas. Athorough data base of isotopic production and fragmen-tation cross sections is thus a critical element of propaga-tion models that are constrained by the abundance mea-surements of isotopes, ¯p’s, ande+’s in CR.

As solar activity changes with a period of 11 years sodoes the intensity of CR, but in opposite direction: withan inverse correlation. The “solar modulation” is a com-bination of effects of convection by the solar wind, diffu-sion, adiabatic cooling, drifts, diffusive acceleration andaffects CR below 20 GeV/nucleon. The theory of solarmodulation is far from being complete [15]. The Ulyssesspacecraft first provided measurements of the solar windand magnetic field outside the ecliptic helping us to un-

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FIGURE 5. The EGRET sky: diffuseγ-ray emission [5].

derstanding the global aspects of modulation, while Pio-neer and the two Voyagers have explored the outer solarsystem. Recently there appear some indications that Voy-ager 1, currently at 13.3×109 km (88 AU) from the sun,may be close to the termination shock, the heliosphericboundary. If true, in a few years it will become the firstspacecraft ever to reach interstellar space.

The diffuse continuum emission is the dominant fea-ture of theγ-ray sky (Fig. 5). It is evidence of CR pro-ton and electron interactions with gas and the interstel-lar radiation field (ISRF), and is created viaπ0-decay,inverse Compton, and bremsstrahlung. This emission inthe range 50 keV – 50 GeV has been systematically stud-ied in by OSSE (Oriented Scintillation Spectrometer Ex-periment), COMPTEL (Imaging Compton Telescope),and EGRET on the CGRO and in earlier experiments[4, 5]. The GLAST (Gamma-ray Large Area Space Tele-scope) will improve the sensitivity for the diffuse emis-sion by a factor of 30.

Increasingly accurate balloon-borne and spacecraftexperiments are demanding propagation models with im-proved predictive capability. Incorporation of the realis-tic astrophysical input increases the chances of the modelto approach reality and dictates that such a model shouldbe numerical. Besides the nuclear data, such a modelhas to include the detailed 3-dimensional maps of theGalactic gas derived from radio and IR surveys, the LocalBubble and local SNRs, the spectrum of the ISRF, mag-netic fields, details of composition of interstellar dust,grains, as well as theoretical works on CR accelerationand transport in Galactic environments. The most ad-vanced model to date, GALPROP, is a three dimensionalmodel [6, 13, 16]. It is widely used as a basis for manystudies, such as search for dark matter signatures, ori-gin and evolution of elements, the spectrum and originof Galactic and extragalactic diffuseγ-ray emission, he-liospheric modulation. The model calculates CR propa-gation for nuclei (11H to 64

28Ni), p’s, e±’s, and computesγ-rays and synchrotron emission in the same framework;it includes all relevant processes and reactions. It is anexcellent tool to cross-test various hypotheses [7, 17].

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FIGURE 6. Boron/carbon ratio in CR as calculated in thereacceleration model. Lower curve – interstellar ratio, uppercurve – modulated (Φ = 450 MV) to compare with data.Adapted from [7].

NUCLEAR PHYSICS IN CR STUDIES

The abundances of stable (3Li, 4Be, 5B, 21Sc,22Ti, 23V)and radioactive secondaries (10

4 Be, 2613Al, 36

17Cl, 5425Mn) in

CR are used to derive the diffusion coefficient and thehalo size [16, 18]. The derived source abundances ofCR may provide some clues to mechanisms and sitesof CR acceleration. However, the interpretation of CRdata, e.g., the sharp peak in the secondary/primary nu-clei ratio (Fig. 6), is model dependent. The leaky-boxmodel fits the secondary/primary ratio by allowing thepath-length distribution vs. rigidity to vary. The diffusionmodels are more physical and explain the shape of thesecondary/primary ratio in terms of diffusive reaccelera-tion (distributed energy gain) in the ISM, convection bythe Galactic wind, or by the damping of the interstellarturbulence by CR on a small scale.

The secondary/primary nuclei ratio is sensitive to thevalue of the diffusion coefficient and its energy depen-dence. A larger diffusion coefficient leads to a lower ratiosince the primary nuclei escape faster from the Galaxyproducing less secondaries and vice versa. The abun-dance of radioactive secondaries (e.g.,10Be/9Be) is sen-sitive to the Galactic halo size, the Galactic volume filledwith CR. The larger the halo the longer it takes for ra-dioactives to reach us thus decreasing the ratio10Be/9Be.

Current CR experiments, such as Advanced Composi-tion Explorer (ACE), Ulysses, and Voyager, deliver ex-cellent quality spectral and isotopic data. Meanwhile,isotopic production cross sections have for a long timebeen the Achilles’ heel of CR propagation models, andnow become a factor restricting further progress. Inter-pretation of CR data requires massive calculations ofisotopic production involvingp’s andα ’s, however, thewidely used semi-empirical systematics are frequentlywrong by a significant factor [22, 23]; this is reflected in

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FIGURE 7. Cross section for the reactionnatSi(p,x)26Al.Calculations: semi-empirical systematics [19, 20], CEM2K[21], evaluated [22]. Adapted from [21].

the value of propagation parameters. Figs. 7 and 8 illus-trate the effect of isotopic cross sections on the derivationof the halo size from radioactive secondaries. Using thesemi-empirical systematics leads to the huge error barswhere the upper limits are consistent with infinite halosize [24]. Using the evaluated cross sections dramaticallyreduces the error bars and gives a consistent value: 4–6kpc [22]. Unfortunately, the evaluated cross sections inthe required energy range are mostly unavailable.

K-capture isotopes in CR (e.g.,4923V, 51

24Cr) can serve asimportant energy markers and can be used to study theenergy-dependenteffects such as diffusive reaccelerationin the ISM and heliospheric modulation [25, 26, 27].Such nuclei usually decay via electron-capture and havea short lifetime in the medium. In CR they are stable orlive longer as they are created bare by fragmentation ofheavier nuclei while theirβ +-decay mode is suppressed.At low energies, their lifetime depends on the balancebetween the processes of the electron attachment fromthe ISM and stripping. The probability of attachment isstrongly energy-dependent, increasing toward low ener-

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FIGURE 8. Determination of the Galactic halo size based onradioactive secondaries: using semi-empirical systematics [24]– dashes, light shaded area shows the range consistent with allratios; using evaluated cross sections – solid, heavy shaded areashows the range consistent with all ratios. Adapted from [22].

FIGURE 9. 51V/51Cr ratio in CR as calculated with/withoutK-capture. Adapted from [26].

gies, while the probability of stripping is flat. This makesthe abundances of K-capture isotopes in CR energy-dependent (Fig. 9). Without K-capture, the ratio51V/51Crin CR would be flat because both nuclei are secondary.The electron K-capture51Cr(EC)51V increases the ratioat low energies. Reacceleration (energy gain) increases iteven further. On the contrary, solar modulation flattensthe ratio (Fig. 10), which is very steep in the ISM.

Study of the light nuclei in CR (Li–O) allows us todetermine propagation parameters averaged over a largerGalactic region, but the local ISM isnot necessarily thesame and thelocal propagation parameters may signif-icantly differ. The best way to study the local ISM isto look at isotopes with shorter lifetimes (e.g.,14C) andheavy nuclei since large fragmentation cross sectionslead to a small “collection area.”

The CR source composition is derived from direct CRdata by correcting for the effects of propagation, spalla-tion, and solar modulation. The elements with low first-ionization potential (FIP) appear to be more abundant inCR sources relative to the high-FIP elements, when com-pared with the solar system material (Fig. 11). This might

FIGURE 10. 51V/51Cr ratio in CR as calculated for differentlevels of solar modulation. Interstellar ratio corresponds toΦ = 0 MV. Adapted from [27].

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FIGURE 11. (Galactic CR sources)/(solar system) abun-dances of different elements vs. FIP. Adapted from [28].

imply that the source material for CR includes the atmo-spheres of stars with temperatures∼104 K [29]. A strongcorrelation between FIP and “volatility” (most of low-FIP elements are refractory while high-FIP elements arevolatile) suggests that CR may also originate in the in-terstellar dust, pre-accelerated by shock waves [28, 30].11Na,31Ga,37Rb and some other elementsZ > 28 breakthis correlation. CR data tend to prefer volatility over FIP,but uncertainties in the derived source abundances (crosssections!) prevent an unambiguous solution.

Isotopic peculiarities of CR composition are also im-portant. For example, the22

11Ne/2011Ne enrichment might

tell us that CR are produced in cores of superbubbles [31]created by multiple correlated SNe.

SCENT OF NEW PHYSICS

Galactic and extragalactic space presents a test rangewhere nature runs its numerous experiments continu-ously for billions of years. This is an arena where all fun-damental forces perform in an exotic show involving yet-to-be-discovered particles, new elements, giant nucleibound by gravitation – neutron stars, and singularities– black holes, and engineering the largest-scale grid ofstructures in the universe. CR and diffuseγ-rays, there-fore, could contain signatures of exotic physics, however,conventional CR present an enormous background fortiny exotic signals.

The growing number of experiments forces us to theconclusion that the universe is dominated by the darkmatter (DM) and dark energy. A preferred candidate fornon-baryonic DM is a weakly interacting massive par-ticle (WIMP). The WIMP is the lightest neutralinoχ0

[32], which arises in supersymmetric models of particlephysics, or a Kaluza-Klein hyperchargeB1 gauge boson[33]. Annihilation of neutralinos creates a soup of par-ticles, which eventually decay to ordinary baryons and

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FIGURE 12. Longitude profile of diffuseγ-ray emission[7]. Lines (top to bottom): total,π0-decay, inverse Compton,bremsstrahlung, extragalactic background.

leptons. The DM particles in the halo or at the Galacticcenter [34] may thus be detectable via their annihilationproducts (e+, p, d, γ-rays) in CR [35]. The approach is toscan the SUSY parameter space to find a candidate ableto fill the excesses in diffuseγ-rays, p’s, ande+’s overthe predictions of a conventional model (as discussedabove). Preliminary results of the “global fit” to thee+’s,p’s, and diffuseγ-ray data simultaneously look promis-ing [36]. In particular, the DM distribution with two-ringstructure allows the EGRETγ-ray data and the rotationcurve of the Milky Way to be fitted, while the ring radii, 5and 14 kpc, surprisingly well coincide with the observedrings of cold H2 gas and stars, respectively.

In terms of conventional physics, the spatial fluctua-tion of CR intensity may also provide a feasible explana-tion. The CR ¯p data can be used to derive the Galactic av-erage proton spectrum (Fig. 4, optimized model), whilethe electron spectrum is adjusted using the diffuseγ-rays[7]. The model shows a good agreement with EGRETspectra of diffuseγ-ray emission (<100 GeV) from dif-ferent sky regions (Fig. 12). The increased Galactic con-tribution to the diffuse emission reduces the estimate ofthe extragalacticγ-ray background [7, 37]. The new ex-tragalactic background [37] shows a positive curvature(Fig. 13), which is expected if the sources are unresolvedblazars or annihilations of the neutralino DM [38, 39].The discrepancy between the radial gradient in the dif-fuse Galacticγ-ray emissivity and the distribution ofSNRs can be solved [40] if the ratio H2/CO in the ISMincreases from the inner to the outer Galaxy. The latter isexpected from the Galactic metallicity gradient.

The difficulty associated with ¯p may also indicate neweffects. The propagation of low-energy particles may bealigned to the magnetic field lines instead of isotropicdiffusion [13]. Our local environment (the Local Bubble)may produce a fresh “unprocessed” nuclei component inCR at low energy [41]; the evidence for SN activity inthe solar vicinity in the last few Myr supports this idea.

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FIGURE 13. Spectrum of extragalactic diffuseγ-ray emis-sion [37]. Adopted from [39].

CONCLUSION

Several topics are expected to become the subject of in-tensive studies in the coming years. PAMELA (Payloadfor Antimatter Matter Exploration and Light-nuclei As-trophysics) is designed to measure ¯p’s, e±’s, and iso-topes H–C over 0.1–300 GeV. Future Antarctic flightsof a new BESS-Polar instrument (Balloon-borne Exper-iment with a Superconducting Spectrometer) will con-siderably increase the accuracy of data on ¯p’s and lightelements. The AMS (Alpha Magnetic Spectrometer) on-board the International Space Station will measure CRparticles and nucleiZ∼<26 from GeV to TeV energies.This is complemented by measurements of heavier nucleiZ > 29 by (Super-)TIGER (Trans-Iron Galactic ElementRecorder). The future GLAST mission will be capableof measuringγ-rays in the range 20 MeV – 300 GeV; be-sides other goals, it should deliver a final proof of protonacceleration in SNRs – long awaited by the CR commu-nity. A breakthrough on SUSY and high-energy interac-tions should come with operation of the new CERN largehadronic collider, LHC. Not surprisingly, the success ofthe state-of-the-art CR experiments depends heavily onthe quality of nuclear data and especiallyp- and α-induced reactions at intermediate energies from tens ofMeV – few GeV. Challenging these new frontiers is thusimpossible without involvement of the nuclear physicscommunity.

This work was supported in part by a NASA Astro-physics Theory Program grant, US DOE, and the CRDFProject MP2-3025.

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