Direct Measurements, Acceleration and Propagation of ......direct measurements of the cosmic ray...

30TH INTERNATIONAL COSMIC RAY CONFERENCE

Direct Measurements, Acceleration and Propagation of Cosmic RaysPASQUALE BLASI

INAF/Osservatorio Astrofisico di ArcetriLargo E. Fermi 5, 50126 Firenze (Italy)[email protected]

Abstract. This paper summarizes highlights of the OG1 session of the 30th International Cosmic RayConference, held in Merida (Yucatan, Mexico). The subsessions (OG1.1, OG1.2, OG1.3, OG1.4 andOG1.5) summarized here were mainly devoted to direct measurements,acceleration and propagation ofcosmic rays.

Introduction

The OG1 session was splitted in 5 subsessions,devoted to direct measurements of cosmic raysby balloons and satellites (OG1.1), cosmic raycomposition (OG1.2), cosmic ray propagation(OG1.3), cosmic ray acceleration (OG1.4) and in-trumentations and new projects (OG1.5). Thenumber of papers discussed in the OG1 sessiongives a feeling of the huge number of results pre-sented during the conference: there were 138 pa-pers presented (66 of which were oral presenta-tions). About 37 of the oral presentations reportedon observational results, while about 29 re-ported on theoretical or phenomenological work.It is obvious that a meaningful summary of thiswork implies a selection of highlights. An apol-ogy is due to all those that will not see their workproperly discussed here. It should also be under-stood that in order to avoid doing a simple list ofthe results it is needed to put things in context, andthis often requires weighing the results accordingto the opinions of the writer, which do not coincidenecessarily with the opinions of the Community atlarge. I hope that this may be a starting point forfurther discussion on the topics that I will touchupon below.

The origin of cosmic rays is a problem thathas been haunting scientists for almost one centurynow. Solving this scientific problem means puttingtogether numerous pieces of a complex puzzle, inwhich the acceleration processes, the inner dynam-

ics of the sources, the propagation, the chemicalcomposition all fit together to provide a satisfac-tory and self-consistent global picture. We are notthere yet, though an increasingly larger number ofpieces are finding their place in the puzzle. The In-ternational Cosmic Ray Conference is a privilegedplace to observe the puzzle taking shape.

This rapporteur paper is organized as follows:in §2 I present a subjective bird’s eye view ofhow things stand in the field, in order to makeit easier for the reader to put in the right contextthe extremely wide range of results presented atthe Conference. In§3 I summarize some impor-tant observational results about spectra and chem-ical composition of cosmic rays (including theelectronic component) that have been presented.In §4 I illustrate some recent developments in theunderstanding of the acceleration of cosmic rays.In §5 I discuss the problem of relating the observedcosmic rays to the sources through propagation inthe Galaxy. The transition from the galactic com-ponent to the extragalactic cosmic ray componentis briefly discussed in§6 together with some is-sues related to the propagation of ultra high energycosmic rays in the Galaxy and in the intergalacticmedium. I conclude in§7.

A bird’s eye view on cosmic rays

The best known property of cosmic rays is their all-particle spectrum. Most experiments agree, at least

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Proceedings of the 30th International Cosmic Ray ConferenceRogelio Caballero, Juan Carlos D'Olivo,Gustavo Medina-Tanco, José F. Valdés-Galicia (eds.)Universidad Nacional Autonóma de México,Mexico City, Mexico, 2009Vol. 6, pages 271-290

ACCELERATION AND PROPAGATION OFCOSMIC RAYS

qualitatively, that the spectrum consists of four re-gions: 1) at low energies (below∼ 10 GeV) theobserved spectrum is flat as it is affected by so-lar modulation. 2) For energies10GeV ≤ E ≤

3 × 1015eV, the spectrum can be fit with a powerlaw with slope∼ 2.7. 3) At energies between3 × 1015GeV and∼ 1018eV the slope grows to∼ 3.1. 4) The upper boundary of region 3 is notwell defined, so I will take some liberties in defin-ing region 4. In terms of Physics this reflects ouruncertainties in defining the region of transition toextragalactic cosmic rays (see§6).

The chemical composition of cosmic rays is acrucial piece of information and is becoming welldetermined at energies below the knee, where di-rect measurements can still be carried out, while itis more uncertain and model dependent at higherenergies. The composition of low energy cos-mic rays provides important hints to the acceler-ation processes and the propagation of cosmic raysthrough the interstellar medium (ISM). Especiallyimportant in this respect are the abundancesand spectra of elements such as Boron, Beryl-lium and Lithium, which are mainly produced assecondaries of primary cosmic rays. The ratio ofsecondary to primary (for instance B/C) cosmic rayfluxes provides a unique tool to characterize thediffusion properties of the ISM. Existing measure-ments of this ratio as a function of energy suggestthat the diffusion coefficient scales with energy asD(E) ∝ Eα, with α ≈ 0.6, at least at rigiditiesbelow ∼ 10 GV, while it is not clear whether athigher energies the slope remains constant or thereis a flattening.

Elements such as Ge and Ga can potentially al-low us to discriminate between volatility based andfirst ionization potential based acceleration pro-cesses, and therefore provide information about thedominant acceleration sites. Other elements (e.g.59Co and59Ni) also provide us with precious in-formation on the mean time between the produc-tion of the material which is accelerated and theactual time when it is accelerated to cosmic rayenergies.

Current direct measurements are filling thegap to the knee region, thereby providing a wayto match and cross-check the indirect measure-ments of spectrum and composition carried out byobserving and modelling extensive air showers at

energies across and above the knee. The data col-lected by the KASCADE experiment suggest thatthe knee in the all-particle spectrum may be anartifact of the superposition of sharper knees inthe single components, mainly in the light chem-icals, such as H and He. The proton spectrummeasured by KASCADE has a pronounced kneeat energy∼ 106 GeV. A knee in the He compo-nent is also seen, but the fluxes become more un-certain while moving to larger masses. It is notknown as yet what could be the explanation forthe knees in these components, though it is plau-sible that they may reflect inefficiency of the accel-erator. In a strictly rigidity-dependent approach,a knee in the iron spectrum could be expected at∼ 3 × 107 GeV. This simple argument opens theway to an equally simple but far reaching implica-tion: the spectrum of Galactic cosmic rays shouldend at energies around∼ 1017 eV, so that cosmicrays of larger energies must be accelerated in ex-tragalactic sources. Unfortunately the KASCADEresults are not fully consistent with those of someother experiments, especially the Tibet array. Themain difficulty of all ground based experiments,including those operating in the ultra high energyrange, is the poor understanding of cosmic ray in-teractions in the atmosphere, which may be veryproblematic to infer basic information as the chem-ical composition of the primary particles.

Three sets of measurements will help us fig-ure out whether the physical picture suggestedby the KASCADE data is correct (assuming thatthe data themselves find proper confirmation): 1)direct measurements of the cosmic ray spectraand chemical composition should extend as far aspossible towards the knee and possibly across it;2) additional data and reliable models for the de-scription of the shower developments (possiblychecked versus future LHC data) are crucial at en-ergies around and above the knee; 3) the chemicalcomposition in the energy region between1017 eVand1019 eV needs to be measured reliably.

Fortunately, important steps ahead in all thesedirections are being done and some important re-sults will be discussed below.

What about the sources? The paradigm basedon supernova remnants (SNRs) as the main sourcesof galactic cosmic rays remains the most plau-sible, but the smoking gun that would turn the

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paradigm into a well established theory is stillmissing. The most important news in this direc-tion is represented by the recent observations ofSNRs in gamma rays by Cherenkov imaging tele-scopes (see [1] and references therein for a re-cent review) and the high resolution observationsof the X-ray emission from the rims of severalSNRs (see [2] and references therein for a recentreview). The former have presented us with someevidences of TeV gamma ray emission, possibly ofhadronic origin. The latter have provided us withstrong evidence of efficient magnetic field amplifi-cation, which is in turn required in order to reachthe high energies observed in cosmic rays, and area consequence of efficient cosmic ray acceleration.From the theoretical point of view, there have beenseveral new developments in our understanding ofthe mechanism of diffusive shock acceleration inSNRs but also related to the propagation of cos-mic rays both in the Galaxy and in the intergalac-tic medium. I will discuss some of these issues inmore detail below.

New Measurements

The direct measurements of the flux of cosmicrays and of their chemical composition, carriedout by using balloons and satellites, has alwaysplayed a crucial role in advancing our understand-ing of both acceleration and propagation of cos-mic rays, at least at energies below the knee. Athigher energies the low fluxes due to the steeplyfalling spectrum make it necessary to use groundarrays which observe cosmic ray induced air show-ers. The two techniques are clearly complementaryand one of the biggest problems has always beento cross-calibrate the two. For the first time thisgoal seems to be at least in sight, in that the di-rect measurements are extending to∼ 10 − 100TeV, therefore approaching the knee region. Nu-merous new results on spectra of different chem-ical elements have been presented, from balloonflights (CREAM, ATIC, Tracer, TIGER, Bess-Polar, PPB-BETS), from satellites (preliminary re-sults from PAMELA) and even some shower ex-periments (Tibet Array and HESS). The overlapbetween all these techniques in the energy regionaround the knee appears to be of crucial impor-

tance, especially to unveil the origin of the kneein the cosmic ray spectrum.

Balloons and Satellites

The CREAM Collaboration has presented impres-sive results collected during a total of 70 days offlight of their balloon experiment. The data werecollected during the record breaking CREAM-Iflight (42 days between 12/16/05 and 01/27/05)and a second flight (CREAM-II) lasted 28 days(between 12/16/05 and 01/13/06). Convincing evi-dence was presented of the excellent charge resolu-tion of the experiment (∆q ∼ 0.2 electron charge),precious tool to reconstruct the spectra of differentchemicals (see [4, 5] for a technical discussion).

In Fig. 1 I reproduce the plots as shown by[3] (see also [6]) illustrating the spectra of protonsand helium nuclei as measured by CREAM-I (redcircles). The CREAM spectra are compared withthose of other experiments as listed in the figurewith different symbols. The spectrum of He nucleias measured by CREAM is compatible with thatmeasured by ATIC-2, but appears to be some-what flatter than that measured by ATIC-1.

The spectra of Carbon and Oxygen measuredby CREAM-II were presented by [7] and [8]. Theresults on the C/O ratio confirm the primary natureof both nuclear species [9]. An overview of theCREAM results and future developments (a thirdand fourth flight) were presented by [3]. The spec-tra of the chemicals presented by the CREAM col-laboration do not show appreciable differences inthe slope, with the possible exception of the he-lium spectrum that might be slightly harder thanthe proton spectrum. In fact this trend is proba-bly present even in the ATIC-2 spectrum. In Fig. 1the shaded area is supposed to show the range offluxes as measured by ground arrays. The widthof the shaded region provides an estimate of theuncertainties due to either the interaction modelsadopted for the analysis or systematics in the dif-ferent experiments. An important point that thisfigure shows is that finally direct and indirect mea-surements are starting to overlap in the knee re-gion. This will be of great importance to under-stand the reason for the appearance of the knee inthe all-particle cosmic ray spectrum.

The ATIC balloon experiment has presentedimpressive results on the B/C ratio and mass com-

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Fig. 1. Spectra of protons (left panel) and helium nuclei (right panel) as measured by CREAM-I (figure from [3])compared with the results of other experiments.

Fig. 2. B/C ratio as a function of energy per nucleon asmeasured by ATIC-2 (squares) [11] and compared withthe results of HEAO-3 and the predictions of two theo-retical models (lines).

position of cosmic rays below the knee. In factthe ratios N/O and C/O were also measured. TheB/C ratio, as I discuss in§5, is a crucial indica-tor of the mode of cosmic ray propagation in theinterstellar medium. Low energy measurements(E < 30 GeV) carried out by HEAO-3 [10] showthat the B/C ratio scales with rigidity as∼ R−0.6,usually interpreted as a proof of the primary (sec-ondary) origin of Carbon (Boron) nuclei.

The ratio as measured by ATIC-2 is reportedin Fig. 2 [11] together with the previous resultsof HEAO-3 and the predictions of two theoreticalmodels (lines) (see [11] for some discussion andreferences). Despite the apparent flattening of themeasured B/C ratio in the ATIC data, the error barsare still too large to infer solid conclusions on thisissue.

The all-particle spectrum and the average massnumber as a function of energy as measured byATIC-1 are shown in Fig. 3 [12] compared withthe results of other experiments, as indicated in thefigure. There is a substantial agreement among allthe data sets shown. At least in part the small off-sets may be explained in terms of systemaic errorsin the energy determination, amplified by the mul-tiplication byE2.5.

The mean logarithmic mass number found byATIC in the energy range102 − 105GeV shows ageneral trend to a heavier composition and appearsto match well with the results of RUNJOB, CASA-BLANCA, DICE and KASCADE in the knee re-gion. At energies above the knee (not reached byATIC) the other experiments show quite differenttrends. This prevents us from reaching a satisfac-tory explanation of the origin of the knee and ofthe transition from galactic to extragalactic cosmicrays (see§6).

Very accurate measurements of the flux of dif-ferent chemical elements below the knee were pre-sented by the TRACER Collaboration [13] and areshown in Fig. 4 (filled dots) for nuclei betweenOxygen and Iron. The fluxes are multiplied bydifferent normalization factors to make the plotclearer, and they are compared with the results ofHEAO-3 and CRN. No appreciable difference be-tween the slopes of the spectra of these nuclei wasdetected, all slopes being around∼ 2.7.

The TRACER Collaboration also presented theB/C ratio in the energy region around∼ 100GeV/amu, being fully consistent with other mea-surements. The predicted error bars on the B/C

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Fig.3. All particle spectrum (left panel) and mean logarithmic mass number (right panel) as measured by ATIC [12].

Fig. 4. Differential spectra of chemical elements fromOxygen to Iron as measured by Tracer [13] and com-pared with previous results from CRN and HEAO-3.

ratio with a 30 days balloon flight of TRACERshould allow to finally pin down the slope of theratio as a function of energy up to∼ 1 TeV/amu.While indicators such as the B/C ratio provideus with important information on the propagationof cosmic rays in the Galaxy, the abundances ofsuper-heavy elements (Z > 30) tell us about theacceleration regions, though their flux is more than∼ 1000 times smaller than the Iron flux. Theflux of these elements has been measured duringtwo balloon flights by the TIGER Collaboration in2001 and 2003 (a total of about 50 days of observa-tions). The fluxes in the energy region between0.3and10 GeV/nucleon are reported in Fig. 5 (from

[14]). The lines represent the predictions of twomodels for acceleration, one based on first ioniza-tion potential (FIP) and the second on volatility, butboth with a standard solar system composition ofthe ambient medium. The abundances of31Ga and32Ge appear to be inconsistent (if taken at the sametime) with both theoretical models. One shouldhowever recall that a standard solar system com-position near the accelerator is all but granted.

Important information on the origin of cosmicrays and their propagation can also be indirectlygathered by observing electrons. Their propaga-tion in the Galaxy is affected by diffusion, as forions, and energy losses (mainly synchrotron andinverse Compton scattering losses). At energieslarger than 20-100 GeV the loss time due to ICSand synchrotron becomes shorter than the diffusiveescape time from the Galaxy, so that the spectrumsteepens by one power compared with the sourcespectrum. At energies larger than∼ 1 TeV the fluxof electrons at Earth is expected (and observed) todecline, presumably as a result of the discretenessin the spatial distribution of the sources. In thissense several groups have been engaged in a searchfor a possible signal of the closest sources of elec-trons around the solar system, the most promisingsources being Vela, the cygnus loop and Mono-gem. The expected signal would consist of a bumpin the diffuse flux of electrons at energies in excessof ∼ 1 TeV. The proximity of the source wouldalso result in a small anisotropy in the arrival di-rections. The spectrum and anisotropies have beenpresented by PPB-BETS.

To date, the spectrum [15] (Fig. 6) does notshow evidence for the possible appearance of a

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Fig. 5. Relative abundances of heavy elements as ob-served by the TIGER experiment [14].

nearby electron source. Even the anisotropy isclaimed to be fully consistent with an isotropicdistribution of arrival directions [15]. The BESS-Polar experiment has presented several interestingresults, ranging from low energy cosmic ray spec-tra to spectra of antiprotons and limits to the fluxof anti-helium nuclei. The flux of cosmic ray pro-tons in the energy region below∼ 10 − 30 GeV isheavily affected by solar modulation. In Fig. 7 I re-port the results presented by [16]: the thick dots arethe recent results of BESS-Polar, compared withthose of BESS-1997 (open circles), at the time ofthe solar minimum. It is evident the effect of theenhanced solar modulation while the sun gradu-ally approaches the next solar minimum. The up-per solid line represents the spectrum of protons inthe interstellar medium as inferred from BESS-98measurements.

The propagation of cosmic ray nuclei in theinterstellar medium also results in the productionof many secondary products (nuclei, antiprotons,electron-positron pairs, gamma rays, neutrinos).Accurate measurements of these secondaries, es-pecially antiprotons and positrons is instrumentalto the search for faint signals, such as those comingfrom the annihilation of non-baryonic dark mat-ter. The flux of anti-protons and the ratio of anti-protons to protons in the energy region below fewGeV as measured by BESS-Polar is reported in

Fig. 6. Spectrum of electrons (multiplied byE3) as ob-served by PPB-BETS [15] compared with the results ofprevious measurements.

Fig. 8. In the left panel, the antiproton spectrum iscompared with some theoretical predictions of thesame quantities for some models (solid line: propa-gation with GALPROP; dotted line: standard leakybox with solar modulation; dash-dotted line: blackhole evaporation). In the right panel, the ratio an-tiproton/proton flux is compared with predictionsof a drift model with different tilt angles of the so-lar magnetic field. The thick dots and empty circlesrefer again to BESS-Polar and BESS-1997 respec-tively. In the right panel the effect of a different so-lar modulation in the two periods is evident again.As expected, this effect almost completely disap-pears in the ratio of the antiproton/proton flux. Thefluxes of antiprotons observed by BESS-1997 andBESS-Polar are both fully consistent with the oneexpected on the basis of a propagation model withsolar modulation, thereby implying significant up-per limits to the flux of antiprotons from, for in-stance, neutralino annihilation in the Galactic darkmatter halo.

BESS has also focused on the detection of anti-nuclei. The quest for why our universe is (almost)completely made of matter instead of a mixtureof matter and anti-matter is a fundamental one,as Nature is expected to have produced a (almost)symmetrical universe. Though it is likely that thesmall excess of matter over anti-matter is what nowmakes most of the present universe, the search forislands of antimatter or traces of anti-nuclei hasnever quite finished. The limit imposed by BESS-

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Fig.8. Left Panel: Antiproton spectrum measured in BESS-Polar compared with BESS(95+97) results. The lines illus-trate predictions of different theoretical scenarios. The lines that passthrough the data points are the predictions of stan-dard propagation calculations (GALPROP and leaky box models). Right Panel: p/p ratio measured by BESS(95+97)and BESS-Polar I (2004) compared with drift model calculations at various Solar magnetic field tilt angles.

Fig. 7. Spectrum of protons as observed by BESS-1997(empty circles) and BESS-Polar (filled circles) [16]. Thedifference between the two spectra is due to the differentlevels of solar modulation at the time of the measure-ments.

Fig. 9. Limits on the flux of anti-Helium obtained byBESS-Polar [16].

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Polar and the limit that will possibly be reached bythe next BESS flight are shown in Fig. 9, togetherwith the results of previous measurements.

The measurement of the cosmic ray spectrumand chemical composition up to energies of∼ 1TeV, the search for dark matter, anti-matter and ex-otic particles, and finally bits of solar and mag-netospheric physics are among the goals of thePAMELA satellite, which has been succesfullylaunched on june 15, 2006. The instruments on-board are collecting data, but only preliminary re-sults were presented at the conference. A reviewof PAMELA preliminary results and expectationshas been presented in [17]. Particularly interest-ing, and suggestive of the quality of the results thatwe should expect, is the spectrum of protons andhelium, reported in Fig. 10.

This preliminary analysis does not show evi-dence for any difference in the slopes of the spec-tra of H and He in the energy region below∼ 500GeV. In both cases the best fit power law has aslope of2.73.

Several simulated results were also presentedby the PAMELA Collaboration, mainly aimed atshowing the potential for discovery of indirect sig-nals of dark matter annihilation (in the form ofanomalous features in the antiproton and positronspectra), and the limits achievable in the search foranti-matter. The limit on the ratioHe/He is ex-pected to improve by about 1 order of magnitudein about three years of PAMELA operation with re-spect to that achieved by BESS-Polar (see Fig. 9).

PAMELA is expected to play a crucial rolein the identification of spectral features in thepositron and antiproton spectra as they can possi-bly result from dark matter annihilation, providedthe mass of the dark matter candidate particle is inthe right energy range (below500 − 1000 GeV).

Ground Experiments

Since most results from ground experiments werepresented in other sessions of the ICRC, the talkson this subject in the OG1 session were sparse.

The HESS Collaboration has presented the re-sults of a very interesting detection of the directCherenkov (DC) light from cosmic rays impactingthe atmosphere. This technique, proposed as a pos-sible tool to measure the chemical composition ofcosmic rays above 10 TeV by [18], has been used

Fig. 10. Preliminary spectra of protons and helium fromPAMELA.

by HESS to measure the flux of heavy nuclei (Fe-like). The direct Cherenkov light is produced bythe primary nucleus while entering the atmosphereand before the first interaction that generates theshower. High up in the atmosphere the densityof air is lower and therefore the Cherenkov coneis more collimated with respect to the Cherenkovcone of the light generated by lower energy parti-cles in the shower. As a result the total Cherenkovemission from a shower is expected to have a broadregion with ahot pixel corresponding to the DClight. This emission has in fact been success-fully detected by HESS. Since the intensity of theCherenkov signal scales with the square of thecharge of the parent nucleus, it is best to seach forthe signal from Fe nuclei provided the energy doesnot exceed a few hundred TeV, in order to avoidthat the shower emission overshines the DC light.The spectrum of Iron nuclei as measured by HESSis reported in Fig. 11 [19] where it is comparedwith the results of other experiments. The two setsof data points refer to QGSJET and SIBYLL as in-teraction models.

The search for the DC light is also being pur-sued by VERITAS [20], while dedicated instru-ments are being planned (e.g. TrICE [21]).

The HESS Collaboration has also presented thepreliminary results of their measurement of theelectron spectrum [22], consistent with measure-ments carried out by other experiments within thesystematic uncertainties.

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Fig. 11. Spectrum of iron nuclei (in fact nuclei withZ > 24 obtained by HESS using the detection of DClight. The HESS results (with SYBILL and QGSJET asmodels for interactions) are compared with the results ofother measurements.

A relevant contribution to the understanding ofthe nature of the knee in the all-particle spectrumhas been provided by Tibet Array. The Collabora-tion has presented the most recent measurementsof the proton and helium spectra in the knee re-gion, and the fraction of heavy nuclei as a functionof energy, in the range106 ≤ E ≤ 107 GeV.

The measurements of the chemical abundancesin this energy region are still controversial. TheTibet data on the proton spectrum appear in roughagreement with those of RUNJOB and JACEE(both with QGSJET and SIBYLL as interactionmodels) but in rather apparent contradiction withthe KASCADE data, especially when the KAS-CADE data are analyzed using SIBYLL. The lattershow a steeper spectrum of protons and a some-what higher normalization of the flux. The dis-crepancies are even more evident in the case ofthe helium spectrum. The Tibet results on heliumroughly match with those of RUNJOB, but notwith data from JACEE and KASCADE. The ab-solute flux of helium as measured by KASCADEis almost one order of magnitude higher than thatmeasured by Tibet Array. The situation in the kneeregion continues to be confused and this preventsthe possibility of unveiling the origin of the knee.

Acceleration of Cosmic Rays

The main mechanism for the acceleration of cos-mic rays (not only galactic) remains diffusive par-ticle acceleration at shocks. Many contributionspresented at the conference have focused on thedetermination of the efficiency of particle acceler-ation, the dynamical effect of the accelerated parti-cles and the magnetic field amplification generatedby the accelerated particles through streaming in-stability or due to turbulent amplification.

I will start by discussing some issues related tothe acceleration of Galactic cosmic rays in SNRs,though some of the conclusions will be of widerapplicability.

One of the most recent advancements in thetheory of particle acceleration at non-relativisticshocks, especially for SNR shocks, has been thecalculation of the dynamical reaction of the accel-erated particles onto the background plasma. Theeffect has been discussed already in the 80’s inthe context of two-fluid models (see [23] for a re-view), and later addressed numerically by directsolution of the time dependent equation of diffu-sive tranport coupled with the equations of mass,momentum and energy conservation of the back-ground plasma (see for instance [24]). In the late90’s a stationary semi-analytical solution of this setof equations was found in the form of an integralequation [25] for a spatially constant diffusion co-efficient. A general semi-analytical method was re-cently proposed by [26], valid for any choice of thediffusion coefficient.

The structure of the shock is changed by theaccelerated particles due to the pressure they ex-ert on the background plasma, though in a col-lisionless manner. For ordinary diffusion coeffi-cients, which are increasing functions of particlemomentum, higher energy particles can travel fur-ther away than low energy particles: a fluid ele-ment approaching the shock surface thereforefeelsan increasing pressure due to accelerated particlesand as a consequence it slows down. This leads tothe formation of aprecursorupstream of the shock(which is now calledsubshock) in which the fluidvelocity, as seen in the (sub)shock reference framedecreases while approaching the shock. The ef-fective compression factorfelt by particles cross-ing the shock and precursor is now a function of

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momentum, being bigger at large momenta andsmaller at low momenta. The immediate conse-quence is that the spectrum of particles acceler-ated at shocks is not a power law, as expected intest-particle theory, but rather a concave functionof momentum, harder at high momenta and softerat low momenta. This nonlinear system is found toself-regulate itself and to be able to reach relativelyhigh efficiency of particle acceleration.

This complex nonlinear system has howeveradditional interesting aspects, concerning the max-imum momentum that the particles can be accel-erated to. As was recognized first in [27, 28],the maximum momentum achieveable in SNRs isexceedingly low compared with the knee energyunless the diffusion coefficient is Bohm-like andmagnetic field amplification takes place. Even inthis case the maximum energy falls short of theknee energy by a factor∼ 100, unless the ampli-fication turns strongly nonlinear, namelyδB/B ∼

100. An investigation of the process of particle ac-celeration at cosmic ray modified shocks with self-generation of strong turbulence was discussed in[29, 30] and presented at this Conference by [31].

The most important clue in this field has how-ever come in the last few years from high reso-lution X-ray observations of the rims of severalSNRs. The thickness of the rims is related tothe loss length of high energy electrons radiatingX-rays by synchrotron emission. The observedbrightness profiles lead to estimates of the down-stream magnetic field of the order of a few hun-dredsµG [32]. These estimates were confirmedand presented here by [33, 34] together with theirimplications for multifrequency observations ofspecific SNRs.

These calculations are based on a numericaltime-dependent solution of the problem of parti-cle acceleration at modified shocks. The strengthof the magnetic field is not self-consistently cal-culated but rather fit to the observations at agiven time (the observation time) and not evolvedin time. The calculations of [34] show that the mul-tifrequency data for supernova RXJ1713.7-3946are explained rather well from radio to X-rays andgamma rays (Fig. 12 from [34]). In particular thegamma ray data from HESS are interpreted as theresult of pion production and decay. The magneticfield required for the fit is126µG, again consistent

with the general trend of strong magnetic field am-plification observed in other remnants.

The strong magnetic field causes the electrondensity to be low, thereby reducing the flux of ICSgamma rays. Similar consequences can be inferredfor the RX J0852.0-4622 (Vela Jr.) [33]. It is alsoworth noticing, in Fig. 12 (and others that havebeen presented for other SNRs) that both the pre-dicted radio-X and gamma ray spectra show a clearindication of a curvature (concavity). This char-acteristic, as discussed above, is one of the mostdistinctive consequences of particle acceleration atmodified shocks. Signatures like this should becarefully looked for in future, better data at allwavelengths. In particular, future gamma ray ob-servations with GLAST might allow us to con-firm or reject the hadronic origin of the gamma rayemission.

Two models have been discussed for the am-plified magnetic field observed in several SNRs.Quantitatively they potentially lead to the samelevel of magnetization, but the principle is differ-ent in the two cases.

The traditional explanation is based on stream-ing instability induced by the accelerated particles.The instability leads to resonant growth of Alfvenmodes [35] and typicallyδB/B ∼ 20 − 30 [29].By using the results of quasi-linear theory for thegrowth rates, [31] showed how to determine thediffusion coefficient and implement it in a self-consistent solution of the problem of accelerationat modified shocks. At the beginning of the Sedovphase this type of instability leads to reach approx-imately proton energies of∼ 106 GeV, while atlater stages of the SNR evolution, the maximummomentum decreases in a way that depends onhow the magnetic field amplification drops.

In [36] it was proposed that non resonantmodes may grow faster than resonant modes insome circumstances. The analysis of Bell wasbased on a MHD treatment of the backgroundplasma and the non resonant modes are oftenconsidered as strictly related to this assumption.The presentation of [37] has demonstrated that thesame dispersion relation is obtained in the contextof a purely kinetic approach, if particle acceler-ation is efficient, as it is expected at cosmic raymodified shocks. The imaginary and real parts ofthe frequency of the propagating waves are plot-

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Fig.12. Multifrequency spectrum of the SNR RXJ1713.7-3946 and the best fit of the calculations of [34].

ted in Fig. 13 in units ofV 2s /crL,0 as a function

of the wavenumberk in units of1/rL,0. HererL,0

is the Larmor radius of the particles in the back-ground magnetic field andVs is the shock velocity,taken here as109cm s−1. The efficiency in accel-eration was assumed to beη ≡ UCR/ρV 2

s = 0.1.The peak of the growth rate if not atkrL,0 ∼ 1which is again a confirmation that the faster grow-ing modes are non resonant. However the sameauthors of [37] also showed that the peak movestowardskrL,0 ∼ 1 when either the shock veloc-ity decreases orη decreases. This suggests that atlater epoques during the SNR evolution the reso-nant mode may become dominant.

The search for the non resonant modes foundby [36] was also carried out by using Particle-in-Cell (PIC) simulations. The results of such studieswere presented by [38]: no evidence was found ofthe fastly growingBell modein their simulations.It remains to be seen whether this result is due tothe anomalous values of the parameters adopted bythe authors (for instance the large density of nonthermal particles needed to satisfy the condition ofefficient acceleration and the artificial value of theratiome/mp), or if actually shows that the instabil-ity may be suppressed due to some physical mech-anism yet to be identified.

It is important to stress that streaming instabil-ity generates the magnetic field amplification up-stream of the shock front. The turbulent field isthen advected downstream and the perpendicularcomponents are compressed at the shock surface.

A second model for the generation of strongfield was discussed by [39]: the model is basedon the (realistic) assumption that density perturba-tions δρ/ρ ∼ 1 are present upstream (see Fig. 14for a schematic view). The density perturbationsinduce corrugations in the shock structurewhich in turn produce turbulent eddies that twistthe field lines frozen in the plasma leading to mag-netic field amplification. The numerical simula-tions that the authors illustrated show thatδB/B ∼

MA, whereMA is the Alfven Mach number. Inconditions which are typical of SNRs one may eas-ily expectδB/B ∼ 100−1000 downstream of theshock.

The effects of such amplified magnetic fieldon the acceleration of particles need some furtherdiscussion: if the field in the upstream region ismainly parallel to the shock normal, and there is nostreaming instability (as assumed in [39]) then theacceleration process is inefficient, being weakly af-fected by the downstream strong fields alone. Infact the acceleration time is the sum of the diffu-sion times upstream and downstream. If the field is

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Fig. 13. Real and Imaginary part of the frequency of thewaves excited by the streaming of cosmic rays at a shockwith velocity 10

9cm s

−1 and efficiency of particle ac-celerationη = 0.1. For these parameters the peak ofthe growth rate occurs atkrL � 1, showing the nonresonant nature of the instability [37].

Fig. 14. Schematic view of the turbulent magnetic fieldamplification scenario proposed by [39].

only amplified downstream, the acceleration timeis dominated by the upstream region, and it re-mains too long to lead to efficient acceleration.The problem can be avoided by assuming that theshock is perpendicular. In this case the upstreamacceleration time is substantially shorter becausethe perpendicular diffusion coefficient is smallerthan the parallel one [40], thereby mimicking am-plification of the magnetic field from the point ofview of acceleration. For perpendicular shocks theamplification by streaming instability is expectedto be suppressed, therefore the two mechanismscould be considered as complementary and mighttake place together though with different efficien-cies as related to the relative orientation of theshock normal and the ambient magnetic field.

Efficient particle acceleration at SNR shocksmodified by the dynamical reaction of cosmic rays,together with the amplification of the magneticfield provide a consistent picture of the origin of

cosmic rays: protons in the SNR environment canbe accelerated to∼ 106 GeV, while elements withhigher charge (Z) may be accelerated to energieswhich areZ times larger. The maximum ener-gies are reached at the beginning of the Sedovphase while at later stages the maximum energydecreases, mainly because the magnetic field am-plification is less efficient (at least for amplificationdue to streaming instability). The spectrum of cos-mic rays observed at the Earth is the superpositionof the cosmic rays trapped behind the shock andreleased after adiabatic decompression and the par-ticles which may leave the system from upstreamdue to lack of confinement in the accelerator.

The calculations presented by [41] representthe first attempt to convolve the results from par-ticle acceleration with given diffusion propertiesof the interstellar medium to determine the all-particle spectrum of Galactic cosmic rays. Goodagreement with data is obtained after summingover all chemical elements, though there are nu-merous parameters that can be tuned to obtain thefit. The most important point is however that theend of the Galactic spectrum is expected to be atenergies around a few1017 eV. I will discuss thispoint in more detail in§6.

Our understanding of cosmic ray accelerationat SNR shocks has certainly improved consider-ably in the last few years, as also shown by theimpressive quality of the fits to multifrequency ob-servations of SNRs from radio to gamma ray wave-lengths. However, it may be useful to briefly dis-cuss some aspects of the problem that are not sowell understood and that are nevertheless crucial toexplain observations and to have a consistent pic-ture of the origin of cosmic rays. I will limit myselfto mentioning three of such aspects.

1. A general trend of the non linear theoriesof particles acceleration at modified shocksis to lead to very large total compressionfactors, incompatible with the values (∼ 7)which provide a good fit to data. It is usu-ally believed that this reduction may be at-tributed to turbulent heating in the precursor[42, 43]. However to date we have no reli-able theory of how to treat this phenomenon,initially put forward to avoid magnetic fieldamplification toδB/B � 1 and currentlyused also in cases where the amplification is

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strongly non linear. One can adopt recipesthat qualitatively work, but do not ensure thecorrectness of the quantitative results.

2. The flux of particles that may escape theshock region from upstream of a modifiedshock can be an appreciable fraction of theenergy flux. We do not know as yet how tocarry out a detailed calculation of this flux,despite the fact that cosmic rays detected atthe Earth might be dominated by this com-ponent rather than by the ones trapped be-hind the shock. The spectrum of particlesthat escape a SNR at each time during theSedov phase is expected to be very peakedat energies around the maximum momentumachievable at that specific time. As proposedby [44] the observed flux might be due to anoverlap of these peaked spectra integrated onthe SNR evolution.

3. As discussed above, the crucial elementwhich makes cosmic ray acceleration pos-sible in SNR shocks is the magnetic fieldamplification. If this process does not takeplace, SNRs can hardly be the sources ofGalactic cosmic rays. The amplificationmay however take place in different ways(resonant and non resonant streaming insta-bility, firehose instability, turbulent amplifi-cation, and possibly others). Each amplifi-cation process leads to a different saturationlevel and different scaling laws with the ageof the SNR. More specifically, at differenttimes in the SNR evolution, different ampli-fication processes may operate. This makesthe calculation of the actual spectrum of CRsfrom SNRs highly non trivial.

It is remarkable that all the work done andpresented at the Conference on shock modifica-tion and its phenomenological consequences wasmainly concentrated upon non relativistic shocksand more specifically SNR shocks.

A paper was presented [45] in which the au-thors stress the difficulty of accelerating particles atrelativistic shocks (in the test particle approxima-tion), which reflects into very steep spectra. Thisfinding adds to the fact, which is becoming increas-ingly more recognized, that the dependence on am-bient conditions is very important for the case of

relativistic shocks. For instance, even the simplecompression of the perpendicular component of aturbulent magnetic field crossing a shock surfacemay induce a substantial steepening of the spec-trum in the relativistic case (see also [46]), whilebeing unimportant for non relativistic shocks.

Propagation of Cosmic Rays

The propagation of cosmic rays in the Galaxyis dominated by diffusion (possibly anisotropic)and advection if there is a wind blowing out-wards. Qualitatively it is very easy to illustratewhat might be expected. Let us assume that thesources inject cosmic rays into the ISM with a rateQp(E) ∝ E−γ , where the indexp stays forpri-mary. At the leaky boxlevel, the equation whichdescribes the stationary density of cosmic rays inthe Galaxy is

Qp(E) =np(E)

τ(E),

whereτ(E) is the time needed for escaping theGalaxy. If the escape is solely due to diffusionand the diffusion coefficient scales asD(E) ∝ Eα,then τ(E) ∝ E−α. It immediately follows thatnp(E) ∝ Qp(E)τ(E) ∝ E−(α+γ). During propa-gation in the ISM secondary nuclei are produced ata rateQs(E) ≈ np(E)σnHv(p) ∝ E−(α+γ) (as-sumingv(p) ∼ c). It follows, again at the leakybox level of approximation, that the equilibriumdensity of secondaries isns(E) ≈ Qs(E)τ(E) ∝

E−(α+2γ). Therefore the ratio of the secondary toprimary equilibrium densities isns/np ∝ E−α ∝

1/D(E). This is the case of theB/C ratio dis-cussed in§3: measuring the energy dependenceof theB/C ratio we can infer the diffusion coeffi-cient, or more in general the escape time as a func-tion of energy, which scales as1/D(E) if diffusionis the only process responsible for escape while itis somewhat more complex if there are other pro-cesses involved (for instance advection in a wind).

As discussed in§3 the most recent measure-ments of the B/C ratio by CREAM, ATIC andTRACER extended to energies of100 − 1000GeV/nucleon, thereby providing us with a uniqueopportunity to understand what is the rate of escapeof cosmic rays as a function of energy right belowthe knee. It is worth recalling that the data points

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with small error bars at energies smaller than∼ 30GeV/nucleon (see Fig. 2) return a slope of the B/Cratio ∼ 0.6. The higher energy data presented bythe three Collaborations have too large error barsso far to understand if such a slope remains un-changed. On the other hand one should recall thatif indeed cosmic rays escaped from the Galaxy pro-portionally toE−0.6, and normalizing the escapingtime in the 10 GeV/nucleon region, one would in-fer a too large anisotropy of cosmic rays around theknee [47]. It is therefore likely that somewhere be-low the knee the behaviour of the escape time withenergy changes to a flatter behaviour. On the otherhand, if this transition exists then one should ex-pect the appearance of a feature in the all-particlespectrum, which does not seem to be there. Theproblem remains open.

The importance played by diffusion in the in-vestigation of the origin of cosmic rays is also clearfrom the wealth of presentations at the Conference,concerning different ways to treat diffusion. Thestandard way to describe diffusion of cosmic raysin the Galaxy has become the GALPROP code,which was used also in the work presented by[48] in order to calculate the elemental abundan-cies throughout the periodic table. GALPROP isalso used to determine spectrum and spatial distri-bution of the secondary emissions, especially radioand gamma, which provide information on the dis-tribution of magnetic field and gas respectively.

Some random-walk-like approaches to diffu-sive motion have been presented in [49, 50] andthen applied for specific purposes such as the cal-culation of the diffuse galactic gamma ray back-ground or the gamma ray emission from diffusesources such as the HESS source in the galacticbulge.

The simple arguments reproduced above,which illustrate the basic aspects of the leaky boxapproaches, are a wild oversimplification of a phe-nomenon which is in fact very complex. Below Iwill discuss some of these complications and howto describe at least some of them.

In general, diffusion acts on top of a regularmotion of charged particles moving in a large scalemagnetic field and is due to a turbulent compo-nentδB. In the case of the Galaxy the large scalefield has a complex structure, made of spiral armsand a poorly known halo. Diffusion parallel to

the background magnetic field is faster than dif-fusion in the direction perpendicular to the orderedfield. The difference between the diffusion coef-ficients in the two directions (parallel and perpen-dicular) decreases when the level of turbulent fieldincreases.

The parallel diffusion coefficient can be evalu-ated in the context of quasi-linear theory providedδB/B � 1. In the non linear regime there isno definite theory for the determination of the dif-fusion coefficients and numerical simulations be-come invaluable tools. In the weakly non linearregime analyical techinques can still be applied andlead to rather unexpected results: for instance asimilar theoretical approach presented by [51] andconsisting of a weakly non linear approach to par-allel diffusion, results in a scaling of the paralleldiffusion coefficient with energy asD‖ ∝ E0.6

despite the fact that the spectrum of turbulence isKolmogorov-like. This might have an importantimpact on the interpretation of the observed slopein the B/C ratio, though this slope would still re-main incompatible with the observed anisotropy ofcosmic rays at the knee.

For typical magnetic fields of fewµG, as inthe Galaxy, numerical simulations can be used toderive the propagation properties of cosmic raysdown to energies of1014 − 1015 eV. The resultsof one such investigation were presented by [52]and revealed several interesting new aspects of theproblem. The simulation consists of propagatinga large sample of charged particles and determinetheir escape time fromtoy modelsof the magneticfield of the Galaxy. At the same time, in order tobetter understand and interpret the results the au-thors also calculate the diffusion coefficients (par-allel and perpendicular to the direction of the reg-ular magnetic field).

The simulations cover the range of turbulencestrength0.5 ≤ δB/B ≤ 2 always assumed tobe distributed according with a Kolmogorov spec-trum, δB(k)2 ∝ k−5/3. The authors find that theenergy dependence of the perpendicular and paral-lel diffusion coefficients is different:D⊥ ∝ Eα,with α ≈ 0.5 − 0.6 and D‖ ∝ E1/3 (basicallythe same slope obtained from quasi-linear theorydespite the non linearity).

The results of the calculations of the escapetimes from the Galaxy clearly illustrate the diffu-

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culty of the problem. The authors investigated sev-eral toy geometries of the regular magnetic field ofthe Galaxy, starting with a purely azimuthal field,from which particle escape can only take placethrough diffusion perpendicular to the field (andtherefore to the disc). Even in this simple case, theescape time is affected not only by (perpendicular)diffusion, but also by drifts induced by gradients inthe regular field. The gradients may be simply theones associated with the curvature of field lines butcould also be due to gradients along the radial di-rection in the disc, and along the z-axis perpendic-ular to the disc. The full set of results are discussedin [52, 53].

In Fig. 15 I reproduce the escape times (toppanel) and the grammage traversed by cosmic rays(bottom panel) as presented by [52] for the sim-ple case of a purely azimuthal regular field. Afew interesting results are apparent: first, the es-cape time obtained with all values ofδB/B havea slope∼ 0.6, consistent with the fact that the es-cape time in this field configuration is∝ H2/D⊥,whereH is the thickness of the magnetized halo.Second, atE ∼ 1017 eV the escape time is ap-preciably affected by the drift induced by the cur-vature of the regular magnetic field lines (solidline). Third, the grammage inferred from the sim-ulation is of order0.5 − 3g cm−2 at 1015 eV. Ifextrapolated to 10 GeV with a slope 0.6 this wouldlead to exceedingly large grammage (or equiva-lently too long escape times) in the energy regionwhere this parameter can be inferred from B/C ra-tio and is∼ 20g cm−2. A similar problem, thoughat higher energies, was previously found by [54].Many other cases discussed by the authors confirmthe generality of these few conclusions and showthat the problem of propagation has still many as-pects which are poorly understood and can hardlybe included in phenomenological approaches in-cluding simple ones such as the leaky box mod-els or more complex ones such as GALPROP. Thepropagation of ultra-high energy cosmic rays in theintergalactic space is in a way simpler to describe,though a major source of uncertainties is due toour ignorance of the magnetic field (strength andtopology) possibly existing between the sourcesand our Galaxy. An appreciable intergalacticmagnetic field can affect both the spectrum andthe anisotropy of cosmic rays. While the overall

Fig.15. Escape times (top panel) and grammage (bottompanel) for cosmic rays propagating in a toy model of theGalaxy [52].

shape of the spectrum is left almost unchanged, be-cause of the universality shown by [55], some fea-tures may appear in the observed spectrum becauseof the so-called magnetic horizon [56, 57]: at thelowest end of the cosmic ray spectrum, the prop-agation time from the nearest source may exceedthe age of the universe thereby suppressing the fluxof cosmic rays. For magnetic fields of less than∼ 1 nG, this effect typically appears below1018

eV (the details depend on the topology of the fieldand the diffusion properties of the particles). Athigher energies the presence of the magnetic fieldmainly affects the anisotropy (especially on smallscales) in the arrival directions. In fact at energies≥ 1019.6 eV the flux received at Earth is expectedto come from nearby sources, and the arrival direc-tions to point back to the sources. However therehas been a lot of discussion on whether this is actu-ally the case (see for instance [58] and [59] for tworather different results), because of the uncertain-ties on the strength of the magnetic field. A paperwas presented at the Conference [60] in which thepropagation in a structured magnetic field was dis-cussed in the assumption that some fraction of the

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energy in the hydrodynamic flows leading to largescale structure formation is converted to magneticfields. The authors reach a conclusion which issomewhat in between those of [58] and [59]: onlysome of the UHECRs should point back to theirsource. All these results should however be takenwith a grain of salt, the uncertainties in the determi-nation of the magnetic field being very large. Fromthe observational point of view, if a correlation wasfound between arrival directions of UHECRs and aclass of sources, this would be the best proof of theweakness of the magnetic fields in the interveningintergalactic medium. It would be harder to con-clude one way or the other in case of absence ofcorrelations.

The uncertainties in the galactic magnetic fieldare also rather disturbing and affect appreciablyour ability to obtain realistic results on the propa-gation of cosmic rays. In [61] the authors proposedto use data on the polarization of the CMB photonsto infer information on the large scale structure ofthe galactic magnetic field. Such a goal would cer-tainly justify the effort.

Where do Cosmic Rays becomeextragalactic?

The theoretical arguments illustrated in§4 suggestthat if cosmic rays are accelerated in SNR shocksthen the maximum energy of nuclei of chargeZshould be∼ Z×1015 eV. This conclusion is basedon the evidences for magnetic field amplification atSNR shocks, as inferred from X-ray observations.A similar conclusion could however be reachedbased on direct observation of the proton spectrumby the KASCADE experiment. The proton spec-trum as measured by the Tibet-Array experimentat energies above the knee is harder than that mea-sured by KASCADE, but the two agree on the factthat at∼ 1015 eV there is a softening of the protonspectrum. Moreover, both agree, at least qualita-tively, on the fact that the chemical compositionbecomes heavier above the knee in the all-particlespectrum.

On the observational side this situation sug-gests that future accurate measurements of thechemical composition at energies above the kneewill be crucial to solve the problem of the originof cosmic rays. From the theoretical side, the most

striking conclusion is that the galactic componentof cosmic rays should end at around∼ a few 1017

eV and in this energy region be iron dominated.This is in clear contradiction with the traditionalankle model of the transition, which postulates thatthe transition takes place at∼ 5× 1018 eV as a re-sult of the intersection of a steep galactic spectrumand a flatter extragalactic (proton dominated) spec-trum.

Recently two other models have been pro-posed, both of which locate the transition regionat energies∼ 1017 − 1018 eV, thedip model[62]and themixed compositionmodel [63]. They aredescribed at length in the rapporteur paper on ses-sion HE and in the Review paper by V.S. Berezin-sky, therefore here I will limit myself to a shortdescription.

In the dip model [64] the extragalactic spec-trum is proton dominated (not more than 15% ofHe nuclei are allowed). The effective injectedspectrum at the extragalactic sources is requiredto beE−γ with γ = 2.6 − 2.7. The dip appearsas a feature due to pair production losses of pro-tons on the cosmic microwave background radia-tion and its location in energy is very well definedand model independent. The shape of the dip isalso very weakly dependent upon most parameters,with the exception of the chemical composition ofthe extragalactic component, as mentioned above.The extragalactic spectrum extends down to lowerenergies, and at the position of the so-called secondknee it is predicted to flatten. This is the regionof the transition from a steep galactic to a flatterextragalactic cosmic ray component. The chemi-cal composition in the transition region is predictedto suffer a sharp transition from iron dominated toproton dominated [65], and the transition is com-pleted at energy∼ 1018 eV.

In the mixed composition model the extra-galactic component corresponds to a flatter injec-tion spectrum∼ E−2.3, with a composition whichis a mixture of different chemicals with abun-dances that are roughly comparable with the sourcecompositions inferred for SNRs but with muchfreedom in this respect. The propagation of thesecomponents from the sources to Earth leads to theformation of a complex spectrum that may fitthe all particle spectrum fairly well. The transi-tion from galactic to extragalactic cosmic rays in

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this model is more gradual and is completed at en-ergy ∼ 3 × 1018 eV. The chemical compositionis expected to vary slowly in the transition region,shifting from iron dominated (at low energies) togradually lighter towards higher energies.

The main discriminating factor between thetwo models is the chemical composition inthe transition region. Present measurements do notallow to make this discrimination as yet.

In the two models illustrated above, the Galac-tic cosmic ray component is obtained by subtrac-tion of the predicted extragalactic flux from themeasured all particle spectrum. In the presentationby [66] the authors have tried a different approach,namely that of calculating the galactic componentby assuming a source spectrum and using GAL-PROP to descrive propagation in the ISM. Themain goal was to show that in general, for bothmodels, the superposition of the galactic and ex-tragalactic components leads to the appearance ofstrong features in the all-particle spectrum. The au-thors claim that the features are more evident in themixed composition scenario. This result should ofcourse be taken as an interesting suggestion to befurther investigated. We do not have enough in-formation about the shape of the spectrum of thedifferent chemicals and their maximum energies inorder to run GALPROP and obtain results whichcan be interpreted in a unambiguous way.

Conclusions

The collection of high quality data is the main drivefor the field of cosmic ray research. In the verylow energy region (below∼ 10 GeV) the accu-rate measurements of the cosmic ray flux by BESShas, among other things, allowed to achieve an ex-cellent understanding of the effects of solar mod-ulation. At energies below the knee in the all-particle spectrum, several experiments (CREAM,ATIC, Tracer) are providing us with large statis-tics of data and correspondingly excellent qualityspectra of nuclei spanning the all periodic table.The domain of ultra-heavy nuclei is being coveredby the TIGER experiment. These direct measure-ments are gradually approaching the energy rangearound the knee thereby providing us with a test ofconsistency (or inconsistency) of data collected in-directly by ground experiments using atmospheric

showers induced by the cosmic ray interactions.One of the goals of the research in this field in theyears to come should be (and in fact it is already)to match the results of direct and indirect measure-ments of cosmic ray fluxes and chemical composi-tion. Thinking of the possibility of ultra-long dura-tion balloon flights to reach closer to or across theknee appears as a worthy effort.

The achievement of accurate measurements ofcosmic ray spectra is also opening the way tothe search for weak signatures of rare phenom-ena, such as propagation of antimatter from nearbyregions of the universe and annihilation of darkmatter in the Galaxy. The latter has profound im-plications on the spectra of positrons and antipro-tons especially, besides creating features in gammarays and at other wavelengths. The launch of thePAMELA satellite in 2006 has been a milestone inthis direction, and hopefully next ICRC will haveplenty of presentations of exciting new results.

The picture that emerges from direct cosmicray measurements can be summarized as follows.There is a satisfactory agreement on the all-particlespectrum as measured by different experiments.The spectra of the chemical species do not showstatistically significant differences in the slopes.The abundances of Ga and Ge do not seem im-mediately compatible with acceleration scenariosbased on pure first ionization potential or volatil-ity. Different determinations of the B/C ratio areconsistent with each other up to the highest mea-sured energy (∼ 1 TeV), but the error bars are stilllarge enough to leave open the possibility of a flat-tening in the slope of the B/C ratio as a functionof energy. A long duration flight, for instance ofTracer, is likely to settle this issue. We recall thatfrom the theoretical point of view a naive extrapo-lation of the observed B/C ratio to the knee regionwould lead to exceedingly large anisotropy.

A few results of measurements carried out withground experiments, such as HESS and the Tibethybrid detector were presented in the OG session.The HESS collaboration presented the positive de-tection of the direct Cherenkov radiation, and usedit to infer the spectrum of iron nuclei (more cor-rectly of nuclei with chargeZ > 24) with energyup to∼ 100 TeV. The measured spectrum appearsto be in good agreement with other results in thesame energy region.

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The Tibet Collaboration discussed the resultsof a measurement of the proton and helium primaryspectra as obtained with the Tibet hybrid experi-ment. The discrepancy between these results andthose of the KASCADE experiment are clear, espe-cially for the helium spectrum. As stressed above,one way of facing these problems is to extend thedirect measurements with high statistics of eventsto the knee region.

The calibration of the ground arrays by an over-lap with direct measurements is a crucial goal topursue, not only to understand the origin of theknee but also to describe correctly the transitionfrom galactic to extragalactic cosmic rays. The twoproblems are tightly related to each other.

There have been numerous presentations at theConference on the theory of acceleration of cos-mic rays. From the phenomenological point ofview it is clear that several independent pieces sup-port the possibility that the bulk of galactic cos-mic rays are accelerated in SNRs: 1) X-ray ob-servations have shown that effective magnetic fieldamplification at SNR shocks takes place; 2) multi-frequency observations of SNR RXJ1713 and Velajunior are best fit if the observed gamma ray emis-sion is of hadronic origin; 3) the spectra of ra-dio and gamma rays show some evidence, thoughprobably not conclusive, of curvature (concavity),a phenomenon which is expected in non linear the-ories of particle acceleration at shock waves, whenthe dynamical reaction of the particles is not negli-gible, namely when acceleration is very efficient.

From the theoretical point of view, the originof the magnetic field amplification is being widelyinvestigated. Two mechanisms might be at workat the same time: streaming instability induced bythe efficiently accelerated cosmic rays and turbu-lent amplification in a shocked medium with den-sity inhomogeneities. Other instabilities, such asfirehose instability, might also be at work. Therehave been several contributed papers on the growthrate of the non resonant streaming instability inthe context of a kinetic approach, and as simulatedwith the help of PIC simulations. The latter do notseem to confirm the large growth rates predicted byquasi-linear theory, but additional work is neededto make sure that the initial conditions are set in aphysically meaningful way.

Efficient magnetic field amplification, when itis due to streaming instability, also implies efficientparticle acceleration, which in turn induces a con-cavity in the spectra of both the accelerated par-ticles and the radiations produced by them. Effi-cient magnetic field amplification is also requiredin order to explain cosmic ray energies at least inthe knee region for protons and correspondinglyhigher for nuclei with higher charge.

All these ingredients are put together in multi-frequency investigations of SNRs, where evidencefor magnetic field amplification comes from X-rayastronomy. Convincing evidence was presentedthat such multifrequency spectra, from radio togamma rays, can be explained in the frameworkof particle acceleration at modified shocks. It wasalso claimed that the propagated spectra of differ-ent chemical components, when summed togetherprovide a good fit to the observed all-particle spec-trum of cosmic rays.

Unfortunately propagation in the Galaxy is allbut well understood, mainly because of our ig-norance of both the regular and turbulent compo-nents of the galactic magnetic field: the competi-tion between parallel and perpendicular diffusion,the presence of a wind, the topology of the mag-netic field in the spiral arms and in between thearms all affect the escape times and their depen-dence on energy. A hint of what might be going oncould come from future extensions of the primaryto secondary ratios to higher energies, possibly ap-proaching the knee region.

Acknowledgements

I am grateful to the organizing Committee ofthe 30th International Cosmic Ray Conference fortheir help. I am also grateful to the numerous sci-entists in Merida that I had the pleasure to talk toin order to better prepare this contribution. FinallyI wish to express my gratitude to all my closer col-laborators, R. Aloisio, E. Amato, V. Berezinsky,D. Caprioli, D. De Marco, S. Gabici, G. Morlino,M. Vietri for continuous stimulating discussions.

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References

[1] S. Funk, VHE Gamma-ray supernova rem-nants, astro-ph/ 0701471.

[2] J. Vink, X-ray high resolution and imagingspectroscopy of supernova remnants . InTheX-ray Universe 2005(2006) p. 319.

[3] E. S. Seo et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 47.

[4] I. H. Park et al., Nucl. Instr. and Meth. A 570(2007) 286.

[5] S. Coutu et al., Nucl. Instr. and Meth. A 572(2007) 485.

[6] Y. S. Yoon et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 55.

[7] R. Zei et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 23.

[8] H. S. Ahn et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 63.

[9] N. H. Park et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 39.

[10] J. J. Engelmann et al. (HEAO Collaboration),Astron. and Astrop. 233 (1990) 96.

[11] A. D. Panov et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 3.

[12] H. S. Ahn et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 79.

[13] P. J. Boyle et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 87.

[14] B. F. Rauch et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 7.

[15] H. S. Yoshida et al., Proceedings of 30thICRC Merida, Mexico, (2007) Vol.2, p. 59.

[16] T. Hams et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 67.

[17] P. Picozza et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 19.

[18] Kieda D. B. Swordy, S. P. and S. P. Wakely,Astropart. Phys. 15 (2001) 287.

[19] R. Buler et al. (HESS Collaboration), Pro-ceedings of 30th ICRC Merida, Mexico,(2007) Vol.2, p. 15.

[20] S. A. Wissel et al. (Veritas Collaboration),Proceedings of 30th ICRC Merida, Mexico,(2007) Vol.2, p. 417.

[21] S. A. Wissel et al., Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 413.

[22] Van Eldik C. Hinton J. (HESS Collabora-tion) Egberts, K, Proceedings of 30th ICRC

Merida, Mexico,(2007) Vol.2, p. 35.[23] M. A. Malkov and L. O’C. Drury, Rep. Prog.

in Phys. 64 (2001) 429.[24] A. E. Bell, MNRAS 225 (1987) 615.[25] M. A. Malkov, Ap. J. 485 (1997) 638.[26] E. Amato and P. Blasi, MNRAS Lett. 364

(2005) 76.[27] P. O. Lagage and C. J. Cesarsky, Astron. and

Astrop. 118 (1983) 223.[28] P. O. Lagage and C. J. Cesarsky, Astron. and

Astrop. 125 (1983) 249.[29] E. Amato and P. Blasi, MNRAS 371 (2006)

1251.[30] Amato E. Blasi, P. and D. Caprioli, MNRAS

375 (2007) 1471.[31] P. Blasi and E. Amato, Proceedings of 30th

ICRC Merida, Mexico, (2007) Vol.2, p. 231.[32] Berezhko E. G. Volk, H. J. and L. T. Kseno-

fontov, Astron. and Astrop. 433 (2005) 229.[33] Puehlhofer G. Berezhko, E. G. and H. J.

Volk, Proceedings of 30th ICRC Merida,Mexico, (2007) Vol.2, p. 255.

[34] E. G. Berezhko and H. J. Volk, Proceedingsof 30th ICRC Merida, Mexico, (2007) Vol.2,p. 259.

[35] A. E. Bell, MNRAS 182 (1978) 147.[36] A. E. Bell, MNRAS 353 (2004) 550.[37] P. Blasi and E. Amato, Proceedings of 30th

ICRC Merida, Mexico, (2007) Vol.2, p. 235.[38] J. Niemiec and M. Pohl, Proceedings of 30th

ICRC Merida, Mexico, (2007) Vol.2, p. 279.[39] J. R. Jokipii and J. Giacalone, Proceedings

of 30th ICRC Merida, Mexico, (2007) Vol.2,p. 229.

[40] J. R. Jokipii, Ap. J. 146 (1966) 480.[41] E. G. Berezhko and H. J. Volk, Proceedings

of 30th ICRC Merida, Mexico, (2007) Vol.2,p. 109.

[42] J. F. McKenzie and H. J. Volk, Astron. andAstrop. 116 (1982) 191.

[43] E. G. Berezhko and D. C. Ellison, Ap. J. 526(1999) 385.

[44] V. S. Ptuskin and V. N. Zirakashvili, Astron.and Astrop. 429 (2005) 755.

[45] Ostrowski M. Niemiec, J. and M. Pohl, Pro-ceedings of 30th ICRC Merida, Mexico,(2007) Vol.2, p. 283.

[46] Pelletier G. Lemoine, M. and B. Revenu,Ap. J. Lett. 645 (2006) 129.

289


[47] M. Hillas, J. of Phys. G 31 (2006) 95.[48] I. V. Moskalenko and A. W. Strong, Proceed-

ings of 30th ICRC Merida, Mexico, (2007)Vol.2, p. 129.

[49] Mastichiadis A. Dimitrakoudis, S. andA. Geranios, Proceedings of 30th ICRCMerida, Mexico, (2007) Vol.2, p. 211.

[50] C.-Y Huang and M. Pohl, Proceedings of30th ICRC Merida, Mexico, (2007) Vol.2,p. 207.

[51] A. Shalchi and R. Schlickeiser, Proceed-ings of 30th ICRC Merida, Mexico, (2007),Id 0046.

[52] P. Blasi, D. De Marco and T. Stanev, Proceed-ings of 30th ICRC Merida, Mexico, (2007)Vol.2, p. 195.

[53] P. Blasi, D. De Marco and T. Stanev, JCAP 6(2007) 27.

[54] D. N. Pochepkin et al., Astron. Lett. 24(1998) 139.

[55] R. Aloisio and V. S. Berezinsky, Ap. J. 612(2006) 900.

[56] R. Aloisio and V. S. Berezinsky, Ap. J. 625(2005) 249.

[57] M. Lemoine, Phys. Rev. D 71 (2005) 3007.

[58] F. Miniati, G. Sigl and T. Ensslin, Phys. Rev.D 70 (2004) 3007.

[59] Grasso D. Springel V. Dolag, K. andI. Tkachev, JCAP 1 (2005) 9.

[60] Das S. Ryu D. Kang, H. and J. Cho, Proceed-ings of 30th ICRC Merida, Mexico, (2007)Vol.2, p. 175.

[61] A. H. Waelkens et al., Proceedings of 30thICRC Merida, Mexico, (2007) Vol.2, p. 223.

[62] A. Gazizov, V. Berezinsky, and S. Grigorieva,Phys. Lett. B 612 (2005) 147.

[63] E. Parizot et al., Astron. and Astrop. 443(2005) 29.

[64] V. Berezinsky et al., Astropart. Phys. 27(2007) 76.

[65] Berezinsky et al.,Signatures of the transi-tion from galactic to extragalactic cosmicrays, arXiv0706.2834:[astro-ph], Acceptedfor publication in Physical Review D.

[66] C. De Donato and G. Medina Tanco, Pro-ceedings of 30th ICRC Merida, Mexico,(2007) Vol.2, p. 219.

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