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006 Cosmic Rays from the Knee to the Ankle – Status and Prospects

Karl-Heinz Kamperta∗

aDepartment of Physics, Bergische Universitat WuppertalD-42119 Wuppertal, Germany

Recent progress in cosmic ray physics covering the energy range from about 1014 eV to 1019 eV is reviewed.The most prominent features of the energy spectrum are the so called ‘knee’ at E ≃ 3 · 1015 eV and the ‘ankle’ atfew 1018 eV. Generally, the origin of the knee is understood as marking the limiting energy of galactic acceleratorsand/or the onset of increasing outflow of particles from the galaxy while the ankle is considered to mark thetransition from galactic to extragalactic cosmic rays. Alternative theories do exist and shall be sketched. A keyobservable to answer the still open questions about the cosmic ray origin and to discriminate between variousmodels is given by measuring the chemical composition or – more directly – by measuring energy spectra ofindividual cosmic ray mass groups. The status of present analyses is critically discussed and new experimentalendeavors carried out in order to improve both the statistics and the quality of data particularly at energies abovethe knee will be summarized.

1. INTRODUCTION

The cosmic ray (CR) energy spectrum extendsfrom a few hundreds MeV to above 1020 eV.Over this wide range of energies the intensitydrops by more than 30 orders of magnitude.Despite the enormous dynamic range covered,the spectrum appears rather structureless andcan be well approximated by broken power-lawsdN/dE ∝ E−γ . Up to energies of a few 1014 eVthe flux of particles is sufficiently high to en-able measurements of their elemental distribu-tions by high flying balloon- or satellite-borne ex-periments. Such studies have provided importantinformation about the origin and transport prop-erties of CRs in the interstellar medium. Twoprominent examples are ratios of secondary toprimary elements, such as the B/C-ratio, whichare used to extract the average amount of matterCR-particles have traversed from their sources tothe solar system, and are relative abundances ofradioactive isotopes, such as 10Be to stable 9Beor 26Al to stable 27Al, which carry informationabout the average ‘age’ of CRs. With many newcomplex experiments taking data or starting upin the near future and with a possibly new gener-

∗email: kampert@uni-wuppertal.de

ation of long flying balloons, this remains a vitalfield of research.

Above a few times 1015 eV the flux drops toonly one particle per square metre per year. Thisexcludes any type of ‘direct observation’ even inthe near future, at least if high statistics is re-quired. On the other hand, this energy is largeenough so that secondary particle cascades pro-duced in the atmosphere penetrate with a foot-print large enough to be detected by an arrayof detectors on the ground. Such an extensiveair shower (EAS) array typically has dimensionsof a fraction of a square kilometre to more than1000 square kilometres and can be operated formany years to detect fluxes down to 1 particle persquare kilometre per century or less.

The most prominent features of the CR energyspectrum fall into the energy range covered byEAS experiments. The steepening of the slopefrom γ ∼= 2.7 to γ ∼= 3.1 at about 3 · 1015 eVis known as the ‘knee’. It was first deduced fromobservations of the shower size spectrum made byKulikov and Khristianson et al. in 1956 [1] butit still remains unclear as to what is the cause ofthis spectral steepening and even as to what arethe sources of the high energy CRs at all. At anenergy above 1018 eV the spectrum flattens again

1

2

Figure 1. The all-particle CR energy spectrum weighted by E3 showing the knee at 3 ·1015 eV, a possiblesecond knee at ∼ 1017 eV, the ankle at about 3 ·1018 eV, and the GZK-region near 6 ·1019 eV. Referencesare given in the text.

at what is called the ‘ankle’. Because of the largesize and/or magnetic field required to accelerateand confine charged particles above 1018 eV, theorigin of CRs above the ankle is generally consid-ered to be of extragalactic (EG) nature. Finally,the question whether the spectrum extends be-yond the Greisen-Zatsepin-Kuzmin threshold of6 · 1019 eV [2] is currently among the foremostquestions in astro-particle physics as is reflectedalso by the number of presentations given at thisconference.

The main purpose of this paper is to review theexperimental data in the energy range below theGZK-threshold, i.e. from about 1014 to 1019 eV.We shall discuss the energy spectrum, chemicalcomposition, and anisotropies in their arrival di-rections and critically examine the astrophysicalimplications by taking into account the system-atical uncertainties of the data.

2. THE KNEE REGION

Mainly for reasons of the required power thedominant acceleration sites of CRs are generally

believed to be shocks associated with supernovaremnants (SNR). Naturally, this leads to a powerlaw spectrum as is observed experimentally. De-tailed examination suggests that this process islimited to E0/Z ∼ 1014 eV [3,4] for standardgalactic SNRs. This value can be extended up-ward with a number of mechanisms, for exam-ple by introducing higher magnetic fields, largersources, quasi-perpendicular shocks, reaccelera-tion by multiple sources, etc. However, theseassumptions and their effects are not free of de-bate and possibly, something more fundamentalmay be incorrect with the suggested supernova(SN) picture and its shock value E0. In any case,if there is a typical maximum energy which de-pends linearly on Z for reasons of magnetic con-finement, then the spectrum of CR nuclei mustbecome heavier with increasing energy as the hy-drogen cuts off first and then increasingly heaviernuclei reach their acceleration (or confinement)limits.

A change in the CR propagation with decreas-ing galactic containment at higher energies hasalso been considered. This increasing leakage re-

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sults in a steepening of the CR energy spectrumand again would lead to a similar scaling with therigidity of particles, but would in addition predictanisotropies in the arrival directions of CRs withrespect to the galactic plane.

Besides such kind of ‘conventional’ source andpropagation models [5,6] several other hypothe-ses have been discussed in the recent literature.These include the astrophysically motivated sin-gle source model of Erlykin and Wolfendale [7]trying to explain possible structures around theknee by a single recent and nearby SN, as well asseveral particle physics motivated scenarios try-ing to explain the knee due to different kindsof CR-interactions, e.g. by photodisintegration atthe source [8] or by sudden changes in the char-acter of high-energy hadronic interactions duringthe development of EAS [9].

Recently, the ‘Cannonball’ model of CRs hasbeen suggested as a radically different theory ofCR origin [10]. It is inspired by mounting obser-vational evidence that, in addition to the ejectionof a non-relativistic spherical shell, the explosionof core-collapse SNae results in the emission ofhighly relativistic bipolar jets of plasmoids of or-dinary matter, the ‘Cannonballs’ (CB). As theCB with a typical half of the Mercury mass propa-gates at relativistic speed through the interstellarmedium, it encounters electrons, protons, and nu-clei kicking them up to higher energies elasticallyby magnetic deflection. These newly born CRsare then subject to propagation effects, similarlyas in ‘classical’ theories. It is argued that this verysimple concept explains all observed propertiesof non-solar CRs at all observed energies. Thereare two important differences to the conventionalmodels: a) because of the specific kinematics ofparticle acceleration, the maximum energy of CRs(and thereby the knee positions) scale with themass A of CRs rather than with their charge Z,b) since the CBs propagate rapidly from the innerSN and GRB realm of the Galaxy into its halo orbeyond converting ISM particles to high energyCRs all along their trajectories, there is a muchlower level of CR-anisotropy expected than in thetraditional SN picture of CRs.

Indeed, the low level of CR anisotropy evenat energies above the knee is a long standing

problem [11]. Generally, the observed spectrumφ(E) and the source spectrum Q(E) are consid-ered to be connected by a relation of the formφ(E) = Q(E) × τesc(E). A simple power-lawfit of the escape time to the available data givesτesc(E) ∝ E−δ with δ ≈ 0.6. Extrapolating τesc

to 1015 eV, for example, would lead to a value al-most as small as the light travel time across thegalactic disk, implying a much larger anisotropythan is observed.

From the discussion above it is obvious, thatan answer to the question about the origin of theknee is of key importance to reveal informationabout the origin of galactic cosmic rays in gen-eral. Experimental access to such questions isprovided by measurements of charged cosmic rays(the classical nucleonic component) and γ-raysby experiments above the atmosphere, and bythe observation of air showers initiated by high-energy particles in the atmosphere.

A wealth of information on potential cosmic-ray sources is provided by recent measurementsof TeV γ-rays employing imaging atmosphericCherenkov telescopes, most notably from theH.E.S.S. experiment. Their observation of themorphologies and energy spectra of the shell typeSNRs RX J1713.723946 [12,13] and RX J0852.0-4622 [14] are well in agreement with the idea ofparticle acceleration in the shock front. The spec-tra extend up to energies of 10 TeV and provideevidence for the existence of particles with en-ergies beyond 100 TeV at the shock front thatemerged from the supernova explosions. How-ever, an unequivocally proof for acceleration ofhadrons is still missing and questions arise alsoabout the low number of established SNRs show-ing TeV γ-ray emission. For example, a recentGalactic plane survey of H.E.S.S. [15] reveals noSNRs brighter than these two in the region cov-ered. This apparent deficit of TeV-bright SNRsmay pose some problems in explaining the highenergy budget of galactic CRs. Remember thatabout 10% of the mechanical energy released bythe population of Galactic supernovae needs tobe converted into CRs if all SNRs are sites ofCR acceleration. Any reduction in the number ofTeV-bright SNRs needs to be compensated for bya corresponding factor in the already large value

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of the CR acceleration efficiency.To undoubtedly establish SNRs as the sites of

CR acceleration and in order to constrain the con-ventional SN acceleration model from other pro-posed mechanisms, precise measurements of theprimary CR energy spectrum and particularly ofthe mass composition as a function of energy areneeded. Significant progress has been made hereas well in recent years, but the situation is farfrom being clear.

2.1. Comparison of direct and indirectmeasurements

Cosmic ray measurements on balloons andspacecraft have an important advantage overground-based air shower experiments: They de-tect the primary CR particles and measure itscharge directly. This is because spacecraft experi-ments perform the measurement above the atmo-sphere and balloon-borne experiments typicallyperform their measurements with residual atmo-spheres of only ∼ 5-10 g/cm2. This is a relativelysmall value compared to the typical hadronic in-teraction length of λI ∼ 90 g/cm2 so that correc-tions for interactions above the instruments areof minor importance, at least for light particles,such as protons and He nuclei. This advantage ispaid for at the expense of lacking statistics at highenergies. For example, the largest of the currentgeneration of balloon-borne detectors, TRACER[16], reaches a sensitive volume of 2× 2× 1.2m3.It has been flown successfully for 14 days expo-sure from the Antarctic in 2003 and from Swe-den in summer 2006. The first 14 days flighttime resulted in an exposure of ∼ 75 m2 sr daysand allowed to measure e.g. oxygen nuclei up to∼ 320TeV and iron nuclei up to ∼ 70TeV.

The largest exposure of all direct experimentshas been reached by the Japanese American Co-operative Emulsion Experiment JACEE [17] andthe RUssian-Nippon JOint Balloon collaborationRUNJOB [18]. JACEE flew a series of thin(∼ 8.5 radiation lengths) emulsion/X-ray filmcalorimeters on 15 flights during 1979-1994 andhas reached an exposure of ∼ 664 m2 hrs from 11analysed flights. Taking the zenith angle accep-tance out to tan θ ∼ 72−79◦ into account, this re-lates to approx. ∼ 80 m2 sr days. RUNJOB flew

Figure 2. Proton (top), helium (centre), and iron(bottom) spectra from direct experiments com-pared to EAS data (based and updated from [19]).The single diagonal error bar in each panel in-dicates the effect of a ±15% uncertainty in theenergy scale.

roughly a similar set of X-ray films and emul-sion chambers on a series of 10 successful balloonflights during 1995-1999 with a total exposure of575 m2 hrs. Both experiments were able to recon-struct proton spectra up to almost 1 PeV.

Figure 2 shows a collection of the proton, he-lium, and iron spectra obtained by various ballon-and satellite-borne experiments compared to datafrom ground based experiments. Obviously, datafrom direct experiments are sparse above 100 TeVand uncertainties become very large with increas-ing energies, particularly for primaries heavierthan protons. Reasonably good agreement be-tween RUNJOB and JACEE is observed in caseof the proton spectrum, but the He-flux mea-

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sured by RUNJOB is about a factor of two lowercompared to other experiments. Comparing theslopes of the p and He spectra yields power lawindices of ∼ 2.7-2.8 for both elements in the en-ergy range 10-500 TeV/nucleon. The iron spec-trum appears somewhat flatter, γFe ≃ 2.6, par-ticularly when taking into account the extrapo-lation to the EAS data. Such a dependence ofγ could be explained by charge dependent effectsin the acceleration or propagation process. Forexample, non-linear models of Fermi accelerationin supernovae remnants predict a more efficientacceleration for elements with a large A/Z ratio.However, uncertainties may still be too large toallow for definite conclusions about differences inthe acceleration and propagation mechanisms ofdifferent primaries. For illustration, the effect ofan assumed (and possibly underestimated) uncer-tainty of ±15% in the energy scale is shown bythe single error bar in each of the panels.

It is remarkable to see direct measurements andEAS data starting to overlap each other. Clearly,EAS data below about 1015 eV are dominatedby systematic uncertainties while direct measure-ments suffer from statistical ones. With thesecaveats kept in mind, the agreement is very good.The EAS data of KASCADE [20], also shown infigure 2, have been reconstructed based on twodifferent hadronic interaction models employed inthe EAS simulations. Except perhaps for iron,the uncertainties caused by the interaction modelare of similar size or even smaller than systematicuncertainties between experiments like JACEEand RUNJOB. Also shown in figure 2 are protonand helium spectra derived from emulsion cham-bers and burst detectors operated within the Ti-bet II air-shower array [21]. The results are inrough agreement with the KASCADE data. Forreasons of clarity, only the results based on simu-lations with the CORSIKA [22] / QGSJet-model[23] are included for the Tibet data. Those ob-tained based on Sibyll [24] are similar within theirerror bars. There are some important peculiari-ties of the Tibet ASγ analysis to be pointed outhere. The data are compared to EAS simula-tions assuming in one case a heavy dominated(HD) and in another case a proton dominated(PD) composition. In the HD-model a rigidity

dependent knee Ek = Z×1.5 ·1014 eV is assumedand in the PD-model all mass components are as-sumed to break off at Ek = 1.5 · 1014 eV. Theseassumptions are surprising, since no experimentever has observed at break in the spectrum atsuch low energies. Furthermore, the experimen-tal data of Ref. [21] start only at energies aboveE ≃ 4 · 1014 eV, i.e. significantly above the as-sumed knee position. Moreover, because of in-sufficient separation power between proton andhelium primaries, the authors have deduced theproton spectrum first by using a neural networkalgorithm. Next, the proton + helium spectrumhas been reconstructed and, finally, the heliumspectrum has been obtained by subtracting thenumber of proton events obtained in the first taskfrom the proton + helium dataset obtained in thesecond task. Clearly, there are huge correlatederrors to be expected in the helium spectrum de-duced that way. Also, it is not clear how theresults depend on the ad-hoc assumptions madeabout the knee position. Because of the steeplyreconstructed proton and helium spectrum, theauthors then conclude, that the main componentresponsible for the change of the power index ofthe all-particle spectrum around 3·1015 eV is com-posed of heavy primaries. However, there is noproof to this statement as the experiment is al-most blind to heavy particles (detection efficiencyof iron ≈ 4 %) .

To conclude this topic, despite some contro-versy a reasonably good agreement between di-rect and EAS experiments has been achieved inrecent years. At present, EAS experiments attheir threshold energies are limited purely by sys-tematic uncertainties, while direct measurementssuffer mostly from lacking statistics but also fromsystematic uncertainties in determining the ab-solute energy scale. There is some hope thatnew EAS experiments located at very high alti-tude will be able to push the measurements downto lower energies and at the same time also re-duce their systematic uncertainties. Direct ex-periments, on the other hand, may be able to in-crease their exposure at high energies. However,given the very steeply falling spectrum, it appearsunlikely that balloon experiments will be able toextend the range of measurements beyond 1 PeV

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any time in the near future. Thus, the chance ofdetecting the knee with direct measurements ofprotons to iron on balloons is not likely to occurwithout significant increases in the payload andflight duration capabilities of high altitude bal-loons. Even with 50 times the present JACEEp-He exposure one would still be unable to makedefinitive measurements about a break in the en-ergy spectrum beyond 200 - 300 TeV [25].

2.2. Air shower data at the kneeAs can be seen from figure 1, a wealth of

data at energies around the knee has been accu-mulated by a large number of experiments op-erated over many years. It is clearly notice-able that the data fall into two groups differ-ing by their fluxes mostly: CASA-MIA, CASA-BLANCA, and DICE (all operated at Dugway,Utah) show distinctly lower fluxes than Tibet,HEGRA, EAS-TOP, and KASCADE and Tunka[26] (not shown in figure 1). This problem has al-ready been addressed in [27] but is still not fullyunderstood. It may be related to different ob-servation techniques (charged particles combinedeither with muons or with Cherenkov light), dif-ferences in the details of EAS simulations, or toother reasons. On the other hand, it should bepointed out that the differences almost vanish,if one of the groups is shifted by about 15% intheir absolute energy scale, i.e. by an amountwell within the systematic uncertainties of theexperiments. The knee energy is found in all ex-periments at approximately 3 PeV with the in-dex changing from γ1 = 2.7 to γ2 = 3.1. OnlyAkeno data are different showing different spec-tral shapes and a very sharp knee at ∼ 5PeV.

It has been realized that the all-particle spec-trum is not very discriminative against astrophys-ical models of the knee and that a deconvolutioninto different primary particles is required. How-ever, this is probably the most difficult task inEAS physics, both because of the level of depen-dence on hadronic interaction models used in EASsimulations and because of the significant (massdependent) fluctuations of EAS observables. Alarge variety of methods is used to infer the pri-mary energy and mass [28], most notably the ra-tio of electron to muon numbers. At energies

10 8

10 9

3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6

Log10(E/TeV)

φ(E

) E

2.5 (

arb.

un.

)Heavy

Light

Figure 3. CR energy spectrum of light (p+He)and heavy (all the rest) primaries from EAS-TOPand MACRO using TeV muons [29]).

higher than approx. 1017 eV, also direct measure-ments of the shower maximum in the atmospherebecome available by observations of fluorescencelight with imaging telescopes, such as operatedby HiRes and the Pierre Auger Collaboration (seeproceedings to this conference).

Extensive analyses of both the energy spectrumand composition have been performed by EAS-TOP and KASCADE. EAS-TOP has analysed itsdata through simultaneous measurements of theelectromagnetic and muonic shower components.These are obtained from the EAS array operatedat Campo Imperatore on the mountain top 2005m.a.s.l. (820 g/cm2) above the underground GranSasso Laboratories in which the MACRO detec-tor has been located under an average depth of1200 m rock [29]. The coincident observation ofthe soft charged particles in the surface array andthe high energy EAS muons (Eµ > 1.3TeV) inthe underground detector permits – despite largefluctuations of the muon number – a reconstruc-tion of the CR energy spectrum for “light” and“heavy” primaries. The result, depicted in figure3, shows that the energy spectrum of the light pri-

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maries is beginning to diminish at about 5 PeV,whilst the heavy component may be signaling itschange in the spectrum at least a decade higherin energy.

The results corroborate those of KASCADEshown in figure 4. KASCADE is located atsea-level (110 m.a.s.l.) in Karlsruhe, Germany,and measures the electromagnetic, muonic, andhadronic EAS components using a very dense de-tector array and a hadronic calorimeter [30]. Theanalysis of the data takes advantage of the ef-fect that for given energy, primary Fe-nuclei re-sult in more muons and fewer electrons at groundas compared to proton primaries. Specifically, inthe energy range and at the atmospheric depthof KASCADE, a Fe-primary yields about 30%more muons and almost a factor of two fewer elec-trons as compared to a proton primary. The basicquantitative procedure of KASCADE for obtain-ing the energy and mass of the CRs is a techniqueof unfolding the observed two-dimensional elec-tron vs truncated muon number spectrum intothe energy spectra of primary mass groups [20].The problem can be considered a system of cou-pled Fredholm integral equations of the form

dJ

d lg Ne d lg N trµ

=∑A

+∞∫

−∞

d JA

d lg E·

· pA(lg Ne , lg N trµ | lg E) · d lg E

where the probability

pA(lg Ne, lg N trµ | lg E) =

+∞∫

−∞

kA(lg N te, lg N tr,t

µ )d lg N te d lg N tr,t

µ

is another integral equation with the kernel func-tion kA = rA · ǫA · sA factorizing into three parts.Here, rA describes the shower fluctuations, i.e.the 2-dim distribution of electron and truncatedmuon number for fixed primary energy and mass,ǫA describes the trigger efficiency of the exper-iment, and sA the reconstruction probabilities,i.e. the distribution of Ne and N tr

µ that is recon-structed for given true numbers N t

e, N tr,tµ of elec-

tron and truncated muon numbers. The proba-bilities pA are obtained from CORSIKA simula-

Figure 4. Unfolded CR energy spectrum of p, He,and C mass-groups from KASCADE. The spectraare obtained by using QGSJET and SYBILL forthe generation of the EAS response matrix pA

[20].

tions using QGSJET-01 [23] and Sibyll 2.1 [24]as high-energy and GHEISHA [31] as low-energyhadronic interaction models and a moderate thin-ning procedure. Smaller samples of fully sim-ulated showers were generated for comparison.The simulated data are then fed into the detec-tor Monte Carlo programme and the response isparameterized as a function of energy and mass.Because of the large shower fluctuations, unfold-ing of all 26 energy spectra ranging from protonsto Fe-nuclei is clearly impossible. Therefore, 5elements (p, He, C, Si, Fe) were chosen as repre-

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sentatives for the entire distribution. More massgroups do not improve the χ2-uncertainties of theunfolding but may result in mutual systematic bi-ases of the reconstructed spectra.

The results of such an unfolding are presentedin figure 4. Shown are the spectra of the p,He, and C mass-groups based on the responsematrices pA obtained from the two interactionmodels. Clearly, there are common features butalso differences in the energy distributions. Ineach of the distributions a distinct break in thespectrum is observed which is increasing towardshigher energy with increasing primary mass. Inboth cases the He flux is higher than the pro-ton flux. This finding may be surprising at firstsight, but it is already suggested by extrapolat-ing the He and proton spectra with their differentslopes from lower energies towards the knee (seefigure 2). The spectrum of the Si group (see fig-ure 14 and 15 in Ref. [20]) indicates a knee ateven higher energies. The Fe spectrum (figure 2)shows large differences when performing the un-folding either with the QGSJET or Sibyll modeldemonstrating that such analyses are limited atpresent mostly by uncertainties of the hadronicinteraction models. Despite these differences inthe individual spectra, the all-particle spectra ofKASCADE (see figure 1), obtained by summingup the energy spectra of all mass groups (p - Fe)coincide very nicely for the two interaction mod-els. Thus, it can firmly be stated that the knee inthe all particle spectrum is caused by light (p andHe) primaries. Obviously, also the mean masscomposition (e.g. expressed in terms on the meanlogarithmic mass [32]) increases above the knee.

A more detailed investigation [20] shows thatthe QGSJET model performs reasonably well athigh energies but exhibits some problems at PeVenergies. Sibyll, on the other hand, describes thedata rather well in the knee region but suffersfrom a muon deficit at higher energies. There-fore, it suggests a more prominent contributionof heavy primaries at high energies. It shouldbe emphasized, that this muon deficit of Sibyllapplies to O(1GeV) muons only. Muons at en-ergies of several 100 GeV, such as observed byunderground experiments like AMANDA and Ice-Cube, seem to be described rather well by Sibyll

Figure 5. Interpretation of the CR spectrum interms of different sources [11]. Shown are the in-dividual galactic sources (component A and B)and the flux expected from extragalactic sources.The galactic components are guided by the KAS-CADE knee shape as far as the point marked x.The dashed line Q is the total if the extended tailB of the galactic flux is omitted.

[33]. Very recently, a new interaction model,called EPOS has been released [34]. Most impor-tantly, it provides a better description of baryon-antibaryon production at high energies. A pre-liminary analysis shows that the muon num-ber increases more rapidly with energy than inQGSJET or Sibyll with the muon density be-ing about 40% higher at 1018 eV compared toQGSJET-01 calculations. It will be interestingto repeat the unfolding of the CR energy spec-tra employing this model to verify whether thepresent deficiencies of the interaction models willbe resolved.

The unfolded KASCADE energy spectra candirectly be compared to phenomenological calcu-lations of astro- and particle physics related mod-els or can be used to infer information about theCR sources. An example is shown in figure 5taken from Ref. [11]. It is concluded that thedata provide support for the supernova pictureof CR origin, i.e. the distinct knee near 3 PeVwould be related to emission by the free expan-sion phase of SNRs. However, a question arisesabout how to fill the gap from the iron knee at

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about 1017 eV to the ankle at ∼ 5 · 1018 eV.These CRs may originate from SN type II ex-plosions into dense stellar winds where the inter-action generates much stronger magnetic fields.This may result in rigidities up to at least 1017 V(component ‘B’ in figure 5), especially from a fewabnormally high speed/low mass ejections [11].

A very important question is whether thepresent data allow to distinguish a knee of con-stant rigidity (E/Z) from that of constant energyper nucleon (E/A), such as is predicted by parti-cle physics interpretations of the knee or by thecannonball model. Unfortunately, Z/A changesonly from 0.5 in case of He to 0.46 for Fe nu-clei. Hence, the question about the rigidity de-pendence needs to be answered basically by com-paring the energy spectra of p and He primaries.Ironically, these are the two primaries which aremost strongly affected by EAS fluctuations, sothat their energy resolutions are deteriorated sub-stantially. In fact, overlaying the p and He spec-tra of figure 4 using E/Z and E/A abscissas doesnot give a clear answer; Sibyll exhibits a slightpreference for charge scaling and QGSJET formass scaling. It is hoped, that the situation willimprove somewhat with better models becomingavailable. Improving on the data side seems moredifficult because of two reasons: statistical errorsare already much smaller than systematical onesand (presently not yet included) data from largerzenith angles are subject to even stronger EASfluctuations.

3. THE SECOND KNEE AND ANKLE:TRANSITION FROM GALACTIC TOEXTRAGALACTIC COSMIC RAYS

Besides the prominent knee in the all-particlespectrum, additional structures are observed atabout 1017 eV and ∼ 3 · 1018 eV, known as thesecond knee and the ankle, respectively (see Figs.1 and 5). The ankle has been reported convinc-ingly by a number of experiments, but there isstill no consensus about the existence of a sec-ond knee. This is because of both the weaknessof the structure making it difficult to detect andbecause of only few experimental data, most ofwhich are either at their upper or lower limit of

Figure 6. All-particle CR energy spectra fromYakutsk [38], Haverah Park [37], Fly’s Eye [36],HiRes II (mono) [39], and Akeno [35].

detectable energies. A blow-up of the data be-tween 1017 eV and 1019 eV is shown in figure6. It includes measurements by Akeno [35], Fly’sEye (stereo) [36], Haverah Park [37], Yakutsk [38],and HiRes II (mono) [39]. Akeno has provided thefirst hint of a change in the index of the power-lawenergy spectrum around 6 · 1017 eV. The steep-ening of the spectrum was confirmed by HaverahPark and is indicated also in the Fly’s Eye andmore recent HiRes data. A recent re-analysis ofthe Yakutsk 1974-2004 data agrees well with theAkeno data providing additional support for theexistence of a second knee at about (6 ± 2) · 1017

eV. The ankle at ∼ 3 · 1018 eV was first ob-served by Haverah Park, Akeno, and Yakutsk andis traditionally explained in terms of the transi-tion from galactic to EGCRs. The key point hereis that one expects the galactic magnetic field tolose its efficiency at about this energy as the gyro-radius of a particle at charge Z in a µ-Gauss field,rg ≃ 1 kpcZ−1B−1

µG, becomes comparable to the

thickness of the galactic disk. It then becomesnatural to think of hard EGCRs starting to pen-etrate into the galaxy and dominating the flux athigher energies (see figure 5 for illustration).

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Figure 5 also provides an intuitive explanationfor the second knee: it would primarily be causedby the break of the galactic Fe component. AsHillas pointed out [11], an extra component ‘B’would be needed in order to make up the well-measured total CR flux at several 1017 eV forwhich he considered SNae Type II explosions intodense stellar winds (see chapter 2.2). Naıvely, thesecond knee in this picture is expected at EFe ≃26×3 ·1015 ≃ 8 ·1016 eV or even lower if the kneeis composed of p and He primaries as suggestedby figure 4. This is almost a factor of 10 lowerthan reported by Akeno and others. A scaling ofthe knee position with E/A would bring the Fe-knee up to approx. 2 · 1017 eV, but still too lowto fit the classical picture.

Ignoring this puzzle for a moment, also char-acteristic changes of the CR composition are ex-pected in this traditional picture of the knees andankle. Up to the knee, the composition would fol-low the standard source composition dominatedby p and He primaries. Between the first andsecond knee the composition would change tobecome iron dominated, and above the ankle itwould be dominated by extragalactic protons.

However, the ‘folklore’ about the second kneeand ankle and its related transition from galac-tic to EGCRs is not free of dispute and hasreceived much attention recently. Back in the80s, Berezinsky and collaborators have pointedout an inevitable feature of the 1018-1019 eVEGCR spectrum: if EGCRs consist of protonsmostly, they would suffer - besides the GZK ef-fect - from energy losses associated with the pro-duction of e+e− pairs in the CMB photon field[40]. This would result in a modulation of theall-particle energy spectrum to what is called a“pair-production dip” between 1 · 1018 - 4 · 1019

eV. In such a way, the turn over from the left-to the right hand side of the ‘dip’ would mimicthe ankle. Moreover, since the Bethe-Heitler pairproduction works effectively only for protons [41],the ankle can then be interpreted as a signature ofa pure proton EGCR component and the galactic-extragalactic transition must occur at much lowerenergies than in the traditional picture, possiblyaround the second knee.

How can the two models be discriminated? The

Figure 7. Comparison of the mean depth ofshower maximum, Xmax, predicted by the dip-and ankle-model of Ref. [42] and the Cannonballof Ref. [10] with data from HiRes [43], [44], Fly’sEye [36], and Yakutsk [45] (see text for details).

most critical observation is provided by a mea-surement of the chemical composition in the en-ergy range around 1018 eV: In the dip model astrong dominance of protons, and in the anklemodel a strong dominance of iron nuclei is ex-pected. A recent confrontation of the two modelsto existing data has been performed by Allardet al. [42]. The authors conclude that the all-particle energy spectrum is reproduced equallywell by the two models. However, based on a com-parison of the mean mass composition, analyzedin terms of the mean depth of the shower max-imum, Xmax, they favour the traditional model.Figure 7 compares the Xmax data of various ex-periments with the dip- and ankle-model of [42].Here, only CORSIKA / QGSJET-01 simulationsare shown, because QGSJET-01 is the interac-tion model providing the most consistent descrip-tion of experimental data in this energy region.Clearly, this direct comparison with QGSJET-01does not seem to give preference to any of the twomodels. Also shown are predictions of the can-nonball model for two choices of penetrability of

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EGCRs into the Galaxy [10]. It should be noted,that in the latter case, Xmax(E) is constructed bya simplified model described in Ref. [46] insteadof using full EAS simulations. Evidently, betterdata are required before definite conclusions canbe drawn about the transition from Galactic toextra-galactic CRs.

4. ANISOTROPIES

Another key observation in cosmic ray astro-physics is the directional distribution of the parti-cles. That distribution will depend on any galac-tic magnetic fields and hence will be energy (rigid-ity) dependent. However, with very limited ex-ceptions, which are not individually statisticallysignificant, there is no observed deviation fromisotropy above the knee of the energy spectrum,and any anisotropies at lower energies are them-selves very small [47,48]. Probably, the most com-prehensive data at energies from a few to severalhundred TeV have been obtained by the TibetASγ experiment. Besides revealing fine details ofknown anisotropies, the data support the pictureof corotation of low energy CRs with the localGalactic magnetic environment and they may in-dicate an anisotropy around the Cygnus region[49]. However, a contamination of TeV γ’s in thedata sample cannot be excluded at present.

A non-uniform distribution in of the arrival di-rections, suggestive of a source direction, in theenergy range 1018.0 - 1018.4 eV has been reportedby the AGASA [50] and similarly by the SUGARcollaboration [51]. However, neither of those ob-servations on their own is clearly statistically sig-nificant. Moreover, the Pierre Auger Collabora-tion has also started to analyse the galactic centreregion. These results, obtained with much largerexposure than of AGASA and SUGAR, do notsupport that finding and instead provide an up-per bound on a point-like flux of CRs from theGalactic Centre. Even in absence of CR pointsources, such data may be regarded as the pos-sible beginning of a new era in cosmic ray astro-physics in which we can begin directional cosmicray astronomy. The possibility of having a sourceto observe may indeed open up new frontiers forthe Pierre Auger Observatory [53,54].

Figure 8. Rayleigh amplitudes A vs primary en-ergy from different experiments. The data ofKASCADE [48] (bold line) represent upper lim-its (95%). The thin lines show expectations fromthe galactic CR diffusion model of Ref. [55].

As already pointed out, the low level of CRanisotropy even at energies above the knee is con-sidered the most serious challenge to the stan-dard model of the origin of galactic CRs fromdiffuse shock acceleration [11]. Figure 8 showsa collection of data expressed in terms of theRayleigh amplitudes A. The thin lines representa CR diffusion model [55] predicting anisotropieson a scale of 10−4 to 10−2 depending on particleenergy and strength and structure of the galac-tic magnetic field. However, the model fails todescribe the all-particle spectrum considerably.Assuming a simple rigidity model of τesc(E) ∝E−0.6, Hillas estimates anisotropies at a level of5 %, 16%, and 180% at 1.5 · 1014 eV, 1015 eV,and 1.5 · 1017 eV, respectively [11]. In case of aE−1/3 scaling, the values would go down to 0.6%,1.1%, and 3.7% which is still in contradiction tothe experimental data of figure 8.

As already mentioned, the CB-model [10] pre-dicts much lower levels of anisotropies than mod-els in which CRs diffuse away from the centralrealms of the Galaxy, where most SN explosionstake place. A CB, on the contrary, is consid-ered a continuous source of CRs along its trajec-tory from the galactic disk into the galactic halo.

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Along its trajectory, the source intensity dependson the local and previously traversed ISM den-sity. Thus, the source of CRs is very diffuse andthe directional anisotropy of CRs at the Earthslocation is expected to be very small and to varylittle with energy.

5. SUMMARY AND OUTLOOK

Diffusive shock acceleration in SNRs is consid-ered a viable mechanism for accelerating cosmicrays and it naturally leads to a power-law spec-trum in rigidity. However, many fundamentalquestions related to the assumption of SNRs be-ing the sources of galactic cosmic rays are stillopen. These questions include, amongst others,the absence of TeV γ-radiation from a large frac-tion of SNRs, the origin of the knee in the cosmicray spectrum, the low level of global anisotropiesin their arrival direction, the transition of galac-tic to extragalactic CRs and its related questionabout the existence of a second knee and aboutthe origin of the ankle.

The deconvolution of the all-particle CR spec-trum into energy spectra of individual mass-groups by current KASCADE data [20] has ad-vanced the field quite a lot. Such kind of data con-tain much more information than the all-particlespectrum and the mean mass of CRs (expressedmostly by 〈Xmax〉 and 〈ln A〉) alone. However,there remain large uncertainties, which still allowalternative interpretations. Most prominently, adefinite answer about an E/Z (rigidity) or E/Ascaling of the knee position cannot be given atpresent. However, there is still some room forimproving the data quality and, despite enor-mous progress already made, there are also bet-ter hadronic interaction models being developedwhich are hoped to eliminate the still existingshortcomings of the present models such as Sibyll2.1 or QGSJET01 [34].

At energies above 1017 eV data become verysparse and we are far from understanding thetransition from galactic to extragalactic CRs. Al-though the ankle in the CR spectrum at about5 · 1018 eV is often interpreted as the signatureof the transition from a steeply falling galacticCR-spectrum to a slightly harder extragalactic

spectrum, alternative explanations are possible.Sometimes the second knee at about 1017.5 eV isconsidered as indication for the transition to ex-tragalactic CRs, but this explanation would re-quire fine-tuning of the injection spectra of thedifferent galactic and extragalactic sources. Twoparticular models were discussed in detail, thedip- [41] and the ankle-model [11]. Current dataon 〈Xmax〉 do not allow to exclude any of the twomodels. The transition from galactic to extra-galactic CRs occurs in the energy region of thesecond knee and is distinctly seen only if iron andproton spectra are measured separately.

In conclusion, the fundamental question aboutthe origin of high energy CRs below the GZK en-ergy remains far from being answered. As a con-sequence, the interest in studying CRs from about1017 to 1019 eV with high quality state of the artEAS detectors has grown worldwide and severalnew experiments are being prepared or plannedfor. These include KASCADE-Grande (alreadyin operation) [56] as well as low-energy extensionsof Auger by High Elevation Auger Telescopes(HEAT) and an infill array with extra muon de-tectors, as well as the Telescope Array (TA) andits low-energy extension TALE [57]. These detec-tors can reliably solve the problem of measuringthe energy spectrum and mass composition in thetransition region and complement the measure-ments performed at the highest energies by thePierre Auger Observatory.

Acknowledgments Its a pleasure to thank theorganizers for their invitation to the CRIS 2006workshop which was conducted in a very pleasantand fruitful atmosphere. The author is gratefulto M. Risse for carefully reading the manuscript.The work of the group at University Wuppertal issupported in part by the Helmholtz VIHKOS In-stitute and by the German Ministry for Researchand Education.

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