Review
Cosmic rays from the knee to the highest energies

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Abstract

This review summarizes recent developments in the understanding of high-energy cosmic rays. It focuses on galactic and presumably extragalactic particles in the energy range from the knee (1015 eV ) up to the highest energies observed (>1020 eV). Emphasis is put on observational results, their interpretation, and the global picture of cosmic rays that has emerged during the last decade.

Introduction

Cosmic rays are ionized atomic nuclei reaching the Earth from outside the Solar System. Although already discovered in 1912, their sources and propagation mechanisms are still a subject of intense research. During the last decade significant progress has been made and a consistent picture of cosmic-ray observations is now evolving. This review describes recent progress in the exploration of the sources and propagation of high-energy cosmic rays, focusing on observational results and the emerging global picture.

Many reviews of cosmic-ray theory and observations are available in the literature of the subject. Most of these reviews concentrate on different aspects and energy ranges of high-energy cosmic rays which are presented in much more detail than is possible here. For example, covering the knee energy region, experimental data are compiled in [1], [2] and a comparison of observations and model predictions can be found in [3]. The data in the range between the knee and the ankle, and their interpretation are discussed in [4]. Focusing on the upper end of the cosmic-ray spectrum, measurement techniques and observations are reviewed in [5], [6], [7], [8]. More theoretical and phenomenological aspects of the physics of ultra high-energy cosmic rays is the subject of the reviews [9] and different source scenarios are discussed in depth in [10], [11] (acceleration scenarios) and [12] (non-acceleration scenarios). An exhaustive compilation of experimental results of the full cosmic-ray energy range can be found in [13] and a recent review, emphasizing measurement and analysis techniques, is given in [14].

In this article, we discuss high-energy cosmic-ray measurements covering the energy range from the knee to the highest energies. By concentrating mainly on observational results over the last decade and their implications for our overall understanding of cosmic rays, this review is complementary to the other articles.

The exploration of cosmic rays is mainly driven by new experimental findings. Hence, we begin this review with a short historical overview, followed by an introduction to the physics of high-energy cosmic rays (Section 1).

In the energy region of interest, cosmic rays are measured indirectly with large detector installations below the atmosphere, registering secondary particles produced in extensive air showers, initiated by high-energy cosmic rays. In Section 2, basic properties of air showers are introduced and major detection techniques are discussed.

Recent experimental results concerning the flux of cosmic rays, their elemental composition, and studies of anisotropies in their arrival directions are presented in Section 3 to 5. The global picture evolving from these measurements and their impact on the present understanding of the origin of high-energy cosmic rays is emphasized in Section 6. The importance of the understanding of high-energy hadronic interactions for the interpretation of air shower data is underlined in Section 7. Concluding remarks (Section 8) complete the review.

Cosmic rays were discovered in the year 1912 by V.F. Hess during several ascends with hydrogen-filled balloons up to altitudes of 5 km [15]. He measured the ionization rate of air as a function of altitude. Electrometers served as standard devices to measure ionizing radiation at this time [16]. Hess found an increase of ionizing radiation with increasing height and he concluded that radiation penetrates from outer space into the atmosphere. For the discovery of the cosmic radiation, V.F. Hess was awarded the Nobel Prize in 1936. In subsequent years W. Kolhörster made further ascends with improved electrometers, measuring the altitude variation of the ionization up to heights of 9 km [17].

In 1929 W. Bothe and W. Kolhörster measured coincident signals in two Geiger–Müller counters [18]. Placing absorber material in between the two counters they also measured the absorption characteristics of the radiation. They concluded that the “Höhenstrahlung” (or cosmic radiation) is of a corpuscular nature, i.e. it consists of charged particles. Similar conclusions were drawn from measurements by J. Clay, who showed that the intensity of cosmic rays depends on the (magnetic) latitude of the observer [19]. This was a clear indication that a large fraction of cosmic radiation consists of charged particles.

Kolhörster continued his work with Geiger–Müller tubes operated in coincidence. In February 1938 he reported the discovery of coincident signals between two tubes set as far as 75 m apart [20]. He concluded that the tubes were hit by secondary particles or showers generated by cosmic rays in the atmosphere. In the late 1930s P. Auger undertook investigations of cosmic radiation at the Jungfraujoch, Switzerland at 3500 m.a.s.l. He used Wilson chambers and Geiger–Müller tubes separated by large distances and operated in coincidence [21]. Similar to Kolhörster, Auger concluded that the registered particles are secondaries generated in the atmosphere, originating from a single primary cosmic ray.

In the 1940s the origin of the primary radiation could be revealed with measurements on balloons at high altitudes. M. Schein showed that the positively charged primary particles were mostly protons [22]. Cloud chambers and photographic plates were carried into the stratosphere and it was found that cosmic rays are made up of fully ionized atomic nuclei moving at speeds closely to that of light [23]. Many nuclei of the periodic table up to Z40 were found and their relative abundances determined. Hydrogen and helium occur most frequently, and the distribution in mass of the heavier nuclei appeared to be similar to that in the solar system. Elements more massive than iron or nickel were found to be very rare.

Since the mid 1940s large detector arrays were installed to measure extensive air showers. For most investigations detectors with a large surface and a short time resolution were required. Early detectors comprised Geiger–Müller counters, progress in the development of photomultipliers lead to the application of scintillation counters and the newly available Cherenkov detectors. It was found that the energy spectrum of cosmic rays follows a power law dN/dEEγ over a wide range in energy. In 1958 G.V. Kulikov and G.B. Khristiansen measured the integral electron number spectrum in air showers using an array of hodoscope counters [24]. They recognized a kink in the spectrum around 6×105 particles, corresponding to primary energies of several PeV (1015 eV ). This structure is now known as the “knee” in the energy spectrum. Since that time there is an ongoing debate about the origin of this structure.

In the 1960s the air shower array of the M.I.T. group at Volcano Ranch, New Mexico was the largest cosmic-ray detector. The set-up comprised 20 stations equipped with scintillation counters arranged on a triangular grid and covering a total area of 12 km2. In 1962 the first event with an energy of about 1020 eV was recorded with the Volcano Ranch array [25]. Bigger air shower arrays were subsequently built (SUGAR [26], Haverah Park [27], Yakutsk [28], and AGASA [29]) and, after some initial attempts, the first successful fluorescence light detector, called Fly’s Eye, was set up in Utah [30]. With these detectors, another feature of the cosmic-ray flux–first discussed in [31]–was firmly established in the early 1990s and is now known as the “ankle” [32], [33].

Finally, it should be mentioned that, in the early years, particle physics was practiced primarily through the study of cosmic rays. In the 1930s investigations of the cosmic radiation lead to the discovery of new elementary particles such as the positron [34] or the muon [35]. The pion was discovered exposing nuclear emulsions to cosmic radiation at mountain altitudes in 1947 [36]. New unstable hadrons were found in cosmic-ray interactions in balloon-borne emulsion chambers [37] in 1971 which, after the discovery of charm particles, were later identified as D mesons [38]. Also, a number of exotic phenomena were observed [39], none of which could be confirmed in accelerator experiments.

Over time a standard description of cosmic rays evolved, which is briefly sketched in the following section.

The solar system is permanently exposed to a flux of highly energetic ionized atomic nuclei — cosmic rays. Their energies extend from the MeV range to at least 1020 eV. The differential energy spectrum of all cosmic-ray particles is depicted in Fig. 1. It falls steeply as function of energy, decreasing by about a factor 500 per decade in energy. The flux decreases from more than 1000 particles per second and square meter at GeV energies to about one particle per m2 and per year at a PeV, and further to less than one particle per km2 and per century above 100 EeV.

The strong decrease in flux poses a big experimental challenge and our knowledge about the particles and their origin is more and more limited with increasing energy (and decreasing flux). At sub-GeV energies individual isotopes are measured with small detectors in outer space and individual elements can be resolved with balloon-borne detectors in the TeV regime. At energies exceeding 100 TeV large detection areas are required to collect a suitable number of particles in a reasonable time. At present, such detectors are realized at ground level only and secondary particles generated in the atmosphere (the extensive air showers) are registered. At PeV energies, groups of elements could be resolved, while at the highest energies even a classification into “light” and “heavy” particles becomes already an experimental challenge.

The energy spectrum follows a power law dN/dEEγ over a wide energy range, indicating non-thermal acceleration processes. The spectrum is rather featureless, as can be inferred from Fig. 1. However, small structures become clearly visible when the ordinate is multiplied with some power of the particle energy, as shall be discussed below (see e.g. Fig. 7). The spectral index is γ2.7 at energies up to several PeV. Then a steepening is observed, the so-called knee, with γ3.1 at higher energies. A further steepening, the second knee, occurs around 4×1017 eV. Finally, at about 4×1018 eV, at the ankle, the spectrum flattens again.

The abundance of elements in cosmic rays is shown in Fig. 2 as function of the nuclear charge number. All the elements of the periodic table have been found in cosmic rays. For the relatively abundant elements up to nickel, energy spectra for individual elements have been measured [1], [2]. Abundances as obtained by several experiments at about 1 GeV/n are depicted. The cosmic-ray composition is compared to the abundance of elements in the solar system. Overall, both distributions look very alike. However, there exist certain differences, which reveal information about the acceleration and propagation of cosmic rays.

The light elements lithium, beryllium, and boron, as well as the elements below iron (Z=26) and below lead (Z=82), are more abundant in cosmic rays than in the solar system. They are assumed to be produced in spallation processes of the more abundant particles of the CNO, iron, and lead groups during the journey of cosmic rays through the Galaxy. Hence, they are frequently referred to as secondary cosmic rays. As the spallation cross section of the relevant nuclei is known at GeV energies, the ratio of secondary to primary cosmic rays is used to infer the propagation path length of cosmic rays in the Galaxy. An example of this is the boron-to-carbon ratio which has been measured as a function of energy [51]. The ratio decreases as a function of energy, which is frequently explained in Leaky Box models by a rigidity-dependent2 decrease of the path length of cosmic rays in the Galaxy Λ(R)=Λ0(R/R0)δ. Typical values are Λ01015g/cm2, δ0.50.6, and R04GV as reference rigidity.

Cosmic-ray particles are assumed to propagate in a diffusive process through the Galaxy, being deflected many times by the randomly oriented magnetic fields (B3μG). The nuclei are not confined to the galactic disc, they propagate in the galactic halo as well. The scale height of the halo has been estimated with measurements of the 10Be/9Be-ratio by the ISOMAX detector [52] to be a few kpc. The abundance of radioactive nuclei in cosmic rays measured with the CRIS instrument yields a residence time in the Galaxy of about 15×106 years for particles with GeV energies [53].

The energy density of cosmic rays amounts to about ρcr1eV/cm3, a value comparable to the energy density of the visible star light ρsl0.3eV/cm3, the galactic magnetic fields B2/2μ00.25eV/cm3, or the microwave background ρ3K0.25eV/cm3. The power required to sustain a constant cosmic-ray intensity can be estimated as Lcr=ρcrV/τesc1041erg/s, where τesc is the residence time of cosmic rays in a volume V (the Galaxy and the galactic halo). With a rate of about three supernovae per century in a typical Galaxy, the energy required could be provided by a small fraction (10%) of the kinetic energy released in supernovae. This had already been discovered by Baade and Zwicky [54] in 1934. The actual mechanism of acceleration remained mysterious until Fermi [55] proposed a process that involved the interaction of particles with large-scale magnetic fields in the Galaxy. Eventually, this lead to the currently accepted model of cosmic-ray acceleration by the first-order Fermi mechanism, which operates in strong shock fronts powered by supernova explosions and propagate from a supernova remnant (SNR) into the interstellar medium [56].

Diffusive, first-order shock acceleration works by virtue of the fact that particles gain an amount of energy ΔEE at each cycle, where a cycle consists of a particle passing from the upstream (unshocked) region to the downstream region and back. At each cycle there is a probability that the particle is lost downstream and does not return to the shock. The higher energy particles are those that have remained longer in the vicinity of the shock and so have had time to achieve higher energy. After a time T the maximum energy achieved is EmaxZeβsBTVs, where βs=Vs/c refers to the velocity of the shock. This results in an upper limit, assuming a minimal diffusion length equal to the Larmor radius of a particle of charge Ze in the magnetic fields B behind and ahead of the shock. Using typical values of Type II supernovae exploding in an average interstellar medium yields EmaxZ×1014eV [57]. More recent estimates give a maximum energy up to one order of magnitude larger for some types of supernovae [58]. It has also been suggested that the cosmic rays interact with the magnetic fields in the acceleration region, yielding to an amplification of the fields, which in turn results in much higher energies being reached during the acceleration process [59]. With this mechanism, cosmic rays are supposedly accelerated up to 1017 eV.

Information on the composition at the source can be obtained from measurements of the abundance of refractory nuclei. They appear to have undergone minimal elemental fractionation relative to one another. Comparing the derived abundance at the source to the abundance in the solar system reveals that the two samples exhibit a striking similarity over a wide range [60]. When uncertainties are taken into account, the abundances of particular isotopes are consistent with being within 20% of the solar values. This indicates that cosmic rays are accelerated out of a sample of well mixed interstellar matter. Hence, cosmic rays are “regular” matter accelerated to extremely high energies.

The understanding of the origin of the knee in the energy spectrum is commonly thought to be a cornerstone for the understanding of the origin of (galactic) cosmic rays. Many approaches are discussed in the literature [3]. A popular explanation is that the knee is associated with the upper limit of acceleration by galactic supernovae, while the ankle is associated with the onset of an extragalactic population that is less intense but has a harder spectrum that dominates at sufficiently high energy. Another popular explanation is leakage of particles from the Galaxy. At energies in the GeV regime measurements indicate a decreasing path length of cosmic rays in the Galaxy. Extrapolating this to higher energies indicates that, above a certain energy, cosmic rays are not contained in the Galaxy (or the galactic halo) anymore. In a simple picture, this can be understood since the Larmor radius of a proton in the galactic magnetic field rL=1.08pcE/PeVZB/μG becomes with increasing energy comparable to and finally exceeds the thickness of the galactic disk.

If the knee is caused by the maximum energy attained during the acceleration process or due to leakage from the Galaxy, the energy spectra for individual elements with charge Z would exhibit a cut-off (or a knee) at an energy EcZ=ZEcp, with the cut-off energy Ecp for protons. The sum of the flux of all elements with their individual cut-offs makes up the all-particle spectrum. In this picture, the knee in the all-particle spectrum is related to the cut-off for protons and the steeper spectrum above the knee is a consequence of the subsequent cut-offs for all elements, resulting in a relatively smooth spectrum above the knee.3 Since the abundance of ultra-heavy nuclei (see Fig. 2) at GeV energies is very low when compared to iron, the end of the galactic component is often assumed to be at energies around 30×Ecp. However, recently it has been proposed that ultra-heavy elements may play an important role at high energies [2] which yields a value of 92×Ecp for the end of the galactic component, coinciding with the second knee at 4×1017 eV.

Another interesting question is that of a natural end of the spectrum at high energy. Already 40 years ago it has been realized that interactions of cosmic rays with photons of the cosmic microwave background (CMB) would result in a cut-off of the spectrum above 6×1019 eV  [63]. All hadronic particles suffer significant energy losses during propagation above this energy. Protons interact with background photons forming mainly a Δ+(1232) resonance [64] and nuclei are broken up due to photodisintegration [65]. A compilation of energy loss lengths of protons and various nuclei is shown in Fig. 3 (left) [66]. The energy loss length of photons depends on the flux of the universal radio background (URB) which is not well known (see, for example, discussion in [67]). Depending on the assumptions on the URB, the energy loss length is significantly smaller than or comparable to that of hadronic particles.

The short energy loss lengths indicate that cosmic rays with energies above 1020 eV should come from sources within a 100Mpc sphere. Astrophysical sources within our Galaxy are disfavored. Even though rapidly spinning young neutron stars could be thought of as accelerating particles to the highest energies observed [69], it would be difficult to explain the apparent isotropic arrival direction of UHECRs to energies beyond 1019 eV. As cosmic rays of energy greater than 1018 eV are no longer confined by galactic magnetic fields, it is natural to assume that they are produced by extragalactic sources.

Considering diffusive shock acceleration, which is thought to accelerate cosmic rays in SNRs, the magnetic field strength B in the source and the size R of the source region are related to the maximum acceleration energy by [10]Emax1018eVZβs(Rkpc)(BμG), where βs is the shock velocity in units of c and Z is the particle charge. This relation is shown in Fig. 3 (right) for various astrophysical objects. The list of the very few viable candidate sources includes active galactic nuclei (AGN) [70], [71], [72], [73], radio lobes of FR II galaxies [74], [75], and gamma-ray bursts (GRBs) [76] (for a review of astrophysical sources, see [11]).

Many alternative, non-acceleration scenarios–called top-down models–have been proposed. In these models, UHECRs are produced in decays of super-heavy objects such as super-heavy dark matter [77], cryptons [78], or topological defects [79]. All of these models postulate new particle physics and predict typically high gamma-ray fluxes at ultra-high energy [80]. Finally there are propagation model scenarios in which the GZK energy loss processes are evaded or shifted to higher energies. Examples are a violation of Lorentz invariance [81], the Z-burst model [82] or postulation of new particles with properties similar to protons [83], [84]. Reviews of the different scenarios can be found in [12], [85].

Measurements of the arrival direction distribution, primary mass composition and flux will be the key ingredients to solving the puzzle of UHECR sources. Given an expected angular deflection of only a few degrees for particles above 1019.5 eV in our Galaxy [86] and the existence of large cosmic voids with negligible magnetic fields [87], high statistics measurements should finally allow cosmic-ray astronomy and reveal correlations with sources or source regions. Similarly, knowing the composition of UHECRs will restrict the classes of source models. For example, a mixed composition would exclude top-down models. Another very important source of complementary information is given by secondary particle fluxes, i.e. gamma-rays and neutrinos, produced in UHECRs sources and during propagation (see, for example, [88], [89], [90], [66], [91], [92]).

Section snippets

Shower properties

In what follows, we will introduce some general properties of extensive air showers that are employed in cosmic-ray measurements. Detailed presentations of this subject can be found in [93].

Energy spectra

The all-particle energy spectrum extending from 1012 eV up to the highest energies is shown in Fig. 7. The flux as obtained from direct measurements above the atmosphere (represented in the figure through results from ATIC, PROTON, and RUNJOB) extends smoothly to high energies in the air shower detection regime. The all-particle spectrum can be approximated by a broken power law Eγ with a spectral index γ=2.7 below Ek4×1015eV. At this energy, the knee, the spectral index changes to γ3.1.

Mean logarithmic mass

At energies below 1014 eV the abundance of individual elements has been measured with detectors above the atmosphere. At higher energies this is presently not possible due to the low flux values and the large fluctuations in the development of extensive air showers. Thus, in the past, mostly the mean mass has been investigated. An often-used quantity to characterize the composition is the mean logarithmic mass, defined as lnA=irilnAi, ri being the relative fraction of nuclei of mass Ai.

Anisotropy

The search for anisotropies in the arrival direction of cosmic rays on different angular scales can contribute to the understanding of the cosmic-ray origin, in particular the identification of source regions or individual sources.

Galactic cosmic rays and the knee

The measurements indicate that the knee in the all-particle energy spectrum is caused by a break in the spectra for the light elements, yielding an increase of the mean mass of cosmic rays in this energy region. Several scenarios are discussed in the literature as a possible origin for the knee, see e.g. [3]. In the following, a current astrophysical picture of the origin of high-energy cosmic rays is sketched, based on recent observations.

One of the most popular explanations for the origin of

Importance of modeling hadronic interactions

There are strong indications of shortcomings in the shower simulations, probably due to the limitations of modeling hadronic interactions.

Detailed studies of the shower development in the atmosphere have been performed with the KASCADE multi-detector set-up and interaction models have been improved [162], [156], [469], [470]. A particularly valuable tool to test high-energy interaction models are correlations between different shower components [471], [472]. Some years ago several models like

Conclusions and outlook

The all-particle flux of cosmic rays is reasonably well known up to the highest energies. Recent measurements by the HiRes and Auger Collaborations established a GZK-like suppression of the flux at energies exceeding 6×1019 eV.

In the knee region, the mean mass of cosmic rays is found to increase as a function of energy. The knee is caused by sequential breaks in the spectra of individual elements, starting with the light elements. At present, a rigidity dependence of the cut-off energies for

Acknowledgements

We thank our colleagues from the Pierre Auger and KASCADE-Grande Collaborations for many fruitful and stimulating discussions and comments on the paper. In particular, we thank Carola Dobrigkeit, Maria Giller and Jim Matthews for reading the manuscript of this article. We are grateful to D. Heck and T. Pierog for providing numerical results of air shower simulations and S. Knurenko, K. Shinozaki, P. Sokolsky, M. Takeda, and G. Thomson for making available data tables of experimental results.

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