# High energy cosmic rays

 Lu Lu and Alan Watson (2016), Scholarpedia, 11(7):32454. doi:10.4249/scholarpedia.32454 revision #154491 [link to/cite this article]
Post-publication activity

Curator: Lu Lu

## Contents

### Introduction

Cosmic rays with the kinetic energy of a well-hit tennis ball strike the top of the earth’s atmosphere about 10 times every second. These rare particles are the most energetic of billions that continuously reach us from outer space: they are predominantly the nuclei of the common elements, from hydrogen to uranium, with energies ranging from ~1 GeV (109 eV) 1 to beyond 100 EeV. To put this energy into context, protons accelerated in the Large Hadron Collider (LHC) reach ~7 TeV, over 7 orders of magnitude lower than the most energetic cosmic rays. At 100 EeV a proton has a speed close to that of light: in a race between it and a light beam lasting one year, the 100 EeV proton would lag the light by only one-hundredth of the diameter of a human hair. By contrast, the LHC proton trails by about a million kilometres, 3 times the distance of the moon from the earth. Thus ultra high-energy cosmic rays (UHECRs) are truly at the energy frontier and by studying them we can hope to find how Nature has designed accelerators that boost particles to energies far beyond what will be reached by man in the foreseeable future.

Figure 1: Schematic energy spectrum of the differential intensity of cosmic rays. Two features are identified: the ‘knee’ is at ~3 × 1015 eV and the ‘ankle’ is at ~4 × 1018 eV. The energy at which a proton striking a stationary target would create the same centre-of-mass energy as at the LHC (7 TeV on 7 TeV) is indicated (Watson, 2009).

Cosmic rays were discovered in 1912 by Victor Hess who was trying to understand why charged bodies lost their charge more quickly than expected. To exclude effects associated with radioactivity in the earth, he carried instruments in a balloon up to 5000 m to measure the rate of production of ions in air, finding that the rate of ionisation increased by a factor of about 3. He concluded that the earth was being bombarded by a penetrating radiation – he imagined some form of X-rays, as these were the most penetrating of the radiations then known. Kolhörster confirmed his findings almost immediately. The names ‘Höhenstrahlung’ or ‘Ultrastrahlung’ were used to characterise the phenomenon until the 1920s when Millikan introduced the term ‘cosmic rays’, the name finally adopted. In the early 1930s it was discovered that cosmic rays were, in fact, mainly positively charged and so not ‘rays’ at all. Most are of low energy with the number falling roughly as E-2.7 up to the highest energies observed.

During the 1930s and 1940s, a number of ‘elementary particles’ such as the positron, the muon, the charged pions, and the first of the so-called ‘strange particles’, were found in cosmic rays, making this field the birthplace of particle physics. Only in 1953, during a conference in Bagnères-de-Bigorre, was a decision taken to focus work on particle physics at accelerators (see Cronin, J. W. 1953 for an account of this meeting).

At low energies, cosmic rays come from all parts of the sky with equal intensities. Thus, in efforts to discover the origin of these enigmatic particles, scientists have studied higher and higher energies, expecting that anisotropies in the arrival directions would eventually be seen. A problem that hinders this work is that the flux falls rapidly with energy. Above 100 GeV the rate is ~1 particle m-2 s-1 but above 3 PeV it is only ~1 particle m-2 year-1. A schematic representation of the cosmic-ray energy spectrum is shown in Figure 1. While the masses and energies of a low energy particle can be measured directly with detectors of a few square metres lofted on balloons to the top of the atmosphere, or on space vehicles2, the higher-energy particles must be studied using a different technique involving the phenomenon of ‘extensive air-showers’.

### Basic ideas about extensive air-showers and their detection

An air-shower develops when a charged particle enters the atmosphere and interacts with a nucleus of oxygen or nitrogen producing secondary particles which in turn interact or decay. For a cosmic-ray proton the first interaction can be represented as

$$\text{p}_\text{cr} + \text{N} \rightarrow \text{p (or neutron)} + \text{N} + nπ \qquad$$(1) .

Here $$\text{p}_\text{cr}$$ is the incoming cosmic-ray, N is a nucleon in an air-nucleus, while $$nπ$$ represents the $$n$$ pions π that are produced. On average, the out-going proton or neutron (arising from a process known as ‘charge exchange’) retains about one-half of the incoming energy, with most of the remainder shared between the pions. Above 100 PeV, hundreds of pions are produced in each collision. All of the elementary particles, including the charged and neutral kaons, the $$ρ^0$$-meson, the $$Λ^0$$ and excited states of nucleons, are created in such collisions. On decay, these give rise to pions (mass ~140 MeV/c2), which are of major importance in the development of the cascade.

Both charged pions (π+ and π-) and neutral pions (π0) exist. The π0 has a lifetime of ~10-16 s in its rest-frame, decaying into two photons (γ),

$$π^0\rightarrow γ + γ \qquad$$(2).

The photons generate pairs of positrons and electrons. These create further photons through the process of bremsstrahlung as described by the following equations,

$$γ + \text{Z} \rightarrow \text{Z} + \text{e}^0 + \text{e}^-$$ and $$\text{e}^\pm + \text{Z} \rightarrow \text{Z} + \text{e}^\pm + γ \qquad$$(3) .

Z represents the charge of the nucleus that must be present to conserve momentum.

The reactions involving photons, electrons and positrons are closely coupled and lead to the formation of a cascade or shower in which the number of particles and photons increases. The growth continues until the rate of energy loss of the charged particles through bremsstrahlung becomes less than that due to ionisation of the atmosphere (~2 MeV per g cm-2). The point at which the ionisation loss begins to dominate is called the shower maximum, Xmax, a key parameter used to define the properties of a shower. At 3 PeV, Xmax is about 500 g cm-2, which is approximately halfway down the atmosphere in the vertical direction3. A reasonably accurate relation between the number of electrons and positrons in the shower and the energy of the initiating particle is E = 2 × 109 Ne eV, where Ne is the number of electrons and positrons at shower maximum. The photon number is approximately 10 times larger. Beyond shower maximum, the cascade is attenuated.

The expectation that air showers would be created by high-energy photons was first pointed out by Schmeiser and Bothe, who showed in 1938 that Geiger counters placed horizontally 40 cm apart were sometimes hit simultaneously by what they called “Luftschauer”. Kolhörster and collaborators observed the same effect using counter separations up to 70 cm. However, the discovery of what are now called extensive air-showers is often credited to Pierre Auger who, in 1938, after a serendipitous observation, went on to detect simultaneous hits even with Geiger counters 300 m apart. Under the assumption that the cosmic rays were photons, Auger used the new results of quantum electrodynamics to argue that the most energetic events were initiated by primaries of ~1 PeV, an increase by ~105 on the highest energies believed to exist at that time4.

The role of pions in the development of a shower was realised following their discovery in the late 1940s. It was recognised that, in addition to an electromagnetic cascade developed by the decay of π0s, there is an entwined cascade – the hadronic cascade – driven by the charged pions and by the out-going particle (‘p’ or ‘neutron’ of equation 1). Previously it was thought that showers were initiated by photons and early observations that they contained muons had been a puzzle.

If the energy of a charged pion is sufficiently great (above ~30 GeV at an altitude of 5000 m) then the pion is more likely to interact than to decay. The processes can be represented by,

$$π^\pm + \text{N} \rightarrow π^\pm + \text{N} + nπ\quad \text{and} \quad π^\pm \rightarrow μ^\pm + ν_μ/\bar{ν_μ} \qquad$$(4) .

Thus, the shower is a complex mixture of electrons, positrons, photons, pions, muons and nucleons. At distance beyond ~100 m from the centre of the shower, the muons and electromagnetic component form the major part of the signal.

The key reasons why the air-shower phenomenon can be used to study particles of very high energy are that the electrons and photons are scattered as they travel through the atmosphere and the charged pions, and hence the muons into which they decay, are emitted at angles from the direction of travel of the parent that initiates the collision. The atmosphere serves to amplify the number of particles and to spread them over a large area so that the shower can be studied using a few detectors located strategically. An example of a cascade is shown in Figure 2. Here a proton of ~10 GeV produces a shower in lead (the Wilson cloud chamber shows the products of the interactions). It is clear that a proton rather than an electron creates the cascade as the particle travels through nearly 8 cm of lead before interacting. In this interaction, which will have been of the type shown in equation 1, neutral and charged pions are produced. The photons from the π0-decays create electrons pairs (equation 2) and these, in turn, more photons. The development of the cascade starts to attenuate after crossing five plates.

In the cloud chamber, the lateral extension of the shower is over an area of a few square centimetres, but in air, the spread is much greater. At 10 EeV, the footprint at the ground is ~25 km2, with 5 × 109 particles dispersed over this area.

Figure 2: Image of a particle shower seen in a Wilson chamber of area 0.5 × 0.3 m2 operated at 3027 m. The chamber contained 16 lead plates each of thickness ~13 mm. The primary particle is a proton with energy ~10 GeV. The first interaction occurs inside the 7th lead plate. Neutral pions feed the cascade, much of which is visible in the gas of the chamber. Charged pions make similar interactions to the proton, or decay into muons, some of which are seen penetrating several lead plates as they move towards the bottom left-hand corner of the picture (Fretter 1949).

Early studies of extensive air-showers were made using Geiger counters and Wilson cloud chambers deployed over areas of ~5000 m2. A major development, made in 1953 by Rossi’s MIT group5, was the introduction of large-area liquid-scintillators with which it was possible to find the shower direction and the number of particles within it.

The particles in the shower travel in a disc, like a giant dinner-plate, with the particle numbers falling-off steeply from the central region towards the edges (see Figure 2). When the disc sweeps across an array of particle detectors, these are struck at different times so that if at least three ‘hits’ are available, a direction perpendicular to the plane of the disc can be found by triangulation. In the early MIT work, the direction was found to ~5°, but sub-degree precision is now achieved. In Figure 2, one might imagine micro-detectors placed on the plates to measure the slightly different times of arrival of particles and thus determine the direction of the primary.

The breakthrough by Rossi’s group opened the route to searches for cosmic ray anisotropies at high energies. After running an array of 15 scintillators laid out over ~0.2 km2 for a few years, and developing innovative analysis techniques, the first ‘large’ array was constructed at Volcano Ranch, New Mexico. There, Linsley spread 19 plastic scintillators over 8 km2 and made the first search for anisotropies above 10 EeV. None was found but he recorded an event from a primary of 100 EeV (Linsley 1963a).

A different approach to exploring the properties of UHECRs is to observe the longitudinal development of the shower in the atmosphere by capturing the fluorescence radiation emitted from nitrogen excited by the particles of the cascade, essentially the process that creates aurora. This concept was proposed independently by Chudakov, Greisen and Suga in 19626 and was realised successfully in the late 1970s through the “Fly’s Eye detector”, developed by a group at the University of Utah. The technique uses the fact that the light from nitrogen is emitted isotropically: thus showers can be observed at great distances using a single detector. A calorimetric estimate of the primary energy is possible, with the atmosphere acting as a calorimeter. The technique enables the development of the shower to be visualised in the atmosphere in a manner analogous what is seen in Figure 2. Stereoscopic viewing of showers has advantages and was realised in the second-generation "HiRes" detector with which an event of 300 EeV was discovered (Bird et al. 1993).

### Motivations for studying high-energy cosmic rays

An early motivation for studying high-energy cosmic rays was the expectation that anisotropies in the arrival directions would be found. However, as more and more information became available about galactic magnetic field strengths, it was realised that protons with energies at least as great as 30 EeV must be studied to pick out point sources. If such a proton moved perpendicular to a field of 3 µG (typical of the galaxy), it would be deflected from a straight line by about 20° as it travelled across 8 kpc (the distance of the earth from the galactic centre). The galactic magnetic field is not as ordered as implied here, and deflections from a rectilinear path can be considerable. As any deflection will be larger by a factor of Z for a heavier nucleus, it is clearly desirable to know the mass of the cosmic ray but, as discussed below, this requires extrapolations to be made about hadronic interactions at energies well-beyond those attainable at the LHC. The discovery of the universal blackbody radiation in 1965 transformed interest in the top end of the energy spectrum. Greisen (1966) and Zatsepin and Kuz’min (1966) realised that it might terminate: the argument is that high-energy protons or nuclei ‘see’ the 2.7 K cosmic microwave photons through which they travel Doppler-shifted by the Lorentz factor of the particle. For a proton of 100 EeV, this is a factor of ~1011 so that a photon of ~7 × 10-4 eV, typical of the background radiation, can excite the Δ+ resonance in the reaction,

$$\text{p}_\text{CR} + γ_{\text{CMB}} \rightarrow Δ^+ \rightarrow \text{p} + π^0 \text{ or } \text{n} + π^+ \qquad$$(5) .
.

If the cosmic ray is a nucleus of atomic mass, $$A$$, then the key process is photo-disintegration,

$$A_\text{CR} + γ_{\text{CMB}} \rightarrow (A - 1) + \text{n} \qquad$$(6) ,

which occurs at a similar energy.

Both interactions limit the distance from which the highest-energy particles can reach us and it depends on the energy and the nuclear species. Distances of ~100 Mpc are relevant and thus sources lying further away are expected to give little contribution at the highest energies. Early searches for the spectral steepening with arrays at Haverah Park (12 km2), Yakutsk (25 km2), Narribri (100 km2) and AGASA (100 km2) failed to establish a suppression and indeed several claims were made for events with energies beyond the most energetic one found by Linsley. It is now clear that early models of shower development, used to derive the energies, led to over-estimates. However, these early claims stimulated much theoretical speculation that the primaries might be photons arising from the decay of such exotic objects as Super-Massive Relic particles, created in the early universe.

### Two Giant Cosmic-Ray Observatories

By the late 1980s it was evident that the flux of cosmic rays above 100 EeV was below 1 per km2 per century and that a detector with an area of many thousands of square kilometres needed to be constructed. In 1991, Cronin and Watson took up the challenges of designing such a device and of forming the collaboration needed to fund and operate it. The resulting instrument, the Pierre Auger Observatory, is located near Malargüe City in Western Argentina, at latitude 35.2º S and mean altitude of 1400 m (an atmospheric depth of ~875 g cm-2): it covers 3000 km2. The Observatory contains 1660 water-Cherenkov detectors7 (10 m2 × 1.2 m) with 24 fluorescence telescopes, located at 4 points on the boundary of the area (Figure 3). It is operated by scientists from 16 countries.

Figure 3: The layout of the Pierre Auger Observatory, located close to the city of Malargüe, Argentina. The 1660 surface detectors are marked with red dots. Four fluorescence detectors (at Los Leones, Los Morados, Loma Amarilla and Coihueco), sited at the periphery of the array, are shown in green. Near the centre are two facilities (CLF and XLF) from which steerable laser beams are available. The area of the Observatory is ~3000 km2: the 58 km2 enclosed by the LHC is shown for comparison8.
Figure 4: The array of plastic scintillators and fluorescence detectors operated by the Telescope Array Collaboration. The red squares indicate the locations of the three fluorescence detectors. Blue squares mark the scintillators.

A novel feature of the Auger Observatory was the inclusion of both particle and fluorescence detectors. Such simultaneous observations, using both methods, have many advantages and this approach was later implemented in the northern hemisphere by the Telescope Array team led by scientists from Japan and the USA9. This array is located in Utah, USA, at 39º N, at 1400 m above sea-level. 507 scintillation detectors (3 m2 × 1.2 cm) are spread on a 1.2 km square grid over ~680 km2 (Figure 4). Three fluorescence detectors overlook the array. The data reported by these two groups, at the International Cosmic Ray Conference in August 2015 were based on exposures10 of 50,000 km2 sr y (Auger) and 5920 km2 sr y (Telescope Array).

Surface detectors at the Observatories are shown in Figure 5. The principles of reconstruction of an event with a hybrid detector are illustrated in Figure 6.

• Figure 5: In the left-hand picture (Auger Observatory), a water-Cherenkov detector and a communication tower, adjacent to one of the fluorescence stations, are shown. Each fluorescence station contains six telescopes equipped with an UV-filter, 440 photomultipliers and a mirror of 11 m2. In the right-hand picture, one of the scintillators of the Telescope Array is seen. Both observatories use GPS receivers to determine when a station is triggered.

The sizes of the signals recorded by the particle detectors reflect the primary energy of the particle that has initiated it. However, it is clear from studying the event in Figure 2 that it is impossible, with a distributed array of detectors, to measure the total number of particles in a shower: the detectors are just too far apart11. The manner in which the signal falls with distance is shown in Figure 6. The signal at a distance of 1000 m from the shower axis, S(1000), can be determined accurately, reflecting the 1500 m detector spacing at the Auger Observatory: for the Telescope Array, where the spacing is 1200 m, the optimum distance is 800 m. To connect S(800) or S(1000) to the primary energy, use is made of the calorimetric measurement of energy possible with the fluorescence detectors. This approach requires two important secondary measurements: one concerns the clarity of the atmosphere and the other the yield of fluorescence photons from the nitrogen excited by the particles in the cascade. In , a laser facility at the Auger Observatory, used for atmospheric monitoring and for checking event reconstruction, is shown. A unique feature of the Telescope Array, a 40 MeV linear accelerator used to fire a 6.4 mJ pulse in front of one fluorescence detector, is seen in Figure 8. The accelerator measurements act as a check on the fluorescence yield measured in the laboratory.

• Figure 6: In the left-hand diagrams a hybrid event is shown, recorded by water-Cherenkov detectors (coloured circles) and by a fluorescence detector, the pertinent one here is at the bottom of the diagram. The cascade profile found with a fluorescence detector is similar to the profile seen in Figure 2 (see also Figure 9). In the right-hand diagram, the fall-off of the signal with distance from the centre of the shower is shown. The signal at 1000 m, S(1000), is used to find the energy of the primary producing the event.
• Figure 7: The Central Laser Facility (CLF) of the Auger Observatory. The steered laser-beam is used to cross-check some of the reconstructed shower observables and to monitor the transparency of the atmosphere
• Figure 8: The left-hand diagram shows the location of the electron accelerator at the Telescope Array relative to one of the fluorescence detectors. The fluorescence emission created by the electron beam in the air, as registered by one of the fluorescence detectors, is shown in the right-hand picture.
• Figure 9: The signals from the shower detected by a fluorescence detector of the Auger Observatory are shown. Note the similarity to the signals in the top right diagram to those from the TA electron accelerator seen in Figure 8. In both figures, each hexagon corresponds to a photomultiplier, one pixel of the camera. The colour shows the time at which the photomultiplier was triggered, with blue being the earliest and red the latest. The red line is the fit of the shower axis. The red point shows the position of Xmax. The number of photons observed is proportional to the energy lost by the shower in the atmosphere. In the bottom right diagram the shower profile, which describes the energy loss with respect to the atmospheric depth, is shown. The calorimetric energy of the shower is found by integrating the area under this curve, an addition being made to account for the ‘missing energy’12 carried into the ground by muons and neutrinos. The depth of shower maximum, Xmax, can readily be found.

The hybrid technique permits accurate reconstruction of key properties of the shower. The accuracies are energy dependent: at 10 EeV, the direction is known to ~1º, the energy to ~15% and the depth of maximum to ~20 g cm-2.

An example of the signals seen in the camera of a fluorescence detector, and the cascade development that is derived, are shown in Figure 9.

### Measurements of the properties of ultra-high energy cosmic-rays

#### The arrival direction distribution of high-energy cosmic-rays:

The expectation that anisotropies in the arrival directions of cosmic rays would be revealed at a sufficiently high energy was a strong motivation for studying extensive air-showers, but finding convincing evidence for anisotropy has proved difficult as the signal is small. Below ~30 EeV, only anisotropies on large angular scales (> 60°) are detectable. The fact that an array of surface detectors can be operated with nearly 100% efficiency is exploited. This makes it relatively easy to look for deviations from a uniform distribution in right ascension (α) in the declination band selected. Near 1 EeV, where the composition is dominated by protons (see section 5.3), the amplitude of the anisotropy is less than ~1%, an important observational fact that models of cosmic-ray origin must explain. Above 8 EeV, a significant amplitude of the first harmonic in right ascension of (4.4 ± 1.0) × 10-2 has been measured by the Auger Collaboration. The probability that such an amplitude has occurred by chance is 6.4 × 10-5. The maximum is in the direction α ~95°, about 180° from that of the Galactic Centre, suggesting that the anisotropy may be associated with an inhomogeneity in the distribution of extragalactic sources. Data are shown in Figure 10.

• Figure 10: Ratio of the observed number of events over the mean as a function of the right ascension with 1σ uncertainties indicated for 19797 events with energies > 8 EeV. The solid line shows the first harmonic and the dashed line the combination of the first and second harmonics.
• Figure 11: Excesses in the arrival direction of ultra-high energy cosmic rays observed in the northern sky by the Telescope Array (19 events with energy > 57 EeV within a radius of 20º) and in the southern sky by the Pierre Auger Observatory (14 events > 58 EeV within 15º of Centaurus A). The Telescope Array ‘hotspot’ has no obvious associated source: after allowing for the number of searches made, the significance is ~5 σ. The Auger ‘warm-spot’ in the region of Centaurus A, after allowing for the number of searches, has a significance of ~3σ.

At the highest energies, it is unclear as to whether there are correlations of arrival directions with extragalactic objects, such as active galactic nuclei, that are possible sources. The Auger Collaboration have described an alignment of a small number of events of energy > 58 EeV with Centaurus A, a powerful radio galaxy only ~4 Mpc from earth: this association is significant at ~3 sigma. The Telescope Array Collaboration have reported a hot-spot, not obviously associated with any object or group of objects, over an angular scale of ~20º for events of similar energy. The significance is ~5 sigma. The all-sky picture from both observatories is shown in Figure 11.

#### The energy spectrum of cosmic rays:

Figure 12: The correlation between the calorimetric energy for 1731 events measured using the fluorescence detectors, EFD, and the ground-based parameter, S(1000). The fitted line is used to obtain the energy of the much larger set of events registered only with the surface detectors.

The hybrid nature of the two Observatories enables a calorimetric energy to be assigned to events measured with both detectors. The relationship for the Auger Observatory, based on events recorded on clear, moonless nights, is shown in Figure 12. Energy spectra from exposures of 50,000 km2 sr y with the Auger Observatory and of 5920 km2 sr y with the Telescope Array are shown in Figure 13. On the y-axis, the flux has been multiplied by E3 to emphasise features in the spectrum. At 5 EeV there is a clear decrease in the rate of fall of event number with energy. This ‘flattening’, first reported by Linsley (1963b), is known as ‘the ankle’. Beyond ~40 EeV, it is evident that the rate declines very rapidly. The first convincing evidence for this suppression was reported from the HiRes device (section 2), a few months before a similar claim from the Pierre Auger Observatory (Abbasi et al. 2008, Abraham J et al. 2008). These results, and those shown in Figure 13, have settled the question as to whether or not the cosmic-ray spectrum steepens at the highest energies. However, a problem remains: is the difference between the measurements from the two Observatories above 30 EeV due to some calibration problem or is there an excess from the northern sky? Could the excess be associated with the Telescope Array hot-spot (Figure 11). It would be an important discovery if the difference has an astrophysical explanation. However, the excess would have to come from a region of the sky inaccessible to the Auger Observatory as recent results show that the spectrum shape is constant over declinations up to +24.80°.

Figure 13: The energy spectra reported by the Pierre Auger and Telescope Array Collaborations. The spectra are compared in the right-hand figure.

Whether the observed suppression of the flux is due to the GZK-effect, or is evidence of a limit to the energy that an accelerator can achieve, will be discussed in section 6.

#### The mass composition of high-energy cosmic-rays:

Determining the mass of the particle that creates an air-shower is a huge challenge and it is here that the excellent precision of reconstruction in the hybrid events is most important. To deduce the mass composition requires comparison of data with what models, that use extrapolations of measurements at accelerators, predict for different primary masses. Key quantities are the cross-section, the multiplicity and the inelasticity of interactions but the relevant ones have been measured at accelerators only to a limited extent. It is clear from Figure 2 that to determine the nature of the incoming particle is going to be difficult, in part because fluctuations in the position of the first interaction and in the positions of subsequent key interactions. The principle method for estimating the mass composition is to compare the evolution of the depth of shower maximum, Xmax, with energy against predictions from different models of shower development. An example of the signals seen in the camera of a fluorescence detector, and the cascade development used to find Xmax, are shown in Figure 9. Measurements of the change of Xmax with energy from the two Observatories are shown in Figure 14. Because heavy nuclei are larger than protons, they interact higher in the atmosphere. In addition, the energy of each nucleon is lower than for a proton of the same energy. Thus, Xmax is, on average, at a shallower depth for iron than for protons.

Figure 14: The depth of shower maxima measured by the Telescope Array and the Auger Observatory, compared with predictions of the SIBYLL model, one of several used to describe the behaviour of showers.

The results from the two Observatories cannot be compared directly because of different approaches to the analyses. However, it is clear that comparisons against the predictions of one particular model of shower development indicate that the mass composition is changing from nearly pure protons at ~1 EeV to a mixed composition at the highest energies accessible with this technique. Using the larger number of events in the Auger data, a detailed analysis of the mass distribution has been possible and the fractions nuclei for four mass components (p, He, N and Fe) and three different hadronic interaction models have been obtained. Iron is found to be largely absent for all models and at all energies up to 40 EeV: protons are the main component near 1 EeV with helium and nitrogen dominant above 10 EeV.

#### Limits to the fluxes of neutrinos and photons:

Limits to the fluxes of neutrinos and photons provide a test of different models of UHECR origin and of the masses of the primaries. In particular, models in which the particles are supposed to arise from the decay of topological defects, such as strings or massive monopoles, would be responsible for many showers being initiated by photons. Photons also come from the decay of π0s produced through interactions with the 2.7 K radiation (equation 5 and 6). Neutrinos come from the products of proton and nucleus interactions. For neutrinos, the detection method exploits the fact that, because of the small cross-section, a neutrino can interact anywhere in the atmosphere with equal probability. Hence, if a shower can be identified at a large zenith angle as being due to a particle that has interacted unusually deep in the atmosphere, it has probably been induced by a neutrino. A strategy that gives a higher sensitivity is to look for showers created by τ leptons produced in rock through the interaction of ντs. As yet no neutrinos have been observed, though present limits are close to the predictions from several sources and are superior to those achieved by other methods. The Auger Observatory is most sensitive at ~1 EeV, the energy at which most neutrinos are expected from proton interactions with the 2.7 K radiation. However, the range of predictions is such that this mechanism cannot be excluded (Figure 15, for more details see Aab et al., 2015). The most straight-forward method to search for photons is to use fluorescence detectors to find showers with unusually large values of Xmax, although this restricts the search to hybrid events and thus bounds are relatively weak. However, techniques have been developed using the surface detectors to study specific shower features and these push limits into the region of predictions (Figure 15) but they remain an order of magnitude above the lower limit for proton primaries.

Figure 15: Upper limit to the flux of ultra-high energy neutrinos (left) and photons (right). In the neutrino plot, the Auger data are compared with limits from other experiments. In the photon plot, both hybrid (blue arrow) and surface-detector based (black arrows) are data from the Pierre Auger Observatory. The predictions from models invoking the decay of Super-Heavy Dark Matter (SHDM), topological defects (TD) and the Z-Burst model are excluded.

### The origin of highest-energy cosmic rays

The questions to be answered concerning UHECR are:

1. What is the cause of the suppression of the spectrum at ~40 EeV?
2. How can the ‘ankle’ feature in the spectrum be explained?
3. How can the relatively small anisotropy, particularly near 1 EeV, and the larger anisotropy above 8 EeV, be understood?
4. How can one account the abundance of nuclei heavier than protons at the highest energy and the dominance of protons near 1 EeV?

It seems likely that several different types of sources, such as gamma-ray bursts (GRBs) and active galactic nuclei (AGNs), may contribute to the high-energy cosmic ray flux while exotic origins, such as the decay of topological defects, are ruled out by the photon searches (section 5.4). It seems reasonable to assume that there will be a variety of UHECR sources, having different spectral shapes and maximum energies. The environments in which the sources lie, and in which acceleration happens, will be reflected in the mass composition observed at earth.

Any accelerator must possess certain generic properties. In a man-made synchrotron, the maximum energy depends on the magnetic field and radius (Emax = ZeBRβc, where Z is the nuclear charge; e, the charge of the electron; B, the magnetic field in a region of radius, R, and βc, the velocity of the particle). A particle must be confined within the acceleration region sufficiently long to gain energy. In astrophysical accelerators, a process called diffusive shock acceleration13 is the likely mechanism with the same relationship applying, Emax = kZeBRβc with k<1 and β denoting the speed of the shock wave. Suitable shocks occur near active galactic nuclei and black holes. Colliding galaxies, AGNs, magnetars, GRBs, and perhaps galactic clusters, might host the right conditions (Hillas 1985).

As the size of the acceleration region must exceed the Larmor radius of the particle being accelerated and the magnetic field must be sufficiently weak to limit synchrotron losses, it follows that the total magnetic energy in the source grows as Γ5, where Γ is the Lorentz factor of the particle, 1/(1 – β)1/2. For a proton of 100 EeV this is >> 1057 ergs, with the magnetic field < 0.1 Gauss. Cosmic-ray sources are likely to be strong radio emitters with radio powers >> 1041 ergs s-1, unless protons or heavier nuclei are accelerated exclusively. Aharonian et al. (2002) showed that this inequality is at least >1044 ergs s-1 and Centaurus A and M87 are two sources that match these criteria.

The spatial distribution of the sources is probably non-random, and in the GZK-region only those within 100 – 200 Mpc are important. With so many free parameters, it is unsurprising that a number of proposals to explain the data have been forthcoming.

For example, Berezinsky (e.g. Berezinsky et al., 2006) has argued for many years that the highest energy particles are protons and that the suppression of the spectrum and the ankle feature reflect the imprints of propagation on the spectra of the particles at the sources. The suppression is due to the (γ + p) process (equation 5), while the ankle is a consequence of pair-production on protons by the 2.7 K radiation. Accepting that protons do not dominate at the highest energies, Aloisio, Berezinsky and Gazizov (2011) have suggested that the break at 2 EeV in the energy-dependence of <Xmax> marks the maximum energy to which sources can accelerate protons: for iron the highest energy is 26 times larger and thus in the region of flux suppression.

Figure 16: The extragalactic cosmic ray fluxes as a function of energy for protons, helium and a range of different nuclei. UFA refers to the work of Unger et al. while GAP relates to Globus et al. In the right-hand plots the predictions for the evolution of Xmax and the variance of ln A as a function of energy are compared with Auger measurements.

A consensus has developed that the observed energy spectrum requires that the source spectrum be rather flat (e.g. Taylor 2014). Recently two groups have extended this idea by including interactions in and around sources (Globus, Allard and Parizot 2015, Unger, Farrar and Anchordoqui 2015). In both models the fate of the accelerated protons and nuclei as they traverse the ambient photon fields is studied. Globus et al. assume that a gamma-ray burst accelerates particles in internal shocks, while Unger et al. offer a generic analysis. It is shown, from both analysis, that the proton component near the ankle is supplemented by protons from the decay of neutrons escaping from sources, unimpeded by magnetic fields. This insight gives a natural explanation for a large fraction of protons from outside of the galaxy near ~1 EeV and thus for the small anisotropy observed.

Comparisons of the results from these analyses are shown in Figure 16. Predictions of the number of neutrinos detectable with IceCube and KM3Net provide a test of these ideas.

### The future of high-energy cosmic-ray research

We are still some way from identifying the remarkable accelerators that Nature has devised to boost particles to energies beyond the reach of man in the foreseeable future.

The next stage is to improve our knowledge of the mass composition beyond 30 EeV: to this end the Auger Collaboration are supplementing their water-Cherenkov detectors with thin scintillators to measure the muon content on an event-by-event basis. Data-taking will start in 2018. Below the ankle, anisotropy studies must be made as a function of particle mass, and methods to infer Xmax in a large fraction of events are needed. The radio emission from air-showers between 43 – 57 MHz is being developed to this end.

A greatly-enhanced rate of collecting the highest-energy events is also needed. Above 50 EeV, only about 4 events are recorded every month by the Auger Observatory and Telescope Array instruments combined and, although the area of the Telescope Array is to be extended by a factor of 4, the picture will not change rapidly. The challenge is to find an economical method of increasing the aperture by 10 to 30 times beyond what has been achieved so far. One approach is to place a fluorescence detector in space (Linsley 1985). Currently the JEM-EUSO project (Santangelo 2012) is being developed to put such a device on the International Space Station and reach an exposure 10 times that achieved using the Auger Observatory. This ambitious mission has three major goals. Firstly, if neutrinos are detected with energies above 100 EeV there will be a dramatic impact on astroparticle physics. Secondly, it is anticipated that sources of UHECRs will be identified. Thirdly, the energy spectrum can be pushed to higher energies because of the large exposure. Where this instrument is more limited is in measuring the mass of the cosmic rays, as the accuracy of the determination of Xmax will be relatively poor.

Another way forward is to use Antarctic ice as a target, as attempted through the ANITA project, the primary motivation of which is to detect ultra-high energy neutrinos. The idea is to search for the GHz emission expected to exit the ice after neutrino interactions within it. During early searches, it was found that GHz radiation produced within air-showers that could be detected after reflection of it from the ice surface. Data from 14 events above 2.8 EeV have been described (Schoorlemmer et al. 2015) but the first neutrino has yet to be found. A flight around Antarctica of over 22 days was completed in early January 2015 and results are awaited.

JEM-EUSO and ANITA are important probes looking at an energy region not yet explored and one can imagine the future as follows. The Pierre Auger Observatory and the Telescope Array are being enhanced to improve the astrophysical data while the JEM-EUSO and ANITA missions will be used to identify neutrinos, extend the cosmic-ray spectrum and possibly find sources of charged cosmic rays. These space and balloon projects must then be followed up by dedicated observatories covering in total more than 30,000 km2. These would be of the hybrid type with a precision of measurement at least equal to that presently available above 10 EeV. Such a project surely requires global cooperation, perhaps to be realised in 10 - 15 years, but it is not too early to discuss plans, form collaborations and carry out R&D. This World Observatory is analogous to the LEP machine at CERN, and the associated detectors that were built to study the W± and Z properties in exquisite detail: like the SPS, JEM-EUSO and ANITA are discovery devices. However, a World Observatory will only become a reality if a team of dedicated people decide to devote a significant part of their careers to making it happen. Dynamic young scientists exist within several collaborations: a few must step forward and lead the next stage.

### Footnotes

1: 1 GeV = 109 eV; 1 TeV = 1012 eV; 1 PeV = 1015 eV and 1 EeV = 1018 eV. The kinetic energy of a mosquito is ~1 TeV

2: An outstanding example of a space experiment is the Alpha Magnetic Spectrometer (AMS-02) placed on the International Space Station in 2011. This instrument has recorded billions of charged cosmic rays with energies up to ~300 GeV. See www.ams02.org.

3: The vertical atmosphere at sea-level is ~1000 g cm-2 thick, corresponding to a pressure of ~1000 mb.

4: For a history of the discovery of air showers, see Additional Reading: Kampert and Watson (2012).

5: Rossi should probably be credited with the discovery of the air-shower phenomenon. In 1934, in Eritrea, he observed the correlated arrivals of particles at widely-spaced detectors but he was unable to follow up this discovery.

6: See Kampert and Watson (2012) for a discussion of the history of the development of this technique.

7: Electromagnetic radiation, known as Cherenkov light, is created when a charged particle passes through a refractive medium at a speed greater than that of light in the medium. The phenomenon is used to detect particles in many situations, with air, water and ice some of the media currently exploited. Details about particle detectors are listed in Additional Reading.

8: Further details about the Pierre Auger Observatory can be found at www.auger.org. Relevant papers by the Auger Collaboration in journals and conferences are listed under Further Reading.

9:Further details about the Telescope Array project can be found at www.telescopearray.org. Relevant papers in journals and conferences by the Telescope Array Collaboration are listed under Further Reading.

10: The exposure of a cosmic-ray telescope is expressed as the product of the collecting area (km2), the solid angle (steradian, sr) and the on-time (years, y).

11: Of course, it would be desirable to have more detectors more closely spaced, but there are limitations set primarily by cost.

12: The addition that must be made to the estimate of the electromagnetic energy, to account for the missing energy, is ~10% .

13: An introduction to the ideas of diffusive shock acceleration can be found in Drury (1994)

### References

• Fretter, W. B. in Proceedings of the Echo Lake Symposium, Office of Naval Research p 37, Washington DC 1949
• Hillas, A. M., Ann Rev Astronomy and Astrophysics 22 425 1985
• Linsley, J, Proceedings of the International Conference on Cosmic Rays, Jaipur, Vol. 4 77 1963b
• Linsley J, in Proceedings of the International Cosmic Ray Conference, La Jolla, Vol. 3 438 1985

• Santangelo, A. for the JEM-EUSO Collaboration, International Symposium on Future Directions in UHECR Physics, CERN 2012, EPJ Web of Conferences Vol. 53 Part 2 090001 2013
• Zatsepin, G. T. and V. A. Kuz’min, Zh. Eksp. Teor. Fiz. Pis’ma Red. (JETP) 4 144 1966

#### From Pierre Auger Collaboration 

• A collection of papers presented at the 2015 International Cosmic Ray Conference, held in The Hague, Netherlands, is available at here. Several of the papers detailed below can be found there, together with papers on a wide range of other topics.
• A detailed description of Auger Observatory:

The Pierre Auger Collaboration, The Pierre Auger Observatory, NIMA 798 172 2015

• The Central Laser Facility:

Fick, B, et al., The Central Laser Facility of the Pierre Auger Observatory, JINST 1 11003 2006

• Distribution of Arrival Directions above 8 EeV:

The Pierre Auger Collaboration, The large scale distribution of ultra high energy cosmic rays detected at the Pierre Auger Observatory with zenith angles up to 80 degrees, ApJ 802 111 2015

• Paper including discussion of possible signal from Cen A:

The Pierre Auger Collaboration, Searches for Anisotropies in the Arrival Directions of the Highest Energy Cosmic Rays detected by the Pierre Auger Observatory, ApJ 804 15 2015

• The energy spectrum (including calibration, spectrum measurement and declination-independence of cosmic ray flux):

Valiño, I., for the Pierre Auger Collaboration, The flux of ultra-high energy cosmic rays after 10 years of operation of the Pierre Auger Observatory, Proceedings of ICRC 2015 (The Hague), Proceeding s of Science (ICRC2015) paper 271

• Mass composition: Measurements of the Depth of Shower Maximum and their Interpretation:

The Pierre Auger Collaboration, Depth of Maximum of air-shower profiles at the Pierre Auger Observatory: Measurements at energies above 1017.8eV, Phys Rev D 90 122005 2014 The Pierre Auger Collaboration, Depth of Maximum of air-shower profiles at the Pierre Auger Observatory: Composition Implications, Phys Rev D 90 122006 2014

• Joint papers with Telescope Array demonstrating that the Xmax measurements from the two projects are in good agreement:

Abbasi, R., Bellido, J. et al for the Pierre Auger Collaboration and the Telescope Array, Report of the Working Group on the Composition of Ultra High Energy Cosmic Rays, submitted to Proceedings of the UHECR 2014 Symposium Unger, M., for the Pierre Auger Collaboration and the Telescope Array, Report of the Working Group on the Composition of Ultra High Energy Cosmic Rays, Proceedings of ICRC 2015 (The Hague), Proceeding s of Science (ICRC2015) paper 307

• Papers describing aspects of radio detection:

Schröder, F., for the Pierre Auger Collaboration, Radio Detection of high-energy cosmic rays with the Auger Engineering Array, Proceedings of the Pisa Conference 2015, to be published in NIM A Pierre Auger Collaboration, Probing the Radio Emission from cosmic-ray-induced air showers by polarization measurements, Phys Rev D 89 052002 2014

#### From Telescope Array Collaboration 

• A detailed description of Telescope Array:

Tokuno, H., et al., New air fluorescence detectors employed in the Telescope Array experiment, NIM A 676 54 2012 Abu-Zayyad, T., et al., The Surface Detector Array of the Telescope Array Experiment, NIM 689 87 2012

• The LINAC at the Telescope Array:

Shibata, T., et al., End to end absolute energy calibration of the atmospheric fluorescence telescopes by an electron linear accelerator,NIM A597, 61 2008

• Discussion of Arrival Directions, including the Hot-Spot:

R., et al., Indications of Intermediate-Scale Anisotropy of cosmic rays with energy greater than 57 EeV in the Northern Sky measured with the Surface Detector of the Telescope Array, ApJ 790 L21 2014 Kawata, K., et al., Ultra-High-Energy Cosmic-Ray Hotspot Observed with the Telescope Array Surface Detectors, Proceedings of ICRC 2015 (The Hague), Proceeding s of Science (ICRC2015) paper 276

• Joint papers with the Pierre Auger Observatory demonstrating that the Xmax measurements from the two projects are in good agreement.

Abbasi, R., Bellido, J. et al for the Pierre Auger Collaboration and the Telescope Array, Report of the Working Group on the Composition of Ultra High Energy Cosmic Rays, submitted to Proceedings of the UHECR 2014 Symposium Unger, M., for the Pierre Auger Collaboration and the Telescope Array, Report of the Working Group on the Composition of Ultra High Energy Cosmic Rays, Proceedings of ICRC 2015 (The Hague), Proceeding s of Science (ICRC2015) paper 307

• Papers on the Energy Spectrum

Abu-Zayyad, T., et al., The Cosmic-ray energy spectrum observed with the surface detectors of the Telescope Array, ApJ Letters 768 1 2013 Ivanov, D., et al., TA Spectrum Summary, Proceedings of ICRC 2015 (The Hague), Proceedings of Science (ICRC2015) paper 349

• Papers discussing the measurement of Xmax made using the Telescope Array

Abbasi, R. U., et al., Study of the Ultra-High Energy Cosmic Rays Composition using the Telescope Array’s Middle Drum Detector and Surface Array in Hybrid Mode, Astroparticle Physics 64 49 2015 Stroman, T. and Tameda, Y., for the Telescope Array Colalboration, Telescope Array Measurement of the UHECR composition from stereoscopic fluorescence detection, Proceedings of ICRC 2015 (The Hague), Proceedings of Science (ICRC2015) paper 361