**3. The GZK cut-off**

collide with another nucleus. The subsequent collisions are similar in nature to the primary

About 33% of pions, created in collisions, are neutral. They are very short-lived and decay very fast into a pair of photons before a next interaction with nuclei in the atmosphere. Next, photons interacting with the nuclei in the air create electron-positron pairs, which thus produce bremsstrahlung photons. This cascading process forms an electromagnetic avalanche. The hadronic shower itself permanently produces neutral pions and thus is developing sec-

With an EAS development into the atmosphere, the number of generated particles successively increases (**Figure 2**). However, the process of multiplication is continued until the average energy of the shower particles is insufficient to produce more particles in subsequent collisions. Some part of energy is also leaking to the atmosphere due to ionization processes. Finally, the number of the particles traveling in the shower starts to decrease. This point of the EAS development is known as shower maximum. Beyond the maximum, the shower particles

*Xmax* can also be used to estimate the composition of the primary cosmic ray. Hadronic interac-

More muons and fewer electromagnetic particles are produced by heavy primary particles rather than do lighter primaries, of the same primary energy. Iron and proton showers can be distinguished using surface detector data alone through the ratio of muons to electromagnetic particles, as well as through the arrival time distribution of particles in the shower front.

**Figure 2.** The schematic of the hadronic and electromagnetic components generation in the EAS development.

. The depth of shower maxi-

for every decade of energy [7]. The measured value of

, and shorter for heavier nuclei. This means EAS

at 1015 eV, the average *Xmax*

collision. This process then leads to a cascade of particles, known as hadronic shower.

ondary electromagnetic cascades along its path.

6 Cosmic Rays

for showers increases by 60–70 g/cm<sup>2</sup>

tion length in air for protons is about 70 g/cm<sup>2</sup>

are gradually absorbed with an attenuation length of ~200 g/cm<sup>2</sup>

are generated by heavier elements higher in the atmosphere.

mum (*X***max**) is a function of energy. With a value of about 500 g/cm<sup>2</sup>

We do not know the composition of the UHECRs. However, the set of stable particles as candidates for the UHECRs, which can trespass cosmological distances saving their energy, is quite limited: heavy or light atomic nuclei, photons and neutrinos. No any standard, electromagnetic mechanism can be responsible for photons and neutrinos (as neutral) acceleration. They can only be a product of the interaction of a still higher energy-charged particle. Therefore, in the framework of conventional astrophysics, we believe that light and heavy nuclei are probably the best candidates for the UHECR.

There is experimental evidence that the Universe was created some ~14 billion years ago from some singularity in a giant explosion known as the "Big Bang." Perhaps the most conclusive evidence for the Big Bang is the existence of the isotropic, with Planck distribution T = 2.73 K radiation permeating the entire Universe known as the **c**osmic **m**icrowave **b**ackground (CMB). Shortly after the CMB discovery, Greisen and independently Zatsepin and Kuzmin predicted that at very high energies, the universe should become opaque to light or heavy nuclei due to the following reactions:

$$\begin{array}{llll}\text{"module due to the following reactions:}\\\\ \text{p} + \text{ $\gamma\_{\text{CMB}}$ } \rightarrow \text{N} + \pi & \text{E}\_{\text{p}} \geq 1.1 \times 10^{20} \,\text{eV} \\\\ \text{p} + \text{ $\gamma\_{\text{CMB}}$ } \rightarrow \text{ $\Delta$ } \rightarrow \text{N} + \pi & \text{E}\_{\text{N}} \geq 2.5 \times 10^{20} \,\text{eV} \end{array} \tag{1}$$

where EN is the energy of nucleon being disintegrated.

The energy budget in the center-mass-frame, for an average CMB energy 6.34 × 10−4 eV and protons with energy above 110 EeV, is sufficient for pion-production, during inelastic collisions with CMB photons.

Since in each such inelastic collision, protons leave a large part of their energy (of the order of 13% on average), their energy goes below 10 EeV (EeV = 1018 eV) after a few tens of Mpc. As an example, if the largest energy cosmic ray ever detected 320 EeV (it is more than 50 J) were a proton produced with an initial energy of 10 ZeV (ZeV = 1021 eV), the distance of its source should be less than 50 Mpc (**Figure 3**). The same effect is expected for heavy nuclei. Nucleons will be stripped off from the nucleus due to inelastic collisions with most of all infrared background and also with CMB. Thus, the highest energy cosmic rays cannot originate at distances larger than a few tens of Mpc.

particles depends on the value and the size of the magnetic field and is limited by the Larmor radius related to their confinement. If the Larmor radius of the particle exceeds the size of the "accelerator," then the particles escape from it. Candidates of astrophysical object, which

Introductory Chapter: Ultrahigh-Energy Cosmic Rays http://dx.doi.org/10.5772/intechopen.79535 9

*E*max = q*BR*c (2)

where *E*max is the maximal energy of particles confined in the magnetic field (J), q is the electric charge (C), *B* is the induction of the magnetic field (T), *R* is the radius of the confined trajectory

Many theories and models propose either sophisticated explanations or require some new physics. One of the models explores ultra-relativistic shock acceleration such as in hot spots of powerful radio galaxies and gamma-ray bursts (GRB) [13]. In the first case, relativistic jets are produced perpendicular to the accretion disk around a supermassive black hole in the central part of an active galactic nucleus. The shock on a jet, several hundred kpc from the central engine, due to collision with the intergalactic medium is considered as being able to accelerate particles up to the highest energies. This hypothesis, however, requires some additional assumptions. Such powerful galaxies are rather rare objects and should be clearly visible in

The second model corresponds to the UHECR another astrophysical puzzle: the gamma-ray bursts. The emission of huge amounts of energies (typically a nonnegligible fraction of the mass energy of the Sun) is observed over a very short time (minutes), as gamma rays but with, in some cases, X-ray and optical contributions. Their distribution is cosmological and uniform. GRB happen relatively frequently: 2–3 per day. However, their distribution within the "GZK sphere" rather does not agree with the UHECRs observations. Other objects are also proposed as potential sources of UHECRs, such as rapidly rotating compact objects (young black holes, neutron stars or "magnetars"), which possibly are the sources of the most intense magnetic fields in the universe. The 10<sup>21</sup> eV energies in such systems are rather difficult to

If we have difficulties to imagine reliable mechanism accelerating particles from low to high energies, let us inverse the situation. Many theories propose top-down mechanism, decay of super-heavy, super-symmetric or Grand Unified Theories (GUT) particles [14]. The only problem is a justification of their existence or their surviving after the Big Bang. They could have survived up to now by some yet unknown mechanism (a very weakly violated quantum number, particles trapped inside huge potential walls called topological defects and released via spontaneous symmetry breaking mechanism). Their decay into a huge number of secondary particles (mainly pions) by hadronization of quark-antiquark pairs could produce the ZeV energies we expect, however they would decay mainly into photons (decays of neutral pions) and neutrinos (decays of charged pions). The current flux limits rule out or strongly disfavor that top-down models can account for a significant part of the observed UHECR

possesses such a large BR factor, are given on the Hillas plot [12].

(m), and c is the speed of light (m/s).

the 50 Mpc distance.

**3.2. "Top-down" production**

reach.

#### **3.1. "Bottom-up" production**

In order to accelerate charge particles to energies above 1020 eV, extremely powerful electromagnetic fields should exist. However, we did not register any stable region with so large potential, which could assure such an extremely energy in a single shot process. One of the earliest theories on the acceleration of cosmic rays proposed was the second order Fermi mechanism [9], where plasma clouds can be treated as a magnetic mirror. A particle trespassing a cloud from the front can be kicked back, like a tennis ball hit by a racket, with energy larger than its initial value. In this way, particles gain energy over many collisions. However, this mechanism is also too slow and too inefficient to account for the observed UHECR.

A more efficient and faster process is acceleration by crossing shock fronts generated in explosive phenomena (first-order Fermi mechanism - ΔE > 0) [10, 11]. However that approach meets difficulties. Let us consider some hypothetical cosmic accelerator. The energy of accelerating

**Figure 3.** Energy degradation for nucleons as a function of distance to the observer for three different injection energies [8].

particles depends on the value and the size of the magnetic field and is limited by the Larmor radius related to their confinement. If the Larmor radius of the particle exceeds the size of the "accelerator," then the particles escape from it. Candidates of astrophysical object, which possesses such a large BR factor, are given on the Hillas plot [12].

$$E\_{\text{max}} = \text{qBRc} \tag{2}$$

where *E*max is the maximal energy of particles confined in the magnetic field (J), q is the electric charge (C), *B* is the induction of the magnetic field (T), *R* is the radius of the confined trajectory (m), and c is the speed of light (m/s).

Many theories and models propose either sophisticated explanations or require some new physics. One of the models explores ultra-relativistic shock acceleration such as in hot spots of powerful radio galaxies and gamma-ray bursts (GRB) [13]. In the first case, relativistic jets are produced perpendicular to the accretion disk around a supermassive black hole in the central part of an active galactic nucleus. The shock on a jet, several hundred kpc from the central engine, due to collision with the intergalactic medium is considered as being able to accelerate particles up to the highest energies. This hypothesis, however, requires some additional assumptions. Such powerful galaxies are rather rare objects and should be clearly visible in the 50 Mpc distance.

The second model corresponds to the UHECR another astrophysical puzzle: the gamma-ray bursts. The emission of huge amounts of energies (typically a nonnegligible fraction of the mass energy of the Sun) is observed over a very short time (minutes), as gamma rays but with, in some cases, X-ray and optical contributions. Their distribution is cosmological and uniform. GRB happen relatively frequently: 2–3 per day. However, their distribution within the "GZK sphere" rather does not agree with the UHECRs observations. Other objects are also proposed as potential sources of UHECRs, such as rapidly rotating compact objects (young black holes, neutron stars or "magnetars"), which possibly are the sources of the most intense magnetic fields in the universe. The 10<sup>21</sup> eV energies in such systems are rather difficult to reach.

#### **3.2. "Top-down" production**

As an example, if the largest energy cosmic ray ever detected 320 EeV (it is more than 50 J) were a proton produced with an initial energy of 10 ZeV (ZeV = 1021 eV), the distance of its source should be less than 50 Mpc (**Figure 3**). The same effect is expected for heavy nuclei. Nucleons will be stripped off from the nucleus due to inelastic collisions with most of all infrared background and also with CMB. Thus, the highest energy cosmic rays cannot origi-

In order to accelerate charge particles to energies above 1020 eV, extremely powerful electromagnetic fields should exist. However, we did not register any stable region with so large potential, which could assure such an extremely energy in a single shot process. One of the earliest theories on the acceleration of cosmic rays proposed was the second order Fermi mechanism [9], where plasma clouds can be treated as a magnetic mirror. A particle trespassing a cloud from the front can be kicked back, like a tennis ball hit by a racket, with energy larger than its initial value. In this way, particles gain energy over many collisions. However, this mechanism is also too slow and too inefficient to account for the observed UHECR.

A more efficient and faster process is acceleration by crossing shock fronts generated in explosive phenomena (first-order Fermi mechanism - ΔE > 0) [10, 11]. However that approach meets difficulties. Let us consider some hypothetical cosmic accelerator. The energy of accelerating

**Figure 3.** Energy degradation for nucleons as a function of distance to the observer for three different injection energies [8].

nate at distances larger than a few tens of Mpc.

**3.1. "Bottom-up" production**

8 Cosmic Rays

If we have difficulties to imagine reliable mechanism accelerating particles from low to high energies, let us inverse the situation. Many theories propose top-down mechanism, decay of super-heavy, super-symmetric or Grand Unified Theories (GUT) particles [14]. The only problem is a justification of their existence or their surviving after the Big Bang. They could have survived up to now by some yet unknown mechanism (a very weakly violated quantum number, particles trapped inside huge potential walls called topological defects and released via spontaneous symmetry breaking mechanism). Their decay into a huge number of secondary particles (mainly pions) by hadronization of quark-antiquark pairs could produce the ZeV energies we expect, however they would decay mainly into photons (decays of neutral pions) and neutrinos (decays of charged pions). The current flux limits rule out or strongly disfavor that top-down models can account for a significant part of the observed UHECR flux. The bounds are reliable as the photon flux limits depend only on the simulation of electromagnetic showers and, hence, are very robust against assumptions on hadronic interactions at very high energy [15]. The photon flux limits have further far-reaching consequences by providing important constraints on theories of quantum gravity involving violation of Lorentz invariance (LIV) [16–19]. And, observing a single photon shower at ultra-high energy would imply very strong limits on another set of parameters of LIV theories [20, 21].

[14] Sigl G. Particle and Astrophysics Aspects of UHECR. Astro-ph/0008364

Rays. Physical Review Letters. 2008;**100**:021102 arXiv:0708.1737. 2015

Physics Letters A. 2007;**A22**:749 astro-ph/0702632

2008;**D78**:063003. arXiv:0807.1210

arXiv:1008.1967

[15] Risse M, Homola P. Search for ultra-high energy photons using air showers. Modern

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[16] Galaverni M, Sigl G. Lorentz Violation and Ultrahigh-Energy Photons. Physics Review.

[17] Galaverni M, Sigl G. Lorentz Violation for Photons and Ultra-High Energy Cosmic

[18] Liberati S, Maccione L. Quantum gravity phenomenology: achievements and challenges. Journal of Physics Conference Series. 2011;**314**:012007 arXiv:1105.6234

[19] Horvat R, Kekez D, Trampetic J. Spacetime noncommutativity and ultra-high energy

[20] Klinkhamer F. Potential sensitivities to Lorentz violation from nonbirefringent modified Maxwell theory of Auger, HESS, and CTA. Physics Review. 2010;**D82**:105024

[21] Girelli F, Hinterleitner F, Major S. Loop Quantum Gravity Phenomenology: Linking

cosmic ray experiments. Physics Review. 2011;**D83**:065013 arXiv:1005.3209

Loops to Observational Physics. SIGMA. 2012;**8**:098 arXiv:1210.1485
