The sheep will guide you home if you're lost (they're generally known as followers but this one's obviously the black sheep of the family)

or....

UNIVERSITY OF BRISTOL

DEPARTMENT OF PHYSICS

         H.H. Wills Physics Laboratory

         University of Bristol

         Tyndall Avenue, Bristol BS8 1TL

Contents

1)Acknowledgements     

2)Abstract     

3)Introduction   

       3.1)A Brief history of Cosmic Rays

4)Current level of knowledge

4.1) Cosmic Ray propagation

4.1.1) The GZK cut-off

4.1.2) Magnetic fields

4.2) Current Energy Spectrum

4.3) Status of UHECR observations

4.4) Anisotropy                                                       

5) Detection of Cosmic Rays

5.1) Methods of detection at different energies

5.2) Extensive Air Showers

5.2.1) Electromagnetic EAS

5.2.2) Hadronic EAS

5.3) Data collection

5.3.1) The Cherenkov Detector

5.3.2) The Fluorescence Detector

5.3.3) Past and current detectors (including HiRes)

5.3.4)Future detectors (OWL, Pierre Auger)

6) Sources of UHECRs

      6.1) Origin of the bulk of the cosmic rays

      6.2) The search for UHECR sources

6.2.1)Methods of particle acceleration

6.2.1a) Direct acceleration (sources)

6.2.1b) Shock acceleration (sources)

6.2.1c) Other acceleration sources

6.3) Top down production of cosmic rays

            6.3.1) Sources of X-particles

7) Restriction of Sources through anticipating new data

8) Conclusion 

9) References

10)Figures (that were not included within main document)

1) Acknowledgements

My first thanks must go to Robin Walker for his constant advice and encouragement throughout the academic year and also thanks for allowing me to undertake this project which I found enormously interesting.  I also wish to thank my parents for further encouragement, the use of the computer and lots of cups of tea.

2) Abstract

Very few ultra high energy cosmic rays have ever been detected.  Consequently for the past ten years many theories on the source of these high energy objects have been published and until data starts to arrive from the new observatories that are being built or have been built no theory can be proved. Within this dissertation I explained each of the most likely theories and highlighted what information would be needed from the new detectors to prove or disprove these theories.  The most likely source appears to be gamma-ray bursts or topological defects but this is far from conclusive. 

3) Introduction

This dissertation will deal with three main areas on the subject of cosmic rays:

1)      Current experience

2)      Detection methods

3)      Sources

The current level of knowledge is very important as this is the basis for the theories on the sources and therefore it has been made clear what is known and how it is used.  The theory of detection has not changed significantly in the past 30 years, only the accuracy has increased.  Detection methods will be discussed stating what information is currently taken and how this helps resolve the ultra high energy cosmic ray (UHECR) issue.

From the data that has been collected many theories have been born, often openly contradicting one other. Events are not common and many of the objects suggested as sources are either completely theoretical, rarely viewed, or incredibly far away, but this has not impeded the number of reports on this subject.    Consequently the section on sources of UHECRs prevails collating ideas on the most popular models, determining the key features of each theory. Following on from this section is a discussion highlighting the results necessary to refute or confirm the various claims made.

This dissertation as a whole should therefore make clear where the contradictions exist, and what would resolve them. Also included is my own personal view on the possibility of each of the sources providing us with ultra high energy cosmic rays (UHECRs).

3.1) A brief history of Cosmic Rays

The history of Cosmic rays extends right back to the beginning of the 20th century when it was discovered that electroscopes discharged even when they were concealed from natural sources of radioactivity. This strange behaviour provoked many theories and several important experiments.  Initially Rutherford managed to prove that most of the observed discharge was due to radioactivity emitted by the rocks surrounding us or by the scientific equipment in the laboratory.  However, as it was known that even gamma-ray radiation halved its intensity after travelling 80m through the air, a fellow physicist, Wulf, ascended the Eiffel Tower (330m) with an electrometer wholly expecting the ionisation effect to all but disappear.

This was not so, and in 1912 and 1913 Hess and then Kolhorster were able to test the level of ionisation higher up in the atmosphere from manned balloons that reached heights of up to 9km.  Their amazing experiments showed that the ionisation did not fall off as expected, but actually increased once their balloons were higher than 1.5km above sea level, increasing rapidly all the way to 9km in altitude.

It became apparent that the source of this radiation was extra terrestrial, from the cosmos, and so was born the phrase "Cosmic Rays".  Soon after it was learnt, from several experiments, that in fact most of these "rays" were actually charged particles, mostly hydrogen nuclei (protons) with a few heavier nuclei and the occasional electron.   It was found at this time that most CRs had an energy of around 10⁹-10¹⁰eV.    Because of this high energy, CRs provided a natural source of very high energy particles which could penetrate the nucleus.  Through the study of the interactions and decays of CRs in cloud chambers and photographic emulsions many new and important particles were discovered, such as the positron, neutron, muon, kaon, and pion.

After about 1953 the first particle accelerators were created and CRs were no longer needed for high energy collisions, thus our interest in CRs shifted to their origin and propagation.  As our ability to reach higher and higher into the atmosphere grew, so did our knowledge of Cosmic Rays.  Cosmic Ray showers were discovered which suggested that many of the CRs seen at the ground level were actually just a small part of a much more energetic particle which decayed higher in the atmosphere.   Eventually one was able to put CR detectors into satellites allowing us to study the primary particles.  With this information an energy spectrum could be plotted up to about 10¹⁴eV, showing the flux to be based on a power law.   Unfortunately, above these energies it was no longer practical to measure the properties of CRs from space because of their rarity; thus ground-based detectors were born. 

Initially the detectors were only meant to be measuring particles up to ~10¹⁸eV and were consequently made relatively small as the particles they were hoping to measure frequently caused air showers.  What they didn’t expect was to receive particles over 5x10¹⁹eV.  This caused problems and at first they put it down to instrument error, but more and more of the particles started arriving and it became clear that a new level of physics was needed to explain these phenomena, thus a new area in physics was created.

4) Current level of knowledge

4.1) Cosmic Ray propagation

4.1.1) The GZK cut-off

To a particle moving at nearly the speed of light the Inter Stellar Medium (ISM) is a hostile place.  The main source of energy loss for particles travelling through the ISM is the Cosmic Microwave Background (CMB) radiation.  To a cosmic ray moving at such high speed the CMB radiation appears as a sea of hot gamma rays due to Doppler blueshifting and consequently any CR tends to interact with the CMB producing large numbers of pions, neutrons, gamma rays and protons through various decay channels losing energy in the process.  In 1966 Greisen [1] and also Zatsepin and Kuzmin [2] predicted that just such an effect would limit the cosmic ray energy spectrum to values below which the CMB did not appear so hostile, this prediction came to be known as the Greisen-Zatsepin-Kuzmin (GZK) cut-off and occurs at ~4x10¹⁹eV for a proton. To be more accurate, higher energy values aren’t excluded more that a limit on the distance to their source is imposed.  It can be seen from [fig 1, [27]] that even protons of energies of 10²²eV are reduced to below 10²⁰eV after travelling only 100Mpc through the ISM.  Of course for different particles the magnitude of this effect varies.  Generally it is considered that a proton, nucleus or photon arriving at the Earth with an energy in excess of 10²⁰eV must have been formed at less than 50Mpc from the Earth [3].

Proposals to avoid the above problem (as it surely must be) range from hypothesising topological defects or superheavy particles that decay within 50Mpc, producing high energy nucleons and photons, to positing new particles that would evade the GZK effect [3].  In the latter scenario, it is thought that protons would be accelerated to above the observed CR energies in a conventional source (see § 6) and upon exiting the source the proton would collide with a hadron or photon.  Of the secondary particles produced one could be a neutral long-lived hadron (dubbed uhecron).  Because of its nature, a uhecron would be a lot less likely to interact with the CMB radiation and would therefore have a lot longer mean free path (the distance travelled before the CR is more likely than not to react with the CMB radiation).  Upon arriving at the Earth the uhecron would however trigger an air shower like any hadron.

There is of course the simpler proposal that the CRs do arrive from our galaxy, but they just appear to arrive from outside our galaxy [4].  This has only recently been suggested, as until recently it was firmly believed that no source within our galaxy could provide the accelerating power.

4.1.2) Magnetic fields

At the high energies that are considered within this report it is generally thought that intergalactic magnetic fields would have little or no effect on the path of UHECRs, though this is a very much open debate as there have been no firm conclusions on the strength of intergalactic fields.   When the CR arrives in the vicinity of our galaxy it also encounters the stronger galactic magnetic fields.  Though these fields are over a shorter distance they may well have a larger effect on the arrival direction of UHECRs and when combined with intergalactic magnetic fields arrival directions may deviate by up to 22^o [5] (at the extreme) when considering a particle arriving from 15Mpc or more. 

4.2) Current energy spectrum

The spectrum as it is known so far is shown in [fig 2, [12]].  This includes energies from 10⁸eV right up to the most energetic particle viewed so far at 3.2x10²⁰eV.  Also included are the arrival rates at different energies, which display very well how difficult it is to capture one of these events when considering 10²⁰eV.  Over this wide range of energies a power law is exhibited, but it can be seen at two major points that this power law changes appreciably.  These two points are known as the knee (~4x10¹⁵eV) and the ankle (~5x10¹⁸eV).   It is widely believed that below the knee supernova explosions produce most of the CRs but above the knee it is harder to explain the results by attributing them to supernova explosions, as the energy necessary is just not conceivable.  §6 will discuss the sources in more detail.

The Fly’s Eye experiment was the first to discuss the area surrounding the ankle, possibly suggesting that it is caused by a composition change in the primary CR. It has also been suggested that above the ankle CRs are no longer confined to the galactic halo due to magnetic fields and therefore extragalactic CRs could be more likely.  Above the ankle a lack of results limits any conclusions but the main point is that CRs should not really exist at these energies.

It is also interesting to note that a possible gap in the energy spectrum may well be developing at 10²⁰eV [fig 3, [6]].  This may be due simply to a lack of results again, but if the gap persists even after a quadrupling of data it may well point towards the need for new physics [6].

4.3) Status of UHECR observations

The highest energy particle was viewed in 1991 by the Fly’s Eye detector and reached an incredible energy of 3.2x10²⁰eV.  At first it was believed that it was due to an instrument error, but soon after, other detectors around the world viewed other high energy events.  Systematic errors suggest an error margin of ~30% for most detectors, thus ruling out any possibility of large instrument error.  So far ~8 events of energy ≥10²⁰eV have been viewed [27].  Unfortunately, beyond the existence of these particles, there is not much agreement.  Each detector has its own personal set of data claiming to suggest different properties of the primary particle.  For example, data from the AGASA array favours nuclei or protons rather than photons and this seems to agree with a report from the Fly’s Eye detector on the highest energy particle [7] though other reports [8] also suggest that the AGASA data does not disallow a gamma-ray primary cosmic ray.

4.4) Anisotropy

Due to the shortage of results at these energies, answers are far from conclusive on the subject of anisotropy.  Anisotropic clustering would suggest that point sources are responsible for CRs rather than if isotropic clustering is discovered which would suggest a source pervading most of the universe [8] such as a topological defect or gamma-ray burst.  If results are found to centre towards the galactic plane then obviously this would suggest a galactic origin and conversely a focusing towards the supergalactic plane would suggest a cosmological source.

So far both AGASA and Fly’s Eye experiment report a small but statistically significant anisotropy of the order of 4% toward the galactic plane at around 10¹⁸eV but there is conflicting data for events above 10²⁰eV, some suggesting isotropy [9] whereas others claim there is small anisotropy [10].  A report published in 1994 using all of the major arrays [26] has also suggested anisotropy, highlighting four clusters that are not directed towards the galactic plane. It must be kept in mind that this is all based on ~8 events in the Northern Hemisphere [27].

5) Detection of Cosmic Rays

5.1) Methods of detection at different energies

As has been mentioned before, it was noted that as measuring instruments were flown higher and higher that it was possible to receive more of the original cosmic rays.  CR primaries are shielded by the Earth’s atmosphere and near ground level their existence can only be inferred by indirect measurements such as ionisation. It has also been noted that it is possible to fly detectors above the atmosphere to study cosmic ray primaries, if they are charged, up to an energy of ~10¹⁴eV.  If they are uncharged, i.e. photons, one can only view them directly up to ~10¹¹eV such as on the Compton Gamma Ray Observatory (CGRO).  In most of the detectors above our atmosphere nuclear emulsion stacks are used, but recently it has been possible to use spectrometric techniques to measure exact chemical composition.  On board the CGRO a combination of spark chambers and NaI calorimeters are used to achieve this.

Once energies above ~10¹⁵eV are attained, the shower of particles produced [fig 4, [28]] as the primary particle or photon interacts with the Earth’s atmosphere, can be detected using a variety of methods based on the ground, or in the case of one detector, in space whilst circling the Earth.  Such showers of particles are called Extensive Air Showers (EAS).

5.2) Extensive Air Showers

A lot of information can be gained from studying the type of particles that arrive at the ground after an EAS.  The muon content is particularly important as this gives an indication as to whether the primary particle initiated an electromagnetic cascade (see below) creating a muon poor shower or initiated a hadronic shower (see below) which will tend to be muon rich.  As the muon content of the EAS increases so does the likelihood that the original CR was a heavy nucleus rather than a proton.

Another invaluable measurement is known as the rise time of the shower.   This technique is used by detectors collecting data solely at ground level and tells us how fast the EAS reaches its maximum (i.e. where the number of particles produced is greatest).   The faster the development of the shower, the more likely it is to be a heavy nucleus.  This is because heavy nuclei can initiate a larger number of interactions when they first strike the atmosphere compared to a single proton.

For detectors that watch for interactions of CRs with the atmosphere directly a similar measurement to rise time is taken to assess the type of nuclei and it is called the longitudinal profile of the shower, depicting the development of the cascade as it penetrates deeper and deeper through the atmosphere.   The depth of the shower maximum (where the most particles are created), within the atmosphere, gives information on the size of the original CR as heavy nuclei tend to have a much shallower shower maximum than, for example, a proton.  The reason for this is the same as for the rise time technique, as heavy nuclei will splinter quickly causing a large shower maximum higher up in the atmosphere.

Of course the shower size itself can also give us clues to what type of CR initiated the EAS.  The total energy of the original particle can be estimated by summing up the total energies of the particles that do reach the ground.  This is affected by large errors, but even with 30 or 40% errors it cannot be denied that UHECRs are striking our atmosphere.

Any detector wishing to observe these events must be spread over a fairly large area, firstly to make sure that they receive sufficient data, and also to make sure they receive all of the shower, which can be spread out over several kilometres.

5.2.1) Electromagnetic EAS

If the primary cosmic ray is a photon or electron the shower will develop into what is known as an electromagnetic cascade (the left side of [fig4]) where the photon ® e⁺e^- pair (or vice-versa) each of which emit a photon through bremsstrahlung[[a] which then decays into a e⁺e^- pair and so on.   What arrives at the ground is a mass of photons, electrons and positrons covering an area exceeding at least 20km².  Particles near the shower core, where the peak particle density is located, can reach 10⁶ particles m^-2.

5.2.2) Hadronic EAS

The alternative is that the primary CR is a particle, possibly a proton, heavier nuclei or exotic particle.  In this case the EAS created is much more complicated and is affected by the type of CR. What follows is a general description of a hadronic cascade.  Initially the particle would collide with atoms in the upper atmosphere such as a nitrogen or oxygen nucleus, creating mostly pions of all charges [fig 4] with some strange particles and the odd antinucleon.  In addition a nucleonic cascade can be created if the CR has enough energy to shatter the first oxygen or nitrogen nucleus.  This is likely to happen with heavy nuclei and is the reason why such showers develop so quickly.

The neutral pions quickly decay into two gamma-rays which carry on to form an electromagnetic shower, but the charged pions decay later into charged muons with their associated muon neutrinos.   Of the muons produced, most reach the earth and can be detected in Cherenkov water chambers, but of those that have time to decay (i.e. are not travelling as fast) decay into either an electron plus neutrino and associated muon neutrino or into the opposite (i.e. positron plus antineutrino and antimuon neutrino).

Overall this produces at ground level a large number of electrons, positrons, gamma rays and some neutrinos and a fair number of muons.

5.3) Data collection

5.3.1) The Cherenkov Detector

A very useful method of measuring the energies of particles at relativistic speed is through the Cherenkov detector. When a particle moves through a medium at a velocity that is greater than the speed of light in that same medium, it emits Cherenkov radiation. As a consequence, a shock wave is created that propagates out at a fixed angle [fig 5, [29]] (similar to the passage of a supersonic plane), with the angle of the shock wave to the passage of the particle being related to the velocity of the particle.

This type of detector can either be used to measure the energies and the muon content of the particles and that reach the ground by measuring the Cherenkov radiation created inside water tanks.  The muon content is found by measuring the number of particle incident both above and below the tanks as such particles can only be penetrating muons when considering an EAS.  Alternatively the detectors can be pointed skywards to detect the development of an electromagnetic shower in the upper atmosphere as the e^-e⁺ pairs created from a γ-ray decay (see below) can easily travel faster than the speed of light in the thin gas at the top of the Earth’s atmosphere.  Detectors using ground based water Cherenkov detectors usually use a large number of tanks spread over several tens of kilometres to increase the likelihood of capturing an EAS.

5.3.2) The Fluorescence Detector

Above ~10¹⁷eV the electrons in the shower have enough energy to excite nitrogen fluorescence that can be detected at ground level (such as the Fly’s Eye experiment).  Unlike surface arrays, atmospheric fluorescence detectors can track the development of a shower through the atmosphere, rather than being limited to ground level.  A fluorescence detector usually consists of a number of metre-sized mirrors, each containing a group of photo-multiplier tubes that concentrate on one section of the sky at a time.  It is possible to have a “stereo” image if two mirror arrays are used, separated by several kilometres, thus giving a more accurate estimation of the arrival direction of the primary CR.  Fluorescence detectors are able to determine both the depth at which the first reaction takes place and the depth at which the maximum number of electrons is produced, helping primary particle identification.  The energy of the original particle can be found to within 25% by saying that most of the energy will be in the form of relativistic electrons and assuming that at the shower maximum they each contain ~1.4GeV [11].

Recently it has become evident that both a water, ground-based, Cherenkov detector and a fluorescence detector combined (known as a hybrid detector) provide the best method of data collection as data regarding the same EAS can be compared from two different sources, thus reducing the errors.  Aside from the problem of accuracy, all detectors face the same problem when dealing with UHECRs over 10¹⁹eV, a lack of results.  Most future plans for detectors involve surveying large amounts of the atmosphere at the same time, such as the Pierre Auger project which plans to cover a total of 6000km² over two sites.  One novel approach, planned by OWL-Airwatch, is to place fluorescence detectors in space, looking down onto the atmosphere, allowing a much larger area of the atmosphere to be viewed.

5.3.3) Past and current detectors (including HiRes)

The detectors that have brought us the results that astounded us in the first place have all since stopped, with only the AGASA array, south-west of Tokyo still running [fig 6].  AGASA is a ground based detector using water-Cherenkov detectors or scintillation counters to measure the cascades that reach the ground.  Other arrays that have contributed to this area of astrophysics in using this technique are Volcano Ranch (USA), Haverah Park (Leeds, UK), Sydney (Australia) and Yakutsk (Siberia).  Only the Fly’s Eye detector in Utah, USA used a completely different approach by using fluorescence detectors high up in the mountains and is responsible for the detection of the highest energy event so far, recorded in 1991.   Currently the Fly’s Eye detector is running under the new name HiRes .

In the past 5 to 10 years new detectors have been developed with the main aim of increasing the number of events collected, as this has been the largest problem faced by past detectors.  Admittedly when the first detectors were made they weren’t expecting to obtain results of such high energy and so were accordingly not made large enough. 

HiRes (previously Fly’s Eye)

HiRes has been operating since 1997 [fig 6] and is based on the original Fly’s Eye detector.  The principle of HiRes is therefore still to detect the nitrogen fluorescence created by incredibly fast charged particles, but the power has been upgraded tenfold by using two mirror arrays sitting on top of two mountains separated by 13km to create a very accurate stereo imaging detector.  Each of the arrays contains 54 mirrors, each 2 metres in diameter which gives the arrays the sensitivity to detect a 4-watt light bulb at 20 kilometres.

5.3.4) Future detectors (OWL, Pierre Auger)

The OWL-Airwatch collaboration

OWL stands for Orbiting Wide-angled Light-collectors.  The basic principle is to use the atmosphere as a large calorimeter and observe the nitrogen fluorescence of an EAS from space.  The project has no set launch date at the moment, though the theory is well worked out and several components have started being built.  In theory one, but hopefully two (for stereo imaging) large Fresnel mirrors will be launched into space and will then be pointed towards the Earth [fig 7, [12]] to detect nitrogen fluorescence caused by UHECRs.  As with a normal fluorescence detector shower development will be recorded, along with arrival direction to an accuracy of 1° (with stereo imaging).  From this information the original particle energy and possible identity will be found.

The reason why this project will be so beneficial to the CR question is that the OWL telescope will be able to monitor 3x10⁹m² of atmosphere, providing us with a predicted 3000 events of energy >10²⁰eV, far greater than any ground based detector.

Pierre Auger Project

This detector is named after the French physicist who discovered air showers in 1938 and will be the largest ground based detector once it is completed in 2001.  The detector is actually split into two sites, one in the northern hemisphere (Utah, USA) and one in the southern hemisphere (Mendoza, Argentina) each covering an area of 3000km².  Each of the arrays will be using 3 fluorescence detectors pointed skywards and 1600 water-Cherenkov detectors spaced 1.5km apart [fig 8, [30]] with a depth of 1.2m into the ground [23].  Because of this depth nearly all of the electromagnetic part of the shower will be absorbed, providing us with an accurate picture of shower development and energy.  The water tanks will also be able to assess the muon content of the shower through separation of the signal amplitudes.  The fluorescence detectors will supply us with an alternative set of results on the same shower, again measuring total energy and shower development.  As the array is spread over 3000km² optical cables are impractical and so each detector will be separate, relying on solar power and transmitting data back to a central station which will decide whether the shower detected was part of an EAS or an isolated event.  A GPS measuring system will help provide information on the arrival direction to an accuracy of ~1.5^o, depending on particle energy. 

Due to the Pierre Auger project data on UHECRs arriving in the southern hemisphere will be taken for the first time, thus enabling us to properly assess whether their arrival direction is isotropic or not.  Of course, because of the size of the detectors, many more events will be viewed with hopefully >60 events a year with an energy of 10²⁰eV or more.

6) Sources of UHECRs

6.1) Origin of the Bulk of the Cosmic Rays

The question of origin of cosmic rays continues to be regarded as an “unsolved problem” even after almost ninety years of research.  Although the general aspects of the question of CR origin are regarded as fairly well understood now, major gaps and uncertainties remain, the level of uncertainty being in general a function that increases with the energy of the CRs.  Below about 1GeV most of the CR spectrum can be attributed to solar activity.  At higher energies, however, most CRs are considered extra-solar, for the rather obvious reason that they do not arrive from the sun.  Several arguments involving energetics, composition, magnetic fields and secondary γ-ray production suggest that the majority of CRs between 1GeV and at least up to the knee region [Fig 2] are confined to the galaxy and are probably produced in supernova remnants (SNRs), though this has recently been called into question [4].  Between the knee and the ankle the situation becomes less clear, although the ankle is sometimes interpreted as a cross over from galactic to extragalactic origin, as above 10¹⁹eV the results suggest that the sources are a lot less confined to the galactic plane and as pointed out previously it is often thought that the magnetic field within our galaxy would not be strong enough to contain these particles, thus suggesting an extragalactic source.  It has also been suggested that the ankle signifies a change to lighter nuclei such as protons [12].

6.2) The search for UHECR sources

For any energy CR there exists only two ways for particles to attain their energies, either through bottom-up scenarios where the particle or photon is accelerated to high energies from rest, or the top-down approach which involves the decay of a superheavy relic particle (with mass ~10²⁴eV) left over from the early universe.  The top-down scenario does appeal to physics beyond the standard model of particle physics, but in the case of UHECRs, all proposals are pushed to their limits. Bottom-up methods of acceleration and candidates for these types of UHECRs will be discussed first, following with the top-down technique, and possible top-down sources.

6.2.1) Methods of particle acceleration

When the acceleration of Cosmic rays is discussed, only two methods are likely to be significant:

1)   Direct acceleration of charged particles by an electric field

2)   First order Fermi acceleration in strong shocks

In the direct acceleration mechanism, the electric field in question can be due to, for example, a rotating magnetic field such as on a pulsar, a rotating accretion disk (onto a black hole) containing magnetic fields or possibly in colliding galaxies where magnetic fields change very rapidly as they reconnect.   The details of the actual acceleration process and the maximum energy to which the particle can be accelerated depend on the particular physical situation under consideration, though they all involve unipolar induction by a moving magnetic field.

Enrico Fermi originally suggested the second method of acceleration in 1949.  He postulated a mechanism of particle acceleration, whereby individual charged particles (“test particles”) in magnetised plasma are subject to repeated collisionless scatterings (“encounters”) with randomly moving inhomogeneities of the turbulent magnetic field, such as within an interstellar cloud.  Although in each individual encounter the particle may either gain or lose energy (depending on whether it was a head-on or following collision), there is on average a net gain of energy after many encounters.

This mechanism of acceleration is now called “second order” Fermi acceleration, because the average fractional energy gain is proportional to (u/c)², where u is the relative velocity of the cloud with respect to the momentum rest frame of the Cosmic rays, and c is the velocity of light.

Because of the dependence on the square of the cloud velocity, second order Fermi acceleration is not very efficient and for most interstellar clouds (where 2nd order Fermi acceleration usually occurs), the acceleration time scale turns out to be much larger than the typical escape time of Cosmic rays in the Galaxy.

A more efficient version of Fermi acceleration is seen when one considers encounters of test particles with plane shock fronts (discovered independently both by Bell in 1978 and Blandford and Ostriker in 1978). Shock fronts occur when an outflow of plasma containing relativistic electrons and magnetic fields encounters the ambient material in the interstellar or intergalactic medium (ISM or IGM).  These outflows are seen to take place in many objects throughout the universe such as supernovae remnants and Active Galactic Nuclei (AGNs). In these cases, the average fractional energy gain of a particle per encounter (defined as a cycle of one crossing and then re-crossing of the shock after the particle has been turned back by scattering) is of the first order (i.e. the fractional energy gain is (u/c) (with u being the propagation velocity of the shock through the ISM) and is therefore known as 1^st  order Fermi acceleration.

All shock acceleration methods (such as DSAM [13]) use 1^st order Fermi acceleration as their foundation, thus two key points are always inferred, whatever the particular shock scenario. Firstly that the shock wave is non-relativistic such that v- and v+ (the upstream and downstream velocities on either side of the shock front, in the rest frame of the shock front) are much less than vp the particle velocity.  Secondly, but no less important, is that the particle distribution is isotropic when viewed in the relevant rest frame (i.e. the upstream or downstream frame, depending on particle position).  This can be sometimes difficult to accept, but is nonetheless plausible.  On the outflow side of the shock the isotropy of particle distribution is the result of random scattering of the particles by tangled magnetic fields.  On the interstellar medium side the isotropy is created by the particles being deflected and scattered by Alfvén[[b] and hydromagnetic waves, which are often caused by the very passage of the relativistic particles themselves.

Because v- and v+ are significantly smaller than vp it can be assumed (for simplicity) that the particle does not react with or even notice the shock front, and as the particle crosses the shock front it gains a small amount of energy due to the differences in v- and v+.  The particle is then scattered, without losing a significant amount of energy before returning to cross the shock front gaining yet more energy.  For each cycle this gives a 1^st order energy gain of (DE/E)=(4/3)(u/c) [14].

A particle may be deflected in such a way that it crosses the boundary of the shock hundreds or even thousands of times, picking up a small amount of energy on each passage. Delving into the mathematics of this theory gives us an energy spectrum of the form N(E) E^-r where r=(R+2)/(R-1).  R is simply the shock compression ratio given by v-/v+=(g+1)(g-1) (g being the ratio of specific heats of the gas).  For typical astrophysical situations one has a fully ionised plasma, thus g=(5/3) and one obtains R=4 and hence r=2.

It is important to note here that the power law index depends only on the shock compression ratio and does not depend on the degree of scattering, so long as the scattering gives a near isotropic distribution of particles in the relevant rest frame.

Of course, there are several issues to complicate this picture, some of the most important are:

a)   The effect of a more realistic shock geometry

b)   Interaction of the particles with the shock structure and the possible consequences for the end particle spectrum

c)   Ultra-relativistic shocks, possibly relevant in g-ray bursts (GRBs)

d)   The likelihood of magnetic fluctuations and Alfvén waves, which are key features of DSAM.

There are ongoing debates in this area, resulting in claims of spectral indices from r=1.5 (due to particles interacting with the shock) to r=2.2 (ultra-relativistic shocks) or much higher [15].

Even though accelerating mechanisms do differ dramatically (both in time and space) it is still possible to derive a general maximum energy equation which then can be adapted to a particular acceleration scenario.  This is because the maximum achievable energy, E_max, of a cosmic ray is limited, in any situation, either by a combination of the size of the accelerating site R, (which has to be larger than the gyroradius of the particles being accelerated) and the strength of the magnetic field B, within the site. 

Hillas [16] first pointed out this condition in 1984 where the following equation is given:

                                               E_max(10¹⁸eV) » βZeB(μG)R(kpc)  

With Ze being the charge of the particle and β being usually having a value of 0.01 to 1 and derives from βc, the characteristic velocity of the accelerating region.  Even with this simple approximation, when one considers the energies achieved by the most energetic cosmic rays, many acceleration sites either are ruled out, or are pushed to the limits.  The Hillas plot [fig 9, [16]] of B vs R clearly compares the various possible acceleration sites, from neutron stars to colliding galaxies.  The lines drawn show the conditions that must be reached within an accelerating site to be able to contain a particle up to an E_max of 10²⁰eV.  One can see that Supernova Remnants (SNRs) cannot provide the necessary conditions for the highest energies, only really being able to confine particles up to ~10¹⁶eV.  White Dwarfs possess the necessary criteria for containing UHE iron nuclei, but these small dead stars are unable to contain highly relativistic protons and thus cannot be considered for the high energies that interest this report.  What follows is a comprehensive discussion of acceleration sites that satisfy the above criteria.

6.2.1a) Direct Acceleration  (sources)

Pulsars (rotating neutron stars)

The large rotating magnetic field (~10⁸T) on a pulsar induces a strong electrostatic potential drop (in principle up to 10²¹V) at the surface of the neutron star, this ionises the surface of the star, producing a large number of electrons which are then accelerated to relativistic speeds. This is known to be true due to the large amount of synchrotron radiation given off by these objects.  Synchrotron radiation is inevitable when electrons are accelerated in the presence of a magnetic field, thus the presence of synchrotron radiation in an object suggests that electrons are being accelerated to high energies whilst in close proximity to a magnetic field, and indeed the Hillas plot [fig9] confirms that particles with energies up to and beyond 10²⁰eV can be contained within Pulsars.

However, in any realistic model the large potential drop along the magnetic field lines is significantly short-circuited by electrons and positrons moving in opposite directions along the field lines, and any high energy charged particle trying to leave suffers severe energy loss due to having to cross the magnetic field lines.  Generally, it has been concluded that it is difficult to envisage the acceleration of charged particles, by an isolated pulsar, to energies beyond ~10¹⁵eV.  Though, recently, the discovery of a magnetar (a pulsar with very high magnetic field) indicates a dipole magnetic field approaching ~10¹¹T which would give an energy budget around 2 to 3 orders of magnitude higher than a pulsar, but of course there is still the not insignificant problem of short-circuiting.  Pulsars in close binary orbit also give a larger energy budget and in principle could power particles up to UHECR energies, but it has been noted in at least two such systems that there is a complete lack of detectable high energy g-ray radiation, thus reducing the likelihood of such binary systems providing UHECRs.  It is possible to reduce severe energy losses as the charged particle attempts to escape the site by invoking relativistic MHD winds which have been observed in the Crab Nebula and may carry UHECRs beyond the accelerating region.  This seems most likely to occur within the first few years of the life of a Pulsar and infers that a large proportion of the escaping particles would be iron nuclei.

Rotating accretion disks

It is generally agreed that at the centre of all Active Galactic Nuclei (AGNs) [fig10, [30]] there lies a very massive (10⁶-10¹⁰M_ο) black hole with its associated accretion disc.  Within this accretion disc there is threaded a magnetic field and as the disc rotates it sets up an electric field not unlike the one operating in pulsars.  From [fig9] it can be found that most AGNs can contain protons up to very high energies, and one can estimate the potential drop to be in excess of 10²⁰V.  Of course AGN cores still incorporate the sapping power of an intense radiation field which causes particles to lose energy via photo-pion production and also through the Compton effect, the radiation field being effectively a condensed Cosmic Background.  It has been proposed [17] that quasar (an incredibly distant, luminous galaxy) remnants, the name given to supermassive black holes in centres of inactive galaxies, are more effective accelerators as the debilitating losses of the radiation field are greatly reduced.  The exact conditions of acceleration have not been made clear as of yet, but it has been suggested that the very highest energies can be reached, and as there are many of these objects within the GZK cut-off distance they present a very promising answer to our problem.

Already it has been found that several of the highest energy events are in line with several extremely distant quasars [3].  For this to be possible a new type of particle must be invoked for it to cross such large distances without being affected by the CBR.  This may help the transfer of energy from the AGN central core as a UHE particle could collide with a hadron or photon whilst still very near the acceleration site creating the new particle and thus avoiding a large amount of the effect of the radiation field.  As all of the quasars referred to in [3] are compact, radio-loud, then the acceleration could be taking place in the radio lobes [fig 10] of the quasar rather than within the core.  This will be discussed shortly.

Colliding galaxies

Along with appearing on the Hillas diagram as being able to contain UHECRs, colliding galaxies may provide acceleration due to their violent nature.  Galaxies can interact in many different ways depending on the speed of collision, and on their respective sizes.  One can commonly find large variations in densities, causing numerous shocks and jet like anomalies.  A good example of this is given by [fig 11, [31]] which shows a supernova type shock created by the collision of two galaxies.  Magnetic field lines can also reconnect providing sudden and large potential drops thus these events can come under the title of acceleration by shocks or by direct acceleration. 

Unfortunately, detailed information on the possible acceleration of UHECRs in galaxy collisions is not very widespread, though it has been noted that many of the highest events are inline with sites of colliding galaxies [5]. In contradiction other reports feel that they are a very unlikely source of UHECRs as any acceleration would take too long a time.

6.2.1b) Shock acceleration (sources)

Active Galactic Nuclei-within the core and jets

It is perfectly possible for the accretion disc around the black hole at the centre of an AGN to be rotating at speeds of 0.1c [18], well in excess of the sound speed (30kms^-1) of the material being carried.  If these flows converge, shocks will be created and particles can be accelerated using the method described earlier.  Unfortunately, this scenario of shock acceleration has not been greatly investigated, generally because the much more powerful shocks at the termination of jets in the same galaxies have occupied most of our attention for the time being.

Jets occur on a small scale within our own galaxy and are considered to be the outflow of material from the centre of galaxies. It has already been noted that the most interesting of these are seen coming from AGNs, with sizes ranging from parsecs to megaparsecs across, their length often being 100 times their diameter. Along the length of the shock small knots can be seen which are now known to be small internal shocks created by the highly relativistic flow of material regularly trying to overtake itself and becoming supersonic. When the material encounters the ISM, which is moving at a much slower speed, it causes a large compressed shock to be set up, also known as a hot spot due to the intense energy released in this termination.  As can be seen from [fig12, [32]] the termination is surrounded by a cocoon of low-density material known as the radio-lobe, as the speed of the ejected material, ν_- increases with respect to the speed of the ISM, ν₊ the size of this cocoon increases.   It has been proposed that the boundary between the cocoon and the true ISM also contains a strong shock often known as a tangential discontinuity.  It is postulated that the cocoon shock accelerates particles already accelerated by the jet termination shock pushing the limit of particle acceleration to possibly greater than 10²⁰eV [15,25] even taking into account energy loss effects.  This opposes estimates of E_max in the region of 10¹⁹eV when relying solely on acceleration due to the jet termination shock.  Acceleration in the cocoon does rely on a relativistic shock speed, as opposed to the original assumption that the shock speed is irrelevant.

The main energy loss problem faced by AGN central regions (the intense radiation field) is significantly smaller in the region of the shock, thus the most likely reason for CRs not reaching the required energies is simply that the accelerating region is not large enough, and therefore cannot contain the particle long enough.

Cluster shocks

Often cluster shocks are very similar to the collision of galaxies as clusters are the name given to a large group of galaxies.  Clusters collide at relative velocities of thousands of km/s.  This is much higher than the speed of sound within the intracluster medium and leads to shocks within the cluster gas.  Following the initial collision, turbulence and bulk flows (jets) develop in the cluster gas, often sustained for 2-5Gyr. Abell 754 is an example where a large shock (or bar like structure) has been created due to the collision between two clusters.

From the description above, it is easy to see that there are many opportunities for particle acceleration, such as in the jets (much like in AGNs) or within the large shocks.  One of the first papers involving a several megaparsec scale, non-relativistic shock in a galaxy cluster was proposed by [19].

Gamma Ray Bursts (GRBs)

Gamma Ray Bursts are known as perhaps the most extreme form of high energy phenomena.  A typical burst last for only a few seconds, and they were first discovered completely by accident by the Vela series of surveillance satellites, whose prime task was actually to monitor nuclear explosions that could violate the test-ban treaties.  Because of the briefness and rarity (no more than 10 or 20 are observed each year) they tend to be hard objects to study.  What is known is that when they occur they become the strongest γ-ray source in the atmosphere (with hardly any emission in the x-ray range) and they are remarkably uniform over the sky and thus suggest that they originate within our own galaxy as well as throughout the cosmos.

It has been proposed [4] that γ-ray bursts are the result of highly relativistic, narrowly collimated jets from the birth or collapse of neutron stars within our own galaxy and terminate in the form of a hotspot [fig13, [4]], where the radiation is narrowly beamed towards earth, i.e. the radiation seen appears to originate in another galaxy but in reality is within our own (distances are hard to gauge due to their duration).  Evidence for GRBs being associated with neutron stars has already been put forward [20] as indications such as possible electron-positron annihilation and electron cyclotron emission lines have been viewed in GRBs and both of these processes occur in neutron stars. 

Because of the highly relativistic speed of the jet, particles contained within are already at high energies due to internal shocks, but they are accelerated to even higher energies due to the shock created when the jet terminates in a hotspot giving a maximum achievable energy in excess of 10²⁰eV.  As these GRBs would be located within the galaxy, there would be no reduction of energy due to propagation through the ISM and therefore would explain the absence of the GZK cut-off.  The only real problem with this theory is that it requires GRBs to be not rare, and occur ~300 times a year, similar to the birth rate of neutron stars.  This is possible if GRBs are strongly beamed, and therefore only a small percentage of the true number of events are viewed.  This in turn could be true due mainly to the exceptionally relativistic speeds of the jet, and is in fact necessary in some observed cases, where if the γ radiation viewed was emitted in all directions, rather than in a narrow cone, it would exceed the energy available in the birth or death of a neutron star.  It is also possible that the beaming is caused by procession of the beam, much like a lighthouse, though this seems less likely.

The next generation of UHECR detectors will be able to confirm this theory as it also implies a certain level of angular clustering (admittedly small) must be involved due to the limit to the number of γ-ray bursts.

6.2.1c) Other acceleration sources

In this section can be found other possible reasons for the acceleration of UHECRs, though none of them will be discussed in detail, partly due to a lack of understanding of the mechanism and also due to an uncertainty in how an air shower would develop when involving such strange objects.  It is possible that manifestations such as topological defects may well be a site for the acceleration of UHECRs.  One example is of the magnetic monopole, which will be explained in more detail later as they have a greater significance for top-down UHECR creation, but here one can speculate that such an object could accelerate charged particles with ease if travelling at a suitably relativistic speed.  Another solution to the UHECR problem is by introducing a highly charged particle known as a vorton, which, due to its intense charge, can be accelerated much more easily in objects such as AGNs (central core and jets).  It is thought that vortons may be part of the dark matter that appears to surround us. 

6.3) Top-Down production of Cosmic Rays

As highlighted above, the acceleration of cosmic rays comes up against several major problems when energies greater than 10²⁰eV are considered, in fact, just one CR above 10²¹eV will eliminate all but a couple of the above scenarios, and of those left they would be stretched to the limit of plausibility.  Bottom-up methods will, of course, face the major energy-limiting factor of whether they are able to contain a UHECR long enough for acceleration.  This, coupled with having often to either invoke a new type of fundamental particle or accelerate beyond 10²¹eV to compensate for energy losses whilst escaping the accelerating region or crossing the ISM has forced astrophysicists to look to other methods of producing UHECRs.

It has been thought for a while that UHECRs may be the result not of acceleration, but of the decay of a supermassive (“X”) particle with mass >10²⁰eV originating from high-energy processes in the early universe. As shall be discussed below, such a “top-down” decay mechanism for the production of extremely energetic particles in the Cosmos today is certainly possible and may indeed be naturally realised within the context of unified theories of elementary particle interactions in the early Universe.

The basic idea of a top-down origin of cosmic rays came from Georges Lemaître [21], in 1950, with his theory of the “primeval atom”, the alternative to the Big Bang theory where a single atom decayed ever smaller, producing the lighter atoms.  In fact, CRs were the main evidence of the primeval atom in the present universe.  Of course, with the discovery of the Cosmic Background Radiation (CBR) high energy particles are limited to short distances of the galactic rather than the cosmic scale thus rendering the theory untenable.  In the modern version of the top-down scenario for cosmic rays, the X particles typically decay to quarks and leptons.  The quarks produce jets of hadrons (of the order of 10⁴-10⁵) [8] containing mainly light mesons (pions) with a small percentage of baryons (mainly nucleons).  The pions decay to photons, neutrinos (plus antineutrinos) and electrons (with positrons).  Thus, energetic photons, neutrinos and charged leptons, together with a small fraction of nucleons, are produced directly with energies up to m_x, the mass of the original particle.  This all happens without resorting to any acceleration method whatsoever.

For UHECRs to be observed today, having originated from an X particle three basic conditions must be satisfied:

1)      The particles must decay at none cosmological distances, within 50Mpc of Earth.

2)      The X particles must be sufficiently massive, i.e. with mass >10²⁰eV.

3)      The number density and rate of decay of the X particles must be large enough to produce a detectable flux of UHECR particles.

The first condition simply results from the GZK cut-off, which limits most particles to a average maximum of 50 Mpc.  It is possible for very high energy neutrinos (who have a longer propagation distance before likely interaction with the CBR) to decay into UHE nucleons and/or photons within 100Mpc of Earth, but of course this is dependent on whether neutrinos have mass, which is yet to be proved conclusively.  The second and third requisites are effectively self-explanatory.

6.3.1) Sources of X particles

Cosmic topological defects (TDs)-magnetic monopoles, cosmic strings, domain walls, superconducting cosmic strings, etc as well as various hybrid systems consisting of these TDs- are predicted to form in the early universe as a result of symmetry-breaking phase transitions envisaged in Grand Unified Theories (GUTs).  TDs are already well known in other symmetry-breaking phase transitions such as in the condensed matter system of superfluid helium where vortex lines are created.  Many topological defects have been seen in liquid crystals too [22].

It is true that the idea of a rapid inflation period in the early universe was to some extent created to remove the problem of such defects, but it has been recently realised that these defects could be produced in the preheating stage just after inflation, producing “harmless” TDs that can exist alongside current theories concerning the development of the universe.  In fact, the inflation theory requires them to a certain extent.

All the topological defects mentioned above could emit X particles, generally when the defect is deformed in some way so energy can be released.  Often the production of X particles is due to the decay or creation of the TDs themselves.  [22] explains very well the various TDs but included here is a short summary of the most important ones together with potential methods of X particle production.

Cosmic strings and superconducting cosmic strings

These are very similar to a one-dimensional piece of string extending possibly the length of the universe.  They are incredibly dense, with a ten kilometre stretch weighing in at one Earth mass.  Emission of X particles can occur at the point of intersection of two string segments, or can be caused if one of the closed loop of string shrinks (due to energy loss) down to a radius similar to the width of the string.  Superconducting cosmic strings are simply cosmic strings with a persistent electric charge and will emit X particles if the current within the string surpasses the saturation value.

Domain Walls

Domain walls separate areas of the universe that are in different states and can decay to form X particles.  This can happen at any point in time and space.

Monopoles

The existence of monopoles is actually required by GUTs and is zero-dimensional supermassive object that carries magnetic charge.  A monopole can form with an anti-monopole to form a monopolonium. Subsequently, if the monopole and anti-monopole overlap within the monopolonium they can annihilate one-another, creating X particles.

From [fig14, [8]] it can be seen that at CR energies above 10²⁰eV γ-rays will all but dominate the spectrum in a TD scenario, with only neutrinos having a higher production rate.  It can also be seen that top-down methods will really only be noticeably present at energies greater than 10¹⁹eV.   From these two observations it should be possible to assess the likelihood of TDs causing UHECRs once more extensive data has been taken and the composition of primary UHECRs has been conclusively determined.  It is true that currently there is a possible clustering towards the supergalactic plane [8] which may well be a confirmation of CRs being caused by X particles.

7) Restriction of Sources through anticipating new data

§6 dealt with the sources that are currently under debate based on the data on UHECRs that is possessed currently. This section will highlight what the possible outcomes are once the new detectors start publishing data. There are several areas that will greatly effect the narrowing down of sources.

a) The energy

If the spectrum carries on at its current rate and no limit is found within the near future then this would quite simply disallow many of the sources that are based on acceleration.  Just one cosmic ray with an energy greater than 10²¹eV would rule out even the most ambitious acceleration mechanisms as the energy is just not available. 

It has been remarked earlier in §4.2 that currently there is a cosmic ray deficiency around the 10²⁰eV mark [fig 3] if the spectrum is expected to continue relatively smoothly.  [fig 15] shows the current best fit line for a conventional accelerating mechanism and here, the deficiency does not appear to be significant.  However, as [6] suggests this may well be the first sign of topological defects being the sources of high energy cosmic rays.  [fig3] shows the best fit line for a top-down scenario and as can be seen, this fits very well.  The inverse is also true that if this gap disappears, top-down scenarios would be unlikely as sources.

b) Arrival direction and isotropy

The simplest observation would be if strong clusters develop in the directions of known high energy objects, such as quasars or colliding galaxies.   This would not only shed light on the strength of intergalactic magnetic fields but would obviously strongly suggest that the objects they are clustering around are the sources.  Of course this may pose a problem if this is combined with very high energies and would subsequently demand a re-evaluation of our knowledge of particle acceleration.

What is more likely and harder to resolve is if anisotropies are present, but not on the level stated above. Small scale clustering may occur directed either to the galactic plane or supergalactic plane.  The former would support sources within our own galaxy such as newly formed neutron stars or pulsars, the latter clustering would support either gamma ray bursts [33] appearing to originate outside our galaxy or topological defects.  With the new detectors the Southern Hemisphere will soon be able to be studied and therefore isotropy will be truly measured.

c) Composition

The best detectors may be able to achieve is to find a percentage of particles that are protons, heavier nuclei or photons as it is unlikely that any single set of shower measurements could conclusively point towards one type of particle at such high energies.  It may prove even more difficult to prove the existence of the more exotic particles that are necessary for some theories.  In general, heavy nuclei cosmic ray primaries would favour galactic disk theories such as gamma-ray bursts in our own galaxy [4].  If most of the cosmic rays that strike our Earth at energies greater than 10¹⁹eV are protons then this would suggest an extra-galactic acceleration site.  Top-down scenarios favour photons as the composition of cosmic ray primaries, especially above 10²⁰eV, though neutrinos also figure highly and protons would not be completely ruled out either.

8) Conclusion

For the small amount of data that has been made available over the past 30 years to high energy astrophysicists the extent of ideas that has been produced is amazing.  This has made the dissertation very interesting to write, provoking often conflicting, but always fascinating ideas.  The next few years will prove ever more interesting for the subject of Ultra High Energy Cosmic Rays.  As new data is published by HiRes, Pierre Auger and possibly the OWL-Airwatch collaboration many of the above theories will vanish, but I believe that the subject will not be resolved.  New results may demand new areas of physics, as in the case of topological defects or possibly the invention of new particles and a rethinking of acceleration methods if the sources are found to be at cosmological distances as suggested for the case of some quasars.  UHECRs may have other effects too.  UHECRs provide a natural probe for intergalactic magnetic fields and in the future it may be possible to use these events as extremely high energy particle colliders far more powerful than any particle accelerator known on Earth.

Many of the reports are very convincing, but there are some that appear more likely than others.  In particular the possibility of gamma-ray bursts being beamed towards Earth sounds very plausible when one studies the data already known on these incredibly high energy phenomena.  Topological defects also seem likely, especially as they have been viewed within our own laboratories and also suggest much higher energies. 

Astrophysicists are beginning to think of UHECRs as one of the great unanswered questions, the other being Dark Matter.  UHECRs are known to exist, but shouldn’t and Dark Matter should exist, but doesn’t (so far).  

9) References

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[30] Pierre Auger picture gallery: http://www.auger.org/gallery.html

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[23] M.Boratav. Extremely high energy cosmic rays and the Auger observatory. 7th International Workshop on Neutrino Telescopes. Venice (April 1996).

[4] A. Dar and R. Plaga, Astron, Astrophys. 349 (1999), 259-266

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[3] G.R. Farrar and P.L. Biermann, Phys. Rev. Lett. 81. (1998), 3579-3582

[33] K.Gibbs. Cosmic rays at extreme energies. (Review talk given at the XXXIInd Rencontres de Moriond, "Very High Energy Phenomena in the Universe", Les Arcs, France (1997)

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[9] A.M. Hillas, Nature 395 (1998) 15

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[31] HS Telescope picture gallery: http://oposite.stsci.edu/pubinfo/gif/Cartwheel.gif

[19] H. Kang et al, Astrophys. J. 456 (1996) 422

[13] J.G. Kirk and P. Duffy, J. Phys. G 25 (1999), R163-R194

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[21] C. G. Lemaître, The Primeval Atom (Van Nostrand, Toronto, 1950)

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[17] A. V. Olinto. Ultra High Energy Cosmic Rays: The theoretical challenge.(2000)                                       (http://www-lpnhep.in2p3.fr/auger/review.html)

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[22] Topological defects: http://www.damtp.cam.ac.uk/user/gr/public/cs_top.html

[27] A. Watson, in Particle and Nuclear Astrophysics and Cosmology in the Next Millennium, edited by E.W. Kolb and R.D. Peccei (World Scientific, Singapore, 1995) p.126

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10) Figures (that were not included in main document)