chapter 1 cosmic rays, their energy spectrum and origin...law spectrum. [1] 4 chapter 1. cosmic rays...

Chapter 1

Cosmic Rays, their Energy

Spectrum and Origin

1 The Problem of Cosmic Rays

Most cosmic rays are not, as the name would suggest, a type of electromagnetic

radiation, but are nucleonic particles that travel through the universe with

velocities that approach the speed of light. These particles have always formed

a controversial topic for the physicists that studied them. The focus of cosmic

ray studies in this thesis is concerned with the most energetic of these particles,

with energies exceeding 1019 eV. Of particular interest is their origin and the

ability of astrophysical objects to accelerate particles to these great energies.

To thoroughly investigate their origin we must first determine any anisotropy

or clustering of cosmic ray arrival directions in our sky, measure the basic

composition or mass of the cosmic rays and resolve the energy spectrum at

these energies.

The Pierre Auger detector has been built with the expectation that it will

fully resolve these three aspects of cosmic ray research. The detector combines

two of the techniques used to measure cosmic rays at these energies. Both of

these techniques measure the properties of the cascade of particles created

by a cosmic ray when it collides with the atmosphere, termed an Extensive

Air Shower (EAS). The surface detector technique measures properties of the

air shower particles as they hit the ground. The complementary fluorescence

technique measures the fluorescence light the air shower produces as it tra-

verses the atmosphere. This thesis will examine in detail two large sources

1

2 CHAPTER 1. COSMIC RAYS

of error present in the fluorescence technique; the Cherenkov contamination

of the fluorescence light and the amount of atmospheric scattering suffered by

these two types of light. The extra information provided by the stereo imaging

of an event should produce a reduction in these sources of error in the shower

analysis procedures for the measurement of the primary particle energies and

the estimation of their composition.

2 The Energy Spectrum of Cosmic Rays

Our current understanding of the problem of cosmic rays can be best under-

stood by reviewing the features of their energy spectrum, shown in Figure 1.1.

This energy spectrum has been constructed from data collected by cosmic ray

observatories operating over the past century. A primary goal of all cosmic

ray observatories is to further resolve the energy spectrum as this will enable

a more complete understanding of the origin and propagation of cosmic rays

throughout the universe. The energy spectrum can be described by a relatively

featureless power law with only two observable changes in spectral slope which

have been named the ‘knee’ and the ‘ankle’. We can break the spectrum up

into three sections based on these two features, both of which seem to indicate

a change in the origin or composition of cosmic rays at crucial energies.

2.1 Below the Knee

The region below the knee of the energy spectrum of cosmic rays is the most

clearly understood. The flux of cosmic rays up to an energy of about 1014 eV

[2], which is just below the knee, is large enough for them to be directly de-

tected from high flying balloon and satellite experiments. In these experiments

the primary cosmic ray is directly intercepted and measured. Thus, measuring

the composition of these cosmic rays is straight-forward and has been found

to consist mostly of Hydrogen and Helium nuclei. The beam also consists of

Lithium, Beryllium and Boron, with heavier nuclei present in smaller concen-

trations. The knee has been observed to occur at an energy of about 3×1015 eV

[3]. Below this energy the spectrum follows the simple power law relationship,

dN

dE∝ E−γ (1.1)

2. THE ENERGY SPECTRUM OF COSMIC RAYS 3

Figure 1.1: The energy spectrum of cosmic rays, showing the only two clearlyobservable features, the knee and the ankle, in an otherwise featureless powerlaw spectrum. [1]


with a slope (γ) ' 2.7 as found, for example, by Aglietta et. al. (2000) [4].

The mathematical theory of shock acceleration within a supernovae produces

a predicted spectral slope of γ = 2 [5]. When we account for the effect galactic

fields and particles will have on the propagation of cosmic rays we arrive at a

spectral slope very close to what has been measured. So it is generally accepted

that the dominant sources of cosmic rays for this region of the spectrum are

galactic supernovae.

2.2 The Knee of the Cosmic Ray Energy Spectrum

The knee of the cosmic ray energy spectrum was first measured by Kulikov

and Khristiansen in 1958 [3]. It is a feature of the spectrum that is still not

completely understood. Astrophysicists believe that it is accompanied by a

change in the proportion of light hydrogen nuclei to heavy iron nuclei, a change

in the chemical composition, but this has not been conclusively proved.

Above 1014 eV cosmic ray particles can no longer be observed directly in

balloon experiments as the particle flux at Earth has dropped too low. How-

ever, at these energies the cosmic rays begin another process in the atmosphere

that allows us to measure them on the ground. This process, called an exten-

sive air shower, was first recognised by Pierre Auger (1939) [6]. It occurs when

the primary cosmic ray collides with an atmospheric nucleus, which creates

an ongoing cascade of secondary particles in the atmosphere. The particles

resulting from these collisions can be measured by an array of detectors spread

across an area of the Earth. Some such detectors are: EAS Top [4], Kascade

[7] and MSU [8].

Various models describing the structure of the knee have been put forward

including, but not limited to, diffusion models, compact source models and

inefficient acceleration mechanisms. Descriptions of how these models generate

the knee have been discussed in Horandel (2002) [9] and Candia et al. (2000)

[10].

2.3 The Ankle of the Cosmic Ray Energy Spectrum

The only other clearly observable feature on the energy spectrum of cosmic

rays is the ankle, a flattening of the spectrum which occurs at about 1018 eV

[11]. This region of the spectrum is more vigorously debated than the knee

3. PROPAGATION 5

as fewer events have been recorded above this energy. A number of major

detectors which operated in this region of the spectrum are, Fly’s Eye [12],

HiRes [13], AGASA [14], Pierre Auger [15], Yakutsk [16], SUGAR [17] and

Haverah Park [18]. The basic detection technique for cosmic rays above the

ankle remains the same as for energies above the knee. However, above this

energy fluorescence light is generated by the passage of the charged air shower

particles through the atmospheric nitrogen, which can be measured by distant

light detectors. This method pioneered by Bunner and Greisen (1967) [19] has

been used by the Fly’s Eye, HiRes and Pierre Auger detectors.

The ankle is believed to be generated as another, extragalactic, source of

protons begins to dominate the spectrum. However, the experiments work-

ing in this energy range are currently unable to get consistent results on the

anisotropy, composition or structure of the energy spectrum above 1019 eV,

which suggests that more data are needed to be able to accurately define the

origin of the most energetic cosmic rays.

3 Propagation

As cosmic rays travel through the galaxy they interact with galactic particles

and fields. For cosmic rays with energies much less than 1019 eV the movement

of the particle within the galactic magnetic field is contained by the galaxy.

These particles will not travel in straight lines from their origin to the Earth,

so the only property that can be directly measured from them is their energy

density. To determine the source of cosmic rays with energies below 1019 eV

we compare the measured energy density with the energy density predicted by

a proposed origin of cosmic rays.

For ultra high energy cosmic rays (UHECR), with energies that exceed

4×1019 eV, the galactic magnetic field has a very small effect on the particle’s

direction and so it may be possible to directly measure the vectorial direction of

their origin. However at this energy the photons of the microwave background

radiation begin to have a relative energy that matches that needed for photo-


pion production to occur through,

p + γ2.7K −→ n + π+

−→ p + π◦

−→ p + e+ + e− (1.2)

The theory related to this process, entitled the GZK cutoff, was first put

forward by Greisen (1966) [20] and by Zatsepin and Kuz’min (1966) [21] and

it concludes that above 4× 1019 eV cosmic rays will strongly interact with the

cosmic microwave background radiation and will not be able to travel further

than approximately 200 Mpc. Since this is small in cosmological terms, if

cosmic rays have an origin that is exclusively extra-galactic, a suppression in

the energy spectrum should be observed. The GZK cutoff has not been either

conclusively proved or discredited. Conflicting information exists in regard to

the flux of cosmic rays that are present at these energies. A study performed

by Baltrusitis et al. (1985) [22] with the Fly’s Eye detector showed that the

flux of cosmic rays above this energy was less than was expected, seeming to

confirm the presence of the GZK cutoff. Later studies performed with the

HiRes detector [23] [24] confirmed this result, but the observations made with

the AGASA detector have reported seeing no sign of the GZK cutoff [25]. In

these studies the number of UHECRs used was small and may not have been

an accurate representation of the flux of cosmic rays at these energies. Also,

the error on the calculation of the cosmic ray energy was very large, ∼ 30%,

above 6 × 1019 eV and it has not been determined if these results actually

agree with each other within their error margin [26]. Clearly the number of

events measured within this energy range is limited and the problem should

be solved after further significant observations have been made.

In addition, a few very high energy events have been observed which shows

that there may be a local source of UHECR, and may indicate that the GZK

suppression will be found to be very much reduced in effect. One of these

events was observed by Fly’s Eye in 1992 with an energy of 3 × 1020 eV [27]

and the AGASA array in 1994 observed another event with an energy of 2×1020

eV [28].

4. ANISOTROPY 7

4 Anisotropy

Below 1018 eV the arrival directions of cosmic rays are close to isotropic. At

these energies the arrival directions of cosmic rays are scrambled by galactic

magnetic fields. Above this energy the arrival directions of cosmic rays begin

to show structure and the map of the sky as seen by cosmic ray detectors for

UHECR (> 1019 eV) is expected to be anisotropic. On the large scale this

structure may show a clustering of cosmic ray arrival directions that coincides

with the galactic or the super galactic planes. Anisotropy associated with

either of these planes will prove that cosmic rays originate from either within

the Milky Way, or travel here from a close-by galaxy. Coincidences in the

arrival directions of cosmic rays associated with smaller scale structures such

as M87 or the whole nearby Virgo cluster of galaxies are also possible. The

detectors that operate above 1019 eV have reported differing results due to the

small number of events that have been measured. Of particular interest is the

anisotropy reported by the AGASA detector, which had the largest body of

high energy events recorded before the Pierre Auger Observatory was built.

The AGASA detector has studied two energy regions, that between 1018−1019

eV, and all the events above 1019 eV. For the lower energy region, ≈ 1018 eV,

AGASA reported an anisotropy in the direction of the galactic center [30].

Above 1019 eV Takeda et al. (1999) [29] reported no significant large-scale

anisotropy in the arrival directions of cosmic rays with either the galactic or

super galactic plane. An event excess that lay close to the super galactic plane

at ∼ 4 × 1019 eV was not significant enough for anisotropy along the super

galactic plane to be observed, but had a chance probability of occurring of less

than 1%, this finding is shown in Figure 1.2 (ii). The number of events used in

this analysis was 40 and the observed excess involved a cluster of three events.

The fluorescence detector HiRes that operates in the same energy region as

AGASA has reported seeing no anisotropy in the arrival directions of cosmic

rays around the energy 4×1019 eV. The study involved 271 events with energies

above 1019 eV [31]. The strongest clustering observed was consistent with an

expected isotropic arrival direction map and, hence, no significant anisotropy

in the arrival directions of cosmic rays was found. A study performed by

Letessier-Selvon et al. (2005) [32] with the data collected from the Pierre Auger

detector was performed in the direction of the galactic center at an energy

of about 1018 eV. No significant clustering above the statistical fluctuations


Figure 1.2: The anisotropy map generated by data from AGASA. The dots,empty circles and empty squares represent events with energies, 1019−4×1019

eV, 4×1019−1020 eV and > 1020 eV, respectively. The dashed lines representthe galactic and super galactic planes and GC is the galactic center. Plot (i) isin the reference plane of the sky, plot (ii) is in the reference frame of the MilkyWay. The gray areas on the map represent areas of the sky AGASA could notproperly observe as the detector is situated in the northern hemisphere [29].

5. COMPOSITION 9

associated with an isotropic sky were observed, which is not consistent with

the results recorded by the AGASA detector.

5 Composition

The current level of knowledge of the composition of cosmic rays is constrained

by the different detection techniques used at the different energies of the spec-

trum. Below the knee, cosmic rays are measured in balloon experiments and

the mass of the cosmic ray particle can be directly measured. Cosmic rays

of these energies consist mostly of protons, but heavier nuclei are present in

smaller proportions. Above 1014 eV, however, the composition of the initial

cosmic ray must be inferred from the properties of the air shower cascade it

has started in the atmosphere. At this energy it is no longer possible to talk

about an individual cosmic ray mass, but rather the general mass trend of the

majority of the cosmic rays measured for an energy range. We now speak of

the composition as being ‘heavy’, composed mostly of iron nuclei, or of being

‘light’, composed mostly of protons.

A heavier nucleus has a shorter interaction length than a single proton

because we can assume that the interaction probability of a nucleus can be

composed of the sum of the interaction probabilities of each individual nucleon

[34]. In general, a heavier nucleus will create a shower with a shallower depth of

maximum and a higher muon content at ground level. The many experiments

operating in the energy range around the knee, 1014 − 1016 eV, measure the

muon content of the air showers they detect as a compositional indicator, but

cannot agree on whether the composition is heavier or lighter. It has been

proposed [35] that this disagreement can be explained by the different nuclear

models used to describe the collision of the cosmic ray with an atmospheric

nucleus, but more information about nuclear interactions at these energies is

necessary to finally resolve this question.

Above the ankle, the fluorescence technique allows us to measure the com-

position of cosmic rays through the ‘elongation rate’, the slope of a plot of

the depth at which the maximum number of charged particles occurs in an air

shower against the logarithm of the energy of the cosmic ray. The expected

depth of maximum, Xmax is simulated for many events, when it is assumed

that cosmic rays are either, always protons or always iron nuclei. Comparing


Figure 1.3: The energy dependence of the mean depth of air shower maximumfor cosmic rays measured by the HiRes detector, or the elongation rate. Thecross-hatched area represents the error associated with the data. There is adefinite trend from a heavy to a light composition when either the QGSJet orSIBYLL models of nuclear interactions are used [33].

6. POSSIBLE SOURCES OF ORIGIN 11

this simulated data to the measured data will show the general trend in the

mass composition of cosmic rays. Abu-Zayyad et al. (2001) [33] performed

this kind of elongation rate analysis on the data generated by the HiRes de-

tector, the results of which can be seen in Figure 1.3. This figure shows that

the average mass of cosmic rays decreases with energy for cosmic rays with

energies greater than 1017 eV because the trend of the data moves towards

agreement with the always proton cosmic ray composition line. This agrees

with the theory that at about 1018 eV a proton-strong extra-galactic source of

cosmic rays begins to dominate the spectrum. However, the AGASA detector,

that operates with a surface technique at the same energies as HiRes, has not

observed any change in the composition of cosmic rays at the highest energies

[36] [37]. It may be that it is the detection techniques that are causing the

discrepancy between the experimental results [34]. The Pierre Auger project,

with its larger collection area and ability to cross correlate the fluorescence and

surface detector techniques is expected to resolve the composition of cosmic

rays at the highest energies.

6 Possible Sources of Origin

The biggest unanswered question in the field of ultra high energy astrophysics

is “where do cosmic rays come from?”. The best way to explore the possible

acceleration sites of cosmic rays is to review a “Hillas diagram” as shown

in Figure 1.4. This diagram explores the size of astrophysical objects with

respect to the strength of their magnetic field and so the ability of such objects

to accelerate and contain UHECR’s, in this case with an energy of 1020 eV.

The first thing we notice about this plot is there are very few astronomical

objects which are potentially able to accelerate particles to 1020 eV. There are

only three types of objects that can accelerate protons to this energy, neutron

stars, active galactic nuclei (AGN) and radio galaxy lobes. The galactic halo

can accelerate iron nuclei to this energy, but the galaxy itself, supernovae and

sunspots are unable to accelerate particles to 1020 eV. These objects are divided

by the acceleration mechanism they employ to generate UHECRs. Neutron

stars, active galactic nuclei and sunspots produce UHECRs through the direct

acceleration of a particle in a magnetic field. The rest of the objects accelerate

particles through shock acceleration, described by first order Fermi principles.


Figure 1.4: The diagonal lines represent the relative size the magnetic field ofan object needs to be to contain cosmic rays that are protons (the solid line),and iron nuclei (the dashed line). Any object that projects above the diagonallines can potentially accelerate particles up to 1020 eV [38].


6.1 Fermi Acceleration Models

The first theory of stochastic particle acceleration proposed by Fermi involves

the interaction of a charged particle with vast magnetised clouds. The particle

is scattered by the clouds with a series of glancing collisions. In these collisions

the velocities of the particle and the cloud will either be in the same direction,

or opposite as shown in Figure 1.5. The particle will gain energy from colli-

sions where the velocities are in the opposite directions and will lose energy

when the velocities are in the same direction. Since the collisions where the

velocities of the particle and the cloud are opposite to each other are the most

likely, on average the particle will gain energy with a relative energy gain ∆EE

proportional to the square of the velocity of the cloud,

∆E

E∝(vcloud

c

)2

(1.3)

For this second order acceleration process, vcloud � c and so the time this

process takes to accelerate a particle to relativistic energies can be larger than

the age of the universe. In response to this the theory has been reworked

to include the effect of a shock wave passing through the cloud, as occurs in

the magnetised cloud surrounding a supernovae. In this case the shock front

must be passing through the interstellar medium with a velocity higher than

the speed of sound. The particle is contained by the magnetic field of the

supernovae shell, but can pass through the shock and remain contained. If the

particle passes through the shock then it will receive a relative energy gain of,

∆E

E∝ vcloud

c(1.4)

In this case of first order acceleration, the time taken for the particle to achieve

relativistic speeds is well within the age of the universe. This form of accel-

eration process naturally derives a power law spectrum that fits the spectrum

of cosmic rays observed on Earth. Thus it is considered very likely that this

is the acceleration mechanism for most cosmic rays.

Supernovae

Supernovae fulfill the requirements imposed by first order Fermi shock accel-

eration. The shock wave of the exploding star travels faster than the speed of


Figure 1.5: The two types of collision that can happen between a magnetisedcloud and a charged particle, (i) velocities of the cloud and particle are inopposite directions, (ii) velocities of the cloud and particle are in the samedirection. Note that there may be any angle between the velocity of the cloudand the particle up to 90◦, the velocities have been drawn parallel for simplicity.


sound and the magnetic fields are of the correct strength. Fransson and Bjorns-

son (1998) [39] examined the radio spectrum from the supernova SN1993J in

the M81 galaxy. They observed the synchrotron-emitting hot spots of the

supernova and were able to determine the injected electron spectrum to be

dN/dE ∝ E−2.1, and that strong particle acceleration was occurring in the

shocks of the supernova shell. The particle production spectrum from a su-

pernova that is accelerating particles due to first order Fermi acceleration

principles can be calculated from the observed cosmic ray particle density

at a specific energy range. Hillas (2005) [40] found that this spectrum was

dN/dE ∝ E−2.04, which is very close to that measured in SN1993J.

Radio Galaxy Lobes

A galaxy that produces radio lobes has a super-massive black hole at its center

that produces enormous jets of particles which radiate in the radio part of the

electromagnetic spectrum. It had long been known that the electromagnetic

spectrum emitted by the hot spots in the lobes of radio galaxies could be

explained as the synchrotron radiation coming from charged particles acceler-

ating by 1st order Fermi acceleration principles. Biermann and Rachen (1993)

[41] showed that the observed spectrum of cosmic rays above 1018 eV will fit

the acceleration of protons in the hot spots of the lobes of Fanaroff-Riley Class

II radio galaxies by first order Fermi principles if the injection spectra is E−2.

Other types of galaxies that have associated radio lobes, like BL-Lac objects

and AGN may also be the origin of cosmic rays, see reference [38] for a more

complete discussion of the acceleration properties of these objects.

6.2 Point Source Models

The point source model of cosmic ray acceleration is the most direct method of

particle energy gain. In this case a rotating magnetic neutron star or a rotating

accretion disk generates an electric field that accelerates the particle. However

the amount of acceleration provided by any one object is highly dependent on

the individual properties of that object and so these sources cannot generate

the power law spectrum observed on Earth in a natural way [38].


6.3 Topological Defects

The basic idea of a topological defect is that particles of type “X” that are

embedded in Space-Time have been left over from the Big Bang. These par-

ticles have a mass mX > 1020 eV. The particles were prevented from decaying

immediately after the Big Bang and decay with some random time frame

comparable to the current age of the universe. The “X” particles decay into a

more traditional form of matter, which have an energy that can be in excess

of 1020 eV quite easily [34]. The theory is attractive because it does not rely

on the acceleration ability of astrophysical objects. If this is the acceleration

mechanism for the highest energy cosmic rays then the GZK cutoff will be very

much reduced in effect as the particles may have excessive energies (≈ 1025 eV)

quite easily and so be able to survive many interactions with the CMBR. The

anisotropy of this acceleration method would be non-existent or may indicate

an empty region of the sky.

7 Chapter Summary

The acceleration source of UHECR is one of the most interesting questions in

high energy astrophysics today. There are three theories that describe how a

particle may be accelerated up to 1020 eV, the stochastic particle acceleration

method, the direct compact source method and the top down theory. If par-

ticles are accelerated through the Fermi acceleration technique then a broad

anisotropy in the direction of the super galactic plane is expected and the

GZK cutoff should be clearly seen. For the direct method of acceleration the

particles should point towards known compact source objects. If the origin

of cosmic rays is something more exotic, like the top-down model, then no

anisotropy should be observed and the GZK cutoff will not be clearly present.

Chapter 2

Extensive Air Showers

1 Components of an EAS

The collision of a cosmic ray particle with an atmospheric nucleus begins

a cascade process in the atmosphere, called an extensive air shower. The

cosmic ray will probably be hadronic and the collision will break the target,

atmospheric nucleus into its constituent nucleons. The enormous momentum

of the cosmic ray will cause these particles to travel in the same basic direction.

The energy of the cosmic ray becomes split up among the nuclear fragments,

which then go on to interact with other atmospheric nuclei, creating a chain

of events that will propagate down through the atmosphere. In addition to

the resulting nuclei, much of the energy of the initial cosmic ray is transmuted

to create pions, both neutral and charged. The neutral pions will decay into

two gamma rays before they can interact with other atmospheric nuclei. The

longer lived charged pions may decay or may interact with atmospheric nuclei.

They decay into muons and neutrinos, but this decay is less probable with

pions of higher kinetic energy. These interactions are documented in Figure

2.1.

1.1 Hadronic

The depth of the first collision of the cosmic ray in the atmosphere is random,

but on average is 70 g/cm2 for a proton and 25 g/cm2 for an α particle [42] at

an energy of ∼ 1017 eV. During the collision the target nucleus will break up

into nucleons as will the cosmic ray itself if it is a nucleus. The collision thus

17

18 CHAPTER 2. EXTENSIVE AIR SHOWERS

Figure 2.1: Schematic diagram of a hadronic air shower showing the productsof each interaction and decay [42].

1. COMPONENTS OF AN EAS 19

creates neutrons (n), protons (p), anti-protons (p), anti-neutrons (n), heavy

mesons (K) and hyperons(Y) as well as any fragmented nuclei that may sur-

vive the collision. These nuclear and heavy particles will collide with more

atmospheric nuclei until their energy has dropped below the threshold energy

of the reaction. The interaction of an air shower hadron with an atmospheric

nucleus creates a number of secondary particles including pions, neutrinos or

electrons. The charged pions have a half-life that is comparable to their prob-

able time of nuclear interaction with an atmospheric nucleus, especially when

they are traveling below relativistic velocities, and this interaction will create

more pions, both charged and neutral. The number of nuclear interactions that

occur in an air shower, drops off rapidly with increasing atmospheric depth

due to the large amount of energy that goes into each interaction. Eventually

the nuclear particles have all been reduced to an energy below that needed for

a nuclear interaction to occur and so are no longer created within the cascade.

1.2 Muonic

The decay of a charged pion creates a charged muon and a neutrino. The

muons do not interact with the atmospheric nuclei and lose energy slowly

through ionisation. At the level of energy of an air shower they have a long

half life compared to the dilated time they spend traversing the atmosphere

and many will continue beyond the level of the Earth’s surface. The muons

are used to detect primary cosmic rays with the surface technique and with

detectors placed beneath the surface of the Earth. There is a chance that

a muon will decay within the atmosphere where it will create an electron or

positron and two neutrinos. The weakly interacting neutrinos created in these

processes continue on through the Earth and are not used in the air shower

detection process.

1.3 Electromagnetic

If the initial cosmic ray is not a hadronic particle, but a gamma ray, the re-

sulting air shower will consist almost entirely of gamma rays, electrons and

positrons, ie. it will be completely electromagnetic. If we study how this

simpler cascade will propagate through the atmosphere we can understand

proton induced air showers because the dominant part of an air shower is


the electromagnetic component. Now, as the initial gamma ray passes close

to a nucleus, it will undergo pair production and create an electron-positron

pair. The positron and the electron will interact with nearby nuclei and cre-

ate gamma rays due to the Bremsstrahlung radiative process. Some of the

positrons will annihilate with atmospheric electrons to create more gamma

rays. These cascade electrons and positrons cause Cherenkov radiation to be

emitted and they also excite nearby molecules causing them to fluoresce. Both

processes are discussed later in this chapter. So, the number of electromag-

netic particles present in the cascade will grow exponentially until the energy

losses dominate. The number of charged particles in an air shower drops off

after this point as the electrons are attenuated by the atmosphere and are no

longer considered part of the cascade process.

For a hadron-induced air shower the short-lived neutral pions created by

the hadrons are very unlikely to interact with atmospheric nuclei and will

decay into two gamma rays traveling in the same direction as the initial π◦.

Those gamma rays initiate the electromagnetic part of the air shower by pair

production. For each neutral pion created by the hadronic section of the air

shower, two gamma ray induced air showers can be said to emanate, so a

proton induced air shower is like a superposition of many gamma ray induced

cascades.

2 Longitudinal Profile of an EAS

The growth and decline of the number of charged particles present in an EAS

can be defined using various mathematical models. These models all relate

the number of charged particles present within an air shower as a function

of shower growth. One such model, the Gaisser Hillas profile is the only

development profile considered in this thesis.

2.1 Gaisser Hillas Profile

The Gaisser Hillas profile was first defined by Gaisser and Hillas in 1977 [43].

This profile uses the atmospheric slant depth to define the position or the

current stage of an air shower’s growth. The slant depth, Xslant, is the atmo-

spheric depth, X, corrected for the geometrical effect of an air shower axis not

2. LONGITUDINAL PROFILE OF AN EAS 21

Figure 2.2: The atmospheric depth, X, is the mass of a column of air witha unit cross sectional area above height h. The slant depth XSlant is theatmospheric depth corrected for the angle, α which the air shower makes withthe Earth’s surface.


Figure 2.3: A plot of a Gaisser Hillas function, Nmax and Xmax are clearlyvisible as 5× 1010 particles and 750 g/cm2, respectively.

being perpendicular to the surface of the Earth.

Xslant =X

sin α(2.1)

Here the angle α is the angle the shower axis makes with the Earth’s surface as

in Figure 2.2. Atmospheric depth is generally used to describe the radiation

absorption capability of the atmosphere. For a uniform absorber, only the

thickness of the absorber needs to be considered. However the atmosphere is

composed of several types of gases and particles with a density profile that

decreases exponentially with increasing height, hence the density of the air

needs to be included when considering its absorbence. This is done by con-

sidering the mass of a vertical column of air with a unit cross-sectional area,

generally measured in grams per square centimeter (g/cm2). Then the mass

per unit area of the atmosphere above a certain height is defined as being the

atmospheric depth.

The Gaisser Hillas function relates the slant depth to the number of parti-

3. FLUORESCENCE LIGHT 23

cles present in the shower through,

N(X) = Nmax

(X −X0

Xmax −X0

)Xmax−X0λ

exp

[Xmax −X

λ

](2.2)

λ and X0 are essentially free parameters, with typical values around, λ =

70g/cm2 and X0 = 0g/cm2. It follows that there will be some depth, Xmax,

where a maximum number of charged particles, Nmax, will exist as in Figure

2.3. The parameter Xmax is used in the elongation plots described in Chapter

1 Section 5 and may be used to infer the mass composition of the primary

cosmic ray.

3 Fluorescence Light

Fluorescence radiation is produced when an external source of radiation causes

the atoms or molecules of a medium to become excited. This external radiation

can be in the form of electromagnetic radiation or charged particles. For

an air shower, the external radiation consists mainly of electrons created by

the cascade process, and the fluorescent medium is nitrogen. The fluorescent

atmospheric nitrogen spectrum calculated by Bunner 1967 [19] is shown in

Figure 2.4 where the distinct lines of emission between 300 nm and 400nm

can be seen. The emission peaks in Figure 2.4 are due to the transition in

N2 and N+2 from a higher molecular energy state to a lower one. The main

emission peaks are at 315 nm, 337 nm and 358 nm and are due to N2, the

remaining peak at 391 nm is due to N+2 . The emission peaks are of course

due to the transition between molecular energy states, the full discussion of

which is beyond this thesis, but can be found in [19]. The photon yield, ε, per

electron given by Nagano 2004 [44] was found from nitrogen gas that had been

excited by electrons, and is written as a function of pressure p at a constant

temperature T in Kelvin:

ε =p

RT (hν)

(dE

dx

)(Φ◦

1 + pp′

)(2.3)

where R is the specific gas constant (N2 : 296.9 m2s−2K−1 and Air : 287.1

m2s−2K−1), dEdx

is the energy loss in eV kg−1m2, hν is the photon energy (eV)

and p′ is the reference pressure. The typical value of ε for a wavelength range


Figure 2.4: The atmospheric fluorescence spectrum due to nitrogen. [19]

4. CHERENKOV LIGHT 25

between 300 and 400 nm is ∼ 3.8 photons/m [44] when in air. The vari-

able Φ◦ corresponds to the fluorescence efficiency in the absence of collisional

quenching and for the ith emission band is given by,

1

Φi(p)=

1

Φ◦i

(1 +

p

p′i

)(2.4)

4 Cherenkov Light

The phenomenon of Cherenkov light can be observed when charged particles

traverse a medium faster than the phase velocity of light in that medium.

It is very much like the shock wave that occurs when a jet plane breaks the

sound barrier in the atmosphere. Whenever a charged particle moves through

a medium it distorts the atoms it passes creating an electric polarisation field,

but as seen in Figure 2.5 (i) the field is symmetrical around the electron and will

cancel itself out, so no radiation may be observed. When the particle is moving

very fast the polarisation field generated by the moving particle is no longer

symmetrical and the electric field will generate a brief pulse of electromagnetic

radiation. Generally the pulsed wavelets will interfere destructively and will

cancel each other out, but if the particle is moving faster than the speed of

light in the medium, the wavelets will add constructively and may be observed

by a distant observer.

It is easy to prove from geometry such as in Figure 2.6 that the angle,

θ, at which the wavelets are coherent is inversely proportional to the relative

velocity of the particle, β = vc, and the refractive index, n, of the medium,

cos θ =1

βn(2.5)

The Cherenkov light is emitted in a cone centered around the trajectory of the

particle, with an opening angle of θ as seen in Figure 2.6. The existence of this

opening angle implies that there exists some threshold velocity of the charged

particle, below which Cherenkov light will not be emitted. This is obvious

from the definition of Cherenkov light and means there will be some limiting

value of energy, Ethres, the charged particle must possess to emit Cherenkov

radiation, given by,


Figure 2.5: When a charged particle moves through a medium, it distorts theatoms it passes. (i) at low velocity the electric field is symmetrical. (ii) at highvelocity a pulse of radiation is emitted as the particle traverses the medium, ifthe particle is traveling above the phase velocity of the medium the radiationwill be coherent [45].

4. CHERENKOV LIGHT 27

Figure 2.6: Huygens principle shows that Cherenkov light is coherent withinthe angle θ. Cherenkov light is emitted in a cone centered around the trajectoryof the charged particle [45].


Ethres = m0c2

[1

2n2− 1

](2.6)

m0 is rest mass of the charged particle.

The derivation of the yield of Cherenkov radiation in a medium may be

found in Jelley 1958 [45]. The yield of the number of photons emitted by a

charged particle within a spectral range of λ1 − λ2 per unit path length is,

dN

dl= 2πα

(1

λ2

− 1

λ1

)·(

1− 1

β2n2

)(2.7)

α is the fine structure constant ' 1137

.

Cherenkov Light Produced by an Air Shower

The Cherenkov light created by an EAS is produced in a very strong froward

pointing cone, experimentally found to have an angular spread to ∼ 20◦. This

spread is created by the distribution of the angular direction of electrons within

an air shower. The strength of the Cherenkov beam and its angular distribu-

tion is thus based on the energy and angular distribution of the electrons in

the shower and this relationship has been explored by a number of physi-

cists [46] [47] [48]. Since the Cherenkov light produced by an air shower is

very bright an Auger detector may see direct Cherenkov light if it views the

shower head-on within 20◦, but it always sees some Cherenkov light that has

been scattered out of the beam. The Rayleigh scattered Cherenkov light nor-

mally dominates, but Mie scattered Cherenkov light will dominate if there are

many aerosols present in the atmosphere. This scattered Cherenkov light is

considered to be noise in the calculation of the amount of fluorescence light

produced by an air shower and must be removed from the calculations. The

only observational difference between fluorescence and Cherenkov light which

the fluorescence detectors of the Pierre Auger Observatory can detect is the

directional nature of Cherenkov light. At large angles to the beam, which are

usually observed by the Pierre Auger fluorescence detectors, Cherenkov light

will normally be measured in much smaller quantities compared to the amount

of fluorescence light measured. So, the Cherenkov light produced by an air

shower can be iteratively removed from most events.

5. ATMOSPHERIC SCATTERING AND ATTENUATION 29

5 Atmospheric Scattering and Attenuation

The process of scattering occurs when a wave passes through a medium that

can be considered to be filled with point discontinuities, such as haze particles

suspended in the air, or the atmospheric molecules themselves, where each

molecule is separated by a region of empty space. The electric field of the inci-

dent wave will cause the suspended particles to vibrate at the same frequency

as the incident wave. The vibrating particles will then radiate a secondary

electromagnetic wave in phase with and of the same wavelength as the inci-

dent wave. Based on the size of the particle with respect to the wavelength

of the incident light, the angular pattern of the intensity of the scattered light

can be described by either Rayleigh or Mie principles [49]. The wavelength

of fluorescence and Cherenkov radiation that is emitted by an air shower falls

between 300 to 400 nm, which means that scattering off of air molecules may

be described by Rayleigh principles, but scattering off of haze aerosols must

be described by Mie principles. For both types of scattering we can simplify

our equations by assuming that the light scattered by each particle escapes

the path of the light beam and is not re-scattered. This is called single scat-

tering and this assumption holds true to a first approximation. The effect of

multiple scattering is being considered by the project, see Roberts (2004) [51]

for a discussion of how it can be applied to the data.

Now, for a homogeneous medium of constant density, the amount of radi-

ance remaining in a beam of light with an original radiance of E0 at position

x along the beam that is undergoing a scattering process is given by,

Ex = E0 exp

(−x

C(λ)

)(2.8)

Here, C(λ) is a constant that describes the basic scattering properties of a

medium for a particular wavelength of light and must be experimentally de-

termined. It can be understood by relating it to the concept of visual range,

which is described in McCartney 1976 [49] as “the distance under daylight

conditions, at which the apparent contrast between a specified type of target

and its background (horizontal sky) becomes just equal to the threshold of the

observer ...”. From this we can infer that the constant C(λ) is the distance

a beam of light must travel before being attenuated to the fraction e−1 of its

original strength.


Figure 2.7: The angular patterns of scattered intensity for a fixed wavelengthwith different particle sizes. (i) Small particle compared to the wavelength,Rayleigh scattering. (ii) Particle size comparable to the wavelength, Mie scat-tering. (iii) Large particle size compared to the wavelength, Mie scattering.[49]


Figure 2.8: The Longtin model of the Mie phase function due to scattering offatmospheric aerosols [50].


Now the quantity transmittance, T, is generally used to describe the at-

tenuation strength of a medium. The transmittance is defined as the ratio

between the beam radiance at position, x, to the beam radiance at the incep-

tion of the beam,

T =Ex

E0

= exp

(−x

C(λ)

)(2.9)

It must be noted that Equation 2.9 holds for both the Rayleigh and Mie

scattering principles and that the total transmittance, Ttot, of the atmosphere is

the product of the transmittance of the molecules, Tm, with the transmittance

of the aerosols, Ta,

Ttot = TmTa (2.10)

5.1 Rayleigh Scattering

The atmosphere is a medium that is not of constant density and so we must

transform our definition of the transmittance into a quantity that removes the

vertical density profile of the atmosphere. The quantity used for this is the

vertical atmospheric depth described in Section 2.1. The atmospheric depth,

X, is the integral of the density of the atmosphere, ρ(h), as a function of height,

h,

X =

∫ ∞

h

ρ(h′)dh′ (2.11)

When we use a single layer model of the atmosphere where the temperature

profile of the atmosphere is assumed to be constant, then Equation 2.11 reduces

to

X = X0 exp

(−h

hm

)(2.12)

Here X0 is the vertical atmospheric depth at some reference height h=0, h

is the height above that level and hm is described as the scale height of the

atmosphere and can be found from,

hm =kT

mg(2.13)

k is Boltzmann’s constant, T is the constant atmospheric temperature, m is

the average mass of an atmospheric molecule and g is the acceleration due to

gravity. In this case the constant C(λ) is defined as the molecular mass atten-

uation length Xm(λ), and for a wavelength of 355 nm, Xm(λ) = 1885g/cm2.


Then the transmittance of a straight light path taken through the atmo-

sphere from height, h, into space will be given by,

Tm =X

Xm(λ) sin α(2.14)

Here α is the elevation angle the light path may have to the ground. When

a non-constant temperature model of the atmosphere is used Equation 2.12

becomes more complicated, but the transmittance is still given by Equation

2.14.

Rayleigh Phase Function

To determine the amount of light scattered in any one direction due to a

particle we must define the Rayleigh angular phase function. The derivation of

this function is beyond the scope of this thesis but may be found in McCartney

1976 [49]. The function has the shape seen schematically in Figure 2.7 (i). It

describes the fraction of incident light that will be scattered in the direction θ

per unit solid angle, dω, and is given by,

dP

dω=

3

16π

(1 + cos2 θ

)(2.15)

5.2 Mie Scattering

As with the description of the distribution of the molecules within the atmo-

sphere, aerosols do not have a constant density. We assume that the density

distribution of aerosols, ρa(h), falls off exponentially with height, through,

ρa(h) = ρ0a exp−h

ha

(2.16)

Here ha is the scale height of aerosols and ρ0a is the density of aerosols at a ref-

erence height, h = 0, and is assumed to be constant everywhere at this height.

We can then describe a similar term to the molecular vertical atmospheric


depth, the particulate vertical atmospheric depth (Xa), by,

Xa =

∫ h1

h2

ρ0a exp−h

ha

dh

= ρ0aha

[exp

−h1

ha

− exp−h2

ha

](2.17)

Now we define a quantity that is equivalent to the mass attenuation length

used in the Rayleigh model by integrating over a horizontal path of length

Λa(λ) at the reference height, where this path length is called the aerosol

attenuation length and must be measured for the atmosphere at specified

wavelengths. It is the horizontal distance the light beam must traverse before

being attenuated to a fraction of e−1 of its original strength.

So, Xa(λ) =

∫ Λa(λ)

0

ρa(0)dx (2.18)

but at the reference height, ρa(0) = ρ0a

∴ Xa(λ) = ρ0aΛa(λ) (2.19)

Now the actual density of aerosols at sea level ρ0a cannot be measured

without prior knowledge of the scattering properties of the aerosol particles,

which is what we are trying to find. So we describe the transmission factor

within any slice of the atmosphere that lies between the heights h1 and h2 as,

Ta = exp

[ha

Λa(λ) sin α

(exp

−h1

ha

− exp−h2

ha

)](2.20)

And we find that the aerosol density factor has disappeared. This definition

of the transmission factor is independent of the density profile of aerosols in

the atmosphere. So the correction for the extra amount of light lost by a light

track that is at an angle α to the ground, is simply given by 1/ sin α.

Mie Phase Function

The phase function for Mie scattering is much more complicated than that

for Rayleigh scattering and cannot be easily described mathematically. The

Pierre Auger project uses the Longtin phase function [50] seen in Figure 2.8

which describes a forward pointing lobe seen in Figure 2.7 (ii).

6. CHAPTER SUMMARY 35

6 Chapter Summary

The extensive air showers that are created by UHECR’s are complicated struc-

tures that span the energy range from atomic molecular excitation to nuclear

collisions at extremely high energies. Air showers enable the measurement of

cosmic rays above 1014 eV, where the flux of cosmic rays has dropped below

a level where it is practical to directly measure cosmic rays with balloon or

satellite detectors. The detection of UHECR relies on our knowledge of all the

molecular interactions that can occur in the atmosphere.

Chapter 3

The Pierre Auger Detector

The Pierre Auger Project in Argentina has been built to study ultra high

energy cosmic rays (UHECR). The Pierre Auger project employs both the

fluorescence and surface detector techniques to measure cosmic rays. The

detector, shown in Figure 3.1, will consist of four fluorescence detectors over-

looking an array of 1600 surface detectors. The array will cover an area of

3000 km2 and will be the largest cosmic ray detector ever built. It is expected

that the large number of UHECR observed by the Pierre Auger detector will

finally resolve the form of the energy spectrum of cosmic rays above 1019 eV.

The surface detector technique can be run continuously, but cannot measure

the energy of a cosmic ray in a model independent way. The fluorescence

technique, first proposed by Bunner and Greisen [19], involves measuring the

track of fluorescence light created by the movement of the charged particles in

an EAS through the atmosphere. This technique is a direct way to measure

the energy deposited by an UHECR in the atmosphere but, unlike the surface

detector technique, it cannot be run during the day or on moonlit nights. The

Pierre Auger Project will make use of the continuous operation of the sur-

face detector technique plus the high precision of the fluorescence technique

to measure cosmic rays.

1 Air Fluorescence Detectors

Fluorescence detectors measure the scintillation radiation produced by the mo-

tion of charged air shower particles through atmospheric nitrogen. There are

only three fluorescence detectors that have been built in the world, Fly’s Eye,

37

38 CHAPTER 3. THE PIERRE AUGER DETECTOR

Figure 3.1: A geographical surface image of the Pierre Auger Detector inthe province of Mendoza in Argentina. The positions of the four fluorescencedetectors as they overlook the array of 1600 surface detectors are shown.

1. AIR FLUORESCENCE DETECTORS 39

HiRes and Pierre Auger. Of these the Fly’s Eye detector is no longer opera-

tional and the Pierre Auger Observatory is still under construction. Compared

to other techniques the fluorescence technique produces a model independent

measurement of the energy and axis geometry of an extensive air shower.

1.1 Fly’s Eye

The Fly’s Eye detector was the first successful project to use the fluorescence

technique to measure UHECR’s. The detector was stationed at the Dugway

Proving Ground in Western Utah, and was operational from 1981 to 1992 [52].

The detector was upgraded to a two station detector in 1986 to consist of Fly’s

Eye I and Fly’s Eye II which were separated by 3.3km. Fly’s Eye I consisted

of 67, 62-inch spherical mirrors that were arrayed around the site. Associated

with each mirror were 12-14 photomultiplier tubes (PMTs) that collected the

light focused by each mirror. Each mirror and PMT unit observed a designated

angular region of the sky so that the total array observed the entire night sky

[12]. Fly’s Eye II consisted of 36 spherical mirrors, with 15 PMTs located at

the focal plane of each mirror. Fly’s Eye II observed one half of the night sky,

in the direction of Fly’s Eye I [11]. The Fly’s Eye detector observed the highest

energy cosmic ray every detected [27] and proved that cosmic rays could be

successfully recorded using the fluorescence method of detection.

1.2 HiRes

In 1993 a single-site prototype High Resolution Fly’s Eye detector (HiRes) was

built on the site of Fly’s Eye I. The prototype HiRes overlooked the Chicago

Air Shower Array (CASA) and the Michigan Muon Array (MIA). This arrange-

ment allowed for a collaboration to exist between the three projects to study

correlations between the different UHECR measurement techniques. The pro-

totype was operational for two years before being succeeded by the completed

detector. The completed HiRes detector consisted of two fluorescence detec-

tors spaced 12.6 km apart. The HiRes I site was completed in 1998 and the

HiRes II site in 1999. HiRes I consists of 22 spherical mirrors 2 m in diame-

ter. The 256 PMTs are positioned at the focal plane of each mirror, behind a

300-400 nm UV bandpass filter. The detector views the full azimuthal range

of 360◦ and an elevation of 2◦ to 17◦ above the horizon. HiRes II consists of


43, 2 m diameter spherical mirrors with 256 PMTs situated at each mirrors

focal plane, behind a UV band-pass filter of the same wavelength range used

in HiRes I. The detector views the full azimuthal range of 360◦ with an eleva-

tion range of 3◦ to 30◦ above the horizon. The HiRes detector continues the

studies begun with the Fly’s Eye detector and first demonstrated the strength

of being able to detect an EAS using both the fluorescence technique and an

array of surface detectors [13].

1.3 Pierre Auger

The Pierre Auger detector is the first fully integrated hybrid detector to em-

ploy two of the techniques used to observe UHECR. Two sites will be built,

the southern site which is under construction in the province of Mendoza in

Argentina and a proposed northern site, to be constructed in southeast Col-

orado, USA [53]. The southern site consists of two types of detectors. The

completed areas of the detector are currently recording events with both fluo-

rescence and surface detectors. The surface array will consist of 1600 surface

Cherenkov detectors that are based on the detectors used by the Havarah Park

array. The four fluorescence detectors that will overlook the array are based

on the detectors pioneered by the Fly’s Eye detector in Utah. The two tech-

niques can only be run together about 10% of the time due to the constraint

of running the fluorescence detectors on clear moonless nights.

2 The Pierre Auger Fluorescence Detectors

The fluorescence detectors of the Pierre Auger Project are designed to enable

scientists to observe the growth of an air shower as it develops throughout

the atmosphere. Three of the four fluorescence detectors are operational at

the site in Argentina. These are Los Leones, completed in 2003, Coihueco,

completed in 2004, and Los Morados completed in 2005. Since fluorescence

light is produced in proportion to the energy the initial cosmic ray deposits

in the atmosphere, these detectors can accurately determine the initial energy

of a cosmic ray in a model independent way. The fluorescence technique can

record the actual depth at which the air shower maximum occurs and is able

to extrapolate the likely mass of the cosmic ray particle from that depth.

2. THE PIERRE AUGER FLUORESCENCE DETECTORS 41

Each detector is composed of 6 spherical mirrors, 3.4 m in diameter accom-

panied by 440 PMTs positioned in the focal plane of a mirror. The six mirrors

of each site combine to view an azimuthal angle of 180◦ and an elevation angle

range of 2◦ to 30◦ above the horizon. The detectors are placed on the edges

of the array of surface detectors as in Figure 3.1 as this configuration provides

the maximum possible detection area with four fluorescence detectors.

2.1 Physical Layout

The fluorescence detectors are each composed of four separate parts as in

Figure 3.2, the UV filter, the corrector ring, the spherical mirror and the

camera [54].

A UV band pass filter, fitted to the aperture of the detector, reduces the

effect of noise signals resulting from the night sky background. This filter is

fitted behind an external shutter which, when closed, provides a light-tight

environment that stops photons flooding the camera when it is not in opera-

tion. The UV filter is composed of 3.25 mm thick glass and acts like a window

to prevent dust from entering the enclosure the mirrors are housed in. The

filter has a transmission curve that peaks at 85% at 350 nm and drops to al-

most 20% at 300 and 400 nm and is thus matched to the spectrum of nitrogen

fluorescence shown in Figure 2.4.

A corrector ring is attached to the diaphragm of the detector to enhance

the light collecting area of the mirrors [55]. The ring is circular with an

external radius of 1.10 m and an internal radius of 0.85 m. It is divided into

24 segments. Each segment is made of UV transmitting glass and is machined

into an asymmetrical profile that will account for the spherical aberration of

the mirror. The ring ensures that the angular size of a light spot is no greater

than 0.5◦, or one third of a camera pixel, anywhere on the focal plane.

The mirrors used for each detector are segmented into 6 x 6 square ele-

ments, each element 60 cm by 60 cm in size, creating a total area of 12.96 m2.

The radius of curvature for each mirror is 3.4 m. Two techniques were used

to manufacture the mirrors, the first used aluminised high quality glass mir-

rors and the second used a special aluminum alloy that was then covered in a


Figure 3.2: The layout of one of the six mirror bays associated with eachdetector. The photons from the EAS pass through the shutter to be filteredby the UV filter. The corrector ring at the diaphragm reduces the effect ofmirror coma aberrations. The camera consists of 440 PMTs which collect thephotons and are connected to data acquisition electronics.


Figure 3.3: A diagram of six Mercedes Stars positioned around a pixel. Theunits are based on simple Winston cones and will collect most of the light thatdoes not fall directly on a pixel.

layer of Al2O3. Both types of mirror are used as the performance of each type

exceeded the initial specifications placed on the mirror. The mirror elements

were mounted on a rigid support structure that allows each part to be aligned

independently.

The camera mounted in front of every mirror consists of (440) hexagonal

PMTs arrayed in 20 columns and 22 rows as shown in Figure 3.4. Every pixel

views an angular size of 1.5◦ by 1.5◦ on the sky. Each PMT is mounted in a hole

drilled in an aluminum block and the PMTs are placed in a hexagonal pattern

to provide the maximum coverage of the image plane. Between each of the

pixels is a space caused by the mounting technique as the holes drilled in the

aluminum block cannot be spaced too close together without compromising

the integrity of the mount. To maximise the light collection capabilities of

the camera, optical reflecting surfaces based on Winston Cones are placed

in between the pixels. These surfaces shown in Figure 3.3 are referred to as

‘Mercedes Stars’ in relation to the shape of each unit. Each star is placed at

the vertex of three camera pixels to form a reflecting surface with a hexagonal

shape that surrounds every PMT. These surfaces increase the light collection

capabilities of a camera at the border of each PMT, from an efficiency of 50%

to 90%.


Figure 3.4: The patterns of allowable pixel patterns that the second level trig-ger associates with an event. Rotation and mirror reflections of each patternare accounted for, as are patterns where one inside pixel is missing.

2.2 Electronics

Behind the recording of an activated PMT are electronics that process the

time and orientation of any signal with respect to the camera and decide if

the flash was generated by a real cosmic ray [15]. Each PMT is connected

to a series of electronic circuits that process the signal before transferring it

to a buffer where digital filters determine its resemblance to an event. The

electronics are composed of the initial, signal receiving analogue electronics

and the trigger processing digital electronics. The analogue aspect consists of

the head electronics and the front-end boards. The head electronics are the

first processing step performed on any signal ‘seen’ by a PMT. They provide

high voltage biasing, signal driving, and a test pulse. The signal from a head

electronics unit is received by one of twenty front-end boards attached to each

camera. Every front-end board digitizes the signals from 22 pixels [56] with a

digitization sampling period of 100 ns. Each digital signal is processed in the

digital part of the front-end board where the first level trigger is implemented.


The First Level Trigger examines the ADC values of each pixel as they

are processed. When the running sum of ten previous samples in the camera

exceeds an adjustable threshold value, the pixel is marked as having a signal.

After this running sum has dropped below the threshold value, the time of

the signal is extended by 20 µs, to give each pixel a common overlap time for

event coincidence [15]. The signal is then passed to a buffer where a possible

coincidence between pixels can be checked by the second level trigger.

The Second Level Trigger (SLT) recognises the pattern the triggered pix-

els make on the camera within a 1 - 32 µs time constraint. Figure 3.4 shows

the five patterns of pixel correlation recognised by the trigger that will ensure

the pixels have formed a straight track. The trigger accepts patterns that are

rotated or mirror imaged to those in Figure 3.4 and allows that one pixel in

the middle of the pattern may be missing [56]. The SLT can read across the

face of the camera in 1 µs, searching each column for recognised patterns of

triggered pixels. When a coincidence between pixels is observed, the signals

are passed to computers associated with each mirror (Mirror PC’s) and are

digitally stored before the third level of trigger is applied to the data.

The Third Level Trigger uses the time structure of each event to ensure

the pulse has run across the pattern in a continuous way. It requires that two

second level triggers have been recorded within a predetermined time frame

and that the combined track length is at least six pixels long. EAS track times

are generally between 400 ns and 10 µs and this test on the timing of coincident

pixels will reject fast Cherenkov flashes, nearby muons and any direct hits on a

PMT. Slower moving noise events are also rejected, such as satellites, aircraft,

planets and stars.

2.3 Reconstruction

After the events have passed the triggering requirements of the electronics they

are stored in the central computing facility at Malargue [57]. These data will

then be processed by the reconstruction software written specifically for the

Pierre Auger Project. The calculation of the initial energy of a cosmic ray

and the determination of its spatial geometry are the properties of the cosmic

ray that are sought by the project. The Offline software is written in C++ to


ensure portability and possesses a modular nature to allow members of the

project to implement their own changes and improvements. The software can

be roughly divided into three sections, the input and manipulation of the raw

data, the application of physical models and the output of the final analysis of

the properties of the cosmic ray. The initial task of the reconstruction software

is to determine the amplitude of the signal across the camera with respect to

a measured background signal, and to perform a final check on the event to

remove any noise events that may have passed the three levels of trigger. The

physical models that define the response of a detector are used to transform the

data to a profile of the real photons that passed the diaphragm as a function of

time. The timing and orientation of the triggered pixels describes the spatial

geometry of the event and, when the atmospheric effects are accounted for,

the number of fluorescence photons produced by an EAS can be derived. This

number is in direct proportion to the amount of energy the initial cosmic ray

has deposited in the atmosphere and hence the initial energy of the particle.

See Chapter 4 for a more in-depth review of the reconstruction software used

by the project.

2.4 Atmospheric monitoring, the Laser system

An estimate of the attenuation suffered by fluorescence light between an air

shower and a detector is vital to the calculation of the amount of energy de-

posited in the atmosphere by a cosmic ray. This requires an accurate knowl-

edge of the scattering effects of atmospheric molecules and aerosols, described

by Rayleigh and Mie principles, respectively. The Rayleigh phase function

(see Chapter 2) is well known and follows the mathematic formula given by

Equation 2.15, while the attenuation coefficients are dependent on the atmo-

spheric density and temperature. These factors are measured for the Auger

project through the use of radio sondes in weather balloons as were launched

by Keilhauer et al. [2003] [58] from Los Leones, Coihueco and the town of

Malargue.

Monitoring the variable aerosol attenuation effect is more difficult. The

main monitoring system is based on that proposed by Roberts [2001] [59] and

consists of a laser positioned at the center of the array, which fires vertical laser

beams into the atmosphere at specific intervals. The laser is a BigSky 355 nm

5mJ frequency tripled yag laser mounted in a temperature stabilising rack.

3. THE PIERRE AUGER SURFACE DETECTORS 47

The laser is connected to a GPS module that fires the laser after a specific

number of nanoseconds past a GPS second. The power of each laser shot is

transmitted to a recording station by a radio or cell phone modem and the

whole array is powered by solar panels. These laser shots are identified from

real events by the GPS nanosecond they occur at. Since the initial intensity

of the laser and its orientation in space are known, it is simply a matter of

accounting for the Rayleigh attenuation suffered by the laser beam and then

reconstructing the aerosol scattering properties.

An additional atmospheric monitoring system was proposed by Cester et

al [2001] [60] and consists of four steerable LIDAR telescopes positioned at

each fluorescence detector site. Each LIDAR telescope contains a pulsed laser

beam and a receiver telescope. The pulsed laser beam is capable of shooting a

5 ns pulse of UV light (at 355 nm) into the atmosphere. The receiver telescope

consists of up to four 0.5 m2 parabolic mirrors each with an associated PMT.

This unit points in the same direction as the laser and measures the return-

ing scatter of the laser pulse as a function of time. The determination of the

backscatter and aerosol attenuation coefficients is completed through the use

of inversions as proposed by Klett and Fernald [61, 62, 63]. The problem with

these techniques is their inability to solve for both the backscatter and atten-

uation coefficients simultaneously. Hence the LIDAR system is complemented

by CIMEL Sun photometers which measure the intensity of well known stars

to determine the atmospheric aerosol optical depth independently [64]. The

backscatter coefficients can also be determined by measuring the Raman light

backscattered from atmospheric nitrogen, but this light is very faint and hard

to measure accurately. Since there is so much ambiguity present in the deter-

mination of the aerosol attenuation coefficients using the LIDAR system, it is

yet not relied on as the main atmospheric monitoring system.

3 The Pierre Auger Surface Detectors

The surface detectors of the Pierre Auger Project are based on those developed

for the Havarah Park array. Essentially the detectors are tanks of water that

act as Cherenkov radiators, with PMTs situated to detect the flash of light

produced by the high energy particles of an air shower as they move through

the tank. The number of tanks deployed as of the 3rd of March 2006 is 1124


Figure 3.5: A diagram of a surface detector showing the positions of the PMTs,the solar panel and the antenna each detector uses to communicate with thecentral facility.

and the number operational is 928. The surface detectors are able to run

continuously as they are not subject to the light produced by either the Sun

or the Moon. However, the tank array can only measure the two dimensional

front of the air shower as it hits the ground and so is limited in its ability

to accurately reconstruct the initial properties of a cosmic ray. The surface

detectors rely on the current level of understanding of particle interactions

at and beyond current accelerator energies. The Large Hadronic Collider is

expected to be able to create collisions with lab frame energies of 4× 1017 eV

[65] which is still three orders of magnitude below the most energetic cosmic

ray detected by the Fly’s Eye detector in 1992. Hence for any cosmic ray

that is detected with an energy above that probed in particle accelerators, the

calculation of the initial properties of the cosmic ray relies on our ability to

accurately extrapolate the interaction properties of highly energetic particles.

3.1 Physical layout

The tanks are placed at regular positions on a triangular grid spaced at 1.5

km intervals. They are constructed from molded polyethylene and are 3.6 m

3. THE PIERRE AUGER SURFACE DETECTORS 49

in diameter and 1.55 m high. They are filled with 12 kL of high purity water.

Three PMTs of diameter 20 cm are placed at the top of each tank, looking

down into the water. Each tank is powered by two solar panels attached to

the top of the tank, and the tanks keep in contact with the central facility

by means of a specifically designed radio system as can be seen in Figure 3.5.

Each tank is an autonomous unit, recording signals from EAS and relaying

recorded signals through the communications antenna positioned on top of

every tank [15].

3.2 Reconstruction

The first step in the reconstruction of an air shower from the data collected

by the surface detectors, is to fit a plane front to the timing information of the

triggered surface detectors. This plane defines the zenith and azimuth angles

of the air shower to an accuracy within two degrees [15]. The location of the

core position of the air shower is determined through an interpolation of the

shower signal in the triggered detectors. A lateral distribution function (LDF)

can then be fit to describe the expected shower particle density at ground

level for any distance from the core. The Pierre Auger Project has access to a

variety of LDF’s to describe the properties of an air shower.

The energy of the initial cosmic ray is related to the normalisation of the

LDF which we approximate to enable us to determine the signal, S(1000),

that would be recorded in a tank 1000 m from the core. The arrival angle

of the air shower needs to be accounted for to improve the use of S(1000) in

determining the primary particle energy. Shower slant angles are accounted for

using constant intensity curves to determine how S(1000) depends on the slant

angle (θ) for fixed energies. This constant intensity curve, CIC(θ), is used to

find S(1000) at the median Auger zenith angle of 38◦. It defines the parameter

S38, the signal in the detector 1000 m from the core when the shower has an

angle of 38◦ to the vertical. S38 is related to S(1000) by,

S38 =S(1000)

CIC(θ)(3.1)

Typical curves for CIC(θ) can be found in Sommers (2005) [66]. The energy

reconstruction of the surface detectors has been calibrated using the fluores-

cence detectors, where the energy of an air shower calculated by the fluores-


cence detectors is plotted against the S38 parameter [66] which has produced

a model independent determination of the energy of an air shower through,

E = 0.16× S1.0638 = 0.16×

[S(1000)

CIC(θ)

]1.06

(3.2)

4 The Stereo Viewing of Air Showers

The Pierre Auger Detector measures cosmic rays using both a surface and

a fluorescence detector technique, allowing for better reconstruction of the

properties of a cosmic ray than could be found by either technique alone. In

addition to this, the higher energy events, above 5× 1018 eV may be collected

in stereo by two or more fluorescence detectors. This stereo viewing of an event

enables extra reconstruction techniques to be applied to the data as detailed

in the following sections.

4.1 Geometry

The precision of the reconstruction of the spatial geometry of an air shower

can be improved when it is calculated from the data collected by two fluores-

cence detectors. To calculate the geometry of an air shower, a plane is fitted

to the arc created by the projection of the triggered pixels on the hemisphere

of the sky for each detector (see Chapter 4 Section 1.2). This shower-detector

plane (SDP) contains the axis of the air shower and a point representing the

detector. In monocular reconstruction, the timing of the camera pixels as they

are triggered is the only resource that can be used to find the geometry of the

shower axis within the SDP. In stereo, the intersection of the two SDP planes

found from the data collected by each detector defines the shower axis as in

Figure 3.6. The arrival time of the light produced by the air shower is used

to increase the accuracy of the reconstruction for an event recorded in stereo.

A χ2 minimisation is performed on the timing information from each detector

and the geometry of the shower axis to determine a more precise result. This

additional reconstruction step is especially useful when the opening angle be-

tween two detector SDPs is very small. In this case the vector cross product

of the two SDPs cannot be relied on to produce an accurate result. Hence, for

small angles of intersection the accuracy of the stereo geometrical reconstruc-

tion is low without the additional information provided by the triggering time

4. THE STEREO VIEWING OF AIR SHOWERS 51

Figure 3.6: The intersection of two SDPs defines the shower axis when anevent has been recorded in stereo.


of each camera pixel for each detector that recorded the event.

4.2 Atmosphere

The correction of the attenuation effect due to the scattering off aerosols in

the atmosphere is of vital importance when using the fluorescence technique to

measure UHECR. The scattering of fluorescence light off aerosols is described

by the Mie theory of scattering. A description of the density of aerosols within

the atmosphere follows no mathematically simplistic model, as aerosols are of

variable density and size at any particular time, in any particular location.

If we assume that changes in aerosol density with height are more important

than those along horizontal distances, then this attenuation may be calculated

from the fluorescence light collected by two detectors. Since a detector that

is positioned further from an air shower will observe light which has trav-

eled through a larger volume of the atmosphere, if the degree of attenuation

correction applied to that shower is higher than the correct value, the light

reconstructed to be produced at the air shower track will appear brighter than

that reconstructed using a detector situated closer to the EAS, and vice versa

for an applied aerosol concentration that is too low. Only when the correct

value of attenuation due to scattering from aerosols is applied to the data, will

the fluorescent light profiles reconstructed by both detectors produced along

the air shower be comparable. These considerations are discussed in detail in

Chapter 5.

This technique could also be used to calculate the amount of scattering and

attenuation that occurs due to Rayleigh scattering, which is a larger effect on

the amount of fluorescence light recorded by a detector. However, at these

wavelengths, Rayleigh scattering is due to atmospheric molecules which are

easier to quantify than the aerosol density. Hence, it is more logical to use this

technique to calculate the amount of Mie scattering suffered by the fluorescence

light generated by an air shower.

4.3 Cherenkov Light

Cherenkov light produced by an EAS is forward directed and very rarely ob-

served by a Pierre Auger fluorescence detector unless scattered out of its trajec-

tory by interactions with molecules or aerosols. To account for this proportion


of scattered Cherenkov light, the amount of Cherenkov light produced by an air

shower is calculated in an iterative manner as described in Chapter 4. When

a shower is pointed towards a detector a great deal of the Cherenkov light cre-

ated by an air shower is observed by the detector and it becomes impossible to

distinguish it from the fluorescence light as the two forms of light are produced

at wavelengths that are within the detectors acceptance, between 300 nm to

400 nm. In such cases that have been viewed in stereo, only one detector

will be highly contaminated with Cherenkov light due to the large distances

between the fluorescence detector sites. Hence it becomes possible to use the

profile of the Cherenkov light produced on the air shower track as correctly

accounted for by the detector not contaminated with Cherenkov light, to cal-

culate the amount of Cherenkov light recorded by the detector swamped with

Cherenkov light. This is because the amount of Cherenkov light produced

by an air shower along its track is unique for any one shower. This technique

may be used in the reconstruction chain for events with incorrectly determined

amounts of Cherenkov light produced along the air shower track in the atmo-

sphere. Chapter 6 details how this technique has been used to improve the

accuracy of the reconstruction of events recorded in stereo between October

2004 to April 2006.

5 Chapter Summary

The Pierre Auger detector is the largest cosmic ray detector ever built, and

it employs two distinct detection methods to produce a “hybrid” detector. It

will study the problem of cosmic rays at the very highest energies, and will

record more events than have been analysed by any other detector to date.

The detector consists of 1600 surface tanks arrayed on a grid over an area of

3000 km2. The four fluorescence detectors associated with the project over

look the array. Each of them contains a series of six mirrors that each view

an angular range of 30◦ x 30◦. This thesis is concerned with the fluorescence

technique of measuring cosmic rays, in particular using the recording of an

air shower from two fluorescence detectors, called the stereo viewing of an

EAS. Additional reconstruction techniques exist when an air shower has been

captured in stereo and can be used to calculate the initial properties of a

cosmic ray with a higher degree of precision.

Chapter 4

The Simulation and

Reconstruction Programs

The fluorescence detectors of the Pierre Auger Project record the light emitted

by an extensive air shower (EAS). This recorded light must be throughly ex-

amined to extract the information it possesses about the primary cosmic ray.

To determine the initial properties of an UHECR, extensive reconstruction of

the recorded light track is required to discover, first the air shower geometry in

space, and finally the initial energy the cosmic ray possessed before it collided

with the atmosphere. The reconstruction of an air shower by the Pierre Auger

Observatory is performed by C++ programs that have been specifically written

for the project. The accuracy of these programs is only as good as our knowl-

edge of the relationship that exists between an EAS and the atmosphere. This

is explored through the use of simulation routines that mimic the effect the at-

mosphere will have on a UV light pulse. The data output by these simulation

routines can be run through the reconstruction routines to test how accurate

the reconstruction routines are, and to compare the simulation output with

real data.

1 The Reconstruction Procedure

The procedure that calculates the initial properties of a cosmic ray from the

recording of the amount of light generated by an extensive air shower, relies

on having a sound knowledge of the physical properties of the atmosphere

and the fluorescence detectors. For the process to work we must know the

55

56 CHAPTER 4. THE AUGER PROGRAMS

light collection properties of the cameras, and be able to find the position

of the air shower with respect to a detector. Then an understanding of the

physics behind atmospheric scattering, fluorescence emission and Cherenkov

production will allow the initial properties of a cosmic ray to be found, as

outlined below.

1.1 Light from camera to light at diaphragm

The cameras for every fluorescence detector used by the Pierre Auger project

measure the number of photoelectrons that have been recorded in a photo-

multiplier ‘pixel’ as a function of time. The triggered signal is time dependent

and will be recorded by the camera pixels in a simultaneous way. The recon-

struction programs break the event time duration into 100 ns time segments

and sum the light recorded by each triggered pixel within each 100 ns. This

generates a profile of the total light recorded by the camera as a function of

time. To convert these electronic ADC counts to the number of photons that

passed the diaphragm (See Chapter 3) of a mirror bay, the detectors are rou-

tinely calibrated with a Tyvek coated drum (2.5 m in diameter, 1.4 m deep).

The drum is coated in Tyvek because Tyvek has good reflectivity in the UV.

The drum contains two pulsed UV LEDs which radiate at 375 ± 12 nm and

are mounted in the center of the drum, pointing towards the back wall of the

drum so that only reflected light can be seen by the camera. The drum is

attached to the outside of a mirror bay aperture and emits a uniform field of

light that is recorded by a camera [67]. These drum calibrations can be used

to remove inconsistencies in the gain between different photomultiplier tubes

and to determine ‘calibration constants’, that describe the conversion from

ADC counts at the camera to photons at the diaphragm.

1.2 Calculating the Air Shower Geometry

The geometry of an air shower track must be precisely calculated to make an

accurate determination of the intrinsic brightness of a cascade. We reconstruct

the shower axis by first noting that the cameras of every detector can be said

to view part of the celestial sphere upon which all shower tracks will seem to

lie. The pattern of an event on the camera will describe an arc across that

sphere which, when using the position of the detector, can be used to calculate

1. THE RECONSTRUCTION PROCEDURE 57

Figure 4.1: The Shower Detector Plane of an event which includes the line ofthe shower axis and the point of the detector. The unit vector normal to theSDP (n [θ, φ]) and the pointing vector of the ith pixel (ri[θ, φ]) are shown.


Figure 4.2: An air shower track on two Coihueco cameras. This event hasbeen reconstructed as an intrinsically bright shower situated many kilometersaway from the detector.


a plane in space, the shower detector plane (SDP) within which the trajectory

of the EAS must lie as seen in Figure 4.1. Each camera pixel points to the

celestial sphere in the direction of ri[θ, φ]. The SDP is ideally formed from

the set of ri[θ, φ] vectors that are defined from an event camera image and

described by the azimuthal and zenith angles of the unit vector normal to the

plane. We find the unit vector normal to the SDP, n [θ, φ] by minimising,

χ2 =∑

i

wi (n [θ, φ] · ri [θ, φ])2 (4.1)

Here the signal amplitude recorded by the ith pixel is taken as the weight,

wi [15]. When the track on the camera, produced by an EAS is long, the

calculation of the SDP will be the most precise. Hence intrinsically bright

showers (i.e. those produced from the highest energy cosmic rays) and showers

that fall close to a detector will have long, well defined tracks across a detectors

camera such as the one seen in Figure 4.2.

Mono Geometrical Reconstruction

To find the orientation of the shower within an SDP when only one fluores-

cence detector has recorded an event, the timing sequence of the arrival light

pulse is used. This determines three additional parameters that describe the

orientation of the shower axis within the SDP as shown in Figure 4.3. These

variables are the shortest distance from the detector to the shower axis (Rp),

the time at which the shower front is at a distance of Rp from the detector

(t0) and the angle the air shower axis makes with the ground within the SDP

(χ0). In addition to these parameters the angle χi is the angle between the

ground and the line from a point P on the shower axis to the detector. It is

the observational angle within the SDP of the ith photomultiplier tube. The

time, ti,exp at which light is expected to arrive at the detector from the air

shower in the field of view of pixel i, is,

ti,exp = t0 −Rp

ctan

(χ0 − χi

2

)(4.2)

This expected arrival time of the light is compared to the measured arrival

time of light in each pixel, ti,meas and minimised to find the best fit of the


Figure 4.3: Within the SDP, variables are used to define the geometry of theair shower. χ0, Rp and t0 define the axis and position of the shower while tiand χi define the position of a point, P, on the shower axis.

shower geometry [15] through the χ2,

χ2 =∑ (ti,exp − ti,meas)

2

σ2i

(4.3)

σi is the uncertainty in the measured time.

Stereo Geometrical Reconstruction

When an air shower has been viewed in stereo, the geometry of the shower

axis can be found by taking the cross product of the two unit vectors normal

to the SDPs that are calculated for each detector. So if the normal vector of

the SDP found for detector 1 is n1[θ, φ] and the normal vector of the SDP

found for detector 2 is n2[θ, φ], then the vector describing the orientation of

the shower axis for the zenith and azimuthal angles θ and φ will be,

A[θ, φ] = n1[θ, φ]× n2[θ, φ] (4.4)

To increase the accuracy of the shower axis geometry the arrival time of

the light pulse at each detector and the pointing direction of each pixel that


recorded the event are used. For the stereo analysis the timing and pixel

pointing information need to be summed for all the detectors (Det) that viewed

an event. Like the mono geometrical reconstruction the difference between

the measured and the expected arrival time of the light pulse are minimised

in a χ2 function. The original SDP normal angles are adjusted according to

typical minimisation principles and then the geometry of the air shower axis

is recalculated for each detector using Equation 4.4. For the Eth detector,

the time of arrival of the light pulse tEi,exp is calculated for the ith 100 ns

time slice of the event as it moved across the camera surface. This is then

compared to the measured arrival time of the light pulse, tEi,meas through the

timing minimisation, χ2time,

χ2time =

Det∑E

∑i

(tEi,meas − tEi,exp

∆tEi,meas

)2

(4.5)

Here, the ∆tEi,meas are the errors in the measured light pulse at the detector.

Using the same adjustments on the SDP, the angle, αEk,exp, between the normal

to the SDP, nE[θ, φ] and the pixel pointing direction, rEk[θ, φ] are calculated

for the kth pixel that recorded a signal, so,

cos αEk,exp = nE[θ, φ] · rEk[θ, φ] (4.6)

This angle should be α = 90◦ and has an error set to be ∆α = 0.35◦ which is

related to the pixel sizes, so the χ2 in the SDP, χ2SDP is then found from,

χ2SDP =

Det∑E

∑k

(α− αEk,exp

∆α

)2

(4.7)

The total χ2 that will be minimised to find the best fit of the stereo axis

geometry is the sum of χ2time and χ2

SDP ,

χ2 = χ2time + χ2

SDP (4.8)

This additional fit to the air shower geometry is most useful when the angle

between two SDPs is very small. In this case the cross product between the

two SDPs will not find the true geometry and our calculation of the air shower

geometry becomes reliant on the timing χ2. When this happens the accuracy


of a stereo reconstruction of the air shower geometry becomes only a little bit

better than that of a mono reconstruction of the geometry, and this is only

because two sets of timing information are available.

1.3 Accounting for the Atmospheric Scattering

Light at wavelengths between 300 nm and 400 nm is relatively unaffected by

atmospheric absorption but is subject to attenuation due to the process of

scattering. In this wavelength range, scattering off molecules can be described

by Rayleigh principles but the scatter off aerosols must be described with the

Mie theory. The Auger reconstruction or simulation programs break the light

recorded by a detector into 16 wavelength bins that range from 280 nm to

415 nm. Each wavelength bin is treated for the effect of atmospheric scatter

separately before being summed to derive the total light produced along an air

shower axis. The molecular phase function of Rayleigh scattering is fixed and

can be described by Equation 2.15 (in Chapter 2). The Rayleigh transmission

factor is dependent on the wavelength of the light being observed and the

density model of the atmosphere. The Pierre Auger project measures the

average density and temperature profiles of the atmosphere every month to

create an accurate representation of Rayleigh scattering. The Mie scattering

parameterisation uses Longtin’s desert aerosol phase function [50] and the

Mie transmission factor is measured at regular intervals by a series of laser

measurements that are carried out every night the detector is operational [68].

1.4 Cherenkov Subtraction

At this point in the reconstruction procedure we can calculate the amount

of light produced by an air shower by accounting for the geometry of the

shower and the scattering and attenuation effects of the atmosphere. If we

assume that all the light calculated to have been emitted by the air shower is

solely due to fluorescence, then we can work out how many charged particles

are present in the cascade. However, there will be Cherenkov light present

in any light profile of the air shower track and, to account for any direct

or scattered Cherenkov light recorded by a detector, an iterative procedure

is employed. The amount of Cherenkov light produced by an extensive air

shower depends on the number of charged particles present in the cascade,


which we can estimate from the amount of fluorescence light recorded by the

detector and a knowledge of the fluorescence yield function as described in

the next section. This gives us an initial guess of the amount of Cherenkov

light that may be present in the measurement of the air shower brightness.

Within this Cherenkov subtraction process, that amount of Cherenkov light

is removed from the light recorded by the detector and the process described

above is repeated for ten iterations. As long as the amount of Cherenkov

light recorded by a detector is a small percentage of the total amount of light

recorded by a detector, which is generally the case, this process will calculate

the amount of Cherenkov light produced by an EAS.

1.5 Calculation of Initial Energy and Other Parameters

At this stage in the analysis we have a distribution of fluorescence photons

emitted at the shower axis as a function of atmospheric depth, L(X). Using

the fluorescence yield, Y (X), given in Nagano et al. (2004) [44], or originally

by Bunner (1967) [19], we can calculate the distribution of charged particles at

a given depth along the air shower axis, Nch(X) which is called the longitudinal

profile,

Nch (X) =L (X)

Y (X) ∆l(4.9)

Here ∆l is the discrete air shower track length that is emitting fluorescence

radiation in an interval around the depth X.

The fluorescence yield function presented by Bunner (1967) [19] and later

by Nagano, et al. (2004) describes the dependence of the yield on the at-

mospheric temperature and pressure, for each of the 16 wavelength bins the

UV light is split into by the reconstruction or simulation program. The flu-

orescence yield is summed over all the wavelength bins to arrive at the total

fluorescence yield at depth X which is used in Equation 4.9

The longitudinal profile described in Equation 4.9 is now fitted with some

function that describes the growth and decline of a cascade throughout the

atmosphere. The parameterisation used in the Pierre Auger project is the

Gaisser-Hillas function [43] and is described in Chapter 2, but is repeated here

for completeness,


N(X) = Nmax

(X −X0

Xmax −X0

)Xmax−X0λ

exp

[Xmax −X

λ

](4.10)

See Chapter 2 Section 2.1 for a discussion on all the relevant terms. An

iron nuclei will interact with the atmosphere at a shallower depth than a

proton, due to its increased cross sectional area. In addition, an iron nuclei

will disintegrate soon after its first interaction with the atmosphere, and every

one of its nucleons will initiate a sub-shower with a fraction of the energy of the

initial cosmic ray. Now, the depth at which the air shower maximum occurs,

Xmax, for a fixed energy is related to how deeply a cosmic ray penetrated

the atmosphere before initiating a cascade and how many nucleons made up

the primary cosmic ray. A plot of Xmax against the cosmic ray energy for

many events will indicate the average mass composition of cosmic rays at

certain energies (see Chapter 1) and is called the elongation rate. Xmax is a

very useful parameter that only the fluorescence technique can measure in an

accurate model independent way.

All of the energy of the initial cosmic ray is split among the particles

and radiation that makes up an air shower. All of the charged particles in

the shower produce fluorescence light. Since we know the fraction of energy

that is expended by those charged particles in producing fluorescence light,

the fluorescence yield, we can calculate the amount of energy the cosmic ray

expended in producing charged particles in the air shower. This energy is

denoted the electromagnetic energy of the cosmic ray, Eem and can be found

by integrating the charged particle distribution,

E =

∫ ∞

0

α(X)Nch(X)dX (4.11)

Here α(X) = dEdX

(X), which is the mean energy loss rate of the particles at

depth X. The rest of the energy of the primary cosmic ray is called the ‘missing

energy’. This energy is not seen through the phenomenon of fluorescence light

because the charged muons do not produce fluorescence light in proportion

to their energy before colliding with the ground. Also, neutrinos produced

in the air shower do not produce fluorescence light. A parameterisation of

this missing energy is given by Song et al. (1999) [69]. It is energy and mass

dependent and at maximum adds some 15 % to the calculation of the inital

cosmic ray energy due to the electromagnetic emission of fluorescence light.

2. RECONSTRUCTION ROUTINES 65

2 Reconstruction Routines

In order to determine the properties of the original cosmic ray we must de-

termine the size and geometry of an air shower. This is done through a com-

plicated set of computer programs which use the image of an air shower on a

detector to determine its geometry. The programs then use the ideas described

above to account for the light attenuation effect of the atmosphere and the

amount of Cherenkov light present within an air shower recording. These ‘re-

construction’ programs form an integral part of the measurement of UHECR

and are rigorously tested to ensure they calculate realistic results. The two

reconstruction programs created for the Pierre Auger Project are called Flores

and the Offline. The Offline software is the most recent of the two programs,

however the Offline was not completed at the start of this project in 2003 and

so my earliest routine uses the Flores software to reconstruct events.

2.1 Flores

Flores is able to read in all FD-DAS, FD-Data Acquisition System compatible

data files generated by either the trigger from a detector that has recorded a

real event, or a simulated data file generated by FDTriggerSim. Flores can only

process the data from one mirror of one detector at a time. It is governed by

three objects, the Data, Actor and Detector objects [70]. The Data objects

control all of the data generated or used by the program, this is where the raw

input data and the processed output data are stored. The Actor objects handle

all of the reconstruction procedures, from the calculation of the geometry of

an air shower, to the calculation of the amount of fluorescence light generated

by the air shower. The Detector objects store all of the data pertaining to the

size and orientation of the entire detector array. Flores is controlled by the Run

Controller, a series of programs that handle the sequencing of the Actors to

determine the reconstruction of an air shower. Figure 4.4 details the sequence

of the Actors within the Run Controller. The raw data and detector geometry

are defined within a Data object that can be accessed at any time during the

processing of the Run Controller. Each Actor recalls the data previously stored

in a Data object and performs reconstruction calculations on the data, then

outputs the results back to a Data object to be accessed by the next Actor.

The CERN package ROOT (’The ROOT Users guide’, http://root.cern.ch/)


Figure 4.4: The basic setup of Flores. The Run Control (represented by thedashed box), controls the sequencing of all the Actors (represented by ellipses).Each Actor can recall or store data in a Data Object and performs the tasksnecessary for the reconstruction of an event.

2. RECONSTRUCTION ROUTINES 67

Figure 4.5: The framework of the Offline consists of discrete modules that canbe processed in any reasonable order the user wishes. The modules access thedata stored in the two data objects, the detector and event objects, but canonly store data to the event data tree.

is used to plot all of the data generated by the program so the last step is to

store all of the data collected in the Data objects to a ROOT compatible file,

or tree.

2.2 Offline

The Offline software is modular and can run multiple events, detectors and

mirrors concurrently. These modules, called processing modules are processed

through the use of the Run-Controller which runs the modules as specified in

an external XML file. Each processing module is set up with three govern-

ing functions, Initial(), Run() and Final(). The Run-Controller accesses each of

these three functions at separate times throughout the procedure. The Ini-

tial() functions are called first and are only processed once for every instance

of the Offline. The Run() functions contain all of the functions that control

the reconstruction of an event and are processed for every event that is run

through any instance of the Offline. The Final() functions are called once at

the end of any instance of the Offline and provide the signals necessary to end

the program. The reconstruction procedure is performed by these modules but

the data stored or needed by the modules are accessed through two objects,

the Event and the Detector. The interaction between these objects and the

processing modules is indicated in Figure 4.5. The Event objects can be ac-

cessed to read or write the information calculated by the processing modules

as they reconstruct an event. These objects store all of the information about


the shower, its size, orientation and the amount of Cherenkov light it has pro-

duced. The Detector objects provide a read-only interface that is able to access

all of the static data members, like the detector description, Cherenkov and

fluorescence models to be used and the description of the atmospheric density

and clarity (i.e. scattering properties). Again, all the data are output to a

ROOT tree where the data can be visually accessed after the reconstruction

procedure has finished. See reference [57] for a more complete account of how

the Offline software works.

3 Simulation Routines

In addition to the reconstruction routines it is very important that the project

run simulations of air showers both to test the accuracy of the reconstruction

routines, and to explore new theories about the extensive air showers created

by UHECRs. Two simulation routines have been used by the project, these

are called FDSim and the Offline simulation software package. The only one of

these simulation packages I used was FDSim, the earliest simulation software

package created for the Pierre Auger Project.

3.1 Simulation of a Shower

When simulating an air shower the same physics as described in Section 1 is

used, but in a different sequence. The initial energy and geometry of the shower

are specified first and these define the amount of Cherenkov and fluorescence

light that will be recorded by a detector. The showers can be simulated from a

simple Gaisser-Hillas parameterisation or through a shower particle simulation

software package such as CORSIKA [71].

3.2 FdSim / FdTriggerSim

There are four basic components that make up the FDSimPreProd software,

‘Atmosphere’, ‘FDSim’, ‘FDTriggerSim’ and the ‘Utils’ as can be seen in Fig-

ure 4.6. The Utils package requires the external XERCES-C package to make

it fully accessible to the other packages. The Atmospheric package relies on

the external CLHEP routines and uses functions defined in the Utils package

to simulate the workings of the atmosphere. FDSim uses the data and func-

3. SIMULATION ROUTINES 69

Figure 4.6: The four packages of the FDSimPreProd software recall data fromeach other as shown. The three external programs, XERCES-C, CLHEP andROOT are necessary for the FDSimPreProd software to run, perform datastorage, and display data with routines that are incapable of being used byC++ . The final output from FDTriggerSim is in the FDEventLib form whichcan be accessed by the reconstruction software Flores.


tions developed in the Utils and Atmosphere packages to create an event. The

results are exported to a ROOT library where they can be displayed. The

FDTriggerSim package applies triggering criteria and transforms the output

from the FDSim package to be compatible with the FDEventLib file format.

FDTriggerSim also outputs data to a ROOT library to be displayed in a human

friendly format. The dependencies of the four programs with each other and

with the external data storage and manipulation programs called the ‘archi-

tecture domain’ are outlined in Figure 4.6

The Atmosphere package contains all of the atmospheric simulations and

data members used in the calculation of the Rayleigh and Mie scattering and

attenuation, the production of Cherenkov light and the routines that calculate

the fluorescence light generated by an air shower. The models for each of these

processes are outlined in Chapter 2.

The Utils are a series of mathematical and physical constants and functions

that are used at various times throughout the implementation of the FDSim

and FDTriggerSim programs. An example of one of the mathematical func-

tions used by the simulation programs is the vectorial distance function that

calculates the distance between two points.

The FDSim components contain the simulation driver and are the base of all

the simulations routines up to the point where FDTriggerSim is implemented.

The FDSim program consists of four objects, the Atmosphere, Shower, De-

tector and Ray Tracing objects which are called throughout the running of

the program. The Atmosphere object is synonymous with the Atmosphere

package and contains all the routines for calculating the physical processes

outlined above. The Shower object handles the longitudinal profile and the

shower geometry. The Detector object contains all the data pertinent to the

size and orientation of the entire array of detectors. The Ray Tracing object

is only used when an accurate account of the amount of light recorded by a

camera is needed. This object handles how the light rays from a shower will

propagate through the detector and determines which camera pixels will see

which sections of the air shower axis. FDSim accesses the data and functions

stored in the Atmosphere and Utils packages respectively and calculates the

amount of fluorescence and Cherenkov light that will be generated by an air


shower. It then propagates that light through the atmosphere for it to be

recorded by any one of the mirrors of any fluorescence detector of the Pierre

Auger project. FDSim can only calculate the light recorded by any one mirror

for any one detector at a time due to the limitations in the Run sequence of

the program.

The FDTriggerSim package performs the electronic and trigger simulation

that will generate output compatible with the FD-Data Acquisition System

(FD-DAS), the mode which input data must be in to be reconstructed with

the Flores software. FDTriggerSim transforms the data output by FDSim to

mimic the format of real data that are recorded by a fluorescence detector.

See reference [72] for more details on how FDSim operates.

3.3 Offline Simulation Software

The Offline software package is the latest simulation and reconstruction pro-

gram written for the Pierre Auger project. The simulation portion of the pack-

age is essentially FDSim updated to be compatible with the Offline Framework

and hence able to run multiple mirror and detector events. By the time the

Offline simulation software was operational, my project no longer required the

use of a simulation routine and so this software was not used in this thesis. The

accuracy of the reconstruction chain must be reliable and is checked through

the use of simulation routines. The simulation programs are run through the

reconstruction chain and compared with the output of real data. This process

keeps the software up to date and accurate.

4 Chapter Summary

The simulation and reconstruction programs written for the use of the Pierre

Auger observatory have gone through a number of updates and overhauls and

will continue to be updated and improved. The current version of the Offline

software can be relied on to calculate the initial properties of an UHECR.

chapter 1 cosmic rays, their energy spectrum and origin...law spectrum. [1] 4 chapter 1. cosmic rays...

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