( PDF ) Estudo da resolução angular do Observatório Pierre Auger

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Claudia Fracchiolla

Estudo da resolu¸c˜ao angular do Observat´orio

Pierre Auger

A study of the Angular Resolution of the Pierre Auger

Observatory

Disserta¸c˜ao de Mestrado

Disserta¸c˜ao apresentada como requisito parcial para obten¸c˜ao do

grau de Mestre pelo Programa de P´os–gradua¸c˜ao em F´ısica das

Part´ıculas Elementares e Campos do Departamento de F´ısica da

PUC–Rio

Orientador : Prof. Ronald Cintra Shellard

Co–Orientador: Prof. Carla Brenda Bonifazi

Rio de Janeiro

Maio de 2007

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Claudia Fracchiolla

Estudo da resolu¸c˜ao angular do Observat´orio

Pierre Auger

A study of the Angular Resolution of the Pierre Auger

Observatory

Disserta¸c˜ao apresentada como requisito parcial para obten¸c˜ao

do grau de Mestre pelo Programa de P´os–gradua¸c˜ao em F´ısica

das Part´ıculas Elementares e Campos do Departamento de F´ısica

do ??xxxx da PUC–Rio. Aprovada pela Comiss˜ao Examinadora

abaixo assinada.

Prof. Ronald Cintra Shellard

Orientador

Departamento de F´ısica — PUC–Rio

Prof. Carla Brenda Bonifazi

Co–Orientador

Departamento de F´ısica — PUC–Rio

Prof. Ronald Cintra Shellard

Coordenador Setorial do ??xxxx — PUC–Rio

Rio de Janeiro, 30 de Maio de 2007

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ou parcial do trabalho sem autoriza¸c˜ao da universidade, do

autor e do orientador.

Claudia Fracchiolla

Graduou–se em F´ısica na Universidade Sim´on Bolivar na

Venezuela. ...

Ficha Catalogr´aﬁca

Fracchiolla, Claudia

Estudo da resolu¸c˜ao angular do Observat´orio Pierre Auger

/ Claudia Fracchiolla; orientador: Ronald Cintra Shellard; co–

orientador: Carla Brenda Bonifazi. — Rio de Janeiro : PUC–

Rio, Departamento de F´ısica, 2007.

v., 64 f: il. ; 29,7 cm

1. Disserta¸c˜ao (mestrado) - Pontif´ıcia Universidade

Cat´olica do Rio de Janeiro, Departamento de F´ısica.

Inclui referˆencias bibliogr´aﬁcas.

1. F´ısica – Tese. 2. Raios c´osmicos . 3. Observat´orio Pierre

Auger. 4. Detector de Superf´ıcie. 5. Resolu¸c˜ao angular. 6.

Anisotropia. I. Shellard, Ronald C.. II. Bonifazi, Carla. III. Pon-

tif´ıcia Universidade Cat´olica do Rio de Janeiro. Departamento

de F´ısica. IV. T´ıtulo.

CDD: 510

Agradecimentos

Resumo

Fracchiolla, Claudia; Shellard, Ronald C.; Bonifazi, Carla. Estudo

da resolu¸c˜ao angular do Observat´orio Pierre Auger. Rio de

Janeiro, 2007. 64p. Disserta¸c˜ao de Mestrado — Departamento de

F´ısica, Pontif´ıcia Universidade Cat´olica do Rio de Janeiro.

O Observat´orio Pierre Auger, cuja constru¸c˜ao na Prov´ıncia de Mendoza, na

Argentina est´a na sua fase ﬁnal, tem por objetivo medir as caracter´ısticas

dos raios c´osmicos de grande energia. O Observat´orio est´a produzindo dados

desde o in´ıcio de 2004, `a medida em que a rede de detectores vai aumen-

tando. Um dos principais temas de pesquisas, usando os dados produzi-

dos pelo detector, ´e o exame da isotropia na dire¸c˜ao de origem dos raios

c´osmicos energ´eticos. Para isto ´e necess´ario entender-mos a resolu¸c˜ao angu-

lar do detector. Nesta tese, estudamos a resolu¸c˜ao angular dos detectores de

Superf´ıcie (ou detectores de radia¸c˜ao de Cherenkov). O principal elemento

que limita a acuracidade angular dos detectores de superf´ıcie ´e a precis˜ao

temporal do registro dos sinais de chegada dos raios c´osmicos. Este estudo

est´a baseado na compara¸c˜ao dos sinais em um conjunto de tanques que

est˜ao muito pr´oximos um do outro (11 metros).

Palavras–chave

Raios c´osmicos . Observat´orio Pierre Auger. Detector de Superf´ıcie.

Resolu¸c˜ao angular. Anisotropia.

Abstract

Fracchiolla, Claudia; Shellard, Ronald C.; Bonifazi, Carla. A study

of the Angular Resolution of the Pierre Auger Observa-

tory. Rio de Janeiro, 2007. 64p. MsC Thesis — Department of

F´ısica, Pontif´ıcia Universidade Cat´olica do Rio de Janeiro.

The Pierre Auger Observatory, in the Mendoza Province in Argentina, is

in it’s ﬁnal phases of construction. It is aimed at the determination of the

characteristics of high energy cosmic rays. The observatory is producing

data since the beginning of 2004, while the size of the array is increasing.

One of the main topics of research, using the data of Auger, is the study of

the isotropy of the arrival direction of the energetic cosmic rays. For that

end it is necessary to have a good estimate of the angular resolution of

the detector. In this thesis we study the angular resolution of the Surface

Detector (or the Cherenkov radiation detector). The main limiting element

on the accuracy of the angular determination is the timing of arrival of the

particles generated by the cosmic ray. This study is based on the comparison

of the signals in a subset of detectors that are deployed very close one from

the other (11 m).

Keywords

Cosmic rays . Pierre Auger Observatory. Surface Detector. Angular

Resolution. Anisotropy.

Sum´ario

1 INTRODUCTION 1

2 Cosmic Rays 3

2.1 Historical Background 3

2.2 Description 4

2.3 Measuring Cosmic Rays 8

3 Extensive Air Showers 18

3.1 EAS development 18

3.2 EAS propagation 19

4 Auger Observatory 24

4.1 Description 24

4.2 Surface Detectors 25

4.3 Fluorescence Detectors 33

4.4 Status 37

5 Angular Resolution 38

5.1 On an event by event basis 38

5.2 Direct Measurement 48

5.3 Hybrids 50

6 Conclusions 53

A SD Reconstruction 59

A.1 Quality Cuts 61

B Complementary Work 63

B.1 FD shift 63

B.2 Calibration of Camera 64

Lista de ﬁguras

2.1 Cosmic Ray Spectrum. 15

2.2 Cosmic Ray Spectrum zoom. 16

2.3 X

max

as a function of energy. 16

2.4 Energy loss of a proton through interaction with cosmic background

radiation 17

2.5 Comparison of the CR spectrum obtained by AGASA and HiRes 17

3.1 Sketch of the EAS 22

3.2 Lateral distribution for muons, electrons and gamma 23

4.1 Pierre Auger Observatory - Southern array 25

4.2 Picture of a SD station 26

4.3 Charged histogram from an SD station 30

4.4 Super Hexagon Array 32

4.5 Fluorescence Detector 33

5.1 Example of T

0 40

5.2 Time diﬀerence for twin tanks 41

5.3 ∆T distribution 42

5.4 ∆T/

√

∆T 42

5.5 RMS of X. 45

5.6 χ

probability distribution. 45

5.7 χ

probability distribution for multiplicity greater than 5. 46

5.8 Angular Resolution for the surface detector as a function of zenith

angle θ (geometrical reconstruction only) 47

5.9 Angular Resolution for the surface detector as a function of zenith

angle θ (complete reconstruction) 47

5.10 Event Selection 48

5.11 Distribution of the theta diﬀerence 49

5.12 Distribution of the phi diﬀerence 49

5.13 Space Angle for doublets reconstructions 50

5.14 Space Angle for Hybrid Reconstruction 51

Lista de tabelas

5.1 ﬁt 43

5.2 Comparison of AR for doublets and TVM 50

5.3 Comparison of AR between SD and Hybrids reconstructions 51

Introduction

The Ultra High Energy Cosmic Rays (UHECR) are particles with ener-

gies above 10

eV, that travel through the galaxy and constantly hit the earth

in every direction. Their study is one of the challenges of modern physics, the

origin and mechanism that produces them are still a mystery.

Many models have been proposed to explain the sources of the highest

energy cosmic rays, but none has succeeded yet. Because the ﬂux of UHECR is

low, the primary of the cosmic ray is very hard to measure. Therefore Extensive

Air Showers (EAS), that are the secondary particles produce when the cosmic

ray interact with molecules of air in the atmosphere, are used to measure them.

To measure the EAS, two techniques exist. The ﬁrst one uses Surface

Detectors (SD) that sample the particles of the showers as they reach the

ground and the second technique uses the fact that, particles of the shower

when interacting with the atmosphere produced ﬂuorescence light. That light

is captured by telescopes called ﬂuorescence detectors. Many experiments have

attempted to measure the spectrum of cosmic rays using these techniques.

However the results are not consistent within diﬀerent detectors, in particular

there is the case of AGASA and HiRes experiments. Therefore arises the need

to build a new observatory, suﬃciently large to collect enough statistics to help

solving these discrepancies and gather reliable results.

The Pierre Auger Observatory was created with these motivations. It uses

the two complementary techniques to detect cosmic rays. The project consists

of two observatories with similar characteristics, one in each hemisphere. The

Southern observatory, located in the province of Mendoza-Argentina, will cover

an area of 3000 km

. It is estimated that each observatory will detect about 30

events per year with energies above 10

eV, allowing to perform studies with

high statistics.

The Pierre Auger Observatory was conceived to explore the energy spec-

trum of the highest energy cosmic rays, their possible sources and composition.

To search the sources of cosmic rays it is of great importance to determine the

distribution of their arrival direction, derived from the data collected by the

SD through a reconstruction of the shower produced by the cosmic ray. To

Chapter 1 2

achieve an optimal measurement of these direction, it is necessary to have a

good estimate of the measurement uncertainties of the detector.

The aim of this thesis is to study the angular resolution of the Surface

Detector of the Pierre Auger Observatory, using the data collected from

2004 until April 2007. We used three diﬀerent methods. The ﬁrst method is

performed on an event by event basis. It is based on the fact that measurements

of the angular resolution depend mainly on the measurement accuracy of the

arrival time of the particles in the detectors. Therefore using the uncertainties

of the zenith (θ) and azimuth (ϕ) angles and the arrival time, it is possible to

calculate the angular resolution of each event. The second method is based on

the comparison of the signals in a sub-array of detectors deployed very close

one from another. Because of the small distance between the pairs of detectors,

they sample the same region of the shower front, allowing a time and signal

measurement comparison. Using the values obtained from this comparison, we

are able to estimate the angular resolution from a direct measurement. The

third method is using the hybrid events, those events that can be reconstructed

by the ﬂuorescence and surface detectors. We estimate the angular resolution

between the hybrid reconstruction and surface reconstruction only.

The second chapter contains an introduction to the concepts that are

used for the development of this work, such as the description of cosmic

rays, their spectrum, chemical composition and at last we discuss also the

problems that still exist to understand the most energetic cosmic rays. In the

third chapter is discuss the deﬁnition of EAS, their composition, development,

propagation and the parameters that are used to obtained information about

the CR primaries. Chapter four shows a full description of the Pierre Auger

Observatory. In chapter ﬁve are explain the methods used to calculate the

angular resolution, the analysis and comparison of the results. The last chapter

contains the conclusions and recommendations for future works.

Cosmic Rays

The high energy cosmic rays are a mystery that is being challenging

scientists ever since they were discovered. They continued to be a reason for

search and improvement on the area of particle physics and astrophysics. This

is why the Pierre Auger Observatory in Argentina is dedicated to search the

answers for one of the greatest mysteries still unsolved.

2.1

Historical Background

Questions about radiation started when the air in instruments for detec-

ting electrical charges became electrically charged (ionized) no matter how well

the containers were insulated. It was thought that radioactivity from ground

minerals was responsible, but if such was the case the eﬀect should have di-

minished with the increase of height. In 1910 Theodore Wulf (1) measured

ionization at the bottom and top of Eiﬀel Tower, which is about 300 me-

ters high. He observed that considerably more ionization existed at the top

than could be expected if it was caused by ground radiation. His results were

not given qualiﬁed acceptance, nor were the experiments of the scientists who

between 1909 to 1911 made balloon ascents to record ionization, claiming that

their instruments developed defects. Reading about these earlier experiments,

the physicist Victor Hess (2) of Vienna University, speculated as to whether

the source of ionization could be located in the sky rather than originated from

ground. The search on cosmic ray began in 1911, when Hess and two assis-

tants ﬂew in a balloon to an altitude of about 5000 meters to measure a very

penetrating radiation. They found that ionization soon ceased to fall oﬀ with

height and began to increase rapidly, so that at a height of several kilometers

it was many times greater than at the earth’s surface. He concluded therefore,

that “a radiation of very high penetrating power enters our atmosphere from

above”. After that discovery, many experiments were conducted. In 1939 Pi-

erre Auger (3) positioned particle detectors high in the Alps, noticing that two

detectors located many meters apart signaled the arrival of particles at the

same time. Pierre Auger had discovered the “extensive air showers”, produced

Chapter 2 4

by the collision of primary high-energy particles with air molecules, creating a

cascade of secondary subatomic particles. Using the information obtained from

the shower, he was able to count the number of particles that hit the ground,

estimating that the energy of primaries was of the order of 10

eV, which was

greater than any particle accelerator could produce. In 1953 Bassi, Clark and

Rossi (4) at the MIT demonstrated that an array of ground level detectors

could reconstruct the incidence direction of an air shower by a relative timing

technique. This lead to the “Volcano Ranch” experiment in New Mexico (5),

the ﬁrst “extensive air shower giant array”. In 1962 a shower was recorded by

this array (5), with primary energy of 10

eV.

In 1965 Arno Penzias and Robert Wilson detected for the ﬁrst time the

cosmic microwave background radiation (CMB) in New Jersey-USA (7). This

radiation is a form of electromagnetic radiation that ﬁlls the entire universe.

It has a thermal 2.7 K black body spectrum which peaks in the microwave

range at a frequency of 160.2 GHz, corresponding to a wavelength of 1.9 mm.

Then in 1966 Kenneth Greisen (8), Vadim Kuzmin and Georgiy Zatsepin

(9), predicted a limit on the cosmic ray spectrum, based on interactions

between the cosmic ray and the photons of the cosmic microwave background

radiation. They predicted that cosmic rays with energies above the threshold

energy of 5 × 10

eV would interact with cosmic microwave background

photons to produce pions. This would continue until their energy fell below

the pion production threshold. Because of the mean path associated with the

interaction, extragalactic cosmic rays from distances greater than 50 Mpc from

the Earth with energies greater than this threshold energy should be very rare

to be observed on Earth. This limit is known as the GZK cutoﬀ.

2.2

Description

Cosmic Rays (CR) are particles with relativistic energies, consisting

mostly of high energy protons, electrons, alpha particles, gamma rays and

heavy nuclei, that travel through the galaxy and hit the Earths atmosphere

constantly in every direction at the rate of about 1000 particles per km

, some

having energies extending up to 10

eV.

2.2.1

Sources

As it has been mentioned times before, one of the main questions

concerning ultra high energy cosmic rays is how they are produce. Many

Chapter 2 5

theories have been proposed to construct models for cosmic rays with such

energies. Models can be divided as:

Bottom-up They proposed the use of acceleration models to achieve the most

energetic cosmic rays (above 10

). Some of the models are described as

follows.

Acceleration in strong ﬁelds This models are based on the existence

of strong electromagnetic ﬁelds caused by objects such as neutron

stars or accretion disks of black holes among others. But it is not

clear how to obtain a power law spectrum with this mechanism (see

section §2.2.2).

Diﬀuse shock acceleration In 1949 Fermi (10) developed a model

where particles achieve high energy at the expense of the kinetic

energy of shock material. The mechanism for acceleration is the

repeated scattering of particles with the moving magnetized shock

front, with some chance to escape the region. He demonstrated that

the average energy change per encounter is positive and proportio-

nal to the particle energy ∆E ≈ αE. After k encounters a particle

with initial energy E

will achieve an energy E = E

(1 + α)

If P

esc

is the probability per encounter that the particle escape,

then the number of particles that survive long enough to reach some

energy E is given by N(> E) ∝ E

−γ

where γ ≈ P

esc

/α, when P

and α are small. The spectral index γ is rather insensitive to the

geometry of the system, thus Fermi acceleration predicts a power-

law spectrum of particle energies.

Acceleration in catastrophic events Gamma Ray Bursts (GRB) are

extremely bright sources of light, emitting gamma rays mainly

during a short period of time (0.1 - 10 s). During this period, they

are the brightest objects in the universe. Despite the fact that many

have been observed, their origin and nature are still a subject of

speculation. There exist similarities between GRBs and UHECR,

that would indicate a common origin.

Top-down In this case the cosmic rays are originated already with energy

ranges (above 10

Exotic sources New ideas have claimed to explain the sources of high

energy cosmic rays. In this case the cosmic rays are produced with

initially extreme energies. Most models propose that the CR are

Chapter 2 6

the product of the decay of supermassive particles. These particles

maybe radiated by topological defects formed early in the universe

as a product of spontaneous symmetry braking implicit in Grand

Uniﬁed Theories (GUT) (11) (12).

2.2.2

Energy Spectrum

The measured ﬂux of cosmic rays spans to 12 orders of magnitude

energy, ranging from GeV to 10

eV. It has been determined by several

experiments and can be well described by an inverse power law in energy,

given by:

∝ E

−(γ+1)

where γ is the spectral index and E the total energy. To a ﬁrst approximation,

the spectrum appears as a featureless power-law with γ ∼ 2.0, but at closer

look, a number of sharp transitions in the slope appears. In ﬁgure 2.1 the

cosmic ray energy spectrum is shown. The power of law holds its ﬂat pattern

from values of 10

eV up to 5 ×10

eV, where a steepening on the curve can

be seen in what is call “the knee”. The position of the knee depends on the

particle type and could be caused by changes in the ﬂux of light cosmic rays. A

variety of models have been proposed to explain that region of the spectrum,

such as a ﬁnite conﬁnement strength of magnetic ﬁelds in our galaxy or a limit

of the acceleration mechanism, related with the Fermi acceleration process.

The relatively sharp change of spectral index leads towards the acceleration

limit hypothesis (13). The existence of the knee can also be explained by

assuming diﬀerent sources of cosmic rays, like galactic gamma ray bursts (14),

which would include a mass dependence of the knee position. A second knee

appears around 10

eV and is supposed to be caused by a second order Fermi

acceleration, which assumes acceleration of cosmic rays trough interactions

with multiple supernova remnants (15). This extended acceleration process

is able to accelerate particles up to energies about 10

eV, where this limit

could be an explanation for this second knee. A hardening of the spectrum for

energy values above 10

eV is called “the ankle”. It is assumed that the ankle

region is where extragalactic cosmic rays start to dominate (model proposed

by Hillas (16)).

It is believed that cosmic rays with energies up to 10

eV that hit

the Earth are produced in our galaxy (Milky Way), probably in supernova

remnants. But there is still no knowledge about the source of the highest energy

MeV = 10

eV; GeV = 10

Chapter 2 7

Figura 2.1: The Cosmic Ray spectrum is shown as a non thermal dependent

power-law

Figura 2.2: The Cosmic Ray spectrum. A zoom of the spectrum for the highest

energy

CR. The ultra high energy cosmic rays, are the most energetic known particles

in the universe, with energies above 10

eV. Correspond to the cosmic rays

of the ankle region (see ﬁgure 2.2). A controversy exists for this range of the

spectrum and is related to the interaction of the highest energy cosmic rays

with the CMB radiation. Because of this interaction, a limit on the energy

Chapter 2 8

was predicted (GZK cutoﬀ), this would imply that cosmic rays with energies

greater than this threshold energy would rarely be observed on Earth. While

the Hires experiment (33) sees the cutoﬀ AGASA (32) predicted a continuation

of a ﬂattened spectrum. With the Pierre Auger Observatory it is expected to

disentangle this controversy.

2.2.3

Chemical Composition

One of the challenging aspects of cosmic rays is the measurement of their

primary mass composition. The chemical composition of CR is a function of

energy.

For low energy cosmic rays, the chemical composition has been measured

using balloons. Measurements have shown that the element abundances in CR

is compared to those of the solar system, though a couple of diﬀerences appear.

The data collected suggest that as we approach the region of the knee of the

energy spectrum of CR (see ﬁgure 2.1), the composition is dominated by heavy

particles such as iron (17). Due to the low ﬂux of high energy cosmic rays,

direct observation of primary particles is impossible above 10

eV, therefore

the information is obtained at ground level, using parameters of secondary

particles of CR that reach the earth, called air showers (see chapter 3). These

parameters can be divided into two categories. The ﬁrst one is related with the

muon content of the shower in conjunction with a second component, either

electron or Cherenkov light ﬂux (18). The other method attempts to infer

information from the depth of maximum shower development (X

max

), using

the lateral or temporal spread of the shower (19), (20). For both methods the

accuracy of the primary particle mass is subject it to severe constrains due to

shower-to-shower ﬂuctuations, hadronic models and other uncertainties.

Many experiments have used these methods to measure the chemical

composition of the high energy cosmic rays. In ﬁgure 2.3 is shown the X

max

as a function of energy. The data suggest that for energies above 10

eV, the

composition changes progressively from heavy to lighter nucleis. Even though

there is consent about the transition from heavier to lighter elements between

all the experiments, they disagree in the range and speed of the transition.

It is certain that there is a great uncertainty in the knowledge of chemical

composition of CR for energies greater than 10

eV. This lack of knowledge

imposes several limitations to the development of theoretical models that could

explained their origin.

2.2.4

Chapter 2 9

Figura 2.3: X

max

as a function of energy obtained from diﬀerent experiments.

The lines indicate the predictions of the hadronic models of high energies

QGSJET01, Sibyll 2.1 y Nexus 3.97 (21)

Propagation

Cosmic ray particles do not travel unhindered through space, they are

subjected to various interactions and their trajectories could be curved by

magnetic ﬁelds or aﬀected by cosmic background radiation, among other

phenomena. The result of these eﬀects will characteristically alter the observed

energy spectrum and arrival directions at the earth. The consequences over the

observation can be resume as:

– Assuming that the sources of the highest energy cosmic rays are extra-

galactic, then the trajectories of CR will be deﬂected by extra galactic

magnetic ﬁelds, also the energy spectrum observed at earth may exhibit

the GZK cutoﬀ cause by the interaction of particles traversing the CMB

radiation. The ﬂux of particles that will be observed above an energy cor-

responding to the threshold for interacting with the cosmic background

radiation is very low. This interaction would implicated a limit in dis-

tance for the source of extremely energetic particles at about 100 Mpc

from the earth.

– Otherwise if the source of high energy CR are nearby, then the charged

particles will traverse the magnetic ﬁelds of the interstellar medium

without being greatly deﬂected. Therefore it could be possible to track

their source through comparison with location of known objects in the

sky, close to the arrival directions of CR, although there is still not

knowledge of such sources in that range of distance.

Chapter 2 10

2.3

Measuring Cosmic Rays

The range of energies covered by cosmic rays is very extensive, hence

diﬀerent techniques must be implemented to measure them properly. They are

usually separated in two categories, depending on the ﬂux: direct and indirect

measurement. In the following sections this techniques will be explained in

detail.

2.3.1

Direct measurement

Below 10

eV, the ﬂux of CR is high enough to be able to measure them

directly. The techniques implemented are similar to the techniques used in high

energy experiments. Normally these detectors are sent to the atmosphere in

aerostatic balloons or sent to orbit by satellites.

Among the most important balloon experiment there is JACEE (Japane-

se-American Collaborative Emulsion Experiment) (22). It measured the CR

spectrum up to energies 10

eV and also the nucleon-nucleon interaction. The

main idea was to measure the primary charged particle and the total energy

through calorimeter, using detectors like emulsion cameras or Cherenkov

counters.

One of the constrains of these type of experiments was the corrections

that need to be done for the atmosphere interactions. To solve this problems,

some experiments were conducted outside the atmosphere. One of these

experiments was “Chicago Egg” (23). It consisted in Cherenkov detector on

an space shuttle. Another experiment was “Ultra Heavy Nuclei Experiment”

(UHN) that ﬂew in Satelite HEAO-3 ( High Energy Astronomy Observatory)

(24).

For values above 10

eV the ﬂux of CR decrease considerably, making it

impossible to measure them in a direct way, this is why other techniques are

implemented.

2.3.2

Indirect measurement

Because of their low ﬂux, CR above EeV (EeV = 10

eV) are diﬃcult to

measure, therefore secondary particles produced by the interaction of cosmic

rays with the earth’s atmosphere are used to detect them.

Two methods are used to measure extensive air showers. The ﬁrst one

uses ground array, detecting particles directly by measuring the number the

secondary particles of the shower that reach the ground, using scintillator

Chapter 2 11

counters or water Cherenkov detectors (WCD), covering a very large area.

Inference can be draw about the energy of the primary cosmic ray. The second

method is based on atmospheric light emission associated with the excitation of

nitrogen molecules by the secondary particles in the shower. This produces light

in two ways: Cherenkov radiation and nitrogen scintillation. Because the angle

for Cherenkov light emission is large the cherenkov light is highly collimated

from its original direction, then it can not be used for measurements. While,

scintillation light comes from the ionized nitrogen molecules that radiate

energy, producing UV photons. This light is isotropic and near the shower max,

the number of particles is big enough, allowing the measurement of light. With

this technique the proﬁle of the shower can be guess using the characteristics

of the cascades.

Pierre Auger and his group were the ﬁrst ones to use resolving time

coincidence circuits in array counters, which provided information about the

shower, but was not able to provide the shower direction. This limitation

was solved when the MIT group (1953)(4) created a method to reconstruct

the arrival direction by measuring the arrival times in scintillation counters

separated a few meters. Later Harvard Agassiz Station (1954 - 1957) (56) used

an array of scintillators to measure the energy spectrum. Since then surface

detectors have been used around the world in experiments like: Volcano Ranch

(USA) (5), Haverah Park (UK) (25) and AGASA (Japan) (29) among the most

important.

Before the discovery of the 2.7 K background radiation it was suspected

that cosmic ray spectrum went up to energies of 10

eV, thus alternative

methods for detection were explored. Ideas of using the earth’s atmosphere

as a scintillator emerged (Suga and Chudakov, 1962). In 1976 Volcano Ranch

detected an event with the ground array. This result led to the development

of FlysEye (26) instrument and later its successor HiRes.

Surface Detectors

One of the principal characteristics of extensive air showers is that they

produce an enormous amount of particles when they reach the Earth, spreading

over large areas. Taking advantage of this, ground arrays were created to detect

these particles. Measuring the lateral distribution function of the showers

by sampling the charged particle component at the earths surface. For this

purpose scintillator counters or water Cherenkov detectors are spread over

large areas. The area required by these arrays is inversely proportional to the

ﬂux of cosmic rays, i.e. the lower the ﬂux, the bigger the array will be. For

UHECR the ground array must cover hundreds of squared kilometers. The

Chapter 2 12

distance (d) at which every surface detector (SD) is placed, depends on the

type of shower, meaning the type of particles that will be detected (for muons

the separation between the SD is much larger), an is usually around hundred

meters. Another important characteristic that is taken into consideration is

the location of the array. The maximum depth of shower is from 800g/cm

see level, thus it has to be guarantied that the location of the array must be

in this range of the shower depth.

The advantage of this type of array is that they provide a good resolution

on the arrival direction. Also they are cheap, stable, do not depend strongly

on weather conditions and last for long periods of time, but they depend on

hadronic models to estimate the energy of the shower and other characteristics.

Fluorescence Detectors

Another characteristic of extensive air showers is that when the particles

enter the earth’s atmosphere with the speed of light, they excite the molecules

of nitrogen in the air, ionizing the particles emitting ”atmospheric light”. The

excited particles emit Cherenkov radiation and ﬂuorescence photons. Though

the ﬂuorescence yield per particle is small, for shower with energies above

1 EeV, a suﬃcient number of photons at the shower max are produce, enough to

be capture by a detector. The light is emitted isotropically along the trajectory

of the shower and is collected by the detectors as a time sequence. With this

sequence is possible to determined the distance to the shower axis and the

incident angle to build the shower detector plane, which is the plane that

contains the shower axis and the detector. Once the geometry is determined,

the number of photons received can be calculated. Using reconstruction

techniques the energy and direction of the shower can be inference.

The advantage of these detectors is that it is not needed a large area,

like the case of SD, but on the contrary are more sensible to climate conditions

and noise.

2.3.3

Most Important Giant Extensive Air Shower Arrays

The ﬁrst of the giant arrays was Volcano Ranch in New Mexico in 1961

(5). Consisted of nineteen plastic scintillator counters, each containing a PMT.

It enclosed an area of 8.1km

, a further unit was shielded by a layer of lead

to measure muons density. Volcano Ranch provided the ﬁrst measurements

of the energy spectrum above 10

eV and also made the ﬁrst predictions of

the arrival direction distribution. It measured the ﬁrst cosmic ray with energy

about 10

eV.

Chapter 2 13

The Haverah Park array in UK (25), was a water Cherenkov detector

array, that covered an area of 12 km

distributed in four central detectors and

six sub-arrays about 2 km from the center. They recorded one of the largest

best measured events with primary of 10

eV.

The Sidney University Ground Air-Shower Recorder (SUGAR) (27) so

far was the only giant array operating in the southern hemisphere

. It

contained 54 stations deployed over 60 km

. Each station consisted of a pair

of scintillators buried below the ground, capable of measuring muons with

E ∼ 0.75 sec θ GeV. The relative arrival time at each detector was derived

from a timing signal beamed across the array. Unfortunately the spacing

between the detectors proved to be too big, so the statistics for one event

were too small.

The Fly’s Eye detector in Utah, USA (26), was actually the ﬁrst expe-

riment to use the FD technique. It consisted of two detectors FEI and FEII

separated by a distance of 3.4 km. FEI consisted of 67 mirrors of 1.6 m dia-

meter with 880 PMT viewing the whole sky. FEII consisted of 36 mirrors and

464 PMT and viewed half the sky in the direction of FEI.

Fly’s Eye traced the development of cascades in the atmosphere by

observing the intensity and time sequence of ﬂuorescence light from the shower.

This array gave important results to the studies of cosmic rays. Its

successor HiRes (1998) had ten times the sensitivity previously achieved in

the region of 10

eV. Consist in two locations for the detectors separated

by 12.5 km, but implemented a reduction in the aperture of each PMT,

counteracting it increase the mirrors diameter, resulting in an increase of the

eﬀective detection area, giving more sensitivity.

The Akeno Giant Air Shower Array (AGASA) (29). The largest array

constructed so far

, covering an area of 100 km

located in Akeno, Japan.

Consisted of 111 scintillation detectors, each of an area of 2.2 m

deployed

with an inter detector spacing about 1 km. Muon detectors of varying sizes are

installed in 27 detectors. Each detector records the arrival time and density of

every incident signal and monitors the performance of the detector. The p-air

inelastic collision cross section, energy spectrum and muon energy spectrum of

horizontal air showers from 3 × 10

to 3 × 10

eV have been measured with

this array.

2.3.4

until the second phase of Pierre Auger Observatory started

until the second phase of the Pierre Auger Observatory started

Chapter 2 14

Open Questions

The UHECR sources, acceleration and propagation process, even mass

composition are uncertain. Here some of the limitations of the diﬀerent aspects

of cosmic rays are presented.

Lets start with acceleration process and energy sources. As it was

mentioned in the previous section an energy source must be extremely large

to be capable of accelerating particles up to 10

eV and the magnetic ﬁelds

of propagation path have to be suﬃciently weak in order that synchrotron

losses are not larger than energy gain. It is believed that cosmic rays with

energies of 10

eV are energized by diﬀusive shock acceleration, with supernova

remnants as the most likely sites. At higher energies it is believed that the

particles are being accelerated by interaction with multiples supernovas as

they move through interstellar medium. However no direct evidence exists of

these phenomena.

It was shown that the maximum energy achievable is given by:

E = kZBRβ

where B is the magnetic ﬁeld needed to keep particles inside acceleration region,

R is the size of the acceleration region, β = v/c is the shock speed, Z is the

charge of the particle. Other options for these phenomena were proposed, like

active galactic nuclei (AGN) or gamma ray burst (GRB). But in this search we

encounter with another problem, distance. After the discovery of microwave

background radiation, Greisen (8), Zatsepin and Kuz’min (9) predicted the

existence of an upper limit on the energy of the proton spectrum around

5×10

eV due to photo-pion production on the microwave background (2.7 K)

through ∆

resonance, which is called the GZK cutoﬀ.

p + γ

2.7K

→ ∆

+(1232)

→ n + π

→ p + π

(2-1)

Another energy loss process is pair production (Bethe-Heitler process)

that could cause a drop in the energy spectrum around 8 × 10

eV.

p + γ

2.7K

→ p + e

+ e

−

(2-2)

Also heavy nuclei primarily undergo successive disintegration by scatte-

ring on the 2.7 K background radiation and the infrared photons with subse-

quent pair production.

A + γ

2.7K

→ (A − 1) → A + e

+ e

−

(2-3)

where A is the nuclei mass. Figure 2.4 is shows the energy losses of a proton.

Chapter 2 15

Figura 2.4: Energy loss of a proton through interaction with cosmic background

radiation for diﬀerent initial values of energy (6).

This implies that primary photons with energies larger than 10

eV can

hardly reach the earth because they will loose all their energy getting here

(supposing the source is at least 50 Mpc from the earths atmosphere).

Another problem for cosmic ray detection is their arrival direction and

distribution. Ultra high energy protons do not suﬀer signiﬁcant energy loss

during their propagation within the limits of our galaxy, but they are deﬂected

by the galactic magnetic ﬁeld. The deﬂection angle is typically α ≈ d × r

with r

= E/ZeB the Larmor radius, and d is the distance the particle

travels, hence the rate of particle loss from the disc increases with energy

and anisotropy might be expected above 10

eV assuming that primaries in

this region are protons.

But since the attenuation length of protons and nuclei below GZK cutoﬀ

energy exceeds 1000 Mpc, the expected arrival distribution of cosmic ray is

isotropic if they are of extragalactic origin. If the energies exceed the GZK

cutoﬀ, the distance to the source is limited to descend of Mpc and the

correlation with their arrival direction with the galactic structure may be

expected, but there is still not knowledge of such sources.

The energy spectrum of Cosmic Rays it has been measured for many of

this experiments. The most controversial result being the comparison between

the AGASA and HiRes spectrum. The spectrum reported by AGASA (32)

shows no existence of the GZK cut-oﬀ, while the HiRes (33) spectrum are

Chapter 2 16

Figura 2.5: AGASA spectrum (triangles) and HiRes (monocular) (HiRes-1

squares and HiRes-2 circles). (33).

consistent with a threshold delimited by the GZK cut-oﬀ. Figure 2.5 shows

the ﬂux of CR as J(E) times E

to stand out the changes in the slope of the

spectrum.

Extensive Air Showers

Air Showers are cascades of particles that propagate through the at-

mosphere. They are generated by the interaction of high energy primary cos-

mic rays with molecules at the top of the atmosphere and travel with velocities

near the speed of light. The number of secondary particles in the cascade in-

creases to subsequent generations of particle interactions, reaching the ground

in a proportion of 3 × 10

particles per primary for energies of 10

eV.

The number of particles along the axis, called longitudinal proﬁle, grows

rapidly up to a maximum. The primary energy is shared equally between the

secondary particles and these would continue to interact and share the energy

until they reach the critical energy. Because of the quick decay of neutral pions,

about 30% of the energy in each generation is transferred to an electromagnetic

cascade. The other two components of extensive air showers are muonic and

hadronic. Figure 3.1 shows the development of a shower.

3.1

EAS development

3.1.1

Hadronic Cascades

The hadronic component of the cascade is mostly formed by charged

pions or kaons, products of decays, collisions or resonances of strange baryons.

This component forms the shower core, feeding the other components. From

decay of neutral pions and eta particles into photons or pair production,

creating the electromagnetic cascade. Lower energy pions and kaons decay

to feed the muonic component.

The hadronic interactions at such high energies is one of the points of

study and a source of error in air shower analysis, since a collider capable to

reproduce such energies does not yet exist.

3.1.2

Chapter 3 18

Muonic Component

The muonic component comes from the decay of charged pions and kaons

into neutrinos and muons, therefore it is sensitive to the baryonic content of

the primary. Neutrinos do not contribute much, they are not detected and

do not interact because of their extremely small cross section. On the other

hand, muons have a long lifetime due to Lorentz factor dilation, therefore they

are able to reach the ground. The number of muons that reach the ground

is about 5 × 10

with energies above 1 MeV for a 10

eV proton induced

shower. Muons with high energy travel more or less in rectilinear path, because

they only suﬀer small scattering which leads to an earlier arrival times at the

ground than electrons. Due to these characteristics the muonic component is

very useful in the reconstruction of the shower development, mass and energy

(in the case of SD detection).

Once the energy of secondary particles falls below some critical value

, ionization losses take over from electromagnetic process and the number

of electrons and photons in the shower decreases, while the number of muons

remains more or less the same. This region of the shower is referred as the

“tail”. Because most shower detectors are located below the altitude at which

the maximum of the electromagnetic component occurs, they observe mostly

the shower tails that have signiﬁcant muonic component.

3.1.3

Electromagnetic Cascade

The electromagnetic component is the dominant process in extensive air

showers development, because the other components end up feeding this one

(more of 1/3 of the energy of hadronic components goes into electromagnetic

cascade). Each high energy photon generates an electromagnetic sub-shower

alternating pair production and bremsstrahlung. These processes are repeated

iteratively, generating a cascade of electron-positron pairs and photons which

will continue until the energy of the secondary electrons reaches a critical

energy, E

≈ 600 MeV/Z, where ionization losses equal those of bremsstrah-

lung. The electromagnetic cascade dissipates about 90% of the primary particle

energy and hence the total number of electromagnetic particles is proportional

to the shower energy.

3.2

EAS propagation

The atmosphere is a calorimeter whose properties vary with altitude and

time, for that reason the quantity that best describes the varying density of

Chapter 3 19

the atmosphere is the vertical atmosphere depth (traversed matter):

(h) =



∞

atm

(z)dz (3-1)

where ρ

atm

(h) = ρ

h/h

is the atmospheric density, with h

µg

the scale-

height of the atmosphere, R the ideal gas constant, µ the average molecular

weight of air, g the gravity, T ≈ 288 K the temperature and z is the height.

However, the development of air showers in the atmosphere is given by the

slant depth which deﬁnes the actual amount of air traversed by the shower. For

inclined showers of zenith angle θ, is given in a good approximation (θ ≤ 80

◦

)

by:

X =

(h)

cos θ

(3-2)

An approximative parametrization of the longitudinal evolution of air showers

was proposed by Gaisser (53) and Hillas (16):

N(X) = N

max



X − X

max

− X



max

−X

exp



max

− X



(3-3)

with X

the point of ﬁrst interaction and λ ≈ 70 g/cm

the hadronic mean

free path in air.

Integrating all charged particles along the slant depth, the calorimetric

energy could be found.

cal



∞

ion

dX ≈

crit



∞

N(X)dX (3-4)

For a photon induced shower, the longitudinal development can be approxi-

mated by:

prim

, t) = 0.31



prim

crit



−1/2

exp [t(1 − 1.5 ln s)] (3-5)

with t = X/X

the atmospheric depth in terms of electromagnetic radiation

lenght X

and s is the shower age:

s =

t + 2 ln



prim

crit



(3-6)

which is equal to zero when the shower is starting and equal to one at its

maximum.

3.2.1

Lateral Distribution of the Shower

The lateral distribution of a shower is mostly determined by electron

multiple scattering, since the electromagnetic component is the most dominant

of the shower

Chapter 3 20

The lateral spread of purely electromagnetic shower can be calculated and

is parametrized by the NKG function after Nishimura, Kamata and Greisen.

≈ C(s)

2πr





(s−2)



1 +



(s−4.5)

(3-7)

where r

denotes the moliere radius and C(s) is a normalization factor given

by:

C(s) =

Γ(4.5 − s)

Γ(s)Γ(4.5 − s)

(3-8)

with s the age of the shower.

On the other hand, the muonic component of EAS depends on the

probability of pions to decay instead of interact. The muon component is also

related to the hadronic component and therefore reﬂects more directly that the

electromagnetic component the properties of initial hadrons. The muon lateral

distribution is ﬂatter than the electron distribution, but at distances far from

the axis , the muon and electromagnetic density start to be comparable and the

energy of the muonic component overcomes the electromagnetic component.

In ﬁgure 3.2 is shown the lateral distribution for charged particles and muons.

Chapter 3 21

Figura 3.1: Sketch of the EAS. It shows the main process of a cascade of

particles, assuming that the primary CR is a nucleon. The cascade divides in

three categories: Hadronic, Muonic and Electromagnetic. (6).

Chapter 3 22

-3

-2

-1

500 1000 1500 2000 2500 3000

Core Distance m

Density m

-2

≥ 10.0 MeV

≥ 1.0 GeV

charged

≥ 0.05 MeV

Figura 3.2: Lateral distribution for muons, electrons and gamma simulated

with Corsika using the hadronic model of interaction QGSJET for a proton

with energy of the order of 10

eV , compare to the experimental data of

AGASA (see text).The ﬁlled line corresponds to the charged particles, and in

dashed line the muons with energies greater than 1 GeV (56).

Auger Observatory

The goal the of Pierre Auger Observatory is to build a detector capable

of solving the puzzle of the spectrum, the origin and composition of UHECR.

To ﬁnd those answers, Auger uses the combination of ﬂuorescence detector

and ground array to measured the highest energy cosmic rays. In the following

section will be describe in detail.

4.1

Description

The Pierre Auger Observatory is a hybrid detector design to study the

higher range of the energy cosmic ray spectrum (above 10

eV). Combines a

very large ground array formed with Water Cherenkov Detectors (WCD) and

ﬂuorescence detectors (FD), that captures the light produced by extensive air

showers in the atmosphere (6). It was conceived to measure the ﬂux, direction

and composition of ultra high energy cosmic rays, very accurately. The simul-

taneous measurements of diﬀerent variables improve the reconstruction of the

shower, reduces possible systematic errors, provide a more accurate time reso-

lution and allows a crosscheck calibration. Apart from that, both techniques

see air showers in a complementary way. The ground array measure the late-

ral distribution of the shower, which permits to separate the electromagnetic

and muonic component, while ﬂuorescence detectors records the longitudinal

proﬁle during its development through the atmosphere.

The complete Observatory will consist of two instruments, located in the

Northern and Southern hemispheres in order to achieve homogeneous coverage

of the whole sky and be able to observe the sources of UHECR with suﬃcient

aperture. The Southern Observatory will cover an area of approximately 3000

, is in its last stage of construction and is operating in a stable. It is

located in the Pampa Amarilla near the town of Malarg¨ue in the province

of Mendoza - Argentina. Will have 1600 WCD arranged in a triangular grid

with 1500 m of separation between each, spread over the total area and four

ﬂuorescence detector buildings, each of them hosting six telescopes, observing

the atmosphere above the whole surface detector area.

Chapter 4 24

In ﬁgure 4.1 it is shown the display of the Southern Observatory in its

actual state.

Figura 4.1: Current layout of the Southern Observatory. In the map is shown

the Cherenkov detectors (dots) and the four ﬂuorescence detector (labels with

the corresponding building name).

The Northern Observatory is design to complete the search pursue by

the Southern Observatory. Auger North will retain the basic functionality and

features of Auger South. The Northern site located in Colorado - USA, will be

3.5 times larger than the Southern Observatory. Covering an area of 10370 km

with a 135 × 77 km squared grid of water Cherenkov detectors overlooked

by three ﬂuorescence buildings, each with six telescopes to provide hybrid

coverage. The total area is incremented in order to obtain more statistics for

events with energies above 10

eV (36).

4.2

Surface Detectors

The principle of work of Surface Detector (SD) is called Cherenkov

radiation, emitted when a charged particle passes through a translucent

medium (like water) at a speed greater than the speed of light in that medium.

This cause an emission of electromagnetic radiation in the form of light. This

light is capture by the detectors in a form of a signal, which is then analyze.

Chapter 4 25

4.2.1

Characteristics and Description

Figura 4.2: Picture of a water Cherenkov detector.

A SD station consists of a cylindrical polyethylene tank, ﬁlled with

pure water. The Cherenkov light is measured by three photomultiplier tubes

(PMT), set in a symmetric pattern on top of the tank, facing downwards. This

arrangement avoids the direct hit of Cherenkov light, collecting a signal which

is homogeneous.

The set of detectors are synchronized by a GPS system that times

the events to allow accurate reconstruction of arrival direction. Stations

communicate with the Central Data Acquisition System (CDAS), through

custom built wireless communication system. The stations are powered by two

solar panels charging two 12 Volts batteries, so each detector is independent

of other detectors in the array.

The surface detector becomes fully eﬃcient for energies above 3×10

and is able to collect data with almost 100% duty cycle. This design was chosen

because of the durability, low cost and reliability (35).

With the SD one obtains a measurement of signal density at ground, and

reconstructs the arrival direction and energy of the air shower by ﬁtting the

measured times to a given shower front model and the observed signal density

as a function of the distance to the shower core respectively.

The speciﬁc characteristics of each station are described as follows:

Chapter 4 26

Tank Stations are formed of rotationally moulded polyethylene tanks of

3.6 m in diameter and 1.5 m high, enclosing a cylindrical volume of

water 1.2 m

. The top of the tank was designed to house the three

photomultipliers and to provide some rigidity, because it needs to support

the stress brought by the solar panels.

The tanks need to be opaque to ensure that there is not light coming in

from out of the tank. However, to reduce the ecological impact and eﬀects

of heating during the sunny days, that could be caused by black tanks,

they are rotomoulded in two layers. The external layer is compounded

with a beige pigment to match the sandy colors of the landscape and the

internal one is black and twice as thick. Also, to protect them against

UV degradation a special resin is used. In ﬁgure 4.2 it is shown a picture

of a WCD.

Tank liner The liner is a Tyvek cylindrical Polyoleﬁn bag, used to contain

the water inside the detector. It protects the water from contamination

and inhibit bacteriological activities. It has high reﬂectivity of Cherenkov

light and acts as a secondary seal against outside light sources. It contains

three windows to enclosed the PMTs.

Water Tanks are ﬁll with ultra pure water to avoid contamination and its

properties will be maintained over the lifetime of the experiment. The

water is produce on a plant implemented in the Observatory. Is produce

with a resistivity better than 10 MΩ-cm. Due to all the handling of the

water (from the plant to the storage tank, to the transport tank and

ﬁnally to the detector) the quality could be degraded. The transparency

of the water is monitored using the decay time of the signals from the

PMTs.

4.2.2

Electronics

All the electronics, except the PMTs, are contained in a waterproof box.

PMTs The photomultiplier tubes used to collect the Cherenkov light are

Photonis XP1805 of 9” each (35). The signal of each PMT is extracted

from the anode and last dynode. The signal from the dynode is ampliﬁed

to a factor of 32.

Front-end electronics and ﬁrst level triggers The signal of each PMT is

sent to an electronic board called Front-End, where the readout of the

Chapter 4 27

signals from each tank is digitized by six 10 bit Fast Analog to Digital

Convertor (FADCs) running at frequency of 40 MHz. The output of each

FADC is a signal digitized in intervals of 25 ns. The digitized signal is sent

to a Programable Logic Device (PLD, i.e. local CPU) used to implement

the two ﬁrst level trigger decisions (see section § 4.2.4).

Station Controller The local electronic is controlled by a CPU board. The

controller is in charge of selecting the trigger signals and send them to

the central station. A Slow Control (SC) is used as interface for the PLD

trigger, so that threshold and PMT voltage can be set and monitoring

information, such as temperature at the PMTs, solar panels among others

can be read.

Timing System The time at which stations are triggered is extremely im-

portant to determine the arrival direction of particles. This timing is

measured at each station using a commercial Motorola GPS board. The

signal is processed by the CPU and a time tagging board, which provides

the event time with a precision of approximately 10 ns. To achieve such

precision, the exact location of the stations are provide to the CPU.

Power Supply The electronic of each station is designed to have power

consumption lower than 10 W, which is obtained from the 12 V batteries,

charged by two solar panels of 60 W each. A power control board is

used to monitor the diﬀerent voltages and currents of the system and to

provide 24 V to the motherboard.

Data Communication System Consists of two integrated radio networks.

One is the microwave network, which is of high capacity and provides

communications from the FD buildings to the central station. It uses

a standard telecommunication architecture, to provide point-to-point

links, consist of microwave transceivers with interface units. The Second

network is a wireless Local Area Network (LAN), used to communicate

with the SD and custom designed for the project. The communication

with the stations is done in a similar way to a cellular phone system.

4.2.3

Calibration

A surface detectors calibration is needed in order to be able to relate the

signal density obtained from the measured Cherenkov light produced inside the

tank with some physical unit. The unit chosen was the charge deposit from

Chapter 4 28

a vertical and central thoroughgoing muon, called vertical-equivalent muon

(VEM).

A VEM is deﬁned as the charge produce when a relativistic vertical

central muon pass through the detector and is collected by the 3 PMTs in the

station.

An advantage of using this unit is that it will not be aﬀected by

experimental circumstances such as changes in the gain of the PMTs or

electronic ﬂuctuations.

The easiest way to determined a VEM from a WCD is to used a muon

telescope, which consist on the use of two scintillators located outside the

detector. One on top and the other one on the bottom of it, on the same axis

of symmetry and working in coincidence. This will allow us to determine the

trajectory of the muon traversing the tank. Therefore enabling to distinguish

the vertical muons. With this information we will produce an histogram of the

charge distribution for the PMTs (38).

Due to the enormous amount of detectors, this method proved to be

expensive and unpractical for the Auger Observatory. For instance it was

necessary to develop other methods.

The best option is to used the charge histogram produced by the

atmospheric muons, that is collected by the three PMTs of the detector (see

ﬁgure 4.3).

It is possible to establish a correlation between the histogram produce

by the background muons in the tank and the histogram obtained with the

muon telescope. Adjusting the peaks from both histograms is possible to infer

the charge of the VEM (37).

In ﬁgure 4.3 it is shown the histogram of the charge distribution by

atmospheric muons and the trigger pulses of the muon telescope.

The VEM value and the other parameters needed for the calibration are

measured every 6 minutes in parallel to regular data taking and returned to

CDAS to allow accurate determination of signal density in each detector and

provide a stable uniform trigger level.

4.2.4

Triggers

The hierarchy of triggers for the surface detectors is established in four

levels. At ﬁrst instance there are two level triggers: local station trigger and

surface array trigger. For the event selection, two higher level triggers are

implemented: physical and quality trigger.

Chapter 4 29

Figura 4.3: Charged and pulse height histogram from an SD station. The ﬁlled-

line is caused by the trigger of a 3-fold coincidence of the PMTs of a special test

detector, located at the central station building. The ﬁrst peak is caused by

the convolution of the trigger on a steeply falling distribution from low energy

particles. The second peak is due to vertical thoroughgoing muons. The dashed

histogram is produce by an external muon telescope, providing the trigger that

selects vertical muons only.

(39)

Local Station Trigger The single station trigger is divided in two level

triggers, T1 and T2. For the ﬁrst level (T1), two diﬀerent triggers are

implemented:

– Time Over Threshold (ToT): requires that at least 13 bins in

a 120 bins window are above 0.2 VEM in coincidence on 2 PMTs

(40). It is eﬃcient for selecting small spread signals, common of high

energy EAS distant from the detector or low energy showers, while

ignoring single muon background.

– Threshold (Th): is a 3 PMTs coincidence of a 1.75 VEM threshold

on at least 1 bin. It is used to detect fast signals (smaller than

200 ns) corresponding to the muonic component generated by

horizontal showers. With frequency of 100 Hz.

The second level trigger (T2) is applied in the station controller to select

the T1 signals likely to come from an EAS. All ToT triggers are directly

promoted to T2, while Th are requested to have a 3.2 VEM threshold

Chapter 4 30

in coincidence for the 3 PMTs. With a reduction of the frequency to

aproximately 21 Hz.

Surface Array Trigger The main central trigger (T3), requires the coinci-

dence of three tanks which have passed the ToT and achived some mini-

mum request of compactness, meaning that one of the tanks must have

two triggered neighbors (3ToT). In case that the event is not ToT but

threshold, then the requirements are of at least four fold coincidence of

any T2.

Physical Trigger The physical trigger (T4) is used to select the real showers

from the T3 data, which could contain some chance coincidence, i.e. those

tanks in the event that even though were trigger, are not part of the real

event conﬁguration (accidental stations). The selection criteria requests:

– 3ToT conﬁguration (3 tanks of the event that are ToT in a compact

conﬁguration)

– Compact conﬁguration of any local trigger, where the station with

highest signal is surrounded by 3 triggered tanks.

The T4 is optimized for showers with zenith angles up to 60

◦

. In the

case of inclined showers, other selection criteria is applied, because this

showers present a diﬀerent topological pattern (42). We will not discuss

this matter, because is not relevant to development of the present work.

Quality Trigger The quality trigger (T5), selects those events that having

passed the T4 criteria can be well reconstructed, meaning that parame-

ters like the core position falls into the array. T5 requires that the tank

with highest signal must have six of its closest neighbors working at the

time of the event. This trigger is of great importance during the deploy-

ment of the SD array, because it is diﬃcult to reach the compactness

need for a good reconstruction and therefore many border eﬀects might

lead to bad reconstruction. Approximately 80% of the T4 events are T5.

4.2.5

Special Tanks in the Array

Within the ground array as it is shown in ﬁgure 4.1, a set of special

detectors has been deployed in order to do some studies relevant to the accuracy

of the SD.

Chapter 4 31

Figura 4.4: A sub-array of detectors, that consists of pairs of tanks separated

by 11 meters and arranged in an hexagonal conﬁguration. They are used to do

crosscheck on the reconstruction.

Doublets (Twin Tanks)

The ﬁrst group of special detectors consists on pairs of tanks separated

only 11 m apart from each other, called “doublets” or twin tanks. Due to the

small distance between the tanks, both detectors will observe the same region

of the shower, therefore enabling crosscheck of reconstructions, like time and

signal measurement comparison.

Currently there exist two sets of doublets. One contain only two pairs

(Moulin-Rouge and Dia-Noche), that were deployed almost since the begining

of the array and have being operating since 2004. While the other set was re-

cently implemented. This set of doublets was deployed to obtain more statistics

in a shorter period of time (than only the 2 pairs already implemented) to al-

low crosscheck calibration for the shower parameters. It has been in operation

since September 2006 and is called “superhexagon”. Consists of a sub-array of

tanks containing nineteen twins, of which seven are triplets (3 tanks arranged

in a triangular grid, also separated 11 m from each other), arranged in an

hexagonal conﬁguration as shown in ﬁgure 4.4.

Inﬁll Tanks

Two more tanks were installed recently in between a triangle grid of tanks

from the regular array. The purpose of this two new deployments is to do some

analysis with a new technique that implements the detection of EAS using

radio frequencies. Also, these inﬁll-detectors will allow us to pursued studies

at lower ranges of energy.

Chapter 4 32

4.3

Fluorescence Detectors

High energy particles, when travelling through the atmosphere ionize

the nitrogen atoms, emitting UV photons. This radiation is called ﬂuorescence

light. If is observed at far distances, then the shower can be seen as a isotropic

source of light moving through the atmosphere. The ﬂuorescence detectors uses

PMTs cameras to capture this light.

The ﬂuorescence detector consists of 4 buildings, called “eyes”, disposed

on the vertices of a diamond-like conﬁguration as seen in ﬁgure 4.1, with a

separation of 65.7 km along the direction North-South and 57.0 km in the East-

West direction. Each building is provided with six independent telescopes with

◦

× 28.6

◦

ﬁeld of view, covering a 180

◦

azimuth angle of each eye, allowing

to view almost the whole area covered by SD array. Each telescope consist on

a Schmidt optical system. Composed of a circular diaphragm, with aperture

of 2.2 m in diameter at the center of curvature of the mirror, UV transmitting

ﬁlter over the diaphragm, to reduce night sky noise, and Schmidt corrector

lenses, to allow an increase on the radius of the telescope diaphragm, while

maintaining the spot size. The camera consists of 20 × 22 photomultiplier

tubes (PMT) for a total of 440 PMTs having a ﬁeld of view of 1.5

◦

each, onto

which light is focused by the spherical mirror. The optical spot size on the

focal surface has a diameter of approximately 15 mm (0.5

◦

) for all directions

of incoming light. To reduce signal losses when the light spot crosses PMT

boundaries, small light reﬂectors (“mercedes stars”) are placed between PMTs.

In ﬁgure 4.5 it is shown a picture of the FD design.

4.3.1

Calibration

The FD measures the arrival direction, time proﬁle sequence, energies of

air showers among other characteristics. However, in order to measure these

parameters with the FD arise the needs of a calibration between the incident

ﬂux of light and signal received by the PMTs, as well as the inclusion of

atmospheric corrections and a good knowledge of the ﬂuorescence yield. The

ﬁrst thing that needs to be taken into consideration is that, to measure the

longitudinal proﬁle and the total energy of the shower, it has to be possible to

convert FADC counts to a light ﬂux. So it is necessary to have a method to

evaluate the response of each pixel to a ﬂux of incident photons. In order to

do this there is the main calibration process, divided in two phases:

Absolute Calibration: Is performed using a calibrated signal to expose the

PMTs at the telescope aperture. The light is 2.5 m diameter drum-

Chapter 4 33

Figura 4.5: The picture on the left exhibits a squematic of the telescope

arregment. On the right is a picture of the details of the camera, PMTs and

mirrors.

shaped light composed of a pair of pulsed UV LEDs, mounted on the

exteriors of FD apertures, providing a known pulsed photon ﬂux of

375±12 nm. The light source ﬁlls the aperture, providing illumination to

each pixel. Knowing the ﬂux from the signal and the response of the data

acquisition system, it is obtained the calibration required for each PMT.

It is estimated that the variation seen in the total ﬂux by the pixels

is less than 1% and there are corrections applied for this variations.

The sensitivity for the Pierre Auger Observatory telescopes pixels is

approximately 4-5 photons/FADC count. An absolute calibration of each

telescope is performed every 3 month, but some parameters have to be

revised more frequently and this is done by the relative calibration (44)

Relative Calibration In this case, optical ﬁbers bring light signals to three

diﬀerent diﬀuser of each telescope:

1. in front of the camera, with a diﬀuser at the center of the mirror

2. along the lateral edges of the camera, body facing towards the

mirror

3. facing 2 reﬂecting foils on the inner side of the telescope shutters

The total integrated charge is measured and compared to the same

quantity measured in a reference run as close as possible to the absolute

calibration, allowing to monitor the short and long term stability of the

FD, relative timing between pixels and gain for each pixel. Normally

this type of calibration is performed twice, at the beginning and end of

Chapter 4 34

each operating night. The overall estimated uncertainty is in the range

of 1 − 3%.

4.3.2

Atmosphere Monitoring

The determination of shower energy requires an accurate estimation of

the eﬃciency of ﬂuorescence light production and subsequent transmission

to a FD. So eﬀects of aerosol content on the atmosphere, dust, clouds, and

other pollutants need to be characterized. To measure the aerosols content a

monitoring routine is needed, which is done by a set of detectors (45):

LIDAR An elastic backscatter LIDAR is located near each eye. They detect

the backscattered signal from the fast pulsed UV lasers. During FD ope-

ration, the LIDAR system performs a routine scan of the sky providing

an hourly measurement of aerosol condition. If a FD detects a shower,

it can send the shower detector plane information to the LIDAR, which

will scan the shower detector plane to give update information.

Central Laser Facility (CLF) The CLF is located near the middle of the

Auger array, at distance that range 26 to 39 km from each eye. This

facility provides a laser generated test beam to investigate properties

of the atmosphere and ﬂuorescence detectors. Tracks recorded by the

CLF are very similar to the ones generated by air showers, and the laser

wavelength of 335 nm is in the middle of the ﬂuorescence spectrum.

Scattered photons from the laser beam by the atmosphere produce

tracks detected by the telescopes, these tracks are used to determined

the aerosol content in the atmosphere. Scattering from the beam is

dominated by Rayleigh (molecular) process. The predictable intensity

of light scattered from the beam at each height can be used to obtain

the vertical aerosol optical depth, trough aerosol attenuation and some

geometrical corrections. Also CLF can send a signal simultaneously to

a SD tank via optical ﬁber to test the relative timing between the FD

and SD. In addition CLF houses a weather station and radiometric cloud

detector (43).

Horizontal Attenuation Monitors (HAM) The HAMs measure the atte-

nuation length at near ground level between the Auger eyes. Each system

consist of a DC light source located at one building and a receiver located

at another building. The digital convertor light sources provides a broad

spectrum of wavelength (300-400 nm) where the FDs are sensitive. The

Chapter 4 35

light detectors consist of UV improved CCD arrays at the focus of 15 cm

diameter mirrors. A measurement of the horizontal attenuation length

at these wavelength is made every hour of FD operation. The HAMs me-

asure mainly the wavelength dependence of the horizontal attenuation

length, described by a power of law as:

HAL

λ1

HAL

λ2



λ1

λ2



(4-1)

where HAL is horizontal attenuation length, γ is the index of power law

and λ the wavelength. The cross-check of horizontal measurements is

done with the LIDAR system.

Aerosol Phase Function Monitors (APF) The aerosol scattering proper-

ties depend on the speciﬁc characteristics of the aerosols. The AFPs are

design to measure the aerosol diﬀerential scattering cross section. This is

made by ﬁring a horizontal collimated beam of light from a Xenon ﬂash-

lamp past the front of an FD. The track that is generated contains a wide

range of light scattering angles (30

◦

− 150

◦

). The APFs include narrow

band ﬁlters that can be used to monitor the wavelength dependence on

the cross section.

Cloud Cameras Clouds can have very large optical depths and aﬀect deeply

the scattering and transmission properties of the atmosphere. The cloud

cameras provide a detailed sky map of clouds distribution. They consist

of infrared cameras which are sensitive to the temperature diﬀerence

between the clear sky and clouds. There are plans to have one camera

for each FD and generate a full sky scan every 15 minutes.

Star Monitors Viewing the attenuation starlight is possible to measure the

total optical depth from observation level to the top of the atmosphere.

And this information can be used to cross-check the total optical depth

measure by laser monitoring systems. Auger uses two kinds of star

monitoring, one ﬁxed, that use a CCD to monitor star images from

elevations of 10

◦

to zenith. Attenuation measures are made by tracking

star images through the ﬁeld of view at diﬀerent slant optical depths.

The second kind uses a narrow ﬁeld of view CCD at the focus of a 20 cm

diameter mirror mounted on a telescope steering mechanism, that allows

to look at the light ﬂux from one star or at the light from the HAM

system. The star monitors will be able to check the aerosol attenuation,

wavelength dependence.

Chapter 4 36

4.4

Status

This section is intended to summarize the actual status of the observatory

and the future plans.

– 1200 tanks deployed and in fully operation

– The deployment of tanks is planed to be ﬁnish by the end of 2007

– All ﬂuorescence detectors are taking data

– First scientiﬁc results already published

Angular Resolution

To determine the arrival direction of cosmic rays with optimal precision,

we must identify the uncertainties of our measurements. The precision with

which is possible to reconstruct the primary cosmic ray arrival direction is the

Angular Resolution (AR).

In the following section we will explain diﬀerent methods to determine

the angular resolution for the surface detector array. The ﬁrst one is done on

an event by event basis, taking into account the uncertainties of zenith (θ)

and azimuth (φ) angles obtained from the reconstruction algorithms (section

5.1); the second one is a direct measurement obtained from the space angle

diﬀerence between two reconstructions of the same shower, using a sub-array

of doublets (section 5.2).

5.1

On an event by event basis

The angular resolution depends mainly on the measurement accuracy of

the arrival time of particles in the tanks, and in second order on the shower

front model, signal and core position uncertainty. Knowing the uncertainties

for individual measurements, it is possible to weight their contribution in the

determination of the arrival direction.

The angular resolution is estimated by the reconstruction (see appendix

A) of the arrival direction of the shower. To determined it, on an event by

event basis, are used the zenith (θ) and azimuth (φ) uncertainties obtained

from the reconstruction, using the relation (47):

F (η) = 1/2 (V [θ] + sin

(θ) V [φ]) (5-1)

where η is the space-angle, and V [θ] and V [φ] are the variance of θ and φ

respectively. If θ and φ/ sin(θ) have Gaussian distribution with variance σ

then F (η) = σ

and η has a distribution proportional to e

−η

/2σ

d(cos(η))dφ.

Therefore is we deﬁne the AR as the angular radius containing 68% of

the shower coming from a point source (47), then:

AR = 1.5



F (η) = 1.5σ (5-2)

Chapter 5 38

To estimate the arrival direction of the primary cosmic ray with the

maximum precision, one must, among other things, adequately model the

measurement uncertainties of each individual tank participating in the event.

For that, a model was design to reproduce the measurement accuracy of the

particle arrival time in the tanks.

5.1.1

Time Variance Model

The Time Variance Model (48) was design to reproduce the uncertainties

of particle arrival time in the tanks. The angular accuracy of the SD events

is driven by the accuracy with which one can measure the arrival time of the

shower front (T

) in each station.

An air shower while traversing the atmosphere is in continual develop-

ment, until it reach a maximum. The development of the shower seems like

a large, thick, cylindrical plate. The shower front can be interpreted as the

radius of curvature of the plate. The shower front model used to determined

the of arrival time (being spherical, cylindrical or planar), inﬂuences on the

determination of the uncertainties of the arrival direction, but not as much as

clock precision, for this reason we used a parabolic model (being the easiest

one)to describe the data.

In (48) is assumed that the particle distribution in the shower front can

be described as a Poisson process over some interval time T . In reality, the

particle distribution in the shower front is not a uniform Poisson process. At

the beginning of the shower the particle arrival frequency is larger than towards

the end. It is however suﬃcient to assume that the frequency is constant over

some interval large enough to have a good fraction of the total number of

particles reaching the ground but less than the total thickness of the shower

front at that location.

The ﬁrst particle arrival time (T

) is used as the estimator for the shower

front arrival

. T

has a distribution function given by:

f(T

) =

−T

(5-3)

where τ is the characteristic decay time. We estimate τ as the ratio of the time

of arrival of the n-th particle (T

) to n: τ = T

/n.

The variance of T

, is given by the sum of the detector clock precision

) and of the variance of T

, which is τ

. Since we estimate the parameter T

from the data itself, the variance of T

becomes:

In fact, an unbiased estimator should be T

−

E[t

], where

E[t

] is the expectation

value.

Chapter 5 39

0.2

0.4

0.6

0.8

220 230 240 250 260 270 280

Time(µs)

Normalize integrated signal

0 0.5 1.0 1.5 2.0 2.5

Figura 5.1: Example of an integrated FADC trace for a detector at 700 m

from the shower core position. T

is the shower front arrival time, T

is the

arrival time of the ﬁrst particles, and T

is the time it takes to reach 50% of

the total integrated signal in the trace (48).

V [T

] =





n − 1

n + 1

+ b

, (5-4)

where b

represents the GPS uncertainty and the resolution of the FADCs of

the tanks.

To obtained (T

), we used the FADCs that record the shower signal in the

tanks. The FADCs give the signal as a function of time, therefore is possible

to build the time parameters. In our case is used the T

, which represents

the time interval that contains 50% of the total signal measured by the PMT

FADC traces (see ﬁgure 5.1). To calculate n, it is assumed that muons are the

particles that contribute the most to the time measurement and is deﬁned as:

n =

V EM

T L(θ)

(5-5)

where S

V EM

(see chapter §4) is the total integrated signal in the FADC traces

in VEM units and TL(θ) is the track length of a shower given as the ratio

of the detector volume and the area subtended by the arriving particles with

zenith angle θ:

T L(θ) =

πrh

πr cos θ + 2h sin θ

(5-6)

with r = 1.8 m is the tank radius and h = 1.2 m is the detector height.

Then we could rewrite equation 5-4 as:

V [T

] = a





n − 1

n + 1

+ b

(5-7)

a and b are the parameters to be adjusted with the adjacent tanks. The

parameter a is a scale factor, containing all the assumption that were taking

into account to write the variance deﬁnition (is expected to be in the order

of one). The parameter b is given by our GPS system resolution (∼10 ns)(49)

Chapter 5 40

and the resolution of our FADC traces (25/

√

12 ns)

(49).

5.1.2

Data Selection

To estimate the parameters a and b a special set of tanks is used, the

”twin”tanks (see chapter § 4). Only events where at least one pair was trigger

are used for the analysis.

We deﬁne the time diﬀerence for these pairs as:

∆T = dT

− dT

(5-8)

where dT

is the time diﬀerence from the tank to the shower front, as shown

in ﬁgure ??.

Figura 5.2: Picture of twin tanks showing the time diﬀerence between tank

and shower front (for each tank).

Using the time diﬀerence dT

, guaranties that the shower front model

does not aﬀect our estimation, because when determining the ∆T variance for

both tanks we eliminate the term corresponding to the uncertainties in the ﬁt,

due to the shower front.

We also applied some selection criteria, over this data to guarantee the

quality of the events. The cuts used are:

1. All events must be T4. (see chapter § 4, section 4.2.4).

2. |∆T | < 200 ns to avoid tails of the distribution and a good overall

reconstruction (see ﬁgure 5.3 ).

3. The distribution of X, where X = ∆T/



V [∆T ] should have a gaussian

normalized distribution, if the model properly represents the uncertain-

ties.

Having a function f(x) deﬁne in an interval d, with a p.d.f. Its variance is deﬁned as

V [x] =

(d)

Chapter 5 41

Figura 5.3: Comparison of the ∆T

distributions for doublet data (red-

solid) and for MC events (blue-dash

line).

Distribution

200

400

600

800

1000

1200

-6 -4 -2 0 2 4 6

Entries

Mean

RMS

1000000

9405

0.1568E-01

0.9736

345.8 / 48

Constant 809.6

Mean 0.5489E-02

Sigma 0.8928

Distribution

Figura 5.4: Distribution of

∆T/



V [∆T ], where V [∆ T ]

= V [T1] + V [T2] with T1 (T2)

calculated using equation 5-7 for the

ﬁrst (second) twin tank, with a = 1

and b = 12 ns.

After applying all the cuts to the data collected since 2004 up to April

2007, we get approximately 17000 events.

5.1.3

The Fit

Given a random sample x

, ..., x

of a random variable X ∼ N(µ, σ

)

with a normal distribution, the likelihood function of θ = (µ, σ

) is:

L(θ, x) =



f(θ, x

) =



2πσ



exp

−

(x−µ)

2σ

(5-9)

with σ

the variance and µ the mean.

Since X has a Gaussian distribution (see ﬁgure 5.4), the parameters are

ﬁt maximizing the likelihood function. Rewriting equation 5-9 for the time

variance case:

L =



k=1



2πV [∆T

]

−

∆T

2 V [∆T

]

(5-10)

where N being the total number of events and V [∆T

] = V [T

1,k

] + V [T

2,k

the sum of the variance of the T

of each member of the doublet, calculated

for each k event, using equation 5-7. It is usually easier to work with the

logarithm of L and it can be proved that both functions maximize for the

same values. Considering the properties of the likelihood functions, maximizing

the likelihood is equal to minimizing  = −2 ln(L). Taking advantage of this

Chapter 5 42

property, it was used a minimization package called Minuit (CERN software

library) to minimize the function:

 =



ln (2πV [∆T

]) +

∆T

V [∆T

]

(5-11)

After the minimization is done, we obtained the values for a and b.

In table 5.1 are shown the values of a and b obtained in (48), where the

ﬁt was done using only the original pairs of doublets (see chapter § 4) and with

data from 2004 to 2006. Compare to the values obtained with the data of the

new doublets, which provides with more statistics.

In ref. (48) Present Work

a = 1.0 ± 0.2 a = 0.6 ± 0.1

b = (12 ± 3) ns b = (13 ± 4) ns

Tabela 5.1: Comparison of the adjusted parameters a and b, between the results

obtained in (48) and the present work .

Comparing this values we can appreciate some diﬀerence, mostly on the

results obtained for the parameter a. This diﬀerence appear mostly because

the calibration suﬀer some modiﬁcation, since the last time the parameters

where ﬁt, and also because the parameter depends on the treatment given

to the FADC traces, i.e., it is aﬀected by the way the T

was deﬁned. For

the case of b, no changes are observed, since the GPS and FADC accuracy

does not change. But although those diﬀerence exist, it will be shown in the

following section that the model is still robust and reproduces well the time

uncertainties.

5.1.4

Validation of the Model

In order to validate the model, several test were done. First it was checked

the robustness of the model, i.e., we veriﬁed that the model does not depend

on variables such as zenith angle, signal and distance to the shower core. For

this we studied the RMS distribution of X, as it was deﬁned in section § 5.1.2

It is expected that if the time variance model reproduces the uncertainties

correctly, we will obtain a constant value of X for any value of the related

parameters.

In ﬁgure 5.5, it is shown the RMS of the distribution of X for diﬀerent

bining in zenith angle, signal, and distance to the core.The distribution is

almost constant for all cases and close to 1, although we see a slight dependence

on the distance distribution that needs further studies. But overall we may

state to say that the model does not have a dependence over this parameters.

Chapter 5 43

Figura 5.5: The RMS distribution of dT

−dT



V [T

] + V [T

] as a function

of the shower zenith angle (top), signal (middle) and distance to shower core

(bottom). See text for details.

Figura 5.6: χ

probability distribution for all T5 events (top), T5 events with

zenith angle greater than 55

◦

(middle) and T5 events with zenith angle smaller

than 55

◦

(bottom). In the last ﬁgure, the distribution is plotted with 2 diﬀerent

scales, the same than the others (red line) and a zoom (dashed line) to see the

details

Chapter 5 44

250

500

750

1000

0 0.2 0.4 0.6 0.8 1

All events

250

500

750

1000

0 0.2 0.4 0.6 0.8 1

Events with θ < 55

250

500

750

1000

0 0.2 0.4 0.6 0.8 1

Events with θ > 55

100

200

300

Figura 5.7: Same ﬁgure as 5.6, but for multiplicities larger than 4.

We also studied the distribution of χ

probability of the T5 events (see

chapter §4, section 4.2.4) for 4 or more stations. In ﬁgure 5.6 it is shown this

distribution for all events, events with zenith angle greater than 55

◦

and smaller

than 55

◦

. This cuts in angle are done, because it is important to show that the

model works ﬁne for all angles, without compensating one set from the other.

It seems that for all cases we obtained a ﬂat distribution, as it was expected.

This means that the variance model properly reproduce the uncertainties of

the arrival time of particles in the tank.

The peak at the beginning of the distribution could be explained for those

tanks in the event that has low signal, therefore the variance is overestimated

causing a large χ

on the distribution. But as it is seen in ﬁgure 5.7, this

behavior improve as we increase the multiplicity, for number of station greater

than 5 the peak almost disappears.

5.1.5

Results

Once the model has been veriﬁed, we could estimated the angular

resolution using the equation 5-1.

In ﬁgure 5.8 we show the angular resolution of all T5 events (see chapter

§4, section 4.2.4) collected from January 2004 to April 2007, for a geometrical

reconstruction

only, using a parabolic shower front. As we can see the value

of the angular resolution is approximately 1.6

◦

in the worst case for 3 stations,

The geometrical reconstruction adjust the parameters; T

, direction of the shower, and

the radius of curvature of the shower front

Chapter 5 45

0.25

0.5

0.75

1.25

1.5

1.75

2.25

0 10 20 30 40 50 60 70 80

θ (degrees)

Angular Resolution (degrees)

3 stations

4 stations

5 stations

6 or more stations

Figura 5.8: Angular Resolution for the surface detector as a function of zenith

angle θ (geometrical reconstruction only), for diﬀerent multiplicities: 3 stations

(circles), 4 stations (squares), 5 stations (up triangles) and 6 or more stations

(down triangles)

0.25

0.5

0.75

1.25

1.5

1.75

2.25

0 10 20 30 40 50 60 70 80

θ (degrees)

Angular Resolution (degrees)

3 stations

4 stations

5 stations

6 or more stations

Figura 5.9: Angular Resolution for the surface detector as a function of zenith

angle θ (complete reconstruction), plotted for diﬀerent multiplicities: 3 stations

(circles), 4 stations (squares), 5 stations (up triangles) and 6 or more stations

(down triangles)

Chapter 5 46

Figura 5.10: Event selection. On the left the original event and on the right after

the selection of pairs. This is a representation of a real event 200627901937

but improve considerably for larger multiplicities, being better than one for

the case of 6 stations or more, corresponding to energies above 10

For zenith angle larger than 60

◦

we have a poor statistics for events with

3 stations only, causing a decrease on the accuracy and a peak on the proﬁle.

Also for horizontal showers the reconstruction is done for events with at least

4 working stations. Therefore for this case the analysis is meaningless.

In ﬁgure 5.9 we show the case of the angular resolution for a complete

reconstruction

. In this case the values of the angular resolution increase

approximately 5%, because for the complete reconstruction there are more free

parameters to be adjusted than in the geometrical reconstruction, including

the core position, which aﬀects the uncertainties on the arrival direction of

particles, and therefore appears a correlation between the uncertainties of the

zenith and azimuth angle and the coordinates of the position of the core. We

also can appreciate a hump around the 40

◦

, especially for 3 station case, that

it is due to the contribution of statistical uncertainties of the core position.

5.2

Direct Measurement

The sub-array of doublets, superhexagon (see chapter §4) as shown in

ﬁgure 4.4, is used to obtain the angular resolution from a direct measurement.

In the analysis we select those events where at least three pairs has

been triggered

and that the shower core falls into the region deﬁne by these

triggered stations, to guarantee a good reconstruction. Two reconstructions

The complete reconstruction adjust geometrical parameters, the core position and

parameters to describe the LDF (see appendix A)

This is to assure a T3 event formed by the doublets

Chapter 5 47

100

150

200

250

300

350

-5 -4 -3 -2 -1 0 1 2 3 4 5

Entries

Mean

RMS

1116

0.4898E-01

0.9841

Constant 323.9

Mean 0.5311E-01

Sigma 0.8960

(Θ

-Θ

)/(V[Θ

]+V[Θ

])

1/2

Figura 5.11: Distribution of the diﬀe-

rence of theta. See text for details.

100

150

200

250

300

350

-5 -4 -3 -2 -1 0 1 2 3 4 5

Entries

Mean

RMS

1130

-0.8454E-02

0.9988

Constant 305.2

Mean 0.1119E-02

Sigma 0.9481

(Φ

-Φ

)/(V[Φ

]+V[Φ

])

1/2

Figura 5.12: Distribution of the diﬀe-

rence of phi. See text for details.

are performed; the ﬁrst one done for a set of stations (green station on ﬁgure

5.10) and the second one for the respective pair stations (yellow stations on

ﬁgure 5.10). These will provide us two semi-independent estimates of θ and φ,

one for each reconstruction. It has to be point out that only stations that are in

pairs are kept for the reconstructions,where a pair means that both twin tanks

were triggered at the time of the event, as it is seen in ﬁgure 5.10. The green

stations correspond to the tanks that were deployed in the array originally and

they send the trigger signal of the event.

In ﬁgures 5.11 and 5.12 it is shown the distribution of C.

C =

− c



+ dc

(5-12)

where c

is θ

or φ

for i = 1, 2 each pair of station, and dc

is the corresponding

uncertainty.

In both cases we obtained a gaussian distribution, center in zero and with

σ close to 1, meaning that the density probability function is normal (in virtue

of the central limit theorem), therefore the uncertainties are well represented.

We determined the angular resolution by estimating the space angle (η)

diﬀerence between both reconstructions, for diﬀerent multiplicities as shown

in ﬁgure 5.14. Fitting the histograms with the function:

exp

−η

2σ

d(cosη)dφ

(5-13)

we get the values of σ for each case. Then the angular resolution is given by:

AR = 1.5σ (5-14)

In table 5.2 is a summary of the values obtained for AR using the three

methods. As it can be seen, these values conﬁrmed those obtained on an event

Chapter 5 48

100

150

0 1 2 3 4 5

3 stations

4 stations

Entries

Mean

RMS

/ ndf

995

1.33

0.78

39.62 / 14

1.06 ± 0.02

0 1 2 3 4 5

5 stations or more

Entries

Mean

RMS

/ ndf

163

1.13

0.77

20.06 / 13

0.79 ± 0.05

0 1 2 3 4 5

Entries

Mean

RMS

/ ndf

0.88

0.61

15.96 / 8

0.60 ± 0.04

Space-angle difference (degrees)

Figura 5.13: Space Angle diﬀerence between the two reconstructions of the set

of doublets for diﬀerent multiplicities: 3 stations (top), 4 stations (middle), 5

stations or more (bottom).

by event basis. Therefore we could conﬁdently say that the uncertainties of

particle arrival time are reproduce correctly. We also can aﬃrm that we have

a pretty good knowledge of the behavior of the detector and the angular

resolution is in the worst scenario (3 stations) is 1.7

◦

and for high energies

(above 10

) is better than one, which prove to have a good resolution.

# σ AR AR

1.5 σ event by event

= 3 1.05 ± 0.03 1.6 1.7

= 4 0.81 ± 0.06 1.2 1.0

≥ 5 0.61 ± 0.05 0.9 0.8

Tabela 5.2: Comparison of the values obtained for the angular resolution, using

the doublets and the time variance model.

5.3

Chapter 5 49

Hybrids

Following the same principle used for the sets of doublets, we estimated

the AR using the Hybrid events. This are the events that can be reconstructed

both by FD and SD. We determined the space angle diﬀerence between the

hybrid and SD reconstruction, using the data since 2004 to April 2007. Fitting

the space angle distribution with equation 5-13, we obtained the value of σ

for the diﬀerent multiplicities and from equation 5-14 we obtained the angular

resolution for each case.

# θ σ

HybSD

SD−Hyb

SD−only

SD−Hyb



HybSD

− σ

Hyb

1.5 σ 1.5σ

= 3 0-30 1.4 1.3 2.0 1.8

= 3 30-50 1.3 1.2 1.8 1.8

= 4 30-50 1.2 1.1 1.7 1.1

= 5 30-50 1.1 1.0 1.5 1.0

≥ 6 30-50 0.9 0.8 1.2 0.7

≥ 6 50-70 0.9 0.8 1.2 0.4

Tabela 5.3: Comparison of the values obtained for the angular resolution, using

the hybrid reconstruction and the SD-only reconstruction.

In order to properly make the comparison, we need to consider the

angular accuracy of the hybrid reconstruction (σ

Hyb

). In order to do this,

we determined the angular resolution using σ

SD−Hyb

, which is obtained by

SD−Hyb



HybSD

− σ

Hyb

, where it is assumed that σ

Hyb

= 0.5

◦

(50). In

table 5.3 are shown the values obtained for σ and the angular resolution

respectively. As it can be seen the results obtained seems to be in reasonable

agreement. For the case of 3 stations, the angular resolution is the same for

both cases, which corroborates that the uncertainties are properly estimated.

For higher multiplicities a slight diﬀerence appears. This is due to two factors,

in ﬁrst place the systematics uncertainties for the hybrid reconstruction are

not taken into consideration, and in second order the low statistics for SD

only

Chapter 5 50

200

400

0 2 4 6

3 stations - θ ∈ (0, 30) 3 stations - θ ∈ (30, 50)

Entries

Mean

RMS

/ ndf

4784

1.83

1.15

303.4 / 29

1.42 ± 0.02

200

400

600

0 2 4 6

Entries

Mean

RMS

/ ndf

5562

1.71

1.11

404.8 / 29

1.29 ± 0.01

100

200

300

0 2 4 6

4 stations - θ ∈ (30, 50) 5 stations - θ ∈ (30, 50)

Entries

Mean

RMS

/ ndf

2125

1.56

1.06

179.6 / 29

1.16 ± 0.02

100

0 2 4 6

Entries

Mean

RMS

/ ndf

816

1.45

0.98

68.4 / 27

1.07 ± 0.03

100

0 2 4 6

6 or more stations - θ ∈ (30, 50) 6 or more stations - θ ∈ (50, 70)

Entries

Mean

RMS

/ ndf

664

1.26

0.91

54.8 / 27

0.90 ± 0.03

100

150

0 2 4 6

Entries

Mean

RMS

/ ndf

959

1.17

0.82

72.5 / 25

0.87 ± 0.02

Space-angle difference (degrees)

Figura 5.14: Space Angle diﬀerence between the hybrids reconstruction and

SD reconstruction for diﬀerent multiplicities: 3 stations (top), 4 stations and

5 stations (middle) 6 or more (bottom).

Conclusions

One of the aims of the Pierre Auger Observatory is to ﬁnd the sources

of the most energetic particles in the universe. For this reason is of great

importance to estimate the arrival direction of cosmic rays with accuracy. To

know the arrival direction with optimal precision we need to take into account

the measurement uncertainties.

This work was developed with the intention to determined the angular

resolution of the surface detector for the Pierre Auger Observatory. For this

purpose we used the data collected since 2004 up to April 2007.

The angular resolution was determined in three diﬀerent ways. One on

an event by event basis, using the time variance model design to estimate the

uncertainties of the arrival time of particles in the tank. It is based on the

shower zenith and azimuth angle uncertainties. With this model it is obtained

an estimation of the uncertainties of individual measurements, allowing to

weight their contribution in the determination of the arrival direction. Several

test were performed to validate the model, all indicating that the model

properly represents the measurement uncertainties. The second method is a

direct measurement of the angular resolution. We determined the diﬀerence

of space angle between two reconstruction. By ﬁtting the distribution of this

diﬀerence space angle, we obtained a value of σ, which is use to determined

the angular resolution. This method is used twice. First it was used the sub-

array of doublets, the superhexagon. Events with at least 3 triggered pair

of stations were used to obtained two semi-independent reconstructions. The

second time we used the hybrids reconstruction and compare it with the SD-

only reconstruction.

The angular resolution of the surface detector was found to be 1.7

◦

for the case of events with only 3 stations triggered, and improving as the

multiplicity (number of stations) increases, being better than 1

◦

for 6 stations,

corresponding to events with energies above 10

. A comparison of the results

obtained with the three methods shows that they are in good agreement,

meaning that we have good knowledge of the behavior of our detector. This

also implies that the time variance model is a good estimator of the time

Chapter 6 52

uncertainties of the surface detector.

For the future it is planned to revised the deﬁnition of the T

and re-

calculate the adjusted parameters (a and b), to observe the changes. Also,

recalculate the AR for the doublet reconstruction after collecting more data,

in order to be able to do a better comparison an diminish the eﬀects of low

statistics. In addition we planned to do some monte carlo and hybrid recons-

truction simulations, to compare the results obtained with the simulations.

It has been though also to follow the same reasoning of the analysis done,

to estimated the signal accuracy of surface detectors.

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2.1 2.1, 2.3.4 2.1, 2.3.4 2.2.1 2.2.1 2.2.1 2.2.2 2.2.2 2.2.2 2.2.2, 3.2 2.2.3

2.2.3 2.2.3 2.2.3 2.3 2.3.1 2.3.1 2.3.1 2.3.2, 2.3.3 2.3.2, 2.3.3 2.3.3 2.3.2,

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5.1, 5.1 5.1.1, 5.1, 5.1.3, 5.1, 5.1.3 5.1.1 5.3 A

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047

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(Nota:) las notas internas de la Colaboraci´on Pi-

erre Auger (GAPs) se encuentran disponible en

(http://www.auger.org/admin/index.html)

SD Reconstruction

In this section we will describe a basic design of shower reconstruction

(51) using the surface detectors measurements. The procedures of this observa-

tions is: measure the secondary particles of an air shower by several detectors

on the ground, remove the accidental noise and reconstruct using the time and

signal reaching the detectors.

The reconstruction of SD events is divided in two parts:

1. Estimation of arrival direction and radius of curvature of the shower front

2. Estimation of core location and shower-size parameter S(1000)

As it was mentioned in the chapter §4, each surface detector contains 3

PMTs that records the signal produce by the shower and converted into VEM

units (see §4.2.3). After this conversion, three parameters are extracted from

the FADC trace: start time of the signal, integrated signal size in VEM units

and rise time.

Integrated Signal (S) Is the signal integrated over 10 µs, starting from

the arrival of the shower front. The signal size (VEM) of the station

is calculated by the average of the signal size of the available PMTs.

Start Time (t

) Deﬁne as the time slot when the integrated signal reaches a

given threshold. It is close to the arrival time of the ﬁrst particle in the

tank.

Rise Time (τ) As ﬁrst approximation, is the interval between the time slots

corresponding to 10% and 50% of the total S (multiple of 25 ns):

τ = t

− t

. Is proportional to the distance to the core.

Chapter A 58

A.0.1

Arrival Direction Reconstruction

The arrival direction is reconstructed for all the events that passed the

T4 requirements.

First, the parameters of the reconstruction are determine in the following

order:

– The core position of the shower is determined as the barycenter deﬁned

by the stations participating on the event, weighted with the squared

root of the signal of each stations.

– The angles θ and φ are estimated from a ﬁt applied over the tanks

participating in the event

Once the parameters have being estimated, the core position is ﬁxed

with these values. A ﬁnal adjust is done using the package Minuit to obtain

the remaining parameters, such as:

– T

= arrival time of the shower core at ground

– R = radius of curvature of shower front

– u = sin θ cos ϕ

– v = sin θ sin ϕ

Then using the time variance and the parametrization:

f(T

, u, v, R) = T

−

+ vy

+ y

− (x

u + y

2Rc

(A-1)

We obtained a minimization of the form:

(f(T

, u, v, R) − t

0,i

)

variance

(A-2)

In the case of 3 or 4 active stations in the event, the radius of curvature is

ﬁx as constant, with a value of 7.5 km. For 5 or more stations all the parameters

are adjusted.

Chapter A 59

A.0.2

Energy Reconstruction

The energy reconstruction is more complex. The estimator used to

determined the energy of a shower is normally, the measured signal at certain

distance of the axis of the shower. This is to avoid the large ﬂuctuations

caused by the shower development. In the case of Auger, the parameter used

is S(1000), which is the signal size at 1000 m.

To estimate S(1000)is used the lateral distribution function (LDF), that

describes the fall of the signal as a function of distance.

The LDF used is a modiﬁcation of the NKG (see chapter §3):

exp

, θ) = S1000



1000





+ 700

1700



(A-3)

where S

exp

is expected signal size, β is the slope of LDF and r is the

distance to the axis in meters.

Once the direction of the shower axis is established, core location and

lateral distribution of the signal are estimated by LDF ﬁt.

The reconstruction can be done in two parts:

Geometrical Reconstruction This reconstruction ﬁts only the parameters

of the arrival direction

Complete Reconstruction Adjust all the parameters together, by doing

both ﬁts at the same time (arrival direction and energy).

A.1

Quality Cuts

After the SD reconstructions, a second selection of the events is done, to

keep only does events that are well reconstructed. The selection is done, by

applying some quality cuts that are deﬁned as follows:

Multiplicity The multiplicity is the number of active stations in an event. If

the number of active stations after the ”cleaning”is less than 3, arrival

direction cannot be estimated in the plane ﬁt, therefore is required that

at least 3 triggered stations.

cluster It is required that al least 3 stations must be neighboring each other,

making a compact triangle.

core location The estimated core location must be inside the array:

– Find the 3 nearest working stations to the core location that form

a triangle with 1500 m separation.

Chapter A 60

– The coordinates os stations and core location are projected on the

ground.

– Calculate the area of the triangle and the quadrangle form by the

3 stations and the core location.

– If the area of the triangle is greater than the quadrangle, the core

location must be inside the array, otherwise is outside.

Complementary Work

B.1

FD shift

The SD system has a potential duty cycle of 100%, while the ﬂuorescence

detector system has a duty cycle limited to about 10%, as data can only be

taken on clear nights with little moonlight.

The systems used to control the data acquisition, calibration of the

cameras and carry out the atmospheric monitoring of the FD buildings are

handled at the operation building and need supervising for the working nights.

Therefore, a schedule of the clear nights of the months is done in advance and

groups of voluntaries are organized to cover these periods.

During the development of the theses I had the opportunity to collaborate

to do an FD shift the Pierre Auger Observatory.

As it was mentioned above, the responsibility of a shifter consist on

controlling the procedures of calibration, regular data taking and detector and

atmospheric monitoring. The procedure for an FD shifts starts usually 2 hours

before the end of the astronomical twilight, which is calculated for every night

of the month.

The normal shift order includes these tasks:

– Checks of the hardware and the software processes;

– Performing the calibration A (sometimes B and C) and its analysis (see

chapter § 4, 4.3.1);

– Recording of shower data, operating the shutter according to the moon;

– Monitoring of the data ﬂow and checking the data quality;

– Stop of data taking and performing the post-run calibration;

– Shut down procedure and e-log update.

During this operation nights of the FD, also the systems for atmosphere

monitoring and sky scanning need to be supervised. I also had the opportunity

to work a couple of night operating the Lidar system. The responsibilities of

a Lidar shifter consist:

Chapter B 62

– Checking the Weather

– Launching Power Control

– Preparing the laser

– Setting the Telescope

– Enable the Lidar DAQ

– Enabling the raman run at Los Leones (before FD shift)

– Starting the weather monitors

– Enabling the autoscan (during FD shift)

– Enabling detection of hybrid and stereo events

– Checking Normal Operations: Every 10 - 15 Minutes

– Shut down procedure and e-log update.

Each of the steps described below have to be executed for each eye in

operation on the speciﬁc night.

To obtained a more detailed information about this procedures, the

following web page contains the manuals of all the procedures and systems

used. http://wiki.auger.org.ar/doku.php?id=fd:main

B.2

Calibration of Camera

During the period I was doing the FD shift in Malarg¨ue, the building

of Loma Amarilla was in its last stage of construction. Therefore the cameras

that are part of the detectors needed to be calibrated in order to start function.

This process consist on aligning the camera that contains the PMTs with

the center of curvature of the lenses and mirrors. This is done, because as it

was mentioned in chapter 4, the light produce in the atmosphere is collected

with the mirrors and reﬂected to the PMTs, therefore to capture the most of

light, the camera must be in the right position.

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