Pierre Auger Observatory: Fluorescence Detector Event...

UNIVERSITA’ DEGLI STUDI DI CATANIA

FACOLTA’ DI SCIENZE MATEMATICHE, FISICHE E NATURALIDOTTORATO DI RICERCA IN FISICA - XVIII CICLO

Domenico D’Urso

Pierre Auger Observatory:Fluorescence DetectorEvent Reconstruction

and Data Analysis

Tutor: Prof. A. Insolia

Tutor: Dott. F. Guarino

Coordinatore: Prof. F. Riggi

Tesi per il conseguimento del titolo

UNIVERSITA’ DEGLI STUDI DI CATANIA

FACOLTA’ DI SCIENZE MATEMATICHE, FISICHE E NATURALIDOTTORATO DI RICERCA IN FISICA - XVIII CICLO

Domenico D’Urso

Pierre Auger Observatory:Fluorescence DetectorEvent Reconstruction

and Data Analysis

Tutor: Prof. A. Insolia

Tutor: Dott. F. Guarino

Coordinatore: Prof. F. Riggi

Tesi per il conseguimento del titolo

logounict.ps

Per correr miglior acque alza le vele

omai la navicella del mio ingegno,

che lascia dietro a se mar sı crudele;

e cantero di quel secondo regno

dove l’umano spirito si purga

e di salire al ciel diventa degno.

Dante Alighieri, Divina Commedia: Purgatorio,

Canto I vv. 1-6.

Acknowledgements

I would like to acknowledge the inestimable help I received in writing

this thesis from my friends of the Naples Auger group. They helped

me in many different ways.

My thanks go out to my supervisor Prof. A. Insolia and to his patience

during these three years.

Especially, I would like to thank Laura for the peaceful background

she gave me in the most endless days.

I would like also to thank all my friends, which never have made me

fill alone.

Finally, I would like to thank my family that have always loved me

with all my caprices, defects and faults.

Contents

Introduction v

1 UltraHigh Energy Cosmic Rays 1

1.1 A few historical notes . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The Physics of UHECR . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Cosmic Ray Spectrum . . . . . . . . . . . . . . . . . . . . 4

1.2.2 Cosmic Ray Mass Composition . . . . . . . . . . . . . . . 8

1.2.3 The GZK Limit . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Possible Sources of UHECR . . . . . . . . . . . . . . . . . . . . . 14

1.3.1 Acceleration and Propagation of cosmic rays . . . . . . . . 18

1.3.1.1 Bottom-up acceleration mechanisms . . . . . . . 18

1.3.1.2 Direct Acceleration Mechanisms . . . . . . . . . . 18

1.3.1.3 The Fermi mechanism . . . . . . . . . . . . . . . 19

1.3.1.4 Top-down acceleration mechanisms . . . . . . . . 23

1.3.1.5 Cosmic ray Propagation . . . . . . . . . . . . . . 23

1.4 Experimental Outlook: Extensive Air Showers . . . . . . . . . . . 25

1.4.1 Shower Development . . . . . . . . . . . . . . . . . . . . . 25

1.4.1.1 The Electromagnetic Component . . . . . . . . . 30

1.4.1.2 The Muon Component . . . . . . . . . . . . . . . 34

1.4.1.3 The Hadron Component . . . . . . . . . . . . . . 35

1.4.2 The Longitudinal Development . . . . . . . . . . . . . . . 37

1.4.3 The Lateral Extension . . . . . . . . . . . . . . . . . . . . 39

1.4.4 Time Structure . . . . . . . . . . . . . . . . . . . . . . . . 42

1.4.5 Fluctuations in Shower Development . . . . . . . . . . . . 44

1.4.6 The Fluorescence Light . . . . . . . . . . . . . . . . . . . . 45

i

CONTENTS

1.4.6.1 Cerenkov, Rayleigh and Mie Contaminations . . 49

1.4.7 UHECR Detection . . . . . . . . . . . . . . . . . . . . . . 53

1.4.7.1 Indirect Techniques . . . . . . . . . . . . . . . . . 54

1.4.8 Fingerprints of primary species in EAS . . . . . . . . . . . 56

1.4.8.1 Muon Component . . . . . . . . . . . . . . . . . 56

1.4.8.2 Elongation Rate . . . . . . . . . . . . . . . . . . 57

1.4.8.3 Temporal Distribution Of Shower Particles . . . . 58

1.4.8.4 Lateral Distribution . . . . . . . . . . . . . . . . 58

2 The Pierre Auger Observatory 59

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.2 The Hybrid Detector . . . . . . . . . . . . . . . . . . . . . . . . . 60

2.3 The Southern Observatory . . . . . . . . . . . . . . . . . . . . . . 63

2.4 The Surface Array . . . . . . . . . . . . . . . . . . . . . . . . . . 65

2.4.1 SD Calibration . . . . . . . . . . . . . . . . . . . . . . . . 66

2.5 The Fluorescence Detector . . . . . . . . . . . . . . . . . . . . . . 67

2.5.1 FD Detector Calibration . . . . . . . . . . . . . . . . . . . 74

2.5.1.1 Absolute Calibration . . . . . . . . . . . . . . . . 75

2.5.1.2 Relative Calibration . . . . . . . . . . . . . . . . 77

2.6 Atmospheric Monitoring . . . . . . . . . . . . . . . . . . . . . . . 80

3 Event Reconstruction with Pierre Auger Data 84

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.2 FD Data Acquisition Strategy . . . . . . . . . . . . . . . . . . . . 86

3.2.1 First Level Trigger . . . . . . . . . . . . . . . . . . . . . . 86

3.2.2 Second Level Trigger . . . . . . . . . . . . . . . . . . . . . 87

3.2.3 Third Level Trigger . . . . . . . . . . . . . . . . . . . . . . 87

3.2.4 The T3 trigger . . . . . . . . . . . . . . . . . . . . . . . . 88

3.3 SD Trigger and Data Selection . . . . . . . . . . . . . . . . . . . . 89

3.3.1 Tank Level Triggers . . . . . . . . . . . . . . . . . . . . . . 90

3.3.2 Event Selection Triggers . . . . . . . . . . . . . . . . . . . 91

3.3.3 T5 quality Trigger . . . . . . . . . . . . . . . . . . . . . . 91

3.4 Hybrid Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.5 SD Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . 94

ii

CONTENTS

3.5.1 SD Geometry Reconstruction . . . . . . . . . . . . . . . . 94

3.5.2 SD Energy Estimation . . . . . . . . . . . . . . . . . . . . 96

3.6 FD Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . 97

3.6.1 Geometrical Reconstruction . . . . . . . . . . . . . . . . . 98

3.6.1.1 Shower Detector Plane Reconstruction . . . . . . 99

3.6.1.2 Shower Axis Reconstruction . . . . . . . . . . . . 100

3.6.2 Longitudinal Profile Reconstruction . . . . . . . . . . . . . 104

3.6.2.1 Energy Estimation . . . . . . . . . . . . . . . . . 106

3.6.3 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . 107

3.7 The Offline Software Framework of the Pierre Auger Observatory 108

4 Application of Gnomonic Projection to the SDP reconstruction

for FD events 111

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

4.2 Reconstruction strategy . . . . . . . . . . . . . . . . . . . . . . . 112

4.2.1 Pixel Selection . . . . . . . . . . . . . . . . . . . . . . . . 113

4.2.2 Definition of coordinates . . . . . . . . . . . . . . . . . . . 114

4.2.3 Gnomonic Projection approach to SDP reconstruction . . 115

4.3 Performances of the method . . . . . . . . . . . . . . . . . . . . . 118

4.3.1 Resolution on SDP reconstruction . . . . . . . . . . . . . 119

4.4 Effect of improved SDP resolution on shower reconstruction . . . 124

4.5 A first look at CORSIKA showers . . . . . . . . . . . . . . . . . . 125

5 FD reconstruction accuracy studies by means of CLF laser shots131

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.2 Analysis Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

5.3 Angular Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5.4 Core Determination . . . . . . . . . . . . . . . . . . . . . . . . . . 138

5.5 Telescope Alignment . . . . . . . . . . . . . . . . . . . . . . . . . 141

5.5.1 Alignment Technique . . . . . . . . . . . . . . . . . . . . . 142

5.5.1.1 CLF Laser Shots Sample Selection . . . . . . . . 143

5.5.1.2 Sheaf Center Determination . . . . . . . . . . . . 143

5.5.2 Alignment Tests . . . . . . . . . . . . . . . . . . . . . . . . 147

iii

CONTENTS

6 Analysis of FD Data 153

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

6.2 Reconstruction Accuracy and

Definition Of Analysis Cuts . . . . . . . . . . . . . . . . . . . . . 154

6.2.1 The Simulated Data Sample . . . . . . . . . . . . . . . . . 154

6.2.2 Definition of Analysis Cuts . . . . . . . . . . . . . . . . . . 155

6.2.2.1 Shower Detector Plane . . . . . . . . . . . . . . . 157

6.2.2.2 Shower Axis . . . . . . . . . . . . . . . . . . . . . 160

6.2.2.3 Longitudinal Shower Profile . . . . . . . . . . . . 160

6.2.3 Application Of Analysis Cuts To Real Data . . . . . . . . 166

6.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

6.3 Reconstruction of Real FD Events . . . . . . . . . . . . . . . . . 172

6.4 Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

6.4.1 All Particle Spectrum . . . . . . . . . . . . . . . . . . . . . 178

6.4.1.1 Detector Aperture . . . . . . . . . . . . . . . . . 179

6.4.1.2 Live Time Determination . . . . . . . . . . . . . 182

6.4.1.3 Spectrum Evaluation . . . . . . . . . . . . . . . . 182

6.4.2 Elongation Rate . . . . . . . . . . . . . . . . . . . . . . . . 186

6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Conclusions 192

Bibliography 194

iv

Introduction

The cosmic ray story begins about 1900: 100 years later most of the main issues

are still open questions, as sources, acceleration mechanisms, propagation and

composition, especially for the extremely high energy cosmic rays, around 1020

eV .

The Pierre Auger Observatory is the biggest experiment on cosmic rays even

conceived and it has been designed in order to solve the fascinating cosmic ray

puzzle. The experiment involves several universities and research institutes from

18 countries, a collaboration with more than 300 physicists. The project consists

of a two-sites observatory, one for each terrestrial hemisphere. The Southern

Observatory will be completed st the end of 2006. It is located i the Pampa

Amarilla, in the Mendoza Province, Argentina. The Northen Observatory will

be built in Colorado. Each site will instrument a 3000 km2 area with an array

of particle detectors, water Cerenkov detectors, overlooked by a group of fluo-

rescence telescopes, disposed at the edges of the area, within 4 buildings, called

eye. Both detection techniques have been well established, separately, by prior

experiments. The combined use of these two techniques can allow: to achieve an

unprecedented reconstruction accuracy, to perform cosmic ray energy measure-

ments almost model independent; to study systematic effects inherent to either

methods alone; to measure a wide set of shower parameters in order to identify

cosmic ray mass composition.

In this thesis, I will discuss original contributions to fluorescence detector

event reconstruction and analysis: new algorithm implmentation for geometrical

reconstruction of fluorescence events; reconstruction accuracy studies; telescope

misalignment measurement; determination of detector reconstruction efficiency

v

and live time; first estimation of all particle data spectrum and elongation rate

with fluorescence data.

The first chapter is an introduction to main aspects of ultra high energy cosmic

ray physics. It describes extended air shower development and the production of

fluorescence light in the case of shower with energy above 1017 eV .

In the second chapter, main characteristics of Pierre Auger Observatory are

presented: the Fluorescence detector, the Surface detector and briefly the atmo-

spheric monitoring.

The event trigger and reconstruction strategy are described in chapter 3.

There is a description of all level trigger used in the Fluorescence and Surface de-

tector data acquisition and of the hybrid trigger strategy, which allows to combine

the use of the two different techniques. Event reconstruction are presented step

by step in the case of pure Surface array events, of pure Fluorescence detector

events and of hybrid events.

Chapter 4 is completely devoted to the discussion of the use of gnomonic pro-

jections in the Fluorescence detector event reconstruction. Gnomonic projections

allow to reduce the usual procedure (derived from Fly’s Eye experiment, first to

use the fluorescence technique to study cosmic ray showers) of computing the

shower detector plane - namely the plane containing the shower trajectory and

the observation point - to a linear fit, once the spherical surface of telescope ac-

tive camera, made by 440 photomultiplier, is projected into a gnomonic plane.

In the same chapter, a few tools, developed to perform the rejection noise photo-

multiplier, are also described. Finally the comparison of this technique and the

standard Fly’s Eye method, over a large set of simulated showers, at different

energies and geometrical configurations, and its effects on the reconstruction of

shower energy and the depth of shower maximum is discussed.

In chapter 5, the improved event reconstruction is tested by means of laser

shots of known geometry produced by a Laser Facility located in the middle

of the ground array, which is able to send a fraction of laser light to a nearby

water detector and to produce an hybrid detection of laser shots. Geometrical

reconstruction accuracy are derived for mono (events recorded only by one eye

of the Fluorescence detector), hybrid (events recorded by both detector) and

stereo (events recorded by at least two eyes). In the second part of chapter 5,

vi

laser shots and gnomonic projections are used to develop a new technique to

measure telescope misalignments observed in the reconstruction accuracy study.

Corrections to telescope pointing directions are then applied to laser shot stereo

reconstruction.

Chapter 6 is dedicated to extract first physical informations from Auger Flu-

orescence data: cosmic ray energy spectrum and elongation rate. The simulated

data sample used to estimate Fluorescence detector aperture have been used to

define useful criteria required to acquire an accurate shower reconstruction and

calculate reconstruction efficiency at different energies. Defined cuts are applied

in the analysis of Fluorescence detector data from january 2004 to november 2005.

The use of the Fluorescence detector apertures available within the Auger Col-

laboration is described. The Fluorescence detector live time has been computed

monitoring detectot evolution and operation in time. Finally, the first estimate

of the all particle spectrum produced with Fluorescence detector data only is

given. The data set used to produce the energy spectrum is also employed to

give a preliminary elongation rate, comparing obtained data with those coming

from simulation of different primary species.

vii

Chapter 1

UltraHigh Energy Cosmic Rays

1.1 A few historical notes

The Earth’s atmosphere is continuosly bombarded by extraterrestrial particles,

the so called Cosmic Rays (CR), which consist of ionized nuclei, mainly protons,

alpha particles and heavier nuclei. Most of them are relativistic and a few par-

ticles have an ultrarelativistic kinetic energy, extending up to 1020 eV . This is a

macroscopic energy, equivalent to that one of a tennis ball moving at 100 km/h.

CR story starts at the beginning of the 20th century when it was found that

electroscopes discharged even in the dark, well away from sources of natural

radioactivity. To solve the puzzle, in 1912 Hess [1] and successively Kolhorster [2]

made a series of manned balloon flights, in which they measured the ionization of

the atmosphere with increasing altitude. What they found out was the startling

result that the average ionization increases with respect to its value at the sea-level

(at 5000 m the difference between observed ionization and that at sea-level was of

∼ 17 × 108 ions m−3) as if a radiation with high penetrating power would arrive

from outside the Earth. Eventually the term Cosmic Rays was used by Millikan

in a seminar at the Leeds University (UK) and, since then, used throughout.

At the beginning, the community believed that CR were “high” energy pho-

tons (at that time the most penetrating radiation known was γ rays). Just in

1929, using a “new” detector able to detect individual cosmic rays, the Geiger-

Muller counter, Bothe and Kolhorster showed that CR were mainly composed by

charged particles and, because of their long range in the matter, these particles

1

1.1 A few historical notes

would have to be very energetic (∼ 109 eV ). From this hypothesis, Bruno Rossi

started to study secondary particle production through interaction of CR with

matter, so called “showers”.

In 1934, on the basis of his observations in Eritrea, Rossi [3] reported of strange

coincidences between different detectors as if very extensive groups of particles

arrived all at once upon the detector. With the use of the first coincidence

circuit at ∼ 5 × 10−6 s, Pierre Auger and his group [4] discovered that some

cascades were initiated by CR, interacting with the atmosphere. Auger called

these cascades Extensive Air Showers (EAS). At that time the primary cosmic

rays were thought to contain a large amount of electrons and a new theory,

developed by Bethe and Heitler [5], was used to infer the primary energy. EAS

studies continued using larger arrays of Geiger-Muller counters, and events with

an energy larger than 1017 eV were detected.

From CR studies the elementary particle physics was born. Indeed, from

cosmic radiation track studies with cloud chamber, Blackett and Occhialini [6]

in 1933 discovered the positron and in 1936 Anderson and Neddermeyer [7] an-

nounced the observation of particles with mass intermediate between that one of

the electron and the proton, the muon. With a new kind of instrument, nuclear

emulsion, in 1947 there was the observation of the pion by Rochester and Butler

[8] and so on till the Σ particle discovery in 1953 [9]. Since then elementary

particle physics was able to use a new kind of “high” energy particle source, ac-

celerators, its future laid in accelerator laboratory rather than in the cosmic ray

observations. The interest in CR shifted to the problems of their origin and their

propagation through the space, from their sources to the Earth.

Although a century of adventurous researches and detailed studies is passed,

cosmic ray radiation still shows unanswered questions. In the last forty years,

many hundreds peculiar events were recorded, in which Extensive Air Showers

were generated by a primary particle whose energy was estimated to exceed 1018

eV (Ultra High Energy Cosmic Rays, UHECR), by different cosmic ray experi-

ments, such as AGASA [10; 11; 12], Fly’s Eye [13] and the High Resolution Fly’s

Eye [14], Haverah Park [15], Yakutsk [16], and more recently the Pierre Auger

experiment [27]. Usually, the most energetic component of UHECR, primary

particles with energy above 5 × 1019 eV is indicated as Extremely High Energy

2

1.2 The Physics of UHECR

Cosmic Rays (EHECR) and its existence opened issues that constitute a puz-

zle still today, whose solution involves astronomy and cosmology, nuclear physics

and elementary particle physics: origin, acceleration mechanisms, propagation,

high energy interaction in the EAS above the highest feasible energy with accel-

erators (LHC experiment will work up to 1012 eV in the center-of-masse frame,

equivalent to ∼ 1017 eV in the laboratory frame).


There is a continuing fascination with the studies of Ultra High-Energy Cosmic

Rays, mostly from several contradictions connected to their obseration.

One of the reason of interest concerns their origin: the places where they

are produced are probably astrophysical sites containing unusual large energies

in their magnetic field structures (see Greisen [17]). Such sources are relatively

rare and mostly far from the Earth. Particles travelling from these sources to

us should interact with Cosmic Background Radiation, deeply modifying the ob-

served energy spectrum, causing the expected Greisen-Zatsepin-Kuzmin (GZK)

cutoff (Greisen [18], Zatsepin and Kuzmin [19]). So the observation of a particle

with energy > 1020 eV would imply that its source lays within ∼ 100 Mpc from

the Earth. At this energy, estimated galactic and extra-galactic fields are such

that they should modify negligibly particle trajectories. Therefore, primary ar-

rival directions should point back directly at sources. But in high energy events

observed till now, there is no clear anisotropy. Even a more important is the

understanding of the mechanism responsible for production and acceleration able

to bring primary particles at this very high energy.

In this energy range, due to the very low flux1 experimental statistics is very

poor. Due to this luck of statistics and experimental uncertainties2, it is not yet

established if the GZK cut-off is actually visible in the data or not.

1The measured CR flux above 1020 eV is of one particle for kilometer square for century.2Most of cosmic ray studies depend on phenomenological models. They are based on Stan-

dard Model physics extrapolated to energies of several order higher than those achievable incurrent and future collider experiments. Furtheremore, processes involved are in kinematicregions unexplored in the study of fundamental interactions.

3


1.2.1 Cosmic Ray Spectrum

The most striking feature of cosmic rays is their energy spectrum, which spans a

very wide range of energies with surprising regularity. As it is possible to see in

fig. 1.1, the differential flux of the all-particle spectrum goes through 32 orders

of magnitude along over 12 energy decades. The regularity is broken mainly in

two regions, the knee at about 3 × 1015 eV and the ankle at about 3 × 1018 eV .

Except a “saturation” region at low energies, cosmic ray spectrum can be well

represented by power-law energy distribution

dN

dE∼ E−γ (1.1)

where γ ∼ 2.7 up to the knee and then ∼ 3.0 up to the ankle. Beyond the

ankle, the spectrum becomes hard to quantify, but it can be again described with

a γ value of 2.7.

The bulk of the CR up to the knee is belived to originate within the Milky

Way Galaxy, by shock acceleration in supernovae remnants. There are some

experimental evidences that the CR composition changes from a light one (mostly

protons) around the knee towards one mainly composed by iron and even heavier

nuclei at E 4 × 1017eV , the second knee [20], in association with a further

spectrum steepening to γ 3.3. This is in agreement with what it is expected

in any scenario where primary particle acceleration and propagation is due to

magnetic fields, whose effects depend on rigidity (namely the ratio of charge to

rest mass Z/A), as long as energy losses and interaction effects are small. That is

true for CR propagation in the Galaxy, in contrast to extra-galactic cosmic ray

propagation at ultra-high energy. The flatter spectrum above the ankle is often

interpreted as a cross over from a steeper Galactic component, no more confined

by Galactic magnetic field at those energies, to a new component. This new

component is generally thought to be extra-galactic [21], although it may also

originate in the Galaxy [22], in an extended halo [23] or in the dark matter halo

[24]. The Galactic origin hypothesis is supported by data recorded by AGASA,

which shows that around 1018 eV the event angular distribution correlates with

the Galactic Center (anisotropy ∼ 4%), while at higher energy the anisotropy

disappears [25]. At the very high end of the spectrum the flux appears uncertain.

4


Figure 1.1: All-particle energy spectrum from a compilation of measurements of

the differential energy spectrum of CR. The dotted line shows an E−3 power-law

distribution for comparison. Approximate integral fluxes are also shown.

5

Chapter1/Chapter1Figs/all-particle_spectrum.ps


Indeed, the most recent experiments, AGASA and HiRes, reported a number of

events above 1020 eV completely in disagreement: HiRes collected only 2 events

instead of about 20 expected for a spectrum similar to that reported by AGASA

[26] (17 events above 1020 eV ) (see fig. 1.2). Figure 1.3 shows the comparison

among Fly’s Eye, HiRes, AGASA and Haverah Park data.

Figure 1.2: High energy cosmic ray spectrum multiplied by E3 to evidence its

features, as seen by AGASA (blue ), by HiRes-II (black ) and HiRes-I (red

). The continuous line is the predicted flux coming out from an isotropic source

model.

This question will be addressed and probably solved by the Auger Observatory

data [27], which combine the two complementary detection techniques adopted

by the aforementioned experiments.

6

Chapter1/Chapter1Figs/hiresvsagasaspectrum.ps


Figure 1.3: Composite energy spectrum including recently reanalysed Haverah

Park data, assuming proton and iron as primaries (λ measures the attenuation

length of the charged particle density at 600 m from the shower core), stereo Fly’s

Eye data, monocular HiRes data from both eyes up to 60 and hybrid HiRes-MIA

data. Different parametrizations are overimposed [26].

7

Chapter1/Chapter1Figs/comparingspectratail.ps


1.2.2 Cosmic Ray Mass Composition

Figure 1.4: Cosmic Ray elemental abundances, measured at Earth, compared to

the Solar System abundances, all relative to silicon.

The chemical abundances of cosmic radiation provide important clues to their

origin and to the processes of propagation from their sources to the Earth. CR

composition is known by direct experiments up to 1014 eV (balloon experiments

at high altitude or experiments on satellites). For that energy range, it comes

out that ∼ 99.8% of primary particles are charged particles, and ∼ 0.2% are

photons and neutrinos. 98% of charged particles are nuclei and 2% are electrons

and positrons. Among the nuclei, protons are 87%, helium nuclei 12% and havier

nuclei 1%. Looking at the distributions of element abundances, cosmic ray abun-

dances are not so different from those of the Solar System. Figure 1.4 shows

the superimposition of this two distributions. It is immediately clear that light

8

Chapter1/Chapter1Figs/abundances_comparison.ps


elements, as lithium, beryllium and boron are grossly overabundant in the cosmic

radiation. There is also an excess of elements just less heavy then those of the iron

group. And finally there is a lack of hydrogen and helium in the cosmic rays with

respect to heavy elements. Some differences can be due to spallation processes:

primary cosmic rays, propagating through the interstellar medium, suffer spalla-

tion collisions with ambient interstellar gas. The net result is the production of

nuclei with atomic and mass numbers just less than those of the common groups

of elements. The overall impression is that cosmic rays have been accelerated

from material of quite similar chemical composition as in the the Solar System.

When it is not possible to perform direct measurements of primary particles

(typically for Eprimary > 1014 eV ), the radiation composition is inferred from

indirect observation. Then conclusions are strongly dependent on models used

to describe the data. Different methods used for mass measurement usually give

different answers.

1.2.3 The GZK Limit

As it is evident from fig. 1.3, cosmic rays of quite enormous energy have been

detected. The first event was observed by Volcano Ranch experiment [28], with

an estimated energy of 1.3 × 1020 eV . In the last forty years, other experiments

registered high energy cosmic rays, Yakutsk, Fly’s Eye, HiRes, AGASA. In

particular, Fly’s Eye observed the most energetic EAS, 3.2± 0.9)× 1020 eV [29].

These events seem to be in disagreement with the GZK-limit. As already

explained, in this energy range, particles should interact with Cosmic Background

Radiation: the relic photon energy is sufficient to excite baryon resonances thus

draining the proton energy via pion production and producing ultrahigh energy

gamma rays and neutrinos. Naively, the GZK-limit gives the radius of the sphere

within which a source has to lie in order to provide us with proton of 1020 eV .

There are three sources of energy loss of ultrahigh energy protons: adiabatic

fractional energy loss due to the expansion of the Universe, pair production (p +

γ → p + e+ + e−) and photopion production (p + γ → π + N), each successively

dominating as the proton energy increases. The adiabatic fractional energy loss

9


at the present cosmological epoch is given by

− 1

E

(dE

dt

)adiabatic

= H0 (1.2)

where H0 ∼ 100 h km s−1 Mpc−1 is the Hubble constant, with h ∼ (0.71 ±0.07)×1.15

0.95 the normalized Hubble expansion rate [30]. The fractional energy loss

due to interaction with the cosmic background radiation at redshift z = 0 is

determined by the integral of the nucleon energy loss per collision multiplied by

the probability per unit time for a nucleon collision in an isotropic gas of photons

[31]. Pair production and photopion production are important for interaction

with the 2.7 K blackbody background radiation. Collisions with optical and

infrared photons give a negligible contribution. For interactions with a blackbody

field of temperature T , the photon density is that of the Plank spectrum [32].

The mean interaction length, xpγ of a proton of energy E is given by

1

xpγ(E)=

1

8βE2

∫ ∞

εmin(E)

n(ε)

ε2

∫ smax(ε,E)

smin

σ(s)(s − m2pc

4)dsdε (1.3)

where n(ε) is the differential number density of photons with energy ε, σ(s)

is the appropriate total cross section for the process in question for a center

momentum (CM) frame energy squared s, given by

s = m2pc

4 + 2εE(1 − β cos θ) (1.4)

with θ the angle between the directions of proton and photon and βc the

proton velocity. Threshold values for processes are smin ≈ 0.882 GeV 2 (E ≈

1018 eV ) for pair production and smin ≈ 1.16 GeV 2 for photopion production,

equivalent to the request of

Ethpγ =

mπ(mp + mπ/2)

ε≈ 6.8 × 1019

( ε

10−3

)−1

eV (1.5)

in the proton rest frame. The cross section for the latter process strongly increases

at the ∆(1232) resonance, which decays into pion channels π+n and π0p. With

increasing energy, heavier baryon resonances occur and the proton might reappear

only after successive decays of resonances. The mean interaction lenghts, derived

from equation 1.3, are plotted as dashed lines in fig. 1.5. Dividing by mean

10


inelasticity of the collision k(E), one obtains the energy-loss distances for the two

processes (solid curves in fig. 1.5)

E

dE/dx=

xpγ(E)

k(E). (1.6)

Figure 1.5: (a) Mean interaction length (dashed lines) and energy-loss distance

(solid lines), E/(dE/dx), for pair production and pion photoproduction in the cos-

mic microwave background radiation (CMBR) (lower and higher energy curves

respectively) [34]. (b) Energy-loss distance of Fe-nuclei in the CMBR for pair

production (leftmost dashed line) and pion photoproduction (rightmost dashed

line). Photodisintegration distances are given for loss of one nucleon (lower dot-

ted curve), two nucleons (upper dotted curve) as well as the total loss distance

(thick curve) estimated by Stecker and Salamon [35]. The thin full curve shows

an estimate over a larger range of energy [36] of the total loss distance based on

photodisintegration cross section of Karakula and Tkaczyk [37].

The resulting interaction lengths are ∼ 6 Mpc and 1 Mpc with an inelasticity

∼ 20% and ∼ 0.1% at E ∼ 1019.6 eV respectively for photopion production and

pair production [33; 34]. Fig. 1.6 shows the proton energy degradation as a

function of the mean flight distance. Notice that, independently of the initial

11

Chapter1/Chapter1Figs/lunghezzagzk.ps


energy of the nucleon, the mean energy values approach 1020 eV after a distance

of ∼ 100 Mpc.

Figure 1.6: Energy attenuation length of nucleons in the intergalactic medium.

Note that after a distance of ∼ 100 Mpc the mean energy is essentially indepen-

dent of the proton initial energy [38].

In the case of nuclei, the situation is a little more complicated. The rele-

vant mechanisms for the energy loss that high energy nuclei suffer during their

propagation toward the Earth are pair production, photopion production and

photodisintegration.

The threshold condition for pair production can be expressed in terms of the

Lorentz factor

12

Chapter1/Chapter1Figs/pattenuazione.ps


γ >mec

2

ε

(1 +

me

Amp

)(1.7)

and that one for photopion production as

γ >mπc2

2ε

(1 +

mπ

2Amµ

). (1.8)

Since γ = E/Ampc2, where A is the mass number, both energy-loss distance

curves in fig. 1.5 are shifted by a factor A. For pair production the energy loss

by a nucleus in each collision near the threshold is approximately ∆E ≈ γ2mec2,

hence the inelasticity is ≈ 2me/(Amp), a factor A lower than for protons. On the

other hand, the cross section depends on Z2, so the overall shift is down by Z2/A

(energy loss distance for pair production for iron nuclei is reduced by a factor

≈ 12.1).

For pion production, the energy loss in each collision near the threshold is

∆E ≈ γ2mπc2, so the inelasticity is a factor A lower than for protons. The cross

section increases approximately as A0.9 giving an overall increase in the energy

loss distance of a factor ∼ A0.1 ≈ 1.5 for iron nuclei (see fig. 1.5).

The dominant mechanism of energy loss for nuclei is photodisintegration. The

photodisintegration distance, defined as A/(dA/dx) calculated by Stecker and

Salomon, is shown in fig. 1.5, together with an estimate made over a larger

energy range by Protheroe [36] of the total loss distance based on cross section

of Karakula and Tkaczyk [37].

Neutrons, even at the higher energies, decay into protons after a free fly of

only ∼ 1 Mpc, so they could be ruled out.

In summary, the GZK−cutoff implies that, if the primary ultrahigh energy

cosmic rays are protons, energetic sources should be close to the Earth, within a

distance of the order of 50 − 100 Mpc.

In the case of high energy γ−rays, the dominant absorption process is pair

production through collisions with the radiation fields permeating the Universe.

On the other hand, electrons and positrons could produce new γ−rays via inverse

Compton scattering. The new γ can initiate a fresh cycle of pair production

and inverse Compton scattering interactions, yielding an electromagnetic cascade.

13

1.3 Possible Sources of UHECR

The development of electromagnetic cascades depends sensitively on the strength

of the extragalactic magnetic field B, which is rather uncertain.

The threshold for the pair production process is of the order of m2e/ε, where ε

is the energy of the radiation field involved. Above 1020 eV , the most relevant in-

teractions are those with radio background, which is almost unknown. Therefore,

the GZK radius of the photon strongly depends on the strength of extragalactic

magnetic fields. In principle, distant sources with a redshift z > 0.03 can con-

tribute to the observed cosmic rays above 5×1019eV if the extragalactic magnetic

field does not exceed 10−12 G [40].

Neutrinos do not suffer any energy degradation during their trip through the

Universe, unless for energies above 1023 eV [42]. As noted by Weiler [43; 44], neu-

trinos can travel over cosmological distances with negligible energy loss and could

produce Z bosons on resonance through annihilation on the relic neutrino back-

ground, within a GZK distance from Earth. In that case, highly boosted decay

products could be observed as super−GZK (above GZK−limit) primaries and

they would point directly back to the source. This model of course requires very

luminous sources of extremely high energy neutrinos through-out the Universe.


The Main astrophysical question connected to cosmic ray studies is the identifi-

cation of possible UHECR sources and plausible acceleration mechanisms to get

particles above 1020 eV .

The CR energy density measured at the top of the atmosphere is dominated

by low energy component between 1 and 10 GeV . At energies of about 1 GeV

the intensities are correlated with the solar activity. At higher energies (10− 100

GeV ) the flux is anticorrelated with solar activity, indicating an extra-solar origin.

Several arguments involving energetics, composition and secondary γ−ray

production suggest that the bulk of CR (between 1 GeV up to PeV ) is confined

to the galaxy and is probably produced in supernova remnants (SNRs). Between

the knee and the ankle the situation becomes less clear. The ankle is sometimes

interpreted as a cross over from a galactic to an extragalactic component. Fi-

nally, beyond 10 EeV , CR are generally expected to be extragalactic. These

14


hypothesis are based on the value of the Larmor radius of a particle, with charge

Ze, traveling in a medium with an estimated value of the magnetic field B

rL ∼ 110E20

ZBµG

kpc (1.9)

where BµG is the magnetic field in units of µG and E20 = 1020 eV . Then,

increasing with the energy, a proton has an higher probability to escape from

the galaxy region. At 1018 eV , it has a Larmor radius of ≈ 1kpc, larger than

the typical galaxy thickness. At higher energies the diffusive approximation for

particle propagation break down, particles propagate in balistic-like way.

A variety of astrophysical objects have been proposed to account for the origin

if the high energy CR as supernovae explosion [50; 51], active galctic nuclei

(AGNs) [53] or pulsar (neutron stars) [52] (For a complete review see [39]).

The maximum attainable energy may be limited by an increased likelihood of

escape from the acceleration region. When the Larmor radius of the particle of

charge Ze (eq. 1.9) approaches the acceleration size, it becomes very difficult to

confine it magnetically. This argument leads to the general condition [49]

Emax ≈ 2βcZeBrL (1.10)

for the maximum energy acquired by a particle traveling in a medium with

magnetic field B, where βc is the characteristic velocity of magnetic scattering

centers. This is known as “Hillas criterion”. The “Hillas criterion” allows to clas-

sify different sources, as summarized in the form of the popular “Hillas diagram”

shown in fig. 1.7.

From fig. 1.7, it is clear that very few sites are able to generate particles with

energy above 1020 eV .

Notice that it is difficult to achieve the maximum energy suggested by eq.

1.10, because energy loss processes should be taken into account. One source of

losses is synchroton radiation, which becames important even for protons at very

high energy in regions of extreme magnetic fields. Other possible losses are due to

photoproduction interaction. If energy loss mechanisms are taken into account,

most of the sources in the “Hillas diagram” are ruled out , as shown in fig. 1.8,

because their rate of energy gain is to slow to overcome energy losses.

15


Figure 1.7: The Hillas diagram showing size and magnetic field strengths of pos-

sible astrophysical sites of particle acceleration. According to eq. 1.10, assuming

the extreme value β = 1, objects below the diagonal lines (from top to bottom)

cannot accelerate protons above 1021 eV and iron nuclei above 1020 eV .

16

Chapter1/Chapter1Figs/hillas_plot.ps


Figure 1.8: Magnetic field strength and shock velocity of most powerful accel-

eration sites shown in fig.1.7. Sources in the shaded region are escluded by the

energy loss mechanism. Only the unshaded region allows acceleration of protons

up to 1020 eV .

17

Chapter1/Chapter1Figs/hillas_plot_con_perdite.ps


1.3.1 Acceleration and Propagation of cosmic rays

There are basically two kinds of acceleration mechanism for UHECR:

1. bottom-up, in which cosmic rays are produced and accelerated in astro-

physical environments;

2. top-down, in which exotic particles, from early universe, decay producing

cosmic rays.

1.3.1.1 Bottom-up acceleration mechanisms

In the bottom-up models, mainly two mechanisms are suggested: direct accel-

eration by electric fields [49] or statistical acceleration (Fermi acceleration) by

magnetized plasma.

In the direct acceleration mechanism, the electric field could be due to a ro-

tating magnetic neutron star (pulsar) or an accretion disk threaded by magnetic

fields, etc. The maximum achievable energy depends on the particular astrophys-

ical environment. Direct acceleration mechanisms are not widely favored because

it is usually not obvious how to obtain the characteristic observed power-law

spectrum.

In statistical acceleration mechanisms, particles gain energy gradually by nu-

merous encounters with moving magnetized plasma. These kinds of models were

pioneered by Fermi [45] in 1949 and are able to produce the typical power-law

spectrum. However, the acceleration is slow and it is hard to keep particles

confined within the Fermi engine.

1.3.1.2 Direct Acceleration Mechanisms

The primary difficulty with the direct acceleration scenarios is the existence of

sufficiently large voltages. Most commonly considered sources are unipolar in-

ductors, such as rapidly spinning magnetized neutron stars or blackholes. In the

case of pulsars, the rotation gives rise an electromagnetic field (EMF) too small

to accelerate iron nuclei to the UHECR energies [46]. A spinning blackhole in the

center of a radiogalaxy generates an electromagnetic field sufficient to accelerate

protons to energies 1019 ÷1020 eV. A difficulty with this scenario, however, is the

18


presence of a dense pair plasma and intense radiation which would cause energy

losses of accelerated particles. Another argument frequently used [47] against

direct acceleration scenarios is that it is not clear how the power-law energy spec-

trum, characteristic for cosmic rays, could emerge. Anyway the accelerator in this

scenario is the unipolar inductor, for example a pulsar (a spinning, magnetised,

neutron star). The surface field will be quite complex but a certain quantity of

magnetic flux Φ can be regarded as open and tracable to large distances from the

star (well beyond the light cylinder). As the star is an excellent conductor, an

EMF will be electromagnetically induced across these open field lines E ∼ ΩΦ,

where Φ is the total open magnetic flux. This EMF will cause currents to flow

along the field and as the inertia of the plasma is likely to be insignificant the only

appreciable impedance in the circuit is related to the electromagnetic impedance

of free space Z ∼ 0.3µ0c ∼ 100Ω. The maximum energy to which a particle can

be accelerated is Emax ∼ eE and the total rate at which energy is extracted from

the spin of the pulsar is Lmin ∼ E2/Z. Taking the Crab pulsar as an example,

Emax is about 30 PeV for protons. As the stellar surface may well comprise iron,

even the Crab pulsar has the capacity to accelerate ∼ EeV cosmic rays. However,

it is not obvious that all of this potential difference will actually be made available

for particle acceleration. In particular, this is unlikely to happen in the pulsar

magnetosphere as a large electic field parallel to the magnetic field wil be shorted

out by electron-positron pairs, which are very easy to produce, and radiative drag

is likely to be severe. In any case seems that pulsars may well contribute to the

spectrum of intermediate energy cosmic rays [48].

1.3.1.3 The Fermi mechanism

The original Fermi mechanism describes the acceleration mechanism suffered by

particles traversing magnetized clouds. It is nowadays called “second-order”

Fermi mechanism, because the average fractional energy gain is proportional to

β2 = (u/c)2, where u is the relative velocity of the cloud with respect to the frame

in which the CR ensemble is isotropic. Because of the dependence on the square

of the cloud velocity, the second-order Fermi mechanism is not a very efficient

process. Acceleration time scale turns out to be much larger than typical escape

19


time (≈ 107 years) of CR in the galaxy. A more efficient version of Fermi mech-

anism is realized when particles encounter plane shock fronts. In these cases,

the average fractional energy gain is of first order in the velocity between the

shock front and the isotropic-CR frame. Currentely, the “standard” theory of

CR acceleration is based on this first-order Fermi mechanism (Diffusive Shock

Acceleration Mechanism, DSAM) [71; 72; 73; 74; 75; 76].

Figure 1.9: CR acceleration at shock front. A planar shock wave is moving with

velocity −u1 while a CR particle is repeatedly crossing the front and scattering

in magnetic irregularities.

In the first-order Fermi mechanism, a large shock wave propagates with veloc-

ity −u1 as indicated in fig. 1.9 and CR particles cross repeatedly the front and

20

Chapter1/Chapter1Figs/fermi_mec_plot.ps


scatter in magnetic irregularities. Relative to the shock front, the downstream

shocked gas is receding with velocity u2, with |u2| < |u1|. In these hypothesys,

before entering in the shock, a CR particle has an energy Ei, a momentum pi and

an incident angle with the shock front propagation direction θi in the laboratory

frame. When the particle crosses the front again, it has energy Ef , momentum

pi and it emerges with an angle θf . In the rest frame of the shock, the particle

has an initial energy

E ′i = γEi(1 − βcosθi) (1.11)

where γ and β are the Lorentz factor and the shock front velocity in units of

speed of light. In the shock frame, there is no change in the energy because all

the scatterings are in the magnetic field, E ′f = E ′

i. In the laboratory frame we

find

Ef = γE ′f (1 + βcosθf) (1.12)

The fractional energy gain in the laboratory frame is then

η =∆E

Ei=

1 − βcosθi + βcosθf − β2cosθicosθf

1 − β2− 1. (1.13)

By considering the rate at which CR cross the shock wave from downstream

to upstream and viceversa, one finds 〈cosθi〉 = 2/3 and 〈cosθf 〉 = −2/3 [75].

Hence the fractional energy gain is

〈η〉 4

3β =

4

3

u1 − u2

c(1.14)

An important feature of diffusive shock acceleration mechanism is that parti-

cles emerge out from the acceleration region with a power-law spectrum, in which

the index depends only on the ratio of the upstream and downstream velocities

(shock compression ratio), not on the shock velocity.

In fact, we can calculate the rate at which CR cross from upstream to down-

stream, given by the projection of the isotropic CR flux onto the plane shock

front

21


rcross =

∫ 1

0

d(cosθ)

∫ 2π

0

dφnCRv

4πcosθ ≈ nCRv

4(1.15)

where nCR is the density of particles undergoing acceleration. The rate of

convection downstream away from the shock is

rloss = nCRu2. (1.16)

The probability of crossing the shock and escaping is then given by

Prob(escape) =rloss

rcross≈ 4

u2

v(1.17)

and the propability of returning to the shock after crossing upstream to down-

stream is

Prob(return) = 1 − Prob(escape). (1.18)

So the probability to cross n times the shock from downstream to upstream

and viceversa is

Prob(cross ≥ n) = [1 − Prob(escape)]n. (1.19)

Therefore, the energy after n shock crossing is

E = E0

(1 + 〈η〉

)n

(1.20)

where E0 is the initial energy. So the number of particles accelerated to

energies greater than E is

Q(> E) ∝∞∑

m=n

[1 − Prob(escape)]m =[1 − Prob(escape)]n

Prob(escape)(1.21)

This leads to

Q(> E) ∝ 1

Prob(escape)

( E

E0

)−γ

(1.22)

with

γ =ln[1 − Prob(escape)]−1

ln 1 + 〈η〉 (1.23)

22


1.3.1.4 Top-down acceleration mechanisms

“Top-down” scenarios avoid acceleration problem by assuming that charged and

neutral primaries arise in the decay of supermassive elementary X particles.

Sources of these exotic particles could be:

1. topological defects, from early Universe phase transitions associated with

the spontaneous symmetry breaking [54; 55; 56; 57; 58; 59];

2. long-lived metastable super-heavy relic particles produced through vacuum

fluctuation during the inflationary stage of the Universe [60; 61; 62; 63];

Topological defects (magnetic monopoles, cosmic strings, domain walls, etc.)

are stable and can survive for ever with massive X particles (≈ 1016 − 1019

GeV ) trapped inside them. Sometimes, they can be destroyed through collapse,

annihilation etc., and their energy would be released in the form of massive quanta

that typically decay into quarks and leptons. In a similar way, superheavy relics

could decay in quarks and leptons. Then CR with energies up to mX can be

produced. These topological defects or superheavy particles would lay in the

galactic halo ragion. Another exotic explanation of the UHECR postulates that

relic topological defectes themselves constitute the primaries [64; 65]. General

features of these exotic scenarios are discussed in several reviews [66; 67; 68; 69;

70? ].

1.3.1.5 Cosmic ray Propagation

Looking at the distributions of element abundances (see fig. 1.4) as measured

below the “knee” region, it is evident that cosmic ray abundances are not so

different from those of the Solar System. Main differences are the overabundances

of light elements like lithium, beryllium and boron,and of element just less heavy

then those of the iron group. These differences can be qualitatively accounted

as result of spallation process of primary cosmic rays with interstellar medium

during their travel to the Earth, producing lighter elements.

For the Li − Be − B group it is possible consider the C − N − O group and

its propagation through the interstellar medium. The model is described by

23


dNp

dX= −Np

λp(1.24)

dNs

dX= −Ns

λs+

NpPsp

λp(1.25)

where Np and Ns are the number of primary particles and secondary ones, X

is the matter quantity (in g/cm2) to pass through, λi are interaction lengths for

different particles, Psp the probability to produce a secondary particle s from a

primary nucleus p, by spallation interactions (Psp = σspallation/σtotal). Solving the

system, one obtains the ratio between primary and secondary abundances, as a

function of X

Ns

Np

=Pspλs

λs − λp

[exp (

Xsp

λp

− Xsp

λs

) − 1]

(1.26)

If we now use the known values for λi and Psp and the measured ratio between

primary group C−N −O and secondary group Li−Be−B, we get that primary

particles should go through 4.3 g/cm2. Hence, with the measured interstellar

medium density, one finds out that primary particles should travel over a distance

of the order of 1 Mpc. So those particles must be confined inside the galaxy for

3 × 106 years.

Generally, propagation mechanism for primary species i can be described

by “Diffusion-Loss Equation” [77], whose solution depends on source contri-

bution and volume in which the species is accelerated. The most simple and

used phenomenological model for the propagation description and for solving the

“Diffusion-Loss Equation” is the “Leaky Box Model”[78]: particles diffuse in a

volume (the galaxy) from which they can escape with a probability function of

the energy. The model predicts different spectral index for different primaries.

In the case of protons, at energies above 4 GeV , one obtains:

Np(E) = Qp(E)τfuga(E) ∝ Qp(E)E−δ (1.27)

with Q(E) primary flux from the sources and δ = 0.6. If we use the known

spectral index (≈ 2.7), it is possible to derive the flux at sources

24

1.4 Experimental Outlook: Extensive Air Showers

Qp(E) ∝ E−γ+δ E−2.1 (1.28)

On the other hand, for iron primaries the flux at sources is

NFe(E) ∝ QFe(E) (1.29)

that is the flux observed has the same spectral index of sources.

The “Leaky Box Model” is able to explain the “knee” feature also, considering

the possibility of particles to leave the galaxy as their energy increases, from

lighter to heavier elements, in agreement with experimental data.

1.4 Experimental Outlook: Extensive Air Show-

ers

For primary cosmic rays with energy above 105 GeV , the flux is so low that the

direct detection is impossible using devices in or above the atmosphere. In such

cases primary particles have enough energy to initiate a cascade whose products

are detectable at ground. These extensive air showers, discovered by Auger and

his group (see sec. 1.1), are used to study cosmic radiation at energies above 105

GeV . The atmosphere is seen as a huge calorimeter, whose properties vary in a

predictable way with altitude and in a relatively unpredictable way with time.

This “calorimeter” provides a vertical thickness of 26 radiation lengths for an

electron and 15 interaction lengths for a proton1.

1.4.1 Shower Development

As long as a primary particle traverses the atmosphere, it dissipates much of

its energy by exiciting and ionizing air molecules along its path, and producing

secondary particles which are able to generate new particles and so on, giving

origin to a cascade. Particle production and the cascade growth continue until

1This is not so different from the number of radiation and interaction lengths at the LHC

detectors. For example, the CMS electromagnetic calorimeter is 25 radiation lengths deepand the hadron calorimeter constitutes 11 interaction lengths.

25


the average energy lost by ionization by secondary particles becomes of the same

order of the average energy needed to produce a new particle generation. At

this point, the shower reaches its maximum development and from now on the

number of particles produced at each generation decreases down to zero.

Figure 1.10: Semplified scheme of extensive air shower development.

A cascade develops through different interaction processes, a simple scheme

is represented in fig. 1.4.1. Main shower components are:

1. hadrons: primary nucleons interact with atmospheric molecules producing

high energy hadrons which interact or decay giving a new generation of par-

ticles. Most part of particles produced in hadronic interactions are mesons,

mainly pions and K.

26

Chapter1/Chapter1Figs/schema_EAS.eps


2. electromagnetic particles: for each hadronic interaction, 1/3 of the incident

particle energy goes into π0, which decay in photons that initiate an elec-

tromagnetic cascade producing e+e− pairs and so on with bremsstrahlung

radiation and new pair production.

3. muons: charged pions and K could decay, if they have not enough energy

to interact, producing muons and neutrinos.

For example, if we consider a 1019 eV proton vertical shower, at the sea level,

there are about 1011 secondary particles with energy above 90 keV in the annular

region extending up to 10 km from the shower core. Of these secondary particles,

99% are photons, electrons and positrons, with a typical ratio of γ to e+e− of 9 to

1 and with a mean energy of 10 MeV . The remaining 1% are muons, neutrinos

and hadrons [80]. About 90% of the primary particle energy is dissipated in the

electromagnetic cascade. The remaining energy is carried by hadrons, muons and

neutrinos [82]. Fig. 1.11 gives an idea of the spatial extension of the different

components.

Usually the muonic and neutrinic part of the cascade is called “hard” compo-

nent, while the electromagnetic and hadronic part is called “soft” component.

Figure 1.11: Spatial extension of shower components.

27

Chapter1/Chapter1Figs/shower_example.ps


The evolution of an EAS is dominated by electromagnetic processes. Photons-

induced showers are even more dominated by electromagnetic channel, as the only

significant muon generation mechanism is the decay of charged pions and kaons

produced in γ−air interactions [83].

The cascade shows a conical form around primary trajectory (“leading particle

effect”), and this trajectory is called “shower axis”. The impact point of the

shower axis on the ground is called “shower core”. The shower reaches the ground

in the form of a giant “saucer” travelling nearly at the speed of light.

To describe an atmospheric cascade one usually defines the following quanti-

ties:

1. N(X), the longitudinal profile, i.e. the number of particles of the shower

(shower size) as a function of the traversed atmospheric depth X;

2. Xmax (measuredin g/cm2), the slanth depth at which the EAS reaches its

maximum, the maximum size Nmax;

3. ρ(r), the particle density at distance r from shower axis, in the plane per-

pendicular to the axis, the lateral distribution.

Longitudinal development, Xmax and lateral distribution depend on the pri-

mary energy and composition. It is not possible to measure the lateral distribu-

tion at different depths, experiments can only measure it at one depth and usually

they can see only a sample of the shower front. Fig. 1.12 shows the lateral and

longitudinal development of a vertical proton shower of 1014 eV in which are indi-

cated hadronic (blue lines), electromagnetic (red lines), muonic (grey lines) and

neutral (green lines) components: (a) a 3D vision of shower development into

the atmosphere, shower front is sampled by an array of particle detector (blue

circle); (b) a top vision of the shower is provided; (c) the particle density of differ-

ent components as a function of the distance from the axis (lateral distribution)

is shown; (d) the shower size as a function of the altitude from the sea level is

represented (for vertical shower is equivalent to the shower size as a function of

the depth, that is the longitudinal profile).

The slant depth is defined by introducing the vertical atmospheric depth at

height h, to take into account the varying density of the atmosphere

28


Figure 1.12: Lateral and longitudinal development of a vertical proton shower of

1014 eV , hadronic (blue lines), electromagnetic (red lines), muonic (grey lines)

and neutral (green lines) components are indicated; (a) a 3D vision of shower

development into the atmosphere is presented, shower front is sampled by an

array of particle detector (blue circle); (b) a top vision of the shower is provided;

(c) it is shown the particle density of different components as a function of the

distance from the axis (lateral distribution); (d) it is represented the shower size

as a function of the altitude from the sea level (for vertical showers is equivalent

to the shower size as a function of the depth, i.e. the longitudinal profile).

Figure 1.13: Slant depths corresponding to various zenith angles θ, considering

the Earth curvature.

29

Chapter1/Chapter1Figs/esempio_lon_lat.ps

Chapter1/Chapter1Figs/x_vs_theta.ps


Xv(h) =

∫ infty

h

ρatm(z)dz (1.30)

where the integration is done over the altitude, z, and ρatm is the atmospheric

density. The slant depth for a shower is then the same integral performed along

particle trajectory. Fig. 1.13 shows the variation of the slant depth with zenith

angle of the trajectory. Neglecting Earth curvature, we can use the approximation

X = Xv(h)/cosθ, where θ is the zenith angle of the primary particle cosmic

ray. The error associated with this approximation is less than 4% for θ 80.

The vertical atmosphere is ≈ 1000 g/cm2 and it is about 36 times deeper for

completely horizontal showers.

1.4.1.1 The Electromagnetic Component

The electromagnetic part of a cascade typically origins by π0 decay

π0 → γ + γ (1.31)

other possible decays, π0 → γ + e+ + e− and π0 → e+ + e− + e+ + e−, are

negligible [81].

Then, the produced photons initiate the cascade, they convert into e+e− pair,

which in turn emit synchrotron photons and so on.

Particle production slows down at a critical energy EC , defined 1 as the en-

ergy at which ionization loss is equal to the breemsstrahlung loss for an electron

(positron). That leads to EC = 710MeV/(Zeff + 0.92) ≈ 86 MeV 2 [87]. At crit-

ical energy ionization loss take over from breemsstrahlung and pair production

as the dominant energy loss mechanism. The changeover from radiation and pair

production losses to ionization losses depopulates the shower.

It is then possible to categorize the shower development in three phases: the

growth phase, in which all particle have energy > EC ; the shower maximum; the

shower tail, where particles only lose energy, get absorbed or decay.

1Several different definitions of the critical energy appear in the literature [86]2For altitude up to 90 km above sea level, the air is a mixture of 78.09% of N2, 20.95%

of O2 and 0.96% of other gases [88]. Such a mixture is generally modeled as an homogeneussubstance with atomic charge Zeff = 7.3 and mass number Aeff = 14.6.

30


The first comprehensive treatment of a electromagnetic shower was elaborated

by Rossi and Greissen [84] and recentely by Gaisser [85].

The electromagnetic interactions of shower particles can be very accurately

calculated by quantum electrodynamics. Then, they are not source of systematic

errors in shower simulations. Main processes are electron (positron) bremsstrahlung

and pair production.

Figure 1.14: Electromagnetic Shower development scheme in the Heitler Model.

The Heitler Model

Most of the general features of an electromagnetic cascade can be understood

in terms of the toy model due to Heitler [89], in which the shower development

is characterized only by bremsstrahlung and pair production processes, and in

31

Chapter1/Chapter1Figs/modello_heitler.eps


which each interaction process produces the conversion of one particle in two.

These processes have the same interaction lenght X0. Hence, the model assumes:

1. in the bremsstrahlung process, final photon and electron (positron) share

the energy of the initial electron (positron);

2. in the pair production process, e+ and e− share the energy of the initial

photon;

3. multiple scattering is neglected and the shower development is unidimen-

sional;

4. Compton scattering is neglected.

In the model, the shower is represented as a tree with branches that bifur-

cate every X0, until they fall below the critical energy (see fig. 1.14). Above

EC , the number of particles grows geometrically, so after n (n = X/X0) steps

(branchings), the total number of particles as a function of the slant depth is

N(X) = 2X/X0 (1.32)

while the energy for each particle is

E(X) =E0

N(X)(1.33)

where E0 is the energy of the particle that initiated the shower (the first

photon). At the maximum, the number of particles should be

N(Xmax) =E0

Ec(1.34)

then we get

Xmax =X0 ln(E0/EC)

ln 2(1.35)

In the real life, high energy photons, electrons and positrons, below 1010 GeV ,

have mean interaction lengths of 37 g/cm2, whereas above this critical energy the

competing LPM [79] and geomagnetic effects lead to interaction lengths between

32


45 and 60 g/cm2 [80]. LPM and geomagnetic effects introduce large fluctuations

in the value of Xmax for photon-induced shower. Nevertheless, the toy model

prediction lies within the range of these fluctuations.

The Heitler model is enlightening for barion-induced shower also. In particu-

lar, for proton showers, the model predicts that Xmax scales logarithmically with

the primary energy, while Nmax scales linearly. In the case of heavy nuclei, us-

ing the superposition principle as reasonable approximation, a shower produced

by nucleus with energy EA and mass A, is modeled by a collection of A proton

shower. Then its maximum is Xmax ∝ ln(E0/A).

The Heitler model, though very simple, is very useful to get a first intuition

about global shower properties, anyway, the details of shower evolution are too

complicated to be described by such a simple analytical model.

To obtain a more precise analytical treatment, the use of diffusion equations

is required. Their solutions are [84]

nedE =dE

Es+1(a1e

λ1(s)t + a2eλ2(s)t) (1.36)

nγdE =dE

Es+1(

a1c

λpair + λ1(s)eλ1(s)t +

a2c

λpair + λ2(s)eλ2(s)t) (1.37)

where nedE and nγdE are the number of electrons (positrons) and photons

with energy between E and E + dE, t is the slant depth traversed in radiation

lenghts (i.e. t = X/X0), λpair is the interaction length for pair production and

λ1(s) and λ2(s) are two functions of the parameter s, called “shower age”. The

shower age is lower than one in the growth phase (“young shower”), is equal

to one at the maximum and is greater than one in the shower tail phase (“old

shower”). For a quantitative analysis ionization loss processes are required. It

is needed to consider the transport equations in air for electrons (positrons) and

photons [85], whose solutions have been obtained by Snyder, Scott [90; 91] and

Greisen [92]. For a large number of particles, these solutions could be expressed

using the Snyder-Scott-Greisen parametrization

N(E0, t) =0.31

[ln(E0/Ec)]1/2exp (t(1 − 1.5 ln s)) (1.38)

where

33


s =3t

t + 2 ln(E0/Ec)(1.39)

The total electron number on the total track length is given by

∫ ∞

0

N(E0, t)dt =E0

Ec

(1.40)

considering constant the energy loss rate by ionization processes. These solu-

tions provide a good description of the longitudinal profile (number of particles

as a function of the depth) of a shower. Neverthless, neglecting processes as

Compton scattering, photoelectric effect and electron-positron annihilation, an

uncorrect estimation of the number of low energy electrons is obtained.

Full Monte Carlo simulation of interaction and transport of each individual

particle would be required to get a complete and precise modeling of the shower

development.

1.4.1.2 The Muon Component

The muon content of a shower is an important feature. It differs from electro-

magnetic component for two main reasons:

1. muons are generated through the decay of cooled charged pions (Eπ± 1

TeV ) and thus the muon content is sensitive to the initial baryonic nature

of the primary. Furthermore, there is no “muonic cascade” so the number

of muons at ground level is much smaller than the number of electrons.

2. muons have a much smaller cross section for radiation and pair production

and so the muonic component develops separately and differently than the

electronic component does.

The ratio of electrons to muons depends strongly on the distance from the

core: for a vertical 1019 eV proton it varies from 17 to 1 at 200 m from the core

to 1 to 1 at 2000 m. The ratio depends also on the inclination. At the zenith

angles greater than 60 the ratio is constant. As the zenith angle grows, the ratio

decreases, until θ = 75, it is 400 times smaller than for a vertical shower. Even

the average muon energy depends on the zenith angle. For horizontal showers,

34


low energy muons are filtered out so the average muon energy is two order of

magnitude greater than for vertical shower. It should be noted that the curvature

of the muon distribution could serve as a discriminator between hadronic models

[113].

High energy muons lose energy through pair production, muon-nucleus inter-

action, bremsstrahlung and knock-on electron (δ− ray) production [114]. The δ−ray production has a short mean free path and a small inelasticity, so it could be

seen as a continuous process. Main energy loss mechanisms are pair production

and bremsstrahlung. Energy loss by pair production is slitghtly more important

than bremsstrahlung at about 1 GeV and becomes increasingly dominant with

the energy.

1.4.1.3 The Hadron Component

Hadronic interactions at ultra high energies constitute one of the most problem-

atic sources of systematic error in the air shower analysis.

The highest primary energy measured thus far is ≈ 1020.5 eV , corresponding to

a nucleon-nucleon center of mass energy√

s ≈ 1014.9 eV/√

A, where A is the mass

number of the primary particle. Hence, ultra high energy cosmic ray interaction

are orders of magnitude beyond the energy range achieveble by present and future

collider experiments.

The typical characteristic of most hadronic interactions occuring in a shower

development is the soft multiparticle production with a small transverse momenta

with respect to the collision axis. Despite the fact that calculations based on ordi-

nary perturbative QCD are not feasible, there are some phenomenological models

that successfully take into account the main properties of the soft diffractive pro-

cesses. These models, inspired by 1/N QCD expansion, are also supplemented

with general theoretical principles like duality, unitarity, Regge behavior and par-

ton structure. Interactions are described by highly complicated modes, known as

Reggeons. Up to 50 GeV , the slow growth of the cross section with√

s is driven

by a dominant contribution of a special Reggeon, the Pomeron. In the energy

range in which we are interested in, semihard interactions arising from the hard

scattering of partons that carry only a very small fraction of the momenta of their

35


parent hadrons can also compete with soft processes. Unlike soft processes, this

semihard physics can be computed in perturbative QCD.

For semplicity, we will follow the example of a proton hitting the atmosphere.

By means of ionization loss processes, a high energy proton has a energy loss

rate in air of 2 MeV/(g/cm2). A visible modification of its motion occurs when

the proton interacts with an atmospheric nucleus. Supposing that the proton

interacts with just a nucleon of the target nucleus, we get the reaction

p + p → p + p + N (π0 + π+ + π−) (1.41)

in which contribution from K, Λ, η, Ω, Σ ... are neglected. A possible

estimation of the number of secondary particles is ns = 2.5E0.25 [115]1.

In such a process, the produced particles carry away about one half of the

primary energy 2. The energy is shared among pions, so at each generation, on

average 1/3 of the energy is carried by π0 and 2/3 by π±. Usually, neutral pions

feed the electromagnetic component of the shower, while charged pions are able to

interact producing a new hadron generation. As for the electromagnetic cascade,

generation by generation, the average energy of generated particles decreases and

the growth of the shower slows down. When the decay or the absorbtion is

competitive with interaction and particle production processes, the cascade goes

to die out.

The hadronic component develops very close to the shower axis. The pions

are emitted forward and backward within a cone which aperture is related to the

energy by [93; 94]

E =2 mπ c2

tg2 η(1.42)

where mπ is the pion mass in the rest frame and η is the angular aperture.

At higher energies it is possible to obtain3

1 There are still a lot of discussion about the estimation of the particle multiplicity.2 As well as the particle multiplicity, the inelasticity is still affected by uncertainties due to

the use of just phenomenological models3If E > 1012 eV then η < 1

36


η = (2 mπc

2

E)1/2 ≈

√2

E(1.43)

with E expressed in GeV units. The muon component derives from the decay

of charged pions. The 75% reaches the ground.

In the case of heavy nuclei of mass A and energy E, we can use the approx-

imation of the superposition model and imagine the shower as a collection of A

proton showers with energy E/A. As already seen, from the Heitler model one

derives that the maximum depth is Xmax ∝ ln(E0/A). In principle, it should be

possible to distinguish primary particles looking at the Xmax.

An important feature of a heavy primary shower is the lower fluctuation of

the longitudinal profile with respect to a proton shower one, because the obtained

profile for a primary of mass A is an average over A proton profiles. An additional

difference with respect to the proton case is the muon population. It is possible

to see that the number of muon produced by a primary of mass A and energy E

is [85]

NAµ ∝ A(E/A)0.85 (1.44)

that can be also expressed as a function of the number of muon produced by

proton shower

NAµ = A0.15Np

µ (1.45)

Hence, an iron nucleus will produce a number of muons 80% greater than that

produced by a proton.

So far it seem that it is possible to distinguish, in principle, light primaries

(protons) from heavy primaries (irons) using the Xmax and the muon population.

1.4.2 The Longitudinal Development

The longitudinal development for a given primary particle of a given energy de-

pends only on the cumulated slant depth X (the thickness of air already crossed).

Fig. 1.15 shows the longitudinal profile of a shower measured at the Auger Ob-

servatory.

Experimental points are fitted by the Gaisser-Hillas function [118]:

37


X [g/cm2]400 600 800 1000 1200 1400

n_e

-1000

0

1000

2000

3000

4000

5000

6000

710× = 723.7+- 3.3maxX

= 3.8e+10 +- 4e+08maxN = 0 +- 00X

/dof 428 / 2702χ) = 19.75emLog(E) = 19.78totLog(E

LongProfile_850018_EyeId_1

Figure 1.15: Longitudinal profile of a shower. A Gaisser-Hillas fit [118] is super-

imposed on the measured profile [120].

S(X) = Smax

( X − X0

Xmax − X0

)(Xmax−X0)/λ

· e(Xmax−X)/λ (1.46)

where S(X), X0, Smax, Xmax and λ are the shower size at slant depth X, the

starting point of the Gaisser-Hillas curve, the maximum size of the shower, the

depth at which the latter is reached and the interaction length for the primary

particle, respectively. The difference Xmax−X0 depends on the energy and on the

primary composition, while X − Xmax indicates the shower age. Xmax increases

logarithmically with energy [119]:

Xmax Xi + 55 log Eprim(g/cm2) (1.47)

where the value of Xi depends on the nature of the primary. As already

seen, with the superposition model, for a primary with mass A, one obtains

38

Chapter1/Chapter1Figs/profilo_long.ps


Figure 1.16: Longitudinal profiles of simulated proton (red) and iron (blues)

showers with energy 1019 eV .

Xmax ∝ log A; in practice, at a given energy, Xmax(p) − Xmax(Fe) 100g/cm2.

In fig. 1.16 longitudinal profiles for proton-showers (red) and iron-showers (blue)

obtained by a sample of simulated events of 1019 eV are shown. It is possible to

see larger fluctuations on proton profiles and a clear shift in Xmax of about 100

g/cm2. In fig. 1.17 is shown the longitudinal profile of a shower induced by a 10

EeV proton at 40.

1.4.3 The Lateral Extension

The transverse development of electromagnetic showers is dominated by Coulomb

scattering of charged particles off nuclei in the atmosphere. The lateral develop-

ment in electromagnetic cascades in different materials scales with the so called

Moliere radius Rm = Es

EcX0, which varies inversely with the medium density

Rm = RM(hOL)ρatm(hOL)

ρatm(h) 9.0g/cm2

ρatm(h)(1.48)

39

Chapter1/Chapter1Figs/profilo_long2.eps


Figure 1.17: Longitudinal profile of a shower induced by a 10 EeV proton at

40: number of particles as a function of the depth X (top); fraction of primary

energy carried as function of X (medium); fraction of primary energy carried as

function of altitude (bottom).

40

Chapter1/Chapter1Figs/example_profile.ps


where Es = mec2(4π/α)1/2 21 MeV [86], EC the critical energy and X0 the

electron interaction lenght in air, ρatm is the atmospheric density and the subscript

OL indicates a quantity taken at a given observation level.

A Very detailed 3D integration of cascade equations has been performed by

Nishimura and Kamata [96; 97] and later worked out by Greisen [95]. They

derived the well-known NKG formula to describe the lateral structure function

for a pure electromagnetic shower

ρ(r) =Ne

R2M

C(s)(r

Rm

)s−2(r

Rm

+ 1)s−4.5 (1.49)

where Ne is the total number of electrons, r is the distance from the shower

axis and

C(s) =Γ(4.5 − s)

2πΓ(s)Γ(4.5 − 2s)(1.50)

The NKG could be extended to describe the electromagnetic component of

barion-induced showers [98]. In such an extension, a deviation of behavior of

Moliere radius is founded, by using the age parameter defined for pure electro-

magnetic cascades. The NKG is generalized changing the definition of the age

parameter in

s = 3(1 +

2β

t

)−1

(1.51)

where the β parameter takes into account the deviations from he theoretical

value.

The modified NKG formula provides a good description of the e+e− lateral

distribution at all stages of the shower development for values of r sufficientely

far from the hadronic core, that is in the interesting region (typical ground array

can only measure densities at r > 100 m from the core, where detectors are not

saturated.

In the case of inclined showers, one usually analyzes particle densities in the

plane perpendicular to the shower axis. But additional asimmetry and geometri-

cal effects are introduced [98; 109]. A lateral distribution function (LDF ) valid

at all zenith angles θ < 70 can be determined by considering

41


t′(θ, ζ) = t sec θ(1 + Hcosζ)−1 (1.52)

where ζ is the azimuthal angle in the shower plane and H = H0 tan θ and

H0 is a constant extracted from fit [98; 110]. For zenith angles θ > 70, the

electromagnetic component at ground is mainly due to muon decay [111; 112].

As a result, the lateral distribution follows that one of the muon component.

In fig. 1.18 it is possible to see the lateral distribution for proton, iron and

photon showers obtained from a sample of 100 1019 eV simulated vertical showers.

Figure 1.18: Lateral distribution for 1019 eV proton (red), iron (blue) and photon

(dashed) obtained from a sample of 100 simulated vertical showers.

1.4.4 Time Structure

At the Volcano Ranch array it was discovered that the arrival times of particles

were spread out over several hundred nanoseconds at several hundred meters from

the shower axis, with an increasing spread with the distance [121]. This can be

understood considering a shower as created along a line source rather than at a

single point high in the atmosphere. The core of the shower can be seen as a “fire

42

Chapter1/Chapter1Figs/ldf.eps


ball” with a slowly increasing radius, moving at the speed of light. The shower

front is slightly curved, resembling a cone with a clear forward front and a more

diffuse backward boundary. Let us call “shower plane” the plane perpendicular

to the shower axis and tangent to the shower front at the axis, moving at speed

of light. The structure of the halo may be descripted in terms of the delay with

respect to the shower plane at ground level:

1. nucleons survive down to lowest energies and their arrival time is spread

out over a long time (tens of microseconds). This component is almost

negligible and not extended far away from the shower axis.

2. muons are generally ultra-relativistic and tend to arrive earlier then elec-

tromagnetic particles because they suffer much less scattering into the air

and so have more direct paths to the ground. Muons are more concentrated

in the forward part of the shower front.

3. electromagnetic halo can be considered as the result of a diffusive process

continously produced from the core. It shows a mean temporal dispersion

roughly proportional to the distance from the shower axis (typically 2.5±1

µs).

The front curvature and thickness decrease as the shower propagates, after

2000 g/cm2 the muon tail is almost a flat disk. Fig. 1.19 shows this evolution.

A proper understanding of the front thickness is important for several reasons:

(a) the thickness determines the accuracy of the shower direction reconstruction;

(b) it dictates the integration time of the recording electronics and the method

used to record the number of particles observed; (c) it may be a useful instrument

to infer the primary composition.

As already said, muons are the first particles to reach the ground; so in the

case of an iron shower, which is richer of muon and that develops higher in the

atmosphere than a proton shower, one obtains a signal which is shorter in time

with respect to a proton shower with the same energy. “Rise-time” measurements

based on this effect are among the most powerful diagnostics of composition for

ground array experimens.

43


Figure 1.19: Evolution of the shower front shape and thickness during its propa-

gation.

Watson and Wilson [122] demonstrated that there are fluctuations in the

shower front thickeness from shower to shower. They discovered that fluctations

are correlated with fluctuations in the lateral distribution.

1.4.5 Fluctuations in Shower Development

Fluctuations (differences between showers produced from the same initial con-

ditions) originate mainly from the depth and the characteristic or the first few

interactions. Fluctuations in later interaction are averaged over a large number

of particles and thus are negligible. In particular, fluctuations arise from the first

interaction point which has a direct effect on the depth of the shower maximum

(see fig. 1.16). Further, fluctuations in the ratio between charged and neutral

pions in the first few generations of the shower affect the rate of the development

of the electromagnetic cascade and the muon content of the EAS.

These fluctuations as observed at ground level have been estimated using

Monte Carlo simulations [123] (usually CORSIKA [173]). For UHECR, fluctu-

ations in the muon component are about 15% and in the electromagnetic com-

ponent only 5%. There is a distance from the core location where the fluctuation

are minimized so that the physical fluctuations in the total measurement is less

than 10%. At 1019 eV this distance is about 1000 m. This feature is exploited in

the energy measurement by ground array.

44

Chapter1/Chapter1Figs/thickness_evolution.ps


1.4.6 The Fluorescence Light

As an extensive air shower develops, most of its energy is dissipated by exciting

and ionizing air molecules along its path. Excited molecules in turn dissipate

the energy gained through not radiative collisions or through internal quenching

processes1. This radiation is improperly called fluorescence light [124] (more tech-

nically, the exact definition is luminescence light) or scintillation light, considering

the atmosphere as a scintillation calorimeter.

To predict the amount of fluorescence light emitted along the shower path,

it is necessary to find the energy loss rate by means of collisional processes that

goes into fluorescence light. Since particles mostly affected by energy losses due

to collisional processes are those with lower ionization power and that electro-

magnetic particles are the dominant component in a cascade 2, it is possible to

assume that the energy loss rate by collision is proportional to the shower size.

Fluorescence light from air results almost entirely from electronic transitions in

the N2 molecule and N+2 molecular ion [124; 125; 126]. It has been experimentally

observed that the light emission comes mainly out from N2 second positive system

(2P ) and the N+2 first negative system (1N) [124; 125; 126], according to standard

spectroscopic notation. Fig. 1.20 shows the measured atmospheric fluorescence

spectrum.

Excitation mechanism for these two system are different. The 1N system can

be excited by direct collision with an high energy particle

N2 + e → N+∗2 + e + e (1.53)

The 2P system cannot be directly excitated beacuse the necessary change

in the resultant electronic spin of the molecule is forbidden. This band can be

excited by collision with low energy particles involving electron exchange with a

resultant spin change, or by decay from higher levels, in processes such as:

1The internal quenching is the process in which isolated molecules can accomplish a down-ward electronic transition without radiation, as for example the transfer of electronic excitationenergy to high vibrational levels of a lower electronic state, with a consequent emission ofinfrared radation.

2typically electron and positron population produced in a shower is higher then other par-ticle population of a factor 2

45


Figure 1.20: Measured atmospheric fluorescence spectrum. It mostly comes from

the 2P and 1N bands of N2 and N+2 , respectively. The spectrum is normalized

to the peak value at 337, 1 nm.

N2 + e(↑) → N∗2 (3Πu) + e(↓) (1.54)

N+2 + e → N∗

2 (3Πu) (1.55)

It should be noted that N2 molecule has got 18 vibrational levels associated

with 2P band, whereas 1N band has only one possible wavelenght.

If we consider m molecules excited at ν level and let be τν , τc, and τi the mean

life time of the system with respect to processes of decay to lower energy level,

collision with other atmospheric molecules and internal quenching, respectively,

the total de-excitation rate is

dm

dt= m(

1

τ0+

1

τc) (1.56)

where τ0 tale che 1/τ0 = 1/τν +1/τc. We can obtain the fluorescence efficency

as a function of the wave length λ

46

Chapter1/Chapter1Figs/spettrofluo.ps


ελ =energy emitted as fluorescence light

energy loss into the atmosphere=

n · Eγ

Edep=

=τ0/τν

1 + τ0/τc

photons per excitation (1.57)

in which n is the number of emitted photons, Eγ their energy and Edep the

total energy deposited in air.

From the molecular theory one finds out τc [125]

τc =1√

2Nσnnv(1.58)

where N is the number of molecules in the volume unit of air, σnn the cross

section for the de-excitation process by mean of collision between two nitrogen

molecules and v (v =√

8kTπM

with k Boltzmann constant, T temperature in Kelvin

and M molecular mass) the mean molecular velocity. Using the ideal gas approx-

imation, we may write τc in terms of the gas pressure

ελ =τ0,λ/τν,λ

1 + p/p′λphotons per excitation (1.59)

where the reference pressure is

p′λ =

√πMkT

σnn,λ

1.87 × 10−4

τ0,λmm Hg (1.60)

In the more realistic case of an atmospheric model with two components, in

which nitrogen molecules could de-excit even by collision with oxigen molecules,

the eq. 1.59 does not formally change with a new definition of p′λ [124]

1/p′λ =τ0,λ

1.87 × 10−4√

πMkT

(fnσnn,λ + foσno,λ

√Mn + Mo

2Mo

)(mm Hg)−1 (1.61)

Mn and Mo being the masses of nitrogen and oxigen molecules, fn and fo

the fractions by volume of the two constituents and σno the cross section for the

aforementioned de-excitation process.

Therefore, the fluorescence efficency becomes

47


n

Edep

[photons

MeV

]= ελ · λ

hc(1.62)

with h Plank constant. It is now possible to introduce the fluorescence yield

Nγ as

Nγ = ελ(p, T ) · λ

hc· dE

dx· ρair

[photons

m

](1.63)

where ρair is the atmospheric density, dE/dx the energy loss rate and ελ(p, T )

is the fluorescence efficency, which is function of the air pressure and temperature.

Recentely, energy, pressure and temperature dependences of Nγ have been

measured between 300 and 400 nm in dry air by means of a Sr β source and

using an electron beam from a synchroton between 1.4 and 1000 MeV [127] (see

fig. 1.21 and 1.22).

The fluorescence yield can be parametrized as a function of the temperature

pressure and energy as [127]

Nγ =

(dEdx

)(

dEdx

)1.4 MeV

× ρair ×(

A1

1 + ρB1

√T

+A2

1 + ρB2

√T

)(1.64)

where A1, A2, B1 and B2 are constants and are

89±1.7 m2 kg−1, 55.0±2.2 m2 kg−1, 1.85±0.04 m3 kg−1 H−0.5 and 6.50±0.33

m3 kg−1 H−0.5, respectively. The systematic error in the measurement is 10% and

the statistical error is 3% [127]

The different dependence of the three most important band in the fluorescence

spectrum (fig. 1.20) from the pressure produces two distinct terms1 in the eq.

1.64.

The angular distribution of the fluorescence light can be approximated as an

isotropic distribution

dn

dldΩ=

NγNe

4π(1.65)

where Ne is the number of electrons in the EAS generating the light.

1Fluorescence bands of 337.1 and 357.7 nm have the same dependence from the pressurewhereas the 391.4 band has a different dependence.

48


Figure 1.21: Fluorescence yield as a function of the electron energy, between 300

and 400 nm in dry air at the pressure of 760 mmHg. The continue curve indicates

the dE/dx.

The resultant fluorescence yield corresponds to a scintillation efficiency of only

0.5%. This poor efficiency is compensated for by the overwhelming amount of

energy being dissipated by a 1020 eV (≈ 1J in 30 µs).

1.4.6.1 Cerenkov, Rayleigh and Mie Contaminations

Fluorescence light produced by an EAS is affected by different contamination

mechanisms: Cerenkov light [128; 129; 130], Rayleigh [132] and Mie [133] scat-

tering.

49

Chapter1/Chapter1Figs/fluomisurata1.ps


Figure 1.22: Fluorescence yield between 300 and 400 nm as a function of the

altitude. This calculation employed two typical atmospheric models: a summer

atmospheric model (•) with a surface temperature of 296 K and a winter model

() with a surface temperature of 273 K [127].

Cerenkov light

Electrons in EAS generate a large amount of Cerenkov light, primarily beamed

in the forward direction [128; 129; 130]. The amount of Cerenkov light at any

point along the shower front depends upon the previous history of the shower.

Thus this light is not proportional to local shower size. Directly-beamed Cerenkov

light dominates the fluorescence light at emission angles relative to the EAS axis

θ of less then 25 [13]. Moreover, as the Cerenkov component builds up with

the propagating shower front, the resultant intense beam can generate enough

scattered light at low altitudes such that it competes with the locally produced

fluorescence light from the “dying” shower.

50

Chapter1/Chapter1Figs/fluomisurata2.ps


An exact calculation of the Cerenkov light signal is complicated and must

be carried out numerically. The number of produced Cerenkov photons can be

approximated, with an accuracy within roughly 10% by the formula [13]

dNγ

dl≈ 33NeF (1.57Es)e

−h/H0 photons/m (1.66)

where Ne is the number of electrons, F (E) the electron fraction with energy

> E [131], Es is the energy threshold for the Cerenkov photon emission by an

electron, h is the production height and H0 is an atmospheric scale factor.

The angular distribution of Cerenkov light depends on the angular distribu-

tion of cascade electrons. In the angular range where Cerenkov light is not the

dominant component (θ < 25), it is an exponential

d2Nγ

dldΩ=

dNγ

dl

e−θ/θ0

2πsinθ(1.67)

whose characteristic angle θ0 depends on the Cerenkov threshold and is given

by

θ0 ≈ 0.83E−0.67 (1.68)

Rayleigh Scattering

Photons produced by fluorescence or by Cerenkov mechanism are scattered

by air molecules, this process is named Rayleigh Scattering. It is proportional to

the local air density. At the sea level, the interaction length at 400 nm is ≈ 23

km [132], which corresponds to a mean free path of xR = 2974 g/cm2. Thus, the

amount of light Rayleigh scattered from a beam of Nγ photons is

dNγ

dl= −ρ

Nγ

xR(400

λ). (1.69)

For an isothermal atmosphere

ρ = ρ0e−h/H0 (1.70)

51


where ρ0 is the local density of the observation site. Taking into account the

angular distribution for the Rayleigh scattering [132], the total scattered light is

given by

d2Nγ

dldΩ=

dNγ

dl

3

16π(1 + cos2θ) (1.71)

Mie Scattering

Mie scattering is the scattering of light by small particle in the atmosphere,

whose size is comparable to the wavelength of the light itself.

It is possible to assume that Mie scattering falls off exponentially with the

altitude. The amount of light Mie scattered from a beam of photons Nγ is ap-

proximately

dNγ

dl= − Nγ

LMe−h/HM (1.72)

where we are using a two parameter model to describe the optical condition of

the atmosphere, in which HM is the scale height and LM is the horizontal aerosol

attenuation length.

The angular distribution is strongly peaked in the forward direction. An

approximate angular form which works very well for angles between 5 and 60

is given by

d2Nγ

dldΩ≈ dNγ

dl0.80e−θ/θM (1.73)

where θM ≈ 26.7.

Attenuation

Fluorescence light must be corrected to take into account Rayleigh and Mie

scattering effects. Let TR and TM be the transmission factor for Rayleigh and Mie

scattering, respectively, as obtained by eq. 1.69 and 1.72, and I0 the intensity

light at source: the visible luminescence light into an angular interval ∆Ω then is

52


I = I0 · TR · TM · (1 + ε)∆Ω

4π(1.74)

where ε is an higher order correction due to multiple scatterings.

Fig. 1.23 shows the relative photoelectron yields produced by scintillation

light and its contamination mechanisms as a function of the altitude, as seen in

the Fly’s Eye experiment [13].

Figure 1.23: Relative photoelectron yields produced by fluorescence light (Sci),

direct Cerenkov (C), Rayleigh scattering (R) and Mie scattering (M) mechanism

as a function of the altitude above the Fly’s Eye experiment [13]. Ne is the shower

size.

1.4.7 UHECR Detection

Cosmic radiation of energy up to 1014 eV could be studied directly by detection

of primary particle by means of ballon and satellite experiments (see fig. 1.24).

53

Chapter1/Chapter1Figs/contributofluo.ps


Figure 1.24: Detection techniques used to study cosmic radiation, different tech-

niques for each energy region are shown.

Going up with the energy, CR flux becomes too low to use direct detection,

since it is impossible to employ wide area detectors on ballons or in the space.

Above 1014 eV CR are investigated through the observation of EAS, using par-

ticle detectors, at ground, of suitable area to measure shower front and lateral

distribution, the sample and the extention depend on the energy region one is

interested in. Therefore, studies on UHECR are carried out with indirect tech-

niques.

1.4.7.1 Indirect Techniques

There are different techniques which can be employed to detect ultrahigh energy

cosmic rays, ranging from direct sampling of particles in the shower to measure-

ments of fluorescence light associated with it, Cerenkov or radio emissions or

radar detection.

Cerenkov detection technicque is used at low energies (≈ 1012 eV ). With this

method one detects the Cerenkov light emitted by electromagnetic component of

54

Chapter1/Chapter1Figs/figtecniche.ps


showers. Of course, this kind of experiments could only work during dark nights

with cloudless sky.

At higher energies, for UHECR, the two mostly employed detection te-

chiniques are the Surface array and the air fluorescence techniques.

Radio emission technique is now tested for the first time with the KASKADE−Grande [138] experiment and will be tested even in the Auger Observatory. More

recently, it has been proposed a technique in which one detect radar echos from

the column of ionized air produced by the shower.

Surface Arrays

Direct detection of shower particles with surface arrays is the most commonly

used method and involves an array of sensors spread over a wide area to sample

particle densities as the shower reaches at the ground. Sensors could be particle

detectors like plastic scintillators (used by AGASA experiment) or Cerenkov

radiators (employed by Haverah Park and AUGER Observatory). The two main

parameters of such detectors are the array surface and the detector spacing. The

total surface is chosen to match the expected incident flux, while the spacing

determines the threshold energy for a vertical shower. For Haverah park, a spacing

of 500 m was used, corresponding to a threshold of ≈ 1016 eV , for the Auger

Observatory a value of 1.5 km fix the trigger efficency to 1 at 1019 eV .

Such detectors measure the energy deposited by particles produced by a

shower, as a function of the time. Then, from energy density measured at the

ground and the relative timing of hits in the different detectors, one can estimate

the energy and the direction of primary CR.

Air Fluorescence Detection

Above 1017 eV , the fluorescence light emission can be used. Since this mecha-

nism has a scintillation efficiency of 0.5%, only at these energies the light emitted

becomes really distinguishable from a background light coming from the stars

and the moon.

55


The technique has been employed for the first time by Greisen [134] and his

group in 1965 but unsuccessfully. The first successful attempt to detect EAS with

fluorescence light observation was done by Utah University group [135]. They de-

tected fluorescence light in coincidence with Volcano Ranch surface array. The

first complete experiment was the Fly’s Eye experiment that started to take data

in 1982. Its name derived from its structure: 67 mirrors with 880 photomulti-

pliers, displaced over a semi-spherical surface. It has now been replaced by its

updated version, the High Resolution Fly’s Eye (HiRes).

From signal timing and intensity measured by such a detector it is possible to

reconstruct the axis and the longitudinal profile of a shower and then the energy

and the shower maximum. Further details will be given in chapter 3.

1.4.8 Fingerprints of primary species in EAS

The measurement of primary particle mass composition is crucial for testing any

theory of cosmic ray origin. However, this is the most difficult task facing an air

shower physicist. So far, no method has been applied for which the conclusion

is not dependent on the shower model used to describe the data. Furthermore,

a mass composition analysis should take into account of the shower-to-shower

fluctuations in measured shower observables.

Up to now, statistical analysis of shower observables known to correlate with

the primary composition have been developed.

1.4.8.1 Muon Component

It is easy to understand that one of the possibility of distinguish between different

particle species is offered by the muon content of showers. Using the superposition

principle to describe an hadronic cascade, it is clear that an iron nucleus should,

on average, produce more muon at ground level than a proton of the same energy,

because the mean energy of created pions is lower in a Fe−shower with respect

to a p−shower. There are different problems related to the measurement of

the muon content of showers as the cost, because large area muon detectors

are needed. Further, the muon content is very dependent on the multiplicity of

56


charged particles. As an example, it is possible to consider the model used by

Gaisser [85]

Nµ(> 1GeV ) = 2.8A(E/Aεπ)0.86 (1.75)

where A is the mass of the primary particle of energy E and επ is the energy

associated with the competition between decay and interaction for pions (∼ 50

GeV ). In this model an iron should produce 76% more muons than a proton.

1.4.8.2 Elongation Rate

Linsley [136] pointed out that the variation of the depth of the shower maximum

with the energy (dlogXmax/dlogE) could be a useful indicator of the energy de-

pendence of the primary mass. In fact, changes in the mean mass composition

of the CR flux as a function of the energy should produce a change in the mean

value of the observable Xmax. This change is known as the elongation rate theo-

rem. For pure electromagnetic showers, Xmax(E) ≈ X0ln(E/ε0) (where ε0 is the

critical energy) and then the rate is dlogXmax/dlogE ≈ X0. For protons, using

the Heitler model, if 〈n(E)〉 is the mean number of secondary particles produced

by the first interaction and λN is its mean free path in the atmosphere, it follows

that

Xmax(E) = λN + X0ln[E/〈n(E)〉]. (1.76)

Assuming that 〈n(E)〉 ≈ n0E∆, the elongation rate can be expressed by the form

given by Linsley and Watson [137]

De = δXmax/δlnE = X0

[1 − δln〈n(E)〉

δlnE+

λN

X0

δln(λN )

δlnE

]= X0(1 − B) (1.77)

Using the superposition model and assuming that

B ≡ ∆ − λN

X0

δln(λN )

δlnE(1.78)

is not changing with the energy, one obtains for a mixed composition

De = X0(1 − B)

[1 − ð〈lnA〉

ð〈lnE〉]

(1.79)

Thus, the elongation rate provides a measurement of the change of the mean

logarithmic mass with energy.

57


1.4.8.3 Temporal Distribution Of Shower Particles

The arrival time of the particles in the shower front is spread out because of

geometrical effects, velocity differences and delay produced by multiple scattering

and geomagnetic deflections (see section 1.4.4). As already said, muons are the

first particles to reach the ground. So for an iron nucleus, a signal shorter in

time with respect to a proton shower is produced. Thus a shower front structure

study could help to solve the mass composition puzzle. However, for techinal

limitations of past experiments, the Auger Observatory will be the first in which

will be possible to study it.

1.4.8.4 Lateral Distribution

The fall off of particles with the distance from the shower axis, the lateral density

distribution (see sec. 1.4.3) is another parameter that can be used to extract

the mass composition. Showers with steeper lateral distribution functions than

average will arise from showers that develop later in the atmosphere, like a proton,

and viceversa.

58

Chapter 2

The Pierre Auger Observatory

2.1 Introduction

The Pierre Auger Observatory (PAO) project is the biggest experiment on cosmic

rays even conceived. It was optimized to answer to all the open questions on

UHECR:

1. the spectrum in the GZK−region;

2. observation of point-like sources of cosmic rays (anisotropy on small scale);

3. estimation of intergalactic magnetic field;

4. observation of large scale anisotropy;

5. mass composition in the GZK−region;

Born in 1992 by two physicists, Jim Cronin and Alan Watson, the project idea

derives its name by the french physicist that discovered the extended air shower

existence.

The experiment involves several universities and research institutes from 18

countries, a collaboration with more than 300 physicists.

Its main characteristics are:

1. Full Sky coverage. The project consists of a two-sites observatory, one for

each terrestrial hemisphere, in order to provide a full sky coverage, crucial

59

2.2 The Hybrid Detector

to study the arrival direction distribution. The Southern Observatory is

now going to be completed in the Pampa Amarilla near Malargue, in the

Mendoza Province, Argentina. The Northern Observatory will be built in

Colorado, USA.

2. Large Aperture. Each site will instrument a 3000 km2 area, for a total

detection area of 6000 km2. Because of its huge aperture, the experiment

should be able to detect ≈ 6000 events in the ankle region, ≈ 60 events

above 1020 eV per year of operation. With a reasonable time of data taking,

the experiment will be able to cope one of the main problems related to

UHECR studies, the lack of statistics.

3. Hybrid Detection. Each observatory will be equipped with an array of

particle detectors, water Cerenkov detectors (tanks), distributed over an

area of 3000 km2 (Surface Detector, SD) overlooked by a group of fluo-

rescence telescopes (Fluorescence Detector, FD). The observatory design

is conceived to maximize the event fraction detectable by both, SD and

FD. The combined use of these two detection techniques will provides a

cross-calibration and a better event reconstruction accuracy.

In the Southern Observatory a new CR detection technique is going to be

tested, based on the detection of an EAS by means of radio emissions by electron-

positon pairs produced by the shower [142]. Probably, the Northern Observatory

will be also instrumented for the EAS radio detection.


The main experimental feature is that the Pierre Auger Observatory is a hybrid

detector (see fig. 2.1), employing two complementary techniques to observe ex-

tensive air shower. SD and FD are able to perform independent measurements

on the same shower: the ground array measures the lateral and temporal distri-

bution of shower particles at the ground level, while the air fluorescence detector

measures the air shower development in the atmosphere, the longitudinal profile,

above the surface array. Both techniques have been well established separately

60


by prior experiments. The ground array is similar to the one operated in the

Haverah Park experiment for over twenty years [15]. The air fluorescence method

has been used for the first time successfully in the Fly’s Eye experiment [13]. One

should note that the air fluorescence method has a duty cycle of 10%, whereas

the SD has a duty cycle of 100%. Therefore only a subsample of Auger data will

be hybrid.

The decision to employ both techniques is based upon the following consider-

ations:

1. Intercalibration. Both techniques are able to measure separately the

primary energy, the arrival direction and estimate the composition of an

EAS. On hybrid data systematic effects inherent to either methods alone

can be studied.

2. Energy spectrum estimation. Both methods have different problems

related to the energy measurement: an air fluorescence detector has in

principle a direct energy calibration, but its aperture is not fixed. On the

other side the surface detector has a fixed aperture but an indirect energy

calibration.

Usually, its energy calibration comes out from EAS Monte Carlo simula-

tions, which strongly depend on models used. Furthermore, one should take

into account fluctuations coming from simulated showers, due mainly to the

thinning level used in the simulation code.

FD aperture grows up with the energy. It also depends on the light back-

ground and on atmospheric conditions, so in principle it changes night by

night.

The combined use of these two techniques could allow to derive energy

calibration constants for the SD from FD energy reconstruction, which is

almost model independent. These constants will be employed in the SD

data analysis to elaborate the spectrum1.

1Since their duty cycle, the number of SD events will be an order of magnitude higher thanFD events.

61


Figure 2.1: Hybrid detection scheme: shower particles are sampled at ground

level by Cerenkov detectors while the fluorescence detector records fluorescence

light produced by shower particles through excitation of nitrogen molecules as

the shower develops in the atmosphere.

62

Chapter2/Chapter2Figs/hybriddetector.ps

2.3 The Southern Observatory

3. Enhanced composition sensitivity. Each technique obtains information

about primary composition by measuring air shower quantities which are

correlated with it: FD directly measures the depth at which the shower

reaches its maximum (Xmax); SD measures particle densities and time

width of the shower front at ground level, which are, partially model in-

dependent, fingerprints of the primary’s nature. Combining muon and elec-

tromagnetic particle densities together with longitudinal profile it is possible

to impose tighter constraints on hadronic interaction models. Moreover, the

knowledge of all these informations allows us to be much less susceptible to

fluctuations leading to misidentification.

The two-sites observatory design aims to get a full sky coverage in order to pick

out cosmic ray sources. In fact, since sources should be not too far for the GZK

limit (see section 1.2.3) and candidate sources are distributed not isotropically,

extremely high energy cosmic rays should point directly to them.


The Southern Observatory is located in the Pampa Amarilla upland. This upland

has an altitude between 1300 and 1500 m above sea level, with an average slope

of 0.5%. The ground array detectors are located over an ancient riverbed, while

the 4 eyes are situated over natural embankment, at edges of the area.

At the moment, the Observatory is going to be completed (see fig. 2.2). It will

be equipped with 1600 water Cerenkov tanks in a 1.5 km spaced triangular grid,

spread out on a 3000 km2 area. The area is overlooked by 4 fluorescence detectors

(eyes) 1, disposed at the edges of the surface array. Each eye is composed by 6

fluorescence telescopes, each one with a field of view of 30 × 30.

The Observatory includes a Central Campus (see fig. 2.3), located in Malargue,

where there are the assembly center, the central data acquisition system (CDAS)

and the offices.

1The names of the 4 eyes are Los Leones, Los Morados, Loma Amarilla and Coihueco.

63


Figure 2.2: Pierre Auger Southern Observatory map. Red dots represent surface

array detectors, labels correspond to 4 fluorescence eye buildings. The lines mark

azimuthal field of view of each telescope. Cyan area represents already operational

parts.

Figure 2.3: Central Campus building in Malargue.

64

Chapter2/Chapter2Figs/mappaauger.ps

Chapter2/Chapter2Figs/centralcampus.ps

2.4 The Surface Array


The Surface Detector is an array of 1600 water Cerenkov tanks in a 1.5 km spaced

triangular grid (see fig. 2.2). This spacing provides a trigger efficency of 100% at

1019 eV . The spacing has been determined by requiring a minimum of 5 triggered

tanks at 1019 eV .

The ground detector unit (tank) is a cylinder of 3.6 m of diameter and 1.2

m in height, viewed by three photomultiplier tubes of 200 mm diameter (see fig.

2.4). Photomulipliers look downward and are placed at 1.2 m from the cylinder

axis, in steps of 120 on the upper cylindrical surface. The design derives by

an optimization of proportionality between Cerenkov light produced and pho-

toelectron yield and signal uniformity. Tanks are built of rotationally moulded

polyethylene that allows them to be resistent to temperatures and occasional lo-

cal animal attacks. They are filled with deionized water, which is enclosed within

a liner. The liner acts as light barrier from outside, while its inner Tyvek surface

is excellent in reflecting Cerenkov light.

Different reasons led the Auger Collaboration to choose water Cerenkov de-

tectors. First, they are able to detect even very inclined showers and offer the

possibility to distinguish between muon component and electromagnetic com-

ponent signals. Furthermore, they are not too expensive compared with other

particle detectors with similar performances, and are built with durable materi-

als and able to keep over 20 years.

Each unit is equipped with the following instruments::

1. solar panels and battery for power autonomy;

2. global position system (GPS) receiver for independent absolute timing;

3. GSM−like transceiver unit for wireless communications.

The signals from each tank are digitized by 10 bit fast analog to digital con-

verter (FADCs) running at 40 MHz.

65


Figure 2.4: Schematic overview of an SD tank.

2.4.1 SD Calibration

To count how many particles are crossing a tank volume in a certain time interval,

one has to know the value of the signal corresponding to one crossings particle.

For this purpose, the concept of Vertical Equivalent Muon (V EM) has been

introduced, defined as the sum of charges collected in the three photomultipliers

(PMTs) for a relativistic down-going vertical muon crossing the detector. One

V EM is then equivalent to a muon track length of 1.2 m, or 0.1 particles/m2.

Tanks are calibrated using atmospheric muons, a well known uniform back-

ground. Atmospheric muon signal is proportional to the path length of the par-

ticles within the tank. A test tank was used to calculate the relation between

of down-going vertical muons (V EM , vertical equivalent muons) and the peak

of the histogram obtained from omni-directional muons. Each tank is calibrated

matching the photomultipliers gain to obtain the expected trigger rate over a

given V EM threshold. This procedure allows to calibrate tanks with a precision

of 5%.

66

Chapter2/Chapter2Figs/schema_tank.ps

2.5 The Fluorescence Detector


The primary purpose of the fluorescence detector is to measure the EAS longitu-

dinal profile. Longitudinal profile provides a direct measurement of the energy of

the shower electromagnetic component, so in a model-independent way. Known

primary energy, from Xmax observation one could infer the primary composition.

FD characteristics have been fixed by requiring an high resolution in Xmax

measurements, 20 g/cm2, in order to investigate CR primary composition1.

FD is composed by 4 eyes, displaced at SD area edges. Each eye with a field

of view of 180 in azimuth and 30 in elevation, is made of 6 telescopes, each

covering 30 × 30. Each eye is housed in a single building. The ground plan

of eye buildings is shown in fig. 2.5. The building has a semicircle ground plan,

with radius of 14 m. Telescopes point radially outward through windows of 3 m

(w) × 3.5 m (h).

Figure 2.5: Layout of an FD building, showing 4 telescopes in their bays.

Telescopes have a light collection system, diaphragm and mirror, and a light

detecting camera, a 440 PMT array (see fig. 2.6).

1On average, the difference between a proton shower Xmax and an iron shower Xmax isabout 100 g/cm2.

67

Chapter2/Chapter2Figs/pianta_occhio.ps


Figure 2.6: Schematic view of an FD telescope. From left to right are shown:

attached to the window shutters and the aperture system with filter and corrector

ring; camera support holding a 440 PMT camera; on the floor the electronic crate;

mirror and its support structure. The indicated reference point defines the center

of the telescope geometry: telescope orientation is defined by datum points on

the ground and the 16 elevation of the central line of sight (axis telescope).

68

Chapter2/Chapter2Figs/schema_telescopio.ps


1. Light Collecting System

The Auger FD design adopts a Schmidt optics [143] to eliminate coma

aberration. Telescope optics is almost completely spherically symmetric, so

pixels far from telescope axis are equivalent to pixels on the axis.

The optics contains a large spherical mirror with radius of R = 3.4 m, with

a diaphragm at the center of curvature whose outer radius is 0.85. The

diaphragm eliminates coma aberration and guarantees an almost uniform

spot size over a large field of view, with a size of the order of 0.5. The

aperture is increased by enlarging to an outer radius of 1.1 m, and the

spherical aberration is compensated by covering the additional area with a

corrector ring (see fig. 2.7). This ring is contained in an aperture box, which

also holds an optical filter transmitting the nitrogen fluorescence wavelength

range and blocking most of the night sky background.

Optics parameters come out from signal/noise calculations for EAS at the

experimental threshold, taking into account the night sky background at

the Southern Observatory.

2. Light Detecting System

A matrix of 440 PMT , called pixels, constitutes the light detecting system

and its main parameters are fixed by reference design of the optics based

on the Schmidt system without corrector plate [144]. Pixels must lie on the

focal surface, that is the spherical surface where the circle of least confusion

has its minimum size. The radius of this focal surface is Rfoc = 1.743

m, with a spot size lower then 0.5. For a better covering of the camera

surface, pixels are hexagonal. As compromise between the resolution and

the minimum circle of confusion, PMTs have a side to side distance of

45.6 mm, corresponding to angular size of 1.5. In order to maximize light

collection and guarantee a sharp transition between adjacent pixels, PMTs

are complemented by light collectors.

Pixel centers are placed over a spherical surface in steps of ∆θ = 1.5 and

∆φ = 1.5 cos 30 ≈ 1.3 (see fig. 2.9). The angular position of the vertices

are obtained by moving in steps of ∆θ/2 and ∆φ/3 with respect to the

69


Figure 2.7: Corrector ring diaphragm and PMT camera for bay 4 in Los Leones

eye.

Figure 2.8: PMT camera

70

Chapter2/Chapter2Figs/corrector_ring.ps

Chapter2/Chapter2Figs/camera.ps


pixel center (see fig. 2.9 (b)). Equal angular steps produce different linear

dimensions, depending on the pixel position on the spherical surface. Thus,

pixels are not regular hexagons. The resulting camera is composed of 440

pixels, arranged in a 20 × 22 matrix (see fig. 2.9 (c)).

Figure 2.9: Geometrical construction of the FD camera: (a) pixel centers are

placed over a spherical surface in steps of ∆θ and ∆φ; (b) positioning of pixel

vertices around the PMT center; (c) the FD camera, a matrix of 20× 22 pixels.

Camera body supports (see fig. 2.10) ensure mechanical stability and pro-

duce a minimal unavoidable obscuration of mirror field of view (less then

0.1 m2).

Pixels are complemented by light collectors, even for mechanical reasons.

The basic element of a light collector is a reflecting mercedes star, with three

71

Chapter2/Chapter2Figs/schema_camera.ps


arms at 120. At each pixel vertex, a mercedes is collocated, producing 6

mercedes for a PMT (see fig. 2.11). The arm length is approximately half

of the pixel side length and its section is an equilateral triangle with base

9.2 mm. In these conditions, a light collection efficency of 94% is obtained

(see fig. 2.12).

PMTs used are hexagonal photomultipliers XP3062 from Photonis [144].

Their characterictics are the followings:

(a) non-uniformity of the response over the photocatode within 15%: the

light spot size for a point source at infinity is about one-third of the

pixel size, so the uniformity is not a critical parameter.

(b) gain: the nominal gain is 5 × 104 − 105.

(c) spectral response: the PMT average quantum efficency is 0.25 in the

wavelength range we are interested in. We allow a deviation of not

more than 10% from this value.

(d) linear response: it is better than 3% over a dynamic range of at least

104 for signals of 1 µs.

(e) longevity: the integrated anode charge corresponding to the half life

of the tube is not less than 500 C with an half life of ∼ 50 years.

(f) single photoelectron: even if it is not necessary, PMT have a single

photoelectron capability, which guarantees a good resolution for the

tube.

In order to achieve a good geometric and profile reconstruction accuracy,

flash-ADC (FADC) to digitize collected light are used. An electronic sys-

tem with a wide dynamic range and 10 MHz ADC sampling has been

developed. Signals are then sampled every 100 ns. This allows a very accu-

rate measurement. In fact, a sample every 100 ns corresponds to a profile

sample of less than 4 g/cm2. The reconstruction is limited by the signal to

noise ratio.

72


Figure 2.10: Schematic view of the camera support.

Figure 2.11: Six mercedes positioned to form a pixel. Each mercedes star has

three arms at 120.

73

Chapter2/Chapter2Figs/camerasupporto2.ps

Chapter2/Chapter2Figs/schema_mercedes.ps


Figure 2.12: Measurement of the light collection efficency with a light spot moved

along a line passed over three pixels: • measurements performed with mercedes;

measurements without mercedes.

2.5.1 FD Detector Calibration

In order to obtain quantitative informations from fluorescence detector data,

detector calibration is essential, because it allows to convert measured FADC

counts into light flux reaching the detector, and then to number of photons emit-

ted by the shower. Detector calibration is performed as a function of light wave-

length.

Two different kinds of calibrations are performed for the FD detector:

1. a relative calibration [148], where the response of the detector to a selecte

light source is checked as a function of the time;

2. an absolute calibration [149], where it is measured the number of photons

corresponding to 1 FADC count for each pixel.

74

Chapter2/Chapter2Figs/efficienza_mercedes.ps


2.5.1.1 Absolute Calibration

In the absolute calibration [145], FD telescopes response to a known light (nom-

inally at ≈ 5%) flux is measured.

The most important absolute calibration procedure is the so-called Drum

Calibration. In the Drum calibration, the fluorescence detector is calibrated by

means of illuminating system, the drum, providing a telescope illumination which

is uniform within 3% (see fig. 2.14). The drum is itself calibrated using a NIST-

calibrated photodiode, that measures the absolute light flux within a precision

of 7%. Drum Calibration provides calibration constants for all FD telescopes.

These calibration constants allow directly to convert FADC counts into inci-

dent photons at diaphragm level, taking into account all possible effects due to

telescope characteristics, from its geometry to its electronics, pixel by pixel.

Figure 2.13: The εPE(λ) behaviour of the photoelectron production by means

of a single photon as a function of the wavelength. Trends of different detector

components involved in the εPE(λ) determination are represented, the contribu-

tion coming from the corrector ring takes into account the effect of the camera

shadow.

75

Chapter2/Chapter2Figs/epsilonPE.ps


Figure 2.14: Drum Calibration scheme: a light source emits light pulses toward

the diffusion panel, which are reflected toward the telescope. Drum inner surfaces

are covered with TYVEK.

There are two additional absolute calibration procedures, mostly used to test

systematic effects affecting Drum calibration:

1. piece-by-piece Calibration: εADC(λ)ij is determined by combining the effi-

cency of every signle part through a ray tracing analysis. In this case the

efficency can be factorized as

εADC(λ)ij = εPE(λ)ij · gij (2.1)

where εPE(λ)ij is the efficency of the i-th PMT in the j-th telescopes for

the photoelectron production by means of a single photon and gij is the

electronic gain (ADC/PE). The εPE(λ)ij behavior is shown in fig. 2.13

while typical values for electronic gains are ≈ 1.8ADC/photon [146; 147].

Uncertainties of the order of 15% are related to this calibration.

2. Rayleigh Calibration: laser shots at 355 nm, with a known intensity at

5%, are used to calibrate the detector. The light source is placed at few

kilometers from FD building, so Mie attenuation effects are negligible in

the analysis.

76

Chapter2/Chapter2Figs/drum_calib.ps


2.5.1.2 Relative Calibration

Relative calibration system is used for monitoring fluorescence detector perfor-

mances as a function of time. During every DAQ (data acquisition) night, three

different relative calibration procedures are employed, corresponding to three dif-

ferent ways to illuminate the telescope by means of light pulses produced by

Xenon flash lamps and indicated as script A, script B and script C (see fig 2.15).

They are usually performed at beginning and at end of DAQ night.

1. Script A: light pulses from the center of the mirror are collected directly

by camera pixels. So A-source calibration signals in each pixel provide an

optimal monitor of the pixel stability.

2. Script B : light pulses are emitted from both sides of the camera body toward

the mirror and then collected by PMT camera. This relative calibration

allows to monitor the mirror-camera system.

3. Script C : light pulses are fed through ports on the sides of the aperture and

are directed onto a reflective TYVEK foil mounted on the inner surface of

the telescope doors. The foil reflects the light back into the telescope optics.

In this way, it is possible to test the whole telescope system.

Script A studies have been performed comparing each night calibration signals

with fixed reference calibration signals. They show that the detecting system,

PMT camera and its electronics, is stable within a few percent both on long

term and on monthly base. The overall uncertainty, as deduced from long term

monitoring of the system, is typically of the order of 1 − 3% (see fig. 2.16).

77


Figure 2.15: Relative calibration schemes: light diffuser is placed at center of the

mirror (Script A), on both sides of the camera (Script B) and in the aperture

box (Script C ).

78

Chapter2/Chapter2Figs/schemacalib.ps


Month0 2 4 6 8 10 12

Mea

n

0.7

0.8

0.9

1

1.1

1.2

1.3

Month0 2 4 6 8 10 12

Sig

ma

%

0

1

2

3

4

5

6

7

8

Figure 2.16: Monthly averaged relative calibration constants from relative cali-

bration A for telescope 4 in Los Leones during 2004, with respect to reference

calibration signals.

79

Chapter2/Chapter2Figs/icrcscriptA.ps

2.6 Atmospheric Monitoring


Experiments based on EAS detection use the atmosphere as a huge calorimeter,

whose properties vary in a predictable way with altitude and in a relatively unpre-

dictable way with time. As in the “usual” calorimeters, one has to get a complete

description of its properties. In fact, to get a precise estimation of the amount of

the fluorescence light emitted by the cosmic ray shower and to be able to convert

production height in atmospheric depth passed through by the shower, a detailed

knowledge of the atmospheric conditions is required. The largest uncertaities in

the fluorescence measurements come from uncertainties in the atmospheric trans-

mission1, air Cerenkov subtraction, light multiple scattering. To minimize the

atmospheric uncertainties, Southern and Northern Observatory will be located in

dry desert areas with excellent visibility.

The Auger Collaboration has developed a full program of atmospheric studies,

by using different and complementary approaches [151].

Air Density Profile Monitoring

In order to obtain an air density profile, essential to transform atmospheric

depth to geometrical altitude and viceversa, the atmosphere has been investigated

in a number of campaign with meteorological radio soundings and with continous

measurements of ground-based weather stations, in order to describe pressure and

temperature as a function of the height and time [150]. The determination of the

air density profile allows to take correctly into account the Rayleigh attenuation

coming from interaction of fluorescence light with atmospheric molecules.

LIDAR Monitoring

The principal device designed to study atmospheric aerosol conditions consists

of a LIDAR system able to measure atmospheric aerosol content by backscattered

light signals [152]. There is a LIDAR station at each FD building, instrumented

with a UV laser source and three parabolic glass mirrors (see fig. 2.17). Each

1As it is shown in eq. 1.74, the collected light by fluorescence detector is related to theemitted light by means of atmospheric transmition factors.

80


parabolic mirror focuses the backscattered laser light into a PMT . LIDAR

systems have two main operation modes: (a) a continuos sky scan on a ≈ 50

cone around the local vertical; (b) “shoot the shower” mode, where laser pulses

are triggered by FD events and shot in the region of the recorded events.

Figure 2.17: LIDAR station near the FD Los Leones building.

Horizontal Attenuation and Aerosol Phase Function Mon-

itoring

LIDAR systems are complemented by Horizontal Attenuation Monitors (HAM),

in which almost horizontal laser shots are used to measure the horizontal attenu-

ation length between FD eyes. Furthermore, the APFs (Aerosol Phase Function

Monitors) has been designed to measure the aerosol differential scattering cross-

section dσ/dΩ, which depends on the characteristic of the aerosols [155]. The

measurement is made by firing a horizontal, collimated beam of light from a

xenon flash lamp across the front of an FD eye. The resulting track contains a

wide range of light scattering angles from beam (30 to 150).

81

Chapter2/Chapter2Figs/lidar.ps


Cloud and Star Monitoring

The Observatory cloud sky coverage is monitored by means of infra-red ob-

servations at wavelength of about 10 µm [153] and by star monitoring systems

[154]. Star monitors measure the brightness of the stars and by comparing it with

the expected one, they provide an independent atmospheric attenuation.

The Central Laser Facility

The Central Laser Facility [156] is located in the middle of the Pierre Auger

Observatory SD array (see fig. 2.18), at distances that range from 26 to 39 km

from FD buildings1. It features a UV laser (355 nm) and optics that direct

a beam of calibrated pulsed light into the sky. Light scattered from this beam

produces tracks in the fluorescence detector. For every hour of FD operation,

several hundred laser shots are fired with different energies and directions. The

laser beam can be steered to any direction with an accuracy of 0.2. By means

of an optical fiber, a fraction of the laser light can be injected into a nearby

SD tank (Celeste) allowing systematic studies of hybrid geometry recontruction

accuracy. CLF tracks have a wide range of uses, from testing detector properties

to monitor atmospheric conditions:

1. geometrical reconstruction accuracy studies;

2. FD − SD time offset measurement;

3. trigger efficency;

4. energy reconstruction studies;

5. aerosol condition studies

The predictable intensity of light scattered from the beam at each height can be

used to measure the aerosol attenuation from the beam to the FD eye, providing

a measurement of the vertical aerosol optical depth (V AOD).

1Its UTM coordinates are N 6095769, E 469378 and H 1412.

82


Figure 2.18: The Central Laser Facility with the nearby Celeste tank.

83

Chapter2/Chapter2Figs/clf_container.ps

Chapter 3

Event Reconstruction with Pierre

Auger Data

3.1 Introduction

The Auger data acquisition system is based on a hierarchical event trigger, capa-

ble to select interesting events and reject uninteresting ones using event topology

and timing informations. The fluorescence and the surface detectors work inde-

pendently and use two completly independent trigger systems. When both FD

and SD are in operation, event candidates, surviving FD trigger selection, are

sent to the SD data acquisition system, that scans the ground array for triggered

tanks to build up hybrid events.

Recorded events could involve:

1. the only surface array, ordinary SD events (see fig. 3.1);

2. only fluorescence detector, mono FD events if seen by one eye or stereo FD

events if seen by at least two eye (see fig. 3.1);

3. both detectors, hybrid events (see fig. 3.1). Hybrid events could be of differ-

ent kinds: 1 FD eye + 1 SD tank or a few SD tanks, not enough to realize

an independ SD reconstruction; 1 FD eye + n SD tanks, with n higher

enough to perform an independent SD reconstruction (golden events); 2 or

more FD eye + SD informations, stereo-hybrid events (platinum events).

84

3.1 Introduction

Figure 3.1: Events recorded by the Pierre Auger Observatory could involve: (1)

only the surface array (left top); only the fluorescence detector, with one (right

top) or more eyes (left medium); both SD and FD in different ways (1 FD eye

+ 1 or more SD tanks, right medium, 2 or more FD eye + 1 or more SD tanks,

left and right bottom, respectively).

85

Chapter3/Chapter3Figs/sd_event.ps

Chapter3/Chapter3Figs/mono.ps

Chapter3/Chapter3Figs/stereo.ps

Chapter3/Chapter3Figs/hybrid.ps

Chapter3/Chapter3Figs/stereo_hybrid.ps

Chapter3/Chapter3Figs/multistereo_hybrid.ps

3.2 FD Data Acquisition Strategy

Once the South Observatory will be complete, it is clear that the fraction

of FD only events will be very small, most of FD events will be hybrid (mono

events with a few tanks).


The fluorescence detector trigger is organized upon several levels. There are

two hardware triggers, the first level trigger (FLT ) and the second level trigger

(SLT ), which select pixel above threshold and require a minimum track on the

camera. There are also two software triggers, the third level trigger (TLT ) and

the T3, which operate a noise event rejection and identify event candidates to

send to the Central Data Acquisistion System (CDAS).

FD signals are digitalized by the by flash−ADC every 100 ns (with a fre-

quency of 10 MHz). Analog signals are converted in 16 bit word, whose the

first twelve store the digitized signals and the latter 4 are control bits (like the

status bit, which says if the pixel is above the threshold, ON , or not, OFF ). Sig-

nal words are stored in a 32 K SRAM memory till a second level trigger signal

occours.

3.2.1 First Level Trigger

The first level trigger is the pixel level trigger. It selects PMT tubes which

are above a threshold. The system distinguishes fluorescence light from night

sky background photons by means of a logic based on a running sum of the

last 10 digitized FADC values [157]. The result of the sum is compared with

a programmable trigger threshold. The threshold automatically varies to hold a

fix trigger rate of 100 Hz, independently pixel by pixel. This system takes into

account for any variation during an acquisition night due to electronics problems

or light background (bright stars in the field of view, etc.). A pixel above the

threshold is labelled as ON and holds its status for 20 µs once the running sum

on its signal has fallen below the threshold.

86


3.2.2 Second Level Trigger

The second level trigger is based upon a pattern recognition procedure on FLT

pixels.

Patterns to look for are defined from a set of five basic configuration of five

pixel each (see fig. 3.2). The complete set of valid patterns is obtained by means

of a rotation of 60 and 120 and by reflection with respect to x and y axis.

Patterns obtained are 39, but for the hexagonal system simmetry one should

consider separately patterns for odd and even rows, the possible configurations

are 78. Requiring only 4 FLT pixels of 5−pixel pattern 1, the list of possible

patterns grows up to 108, leaving out equivalent configurations. The procedure

takes 1 µs to perform a complete scan of the camera. The scan proceeds column

by column, taking for each one a 20 × 5 pixel matrix. In the latter sub-matrix,

the SLT tests possible patterns associated with triggered pixels.

Once a track is compatible with a reference pattern, a SLT signal is issued.

The event is held in the memory till it is processed by the following trigger level.

The memory has a capacity of 32 events. The SLT rate is below 1 Hz for each

telescope.

3.2.3 Third Level Trigger

The first FD software trigger is the TLT . The TLT manages the event readout

and applies a noise rejection algorithm. For events passing the noise rejection

algorithm, a list of triggered pixels and their closest neighbours (to avoid any

signal losses) is compiled. At the end, the complete event data is stored in

an event file. If the event data are coming from more than one mirror, the

TLT integrates it in a single event structure, eye-event structure. Now the data

contain:

1. FLT data, FLT pixels, at what time and how long they are above threshold.

1In this way it is possible to take into account pixels fired marginally or with some hardwareproblem.

87


Figure 3.2: Second Level Trigger patterns: from these basic 5−pixels tracks, the

whole set of patterns by rotation of 60 and 120 and by reflection are generated.

Considering even traces with one hole in the pattern, one obtains a total of 108

patterns.

2. SLT data, a column pattern codes which indicate the recognized pattern

for the track and the first column of the first pixel at which the pattern has

been associated.

3. FADC data, digitized data traces. Each trace contains 1000 FADC values,

each one corresponding to 100 ns. The first 250 time bins correspond to

the data time previous to the event trigger. These pre-trigger data allows

to calculate the pedestal and its fluctuations for each pixel.

With the TLT the event rate goes down to about 100 events per hour for each

telescope.

3.2.4 The T3 trigger

Events surviving TLT are processed by T3 trigger to send a “shower candidate”

trigger signal to the SD acquisition system. This trigger level makes a more strict

noise rejection based on timing and a simple pulses analysis. Furthermore, the

T3 performes an on-line geometrical reconstruction.

88

Chapter3/Chapter3Figs/slt_tracce.ps

3.3 SD Trigger and Data Selection

Shower candidates are identified by looking for events with finite pulse widths

and finite transit times between PMT (shower front is moving in the field of view

if the detector), which depend on shower energy and geometry.

Rejected events could be due to: accidental triggers, small track and no signal

in the triggered pixels; coherent noise, usually associated with weather condi-

tions (lightning and storms in the field of view), characterized by noise signals

distributed almost over all the camera; cosmic ray hitting directly the detector,

high and short pulses and negligible transit times among pixels.

Usign the pixel list coming from SLT , T3 operates a fast signal analysis, based

on searching the FADC trace maximum. Then the noise rejection algorithm is

applied.

The system makes in two steps an on-line reconstruction: a fit to a track on

the camera, to determine the plane containing almost all triggered pixel pointing

direction (the so called shower detector plane SDP ) and so its projection on the

ground (landing line); a time fit on pixel timing and their observation angles to

estimate the expected arrival time for light emitted by shower front at ground

level (landing time).

The resulting T3 trigger rate is between 5 and 10 shower candidates per hour

for each telescope.


Cerenkov photons produced by shower front secondary particles traversing the

SD tank, are recorded by three downward facing PMTs (see sec. 2.4). A low

and high gain signal from each photmultiplier is sent to front-end electronics.

High gain signal is evaluated every 25 ns by the trigger/memory circuitry for

interesting patterns, which stores the data in a buffer memory and informs the

detector station micro-controller when a trigger occurs.

Surface detector trigger levels have a similar hierarchical design structure of

those of the fluorescence detector. The trigger system has been designed to allow

the ground array to operate at a wide range of primary energies, for vertical and

very inclined showers, with a full efficiency for primary particles above 1019 eV .

89


There are two trigger levels implemented directly at tank level, T1 and T2. A

further trigger level, T3, is formed at observatory campus based upon the spatial

and temporal correlation of the 2 level triggers. All data surviving T3 are stored.

Additional trigger levels are implemented in order to select physical events (T4,

physics trigger) and accurate events (T5, quality trigger).

3.3.1 Tank Level Triggers

The trigger/memory circuitry produces a first level trigger based upon hardware

analysis of the high gain PMT signals. The T1 uses two important shower

waveform properties: 1) on average, for any fixed number of Cerenkov photons

detected, those from higher energy showers will be more spread out in time with

respect to those from lower energy showers1; 2) signals coming from electrons and

photons are usually smaller than those of muons2.

At tank level, the T1 uses two different trigger modes:

1. Time over Threshold (ToT ) trigger, which requires that 13 bins in a 120

bins window are above a threshold of 0.2 IestV EM

3 in coincidence on 2 PMT

[159]. This trigger has a rate of about 1.6 Hz. It efficiently selects small

but spread signals, as those coming from high energy distant EAS or low

energy showers, rejecting signals form muon background.

2. 3−fold coincidence of a 1.75 IestV EM threshold. It is more noisy, having a

rate of about 100 Hz, but it is needed to detect fast signals (< 200 ns)

produced by the muonic component of very inclined showers.

T2 is applied in the station controller to select from T1 signals those likely

to have come from EAS and to reduce to 20 Hz the event rate to be sent to the

central station. All of ToT trigger are directly promoted to T2, whereas 3−fold

T1 have to satisfy a higher threshold of 3.2 IestV EM on all of 3 tank’s PMT . The

rate for this trigger level is about 20 Hz.

1A fixed energy contour is farther from shower core in a larger energy showers2At observation level, the energy of muons is usually higher than that of photons and

electrons3The estimated current for a Vertical Equivalent Muon (Iest

V EM ) is the reference unit for thecalibration of FADC signals [160].

90


All T2 tanks are used for the hybrid trigger.

3.3.2 Event Selection Triggers

At Observatory campus, the T3 is applied using two different modes:

1. 3 tanks satisfying the ToT conditions and a minimum compactness, that is

one of them must have one of its closest neighbours and one of its second

neighbours triggered. The 90% of events selected by the so called 3ToT are

physical events. It is very efficient for vertical showers.

2. 4−fold coincidence of any T2 with a moderate compactness requirement,

that is among 4 tanks, one can be as far as 6 km away from others within

an appropriate time window. Only 2% of events selected by this mode are

real showers, but it is absolutely needed to detect horizontal showers, which

produce fast signals with a wide-spread topological patterns.

A physical trigger (T4) is needed to select showers from T3 data. For zenith

angles below 60, there is an official physical trigger implemented offline, based on

the compactness of triggered tanks and on the spread in time of FADC traces,

which is enough to satisfy a ToT condition. The present T4 implementation

requires either a compact 3 ToT (see fig. 3.3), which ensures that more than 99%

of selected events are showers, or a compact configuration of any local trigger

called 4C1 (at least one fired station has 3 triggered tanks out of its 6 first

neighbours, see fig. 3.4).

The 3ToT T4 trigger loses less than 5% of showers below 60. The 4C1 trigger,

which event rate is about 2% of the previous one, allows to keep the 5% of the

showers below 60 lost by the former and to select low energy showers above 60.

The definitions of T4 criteria for horizontal showers is still under study [161]

3.3.3 T5 quality Trigger

To compute the detector acceptance and build the spectrum, among events sur-

viving T4 trigger level, only those reconstructed with a known energy and angular

accuracy have been used. Various studies have been performed to identify under

91


Figure 3.3: The two possible 3ToT compact configurations (with addition of all

simmetry transformations of the triangular grid).

Figure 3.4: The three minimal 4C1 configurations (with addition of all symmetry

transformations of the triangular grid).

92

Chapter3/Chapter3Figs/3ToTfig.ps

Chapter3/Chapter3Figs/4C1fig.ps

3.4 Hybrid Trigger

which conditions events could satisfy this requirement. This is the task of the

quality trigger (T5).

At moment the T5 implementation requires that the tank with highest sig-

nal must have at least 5 working tanks among its 6 closest neighbours when the

event is recorded. Furthermore, the reconstructed core must be inside an equilat-

eral triangle of working stations. These requirements guarantee that no crucial

informations are missed for shower reconstruction. The study of T5 effects on

reconstruction accuracy and in particular on the signal at 1000 m from the core

(S(1000)) is described in [162]. The maximum systematic uncertainty in the re-

constructed S(1000) due to event sampling into the array or the effect of a missing

internal tank is around 8%.

The total trigger chain allows to reduce the event rate in a single tank from

3 kHz, mainly due to muon background, down to 3 per day, due to real showers,

corresponding to a rejection factor of 108.

3.4 Hybrid Trigger

The main Pierre Auger Observatory feature is its hybrid detection technique:

the possibility to measure the same event by fluorescence and surface detector.

Therefore, in the data acquisition system the hybrid trigger design has a very

important role. In the selected design, the FD T3 signal gives an external trigger

to the surface detector [158]. This choice allows to get hybrid events even with

a single SD station. This is very important, because SD timing information

greatly improves the FD reconstruction, though there is only a single SD tank

data. In fact, the FD axis reconstruction is based upon a minimization of a

function which depends on three parameters (see sec. 3.6.1.2), that determine

the curvature of the pixel time distribution versus their elevation angle. The

timing information coming from the SD introduce new terms in the function

with a different dependence on parameters. So, there will be a fraction of events

that are, in principle, hybrid but that cannot be reconstructed from SD array.

This strategy allows an hybrid reconstruction of low energy events, close to the

FD trigger threshold (E ≥ 3 · 1017 eV ). In fact, this energy range is below the

93

3.5 SD Event Reconstruction

SD trigger threshold but the probability that at least a tank gives a T2 trigger

signal is very high (∼ 100%).

At last FD trigger level, FD events, labelled as shower candidates by T3,

are analyzed on-line and their SDP projection and light arriving time at ground

level are computed. When both SD and FD are in operation, T3 signal and

preliminary reconstruction results are sent to CDAS to trigger the SD. The

landing time and the SDP allow CDAS to calculate the impact time of the

shower front in the SD tank region. Then CDAS looks for compatible SD T2

tanks across the array, with a trigger time within 20 µs of the calculated time.

Triggered tanks, identified by this procedure, are collected and their data are

gathered in an event structure labelled FD−trigger.

Of course, time and resources available to perform on-line reconstruction are

limited, so into T3 software is implemented a semplified version of the more

sophisticated reconstruction methods used for the offline analysis.

In order to not degrade SD trigger performances, T3 signals should arrive to

CDAS within 5 s, that is the maximum SD T2 transit time across the radio

network.


The SD event reconstruction can be schematized in two main steps: the plane

fit, to obtain the geometry of the incident shower, and the lateral distribution fit,

to estimate the energy.

3.5.1 SD Geometry Reconstruction

To calculate the plane fit it is necessary to determine the time window for the

signal, the core on the ground and the shower axis.

A well tested method to fix the time window is to calculate t25 and t50, defined

as the time at which the FADC signal reaches the 25% and the 50% of its

maximum, respectively, to define ts = t25 − 1.5(t50 − t25), and then the start of

the signal is the time t0 at which there is the first FADC count above a fixed

94


threshold, usually 5 photelectrons [139]. To prevent contaminations, the time

window is closed after t50 +K(t50−t0), where K is a parameter to be determined.

Afterwards, one can make a first estimation of the shower core. It comes out

by means of an average of the triggered tank positions, weighting the i−th tank

with its signal Si. If we define a coordinate system for the Observatory, centered

in O, let be b the vector from the origin of the coordinate system to the shower

core and xi the vector from O to the i−th tank, one obtains

b =

∑i Wi xi

Wi(3.1)

where Wi =√

Si.

Then we proceed to the axis determination. We fix the shower core as the

reference point from now on and we associate with it a time T0, worked out from

the weighted average of triggered tank times, as done for the core. For each time

t, the shower front can be represented as a point x(t) moving along the shower

axis a at light velocity, so we can write

x(t) −b = −c(t − T0)a (3.2)

where the versor for the shower axis is pointing toward the source. If we make

the approximation of a flat shower front, the time t at which the front passes

through a point P on the ground, identified by the vector x(t) is given by

ct = cT0 − ( x(t) −b) · a (3.3)

If we assume that there are only the errors associated with the time of triggered

tanks, σt, it is possible to estimate the shower axis minimizing the relation [140]

χ2 =1

σ2t

∑i

[ti − t( xi(t))]2] =

1

c2σ2t

∑i

[cti − cT0 + xi · a]2 (3.4)

where xi, ti and t( xi(t)) are the position and the time measured and expected

for the i−th tank, respectively.

Let be a = (u, v, w), xi = (xi, yi, zi) and cσt = σ, eq. 3.4 becomes

χ2 =1

σ2

∑i

[cti − cT0 + xiu + yiv + ziw]2. (3.5)

95


Minimizing the previous equation, it is possible to get a = (u, v, w), of course

with the condition

u2 + v2 + w2 − 1 = 0. (3.6)

In the above minimization, the error definition plays a leading role. Since

time dispersion increases going away from the core, in the first approximation

quadratically, tanks very far away could cause the failure of this procedure. The

errors are usually defined as a function of the signal. One adopted solution,

derived from simulation studies, is [139]

σi(ns) = 1800/(Si)0.85 (3.7)

where Si is the signal recorded by the i−th tank. If necessary the procedure is

reiterated using a parabolic approximation for the shower front [139].

3.5.2 SD Energy Estimation

The crucial point in the SD event reconstruction is the determination of the

lateral distribution function (LDF ). Each experiment should use an appropri-

ate LDF , which depends on ground array design and characteristics, on shower

zenithal angle and energy and on the primary particle composition, too.

To estimate the primary energy one should phenomenologically find a depen-

dence between the LDF behavior and the shower energy. To do so, one should

massively use shower simulations, in which there are some assumptions and ex-

trapolation on hadronic physics involved. This model-dependence is the Achilles

heel of the SD data analysis.

The dependence of the measured signal S at a distance r from the core is

given by [140]

S(r) = S1000fLDF (r) (3.8)

where fLDF (r) is the lateral distribution function and S1000 is the signal measured

at r = 1000 m from the core. Of corse the LDF has the normalization condition

fLDF (r) = 1. The signal uncertainty is assumed as [141]

σS = 1.06√

S (3.9)

96

3.6 FD Event Reconstruction

The LDF used is the so called “NKG − LDF ′′, derived from the Greisen-

Nishimura-Kamata function [92; 96; 97]

fLDF (r) =( r

r1000

)β( r + r700

r700 + r1000

)β+γ

(3.10)

where r700 and r1000 are 700 and 1000 m, respectively, while β and γ are param-

eters depending on the zenithal angle θ. At the moment their estimations are

[140]

β(θ) = 0.9 sec θ − 3.3 (3.11)

γ = 0. (3.12)

By Monte Carlo studies, the energy is worked out defining a and b

a = 0.37 − 0.51 sec θ + 0.30 sec2 θ (3.13)

b = 1.27 − 0.27 sec θ + 0.08 sec2 θ (3.14)

and finally expressed in EeV

E = a(S1000)b [EeV ]. (3.15)


The reconstruction of fluorescence events is mainly divided in two steps: geomet-

rical reconstruction and profile reconstruction. In the geometrical reconstruction

the shower track and timing informations to derive the shower axis are used. In

the latter, employing shower geometry informations and signals recorded by the

fluorescence detector, the shower profile is estimated.

The main goal of FD event reconstruction is the estimation of the shower

energy, which is almost model-independent: FD directly measures the deposited

energy in the atmosphere by the electromagnetic component of a shower, which

carries away more than 95% of the shower energy (it depends on the primary

particle composition and energy). The hybrid detection allows to build up a

corrispondence between the SD energy estimation parameter, i.e. S(1000), and

97


the energy measured by FD. So, in this way, it is possible to perform an energy

calibration of the ground array.

The biggest limit of the FD reconstruction is the geometrical step: geomet-

rical mono event reconstruction has large uncertainties. Geometrical reconstruc-

tion is quite accurate in the case of stereo events. Anyway, if one consideres

only stereo events, the number of available events would be limited. The hybrid

design solves that problem: the ground array receives an external trigger by FD

when it finds a T3 event, so the system associates any possible tank correlated

with it. Therefore, most of FD events will be hybrid event, and 60% of them

will involve only a few SD tanks (sub-threshold shower). Accuracy studies show

an higher reconstruction quality of hybrid events, with respect to mono events,

almost equivalent to that one achievable with stereo events.

In following sections, I will present a review of FD event reconstruction, in the

case of geometrical reconstruction for mono, hybrid and stereo events. Detector

reconstruction performances in the three different cases will be presented in sec.

5.2.

In reconstruction processes, one usually uses FADC signal with subtracted

noise, converted to photons at diaphragm1. In following sections I will use the

terms signal, charge and light without any distinction but I will always refer to

“photons” as the results of the merge of Drum calibration constants and FADC

traces.

3.6.1 Geometrical Reconstruction

Geometrical reconstruction is a two-step process (see fig. 3.5):

1. the determination of the Shower Detector Plane (SDP ), namely the plane

defined as that plane containing the shower axis and the observation point;

2. the shower axis reconstruction, within the SDP .

1By using calibration constants coming from the Drum absolute calibration, one convertsdirectly FADC counts into photons with a wavelength of 370 nm, incoming at diaphragm level.

98


The shower geometry would be completely fixed once we determine the SDP ,

by means of its normal versor, and the axis position and orientation within the

SDP.

Figure 3.5: Geometry of an EAS trajectory. The Shower Detector Plane contains

both the shower axis and the observation point.

3.6.1.1 Shower Detector Plane Reconstruction

The Shower Detector plane contains the shower axis and the observation point,

then directions of pixels that receive light from the shower should lie within the

plane. The usual way to reconstruct the SDP finds the plane that best describes

pixels interested by the shower.

99

Chapter3/Chapter3Figs/schema_rico_fd.ps


The SDP normal vector, n is found minimizing:

χ2 =∑

i

(ri · n) · wi (3.16)

where ri is pointing direction of the i−th PMT and wi is a weight proportional

to its signal. The sum runs over all triggered pixels. Using SDP reconstruction,

it is possible to discard triggered pixels away from the fit.

3.6.1.2 Shower Axis Reconstruction

The second reconstruction step is the determination of the shower axis within

the SDP . The shower axis is estimated using the timing information from FD

signals. As already said, events could involve the ground array and the fluo-

rescence detector in different ways producing mono, hybrids, stereo and stereo-

hybrid events. In this reconstruction step one can use additional informations

from the ground array or by different eyes when they are available, to improve

reconstruction performances.

Mono Reconstruction

In the SDP plane, we can define RP , χ0 and T0 as the minimum distance

between the axis and the observation point (impact parameter), the angle between

the trajectory and the horizontal plane, passing from the detector, within the

SDP , and the time at which the shower front plane passes through the detector

center, respectively (see fig. 3.5 and fig. 3.6).

So, the light reaching the PMT at time ti from any point with viewing angle

θi is delayed from the arrival time T0. The delayed time is

δt(θi) = tiT0 =RP

c sinθi− RP

c tanθi=

RP tan(θi/2)

c(3.17)

where c is the speed of light, ti is the i−th tube trigger time and θi is related

to χ0 by

θi = χ0 − χi (3.18)

where χi is the tube elevation angle in the plane (see fig. 3.6).

100


Figure 3.6: EAS geometry within the SDP . The picture includes an SD station

involved in the event, outside the SDP .

The set of axis parameters (Rp, χ0, T0) is determined by minimizing

χ2 =∑

i

wi(ti − tth)2 (3.19)

where ti is the i−th tube time, wi is a weight proportional to its signal and

tth is

tth = T0 +Rp

ctan

(χ0 − χi

2

). (3.20)

Actually, the adopted strategy is to use as ti the time of the center of signal

of the i−th PMT .

Fig. 3.7 shows a time fit example.

Hybrid Reconstruction

Since the ground array is going to be completed, most of FD events could be

reconstructed using SD information to improve the time fit performance. The

101

Chapter3/Chapter3Figs/schema_timefit.ps


[deg]iχ5 10 15 20 25 30 35

[n

s]×

tim

e

25000

30000

35000

40000

45000

50000

= 67.50120χ

= 24390.6pR

= -1855.390T

^2/dof = 206.156 /34χ

TimeFit- Eye 1Run69Event104

Figure 3.7: Time fit example: experimental points superimposed to the fit result.

The fitted function depends on three parameters. The fit stability depends on

the capability to determine precisely the slight curvature of the pixel time distri-

bution. An SD timing information can fix the problem, because corresponds to

the arrival time on the ground array of the shower front, so it is much strongly

related with the distribution curvature.

expected arrival time tk of the shower front at the k−th tank as a function of

axis parameters is

tk = T0 +Rgnd,k · S

c(3.21)

where Rgnd,k is the vector from the eye to the SD tank k and S is the shower

axis versor. So, axis parameters could be derived minimizing

χ2 = χ2FD + χ2

SD (3.22)

using terms from FD and SD data. In fig. 3.8 is presented an example of

hybrid time fit, showing an evident improvement with respect to the mono fit.

102

Chapter3/Chapter3Figs/esempio_timefit_fd.ps


In fact, the stability of the mono reconstruction fit is based upon the capability

to determine the curvature of the time-fit distribution. The timing information

coming from the SD introduce new terms in the function with a different depen-

dence on parameters. Above all, a tank time corresponds to the arrival time on

the ground array of the shower front, so it suffers much strongly a delay effect

due to the time fit curvature.

[deg]iχ45 50 55 60 65 70 75 80

s]

µ

[×

tim

e

25

30

35

40

45

50

= 110.5+- 0.110χ

= 20737 +- 22pR

= 5332.54 +- 73.60T

TimeFit Id 850018 Eye Id: 1

Figure 3.8: Hybrid Time fit example: experimental points form SD and FD are

used in the hybrid fit determination.

It is clear that in this case is crucial an accurate knowledge of a possible

FD − SD time offset.

Stereo and StereoHybrid Reconstruction

Geometrical stereo reconstruction uses informations coming from at least two

eyes. In each eye, the SDP reconstruction is performed separately, as usual. The

shower axis is then determined by their intersection. If there are more than two

103

Chapter3/Chapter3Figs/esempio_timefit_hybrid.ps


eyes involved1, one should select eyes whose SDP versors ni and nj have the

lowest scalar product module. The selection should consider only SDP recon-

structed with a good accuracy. With this procedure, only geometrical parameters

of the shower axis are determined. T0 is estimated minimizing the usual time fit

formula or that one used in hybrid case, if the event is also hybrid, but fixing Rp,

χ0 and S. In principle, T0 estimation could be done for both eye used to fix the

shower axis2. Its final value will be the weighted mean of this two estimation.

3.6.2 Longitudinal Profile Reconstruction

In order to extract physical information from recorded data, once the shower ge-

ometry has been reconstructed, it is possible to determine the shower longitudinal

development. To perform the reconstruction of the shower longitudinal profile,

we proceed in three reconstruction steps:

1. Determination of the light profile, that is the number of photons reach-

ing the detector at diaphragm each FADC time bin. For each FADC time

bin ti, we consider the expected direction from which the fluorescence light

is coming from, given by the vector Ri pointing from the eye to the shower

axis and forming an angle χi with the horizontal plane within the SDP

calculated from

χi = χ0 − 2 tan( c

Rp

(ti − T0))

(3.23)

inverting eq. 3.17. Then, the total charge recorded by FD telescopes is

computed, summing over all pixels, triggered and not, whose angle between

their pointing directions and Ri is lower than a value ζ . The value of

the parameter ζ is dynamically computed, event by event, maximizing the

signal to noise ratio over all the light profile. The result is the determination

of the light profile reaching the detector as a function of time (see fig:3.9).

1In august 2005, for the first time a 3−eyes event has been recorded. From that date, a 4tri-ocular event has been recorded

2One of two involved eyes in a stereo event could have recorded a short track of 5−7 pixels,which are enough to estimate an SDP but not to perform the time fit.

104


Figure 3.9: Light profile reaching the detector as a function of time.

2. Light at track back-propagation. Starting from the computed light flux

at diaphragm level, photons are back-propogated into the atmosphere up

to their production point along the shower trajectory. At this stage we take

into account any atmospheric attenuation suffered by light in its travel from

source to detector (see sec. 1.4.6.1). In this way, we calculate fluorescence

photons produced by the shower along its propagation into the atmophere,

so we obtain the number of photons as a function of the traversed slant

depth.

3. Shower size determination. Knowing the number of photons generated

by the EAS along its path, it is easy to invert eq. 1.65 and to extract the

number of electromagnetic particles from which they have been produced,

and the the shower size as a function of the slant depth (see fig:3.10).

Usually the longitudinal profile is then fitted by a Gaisser-Hillas function

(see sec. 1.4.2).

Once the shower longitudinal profile is computed, one should subtract the

Cerenkov light. From the reconstructed profile, one can estimate Cerenkov contri-

105

Chapter3/Chapter3Figs/lightflux.ps


Figure 3.10: Number of electromagnetic particles as a function of the traversed

slant depth.

butions. We subtract these contribution to the light at track profile, re-calculate

the shower size and again we fit it with a Gaisser-Hillas function. The process is

then re-iterated till the quantity of Cerenkov photons become negligible.

3.6.2.1 Energy Estimation

Directly related to the shower longitudinal profile is the primary particle energy

estimation. As already said, from the shower profile one can calculate directly

the energy of the electromagnetic component of a shower integrating the profile

Eem =

∫ ∞

X1

dne

dE(E, X)

dE

dX(E)dEdX (3.24)

where dne/dE is the electromagnetic particle spectrum as a function of the tra-

versed slant depth and dE/dX is the rate of energy loss by ionization, both

function of the particle energy. Eq. 3.24 can be rewritten as

Eem =

∫α(X)Ne(X)dX (3.25)

106

Chapter3/Chapter3Figs/longprofile.ps


where

α(X) =1

Ne

∫ ∞

X1

dne

dE(E, X)

dE

dX(E)dE (3.26)

is the mean ionization loss rate per shower particle at depth X. α(X) is

only slightly dependent on X, in particular in the initial stage of the shower

development, where the number of electromagnetic particles is relatively small.

It is possible to consider the function as a constant with a value of about 2.19

MeV/(g/cm2) as derived in [163]. This point is a potential source of systematic

effects.

To infer the shower total energy E, it is possible to use a recent parametriza-

tion [163] of the unseen energy in terms of Eem in 1018 eV units

Eem

E= 0.959 − 0.082E−0.150

em (3.27)

obtained averaging over corrections for proton and iron primaries. This aver-

age introduces a 5% energy uncertainty. This correction is clearly not applicable

to a case of a pure electromagnetic shower, which profile is not described by

a Gaisser-Hillas parametrization as well as that one coming from an hadronic

shower.

3.6.3 Systematic Uncertainties

There are several sources of uncertainties in the energy reconstruction of an FD

event. The sources the most important are:

1. Absolute telescope calibration ∼ 12%. This value is mainly due to the

calibration of the drum itself. In the near future it could be reduced to 7%.

2. Fluorescence yield ∼ 10% systematic and ∼ 3% statistical uncer-

tainties [127]. Actually, in order to obtain a much better precision, a new

set of measurements is going to be performed [164].

3. Atmospheric Modeling ∼ 30 g/cm2 on Xmax determination. for

inclined showers [150]. Errors in the knowledge of atmospheric density

profiles introduce systematic error into slant depth calculation. Of course,

the error depends on shower zenith angle. Effects on fluorescence yield

107

3.7 The Offline Software Framework of the Pierre Auger Observatory

and Rayleigh transmission are negligible compared with their systematic

uncertainties.

4. Mie scattering ∼ 15% and ∼ 10 g/cm2 on Xmax estimation [165] (see

sec. 1.4.6.1). Aerosol light absorbption plays an important role in the pro-

file reconstruction. The concentration and the composition of atmospheric

aerosol is highly variable even on short time scales. Their effects depend

event on shower geometry. A large amount of work have been done by the

Pierre Auger Collaboration on atmospheric monitoring.

5. Unseen Energy ∼ 5%. It depends on the primary mass. As already

explained, the parametrization used is obtained averaging over proton and

iron primary particles.

6. Other Effects. There are further sources of systematic uncertainties like

the model dependence of Cerenkov calculations or in the electromagnetic

energy integration.

Of course, any systematic effect in the geometric reconstruction will induce a

systematic effect into shower profile reconstruction.

3.7 The Offline Software Framework of the Pierre

Auger Observatory

Within the Pierre Auger Collaboration, a general purpose software Framework

[167] has been designed in order to implement algorithms and configuration in-

structions to build the variety of applications required by event simulation and

reconstruction tasks.

The framework is flexible as well as robust to support the collaborative effort

of a large number of physicists developing a variety of applications over a 20 year

experimental run. It is able to handle different data formats in order to deal with

event, monitoring informations and air shower simulation code outputs.

The framework is implemented in C++ and takes advantage of object oriented

design and common open source tools, while keeping the user-side simple enough

108


for C + + novice to learn in a reasonable time. Code implementation has taken

place over the last two years and it is now being employed in analysis of data

gathered by the observatory.

The Offline framework comprises three principal part:

1. a collection of processing modules which can be assembled and sequenced

through instructions provided in an XML file [168];

2. an event structure through which modules can relate all pieces of experi-

mental information and which accumulates all simulation and reconstruc-

tion results;

3. a detector description which provides a gateway to data describing the

configuration and performance of the observatory as well as atmospheric

conditions as a function of time.

Processing algorithms, developed by the Collaboration, can be inserted in so-

called modules, which can be put together defining an analysis Module Sequence

by means of an XML file. This modular design allows to easily exchange code,

compare algorithms and build up a variety of applications by combining modules

in various sequences.

Cuts, parameters and configuration instructions used by modules or by the

framework itself are stored in XML files.

The Offline is built on a collection of utilities, including a XERCES−based

[170] parser, an error logger and a set foundation classes to represent objects

such as signal traces, tabulated functions and particles. The utilities collection

also provides a geometry package in which objects such as vectors and points keep

track of the coordinate system in which they are represented. This allows for their

abstract manipulation, as any coordinate trasformation which may be required in

an operation between objects is automatically performed. The geometry package

also includes support for geodetic coordinates.

The event data structure contains all raw, calibrated, reconstructed and Monte

Carlo data and acts as the principale backbone for comunication between mod-

ules. The event structure is built up dynamically as needed and is instrumented

109


with functions allowing modules to interrogate the event at any point to discover

its current constituents.

The detector description provides an intuitive interface from which module

authors may retrieve information about the detector configuration and perfor-

mance. The interface is organized following the hierarchy normally associated

with the observatory instruments. Generally, static detector informations are

stored in XML files, while time-varying monitoring and calibration data are

stored in MySQL [169] databases.

110

Chapter 4

Application of Gnomonic

Projection to the SDP

reconstruction for FD events

4.1 Introduction

In this chapter I will describe a new approach to the Shower Detector Plane

reconstruction of FD events, developed by myself in collaboration with the Auger

Napoli group. This work has the aim to offer an alternative approach to the

problem of SDP finding.

The first step to be performed in the reconstruction of FD events is the de-

termination of the Shower Detector Plane, defined as the plane containing the

shower axis and the center of the FD detector. The accuracy of this procedure is

crucial for a reliable reconstruction of both mono and stereo events.

The strategy adopted in the SDP determination process is based on the idea

that shower track images, as seen by the fluorescence detector, are great circles

on the surface of FD cameras. Great circles can be projected to a straight line on

the tangent plane to the spherical surface of the camera by means of a gnomonic

projection. This line is on the SDP plane, then the problem of SDP finding is

reduced to a track finding and to a a least squares linear fit to the projected

coordinates derived by pixel pointing directions.

111

4.2 Reconstruction strategy

The procedure I propose has been fully implemented in the Auger Offline

Analysis framework and is based on a robust analytical treatment of projections

and fitting.

In order to study the performances of this approach, a wide set of simulated

showers has been produced and analysed. The angular resolution on the recon-

structed SDP has been studied as a function of shower energy and distance, and

compared with the results obtained with the standard Offline reconstruction.

Results show that the gnomonic algorithm appears to be more stable and

accurate, especially for showers with large core distances from the FD detector.

Then the effect of the improved SDP reconstruction on the determination of the

shower axis, energy and longitudinal profile is discussed.

In the following I describe the reconstruction strategy and make a detailed

comparison of the performances of this approach with the standard Auger Offline

framework reconstruction.


The default version of the SDP reconstruction module in the Offline Framework

defines the SDP plane as the plane that minimizes the sum of the scalar products

of the vector normal to the trial SDP plane and the direction of single triggered

pixels, as explained in sec. 3.6.1.1.

In order to be able to define data, different from single pixel directions, to

be used in the reconstruction, a few changes were made to the offline framework

that allowed us to add a pixel selection and a “coordinate” definition module.

A default module for coordinate definition is also provided, that simply returns

directions, charges and the times of the barycentre of the reconstructed pulse

for the pixels. The default SDP reconstruction module was modified to access

these data. With this choice the present default Offline Framework reconstruction

chain is unchanged, but I added the possibility to the user to define his own input

data to the algorithm as discussed in section 4.2.2. Furthermore, I implemented

a module for making a pixel pre-selection before the SDP finding process.

112


In this way I was able to switch from the Offline Standard to my proposed

reconstruction and make a full comparison of reconstruction results with all pos-

sible combinations of pixel selection, coordinate definition and SDP finding al-

gorithms, by simply changing the Module Sequence.

4.2.1 Pixel Selection

Before SDP reconstruction is performed, a pixel pre-selection is done with a

dedicated module. Pixel validation is made in two steps as discussed in the

following.

Fig. 4.1 illustrates the effect of the procedure. It refers to event 4 of run 73

recorded by the Auger Engineering Array1 and was chosen for illustration because

it is one of the few events in which pixel are rejected by all the selection steps. In

the plot the pixel position (camera row) versus pixel time (in 100 ns time bins)

is reported:

1. Pixels not isolated in space and time are selected, by requiring that valid

pixels should not be more than four camera rows or columns away from any

other (red × in the plot are rejected by this requirement) and the time of

barycenter of reconstructed pulse should not be more than 6 microseconds

away from other pixels (black + are rejected).

2. Pixel times must be correlated with a shower candidate as illustrated in Fig.

4.1. Theta angles vs time data are fitted to a straight line and the σ of the

distribution of distances of data points from fit is considered. Points away

from the fit are rejected in two iterations: in the first iteration I use loose

cuts, 4.5σ (green triangles), that are made more stringent in the second

iteration, 3σ (blue x).

1The Southern Observatory building started by instrumenting an Engineering Array (EA)inwhich testing different FD and SD detector designs. EA was equipped with 40 water Cerenkovtanks in a 750 m spaced triangular grid, overlooked by two telescope prototypes, bay4 and bay5located in the first constructed eye, Los Leones.

113


Figure 4.1: Example of pixel selection procedure: the pixel position (camera row)

versus pixel time (in 100 ns time bins) is shown.

4.2.2 Definition of coordinates

In order to optimize the reconstruction I tested the procedure by using two dif-

ferent definition of coordinates. To do that, I implemented a new data structure

in the Offline framework, namely Coordinate Data, to store defined coordinates.

In the first and simplest case I used each pixel as coordinate to be used in the

reconstruction, as usual in the standard Offline implementation. In the second

approach, aiming at fully exploiting the combined spatial and time informations

provided by the system, the light spot position on the camera was reconstructed

as a function of time. At every time bin in the FADC traces, charge is collected

from all pixels with a reconstructed pulse by the PulseFinder module within two

degrees from the pixel with the highest signal at that particular time bin and

a charge weighted average direction is reconstructed. A coordinate is therefore

defined which stores time, direction, charge and relative errors.

Figure 4.2 shows a typical event pattern as seen using single pixels (left) and

114

Chapter4/Chapter4Figs/Ctimerejec.ps


light spot position vs. time (right) as coordinate. In the case of using single

pixels, each coordinate contains direction, charge, barycentre of reconstructed

pulse and relative errors for the pixels. A set of functions for retrieving these

informations is implemented in the data structure.

Figure 4.2: Typical event pattern as seen on the camera surface by using single

pixels (left) and light spot position vs. time (right)

4.2.3 Gnomonic Projection approach to SDP reconstruc-

tion

The intersection of the shower detector plane with the Fluorescence Detector

camera is a great circle that can be projected to a straight line segment on a

plane tangent to the spherical surface of the camera by means of a gnomonic

projection.

Gnomonic projections, are very useful in plotting great circle routes on a

globe, between arbitrary destinations on a plane map tangent to the globe. This

is due to the fact that they have the nice property that all great circles on a

sphere are represented by straight lines on the map plane. Lines are constructed

by projecting every point on the sphere onto the tangent plane from the center

115

Chapter4/Chapter4Figs/eventi.ps


of the globe (as shown in figure 4.3). For these reasons, they are widely used to

trace stars and meteorites trajectories. In my work their implementation in the

SLALIB− Positional Astronomy Library [171] has been employed.

Figure 4.3: The gnomonic projection is a nonconformal map obtained by pro-

jecting points P1 (or P2) on the surface of sphere from its center O to point P

in a plane that is tangent to a point S. Since this projection obviously sends

antipodal points P1 and P2 to the same point P in the plane, it can only be used

to project one hemisphere at a time. In a gnomonic projection, great circles are

mapped to straight lines.

A gnomonic projection is independent from the choice of the tangent point of

the plane to the sphere. It is possible to project a semi-sphere at once.

When an event is analysed, for each eye, event images on camera surfaces are

mapped, using a gnomonic projection, on the plane tangent to the first triggered

camera, normal to the telescope axis.

Figure 4.4 shows camera meridians and parallels as seen on the projection

plane together with a simulated and reconstructed vertical shower 10 degrees

away from the camera axis.

The employment of such projection allows the use of a simple analytical pro-

cedure to perform SDP finding. Actually, projected coordinates are fitted by

means of a linear least squares fit and through an an iterative procedure pixels

away from the fit are rejected. After the first SDP linear fit, the σ of the distri-

116

Chapter4/Chapter4Figs/gnomosfera.ps


Figure 4.4: Projection of camera meridians and parallels. The SDP reconstruc-

tion of a simulated vertical shower 10 degrees away from the camera axis is also

shown.

bution of distances of data points from the SDP fit is considered and pixels at a

distance from the fit greater than 4.5σ are cut away.

If any pixels are rejected, coordinates are computed again from remaining

pixels and the fitting procedure is repeated until no further rejection occours. In

these iterations a more stringent cut (3σ from fit) is used for rejection.

Whithin this algorithm, the SDP is the plane containing the fitted line and

the camera center. The reconstructed SDP plane is then identified by its normal

versor, which is finally returned in the Auger reference frame.

117

Chapter4/Chapter4Figs/meridiani.ps

4.3 Performances of the method


In order to check the performances of the method I used simulated showers of

known energy and geometry. Showers were generated using the FDSim - FDTrig-

gerSim1 [172] chain, version v2r2 updated from cvs on july 2, 2004 after some

corrections. The analysis was performed with the Auger Offline snap-20040625

updated from cvs on july 8, 2004 after some bug fixing.

Since FDTriggerSim simulated showers are generated using the calibraton

constants of bay 4 in the Engeneering Array and these constants were not present

in the database used by the Offline framework2, I set the event time of generated

events at january 2000 (when the FD was not operating) and added a special

entry in my local copy of the database at that date, with the constants used in

the simulation. With this choice I was able to analyze simulated showers with

appropriate calibration constants.

A sets of 1000 Gaisser Hillas parametrized vertical showers produced by proton

primaries was simulated at various distances in the middle of the field of view

of bay 4 at Los Leones. In both simulation and reconstruction processes I used

a clean atmosphere as distributed by the Auger simulation task group, in which

the aerosol horizontal atenuation length is 25 km and the vertical scale height is

2 km.

The energies of simulated showers were fixed at 1018 1019 and 1020 eV, the

distances from the shower core and the FD were selected between 5 and 40 km,

according to the shower energy. All events were analysed with the default Offline

reconstruction and with my approach, using the two definition of coordinates

described in sec. 4.2.2 for both approaches.

1The possibility to perform event simulation within the Offline framework has been imple-mented only during this year. Up to now, event simulation containing the detector responsehas been made by using FDSim - FDTRiggerSim package for the FD and SDSim for the SD.

2In order to take into of the time-varying telescope calibration constants, they are storedin a MySQL database

118


4.3.1 Resolution on SDP reconstruction

Figure 4.5 shows the difference between true and reconstructed theta of the vector

normal to the SDP plane for standard Offline reconstruction and my approach for

a typical simulated data sample. In the four panels the results for the gnomonic

approach (top) and the Offline standard analisys (bottom) are shown. For each

approach, the results obtained by using coordinates derived from the light spot

as a function of time are shown on the left, those using pixel directions on the

right.

It should be noted that the number of entries in the plots is different. This is

due to a cut I applied in filling the histograms: only events whose SDP angle theta

is reconstructed within 5 degrees from the true one have been considered. With

this choice, the RMS reported in the plots do not take into account those events,

and the reconstruction efficiency of the default Offline reconstruction comes out

to be lower, as shown later.

This comparison demonstrates that the reconstruction approach based on

gnomonic projection together with the use of light spot coordinates is the best

performing. In the following only the comparison between this approach and the

Offline standard will be shown.

Figure 4.6 (top) shows the resolution on the azimuthal angle “phi” of the

SDP vector. Gnomonic result is again better than the standard Offline. The

difference in space between the reconstructed SDP vector and the true one are

also shown (bottom).

Figure 4.7 shows the reconstruction of mean values and RMS of the recon-

structed SDP angle (“Theta”, “Phi” and angle in space from top to bottom) as

a function of shower distance for the three different energies. Here and in the

following plots, I use circles for 1018 eV showers, squares at 1019 and triangles at

1020 eV. Moreover, curves from gnomonic reconstruction are reported with empty

red points and the standard Offline results with solid blue points. At all distances

and energies the accuracy of reconstruction obtained with the gnomonic approach

(both mean values and resolution of distributions) is better than those obtained

with the default Offline reconstruction. Finally, as shown in figure 4.8, the SDP

119


Figure 4.5: Differences of theta SDP reconstructed and expected values for the

two reconstruction approaches and for the two definitions of coordinates. Top:

gnomonic approach; Bottom: Offline standard algorithm. For each approach, the

results obtained by using coordinates derived from the light spot as a function of

time are shown on the left, those using pixel directions on the right.

reconstruction efficiency of the present approach is higher due to the fact that

badly reconstructed events are rejected.

120

Chapter4/Chapter4Figs/CfrSDP-Tot.ps


Figure 4.6: Reconstruction results for phi SDP for the gnomonic approach (left)

and for the Offline standard (right) for azimuthal angle (top) and for the SDP

angle in space (bottom).

121

Chapter4/Chapter4Figs/CfrSDP-PhiEtaDistance_12000_MinPixels_5.ps


Figure 4.7: SDP Resolution for theta (top), phi (middle), angle in space (bottom)

for the gnomonic approach (left) and for the Offline standard (right) for the three

energy bins.

122

Chapter4/Chapter4Figs/CfrTotal-MEAN-RMS-SDP_MinPixels_5.ps


Figure 4.8: Reconstruction efficiency for the gnomonic approach (red empty

points) and for the default offline reconstruction (blue solid points).

123

Chapter4/Chapter4Figs/SDP_Reconstruction_Efficency_MinPixels_5.ps

4.4 Effect of improved SDP resolution on shower reconstruction

4.4 Effect of improved SDP resolution on shower

reconstruction

The reconstruction of the shower detector plane is only the first step in the FD

event reconstruction procedure, and has an impact on the way next steps are

performed. For this reason I compare the reconstruction of shower axis, core

position, Xmax and Nmax for the two SDP reconstruction approaches.

Figure 4.9 shows the comparison of reconstructed shower geometry for the

two SDP approaches. It is clear that the achieved performances are very similar

and not sensitive to the SDP reconstruction accuracy, being dominated by the

errors on the time fit procedure. A test on real laser shots (see sec.5.2) shows that

core reconstruction on real events is better performed if the gnomonic approach

is used. Moreover the more accurate pixel selection procedure has an impor-

tant drawback as shown in figure 4.10 where the final geometrical reconstruction

efficiency is shown for both SDP reconstruction approaches for the three consid-

ered energies. Gnomonic reconstruction efficiency is higher, expecially for 1020

eV showers at distances greater than 30 km, where the time fit of the standard

offline reconstruction stream often fails to converge.

In addiction, one finds that the reconstruction of other physical shower proper-

ties benefit from the SDP reconstruction strategy. Figure 4.11 shows an example

of the reconstruction performances in the determination of Xmax and Nmax. The

Xmax accuracy obtained by using the gnomonic SDP reconstruction approach

is 20 g/cm2 less than that one obained with the default reconstruction. This

improvement is very important for mass composition studies. In fact, the most

traditional method developed so far make use of the depth of the shower maxi-

mum and derives an observed mean mass composition as a function of the primary

energy (elongation rate, see section 1.4.8). Furthermore, shower profiles produced

by iron and proton primaries have an average difference on the maximum shower

depth of about 100 g/cm2. Then it is needed to achieve the better accuracy on

Xmax determination.

Figure 4.12 shows the evolution of mean values and RMS of Nmax and Xmax

as a function of distance for the two approaches.

124

4.5 A first look at CORSIKA showers

Figure 4.9: Reconstructed χ0 and Rp for the two approaches


An accurate test of apparatus simulation and event reconstruction chain is an

essential step to estimate the reliability of presented results. In the previous

paragraphs this kind of studies have been carried out on the basis of Gaisser-

Hillas profiles, processed by FDSim/FDTriggerSim and Offline packages. In this

section, I focus on Monte Carlo generated air showers since it provides a highly

realistic input. The data set used consists of 1800 vertical cascades produced by

particles with the fixed energy of 1 EeV, simulated using the CORSIKA [173]

program (version 6.015) with the QGSJET [174; 175; 176; 177] interaction model.

Simulations were performed at the Lyon Computer Centre. The primary nuclei

were protons and irons, each of them initiating 900 cascades. The CORSIKA

output provides the number of charged particles at atmospheric depths sampled

with 5 g cm−2 intervals, which are fitted using the Gaisser-Hillas function to

extract Xmax and Nmax. Then the same procedure as reported in sec. 4.3 has

125

Chapter4/Chapter4Figs/CfrRpChi0Distance_12000_MinPixels_5.ps


Figure 4.10: Shower axis reconstruction efficiency for the gnomonic approach (red

empty dots) and for the default offline reconstruction (blue solid dots).

been followed: showers have been simulated using the full FDSim-FDTriggerSim

chain and have been afterwards reconstructed with the Offline default program

and with gnomonic reconstruction chain.

Figures 4.13 and 4.14 show an example of the reconstruction performances for

Xmax and Nmax at 10 km core distance for gnomonic and default offline approach

respectively. Also in this case the results obtained by using the gnomonic SDP

reconstruction approach are more accurate. In particular, the reconstruction

126

Chapter4/Chapter4Figs/AXIS_Reconstruction_Efficency_MinPixels_5.ps


Figure 4.11: Reconstruction results for Nmax (top) and Xmax (bottom) for the

gnomonic approach (left) and for the Offline standard (right).

accurancies on shower profile parameters are greatly improved. The achieved

accuracy on Xmax is 33.18 gcm−2 for 1 EeV protons and 15.87 gcm−2 for iron in

the case of the gnomonic reconstruction, to be compared with 46.25 gcm−2 for

proton and 22.10 gcm−2 for iron in the case of standard Offline reconstruction.

This means that using the gnomonic reconstruction the accuracy of Xmax is about

40% better than that obtained using the standard Offline. The effect on mass

composition measurements is obvious.

127

Chapter4/Chapter4Figs/CfrNmaxXmaxDistance_12000_MinPixels_5.ps


Figure 4.12: Reconstruction results for Nmax (top) and Xmax (middle) and zenith

angle (bottom) of reconstructed showers for the gnomonic approach (red empty

dots) and for the Offline standard (blue solid dots) as a function of shower distance

for the three energies.

128

Chapter4/Chapter4Figs/CfrTotal-MEAN-RMS-NmaxXmaxThetaAXIS_MinPixels_5.ps


Figure 4.13: Reconstruction results for Xmax related to the gnomonic (top) and

Offline default (botton) approach for 1EeV protons (left) and irons (right) at 10

km core distance in the middle of the field of view of bay 4 at Los Leones.

129

Chapter4/Chapter4Figs/corsika-gnomo.ps


Figure 4.14: Reconstruction results for Nmax related to the gnomonic (top) and

Offline default (botton) approach for 1EeV protons (left) and irons (right) at 10

km core distance in the middle of the field of view of bay 4 at Los Leones.

130

Chapter4/Chapter4Figs/corsika-default.ps

Chapter 5

FD reconstruction accuracy

studies by means of CLF laser

shots

5.1 Introduction

The angular accuracy achievable by the Pierre Auger Observatory is related to

the quality of anysotropy measurements and searches for point sources.

Auger uses two different detectors, so geometric accuracy studies should be

independently performed for each of them. It is clear that events reacher of

informations, like hybrids, have smaller reconstruction uncertainties then those

observed with FD or SD only.

The Central Laser Facility provides a large amount of laser shots recorded

from both FD and SD with known energies and geometries, its data are very

useful to estimate the angular accuracy an to tune the fluorescence and hybrid re-

construction algorithms. The monocular and hybrid resolutions can be extracted

from CLF laser shot analysis. For the surface detector, the angular accuracy

is determined from the comparison of the hybrid geometrical fit with that one

obtained from SD data alone [180].

In sec 5.2 I will discuss the analysis, done in collaboration with the Auger

Napoli group, of a sample of CLF laser shots in order to estimate the Auger

angular accuracy for monocular, hybrid and stereo FD events.

131

5.2 Analysis Strategy

It will be shown that good reconstruction accuracies are achievable. These

accuracies allowed to observe a FD camera misalignment. It is clear that a

good geometrical reconstruction accuracy also depends on the detailed knowl-

edge of telescope pointing directions. Within the Auger Collaboration, two tele-

scope alignment measurements have been performed by Milan and Prague Auger

groups, based on bright star monitoring [188] [189]. Their results are in very good

agreement except in a few cases, for instance bay3 in Coihueco. This particular

bay has the CLF in the field of view, so it is possible to test its pointing direction

by means of laser track analysis. In section 5.5, a new technique to perform an

independent measurement of telescope misalignment, based upon the features of

gnomonic projections and developed within the Catania group, will be illustrated.


In order to understand the limits of each FD reconstruction typology, a sam-

ple of CLF FD events has been reconstructed with mono, stereo and hybrid

reconstructions. Reconstructed geometries are compared with expected ones. I

selected a set of vertical CLF shots from october to december 2004 requiring that

laser shots did not show the presence of an extended cloud. The presence of a

cloud on an FD event has a big impact on event reconstruction. Thin clouds do

not affect event topology, but introduce big distortions on the light flux (see fig:

5.1). Thick clouds can even affect event topology and prevent the geometrical

reconstruction (see fig: 5.2).

The analysis has been performed by using the Offline framework v1r0 available

in february 2005. Modules described in chapter 4 have been used to perform the

pixel pre-rejection and the SDP reconstruction step. A new stereo reconstruction

module has been developed for the stereo reconstruction. In this module the axis

and the core position have been calculated directly from the intersection of shower

detector planes. T0 is calculated by the usual time fit, but keeping constant Rp

and χ0 derived from SDPs intersection. In addition to previous requirements, at

least 10 pixels in the axis reconstruction have been requested.

Figure 5.3 shows a map of the complete Observatory in UTM coordinates

[186], Easting and Northing. There are also indicated sets of CLF shots recon-

132


h1Entries 1630Mean 411.4RMS 130.2

Time [ns]0 100 200 300 400 500 600 700 800 900 1000

ph

oto

ns

at d

iap

hra

gm

/m^2

0

100

200

300

400

500

600

700

800

h1Entries 1630Mean 411.4RMS 130.2CLF PROFILE WITH CLOUD

Figure 5.1: Effect of a thin cloud on a CLF laser profile in the LosLeones field of

view (left) and on CLF event topology (right).

h1Entries 1575Mean 437.2RMS 89.5

Time [ns]0 100 200 300 400 500 600 700 800 900 1000

ph

oto

ns

at d

iap

hra

gm

/m^2

0

500

1000

1500

2000

2500

3000

h1Entries 1575Mean 437.2RMS 89.5CLF PROFILE WITH THICK CLOUD

Figure 5.2: Effect of a thick cloud on a CLF laser profile in the LosLeones field

of view (left) and on CLF event topology (right).

133

Chapter5/Chapter5Figs/clf_con_nuvola_sottile.ps

Chapter5/Chapter5Figs/clf_topology.ps

Chapter5/Chapter5Figs/clf_con_nuvola_doppia.ps

Chapter5/Chapter5Figs/fungo.ps

5.3 Angular Resolution

structed as mono from Los Leones (LL) and Coihueco (CO). It is clear that

core position as seen from each eye is very well defined in azimuth, since this is

fixed by the SDP reconstruction. In fact, the azimuthal angle is determined by

the intersection of the shower detector plane with the horizontal plane passing

through the eye, and it is directly related to the azimuthal angle of the normal

versor to the plane, which is affected by a very small uncertainty. On the other

side, the core distance from the eye has a wider distribution, because it is fixed

by a more complex minimization procedure.

Therefore I studied core resolutions in a two dimensional cartesian coordinate

system centered at the expected position , the CLF source. The system has its y

axis along the direction from CLF position to the eye (longitudinal component)

and its z axis coincident with vertical in the CLF position. Then, the x axis

measures the transverse component of the core position.

A test over a sample of CLF laser shots detected by Los Leones was performed

to check the effect of different SDP reconstruction strategies on real data.

Figure 5.4 shows on the same scale the distributions of the differences of dis-

tance of reconstructed core position from the eye and the expected one, by using

the default SDP determination method (left panel) and the gnomonic approach

(right panel). As already seen in the test over simulated events, gnomonic ap-

proach improves the reconstruction accuracy, even on real events; the RMS of

the gnomonic distribution is smaller than the default distribution. In particular,

non gaussian tails of the distributions are strongly reduced. So in the following

only results obtained with gnomonic SDP reconstruction will be shown.


Figures 5.5, 5.6 and 5.7 show distributions of the angle η between the recon-

structed direction and the expected one for mono, hybrid and stereo reconstruc-

tions, respectively, for each CLF shot.

For both eyes, the angular resolution of monocular events is better than 1.5

degrees. Stereo and hybrid resolutions are very similar and of the order of 0.6.

Such a high angular reconstruction accuracy is one of the most important features

of the Auger Observatory. It will allow to improve the measurement of CR arrival

134


Easting [km]

Nor

thin

g [k

m]

Figure 5.3: A map in UTM coordinates, Easting and Northing, of the complete

Pierre Auger Southern Observatory. There are also indicated sets of CLF shots

reconstructed as mono from Los Leones (LL) and Coihueco (CO).

135

Chapter5/Chapter5Figs/site2.eps


core distance

Entries 1290

Mean -0.04849

RMS 2.013

Core resolution [km]-10 -8 -6 -4 -2 0 2 4 6 8 10

En

trie

s

0

10

20

30

40

50

60

70

80

core distance

Entries 1290

Mean -0.04849

RMS 2.013

Default Core distance resolution core distanceEntries 1299

Mean -0.07623

RMS 1.381

Core resolution [km]-10 -8 -6 -4 -2 0 2 4 6 8 10

En

trie

s0

20

40

60

80

100

core distanceEntries 1299

Mean -0.07623

RMS 1.381

Gnomonic Core distance resolution

Figure 5.4: Distributions of differences of the distance of the reconstructed core

position from the eye and the expected one, by using the default SDP determi-

nation method (left panel) and the gnomonic approach (right panel).

Figure 5.5: The angle η between the reconstructed direction and the expected

one obtained by mono analysis for Los Leones (left panel) and Coihueco (right

panel).

136

Chapter5/Chapter5Figs/441_mono_LL.eps

Chapter5/Chapter5Figs/mono_clf_axis_2.ps



one obtained by hybrid analysis for Los Leones (left panel) and Coihueco (right

panel).


one obtained by stereo analysis for Los Leones.

137

Chapter5/Chapter5Figs/hybrid_clf_axis_2.ps

Chapter5/Chapter5Figs/stereo_clf_axis_2.ps

5.4 Core Determination

direction determination and in particular the anysotropy studies. It should be

noted that AGASA studies have been done with an angular accuracy of about

2 [187].


To study core determination accuracy, a reference frame with the origin in the

CLF position as defined above is introduced. Figure 5.8 shows the transverse

and longitudinal components of the core position with respect to the real CLF

position for the selected sample using the mono reconstruction. As already seen,

the transverse distribution is very well defined while the longitudinal distribution

is clearly affected by large uncertainties. In fact an RMS of about 30 m for the

transverse component and about 1000 m for the longitudinal one are obtained.

h_transvEntries 86Mean 22.35RMS 26.09

[m]-300 -200 -100 0 100 200 3000

2

4

6

8

10

12

14

16

18

20

h_transvEntries 86Mean 22.35RMS 26.09

mono_gnomonic_eye_1 transverse distribution h_longEntries 86Mean -180.4RMS 1028

[m]-3000 -2000 -1000 0 1000 2000 3000

0

1

2

3

4

5

h_longEntries 86Mean -180.4RMS 1028

mono_gnomonic_eye_1 longitudinal distribution

Figure 5.8: Transverse and longitudinal components of the core position with

respect to the real CLF position obtained by mono reconstruction.

In the hybrid case, reconstruction accuracies become better (fig. 5.9). The

transverse distribution is very similar to the monocular one, because it depends

on the SDP reconstruction step only. The obtained distribution is a little bit

138

Chapter5/Chapter5Figs/mono_clf_core_LL.eps


h_transvEntries 157

Mean 19.5

RMS 51.43

[m]-300 -200 -100 0 100 200 3000

5

10

15

20

25

30h_transvEntries 157

Mean 19.5

RMS 51.43

hybrid_gnomonic_eye_1 transverse distribution h_longEntries 157

Mean -14.39

RMS 52.28

[m]-300 -200 -100 0 100 200 3000

2

4

6

8

10

12

14

h_longEntries 157

Mean -14.39

RMS 52.28

hybrid_gnomonic_eye_1 longitudinal distribution


respect to the real CLF position obtained by hybrid reconstruction.

larger (∼ 50 m) with respect to the case of mono reconstruction ( 30 m) because

the are several events that can be reconstructed as hybrid but cannot as mono.

The longitudinal distribution totally changes and now is comparable to trans-

verse one (∼ 50 m). Figure 5.10 shows the comparison of reconstructed core

distance distributions (longitudinal component) between mono and hybrid verti-

cal CLF laser shots.

At geometrical level, the stereo reconstruction is affected only by SDP un-

certainties from the two eyes. Both ditributions, longitudinal and transverse, are

very well defined with an RMS of ∼ 50 m(see fig. 5.11). As expectd, the Los

Leones transverse distribution is directly related to the Coihueco longitudinal one

and viceversa. In fact, the Los Leones longitudinal distribution can be obtained

from the projections of Coihueco core distributions on the longitudinal axis of the

reference frame relative to Los Leones eye; since the two eye viewing angles are

almost orthogonal (see fig. 5.3), the longitudinal distribution of one eye is quite

similar to the transverse one of the other.

All LosLeones transverse components have a mean value of 20m, comparable

139

Chapter5/Chapter5Figs/hybrid_clf_core_LL.eps


[m]-3000 -2000 -1000 0 1000 2000 3000

distanceEntries 147Mean -1.588RMS 243

[m]-3000 -2000 -1000 0 1000 2000 30000

10

20

30

40

50

60

distanceEntries 147Mean -1.588RMS 243

~ 50 m)σhybrid CLF (

~ 1140 m)σMonoFD CLF (

Core distance resolution

Figure 5.10: Core distance distributions obtained by the reconstruction of a sam-

ple of mono CLF vertical laser shots and hybrid vertical laser shots.

h_transvEntries 187

Mean 19

RMS 51.69

[m]-300 -200 -100 0 100 200 3000

5

10

15

20

25

30

h_transvEntries 157

Mean 19.07

RMS 51.8

stereo_gnomonic_eye_1 transverse distribution h_longEntries 185

Mean -57.46

RMS 35.79

[m]-300 -200 -100 0 100 200 3000

5

10

15

20

25

30h_longEntries 157

Mean -57.56

RMS 35.73

stereo_gnomonic_eye_1 longitudinal distribution


respect to the real CLF position obtained by stereo reconstruction.

140

Chapter5/Chapter5Figs/rp_mono_hybrid_comparison.eps

Chapter5/Chapter5Figs/stereo_clf_core_LL.eps

5.5 Telescope Alignment

with the RMS of the distribution. In the case of stereo reconstruction this offset

is evident even in the longitudinal component. These offsets are due to telescope

misalignments.


Telescope positions are known with a precision of a few centimeters within the

FD eye buildings. Figure 5.12 shows the difference of the zenith angle of the

vector normal to the SDP plane with respect to its nominal value, for LosLeones

bay 4. The reconstructed values are fully consistent with expectations, showing

no evidence for a camera rotation around the telescope axis. The same is true for

Coihueco bay 3. In this conditions, FD telescope pointing directions are fixed by

the pointing directions of their axes and possible misalignments can be studied

by measuring the “real” pointing direction of telescope axes.

SDPθEntries 1358Mean -0.02541RMS 0.0603

/ ndf 2χ 75.45 / 64Prob 0.1549Constant 2.09± 55.69 Mean 0.00157± -0.02399 Sigma 0.00132± 0.05403

[degrees]-0.3 -0.2 -0.1 0 0.1 0.2 0.3

En

trie

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1

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SDPθEntries 1358Mean -0.02541RMS 0.0603

/ ndf 2χ 75.45 / 64Prob 0.1549Constant 2.09± 55.69 Mean 0.00157± -0.02399 Sigma 0.00132± 0.05403

Zenithal SDP Angle for Vertical CLF Laser Shots

Figure 5.12: Theta SDP reconstruction for vertical CLF events.

Since CLF provides FD events of known geometry that can be reconstructed

with high accuracy, CLF laser shots can be used to study camera misalignment.

The azimuthal angle of the normal versor to the SDP (φSDP ), in the case of

FD track produced by vertical events, is directly related to the azimuthal angle

141

Chapter5/Chapter5Figs/CLF_theta_SDP.eps


[degrees]-1.5 -1 -0.5 0 0.5 1 1.5

Los LeonesEntries 3575

Mean 0.04075

RMS 0.03446

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5

En

trie

s

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10

210

310


Mean 0.04075

RMS 0.03446

phiSDP

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5

CoihuecoEntries 5054

Mean 0.09335

RMS 0.03119

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5

En

trie

s

1

10

210

310


Mean 0.09335

RMS 0.03119

phiSDP

Figure 5.13: Distribution of differences between the reconstructed azimuthal angle

of the normal versor to the SDP and the expected one, obtained by analyzing a

sample of mono vertical laser shots for Los Leones (left) and for Coihueco (right).

of the telescope axis. Then a shift in its distribution comes from a shift in the

azimuthal angle value of the telescope axis. Figure 5.13 shows the distribution

of differences between the reconstructed φSDP and the expected one, obtained by

analyzing all mono vertical laser shots recorded during november 2004 by bay4

in Los Leones and bay3 in Coihueco, respectively: for the Coihueco eye the mean

value of the distribution is affected by a clear offset.

5.5.1 Alignment Technique

Within the Catania Auger group, a new technique to perform an independent

measurement of telescope pointing directions has been developed, by using CLF

laser shots and the features of the gnomonic projections.

FD shower track images are great circles on the FD camera spherical sur-

face and so can be projected to straight lines on a plane tangent to the camera

spherical surface, by means of a gnomonic projection as described in section 4.2.3.

Therefore, in the gnomonic plane, at each FD track corresponds a straight line

142

Chapter5/Chapter5Figs/naPhiSDPLL1.eps

Chapter5/Chapter5Figs/naPhiSDPCO1.eps


described by

y = a + bx (5.1)

where the coefficients a and b are derived from a linear fit performed over the

projected track. Since all track start at CLF laser source, laser shots at differ-

ent zenith angles form a proper sheaf of straight lines. The sheaf center is the

projection on the gnomonic plane of the corresponding pointing direction from

the eye to the CLF position. So, by measuring the sheaf center coordinates and

extracting the corresponding pointing direction, from the FD eye to the laser

source, it is possible to compare this direction with the expected one.

Alignment of telescopes which have CLF position in their field of view, bay4

in Los Leones and bay3 in Coihueco have been studied. It should be noted that

all the technique is based on the gnomonic SDP reconstruction approach. Then

the only SDP reconstruction is needed to compute sheaf center coordinates. For

this reason, it is possible to expect a precision of the order of that one of the

SDP accuracy (∼ 0.01) in the measurement.

5.5.1.1 CLF Laser Shots Sample Selection

CLF produces laser shots of known geometry, with an uncertainty of 0.02. The

facility produces laser pulses in different angular configurations, 5 azimuthal val-

ues and with a zenith angle ranging from 0 to 85 in steps of 10.

Figure 5.14 shows the azimuthal configuration selected (corresponding to

192.72 in the coordinate system of figure 5.3), which allows a stereo detection

with quite similar view angles. All CLF laser shots of december 2004, at different

angles, from 0 to 40, have been studied.

5.5.1.2 Sheaf Center Determination

Figure 5.15 shows a sample of CLF laser shot traks seen by LosLeones, projected

in the gnomonic plane. Different colours are used to distinguish among different

zenith angle configuration: black (θz = 0), red (θz = 10), green (θz = 20), blue

(θz = 30), yellow (θz = 40).

143


Figure 5.14: Projection on the ground of the selected laser shot angular config-

uration. Angles αLL e αCO are formed by the projection and the direction from

Los Leones (red) and Coihueco (blue), respectively.

Coefficients of lines in fig. 5.15 can be expressed as a function of sheaf center

coordinates (s, l)

b =l

s− a

s(5.2)

assuming s = 0. At each line it is possible associate a pair (a, b), satisfying eq.

5.2. Let be A = l/s and B = −1/s, then these pairs can be represented by a

point in a XY plane (coefficient plane), where they lie along a straight line (see

fig. 5.16)

Y = A + BX. (5.3)

With this position sheaf center coordinates are

s = − 1

Bl = −A

B. (5.4)

By a linear fit in the coefficient plane, sheaf center coordinates in the gnomonic

plane are derived.

The number of events in each angular configuration is different, most of the

events are in the vertical configuration. In principle each class of events in the

fit should be weighted by its number of events, however the same weight to

144

Chapter5/Chapter5Figs/azimuth_CLF.eps


x-0.2 -0.1 0 0.1 0.2 0.3 0.4

x-0.2 -0.1 0 0.1 0.2 0.3 0.4

y

-0.4

-0.3

-0.2

-0.1

-0

0.1

Figure 5.15: CLF laser shot tracks seen by Los Leones bay4 in the gnomonic

plane. The coordinate system is centered in corrispondence with the telescope

axis. Different colours are used for each zenith angle: black (θz = 0), red

(θz = 10), green (θz = 20), blue (θz = 30), yellow (θz = 40).

each angular configuration is assigned, since each of them could suffer different

systematic effects, due to the shadow of camera supports. In this way I averaged

any detection systematic effects.

Once the sheaf center has been determined in the gnomonic plane, the cor-

rispondent pointing direction is compared with the expected one and correction

angles for the telescope axis are derived. Corrections are applied and a new com-

parison has done. The procedure is reiterated till corrections become smaller

than 0.001. Usually, at the third iteration, the obtained corrections are smaller

than 0.00001.

In tab. 5.1 telescope pointing directions obtained by the described technique

and those obtained by Milan and Prague Auger groups are summarized. As

expected, it is possible to achieve a precision of the order of ∼ 0.01 in the

telescope alignment measurement performed by using gnomonic projections, i.e.

145

Chapter5/Chapter5Figs/Fascio1LL609.eps


X-8 -6 -4 -2 0 2 4 6 8 10

X-8 -6 -4 -2 0 2 4 6 8 10

Y

-60

-50

-40

-30

-20

-10

0

10

CLF 0 degreesCLF 10 degreesCLF 20 degreesCLF 30 degreesCLF 40 degrees

Los Leones

Figure 5.16: Representation in the XY plane of the sheaf shown in fig. 5.15:

each point is associated with a line belonging to the sheaf.

146

Chapter5/Chapter5Figs/RettaCoeff1LL609.eps


Eye Nominal Values Milan Group

Elevation (θ) Azimuth (φ) Elevation (θ) Azimuth (φ)

Los Leones bay4 16 105 15.918 ± 0.001 104.953 ± 0.003

Coihueco bay3 16 75 16.103±0.006 75.099 ± 0.009

Eye Prague Group Catania Group

Elevation (θ) Azimuth (φ) Elevation (θ) Azimuth (φ)

Los Leones bay4 15.94 ± 0.09 104.91 ± 0.07 16.16 ± 0.01 104.95 ± 0.01

Coihueco bay3 15.84 ± 0.06 74.97 ± 0.09 16.28 ± 0.02 74.91 ± 0.01

Table 5.1: Nominal and measured values, by Milan, Prague and Catania Auger

groups, of elevation and azimuthal angles for Los Leones bay4 and Coihueco bay3.

the limit of the SDP accuracy. The performed alignment measurement confirms

the Prague results on Coihueco bay3.

5.5.2 Alignment Tests

All mono CLF vertical laser shots recorded during november 2004, shown in fig.

5.13, have been reconstructed using the results of the three alignment measure-

ments. Distributions of the differences between the reconstructed φSDP and the

expected one show that corrections obtained by the present technique are in good

agreement with those measured by Prague group (fig. 5.17, 5.18 and 5.19). Core

position offsets in the stereo reconstruction of the used sample of vertical laser

shots are only determined by the azimuthal correction. Alignment tests clearly

show that the gnomonic alignment can take into account correctly azimuthal mis-

alignment for both eyes (figures 5.20 and 5.21). On the other side, Milan group

corrections fail for Coihueco (see the longitudinal distributions, figure 5.22 and

the transverse distribution, figure 5.23). Prague group corrections are able to re-

duce core position offsets, but not at level of the gnomonic alignment. The use of

hybrid and stereo reconstruction of CLF shots allows to study the correction for

the elevation angle. This study is more difficult because needs a good knowledge

of FD-SD time offset in the case of hybrid and CLF inclined shots in the case of

stereo analysis, and will be performed in the future.

147


[degrees]-1.5 -1 -0.5 0 0.5 1 1.5


Mean -0.006432

RMS 0.03433

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5

En

trie

s

1

10

210

310


Mean -0.006432

RMS 0.03433

phiSDP - Milan Group

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5


Mean 0.1923

RMS 0.03088

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5

En

trie

s1

10

210

310


Mean 0.1923

RMS 0.03088

phiSDP - Milan Group

Figure 5.17: Differences between the reconstructed azimuthal angle of the normal

versor to the SDP and the expected one, for a sample of mono vertical laser shots

for LosLeones (left) and for Coihueco (right) applying Milan group corrections.

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5


Mean -0.04929

RMS 0.03417

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5

En

trie

s

1

10

210

310


Mean -0.04929

RMS 0.03417

phiSDP - Prague Group

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5


Mean 0.06307

RMS 0.03077

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5

En

trie

s

1

10

210

310


Mean 0.06307

RMS 0.03077

phiSDP - Prague Group



sample of mono vertical laser shots for Los Leones (left) and for Coihueco (right)

applying Prague group corrections.

148

Chapter5/Chapter5Figs/miPhiSDPLL.eps

Chapter5/Chapter5Figs/miPhiSDPCO.eps

Chapter5/Chapter5Figs/proPhiSDPLL.eps

Chapter5/Chapter5Figs/proPhiSDPCO.eps


[degrees]-1.5 -1 -0.5 0 0.5 1 1.5


Mean -0.008401

RMS 0.03484

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5

En

trie

s

1

10

210

310


Mean -0.008401

RMS 0.03484

phiSDP - Catania Group

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5


Mean 0.007164

RMS 0.03185

[degrees]-1.5 -1 -0.5 0 0.5 1 1.5

En

trie

s

1

10

210

310


Mean 0.007164

RMS 0.03185

phiSDP - Catania Group



sample of mono vertical laser shots for Los Leones (left) and for Coihueco (right)

applying Catania group corrections.


Mean 3.044

Sigma 16.59

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s

0

10

20

30

40

50

60


Mean 3.044

Sigma 16.59

Longitudinal distribution - Catania Group Los LeonesEntries 137

Constant 64.7

Mean -2.093

Sigma 12.36

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s

0

10

20

30

40

50


Mean -2.093

Sigma 12.36

Transverse distribution - Catania Group

Figure 5.20: Longitudinal and transverse distributions obtained by analyzing

CLF stereo vertical laser shots with Catania group alignment corrections for Los

Leones.

149

Chapter5/Chapter5Figs/maPhiSDPLL.eps

Chapter5/Chapter5Figs/maPhiSDPCO.eps

Chapter5/Chapter5Figs/ma_LL_XYcore1.eps


CoihuecoEntries 137

Mean 0.1353

RMS 63.48

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s

0

10

20

30

40

50

CoihuecoEntries 137

Mean 0.1353

RMS 63.48

Longitudinal Distribution - Catania Group CoihuecoEntries 137

Mean 4.967

RMS 31.42

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s0

10

20

30

40

50

60

70

CoihuecoEntries 137

Mean 4.967

RMS 31.42

Transverse Distribution - Catania Group


CLF stereo vertical laser shots with Catania group alignment corrections for

Coihueco.

Los Leones

Entries 137

Mean 106.7

RMS 33.27

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s

0

10

20

30

40

50

Los Leones

Entries 137

Mean 106.7

RMS 33.27

Longitudinal Distribution - Milan Group Los Leones

Entries 137

Mean -0.5864

RMS 65.21

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s

0

10

20

30

40

50

Los Leones

Entries 137

Mean -0.5864

RMS 65.21

Transverse Distribution - Milan Group


CLF stereo vertical laser shots with Milan group alignment corrections for Los

Leones.

150

Chapter5/Chapter5Figs/ma_CO_XYcore1.eps

Chapter5/Chapter5Figs/mi_LL_XYcore1.eps


CoihuecoEntries 137

Mean -25.96

RMS 62.74

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s

0

10

20

30

40

50

60

70

CoihuecoEntries 137

Mean -25.96

RMS 62.74

Longitudinal Distribution - Milan Group CoihuecoEntries 137

Mean 102.7

RMS 30.68

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s0

10

20

30

40

50

60

70

80

CoihuecoEntries 137

Mean 102.7

RMS 30.68

Transverse Distribution - Milan Group


CLF stereo vertical laser shots with Milan group alignment corrections for

Coihueco.

Los Leones

Entries 137

Mean 31.2

RMS 32.44

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s

0

10

20

30

40

50

60

70

Los Leones

Entries 137

Mean 31.2

RMS 32.44

Longitudinal Distribution - Prague Group Los Leones

Entries 137

Mean -20.06

RMS 65.11

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s

0

10

20

30

40

50

Los Leones

Entries 137

Mean -20.06

RMS 65.11

Transverse Distribution - Prague Group


CLF stereo vertical laser shots with Prague group alignment corrections for Los

Leones.

151

Chapter5/Chapter5Figs/mi_CO_XYcore1.eps

Chapter5/Chapter5Figs/pro_LL_XYcore1.eps


CoihuecoEntries 137

Mean 11.64

RMS 62.76

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s

0

10

20

30

40

50

60

70

CoihuecoEntries 137

Mean 11.64

RMS 62.76

Longitudinal Distribution - Prague Group CoihuecoEntries 137

Mean 34.37

RMS 29.61

[m]-800 -600 -400 -200 0 200 400 600 800

En

trie

s

0

10

20

30

40

50

60

CoihuecoEntries 137

Mean 34.37

RMS 29.61

Transverse Distribution - Prague Group


CLF stereo vertical laser shots with Prague group alignment corrections for

Coihueco.

152

Chapter5/Chapter5Figs/pro_CO_XYcore1.eps

Chapter 6

Analysis of FD Data

6.1 Introduction

One of the main goals of the Pierre Auger Observatory is the measurement of

the flux of cosmic rays above 1018 eV , to address the question of the presence

of the GZK−cutoff in the CR all particle spectrum. For this purpose it is very

important an accurate knowledge of detector and analysis efficiencies, of detector

aperture and of detector live time. In this chapter I will present the first attempt

to estimate a cosmic ray flux by using FD data within the Auger Collaboration.

In section 6.2, I will discuss the study aiming at defining the minimum set of

analysis cuts needed to achieve accurate physical results. For selected cuts, the

reconstruction efficiency as a function of energy has been computed. In section

6.3, the analysis of mono FD data recorded from january 2004 to november 2005

is shown, and on this data sample cuts defined in section 6.2 are applied. Finally,

in section 6.4.1, time exposure, reconstruction efficiency and detector aperture

have been used to estimate the all particle energy spectrum. An elongation rate

plot to estimate primary mass composition is also presented in section 6.4.2.

153

6.2 Reconstruction Accuracy andDefinition Of Analysis Cuts

6.2 Reconstruction Accuracy and

Definition Of Analysis Cuts

The dependence of Observatory’s aperture on numerous parameters has been

studied by means of detailed simulations [178] [179]. FD aperture has been

independently evaluated by two groups within the Auger collaboration with two

different approaches [178; 190]. Aperture studies are based upon the analysis of

large samples of simulated data and their differences will be discussed in section

6.4.1.3. The simulated sample used in [178] is available since march 2005 and it

has been used to estimate the reconstruction efficiency presented in this chapter.

In the following sections I will present the details of the analysis, and I will test

the application of the procedure to a set of real data (sec 6.3).

6.2.1 The Simulated Data Sample

There are important issues emerging from trigger aperture studies, that can be

used into the reconstruction efficiency determination:

1. The FD trigger aperture is almost independent from primary mass compo-

sition. Showers produced by proton and iron primary particles have been

used to test the FD trigger detector with very similar results.

2. The use of two different atmospheric conditions has shown an effect at

trigger level which, as expected, depends on the primary energy. The two

atmosphere have a vertical aerosol optical depth (VAOD) at 3 km above

FD level of 0.03 and 0.06, respectively. At 1018 eV , the trigger aperture for

the cleaner atmosphere is higher than the other one of 15%. The effect is

smaller at higher and lower energies. In fact at lower energies the detector

produces a trigger mainly on near showers, so aerosol effects on fluorescence

light propagation become negligible. At higher energies, the detector always

produces a trigger signal and the effect of atmosphere conditions affects the

energy determination only.

154


The employed atmospheres are usually referred to as “clean” and “dirty”, be-

cause they have a lower and an higher VAOD with respect to the typical Malargue

atmosphere [181].

Keeping in mind these considerations, the selected data sample used in the

following consists of simulated proton showers produced by using FDSim [172]

with these characteristics:

1. no detailed shower Monte Carlo simulation but a Gaisser-Hillas parametriza-

tion [182];

2. 10000 showers times 8 energy bins at fixed values of Log(E/eV ) = 17, 17.5,

18, 18.5, 19, 19.5, 20, 20.5;

3. zenith angle within 60 degrees, with a cos θd(cos θ) zenith distribution and

uniform azimuth distribution;

4. showers propagated through an atmosphere with a VAOD at 3 km above

the FD level of 0.03, described by a two-parameter Mie model (see sec.

1.4.6.1) with an aerosol horizontal attenuation length LM of 25 km and an

aerosol scale height HM of 2.0 km;

5. shower cores uniformly distributed within the field of view of a single tele-

scope, bay4 of the Los Leones eye and up to distance from the eye that

depends on the energy (6 km at 1017 eV up to 80 km for E > 1019.5 eV );

6.2.2 Definition of Analysis Cuts

In order to define the criteria required to achieve an accurate shower reconstru-

tion, the main shower parameters ( SDP , shower axis, Xmax and shower energy)

have been studied. It was possible to define cuts that allow to reach a good re-

construction accuracy and to evaluated the detector reconstruction efficiency at

different levels.

The analysis has been done using the Offline Framework v1r1, available in

april 2005. Simulated events are reconstructed as monocular events. In the re-

construction module sequence, SDP reconstruction modules described in chapter

155


4 have been used. In this way I used a pixel pre-rejection and the gnomonic pro-

jections to reconstruct the shower detector plane. In collaboration with L’Aquila

group, I inserted in the Offline a module to reject noise events: the module imple-

ments a Hough filter [184], proposed by L’Aquila group as an on-line filter [185].

The simulation software is not able to produce such events and as expected the

module did not reject any simulated event. On the other side, among real data

there are a lot of these dense noise events (see fig. 6.1) and the implemented

algorithm rejects them very efficiently.

• At geometrical level, one should not directly consider the axis determination

accuracy, but it is also important to study SDP determination. In fact,

in the case of stereo events it is enough to be able to estimate the shower

detector plane for both eyes to get a shower axis reconstruction with a very

small uncertainty.

• To check the quality of the time fit procedure a linear interpolation over

the distribution of pixel timing as a function of pixel elevation angles χi

within the SDP (in the following I will refer to it simply as χi−plot) in

addition to the traditional minimization was performed. The underlying

idea is that, if data do not exhibit a clear curvature (see fig. 3.7), it is not

possible to perform a reliable 3 parameters minimization, In such a case,

data are well fitted by the linear interpolation and the quality of this linear

approximation can be evaluated by its χ2. So high χ2 values correspond to

FD tracks with a clear curvature and a cut can be easily defined.

I studied the reconstruction accuracy of the axis as a function of different

parameters:

1. number of pixels used to calculate the variable under esamination;

2. angular width of the visible part of the recorded shower;

3. event time length;

4. quality of the linear interpolation of the χi−plot.

156


• In order to test the quality of the reconstruction of longitudinal profile,

Xmax and energy determination are studied as a function of χ2 coming

from the Gaisser-Hillas fit over the longitudinal profile.

Figure 6.1: A typical dense noise event as seen from fluorescence camera.

Coloured pixels are triggered T1 pixels.

6.2.2.1 Shower Detector Plane

Figure 6.2 shows the mean value of the angle ηSDP between the reconstructed

normal versor to the shower detector plane and the expected one, as a function

of the number of pixels used in the SDP reconstruction.

A cut at 5 pixels provides an SDP accuracy on average of 2 (see fig. 6.2)

with an high efficiency. Individual events may have large reconstruction errors

as shown in 6.3 (yellow distribution). The cut removes all badly reconstructed

events, keeping the 93% of the starting sample.

At other energies, the distributions show a very similar behaviour to the one

in fig. 6.2, so it is possible to generalize the cut and to require for all available

energies a minimum of 5 pixels for the SDP reconstruction.

157

Chapter6/Chapter6Figs/dense_noise_event.ps


# NSDPPixels10 20 30 40 50

hpro7Entries 2265Mean 17.72RMS 10.28

# NSDPPixels10 20 30 40 50

Eta

SD

P [

deg

rees

]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

hpro7Entries 2265Mean 17.72RMS 10.28

SDP

Figure 6.2: Simulated Shower Energy 1019 eV : mean value distribution of the

angle ηSDP between the reconstructed normal versor n to the shower detector

plane and the expected one as a function of the number of pixels used in the

recontruction. Notice that a cut at 5 pixels provides an SDP accuracy on average

of 2.

158

Chapter6/Chapter6Figs/meansdp_vs_nsdppixels_new.ps


EtaSDP [degrees] 0 10 20 30 40 50 60 70 80

hpro5Entries 2411

Mean 1.636

RMS 4.122

EtaSDP [degrees] 0 10 20 30 40 50 60 70 80

En

trie

s

1

10

210

310

hpro5Entries 2411

Mean 1.636

RMS 4.122

SDP Accuracy vs NSDPPixles

All Events

NSDPPixels>=5

Figure 6.3: Superimposed ηSDP distributions at 1019 eV with the request of a

minimum of 5 pixels (red distribution) and without it (yellow distribution). The

cut reduces the total number of events for which we are able to make an SDP

estimation from 2385 to 2216. The resulting efficency is 93%.

159

Chapter6/Chapter6Figs/cut_sdp_vs_nsdppixels_new.ps


6.2.2.2 Shower Axis

The next step is the analysis of the shower axis reconstruction accuracy. We

analyzed the distribution of the angle ηaxis between the reconstructed shower

direction and the expected one as function of several parameters at different

energies: the number of pixels used to reconstruct the axis; the angular width of

the recorded shower track; its time length; the χ2 of the linear interpolation of

the χi−plot.

Of course, these variables are directly related one to another, in particular the

angular aperture with the ηaxis. Figure 6.4 shows the mean ηaxis distributions at

1019 eV as function of the 4 variables. It is clear that a cut on the time length

distribution would be less effective since the distribution is much flatter then the

others.

The analysis of the effect of the cuts on the three remaining parameters on

mean and RMS distributions of ηaxis at different energies shows that the best

performing and the most efficient cut is that on the number of pixels employed

in the shower axis reconstruction (see fig. 6.5).

A cut at shower axis level, that requires at least 15 pixels available in the

shower axis reconstruction, can be used to achieve an average accuracy of 5.

At 1019 eV (see fig. 6.6), this request reduces the number of accepted events

from 1776, for which had been possible to perform a shower axis estimation, to

929, with an efficiency of 52%. As expected, the efficiency associated with this

cut is lower than the previous one, because of the uncertainties related to the

determination of the time curvature.

6.2.2.3 Longitudinal Shower Profile

In order to test the longitudinal profile quality, Energy and Xmax accuracies have

been investigated with respect to the geometrical accuracy and to the χ2 of the

Gaisser-Hillas fit performed over the longitudinal profile.

If we focus again on the case at 1019 eV , a direct correlation between bad

energy and/or Xmax estimations and a badly reconstructed geometry is not evi-

dent. There are a few events with reconstructed values completely out of range

for both energy and Xmax, even with a good angular and distance estimation.

160


eV19Uniform Distribution on Surface at 10

# AXISPixels0 10 20 30 40 50

hpro1Entries 1776

Mean 17.93

RMS 9.348

Underflow 0

Overflow 0

Integral 288.6

# AXISPixels0 10 20 30 40 50

Eta

AX

IS [

deg

rees

]

0

10

20

30

40

50

60

hpro1Entries 1776

Mean 17.93

RMS 9.348

Underflow 0

Overflow 0

Integral 288.6

AXIS Accuracy vs NAXISPixles

AngularAperture [degrees] 0 10 20 30 40 50 60

hpro2Entries 1776

Mean 19.69

RMS 8.574

Underflow 0

Overflow 0

Integral 511.3

AngularAperture [degrees] 0 10 20 30 40 50 60

Eta

AX

IS [

deg

rees

]

0

10

20

30

40

50

60

hpro2Entries 1776

Mean 19.69

RMS 8.574

Underflow 0

Overflow 0

Integral 511.3

AXIS Accuracy vs AngularAperture

TimeDuration [ns] 0 10000 20000 30000 40000 50000

hpro3Entries 1776

Mean 1.72e+04

RMS 8867

Underflow 0

Overflow 0

Integral 529.1

TimeDuration [ns] 0 10000 20000 30000 40000 50000

Eta

AX

IS [

deg

rees

]

0

10

20

30

40

50

60

hpro3Entries 1776

Mean 1.72e+04

RMS 8867

Underflow 0

Overflow 0

Integral 529.1

AXIS Accuracy vs TimeLenght

NormChiSq 0 2 4 6 8 10 12 14 16 18 20 22

hpro4Entries 1776

Mean 6.546

RMS 3.235

Underflow 0

Overflow 0

Integral 385.4

NormChiSq 0 2 4 6 8 10 12 14 16 18 20 22

Eta

AX

IS [

deg

rees

]

0

5

10

15

20

25

30

35

40

hpro4Entries 1776

Mean 6.546

RMS 3.235

Underflow 0

Overflow 0

Integral 385.4

2χAXIS Accuracy vs

Figure 6.4: Mean value distributions of ηaxis at 1019 eV as a function of the 4

variables: number of pixels used in the axis reconstruction, the angular width,

the time length and the χ2 of the linear interpolation of the χi−plot.

161

Chapter6/Chapter6Figs/meanaxis_vs_all_new.ps


Figure 6.5: Distribution of ηaxis mean (left panel) and rms (right panel) as a

function of the energy obtained by requiring 17 (blue ), 15 pixels (red ) and 6

(red ) for the angular width, the number of pixels used in the axis determination

and the χ2, respectively.

Events with an estimated Xmax out of range are mostly the same for which the

energy estimation is incorrect.

The dependence of energy and Xmax accuracy on the χ2 of the Gaisser-Hillas

fit has been investigated. The study has shown that it is difficult to fix a univocal

cut on the whole energy range.

A very useful cut, able to clean energy and Xmax distributions with an high

efficiency, is the request that the reconstructed Xmax is within the detector field

of view. Applying this cut (see figs. 6.7 and 6.8), events whose energy and Xmax

estimations out of range are removed, reducing the number of events to 812 for

the case of simulated shower at 1019 eV , with an efficency of 87%. This simple

geometrical cut allows to achieve an Xmax accuracy of ∼ 50 g/cm2 and of 5% in

energy.

162

Chapter6/Chapter6Figs/cut_mean_rms_all_energies.ps


eV 19Uniform Distribution on Surface at 10

EtaAXIS [degrees]0 20 40 60 80 100 120

hAXISEntries 1776

Mean 7.551

RMS 12.39

Underflow 0

Overflow 0

Integral 1776

EtaAXIS [degrees]0 20 40 60 80 100 120

En

trie

s

1

10

210

310

hAXISEntries 1776

Mean 7.551

RMS 12.39

Underflow 0

Overflow 0

Integral 1776

All Events

NAXISPixels>=15

AXIS Space angle distribution - AXISPixels>=15

Figure 6.6: Superimposed ηaxis distributions at 1019 eV with the request of a

minimum of 15 pixels (red distribution) and without it (yellow distribution).

The cut reduces the total number of events for which we are able to make a

shower axis estimation from 1776 to 929. The resulting efficency is 52%.

163

Chapter6/Chapter6Figs/AXISdistribution_19.0.ps



]2(Xmax_rec-Xmax_exp) [g/cm-1200-1000-800 -600 -400 -200 0 200 400 600

]2(Xmax_rec-Xmax_exp) [g/cm-1200-1000-800 -600 -400 -200 0 200 400 600

En

trie

s

1

10

210

Xmax distribution

All Events

Xmax in the FOV

Figure 6.7: Distribution of the differences between the reconstructed Xmax and

the expected one at 1019 eV with the request of a minimum of 15 pixels (from

geoemtrical analysis) and a reconstructed Xmax within the detector field of view

(red distribution) superimposed with the distribution obtained by imposing only

the geometrical cut (yellow distribution). The cut reduces the total number of

events for which we are able to make an Xmax estimation from 929 to 812. The

resulting efficency is 87%.

164

Chapter6/Chapter6Figs/Xmaxdistribution_19.0.ps



(Energy_rec-Energy_exp)/Energy_exp [%]-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3

hEnergyEntries 929

Mean -0.008756

RMS 0.05636

Underflow 0

Overflow 0

Integral 929

(Energy_rec-Energy_exp)/Energy_exp [%]-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3

En

trie

s

1

10

210

310

hEnergyEntries 929

Mean -0.008756

RMS 0.05636

Underflow 0

Overflow 0

Integral 929

All Events

Xmax in the FOV

Energy distribution

Figure 6.8: Distribution of the differences of the reconstructed and the expected

energy divided by the expected energy at 1019 eV with the request of a minimum

of 15 pixels (from geoemtrical analysis) and a reconstructed Xmax within the de-

tector field of view (red distribution) superimposed with the distribution obtained

by imposing only the geometrical cut (yellow distribution). The cut reduces the

total number of events for which we are able to make an energy estimation from

929 to 812. The resulting efficency is 87%.

165

Chapter6/Chapter6Figs/Energydistribution_19.0.ps


6.2.3 Application Of Analysis Cuts To Real Data

Figures 6.9, 6.10, 6.11 and 6.12 show zenith angle and Xmax distributions obtained

from Los Leones and Coihueco data, separately, by requiring at least 5 pixels

to perform SDP reconstruction (blue distributions), 15 pixels for the shower

axis determination (red distributions) and finally the estimated Xmax within the

detector field of view (green distributions).

After the event selection, it is possible to note that distributions for zenith

angle and Xmax for both eyes are not affected from the features due to badly

reconstructed events, as the spikes clearly visible in figures 6.9, 6.10, 6.11 and

6.12. Furthermore, distributions derived from the two eyes are very similar.

Figure 6.9: Zenithal distributions obtained from LL 2004 data requiring at least

5 pixels to perform SDP reconstruction (blue distributions), 15 pixels for the

shower axis determination (red distributions) and finally the estimated Xmax

within the detector field of view (green distributions).

166

Chapter6/Chapter6Figs/theta_reali_LL.ps


Figure 6.10: Xmax distributions obtained from LL 2004 data requiring at least




167

Chapter6/Chapter6Figs/xmax_reali_LL.ps


Figure 6.11: Zenithal distributions obtained from CO 2004 data requiring at

least 5 pixels to perform SDP reconstruction (blue distributions), 15 pixels for

the shower axis determination (red distributions) and finally the estimated Xmax


168

Chapter6/Chapter6Figs/theta_reali_CO.ps


Figure 6.12: Xmax distributions obtained from CO 2004 data requiring at least




169

Chapter6/Chapter6Figs/xmax_reali_CO.ps


It should be noted that these distributions are obtained without any run pre-

selection. The reason is that present cuts are able also to reject events affected

by extended clouds or very bad atmosphere conditions. Figures 6.13 and 6.14

show two typical cases of FD events with clouds in the detector field of view.

In the first case, the reconstruction program is not able to perform any Gaisser-

Hillas fit over the profile. In the latter case, a Gaisser-Hillas fit to the data is

performed, however the resulting parameters have not physical values and the

event is rejected by the analysis cuts.

X [g/cm2]3980 4000 4020 4040 4060 4080 4100 4120

n_e

0

2000

4000

6000

8000

10000

1010× = -1.601e-35+- 0maxX

= -1e+03 +- 0maxN = -1.601e-35 +- 00X

^2/dof -999 / 0χEem [eV] 1.4e+18 +/- 0

[eV] 1.5e+18 +/- 0totE

Longitudinal Profile - Eye 1 Run624Event2374

Figure 6.13: Event longitudinal profile showing the presence of clouds in the field

of view of the eye. In this case, the reconstruction program is not able to perform

any fit over the profile curve.

170

profilo_nuvola2.ps


X [g/cm2]2780 2800 2820 2840 2860 2880 2900 2920 2940

n_e

0

500

1000

1500

2000

2500

3000

1010× = 578.3+- 11.54maxX

= 1.2e+21 +- 3e+20maxN = 0 +- 0

0X

^2/dof 2.38e+03 / 118χEem [eV] 1.5e+30 +/- 4e+29

[eV] 1.6e+30 +/- 4e+29totE

Longitudinal Profile - Eye 1 Run624Event2373

Figure 6.14: Event longitudinal profile showing the presence of clouds in the field

of view of the eye. In this case, the reconstruction program performs a Gaisser-

Hillas fit, however the event is rejected by analysis cuts (Xmax derived from fit

should be within the the detector field of view).

171

Chapter6/Chapter6Figs/profilo_long_con_nuvola.eps

6.3 Reconstruction of Real FD Events

Log10( Energy [eV]) Reconstruction Efficiency

17.0 0.035

17.5 0.182

18.0 0.359

18.5 0.401

19.0 0.340

19.5 0.287

20.0 0.259

20.5 0.221

Table 6.1: Reconstruction efficiency at different energies.

6.2.4 Summary

For mono reconstruction analysis the following requirements have been estab-

lished:

1. Shower Detector Plane : accuracy < 2, at least 5 pixels;

2. Shower Axis: accuracy < 5, at least 15 pixels;

3. Xmax and shower Energy: Xmax and energy accuracy < 50 g/cm2 and 5%

respectively, Xmax in the detector field of view.

With these cuts, the reconstruction efficiency at different energies has been

computed. In tab. 6.1 determined reconstruction efficiencies are reported.


To estimate the CR flux, all 2004 and 2005 FD data have been analyzed by

using the criteria defined above. All events have been reconstructed as monocu-

lar events. Figure 6.15 shows the reconstructed event rate evaluated at different

reconstruction levels as a function of run number. Represented event rates are

normalized to the number of active bays in the acquisition run. The rate of events

surviving the analysis cuts is very stable over the whole data set. Few runs have

172


been discarded due to laser event contaminations and/or serious hardware prob-

lems. No further run selection has been applied. Although within the Auger

Event Rates at different reconstruction levels - no run selection

Run Number0 200 400 600 800 1000 1200

Run Number0 200 400 600 800 1000 1200

Eve

nts

per

ho

ur

0

50

100

150

200

250

EvtPulsed Rate

Run Number0 200 400 600 800 1000 1200

Run Number0 200 400 600 800 1000 1200

Eve

nts

per

ho

ur

0

20

40

60

80

100

120

140

160

EvtSDP Rate

Run Number0 200 400 600 800 1000 1200

Run Number0 200 400 600 800 1000 1200

Eve

nts

per

ho

ur

0

20

40

60

80

100

120

140

160

EvtTimeFit Rate

Run Number0 200 400 600 800 1000 1200

Run Number0 200 400 600 800 1000 1200

Eve

nts

per

ho

ur

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

EvtCUTS Rate

Figure 6.15: Event rates at different reconstruction levels: event with a list of

pixels with a reconstructed signal (top left panel); event with a reconstructed

shower detector plane (top right panel); event with a shower axis estimation

(bottom left panel); event surviving the requirements of analysis cuts (bottom

right panel).

Collaboration the atmospheric aerosol content is measured on an hourly base, a

database with atmospheric trasparency is available since a short time and the in-

terface between the atmospheric database and the reconstruction program is still

not complete. Figure 6.16 shows the measured vertical aerosol optical depth at 3

km above the FD level as extracted from the database, from january 2004 to oc-

173

Chapter6/Chapter6Figs/event_rate_no_selection.eps


Jan04Feb Mar Apr MayJun Jul AugSepOct NovDec Jan05

Feb Mar Apr MayJun Jul AugSep Oct Nov Dec050

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

DATABASE: VAOD

Clean Atmosphere

Dirty Atmosphere

DATABASE: VAOD

Figure 6.16: Distribution of the mean value of measured VAOD at 3 km above

the FD level for each night, from january 2004 to october 2005. The red line

indicates the corresponding VAOD of the “clean” atmosphere while the green one

the corresponding value of the “dirty” atmosphere.

174

Chapter6/Chapter6Figs/vaod.ps


tober 2005. The red and the green lines indicate the VAOD corresponding to the

“clean” and “dirty” atmospheres, used in the simulated data sample employed to

estimate detector reconstruction efficiency. A seasonal variation of VAOD data

is clearly visible. It is also clear that the value corresponding to the “clean”

atmosphere overestimates the average value, so in most of cases the energy cor-

rection due to atmospheric attenuation is overestimated. To be consistent with

analysis reconstruction efficiency discussed before, the “clean” atmosphere has

been used in the analysis. This introduces systematic uncertainty in the energy

determination which has been estimated to be of the order of 15% [165].

Figures 6.17, 6.18, 6.19 show reconstruction results obtained from the analysis

of the whole set.

0 10 20 30 40 50 60 70 80 900 10 20 30 40 50 60 70 80 900

20

40

60

80

100

120

140

thetaAXIS_eye_LL thetaAXISEntries 2959Mean 30.9

RMS 15.02

thetaAXIS_eye_LL

Figure 6.17: Zenithal distribution obtained from LL data requiring 5 pixels to

perform SDP reconstruction, 15 pixels for the shower axis determination and the

estimated Xmax within the detector field of view.

175

Chapter6/Chapter6Figs/ThetaAXIS_pulito_eyeLL_clean.eps


0 200 400 600 800 1000120014001600180020000 200 400 600 800 1000120014001600180020000

50

100

150

200

250

300

XMax XMaxEntries 2959Mean 704.8

RMS 100.5

XMax

Figure 6.18: Xmax distribution obtained from LL data requiring 5 pixels to per-

form SDP reconstruction, 15 pixels for the shower axis determination and the

estimated Xmax within the detector field of view.

176

Chapter6/Chapter6Figs/XMax_pulito_eyeLL_clean.eps


Log (Energy [eV])0 5 10 15 20 25

Clean Atmosphere

Entries 2973Mean 17.85

RMS 0.6375

Log (Energy [eV])0 5 10 15 20 25

En

trie

s

0

200

400

600

800

1000

1200

1400

Clean Atmosphere

Entries 2973Mean 17.85

RMS 0.6375

energy_eye_LL - VAOD(3 km) = 0.030

Figure 6.19: Energy distribution reconstructed from Los Leones FD data with a

V AOD = 0.030

177

Chapter6/Chapter6Figs/Energy_eyeLL_0.030.eps

6.4 Analysis Results


6.4.1 All Particle Spectrum

In an ideal case in which detector configuration, detector efficiency and at-

mospheric conditions do not depend on time, the CR flux in the energy bin

[E, E + dE] is given by

φ(E) =N(E)

Aperture(E) · LiveTime · ReconstructionEfficiency(E) · E (6.1)

where N(E) is the number of events recorded with energy in the selected

energy bin.

In a more realistic case, for an estimation of the CR flux with the FD detec-

tor, these terms and their dependence on time, atmospheric conditions, shower

geometry, primary mass compositions, Monte Carlo, etc, have to be taken into

account.

1. Detector Aperture. FD detector has the great advantage with respect to

the ground array to have a direct energy calibration. But the detector has

not a fixed aperture. The fluorescence detector aperture grows up with the

energy and depends on atmospheric conditions during data taking. As a

consequence, the detector aperture should to be studied as a function of the

energy in different atmospheric conditions and possible detector configura-

tions. Of course, its dependence on primary mass composition and Monte

Carlo codes should be also considered.

2. Time Exposure. For each FD eye, data acquisition time should be com-

puted. Detector status should be continously monitored. FD acquisition

status could be different night by night, hour by hour, because one or more

of telescopes could be out of operations for a certain time interval during

a night. The computing of the detector live time has to take into account

the possible different status of data acquisition.

3. Reconstruction Efficiency. Once a set of analysis cut is fixed, it is possible

to obtain a detailed knowledge of the reconstruction efficiency at different

energies.

178


In section 6.2, I have already computed the reconstruction efficiency at dif-

ferent energies. To evaluate the determinator of eq. 6.1 in a realistic case, all

possible configurations of an FD eye must be considered. The eye acquisition

configuration can be described by a pattern of active telescopes defined as a 6−bit

word. For instance, if there are 4 active telescopes, bay1, bay2, bay5, bay6, the

pattern will be 1,1,0,0,1,1. There are 64 possible patterns. In addition, tele-

scopes have been equipped with corrector rings at different times. From january

2004 to november 2005, four periods can be distinguished. Therefore the term

Aperture(E) · LiveTime · ReconstructionEfficiency(E) (6.2)

can be expressed as4∑

j=1

64∑i=1

Ai,j(E) · Ti,j · εi,j (6.3)

where the sum is performed over the 26 configurations of active bays, Ai,j(E),

Ti,j and εi,j are aperture, live time and reconstruction efficiency of each configu-

ration, respectively.

Next sections will be devoted to discuss the detector aperture and the deter-

mination of the detector live time.

6.4.1.1 Detector Aperture

Within the Auger Collaboration, two sets of simulated showers have been pro-

duced in order to estimate the detector aperture. The first one uses a parametriza-

tion of longitudinal profiles of air showers, that allows to simulate shower profiles

at each energy in a fast way, avoiding the use of a complex and heavier simu-

lation code like CORSIKA. By using these simulated showers, L’Aquila Auger

group made a detailed study of the FD detector trigger aperture [178]. Detector

response has been checked in different conditions:

1. Two different shower cores ditributions. Showers have been produced uni-

formely in distance and in area, within the field of view of a single telescope,

bay4 of the Los Leones eye and up to distance from the eye that depends

on the energy (6 km at 1017 eV up to 80 km for E > 1019.5 eV ). The

reason for this is to evaluate detector response at different distances with

179


high statistics (uniform in distance) and its behavior in the more realistic

case of a uniform distribution of shower cores (uniform in area).

2. Two different atmospheric conditions. To investigate the dependence of the

detector aperture on atmospheric conditions the “clean” and the “dirty”

atmospheres, defined above, have been employed

3. Two primary particles. Simulated showers are produced for proton and iron

primaries, in order to estimate the aperture dependence on comic ray mass

composition.

4. Two telescope configurations. A growing fraction of Auger FD telescopes

makes use of corrector rings to enhance their aperture without introducing

optical aberrations. To understand the effect on detector aperture both

configurations, with and without them, have been investigated.

For each possible combination of these parameters, 10000 simulate showers have

been produced at fixed values of Log(E/eV ) = 17, 17.5, 18, 18.5, 19, 19.5, 20,

20.5, with zenith angle within 60 degrees, with a cos θd(cos θ) zenith distribution

and uniform azimuth distribution. The aperture trigger function is computed

with a semi-analytical approach: a single telescope aperture is computed with

high statistics and is analytically generalized to the whole eye.

Recently - November 2005 - a second set has been completed by using the

CORSIKA Monte Carlo and it is composed by [190]:

1. 50000 proton showers;

2. energy spectrum from 1017.5 eV to 1020.5 eV , according to dN/dE ∝ E−1;

3. zenith distribution from 0 to 60, according to dN/(d cos θ) ∝ cos θ;

4. uniformely distributed over an area of 80 km × 80 km.

5. showers propagate through the “clean” atmosphere.

6. FD telescopes with corrector rings.

180


Of course, the CORSIKA data set is more realistic and the wider genera-

tion area allows to avoid a systematic effect derived from extrapolation from the

single telescope aperture to the complete eye aperture. On the other hand, the

Gaisser-Hillas data set allowed to check detector response as function of different

parameters and in principle to obtain a more general result.

It is possible to note some differences between the trigger efficency estima-

tion performed by means of CORSIKA showers and that one obtained by fast-

simulated Gaisser-Hillas profiles as shown in fig. 6.20.

Figure 6.20: Comparison between the FD Second Level Trigger (SLT ) estimation

obtained by using CORSIKA showers (blue ) and fast-simulated Gaisser-Hillas

profiles (red ) at 1019 eV . There is a difference in the trigger aperture of a few

percent.

I have done a comparison between the apertures computed with the two dif-

ferent data sets. Figure 6.21 shows the FD mono detector aperture computed

with the CORSIKA data set [190] (cyan triangles) by Wuppertal Auger group,

with Gaisser-Hillas parametrized profiles taking into account corrector rings (blue

stars) and without corrector rings (red triangles) by L’Aquila Auger group. As

181

Chapter6/Chapter6Figs/newghvscorsika.ps


expected, the use of correcor rings enlarges detector aperture. Wuppertal results

are systematically higher than L’Aquila ones. Part of the discrepancy is due to

the effect already shown in figure 6.20 in a particular case. Another contribution

is due to a systematic underestimate of the simple semi-analytical approach. A

more refined semi-analytical approach is under development.

It should be noted that both aperture determination are given in the ideal case

of the complete eye with all 6 telescopes in operation. In principle, the aperture of

each configuration should be computed, in absence of such a detailed information,

I used the reasonable assumption to scale down the total eye aperture by 1/6 for

each missing telescope. This does not take into account for correlations between

neighbouring telescopes.

6.4.1.2 Live Time Determination

In order to estimate the detector live time, I followed the detector evolution in

time.

In principle, different telescope configurations could characterize a run, be-

cause during data acquisition some bay could go out of operation for hardware

problems, or their shutters may be closed when the moon is in their field of view.

The latter case may happen at the start, at the end and during the run. Then for

each run, the active telescope patterns and their live time have been computed.

A continous scan of active bays is performed: at each second the eye data taking

configuration pattern is checked and is corresponding live time is incremented.

In this way, 64 eye patterns for the four time periods corresponding to corrector

ring commissioning, live time values are computed.

6.4.1.3 Spectrum Evaluation

Reconstruction efficiency and detector aperture are measured at a fixed energy in

steps of 100.5 eV . So, FD data will be grouped in 8 energy intervals ([16.75, 17.25[

and so on). Since efficiency and aperture estimation have been extracted from a

data sample with a zenith angle lower than 60 degrees, events with zenith angle

higher than 60 have been rejected. With this binning each energy interval is

much wider than energy bins of existing data. To perform a comparison, the flux

182


Log (Energy [eV])17 18 19 20 21

Log (Energy [eV])17 18 19 20 21

sr]

2A

per

ture

[km

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

FD Mono Aperture Comparison

Figure 6.21: Comparison of FD mono detector apertures obtained by Wupper-

tal Auger group with CORSIKA simulated showers and that one obtained by

L’Aquila Auger group with parametrized Gaisser-Hillas profiles.

183

Chapter6/Chapter6Figs/confronto_aperture.eps


estmation will not be given at the bin center, but at its average energy, computed

weighting for an assumed CR spectrum ∝ E−3.

Since the aperture values provided by the L’Aquila Auger group are given with

and without corrector rings, it was possible to evaluate the sum in eq. 6.3. Figure

6.22 shows the resulting spectrum (violet triangles). Only statistical errors are

given. Spectra obtained assuming the whole eye equipped with corrector rings at

all times (blue circles) and without them (red circles) are also shown to illustrate

their effect on the spectrum. A fit with a spectrum with a spectral index of 3 is

also represented (black line). Due to his lower aperture, the estimated spectrum

without corrector ring is systematically higher than the others. As expected,

the real case , in which acquisition times with and without corrector ring are

considered separately, lies between the two extreme cases.

The effect of corrector rings is clearly not negligible. Since the corrector ring

aperture is not given yet by Wuppertal Auger group, I made further assumptions.

To take into account the effect of the corrector ring, I have assumed that

L’Aquila and Wuppertal apertures without corrector rings would have the same

ratio to their apertures with corrector rings. In this way, I have derived a Wup-

pertal aperture without corrector rings as

ACORSIKA =ACR

CORSIKA · AGH

ACRGH

(6.4)

where ACRCORSIKA and ACORSIKA are the Wuppertal apertures with and without

corrector rings, while ACRGH and AGH are L’Aquila apertures with or without

corrector rings. To do this, Wuppertal aperture has been interpolated in order to

extract the values at the same energies available in the Gaisser-Hillas data set and

for the reconstrcution efficiency. The same reconstruction efficiencies calculated

for GH shower set have been used for the CORSIKA set. In principle, they

should be computed on the CORSIKA data sample.

Figure 6.23 shows the resulting spectrum estimations for the two detector

apertures (blu circles for Gaisser-Hillas showers and red circles for CORSIKA

showers).

The flux estimation is affected by an error of the order of 20% coming from

the present knowledge of detector aperture. The energy estimation is affected by

184


Log (Energy [eV])16.5 17 17.5 18 18.5 19 19.5 20

Log (Energy [eV])16.5 17 17.5 18 18.5 19 19.5 20

-1 s

r s

GeV

)2

Flu

x (m

-2710

-2610

-2510

-2410

-2310

-2210

-2110

-2010

-1910

-1810

-1710 LL without Corrector Ring

LL with Corrector Ring

LL with Corrector Ring Detailed

All particle spectrum from LL FD Mono Data - Corrector Ring Effects

Figure 6.22: Estimation of the all particle spectrum considering the two extreme

cases in which a corrector ring is used by all bays within the eye (red circles) or

by none of them (blue triangles) and the real case (violet triangles).

185

Chapter6/Chapter6Figs/spettro_Confronto_CR.eps


different systematic uncertainties (see section 3.6.3) mainly due to the fluores-

cence yield (∼ 15%), to the FD absolute calibration (∼ 12%) and to atmosphere

attenuation - Mie scattering - (15%). In addition, a further uncertainty of ∼ 15%

due to the use of fixed “clean” atmosphere in the data analysis should be in-

cluded. These ones, together with other smaller FD uncertainties, give a total

systematic uncertainty of the order of 30% in the energy. With these uncertain-

ties, it is possible to estimate the two extreme all particle spectra, reported in

fig. 6.24, which correspond to the aperture uncertainties, The figure also shows

the first Auger spectrum presented at ICRC 2005 [191], produced with only SD

data. Auger spectrum starts at higher energies with respect to this estimation

because the SD, in comparison with the FD, has an higher trigger threshold.

On the same plot, published spectra by AGASA and HiRes are also shown.

6.4.2 Elongation Rate

The distribution of positions of shower maximum (Xmax) in the atmosphere has

been shown to be sensitive to the composition of CRs. It is well known that for

any particular species of nucleus the position of shower maximum deepens with

increasing energy as the logarithm of the energy (see sec. 1.4.8.2). The slope

d(Xmax)/d(logE) is known as the elongation rate (De). While the details depend

on the hadronic model assumed, all modern hadronic models give approximately

the same De (between 50 and 60 g/cm2 per decade of energy, independent of

particle species) and agree within about 25 g/cm2 on the absolute position of the

average shower Xmax at a given energy for a given species. The sensitivity of the

Xmax method to composition comes from the fact that the mean Xmax for iron

and protons is different by about 80-100 g/cm2, independent of hadronic model,

with protons producing deeper showers with larger fluctuations. A change in

the composition from heavy to light would then result in a larger De than 50-60

g/cm2 per decade, and a change from light to heavy would lead to a lower and

even negative De.

The general dependence of Xmax on energy can be seen in a simple branching

model in which Nmax ∝ E0 and Xmax ∝ lnE0, where E0 is the primary cosmic

ray energy [85]. In this model if the primary particle is a nucleus, the shower

186


Log (Energy [eV])16.5 17 17.5 18 18.5 19 19.5 20

Log (Energy [eV])16.5 17 17.5 18 18.5 19 19.5 20

-1 s

r s

GeV

)2

Flu

x (m

-2610

-2510

-2410

-2310

-2210

-2110

-2010

-1910

-1810LL Wuppertal Aperture

LL L’Aquila Aperture

Aperture Effect on Reconstructed CR Energy Spectrum

Figure 6.23: Estimation of the all particle spectrum with the FD mono aper-

ture calculated with parametrized Gaisser-Hillas profiles (red circles) and with

CORSIKA showers (blue circles).

187

Chapter6/Chapter6Figs/spettro_confronto_2_aperture.eps


Log (Energy [eV])17 18 19 20 21

Log (Energy [eV])17 18 19 20 21

-1 s

r s

GeV

)2

Flu

x (m

-2910

-2810

-2710

-2610

-2510

-2410

-2310

-2210

-2110

-2010

-1910

-1810 Auger FD-only Spectrum Estimation

AUGER Spectrum at ICRC 2005

AGASA Spectrum

HiRes Spectrum

All particle spectrum from LL FD Mono Data

Figure 6.24: Two extreme all particle spectra corresponding to the aperture

uncertainties are shown. All particle spectra published by AGASA, HiRes and

the first Auger estimation given at ICRC 2005 [191], produced with only SD

data.

188

Chapter6/Chapter6Figs/spettro_bande_apertura.eps


is assumed to be a superposition of subshowers, each initiated by one of the

A independent nucleons. The primary energy must be divided among the A

constituents, so in this case Xmax ∝ ln A × E0. A more complete discussion leads

to Linsley’s expression for the De:

De = X0(1 − B)

[1 − ð〈lnA〉

ð〈lnE〉]

(6.5)

It includes both the energy dependence of the cross section and the energy

dependence of the multiplicity and inelasticity.

The technique for extracting the CR composition used then reduces to com-

paring the Xmax distribution of the data after appropriate cuts that guarantee

good resolution in this variable, with simulated data generated with either a pro-

ton or iron parent particle. The simulated data are the result of a detector Monte

Carlo and include all the reconstruction uncertainties.

While CR hadronic composition presumably can range anywhere between the

two extremes of pure proton and pure Fe, the 30 g/cm2 resolution of the detector

and the existence of significant shower fluctuations lead us to compare the data

with a simplified two-component model. Events are generated using CORSIKA

6.005 and 6.010 [] and using QGSJet01 [] for high energy hadronic model and

GHEISHA for low energy hadronic model (> 80 GeV). In all simulations, the

CORSIKA EGS4 option is selected, enabling explicit treatment of each electro-

magnetic interaction for particles above a threshold energy. Electrons, positrons,

and photons were tracked down to energies of 100 keV. Hadrons and muons were

tracked to 300 MeV. The showers were initiated from 0 to 53 degree with sam-

pling at 5 g/cm2 of vertical atmospheric depth and the thinning level was set at

10−6. For this study 100 iron showers and 100 proton showers are used in each

0.5 step of log E from 1018 to 1020 eV (simulation were performed at the Lyon

Computer Center).

Figure 6.25 shows the preliminary elongation rate obtained with selected data

set (black stars), compared with those expected from the two extreme cases of

cosmic ray mass composition, proton or iron primary particles. Simulated re-

sults are presented taking into account detector and reconstruction effects (red

solid circles and blue solid squares for protons and irons, respectively). The red

189


Log10(E[eV])17.5 18 18.5 19 19.5 20 20.5 21

Log10(E[eV])17.5 18 18.5 19 19.5 20 20.5 21

XM

ax [

g/c

m^2

]

600

650

700

750

800

850

900

protonironreal data

pure protonpure iron

ELONGATION RATE

Figure 6.25: Preliminary elongation rate estimation obtained with selected data

set (black stars), compared with those expected from the two extreme cases of cos-

mic ray mass composition, proton or iron primary particles, taking into account

detector effects (red solid circles and blue solid squares for protons and irons,

respectively) and not (red and blue lines for protons and irons, respectively).

190

Chapter6/Chapter6Figs/ElongationRate.ps

6.5 Conclusions

and blue lines (protons and irons, respectively) are the results of CORSIKA

simulation without the filter of the Offline reconstruction

The preliminary elongation rate is, of course, affected by the same uncertain-

ties discussed on the energy determination. In addition, a further uncertainty on

Xmax determination of ∼ 30 g/cm2, mainly due to the knowledge of atmospheric

density profile, should be also included.

6.5 Conclusions

The spectrum presented in figure 6.24 is only the first attempt to build up a cosmic

ray spectrum with only FD data within the Auger Collaboration. It is affected by

different systematic uncertainties, on the energy determination (30%) and on the

detector aperture determination (20%). Only the two extreme spectra are given.

The work on this topic is still in progress. All the details of the calculation should

be refined, from the computing of the detector live time to the use of measured

atmospheric conditions, from the estimation of the reconstruction efficiency to

the detector aperture.

The presented elongation rate is only a preliminary estimation. The simulated

data set used to compare with real data is clearly limited. The estimation is

affected by systematic uncertainties, already discussed, on energy determination

and by further uncertainties related to the Xmax determination of ∼ 30 g/cm2,

due to the knowledge of atmospheric density profile.

191

Conclusions

The Pierre Auger Southern Observatory is going to be completed. Since septem-

ber 2003, the Observatory is recording extended air showers by means of two

independent and complementary detectors. In august 2005, the first shower has

been detected by 3 fluorescence 3. Within the Pierre Auger Collaboration, de-

tector features are studied with more and more details. Analysis tools are under

development and optimization.

In this scenery, I have studied details of Fluorescence detector event recon-

struction and new algorithms have been developed in order to enhance recon-

struction performances. The geometrical reconstruction of Fluorescence Detec-

tor events have been improved by implementing the use of gnomonic projections

to perform the first geometrical reconstruction step, the shower detector plane

determination. The new approach has been tested with very good results over a

wide set of simulated showers and laser shots. The study has also shown a visible

effects of the improved shower detector plane determination on the reconstruction

of shower energy and of the depth of shower maximum.

The improved Fluorescence detector geometrical reconstruction has been tested

by mean of laser shots of known geometry, in order to estimate reconstruction

accuracy. All possible event reconstruction typology have been tested (mono, hy-

brid and stereo). Results have shown an incomparable reconstruction accuracy.

In particular, the stereo reconstruction allows a very accurate core determination.

For this reason, it was possible to observe a telescope misalignment, which has

been measured by using features of gnomonic projections and a sample of laser

shots. The obtained corrections for telescope axis have been employed in laser

shot stereo reconstruction, showing that the gnomonic alignment technique can

correctly take into account misalignments for two eyes.

192

The Fluorescence event reconstruction has been used to extract first physical

informations from Auger fluorescence data: first estimate of the all particle en-

ergy spectrum and of the elongation rate. Reconstruction efficiency and analysis

cuts required to achieve a good reconstruction accuracy have been computed on

the same simulated data set used within the Auger Collaboration to evaluate

the Fluorescence detector aperture. Defined cuts are applied to fluorescence data

recorded from january 2004 to november 2005. Monitoring during this period

detector evolution and data taking configuration as a function of the time, detec-

tor live time have been computed. Finally, by using detector apertures available

within the Auger Collaboration, the first attempt to build up a cosmic ray spec-

trum with only fluorescence data within the Auger Collaboration has been done.

The produced spectrum is affected by different systematic uncertainties on the

detector aperture (20%) and on the energy determination (30%). The two ex-

treme spectra computed for the aperture uncertainties is given. With all the cited

limits, the estimated spectrum seems compatible with those evaluated by prior

experiments and by Auger Collaboration on Surface detector data for the ICRC

2005. With the same data set, a preliminary estimate of the elongation rate is

given. The simulated data sample, used to perform the comparison with the two

extreme casa of cosmic ray mass composition (pure proton or pure iron radiation)

is clearly small. In addition to energy uncertainties, systematic errors related to

the Xmax determination (30 g/cm2), due to the knowledge of atmosphere density

profile, should be considered.

All the work on these topics is still in progress. All the details of the calcu-

lation should be refined: the detector live time computing; the use of measured

atmosphere conditions; the estimation of the reconstruction efficiency; the eval-

uation of the detector aperture; Xmax and energy reconstruction. The sample

of simulated showers should be enlarged to an higher statistics and to different

geometrical configurations.

193

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