Measurement of the ultra high energy cosmic ray flux from data of very inclined showers at the Pierre Auger Observatory [Elektronische Ressource] / vorgelegt von Hans Peter Dembinski

Sujets

• Physik

Informations

• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2009
• Nombre de lectures: 3
• Langue: English
• Poids de l'ouvrage: 13 Mo

Extrait

Measurement of the Ultra High Energy
Cosmic Ray Flux from Data of very
inclined showers at the Pierre Auger
Observatory
Von der Fakulta¨t fur¨ Mathematik, Informatik und Naturwissenschaften
der RWTH Aachen University zur Erlangung des akademischen Grades
eines Doktors der Naturwissenschaften genehmigte Dissertation
vorgelegt von
Diplom-Physiker
Hans Peter Dembinski
aus Rostock
Berichter: Univ.-Prof. Dr. Thomas Hebbeker
Univ.-Prof. Dr. Martin Erdmann
Tag der mundl¨ ichen Pruf¨ ung: 3.12.2009
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfu¨gbar.Contents
1 Introduction 1
2 Conventions 3
3 Ultra-high energy cosmic rays 9
3.1 Cosmic rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1.1 Cosmic rays up to 100 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1.2 Cosmic rays above 100 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Extensive air showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 Heitler-model of the hadronic cascade . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Very inclined air showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3.1 Muon component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3.2 Lateral shower profile at ground level . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.3 Time structure of the shower front . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.4 Muon generated electromagnetic particles . . . . . . . . . . . . . . . . . . . . . . 31
4 Pierre Auger Observatory 33
4.1 Surface detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 Signal calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.2 Trigger system and data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Fluorescence detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.1 Signal calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.2 Trigger system and data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 Extensions and new developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5 Air shower and event simulation 47
5.1 Simulation of air showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.1.1 Hadronic interaction models at low energies . . . . . . . . . . . . . . . . . . . . . 48
5.1.2 Hadronic interaction models at high energies . . . . . . . . . . . . . . . . . . . . 49
5.1.3 Thinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.2 Simulation of surface detector events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.1 Un-thinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.3 Mass production of very inclined air showers . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3.1 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.2 Comparison with older productions . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4 Modeling very inclined air showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4.1 Number of muons on the ground . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.4.2 Universality of the normalized muon density profile . . . . . . . . . . . . . . . . . 69
5.4.3 Parameterisation of the muon density profile . . . . . . . . . . . . . . . . . . . . 69
iCONTENTS
5.4.4 Comparison with another model . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.5 Surface detector response to very inclined air showers . . . . . . . . . . . . . . . . . . . . 81
5.5.1 Properties of the Auger Water-Cherenkov detector . . . . . . . . . . . . . . . . . 81
5.5.2 Modeling the signal response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.5.3 Analysis of the electromagnetic signal component . . . . . . . . . . . . . . . . . 86
5.5.4 Comparison with another model . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6 Reconstruction of cosmic ray properties 91
6.1 Vertical and very inclined showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.2 SD event reconstruction of very inclined showers . . . . . . . . . . . . . . . . . . . . . . 93
6.2.1 Idealised reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2.2 Realistic SD reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2.3 Reconstruction resolution and bias . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2.4 Comparison with references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.2.5 Constant intensity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.2.6 Bias correction of the energy estimator . . . . . . . . . . . . . . . . . . . . . . . 127
6.2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.3 FD event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.3.1 Pulse finding and rejection of random pixels . . . . . . . . . . . . . . . . . . . . . 129
6.3.2 Reconstruction of the shower axis . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.3.3 Reconstruction of the shower energy . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.3.4 Systematic uncertainty of the energy . . . . . . . . . . . . . . . . . . . . . . . . . 134
7 Energy calibration of the Surface Detector 137
7.1 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.1.1 SD event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.1.2 FD event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.1.3 Cut optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.2 Calibration method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.2.1 Model components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.2.2 Statistical and numerical bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.3 Application to data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
8 Flux of ultra-high energy cosmic rays 175
8.1 Exposure of the surface detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.2 Unfolding of the cosmic ray flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8.2.1 Unfolding problem and solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8.2.2 RUN-algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
8.2.3 Application to data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
8.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
9 Acknowledgements 199
A Analytical and numerical calculations 201
A.1 Point of shower maximum and particle interaction lengths . . . . . . . . . . . . . . . . . 201
A.2 Exp-normal distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
A.3 Effective area of a SD station and average muon signal . . . . . . . . . . . . . . . . . . . 203
A.4 Projection of surface detector stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
A.5 Calculation of the data modelf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207tot
B Air shower simulation: Technical summary 209
C SD station: signal response model 211
iiCONTENTS
D Reconstruction of SD and FD events: technical details 213
E SD event reconstruction: background rejection 217
F Event selection: examples of rejected events 221
G Cosmic ray flux: tables and consistency checks 227
iiiCONTENTS
ivChapter 1
Introduction
When Victor Hess discovered the cosmic radiation in 1912 [1], he laid a foundation for the upcoming field
of high energy particle physics. For about 40 years, the cosmic radiation was the only source of particles
with energies of several GeV. The analysis of cosmic rays and their reactions with matter led to several
discoveries, for instance the positron in 1933 [2], the muons in 1936 [3], and the pions in 1947 [4].
In the 1950’s, the main focus of particle physicists shifted towards man-made particle accelerators,
which offered several advantages over the cosmic radiation. The key development was the synchrotron
as a scalable accelerator for particles up to multi-GeV energies. The Cosmotron, completed in 1953, was
one of the first [5]. Artificial accelerators provide almost monochromatic beams of high intensity with a
defined particle content, in contrast to the cosmic radiation, and overall much more control over the particle
interactions.
Cosmic rays remained of considerable interest for astrophysicists as messenger particles of very pow-
erful astrophysical processes. In 1939, Pierre Auger discovered cosmic ray induced particle showers in the
atmosphere, called extensive air showers [6]. He analysed coincident