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3D Reconstruction of Extensive Air Showers at thePierre Auger Observatory
Miguel Figueiredo Vaz Pato
Dissertação para obtenção do Grau de Mestre em
Engenharia Física Tecnológica
Júri
Presidente: Professor João Seixas
Orientador: Professor Mário Pimenta
Vogal: Doutora Soa Andringa
Julho 2007
i
Acknowledgements
I am thankful to my supervisor Mário Pimenta mostly for the much I have learned with him and the full
support given during the development of the thesis. And to Soa Andringa, that accompanied at close
distance the whole work and made possible many aspects therein.
The thesis was entirely developed in Lisbon at Laboratório de Instrumentação e Física Experimental
de Partículas (LIP), to which I am very grateful for the exceptional research conditions oered. I would
also like to thank to LIP members Catarina, Bernardo, Patrícia, Pedro Assis and Ruben for numerous
fruitful discussions and help in technical issues. I address special thanks to André and Sara as well.
Last but not the least, I am grateful to my parents, brother and sister and my friends for putting up
with me! És szeretnèk különösen köszönetet mondani Gabriellànak.
ii
iii
Resumo
É apresentada uma síntese acerca de raios cósmicos de energia ultra elevada e dos respectivos desaos
de detecção, bem como o actual estado da arte das observações neste particular domínio. O Observatório
Pierre Auger é descrito de forma detalhada e, em seguida, propõe-se um método tridimensional original
para reconstruir cascatas atmosféricas extensas a partir de dados de uorescência e de natureza híbrida.
Este novo método utiliza o tempo de amostragem ao nível dos telescópios como terceira dimensão espacial,
produzindo uma imagem 3D da cascata atmosférica. Reconstrói-se então o perl da cascata considerando
a óptica detalhada dos telescópios e a luz de uorescência e de erenkov (directa e difusa). Os resultados
das reconstruções da geometria e do perl são vericados através de simulação de cascatas iniciadas por
protões e, nalmente, usam-se dados reais para efectuar a medição de pers laterais.
Palavras-chave: raios cósmicos de energia ultra elevada, cascatas atmosféricas extensas, Observatório
Pierre Auger, luz de uorescência, radiação de erenkov, perl lateral da cacasta
Abstract
A brief review on ultra high energy cosmic rays and the associated detection challenges is drawn
together with the present status of observations in the eld. The Pierre Auger Observatory is described
in a detailed manner and, afterwards, an original three dimensional procedure to reconstruct extensive
air showers from uorescence and hybrid data is proposed. This new method uses the sampling time at
the telescopes as a third dimension in space producing a 3D image of an air shower. The shower prole
is then reconstructed by considering the detailed optics of the telescopes and uorescence and (direct
and scattered) erenkov light. The results from both geometry and prole reconstructions are checked
through proton simulation and, nally, real data is used to perform the measurement of shower lateral
proles.
Keywords: ultra high energy cosmic rays, extensive air showers, Pierre Auger Observatory, uores-
cence light, erenkov light, shower lateral prole
iv
v
Contents
1 Introduction 1
2 UHECR within the cosmic ray eld 3
2.1 Energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Theoretical problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Acceleration and production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Relevance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 UHECR detection 9
3.1 Extensive air showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1.1 Electromagnetic showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1.2 Hadronic showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Indirect detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2.1 Ground arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2.2 Light detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Present status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 The Pierre Auger Observatory 21
4.1 Southern site description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.1 Surface Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.2 Fluorescence Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.3 Laser facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.4 Atmospheric monitoring devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 Event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.1 Surface Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.2 Fluorescence Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.3 Hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.3 Future steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.1 Southern site enhancements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.2 The northern site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5 The 3D FD reconstruction 38
5.1 Geometry reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.1.1 The 3D method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.1.2 Some applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40vi
5.2 Prole reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2.1 The 3D shower prole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2.2 Light at diaphragm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2.3 Spot and mercedes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2.4 Expected and observed signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6 Lateral prole measurements 57
6.1 Systematic study of the 3D reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.2 Lateral sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7 Conclusion and prospects 65
vii
List of Figures
2.1 Energy spectrum of cosmic rays above 108 eV [2]. . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Degradation of proton energy during propagation through the universe [2]. . . . . . . . . . 6
3.1 The Heitler's model in electromagnetic cascades (a) and in hadronic showers (b) [8]. . . . 11
3.2 A ctious event as recorded by a ground array [1]. . . . . . . . . . . . . . . . . . . . . . . 12
3.3 The uorescence spectrum of the atmospheric nitrogen [12]. . . . . . . . . . . . . . . . . . 14
3.4 An air shower as seen by a uorescence detector [1]. . . . . . . . . . . . . . . . . . . . . . 16
3.5 Percentage of missing energy for dierent energies and primaries as calculated in Monte
Carlo simulations. Open circles represent proton showers, open squares He nuclei, lled
circles CNO and lled squares Fe [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.6 The energy spectrum of cosmic rays with the conicting results from AGASA and HiRes in
the UHE range. The actual ux is multiplied by E2.5 to ease the visualisation of spectrum
features [22]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.7 The energy spectrum as measured by HiRes (a) and the PAO (b). . . . . . . . . . . . . . 18
3.8 The transition to a light composition trend that occurs in the ankle region [21]. The
simulation results from proton and iron showers are indicated by the upper and lower
parallel lines respectively, while the full circles represent the experimental data. . . . . . . 19
4.1 The Pierre Auger Observatory southern site in Argentina [24]. The dots represent SD
tanks, while the lines show the eld of view of the FD telescopes. As of 31st March 2007,
1215 tanks and all 24 telescopes were fully installed and operational [39]. . . . . . . . . . . 22
4.2 A water erenkov tank of the Surface Detector [24]. . . . . . . . . . . . . . . . . . . . . . 22
4.3 The Schmidt telescope used in the FD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.4 The (β, α) coordinates and their relation to spherical coordinates (θ, φ). In this particular
case, φt = 90 (adapted from [45]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.5 The dimensions of an FD pixel and the mercedes structures in (β, α) coordinates. . . . . . 26
4.6 An entire FD camera with its 440 pixels and mercedes stars. The telescope axis centre is
signaled with a full circle and the origin with an open one. . . . . . . . . . . . . . . . . . . 27
4.7 The spot on θ ∈ [0, 5] and φ = 2 as previewed by KG simulation [47]. The plot
compares the incident direction of each photon (θin, φin) with the direction in the focal
surface (θfs, φfs). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.8 The position of the laser facilities (CLF and XLF) in the southern site. Other atmospheric
monitoring devices are also signaled [50]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.9 The Central Laser Facility (on the right) and the Celeste SD tank (on the left) [40]. . . . 29
4.10 The FD geometry reconstruction setup (adapted from [63]). . . . . . . . . . . . . . . . . . 31
viii
4.11 Timing t to equation (4.6) of the monocular event SD 2521005 (FD 2/1066/35) recorded
on 2006/08/01 [58]. In this case, Rp ' 5.3 km, χ0 ' 65.5 and T0 ' 24800 ns. . . . . . . . 32
4.12 The light prole at the diaphragm as a function of time for the event SD 2521005 (FD
2/1066/35) recorded on 2006/08/01 [58]. The actual quantity represented is the light ux
that crossed the diaphragm. The several components of direct and scattered light are
represented as well (see text). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.13 The reconstructed longitudinal prole and the Gaisser-Hillas t [44]. . . . . . . . . . . . . 33
4.14 Comparison of monocular and hybrid reconstructions using laser shots [64]. On the left
the dierence between the reconstructed Rp and the actual one is plotted, while on the
right the same dierence for χ0 is presented. . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.15 Calibration between S38 and the energy reconstructed by the uorescence technique [25]. 36
5.1 The 3D geometry setup and event visualisation. . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 The distribution of dCP−eye and log10EKG in the data collected from January 2006 until
September 2006 with KG and 3D prole reconstructions and χ3D0 ≥ 45. The red and blue
lines indicate the border of the empirical cut (5.3) with d∗CP−eye = 5 km and d∗CP−eye = 10
km, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.3 Comparison between the Rp, χ0 and T0 values as reconstructed by the standard and 3D
approaches. Data collected from January 2006 until September 2006 with KG and 3D
prole reconstructions, χ3D0 ≥ 45 and passing cut (5.3) with d∗CP−eye = 10 km was used
to produce the plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.4 Distributions of rmin, rmed and rmax in (a) and their dependence on χ0 in (b). The data
set used is the same as in gure 5.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.5 3D visualisation of event SD 2553671 (FD 2/1081/2704). In this case, Rp ' 9.7 km and
χ0 ' 33.1. Note the dierence between the reconstructed volumes here and those of the
event presented in gure 5.1(b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.6 Dependence of rmax on Rp for the same data set as in gure 5.3 but passing the quality
cut χ0 ≥ π2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.7 The Ixx/Iyy and Izz/r2med distributions for the same data set as in gure 5.3 but requiring
rmed 6= 0 and at least one Iii 6= 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.8 The distributions of√Ixx + Iyy − Izz (a) and
√Izz (b) for the same data set as in gure
5.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.9 The geometric setup used in the 3D prole reconstruction. . . . . . . . . . . . . . . . . . . 46
5.10 Gaussian t to the Nγ,ik distribution for Nγ,ik < 0. All data collected throughout July
2006 was used to produce the plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.11 In (a) and (b), the dependence of the observed (grey shaded area) and expected (red line)
signals on XNP and RCP are presented for the 1018.5 eV simulated event SD 78 (from
job 0). The direct and Rayleigh scattered erenkov expected fractions are signaled by the
green and blue lines respectively. This event presents Rp ' 7.6 km and χ0 ' 90.8. The
behaviour of the ratio e/o with XNP (c) and RCP (d), the χik distribution (e) and the
dependence of the mean lnP1
(Nγ,ik, Nγ,ik
)on RCP (f) are also shown for the same event. 55
ix
5.12 Observed (grey shaded area) and expected (red line) signals for the 1018.5 eV simulated
event SD 14 (from job 0). As in gure 5.11, the green and blue lines represent direct
and scattered erenkov contributions at the telescopes respectively. This event presents
Rp ' 1.6 km and χ0 ' 139.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.1 In (a) and (b), the dependence of the observed (grey shaded area) and expected (red line)
signals on XNP (a) and RCP (b) for 30 1018.5 eV simulated events. The direct and Rayleigh
scattered erenkov expected fractions are signaled by the green and blue lines respectively.
Dashed lines refer to expected signals calculated with the KG parameters, while solid lines
represent the use of the simulated parameters. The value of RM was xed to 9.6 gcm−2 to
produce these plots. The behaviour of the ratio e/o with XNP (c) and RCP (d), the χikdistribution (e) and the χ2/Ndf values per event (f) are also shown for the same simulation
set. Notice that in plot (d), for RCP & 25 gcm−2, the quantity of detected volumes is low
and thus there are signicant uctuations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2 The behaviour of the estimators χ2 (RM ) /Ndf (in black) and lnL (RM ) (in red) with the
eective parameter RM for the close simulated event SD 78 (from job 0) (a) and the distant
one SD 10 (from job 0) (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.3 In (a) and (b), the dependence of the observed (grey shaded area) and expected (red
line) signals on XNP and RCP are presented for the 15 events from the Lecce-L'Aquilla
simulation and passing the cut (5.3) with d∗CP−eye = 10 km. The direct and Rayleigh
scattered erenkov expected fractions are signaled by the green and blue lines respectively.
The behaviour of the ratio e/o with XNP (c) and RCP (d), the χik distribution (e) and
the dependence of the mean lnP1
(Nγ,ik, Nγ,ik
)on RCP (f) are also shown for the same
simulation sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.4 In (a) and (b), the dependence of the observed (grey shaded area) and expected (red line)
signals on XNP (a) and RCP (b) for 50 events collected in June/July 2006 and passing the
cut (5.3) with d∗CP−eye = 5 km. The direct erenkov expected fraction is signaled by the
green line, while Rayleigh and Mie scattered erenkov components are represented in blue
and magenta respectively. The value of RM was xed to 9.6 gcm−2 to produce these plots.
The behaviour of the ratio e/o with XNP (c) and RCP (d), the χik distribution (e) and the
dependence of the mean lnP1
(Nγ,ik, Nγ,ik
)on RCP (f) are also shown for the same data
set. Notice that in plot (c) the ratio e/o grows for XNP & 1150 gcm−2, possibly because
the Mie light fraction (5.24) is over estimated in this region − recall that the component
shown in magenta is only a mean one. Besides, the statistics in that region is small and
consequently large uctuations are expected. . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.5 In (a) and (b), the dependence of the observed (grey shaded area) and expected (red line)
signals on XNP (a) and RCP (b) for 50 events collected in July 2006 and passing the cut
(5.3) with d∗CP−eye = 10 km. The direct erenkov expected fraction is signaled by the
green line, while Rayleigh and Mie scattered erenkov components are represented in blue
and magenta respectively. The value of RM was xed to 9.6 gcm−2 to produce these plots.
The behaviour of the ratio e/o with XNP (c) and RCP (d), the χik distribution (e) and
the dependence of the mean lnP1
(Nγ,ik, Nγ,ik
)on RCP (f) are also shown for the same
data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
x
6.6 The behaviour of the estimators χ2 (RM ) /Ndf (in black) and lnL (RM ) (in red) with the
eective parameter RM for two real showers recorded in July 2006. Plot (a) corresponds
to event SD 2425381 with dCP−eye ' 4.7 km, while (b) corresponds to event SD 2425226
with dCP−eye ' 7.5 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
xi
Abbreviations
ADC Analog to Digital Converter
AGASA Akeno Giant Air Shower Array
AMIGA Auger Muons and Inll for the Ground Array
AMS Alpha Magnetic Spectrometer
APF Aerosol Phase Function Monitors
CDAS Central Data Acquisition System
CLF Central Laser Facility
CMB cosmic microwave background
CORSIKA COsmic Ray SImulations for KAscade
EAS extensive air shower
FD Fluorescence Detector
GPS Global Positioning System
GZK Greisen-Zatsepin-Kuzmin
HAM Horizontal Attenuation Monitors
HEAT High Elevation Auger Telescopes
HiRes High Resolution Fly's Eye
IACT imaging atmospheric erenkov telescope
ICRC International Cosmic Ray Conference
KG Karlsruhe group
LDF lateral distribution function
LIDAR LIght Detection And Ranging
MAGIC Major Atmospheric Gamma-ray Imaging erenkov (telescope)
NKG Nishimura-Kamata-Greisen
PAO Pierre Auger Observatory
PMT photomultiplier tubes
SD Surface Detector
SDP shower detector plane
UHE ultra high energy
UHECR ultra high energy cosmic rays
UV ultraviolet
VEM vertical equivalent muon
VHE very high energy
XLF second Central Laser Facility
xii
xiii
Chapter 1
Introduction
Since its discovery in 1912 by Victor Hess, a great deal was understood about the phenomenon of cosmic
rays. For several decades the eld led the research on high energy particle physics in a time when
particle accelerators underwent an early phase of development. Nowadays, the area of cosmic rays is
split into several dierent branches dened according to the energy range pursued. The lower energy
range is reasonably well documented and understood, although there are still some problems to attack.
But, by far, the ultra high energy cosmic ray (UHECR) eld has remained over the years the hardest
to study. The reason behind this diculty is essentially two-fold. On the one hand, the ux of ultra
high energy cosmic rays hitting the atmosphere of the Earth is extremely low and, so, large detection
areas are required. On the other hand, the extensive air showers (EAS), formed while UHECRs cross
the atmosphere, call for detectors that present several technical challenges. Hence, there are still many
open issues in the UHE range: the energy spectrum, the primary composition, the arrival directions, the
sources and the propagation throughout the universe.
Even though several experiments were of extreme importance to the research in UHECRs, the Pierre
Auger Observatory (PAO) is expected to help in the solution of some of the above mentioned puzzling
questions. Indeed, by the end of this year (2007), when fully operational, the Observatory will become, by
far, the largest cosmic ray experiment ever and is supposed to benet from the use of a hybrid technique
that combines the two most successful detection types in the eld. The PAO comprises both a Surface
Detector (SD), that samples the shower lateral prole at the ground, and a Fluorescence Detector (FD),
that records the light emitted during shower development. Moreover, as proved by earlier experiments,
the control of systematics in a ground-based observatory is vital and, thus, the Pierre Auger Observatory
is equipped with several complementary systems to monitor the atmosphere and estimate systematic
uncertainties.
The research in UHECRs undergoes today a very exciting period since the quantity and quality
of the experimental data gathered until now are on the verge of allowing thorough tests of theoretical
models. And the theoretical relevance of this eld spans dierent branches, including particle physics,
astrophysics, cosmology and fundamental physics.
The present work introduces a three dimensional method for the reconstruction of extensive air showers
using the Fluorescence Detector at the Pierre Auger Observatory. As an application, the measurement of
shower lateral proles is performed in simulation and data. Part of the work developed during the thesis is
subject of a poster accepted for presentation at the 30th International Cosmic Ray Conference (Mérida,
México) in July 2007 and of an oral presentation to be held at the 6th New Worlds in Astroparticle
1
Physics (Faro, Portugal) in September 2007. The structure of the thesis is organised as follows. Chapter
2 contains a brief review on the most important UHECR features. The indirect detection techniques are
then explained in chapter 3 where a short summary of the present observations is presented as well. The
fourth chapter is dedicated to a description of the Pierre Auger Observatory with special emphasis on the
Fluorescence Detector. In chapter 5 the 3D reconstruction procedure is proposed and chapter 6 follows
with the measurement of shower lateral proles in both simulation and data. Finally, chapter 7 draws
the main conclusions and the future prospects of the work developed.
2
Chapter 2
UHECR within the cosmic ray eld
According to a broad denition, cosmic rays are energetic particles of extraterrestrial origin that hit the
top of the atmosphere of the Earth. They include many kinds of particles, both charged and neutral,
namely protons, atomic nuclei, electrons, antiprotons, positrons, photons and neutrinos [1, 2].
At low energies (. 1014 eV), the relative composition of cosmic rays is well known: they are mostly
protons and there are signicant quantities of He, C, N, O, Si and Fe nuclei [3]; minimal amounts of
nuclei heavier than Fe are also present [2]. The Sun is the main source of low energy cosmic rays as it is
the most signicant astrophysical object in the neighbourhood of our planet. Indeed, the abundances of
elements found in this energy range follow the solar composition except in some cases where spallation
prevents the elements from arriving at Earth.
In the intermediate range 1014 eV . E . 1018 eV , the composition still remains subject of contro-
versy, while the sources of these cosmic rays are believed to be the sun and supernova remnants in our
galaxy.
At ultra high energies, which may be understood as E & 1018 eV although there is not a strict
denition, the panorama is quite dierent. There are both technical diculties in the detection of
UHECR and theoretical challenges to explain their existence. Up to now the composition of this kind of
cosmic rays is poorly known and there are no identied sources. It is, therefore, an interesting and open
area of physics, with tight bounds to high energy particle physics and to astrophysics as well.
2.1 Energy spectrum
The energy of the cosmic rays detected up to now spans 15 orders of magnitude: from 106 eV to 1020 eV
[2]. The spectrum for energies above 108 eV is shown in gure 2.1 and it exhibits 33 orders of magnitude
in ux. In fact, while cosmic rays of 1011 eV are seen at a rate of 1 m−2s−1, those of 1018 eV only hit
Earth at 1 km−2yr−1 ' 3 · 10−14 m−2s−1. This outstanding range both in energy and in ux is simply
due to the wide variety of cosmic ray sources, from the Sun to extragalactic objects.
The spectrum is well tted to a simple power law [2]:
dN
dE∝ E−γs (2.1)
where γs is called the spectral index. Overall, γs is close to 3, but there are two major deviations: the
so-called knee at 5 · 1015 − 5 · 1016 eV and the ankle at about 1018 eV.
For E . 1015eV, the spectral index is approximately 2.7. This region includes cosmic rays coming
from the Sun and other galactic sources such as supernova remnants. Then, at the knee region there is a3
Figure 2.1: Energy spectrum of cosmic rays above 108 eV [2].
gradual increase of γs up to 3.0; the ux presents now a quicker decrease with energy and this behaviour
remains until the ankle. Besides, as energy increases, the lighter components gradually disappear, because
they are the rst not to be conned by the galactic magnetic eld. This is due to their greater magnetic
rigidity E|q| . Indeed, a particle of charge q and rest mass m under a magnetic eld B perpendicular to the
particle velocity v feels a radial force given by F = |q|vB = γmv2
r , where r is the radius of the trajectory.
Since p = γmv and E2 = p2c2 +m2c4,
r =√E2 −m2c4
|q|Bc' E
|q|Bc(2.2)
The approximation is valid at knee energies for all known particles because E mc2. Thus, lighter cosmic
rays are usually less charged and r is greater − they are less bounded to the galaxy by its magnetic eld.
At the ankle, there is a decrease of the spectral index back again to 2.7 − the spectrum attens.
Although there is no consensus about this feature, the ankle is believed to correspond to a transition
from galactic to extragalactic sources: at these energies not even the heavier nuclei (such as Fe) are
conned to the galaxy 1 . And this energy range originates so high magnetic rigidities that the particles
roughly point back to their sources. Then, if cosmic rays of E & 1018 eV are mainly from galactic origin,
1The transition implies a decrease in the galactic component rather than its disappearance, since galactic ultrahigh energy cosmic rays may still hit Earth although less bounded to the galaxy.
4
there should exist anisotropy to the galactic plane from events above the ankle. As for ultra high energy
composition, protons are feasible candidates because heavier nuclei are more likely to interact or lose
energy while crossing the interstellar space. Nevertheless, this is still an open question.
Finally, at energies beyond 1019 eV there is no sucient statistics to recognise any feature in the
spectrum [2]. However, some refer a third irregularity − the toe − even though its cause is not yet clear.
2.2 Theoretical problems
The ultra high energy regime gives rise to two main theoretical dilemmas. On the one hand, it is
challenging to explain how particles travel cosmological distances through interstellar space and arrive at
our planet with such impressive energies − this is the propagation dilemma. On the other hand, there is
the question of production and acceleration of particles up to multi-joule energies.
2.2.1 Propagation
The rst requirement one should impose on UHECR candidates is that they are stable and present
minor losses of energy while propagating. Among known particles, natural possibilities are then protons,
electrons, photons, neutrinos and atomic nuclei.
These particles, except for neutrinos, must undergo a cuto mechanism that is based on simple,
well-established results from particle physics. The rst intervenient of this mechanism is the cosmic
microwave background (CMB), discovered by A. Penzias and R. Wilson in 1966. It consists of almost
isotropic radiation with an energy spectrum very similar to that of a black body at TCMB ' 2.73 K,
presenting a mean wavelength < λCMB >' 1.96 mm which corresponds to a mean energy < ECMB >=hc
<λCMB>' 6.34 ·10−4 eV [1]. Because of its isotropy, the CMB should be scattered uniformly around the
universe so that travelling particles are in contact with it. In this way, little after the discovery of the
CMB, K. Greisen and (independently) G. Zatsepin and V. Kuzmin [4, 5] used well-known results from
special relativity to predict that suciently energetic protons interact with the CMB and lose part of
the initial energy. They found a minimum initial energy of the proton above which the interaction may
occur − the so-called GZK cuto.
Let us analyse, for instance, the process pγCMB → pπ0, where < ECMB > is the supposed energy
of the cosmic photon 2 . The threshold condition for this reaction to occur states that the nal proton
and the pion must be at rest in the center of mass reference system, that is, s = (mp +mπ0)2. Since
pCMB =< ECMB > and pp = βpEp (βp is the initial proton velocity in c units), one also computes the
center of mass energy as
s = (pCMB + pp)µ (pCMB + pp)µ = (< ECMB > +Ep)
2 − (~pCMB + ~pp)2
= m2p + 2 < ECMB > Ep (1− βpcosθ) (2.3)
where the calculation was performed in the laboratory reference system and θ is the angle between the
initial proton and the CMB photon. The GZK cuto is found by restricting (2.3) to the threshold
condition:
EGZKp =m2π0 + 2mpmπ0
2 < ECMB > (1− βpcosθ)(2.4)
2The cosmic microwave background radiation presents an energy spectrum spanning all positive energies, butit is fairly concentrated over its mean value, < ECMB >. So, it is reasonable to consider the referred process withγCMB of energy < ECMB >.
5
Considering frontal collisions (θ = π) and UHE protons (βp ' 1), EGZKp ' 1.07 · 1020 eV. As seen
above, the center of mass energy is√s = mp + mπ0 ' 1073 MeV, which is inside the energy range
of standard particle accelerators. Consequently, the total cross section σ(pγ → pπ0
)can be obtained
experimentally and, nally, the mean free path of the proton (the distance it travels before interacting
with a photon from CMB radiation) is given by Lp =[nCMB · σ
(pγ → pπ0
)]−1, nCMB being the CMB
photon density. Using nCMB ' 411 cm−3 [1] and σ(pγ → pπ0
)' 200 µb [4], one gets Lp ' 1.22 · 1023
m' 3.95 Mpc (1 pc' 3.26 light-years). On average terms, after this distance the proton interacts and
loses 0.13 of its initial energy [4]. It continues interacting on 3.95Mpc intervals until its energy falls below
the GZK cuto, as gure 2.2 shows. The main conclusion from gure 2.2 is that, independently of the
source energy, the proton cannot travel more than ∼ 100 Mpc [2] with post-GZK energies; in other words,
the universe is opaque to protons of energies greater than the GZK cuto. Therefore, protons arriving
at Earth with post-GZK energies must come from a source situated less than ∼ 100 Mpc away.
Figure 2.2: Degradation of proton energy during propagation through the universe [2].
Of course, the GZK mechanism is of statistical nature. It is possible that a proton from a source
several Gpc away hit the atmosphere with post-GZK energies, but that constitutes an extremely unlikely
scenario. The GZK eect foresees, in fact, a sharp decrease, rather than an uncontinuous cut, on the
cosmic ray spectrum for extremely high energies.
For the process pγCMB → pπ0, analysed in the previous paragraphs, one should consider as well the
∆+(1232MeV ) resonance, pγCMB → ∆+ → pπ0, which yields EGZKp ' 2.51 · 1020 eV. Moreover, there
are other reactions to take into account when studying the proton GZK cuto, such as pγCMB → nπ+
and pγCMB → e+e−p, with EGZKp ' 1.12 ·1020eV and EGZKp ' 7.57 ·1017eV, respectively. However, their
cross sections are low in comparison to that of pγCMB → pπ0 and so the latter is the most important
process in the proton case. Notice that the above referred reactions are all possible with photons other
than those of CMB − the importance of the CMB steams from being uniformly spread around the
universe and not locally clustered as other kinds of electromagnetic radiation.
6
A GZK-like mechanism also applies to photons(γγCMB → e+e−, E
′GZK′
γ ' 4.12 · 1014 eV)and to
nuclei whose nucleons are lost by spallation on CMB [6]. As for neutrinos, they do not couple directly
to photons according to the standard model since they are neutral and then, in principle, they do not
interact with CMB photons. There are higher order diagrams for the dispersion νγ → νγ but they have
low amplitudes due to the several vertices present. But neutrinos may suer a GZK-like eect due to the
existing cosmic neutrino background formed in the expansion of the universe. In fact, extremely energetic
neutrinos can interact with the just mentioned relic background that, considering all three neutrino
avours, presents a mean density nνr = 3 · 311nCMB ' 336 cm−3, a temperature Tνr =
(411
)1/3TCMB '
1.95 K and a mean energy < Eνr >∼ 10−4 eV [7]. Considering the annihilation ννr → Z0, one gets a
GZK cuto several orders of magnitude above the proton GZK cuto: E′GZK′
ν ' 2.08 · 1025 eV.
The GZK paradox consists in the fact that several events with energies above 1020 eV were detected
and that there are no candidate near sources. Indeed, a source of such extreme energies should be easily
visible to astronomers, that cannot nd a candidate source of multi-joule cosmic rays within ∼ 100 Mpc
of the Earth. A rst solution to this paradox is to consider that post-GZK cosmic rays are mainly
neutrinos, although it is not commonly accepted that neutrinos are responsible for such a signicant
quantity of events. Moreover, neutrinos cannot be accelerated by known physical processes. Thus, they
must come from the decay of particles with even higher energies, which leads to the next challenge −that of understanding how particles can reach ultra high energies.
2.2.2 Acceleration and production
Two dierent types of models attempt to explain the existence of ultra high energy particles: bottom-up
scenarios, which deal with acceleration processes, and top-down models, that involve the decay of super
massive particles.
As for bottom-up scenarios, particle acceleration is achieved through electromagnetic processes, which
must follow a primitive requirement: the particle, of charge q, must be conned to the acceleration site
of typical dimension R and average magnetic eld B. Equivalently, Emax ' |q|BcR [1, 3], as in equation
(2.2). Above this energy the particle abandons the site and cannot be further accelerated. Typical
processes of acquiring energy are synchrotron-like ones, where particles are accelerated by electric or
variable magnetic elds and their trajectories bent by magnetic elds. This phenomenon may occur in
astrophysical sites, but there are signicant energy losses to take into account [2]. Besides, there exist
other more complex acceleration mechanisms that may take place in a large number of astronomical
sources. These sources can accelerate particles up to a certain maximum energy according to their
BR product; however, it seems extremely dicult to nd cosmological objects able to hit 1020 eV even
disregarding the GZK feature.
The top-down models look at the ultra high energy question through a dierent angle. These models
are based on super massive particles (of masses up to ∼ 1025 eV [6]) presumably originated in the early
universe and that managed to survive until now. The decay of such particles would produce several mesons
and hadrons; charged mesons yield neutrinos (π+(π−) → l(l)νl(νl)) while neutral mesons yield photons
(π0 → γγ). Therefore, top-down models usually foresee large uxes of ultra high energy neutrinos and
photons rather than protons and nuclei. This feature is quite dierent from the previsions of bottom-up
scenarios and it is an useful feature to test dierent models.
7
2.3 Relevance
The research in the UHECR eld is relevant to several areas of modern physics, namely particle physics,
astrophysics, cosmology and fundamental physics.
In the particle physics eld, the study of UHECR makes possible the study of reactions at high√s.
Indeed, considering in the laboratory reference system a particle of mass m1 and energy E1 hitting a
target particle of mass m2 at rest, s = (p1 + p2)µ (p1 + p2)µ = m21 + m2
2 + 2m2E1. If the two particles
are protons and the moving one has an ultra high energy of E1 ∼ 1019 eV, then√s ∼ 137 TeV, while in
the Large Hadron Collider (LHC) the same collision will be possible up to√s ∼ 14 TeV or, equivalently,
E1 ∼ 1017 eV. Of course, the main setback in cosmic ray physics is that the uxes and energies observed
cannot be controlled as in a particle accelerator.
As for astrophysics, since UHECRs point back to their origins, important sources can be further
studied and acceleration mechanisms understood. New astronomy channels may be opened soon and
there is also the possibility of performing cosmology studies as UHECR are potential messengers of
earlier stages of the universe.
Finally, a wide variety of fundamental physics models, such as SUSY, extradimensions and Lorentz
violation, may be tested using UHECR data.
8
Chapter 3
UHECR detection
The detection of cosmic rays with energies below 1014 eV may be direct [2] since the ux is high at that
energy range. Indeed, as pointed out in section 2.1, cosmic rays of 1011 eV arrive at a rate of approximately
1 m−2s−1, which means that small detectors are enough to gather signicant statistics. However, at low
energy, the atmosphere makes ground-based experiments inadequate and therefore balloon or satellite-like
detectors are required. A modern example of this kind of detectors is the Alpha Magnetic Spectrometer
2 (AMS2), which is planned to be installed in the International Space Station by 2009 and that will be
able to measure the energy and the direction of charged cosmic rays and photons.
At energies above 1014 eV there is a fortunate combination of two factors that calls for an indirect
detection. On the one hand, the low ux (roughly 10 m−2day−1 for E > 1014 eV [2]) demands for great
exposure areas that cannot be easily launched above the top of the atmosphere. On the other hand,
cosmic rays of this energy range hit the atmosphere and originate the so-called extensive air showers
(EAS). These showers may be detected by ground-based experiments whose main challenges are the
reconstruction of energy, nature and direction of the primary particle, the original cosmic ray.
3.1 Extensive air showers
High energy cosmic rays (E & 1014 eV) interact with atmospheric nuclei typically on the top of the
atmosphere and originate large cascades of dierent kinds of particles − the extensive air showers. In this
process the atmosphere works as a calorimeter: it gradually absorbs the energy of the created particles.
But it is much more complicated than a lead calorimeter, because of the quite variable density and loads
of meteorological phenomena to take into consideration. Note as well that some kinds of cosmic rays,
like neutrinos, have such a small interaction cross section that may not interact in the atmosphere and
go undetected.
The dynamical features of an EAS are best parameterised by the slant depth X measured in gcm−2:
X(~r0, ~r) =∫ ~r
~r0
ρ (~r′) d~r′ (3.1)
where ρ is the density of the atmosphere and ~r0 is the rst contact point of the cosmic ray with the
atmosphere. Usually X is computed as a function of the altitude h of the point ~r and the zenith angle θ
of the trajectory using the approximation
X '∫∞hρ(h)dhcosθ
≡ Xv
cosθ(3.2)
which is valid for almost vertical showers. The slant depth is more convenient to use than a simple
distance because of the variable atmospheric density. As a reference, a vertical shower crosses a slant9
depth of approximately 1000 gcm−2 until it reaches sea level, while a skimming one traverses up to 36000
gcm−2.
3.1.1 Electromagnetic showers
Electromagnetic showers are the ones originated by photons, electrons or positrons and are fed mainly
by two electromagnetic processes: bremsstrahlung (e± → e±γ), where the electron (or positron) is
deaccelerated in the presence of electromagnetic elds and radiates, and pair production (γ → e+e−),
where a photon of energy higher than 2me ' 1022 KeV creates a pair electron-positron in the presence
of matter (the atmospheric nuclei) for momentum conservation. These processes create a chain reaction
that evolves until the electrons and positrons start to lose their energy essentially by collisions rather
than by bremsstrahlung radiation. From that moment on, the creation of new generations of particles
stops and the cascade declines.
The development of electromagnetic showers is fairly described by Heitler's model, illustrated in gure
3.1. This very simple but meaningful model denes several splitting levels separated by a length d; at
each level the reactions γ → e+e− and e± → e±γ are assumed to occur with equal distribution of energy
and in an elastic manner [8]. The length d is given by d = Xlln2 (Xl ' 37 gcm−2 being the radiation
length of the electron in the air) since that is precisely the length after which the electron has lost half
of its initial energy − in fact, Ee(X) = Ee(X0)e−(X−X0)/Xl . Therefore, according to the model, at a
certain slant depth
Xj = jXlln2 (3.3)
there are N = 2j particles in the cascade (electrons, positrons and photons) all of which with an energy
E0/2j , where E0 is the energy of the primary particle. This behaviour ends when the shower hits its
maximum or, in other words, when E0/2j falls below ε0, the critical energy 1 . In this way, one may
calculate the primary energy if one knows the number of particles Nmax at shower maximum Xmax:
E0 = ε0Nmax (3.4)
Moreover, (3.3) and (3.4) together yield
Xmax = jmaxXlln2 = log2NmaxXlln2 = ln
(E0
ε0
)Xl (3.5)
Equations (3.4) and (3.5) contain the two most important previsions of Heitler's model: (a) the
number of particles at shower maximum is proportional to the primary energy and (b) the slant depth of
shower maximum presents a logarithmic increase with the primary energy. Nevertheless, the model tends
to overestimate the number of electrons in the shower [8]. For further information in electromagnetic
shower development detailed simulation is needed.
3.1.2 Hadronic showers
Hadronic showers are originated by the interaction of a primary nucleon or nucleus with atmospheric
nuclei. Part of the primary energy is converted by strong interaction in secondary mesons [1] − almost
entirely charged and neutral pions and some kaons as well. The remaining energy goes to secondary
nucleons that will initiate other showers. The pions produced during the cascade may either decay or
interact depending on their energy. The decay length is given by Ldecay = cγτ = Eτmc (in m), while the
1Energy at which the electron energy loss by bremsstrahlung and by ionization are equal. Following [12, 13],the electron critical energy in air is ε0 ' 81 MeV.
10
(a) (b)
Figure 3.1: The Heitler's model in electromagnetic cascades (a) and in hadronic showers (b) [8].
interaction length for pions in air is Xπint ' 120 gcm−2 for Eπ < 1014 eV [1, 8]. The determination of
the dominant process for a specic energy is performed comparing Xπint to Ldecay, both in gcm−2 units.
Anyway, due to their very short mean life, π0 essentially decays: π0 → γγ. The resulting photons start
sequential electromagnetic subshowers, feeding the electromagnetic component of the cascade. As for
charged pions, their mean life is suciently large to allow that some, low energy ones, decay and the
others, high energy ones, interact. Decaying charged pions originate mainly muons and muon neutrinos
[9] (π+(π−) → µ+(µ−)νµ(νµ)) giving rise to the muonic component. Finally, the charged pions that
interact with atmospheric nuclei originate 13 π0 and 2
3 π± [1], continuing the hadronic component. As
the shower evolves, the energy of charged pions decreases and more and more of them decay instead of
interacting. That is why in a hadronic shower there are more electrons, positrons, photons, neutrinos and
muons than hadrons. Specically, for each hadron in the cascade there are in mean terms ∼ 102 muons
and neutrinos and ∼ 104 electrons, positrons and photons [10].
As in the electromagnetic case, the hadronic shower hits a maximum, characterised by Xmax and
Nmax, when the charged pions energy falls below the energy at which decay and interaction occur with
equal probability. Although these showers are complex, a modied Heitler's model may be applied using
Xπint instead of Xl [8]. Again, shower simulation codes, such as CORSIKA (COsmic Ray SImulations for
KAscade), are needed to study hadronic shower development with more detail.
The distinction between proton (hadronic) and photon (electromagnetic) initiated showers of the same
primary energy is achieved considering that proton cascades present Xmax lower than photon ones.
3.2 Indirect detection
Indirect detection of UHECR is possible through the measurement of EAS features. Two dierent kinds
of detection techniques are usually implemented: ground arrays, that sample the transverse prole of the
cascade at the surface level, and light detectors, that record the light emitted during the development of
the EAS.
3.2.1 Ground arrays
Ground arrays are sets of individual particle detectors scattered around Earth surface and that can
cover considerably large eective areas. The detectors may be electromagnetic (sensitive to photons and
electrons), muonic or hadronic − usually scintillators and/or water erenkov tanks are used [11]. This
11
technique presents a threshold energy of approximately 1014 eV since only high energy cosmic rays are
able to originate air showers large enough to detect at the ground. Moreover, the target energy range
of a ground array experiment determines the optimal altitude of the site: the shower maximum should
occur just above the array in order to measure greater quantity of particles with less uctuations [1].
Therefore, EAS of primary energies of 1014−1015 eV are best recorded at high altitudes, while ultra high
energy cascades should be detected at lower altitudes − otherwise, the shower maximum is missed and
the reconstruction becomes dicult.
As an EAS crosses the experiment site, each detector measures a particle density as exemplied in
gure 3.2; to convert this information into the transverse prole of the cascade its direction is needed. At
rst approximation, the air shower is a at disk propagating at the speed of light as a plane front and,
thus, the hit time and the position of the individual detectors are used to calculate this direction. In
practice, however, one must take into account a more realistic propagation shape, which is curve rather
than at. Given the direction, the measured densities may be tted to a transverse prole − whose
specic parameterisation is highly inuenced by the experiment conguration − and the shower core
is determined. Afterwards, the detectors that deviate from the tted prole may be excluded and the
process of determination of shower direction and shower core is repeated iteratively until it converges.
Figure 3.2: A ctious event as recorded by a ground array [1].
In what refers to primary energy reconstruction, one usually turns to shower simulation that demon-
strates that the particle density at a certain distance from the shower axis is roughly proportional to the
primary energy and that this behaviour is almost independent from the primary mass number. So, the
measured particle density at 500 − 1000 m from the axis yields the primary energy estimate through a
constant of proportionality given by Monte Carlo calculations.
Finally, the nature of cosmic rays is not straightforward to determine, although a hint on the primary's
mass number is given by the relative abundance of the muon component on the EAS: the bigger this
relative abundance, the heavier is the primary.
Some setbacks are inherent to the ground array detection technique. For instance, it is not possible to
perform direct studies on the longitudinal development of the shower. Besides, the energy reconstruction
is based on Monte Carlo simulations, which assume that the primary nature is known and use extrapolated
cross sections from low energy calorimeter measurements. Another disadvantage is the non-reliability in
the determination of the cosmic ray nature. However, ground arrays are not strongly inuenced by
meteorological, atmospheric nor luminosity conditions and, thus, can make measurements continuously
12
presenting a duty cycle of virtually 100%. Adequate rst estimates on primary energy and on shower
direction are also advantages of the ground arrays [2].
One of the most signicant ground array experiments was the Akeno Giant Air Shower Array (AGASA),
situated in Japan. The site covered a total area of approximately 100 km2 with 111 surface detectors
of 2.2 m2 each separated by ∼ 1 km and 27 underground muon detectors [14]. AGASA studied most
features of UHECR, in particular the far end of the cosmic ray spectrum.
3.2.2 Light detectors
The development of air showers through the atmosphere gives rise to the emission of two kinds of elec-
tromagnetic radiation that may be collected by optical devices on the ground: erenkov and uorescence
light. The production and attenuation of these types of light are controlled by the atmosphere, which is
an integral part of ground-based light detectors. Therefore, in the next paragraphs relevant atmospheric
properties are detailed to some extent, before describing erenkov and uorescence detection techniques.
Light production and attenuation in the atmosphere
As stressed above, an extensive air shower crossing the atmosphere emits both uorescence and erenkov
light. The uorescence depends only slightly on atmospheric characteristics, but most shower parame-
ters are functions of the atmospheric temperature, pressure and/or density. These variables have well-
understood behaviours with height and are adequately described by models such as the US standard
atmosphere.
In this section, the production of erenkov and uorescence light is briey described as well as the
most inuent scattering processes, Rayleigh and Mie, that are responsible for both the existence of
scattered erenkov light and the attenuation of electromagnetic radiation from its emission point until
the detector.
erenkov light erenkov radiation is emitted by charged particles while travelling in a medium of
refraction index n at a speed v greater than the phase velocity of light in the medium, cn . It is emitted on
a cone along the propagation direction with maximum opening angle θ = arcos(c/nv
). In an extensive
air shower most charged secondary particles travel almost at the speed of light in vacuum c and so, as
nair ' 1.0003 [1], θ ' 1.4. Although the mentioned value for nair corresponds to the refraction index of
the air at sea level, it is useful in getting a rst approximation on the erenkov opening angle. However,
due to the charged particles transverse momentum, erenkov light is seen at the ground with an angle
up to ∼ 20 with respect to shower axis in the case of UHE protons [12].
Atmospheric nitrogen uorescence Another remarkable process occurs as an EAS develops in the
atmosphere: the shower charged particles excite N2 molecules and N+2 ions that afterwards return to
their ground states by isotropic emission of electromagnetic radiation in the ultraviolet and visible bands.
This phenomenon is called scintillation [21], but the above described radiation is known in the cosmic ray
eld as uorescence light even though uorescence is the process in which an atom or molecule absorbs
photon(s) of certain wavelength λ and re-emits photon(s) of λ′ > λ. When the charged particles of an air
shower excite the atmospheric nitrogen (N2 and N+2 ), two competing phenomena may occur: either the
excited molecules collide with other atmospheric components such as the oxygen or they emit uorescence
light, in the 300-400 nm band. In this wavelength range, N2 and N+2 are indeed the main contributors to
13
uorescence production and their spectrum, shown in gure 3.3, presents three strong spectral lines: at
337 nm, 357 nm and 391 nm [12].
Figure 3.3: The uorescence spectrum of the atmospheric nitrogen [12].
But the nitrogen uorescence spectrum is not enough to reconstruct the shower longitudinal prole:
one needs to relate the photons produced with the charged particles in cascade development. This relation
is accomplished by the uorescence yield yfγ that is approximately 4 γ/e/m in the 300-400 nm band
[12, 20]. It has a mild dependence on atmospheric density and temperature and it may be parameterised
through the energy deposited by the shower along its longitudinal development.
Rayleigh scattering When an electromagnetic beam crosses a gas, it is scattered o by the gas'
molecules and/or atoms − if the size of these scattering centres is small in comparison with the beam
wavelength λ, then Rayleigh scattering takes place presenting a cross section proportional to λ−4. As-
suming dNγ photons crossing the atmosphere along the path dl, their extinction rate due to Rayleigh
scattering is given by [16]:dNγdl
= −ρNγXR
(400nmλ
)4
(3.6)
being XR = 2974 gcm−2 the characteristic Rayleigh pathlength [18]. The radiation is preferentially
deected in the forward and backward directions according to the angular distribution [17]:
d2NγdldΩ
=3
16π(1 + cos2θ
) ∣∣∣∣dNγdl∣∣∣∣ (3.7)
where θ is the angle between the original beam direction and the scattered one.
Since dX = ρdl (confer (3.1)), the integration of (3.6) results in Nγ (X2) = Nγ (X1) e−|X1−X2|XR
( 400nmλ )4
,
where 1 and 2 refer to the initial and nal points of the trajectory, respectively. Or in terms of a
transmission coecient:
TR = e− |X1−X2|
XR( 400nm
λ )4
(3.8)
Mie scattering The Mie scattering occurs when the scattering centres have sizes similar to the wave-
length of the radiation and this is, for instance, the case of UV light crossing the aerosol content of the
atmosphere. Aerosols are natural and human-made particles with various sizes and dierent vertical den-
sity proles, namely low altitude clouds, pollutants and dust. The Mie cross section is not as dependent
14
on the wavelength λ as the Rayleigh one is and its extinction rate is [16]
dNγdl' −Nγe
− hhM
lM (λ)(3.9)
where h is the height and hM and lM are characteristic distances of aerosol distributions. The angular
dependence, which is strongly peaked forward, is given by [16]:
d2NγdldΩ
' aM · e−θθM
∣∣∣∣dNγdl∣∣∣∣ (3.10)
with θM = 26.7. The parameter aM is forced to 0.891 so that∫ 2π
0
∫ π0aM · e−
θθM sinθdθdφ = 1.
The transmission coecient is obtained integrating (3.9):
TM = e− 1lM (λ)
∣∣∣∣∫ 21 e− hhM dl
∣∣∣∣ (3.11)
Following [16], hM ' 1.2 km and lM (λ = 400 nm) ' 14 km. With the approximation dl ' dh/cosθ′ (θ′
being the angle between the beam trajectory and the vertical), (3.11) yields:
TM = e− hMlM (λ)cosθ′
∣∣∣∣∣e− h1hM −e
− h2hM
∣∣∣∣∣ (3.12)
The Mie attenuation is specially important in polluted sites and within the rst ∼4 km of atmosphere.
Besides, the values given in this section for aM , θM , hM and lM must be understood as mean ones,
because the aerosol content of the atmosphere is highly variable in space and time. So, a large cosmic
ray experiment must have several regular atmospheric surveys in order to update such parameters in a
daily basis.
erenkov technique
Optical detectors may collect erenkov radiation directly if the shower approximately points at them
− otherwise, only Rayleigh and Mie scattered light can be observed. The main advantage of measuring
direct erenkov light is the substantial photon density that is greater than the electron density at the
ground and proportional to the number of charged particles created during shower development. Besides,
the analysis of the lateral distribution of this kind of radiation may be used in the estimation of the
shower maximum and primary energy.
A modern example of an imaging atmospheric erenkov telescope (IACT) is the Major Atmospheric
Gamma-ray Imaging erenkov (MAGIC) device, settled in the island of La Palma, Canarias, Spain and
taking data since late 2004 [19]. The rst telescope includes a 236 m2 mirror with 17 m of diameter and a
camera of 576 photomultiplier tubes (PMT) in order to image the erenkov light emitted during shower
development. A second telescope is now under construction. Rather than focusing on UHECR, MAGIC
is designed to study very high energy (VHE) gamma rays (1011 eV . E . 1014 eV ) that, being neutral,
suer no magnetic deection and enable the study of astrophysical sources.
Fluorescence technique
Since uorescence light is isotropic, it can be detected far away from the emission point [1] as long as
it is abundant enough − the threshold energy for uorescence detection is situated around 1017 eV. The
detectors usually consist of large mirrors that concentrate the collected light in a PMT camera whose
task is to divide the image into pixels, as shown in gure 3.4, and record the photon densities and arrival
times of each pixel. Therefore, this technique allows the imaging of the shower longitudinal prole.15
Figure 3.4: An air shower as seen by a uorescence detector [1].
Before, however, one has to proceed to the geometry reconstruction. Firstly, the positions of the
activated pixels are used to nd the shower-detector plane (SDP), that contains both the detector and
the shower axis. Then, if there is only one uorescence detector, the exact geometry of the axis within
the SDP is tted with the help of the pixels' arrival times. In the case of stereoscopic observations, i.e.
more than one uorescence detector triggered, the existing SDPs may be intersected to determine the
shower axis with better precision. Another way to improve the timing t necessary to single uorescence
detectors is to use the information given by a ground array that has seen the event.
Once the event geometry is xed, several factors must be taken into account to derive the shower
longitudinal prole from the raw signal received by the detector. To begin with, direct and scattered
(Rayleigh and Mie) erenkov light is calculated using the geometry and subtracted from the original
signal in order to obtain the uorescence fraction. This fraction must be corrected according to the solid
angle seen by the device because uorescence light is isotropic. Then, Rayleigh and Mie attenuation
undergone by photons while propagating from the emission point to the detector is considered − to
minimise this attenuation uorescence-based experiments are usually settled in non-polluted, dry places.
Besides, regular monitoring of atmospheric conditions (aerosol and cloud measurements in special) is
essential to compute attenuation in a precise manner. Lastly, using the uorescence yield, the number
of electrons in the shower as a function of the slant depth, Ne(X), this is the longitudinal prole, is
reconstructed, allowing the determination of Xmax and Nmax.
In what regards energy reconstruction, the total energy from the cascade electromagnetic component
is proportional to∫∞
0Ne(X)dX, being the constant of proportionality given by the electron mean loss.
But to nd the primary energy one has to estimate the so-called missing energy − the energy taken by
hadrons, muons and neutrinos, that are invisible to uorescence techniques. Although the calculation of
the missing energy is model-dependent, Monte Carlo simulations show that it represents less than 10%
at primary energies greater than 1018 eV. Figure 3.5 sketches the evolution of this undetected energy
both with primary nature and primary energy. The heavier the primary, the more important is the
missing energy. Indeed, at the same primary energy heavier nuclei present smaller energy per nucleon
and consequently the charged pions and other mesons produced are more likely to decay than interact
[1], thus feeding the muonic component which is almost invisible to uorescence detectors. Moreover,
as primary energy increases, the missing energy declines because the interaction of secondary mesons is
more probable and that feeds the electromagnetic, detectable component of the cascade. To sum up, at
16
ultra high energies the electromagnetic energy is a good estimate on the primary energy (within < 10%)
and that is why uorescence detectors are highly ecient for UHECR showers.
Figure 3.5: Percentage of missing energy for dierent energies and primaries as calculated in Monte Carlosimulations. Open circles represent proton showers, open squares He nuclei, lled circles CNO and lledsquares Fe [1].
Besides the high eciency just mentioned, the main advantage of uorescence techniques is the ability
to study the longitudinal prole which allows the calculation of Xmax. Nevertheless, this kind of detection
is extremely sensitive to atmospheric and meteorological conditions and may only be used in moonless
nights − about 10% of duty cycle. Moreover, one relies on simulations to estimate the missing energy
even though this may be much greater in showers initiated by exotic particles. Finally, as in the ground
arrays case, it is not possible to identify the primary nature on a event-by-event basis [2] since several
features of a shower, such as Xmax, present important statistical uctuations. Therefore, only a 'mean'
primary nature may be determined.
A successful example of a uorescence-based experiment was the Fly's Eye (then, High Resolution
Fly's Eye, HiRes), settled in the USA and operated from 1981 until 1993. Originally, it consisted of one
uorescence eye with 67 spherical mirrors of ∼ 1.6 m diameter corresponding to 880 PMTs with a 25 ns
time resolution. Each PMT covered a 5x5 eld of view in hexagonal-shaped pixels in order to maximise
light collection and achieve full coverage of the night sky [21]. In 1986 a second eye, with 36 mirrors
and situated 3.4 km away from the rst one, was installed allowing stereoscopic observations. Fly's Eye
is responsible for the knowledge of several features of UHE physics and for the detection of the most
energetic phenomenon ever recorded − 3.2 · 1020 eV.
3.3 Present status
There are currently three main topics in ultra high energy cosmic ray physics that still remain unanswered:
the energy spectrum, the composition and the arrival directions. This section will briey describe the
present status of observations at this energy range gathering data from dierent experiments, including
the Pierre Auger Observatory. The PAO comprises both a Surface Detector (SD) and a Fluorescence
Detector (FD), allowing the use of a hybrid technique that combines the two detection types described
in 3.2.
Over the last years, the energy spectrum at the highest energies has been thoroughly studied by
two major experiments, AGASA and HiRes. These groups present conicting results. For instance,
while HiRes sees the ankle at ∼ 3 · 1018 eV [21], AGASA seems to locate this structure at about 1019
17
Figure 3.6: The energy spectrum of cosmic rays with the conicting results from AGASA and HiRes inthe UHE range. The actual ux is multiplied by E2.5 to ease the visualisation of spectrum features [22].
(a) The ratio between the observed ux using HiResdata and the expected one if there were no GZK cuto[23]. There exists a clear break at about 1019.8 eV.
(b) The energy spectrum as measured by the PAOwith data prior to 2007 [30]. The three spectra pre-sented correspond to dierent sets of data: SD events,hybrid events and inclined showers (of zenith anglesgreater than 60).
Figure 3.7: The energy spectrum as measured by HiRes (a) and the PAO (b).
eV [1]. Figure 3.6 shows the cosmic ray spectrum as measured by several experiments. The actual
quantity represented is the ux times E2.5 to better distinguish spectrum features: little errors in energy
determination correspond to large errors in the yy axis. In the rst place, it is clear that AGASA predicts
a greater ux than HiRes in the whole UHE range. The dierence corresponds to 30− 40% of systematic
error in energy reconstruction [1, 3] which may be corrected if one assumes that AGASA overestimates
the event energy by ∼ 20% and HiRes underestimates it by ∼ 20%. These values are in agreement
with the expected systematic uncertainties for the two experiments [3]. Anyhow, AGASA results seem
to deny the existence of a GZK feature, whereas HiRes data is consistent with a GZK cuto at 1019.8
eV as represented in gure 3.7(a). The lastest Pierre Auger Observatory spectrum dates from 2007
[27, 28, 29, 30] and is shown gure 3.7(b). It seems to indicate a cuto above 1019.6 eV [30], altough there
are still signicant statistical and systematic errors. In what refers to events with energies above 1020 eV,
the AGASA group claims 11 events, but HiRes in single eye mode, with great exposure, detected only
one. As of 2007, the maximum primary energy recorded at the PAO was 1020.25 eV [30].
From this analysis it is obvious that the UHE spectrum may be further studied only with improved
statistics and a better control of systematic errors specially in energy reconstruction. The PAO is believed
to solve the statistics problem with the expected 60 events per year with energies above 1020 eV [3];18
besides, it has the necessary equipment to perform detailed monitoring of systematics.
The cosmic ray composition at the highest energies is still an open topic as well. In the knee region,
between 5 · 1015 eV and 1016 eV, several experimental groups conrm a shift to a heavier composition
[1]. On the contrary, the ankle signals the transition to a lighter cosmic ray trend, as pointed out in
section 2.1. On the one hand, uorescence-based experiments, such as HiRes, may study the composition
through the evolution ofXmax with the primary energy E0. Lighter cosmic rays are more likely to interact
deeper in the atmosphere (presenting a greater Xmax) than heavier ones. However, hadronic interaction
models predict a slope dXmaxdlog10E0
, the so-called elongation rate, almost independent from primary nature:
50-60 gcm−2decade−1 [1, 21]. As the elongation rate measured by HiRes is somewhat larger than these
values, one concludes that the composition at the ankle is becoming lighter and that UHECR are more
consistent with protons than with iron nuclei − see gure 3.8. On the other hand, ground arrays may
infer the composition through the relation between muonic and electromagnetic components: heavier
primaries initiate showers with more muons than those present in cascades originated by lighter cosmic
rays. AGASA does not conrm nor contradict a transition to a lighter component above the ankle [1].
Figure 3.8: The transition to a light composition trend that occurs in the ankle region [21]. The simulationresults from proton and iron showers are indicated by the upper and lower parallel lines respectively, whilethe full circles represent the experimental data.
Another important composition study is that of knowing the fraction of γ-initiated showers at ultra
high energies. Indeed, as stressed in section 2.2.2, such a study tests top-down models, since these
preview a signicant ux of ultra high energy photons. Two ground array experiments, Haverah Park
and AGASA, estimated an upper limit to the fraction of γ-initiated showers above 1019 eV obtaining 48%
and 28%, respectively [32]. As of 2007, the Pierre Auger Observatory data points at 13% [34]; this result
is determined by comparison between the mean values of some ground parameters observed in hybrid
data and the corresponding values from simulated photon showers. Using observed and simulated Xmax
also in hybrid data, the limit is set on 16% [35].
The distribution of arrival directions is the third hot topic in UHECR observations. As explained
in chapter 2, UHE charged particles have great magnetic rigidity and are deected up to a few degrees
from their initial directions, usually less than the angular resolution of the experiments designed to this
19
energy range [3]. Therefore, the distribution of arrival directions is meaningful in the study of cosmic
ray sources. As in the spectrum case, AGASA and HiRes present contradictory results. While HiRes
is compatible with an isotropic distribution, AGASA recorded 47 events with energy above 4 · 1019 eV
of which three doublets and one triplet [1]. Each set of events dier less than 2.5 in arrival direction.
Again, the statistics is still very low, but AGASA indicates a certain degree of anisotropy even if the
clusters directions do not seem to point at signicant astronomical sites. The rst PAO indications on
this subject [36, 37], dated from 2005, are consistent with isotropy. New results are expected within one
year.
20
Chapter 4
The Pierre Auger Observatory
The Pierre Auger Observatory 1 was proposed to the scientic community in 1992 by Alan Watson and
James Cronin in order to study the ultra high energy range with unprecedent statistics − about 60 events
per year with energies above 1020 eV [3]. The Observatory consists of two dierent sites: one in each
hemisphere, both situated at mid-latitudes. This geographical choice allows an uniform, full sky coverage
that is essential to anisotropy studies [11]. The northern site will be located in Lamar, Colorado, USA,
but still undergoes an early phase prior to construction. The southern site is situated on the Pampa
Amarilla near the Andes − Malargüe, Province of Mendonza, Argentina − at about 1400 m above sea
level. It is now in an advanced stage of construction and, when fully operational (by the end of 2007), it
will enclose a total area of 3000 km2. The whole present work refers uniquely to the southern site.
The innovative character of the PAO steams from the use of a hybrid technique. Indeed, the southern
site, represented in gure 4.1, comprises a ground array of 1600 water erenkov tanks (the so-called
Surface Detector, SD) and a set of 24 telescopes placed into four uorescence eyes (the Fluorescence
Detector, FD), combining the two most successful UHECR detection techniques, described in section 3.2.
Therefore, the PAO is able to study longitudinal and lateral proles of cosmic ray showers presenting the
advantages of both detection types. In addition, an improved geometrical reconstruction is achieved for
hybrid events − those simultaneously seen by the SD and the FD. Moreover, these events may be used to
perform a calibration in energy between both techniques. Such a calibration frees the PAO from Monte
Carlo simulations (vastly used in ground array experiments) and may explain why the results obtained
so far with ground arrays and uorescence detectors, such as AGASA and HiRes respectively, do not
coincide. However, the hybrid detection requires the synchronisation between the Surface Detector and
the Fluorescence Detector, which is a sensitive task.
Finally, the control of systematics, as pointed out in 3.3, plays a decisive role in cosmic ray data
analysis. The Pierre Auger Observatory is, thus, equipped with several complementary systems to monitor
the most signicant atmospheric eects and estimate accurately the systematic uncertainties, unlike most
earlier experiments.1Pierre Auger was the French scientist responsible for the concept of ground arrays: he detected particles
arriving at the ground in coincidence and separated by several meters. In 1939, Auger also proved the existenceof 1015 eV cosmic rays.
21
Figure 4.1: The Pierre Auger Observatory southern site in Argentina [24]. The dots represent SD tanks,while the lines show the eld of view of the FD telescopes. As of 31st March 2007, 1215 tanks and all 24telescopes were fully installed and operational [39].
4.1 Southern site description
4.1.1 Surface Detector
The Surface Detector is an 1600 water erenkov tanks array in an 1.5 km spacing triangular grid covering
an area of roughly 3000 km2. The grid spacing was chosen to achieve full eciency (ve triggered tanks)
at 1019 eV, even though 3 · 1018 is enough to achieve it for non-horizontal showers [24, 11]. As of 31st
March 2007, 1297 tanks were positioned in the eld, 1272 lled with water and 1215 with electronics
installed [39].
Figure 4.2: A water erenkov tank of the Surface Detector [24].
Each water erenkov tank − see gure 4.2 − is a 10 m2 base, 1.5 m tall plastic cylinder lled with 12
m3 of puried water up to an 1.2 m height [24, 41]. The inner surface of the tank presents high reectivity
to maximise the collection of erenkov light, which is done by three 9 inch PMTs located on the top. The
electronics apparatus is powered by two 12 V batteries charged by two solar panels. The connection to
the Central Data Acquisition System (CDAS) is set up through a communication antenna and the timing22
information is obtained from a GPS unit. The whole tank was designed to be highly robust in order to
face the extreme environment of the Pampa: dust, sand, rain, hail, snow, salinity, humidity, wind and
day-night temperature variations of 20C.
When an EAS crosses the SD, charged shower particles travel in the water of the tanks at a speed
greater than the phase velocity of light in the medium, thus emitting erenkov light. Photons are
not charged but, when crossing a depth in water of ρwater∆l ' 1 gcm−3 · 1.2 m = 120 gcm−2 which
corresponds to ∼ 3.2 radiation lengths (see section 3.1.1), almost all convert into relativistic electron-
positron pairs that radiate erenkov light. This light is collected by the three PMTs and the signal
is analysed in terms of vertical equivalent muons (VEM), i.e. the average charge deposited by a high
energy vertical down-going muon. In this way, only the neutrino part (and eventually an unknown
neutral, weakly interacting fraction) of the shower goes undetected. Besides, the discrimination between
muons and electrons or photons is possible: muons are less scattered in the atmosphere producing earlier,
quicker and higher amplitude signals when compared to those of electrons or photons [1]. Finally, to
select potentially physical events several triggers in time, space and quality are applied (see, for instance,
[11]) and, afterwards, interesting events are sent to the CDAS.
4.1.2 Fluorescence Detector
The Fluorescence Detector comprises four sites located on the top of small hills in the array's boundaries:
Los Leones, Los Morados, Loma Amarilla and Coihueco. Each site houses a six telescopes uorescence eye
overviewing the array 180 in azimuth and 28.6 in elevation [42]. The communication with the CDAS
and the SD is established through the antenna tower built on each uorescence site. Data taking began
at Los Leones and Coihueco eyes in January 2004 and at Los Morados in March 2005, while the Loma
Amarilla eye was only nished by February 2007 [42, 38]. Besides the optical telescopes, the atmosphere
is an integral part of the Fluorescence Detector as well. Since it was characterised in 3.2.2, this section
will only present a detailed description of this telescopes.
The optical devices used in the FD, protected from rain and wind by individual shutters, are Schmidt
telescopes with a eld of view of 30 in azimuth and 28.6 in elevation [24]. As exemplied in gure 4.3,
each telescope consists of several separate parts.
First of all, an 80 cm x 40 cm ultraviolet lter is installed after the shutter in order to transmit in the
280-430 nm band, thus blocking visible light. The lter reduces the night background light and ensures
an acceptable signal-to-noise ratio. Moreover, it acts as a window protecting the devices from dust and
rain.
Then, the ultraviolet radiation crosses a circular diaphragm with a radius of 0.85 m that is surrounded
by a corrector ring with outer radius 1.10 m. The corrector ring, composed of 24 ultraviolet transmitting
glass segments, almost doubles the eective area and is constructed in such a manner that it allows a
good quality of the optics [43, 44].
Between the diaphragm and the mirror there is the 440 PMT camera (described below) that allows
the imaging of the shower prole. The light is collected by a 3.5 m x 3.5 m spherical mirror with 3.4
m of radius [43, 42] presenting a mean reectivity around 90% in the 300-400 nm band [44]. The large
dimensions of the mirror require that it consists of several segments − hexagonal and square-shaped
segments were chosen in order to maximise light collection and sky coverage.
The PMT signals are sampled in 100 ns time bins and are then subjected to two basic levels of trigger −see, for instance, [44] − that rule out random coincidences and select potentially physical events. Besides,
23
(a) Schematic representation [43]. (b) Detailed view of the PMT cameraon the right and the mirror with square-shaped segments on the left [24].
Figure 4.3: The Schmidt telescope used in the FD.
the telescopes must undergo several calibration processes so that the energy reconstruction accuracy is
better than 15% [42] − this requirement is of extreme importance in the study of the far end of the
cosmic ray spectrum as discussed in section 3.3.
PMT camera
The PMT camera lies on the spherical focal surface of the telescope and consists of a 6 cm x 94 cm x 86 cm
aluminum body supported by two legs and housing 22 rows x 20 columns of hexagonal PMTs [43]. Each
PMT corresponds to a pixel so that the camera presents a total of 22x20=440 pixels. Light collection is
maximised surrounding each PMT with six mercedes stars: these are inclined reecting surfaces designed
to direct ∼ 90% of the incident light into the centre of the PMT, thus smoothing the transition between
pixels.
As the camera lies on a spherical surface, the pixels are not regular hexagons in spherical coordinates
but have variable size in order to best cover the focal surface [44]. So, to ease the data analysis it is
convenient to dene a coordinate system in which the camera is rectangular and the pixels regular. The
new coordinates (β, α), proposed in [45], are represented in gure 4.4 and their relation to spherical
coordinates (θ, φ) is given by the equations:
β = arcsin (sin (φt − φ) sinθ) (4.1)
α = αc − αm + arcsin
(cosθ
cosβ
)(4.2)
where φt and αm = 16 are respectively the azimuth and the elevation angles of the telescope axis and
αc =√
3
2 is the oset angle between the camera centre and the telescope axis [46].
In these coordinates, each pixel of the camera is a regular hexagon of radius rpix =√
3
2 , side length
lpix =√
3
2 and side-to-side dimension dpix = 1.5 as shown in gure 4.5. The mercedes structures form
a similar inner hexagon scaled by 0.8. For each telescope, the camera is a 22 rows x 20 columns grid of
24
Figure 4.4: The (β, α) coordinates and their relation to spherical coordinates (θ, φ). In this particularcase, φt = 90 (adapted from [45]).
pixels whose central points have coordinates
βij =
1.5 · (10− i) if j odd
1.5 · (10− i) + 0.75 if j even(4.3)
αij = 1.5√
3
2· (j − 11) (4.4)
being i ∈ [1, 20] the column number and j ∈ [1, 22] the row number. The whole camera is represented in
gure 4.6 and, as αc =√
3
2 = rpix, the telescope axis centre coincides with the centre of a mercedes star.
Moreover, the camera limits in (β, α) are given by:
βmin = 1.5 · (10− 20)− dpix2
= −15.75 βmax = 1.5 · (10− 1) + 0.75 +dpix
2= 15
αmin = 1.5√
3
2· (1− 11)− rpix ' −13.86 αmax = 1.5
√3
2· (22− 11) + rpix ' 15.16
The eld of view of the camera is then 30.75 in β and ∼ 29.01 in α.
For practical reasons, each pixel must be labeled by a number Npix ranging from 1 to 440. Usually
the relation Npix = 22 · (i− 1) + j is used to dene the pixel number given the respective column i and
row j. Inversely, there are also unambiguous relations that yield the column and row given the pixel
number Npix: i = int[Npix−1
22
]+ 1 and j = mod [Npix − 1, 22] + 1.
Having the detailed camera description presented in the above paragraphs, one may convert the (θ, φ)
direction of an incident photon into the number of the pixel it hit and, additionally, verify whether the
photon undergone a mercedes reection or not. This is an important tool when taking into account the
details of FD optics in order to analyse shower events, as done further ahead in this work.
Spot
A photon entering the diaphragm with a certain direction may be misplaced in the PMT camera. The
so-called spot is precisely the circle of least confusion that measures the degree of this misplacement. The25
Figure 4.5: The dimensions of an FD pixel and the mercedes structures in (β, α) coordinates.
main advantage in using Schmidt optics is that the spot is independent from the incident direction and
is not worsened (on the contrary, it is improved) by the introduction of the correction rings. On the focal
surface the spot radius is ∼7.5 mm or ∼ 0.25 which corresponds to ∼ 16 of the pixel size [43, 42]. This
eect is mainly due to mirror aberration and is expected to have radial behaviour or, in other words,
depend on the distance to the camera centre.
Further detail on the spot is achieved with simulation of FD optics. The Karlsruhe group (KG)
simulation [47] allows the study of the spot on dierent positions. Figure 4.7 shows the misplacement of
the incident photons in a particular region of the focal surface. The knowledge of this kind of information
is important in careful uorescence data analysis.
4.1.3 Laser facilities
There are two laser facilities at the Pierre Auger Observatory, both near the centre of the array as
represented in gure 4.8: the Central Laser Facility (CLF), nearly equidistant from Los Leones, Los
Morados and Coihueco eyes and working since July 2003, and the second Central Laser Facility (XLF),
nearly equidistant from Los Morados, Loma Amarilla and Coihueco sites and nished in January 2007
[48, 38]. This section will shortly describe the CLF which is thoroughly documented elsewhere [48, 49].
The Central Laser Facility, strongly based on the HiRes collaboration laser devices, is situated 26
km away from Los Leones, 30 km from Los Morados and Coihueco and 40 km from Loma Amarilla.
Figure 4.9 shows the facility and its adjacent SD tank, named Celeste. The CLF is a fully independent
unit, controlled wirelessly through a microwave internet link, and has its own weather station in order to
determine air temperature, pressure, humidity, wind speed and wind direction [49]. This station, together
with the ones installed at all FD eyes, allows a realistic weather monitoring over the whole site aperture.
A 355 nm linearly polarised laser is installed in the CLF. The laser wavelength is ideal for the
uorescence technique since it is approximately in the middle of the nitrogen uorescence spectrum;
therefore, two mirrors reecting only 355 nm radiation are used to eliminate other wavelengths. The
laser is red in 7 ns pulses up to a maximum energy of 7 mJ − at this energy the pulse mimics an EAS
originated by a 1020 eV cosmic ray [49]. In order not to privilege a certain direction, the initially linearly
polarised laser is depolarised before being red in vertical beams or steered in any direction with 0.2
26
Figure 4.6: An entire FD camera with its 440 pixels and mercedes stars. The telescope axis centre issignaled with a full circle and the origin with an open one.
precision [51]. As a beam crosses the atmosphere its light is scattered o by Rayleigh and Mie processes
and this scattered radiation is detected by the FD telescopes. Besides, a 40 m long optical ber may
drive the laser signal to the Celeste tank.
The potential of a laser facility within a large cosmic ray observatory is immense. The main motivation
to build the CLF was the atmosphere monitoring: a measurement of the aerosol optical depth as a function
of height is possible with the tracks of a vertical laser beam seen by the FD eyes. The behaviour of this
measurement with time and position in the array is monitored as well since it is crucial to the FD data
reconstruction. But atmospheric monitoring is not the only task assigned to the CLF. For instance, the
time synchronisation between the four FD eyes is performed with vertical beams. And almost horizontal
beams directed to each eye are used to determine the time oset between the FD eyes and the SD: 289±43ns for Los Leones, 363±43 ns for Los Morados and 307±49 ns for Coihueco [52] 2 , being the SD the
last to record the events. Moreover, as the position and direction of the laser beams are known with
higher accuracy than the expected FD resolution, the geometrical reconstruction and the alignment of
the telescopes may be tested and hybrid and FD-only reconstructions compared. Also the FD trigger
as a function of energy, shower direction and atmospheric conditions can be evaluated by computing
the fraction of laser events recorded by the eyes. Finally, a determination of the photometric resolution
becomes possible with the CLF if one compares the actual and reconstructed energy of the laser. This
comparison may also work as an atmospheric quality parameter.2The eye at Loma Amarilla was only nished in February 2007 and, thus, no estimate on its time oset to the
SD is available yet.
27
Figure 4.7: The spot on θ ∈ [0, 5] and φ = 2 as previewed by KG simulation [47]. The plot comparesthe incident direction of each photon (θin, φin) with the direction in the focal surface (θfs, φfs).
4.1.4 Atmospheric monitoring devices
As pointed out earlier in this work, the uorescence technique is extremely sensitive to all atmospheric
features. At the moment, the dependence of the atmospheric density, temperature and pressure on the
position is well monitored by radiosondes launched above the southern site and by the weather stations
at the uorescence sites and the CLF [42]. Besides, molecular processes such as Rayleigh scattering are
understood and accurately accounted for. However, the aerosol content of the atmosphere − low altitude
clouds, dust, smoke and other pollutants driven by the wind − must be constantly monitored since it
varies rapidly. It is known that aerosols scatter (Mie scattering) in a signicant manner both uorescence
and erenkov light. So, at the Pierre Auger Observatory there is a hourly monitoring of aerosol conditions
as a function of height, wavelength and position in the array − indeed, there are ve monitor stations (in
the CLF and in the four FD sites) [51]. Several other monitor devices are available and distributed around
the site according to gure 4.8: the CLF (as explained in the last section), backscatter LIDARs (LIght
Detection And Ranging), Horizontal Attenuation Monitors (HAMs), Aerosol Phase Function Monitors
(APFs), cloud cameras and star monitors.
A backscatter LIDAR is a steerable ensemble of a 355 nm laser and a telescope [53, 51]. After the
laser is red, the telescope records the elastic backscattered light providing a measurement of the aerosol
optical depth in the direction of ring. An interesting possibility of LIDAR systems is the 'shoot-the-
shower' mode: an FD eye detects an event and sends the geometry information to the LIDAR which
scans the event shower detector plane upon conrmation of the SD. In this way, detailed, updated aerosol
monitoring is achieved for a specic event. Presently, three LIDAR systems are operational at Los Leones,
Los Morados and Coihueco eyes and the fourth will be installed at Loma Amarilla. The Pierre Auger
Observatory is also equipped with Raman LIDARs, that record the light backscattered (and frequency
shifted) by Raman scattering. This system allows a more precise measurement of the aerosol transmission
and the identication of the dierent constituents of the atmosphere. But the required lasers are quite
intense and, therefore, pollute the eld of view of the telescopes − that is why Raman LIDARs are only
red when the FDs are not collecting data [51]. Further details on Raman LIDARS can be found in [54].
The Horizontal Attenuation Monitors were designed to quantify the attenuation length in horizontal
paths between FD sites. They consist of a UV light source and a corresponding detector. As of 2005,
28
Figure 4.8: The position of the laser facilities (CLF and XLF) in the southern site. Other atmosphericmonitoring devices are also signaled [50].
Figure 4.9: The Central Laser Facility (on the right) and the Celeste SD tank (on the left) [40].
one HAM system was implemented between Los Leones and Coihueco eyes [51].
As for APFs, their task is to study the Mie scattering cross section so that the aerosol scattered
erenkov light is correctly accounted for in the uorescence proles of FD events. This is achieved by
recording the FD signal originated by a horizontal, collimated beam shot in front of the eye. For now,
Los Morados and Coihueco sites are equipped with APFs.
Finally, cloud cameras and star monitors complement the atmospheric aerosol monitoring. The former
provide a map of cloud distribution over the array and on the FD eld of view, while the latter use the
attenuation of star light to determine the total optical depth until the top of the atmosphere.
The extensive programme of atmospheric monitoring at the southern site is expected to allow a good
control and determination of systematic errors− and this is one of the main advantages of the Pierre Auger
Observatory when compared to other experiments. Moreover, there are several redundant monitoring
instruments. For instance, CLF, LIDAR systems and star monitors are all capable of measuring the
vertical optical depth. The choice for redundancy is yet another way to perform an undoubted control
over systematics.
29
4.2 Event reconstruction
4.2.1 Surface Detector
An ultra high energy cosmic ray produces an EAS that triggers several tanks with dierent charge signals
(measured in VEM) and hit times. As stressed in 3.2.1, the SD event reconstruction is two-fold. The
rst step is that of computing the zenith and azimuth angles of the shower direction (θs, φs) given the
arrival times of the tanks. Assuming a plane front propagation, θs and φs are found with a 2 accuracy
[44]. Renements to this determination are achieved by using a spherical parameterisation of the shower
front that Monte Carlo simulations prove to lead to a better direction reconstruction [44, 55].
Fixed θs and φs, the next step is to t the signals measured in the tanks to a certain lateral distribution
function (LDF). The analysis of events from 2004 and 2005 shows that the following Nishimura-Kamata-
Greisen (NKG) distribution is the best t to the data [56, 57]:
S(rc) = S(1000) · 3.47β ·[rcrs
(1 +
rcrs
)]−β(4.5)
where rs = 700 m, β = 2.4 − 0.9 (secθs − 1), rc is the distance to the core and S(1000) is the signal in
VEM at 1000 m from the shower axis. The t to this function, which is valid up to zenith angles of 60,
yields an estimate on the core position and on S(1000).
In order to determine the energy of an SD event, one needs an energy estimator that must be almost
independent from primary nature, longitudinal shower development and geometry and simultaneously
present a clear behaviour with energy in the EeV range. Close to shower axis the features of an EAS have
somewhat important uctuations; besides, with an 1.5 km spacing, measurements less than 100 m from
the core are not frequent [44]. The measured signal at greater distances from the core is used in giant
ground arrays as energy estimator. Since Monte Carlo simulations show that S(1000) is the parameter
with smaller shower-by-shower uctuations, this is used at the Pierre Auger Observatory [44, 57, 63].
However, because S(1000) falls with the zenith angle θs due to the larger slant depths, the estimator
S38 = S(1000)/CIC (θs), where CIC (θs) is the so-called constant intensity curve (see [25] for further
details), is applied as energy estimator in SD analysis. One of the main aims of the Observatory is to
calibrate S38 using the energy reconstructed by the FD in order not to depend on shower simulations.
Finally, showers with zenith angles greater than 60 are deected by Earth's geomagnetic eld in a
signicant way. Therefore, the lateral distribution of such showers is asymmetric − in other words, it
is not just a function of the distance to the axis − and (4.5) becomes inadequate [44, 56]. Dierent
methodologies are needed to treat those cases.
4.2.2 Fluorescence Detector
The analysis procedure of an FD event comprises two separate steps: rstly, the geometry of the shower
is determined and then the reconstruction of the longitudinal prole and energy is performed. The whole
process will be referred to as standard reconstruction along this work.
Geometry reconstruction
The geometry reconstruction begins with the determination of the shower detector plane (SDP), repre-
sented in gure 4.10. Each triggered FD pixel views a direction ~ri and records a total signal qi. An
approximation on the SDP normal ~nSDP is found by minimising the quantity∑i qi (~nSDP · ~ri)2 where
30
the sum is over the triggered pixels [44]. Then, the pixels that are more than 2 away from the approxi-
mated SDP are excluded and the process is repeated iteratively [11]. This method has been tested with
laser beams generated by the CLF and it proved to determine the SDP with an accuracy less than ∼ 0.5
[44, 11, 42].
Figure 4.10: The FD geometry reconstruction setup (adapted from [63]).
Afterwards, it is necessary to constrain the shower axis within the SDP. In monocular events, when
only one eye is triggered, the timing information of the pixels is essential to accomplish this task. Each
pixel records signal during several 100 ns time bins, but only the centroid time ti,c is used in the standard
reconstruction procedure. Assuming that a shower evolves along a line at the speed of light c, one would
expect for the centroid times of each pixel (see gure 4.10):
ti = Temission + Tpropagation = T0 −Rpctg (χi − δ) +
d
c
= T0 +Rpc
(1− sin (χi − χ0 + π/2)cos (χi − χ0 + π/2)
)= T0 +
Rpc
(1− cos (χi − χ0)−sin (χi − χ0)
)= T0 +
Rpctg
(χ0 − χi
2
)(4.6)
where T0 is the time when the shower is at closest distance Rp from the eye, χi is the viewing direction of
the pixel projected onto the SDP and χ0 is the angle of the shower axis within the SDP. A t to equation
(4.6) letting the parameters T0, Rp and χ0 vary is performed by minimisation of∑i qi(ti − ti,c
)2[44]
− an example is shown in gure 4.11. In this way, the geometry of the shower is completely dened.
However, several technical problems may arise when certain events − usually distant ones − produce
short tracks in the eld of view of the eye [12]. In fact, these showers yield so reduced intervals of χ0−χi2
that the t to (4.6) may not be sensible enough to the curvature of tg(χ0−χi
2
)and a wide range of Rp
and χ0 values may be reconstructed. The problem becomes specially acute in the case of small χ0−χi2
values.
The just-mentioned ambiguity may be broken with stereoscopic observations. As explained in section
3.2.2, these events achieve improved geometrical precision by intersecting the SDPs from each eye, thus
avoiding the troublesome timing t to equation (4.6).
31
Figure 4.11: Timing t to equation (4.6) of the monocular event SD 2521005 (FD 2/1066/35) recordedon 2006/08/01 [58]. In this case, Rp ' 5.3 km, χ0 ' 65.5 and T0 ' 24800 ns.
Longitudinal prole and energy reconstruction
Once the geometry of the shower is xed, the longitudinal prole reconstruction may begin. It comprises
two phases: the computation of the light prole at the diaphragm as a function of time and the determi-
nation of the number of charged particles in the shower as a function of the slant depth, i.e. the proper
longitudinal prole.
In the rst phase, the ADC counts registered by the PMTs must be converted into equivalent 370 nm
photons at the diaphragm − this is done using the conversion factor CADC/370 ' 5 ADC−1 determined
during FD calibration and that includes both the detector eciency ε(λ) and the nitrogen uorescence
spectrum [59]. Then, one needs to calculate the contributions of the dierent pixels. Even though
the geometry reconstruction takes the shower propagation to be a line, the spot caused by imperfect
optics results in the distribution of signal over several pixels at the same instant. To decide which
PMTs contribute to the light prole, the signal-to-noise ratio is maximised. Firstly, each time tk yields a
direction in the sky χk by inversion of (4.6). Considering at each time slot all pixels pointing at directions
less than dSN degrees from χk as signal, the signal-to-noise ratio is computed and the value dSN,max that
maximises the ratio is discovered. Now the number of equivalent 370 nm photons − the light prole −at the diaphragm is determined, in a conservative manner, using at each time slot k the pixels within a
certain angle (related to dSN,max) from χk [59]:
Nγ (tk) =∑i
Nγ,ik =∑i
CADC/370 · (NADC,i (tk)−Nped,i) (4.7)
where NADC,i (tk) is the number of ADC counts of pixel i at time tk and Nped,i ' 100 ADC is the pedestal
or baseline value for the PMT i. An example of a light prole at the diaphragm is shown in gure 4.12.
The reconstruction of the proper longitudinal prole uses both the prole (4.7) and the shower ge-
ometry as inputs. The light prole at the telescope diaphragm, given by (4.7), is a mix of uorescence,
erenkov and scattered erenkov light (and eventually background noise that is taken to be small). To
isolate the uorescence component, an iterative method is used. The rst guess is that all light at the
diaphragm is of uorescence origin. The photons are propagated backwards until the emission points by
considering Rayleigh and Mie processes and then the uorescence yield is used to have a rst estimate
on the shower longitudinal prole, N (1)e,max (X). With this prole and the shower geometry, the expected
components of direct and (Rayleigh and Mie) scattered erenkov light at the diaphragm are determined32
Figure 4.12: The light prole at the diaphragm as a function of time for the event SD 2521005 (FD2/1066/35) recorded on 2006/08/01 [58]. The actual quantity represented is the light ux that crossedthe diaphragm. The several components of direct and scattered light are represented as well (see text).
and subtracted from the initial light prole (4.7). The method is iterated until convergence (up to four
times in total) [59]; it works adequately for showers that produce low erekov contamination at the
detector, but completely diverges otherwise [12]. Anyhow, the nal longitudinal prole N (l)e,max (X) is
tted to the Gaisser-Hillas formula:
Ne (X;Nmax, Xmax, X0, λGH) = Nmax
(X −X0
Xmax −X0
)Xmax−X0λGH
eXmax−XλGH (4.8)
where X0 and λGH are t parameters (weakly) correlated to the rst interaction point and the proton
interaction length in air, respectively [60]. In principle, the t is performed with four parameters − Nmax,Xmax, X0 and λGH − but the restrictions X0 = 0 gcm−2 and λGH = 70 gcm−2 are usually imposed for
the sake of convergence. Figure 4.13 presents the reconstructed longitudinal prole of a shower and the
corresponding Gaisser-Hillas t.
Figure 4.13: The reconstructed longitudinal prole and the Gaisser-Hillas t [44].
A non-iterative procedure to calculate the longitudinal prole given the light at the diaphragm was
recently proposed and is already in use [61, 58]. Since the uorescence production is proportional to the
energy deposited by the shower in the atmosphere dEdX , it is convenient to reconstruct the dE
dX (X) prole
rather than the Ne (X) mentioned in the above paragraphs. However, the erenkov light, both direct33
and scattered, depend on the Ne (X) prole 3 ; so, there is the need to relate dEdX to Ne. According to
[62, 46]:dE
dX(Xi) = Ne (Xi)αKGi (4.9)
where αKGi ≡ αKG (si) = 1.06724 ·(
43.2535(1.34508+si)
11.3005+2.44755+0.122845si
)MeVgcm−2 and si = 3
1+2Xmax/Xiis
the shower age parameter. At this point, one may relate in a matricial manner the dEdX prole of the
shower and the three components of detected light: uorescence, direct erenkov and scattered erenkov
light. Considering line propagation as in the geometry reconstruction, the rst two kinds of light arriving
at the detector at a certain instant come from a specic segment of the shower, while the scattered part
builds up during cascade development and must therefore be summed over all shower history [61]:
y = Cx (4.10)
being y and x vectors and C a matrix given by
Cij =
0 if i < j
cdi + csii if i = j
csij if i > j
where y is the light received at the diaphragm as a function of time, x is the prole dEdX (X), cdi is the
direct light contribution (uorescence and erenkov) at time slot i and csij is the scattered erenkov
fraction (due to Rayleigh and Mie scatterings) detected at time slot i but emitted in Xj slant depth
bin. The dEdX (X) prole is found by inverting (4.10) and, afterwards, one ts it to a (slightly) modied
Gaisser-Hillas formula:
dE
dX
(X;
dE
dX
∣∣∣∣max
, Xmax, X0, λGH
)=
dE
dX
∣∣∣∣max
(X −X0
Xmax −X0
)Xmax−X0λGH
eXmax−XλGH (4.11)
Further details on this procedure are given in [61].
Finally, the energy estimate is determined by integrating the best t to the reconstructed longitudinal
prole. In the case of the Ne (X) prole, the energy is given by
E '< dE
dX>
∫ ∞X0
Ne (X) dX (4.12)
where the mean energy deposit is < dEdX >' ε0
Xl' 2.2 MeV
gcm−2 [12, 9]. As for the dEdX (X) prole, the
estimated energy is simply the integral of the curve:
E =∫ ∞X0
dE
dX(X) dX (4.13)
As a nal remark, note that the energy calculated with (4.12) or (4.13) is about 10% less than the
actual energy of the cosmic ray − recall the discussion on the missing energy in section 3.2.2.
4.2.3 Hybrid
The hybrid technique is being used for the rst time ever at the Pierre Auger Observatory. It diers from
the FD-only reconstruction described in the previous section uniquely on the second step of the geometry
3While direct erenkov light is proportional to Ne (X), the scattered component grows with the integral ofNe (X).
34
(a) (b)
Figure 4.14: Comparison of monocular and hybrid reconstructions using laser shots [64]. On the leftthe dierence between the reconstructed Rp and the actual one is plotted, while on the right the samedierence for χ0 is presented.
reconstruction, i.e. on the denition of the shower axis within the SDP. If, besides the FD, one SD tank
is triggered − as in gure 4.10 − , the arrival time of the shower front to the ground, tgrd, constrains the
T0 parameter in the timing t to equation (4.6) [63]:
T0 = tgrd −~rgrd · ~sc
(4.14)
where ~rgrd is the position of the tank and ~s is the normalised shower direction. The constraint allows
a more accurate reconstruction of Rp and χ0 or, in other words, of the shower geometry. In the case of
more than one triggered SD stations, a better precision is achieved and eventual restrictions on the core
position are possible [44, 12]. Note that the measurements needed from the surface detector are arrival
times and not deposited charges which makes the hybrid technique rather clean and straightforward
even though a careful synchronisation between the FD eyes and the SD is crucial as reported in 4.1.3.
Moreover, this reconstruction works quite well even if the shower produces short tracks within the eld
of view of the FD. Indeed, the use of ground stations, that correspond to small χi, allows a better t to
equation (4.6).
Since the SD presents a duty cycle of 100%, FD events are almost all hybrid ones as well. Approx-
imately 10% of the SD data are hybrid and, when nished, the Pierre Auger Observatory is expected
to collect about 4000 of these events per month [64]. An important energy feature is that the hybrid
mode triggers at somewhat low energies when compared to the SD trigger, because only one active tank
is required. This means that events that would not have triggered the surface detector are recovered and
analysed with improved geometrical precision through the hybrid technique.
The hybrid detection was put to test using laser beams shot from the CLF, whose direction is almost
vertical (χ0 = 90±0.01) and the Rp (in this case, also the 'core' position) is known with a 5 m precision.
During CLF routine operation, several vertical laser beams are shot into the sky and one of them is also
driven into the Celeste tank, thus allowing the comparison of monocular and hybrid (with one tank only)
reconstructions [64]. The results of the resolutions in Rp and χ0 are plotted in gure 4.14 and are rather
impressive: the hybrid technique provides a geometry reconstruction with a ∼10 times better resolution
and no systematic shift.
The improved geometry precision makes hybrid data very clean to perform anisotropy studies and also35
allows a better accuracy in the determination of the shower longitudinal prole and primary energy. Thus,
most physical studies use preferentially hybrid data sets, even though they represent smaller statistics.
But maybe the most important feature of the hybrid technique is the possibility to calibrate the S38
parameter of SD analysis with the energy reconstructed by the FD, as demonstrated in gure 4.15 for
a specic set of hybrid data [25]. The calibration provides an energy conversion almost simulation-
independent and constitutes the rst step in getting an unbiased energy measurement and therefore a
reliable spectrum such as the one presented before in gure 3.7(b).
Figure 4.15: Calibration between S38 and the energy reconstructed by the uorescence technique [25].
4.3 Future steps
The next steps for the Pierre Auger Observatory are the installation of enhancements on the southern
site and the construction of the northern one. Brief details on these fronts are given below.
4.3.1 Southern site enhancements
The main physical motivation to enhance the southern site is the possibility of exploring the region of the
cosmic ray spectrum around the ankle, i.e. 1017 − 1019 eV. In this energy range cosmic ray sources are
believed to change from galactic to extragalactic ones and that transition is not yet totally understood
nor experimentally documented [65, 66, 67]. Presently, the FD and the SD achieve full eciency at 3·1018
eV [24, 68]. So enhancements were planned to aim at lower energies.
But lowering the threshold energy is not enough to study the ankle region − both a good energy
resolution and (statistical) capability to identify primaries are crucial. Primary identication may be
performed knowing the muon content of the air shower. Therefore, one of the southern site enhance-
ments is the Auger Muons and Inll for the Ground Array (AMIGA) which plans to install underground
muon counters and additional SD tanks, as explained below. Another reliable composition study is the
dependence of the shower maximum on energy. For lower energy cascades, the shower maximum occurs
higher in the atmosphere and, consequently, an extended FD eld of view is needed − the issue is being
delt with by the High Elevation Auger Telescopes (HEAT). Both HEAT and AMIGA were approved by
the Auger Collaboration and are now under construction.
The HEAT initiative will deploy three telescopes similar to the ones already in use behind of the
Coihueco site. The telescopes will be inclined so that the region between 28 and 58 in elevation is
36
covered [66]. The azimuth spacing between the telescopes is still under discussion, but they will work
independently from Coihueco eye in trigger matters. HEAT will allow the full detection of EAS with
primary energies below 1019 eV. In fact, those cascades emit fainter uorescence light and simultaneously
peak earlier in their development. So, extending the eld of view, i.e. looking at higher elevations closer
to the eyes, will make the FD sensible to lower energies. Specically, the threshold energy will be 7 · 1017
eV and may fall to 2 ·1017 eV with ground array inlls such as AMIGA and considering a hybrid threshold
[67]. Last but not the least, the composition study through the Xmax (E) dependence in the 1017 − 1019
eV range may help to unravel the mystery behind the transition that takes place around the ankle.
AMIGA, on the other hand, consists of an inll of both water erenkov tanks and underground muon
counters ∼ 6.0 km in front of Coihueco eye [69]; the additional detectors will be placed in 433 m and 750
m grids. The muon counters will contain several 400 cm x 4.1 cm x 1.0 cm strips buried ∼ 3 m under the
ground. AMIGA will achieve SD full eciency at lower energies than the current 3 ·1018 eV: 1016 eV with
433 m spacing and 3 · 1017 eV with 750 m [66]. Besides, AMIGA will improve the event reconstruction
and complement composition studies performed by HEAT.
Another southern site potential enhancement is the radio detection through antennas that aims at
recording . 100 MHz signals emitted during EAS development. This technique monitors the electro-
magnetic properties of a cascade as it crosses the atmosphere, being complementary to the SD and the
FD and presenting an 100% duty cycle [70]. Moreover, it exhibits a good pointing accuracy and, thus,
allows anisotropy and source studies. However, radio detection is not yet fully developed and is highly
inuenced by signicant background in the . 100 MHz frequency band due to storms and human-made
noise. Since November 2006 a prototype antenna has been operating near the CLF, but up to now it
proved to be too sensitive to storms ∼ 100 km away [38].
4.3.2 The northern site
In June 2005 the Auger Collaboration chose Lamar, Colorado, USA to be the site for the northern part of
the Observatory [71]. Located 1300 m above sea level, it is an approximately rectangular site of 134 km
x 77 km enclosing a total area of ∼ 10300 km2 and extension is possible up to 22000 km2. The northern
Fluorescence Detector will comprise two eyes with telescopes similar to those used in the southern site.
The Surface Detector will consist of a 4000 water erenkov tanks array in an 1.6 km spacing rectangular
grid. This second site will focus on the 1020− 1021 eV range, presenting a threshold energy of about 1019
eV. The construction is scheduled to start on 2009 and from then on signicant statistics will be added
to the PAO data, specially SD data since the northern ground array is more than three times bigger than
the one in Argentina. Besides, with full sky coverage, the Pierre Auger Observatory will become the rst
experiment able to perform comprehensive anisotropy and other astrophysical studies.
37
Chapter 5
The 3D FD reconstruction
The standard FD event reconstruction, described in 4.2.2, does not use all the information recorded by
the telescopes. In the geometry reconstruction, only the centroid times of the triggered pixels are used
and, so, the time structure of the signal inside each pixel is neglected. Besides, the line propagation
approach, that may be sucient for distant showers, is responsible for the mistreatment of the lateral
proles in close-by events. As for the prole reconstruction, at each time slot the contributions of nearby
pixels are summed, even though the same observation times in dierent pixels correspond to dierent
emission times.
It is therefore necessary to develop a new reconstruction procedure that deals properly with all avail-
able FD information. The 3D reconstruction [72] is a possible approach. Indeed, it uses all relevant time
bins inside each pixel and considers a disk (rather than line) shower propagation. This improved geometry
reconstruction allows the study of the 3D features in cascade development and the reconstruction of a
3D shower prole instead of separate longitudinal and lateral analyses.
5.1 Geometry reconstruction
5.1.1 The 3D method
While each pixel of the FD camera corresponds to a direction in the sky, the third dimension− the distance
to the eye − is determined by the timing information. The idea of the 3D geometry reconstruction is to
use both pixel direction and time to locate in space the volume from where the photons observed by each
pixel at each time slot were originally emitted. An important dierence from the standard procedure is
the shower propagation hypothesis: instead of considering line propagation, the cascade is assumed to be
a plane disk, moving at the speed of light in vacuum c.
The 3D geometry reconstruction is initiated by constraining ~nSDP , Rp and χ0 to the values given by
the standard method and retting the data to equation (4.6) with T0 as the only t parameter. Then,
as exemplied in gure 5.1(a), each triggered pixel i, of central direction (θi, φi), at each time slot k is
associated to an unambiguous point ~rik:
tk = Temission + Tpropagation = T0 −rikccosαi +
rikc⇔
rik =c (tk − T0)1− cosαi
(5.1)
where tk is the central time of slot k, αi is the angle between −~rik and the shower axis ~s and rik is the
distance from the eye in (θi, φi) direction. The point dened in this way is the central point of the volume
whose vertices are determined by (5.1) using tk ± 50 ns and the directions (θvi , φvi ) corresponding to each
38
r
r
A
AAAAAK
eye
~rik
~s
αi
T0
shower front
@@
@@
@@
@
@@
@@@
(a) The 3D geometry reconstruction setup. Eachpixel i at each time slot k corresponds to anunique volume with central point ~rik.
(b) 3D visualisation of event SD 2521893 (FD4/1731/2757) recorded on August 2006. The full cir-cles represent the central points of the volumes andthe color code is referred to observation times.
Figure 5.1: The 3D geometry setup and event visualisation.
vertex of the hexagonal pixel (v = 1, ..., 6). Therefore, for each pixel at each time slot there exists an
irregular volume in the space.
Fixed all 'detected' volumes for an event, a new estimate on the shower axis ~s and core position ~rsmay be computed through inertia calculations. Using the number of 370 nm photons at the diaphragm,
Nγ,ik = CADC/370 · (Ni,ADC (tk)−Ni,ped), as the 'mass', one may calculate the centre of mass of the
central points ~rik:
~rcm =
∑i,kNγ,ik~rik∑i,kNγ,ik
Moreover, the inertia matrix of the set of central points is given by
I =
Ixx Ixy Ixz
Ixy Iyy Iyz
Ixz Iyz Izz
(5.2)
being
Ixx =
∑i,kNγ,ik
(dy2ik + dz2
ik
)∑i,kNγ,ik
Ixy = −∑i,kNγ,ikdxikdyik∑
i,kNγ,ikIxz = −
∑i,kNγ,ikdxikdzik∑
i,kNγ,ik
Iyy =
∑i,kNγ,ik
(dx2
ik + dz2ik
)∑i,kNγ,ik
Iyz = −∑i,kNγ,ikdyikdzik∑
i,kNγ,ikIzz =
∑i,kNγ,ik
(dx2
ik + dy2ik
)∑i,kNγ,ik
with dxik = (~rik − ~rcm) · ~ex, dyik = (~rik − ~rcm) · ~ey and dzik = (~rik − ~rcm) · ~ez.The main inertia axis − the third eigenvector of I − is the new estimate on ~s and together with ~rcm
it yields the core position ~rs. From ~s, ~rs and the eye position, one easily nds the geometric parameters
~nSDP , Rp and χ0 that are once again used in the timing t with T0 as the only parameter. The method
is repeated iteratively until convergence of both ~s and ~rs.39
Figure 5.2: The distribution of dCP−eye and log10EKG in the data collected from January 2006 until
September 2006 with KG and 3D prole reconstructions and χ3D0 ≥ 45. The red and blue lines indicate
the border of the empirical cut (5.3) with d∗CP−eye = 5 km and d∗CP−eye = 10 km, respectively.
Note that the geometry generated by equation (5.1) is such that the constant observation times
(tk =constant) correspond to rikc (1− cosαi) =constant, i.e. the bisectrix between the shower axis and
the observation line.
The visualisation of the complex 3D output of the new geometry reconstruction is done using the
map3d package [73], as exemplied in gure 5.1(b). Besides all vertices of the volumes and the central
points, also the so-called near points may be represented. The near point of a volume is the point at
minimum distance from the shower axis; it represents a more physical position in the cascade structure
than the central point. Several features associated to each volume − observation time, Nγ,ik, eye − can
as well be represented using a color code.
The 3D method is supposed to be particularly accurate for events simultaneously close to the detector
and with high energies. The mean distance of the central points of the volumes to the respective eye
dCP−eye and the KG-reconstructed energy EKG are used to select the referred events:
log10EKG − 17.5 >
d2CP−eye
d∗2CP−eye∧ dCP−eye 6= 0 (5.3)
The distribution of dCP−eye and EKG as well as the empirical cut (5.3) with d∗CP−eye = 5 km and
d∗CP−eye = 10 km are presented in gure 5.2 for the data collected from January 2006 until September
2006 with KG and 3D prole reconstructions and χ3D0 ≥ 45. In order to check if the new geometry
reconstruction is working properly, a comparison between the values of Rp, χ0 and T0 as given by
the standard (KG) and 3D methods applied to the data set of gure 5.2 with d∗CP−eye = 10 km was
performed and is plotted in gure 5.3. Except for some (potentially interesting) events, the 3D approach
yields essentially the same geometry as the standard procedure, which is natural. There seems to be a
slight tendency of the new method to reconstruct smaller Rp, but further cross-checks must be done −see next section.
5.1.2 Some applications
The 3D shower structure allows a study on lateral proles. Indeed, minimum and medium lateral dimen-
sions rmin and rmed may be dened for each shower. The positions of the near points (np) and central40
(a) (b)
(c)
Figure 5.3: Comparison between the Rp, χ0 and T0 values as reconstructed by the standard and 3Dapproaches. Data collected from January 2006 until September 2006 with KG and 3D prole reconstruc-tions, χ3D
0 ≥ 45 and passing cut (5.3) with d∗CP−eye = 10 km was used to produce the plots.
41
points of the volumes yield these variables directly:
rmin =
∑i,k dPL (~rnp,ik, ~s, ~rs)
Nvolrmed =
∑i,k dPL (~rik, ~s, ~rs)
Nvol
where the sums are over all good volumes, Nvol is the number of those volumes and dPL (~r,~s, ~rs) is the
distance from point ~r to the shower axis given by ~s and ~rs.
Another lateral parameter is the so-called rmax which is of an essentially dierent kind from rmin and
rmed and represents roughly the radial distance that includes most detected volumes. Its denition is
as follows. A Monte Carlo method was designed to determine the volume of the irregular solid seen by
each pixel i at each time slot k. Each solid ik is surrounded by a cylinder of volume Vcyl,ik inside which
Ntot,ik points are randomly generated according to the volume element rdrdθdh = d(r2
2
)dθdh. Of the
total Ntot,ik, only Nin,ik points ~r(l)ik are in the detected volume ik and, therefore,
Vik '∑Nin,ikl=1 1Ntot,ik
Vcyl,ik =Nin,ikNtot,ik
Vcyl,ik (5.4)
σ (Vik) =∂Vik∂Nin,ik
√Nin,ik +
∂Vik∂Ntot,ik
√Ntot,ik = Vik
(1√Nin,ik
+1√
Ntot,ik
)(5.5)
where Ntot,ik was xed to 1000 independently from i and k. Then, a cylinder of radius r(m)cyl around the
shower axis is dened and the following estimator computed:
η(r
(m)cyl
)=
∑i,k Vact,ik∑i,k Vik
being Vact,ik the active volume ik, i.e. the volume of the solid ik inside the cylinder of radius r(m)cyl :
Vact,ik =∫Vik
factdV 'Nin,ik∑l=1
fact
(~r
(l)ik
) VikNin,ik
=Nin,ik∑l=1
fact
(~r
(l)ik
) Vcyl,ikNtot,ik
(5.6)
with fact(~r
(l)ik
)=
1 if dPL(~r
(l)ik , ~s, ~rs
)≤ r(m)
cyl
0 otherwise.
Physically, η(r
(m)cyl
)is simply the fraction of the detected volume within r
(m)cyl from shower axis.
Finally, rmax is found by looping on r(m)cyl with step ∆rcyl = 10 m:
rmax = r(m)cyl −
∆rcyl2
:η(r
(m)cyl
)− η
(r
(m−1)cyl
)∆rcyl
≤ 10−3 ∧ η(r
(m)cyl
)≥ 0.1 (5.7)
With this denition, all the signicant volumes ik of the event are inside the cylinder of radius rmaxaround the shower axis. It is obviously possible that there are volumes further away than rmax, but they
are assumed not to be physically signicant.
The comparison between rmin, rmed and rmax is presented in gure 5.4(a). As expected, rmin ∼ 0 since
the near points are supposed to be close to shower axis if this was correctly reconstructed, while rmed and
rmax have more sparse distributions. These three parameters and their dependence on geometric variables
constitute an useful tool in the identication of non-standard events. To begin with, the behaviour of
rmin, rmed and rmax with χ0 is plotted in gure 5.4(b). There is a decrease of both rmed and rmax until
χ0 = π2 and a stabilisation afterwards. The rmin parameter, however, is close to 0 along the whole range
in χ0. In other words, events with χ0 <π2 present large, spread volumes containing parts of the shower
axis − the 3D structure of such an event is shown in gure 5.5. The reason behind this situation is the42
(a) (b)
Figure 5.4: Distributions of rmin, rmed and rmax in (a) and their dependence on χ0 in (b). The data setused is the same as in gure 5.3.
signal pile up that occurs for showers approaching the FD eye, i.e. χ0 <π2 . In fact, in the extreme case
where a shower evolves towards the eye parallel to the viewing direction of a pixel i, both the standard
and the 3D methods are problematic. In the standard procedure, as χ0 = χi, (4.6) yields ti = T0: all the
photons produced along the shower axis arrive at pixel i at the same instant ti. Notice that the standard
geometry reconstruction does not fail because Rp, χ0 and T0 are known (Rp = 0, χ0 = χi and T0 = ti),
but the shower prole determination becomes impossible. The 3D approach, on the other hand, diverges
in the extreme case since αi = 0 and (5.1) reads rik →∞ − that is why smaller χ0 correspond to larger
volumes. Another important remark on events with χ0 <π2 is that the erenkov radiation emitted during
cascade development may arrive directly at the FD telescopes and, consequently, this contribution must
be taken into account together with uorescence light in the reconstruction of the shower prole and in
energy estimation.
Figure 5.5: 3D visualisation of event SD 2553671 (FD 2/1081/2704). In this case, Rp ' 9.7 km andχ0 ' 33.1. Note the dierence between the reconstructed volumes here and those of the event presentedin gure 5.1(b).
Figure 5.6 shows the relation between rmax and Rp with the quality cut χ0 ≥ π2 in order to eliminate
the events described in the previous paragraph. The plot seems to indicate that rmax ∝ Rp which is
natural since a pixel overviews greater volumes at greater distances from the eye. The deviation from
this behaviour is a possible criterion to classify cosmic ray events and identify strange ones.
43
Figure 5.6: Dependence of rmax on Rp for the same data set as in gure 5.3 but passing the quality cutχ0 ≥ π
2 .
Also the inertia coecients Ixx, Iyy and Izz, dened in the last section, play an important role in
the characterisation and classication of events. From the analysis of these parameters in data, the rst
conclusion is that Ixx/Iyy ∼ 1 as shown in gure 5.7. Therefore, the shower 3D structure is cylindrically
symmetric within a very good approximation. Moreover, the fact that Ixx ∼ Iyy means the use of the
observation time as a third dimension in FD analysis introduces no signicant bias in the 3D geometry
reconstruction.
Figure 5.7: The Ixx/Iyy and Izz/r2med distributions for the same data set as in gure 5.3 but requiring
rmed 6= 0 and at least one Iii 6= 0.
A study of the three dimensional shape of shower development may as well be performed using
inertia relations. If the shower structure were a massive, uniform cylinder of radius r and height h,
then the moments of inertia along the main inertia axes would be Icylxx (r, h) = Icylyy (r, h) = r2
4 + h2
12 and
Icylzz (r) = r2
2 . In the case of a cone of radius r and height h, Iconexx (r, h) = Iconeyy (r, h) = 320r
2 + h2
10 and
Iconezz (r) = 310r
2. The typical lateral dimension of a shower is given by rmed and so one may verify if the
3D structure is similar to that of a cylinder of radius rmed, a cone of radius rmed or a cone of radius
2rmed in which cases the following relations are expected: Izzr2med
= Icylzz (rmed)
r2med= 1
2 ,Izzr2med
= Iconezz (rmed)
r2med= 3
10
and Izzr2med
= Iconezz (2rmed)
r2med= 6
5 . Figure 5.7 shows the distribution of Izzr2med
in events from August 2006. The
data is consistent with cylinders of radius rmed and not with any of the cones considered above. However,
44
(a) (b)
Figure 5.8: The distributions of√Ixx + Iyy − Izz (a) and
√Izz (b) for the same data set as in gure 5.7.
the considerable dispersion around the mean value indicates a mix of dierent geometries − probably
not only cylinders or cones − present in the data set. Note that the inertia coecients, namely Izz,
are calculated with weight Nγ,ik that is not uniformly distributed as the mass is in a massive, uniform
cylinder or cone. Thus, the coecients are a convolution of the Nγ,ik distribution and the geometric
structure and should not be misunderstood as simple geometric parameters such as rmin, rmed or rmax.
Anyway, the trail of the Izzr2med
histogram, this is, events far away from cylinder-like behaviour, corresponds
to two dierent populations of showers: those badly reconstructed and those potentially interesting that
present remarkable moments of inertia.
Finally, the longitudinal and lateral dimensions of a shower may be accessed using√Ixx + Iyy − Izz
and√Izz respectively, since
√Ixx + Iyy − Izz ∝ h and
√Izz ∝ r in both a cylinder and a cone. The
distributions of such parameters are presented in gure 5.8 and they allow the identication of particularly
'fat' and/or extense events.
Many more geometric tests and studies will be done in the near future.
5.2 Prole reconstruction
The volumes Vik determined by the 3D geometry reconstruction correspond to the regions in space from
where the detected photons were originally emitted. Using these volumes and a 3D prole, one may
compute the expected signal at pixel i and time slot k taking into account uorescence light, direct
and scattered erenkov emission, light attenuation and the detailed FD optics. While in the standard
reconstruction the observed photons are propagated backwards to obtain the shower prole, the 3D
approach uses a given prole to calculate the expected signals at the PMTs and then a comparison
between observation and expectation determines the best 3D prole.
5.2.1 The 3D shower prole
As mentioned above, the 3D reconstruction procedure calls for a three dimensional prole that describes
the evolution of the shower at each point in space. Since the shower longitudinal and lateral develop-
ments are known to be best parameterised in depth units, each point ~r is associated to a pair (X,R) as
45
schematically represented in gure 5.9:
X =
∫∞h(~ps)
ρ(h)dh
cosθs
[gcm−2
](5.8)
R = ρ (~r) dPL (~r,~s, ~rs)[gcm−2
](5.9)
where ~ps is the closest point of the shower axis to ~r and θs is the angle between ~s and the vertical.
Expression (5.8) is valid for almost vertical showers. Furthermore, the denition of R does not contain
an integral between ~r and ~ps as (5.8) does. This is because the shower particles do not follow the path
from ~r to ~ps and so the local density ρ (~r) is taken into account instead of performing the integral. Note
the use of capital letters for depth-like parameters (measured in gcm−2) and small letters for distances
(in m) − an exception is Rp, dened in section 4.2.2.
r
rr@@R
A
AAAAAK
HHY
eye
~s
α
θs
R
X
At
~et
~r − ~reyeθ
ps
r
@@
Figure 5.9: The geometric setup used in the 3D prole reconstruction.
The 3D prole is simply the product of a longitudinal prole, that gives the number of electrons at
slices of dierent slant depths, and a lateral distribution function, that spreads the electrons around each
slice:
Ne (~r;Nmax, Xmax, X0, λGH) = Ne (X,R;Nmax, Xmax, X0, λGH)
= Ne (X;Nmax, Xmax, X0, λGH) · LDF (X,R;Xmax)[ em2
](5.10)
Whereas the longitudinal prole is parameterised from CORSIKA simulations by the Gaisser-Hillas
formula (4.8), there are several possible lateral distributions, that are required to be normalised, i.e.∫ 2π
0
∫∞0LDF (X, r) · rdrdφ = 1. The lateral spread is scaled by the so-called Molière radius, a natural
transverse length given by multiple scattering [13, 74]: RM = EsXlε0' 9.6 gcm−2 (recall the denition
of the electron radiation length in air Xl and the critical energy ε0 in chapter 3), or in distance terms
rM = RMρ(~r) , where Es =
√4παfs
mec2 ' 21 MeV is the scale energy for electrons and αfs = e2
4πε0~c '1
137 is
the ne structure constant. About 90% of the shower energy is contained in one Molière radius around
the axis [9].
A lateral distribution suitable for electromagnetic showers is described by the Nishimura-Kamata-
Greisen (NKG) formula [74]:
LDFNKG (X, r;Xmax) =1r2M
(r
rM
)s−2(1 +
r
rM
)s−4.5 Γ(4.5− s)2πΓ(s)Γ(4.5− 2s)
[1m2
](5.11)
46
being r the distance to the axis and s = 31+2Xmax/X
the shower age. The respective NKG cumulative func-
tion at shower maximum (s = 1) is FNKG (Xmax, r) =∫ 2π
0
∫ r0LDF (Xmax, r) · rdrdφ = 1−
(1 + r
rM
)−2.5
.
So, an universal lateral distribution based on this formula and on CORSIKA simulations of hadronic pri-
maries was proposed by D. Góra et al. [13]. Independently from primary energy, primary (hadronic)
particle and zenith angle, the shower lateral cumulative function was found to be adequately parame-
terised by:
FGora (X, r;Xmax) = 1−(
1 + a(s)r
rM
)−b(s)(5.12)
with
a(s) = 5.151s4 − 28.925s3 + 60.056s2 − 56.718s+ 22.331
b(s) = −1.039s2 + 2.251s+ 0.676
Since (5.12) presents cylindrical symmetry around the shower axis, its corresponding LDF is given
by:
LDFGora (X, r;Xmax) =1
2πrdFGoradr
=1
2πra(s)b(s)
rM
(1 + a(s) r
rM
)1+b(s)
[1m2
](5.13)
However, as pointed out in [13, 15, 74], the cascade particles at certain depth X are spread according
to the value rM computed at depth X − 2Xl. Thus, in depth-like variables X and R, (5.13) becomes
LDFGora (X,R;Xmax) =1
2πR/ρ (~r)a(s)b(s)
RM/ρ (~r′)(
1 + a(s) R/ρ(~r)RM/ρ(~r′)
)1+b(s)
=1
2πRa(s)b(s)ρ (~r) ρ (~r′)
RM
(1 + a(s) Rρ(~r′)
RMρ(~r)
)1+b(s)
[1m2
](5.14)
where ~r′ is the point corresponding to ~r but at slant depth X − 2Xl. Note that (5.14) is in units 1/m2,
as required for a distribution of particles in a plane.
5.2.2 Light at diaphragm
Given a hypothetical 3D prole, the number of photons at the diaphragm is determined integrating in
each volume Vik the density of emitted photons that arrive at the telescope. Similarly to rmax calculation,
a Monte Carlo method is used to perform the integration. Firstly, a cylinder of volume Vcyl around the
shower axis is dened with radius rcyl = max (rmax, 3rM,max), where rM,max is the maximum value of rMcalculated in all central points ~rik, and height hcyl enough to include all detected volumes. The cylinder
is such that most shower particles are inside it. Then, Nvol · N1 points ~r(q) are uniformly generated in
the cylinder according to the element volume rdrdθdh and, as in equation (5.6), the number of expected
photons at the diaphragm coming from Vik is
Nγ,ik (Nmax, Xmax, X0, λGH) =∫Vik
dNγdV
(~r;Nmax, Xmax, X0, λGH) dV
'Nin,ik∑l=1
dNγdV
(~r(l);Nmax, Xmax, X0, λGH
) VcylNvol ·N1
(5.15)
where ~r(l) are the Nin,ik generated points that are inside Vik. Ignoring the (small) contribution of multiple
scattering, the density dNγdV is a sum of uorescence
(dNfγdV
), direct
(dN
dγ
dV
)and Rayleigh
(dN
Rγ
dV
)and
47
Mie(dN
Mγ
dV
)scattered erenkov fractions:
dNγdV
=dNf
γ
dV+dNd
γ
dV+dNR
γ
dV+dNM
γ
dV(5.16)
Recall that, unlike erenkov emission, uorescence is isotropic and, consequently, its scattering is not
very important to the angular distribution of the light.
As the above described Monte Carlo integration is performed for each telescope triggered by the event,
the treatment of information coming from dierent telescopes (and eventually from dierent eyes as well)
is straightforward.
Fluorescence
Although all charged particles in a cascade are responsible for the production of uorescence light, elec-
trons present the most signicant contribution. The electrons that contribute to this kind of light have
energies lower than the critical energy ε0 ' 81 MeV and above the uorescence threshold Efthr ' 1.4
MeV; therefore, the density of uorescence photons at (X,R) in the wavelength band [λ1, λ2] is simply
given by
Ne (X;Nmax, Xmax, X0, λGH) · LDF (X,R;Xmax) ·∫ ln(ε0/MeV)
ln(Efthr/MeV)yfγ (E, h, λ1, λ2) fe(E, s)dlnE
[ γm3
](5.17)
where yfγ is the uorescence yield and fe = 1Ne
dNedlnE is the electron energy distribution in an EAS that is
parameterised from CORSIKA simulations in [17]:
fe(E, s) = a0(s)E
(E + a1(s)) (E + a2(s))s
with E in MeV units and
a0(s) =
[∫ ∞ln(Ecut/MeV)
E
(E + a1(s)) (E + a2(s))sdlnE
]−1
a1(s) = 6.42522− 1.53183s a2(s) = 168.168− 42.1368s
The yield dependence on E and h (through the density ρ(h) and the temperature T (h)) may be dis-
regarded at rst approximation and, integrating over the nitrogen uorescence spectrum, yfγ ' 4 γ/e/m.
So, (5.17) becomes simple to compute and∫ ln(ε0/MeV)
ln(Efthr/MeV) fe(E, s)dlnE represents the fraction of electrons
contributing to uorescence at shower age s. As a reference, at shower maximum (s = 1), this fraction is
about 0.7.
Afterwards, the light angular distribution must be taken into account: since uorescence is an isotropic
phenomenon, 1
Nfγ
dNfγdΩ = 1
4π . Thus, when computing the expected number of photons at the diaphragm,
one nds the term1
Nfγ
dNfγ
dΩ∆Ω (~r)
where ∆Ω is the solid angle seen by the telescope:
∆Ω (~r) =At
|~r − ~reye|2[stereorad]
being At = π · 1.12 m2 the total area of the diaphragm including the corrector ring. In principle, instead
of At, one should use the eective collection area Atcosθ (~r), where θ is the angle between the incident48
photon and the normalised telescope axis ~et − see gure 5.9. But the cosθ contribution is already included
in the calibration factor C370/ADC introduced in section 4.2.2.
Finally, the light attenuation from the emission point until the detector is accounted for using the
transmission coecients TR and TM , given respectively by equations (3.8) and (3.12). The densitydNfγdV
is then
dNfγ
dV(~r;Nmax, Xmax, X0, λGH) = Ne (X;Nmax, Xmax, X0, λGH) · LDF (X,R;Xmax) · yfγ ·
·∫ ln(ε0/MeV)
ln(Efthr/MeV)fe(E, s)dlnE ·
1
Nfγ
dNfγ
dΩ∆Ω (~r) · TR
(~r, ~reye, λ
feff
)· TM
(~r, ~reye, λ
feff
) [ γm3
](5.18)
where λfeff = 370 nm is the eective uorescence wavelength for which the detector eciency is unitary.
Notice thatdNfγdV has indeed units of photon density, so that (5.15) yields a number of photons.
Direct erenkov
Following a similar reasoning as in the uorescence case, the density of erenkov photons with λ ∈ [λ1, λ2]
emitted at (X,R) and that arrive directly at the detector is essentially
dNdγ
dV∼ Ne (X;Nmax, Xmax, X0, λGH) · LDF (X,R;Xmax) ·
∫ ∞ln(Ethr(h)/MeV)
yγ (E, h, λ1, λ2) fe(E, s)dlnE ·
· 1
Ndγ
dNdγ
dΩ∆Ω (~r) · TR
(~r, ~reye,
λ1 + λ2
2
)· TM
(~r, ~reye,
λ1 + λ2
2
) [ γm3
]being E
thr(h) = mec2√
2(n(h)−1)the electron threshold energy for erenkov emission and n the refraction
index. The yield yγ is described in [17] and approximately given by:
yγ (E, h, λ1, λ2) ' 2παfs
(2 (n(h)− 1)− m2
ec4
E2
)(1λ1− 1λ2
) [ γ
e.m
](5.19)
As for the angular dependence, the erenkov radiation is forward directioned in a cone centred along
shower axis. Since the light distribution presents azimuthal symmetry,
1
Ndγ
dNdγ
dΩ(α, h, s) =
1
Ndγ
dNdγ
2πsinαdα≡ A (α, h, s)
2πsinα
[1
stereorad
]where α is the angle between the shower axis and the viewing direction− see gure 5.9− andA (α, h, s) ≡
1
Ndγ
dNdγ
dα is parameterised in [17] for α ∈ [5, 60] using CORSIKA showers:
A (α, h, s) =as(s)αc(h)
e−α
αc(h) +bs(s)αcc(h)
e−α
αcc(h)
[1rad
](5.20)
being the second term specially important for large angles α (close to 60) and:
as(s) = 0.42489 + 0.58371s− 0.082373s2 bs(s) = 0.055108− 0.095587s+ 0.056952s2
αc(h) = 0.62694
(Ethr(h)MeV
)−0.60590
αcc(h) = (10.509− 4.9644s)αc(h)
The angles α, αc and αcc are all measured in rad for consistency of expression (5.20). Even though the
parameterisation (5.20) was obtained for the range [5, 60], it is used for α > 60 as well since that is the
procedure followed in the Oine analytical erenkov model [46]. Nevertheless, the erenkov emission is
in principle very small at large α angles when compared to the emission in the parameterisation range.49
The main dierence between the detection of uorescence and erenkov light is in the fact that the
FD telescopes were designed to record the former and that the calibration takes the nitrogen uorescence
spectrum into account. So, the erenkov spectrum must be convoluted with the detector eciency ε(λ)
in the lter wavelength band [280, 430] nm. In mean terms, the eciency in the detection of erenkov
radiation is somewhat low:
ε =(
1280 nm
− 1430 nm
)−1 430 nm∑λn=280 nm
(1
λn − ∆λ2
− 1λn + ∆λ
2
)ε(λn) ' 0.45
where ∆λ = 5 nm. Nevertheless, the erenkov light may be studied by itself, rather than being considered
simply as noise to uorescence collection. Besides, in order to write down the density of direct erenkov
photons at the diaphragm, one needs the eective erenkov wavelength given the detector eciency ε(λ):
λeff =1ε
(1
280 nm− 1
430 nm
)−1 430 nm∑λn=280 nm
(1
λn − ∆λ2
− 1λn + ∆λ
2
)ε(λn)λn ' 356 nm
Finally,
dNdγ
dV(~r;Nmax, Xmax, X0, λGH) = Ne (X;Nmax, Xmax, X0, λGH) · LDF (X,R;Xmax) ·
·∫ ∞ln(Ethr(h)/MeV)
430 nm∑λn=280 nm
yγ
(E, h, λn −
∆λ2, λn +
∆λ2
)ε(λn) · fe(E, s)dlnE ·
· 1
Ndγ
dNγd
dΩ(α, h, s) ∆Ω (~r) · TR
(~r, ~reye, λ
eff
)· TM
(~r, ~reye, λ
eff
) [ γm3
](5.21)
When a shower propagates towards the detector, this is when χ0 <π2 , the direct erenkov light is
important and quite intense because it is highly collimated. However, in the other cases the fraction of
this kind of radiation is very small since A (α, h, s) falls quickly with α.
Scattered erenkov
The erenkov light emitted during shower development is scattered o by Rayleigh and Mie processes
and, consequently, the scattered erenkov radiation becomes important to consider in all geometry setups.
The rst step in the calculation of this contribution at the telescopes is the construction of the beam of
erenkov photons produced along the cascade. The beam is assumed to have dependence uniquely on
the slant depth X and the propagation direction is taken to be parallel to the shower axis. Therefore,
for each event the beam is given by:
Nγ (X,λ1, λ2;Nmax, Xmax, X0, λGH) =
∫ X
X0
Ne (X ′;Nmax, Xmax, X0, λGH) ·
·∫ ∞ln(Ethr(h)/MeV)
yγ (E, h′, λ1, λ2) fe(E, s′)dlnE · TR(X ′, X,
λ1 + λ2
2
)· TM
(X ′, X,
λ1 + λ2
2
)dX ′
ρ(h)(5.22)
Now, as in the previous sections, the density of Rayleigh scattered erenkov photons is:
dNRγ
dV(~r;Nmax, Xmax, X0, λGH) =
430 nm∑λn=280 nm
Nγ
(X,λn −
∆λ2, λn +
∆λ2
;Nmax, Xmax, X0, λGH
)·
·LDF (X,R;Xmax) · 1
NRγ
d2NRγ
dldΩ(~r, λn) ∆Ω (~r) · TR (~r, ~reye, λn) · TM (~r, ~reye, λn) · ε (λn)
[ γm3
](5.23)
50
where the LDF is not the same as in equations (5.18) and (5.21) since in principle the scattered erenkov
light does not present the same lateral distribution as the electrons in an EAS. The angular term1
NRγ
d2NRγ
dldΩ follows from equations (3.6) and (3.7):
1
NRγ
d2NRγ
dldΩ(~r, λ) =
316π
(1 + cos2θs
) ρ(h)XR
(400 nm
λ
)4 [1
m.stereorad
]being θs = α because the beam photons are considered to propagate parallel to the shower axis. The
Rayleigh scattered light presents lobes in the forward and backward directions, but the angular distribu-
tion is not exceedingly dierent from an isotropic one. Indeed, < 316π
(1 + cos2θs
)>= 3
16π
(1 + 1
2
)= 9
32π
and this value is close to 14π .
As for Mie scattered erenkov light, an equation similar to (5.23) is obtained:
dNMγ
dV(~r;Nmax, Xmax, X0, λGH) =
430 nm∑λn=280 nm
Nγ
(X,λn −
∆λ2, λn +
∆λ2
;Nmax, Xmax, X0, λ
)·
·LDF (X,R;Xmax) · 1
NMγ
d2NMγ
dldΩ(~r, λn) ∆Ω (~r) · TR (~r, ~reye, λn) · TM (~r, ~reye, λn) · ε (λn)
[ γm3
](5.24)
where, according to (3.9) and (3.10),
1
NMγ
d2NMγ
dldΩ(~r, λ) = aM · e−
θsθM
e− hhM
lM (λ)
[1
m.stereorad
]The above formula was implemented with aM = 0.891, θM = 26.7, hM = 1.2 km and lM = 14 km
as in chapter 3, but these values correspond to a mean Mie contribution. Indeed, when integrated in the
Auger Oine machinery, the method will use the values updated in a daily basis.
5.2.3 Spot and mercedes
While travelling from the diaphragm until the PMT camera (after reection in the mirror), the photons
undergo two dierent eects due to FD optics: the spot and the mercedes reection. Another important
issue would be the camera shadow, but that is already included in the calibration factor C370/ADC .
A photon coming from a given volume ik may be misplaced in the PMT camera according to the spot
presented in section 4.1.2 − the photon may jump into a pixel i′ 6= i which means it will be associated
with another volume i′k of the same time slot. This eect must be described accurately in order to
calculate the expected photon distribution at the PMTs. In the Monte Carlo integration, each of the
Nvol ·N1 randomly generated points ~r(q) corresponds to a certain direction(θ(q), φ(q)
)in the camera. For
each direction, N2 new directions(θ(r), φ(r)
)=(θ(q), φ(q)
)+(δθ(r), δφ(r)
)are generated according to the
simulated spot and associated to the respective volumes.
As for the mercedes stars, since its reectivity is non-unitary and the calibration constant C370/ADC is
determined by illuminating the whole FD camera uniformly, there must be a correction factor fcorr (θ, φ)
to take into account the sensitivities of the dierent parts of the PMTs. Following [59],
fcorr (θ, φ) =
0.87 if (θ, φ) in mercedes
1.08 otherwise(5.25)
51
Finally, one may write the expected number of detected photons for volume Vik:
Nγ,ik (Nmax, Xmax, X0, λGH) = Nγ,ik (Nmax, Xmax, X0, λGH) · 1N2
∑(θ(r),φ(r))∈pixel i
fcorr
(θ(r), φ(r)
)+∑j 6=i
Nγ,jk (Nmax, Xmax, X0, λGH) · 1N2
∑(θ(r),φ(r))∈pixel i
fcorr
(θ(r), φ(r)
)(5.26)
where the second term represents the contribution from neighbour pixels.
5.2.4 Expected and observed signals
Following the previous sections, the expected signal for a given volume ik is a sum of the dierent light
contributions:
Nγ,ik = Nfγ,ik + Nd
γ,ik + NRγ,ik + NM
γ,ik (5.27)
where multiple scattering processes are overridden. The respective observed signal Nγ,ik is also a sum of
those fractions and eventually some noise and is measured in equivalent 370 nm photons at the diaphragm
as explained in section 4.1.2. To monitor the relative behaviour of the expected and observed quantities
(Nγ,ik and Nγ,ik respectively), several quality estimators were used.
Firstly, consider a certain parameter pik − for instance, the slant depth of the central points of the
volumes, X (~rik). Binning the pik distribution, the expected-to-observed ratio is dened as
e/o (p) =Nγ (p)Nγ (p)
(5.28)
Although useful, the ratio does not take into account the errors associated to expected and observed
values. Nor does it allow a volume-to-volume comparison, i.e. between Nγ,ik and Nγ,ik. Thus, the χikestimator is applied as well:
χik =Nγ,ik −Nγ,ik√
σ2(Nγ,ik
)+ σ2 (Nγ,ik)
(5.29)
being σ2(Nγ,ik
)= N2
γ,ik
(1√Nin,ik
+ 1√Nvol·N1
)2
(confer equations (5.5) and (5.15)) and
σ2 (Nγ,ik) = σ2(C370/ADC · (NADC,i (tk)−Nped,i)
)=√|Nγ,ik|
2
+ C2370/ADC · σ
2 (Nped,i)
' |Nγ,ik|+ C2370/ADC · σ
2 (Nped,i)
Nγ,ik is a sum of a signal Ns,ik and a background Nb,ik, where the pedestal Nped,i appearing on
equation (4.7) has already been subtracted to obtain Nb,ik. To nd the distribution of this background,
the negative-valued signals Nγ,ik in events recorded throughout July 2006 are tted to a gaussian as
shown in gure 5.10. Thus, the background Nb,ik is roughly a normalised gaussian distribution Pb with
mean µb = 0 and standard deviation σb = 25: Pb(x) = Gaus (x;µb, σb) ≡ 1√2πσb
e− (x−µb)
2
2σ2b . Besides, the
term C2370/ADC · σ
2 (Nped,i) is equal to the standard deviation σb and, hence, σ2 (Nγ,ik) ' |Nγ,ik|+ 252.
Using χik, a χ2 =∑i,k χ
2ik is dened for each event. Given Nvol and the number of t parameters
Npar, the number of degrees of freedom is Ndf = Nvol −Npar and χ2/Ndf represents an estimator of the
concordance between observation and expectation.
52
Figure 5.10: Gaussian t to the Nγ,ik distribution for Nγ,ik < 0. All data collected throughout July 2006was used to produce the plot.
However, when Nγ,ik and Nγ,ik are small, they do not follow gaussian distributions and χ2 is not valid.
So, one must proceed to a likelihood function, which is the product of the probabilities of observing Nγ,ikwhen Nγ,ik is the expected value:
L =∏i,k
P1
(Nγ,ik, Nγ,ik
)(5.30)
Since Nγ,ik = Ns,ik + Nb,ik, the probability P1
(Nγ,ik, Nγ,ik
)is the convolution of the probabilities
of observing Ns,ik as signal and Nb,ik = Nγ,ik −Ns,ik as background:
P1
(Nγ,ik, Nγ,ik
)=
Nγ,ik∑Ns,ik=0
Ps
(Ns,ik, Nγ,ik
)· Pb (Nγ,ik −Ns,ik) (5.31)
For Nγ,ik ≤ 10, Ps is a normalised Poisson distribution of mean νs = Nγ,ik: Ps (x, νs) = Poisson (x; νs) ≡νxs e−νs
x! . When Nγ,ik > 10, Ps is well described by a gaussian distribution with µs = σ2s = νs and, therefore,
(5.31) becomes a convolution of two gaussians:
P1
(Nγ,ik, Nγ,ik
)=
∫ Nγ,ik
0
Gaus
(Ns,ik; Nγ,ik,
√Nγ,ik
)·Gaus (Nγ,ik −Ns,ik; 0, 25) dNs,ik
= Gaus
(Nγ,ik; Nγ,ik,
√252 + Nγ,ik
)=
1√2π(
252 + Nγ,ik
)e− (Nγ,ik−Nγ,ik)2
2(252+Nγ,ik)(5.32)
After determining each P1
(Nγ,ik, Nγ,ik
), the likelihood function (5.30) is more easily analysed in
terms of its logarithm:
lnL =∑i,k
lnP1
(Nγ,ik, Nγ,ik
)(5.33)
5.3 Validation
The validation of both geometry and prole 3D reconstructions is performed using the low energy simu-
lation from the Lecce-L'Aquilla Auger group [60, 75]. The simulation consists of 1017, 1017.5, 1018 and
1018.5 eV protons showers generated with CORSIKA and then integrated in the PAO detector simu-
lation chain [46]. The shower cores were uniformly distributed on the ground in the eld of view of
telescope 4 from Los Leones eye and no Mie scattering was considered. Moreover, all light arriving at53
the telescopes was spread according to the Góra cumulative function (5.12) in order to mimic the shower
lateral prole. The longitudinal proles, on the other hand, follow a shifted Gaisser-Hillas formula
Ne (X −X1;Nmax, Xmax, X0, λGH), where X1 is the depth of the rst interaction point.
To illustrate the results from the 3D reconstruction some events are analysed xing Nmax, Xmax,
X0, X1 and λGH to the respective simulation values, considering no Mie attenuation factor TM nor Mie
scattered erenkov light and using the Góra LDF for uorescence, direct and scattered erenkov light.
The latter assumption is probably not true, but reproduces what was done in the detector simulation
chain when spreading all light according to the Góra cumulative function. Figures 5.11(a) and 5.11(b)
represent the observed (grey shaded area) and expected (red line) signals as functions of the depth-like
variables XNP ≡ X (~rnp,ik) and RCP ≡ R (~rik) for a 1018.5 eV simulated event. The green and blue lines
indicate, respectively, the direct and Rayleigh scattered erenkov contributions for the total expectation
in red. The concordance between observed and expected behaviours is evident. The event triggered
telescopes 3 and 4 from Los Leones eye and that is the reason of the peak at X ∼ 675 gcm−2: in this
region the signals detected by both telescopes add up. As for the depression at X ∼ 950 gcm−2, it is
due to the fact that two pixels did not pass the trigger requirements. Besides, notice that the observed
values may fall below 0 since the PMT pedestal uctuates; however, the expected quantities are always
non-negative because they are calculated as a physical number of photons.
In order to monitor the concordance between observed and expected signals for the referred event,
the ratio e/o is presented in gures 5.11(c) and 5.11(d), while gures 5.11(e) and 5.11(f) show the
χik distribution and the dependence of the mean lnP1
(Nγ,ik, Nγ,ik
)(confer equation (5.33)) on RCP .
Although with some uctuations, e/o is reasonably close to 1 in the whole range of X and R. As for χik,
one would expect a gaussian distribution centred in 0 and with unitary standard deviation, but there are
clearly some volumes that deviate from this behaviour. Nevertheless, most volumes correspond to almost
null χik values, which is a reection of the empirically good concordance shown in gures 5.11(a) and
5.11(b). Finally, the mean values of lnP1
(Nγ,ik, Nγ,ik
), plotted in gure 5.11(f), are upper limited by the
probability P1
(Nγ,ik, Nγ,ik
)that depends on Nγ,ik, but yields approximately −lnP1
(Nγ,ik, Nγ,ik
)'
4.1− 4.2. Furthermore, the highest RCP are associated to volumes where the expected signal is close to
0 and the observed one is in the order of the background, i.e. σb = 25 − the plateau at greater RCP has
then a value of ∼ lnP1 (25, 0) = −4.64.
Figure 5.12 illustrates a 1018.5 eV simulated event where the observed signal is dominated by Rayleigh
scattered erenkov light. In face of the narrow slant depth window overviewed by the telescope in
this case, it is encouraging that the 3D method predicts to a quite good approximation the observed
distribution, while the KG reconstruction measures an energy somewhat lower than that simulated (∼1017.89 eV).
54
(a) (b)
(c) (d)
(e) (f)
Figure 5.11: In (a) and (b), the dependence of the observed (grey shaded area) and expected (red line)signals on XNP and RCP are presented for the 1018.5 eV simulated event SD 78 (from job 0). The directand Rayleigh scattered erenkov expected fractions are signaled by the green and blue lines respectively.This event presents Rp ' 7.6 km and χ0 ' 90.8. The behaviour of the ratio e/o with XNP (c) and
RCP (d), the χik distribution (e) and the dependence of the mean lnP1
(Nγ,ik, Nγ,ik
)on RCP (f) are
also shown for the same event.
55
Figure 5.12: Observed (grey shaded area) and expected (red line) signals for the 1018.5 eV simulated eventSD 14 (from job 0). As in gure 5.11, the green and blue lines represent direct and scattered erenkovcontributions at the telescopes respectively. This event presents Rp ' 1.6 km and χ0 ' 139.3.
56
Chapter 6
Lateral prole measurements
In order to perform a measurement of the shower lateral prole, one must ensure in the rst place
that no signicant bias is being introduced by the 3D reconstruction. This is accomplished through a
systematic study of the method proposed in the last chapter using a sample of several simulated events.
But to proceed to an analysis of real data, where a priori there is no indication on the parameters
Nmax, Xmax, X0 or λGH as in the simulation, one needs to start from the parameters reconstructed
by the KG (standard) procedure. Using these parameters, the next step is to understand the lateral
sensitivity achieved by the 3D reconstruction and dene the set of quality cuts required to have reasonable
sensitivities.
6.1 Systematic study of the 3D reconstruction
The comparison between expectation and observation, already performed for isolated events in sec-
tion 5.3, is presented in gure 6.1 for 30 1018.5 eV events from the simulation of the Lecce-L'Aquilla
group. The expected signals computed with both the simulated and the KG-reconstructed parameters
(Nmax, Xmax, X0, λGH) are plotted. The sample of events was selected requiring 3D and KG prole re-
constructions, χ3D0 ≥ 45 and
∣∣log10Esim − log10E
KG∣∣ ≤ 0.5. The latter quality cut is needed to prevent
the events misreconstructed by the KG method from contaminating the 3D analysis. When processing
real data this cut is obviously inappropriate.
Firstly, the results with the simulated parameters seem to describe inaccurately the depths below
∼ 550 gcm−2 as evident in gures 6.1(a) and 6.1(c), but this feature is absent when using the KG
reconstruction. A misinterpretation or bad handling of the simulation depth parameters is probably the
reason for such dierence.
Another interesting feature is shown in gure 6.1(d): the ratio e/o corresponding to the use of simu-
lated parameters is slightly above 1 for RCP . 10 gcm−2 and below afterwards. Such a behaviour may
be explained by the s-dependence of the Góra LDF. Indeed, in the denition s = 31+2Xmax/X
one uses
the shower maximum Xmax from simulation and X from the reconstructed method, thus introducing a
bias. So, it is more adequate to use the KG-reconstructed Xmax − the result is presented in red in gure
6.1(d) and is more at and close to 1. Notice that above RCP ∼ 25 gcm−2, the wide uctuations on the
ratio e/o are due to the low number of detected volumes.
In what refers to gures 6.1(e) and 6.1(f), it is clear that the use of the KG parameters instead of the
simulation ones reduces the χ2/Ndf values. Besides, the χik distribution seems slightly better as well.
57
(a) (b)
(c) (d)
(e) (f)
Figure 6.1: In (a) and (b), the dependence of the observed (grey shaded area) and expected (red line)signals on XNP (a) and RCP (b) for 30 1018.5 eV simulated events. The direct and Rayleigh scatterederenkov expected fractions are signaled by the green and blue lines respectively. Dashed lines refer toexpected signals calculated with the KG parameters, while solid lines represent the use of the simulatedparameters. The value of RM was xed to 9.6 gcm−2 to produce these plots. The behaviour of the ratioe/o with XNP (c) and RCP (d), the χik distribution (e) and the χ2/Ndf values per event (f) are alsoshown for the same simulation set. Notice that in plot (d), for RCP & 25 gcm−2, the quantity of detectedvolumes is low and thus there are signicant uctuations.
58
(a) (b)
Figure 6.2: The behaviour of the estimators χ2 (RM ) /Ndf (in black) and lnL (RM ) (in red) with theeective parameter RM for the close simulated event SD 78 (from job 0) (a) and the distant one SD 10(from job 0) (b).
6.2 Lateral sensitivity
Analysing the lateral distribution functions presented in section 5.2.1 such as (5.13), one concludes that
a straightforward way to study the lateral sensitivity is to dene RM as an eective parameter. By
varying RM and computing the respective estimators χ2 (RM ) /Ndf and lnL (RM ), a preliminary t
is performed to nd the best parameter value R∗M for which χ2 (R∗M ) /Ndf and lnL (R∗M ) are mini-
mal. The uncertainties σ+ and σ− on R∗M are then xed by an unitary variation ∆(χ2 (RM ) /Ndf
)≡
χ2 (RM ) /Ndf − χ2 (R∗M ) /Ndf = 1, that corresponds to ∆lnL (RM ) ≡ lnL (RM )− lnL (R∗M ) = Ndf/2 −this correspondence is easily shown by replacing P1 in equation (5.33) by a gaussian distribution.
Figure 6.2 shows the study of the lateral sensitivity for two 1018.5 eV simulated events using the KG
reconstructed parameters. The events dier essentially on the mean distance of the central points of the
volumes to the respective eye, dCP−eye: event SD 78 (from job 0) presents dCP−eye ' 8.4 km, while
in event SD 10 (from job 0) dCP−eye ' 26 km. It is clear that the closer event enables a reasonable
determination of the eective parameter RM(RM = 9.6 + 4.1− 3.0 gcm−2
), whereas in the other one
the 3D reconstruction has no sensitivity(RM = 15.6+ > 15.0− 15.6 gcm−2
).
Notice that, in regard of the discussion in section 5.2.4 about the dierences between χ2/Ndf and lnL,the black and red curves in gure 6.2 do not present exactly the same behaviour as expected, but they
yield similar sensitivity results in those examples.
6.3 Data
The lateral sensitivity was studied in real data collected throughout July 2006 requiring KG and 3D
prole reconstructions and χ3D0 ≥ 45. Since in the data Mie scattering is important, the analysis takes
into account both the Mie attenuation factor (3.12) and the Mie scattered erenkov light fraction (5.24).
Moreover, in order to analyse events where the 3D method is potentially more sensitive to the lateral
distribution, the empirical cut (5.3) (with d∗CP−eye = 5 km and d∗CP−eye = 10 km) is applied to select
events simultaneously close to the detector and with high energies.
The simulation from the Lecce-L'Aquilla group does not contain many events passing the empirical
cut (5.3): only 3 showers for the cut with d∗CP−eye = 5 km and 15 with d∗CP−eye = 10 km. Consequently,
there is the need to generate a signicant number of events in the region where the 3D method is more
accurate. CORSIKA showers are being run and integrated in the Auger Oine detector simulation
59
at dierent distances away from the FD eyes. Nevertheless, the 15 showers passing the cut (5.3) with
d∗CP−eye = 10 km are presented in gure 6.3. Furthermore, gure 6.4 shows the expected and observed
signals of 50 showers passing the cut (5.3) with d∗CP−eye = 5 km, while gure 6.5 refers to 50 showers
passing the same cut with d∗CP−eye = 10 km. The most evident and interesting feature is that presented
by gures 6.3(d), 6.4(d) and 6.5(d): the ratio e/o decreases steeply with RCP . Indeed, both simulation
and data seem to present a more sparse lateral distribution than expected, with lower signals near the
axis(RCP . 5 gcm−2
)and higher ones away from it. The reason for this behaviour is still not clear.
Another remark should be made in regard of the χik distributions in plots 6.3(e), 6.4(e) and 6.5(e).
In the rst place, those distributions present only the volumes where Nin,ik 6= 0 (for consistency of the
χik value). Besides, the t presented in gure 6.3(e) is not totally rigorous since there seem to exist two
dierent populations of volumes ik. Anyhow, and taking into account 6.4(e) and 6.5(e) as well, the mean
value of χik is negative, which means that Nγ −Nγ is a fairly constant positive value. Such shift is not
yet fully understood but is probably linked to the way the observed number of photons is obtained.
As in the simulation analysis, the sensitivity to the RM eective parameter was studied in two real
showers and is shown in gure 6.6. In both cases 9.6 gcm−2 seems to be included in the measurement.
60
(a) (b)
(c) (d)
(e) (f)
Figure 6.3: In (a) and (b), the dependence of the observed (grey shaded area) and expected (red line)signals on XNP and RCP are presented for the 15 events from the Lecce-L'Aquilla simulation and passingthe cut (5.3) with d∗CP−eye = 10 km. The direct and Rayleigh scattered erenkov expected fractions aresignaled by the green and blue lines respectively. The behaviour of the ratio e/o with XNP (c) and RCP(d), the χik distribution (e) and the dependence of the mean lnP1
(Nγ,ik, Nγ,ik
)on RCP (f) are also
shown for the same simulation sample.
61
(a) (b)
(c) (d)
(e) (f)
Figure 6.4: In (a) and (b), the dependence of the observed (grey shaded area) and expected (red line)signals on XNP (a) and RCP (b) for 50 events collected in June/July 2006 and passing the cut (5.3) withd∗CP−eye = 5 km. The direct erenkov expected fraction is signaled by the green line, while Rayleighand Mie scattered erenkov components are represented in blue and magenta respectively. The value ofRM was xed to 9.6 gcm−2 to produce these plots. The behaviour of the ratio e/o with XNP (c) and
RCP (d), the χik distribution (e) and the dependence of the mean lnP1
(Nγ,ik, Nγ,ik
)on RCP (f) are
also shown for the same data set. Notice that in plot (c) the ratio e/o grows for XNP & 1150 gcm−2,possibly because the Mie light fraction (5.24) is over estimated in this region − recall that the componentshown in magenta is only a mean one. Besides, the statistics in that region is small and consequentlylarge uctuations are expected.
62
(a) (b)
(c) (d)
(e) (f)
Figure 6.5: In (a) and (b), the dependence of the observed (grey shaded area) and expected (red line)signals on XNP (a) and RCP (b) for 50 events collected in July 2006 and passing the cut (5.3) withd∗CP−eye = 10 km. The direct erenkov expected fraction is signaled by the green line, while Rayleighand Mie scattered erenkov components are represented in blue and magenta respectively. The value ofRM was xed to 9.6 gcm−2 to produce these plots. The behaviour of the ratio e/o with XNP (c) and
RCP (d), the χik distribution (e) and the dependence of the mean lnP1
(Nγ,ik, Nγ,ik
)on RCP (f) are
also shown for the same data set.
63
(a) (b)
Figure 6.6: The behaviour of the estimators χ2 (RM ) /Ndf (in black) and lnL (RM ) (in red) with theeective parameter RM for two real showers recorded in July 2006. Plot (a) corresponds to event SD2425381 with dCP−eye ' 4.7 km, while (b) corresponds to event SD 2425226 with dCP−eye ' 7.5 km.
64
Chapter 7
Conclusion and prospects
The original work presented in this thesis was entirely developed in the context of the Pierre Auger Ob-
servatory, that is today the leading experiment in the eld of ultra high energy cosmic rays. The technical
documents and tools produced by the PAO Collaboration were extremely valuable in understanding the
physics behind cosmic ray detection and in event analysis. Moreover, the data and simulation sets used
were also provided by the Collaboration.
A three dimensional method to reconstruct EAS from uorescence and hybrid data was conceived
for event analysis at the PAO. The innovative idea of this method consists in using the sampling time
at the telescopes as a third dimension in space. Hence, instead of assuming line propagation in shower
development, all the available information recorded by the FD telescopes is used to locate the shower
in space. An iterative method for the geometry reconstruction of extensive air showers was then built
based upon inertia considerations and a 3D event display was developed using existing software. Once
the geometry is xed, the reconstruction of the shower 3D prole follows. Such reconstruction was
accomplished through Monte Carlo calculations by considering the detailed optics of the telescopes and
by taking into account uorescence and (direct and scattered) erenkov light.
The 3D method constitutes a powerful tool in the reconstruction of EAS and related studies and it
was validated using the proton simulation from the Lecce-L'Aquilla group. Furthermore, the sensitivity of
the method to the eective parameter RM was performed in order to get a rst preliminary measurement
of the shower lateral prole. Both simulation and data samples were considered in that analysis.
The tool developed allows a systematic study of EAS features and a comparison between existing
simulation and data − recall that the Pierre Auger Observatory has already further exposure than
AGASA. Firstly, a more consistent analysis of larger simulation and data samples may open the possibility
of understanding the consequences of dierent hadronic models in shower development. Furthermore, the
lateral distribution of direct and scattered erenkov light must be understood and parameterised, but
such task requires a three dimensional simulation yet to be implemented. Another relevant channel is the
search for new physics by identifying particularly 'fat' or irregular events that may correspond to double
bangs, decays of new particles or other exotic phenomena.
65
Bibliography
[1] T. Stanev, High Energy Cosmic Rays, Springer Praxis Books, 2004.
[2] J. Cronin, Cosmic rays: the most energetic particles in the universe, Reviews of Modern Physics,
71(2), 165, 1999.
[3] A. Olinto, Ultra high energy cosmic rays and the magnetized universe, Journal of the Korean Astro-
nomical Society, 37, 413-420, 2004.
[4] K. Greisen, End to the cosmic-ray spectrum?, Physical Review Letters, volume 16(17), 748, 1966.
[5] G. Zatsepin and V. Kuzmin, Upper limit of the spectrum of cosmic rays, Journal of Experimental
and Theoretical Physics, 4(3), 78, 1966.
[6] M. Boratav, Probing theories with cosmic rays, Europhysics News, 33(5), 2002.
[7] L. Bergström and A. Goobar, Cosmology and Particle Astrophysics, John Wiley & Sons, 1999.
[8] J. Matthews, A Heitler model of extensive air showers, Astroparticle Physics, 22, 387-397, 2005.
[9] W. Yao et al., Review of Particle Physics (Particle Physics Booklet), Journal of Physics, G 33, 1,
2006.
[10] S. Andringa, public seminar at Centro de Física Teórica e Computacional, 2007.
[11] F. Salamida, Ultra High Energy Cosmic Rays in AUGER: Hybrid Simulation and Reconstruction,
PhD thesis at Università degli Studi dell'Aquilla, 2006.
[12] B. Dawson, Pierre Auger Project Note GAP-96-017.
[13] D. Góra et al., Universal lateral distribution of energy deposit in air showers and its application to
shower reconstruction, astro-ph/0505371v1, 2005 (also Pierre Auger Project Note GAP-2005-093).
[14] AGASA website, http://www-akeno.icrr.u-tokyo.ac.jp/AGASA/.
[15] J. Matthews, Pierre Auger Project Note GAP-98-002.
[16] P. Sokolsky, Introduction to Ultra High Energy Cosmic Ray Physics, Westview Press, 2004.
[17] F. Nerling, Description of Cherenkov Light Production in Extensive Air Showers, PhD thesis at
Universität Karlsruhe, 2005 (also Pierre Auger Project Note GAP-2005-063).
[18] J. Diaz, M. Amaral and R. Shellard, Weakly interacting particles viewed by uorescence detectors.
[19] MAGIC website, http://wwwmagic.mppmu.mpg.de/index.en.html.
66
[20] B. Dawson, Pierre Auger Project Note GAP-2002-067.
[21] HiRes website, http://hires.physics.utah.edu/.
[22] http://www.astro.psu.edu/users/nnp/cr.html.
[23] R. Abbasi et al., Observation of the GZK Cuto by the HiRes Experiment, astro-ph/0703099v1,
2007.
[24] P. Mantsch for the Pierre Auger Collaboration, The Pierre Auger Observatory Progress and First
Results, 29th International Cosmic Ray Conference, Pune, India, 2005.
[25] P. Sommers for the Pierre Auger Collaboration, First Estimate of the Primary Cosmic Ray Energy
Spectrum above 3 EeV from the Pierre Auger Observatory, 29th International Cosmic Ray Confer-
ence, Pune, India, 2005.
[26] A. Tripathi et al., A Preliminary Estimate of the Cosmic Ray Energy Spectrum from Pierre Auger
Observatory Data, 29th International Cosmic Ray Conference, Pune, India, 2005.
[27] M. Roth for the Pierre Auger Collaboration, Measurement of the UHECR Energy Spectrum using
data from the Surface Detector of the Pierre Auger Observatory, 30th International Cosmic Ray
Conference, Mérida, México, 2007.
[28] P. Luis for the Pierre Auger Collaboration, Measurement of the UHECR spectrum above 1019 eV at
the Pierre Auger Observatory using showers with zenith angles greater than 60, 30th International
Cosmic Ray Conference, Mérida, México, 2007.
[29] L. Perrone for the Pierre Auger Collaboration, Measurement of the UHECR energy spectrum from
hybrid data of the Pierre Auger Observatory, 30th International Cosmic Ray Conference, Mérida,
México, 2007.
[30] T. Yamamoto for the Pierre Auger Collaboration, The UHECR spectrum measured at the Pierre
Auger Observatory and its astrophysical implications, 30th International Cosmic Ray Conference,
Mérida, México, 2007.
[31] J. Matthews for the Pierre Auger Collaboration, A description of some ultra high energy cosmic
rays observed with the Pierre Auger Observatory, 29th International Cosmic Ray Conference, Pune,
India, 2005.
[32] M. Risse et al., Photon air showers at ultra-high energy and the photonuclear cross-section, astro-
ph/0512434v1, 2005.
[33] M. Risse for the Pierre Auger Collaboration, Upper limit on the primary photon fraction from the
Pierre Auger Observatory, 29th International Cosmic Ray Conference, Pune, India, 2005.
[34] J. Doe for the Pierre Auger Collaboration, Search for Ultra-High Energy Photons with the Pierre
Auger Observatory, 30th International Cosmic Ray Conference, Mérida, México, 2007.
[35] M. Risse and P. Homola, Search for ultra-high energy photons using air showers, astro-ph/0702632v1,
2007.
67
[36] A. Letessier-Selvon for the Pierre Auger Collaboration, Anisotropy Studies Around the Galactic
Center at EeV Energies with Auger data, 29th International Cosmic Ray Conference, Pune, India,
2005.
[37] B. Revenu for the Pierre Auger Collaboration, Search for localised excess uxes in Auger sky and
prescription results, 29th International Cosmic Ray Conference, Pune, India, 2005.
[38] Pierre Auger Progress Report December 2006 & January 2007.
[39] Pierre Auger Progress Report February 2007 & March 2007.
[40] Pierre Auger Observatory ocial website, http://www.auger.org.
[41] X. Bertou for the Pierre Auger Collaboration, Performance of the Pierre Auger Observatory Surface
Array, 29th International Cosmic Ray Conference, Pune, India, 2005.
[42] J. Bellido for the Pierre Auger Collaboration, Performance of the Fluorescence Detectors of the
Pierre Auger Observatory, 29th International Cosmic Ray Conference, Pune, India, 2005.
[43] G. Matthiae, Pierre Auger Project Note GAP-2001-037.
[44] J. Abraham et al., Properties and performance of the prototype instrument for the Pierre Auger
Observatory, Nuclear Instruments and Methods in Physics Research, A 523, 50-95, 2004.
[45] M. Giller et al., Pierre Auger Project Note GAP-2000-032.
[46] Auger Oine Software.
[47] Karlsruhe group optics simulation.
[48] B. Flick et al., Pierre Auger Project Note GAP-2004-003.
[49] B. Flick et al., The Central Laser Facility at the Pierre Auger Observatory, Journal of Instrumenta-
tion, 1 P11003, 2006.
[50] L. Wiencke for the Pierre Auger Collaboration, Extracting rst science measurements from the south-
ern detector of the Pierre Auger Observatory, astro-ph/0607449v1, 2006.
[51] R. Cester et al. for the Pierre Auger Collaboration, Atmospheric aerosol monitoring at the Pierre
Auger Observatory, 29th International Cosmic Ray Conference, Pune, India, 2005.
[52] P. Younk et al., Pierre Auger Project Note GAP-2006-005.
[53] A. Filipi£i£ et al., Pierre Auger Project Note GAP-2002-004.
[54] V. Rizi et al., Pierre Auger Project Note GAP-2002-004.
[55] C. Bonifazi for the Pierre Auger Collaboration, Angular Resolution of the Pierre Auger Observatory,
29th International Cosmic Ray Conference, Pune, India, 2005.
[56] D. Barnhill et al. for the Pierre Auger Collaboration, Measurement of the Lateral Distribution Func-
tion of UHECR Air Showers with the Pierre Auger Observatory, 29th International Cosmic Ray
Conference, Pune, India, 2005.
68
[57] P. Ghia for the Pierre Auger Collaboration, Statistical and systematic uncertainties in the event
reconstruction and S(1000) determination by the Pierre Auger surface detector, 29th International
Cosmic Ray Conference, Pune, India, 2005.
[58] I. Maris et al., ADST and EventBrowser Reference Manual - Data Summary Trees and Shower
Visualization for Reconstructed Auger Events, 2006.
[59] D. Allard et al., Pierre Auger Project Note GAP-2006-026.
[60] L. Perrone, S. Petrera and F. Salamida, Pierre Auger Project Note GAP-2005-087.
[61] M. Unger, Pierre Auger Project Note GAP-2006-010.
[62] F. Nerling et al., Universality of electron distributions in high-energy air showers − Description of
Cherenkov light production, Astroparticle Physics, 24, 421-437, 2006.
[63] K. Kampert for the Pierre Auger Collaboration, The Pierre Auger Observatory − Status and
Prospects, astro-ph/0501074, 2005.
[64] M. Mostafá for the Pierre Auger Collaboration, The Hybrid Performance of the Pierre Auger Ob-
servatory, 29th International Cosmic Ray Conference, Pune, India, 2005.
[65] B. Dawson, The Pierre Auger Observatory at 1018 eV.
[66] A. Etchegoyen et al., Pierre Auger Enhancements: Transition from Galactic to Extragalactic Cosmic
Ray Sources.
[67] Proposal of HEAT, Enhancement of the PAO Fluorescence Detector by Additional Telescopes with
Elevated Field of View: High Elevation Auger Telescopes (HEAT), 2006.
[68] H. Klages for the Pierre Auger Collaboration, HEAT: Enhancement Telescopes for the Pierre Auger
Southern Observatory, 30th International Cosmic Ray Conference, Mérida, México, 2007.
[69] A. Etchegoyen for the Pierre Auger Collaboration, AMIGA, 30th International Cosmic Ray Confer-
ence, Mérida, México, 2007.
[70] Auger Radio website, http://www.augerradio.org/wiki/moin.cgi/.
[71] The Pierre Auger Northern Observatory Design Report, 2007.
[72] S. Andringa, M. Pato and M. Pimenta for the Pierre Auger Collaboration, 3D Reconstruction of
Extensive Air Showers from Fluorescence Data, 30th International Cosmic Ray Conference, Mérida,
México, 2007.
[73] R.S. MacLeod and C.R. Johnson, Map3d: Interactive Scientic Visualization for Bioengineering
Data. In IEEE Engineering in Medicine and Biology Society 15th Annual International Conference,
pages 30-31, IEEE Press, 1993.
[74] D. Góra et al., Pierre Auger Project Note GAP-2004-034.
[75] M. Settimo, L. Perrone and I. Mitri, Pierre Auger Project Note GAP-2006-015.
69