Detecção de múons com o AMIGA no
Observatório Pierre Auger
Muon detection with AMIGA at the Pierre
Auger Observatory
CAMPINAS 2018
Muon detection with AMIGA at the Pierre
Auger Observatory
Detecção de múons com o AMIGA no
Observatório Pierre Auger
Tese apresentada ao Instituto de Física Gleb Wataghin da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obtenção do título de Doutor em Ciên-cias.
Thesis presented to the Institute of Physics Gleb Wataghin of the University of Camp-inas in partial ful llment of the requirements for the degree of Doctor in Science.
Supervisor/Orientador: Prof. Dr. Ernesto Kemp Este exemplar corresponde à versão final
da tese defendida pelo aluno Bruno Daniel, e orientada pelo Prof. Dr. Ernesto Kemp.
Campinas 2018
DanTese (doutorado) – Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin.
Dan1. Observatório Pierre Auger. 2. Raios cósmicos. 3. Múons. I. Kemp,
Ernesto, 1965-. II. Universidade Estadual de Campinas. Instituto de Física Gleb Wataghin. III. Título.
Informações para Biblioteca Digital
Título em outro idioma: Detecção de múons com o AMIGA no Observatório Pierre Auger Palavras-chave em inglês:
Pierre Auger Observatory Cosmic rays
Muons
Área de concentração: Física Titulação: Doutor em Ciências Banca examinadora:
Carola Dobrigkeit Chinellato Anderson Campos Fauth Ettore Segreto
Edivaldo Moura Santos Luiz Vitor de Souza Filho
Data de defesa: 22-02-2018
Programa de Pós-Graduação: Física
“GLEB WATAGHIN”, DA UNIVERSIDADE ESTADUAL DE CAMPINAS, EM 22/02/2018.
COMISSÃO JULGADORA:
- Profa. Dra. Carola Dobrigkeit Chinellato – (Presidente) – IFGW/UNICAMP - Prof. Dr. Anderson Campos Fauth - IFGW/UNICAMP
- Prof. Dr. Ettore Segreto- IFGW/UNICAMP
- Prof. Dr. Edivaldo Moura Santos – UNIVERSIDADE DE SÃO PAULO - USP - Prof. Dr. Luiz Vitor de Souza Filho – UNIVERSIDADE DE SÃO PAULO - USP
A Ata de Defesa, assinada pelos membros da Comissão Examinadora, consta no processo de vida acadêmica do aluno.
CAMPINAS 2018
people to name individually), which helped me in many subjects, especially in making my routine more fun. I am sure the time we spent having coee would be enough for another Ph.D., but their friendship and moments we shared are much more valuable. Special thanks to Lucas, who shared the o ce with me for many years and became a friend I will carry for the whole life.
Another acknowledgement to all the people who collaborated directly to this work. To my advisor, Professor Ernesto Kemp, not always physically present, but con-stantly in uencing my way of thinking and acting. People from the ITEDA in Buenos Aires, who welcomed me and taught many things that made a big dierence at the end. Professor Antonella Castellina from Torino, for being part of the most transforming ex-perience I had in my life when I lived in a dierent culture and worked in a dierent methodology. Professor Carola Chinellato, who helped me a lot with all the bureau-cracy and other issues I had. All other professors and colleagues from the Pierre Auger collaboration.
Finally, I acknowledge all institutions who made this work possible. The State University of Campinas (UNICAMP) for the infrastructure for my research and courses. The Pierre Auger Collaboration, in which I had the pleasure to take part. The fund-ing agencies CNPq (process 141048/2012-3) and FAPESP (processes 2012/15476-8 and 2013/17546-6).
O Observatório Pierre Auger foi construído para estudar os raios cósmicos de energia ultra-alta, de forma que se possa entender sua origem, mecanismos de aceleração, propagação e composição química. É utilizada uma técnica híbrida, cobrindo uma área de 3000 km² com um conjunto de 1600 estações de detecção de radiação Cherenkov na água e 24 telescópios de uorescência. Resultados de grande relevância foram obtidos desde o início de sua operação em 2004, principalmente sobre as características do es-pectro de energia, composição e anisotropia dos raios cósmicos com energia acima de 3 EeV. O estudo destas partículas é fundamental para o entendimento da astrofísica e física hadrônica a energias que estão além do alcance dos aceleradores de partículas atuais. Uma extensão do observatório foi construída para permitir a detecção de eventos com
energias mais baixas, até 1017 eV, fornecendo informações detalhadas sobre a composição
de massa na região de energia abaixo do tornozelo do espectro. Para isto foram incluídos mais três telescópios de uorescência e uma região com 60 detectores Cherenkov com metade do espaçamento (750 m) que no restante do observatório, denominada AMIGA. Ao lado de cada estação do AMIGA serão enterrados 30 m² de cintiladores, que permi-tirão a contagem direta de múons em chuveiros atmosféricos. Esta tese está relacionada ao desenvolvimento do AMIGA, principalmente à detecção dos múons. Simulações de chuveiros atmosféricos foram realizadas, para auxiliar na compreensão das característi-cas das diferentes componentes (muônica, eletromagnética e hadrônica) na superfície e embaixo da terra, à profundidade dos contadores de múons. Usando dados obtidos nos primeiros meses de operação da célula unitária de sete estações do AMIGA, a técnica de contagem de múons foi estudada. Os detectores gêmeos instalados em duas estações foram usados para checar a consistência das medidas e calcular a acurácia da contagem de múons, resultando na descoberta de problemas de calibração em alguns módulos. Uma análise da blindagem embaixo da terra também foi realizada com dados de cintiladores a profundidades diferentes, fornecendo parâmetros que auxiliaram na escolha da posição ideal para os detectores, que deve maximizar o sinal de múons e reduzir a contaminação eletromagnética.
of the Observatory was also built to extend the measurements to the energy region down
to 1017 eV, thus getting new insights in the region below the ankle of the spectrum,
with the addition of composition information. It includes three additional uorescence detectors (HEAT) and an in ll of 60 water-Cherenkov stations (AMIGA - Auger Muons and In lled Ground Array) placed at a mutual distance of 750 m (half the standard one). Aside from each station of the in ll, 30 m² buried scintillator counters will allow counting muons directly. This thesis is related to the development of AMIGA, especially in what regards the muon detection. Air-shower simulations were performed to provide insights on the behavior of the dierent particle components at the surface and underground at the depth of the muon counters. Using data collected in the rst months of operation of the AMIGA unitary cell of seven stations, the muon counting technique was reviewed. The twin detectors deployed at two locations were used to check the consistency of the measurements and to obtain the accuracy of the muon counters, resulting in the discovery of calibration problems in some of the detectors. A shielding analysis was performed with data of scintillators placed at dierent depths, providing information which contributed to the choice of the ideal point to maximize the muon signal and minimize electromagnetic punch-through.
1 Introduction 10
2 Ultra-high energy cosmic rays 12
2.1 Origin: where do UHECRs come from? . . . 12
2.2 Propagation: how do UHECRs reach the Earth? . . . 15
2.3 Energy spectrum: what are the energies of UHECRs reaching the Earth? . 15 2.4 Mass composition: what type of particle are the UHECRs? . . . 18
2.5 Extensive air-showers: what happens when UHECRs reach the atmosphere? 20 2.5.1 Main features of a shower . . . 21
2.5.2 Hadronic interaction models and the muon excess . . . 22
2.6 Experimental techniques: how can UHECRs be detected? . . . 23
3 The Pierre Auger Observatory 26 3.1 Fluorescence detector . . . 26
3.2 Surface detector . . . 31
3.2.1 Energy reconstruction . . . 32
3.3 Enhancements of the Observatory . . . 32
3.3.1 AMIGA . . . 35
3.4 The AugerPrime upgrade . . . 39
3.4.1 Surface scintillator detector . . . 40
3.4.2 Other features of AugerPrime . . . 41
4 Air-shower simulations 43 4.1 Air-shower particles at the surface . . . 44
4.1.1 The electromagnetic component . . . 47
4.1.2 The muonic component . . . 52
4.2 Particle propagation underground . . . 59
4.2.1 General features of particles underground . . . 59
4.2.2 Electromagnetic shielding . . . 62
4.2.3 Muon absorption . . . 62
5.3 AMIGA shielding analysis . . . 98 5.3.1 Preliminary study of the AMIGA modules at the depth of 1.3 meters 98 5.3.2 AMIGA shielding: simulation predictions . . . 107
6 Final Remarks 111
Chapter 1
Introduction
The Pierre Auger Observatory [1] was built to study ultra-high energy (higher
than 1 × 1018 eV) cosmic rays (UHECR) in order to understand their origin, acceleration
processes, propagation and mass composition. A hybrid technique is exploited, including
an array of 1600 water-Cherenkov stations (SD) over a 3000 km2 area [2], overlooked by
24 uorescence telescopes (FD) [3]. Very important results have been obtained since the beginning of the data taking, in 2004, in particular on the features of the energy spectrum [4], the composition [5] and anisotropy of cosmic rays above 3 EeV [6], but there are still many open questions. The study of these particles is fundamental to improve our knowledge in astrophysics and hadronic physics at energies above the reach of current accelerators.
A low energy enhancement of the Observatory was built to extend the measure-ments to the energy region down to 1017 eV, thus getting new insights in the region below
the ankle, believed to host the transition between Galactic and extragalactic particles [7], with the addition of composition information. It includes three additional uorescence de-tectors (HEAT - High Elevation Auger Telescopes [8]) and an in ll of 60 water-Cherenkov detectors (AMIGA - Auger Muons and In lled Ground Array [9]) placed at the mutual
distance of 750 m (half the standard one). Aside each station of the in ll, 30 m2 buried
scintillator counters will allow counting muons directly.
The upgrade of the Observatory, AugerPrime [10], has also started to be con-structed. It will allow increasing the quality of the composition measurement and solve other open issues, both from the astrophysical point of view (determination of the mass composition, origin of the ux suppression and the identi cation of sources) and from the particle physics one (the study of hadronic interactions at ultra-high energies). After studying and testing new techniques to reach this aim, the collaboration decided [10] to use scintillators above the SD stations. The upgrade will include other features, like an extension in the time of operation of the uorescence telescopes, the inclusion of a fourth photomultiplier tube (PMT) with larger dynamic range and new electronics on the surface detector stations, and the installation of AMIGA scintillators in all stations of the in ll
with data of scintillators placed at dierent depths, to contribute to the choice of the ideal point to maximize the muon signal and minimize the electromagnetic punch-through.
The main content of the text is divided into four parts. In chapter 2, a brief introduction to the main features of ultra-high energy cosmic rays is provided, with a review of the most recent results obtained by the Pierre Auger Observatory and other experiments. Chapter 3 contains a description of the detection techniques applied in the Observatory. In chapter 4, air-showers induced by ultra-high energy particles are studied with simulations, going to the surface depth and a few meters underground. All the analyses with preliminary data from AMIGA are presented in chapter 5. Conclusions and nal remarks are presented in chapter 6.
Chapter 2
Ultra-high energy cosmic rays
Since their discovery at the beginning of the 20th-century, cosmic rays have been very important to Physics. Many elementary particles (positrons, muons, pions, etc) were discovered in cosmic-ray experiments [11, 12]. When these particles reach the atmo-sphere they collide inelastically with their atoms, producing other particles and generating a cascade with an extension of thousands of meters in radius as it reaches the ground in the case of ultra-high energies (more than 1018 eV). The importance of ultra-high energy
cos-mic rays is related to the possibilities in astrophysics and astronomy studies. But the rst interactions in these extensive air-showers occur at energies which cannot be reached by current particle accelerators, becoming very important to study hadronic interactions. So they can also provide information about processes happening in astrophysical sources ob-served with other messengers, like photons and neutrinos. The biggest challenge consists in understanding and disentangling their origin, acceleration mechanisms, propagation until the Earth, energy spectrum and mass composition.
In this chapter, ultra-high energy cosmic rays are described, with a review of the most recent results obtained by the Pierre Auger Observatory and other experiments. A review by B.Dawson, M. Fukushima and P. Sokolsky [13] is used as our main reference. All the main topics are covered: origin, acceleration mechanisms, propagation, energy spectrum and mass composition. As it serves as a base for the following chapters, an introduction to the physics of extensive air-showers and their detection is also provided. More details on fundamental concepts can be found in the basic literature [14, 15, 16].
2.1 Origin: where do UHECRs come from?
Figure 2.1 is the Hillas diagram [17], which shows astrophysical objects capable of accelerating particles up to ultra-high energies. It is based on the Fermi mechanism for acceleration. Very large radius and/or intense magnetic elds are required, resulting in only a few candidates. There are also "top-down" models [18], where UHECRs have a cosmological origin, like the decay of super-heavy dark matter particles, but most of
Figure 2.1: Hillas diagram showing candidate sources of ultra-high energy cosmic rays [17].
these models are disfavored by measurements at almost all energies. Beyond the fact that statistics are very low, the search for sources of UHECRs gets even more di cult due to the magnetic elds which de ect their trajectories.
In the rst years of operation of Auger an important result was published [19]: a correlation between the most energetic events and active galactic nuclei. However, even with 0.0017 probability of happening by chance, with the increase in the number of events this correlation decreased from 61.5% to 28.1% [20]. The updated result is only 2σ above the expectation from isotropy. Many other searches for event clustering and cross-correlations with various astronomical catalogs were performed, but all results were compatible with isotropy [13]. The Telescope Array (TA) performed similar searches and obtained similar results [21, 22], except for an excess in a medium angular scale for energies above 5.7 × 1019 eV, shown in gure 2.2. The 'TA's hot-spot' is being attributed
to the M82 starburst galaxy.
Large-scale anisotropies in arrival directions have been reported in many recent works [23, 21]. A very relevant result was published recently [6] showing that there is a dierence of 13% in the ux of cosmic rays with energies above 8 EeV from opposite directions of the sky. Figure 2.3 shows this dipole, where it is possible to see that the
excess of particles comes from a direction 120o from the galactic center. It is a strong
Figure 2.2: Excess of events detected by the Telescope Array experiment [22]. Arrival directions are presented in equatorial coordinates.
Figure 2.3: Dipole in the arrival direction distribution of UHECRs reported by the Pierre Auger Collaboration [6]. The plot is in galactic coordinates, with the cross indicating the excess in the ux.
with a proton of energy above 5 × 1019 eV, decaying into a neutral pion and a proton
with lower energy (or a charged pion plus a neutron). Heavier nuclei may also suer photo-disintegration at these energies [29]. These interactions decrease the probability for cosmic rays at this energy range to reach the Earth, especially those which traveled a long distance. Therefore, a suppression in the ux of UHECRs is expected above the GZK threshold energy. The existence or not of a suppression was under discussion for some years, but the most recent experiments con rmed its existence, as presented in the next section.
2.3 Energy spectrum: what are the energies of
UHE-CRs reaching the Earth?
Cosmic rays reach the Earth in a broad range of energies and uxes. The spectrum can be described as a power-law in energy with changes in the spectral index at some points, like the knee and ankle, shown in the compilation of measurements of gure 2.4. Figures 2.5 and 2.6 present in more details the results for Auger [4] and TA [30] for ultra-high energies. Both observe the ankle around 5 × 1018eV, but with a dierence in the
ux of 20%, probably due to a shift in the energy scale (within systematic uncertainties). The ux suppression is also observed by these experiments, but with an inconsistency in its energy. The agreement about the position of the ankle and the disagreement about the suppression may be due to a systematic uncertainty dependent on the energy or to a real dierence between cosmic rays arriving at the northern and southern hemispheres [13]. The last hypothesis is favored by the recent result of the dipole discussed in section 2.1 [6].
The interpretation of the spectrum relies on understanding the features of the ankle and suppression. The ankle can be explained by pair production on the cosmic microwave background, assuming a pure proton composition for UHECRs [32]. This assumption is in agreement with TA's measurement of the composition [33], but not with Auger's result [5, 34]. Another explanation is based on a model with source production
Energy (eV) 9 10 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 -1 sr GeV sec) 2 Flux (m -28 10 -25 10 -22 10 -19 10 -16 10 -13 10 -10 10 -7 10 -4 10 -1 10 2 10 4 10 -sec) 2 (1 particle/m Knee -year) 2 (1 particle/m Ankle -year) 2 (1 particle/km -century) 2 (1 particle/km FNAL Tevatron (2 TeV)CERN LHC (14 TeV)
LEAP - satellite Proton - satellite Yakustk - ground array Haverah Park - ground array Akeno - ground array AGASA - ground array Fly’s Eye - air fluorescence HiRes1 mono - air fluorescence HiRes2 mono - air fluorescence HiRes Stereo - air fluorescence Auger - hybrid
Cosmic Ray Spectra of Various Experiments
Figure 2.5: Energy spectrum obtained by a combination of dierent techniques at the Pierre Auger Observatory [4]. The t of the spectral indexes are shown for two regions.
and propagation assumptions, to t both the mass composition and the spectrum [35]. In the case of the suppression, the GZK eect is successful in explaining both Auger's and TA's data. But there may also be any feature of the acceleration mechanisms that limits the energy range of the UHERCs, contributing to the suppression. Some of these open questions about the energy spectrum are related to uncertainties about the mass composition, showing how important it is to obtain an accurate result on this subject.
2.4 Mass composition: what type of particle are the
UHECRs?
For low energy cosmic rays, the mass composition is very well known. Most of them are protons [15]. For ultra-high energies, direct measurements are not viable, due to the very low uxes. The mass estimation, in this case, is based on predictions from Monte Carlo simulations, which depend on hadronic interaction models. But even the most recent models, tuned with measurements from the LHC [36], are just extrapolations to ultra-high energies since the current accelerators cannot reach such values. Recent studies of the Pierre Auger Observatory [37, 38] showed an inconsistency between the observed and predicted number of muons at the surface, which highlights the need for improvement in hadronic interaction models. An accurate determination of the mass composition will only be possible with a better understanding of the shower physics at ultra-high energies and improved discrimination between the shower components. Even with all these limitations, it is still possible to relate shower features to the mass of the primary particle, to get insights on the composition.
One of the most used observables for this type of study is the depth of shower
maximum (Xmax). It consists in the slant depth in the longitudinal development of the
shower where the number of particles reaches its maximum. Its value is sensitive to the energy and mass of the primary particle. Fluorescence techniques allow the
measure-ment of hXmaxi with a very good resolution in a hybrid detector. Figure 2.7 shows the
measurement of the FD of the Pierre Auger Observatory [5]. The mean value and
stan-dard deviation of hXmaxi are compared to the expectation from three dierent hadronic
interaction models for proton and iron primaries. At lower energies, the data are close to the prediction for protons, and particles seem to become heavier with the increase in energy, inconsistent with the proton predictions. The result cannot be described as a simple combination of proton and iron, but a good model can be obtained introducing
intermediate masses [39]. The measurement of hXmaxi by TA [33] is not identical to the
one of Auger and results point to a light component at any energy. But a recent analysis [40] showed that TA data is within the systematic uncertainties compatible with a mixed composition, like the one measured by the Auger detectors.
Figure 2.7: Depth of maximum in the shower development hXmaxi) measured with the
FD of the Pierre Auger Observatory [5]. Plot on the left is the average value and the right one is the standard deviation. Predictions from hadronic interaction models are also shown.
Composition studies based on measurements from surface detectors have a lower resolution but have the advantage of higher statistics. The Pierre Auger Collabo-ration explored the properties of the rise-time of the signal (the time it takes to increase from 10% to 50%) of its water-Cherenkov detectors (WCDs), which presents an azimuthal asymmetry. This feature was exploited to study the shower development [41]. A result
similar to the one with hXmaxi was obtained, but with an interpretation with a strong
dependence on the hadronic interaction models.
The shower development can also be studied in terms of the muon production
depth (MPD). The depth of maximum in its development, Xµ
max, is also sensitive to the
mass of the primary particle. Using inclined showers, which are dominated by muons, the
Auger Collaboration studied the mass composition of cosmic rays above 1019.3 eV [42].
Results ( gure 2.8) show a mass increasing with the energy, but again the theoretical models present inconsistencies. This type of study will be more eective with the upgrade of Auger, since the new scintillator detectors will allow an accurate muon measurement. Advances in this subject have already been obtained, exploring data of the AMIGA muon counters [43].
Other studies related to the characterization of the primary particle are the searches for neutrino and photon events. These particles may be produced in hadron interactions during their propagation, like the photo-pion production in the interaction with the CMB [27, 28]. "Top-down" models also predict signi cant photon uxes [18].
Figure 2.8: Average depth of maximum in the muon production (left) ant its standard deviation (right), obtained with the surface detector of the Pierre Auger Observatory [42]. The searches for neutrinos in Auger [44, 45] are based on young showers (Xmax close to the
surface) with large zenith angles or skimming the Earth. No candidate shower was found. In the case of photons, for lower energies, hybrid data are used in a multivariate analysis
including hXmaxi and parameters of the lateral distribution function (LDF) [46]. A few
candidates were found, but consistent with the misclassi cation for hadronic showers.
Above 1019 eV data from the surface detector are used and ve candidates were found,
but again consistent with a misclassi cation [45]. Although the results are negative, these studies allow setting limits on the uxes of neutrinos and photons.
2.5 Extensive air-showers: what happens when
UHE-CRs reach the atmosphere?
When UHECRs reach the atmosphere they collide inelastically, giving rise to other high energy particles. These new particles suer other inelastic collisions in a chain process, originating a cascade called extensive air-shower (EAS) [14, 16]. The production of new particles during the shower development is possible while pair production and bremsstrahlung dominate over ionization processes. The critical energy in the air, around 80 MeV, is the threshold from which this condition is satis ed. At this point of maximum in the shower development, the cascade may contain billions of particles. They reach the surface with extensions up to tens of km2, allowing the indirect detection of cosmic rays,
through the reconstruction of the shower from signals recorded at dierent positions on the ground.
Figure 2.9 shows a schema of EAS splitting its components, which are formed by the secondary particles of the interactions. The electromagnetic and muonic compo-nents are the most important from the experimental point of view. The electromagnetic one carries 90% of the total energy. It originates mostly from the decay of neutral pions. Muons are very penetrating and abundant at surface level where the detection takes place
Figure 2.9: Schema of an extensive air-shower with its dierent components [47]. in some techniques. They come from charged pions ( 90%) and kaons ( 10%) created in the rst and following interactions. There is still the hadronic component, with the re-maining hadrons, as its name suggests. A more detailed description of these components, including a study with simulations, is performed in chapter 4.
2.5.1 Main features of a shower
The longitudinal development of the shower is given in terms of the quantity of matter traversed, the slant depth in g/cm2, denoted by X, as already mentioned in the
previous section. This longitudinal pro le can be described by the Gaisser-Hillas function [48], like at the example from gure 2.10. It is possible to see an increasing number of
particles until a maximum is reached. This point de nes the Xmax parameter, related
to the mass and energy of the primary cosmic ray. It is associated to a critical energy for which the absorption dominates the production processes and the particle density starts to decrease. The determination of the longitudinal pro le is very accurate with uorescence detectors, described for the Pierre Auger Observatory in section 3.1.
At each step of the development, particles scatter in an angle dependent on the transverse momentum of the particle. Being relativistic, these angles are very small, but the very high number of interactions makes the shower spread and reach the surface with a few km² of extension. The lateral distribution, that is the particle density as a function of the radial distance from the shower center, decays exponentially. A model credited to Nishimura, Kamata and Greisen (NKG [49, 50]) is the most used for describing it. In
Figure 2.10: Longitudinal pro le of an air-shower with the t of a Gaisser-Hillas function, taken from [1].
practice, the LDF is t to data from surface detectors to parameterize the signal collected with some stations. Figure 2.11 shows an example of lateral distribution obtained by the Pierre Auger Observatory, where the signal at a reference distance of 1000 meters is used to estimate the energy of the shower, as explained in next chapter.
2.5.2 Hadronic interaction models and the muon excess
Some of the results presented in this chapter are dependent on the theoretical knowledge of various features of the shower. Monte Carlo simulations provide the expected behavior of observables and allow us to draw conclusions from the data. The interpretation of the mass composition results from section 2.4, for example, is totally based on the Xmax
obtained in shower simulations for dierent primary particles. Therefore, an accurate model is required to describe the shower propagation. But the particle interactions at the top of the atmosphere occur at energies for which there is no data from accelerators, so the cross-sections and other features are not well established. What is done is an adaptation of the results for the highest energies available, that is not necessarily valid. Currently, the most used models for hadronic interactions at ultra-high energies are the EPOS-LHC [51], QGSJET-II-04 [52] and Sibyll [53]. They are all based on updated measurements of the LHC [36], but contain a few dierences in the treatment of pion-air and kaon-air collisions [54]. Their description of the depth of maximum in the shower development is not identical [5], making the interpretation of the mass composition even more inaccurate, as already seen in gure 2.7.
Recent analyses are pointing to inconsistencies in the measured numbers of muons at the surface when compared to the predictions by simulations. Very inclined showers are dominated by muons at the surface since the electromagnetic component is
Figure 2.11: Lateral distribution function for an event of the Pierre Auger Observatory [1]. A NKG-like function is t to the data.
attenuated through the long path traversed. Selecting hybrid events with zenith angles between 62°and 80°, the Pierre Auger Observatory found that the models underestimate the number of muons by 30% to 80% [38]. This result is presented in gure 2.12. In an-other study [37], with vertical events, the number of muons from a simulation with mixed composition was dierent from what is observed, although the energies are consistent in both EPOS-LHC and QGSJET-II-04 models. Results from the Telescope Array experi-ment are in agreeexperi-ment with Auger [55], having also observed an excess of muons when compared to predictions. It is clear from these results that even the most updated versions of the hadronic interaction models fail to describe the muon numbers. It is important to remember they are based on extrapolations from lower energy measurements. To allow the interpretation of mass composition results, the muon de cit in models must be solved and the uncertainties in muon measurements must decrease. Improvements in the Pierre Auger Observatory are already being built with the aim of counting these particles, as described later in this text.
2.6 Experimental techniques: how can UHECRs be
de-tected?
Particle physics experiments started at the end of the 19th century, with the discovery of X-rays and other types of radiation. The rst observation of cosmic rays is credited to Victor Hess [14], which realized that the ionizing radiation in the atmosphere increased with altitude during his balloon ights. In the following decades, many features of elementary particles and their interactions were con rmed or discovered in cosmic ray
Figure 2.12: Average muon content as a function of the average shower depth, as measured by the Pierre Auger Observatory with highly inclined events [38].
experiments. Nowadays they still play a very important role in high energy physics, due to the limited range of energy achievable with particle accelerators.
The higher the energy of the cosmic ray, the more di cult its detection be-comes, because of the decrease in ux. At ultra-high energies, for example, it is of the
order of 1 particle per m2 per century. A very large area is required to compensate this
ux, so a direct detection is not viable. In this case, the extensive air-showers are of great value, allowing the detection with indirect techniques.
As rst used at the Volcano Ranch experiment [14], the detection of cosmic rays at the surface is based on a geometric reconstruction of the shower. With the time dierence of the signals recorded at dierent positions at ground level, a plane front for the shower can be determined, and hence the arrival direction of the primary particle. The lateral distribution of the shower can also be obtained. This technique was applied in various other experiments (Haverah Park [56], Yakutsk [57], AGASA [58], TA and the Pierre Auger Observatory, for the highest energies), using dierent types of detectors. With the coverage of a large area, a good event rate can be reached. More details on the surface detector of the Pierre Auger Observatory are provided in section 3.2.
Another technique for indirect detection of UHECRs is the observation of the uorescence light emitted while particles propagate through the atmosphere. The longi-tudinal pro le of the shower is obtained, allowing the reconstruction of the energy of the primary cosmic ray with a very high accuracy. The rst experiments to use uorescence detectors were the Fly's Eye [14] and its successor HiRes [59], but they are also used in
statistics.
More recently other features are being explored for the detection of UHECRs, like the radio emission in showers. This technique advanced a lot in last years, showing promising results [60, 61]. The combination of dierent types of detectors, including radio, can bring various bene ts, as proved in the case of the PAO with the surface and uores-cence detectors. The combination of data from dierent experiments can also contribute to the study of UHECRs, like already done between the Auger and TA collaborations recently (e. g., [40]). Another innovative idea is the operation of a detector from a space station, with uorescence telescopes pointed to the surface of the Earth [62]. This would greatly increase the current coverage and the event rate, but technological and nancial issues are still a great challenge, making this type of proposal more di cult to become real.
Chapter 3
The Pierre Auger Observatory
The concept of the Pierre Auger Observatory comes from a suggestion of Alan Watson and Jim Cronin in 1992 [63]. Its construction was possible due to an international eort, with 19 participating countries, including Brazil. A at location with favoring altitude, clean sky and low level of luminosity was required for the construction. So the city of Malargüe in Argentina was chosen for the southern site [64] and the northern site (which was not built) would be in the USA, in Colorado [65]. The Observatory not only covers a very large area of the surface, but it was the rst experiment to use a hybrid technique, with an array of water-Cherenkov detectors and four sets of uorescence telescopes working together to obtain a high event rate with an accurate reconstruction [66]. Data taking started in 2004 and the construction was nished in 2008. The current status of the detectors is shown in gure 3.1. An upgrade called AugerPrime started in 2015, aiming the operation of the experiment for the next years up to 2025 [10].
This chapter is fully devoted to the Pierre Auger Observatory. The surface and uorescence detectors will be described in details. Then some of the enhancements of the Observatory will be presented, focusing on AMIGA, which is closely related to the main subject of this thesis. The AugerPrime upgrade will also be brie y presented. A detailed description of the Observatory is given in reference [1], covering topics not covered in this text, like electronics for data acquisition and communications.
3.1 Fluorescence detector
The 27 uorescence telescopes of the Pierre Auger Observatory [3], pointing to the directions represented by blue lines in gure 3.1, are divided in four stations like the one from gure 3.2. In nights with appropriate climate conditions and with low light background, which depends on the moon, the shutters are opened for data taking. The longitudinal pro le of the shower is registered, from which it is possible to obtain the
very important Xmax (depth of maximum of the shower development) parameter and
Figure 3.1: Current status of the Pierre Auger Observatory [1]. Grey dots represent each station of the surface detector. Blue lines delimit the eld of view of the uorescence telescopes are pointing. The AMIGA, HEAT and AERA enhancements are also indicated.
Figure 3.2: Los Leones building with the uorescence telescopes exposed [1]. Shutters were open during daytime for maintenance.
of this measurement. The amount of light detected is converted to energy deposited in the atmosphere, considering the dierent contributing sources ( uorescence, Cherenkov and multiply scattered light). The pro les are tted with a Gaisser-Hillas function [48],
from which Xmax can be extracted. The integral of the function provides the calorimetric
energy of the shower and a correction for the energy carried away by neutrinos and high energy muons provides the total energy. The geometrical reconstruction of the event also uses information from the surface detector.
Each telescope ( gures 3.4 and 3.5) has an aperture of 30 × 30°, provided by a spherical segmented mirror with 3.4 m of curvature with an array of photomultiplier tubes in its focus. The PMTs are arranged in a matrix with 22 × 20, totalizing 440 pixels. Light enters through the spherical window, passing through lenses for optical correction and a UV lter, and reach the focus due to re ection at the mirror. An example of an event recorded is showed in gure 3.6.
The monitoring of climate conditions is very important for the operation of the FD, not only to protect the telescopes from wind and rain but due to their direct in uence in data reconstruction. Variations in pressure, temperature and humidity of the atmosphere may aect particle interactions and uorescence emission or detection. The eect of molecular and aerosol conditions is monitored using various types of lasers, like the one from the Central Laser Facility (CLF), that shoots a depolarized beam in a quarter-hourly sequence. There are also lidars installed close to each FD station. Details
Figure 3.3: Example of a shower pro le measured by the uorescence detector [1].
Figure 3.5: Fluorescence telescope viewed from inside the FD building [1].
Figure 3.6: An example of air-shower trace recorded by the uorescence detector [1]. Each dot represents a pixel (or a PMT) and the colors are related to time.
Figure 3.7: Schema with the spherical shower front reaching the stations of a surface detector [1].
about atmospheric monitoring are given in reference [67].
3.2 Surface detector
As already mentioned, the detection of cosmic rays at ground level is possible through the geometrical reconstruction of air-showers. At the Pierre Auger Observatory,
an array of 3000 km2 with 1600 water-Cherenkov detectors separated by 1500 m in a
triangular grid is used [2]. When a signal is registered by three or more neighboring stations inside a time window compatible with an air-shower, data is sent by radio to the central building [68]. The geometrical reconstruction, performed o ine, takes into account the intensity of the signals, position and time of detection for each station. The shower front is initially considered as plane and the arrival direction of the primary particle is obtained. The result is improved with a recursive χ2 minimization considering a spherical
shower front like shown in the schema of gure 3.7.
Another important information taken from the SD is the lateral distribution of the shower, the signal of the detectors as a function of the distance to the shower core. This distance is measured in shower coordinates, de ned by a plane orthogonal to the central axis of propagation. A function with the NKG [49, 50] shape, with a normalization at 1000 m, describes well the data. It is written as
S(r) = S(1000) r 1000 β r + 700 1000 + 700 β+γ (3.1) The S(1000) parameter is used for the energy calculation, explained later. Signal is converted to units of vertical equivalent muons (VEM), with a calibration performed with the ux of atmospheric muons [69]. Figure 3.8 shows an example of reconstructed event, with the most important plots obtained by the O ine [70] framework developed by the
collaboration.
The water-Cherenkov detectors [71] of the SD, shown in gures 3.9 and 3.10, are cylindrical tanks with 3.6 m of diameter and 1.6 m height. They are instrumented with a communication antenna, battery box and solar panel, working without the need of cables for transmitting data or energy. Inside the polyethylene structure, there is a sealed liner bag of 1.2 m height, with a re exive inner surface. It contains 12000 liters of ultra-pure water. Three 9 inches photomultiplier tubes are coupled to the liner, facing downwards. They detect the light emitted in water due to the Cherenkov eect, which occurs when charged particles propagate faster than the speed of light in that medium.
3.2.1 Energy reconstruction
The greatest advantages of the Pierre Auger Observatory when compared to previous and current experiments is the very large coverage and the use of a hybrid technique. The surface detector provides parameters to improve the reconstruction of events from the uorescence detector and vice-versa. The telescopes measure the energy of the shower with high accuracy. The SD has a duty cycle close to 100%, compensating the 15% of the FD. With events detected with both techniques, it is possible to obtain an energy calibration for the SD.
The reconstruction of the energy of the shower detected by the SD is based on the S(1000) parameter, obtained in the t of the lateral distribution of the signal. The distance of 1000 m from the shower core was chosen because it is the point where the shower-to-shower uctuations are minimum (for a distance between stations of 1500
m) [72]. S(1000) is dependent on the zenith angle but an attenuation curve fCIC(θ) can
be obtained with a Constant Intensity Cut method [73]. Taking the median angle of
38°, a new parameter is de ned, S38, which is the signal a particular shower with size
S(1000) would have produced had it arrived at 38°. It can be obtained by the relation
S38 = S(1000)/fCIC(θ) and related to the energy of the FD (EF D) . For this, a selection
of good quality hybrid events is performed. Figure 3.11 shows the relation between S38
and EF D, which can be parameterized with a single power law. In summary, for each
event of the SD S(1000) is obtained with the LDF t, then it is converted to S38 and the
energy is obtained from the curve in gure 3.11.
3.3 Enhancements of the Observatory
Although the Pierre Auger Observatory was designed to study cosmic rays with energies higher than 3 × 1018 eV, the region right above the knee of the spectrum is
also of big importance. It includes the ankle of the spectrum, as discussed in chapter 2, and these energies are close to the range of current particle accelerators. To improve the
Figure 3.8: Results of the reconstruction of an event of the surface detector. This is an output obtained with the O ine software [70]. Diagram on the top contains the SD array with circles representing stations with a diameter proportional to their signals. Colors are related to the arrival time at each of them and the red arrow is the arrival direction of the shower. Plot on the middle is the lateral distribution of the signal, with the green line representing the NKG function from the t. Plot on the bottom is the dierence in time from signals to the expectation from a plane shower front.
Figure 3.9: Water-Cherenkov station of the surface detector [1].
Figure 3.11: Relation between S38 and the energy of the FD [1]. It allows the calculation
of the energy for any event, given S(1000) and the zenith angle of the shower.
e ciency of Auger in detecting air-showers of such energy, two enhancements were built: AMIGA (Auger Muons and In lled Ground Array [43]) and HEAT (High Elevation Auger Telescopes [8]). The rst one is the subject of this thesis, described in further details later. HEAT is a set of three uorescence telescopes ( gure 3.12), very similar to those from the
regular FD, but which can be tilted to observe the atmosphere at greater heights (30o to
58o). AMIGA and HEAT provide high-quality hybrid measurements of air-showers with
energies extended down to 1017.5 eV.
The construction and operation of an experiment like the Pierre Auger Ob-servatory involve a huge eort in terms of the development of new instruments. In this process, there are opportunities to test new technologies. The detection of air-showers using radio antennas is an example of a technique with signi cant advances in the last years at the Observatory, taking advantage of all its infrastructure and other detectors. An engineering radio array (AERA [74]) was built, with 153 detection stations ( gure
3.13), spread over an area of 17 km2 with spacings between 150 and 750 m. Dierent
types of antennas were tested, aiming the validation of the technique for UHECRs. Lat-est results of AERA [60, 61] are very promising, showing that the reconstruction of the primary cosmic ray with radio is reliable.
3.3.1 AMIGA
While the original proposal for the Pierre Auger Observatory was to study
Figure 3.12: Fluorescence telescopes of the HEAT extension of the Pierre Auger Obser-vatory [1].
Figure 3.13: Antennas of the AERA project from the Pierre Auger Observatory, for the detection radio signals from air-showers [1].
bers to collection and transmission of light like represented in gure 3.17. The photons are guided to a 64-pixel photomultiplier tube positioned at the center of each module. The scintillators work as counters, i.e., they count signals above a tunable threshold.
Figure 3.14: Trigger e ciency of the surface detector for the regular (1500 m between stations) and in ll (750 m) arrays [75]. The 3ToT trigger consists in the time coincidence of the signals of three neighbor stations.
The In ll array of water-Cherenkov detectors is complete since September 2012, with 61 stations overlooked by the HEAT telescopes in the western part of the surface detector array, shown in the map of gure 3.18. Data taking started in 2008 and results have already been obtained [77], like the energy spectrum presented in the previous chapter.
A unitary cell (UC) of seven stations with muon counters forming a hexagon ( gure 3.19) was completed in 2014. Two locations are instrumented with a pair of
independent counters called twins (with 30+30 m2), to allow a direct measurement of the
muon counting accuracy [79]. The Phil Collins station contains modules buried at a depth of 1.3 m, to study the electromagnetic shielding of the detectors. Silicon photomultipliers (SiPMs) are also being tested in some of the counters, as a cheaper alternative to the
Figure 3.15: Deployment of the prototype detectors of an AMIGA station [76]. Main features of the preliminary design are indicated.
Figure 3.16: Con guration of the AMIGA stations, with the water-Cherenkov detector and buried scintillator modules [43].
usual multichannel PMTs [80].
Various other features of the AMIGA muon detectors will be explored in chap-ter 5. Data of the UC will be used to discuss the muon counting technique and event reconstruction. The accuracy will also be determined with the twin counters and a study of the depth of the scintillators will be performed.
Figure 3.18: Map of the AMIGA In ll and unitary cell of muon counters [78].
3.4 The AugerPrime upgrade
Even with the large dataset of Auger obtained in more than one decade of operation, a few questions regarding UHECRs are still open. The main problem lies in the mass composition measurement. Without information about the mass of particles, it is impossible to study its de ection in magnetic elds and consequently the sources of cosmic rays. Astrophysical models depend on the composition to provide the interpreta-tion of features like the suppression in the ux. And the study of hadronic interacinterpreta-tions in air-showers is closely related to it. The best measurement of mass composition available is based on the depth of maximum in the showers detected with the FD. But its inter-pretation is dependent on theoretical models, which are not very accurate, as discussed in section 2.5.2. A measurement with the SD based on muons would provide another es-timator with higher statistics, but the signal produced in the water-Cherenkov detectors by electrons and muons cannot be discriminated. To overcome all these issues, the Auger collaboration planned an upgrade of the Observatory. Its main goal is to improve the quality of the mass composition measurement up to 100 EeV. The AugerPrime upgrade is already under construction and the preliminary design report is already available [10].
Figure 3.19: Muon counters of the unitary cell of AMIGA [78].
3.4.1 Surface scintillator detector
Dierent techniques were considered for the muon measurement in the up-grade. For more than one year prototype detectors were tested in the eld, exploiting e.g. (a) muon counters underground, similar to those from AMIGA, (b) scintillators on the top of the tanks, (c) resistive plate chambers (RPC) and (d) modi ed water-Cherenkov detectors with segmentation. After evaluating the results obtained and the viability of each proposal, the collaboration decided [10] that option (b) would be used in the upgrade of the surface detector.
The Surface Scintillator Detector (SSD) [81] will be composed by two modules
of 2 m2, placed at the top of the SD stations ( gure 3.20). Each module contains 12
scintillator bars with optical bers inside to collect light and lead it to a photomultiplier tube, similar to what is done in AMIGA. But in this case, the signal of all bers is read in an integrated way with a dynamic range compatible to the signal of the SD (the signal in one of the modules is attenuated by a factor of 4 and the other is ampli ed by a factor of 32 for this). This system must be robust enough to resist more than a decade of operation in the Pampas, under extreme weather conditions.
The measurements of the SSD will complement data from the surface detector. Sampling the shower in the same position with detectors with dierent responses to muons and electromagnetic particles will allow the discrimination between this two components in
Figure 3.20: A station of the surface detector equipped with the scintillators for the AugerPrime upgrade [81].
the signal. This is performed using a matrix inversion approach [82]. After that, exploring the shower universality features [83], the composition of UHECRs can be studied with an accuracy comparable to the FD measurements [10].
3.4.2 Other features of AugerPrime
The upgraded surface detector will provide a measurement of mass and charge of the primary in a shower-by-shower mode. For this, it will receive other enhancements besides the SSD. The electronics for data acquisition (now responsible for the water-Cherenkov and scintillator detectors) will be upgraded for better timing accuracy, higher sampling frequency and increased processing capability [84]. A fourth photomultiplier tube, named SPMT (small PMT [85]), will be included in the SD stations to extend the dynamic range. With this, the saturation in the signal, which aects most of the stations close to the shower core, is expected to decrease signi cantly.
Another feature of AugerPrime will be the extension of the duty cycle of the FD. Decreasing the high voltage at the PMTs allows the operation with high night sky background, without irreversible damage to the device. Operating with a moon fraction of about 90%, the duty cycle will go to 29%, which is almost 50% higher than the current value.
AMIGA will also play an important role in AugerPrime. It will provide direct muon measurements in a subset of showers to validate and ne-tune the technique used
by the SSD to obtain the muonic component. The muon counters will be installed at 1.3 m underground in all 61 stations of the In ll.
This chapter shows the predictions from simulated air-showers for the behav-ior of particles at the surface and underground produced by ultra-high energy cosmic ray interactions with the atmosphere. Particular attention is given to the muonic and electro-magnetic components, studying their energy spectra, lateral distribution and sensitivity to changes in the energy, zenith angle and mass of the primary particle. Aiming the de-tection of muons by the AMIGA extension of the Pierre Auger Observatory, the particle absorption and electromagnetic contamination underground are estimated. A simpli ed analysis of the viability of using muons on composition studies is also performed.
The air-shower simulations were performed with the CORSIKA software [86]. All of them were already available at the computing cluster of the Physics Institute of UNICAMP. Simulating new showers requires a lot of time and disk space, so reusing them can save a lot of resources. Since the main goal of this study was to get insights in the behavior of particles at the surface and underground without comparing it to real data, only the QGSJETII-04 model [52] for hadronic interactions was used. As discussed in section 2.5.2, dierent models would provide dierent numbers of particles (none of them describing data accurately), but this comparison is out of the scope of this thesis. Also,
in most of the analyses, only protons of 1018 eV (a typical energy for AMIGA events)
were considered as primaries, which was taken as a standard. Iron showers are studied only in section 4.4, where composition features are explored. Zenith angle is uniformly distributed in sec(θ) from 0°to 60°.
Using a list provided by CORSIKA, the simulations use an unthinning algo-rithm [87] to distribute the particles at the surface around each station. The O ine framework [70] controls all the process, from reading the input les until the event re-construction. It includes all the standard methods of Auger for detector simulation and reconstruction. But in our case, instead of considering a simulated signal as the output for the analyses, a simple particle counting based on the geometry of a detector is used. In this way, it is expected to get a more general result. An exception is section 4.3, where the energy deposited by particles in a plastic scintillator is studied.
x (m) -20 -10 0 10 20 y (m) -20 -10 0 10 20 0 2 4 6 8 10 12 14 16 18 20
Particles distribution on surface
Figure 4.1: Example of particle distribution on the ground for a single station at 450 m from the shower core.
Figure 4.1 shows how particles are distributed at the surface for a single event. The surface detector station is at the center of the histogram, with a radius if 1.8 m. Parti-cles are injected in a very large area because they are propagated until 2.3 m underground and border eects must be avoided. Figure 4.2 is a three-dimensional representation of detection of a single muon (red line), with the SD station at the top (Cherenkov light is produced inside it, represented in green) of a big brown cylinder of ground. These are the components of the standard GEANT4 [88] simulation used in O ine for AMIGA, developed in the scope of this thesis. In most of our analyses, this is the last step of the simulation. After that, a list of particles is generated and saved to be studied. They could also be injected in the scintillators to continue the simulation.
4.1 Air-shower particles at the surface
After interacting with the atmosphere, millions of particles of an air-shower reach the surface, where they can be detected by ground arrays like the Pierre Auger Ob-servatory's SD. There are many types of secondary particles, but in the following analysis, only the most important (considering their contribution to the detection) are considered: muons, electrons (or positrons), photons and hadrons (mesons, protons, neutrons, etc).
Figure 4.2: Muon crossing the GEANT4 volume of the O ine simulation for AMIGA. A cylinder with a radius of 25 m and 4.1 m high (1.8 m from the WCD plus 2.3 m of ground) is considered for each station.
Figure 4.3 shows the density of particles at the surface (at the Observatory's altitude) as a function of the distance from the shower core, obtained with 300 simulated
proton showers of 1018 eV. As expected [16], the electromagnetic component is
predomi-nant over the muonic and hadronic contributions. In this plot and others in this chapter, the density is the mean value calculated for each bin of distance and the error bars are the uncertainties on the mean value (standard deviation divided by the square root of the number of entries), which is very small in most cases, since there are a lot of entries. Each plot may contain information from various stations from all simulated showers.
It is also important to look for the dependence of this result with the zenith angle θ of the primary cosmic ray. It is shown in gures 4.4 and 4.5 at 500 and 1000 meters from the shower core. Up to 30°, the densities seem to keep constant and the proportions for each type of particle are the same as before. But after that, there is a clear decrease in the numbers of particles. This is due to the increase in the path traversed by them in the atmosphere, increasing their attenuation. An indication of this fact is the dierence in the behavior of muons, which are much more penetrating than other particles, presenting just a slight decrease for inclined events, even surpassing the number of electrons close to 60°.
It is clear that in absolute numbers there are much more electromagnetic parti-cles than any other type. But their importance is more related to their contribution to the signal of the detector, which depends on the energy distribution and type of interaction. In the case of the water-Cherenkov detectors of the Pierre Auger Observatory, muons are responsible for 50% of this signal and electromagnetic particles make up the other 50% [41]. These two components of the shower need to be studied in more details.
Distance from shower core (m) 200 400 600 800 1000 1200 1400 ) -2 Particle density (m 2 − 10 1 − 10 1 10 2 10 3 10 4 10 Photons Electrons Muons Hadrons Particle densities at surface
Figure 4.3: Densities of particles at the surface measured at dierent distances from the shower core. All range of zenith angle is considered.
Zenith angle (degrees)
0 10 20 30 40 50 60 ) -2 Particle density (m 2 − 10 1 − 10 1 10 2 10 3 10 Photons Electrons Muons Hadrons
100) m from the shower core
±
Particle densities at (500
Figure 4.4: Dependence of the particle density around 500 m from the shower core with the zenith angle.
Zenith angle (degrees) 0 10 20 30 40 50 60 2 − 10 1 − 10
Figure 4.5: Dependence of the particle density around 1000 m from the shower core with the zenith angle.
4.1.1 The electromagnetic component
The electromagnetic cascade is initiated by γ rays from π0 decays [16]. These
photons interact in the atmosphere through photoelectric eect, Compton eect and pair production, although the rst two have a very small cross-section at high energies in comparison to the latter. The electrons or positrons produced interact by ionization and bremsstrahlung, creating photons. These new photons produce other electron-positron pairs, that emit photons by bremsstrahlung if they still have high energies. In this process, the number of particles increases at each step, while the individual energies decrease. At a certain point, this electromagnetic cascade reaches a maximum in the number of particles, due to the reduction in energy and the domination of absorption processes over pair production and bremsstrahlung. The longitudinal pro le of a shower, with
this maximum denoted by Xmax, can be described by the Gaisser-Hillas function [48], as
already mentioned. Concerning the lateral spread of the particles, it can be described very well by the Nishimura-Kamata-Greisen (NKG) function [50, 49].
Figure 4.6 presents the mean lateral distribution of particles for dierent ener-gies of the primary particle. The exponential decrease is in agreement with the model [89]. The increase in densities with energy is also expected since more particles are produced. Electromagnetic particles reach the surface with energy distributions like those from gure 4.7, obtained from simulations of proton showers. The cuto in the spectrum at 1 MeV is a choice at CORSIKA to spare computational time since the contribution of these particles to the total signal can be neglected. Figure 4.8 shows the dependence of
Distance from shower core (m) 200 400 600 800 1000 1200 1400 ) -2 Particle density (m 2 − 10 1 − 10 1 10 2 10 3 10 4 10 eV 18.5 10 eV 18.0 10 eV 17.5 10
Electron/positron densities at surface
Distance from shower core (m) 200 400 600 800 1000 1200 1400 ) -2 Particle density (m 2 − 10 1 − 10 1 10 2 10 3 10 4 10 eV 18.5 10 eV 18.0 10 eV 17.5 10
Photon densities at surface
(energy/MeV) 10 log 0.5 − 0 0.5 1 1.5 2 2.5 3 3.5 Entries 0 1000 2000 3000 4000 5000 6000
Figure 4.7: Energy distributions of electrons/positrons (top) and photons (bottom) at the surface for proton showers of 1018 eV.
the mean energy with the distance from the shower core. But this result is biased by the threshold. The dependence is better represented by the plot from gure 4.9, where it is possible to see the number of high-energy particles decreasing with the core distance, but with a maximum (hotter bins) always around 10 MeV.
There is a very particular feature in the lateral development of the electromag-netic component, studied in more detail in [90]. Far from the core most of the electrons or photons come from low energy sub-showers initiated close to the surface. Older particles, generated at high altitudes, are concentrated close to the core of the shower. It ends up that the electromagnetic component at an intermediate distance is a combination of these two populations. The plots in gure 4.10, taken from [90], show the energies and depth of production of the initiators of the electromagnetic sub-showers, representing very well the eect described. This may also aect the lateral behavior of the energy.
Figures 4.11 and 4.12 show the dependence of the average energies of electro-magnetic particles with the primary energy and zenith angle. Apparently, the energy does not aect the behavior of the particles at the ground, but it is important to remember ( gure 4.6) that their densities change considerably with the energy of the primary. Re-garding the zenith angle, there is an increase in energy for more inclined events, which can be seen more clearly in gure 4.13. This feature may be just a consequence of the
Distance from shower core (m) 200 400 600 800 1000 1200 1400
Mean energy (MeV)
5 10 15 20 25 30 35 40 45 Photons Electrons
Average energies of EM particles at the surface level
Figure 4.8: Average energy of electromagnetic particles at the surface for proton showers of 1018 eV at dierent distances from the shower core.
Distance from shower core (m) 200 400 600 800 1000 1200 1400 (energy/eV) 10 log 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 1 10 2 10 3 10 4 10
Electromagnetic particles at surface
Figure 4.9: Energy of electrons at the surface for proton showers of 1018 eV for dierent
distances from the shower core. The color scale represents the number of counts in each bin.
Figure 4.10: Energy and depth of production of initiators of electromagnetic sub-showers, close to the core in the top panel and at 1000 meters in the bottom. The results come from vertical proton showers of 5 × 1019 eV, taken from [90].
Distance from shower core (m)
200 400 600 800 1000 1200 1400
Mean energy (MeV)
5 10 15 20 25 30 35 40 eV 18.5 10 eV 18.0 10 eV 17.5 10
Electron/positron energies at surface
Distance from shower core (m)
200 400 600 800 1000 1200 1400
Mean energy (MeV)
5 10 15 20 25 30 35 40 eV 18.5 10 eV 18.0 10 eV 17.5 10
Photon energies at surface
Figure 4.11: Average energies of electromagnetic particles at the surface level for simulated air-showers with dierent primary particle energies.
energy threshold at 1 MeV for electromagnetic particles, but the increase in energy can also be related to a change in the origin of the electrons from pure electromagnetic to muon decay.
As a summary from these simulations, it is possible to say that the densities of electromagnetic particles are very sensitive to the energy and zenith angle of the primary cosmic ray and also to the distance from the shower core where they are measured. Their energy spectra could also be studied, but its dependence on other parameters is not very clear. The average energies have unexpected behaviors, but at least it is clear that there are not very large variations with the radial distance. Reducing or removing the energy threshold of the simulation would make the results clearer.
4.1.2 The muonic component
The main subject of this thesis is the study of muons. It is important to understand in detail their behavior in the propagation through the atmosphere and the main features of particles arriving at ground level. They are mostly produced in decays
Distance from shower core (m)
200 400 600 800 1000 1200 1400
Mean energy (MeV)
10 20 30 40 o < 20 θ < o 0 o < 45 θ < o 20 o < 60 θ < o 45
Distance from shower core (m)
200 400 600 800 1000 1200 1400
Mean energy (MeV)
10 20 30 40 50 60 o < 20 θ < o 0 o < 45 θ < o 20 o < 60 θ < o 45
Photon energies at surface
Figure 4.12: Average energies of electrons/positrons (top) and photons (bottom) at surface level for simulated air-showers in dierent ranges of zenith angle.
)
θ
sec( 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
Mean energy (MeV)
10 20 30 40 50 60 70 80 90 100 Photons Electrons
100) m from the shower core ±
Average energies of EM particles at (500
Figure 4.13: Dependence of the energy of the electromagnetic particles on the zenith angle around 500 m from the shower core at the surface.
of charged pions and kaons all over the longitudinal development of the shower. The total amount of muons produced is dependent on the mass of the primary particle, so they carry valuable information for composition and hadronic interaction studies. The fact that they are much more penetrating in the atmosphere than electromagnetic particles is what makes them so important for practical purposes, in what regards the detection on the surface.
Decay (into electron/positron plus neutrinos), ionization, bremsstrahlung, di-rect electron pair production and photo-nuclear interactions are the most important pro-cesses muons are subject to in their propagation. At low energies ( 10 GeV), ionization dominates the energy loss. Above 100 GeV radiative processes start having an important role and the rate of energy loss increases. This behavior is represented in gure 4.14, for propagation in dierent materials [91].
The energy spectrum of muons at the surface for all simulated proton showers
of 1018 eV is presented in gure 4.15. Most of the particles have energies of a few GeV,
where ionization dominates the energy loss. But values can reach 100 GeV, with a very low rate, corresponding to muons produced close to the shower core and at high altitudes, due to decays of hadrons with very high energies [89]. The mean energy versus core distance is plotted in gure 4.16, showing no strong dependence on the primary particle energy.
The lateral structure of the muonic component is similar to the electromagnetic one, with an exponential decrease in the density of particles going farther from the core. Figure 4.17 shows the lateral distribution for dierent energies. As expected, higher energy
Figure 4.14: Average energy loss of muons in hydrogen, iron and uranium. For iron the contribution of the radiative processes (bremsstrahlung, direct electron pair production and photo-nuclear interactions) and ionization are shown separately. The plot was taken from [91]. (energy/MeV) 10 log 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Entries 0 10000 20000 30000 40000 50000 60000 70000 80000
Energy spectrum of muons at surface level
Figure 4.15: Muon energy spectrum at the surface for 1018 eV proton showers. All
dis-tances from the shower core and all zenith angles are considered. A threshold of 50 MeV is imposed in the CORSIKA simulation.
Distance from shower core (m) 200 400 600 800 1000 1200 1400
Mean energy (MeV)
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 eV 18.5 10 eV 18.0 10 eV 17.5 10
Muon energies at surface
Figure 4.16: Mean muon energies at the surface for proton showers of dierent energies. primaries produce more muons at the surface. These distributions can be described very well by the function below, proposed in [92] for the KASCADE-Grande experiment:
ρµ(r) = k r r0 −α 1 + r r0 −β 1 + ( r 10ro )2 −γ . (4.1)
The ro parameter is a reference distance where the shower-to-shower uctuations is
min-imum for a given distance between stations in a surface detector. In gure 4.18 this function is successfully tted to a mean LDF of simulated showers.
Now looking to the lateral distribution of muons dividing data into intervals of zenith angle ( gure 4.19), it is possible to note a lower density of particles at the surface for more inclined events. This is because of the larger path traversed from the top of the atmosphere until the ground. In these cases, muons lose more energy and more of them decay. This eect is more evident close to the shower core. Another feature of muons from inclined events is their higher average energy, related to the decrease in the number of low energy particles and the increase in the decay rate of high energy pions [91]. This property is con rmed in the plots from gures 4.20 and 4.21.
These simulations allowed us to see that muons have a lateral distribution which is very sensitive to the energy of the shower (also to its mass, as discussed later in section 4.4). Their energies are around a few GeV, without a strong dependence on the energy of the primary, but dependent on the distance to the shower core and zenith angle (both features are related to the size of the path traversed in the atmosphere).
