Cosmic Ray Showers with Anomalous Longitudinal Profile

Transcription

1 Charles University in Prague Faculty of Mathematics and Physics MASTER THESIS Jiří Blažek Cosmic Ray Showers with Anomalous Longitudinal Profile Institute of Particle and Nuclear Physics Supervisor of the master thesis: Study programme: Specialization: RNDr. Petr Trávníček, Ph.D. Physics Nuclear and Particle Physics Prague 14

2 I would like to express my sincere thanks and gratitude to my supervisors, RNDr. Petr Trávníček, Ph.D. and RNDr. Michael Prouza, Ph.D., for their guidance and ongoing patience shown during the work on this thesis. I would also like to thank Mgr. Ivana Ebrová, Ph. D., for her help with the analysis of the FRAM data.

3 I declare that I carried out this master thesis independently, and only with the cited sources, literature and other professional sources. I understand that my work relates to the rights and obligations under the Act No. 11/ Coll., the Copyright Act, as amended, in particular the fact that the Charles University in Prague has the right to conclude a license agreement on the use of this work as a school work pursuant to Section 6 paragraph 1 of the Copyright Act. In... date... signature of the author

4 Název práce: Spršky kosmického záření s anomálními podélnými profily Autor: Jiří Blažek Katedra: Ústav částicové a jaderné fyziky, Matematicko-fyzikální fakulta, Univerzita Karlova Vedoucí diplomové práce: RNDr. Petr Trávníček, Ph.D., Fyzikální ústav AV ČR Abstrakt: Cílem práce bylo studovat vysokoenergetické spršky kosmického záření s anomálním podélným profilem vzešlé z Monte-Carlo simulací a následně uplatnit použité techniky při zkoumání výsledků z Observatoře Pierra Augera v Argentině. Nejprve byl podán velmi stručný úvod do způsobu popisu vysokoenergetických spršek. Dále byla provedena systematická analýza přibližně nasimulovaných spršek třemi různými technikami. Ve třetí části byl nastíněn způsob fungování Observatoře Pierra Augera, vysvětlena důležitost monitorování okamžitého stavu atmosféry pomocí programu Shoot-the-Shower a podrobně popsán dalekohled FRAM, který umožnil identifikaci spršek s opticky jasnou částí oblohy v pozorovaném směru. Tento vzorek spršek byl prostudován a bylo vybráno několik zajímavých událostí vhodných k dalšímu zkoumání. Klíčová slova: Observatoř Pierra Augera, spršky kosmického záření, chemické složení, anomální podélný profil, Gaisser-Hillasova funkce Title: Cosmic Ray Showers with Anomalous Longitudinal Profile Author: Jiří Blažek Department: Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University Supervisor: RNDr. Petr Trávníček, Ph.D., Institute of Physics ASCR Abstract: The aim of this work was to study high-energy cosmic ray showers with anomalous longitudinal profiles generated by Monte-Carlo simulation and subsequently use the acquired analysis techniques on results from the Pierre Auger Observatory (PAO) in Argentina. Firstly, a short introduction of various descriptions of the extensive air showers was given. Then a systematic analysis was performed on approx simulated showers with three different techniques. A brief explanation of the functionality of the PAO was given, then the importance of monitoring the immediate state of the atmosphere using the Shootthe-Shower program was elucidated and the FRAM telescope was described in detail. FRAM enabled an identification of showers with a clear atmospheric background, this sample of showers was then analyzed and several interesting events warranting a further study were chosen. Keywords: Pierre Auger Observatory, Extensive Air Showers, Chemical Composition, Anomalous Longitudinal Profile, Gaisser-Hillas Function

5 Contents Thesis Overview 1 Introduction The Early Days The Nature of Cosmic Rays The Usefulness of Anomalous Profiles Extensive Air Showers 7.1 Development of a Shower Electromagnetic Showers The Heitler Model Hadronic Showers Gaisser-Hillas Profile The Extended Heitler Model Simulation The CONEX Simulation Program Analysis of the Simulation Results Search for Inflection Points Search for Peaks Statistical Approach A Relation of Maxima Separation to the Distance of the Initial Interaction Points The Pierre Auger Observatory Purpose of the Experiment The Hybrid Detection Method The Configuration of the Pierre Auger Observatory Chemical Composition of Cosmic Rays Shoot-the-Shower Type Experiments The FRAM telescope Analysis of the Results Conclusion 45 Bibliography 46 Appendix 5 1

6 Thesis Overview The aim of the diploma thesis is to estimate the rate of anomalous cosmic ray showers using one-dimensional Monte Carlo simulations (performed by the program CONEX) and to demonstrate how similar analysis methods could be applied to experimental data in the case of the Pierre Auger Observatory. Of critical importance is the discrimination of events influenced by the presence of clouds which can cause a creation of an artificial anomalous light profile observed by the fluorescence telescopes. To be able to explain the whole concept several theoretical as well as experimental subjects are described. In the introductory chapter 1 a short history of the research of cosmic rays is presented and the possible usefulness of anomalous shower profiles, if found, is alluded to. A short overview of few simple models describing the properties of extensive air showers is presented in the chapter, with the emphasis on the models predictions on quantities X max and N max which play a pivotal role in the analysis of longitudinal shower profiles. The chapter 3 recounts the process of identification of anomalous profiles from a large statistical sample generated by Monte-Carlo methods. Three different techniques are used and the influence of various values of cuts on the profile quality is studied. In the chapter 4 the purpose and functionality of the Pierre Auger Observatory is briefly described and the FRAM telescope (section 4.6) is introduced as an useful tool for monitoring the immediate state of atmosphere. Based on the FRAM results an analysis is performed on showers observed through a non-absorbing atmospheric background and several interesting events are identified (tables 4.1 and 4.). The profiles of all the analyzed showers from the FRAM sample are shown in the Appendix.

7 1. Introduction 1.1 The Early Days The research of a radiation of extraterrestrial origin began with experiments of Victor Hess during the years Previous research into the nature of radioactive radiation suggested that the ionization, measured with electroscopes, is not declining with height as fast as it should be, assuming purely terrestrial radioactive origin and using the known γ absorption coefficients [1]. Another study conducted by G. Simpson and C. Wright showed that there exist noticeable levels of radiation over a sea body, but at the same time the amount of radioactive material present there is negligible. These results hinted at the presence of an ionizing component not originating from terrestrial sources. Victor Hess performed a series of experiments with his two assistants using balloons, flying up to 5 m above sea level. They discovered an initial decrease of ionization as a function of height, but the curve reached a minimum at approximately 7 metres and further increased considerably []. This result signified a breakthrough and was later confirmed by Kolhörster, using atmospheric unpiloted balloons reaching up to 9 metres above sea level, where the ionization was increased tenfold with respect to sea level [4]. Hess performed his experiments also during the night and was able to measure an ionization during solar eclipse, finding no differences from daytime observations. That enabled him to eliminate the Sun as a major source of measured radiation. The concept of extraterrestrial rays took a while to settle in, but was finally universally accepted and the term cosmic rays was introduced by Robert Millikan in 195. Victor Hess received a Nobel prize for his discovery in Notable is also the contribution of Domenico Pacini of the University of Bari, who came to similar conclusions simultaneously to Hess using a electroscope submerged in water. 1. The Nature of Cosmic Rays During the late 19s the existence of cosmic rays was firmly established, but their nature remained elusive - it was not clear whether they consist of charged particles or gamma rays on the ground level and likewise what is the nature of the primary particle(s). One of the first arguments in favor of the charged particles hypothesis was an experiment performed by Clay in 198, who found that cosmic ray intensity increases with geomagnetic latitude. This behavior is expected assuming the primary cosmic rays are charged, otherwise the latitude would have no effect [3]. Another very important discovery was made by D. Skobeltsyn, who observed cosmic rays for the first time in a Wilson cloud chamber. Bothe and Kolhörster later verified that the rays tracks are indeed curved and thus the observed cosmic rays on sea level are charged particles. The actual charge of the primary particles was still unknown however. The answer came with careful measurements of the so called east-west asymmetry. Charged particle incoming on a plane of fixed magnetic latitude will be either attracted or deflected according to their respective charge (assuming their energy 3

8 Figure 1.1: Cosmic ray fluxes for several elements. The figure was created by P. Boyle and D. Muller [37]. is low enough so they can be affected by the magnetic field). This leads to an overabundance of positively charged particles incoming from the west. In 1934 a significantly larger intensity of cosmic rays was indeed found coming from the west direction [5], thus confirming that the primary particles are positively charged. In 1938, Pierre Auger was able to prove using coincidence counters that particles observed in the distance of up to 3 meters were in fact part of one event originating higher in the atmosphere and he estimated the primary particle s energy to be about 1 15 ev. This discovery brought about the research of the so-called extensive air showers (EAS). Another open question regarding the nature of cosmic rays was that of the chemical composition at various energies. This interesting problem was partly resolved by various balloon and satellite experiments on energies reachable by such configurations. The resulting chemical composition of cosmic rays is shown in Fig. 1.1 for the region of relatively small energies. Notable is the dominance of protons, followed by a portion of around 1% of Helium and even smaller percentage of heavier elements. Their relative contribution increases with energy however and the shape of the spectrum at very high energies still poses an open and interesting problem today. 1.3 The Usefulness of Anomalous Profiles The current research about the mass composition of cosmic rays in the ultra high energy region centers around the study of the value of slant depth, called X max, where a shower reaches a maximum in its longitudinal profile (which describes the 4

9 number of charged particles, or, equivalently, the energy deposited, per an unit of air-mass passed). The measure of the X max fluctuations σ(x max ) and other derived or independent quantities may also be showing a sensitivity to the mass composition. One of the main basic underlying assumptions is that the smaller the mass of the primary cosmic ray nucleus the deeper the shower penetrates into the atmosphere (see section.4 for a discussion of the reason) and thus, given a specific energy, one should be in principle able to estimate the mass spectrum by comparing the measured shower statistic to the prediction of the hadronic interaction models. Figure 1.: X max (left) and RMS(X max ) (right) as a function of energy. The number of events in each bin is shown. Red, resp. blue, lines represent various hadronic models predictions for proton, resp. for iron, obtained from Monte-Carlo (MC) type simulations of the shower development. Figures taken from [36]. Two of various relevant results from the Pierre Auger Observatory (PAO) are shown in Fig. 1.. The figures indicate a prevalence of protons (or, more generally, of light nuclei) in the lower energies of the UHECR spectrum and a starting trend towards heavier nuclei for the most energetic events. This interpretation is however heavily dependent on the predictions of the hadronic interaction models, which are not in perfect agreement in this energy region. The discrepancy in their predictions is more pronounced in the study of other mass-sensitive parameters, such as X µ max, as is discussed in section 4.4. All interaction models fit well the accelerator data obtained on lower energies, but they differ on the physical assumptions taken to extrapolate their effectiveness to the ultra-high energy region. Incidentally, it is not clear whether the trend shown in Fig. 1. is caused by a gradual change in the mass spectrum or by an unexpected behavior of hadronic interactions at ultra high energies (or a combination of both). The model predictions furthermore depend on assumptions about the cosmic ray mass composition and vice versa. Disentangling this model-data reliance has proved to be difficult at the present state of data acquisition and model iteration, the models cannot be used to consistently interpret all data in terms of cosmic ray mass composition. A model independent information about the chemical composition would thus be very useful in constraining the parameter space of the various hadronic interaction models. A correlated beam of particles originating from a specific (possibly extra-galactic) source with a known acceleration mechanism (and known composition) could, if found, provide a set of constraints. A search for an anisotropy in 5

10 the arrival direction of cosmic rays is coincidentally one of the principal scientific goals of the Pierre Auger Observatory and various other experiments. Another useful tool for placing constraints on the mass composition is the study of showers of anomalous profiles. When a primary particle interacts high in the atmosphere and forms a shower, the shower s longitudinal profile usually acquires a largely universal shape with one maximum. Sometimes, however, a secondary light particle created during a highly inelastic collision receives a relatively large portion of the primary particle s energy and propagates deeply into the atmosphere before interacting and forming a second large sub-shower. Such shower profiles could then exhibit double maxima and are then regarded as anomalous. The critical observation is that the primary particle must be light in order for the secondary maximum to be visible. The reason being that a heavier particle (meaning usually an iron nucleus in the context of this work) has a very low probability creating a secondary light particle with a significant portion of energy due to kinematical constraints. A large composite nucleus such as iron can be seen as a system of (56) independent nucleons, which each trigger their own sub-showers, adding up and creating a largely universal longitudinal shower profile. Sub-showers with relatively small energy then get averaged over and are lost in the composite signal. Due to this fact, an observation of the anomalous events would then constitute an evidence of the presence of light nuclei in the mass spectrum of cosmic rays in a given energy region. The possibility of the appearance of showers of this type is not surprising. The probability of a proton propagating through an atmosphere over a distance X with a (energy dependent) interaction length λ is given by P (X) = e X λ. (1.1) Assuming that a distance of X = g/cm is needed to clearly separate the maxima, the predicted rate of occurence from the equation 1.1 is of the order for the energy range ev (corresponding to the interaction lengths predicted by the EPOS-LHC interaction model). This ratio decreases with energy, as the respective cross section rises. Anomalous showers are incidentally also found in the Monte-Carlo simulations performed while using the various interaction models, as described by the chapter 3 of this work. Actual observation of these events on shower-monitoring experiments is difficult however, since an absorbing atmospheric layer between the detector and the shower axis can easily block a portion of the incoming light and create a false double-maxima profile. Several experiments are in operation with the purpose to identify possible anomalous showers with clear atmospheric conditions. One such experiment, the FRAM telescope, and some of its results are described in detail in the section

11 . Extensive Air Showers.1 Development of a Shower When an incoming cosmic ray particle hits a target air molecule, it triggers a cascade of secondary particles, which further interact with the molecules of the atmosphere and (eventually) lose energy through ionization. Such phenomenon was first observed by Viktor F. Hess during a series of balloon experiments [] and later confirmed by other atmospheric measurements. Later it was established [6] that for energies above approximately 1 14 ev such experimental approach becomes impractical, because the flux of incoming cosmic rays becomes too small to measure effectively. Primary particles at such energies are however able to produce sufficient number of energetic secondary particles so that the resulting air shower is able to propagate to altitudes on a mountain level and with even higher energies it is able to reach the sea level. Due to the acquired transversal momenta of the secondary particles and their further subsequent scattering on air molecules the shower gains a significant lateral spread at the observational level, which exhibits itself by a large number of particles arriving almost simultaneously over a large area. Such phenomenon is then called an Extensive Air Shower (EAS). Depending on the incoming cosmic ray particle, two types of showers can be recognized. An incoming γ ray or an electron (positron) results in a purely electromagnetic shower, while a primary hadron triggers a hadronic shower, which mixes both the hadronic and the electromagnetic component. The presence of the latter is explained mainly by the production of neutral pions (comprising about 1/3 of the total number of pions produced) by a strong interaction and their subsequent near instantaneous decay into γ, which further triggers an electromagnetic sub-shower.. Electromagnetic Showers In a purely electromagnetic shower there are two dominant processes contributing to the formation of the cascade: Bremsstrahlung, during which an electron traversing matter emits a photon, and a pair production, during which a (high energy) photon traveling through matter creates an electron plus positron pair. The production of particles continues until ionization losses of the electrons and positrons become higher than the radiative losses feeding the shower evolution. This happens at the so called critical energy, E c, which for air equals ɛ 81 MeV. After this point, the shower dissipates via ionization losses. This behaviour can be modeled by a pair of integro-differential (cascade) equations [9]. dφ γ (E) dx = 1 1 φ γ (E) + φ e λ pair λ (Ẽ)dn e γ dẽ (.1) brems de E 7

12 dφ e (E) dx = 1 1 φ e (E) + φ e λ brems E λ (Ẽ)dn e e brems de dẽ 1 + φ γ λ (Ẽ)dn γ e pair de dẽ E (.) Where φ e, respectively φ γ, is the flux of electrons and positrons, resp. γ photons. dx is a slant depth measured in g/cm and connected with the traversed path in the atmosphere with a density ρ(l) by the relation ρ(l)dl = dx. λ brems, respectively λ γ, is the radiation length, resp. the conversion length. This set of coupled equations can be solved analytically under two distinct sets of assumptions. This was done first by the pioneering work [9]. A succinct modern treatment can be found in [7]. Following these works, the respective approximations are be labeled A and B. In the case of app. A: ˆ The interaction lengths are constant in regards to energy. ˆ Only bremsstrahlung and pair production processes are taken into account. Processes like the Compton scattering and electron/positron pair annihilation are neglected. ˆ Energy loss by ionization is neglected. ˆ The principle of scaling: particle production depends only on energy ratio of the energy of the primary particle Ẽ and that of the secondary particle E, ie. X lab = Ẽ/E. This assumption is actually superfluous, since it is a consequence of the previous assumptions which strip eq..1 and. of any energy scale. On the other hand, this assumption alone is sufficient to ensure the solution taking the form: φ(x, E) = A e X/Λ E (1+γ), ie. exponential behaviour with depth and a power law in energy. If the scaling was correct perfectly, measurements at low energy would be sufficient for predictions at all energies. Cosmic ray data however suggest only an approximate validity of scaling. Using these assumptions one arrives at a rather complicated formula for the resulting flux. It can be however simplified by using a saddle point approximation, with the extremum being characterized by the condition dλ 1 ds (s)x + ln E /E + 1 s = (.3) where λ 1 (s) is a complicated implicit function to be taken at a value s corresponding to the respective slant depth X. The parameter s is called a shower age. One can now deduce several interesting results. First, one finds the proportionality φ e (X, E) 1 ( ) s+1 E e λ1x, (.4) E E 8

13 where E is the energy of the primary particle triggering the shower. There is however a very accurate approximation introduced by Greisen for the dependence of λ 1 (s): λ 1 (s) = 1/(s 1 3 ln s) 1 X (.5) Where X is a radiation length in a given medium and represents a very important scale (X 37g/cm in air). Inserting eq..5 into.3 one gets s = which gets often simplified to 3X X X + X ln E /E (.6) s = 3X X + X max. (.7) Which, taking into account that the shower maximum corresponds to s = 1, finally leads to the well known relation X max = X ln (E /E) (.8) This has several implications. Firstly, since X max is a increasing function of E, showers with higher energies (meaning the energy of the primary particle) reach their maxima slower than showers with lower energies. Next, the energy dependence of the spectrum turned out to be a power law (as evident from eq..4), in accordance with the implications of the fourth assumption of approximation A. Lastly, when integrating eq..4 over a range of energies from some E min to E, one finds that the number of electrons at maximum is roughly proportional to E. By further studying the equations for the respective fluxes one also finds that showers initiated by an electron or positron and showers initiated by a photon share a very similar development, suggesting they reach a form of dynamic equilibrium injecting each other with new particles [7]. Under the approximation B, following assumptions are taken: ˆ The interaction lengths are again constant in regards to energy. ˆ Validity of the scaling principle is once again assumed. ˆ The ionization loss is not neglected and is instead modeled as a energy independent loss of ɛ per unit of radiation length. This quantity coincides with the already established critical energy, E c, equal to 81 MeV in air. Accordingly, a new term has to be added to the cascade eq.. representing the ionization loss. In this case, no more simple solutions in the form of a power law exists, but analytical solutions can still be found. It is important to notice that for large energies E >> ɛ the collision losses can safely be neglected and the 9

14 solutions must coincide with those of approx. A. Approximation B is thus useful for studying the behaviour on energies comparable to ɛ. The result is that for such energies the profiles obey following relations: (full derivation is again given in [7], the equations are quite similar to those used in approx. A) dn e de ln E c E, (.9) dn γ de E c E. (.1) Incidentally, one can integrate the exact version of eq..4 over the appropriate range of energies and obtain an universal electromagnetic longitudinal shower profile, often called a Greisen profile: N Greisen =.31 [X (1 ln(e /ɛ) exp 3 ( ))] log 3X X + ln(e /ɛ) (.11).3 The Heitler Model Many of the features discussed in the previous section can be obtained also by using a surprisingly simple model of the propagation of the shower. The underlying assumptions are: ˆ The primary particle s energy is much greater than the critical energy, E >> E c. ˆ The radiation length of a electron (or a positron) and the conversion length of a photon are equal. ˆ Each particle travels one radiation length and then decays into two secondary particles (e e + γ, γ e + e + ), each receiving half of the parent s particle energy. ˆ There exists an energy E c such that electrons and positrons with E < E c lose all their energy through ionization. This scheme is ilustrated in.1. Under such model, after the particles travel t radiation lengths, the shower will have t particles. The energy distribution will be constant, with each particle having the same energy E = E t. At some t max, the energy will fall under the critical value E c, with the corresponding air thickness X max : E tmax = E c => X max = t max X = ln E /E c (.1) ln This result, together with the formula for the number of particles at maximum depth (N max = tmax = E /E c ) can be compared to the previous results obtained through more rigorous treatment. In both cases, X max grows logarithmically with energy, which is also an experimentally observed feature. 1

15 Figure.1: A schematic example of an electromagnetic shower. from [15]. Sketch taken.4 Hadronic Showers As a consequence of the presence of the strong force in the initial interaction, hadron showers differ substantially from their electromagnetic counterparts. A strongly interacting particle with sufficient energy scatters inelastically on an air nucleus and can produce a large variety of particles from the hadron sector, with π mesons being the most abundant type. The resulting extensive air shower is guided by a few initial interactions, resulting in large possible fluctuations due to their complex nature. Of particular importance is the production of neutral π and η mesons. These particles decay rapidly into γ and thus create an electromagnetic sub-component of the shower, which is being continually enhanced during its evolution. Due to the almost instantaneous decay of these mesons they don t propagate very far in the atmosphere and therefore the electromagnetic spectrum is driven by the first few high-energetic interactions [8]. Hadron showers also have an muonic component stemming from the decay of charged mesons. Charged pions have to be relatively low-energetic (in the range of 3 1 GeV) for their decay probability to be higher than their interaction probability, meaning that the muonic component originates from the deeply penetrating hadrons which have lost a sufficient amount of energy through multiple interactions. The number of muons as a function of altitude is plotted in Fig... Energy deposit associated with the production of weakly interacting particles such as neutrinos and neutrons escapes the detection region and is not measured by the surface detectors. Lastly, some energy gets dissipated in interactions with air nuclei. Thus, only a fraction of the initial energy is observable through the detection of ionization losses of charged particles (particularly the electrons and positrons). Another important feature of the hadronic showers is the energy dependence of the cross section, inelasticity and other parameters. The quantity corresponding to the radiation length (as explained in section.) is the mean free path Λ, which equals approximately 8g/cm for a proton of energy 1 15 ev in air [1] and thus is roughly double that of its electromagnetic counterpart. One would thus expect the hadronic showers to be comparatively more deeply penetrating, or equivalently, their longitudinal profile (of energy deposit per depth, de/dx) 11

16 6 1 number of Muons H [m] Figure.: A sample shower showing number of muons depending on the altitude. The peak is reached at approx. 1 km. Simulation done in CONEX using a proton with an initial energy 1 19 ev, zenith angle 6, high energy model EPOS LHC. to have a higher maximum X max compared to the electromagnetic shower of the same energy. Furthermore, as the electromagnetic component is constantly being fed new particles from the π decay, one would expect a further shift in X max. This not observed however [11], as the hadronic interactions have a comparatively much higher multiplicity and the initial energy is thus distributed to product particles faster, ie. they reach the critical energy in fewer generations..5 Gaisser-Hillas Profile Various experimental data of extensive air showers measured using the detection of fluorescence light are often fitted using a four-parametric Gaisser-Hillas function [1]: ( X X N GH (X) = N max X max X ) Xmax X λ ( ) Xmax X exp λ (.13) The parameters N max, resp. X max modify the normalization, resp. location of the shower maximum, while the parameters X and λ modify its shape. It is important to note that while the latter parameters may appear to have an obvious physical meaning (namely, that of a location of the first interaction and that of a interaction length), their values are governed by the output of the fitting procedure and the best fit often corresponds to unphysical values (X can often obtain negative values, meaning the interaction would occur before the particle entered a (massive) medium). As can be seen from various simulations done in CONEX [14] and CORSI- KA [13] simulation packages, the eq..13 describes the shower profile well for a large region of slant depths but fails for the deeply penetrating ( long tail ) component. For this reason, a 6-parametric Gaisser-Hillas function is sometimes introduced, parametrizing the interaction length λ in the following way: 1

17 λ = λ + λ 1 X + λ X. (.14) The Gaisser-Hillas profile describes well the bulk of simulated and measured showers. However, the development of a hadronic shower is still subject to large fluctuations and significant differences to the profile in eq..13 can occur. A particle can interact inelistically high in the atmosphere, triggering a sub-shower, while at the same time creating a deeply penetrating leading particle, which carries a significant portion of the initial energy. The leading particle then interacts inelistically deep in the atmosphere, triggering another sub-shower of comparable energy. The resulting profile would then show a clearly separated double maxima. Such events can be seen in simulations [19]. Incidentally, one of the aims of this work is to quantify the percentages of those showers with anomalous profiles that could be in principle observable..6 The Extended Heitler Model A construction similar to the aforementioned simple Heitler model (developed for electromagnetic showers) is also possible for hadron initiated showers. In this simple model the hadronic cascade consists purely of pions. Analogically to the electromagnetic case, it is assumed that a charged pion travels one interaction length (approximately 1 g/cm for the energy range of 1-1 GeV [16]) before it interacts, producing another n mult pions. The interaction length λ is assumed to be constant. A fraction of these pions will be neutral which will, after their near instant decay, transfer portion of the total energy into an electromagnetic component. This fraction is assumed to be 1/3 (see [15] for a discussion about the validity of this value and for instructive construction of the extended hadronic model). Figure.3: A schematic example of a hadron shower in a simple model. Sketch taken from [15]. be After n generations, the number of charged pions present in the shower will ( ) n Nπ ch = 3 n mult, (.15) 13

18 while the energy per charged particle is E ch π = E ( 3 n mult) n. (.16) Charged pions of higher generations will eventually have sufficiently low energy to become more likely to decay than to interact again. In this model it is assumed that the pions decay immediately after obtaining this critical energy E c π into muons. The exact value of E c π depends on the density of the medium where the interaction occurs but for the purposes of studying air showers GeV is a good estimate [15]. The number of generations n c required to reach this energy is given by n c = ln (E /E c π) ln ( 3 n mult). (.17) Using n mult = 1, this expression gives n c = 3 6 for log 1 E = The muon number (N µ = Nπ ch ) can be inferred from eq..17: where N µ = ( ) nc 3 n mult = ( E E c π ) β, (.18) β = ln ( n 3 mult) < 1. (.19) ln n mult Again, using the value n mult = 1, one gets β =.85. The muon number thus depends on E less than linearly. It is now also possible to estimate the electron number N max e and E ch π N max e = N µ E c π there follows from the conservation of energy. Since E = E e.m. + E ch π Ne max = E N Ee.m. c µ (.) Ee.m. c is directly proportional to E, but also depends on the pion multiplicity through the muon number and also possibly on the ratio of neutral pions produced (which was assumed to be equal to 1/3 in eq..15). Ideally, it would be possible to infer useful characteristics of the strong interaction by measuring the electron number N e, computing Ne max and then examining the structure of eq..18, for instance. However, as shown in [17], the quantity ln N e depends on Ne max only logarithmically compared to linear dependence on X max. This makes the aforementioned task difficult. It is also interesting to further extend the model to accommodate initial particles more complex than a proton - atomic nuclei. In the most simplified view, an incoming nucleus with an atomic number A and total energy E can be taken as a sum of A protons, each with E /A energy. They all interact at the same point in time and then subsequently act independently as A separate showers. In comparison to shower initiated by a proton of the same energy E, this scenario has lower initial energies of the sub-showers. As alluded to in [15], several useful expressions can be derived from the modified model: E c π N A µ = N p µa.15 (.1) 14

19 and X A max = X p max λ γ lna, (.) where λ γ is the splitting length of the γ photon. Eq..1 is a consequence of the muon number depending less than linearly on E. Because of the lower initial energy of the respective sub-showers (compared to a single proton with energy E ) fewer generations of particles are generated and less total energy is lost to the electromagnetic component. For the same reason the showers produced by heavier nuclei do not penetrate comparatively as deeply, as eq.. shows. These properties would ideally provide the tools for identifying the chemical composition of the incoming cosmic rays. That would, however, require very precise measurements of X max and N µ, which is difficult to achieve. Moreover, the interpretation of the measurements largely depends on simulations, which are in turn dependent on the various high energy models of the strong interactions. These models are however only extrapolations from energy regions explored by colliders and experiments such as the KASCADE-Grande exp. [18] and are thus carrying large uncertainties in their predictions. 15

20 3. Simulation One of the principal aims of this work is to give a quantitative prediction on the number of anomalous double maxima showers that should be observed on the Pierre Auger experiment or any other observatory studying UHECR. As already alluded to in previous chapters, it is presently impossible to obtain such a prediction from first principles of the theory of strong interactions and one thus has to rely on simulations using various approximative models of strong interaction, which have to be furthermore extrapolated into the UHECR energy region. A program CONEX was chosen as an optimal tool to simulate the hadronic showers. 3.1 The CONEX Simulation Program CONEX is a simulation program designed to vastly cut the computing time required compared to other simulation packages while maintaining a high level of accuracy of its predictions at the expense of keeping track only of the longitudinal features of a shower [3]. Alternative simulation packages like CORSIKA [31] are used for a complete determination of an extensive air shower development by employing a full Monte Carlo (MC) treatment. Both resulting profiles (longitudinal and lateral), modeled in high detail, show a good agreement with experimental data [39]. However, for high energies of the primary particles the computing time becomes unreasonably high if a large statistical sample is required. CONEX circumvents these limitations by introducing a hybrid approach to the shower simulation: at high energies, a Monte Carlo treatment is employed again, using the available high energy hadronic interaction models (EPOS LHC, QGSJETII- 4, QGSJET1 or SIBYLL.1 in the present iteration) to simulate the first few particle generations in detail and recording them on a number of chosen depth levels. When the particles energies fall under a certain threshold energy E thr, acting as a free parameter in the simulation, they are binned into energy-depth tables, which represent the source terms in the subsequent treatment using numerical solutions to electromagnetic and hadronic [3] cascade equations. The depth X represents a projection of the slant depth of a given particle onto a shower axis. The cascade then continues to be solved numerically on a number of pre-chosen depth levels, until all sources fall under their respective critical energies. The energy lost from the hadronic shower through the π and η decay is binned into the electromag. source terms on the next depth level and similarly CONEX deals with the hadronic terms created in the electromagnetic cascade equations (such as through a photo-nuclear interaction and through muon pair production, which is also considered a hadronic process for the purposes of the simulation). Despite this simplifying approach, CONEX displays a good agreement with more detailed MC simulation methods [3]. The generated output contains various shower characteristics, some of them dependent on the depth X. Some examples being the number of charged particles above a given energy cut N ch (X), the muon number N µ (X) and the energy deposit de/dx(x). The quantity de/dx is especially useful in comparing the simulation results to direct measurements of the ionization energy losses by the fluorescence 16

21 detectors. The program also automatically performs a fit on the generated profile of N ch using a six parameter Gaisser-Hillas function.5 and returns the result. Fig. 3.1 plots a sample output of a simulation. number of charged particles proton (EPOS) lg(e/ev)=. zenith=6. azimuth=. N max = 5.9e+1 X max = 813 g/cm X X int λ = 7 g/cm = 36 g/cm = 88 g/cm X [g/cm ] Figure 3.1: A sample CONEX profile generated using an initial proton of energy 1 ev is shown as dots, plotted red line is a Gaisser-Hillas fit. On the right are displayed its parameters (λ 1 and λ are omitted for clarity), X int represents a stored value of the depth of the first interaction of the initial particle. CONEX is also capable of tracking the position, energy and other parameters of the most energetic (leading) particle resulting from the first interaction. Various pieces of information about the interaction itself such as the inelasticity (fraction of the total energy not carried away by the leading particle), the multiplicity (number of particles created in the interaction) and others are also stored. After the leading particle interacts, CONEX again stores the position and interaction parameters and tracks the (possibly new) most energetic particle, then continues on to the next iteration. This procedure provides useful information in the analysis of the development of the most energetic sub-shower, which can be used eg. for estimating hadronic cross sections and the validity of the hadronic interaction models used in the simulation. The information about the interaction depths of leading particles is also used in section 3.5 later in this work when analyzing the properties of anomalous shower profiles showing double maxima. 3. Analysis of the Simulation Results Showers showing two maxima as described in section 1.3 are very rare. To estimate the ratio of these anomalous showers on a given energy a large number 17

22 of events must be generated. An energy range ev of a primary proton was investigated in this work, with a step increase of log 1 (E/eV) =.5, seven energies in total. For each energy, approximately 1 5 showers were generated. The zenith angle was set to be θ Z = 6, to enable a sufficient development of the shower in the atmosphere, azimuthal angle was not specified as it is not relevant. The hadronic interaction model used was EPOS LHC [33]. With the simulation results in hand, the principal question is how to define and subsequently find anomalous showers with double maxima. It is clear that every such definition must depend on a set of parameters, values of which are difficult to set correctly due to the inexact nature of the anomalous showers. For this reason, the parameters were varied in the analysis to give a range of possible predictions. Three independent methods were employed: ˆ A search for inflection points. Since CONEX outputs a smooth non-fluctuating longitudinal shower profile, it is possible to estimate the number of double maxima profiles by the number of showers with four inflection points (as opposed to an ideal G.-H. profile, which would contain only two inflection points). ˆ A straightforward search for the number of peaks using the TSpectrum ROOT routine. ˆ A statistical approach. An 8-parameter Gaisser-Hillas fit, obtained by adding two 4-parameter Gaisser-Hillas profiles, is applied to simulated showers and fits showing a (significant) improvement over the default CONEX fit (measured in the difference of χ values) are identified as anomalous. In the following sections, each method is described in more detail and the results are presented. 3.3 Search for Inflection Points The CONEX output bins the charged particle profile into approx. bins, spanning from X = gcm to roughly X = gcm. An inflection point is identified as a region of at least K bins where the second order central difference (a numerical equivalent of the second derivation) changed its sign. The method is solely dependent on the value of K, which specifies the minimal proportion of the found extreme (a maximum is identified by the presence of two inflection points, which couldn t be less than K bins afar or else they would get ignored) and the minimal distance between extremes (two maxima cannot be closer than K bins). Showers exhibiting 4 inflection points or more are then identified as anomalous. In the Fig. 3. the relative ratios of anomalous shower profiles are shown as a function of the energy of the primary particle, each data set representing a different value of K. The acquired ratio first decreases with energy. This is an expected effect, since the cross section rises with energy (and so the interaction length decreases). In the last two energy bins however a significant rise is observed. This is consistent across all the methods results with a proton as a primary particle presented in this chapter. The reason for this behavior is not clear. A study examining this effect with all the up-to-date interaction models could possibly yield interesting 18

23 results, but gathering a shower statistic required for such an analysis was beyond the scope of this work. 3 1 /N tot ].5 Ratio [N 4inf log (E/eV) 1 Figure 3.: A ratio of anomalous profiles identified with the inflection point method plotted against the initial particle s energy. The results obtained with three different parameters are shown: blue circles correspond to K = 5, red triangles to K = 7 and green squares to K = Search for Peaks This approach makes use of a TSpectrum ROOT class, a method developed originally for background removal and peak finding in nuclear γ ray spectra [34]. The function first removes the background. The CONEX shower profiles technically do not contain any background, but the use of the removal function is still advantageous in regards to obtaining the approximately correct number of peaks the method searches for Gaussian-profiled peaks, which differ from the Gaisser-Hillas profiles exhibited by the cosmic ray showers. A deconvolution algorithm is then used iteratively to estimate the number of peaks. The scheme depends on several parameters such as number of iterations in the background removal procedure, number of deconvolution iterations, estimated gaussian standard deviation σ for the looked-for peaks and the threshold value for candidate peaks found. The iterative parameters were left at default values and σ was after some experimentation set to σ = 1. The threshold value T possesses a clear physical meaning: the peaks with amplitude less than T N H max, where N H max denotes the amplitude of the highest peak in the spectrum, are discarded. T thus controls the size (or, respectively, energy, see eq..1) of the sub-showers, which could be considered anomalous. The following Fig. 3.3 shows the relative ratios of the anomalous profiles in dependence on primary energy for three values of T (T =.5, T =. and T =.5). 19

24 /N tot ] 1 3 Ratio [N peaks log (E/eV) 1 Figure 3.3: A ratio of anomalous profiles identified with the peak search method plotted against the initial particle s energy. The results obtained with three different parameters are shown: blue circles correspond to T =.5, red triangles to T =. and green squares to T = Statistical Approach This method attempts to identify the double maxima profiles by the χ difference of the CONEX 6-parametric fit and double Gaisser-Hillas 8-parametric fit. This procedure is analogous to the method used in the reference paper [35], but differs in several important points, which are described later in the text. The 8-parametric double Gaisser-Hillas (DGH) profile has the form of N DGH (X) = N 1 GH(X) + N GH(X), (3.1) where NGH 1 and N GH are standard 4-parametric Gaisser-Hillas functions described by eq..13, X is a slant depth. The expanded 6-parametric profile used by CONEX further parametrizes the term λ as in eq..14, ie. λ = λ + λ 1 X + λ X, to better describe the behaviour of the profile on high shower depths dominated by a muonic long tail, where the 4-param. G.-H. profile often fails to be accurate. This behavior is also inherited by the 8-param. profiles with double maxima. The long tail of the profile was not fitted however since only a good agreement (between the fit and the simulated profile) in the region around the two maxima is of importance for estimating the ratio of anomalous profiles. In terms of the χ function, the parameter dependency looks as χ DGH = χ DGH(N 1 max, X 1 max, X 1, λ 1, N max, X max, X, λ ) (3.) and the function is computed from the simulated shower profile N(X) by the Ansatz χ DGH = n (N i (X i ) N DGH (X i )), (3.3) V i i= where n is total number of simulated data points and V i sets the normalization of the distribution. Using Poisson-like values V i = N i the eq. 3.3 would become

25 the standard formula for calculating χ. In the work [35] the shower shape parameters X 1, and λ 1, were fixed at values typical for non-anomalous profiles to improve the stability of the fit, in effect reducing the fit to 4 parameters. In our analysis however, a full 8-parametric fit is attempted with the purpose of obtaining comparatively better fit results. This is justifiable due to CONEX producing an exact shower profile of more than bins, so the problem is well defined. This method places higher requirements on the stability of the fits however, so consequently a longer computing time is required in comparison to the fixed parameters method. Following the approach in [35], a choice was made for V i so that V i = kn i /E, (3.4) where E is the energy of the initial particle and k is set in such a way that the condition Vi / N i =.1 is satisfied. This re-scaling of the equation 3.3 helps to remove the energy dependency of χ, which otherwise in the Poissonian Ansatz grows significantly with energy. This behavior is due to the total number of shower particles being related to initial particle s E, making comparisons between different energies difficult. After the re-scaling however, it is possible to introduce energy-independent cuts for the identification of anomalous profiles. Their exact values will be discussed later in this section. Finally, in the paper [35] the generated profile was further fluctuated by V i using Gaussian random numbers simulating a real detector response and easing the fitting procedure. This was not done in this thesis, as the intristric fraction of anomalous showers being generated in the atmosphere and a capability of a particular experiment to observe it are viewed as two separate problems. In this section an analysis of an exact profile generated by CONEX was desired, to estimate the fraction of anomalous showers without any restrains possibly introduced by the observing techniques of surface experiments. During the fitting procedure several measures are taken to improve the stability of the fits. Firstly, approx. 15 last bins are cut from the profile (a loss of roughly 7% of the data), due to the already mentioned poor accuracy of 4-parametric Gaisser-Hillas profiles on the long tail of the spectrum. This significantly improves the fit convergence and does not lessen the quality of the fits themselves, since for the purposes of the analysis of anomalous showers, a fit correct mainly in the region containing the double maxima is the most desired outcome. It would be possible to attempt to fit two 6-parametric Gaisser-Hillas profiles to make use of all the data available, but it would introduce significant difficulties in the fitting procedure due to an increased complexity of the problem. The result, an expected fraction of anomalous showers seen by the fluorescence detectors, would likely not be much improved due to the relatively small significance of the long tail on the X 1 max and X max difference. Then the ROOT TSpectrum method is applied to the generated profiles and the resulting peak position(s) are taken as a first parameter value for the ROOT fit() function, which improves the stability of the fit. Lastly, since the fit often doesn t converge on a first call, an iterative procedure is used when the results of the previous iteration are used as initial parameters for the next iteration. This is expensive in terms of computer time, but ensures that the vast majority of fits eventually converge to a meaningful set of values of parameters in eq

26 Lastly, χ is computed as in eq. 3.3 for the 8-parameter fit and compared to χ calculated for the 6-param. fit, which is given by CONEX output for the respective showers. The CONEX fit uses also the re-scaling shown by eq. 3.4 and is thus different quantity from the χ found in the CONEX output. In Fig. 3.4 several examples of found showers exhibiting anomalous profiles are shown, together with several plotted fit results. To obtain a meaningful estimate for the number of anomalous shower profiles that should be, in principle, observed by surface detectors, several cuts need to be applied to the shower statistics calculated in preceding steps. Firstly, there should be a clear separation of the two maxima (or possibly mere regions containing inflection points), denoted by X max. Secondly, it is possible to require the χ of the DGH fit to be a improvement over the χ of the CONEX fit by a certain margin, denoted by χ. These two quantities serve as the two main parameters of the statistical approach being presented in this section and several combinations of their values were used in the following presented results. First X max was varied while χ was set to χ =.1. The results are shown in Fig As can be seen from Fig. 3.5, the calculated fraction is only weakly dependent on the maxima separation cut for energies of E = 1 19 ev and higher. In the work [35] a cut value of X max = 3 g/cm was used. Such a strict separation requirement is however not necessary in this work, since the analysis is carried on exact non-fluctuated profiles. Also please note that due to this fact the respective values of χ turn out to be much smaller (under the re-scaling described by eq. 3.4) than in the cited work where a discrimination cut of δχ = 5 was used. In our analysis the values usually obey χ << 1 and typically χ <.1. Next the discrimination cut X max = 1 g/cm was set and the parameter χ was varied. The results can be seen in the Fig The results of all of the above-mentioned methods behave in a consistent way and give a compatible order of magnitude prediction. The value of this estimate is dependent on various cuts used for identification of anomalous profiles and thus carries a large systematic error. The exact value is not important however, since any evidence of observed anomalous profiles in the UHECR region by a fluorescence detector would point out to a presence of light nuclei component in the cosmic rays, as was already discussed in the introductory section 1.3. To illustrate the validity of this point also through the methods carried out in this chapter, a statistic of approx. 1 4 showers with an iron nucleus as an initial particle was generated. Then the inflection point search method was performed, as described in section 3.3. The results are plotted in Fig A Relation of Maxima Separation to the Distance of the Initial Interaction Points Another interesting question about the development of the so called anomalous showers is how many of the visible sub-showers are caused by the leading particles. A leading particle labeled as n = 1 is defined as the most energetic particle created in the first interaction of the initial particle. A leading particle labeled n = refers to the most energetic particle created in the first interaction of the leading particle labeled n = 1 and so on. Since CONEX tracks the positions (slant depths)

27 Figure 3.4: A sample example of profiles identified as anomalous, generated by an initial proton of energy E = 1 ev. Black line is a CONEX generated shower profile, blue dashed lines are 4-param. distributions N 1 GH (X) and N GH (X), red line is their sum N DGH (X). Red triangles are the results of the TSpectrum method, where successful. 3

28 ] 1 tot / N 3.5 Ratio [N 4inf log (E/eV) 1 Figure 3.5: A ratio of anomalous profiles identified with the χ comparison method plotted against the initial particle s energy. The results obtained with three different parameters are shown: blue circles correspond to X max = 5 g/cm, red triangles to X max = 1 g/cm and green squares to X max = 15 g/cm. 3 ] 1 tot / N Ratio [N 4inf log (E/eV) 1 Figure 3.6: A ratio of anomalous profiles identified with the χ comparison method plotted against the initial particle s energy. The results obtained with three different parameters are shown: blue circles correspond to χ =.5, red triangles to χ =.1 and green squares to χ =.. of the interactions, it is possible to analyze the difference of the interaction of the primary particle X initial and the slant depth X N at which the leading particle n = N created a significant sub-shower (ie. the interaction was deeply inelastic, the created particles are assumed to then decay or interact quickly so that a subshower develops). The difference should be (when all quantities are well defined) strongly correlated to the difference of the parameters X 1 max and X max (= X max ) obtained by the 8-param. double Gaisser-Hillas fit. For this purpose the data from all energies were pooled together and the cuts χ =. and X max = g/cm were applied. An interaction was considered 4

29 ] 1 3 tot.5 / N Ratio [N 4inf log (E/eV) 1 Figure 3.7: A ratio of anomalous shower profiles with a Fe nucleus as an initial particle plotted against energy. Black squares represent profiles identified with the inflection point method using K = 5. Red triangles represent profiles identified with the peak search method using T =.5. Blue dots serve as a reference and represent a ratio of anom. showers initiated by a proton and identified by the inflection point method using K = 5. as creating a sub-shower when at least 15% energy of the leading particle was carried away by the products of the interaction (ie. the inelasticity was bigger than.15). Results obtained after applying these cuts are shown in Fig As can be seen, there exists a large set of events clustered around the x = y line, indicating that the sub-showers visible in the shower profiles were indeed created by a Nth generation of leading particles. A very large cluster of events with small X N X initial but large X max is also visible. These events indicate a set of sub-showers not initiated by the leading particles, the quantity X N (and consequently X N X initial ) is not well defined. A sample possible scenario explaining such events would be an initial particle undergoing a deeply inelastic scattering, creating two product particles with large fractions of the parent particle s energy. The higher energetic particle, labelled as leading, interacts immediately and contributes to the shower generated by the parent particle. The second (slightly) less energetic particle then propagates deeply through the atmosphere and creates a sub-shower far from the initial interaction. Its position then doesn t get registered by the CONEX tracking algorithm. Another possible explanation for such events is that the leading particle triggered a sub-shower at a point which didn t tracked by CONEX, since only several interaction points were recorded. 5

30 [g/cm X max fitted ] X N X initial [g/cm^] Figure 3.8: A plot showing a correlation between X max and X N X initial. Red line represents the x = y axis. Plot contains events from all energies, the data size was significantly reduced due to strict cuts. 6

31 4. The Pierre Auger Observatory 4.1 Purpose of the Experiment The Pierre Auger Observatory was designed to measure Ultra-High Energy Cosmic Rays (UHECR), which are usually defined as incoming particles with energies above 1 18 ev. Such particles exceed the energies reachable at particle accelerators by several orders of magnitude and thus their study in principle offers opportunities for a possible discovery of new physics phenomena. This energy region is, however, interesting also from an astro-physical point of view. It is expected that protons of energies above approximately 1 19 ev are traveling through the galactic medium in straight lines and can thus pinpoint the location of their sources, enabling (among other useful research topics) the study of a possible anisotropy of the UHECR. It is hoped that information about the spatial distribution of the sources and their respective identification will provide an insight about the acceleration mechanisms that take place in these astronomical objects. The cosmic ray energy spectrum displays a feature called an ankle, showing a hardening of the slope (the dependence of incoming flux on energy) at around ev [] (recent results from the KASCADE experiment in Karlsruhe have shown an even earlier hardening at around 1 17 for the light particles [1]). It is widely assumed that this phenomenon is at least partly explained by the emergence of an extra-galactic component in the flux, which would then be dominated by light nuclei. Figure 4.1 shows a spectrum reconstruction done by the Pierre Auger collaboration, data are taken from years 5 1. Figure 4.1: Energy spectrum obtained by the Auger Collaboration. Figure taken from []. As can be seen, another important feature of the spectrum is the flux suppression observed at approx. at ev. A possible explanation is an energy loss of protons with extra-galactic origin caused by the pion production off the 7

32 cosmic microwave background: p + γ CMB p + π (a similar process, a pair production p + γ CMB p + e + e +, is less efficient). The threshold energy is approx ev and the corresponding mean path is roughly 5 Mpc, meaning that protons originating outside of a sphere with this radius should be strongly suppressed. This effect is called a Greisen-Zatsepin-Kuzmin (GZK) effect and the corresponding limit a GZK cut off [], [3]. Recent results from the Auger [5] and HiRes [4] experiments show similar suppression. Observing events above the cut-off energy would then indicate an origin inside the GZK horizon. To summarize, the Pierre Auger Observatory hopes to address the following questions through the study of ultra-high energy cosmic rays: ˆ Is there an anisotropy in the origin of the UHECR? Would it be possible to identify any point sources? Is there a correlation to known astronomical objects? ˆ What is the chemical composition of the incoming flux? ˆ Does the GZK limit hold? How is the case with heavy nuclei? ˆ Is the observed ankle indeed caused by an extra-galactic component? ˆ What are the acceleration mechanisms for UHECR production? 4. The Hybrid Detection Method Early measurements of the cosmic days were done in arrangements using balloons and later satellites. But due to the incoming flux of cosmic rays steeply declining with energy, the detection of UHECR becomes very difficult (particles with energies above 1 19 ev pass through a given square kilometer only once a year). This necessitated a different approach in CR measuring experiments - the particles were observed indirectly through the study of extensive air showers, which required large detection areas being covered over long periods of time to get a meaningful statistic (the spectrum declines approximately as E 3, so to detect a 1 times more energetic particle, 1 times larger covered area is needed). Two configurations were historically used in the experiments. One is a (large) array of radiation detection stations filled with a target material (either purified water or a plastic scintillator) paired with photomultipliers and related data readout system. A passing particle emits a light signal (sufficiently energetic particles travel through water with a speed greater than the speed of light in the medium, producing a Cherenkov radiation) which then gets picked up and converted into an electric signal by the photomultiplying tubes. A coincidence of several station signals is used to identify a shower. These types of experiments are called surface detectors (SD) and are capable of having nearly 1% operating uptime, while also being only weakly affected by atmospheric conditions. The second approach takes advantage of the fact that nitrogen molecules emit a near ultraviolet fluorescence light when passed by particles in an electromagnetic component of an extensive air shower. The size of this light signal is directly proportional to the shower particle energy through a constant called a fluorescence yield. An UV telescope installed on the surface is then able to measure 8

33 the ionization losses of an air shower, effectively using the atmosphere as a giant calorimeter. The fluorescence detectors (FD) are able to measure the longitudinal profile of the shower and then by integration over the whole path the total deposited energy can be inferred, thus determining the initial particle s energy. Fluorescence detectors can only operate during clear nights with the moon being not too prominent. The Pierre Auger Observatory has taken a novel approach in combining both aforementioned experimental setups, producing the so-called hybrid detection method. The SD and FD setups are used in a highly complementary way. ˆ The two shower parameters most indicative of cosmic ray composition are shower maximum X max, which is directly measured by the FDs, and muonic content N µ, which can be directly measured by the SDs. ˆ The shower energy is estimated by both methods independently, thus allowing for cross-checking and fine-tuning the analysis. The FD has a lower uncertainty, connected mainly with the determination of the fluorescence yield parameter. The SD, in its modern form, relies on the reconstruction of a shower using simulations and thus depends on assumptions regarding the initial particle type and the nature of hadronic interactions (ie. which high energy strong interaction model is used, what are its parameters). This dependency is however strongly supressed in the analysis on the Pierre Auger Observatory, since a calibration procedure using FD reconstructed energy profiles is employed. ˆ The SD method is superior in determining the geometry of the shower, while the FD is superior in determining its energy. 4.3 The Configuration of the Pierre Auger Observatory The Pierre Auger Observatory is located near the city of Malargue in Mendoza province, Argentina. Its southern latitude is 35, while situated at the altitude of 14 meters above the sea level. It covers a surface area of roughly 3 km, with 16 water tanks located on a triangular grid, spaced by 1.5 km. The tanks have a 1.8 m radius and 1. m height, containing 1 m 3 of highly purified water. Three photomultiplier tubes are installed above the water. Each station contains a solar panel and a buffer battery providing power for the locally placed electronics. A GPS signal is used to provide synchronization for coincidence measurements. Calibration is done using a characteristic signal emitted by a cosmic ray muon passing the tank vertically. There are altogether 4 fluorescence detectors installed, grouped up by six at four separate locations standing at the array s periphery and overlooking the SD array. Each location is situated at a slight elevation and is referred to by name -Coihueco, Los Leones, Loma Amarilla and Los Morados. Each detector is a wide-angle Schmidt telescope with aperture diameter of. m. Each telescope has a filed of view of 3 in azimutal and zenith angle, with the centre of field being roughly 16 above horizon. The groups of six telescopes are arranged in 9

34 a half-circular fashion (shown in Fig. 4.) so that combined they view full 18 angle in the direction of the SD array. Due to the measurements being possible only on relatively moonless, clear nights, the FD is only operational about 1% of the time. Detailed description on the FD construction and functionality is given in [6]. Fig. 4.3 shows the layout of the whole observatory. Figure 4.: Spatial arrangement of a fluorescence detection site. Figure taken from [6]. Figure 4.3: The layout of the Auger experiment. Light dots represent SD tank stations, the grayed areas represent field of view of the four named fluorescence detectors, each consisting of six separate telescopes. Figure taken from [6]. Three additional fluorescence telescopes, called High Elevation Auger Telescopes (HEAT), were added to the Auger experiment in the year 9 [7]. They possessed a field of view of 3, same as the previously installed FDs, but were also newly being able to be tilted for up to 3 in the zenithal direction. This enabled the observation of showers with energies down to 117 ev, lowering the 3

35 observable energy threshold by about a magnitude. This is a consequence of the fact that lower energy showers have their maximum higher in the atmosphere and their maxima thus could have been too high in altitude to be observed by the original FD setup. Furthermore, as discussed in section.6, showers initiated by heavier nuclei also have their maxima shifted to the higher altitudes (lesser slant depths). The installation of HEAT telescopes thus made possible the observation of the very interesting region of expected galacatic and extra-galactic cosmic ray transmission, enabling a cross checking with results of previous experiments already exploring this region such as HiRes and KASCADE. Figure 4.4 schematically depicts the elevated field of view of HEAT. Figure 4.4: A schematic depiction of the respective field of view of one standard FD and two HEAT detectors. Figure taken from [7]. 4.4 Chemical Composition of Cosmic Rays As mentioned previously one of the main questions to be answered by the Pierre Auger Observatory is the chemical composition of the cosmic rays in the UHECR energy region. As already seen at section.6, the quantity X max of a shower induced by a particle with energy E is expected to be sensitive to the particle s mass A through the relation X max ln E ln A (see eq..). Another quantity sensitive to A is the standard deviation of X max, σ(x max ), which is also observable at the PAO [9]. Comparing their measured values to predictions of various hadronic interaction models for light and heavy nuclei (which should differ) can in principle answer the posed question about the cosmic ray mass composition. The latest published comparison ([9]) between data ([8], see also Fig. 1.) and model predictions is hinting at the prevalence of the light nuclei component in the flux at energies near E = 1 18 ev and then an increase of the heavy nuclei component to a point where it becomes dominant at around E = ev (see Figure 1.). It is still not possible to draw definitive conclusions about the chemical composition, as the interpretation of the data relies on predictions of the interaction models, which are fitted to show good agreement with data from 31

36 accelerator experiments. They differ significantly in their predictions in the ultrahigh energy region however. The use of the quantities X max and σ(x max ) in inferring the chemical composition of the cosmic ray flux is not equivalent. The mean distribution X max depends on lna linearly via the equation (see [9] for details) X max = X max p + f E lna, (4.1) where X max p is the mean distribution for proton-induced showers and f E is a parameter depending on energy and also on the specific hadronic interaction model used. With the distribution of dispersion σ (X max ) the situation is more complicated. The equivalent equation reads σ (X max ) = σ sh + f Eσ lna, (4.) where σsh is the measure of the intrinsic shower to shower fluctuations and σlna is the measure of the variance of lna in the incoming flux of particles interacting in the highest layers of the atmosphere. If the cosmic ray consisted solely of a single type of nucleus, the quantity σ (X max ) would depend only on the mean mass distribution lna and could be used as a good measure of the average composition. If the term σlna is not negligible however, the interpretation of σ (X max ) in terms of chemical composition is not so straightforward. Nevertheless, with this fact in mind while assessing the results, the equations 4.1 and 4. can be inverted to obtain the quantities lna and σlna in terms of X max and σ (X max ). This new set of equations depends on various parameters of the interaction models, which could be fitted doing a large number of MC simulations. The observed distributions of X max and σ (X max ) can then be inserted into the inverted equations to obtain a model-dependent prediction. This provides an useful information about the mass composition and its reliance on a particular model used. The latest published result ([9]) from the PAO collaboration is shown in Fig. 4.5, with the interaction model being EPOS Other models differ significantly on the absolute placement of the data on the y axis, but roughly agree on the shape of the spectrum. The methods used for determining the mass composition by studying the distribution of X max and related quantities rely on the data from the fluorescence detectors and thus suffer from relatively small statistics. A number of approaches however also makes use of the surface detector data and the related larger sample of observed showers. One of them is the study of Muon Production Depths (MPDs). Newly created muons travel approximately at the speed of light and are registered by the surface detectors after a time period proportional to the distance covered from their creation point. By carefully analyzing the recorded detection times it is possible to infer the shape of the profile of muon creation rates in dependence on the air mass covered along the shower axis. Muons are generated by the decay of the π and K mesons and as such carry direct information about the shape of the hadronic part of a shower. The observed profiles can be fitted by a 4-parametric Gaisser-Hillas function, obtaining an important quantity X max, µ which signifies a point along the shower axis where the muon creation was maximal. By comparing the predictions of hadronic interaction models with the measured distribution X max µ and its dispersion, one can in principle 3

37 Figure 4.5: In the left figure is shown the dependence of ln A on energy. Full circles indicate Auger data, grayed band plots systematic uncertainties. The right figure shows the dependence of σlna on energy. An exclusion line is graphed to show the lower limit. EPOS 1.99 was used as an interaction model. Figure taken from [9]. gain insight about the various properties of the hadronic part of the shower, including the mass composition of the incoming cosmic rays. Equivalently, further constraints on the interaction models could be placed using this approach. Latest results from the PAO collaboration ([4]) are shown in Fig The flatness of the observed curve would suggest a change in the mass composition with energy. However, due to the large uncertainties present in the data a constant composition cannot be ruled out. Notable is the fact that the interaction models in this case agree on the rate of change of X µ max with energy (the so-called elongation rate). Showers with an anomalous profile could also prove to be an useful tool in the determination of a possible presence of light nuclei in the cosmic rays. As already alluded to in section.6 (using the simple superposition model) nucleons with mass A act on average as A independent protons, with a single particle carrying on average a E/A fraction of the primary energy. For iron, expected to be the most prevalent heavy nucleus present in CR, this constitutes to 1/56 % of a shower energy, ie. such a particle cannot create a significant sub-shower. Thus an observation of a statistically significant sample of showers with anomalous profiles would provide a model-independent evidence of the presence of light nuclei in a particular energy region of the UHECR. 33

38 Figure 4.6: X max µ as a function of energy. Numbers indicate the size of the chosen data set in each energy bin, gray lines represent the systematic uncertainty. Predictions of two hadronic interaction models for two particle types are shown. Figure is taken from [4]. 34

39 4.5 Shoot-the-Shower Type Experiments The immediate state of the atmosphere in the vicinity of an observed shower has a direct impact on the amount of light the fluorescence detectors are able to measure. Considering the fact that the majority of detectors operate on high zenith angles, the light signal has to traverse a relatively large portion of the atmosphere before being detected. To control for this atmospheric influence, the Pierre Auger Observatory employs several atmospheric-monitoring measures, such as cloud cameras 1, lasers, APF 3, back-scattering lasers (LIDARs) and others. The data resulting from these programs is used for the calibration of the observed shower profiles during analysis. Given the fact that only several data points at static geographic locations are available during one given night and that the atmospheric conditions can change dramatically in time and the area covered by the PAO is vast, to study the atmospheric influence on a particular shower, more directly focused methods are needed. For this purpose, the PAO introduced a rapid monitoring program which uses LIDARs and the FRAM (F/Photometric Robotic Atmospheric Monitor) telescope to make immediate direct scans in the direction of an observed shower - hence the program s name Shoot-the-Shower (StS). There are several general types of showers considered interesting to trigger the StS observation - either (very rare) showers with a very high energy, showers that may constitute a candidate for an ultra-high energy photon as a primary particle and showers that exhibit an anomalous longitudinal profile during the preliminary data analysis done immediately after the shower observations. The last type constitutes the bulk of measurements done by the StS experiments. 4.6 The FRAM telescope The basic functionality of the FRAM telescope (Photograph 4.7), when being used as a StS instrument, consists of waiting for the central campus computer to perform a fast preliminary reconstruction of a shower, then, if the shower parameters pass a set of cuts, shooting the night sky in the direction of the axis of the shower. Then an offline analysis can be performed on the acquired data set, comparing visible stars to their cataloged equivalents and determining the integral atmospheric extinction in a given direction. This procedure allows the software to asses whether an absorbing layer (clouds or aerosols) was present. The advantage of this approach is that such a detection technique is completely non-invasive, in contrast to the measurements of the back-scattering lasers, which could potentially be visible in the FD telescopes. The disadvantage is that the measured extinction coefficient is an integral value, covering the whole air mass between the telescope and the edge of the atmosphere. As such it cannot be used on its own to determine whether an observed absorbing layer was located in front 1 The detection of infrared radiation originating from clouds, contrasted to radiation from (dark) space. A controlled strong signal is being sent at an specific angle, observed by the fluorescence detectors and then used as a reference for calibration. 3 Aerosol Phase Function - the detection of scattered light on a aerosol layers originating from a xenon flash lamp source. 35

40 Figure 4.7: A photograph of the FRAM telescope taken during a maintenance. The instrument is enclosed by a cover with a movable roof. (from the point of view of the telescope) of the shower with an anomalous profile or behind. It is, however, able to positively determine anomalous showers that happened on a clear sky background. The following text will go into more detail describing the functionality of FRAM. The FRAM telescope is located at the Los Leones FD site and is thus only able to see one fourth of the events registered by the PAO fluorescence detectors. After a shower is observed, the controlling software at the main campus site waits for the signal from the surface detectors to be processed and then performs a preliminary hybrid reconstruction on an yet-not calibrated data set, greatly enhancing the accuracy over a reconstruction from a fluorescence signal alone. This process can take up to 1 minutes. A signal with the reconstructed shower s parameters is then send to the PC controlling the StS program, which decides whether a shower is worth shooting based on several sets of cuts corresponding to the cases of interest discussed earlier. The basic requirement, besides several ordinary quality cuts, for a shower to be considered anomalous is to have its reconstructed longitudinal profile be better fitted by a 8-parametric Gaisser-Hillas function (eq. 3.1) than by a 4-parametric G.-H. function (eq..13) by a certain margin dχ improv., computed as a difference of their respective χ functions. The value of this parameter has changed during the time FRAM was operational and will probably change further in the future based on some results of this work, to help better discriminate the most promising showers. When a shower passes the trigger cuts, FRAM stops the activity it is currently performing and moves to shoot the new shower. This behavior is one of the 36

41 contributing reasons that roughly 3% of shot showers have to be discarded during the analysis due to incomplete profiles. This is a relict of implementation the shooting of ToO (Target of Opportunity) events was programmed in the framework of the RTS (Remote Telescope System, nd version) software, which is used mainly for observing optically transient Gamma-Ray Bursts. In this field a later signal from a controlling computer typically signifies a more precise measurement of the position of the source, making an interruption of the current activity advantageous. This is not the case when recording the atmospheric data around a freshly developed air shower however, so this behavior will be changed in the future. A wide-field (WF) camera with a field of view of approx. 7 7 is used to record images, each with a 3 seconds exposure. A whole recorded trajectory of the shower is covered and the area of sky in close proximity the observed profile boundaries is also recorded. This allows to check whether an absence of light signal from that direction may be due to an absorbing layer. Lastly, an image of the reconstructed arrival direction of the primary particle is taken. When this procedure is done, FRAM resumes its previous activity. The acquired data set is stored locally and analysed at a later date. The process of data analysis itself consists of comparing measured brightness of identified stars with their values from the reference catalog Tycho [38]. The process is not straightforward however and a correction for several complicating effects is needed. In the present state of analysis, the extinction coefficient is fitted as a function of the air mass. It is then reparametrized as a function of altitude and compared to data set. If the two values differ by a certain cut value, the bin is tagged as cloudy. Looking over the whole acquired profile and using a quantitative analysis with reasonably set cuts, it is possible to identify events developed in a clear atmospheric background, ie. clear sky. A sample randomly chosen output is shown in the Figure 4.8. This work has been recently advanced by several members participating in the FRAM data analysis working at the Astroparticle Physics Department of the Institute of Physics ASCR and the preliminary results have been made available internally for the PAO collaboration ([4], [41]). Figure 4.9 shows a shower with an identified anomalous profile which was caused by a clouded sky. Figure 4.1 shows a more likely candidate for an anomalous shower. 37

42 Figure 4.8: An example of a single FRAM output, showing a thinly clouded night. Each data point represents one successfully identified star and the value on the y axis is taken as the difference between a star brightness in magnitudes (corrected for color index) taken from a catalog and the apparent brightness as observed by FRAM. The overall normalization of the y axis is arbitrary. The axis x represents the height above horizon in degrees. The solid red line plots the overall extinction model fitted to the data. The large filled circles represent the averages of the respective bins of altitude, their coloring scheme is given by their distance from the extinction model, where blue shows a good agreement, while yellow and green refer to a larger distance and may point to cloudy sectors of the recorded sky. The horizontal green line shows a region with a completed astrometry, the green triangles indicate the range of the individual shots taken by FRAM. Data points plotted in red represent (more than 3σ) outliers and were removed before re-running the analysis. This particular example points to a thin cloud layer between 3 and 35 degrees in elevation. 38

43 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure 4.9: An example of a shower that gets incorrectly identified as anomalous. The upper figure presents a FD profile that shows a better fit with a double G.-H. function (solid blue line) compared to a standard 4-param. G.-H. function (red line fit done by the Offline software). The dotted blue lines represent fitted sub-showers. The lower figure shows the corresponding data obtained by FRAM, where absorbing atmospheric layers are clearly visible. The blue horizontal lines indicate regions of the sky where camera shots were taken, but no astrometry could be done, possibly due to the presence of clouds. 39

44 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure 4.1: An example of a shower that can be considered a candidate for an event (obsid 84799, listed in 4.1) with a clearly identifiable anomalous profile. Upper figure shows an observed FD profile and the lower figure the corresponding FRAM data with no absorbing layers visible above 5. More careful analysis of these types of showers is still needed. 4

45 4.6.1 Analysis of the Results The data set was collected during two phases which differed in the FRAM functionality - during the first phase, consisting of the years 11, 1 and up to August 13, many showers were shot with a wrong pointing, missing the actual trajectory of the shower. During this period the data was collected, but a serious analysis was done only during the year 13, when the geometry problems were discovered. In some cases though the pointing was still largely correct and showers with clear skies can be still identified after a careful assessment. Due to a longer data acquisition period the collected data sample is comparable to the output of the second phase, dating from September 13 onward, where the pointing problems were finally reliably fixed and the data form a much more consistent set. During the first phase, 143 showers have been recorded by FRAM. Of those, only 46 events had correct astrometry and geometry. Further, 119 of those had not successfully shot the whole observed trajectory of the shower, leaving 17 events for analysis. 18 of them were identified as cloudy or partly cloudy, leaving 19 showers with clear atmosphere. During the second phase, showers were recorded altogether. 164 of those had correct astrometry and geometry, a large improvement over the first phase (it is also important to stress that the cuts defining the StS algorithm changed between the two phases). Full data on the whole shower trajectory was acquired in 114 events. Of these, 91 events were identified as cloudy or partly cloudy and 3 as cloudless. An analysis similar to the method described in 3.5 was then performed on the showers with identified clear sky. The output of the PAO analysis software doesn t use the energy-scaling convention for the χ distribution calculation shown in but rather the standard form χ DGH = n (N i (X i ) N DGH (X i )). (4.3) σn DGH (X i ) i= And similarly for the single G.-H. function. This form was also used in the analysis of the FRAM results presented here. While it is true it would be beneficial to use the rescaled form shown in eq. 3.4 in the preliminary reconstruction of the FD signal to have a single cut value covering the whole energy range, it is not really of much practical use since the observed statistics of the ultra-high energy events is very low. Currently, the cut value dχ improv. is set so that it works relatively well for discriminating anomalous showers with energies around 1 18 ev. On higher energies, the fitted profiles and their respective χ functions grow more sensitive to variations from an universal profile, assuming the related dispersions follow a Poissonian distribution. Showers with anomalous profiles aren t then always discriminated properly, since the trigger cut value stays the same and more false positive events could be potentially recorded by FRAM. However, due to their number being very small, they do not present a significant burden and they are later discarded during individual analysis of the showers. A 8-parametric double Gaisser-Hillas fit was performed on the selected showers, dχ improv. was obtained from the results, computed over a domain selected as the conjunction of the domains of the three respective G.-H. functions (two coming from the fitted double G.-H. profile). This value was then rescaled in 41

46 a standard way as dχ improv. = dχ improv. n def, (4.4) where n def the number of bins where all three functions are defined. This rescaling enables a direct comparison between showers with varying length of a profile recorded and makes the use of a single cut value for all profile sizes possible. This was not the case at all times however, since the set of reconstruction parameters sent to the StS instruments contains a χ value computed as in eq. 4.3 and the dχ improv. selection cut was applied to this value. This was obviously inefficient (interesting profiles with a relatively smaller number of degrees of freedom could have been discarded) and it is presently being corrected as a direct result of the work done on analysis of the FRAM data in this thesis. The table 4.1 sums up the results of the first phase of FRAM s operational period. The first column denotes the unique FRAM observational identification number. In the second column the shower energy obtained from the FD reconstruction by the OFFLINE software is shown. δx max represents the difference between the fitted X max values of the two respective sub-showers, E s1 and E s represent their respective energies obtained by a numerical integral over the fitted sub-shower profiles. Their sum doesn t have to add up to the energy listed in the second column, since the final double Gaisser-Hillas function obviously differs from the 4-parametric G.-H. function fitted by OFFLINE. The double maxima function also always represents a better fit for the data. A set of cuts was applied to the fit results. The secondary shower energy (or, equivalently, size, since the number of charged particles is proportional to the deposited energy) had to be at least 15% the value of the primary particle s energy. The δx max was required to be greater than 15 g/cm and the value of dχ improv. had to be greater than.. These cuts are consistent with the range of parameters used in the section 3.5 during the analysis of the MC generated showers. The final column of Table 4.1 attempts to ascertain a qualitative subjective statement about the possibility of the shower being a candidate for an actual clearly anomalous event. The most common status is inconclusive, which means that the obtained fit doesn t represent a significant enough improvement over a single G.-H. fit, and sec. shower energy too small, which means that the secondary sub-shower is difficult to be separated from random profile fluctuations. Incidentally, secondary sub-showers with a small energy portion (the cut was set to 15%, in order to be consistent with methods applied in chapter 3.5) compared to the primary shower would not point to a presence of light nuclei in the cosmic ray mass spectrum, since the creation of such events from an iron primary particle becomes statistically possible. Oftentimes, a shower didn t pass several of the cuts. Only one reason is still listed though for the sake of clarity. To the 18 events with confirmed clear sky, one interesting event was added (obsid Fig. A.11 in the Appendix) where the sky area recorded by FRAM also shows no clouds, but the pointing geometry was not precisely correct. The shower profile however exhibits a remarkably good fit with the double G.-H. function and so the event possibly warrants further study. Two showers, with obsid and 85541, passed the three required cuts. The shower marked as is shown in Fig. 4.1 together with its extinction 4

47 obsid E [EeV] δx max [g/cm ] E s1 [EeV] E s [EeV] dχ improv. Status small sec. shower energy inconclusive inconclusive inconclusive ok inconclusive small sec. shower energy inconclusive small sec. shower energy ok small δx max small sec. shower energy small δx max small δx max inconclusive / ok inconclusive inconclusive inconclusive / ok small δx max Table 4.1: Table of FRAM results from phase 1. The corresponding longitudinal profiles (A.1 A.19) and an extended version of the table (A.1) are included in the Appendix. profile. The shower marked as is shown in Fig.A.1 in the Appendix. A further detailed analysis on these events must be performed to be able to indeed identify them as anomalous. Foremostly, the data from other various atmospheric monitoring instruments installed at the PAO need to be cross-checked to make sure they are consistent with the extinction profile observed by FRAM. Two other showers, with obsids 14 and (Figures A.15 and A.18), were identified as interesting and could pass the selection if the cut on dχ improv. was lowered to.14. The shower listed as 5168 (Fig. A.19) is interesting in the sense that it would represent a (very rare) anomalous event with the energy of approx ev. The quality of the fit is roughly at the cut value, but it doesn t pass the other two requirements. The same analysis was also done for the second phase of the FRAM measurements, the cut values were kept the same. Table 4. lists the results. Two showers, with obsid 737 (Fig. A.1) and 113 (Fig. A.37), passed all three cut requirements. One more, with the obsid 966 (Fig. A.35) passed two and is close to the cut value for the energy portion of the secondary shower. 43

48 obsid E [EeV] δx max [g/cm ] E s1 [EeV] E s [EeV] dχ improv. Status inconclusive ok small sec. shower energy inconclusive inconclusive inconclusive inconclusive inconclusive inconclusive inconclusive small sec. shower energy inconclusive small sec. shower energy inconclusive inconclusive small sec. shower energy / ok inconclusive ok inconclusive inconclusive small sec. shower energy inconclusive inconclusive Table 4.: Table of FRAM results from phase. The corresponding longitudinal profiles (A. A.4) and an extended version of the table (A.) are included in the Appendix. 44

49 Conclusion The principal aim of this work was to study the properties of anomalous shower profiles on a large sample statistic acquired from time-efficient Monte-Carlo simulations and then attempt to apply similar analysis methods to actual experimentally observed data. In the second chapter of this work, a cursory introduction about various simple models describing the properties of extensive air showers was given. A special emphasis was put on predictions about the longitudinal shower profiles and their characteristics X max and N max. The third chapter describes the collection and analysis of a large sample of shower profiles with protons as a primary particles with energies in the range of ev. EPOS LHC was used as the high energy hadronic interaction model. Three different methods, each with a varying cut parameter, were then applied to identify the showers with anomalous profiles. The results (figures 3., 3.3, 3.5 and 3.6) proved to be approximately compatible with each other. The predictions on the rate of occurrence of anomalous showers are of the order 1 3 and decrease with energy. However, a significant rise in the two highest energy bins was observed and the explanation of this phenomenon is not clear. A sample statistic consisting of iron nuclei as the primary particles was generated to illustrate the usefulness of anomalous profiles in determining the mass spectrum of cosmic rays. All three identification methods were applied to this data sample and the resulting portion (Fig. 3.7) of anom. profiles was significantly lower than in the case of a primary proton (two of the methods found no matches using the same cuts as in the proton case). The fourth chapter gives a very brief overview of the Pierre Auger Observatory, describing its main scientific goals and the unique hybrid detection method used. A few interesting results related to the question about cosmic ray mass spectrum are presented. Next a motivation behind installing and operating various Shootthe-Shower type experiments is given, in particular the functionality of the FRAM telescope is explained in detail. A recently upgraded code used for discriminating showers on a cloudless background identified 19 such showers during a first phase of FRAM operation and 3 showers during the second phase. These shower profiles were then fitted with a (8 parametric) double Gaisser-Hillas function and a selection was made based primarily on the quality of the fit, but also on several other related criteria (see tables 4.1 and 4. for the results). Two showers from each phase were chosen as promising candidates for an observed anomalous profile, while several others were identified as interesting cases that warrant further inspection. To actually identify these events as anomalous further detailed analysis must be performed however. To summarize the author s own contribution: A set of predictions was made on the expected ratio of anomalous events assuming a proton as a primary particle and using a particular interaction model (EPOS LHC). The predicted ratios depended on various cut parameters. Similar analysis was then carried on showers observed by the PAO and already identified as cloudless by the FRAM analysis methods. Several promising candidates were chosen based on a set of cuts and an input was provided about a possible improvement of the selection criteria being used by FRAM to decide whether to shoot the shower. 45

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53 List of Tables 4.1 Table of FRAM results from phase Table of FRAM results from phase A.1 An extended table of FRAM results from phase A. An extended table of FRAM results from phase

54 Appendix 5

55 obsid run event E [EeV] δxmax [g/cm ] Es1 [EeV] Es [EeV] dχ improv. (Offline) dχ improv. dχ improv. Status small sec. shower energy inconclusive inconclusive inconclusive ok E inconclusive small sec. shower energy E inconclusive E small sec. shower energy E ok small δxmax small sec. shower energy small δxmax small δxmax E inconclusive / ok E inconclusive inconclusive N/A inconclusive / ok E small δxmax Table A.1: An extended table of FRAM results from phase 1. In addition to quantities already explained in section 4.6, several more columns are added: Event and Run identify the shower in the PAO data files. dχ improv. (Offline) is the value (previously) used for selecting showers for observation with FRAM. It is calculated by the Offline software, firstly using the equation 4.3 to compute the fit quality both for a single G.-H. fit and a double G.-H. fit and then subtracting the two values. In several cases the fitting procedure did not converge. dχ improv. is calculated in the same way using double G.-H. fits created during the course of this work. These two values are not directly comparable, since they were not necessarily computed over the same domain (ie. with the same number of degrees of freedom). dχ improv. is calculated from the latter value and is used as a basis for selection cuts. The corresponding longitudinal profiles are included further in the Appendix. 51

56 obsid run event E [EeV] δxmax [g/cm ] Es1 [EeV] Es [EeV] dχ improv. (Offline) dχ improv. dχ improv. Status inconclusive E ok small sec. shower energy E inconclusive inconclusive inconclusive inconclusive inconclusive inconclusive inconclusive small sec. shower energy inconclusive small sec. shower energy inconclusive inconclusive E small sec. shower energy / ok inconclusive ok inconclusive inconclusive small sec. shower energy E inconclusive inconclusive Table A.: An extended table of FRAM results from phase. Explanation of the listed values is given in section 4.6 and in the caption of Table A.1. The corresponding longitudinal profiles are included further in the Appendix. 5

57 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.1: A shower with the obsid 684. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

58 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

59 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.3: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

60 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.4: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

61 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.5: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

62 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.6: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

63 FD profile de/dx [PeV/(g/cm )] X [g/cm ] Figure A.7: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

64 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.8: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

65 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.9: Obsid

66 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.1: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

67 FD profile de/dx [PeV/(g/cm )] X [g/cm ] Figure A.11: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

68 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.1: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

69 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.13: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

70 FD profile de/dx [PeV/(g/cm )] X [g/cm ] Figure A.14: A shower with the obsid 1. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

71 FD profile de/dx [PeV/(g/cm )] X [g/cm ] Figure A.15: A shower with the obsid 14. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

72 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.16: A shower with the obsid 178. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

73 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.17: A shower with the obsid 134. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

74 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.18: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

75 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.19: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.1. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

76 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.: A shower with the obsid 737. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

77 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.1: A shower with the obsid 737. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

78 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

79 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.3: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

80 FD profile de/dx [PeV/(g/cm )] X [g/cm ] Figure A.4: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

81 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.5: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

82 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.6: A shower with the obsid 757. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

83 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.7: A shower with the obsid 757. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

84 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.8: A shower with the obsid 759. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

85 FD profile de/dx [PeV/(g/cm )] X [g/cm ] Figure A.9: A shower with the obsid 771. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

86 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.3: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

87 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.31: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

88 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.3: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

89 )] de/dx [PeV/(g/cm FD profile X [g/cm ] Figure A.33: A shower with the obsid 878. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

90 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.34: A shower with the obsid 964. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

91 FD profile de/dx [PeV/(g/cm )] X [g/cm ] Figure A.35: A shower with the obsid 966. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

92 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.36: A shower with the obsid 113. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

93 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.37: A shower with the obsid 113. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

94 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.38: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

95 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.39: A shower with the obsid 737. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

96 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.4: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

97 FD profile de/dx [PeV/(g/cm )] X [g/cm ] Figure A.41: A shower with the obsid 116. Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig

98 FD profile )] de/dx [PeV/(g/cm X [g/cm ] Figure A.4: A shower with the obsid Upper figure shows a fluorescence profile recorded by the Los Leones FD site. The red line represents a 4-parametric Gaisser-Hillas fit done by the Offline reconstruction software. The two dotted blue lines show the fitted G.-H. profiles, the solid blue line is their sum. Details on the fit results are available in the Table A.. The lower figure shows the corresponding extinction profile as recorded by FRAM. Some details on the meaning of the various contents of the figure are described in the caption of Fig