Properties of the surface detector data recorded by the Pierre Auger ...
Properties of the surface detector data recorded by the Pierre Auger ...
Properties of the surface detector data recorded by the Pierre Auger ...
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<strong>Properties</strong> <strong>of</strong> <strong>the</strong> <strong>surface</strong><strong>detector</strong> <strong>data</strong> <strong>recorded</strong> <strong>by</strong> <strong>the</strong><strong>Pierre</strong> <strong>Auger</strong> observatoryMASTERARBEITzur Erlangung des akademischen GradesMaster <strong>of</strong> Science(M.Sc.)dem Fachbereich Physik derUniversität Siegenvorgelegt vonStefan GrebeOktober 2008
CONTENTSContents1 Introduction 11.1 Cosmic rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.3 Extensive air showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.4 Detection methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Scope <strong>of</strong> this <strong>the</strong>sis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 <strong>Pierre</strong> <strong>Auger</strong> observatory 72.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Surface <strong>detector</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Surface <strong>detector</strong> stations . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Calibration and monitoring . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.3 AMIGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Fluorescence <strong>detector</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 Radio <strong>detector</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 First results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Event reconstruction using <strong>the</strong> <strong>surface</strong> <strong>detector</strong> <strong>data</strong> 163.1 Trigger chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Tank trigger probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3 Event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.1 CDAS and Offline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.2 Angular reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.3 Energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.4 Fine-tuning <strong>of</strong> <strong>the</strong> LDF . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4.1 Variations on different time-scales . . . . . . . . . . . . . . . . . . . . . 253.4.2 Attributes <strong>of</strong> <strong>the</strong> array . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Stability <strong>of</strong> <strong>the</strong> reconstruction 284.1 Method and <strong>data</strong> set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Reconstruction without individual stations . . . . . . . . . . . . . . . . . . . . . 294.2.1 Stability <strong>of</strong> events with E > 57EeV . . . . . . . . . . . . . . . . . . . . 294.2.2 Stability <strong>of</strong> events with E > 25EeV . . . . . . . . . . . . . . . . . . . . 334.2.3 Test <strong>of</strong> <strong>the</strong> asymmetry correction . . . . . . . . . . . . . . . . . . . . . . 354.2.4 The optimum ground parameter . . . . . . . . . . . . . . . . . . . . . . 36
IVCONTENTS4.3 Reconstruction without sets <strong>of</strong> <strong>detector</strong>s . . . . . . . . . . . . . . . . . . . . . . 404.3.1 Reconstruction with <strong>the</strong> unitary cell only . . . . . . . . . . . . . . . . . 404.3.2 Simulating borders <strong>of</strong> <strong>the</strong> array . . . . . . . . . . . . . . . . . . . . . . . 434.4 Less dense arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Azimuth angle distribution 495.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2 Azimuth angle distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.2.1 Hexagonal structure <strong>of</strong> <strong>the</strong> array . . . . . . . . . . . . . . . . . . . . . . 505.2.2 Direct light in inclined showers . . . . . . . . . . . . . . . . . . . . . . 545.2.3 Determination <strong>of</strong> amplitudes and phases . . . . . . . . . . . . . . . . . . 545.3 Model for <strong>the</strong> hexagonal effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.3.1 Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.3.2 Asymmetry correction . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.3.3 Signal fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.3.5 Limits <strong>of</strong> <strong>the</strong> model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.4 Description <strong>of</strong> <strong>the</strong> asymmetry in 2! . . . . . . . . . . . . . . . . . . . . . . . . 645.4.1 Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.4.2 Rayleigh analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.4.3 Energy and " dependency . . . . . . . . . . . . . . . . . . . . . . . . . 705.4.4 Different areas <strong>of</strong> <strong>the</strong> array . . . . . . . . . . . . . . . . . . . . . . . . . 735.4.5 Time dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.4.6 Events with less strict cuts . . . . . . . . . . . . . . . . . . . . . . . . . 765.4.7 Attributes <strong>of</strong> <strong>the</strong> effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.5 Origin <strong>of</strong> <strong>the</strong> asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.5.1 CDAS reconstruction algorithm . . . . . . . . . . . . . . . . . . . . . . 815.5.2 Border effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.5.3 Tilt <strong>of</strong> <strong>the</strong> array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.5.4 PMT effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.5.5 Terrestrial magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . 855.5.6 Solar panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866 Summary and outlook 88List <strong>of</strong> Figures 95List <strong>of</strong> Tables 97List <strong>of</strong> Acronyms 98Acknowledgment 103
Chapter 1Introduction1.1 Cosmic raysCosmic rays are particles with high energies coming from outer space. These particles are permanentlyhitting and penetrating <strong>the</strong> earth’s atmosphere, <strong>the</strong>re<strong>by</strong> initiating extensive air showers <strong>of</strong>secondary particles.Cosmic rays are mainly positively charged and <strong>the</strong>ir exact composition depends on <strong>the</strong> part <strong>of</strong> <strong>the</strong>energy spectrum, which is observed. In general, about 85% <strong>of</strong> <strong>the</strong> particles arriving at <strong>the</strong> top <strong>of</strong><strong>the</strong> atmosphere are protons, about 12% are helium nuclei, about 2% are electrons and about 1%are nuclei, which are heavier than helium [1]. Cosmic rays cover an energy range <strong>of</strong> 11 orders<strong>of</strong> magnitude from 10 9 eV up to 10 20 eV. For energies below 10 14 eV, <strong>the</strong> best <strong>data</strong> have beenobtained from direct measurements in space experiments; for higher energies, <strong>the</strong> <strong>data</strong> are derivedfrom ground based experiments, which measure <strong>the</strong> secondary particles <strong>of</strong> extensive air showers,or interactions <strong>of</strong> <strong>the</strong> particles with <strong>the</strong> molecules in <strong>the</strong> atmosphere.In this chapter, a short historic introduction about <strong>the</strong> discovery <strong>of</strong> cosmic rays and <strong>the</strong> determination<strong>of</strong> <strong>the</strong>ir properties is given. Then, <strong>the</strong> particles, <strong>the</strong>ir energy spectrum, <strong>the</strong> extensive airshowers produced, and <strong>the</strong> detection techniques used are described. In <strong>the</strong> last part, <strong>the</strong> scope <strong>of</strong>this <strong>the</strong>sis is defined.1.1.1 HistoryIn 1785, H. Coulomb found, that a simple electroscope looses its charge with time though beingwell insulated. After <strong>the</strong> discovery <strong>of</strong> radioactivity <strong>by</strong> H. Becquerel in 1896, it was believed, that<strong>the</strong> electric discharge is due to radioactivity in <strong>the</strong> soil or due to radioactive gases. In a series <strong>of</strong>experiments, <strong>the</strong> phenomenon and its dependence on <strong>the</strong> altitude above ground has been studied.In 1910, T. Wulf compared <strong>the</strong> radiation at <strong>the</strong> bottom and on <strong>the</strong> top <strong>of</strong> <strong>the</strong> Eiffel Tower and founda significant drop <strong>of</strong> <strong>the</strong> ionization rate at <strong>the</strong> top [2].The cosmic radiation has been discovered <strong>by</strong> V. Hess in 1912 [3], as he increased <strong>the</strong> distanceto <strong>the</strong> ground up to 5300 m <strong>by</strong> performing balloon flights. Hess measured <strong>the</strong> discharging effectswith electroscopes. He found a decrease <strong>of</strong> <strong>the</strong> effect up to an altitude <strong>of</strong> 1500 m, <strong>the</strong>n it startedto increase again and became even larger at an altitude <strong>of</strong> 3600 m than on <strong>the</strong> ground. This measurementestablished <strong>the</strong> extraterrestrial origin <strong>of</strong> <strong>the</strong> radiation, which R. Milikan called ”cosmicrays”, after he had discovered in 1925, that <strong>the</strong> radiation interacts with <strong>the</strong> particles in <strong>the</strong> earth’satmosphere [4]. In <strong>the</strong> interactions, new particles are produced, which in turn may interact withatmospheric constituents. All particles produced in interactions in <strong>the</strong> atmosphere are called “sec-
2 Introductionondary particles”, which could for <strong>the</strong> first time be detected <strong>by</strong> cloud chambers and photographicplates.In 1938, P. <strong>Auger</strong> found, that cosmic radiation events were coincident in time, <strong>by</strong> measuring secondaryparticles with spatially separated <strong>detector</strong>s on ground level [5]. He postulated, that <strong>the</strong>ywere associated with a single event, an “extensive air shower”. Today, <strong>the</strong> largest experiment tomeasure extensive air showers is named after <strong>the</strong>ir discoverer, <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory.1.1.2 Energy spectrumCosmic rays arriving at <strong>the</strong> top <strong>of</strong> <strong>the</strong> earth’s atmosphere cover a range <strong>of</strong> about 11 orders <strong>of</strong>magnitude in energy and <strong>of</strong> about 30 orders <strong>of</strong> magnitude in flux. The relation between <strong>the</strong> flux Iand <strong>the</strong> energy E is given <strong>by</strong> a power lawdIdE ∼ E−# , (1.1)where <strong>the</strong> spectral index # depends on <strong>the</strong> energy. For cosmic rays with energies between 10 11 eVand 10 15 eV # equals 2.7. For higher energies # changes to 3.1 and returns to <strong>the</strong> value <strong>of</strong> 2.7 atE ≈ 10 18 eV (see Figure 1.1). The regions, where <strong>the</strong> spectral index changes are referred to as <strong>the</strong>Figure 1.1: Primary cosmic ray spectrum [6].“knee” and <strong>the</strong> “ankle”.For energies beyond 6 · 10 19 eV, Greisen, Zatsepin and Kuzmin predicted a cut-<strong>of</strong>f <strong>of</strong> <strong>the</strong> flux
1.1 Cosmic rays 3[7]. At <strong>the</strong> GZK cut-<strong>of</strong>f, primary cosmic rays are expected to interact with cosmic microwavebackground photons. Up to now, <strong>the</strong> number <strong>of</strong> events with energies above <strong>the</strong> predicted energythreshold, detected with <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory, is compatible with <strong>the</strong> GZK cut-<strong>of</strong>f.1.1.3 Extensive air showersWhen high energy primary cosmic rays enter <strong>the</strong> atmosphere, <strong>the</strong>y collide with nuclei in <strong>the</strong> upperatmosphere and generate less energetic secondary particles. These secondary particles are also interactingwith constituents <strong>of</strong> <strong>the</strong> atmosphere and, thus, initiating cascades <strong>the</strong>mselves. During <strong>the</strong>development <strong>of</strong> an extensive air shower, <strong>the</strong> secondary particles <strong>of</strong> each new generation carry lessenergy per particle than <strong>the</strong> generation before. The number <strong>of</strong> particles increases up to <strong>the</strong> showermaximum X max , where <strong>the</strong> energy <strong>of</strong> <strong>the</strong> particles becomes too small to produce new particles (seeFigure 1.2). Beyond <strong>the</strong> shower maximum, <strong>the</strong> number <strong>of</strong> particles decreases exponentially withFigure 1.2: Schematic drawing <strong>of</strong> <strong>the</strong> longitudinal development <strong>of</strong> an extensive air shower [8].<strong>the</strong> atmospheric depth. The altitude <strong>of</strong> <strong>the</strong> shower maximum depends on <strong>the</strong> energy and <strong>the</strong> type<strong>of</strong> <strong>the</strong> primary particle, as well as on <strong>the</strong> mass densities in <strong>the</strong> atmosphere.The cascade <strong>of</strong> secondary particles comprises <strong>of</strong> three different components: <strong>the</strong> hadronic, <strong>the</strong>muonic, and <strong>the</strong> electromagnetic (see Figure 1.3). The hadronic component in extensive air showersis small (1%), but has a large impact on <strong>the</strong> shower development, as it feeds <strong>the</strong> o<strong>the</strong>r components.In strong interactions, mainly pions are generated and with smaller cross sections alsokaons, protons and neutrons. The charged pions perform most likely fur<strong>the</strong>r hadronic interactions,whereas <strong>the</strong> neutral pions decay with high probability into two photons. Since <strong>the</strong> transversal momenta<strong>of</strong> <strong>the</strong> hadrons are very small, <strong>the</strong>y propagate along <strong>the</strong> line <strong>of</strong> flight <strong>of</strong> <strong>the</strong> primary particleand form, toge<strong>the</strong>r with o<strong>the</strong>r, only slightly deflected particles, <strong>the</strong> shower core.The muonic component rises mainly from weak interactions <strong>of</strong> <strong>the</strong> hadronic component. The crosssection decreases during <strong>the</strong> shower development, as <strong>the</strong> cross sections <strong>of</strong> <strong>the</strong> competing stronginteractions arise with increasing particle densities in lower atmosphere layers. The dominatingmechanisms for <strong>the</strong> production <strong>of</strong> muons are! ± −→ µ ± + $ µ ($ µ ),K ± −→ µ ± + $ µ ($ µ ),K ± −→ ! ± + ! 0 .
1.2 Scope <strong>of</strong> this <strong>the</strong>sis 5pends on <strong>the</strong> distance r to <strong>the</strong> shower axis% e (r)=( )& (4.5 − s)& (s) · & (4.5 − 2s) · N e r s−2 (2!r 2 · 1 + r ) s−4.5, (1.2)r M r Mwhere N e is <strong>the</strong> number <strong>of</strong> electrons at observation level, r M <strong>the</strong> Molière radius and s <strong>the</strong>parametrization <strong>of</strong> <strong>the</strong> shower age. At <strong>the</strong> point <strong>of</strong> <strong>the</strong> first interaction <strong>of</strong> <strong>the</strong> shower with a particle<strong>of</strong> <strong>the</strong> atmosphere, s equals 0. It reaches 1 at <strong>the</strong> shower maximum and s equals 2 at <strong>the</strong> point,where <strong>the</strong> shower dies out.1.1.4 Detection methodsFor <strong>the</strong> detection <strong>of</strong> cosmic rays, its various interactions with matter are used. Depending on <strong>the</strong>energy and <strong>the</strong> particle type, <strong>the</strong> appropriate <strong>detector</strong> is selected. For charged particles, <strong>the</strong> dominatingmechanisms <strong>of</strong> energy loss are bremsstrahlung and ionization. They can be measured withgas <strong>detector</strong>s, scintillators and calorimeters. The emitted Cherenkov radiation can be measuredwith threshold counters or ring imaging Cherenkov counters [10].Cosmic rays can be detected <strong>by</strong> measuring <strong>the</strong> primary particle directly, or <strong>by</strong> measuring <strong>the</strong> secondaryparticles <strong>of</strong> extensive air showers. For energies below 10 14 eV, only small <strong>detector</strong>s arerequired to collect high statistics in a reasonable time, due to <strong>the</strong> high flux <strong>of</strong> particles. In thiscase, <strong>the</strong> cosmic rays can be detected directly <strong>by</strong> particle <strong>detector</strong>s flown aboard satellites or inhigh altitude balloons.For <strong>the</strong> detection <strong>of</strong> cosmic rays with E > 10 14 eV, two different techniques are common: <strong>the</strong>observation <strong>of</strong> longitudinal shower pr<strong>of</strong>iles and <strong>the</strong> observation <strong>of</strong> lateral shower pr<strong>of</strong>iles on <strong>the</strong>ground. The <strong>Pierre</strong> <strong>Auger</strong> observatory comprises both techniques and performs hybrid measurements<strong>of</strong> extensive air showers with fluorescence telescopes and a ground array (see Figure 1.4)The secondary particles <strong>of</strong> extensive air showers excite <strong>the</strong> nitrogen atoms in <strong>the</strong> atmosphere.When <strong>the</strong> atoms fall back into <strong>the</strong>ir ground state, <strong>the</strong>y emit ultraviolet fluorescence light. Theamount <strong>of</strong> emitted light is proportional to <strong>the</strong> number <strong>of</strong> secondary particles and thus, correlateswith <strong>the</strong> energy <strong>of</strong> <strong>the</strong> primary cosmic ray. This light is measured <strong>by</strong> fluorescence telescopes,which observe <strong>the</strong> atmosphere above <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory.The o<strong>the</strong>r technique uses <strong>the</strong> production <strong>of</strong> Cherenkov light in water-filled <strong>surface</strong> <strong>detector</strong> stations.The secondary particles are reaching <strong>the</strong> ground with almost <strong>the</strong> speed <strong>of</strong> light. When <strong>the</strong>ycross <strong>the</strong> water, <strong>the</strong>ir speed is greater than <strong>the</strong> speed <strong>of</strong> light in that medium and this results in <strong>the</strong>emission <strong>of</strong> Cherenkov light, which is measured with photomultipliers. Arrays <strong>of</strong> <strong>surface</strong> <strong>detector</strong>stations measure <strong>the</strong> lateral distribution <strong>of</strong> <strong>the</strong> particles at <strong>the</strong> ground.1.2 Scope <strong>of</strong> this <strong>the</strong>sisThe work on hand constitutes an effort to achieve a better understanding <strong>of</strong> <strong>the</strong> properties <strong>of</strong> <strong>the</strong><strong>surface</strong> <strong>detector</strong> <strong>data</strong> <strong>recorded</strong> <strong>by</strong> <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory. Since <strong>the</strong> construction phase <strong>of</strong><strong>the</strong> regular <strong>surface</strong> <strong>detector</strong> array has been finished in <strong>the</strong> middle <strong>of</strong> 2008, more than 4500 eventsare <strong>recorded</strong> every day, in an energy range from 0.1 EeV to 100 EeV. The events are reconstructedwith two independent reconstruction algorithms, online (CDAS, central <strong>data</strong> acquisition system)and Offline, and analyzed <strong>by</strong> <strong>the</strong> members <strong>of</strong> <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> collaboration. The aim is, to solvefundamental questions about <strong>the</strong> highest energetic cosmic rays with this <strong>data</strong>. Before <strong>the</strong>se resultscome into reach, a detailed knowledge <strong>of</strong> <strong>the</strong> <strong>detector</strong> and its features is essential.Two main aspects have to be considered, <strong>the</strong> accuracy <strong>of</strong> <strong>the</strong> reconstruction for <strong>the</strong> individual
6 IntroductionFigure 1.4: Schematic view <strong>of</strong> <strong>the</strong> measurement <strong>of</strong> an extensive air shower <strong>by</strong> a fluorescence telescopeand <strong>surface</strong> <strong>detector</strong> stations [12].events, which fulfill <strong>the</strong> trigger conditions and <strong>the</strong> dependence <strong>of</strong> <strong>the</strong> trigger rate on <strong>the</strong> energy,<strong>the</strong> zenith angle, <strong>the</strong> azimuth angle or <strong>the</strong> core position in <strong>the</strong> array.In <strong>the</strong> following Chapter 2, <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory and its <strong>detector</strong> techniques are described.The focus is on <strong>the</strong> <strong>surface</strong> <strong>detector</strong>, its stations and its calibration. Chapter 3 contains a description<strong>of</strong> <strong>the</strong> trigger chain and <strong>the</strong> reconstruction method for <strong>surface</strong> <strong>detector</strong> events. At <strong>the</strong> end <strong>of</strong> <strong>the</strong>chapter, several known properties <strong>of</strong> <strong>the</strong> <strong>data</strong> are presented.In Chapter 4, <strong>the</strong> stability <strong>of</strong> <strong>the</strong> CDAS reconstruction algorithm is checked for events with E >25EeV. The energies and arrival directions <strong>of</strong> highest-energy <strong>Auger</strong> <strong>surface</strong> <strong>detector</strong> events arecompared to <strong>the</strong> values, obtained with modified sets <strong>of</strong> <strong>detector</strong>s, used in <strong>the</strong> reconstruction.In Chapter 5, <strong>the</strong> azimuth angle distribution is analyzed in detail. In addition to <strong>the</strong> variations in<strong>the</strong> number <strong>of</strong> events due to <strong>the</strong> hexagonal structure <strong>of</strong> <strong>the</strong> array, an asymmetry in <strong>the</strong> number <strong>of</strong>events with a period <strong>of</strong> 2!, is observed and investigated in more detail.Finally, Chapter 6 summarizes <strong>the</strong> contents <strong>of</strong> this <strong>the</strong>sis, including a brief outlook on possiblefur<strong>the</strong>r studies.
Chapter 2<strong>Pierre</strong> <strong>Auger</strong> observatoryThe <strong>Pierre</strong> <strong>Auger</strong> observatory has been designed in order to answer fundamental questions abouthighest-energy cosmic rays. Nowadays, 100 years after <strong>the</strong>ir discovery <strong>by</strong> V. Hess [3], <strong>the</strong>irsources are still not identified and <strong>the</strong> acceleration mechanisms are not yet understood.2.1 OverviewThe observatory is named after <strong>Pierre</strong> <strong>Auger</strong>, who discovered extensive air showers in 1938 [13]with spatially separated <strong>detector</strong>s. These days, more than 300 physicists from universities andresearch institutes <strong>of</strong> 18 countries work with <strong>the</strong> observatory.The <strong>Pierre</strong> <strong>Auger</strong> observatory will have two sites, one in each hemisphere to be able to observeultra-high energy cosmic rays (UHECRs) over <strong>the</strong> entire sky. The nor<strong>the</strong>rn site (<strong>Auger</strong> North) isplanned for sou<strong>the</strong>ast Colorado, USA, near <strong>the</strong> city <strong>of</strong> Lamar. It will be a hybrid <strong>detector</strong> consisting<strong>of</strong> water Cherenkov <strong>detector</strong>s and fluorescence telescopes. Studies for <strong>the</strong> design <strong>of</strong> <strong>the</strong>telescopes, <strong>the</strong> <strong>surface</strong> stations and <strong>the</strong>ir spacing are under way. In this <strong>the</strong>sis, <strong>the</strong> focus is on<strong>Auger</strong>-South and its <strong>data</strong>. In all fur<strong>the</strong>r chapters <strong>the</strong> word observatory is used instead <strong>of</strong> sou<strong>the</strong>rnsite <strong>of</strong> <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory.The observatory is located in <strong>the</strong> Pampa Amarilla near <strong>the</strong> town <strong>of</strong> Malargüe in <strong>the</strong> province <strong>of</strong>Mendoza, Argentina. The assembling is almost finished and <strong>data</strong> taking started at <strong>the</strong> beginning<strong>of</strong> 2004. The observatory has a size <strong>of</strong> 3000km 2 and allows <strong>the</strong> detection <strong>of</strong> primary particles inan energy range from 10 17 eV to 10 21 eV.With its clear nights and minimal light pollution, <strong>the</strong> site in <strong>the</strong> Pampa Amarilla provides uniqueconditions for <strong>the</strong> detection <strong>of</strong> cosmic rays. The observatory is located at a plain plateau at an altitude<strong>of</strong> 1420 m above sea-level, which reduces <strong>the</strong> distance to <strong>the</strong> shower maximum (see Chapter1.1.3), which is typically situated a few kilometers higher in <strong>the</strong> atmosphere. The <strong>surface</strong> <strong>detector</strong>array consists <strong>of</strong> 1600 water Cherenkov tanks, located at altitudes between 1340 m and 1610 m,and is surrounded <strong>by</strong> four fluorescence <strong>detector</strong> buildings. Each building, called eye, is equippedwith 6 telescopes, which survey <strong>the</strong> sky above <strong>the</strong> ground array in moonless and cloudless nights(see Figure 2.1) [15].The observatory combines two complementary observation techniques: <strong>the</strong> detection <strong>of</strong> <strong>the</strong> secondaryparticles at ground level and <strong>the</strong> observation <strong>of</strong> fluorescence light, produced <strong>by</strong> <strong>the</strong> airshower in <strong>the</strong> atmosphere. The detection <strong>of</strong> showers, using both techniques, allows to crosscalibrate<strong>the</strong> individual <strong>detector</strong>s. Events detected simultaneously with <strong>the</strong> <strong>surface</strong> <strong>detector</strong> and<strong>the</strong> fluorescence <strong>detector</strong> are called hybrid events.
8 <strong>Pierre</strong> <strong>Auger</strong> observatoryFigure 2.1: The <strong>Pierre</strong> <strong>Auger</strong> observatory near <strong>the</strong> city <strong>of</strong> Malargüe. The circles illustrate <strong>the</strong> positions<strong>of</strong> <strong>the</strong> 1600 water Cherenkov <strong>detector</strong>s forming <strong>the</strong> <strong>surface</strong> <strong>detector</strong> array. The array is overlooked<strong>by</strong> 24 fluorescence telescopes, situated in 4 buildings. The fields <strong>of</strong> view <strong>of</strong> <strong>the</strong> individualtelescopes are indicated <strong>by</strong> lines [14].After <strong>the</strong> first detection <strong>of</strong> a particle at an energy <strong>of</strong> about 10 20 eV reported <strong>by</strong> Linsley in 1963[16], many questions about <strong>the</strong>se rare particles are still not answered. Due to <strong>the</strong> low flux <strong>of</strong> particlesin this energy range (one particle per century and km 2 for E ≈ 10 19 eV), a huge <strong>detector</strong>is required to be able to collect a large amount <strong>of</strong> statistics, for an analysis in a reasonable time.After <strong>the</strong> completion <strong>of</strong> <strong>the</strong> two sites in <strong>the</strong> south and in <strong>the</strong> north, <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatorywill measure <strong>the</strong> cosmic ray flux with more statistics, within 50 days <strong>of</strong> operation, than all <strong>data</strong>combined <strong>of</strong> all <strong>the</strong> o<strong>the</strong>r experiments in <strong>the</strong> last 30 years.2.2 Surface <strong>detector</strong>The <strong>surface</strong> <strong>detector</strong> (SD) array <strong>of</strong> <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory (PAO) consists <strong>of</strong> 1600 waterCherenkov <strong>detector</strong>s, covering 3000km 2 with a spacing <strong>of</strong> 1500 m on a triangular grid. The distancebetween <strong>the</strong> stations is a compromise between cost considerations and <strong>the</strong> energy thresholdfor <strong>the</strong> detection <strong>of</strong> cosmic rays.In addition, 15 pair tanks and 7 triplets have been installed to study signal fluctuations. For pairtanks, a second <strong>detector</strong> is installed at a distance <strong>of</strong> 11 m next to ano<strong>the</strong>r <strong>surface</strong> station. Tripletsare arranged in an equilateral triangle with a spacing <strong>of</strong> 11 m as well. In <strong>the</strong> reconstruction algorithm,only <strong>the</strong> signals <strong>of</strong> stations belonging to <strong>the</strong> regular grid are used.2.2.1 Surface <strong>detector</strong> stationsA schematic view <strong>of</strong> a <strong>surface</strong> <strong>detector</strong> station is shown in Figure 2.2. The main component <strong>of</strong>
2.2 Surface <strong>detector</strong> 9Figure 2.2: Schematic view <strong>of</strong> a <strong>surface</strong> <strong>detector</strong> station [17].each station is a cylindrical plastic water tank <strong>of</strong> 3.6 m in diameter. It is filled with 12 t <strong>of</strong> ultrapure water, which is required to achieve <strong>the</strong> lowest possible attenuation <strong>of</strong> <strong>the</strong> UV Cherenkov lightand to guarantee a stable operation over <strong>the</strong> running period <strong>of</strong> 20 years. The water is enclosed <strong>by</strong>a sealed liner with a diffusively reflecting inner <strong>surface</strong>.Three photomultipliers (PMTs), each nine inch in diameter, symmetrically mounted in a regularmanner at <strong>the</strong> upper side <strong>of</strong> <strong>the</strong> tank (1.2 m from <strong>the</strong> center), are looking down to <strong>the</strong> water and arecollecting <strong>the</strong> produced Cherenkov light. The height <strong>of</strong> a tank is 1.55 m and it is filled with waterup to a level <strong>of</strong> 1.2 m. The water absorbs on average 85% <strong>of</strong> <strong>the</strong> energy <strong>of</strong> <strong>the</strong> secondary particleshitting <strong>the</strong> station, if it has a distance <strong>of</strong> more <strong>the</strong>n 100 m to <strong>the</strong> shower core.Two solar panels on top <strong>of</strong> <strong>the</strong> tank provide <strong>the</strong> power for <strong>the</strong> electronics. The energy is accumulatedin two batteries, hosted in a battery box in <strong>the</strong> south <strong>of</strong> <strong>the</strong> station, to protect <strong>the</strong>m fromdirect sunlight. Each station has an antenna and communicates via a wireless system with <strong>the</strong>central <strong>data</strong> acquisition system (CDAS) in Malargüe. The location <strong>of</strong> each station is known withan accuracy <strong>of</strong> less than 1 m as measured <strong>by</strong> a differential GPS system.Each <strong>of</strong> <strong>the</strong> three PMTs in a station has two outputs: <strong>the</strong> signals <strong>of</strong> <strong>the</strong> anode and <strong>the</strong> last dynode,<strong>the</strong> latter amplified <strong>by</strong> a factor <strong>of</strong> 32. The two signals are filtered and digitized using 10 bit flashanalog-digital converters (FADC) in 1024 bins, each representing a time interval <strong>of</strong> 25 ns. Ringbuffer memories save <strong>the</strong> digitized <strong>data</strong> and allow first and second level triggers to be processed.The whole electronics, except for <strong>the</strong> front-end board, are implemented in a unified board (UB)[18].2.2.2 Calibration and monitoringThe time resolution <strong>of</strong> <strong>the</strong> <strong>surface</strong> <strong>detector</strong> is affected <strong>by</strong> two factors: <strong>the</strong> uncertainty <strong>of</strong> <strong>the</strong> synchronizationbetween <strong>the</strong> stations (8 ns, achieved with <strong>the</strong> differential GPS system) and <strong>the</strong> uncer-
10 <strong>Pierre</strong> <strong>Auger</strong> observatorytainty <strong>of</strong> <strong>the</strong> starting points <strong>of</strong> <strong>the</strong> FADC traces (7 ns). Therefore, <strong>the</strong> total time resolution <strong>of</strong> <strong>the</strong><strong>surface</strong> <strong>detector</strong> adds up to 10 ns [15].The measured signals <strong>of</strong> <strong>the</strong> FADCs have to be converted into physical units. The signal <strong>of</strong> aPMT depends on several parameters like <strong>the</strong> water quality, <strong>the</strong> liner reflectivity, <strong>the</strong> coupling <strong>of</strong><strong>the</strong> PMT to <strong>the</strong> water, <strong>the</strong> gains <strong>of</strong> <strong>the</strong> PMT and <strong>the</strong> amplification factor. Each <strong>surface</strong> station iscalibrated individually and continuously <strong>by</strong> measuring <strong>the</strong> charge deposit <strong>of</strong> atmospheric muons.The signals caused <strong>by</strong> <strong>the</strong> muons are proportional to <strong>the</strong> track lengths in <strong>the</strong> water, as <strong>the</strong>y arenot absorbed in <strong>the</strong> <strong>detector</strong> station. The energy deposited <strong>by</strong> a single vertically and centrallythrough-going muon is used as a reference and defined as 1 VEM (vertical equivalent muon). As<strong>the</strong> atmospheric muons arrive isotropically from all directions, <strong>the</strong>y have different trace lengths in<strong>the</strong> water. The charge distribution has a peak at (1.09 ± 0.02)VEM for <strong>the</strong> sum <strong>of</strong> <strong>the</strong> three PMTsFigure 2.3: Histograms <strong>of</strong> charge (left) and pulse height (right) for a single SD station, triggered <strong>by</strong> a3-fold coincidence from all 3 PMTs (solid line). The histogram with <strong>the</strong> dashed line shows<strong>the</strong> spectrum <strong>of</strong> an external muon telescope for <strong>the</strong> same events. The first hump is due to <strong>the</strong>triggering <strong>of</strong> low-energy particles from EAS and shows <strong>the</strong> typical exponential slope. Thesecond hump is caused <strong>by</strong> <strong>the</strong> atmospheric muons [19].and at (1.03 ± 0.02)VEM for individual PMTs, as <strong>the</strong>y are only sensitive to <strong>the</strong> fraction <strong>of</strong> lightdeposited in <strong>the</strong>ir proximity.Switching a station on, <strong>the</strong> high voltage <strong>of</strong> each PMT is tuned until <strong>the</strong> signal rate is 100 Hz at150 channels above baseline. A pedestal <strong>of</strong> 50 channels is added to <strong>the</strong> signal to observe possiblefluctuations <strong>of</strong> <strong>the</strong> baseline.The calibration to VEM units is a three step process [19]:• The gains <strong>of</strong> <strong>the</strong> PMTs are set to have <strong>the</strong> peak I peakV EMin <strong>the</strong> pulse height histogram at50 channels for each individual PMT (see Figure 2.3).• The I peakV EMis monitored in units <strong>of</strong> channels and adjusted to <strong>the</strong> electronics-level trigger tocompensate for drifts, which occur after setting <strong>the</strong> value.• The peak in <strong>the</strong> charge histogram Q peakVEM (see Figure 2.3) is determined and used to get <strong>the</strong>conversion for <strong>the</strong> signal from Q peakV EMin units <strong>of</strong> VEM.
2.2 Surface <strong>detector</strong> 11During <strong>data</strong> taking <strong>the</strong> individual PMT rates are monitored <strong>by</strong> determining <strong>the</strong> events, with allworking PMTs in a station, above 1.75 VEM. The estimated rate is at 110 Hz. These T1 events areused to check, if each individual PMT has a counting rate <strong>of</strong> 70Hz above 2.3 VEM. An unmatchedPMT, with a too high baseline, would have a higher rate than 70Hz above 2.3 VEM. The VEMvalue for a PMT not conforming to <strong>the</strong> 70 Hz will be modified and matched in an iterative process[20].To determine <strong>the</strong> charge <strong>of</strong> a VEM, <strong>the</strong> signals <strong>of</strong> <strong>the</strong> PMTs are integrated over 625 ns, if <strong>the</strong> signalpeaks exactly at <strong>the</strong> threshold <strong>of</strong> 1.75 VEM. The obtained value is divided <strong>by</strong> a factor <strong>of</strong> 1.75 toget 1 VEM, which has now a precision better than 2%. This method is not applied at a threshold<strong>of</strong> 1 VEM directly, because <strong>of</strong> a too high rate.2.2.3 AMIGAThere are clear indications that simulations underestimate <strong>the</strong> muon content <strong>of</strong> extensive air showersand, hence, are biasing <strong>the</strong> SD energy estimator. A direct measurement <strong>of</strong> <strong>the</strong> muons wouldreduce <strong>the</strong> systematic error <strong>of</strong> <strong>the</strong> reconstructed energies and, in addition, <strong>the</strong> muon fraction is anexcellent indicator <strong>of</strong> <strong>the</strong> type <strong>of</strong> <strong>the</strong> primary particle and might help to solve <strong>the</strong> question <strong>of</strong> <strong>the</strong>composition <strong>of</strong> cosmic rays [21].At <strong>the</strong> moment, <strong>the</strong> observatory is upgraded with a muon <strong>detector</strong> and additional <strong>surface</strong> <strong>detector</strong>stations. AMIGA (<strong>Auger</strong> Muons and Infill for <strong>the</strong> Ground Array) is an enhancement <strong>of</strong> <strong>the</strong> existing<strong>surface</strong> <strong>detector</strong>. In a hexagon with an area <strong>of</strong> 23.5km 2 , additional <strong>surface</strong> <strong>detector</strong>s havebeen installed, with a graded spacing <strong>of</strong> 433 m and 750 m (see Figure 2.2.3). The spacing allowsto measure primary particles down to an energy <strong>of</strong> 0.1 EeV. The expected number <strong>of</strong> detectedevents per year is given in Table 2.1. In 2009, 30m 2 muon scintillation counters will be buried in aE 0 [EeV] Area [ km 2] No. events year −10.1 5.9 160000.3 23.5 8500Table 2.1: Expected number <strong>of</strong> events per year with <strong>the</strong> completely installed AMIGA [22].depth <strong>of</strong> ∼ 3m next to 7 <strong>surface</strong> <strong>detector</strong> stations (one unitary cell). This prototype will take <strong>data</strong>for one year and <strong>the</strong>n muon counters will be deployed next to each <strong>of</strong> <strong>the</strong> 85 <strong>surface</strong> stations in<strong>the</strong> 23.5km 2 hexagon (shown in Figure 2.2.3) to determine <strong>the</strong> muon component <strong>of</strong> extensive airshowers. The center <strong>of</strong> AMIGA will be located 6 km away from <strong>the</strong> Coihueco building and willbe overlooked <strong>by</strong> <strong>the</strong> fluorescence telescopes.Each muon counter will comprise 64 strips <strong>of</strong> a highly segmented plastic scintillator with opticalfibers ending on a 64-pixel multi-anode PMT. In <strong>the</strong> current design, <strong>the</strong> strips are 400 cm long,4.1 cm wide and have a height <strong>of</strong> 1.0 cm. At each tank, 3 or 4 counters will be installed and aprinted circuit board (PCB) with a <strong>data</strong> handling field programmable gate array (FPGA) will beattached to <strong>the</strong> PMTs. A micro-controller for monitoring and communication will process <strong>the</strong> <strong>data</strong>and send it to a second FPGA above ground, if <strong>the</strong> corresponding <strong>surface</strong> <strong>detector</strong> station has beentriggered <strong>by</strong> an extensive air shower. A microcomputer will transmit <strong>the</strong> tank and muon counter<strong>data</strong> to <strong>the</strong> central <strong>data</strong> acquisition system at <strong>the</strong> <strong>Auger</strong> campus.The aim is, to use <strong>the</strong> information <strong>of</strong> <strong>the</strong> number <strong>of</strong> muons at each station to calculate <strong>the</strong> estimatednumber <strong>of</strong> muons N µ (600) 600 m away from <strong>the</strong> shower axis, <strong>by</strong> using <strong>the</strong> parameterized muonlateral distribution function [23], currently used <strong>by</strong> KASCADE-Grande. In addition N µ (600) is an
12 <strong>Pierre</strong> <strong>Auger</strong> observatoryexcellent indicator for <strong>the</strong> type <strong>of</strong> <strong>the</strong> primary particle [22].Figure 2.4: The extensions near <strong>the</strong> Coihueco building: The dots illustrate <strong>the</strong> <strong>surface</strong> stations and <strong>the</strong>lines indicate <strong>the</strong> field <strong>of</strong> view <strong>of</strong> <strong>the</strong> HEAT and <strong>the</strong> former installed fluorescence telescopes.All stations indicated with a name belong to <strong>the</strong> 1.5 km grid, <strong>the</strong> o<strong>the</strong>rs are spaced 750 m and433 m apart. All stations inside <strong>the</strong> huge hexagon will have in addition a 30m 2 buried muoncounter, after AMIGA is completed [24].2.3 Fluorescence <strong>detector</strong>During <strong>the</strong> night, <strong>the</strong> atmosphere above <strong>the</strong> array is monitored <strong>by</strong> 24 Schmidt telescopes placed in4 buildings (eyes) at <strong>the</strong> border <strong>of</strong> <strong>the</strong> ground array (see Figure 2.1). Each telescope has a field <strong>of</strong>view <strong>of</strong> 30 ◦ × 30 ◦ , resulting in a lateral view <strong>of</strong> 180 ◦ per eye, towards <strong>the</strong> center <strong>of</strong> <strong>the</strong> array, from1 ◦ to 31 ◦ above <strong>the</strong> horizon.The secondary particles <strong>of</strong> extensive air showers excite <strong>the</strong> nitrogen molecules in <strong>the</strong> atmospherealong <strong>the</strong>ir path. When <strong>the</strong> excited molecules fall back to ground state, fluorescence light is emitted.If <strong>the</strong> shower axis is in <strong>the</strong> field <strong>of</strong> view <strong>of</strong> a telescope, <strong>the</strong> produced light passes a UVtransmitting filter at <strong>the</strong> diaphragm with an aperture <strong>of</strong> 3.8m 2 . The filter is transparent for wavelengthsin <strong>the</strong> range <strong>of</strong> 300 nm to 400 nm, The optical aberrations are minimized, using a ring<strong>of</strong> corrector lenses installed around <strong>the</strong> diaphragm. The transmitted light is reflected <strong>by</strong> a 12m 2mirror and measured <strong>by</strong> a camera, equipped with 440 hexagonal PMTs. The PMTs are arrangedin a 22 × 20 matrix. Each PMT overlooks a region <strong>of</strong> <strong>the</strong> sky <strong>of</strong> 1.5 ◦ in diameter. The signals <strong>of</strong><strong>the</strong> PMTs are amplified and filtered using an analog board, which is connected to a digital board.The fluorescence <strong>detector</strong> has a 4 level trigger and <strong>the</strong> real events are sent from <strong>the</strong> eye PCs (mainPC in each building) to <strong>the</strong> central <strong>data</strong> acquisition system (CDAS) [26].Before and after each run, a three step relative calibration is performed to observe any changesin <strong>the</strong> system. Firstly, <strong>the</strong> PMTs are illuminated directly with a laser located at <strong>the</strong> center <strong>of</strong> <strong>the</strong>
2.3 Fluorescence <strong>detector</strong> 13Figure 2.5: Schematic view <strong>of</strong> a fluorescence telescope unit [25].mirror, to check <strong>the</strong>ir responses. Secondly, a laser mounted at <strong>the</strong> top <strong>of</strong> <strong>the</strong> camera points at <strong>the</strong>mirror and <strong>the</strong> reflected beam is used to test <strong>the</strong> mirror-camera system. In <strong>the</strong> third step, <strong>the</strong> lighthas to pass <strong>the</strong> diaphragm, before being reflected at <strong>the</strong> mirror and coming to <strong>the</strong> camera. This allowsto test <strong>the</strong> whole telescope system. The absolute calibration is performed only 3 or 4 times ayear <strong>by</strong> illuminating <strong>the</strong> cameras with a well known diffuse light source. The absolute calibrationhas an uncertainty <strong>of</strong> 12%.As <strong>the</strong> number <strong>of</strong> detected photons is strongly correlated with <strong>the</strong> atmospheric conditions, anatmospheric monitoring system is installed. In order to determine <strong>the</strong> aerosol content in <strong>the</strong> airbackscatter LIDARs (light detection and rangings) are constructed next to each telescope building.Each LIDAR consists <strong>of</strong> an UV-laser and a PMT, that detects <strong>the</strong> photons <strong>of</strong> <strong>the</strong> UV laser pulses,which are backscattered in <strong>the</strong> atmosphere. Fur<strong>the</strong>rmore, density and temperature pr<strong>of</strong>iles <strong>of</strong> <strong>the</strong>atmosphere are available from balloon measurements. The atmospheric monitoring <strong>data</strong> is used,to correct for attenuation effects.Ano<strong>the</strong>r tool is <strong>the</strong> central laser facility (CLF), a strong laser located at <strong>the</strong> center <strong>of</strong> <strong>the</strong> array.The CLF is used to check <strong>the</strong> relative timing between <strong>the</strong> SD and <strong>the</strong> FD <strong>by</strong> inserting a signal viaa glass fiber into <strong>the</strong> closest SD station, at <strong>the</strong> same time as <strong>the</strong> laser shoots vertically in <strong>the</strong> sky.The well known position <strong>of</strong> <strong>the</strong> laser beam is used to test <strong>the</strong> angular reconstruction <strong>of</strong> <strong>the</strong> FD andto cross-check <strong>the</strong> calibration <strong>of</strong> <strong>the</strong> individual telescopes.At <strong>the</strong> moment, <strong>the</strong> FD is upgraded with three high elevation <strong>Auger</strong> telescopes (HEAT) near<strong>the</strong> Coihueco building. When <strong>the</strong> construction is being finished, <strong>the</strong>y will observe <strong>the</strong> atmosphereabove <strong>the</strong> new infill <strong>detector</strong> area, with an elevated field <strong>of</strong> view from 30 ◦ to 60 ◦ above <strong>the</strong> horizon.Toge<strong>the</strong>r with <strong>the</strong> telescopes hosted in <strong>the</strong> Coihueco building, <strong>the</strong> atmosphere can be monitored
14 <strong>Pierre</strong> <strong>Auger</strong> observatoryfrom <strong>the</strong> horizon up to an angle <strong>of</strong> 60 ◦ and this allows to measure <strong>the</strong> main part <strong>of</strong> <strong>the</strong> showerdevelopment in <strong>the</strong> atmosphere, for a sizable number <strong>of</strong> extensive air showers.Since all telescopes (normal FD and HEAT) are very sensitive to light, <strong>data</strong> taking is only possiblein periods <strong>of</strong> a bit more than two weeks around new moon, without rain and storm, as well as nottoo heavy clouds. The duty cycle is less than 12%. As <strong>the</strong> FD performs a calorimetric measurement,<strong>the</strong> longitudinal shower pr<strong>of</strong>ile and <strong>the</strong> location <strong>of</strong> <strong>the</strong> shower maximum can be detected.The estimated systematic uncertainty in <strong>the</strong> reconstructed shower energy is 25% and <strong>the</strong> angularresolution is in <strong>the</strong> range <strong>of</strong> 0.5 ◦ [27].2.4 Radio <strong>detector</strong>sThe charged particles <strong>of</strong> air showers passing through <strong>the</strong> terrestrial magnetic field emit electromagneticradiation, that can be detected <strong>by</strong> ground-based antennas [28] [29]. The radiation isemitted coherently and as <strong>the</strong> amount <strong>of</strong> radiation is proportional to <strong>the</strong> number <strong>of</strong> particles in <strong>the</strong>EAS, <strong>the</strong> energy <strong>of</strong> <strong>the</strong> primary particle and <strong>the</strong> shower maximum can be determined.The emission mechanism is still an open question and different models try to describe it. Onemodel is based on <strong>the</strong> fact, that <strong>the</strong> particles in <strong>the</strong> air shower travel faster than <strong>the</strong> speed <strong>of</strong>light and emit coherent Cherenkov radiation in <strong>the</strong> range <strong>of</strong> radio frequency. In neutral showers,<strong>the</strong> signals <strong>of</strong> positively and negatively charged particles would cancel each o<strong>the</strong>r, but due to <strong>the</strong>enrichment <strong>of</strong> negative charge in <strong>the</strong> EAS, caused <strong>by</strong> <strong>the</strong> recombination <strong>of</strong> positrons with <strong>the</strong> electronsin <strong>the</strong> air, radiation at radio frequency is emitted in <strong>the</strong> forward direction.Ano<strong>the</strong>r model assumes, that <strong>the</strong> geomagnetic field deflects <strong>the</strong> particles and induces synchrotronradiation. This process can also be interpreted as a transverse current, coming from <strong>the</strong> separation<strong>of</strong> positively and negatively charged particles <strong>by</strong> <strong>the</strong> geomagnetic field [30].The advantages <strong>of</strong> radio <strong>detector</strong>s are <strong>the</strong> possibility to measure <strong>the</strong> longitudinal pr<strong>of</strong>ile <strong>of</strong> EAS,comparable to fluorescence measurements, but with a much higher duty cycle and <strong>the</strong> low costsetup.At <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory, different prototypes <strong>of</strong> radio <strong>detector</strong>s are tested. Currently, externaltriggers from <strong>the</strong> SD are used. The challenge is to develop a self-triggered system coveringan area <strong>of</strong> 20km 2 . In order to achieve this, several technical issues, like handling <strong>the</strong> <strong>data</strong> streamand installing a wireless system for <strong>the</strong> <strong>data</strong> transfer, have to be resolved.2.5 First resultsThe observatory is taking <strong>data</strong> in a stable mode since 1st <strong>of</strong> January 2004, starting with 154 <strong>surface</strong><strong>detector</strong> stations. The construction has been finished in <strong>the</strong> middle <strong>of</strong> 2008. Since <strong>the</strong> starting <strong>of</strong><strong>data</strong> taking more than 1.5 Mio. events have been detected and first results have been published.The most interesting recent observation is <strong>the</strong> “Correlation <strong>of</strong> <strong>the</strong> highest energy cosmic rays withnear<strong>by</strong> extragalactic objects” [31]. A brief summary <strong>of</strong> <strong>the</strong> results is given, as <strong>the</strong> stability <strong>of</strong> <strong>the</strong>reconstruction <strong>of</strong> exactly <strong>the</strong>se events is analyzed in Chapter 4.In <strong>the</strong> study, which arouse public interest, <strong>the</strong> arrival directions <strong>of</strong> <strong>the</strong> highest-energy cosmic rays,detected <strong>by</strong> <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory, are compared with <strong>the</strong> positions <strong>of</strong> active galactic nuclei(AGN), listed in <strong>the</strong> 12th edition <strong>of</strong> <strong>the</strong> Véron-Cetty and Véron catalog [32]. The energies are soextreme, that <strong>the</strong> particle origins or places <strong>of</strong> acceleration have to be located in <strong>the</strong> most violentplaces in <strong>the</strong> universe. One possible location is within AGNs, compact regions at <strong>the</strong> centre <strong>of</strong>galaxies, which ejecting plasma jets into intergalactic space. The charged particles are deflected
2.5 First results 15Figure 2.6: Sky map <strong>of</strong> <strong>the</strong> celestial sphere in galactic coordinates. The asterisks illustrate <strong>the</strong> positions<strong>of</strong> <strong>the</strong> 442 AGN (318 within <strong>the</strong> field <strong>of</strong> view <strong>of</strong> <strong>the</strong> observatory) with redshift z ≤ 0.017 (D ≤71Mpc) from <strong>the</strong> 12th edition <strong>of</strong> <strong>the</strong> Véron-Cetty and Véron catalog [32]. The black circles<strong>of</strong> 3.1 ◦ in diameter are centered around <strong>the</strong> reconstructed arrival directions <strong>of</strong> <strong>the</strong> 27 eventswith a reconstructed energy above 57 EeV. Darker colors indicate higher relative exposure and<strong>the</strong> solid line shows <strong>the</strong> limit <strong>of</strong> <strong>the</strong> field <strong>of</strong> view, for " < 60 ◦ . The dashed line displays <strong>the</strong>super-galactic plane [31].<strong>by</strong> intergalactic magnetic fields. For particles with energies above a few tens <strong>of</strong> EeV, <strong>the</strong> deflectionsare small enough to identify <strong>the</strong> sources.The study is performed with all events, <strong>recorded</strong> between 1 January 2004 and 31 August 2007,with a reconstructed energy above 40 EeV, a zenith angle smaller than 60 ◦ and satisfying predefinedquality criteria. A three-dimensional scan has been performed to compute <strong>the</strong> degree <strong>of</strong>correlation between <strong>the</strong> arrival directions <strong>of</strong> <strong>the</strong> events and <strong>the</strong> positions <strong>of</strong> <strong>the</strong> AGN. The freeparameters are <strong>the</strong> maximum AGN redshift z max , <strong>the</strong> maximum angular separation ' and <strong>the</strong>threshold for <strong>the</strong> energy <strong>of</strong> <strong>the</strong> cosmic rays E th . The minimum probability <strong>of</strong> <strong>the</strong> hypo<strong>the</strong>sis <strong>of</strong>isotropic arrival directions was found for z max = 0.017 (corresponding to a maximum distance <strong>of</strong><strong>the</strong> source <strong>of</strong> D ∼ 71Mpc), ' = 3.1 ◦ and E th = 57EeV. With <strong>the</strong>se parameters, 20 out <strong>of</strong> 27cosmic ray events correlate with at least one <strong>of</strong> <strong>the</strong> 442 selected AGN (see Figure 2.6). For anisotropic flux only 5.6 are expected.It is possible, that o<strong>the</strong>r sources emit and accelerate <strong>the</strong> UHECRs, but <strong>the</strong>ir local distributions haveto be similar to <strong>the</strong> positions <strong>of</strong> <strong>the</strong> AGN. The AGN are in this case only tracers to <strong>the</strong> real sources.The statistic <strong>of</strong> 27 events is not very high and limited <strong>by</strong> <strong>the</strong> threshold energy E th , which is necessarybecause lower energetic particles are deflected much more <strong>by</strong> <strong>the</strong> intergalactic magnetic fieldsand <strong>the</strong> detected arrival directions do not point to <strong>the</strong> sources <strong>of</strong> <strong>the</strong> CRs.The <strong>Auger</strong> collaboration showed for <strong>the</strong> first time, that astronomy <strong>of</strong> charged particles at highestenergies is practicable and that <strong>the</strong> identification <strong>of</strong> <strong>the</strong> sources as well as <strong>the</strong> comprehension <strong>of</strong> <strong>the</strong>accelerating mechanisms come into reach. The next step is to detect more events to reach higherstatistics and to build <strong>the</strong> nor<strong>the</strong>rn site to get full sky coverage.
Event reconstruction using <strong>the</strong> <strong>surface</strong> <strong>detector</strong> <strong>data</strong>Chapter 3Event reconstruction using <strong>the</strong> <strong>surface</strong><strong>detector</strong> <strong>data</strong>In this chapter, <strong>the</strong> trigger chain, <strong>the</strong> reconstruction algorithm and <strong>the</strong> characteristics <strong>of</strong> <strong>the</strong> <strong>surface</strong><strong>detector</strong> are described. The Cherenkov light, produced <strong>by</strong> secondary particles <strong>of</strong> extensive airshowers crossing <strong>the</strong> water <strong>of</strong> <strong>surface</strong> stations, is collected <strong>by</strong> three photomultiplier tubes (PMTs)and converted into electric signals. The integrated signals are proportional to <strong>the</strong> energy depositsin <strong>the</strong> water. If <strong>the</strong> signals <strong>of</strong> three or more stations conform to predefined trigger criteria, it ispossible to reconstruct <strong>the</strong> energy and <strong>the</strong> arrival direction <strong>of</strong> <strong>the</strong> primary particle.For each detected event, 13 histograms from each station, containing <strong>the</strong> information from <strong>the</strong>calibration, are sent to <strong>the</strong> central <strong>data</strong> acquisition system (CDAS). As an example <strong>the</strong> signals<strong>of</strong> one station are shown in Figure 3.1. The online calibration (described in Section 2.2.2) isperformed in order to obtain <strong>the</strong> same pulse height histograms for all PMTs in all stations. Thisdefinition <strong>of</strong> a uniform trigger condition for all stations ensures to achieve a uniform event rateover <strong>the</strong> whole array.3.1 Trigger chainThe <strong>Auger</strong> trigger chain is hierarchical and consists <strong>of</strong> <strong>the</strong> two local triggers (T1 and T2), <strong>the</strong> arraytrigger (T3), <strong>the</strong> physics event trigger (T4) and <strong>the</strong> quality trigger (T5).The local triggers are part <strong>of</strong> <strong>the</strong> electronics, installed in each <strong>surface</strong> <strong>detector</strong>. The T1 can besatisfied <strong>by</strong> two conditions:• Time-over-threshold (ToT): The amplitude <strong>of</strong> <strong>the</strong> signals <strong>of</strong> 2 PMTs have to be above <strong>the</strong>threshold <strong>of</strong> 0.2 VEM, in at least 13 time bins <strong>of</strong> 25 ns, in an interval <strong>of</strong> 3 µs.• Single threshold (ST): The amplitudes <strong>of</strong> <strong>the</strong> signals <strong>of</strong> all three PMTs in one station exceed<strong>the</strong> threshold <strong>of</strong> 1.75 VEM, in at least one time bin.The ToT trigger is very efficient for <strong>the</strong> detection signals, which are long and have small amplitudes,how <strong>the</strong>y occur in low energy showers and in stations far <strong>of</strong>f <strong>the</strong> core <strong>of</strong> high energyextensive air showers. The ToT trigger has a rate <strong>of</strong> 1.6 Hz and is not sensitive to <strong>the</strong> muoniccomponent, since <strong>the</strong>ir signals are too short (< 200ns and < 8 bins respectively). The muonsconform to <strong>the</strong> ST trigger demands and trigger with a rate <strong>of</strong> 100 Hz. The single threshold triggeris necessary to measure muons <strong>of</strong> horizontal showers. If a station conforms to both criteria, it is
3.1 Trigger chain 17Base PMT 1, LS 1640Base PMT 2, LS 1640Base PMT 3, LS 1640Charge PMT 1, LS 1640Charge PMT 2, LS 1640Charge PMT 3, LS 1640Charge PMT 4, LS 1640Peak PMT 1, LS 1640Shape PMT 1, LS 1640Figure 3.1: Raw histograms <strong>of</strong> station 1640, with an integrated signal <strong>of</strong> 10.3 VEM. The <strong>data</strong> belongs toevent 200821400018 and is a randomly picked example. Top: baseline histograms for all threedynode channels; middle: charge histograms <strong>of</strong> <strong>the</strong> three PMTs; bottom left: summed chargehistogram; bottom middle: pulse height (peak) histograms <strong>of</strong> <strong>the</strong> three PMTs; bottom right:average pulse shape <strong>of</strong> <strong>the</strong> three PMTs.
18 Event reconstruction using <strong>the</strong> <strong>surface</strong> <strong>detector</strong> <strong>data</strong>flagged as a ToT and not as a ST triggered event.Signals passing <strong>the</strong> ToT trigger are directly promoted to <strong>the</strong> T2 trigger, whereas for ST signals <strong>the</strong>crossing <strong>of</strong> a higher threshold <strong>of</strong> 3.2 VEM for all PMTs is required. The T2 trigger rate is reducedto 20 Hz and <strong>the</strong> <strong>data</strong> is transferred to <strong>the</strong> CDAS on <strong>the</strong> campus in Malargüe. The T2 trigger rateallows to monitor <strong>the</strong> performance <strong>of</strong> <strong>the</strong> array and to calculate <strong>the</strong> exposure [33].Coincidences <strong>of</strong> three or more stations, which passed <strong>the</strong> T2 trigger, satisfy <strong>the</strong> array trigger T3.It can be achieved <strong>by</strong> two different criteria:• The coincidence <strong>of</strong> three ToT triggered <strong>detector</strong>s in a compact position defines <strong>the</strong> 3ToT.One <strong>of</strong> <strong>the</strong> stations must have one <strong>of</strong> its closest and one <strong>of</strong> its second closest neighborstriggered. The 3ToT trigger selects 90% physics events and is very sensitive to verticalshowers.• If four T2 triggers are fired in coincidence and in moderate distance (up to 6 km in an appropriatetime window), <strong>the</strong> 3C1 trigger is set. This trigger is necessary in order to detecthorizontal showers with fast and wide-spread signals. Due to <strong>the</strong> less strict requirements,many accidental coincidences conform to <strong>the</strong> trigger condition and <strong>the</strong> fraction <strong>of</strong> real showersis only 2% [34].All T3 triggered events are stored and <strong>the</strong> physics trigger (T4) performs <strong>the</strong> real shower selection<strong>of</strong>fline. Two different trigger modes are implemented on <strong>the</strong> T4 level. The first, called 3ToT T4trigger, requires a 3ToT trigger and a zenith angle below 60 degree. The o<strong>the</strong>r trigger condition iscalled 4C1 and is fulfilled, if at least one station and three <strong>of</strong> six direct neighbors have passed <strong>the</strong>T3 trigger. For both criteria <strong>the</strong> time difference between <strong>the</strong> signals has to be compatible with <strong>the</strong>speed <strong>of</strong> light.By using only <strong>the</strong> 3ToT T4 trigger, less than 5% <strong>of</strong> <strong>the</strong> real showers below 60 ◦ are lost. The 4C1trigger ensures to detect <strong>the</strong>se showers and is also sensitive to showers beyond 60 ◦ (see Figure3.2).Before reconstructing <strong>the</strong> events, <strong>the</strong> signals <strong>of</strong> stations, which are in accidental coincidence, haveFigure 3.2: Zenith angle (left) and energy (right) distribution for events passing <strong>the</strong> T4 trigger. Eventspassing <strong>the</strong> 3ToT are displayed in <strong>the</strong> red shaded area and 4C1 events in <strong>the</strong> blue dashed area.Events fulfilling both criteria are counted as 3ToT events [34].to be removed. Accidental tanks are triggered in <strong>the</strong> same time window as <strong>the</strong> stations triggered <strong>by</strong>an extensive air shower, but <strong>the</strong>ir signals are caused <strong>by</strong> atmospheric muons or o<strong>the</strong>r background
3.2 Tank trigger probability 19effects. The start times <strong>of</strong> <strong>the</strong> three stations with <strong>the</strong> highest signals are used to define a seed, that isan elementary triangle (one station with 2 neighbors in a non-aligned configuration). The signals<strong>of</strong> <strong>the</strong> o<strong>the</strong>r triggered stations are added and kept, if <strong>the</strong>y are compatible with a plane showerfront derived from <strong>the</strong> seed, o<strong>the</strong>rwise <strong>the</strong> stations are classified as accidental and not used in <strong>the</strong>reconstruction [35]. If a station has no triggered neighbor within a circle <strong>of</strong> 1800 m, or only onetriggered neighbor within a circle <strong>of</strong> 5000 m, it is considered as isolated and <strong>the</strong> <strong>data</strong> is removedas well.From <strong>the</strong> obtained T4 events 99% are reconstructed and used for fur<strong>the</strong>r studies. The events witha zenith angle above 60 degree are more difficult to handle and <strong>the</strong> development <strong>of</strong> a T4 is workin progress.The last element in <strong>the</strong> chain is <strong>the</strong> T5 quality trigger. It is used to select events with high energyand angular accuracy. Several studies have been performed to define a reasonable criterion [36].At <strong>the</strong> moment mainly two definitions are used (see Figure 3.3):• The strict-T5: The station with <strong>the</strong> highest signal is surrounded <strong>by</strong> 6 active stations. Theydo not have to be triggered, but have to be active at <strong>the</strong> time, when <strong>the</strong> shower is detected.• The ICRCT5: Five <strong>of</strong> six direct neighbors <strong>of</strong> <strong>the</strong> station with <strong>the</strong> highest signal have to beactive and <strong>the</strong> reconstructed shower core has to be inside an equilateral triangle <strong>of</strong> activestations.Figure 3.3: The ICRCT5 (left) requires five <strong>of</strong> six active stations in <strong>the</strong> first crown and a reconstructedcore position in an active triangle <strong>of</strong> <strong>detector</strong>s. Core positions inside <strong>the</strong> right triangle satisfy<strong>the</strong> ICRCT5, core positions inside <strong>the</strong> left triangle not. The right picture shows <strong>the</strong> conditionfor <strong>the</strong> strict-T5, an active unitary cell.3.2 Tank trigger probabilityIn <strong>the</strong> previous section <strong>the</strong> whole trigger chain has been discussed. The signals obtained in <strong>the</strong>tanks are used to reconstruct <strong>the</strong> arrival directions and <strong>the</strong> energies <strong>of</strong> <strong>the</strong> primary cosmic rays.Before <strong>the</strong> algorithm is described, it is worth to have a look at <strong>the</strong> tank trigger probability andshower fluctuations.The signal <strong>of</strong> each station is affected <strong>by</strong> several fluctuations, as <strong>the</strong> shower-to-shower fluctuations,<strong>the</strong> sampling <strong>of</strong> Cherenkov photons, production <strong>of</strong> photoelectrons and noise [37]. Due to <strong>the</strong>fluctuations, measured signals can be higher or lower, and signals above <strong>the</strong> trigger threshold canfall below <strong>the</strong> threshold and <strong>the</strong> o<strong>the</strong>r way around. This causes a bias, because in <strong>the</strong> thresholdregion, only signals with positive fluctuations are <strong>recorded</strong>.
20 Event reconstruction using <strong>the</strong> <strong>surface</strong> <strong>detector</strong> <strong>data</strong>The trigger probability P exp (S) is defined asP exp (S)= N T + (S)N on (S) ,where N T + (S) is <strong>the</strong> number <strong>of</strong> triggered stations with a signal S and N on (S) <strong>the</strong> number <strong>of</strong> activestations in <strong>the</strong> selected signal bin. An example <strong>of</strong> a lateral trigger probability (LTP) for " = 45 ◦and S 1000 = 4.5VEM is shown in Figure 3.4, whereas S 1000 is <strong>the</strong> signal, obtained at a distance <strong>of</strong>1000 m from <strong>the</strong> shower core (see Chaper 3.3.3). The efficiency to trigger a station decreases forincreasing zenith angles, decreasing signal size and increasing distance to <strong>the</strong> shower core.Figure 3.4: Left: Comparison between <strong>the</strong> experimental (symbols) and unbiased (solid line) trigger probabilityfor " = 45 ◦ and S 1000 = 4.5VEM. Right: Lateral trigger probability for three differentvalues <strong>of</strong> S 1000 (3 (boxes), 10 (circles) and 30 VEM (triangles)) and zenith angles <strong>of</strong> 0 ◦ and45 ◦ (closed and open symbols) [37].3.3 Event reconstruction3.3.1 CDAS and Offline<strong>Auger</strong> has two independent reconstruction s<strong>of</strong>twares available, <strong>the</strong> CDAS online reconstructionand <strong>the</strong> <strong>Auger</strong> Offline s<strong>of</strong>tware. The <strong>Auger</strong> Offline s<strong>of</strong>tware is able to perform SD and FD reconstruction,as well as <strong>the</strong> comparison with Monte Carlo simulations. The CDAS code is onlyfor SD <strong>data</strong> reconstruction. CDAS is used to generate <strong>the</strong> Herald file, which contains all reconstructedT4 events. This Herald file is used for anisotropy studies and source identifications. Themost interesting recent result, published <strong>by</strong> <strong>the</strong> <strong>Auger</strong> collaboration (see Chapter 2.5), is basedon <strong>the</strong> <strong>data</strong> reconstructed <strong>by</strong> CDAS. Therefore, it is important to check <strong>the</strong> stability <strong>of</strong> <strong>the</strong> CDASreconstruction algorithm (see Chapter 4).In this chapter <strong>the</strong> reconstruction algorithm <strong>of</strong> <strong>the</strong> CDAS code is described, as all steps <strong>of</strong> <strong>the</strong>analysis in this <strong>the</strong>sis are performed with CDAS. The Offline reference manual for <strong>the</strong> SD reconstructioncan be found in [38]. A comparison <strong>of</strong> <strong>the</strong> different reconstruction s<strong>of</strong>twares is presentedin [39] and a guideline for SD analysis is given in [40].For each day a ROOT file with all T4-events is available. These files contain <strong>the</strong> raw histogramsfrom each station, <strong>the</strong> FADC traces <strong>of</strong> each PMT, <strong>the</strong> time <strong>of</strong> detection and fur<strong>the</strong>r informationssupplied <strong>by</strong> <strong>the</strong> <strong>detector</strong>s. The stored events can be reconstructed with <strong>the</strong> standard, or a modified
3.3 Event reconstruction 21algorithm.The most important parameters in order to characterize a shower, obtained <strong>by</strong> <strong>the</strong> standard CDASreconstruction, are stored in <strong>the</strong> Herald file. This file contains 39 informations like event-id, reconstructedenergy and arrival direction. The file and detailed informations can be found at [41].3.3.2 Angular reconstructionAll triggered stations used in <strong>the</strong> reconstruction are called selected stations. The determination <strong>of</strong><strong>the</strong>se stations has been described in Chapter 3.1 and a detailed description can be found in [42].The arrival times <strong>of</strong> <strong>the</strong> shower front at <strong>the</strong> selected stations are used to calculate <strong>the</strong> arrival direction<strong>of</strong> <strong>the</strong> primary cosmic ray. The times are extracted from <strong>the</strong> PMT FADC traces and <strong>the</strong>coordinates <strong>of</strong> <strong>the</strong> stations are known at <strong>the</strong> level <strong>of</strong> 1 m from <strong>the</strong> GPS antennas mounted on <strong>the</strong>tanks. The <strong>data</strong> can be compared to different shower front models, like plane, spheric or parabolic.For a plane shower front, orthogonal to <strong>the</strong> shower axis, <strong>the</strong> time difference (t i between <strong>the</strong> predictedand measured arrival times at station i, can be written as [43]:(t i = t i −(T 0 − u(x i − x core )+v(y i − y core )c). (3.1)T 0 is <strong>the</strong> shower core arrival time at ground, c <strong>the</strong> speed <strong>of</strong> light, u equals sin" cos ) and v equalssin" sin). The predicted arrival time is calculated <strong>by</strong> assuming a plane shower front, given <strong>by</strong> <strong>the</strong>signals <strong>of</strong> <strong>the</strong> three stations with <strong>the</strong> highest integrated signals. The angles in spherical coordinates,) for <strong>the</strong> azimuth angle and " for <strong>the</strong> zenith angle, are <strong>the</strong> common nomenclature for <strong>the</strong> arrivaldirection. The position <strong>of</strong> <strong>the</strong> shower core (x core ,y core ) is calculated from <strong>the</strong> barycenter <strong>of</strong> alltriggered tank positions (x i ,y i ), weighted <strong>by</strong> <strong>the</strong> square root <strong>of</strong> <strong>the</strong>ir signals (see Figure 3.6 right).The typical accuracy <strong>of</strong> <strong>the</strong> core position is better than 150 m. For a spherical shower front,ri 2/(2Rc) has to be added to Equation 3.1, with <strong>the</strong> shower curvature R and r i <strong>the</strong> distance between<strong>the</strong> core and station i.is <strong>the</strong> uncertainty <strong>of</strong> <strong>the</strong> arrival time t i , <strong>the</strong> angles" and ) are determined. The uncertainties , ti depend on <strong>the</strong> distance <strong>of</strong> <strong>the</strong> station to <strong>the</strong> coreand increase from 20 ns at <strong>the</strong> core to 50 ns at a distance <strong>of</strong> 1000m. The parameterization <strong>of</strong>, ti =(22 + 0.03 · r)ns, with <strong>the</strong> distance r <strong>of</strong> <strong>the</strong> station to <strong>the</strong> shower core in meter, is included in<strong>the</strong> reconstruction [43].The angular resolution is better than 1.8 ◦ for events below 3 EeV and decreases to 1.2 ◦ for eventsabove 3 EeV. Events with energies above 10 EeV are reconstructed with an angular accuracy betterthan 0.9 ◦ [44].By minimizing * 2 = + i ((t i ) 2 /, 2t i, where , ti3.3.3 Energy reconstructionThe reconstruction <strong>of</strong> <strong>the</strong> energy is a two step process. First <strong>the</strong> signal S(1000) at a distance <strong>of</strong>1000 m from an a priori unknown core position is estimated from <strong>the</strong> <strong>surface</strong> <strong>detector</strong> <strong>data</strong> and<strong>the</strong>n <strong>the</strong> energy E is calculated, using hybrid events (measured simultaneously with <strong>the</strong> SD and<strong>the</strong> FD) to calibrate <strong>the</strong> <strong>surface</strong> <strong>detector</strong>.The primary particle interacts with <strong>the</strong> air molecules and produces an extensive air shower. A“pancake” <strong>of</strong> secondary particles arrives at ground level, whose number <strong>of</strong> secondary particlesscales roughly with <strong>the</strong> primary energy. As <strong>the</strong> <strong>surface</strong> <strong>detector</strong> samples only a small part <strong>of</strong> <strong>the</strong>particles arriving at ground level, a fit <strong>of</strong> <strong>the</strong> lateral distribution has to be performed (see Figure3.6 left). The lateral dependence <strong>of</strong> <strong>the</strong> signals is modeled asS(r)=S(1000) · f LDF (r), (3.2)
22 Event reconstruction using <strong>the</strong> <strong>surface</strong> <strong>detector</strong> <strong>data</strong>where f LDF (r) is <strong>the</strong> parameterized lateral distribution function (LDF) normalized to <strong>the</strong> signalS(1000) with a distance <strong>of</strong> 1000 m from <strong>the</strong> shower axis. The shower front curvature and particledistribution depend on several parameters. High-developing showers have a flat lateral distribution,whereas low-developing showers produce steep lateral distributions. At a distance <strong>of</strong> 1000 mfrom <strong>the</strong> shower axis, <strong>the</strong> signal is almost independent <strong>of</strong> <strong>the</strong> primary mass and fluctuations [45].To obtain <strong>the</strong> lateral distribution function, <strong>the</strong> signals <strong>of</strong> <strong>the</strong> stations, converted into units <strong>of</strong> VEM,are plotted against <strong>the</strong> distances <strong>of</strong> <strong>the</strong> stations to <strong>the</strong> shower axis (see Figures 3.5 and 3.6). Beforeshower coreshower frontdDD<strong>the</strong>tadFigure 3.5: The distances d <strong>of</strong> <strong>the</strong> stations to <strong>the</strong> shower axis or shower core and <strong>the</strong> distances D to <strong>the</strong>point, where <strong>the</strong> shower core hits <strong>the</strong> ground. The left station is an early <strong>detector</strong>, as <strong>the</strong> stationis triggered before <strong>the</strong> core reaches <strong>the</strong> ground, whereas <strong>the</strong> right station is a late <strong>detector</strong>.performing <strong>the</strong> fit, <strong>the</strong> signals are corrected for <strong>the</strong> forward-backward asymmetry. Early and latetriggered stations, at <strong>the</strong> same distance to <strong>the</strong> shower core, exhibit a different behavior. AfterLateral distribution function fit310210101200 400 600 800 1000 1200 1400 1600 1800 2000 2200Figure 3.6: Pictures from <strong>the</strong> CDAS Event Display: event 200821400018,E = 12.03EeV, " = 51.5 ◦ . Theleft plot shows <strong>the</strong> signals <strong>of</strong> <strong>the</strong> triggered stations (rectangles), <strong>the</strong> silent stations (triangles)and <strong>the</strong> LDF with <strong>the</strong> error band. The right shows a top view <strong>of</strong> <strong>the</strong> triggered stations. Thesize <strong>of</strong> <strong>the</strong> circles is proportional to <strong>the</strong> logarithm <strong>of</strong> <strong>the</strong> detected signal. The stations markedwith a cross, are flagged as accidental and <strong>the</strong> two black stations at <strong>the</strong> right were not active,at <strong>the</strong> time <strong>the</strong> event was detected.reaching <strong>the</strong> shower maximum a few kilometers above <strong>the</strong> <strong>surface</strong> <strong>detector</strong>, extensive air showersthin out. The number <strong>of</strong> particles decreases and at <strong>the</strong> observation level early stations measurehigher signals than late <strong>detector</strong>s, as <strong>the</strong>y detect <strong>the</strong> particles <strong>of</strong> a not so far developed shower
3.3 Event reconstruction 23[46].In CDAS several lateral distribution functions (LDF) are available. The standard one is <strong>the</strong> loglog-parabolaS(r)=S 1000 ×{ ( )r -1000m× ( r1000m() 2·#·lg(300m1000m)×( 300mr1000m1000m) -+#·lg( r1000m)) −#·lg( 300m1000m)r < 300mr > 300mwith r <strong>the</strong> distance between <strong>the</strong> station with <strong>the</strong> highest signal and <strong>the</strong> core. The parameterization<strong>of</strong> <strong>the</strong> slope parameter is(3.3)- = 0.7 × arctan (6.0 × (0.65 − cos ")) − 3.0 (3.4)and # is a piecewise defined function (see Figure 3.7), whereas <strong>the</strong> single functions are all linear,but with different slopes. In <strong>the</strong> fit <strong>of</strong> <strong>the</strong> LDF <strong>the</strong> uncertainties <strong>of</strong> <strong>the</strong> signals are taken as [47], S (") = (0.32 + 0.42 · sec ") √ S. (3.5)After obtaining S(1000), which depends on <strong>the</strong> energy and <strong>the</strong> zenith angle only, <strong>the</strong> next stepis to separate <strong>the</strong>se two dependencies. This is achieved with <strong>the</strong> Constant Intensity Cut (CIC)Figure 3.7: - (left) and # (right) as a function <strong>of</strong> <strong>the</strong> zenith angle. The light line represent <strong>the</strong> parameterization<strong>of</strong> -.method [48]. The main assumption is <strong>the</strong> isotropic arrival <strong>of</strong> cosmic rays from <strong>the</strong> sky. Above fullacceptance <strong>the</strong> zenith angle distribution is <strong>of</strong> <strong>the</strong> form const · sin " cos ". The sine-term is caused<strong>by</strong> <strong>the</strong> increasing spherical element and <strong>the</strong> cosine term <strong>by</strong> <strong>the</strong> decreasing effective array size,with increasing zenith angle. By dividing <strong>the</strong> "-distribution in bins, whose borders are chosento contain <strong>the</strong> same number <strong>of</strong> events in each bin, <strong>the</strong> method <strong>of</strong> <strong>the</strong> CIC can be applied. Aftersorting <strong>the</strong> events in each bin according to <strong>the</strong>ir S(1000) values, <strong>the</strong> signals <strong>of</strong> constant intensity(e.g. <strong>the</strong> 500th event in each selected bin) are plotted against <strong>the</strong> mean " <strong>of</strong> each bin. The obtainedplot showsS(1000)=S 38 · f ( cos 2 (") ) = S 38 · (1+ ax + bx 2) , (3.6)with x = cos 2 " − cos 2 38 ◦ and <strong>the</strong> fit parameters a and b. Now <strong>the</strong> energy estimator S 38 , <strong>the</strong> value<strong>of</strong> S(1000) at a reference angle <strong>of</strong> 38 ◦ , can be obtained:S 38 = S(1000)f (cos 2 ") . (3.7)
24 Event reconstruction using <strong>the</strong> <strong>surface</strong> <strong>detector</strong> <strong>data</strong>The selection <strong>of</strong> 38 ◦ is justified, as it is <strong>the</strong> mean value <strong>of</strong> <strong>the</strong> "-distribution (see Chapter 3.4). Theenergy estimator S 38 does not depend on " any longer and is only a function <strong>of</strong> <strong>the</strong> energy <strong>of</strong> <strong>the</strong>primary particle.In a last step S 38 has to be linked with <strong>the</strong> energy. This can be achieved based on Monte Carlosimulations or <strong>by</strong> cross-calibrating with hybrid events. The energies obtained with both methodsare available in <strong>the</strong> Herald <strong>data</strong> set. With <strong>the</strong> FD calibration (see Figure 3.8) <strong>the</strong> energy <strong>of</strong> <strong>the</strong>Figure 3.8: Correlation between lgS 38 and lgE FD for <strong>the</strong> 661 hybrid events used in <strong>the</strong> fit. The solid lineis <strong>the</strong> best fit to <strong>the</strong> <strong>data</strong> [49].primary is calculated withE = p · (S 38 ) q . (3.8)The best fit yields p =(1.49 ± 0.06(stat) ± 0.12(syst)) × 10 17 eV and q = 1.08 ± 0.01(stat) ±0.04(syst) with a reduced * 2 <strong>of</strong> 1.1 [50].3.3.4 Fine-tuning <strong>of</strong> <strong>the</strong> LDFIn addition to <strong>the</strong> log-log parabola (Equation 3.3) two o<strong>the</strong>r LDFs describe <strong>the</strong> signal distribution.Firstly, a modified NKG-function is <strong>the</strong> standard LDF in <strong>the</strong> standard reconstruction s<strong>of</strong>tware,called Offline(S(r)=S 1000 ×r1000m) ( )- r + 700m-+#× . (3.9)1700mSecondly, an LDF obtained <strong>by</strong> <strong>the</strong> Haverah Park experiment, which was a large air shower experimentnear Leeds/UK [51] with a dense array <strong>of</strong> water Cherenkov <strong>detector</strong>s in <strong>the</strong> center, can beused. The obtained LDF for air showers isS(r)=S 1000 ×{ (( 1800r1000m) #×() -+ r4000mr1000m) -+#+rr < 800m4000mr > 800m.(3.10)
3.4 Data 25In addition to <strong>the</strong> choice <strong>of</strong> different lateral distribution functions, it is possible to use a calculatedor a fitted slope parameter - for <strong>the</strong> energy reconstruction. Equation 3.4 shows <strong>the</strong> formula, whichis used to calculate <strong>the</strong> value <strong>of</strong> <strong>the</strong> slope parameter for a given zenith angle. If a shower triggersmany stations, <strong>the</strong> slope parameter <strong>of</strong> <strong>the</strong> LDF can be fitted to <strong>the</strong> <strong>data</strong> points. In <strong>the</strong> standardreconstruction <strong>the</strong> fit is performed, if a certain number <strong>of</strong> stations, with defined distances to <strong>the</strong>shower axis, have been triggered.3.4 DataThe <strong>surface</strong> <strong>detector</strong> is operating in a stable mode since 1st January 2004 and has detected morethan 1.5 · 10 6 events, out <strong>of</strong> which more than 20000 have an energy above 3 EeV. At 3 EeV <strong>the</strong>array reaches full acceptance. Below this energy, <strong>the</strong> array is not fully efficient and <strong>the</strong> probabilityto detect an event depends <strong>of</strong> <strong>the</strong> zenith angle and <strong>the</strong> core position, in reference to <strong>the</strong> neareststation.The zenith and azimuth angle distributions are shown in Figure 3.9. The zenith angle distributiondiffers from <strong>the</strong> typical sin" cos"-distribution, as it is created without any energy cut. Due to<strong>the</strong> absorption <strong>of</strong> inclined showers, <strong>the</strong> maximum is shifted to lower zenith angles, below fullacceptance. The azimuth angle distribution is analyzed in detail and <strong>the</strong> results are presented inChapter 5.2.counts41004000hPhicounts4000035000hTheta39003000038003700250002000015000360010000350050003400-150 -100 -50 0 50 100 150.00 10 20 30 40 50 60 70 80 90"Figure 3.9: Azimuth angle distribution (left) for all events with " < 60 ◦ and zenith angle distribution(right) without any cuts.3.4.1 Variations on different time-scalesThe <strong>data</strong>, <strong>recorded</strong> <strong>by</strong> <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory, is influenced <strong>by</strong> <strong>the</strong> temperature at <strong>the</strong> groundand <strong>the</strong> conditions in <strong>the</strong> atmosphere above <strong>the</strong> array. The T1 and T2 trigger rates are monitoredcontinuously and <strong>the</strong> gains <strong>of</strong> <strong>the</strong> PMTs are adjusted to reduce temperature effects. Anyhow <strong>the</strong>ToT rates <strong>of</strong> <strong>the</strong> individual stations correlate with <strong>the</strong> temperature and <strong>the</strong> T5 trigger rate perhexagon varies from 1.1 event per day in winter, to 1.4 events per day in summer [41]. In addition,<strong>the</strong> ToT rates <strong>of</strong> <strong>the</strong> individual stations decrease with time and, thus, decrease <strong>the</strong> T5 rate <strong>of</strong> <strong>the</strong>whole array. Figure 3.10 shows <strong>the</strong> decline <strong>of</strong> <strong>the</strong> ToT rate <strong>of</strong> station 119 and <strong>the</strong> development <strong>of</strong>
26 Event reconstruction using <strong>the</strong> <strong>surface</strong> <strong>detector</strong> <strong>data</strong><strong>the</strong> T5 rate in <strong>the</strong> sub-array, which is taking <strong>data</strong> since December 2004. The reason <strong>of</strong> this agingeffect <strong>of</strong> <strong>the</strong> array has to do with <strong>the</strong> water quality in <strong>the</strong> tanks, but is not yet entirely understood.Figure 3.10: The left plot demonstrates <strong>the</strong> development <strong>of</strong> <strong>the</strong> ToT rate <strong>of</strong> <strong>the</strong> Piuquen <strong>detector</strong> sinceits deployment. The right graph shows <strong>the</strong> decreasing T5 rate <strong>of</strong> <strong>the</strong> sub-array, which isoperating since December 2004 [52].3.4.2 Attributes <strong>of</strong> <strong>the</strong> arrayThe location in <strong>the</strong> Pampa Amarilla provides almost perfect conditions for <strong>the</strong> detection <strong>of</strong> extensiveair showers. To analyze <strong>the</strong> <strong>data</strong>, collected <strong>by</strong> <strong>the</strong> <strong>surface</strong> <strong>detector</strong>, it is important to considermany <strong>of</strong> <strong>the</strong> <strong>detector</strong> characteristics.The height <strong>of</strong> <strong>the</strong> tanks is defined <strong>by</strong> <strong>the</strong> topography. The whole array is tilted, with <strong>the</strong> higheststations located in <strong>the</strong> west (see Figure 3.11 left). This causes a large scale anisotropy in <strong>the</strong> <strong>data</strong>,as <strong>the</strong> effective size <strong>of</strong> <strong>the</strong> array, seen <strong>by</strong> <strong>the</strong> shower, depends on <strong>the</strong> azimuth angle [53]. Thedifferent ground altitudes affect <strong>the</strong> energy determination as well, since <strong>the</strong> showers are detectedat a different depth, but this effect is <strong>of</strong> little relevance, as shown in [54].In addition, <strong>the</strong> grid <strong>of</strong> <strong>the</strong> stations is not perfect, as many stations had to be installed displaced,due to rivers or rocks. Figure 3.12 shows <strong>the</strong> differences in size <strong>of</strong> <strong>the</strong> triangles, formed <strong>by</strong> threeneighboring stations, from <strong>the</strong> average <strong>of</strong> 0.975km 2 . The displacements lead to irregular triggercharacteristics and have to be considered in <strong>the</strong> analysis, using events with energies below fullacceptance.Due to <strong>the</strong> large distances between <strong>the</strong> stations and wea<strong>the</strong>r conditions, which allow <strong>the</strong> accessto <strong>the</strong> array in only one third <strong>of</strong> <strong>the</strong> days, some stations show problems. The worst case is a blacktank, a station, which sends no information to <strong>the</strong> central <strong>data</strong> acquisition system. The number <strong>of</strong>black tanks varies with time around ≈ 15.For cosmic rays with energies above ≈ 30EeV, <strong>the</strong> dynode and anode PMT signals <strong>of</strong> <strong>the</strong> closestto-<strong>the</strong>-coretanks are saturated in more than 50% <strong>of</strong> <strong>the</strong> events. A method has been developed torecover <strong>the</strong>se signals. The effect on S(1000) is smaller than 1% at low energies and about 3% athigh values <strong>of</strong> S(1000) [55].An occurring and not yet solved problem is <strong>the</strong> so-called raining behavior <strong>of</strong> approximate half<strong>of</strong> <strong>the</strong> PMTs [56]. In <strong>the</strong> summer <strong>the</strong> PMTs, marked in Figure 3.11 right, show a drop <strong>of</strong> <strong>the</strong>VEM value <strong>of</strong> <strong>the</strong> order <strong>of</strong> ≤ 30% and an increase <strong>of</strong> <strong>the</strong> ToT rate. The influence <strong>of</strong> this effect islimited to <strong>the</strong> acceptance <strong>of</strong> <strong>the</strong> <strong>detector</strong> and does not affect <strong>the</strong> reconstructed energies and arrivaldirections <strong>of</strong> <strong>the</strong> events.
3.4 Data 27altitude1005010050north - south40000300002000000-5010000-100-150-500-200300002000010000north -south0-10000-20000-30000 -20000-10000 0east - west300002000010000-100-150-10000-20000-30000-40000 -30000 -20000 -10000 0 10000 20000 30000east - westFigure 3.11: Left: The altitude <strong>of</strong> <strong>the</strong> stations in meter in reference to <strong>the</strong> center <strong>of</strong> <strong>the</strong> array. Right:Stations, which had one or more raining PMTs in March 2008, are visualized with asterisks.number <strong>of</strong> triangles210Entries 2638Mean -1.435e-13RMS 1.459101-15 -10 -5 0 5deviation / %Figure 3.12: Histogram <strong>of</strong> <strong>the</strong> triangle sizes for <strong>the</strong> <strong>surface</strong> <strong>detector</strong>. The deviations in percent are caused<strong>by</strong> displaced stations.
Stability <strong>of</strong> <strong>the</strong> reconstructionChapter 4Stability <strong>of</strong> <strong>the</strong> reconstructionThe accuracy and stability <strong>of</strong> <strong>the</strong> reconstruction algorithm are essential requirements for discoverieswith <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory. The goal <strong>of</strong> <strong>the</strong> studies presented here is to check <strong>the</strong>stability <strong>of</strong> <strong>the</strong> CDAS online reconstruction algorithm (see Chapter 3.3.1) for cosmic rays withE > 25EeV.The events are reconstructed with modified sets <strong>of</strong> <strong>detector</strong>s. The reconstructed energy and <strong>the</strong>arrival direction <strong>of</strong> <strong>the</strong> standard reconstruction are taken as a reference and compared to <strong>the</strong> results<strong>of</strong> <strong>the</strong> modified reconstructions. Leaving out individual <strong>surface</strong> <strong>detector</strong> stations in <strong>the</strong> reconstructionsimulates non-operational stations. In order to assess <strong>the</strong> influence <strong>of</strong> <strong>the</strong> border <strong>of</strong> <strong>the</strong> array,<strong>detector</strong>s in certain configurations are left out. In fur<strong>the</strong>r steps <strong>the</strong> impact <strong>of</strong> <strong>the</strong> asymmetry correctionis evaluated and a study is performed to determine <strong>the</strong> optimum ground parameter r opt forextensive air showers with energies above 25 EeV. The optimum ground parameter is <strong>the</strong> distancefrom <strong>the</strong> shower axis, where <strong>the</strong> fluctuations <strong>of</strong> <strong>the</strong> signal S(r opt ) have <strong>the</strong> minimum. In <strong>the</strong> lastpart, less dense arrays are generated <strong>by</strong> leaving out whole sets <strong>of</strong> <strong>detector</strong>s. The results give hintswith respect to <strong>Auger</strong> North, as <strong>the</strong> spacing between <strong>the</strong> <strong>surface</strong> stations will be wider <strong>the</strong>re.4.1 Method and <strong>data</strong> setThe reconstruction is performed using CDAS version v4r6p2. In <strong>the</strong> CDAS reconstruction code,all triggered stations used for <strong>the</strong> reconstruction are classified as selected stations. In <strong>the</strong> firstpart <strong>of</strong> <strong>the</strong> analysis, <strong>the</strong> reconstruction is performed repeatedly for each event, each time leavingout one selected station. The results are categorized according to <strong>the</strong> distance between <strong>the</strong> coreand <strong>the</strong> station, which has been left out in <strong>the</strong> reconstruction: <strong>the</strong> central tank, a tank <strong>of</strong> <strong>the</strong> firstcrown, <strong>of</strong> <strong>the</strong> second crown or a tank which is located far<strong>the</strong>r away (see Figure 4.1). The reconstructedenergy and <strong>the</strong> arrival direction <strong>of</strong> <strong>the</strong> standard reconstruction are taken as a reference andcompared to <strong>the</strong> results <strong>of</strong> <strong>the</strong> modified reconstructions. For example, for an event with twelvetriggered stations, twelve tests are performed and twelve deviations in energy and arrival directionare obtained. In those parts <strong>of</strong> <strong>the</strong> analysis, where more <strong>the</strong>n a <strong>detector</strong> is excluded, <strong>the</strong> number <strong>of</strong>tests per event depends on <strong>the</strong> number <strong>of</strong> selected <strong>detector</strong> sets.For <strong>the</strong> analysis, all events <strong>recorded</strong> <strong>by</strong> <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory between 1 January 2004 and4 April 2008, with a reconstructed zenith angle smaller than 60 ◦ , are used. In <strong>the</strong> reconstructionalgorithm, different LDF functions can be selected to determine S(1000), <strong>the</strong> signal at 1000 m coredistance (see Chapter 3.3.4). In addition, <strong>the</strong> slope parameter can be determined in different ways.In CDAS, log-log parabolas are used. In <strong>the</strong> standard option “LDFOptimal”, <strong>the</strong> slope parameter
4.2 Reconstruction without individual stations 29Figure 4.1: The station with <strong>the</strong> highest signal is called central tank. It is surrounded <strong>by</strong> <strong>the</strong> six stations <strong>of</strong><strong>the</strong> first crown. The second crown consists <strong>of</strong> <strong>the</strong> twelve stations surrounding <strong>the</strong> first crown.Crown n is formed <strong>by</strong> 6 · n stations.- is extracted from <strong>the</strong> LDF fit, if enough stations are available in predefined bins <strong>of</strong> distance to<strong>the</strong> shower axis. O<strong>the</strong>rwise, - is calculated from a function depending on <strong>the</strong> zenith angle. In <strong>the</strong>analysis presented here, <strong>the</strong> use <strong>of</strong> <strong>the</strong> “LDFOptimal” option generates a systematic error. If thiscriterion <strong>of</strong> enough triggered stations in <strong>the</strong> predefined bins is fulfilled for an event, <strong>the</strong> exclusion<strong>of</strong> a <strong>detector</strong> may cause, that it is not satisfied any longer. In this case, <strong>the</strong> energy would first becalculated with a fitted - and after <strong>the</strong> removal with <strong>the</strong> calculated slope parameter. To avoid this,all events are reconstructed with <strong>the</strong> calculated -.The deviation in energy is always given as <strong>the</strong> percentage <strong>of</strong> <strong>the</strong> energy and is calculated from <strong>the</strong>formula:(EE = E Original − E Modified.E OriginalThe arrival direction is described <strong>by</strong> two angles, <strong>the</strong> zenith angle " and <strong>the</strong> azimuth angle ). Foreach event <strong>the</strong>se two angles define a vector, which points back to <strong>the</strong> incoming direction <strong>of</strong> <strong>the</strong>primary cosmic ray. The deviations in arrival direction are all positive, as <strong>the</strong>y are defined as <strong>the</strong>space angles between <strong>the</strong> two vectors, that are obtained <strong>by</strong> <strong>the</strong> reconstructions using <strong>the</strong> originaland <strong>the</strong> modified set <strong>of</strong> <strong>detector</strong>s, respectively.4.2 Reconstruction without individual stationsEvents with energies above 10 EeV trigger at least six <strong>surface</strong> stations and events with E > 25EeVtrigger seven <strong>surface</strong> stations (one unitary cell) or more, if <strong>the</strong> core positions are not near<strong>by</strong> <strong>the</strong>border <strong>of</strong> <strong>the</strong> array. The main assumption is, that <strong>the</strong> removal <strong>of</strong> one <strong>detector</strong> station should notchange fundamentally <strong>the</strong> results <strong>of</strong> <strong>the</strong> reconstruction.4.2.1 Stability <strong>of</strong> events with E > 57EeVEvents with energies above a few tens <strong>of</strong> EeV have a large rigidity and <strong>the</strong> search for correlationswith point sources is possible. The events with E > 57EeV <strong>recorded</strong> <strong>by</strong> <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong>observatory show correlations with near<strong>by</strong> AGN (see Chapter 2.5). Above this energy 33 eventshave been detected. Altoge<strong>the</strong>r, <strong>the</strong>y triggered 514 <strong>surface</strong> <strong>detector</strong> stations. Figure 4.2 shows<strong>the</strong> normalized deviations in energy and space angle between <strong>the</strong> original and <strong>the</strong> modifiedreconstruction. The RMS values <strong>of</strong> <strong>the</strong> distributions <strong>of</strong> <strong>the</strong> individual crowns are given in Table
30 Stability <strong>of</strong> <strong>the</strong> reconstructioncounts210Entries 514Mean 0.1092RMS 2.385Underflow 0Overflow 0counts210Entries 514Mean 0.1122RMS 0.1244Underflow 0Overflow 0101011-25 -20 -15 -10 -5 0 5 10 15 20 25Difference in energy [percent]0 0.2 0.4 0.6 0.8 1 1.2Difference in space angle [degree]Figure 4.2: Differences in energy (left) and space angle (right) between <strong>the</strong> original and modified reconstructionsfor events with E > 57EeV.4.1 and <strong>the</strong> RMS for all reconstructions is displayed in <strong>the</strong> legend <strong>of</strong> Figure 4.2. For 8 out <strong>of</strong><strong>the</strong> 514 modified reconstructions <strong>the</strong> deviations in energy are larger than 10% (see Table 4.2).Stations leading to a change <strong>of</strong> <strong>the</strong> arrival direction <strong>of</strong> more than 0.6 ◦ are listed in Table 4.3. Thethresholds <strong>of</strong> 10% and 0.6 ◦ are chosen, as for such events, <strong>the</strong> deviations are a factor <strong>of</strong> 1.5 largerthan <strong>the</strong> errors <strong>of</strong> <strong>the</strong> reconstructed S(1000) and space angle (see Figure 4.3).counts80 Entries 369 45 Entries 36970counts4060504030201000 2 4 6 8 10 12 14( S(1000) [percent]353025201510500 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Space angle [degree]Figure 4.3: (S(1000) (left) and space angle between (),") and () + ()," + (") (right) for T5 triggerevents with E > 57EeV.The central stations and <strong>the</strong> stations <strong>of</strong> <strong>the</strong> first crown measure <strong>the</strong> largest signals. For thisreason <strong>the</strong> relative errors <strong>of</strong> <strong>the</strong>ir signals are smaller and <strong>the</strong>ir weighting in <strong>the</strong> LDF fit is higher,than for stations with a larger distance to <strong>the</strong> shower axis. The removal <strong>of</strong> a station <strong>of</strong> <strong>the</strong> unitarycell has <strong>the</strong>refore a stronger influence on <strong>the</strong> reconstruction <strong>of</strong> <strong>the</strong> energy than <strong>the</strong> removal <strong>of</strong> moredistant <strong>detector</strong>s. The obtained differences in energy show exactly this behavior. The removal <strong>of</strong>stations <strong>of</strong> <strong>the</strong> unitary cell leads to deviations up to 15% and that <strong>of</strong> stations far<strong>the</strong>r <strong>of</strong>f leads todifferences <strong>of</strong> only up to 3%.
4.2 Reconstruction without individual stations 31crown 0 1 2 > 2energy mean -0.63 0.38 0.04 -0,01energy RMS 5.18 3.18 0.47 0.29space angle RMS 0.25 0.22 0.11 0.10Table 4.1: <strong>Properties</strong> <strong>of</strong> <strong>the</strong> energy and space angle distributions shown in Figure 4.2.event ID tank ID - crown (deviation in %)200629604873 370 - 1 (10,8%)200629900147 1061 - 1 (−11.5%), 1068 - 0 (−11.0%)200723401180 383 - 0 (10.1%)200729501686 145 - 0 (−12.3%), 149 - 1 (−13.8%), 192 - 1 (−10.6%)200734500536 1483 - 1 (11.2%)Table 4.2: Deviation in energy between <strong>the</strong> original and <strong>the</strong> modified reconstruction. All events for which<strong>the</strong> modification leads to a deviation in energy larger than 10% are listed. The number after <strong>the</strong>hyphen denotes <strong>the</strong> crown (0 = central station).event ID tank ID - crown (deviation in ◦ )200508101056 499 - 1 (0.65 ◦ )200529501100 950 - 0 (0.63 ◦ ), 957 - 1 (0.69 ◦ )200530605022 562 - 1 (0.70 ◦ )200605500287 133 - 1 (0.67 ◦ )200729501686 149 - 1 (0.69 ◦ )Table 4.3: Angular deviation between <strong>the</strong> original and <strong>the</strong> modified reconstruction. All events, for which<strong>the</strong> modification leads to a deviation larger than 0.6 ◦ , are listed.
32 Stability <strong>of</strong> <strong>the</strong> reconstructionThe removal <strong>of</strong> <strong>the</strong> central station decreases <strong>the</strong> reconstructed energy in average <strong>by</strong> 0.63% (seeTable 4.1) mainly due to saturation effects. For stations close to <strong>the</strong> shower core (< 100m forshowers in <strong>the</strong> EeV range and a few hundred meters for showers at higher energy) most PMT signalsare saturated. The integrated signal is smaller and <strong>the</strong> LDF is pulled down at small distancesto <strong>the</strong> shower axis. To avoid this, a saturation correction is implemented in <strong>the</strong> reconstructionalgorithm. The results show, that <strong>the</strong> correction can be improved for <strong>the</strong> highest-energy cosmicrays.For <strong>the</strong> differences in arrival direction <strong>the</strong> statement is similar, but not as distinct as for <strong>the</strong> energies.The angular deviations decrease with increasing distance <strong>of</strong> <strong>the</strong> removed station to <strong>the</strong>shower axis. In <strong>the</strong> angular reconstruction, <strong>the</strong> arrival direction is calculated from <strong>the</strong> positions<strong>of</strong> <strong>the</strong> tanks and <strong>the</strong> arrival times <strong>of</strong> <strong>the</strong> signals detected <strong>by</strong> <strong>the</strong>m. The errors <strong>of</strong> <strong>the</strong> arrival times, ti are estimated from <strong>the</strong> time residuals <strong>of</strong> <strong>the</strong> shower fit. At <strong>the</strong> core , ti is about 20ns [43] andit increases with <strong>the</strong> core distance r. In <strong>the</strong> reconstruction code <strong>the</strong> following parametrization isincluded:, t = 22ns + 0.03 ns · r with r in meter. (4.1)mThe maximum space angle differences for <strong>the</strong> selected events are 0.7 ◦ for stations <strong>of</strong> <strong>the</strong> unitarycell and up to 0.4 ◦ for stations far<strong>the</strong>r <strong>of</strong>f.The variations in energy and arrival direction are caused <strong>by</strong> changes in <strong>the</strong> LDF and <strong>the</strong> showerfront fit, as well as shifts <strong>of</strong> <strong>the</strong> core position, after leaving out individual stations. Figure 4.4shows <strong>the</strong> displacements <strong>of</strong> <strong>the</strong> cores. For <strong>the</strong> analyzed events, <strong>the</strong> displacements reach up tocounts102Entries 514Mean 7.555RMS 14.46Underflow 0Overflow 01010 20 40 60 80 100 120 140Displacement <strong>of</strong> core position [m]Figure 4.4: Shifts <strong>of</strong> <strong>the</strong> reconstructed core position between original and modified reconstruction forevents with E > 57EeV100 m.The analysis presented so far gives evidence that <strong>the</strong> CDAS reconstruction <strong>of</strong> ultra high energyevents is very robust against <strong>the</strong> removal <strong>of</strong> individual <strong>detector</strong>s. The influence <strong>of</strong> a single failingtank is negligible for <strong>the</strong> detection <strong>of</strong> particles with energies above 57EeV. No station removalinduces an angular deviation <strong>of</strong> more than 1 ◦ [31], which corresponds to <strong>the</strong> estimated resolution<strong>of</strong> <strong>the</strong> SD. The absolute energy has an uncertainty <strong>of</strong> 22% for this energy range [31] and alldeviations are below this systematic uncertainty. There isno event, for which excluding one station
4.2 Reconstruction without individual stations 33from <strong>the</strong> reconstruction leads to an energy below 57EeV, <strong>the</strong> current energy cut for <strong>the</strong> search forcorrelations with source candidates. There is also no event with an reconstructed energy below57EeV, for which <strong>the</strong> removal <strong>of</strong> a single station leads to an energy above <strong>the</strong> energy threshold.4.2.2 Stability <strong>of</strong> events with E > 25EeVThe same test as described in <strong>the</strong> previous section is applied to all events above 25 EeV. In a firsttest, all events are used, regardless whe<strong>the</strong>r <strong>the</strong>y satisfy <strong>the</strong> T5 trigger condition or not. In a secondstep, only events satisfying <strong>the</strong> ICRC-T5 trigger are used. An event is classified as a ICRC-T5event, if five stations <strong>of</strong> <strong>the</strong> first crown were active at <strong>the</strong> time <strong>of</strong> detection and if <strong>the</strong> reconstructedcore position is inside an equilateral triangle <strong>of</strong> active <strong>detector</strong>s. In <strong>the</strong> third step, <strong>the</strong> strict-T5trigger condition is required. The station with <strong>the</strong> highest signal has to be surrounded <strong>by</strong> six activestations. Figure 4.5 shows, from top to bottom: all events (including non-T5 events), ICRC-T5events and strict-T5 events. With each quality cut, <strong>the</strong> number <strong>of</strong> events decreases and <strong>the</strong> robustness<strong>of</strong> <strong>the</strong> remaining events increases. This is clearly visible in Table 4.1. The RMS values <strong>of</strong>T5 cut crown 0 1 2 > 2no cutenergy 10.04 7.71 3.76 2.71space angle 0.45 0.34 0.21 0.20ICRC-T5energy 7.88 5.51 1.38 1.41space angle 0.42 0.30 0.20 0.19strict-T5energy 7.51 4.22 0.96 1.42space angle 0.41 0.29 0.19 0.19Table 4.4: RMS values <strong>of</strong> <strong>the</strong> energy and space angle distributions shown in figure 4.5.<strong>the</strong> histograms shown in Figure 4.5 become smaller with increasing core distance and with eachquality cut applied.For all events, including those which fulfill no T5 trigger condition, 3% <strong>of</strong> <strong>the</strong> tests lead to deviationslarger than 22%, <strong>the</strong> uncertainty <strong>of</strong> <strong>the</strong> absolute energy scale. For non-T5 events, <strong>the</strong> removal<strong>of</strong> one tank results in a reconstruction without at least two stations, <strong>the</strong> subtracted and <strong>the</strong> inactiveone. If <strong>the</strong>se missing <strong>detector</strong>s are neighbors, <strong>the</strong> core position, <strong>the</strong> LDF and hence <strong>the</strong> arrivaldirection and <strong>the</strong> energy are affected heavily.A check <strong>of</strong> all strict-T5 events shows, that deviations above 22% in energy (19 <strong>of</strong> 4650 modifiedreconstructions) and 1.6 ◦ in space angle (45 <strong>of</strong> 4650 modified reconstructions) occur, if at leastone <strong>of</strong> <strong>the</strong> following conditions is fulfilled:• one <strong>detector</strong> is saturated,• at least in one <strong>detector</strong> <strong>the</strong> signals <strong>of</strong> <strong>the</strong> three PMTs differ in more than 20%.To get a more quantitative result, Gaussian fits to <strong>the</strong> distributions <strong>of</strong> <strong>the</strong> strict-T5 events areperformed. As usual, <strong>the</strong> assignment <strong>of</strong> <strong>the</strong> stations to <strong>the</strong> crowns are considered and in additiondifferent energy cuts are implemented. The distributions <strong>of</strong> all events above four different energythresholds (E > 25EeV, 35EeV, 45EeV and 55EeV) are fitted. Table 4.5 shows all mean values Eand standard deviations , <strong>of</strong> <strong>the</strong> fits. The mean values E are <strong>the</strong> average differences <strong>of</strong> <strong>the</strong> energy,reconstructed with <strong>the</strong> original and modified set <strong>of</strong> <strong>detector</strong>s. The removal <strong>of</strong> <strong>the</strong> central stationincreases <strong>the</strong> energy. Omitting stations far<strong>the</strong>r <strong>of</strong>f induces a minimal shift to lower energies.
34 Stability <strong>of</strong> <strong>the</strong> reconstructioncounts310Entries 6943Mean 0.3785RMS 6.43Underflow 60Overflow 43counts310Entries 6943Mean 0.3261RMS 0.7285Underflow 0Overflow 22210210101011-60 -40 -20 0 20 40 60Difference in energy [percent]0 1 2 3 4 5 6 7 8 9 10Difference in space angle [degree]counts310Entries 5740Mean 0.166RMS 4.47Underflow 1Overflow 9counts310Entries 5740Mean 0.2259RMS 0.4422Underflow 0Overflow 721021010101-60 -40 -20 0 20 40 60Difference in energy [percent]10 1 2 3 4 5 6 7 8 9 10Difference in space angle [degree]counts310Entries 4650Mean -0.01543RMS 3.681Underflow 1Overflow 3counts310Entries 4650Mean 0.2019RMS 0.3334Underflow 0Overflow 3210210101011-60 -40 -20 0 20 40 60Difference in energy [percent]0 1 2 3 4 5 6 7 8 9 10Difference in space angle [degree]Figure 4.5: Differences in energy (left) and space angle (right) for all events above 25 EeV (top), ICRCT5events (middle) and strict-T5 events (bottom).
4.2 Reconstruction without individual stations 35crown E > 25EeV E > 35EeV E > 45EeV E > 55EeV0 E −1.40 ± 0.32 −1.13 ± 0.38 −0.74 ± 0.45 −0.33 ± 0.810 , 5.9 ± 0.24 5.43 ± 0.32 4.74 ± 0.58 5.57 ± 0.931 E 0.12 ± 0.04 0.14 ± 0.04 0.12 ± 0.06 0.04 ± 0.071 , 1.12 ± 0.02 1.18 ± 0.03 1.38 ± 0.08 1.23 ± 0.072 E 0.19 ± 0.04 0.18 ± 0.05 0.04 ± 0.07 0.11 ± 0.042 , 0.79 ± 0.02 0.80 ± 0.02 0.79 ± 0.02 0.77 ± 0.02> 2 E 0.11 ± 0.04 0.07 ± 0.04 0.03 ± 0.05 −0.09 ± 0.06> 2 , 0.77 ± 0.02 0.77 ± 0.02 0.78 ± 0.02 0.76 ± 0.03Table 4.5: Values <strong>of</strong> <strong>the</strong> Gaussian fits to <strong>the</strong> energy histograms.The Gaussian fits show <strong>the</strong> strong correlation between <strong>the</strong> stations core distances and <strong>the</strong>irimpact on <strong>the</strong> reconstructed energies and arrival directions. For <strong>the</strong> station with <strong>the</strong> highest signal, is around 5%, for <strong>the</strong> first crown it is around 1.2% and for <strong>the</strong> far-<strong>of</strong>f <strong>detector</strong>s it is close to0.8%. Fur<strong>the</strong>rmore, <strong>the</strong> fit results show <strong>the</strong> independence <strong>of</strong> <strong>the</strong> , and E values from <strong>the</strong> energythreshold. Never<strong>the</strong>less, <strong>the</strong> comparison <strong>of</strong> <strong>the</strong> RMS values <strong>of</strong> Figure 4.2 and 4.5 (bottom) showsa smaller number <strong>of</strong> excessive deviations at high energies. This is no contradiction, as <strong>the</strong> RMSvalue is more sensitive to outliers than ,.4.2.3 Test <strong>of</strong> <strong>the</strong> asymmetry correctionIn this part, all strict-T5 events with zenith angles between 45 ◦ and 60 ◦ are analyzed. In orderto find out if <strong>the</strong>se events are responsible for <strong>the</strong> large deviations, a comparison <strong>of</strong> <strong>the</strong> results excludingei<strong>the</strong>r early or late triggered stations from <strong>the</strong> reconstruction has been performed. This isa check <strong>of</strong> <strong>the</strong> forward-backward correction, which is implemented in <strong>the</strong> CDAS reconstructionalgorithm (see Chapter 3.3.3). For <strong>the</strong> early part, all stations located in a range <strong>of</strong> ) ± 30 ◦ andfor <strong>the</strong> late part, all stations in <strong>the</strong> range <strong>of</strong> () + 180 ◦ ) ± 30 ◦ are selected. The analysis distinguishesbetween <strong>detector</strong>s <strong>of</strong> <strong>the</strong> first crown and those far<strong>the</strong>r away. Figure 4.6 shows <strong>the</strong> fitteddistributions and Table 4.6 lists <strong>the</strong> parameters <strong>of</strong> <strong>the</strong> Gaussian fits.Fit x ,early and 1. crown 0.30 ± 0.24 1.56 ± 0.39early and > 1. crown −0.21 ± 0.04 0.48 ± 0.04late and 1. crown 1.25 ± 0.26 2.20 ± 0.28late and > 1. crown 0.11 ± 0.04 0.62 ± 0.04Table 4.6: Values <strong>of</strong> <strong>the</strong> fits to <strong>the</strong> distributions for <strong>the</strong> early and late part <strong>of</strong> <strong>the</strong> shower.For <strong>the</strong> early and <strong>the</strong> late part <strong>of</strong> <strong>the</strong> showers no bias is visible. Nei<strong>the</strong>r <strong>the</strong> mean nor <strong>the</strong> ,values have a systematic <strong>of</strong>fset. There is no hint <strong>of</strong> a problem with <strong>the</strong> correction <strong>of</strong> <strong>the</strong> forwardbackwardasymmetry.
36 Stability <strong>of</strong> <strong>the</strong> reconstructioncounts12108Entries 105Mean 0.4769RMS 4.278Underflow 0Overflow 0counts120 Entries 283Mean -0.1191100RMS 1.23Underflow 0Overflow 0806604402200-25 -20 -15 -10 -5 0 5 10 15 20 25Difference in energy [%]0-25 -20 -15 -10 -5 0 5 10 15 20 25Difference in energy [%]counts10 Entries 105Mean -0.008773RMS 5.1368Underflow 0Overflow 06counts90 Entries 304Mean 0.202780RMS 1.03670Underflow 0Overflow 0605044030220100-25 -20 -15 -10 -5 0 5 10 15 20 25Difference in energy [%]0-25 -20 -15 -10 -5 0 5 10 15 20 25Difference in energy [%]Figure 4.6: Deviations in energy resulting from excluding individual stations <strong>of</strong> <strong>the</strong> first crown (left) andfar<strong>the</strong>r <strong>of</strong>f (right) for <strong>the</strong> early (top) and late part (bottom) <strong>of</strong> <strong>the</strong> showers.4.2.4 The optimum ground parameterIn order to reconstruct <strong>the</strong> energy <strong>of</strong> primary cosmic rays with <strong>the</strong> <strong>surface</strong> <strong>detector</strong>, <strong>the</strong> LDF isfitted to <strong>the</strong> signals <strong>of</strong> <strong>the</strong> stations and <strong>the</strong> signal S(1000), at a distance <strong>of</strong> 1000 m from <strong>the</strong> showeraxis, is determined. Monte Carlo simulations have shown, that <strong>the</strong> shower-<strong>by</strong>-shower fluctuationsare minimized for a distance <strong>of</strong> 1000 m from <strong>the</strong> shower axis, in <strong>the</strong> energy range <strong>of</strong> <strong>the</strong> <strong>Pierre</strong><strong>Auger</strong> observatory [57]. For <strong>the</strong> highest-energy events and for events with saturated stations, <strong>the</strong>optimum ground parameter r opt differs from 1000 m. Studies presented in [58] and [59] show, thatr opt increases for increasing energies.In Figure 4.7, <strong>the</strong> deviations in S(1000) are compared to <strong>the</strong> deviations in S(1600) for all strict-T5events above 25 EeV and with " < 60 ◦ . The LDF fit is performed with a fitted slope parameter, asfor a fixed - <strong>the</strong> variations <strong>of</strong> S(1000) and S(1600) are <strong>the</strong> same. The selection <strong>of</strong> <strong>the</strong> fitted slopeparameter can be used, as <strong>the</strong> strict-T5 events have enough triggered stations for a reliable fit.The mean deviations <strong>of</strong> <strong>the</strong> S(1600) values are much smaller than for S(1000). The RMS valuedecreases from 6.0 to 3.2 and <strong>the</strong> mean value increases from −0.58 to 0.75. For S(1000), <strong>the</strong>removal <strong>of</strong> <strong>the</strong> central station leads to an increase <strong>of</strong> S(1000) up to 60%. This is caused <strong>by</strong>saturated stations, which pull <strong>the</strong> LDF down at distances near <strong>the</strong> core. To illustrate this fur<strong>the</strong>r,only events with saturated stations are used to create Figure 4.8. The removal <strong>of</strong> <strong>the</strong> central stationleads to an increase <strong>of</strong> S(1000) and to a decrease <strong>of</strong> S(1600) in average. For an optimum groundparameter <strong>the</strong> mean value <strong>of</strong> such a distribution should be zero and <strong>the</strong> RMS should be as smallas possible. The estimation <strong>of</strong> a mean value close to zero is based on <strong>the</strong> assumption <strong>of</strong> <strong>the</strong> sameprobability for an increase or decrease <strong>of</strong> <strong>the</strong> energy, if reconstructing without individual stations.In <strong>the</strong> next step, <strong>the</strong> same procedure is applied again to all events above 25 EeV, excluding allevents with saturated stations. In <strong>the</strong> histograms in Figure 4.10, <strong>the</strong> deviations from S(1000) to
4.2 Reconstruction without individual stations 37counts310Entries 4650Mean -0.584RMS 6.008Underflow 15Overflow 1counts310Entries 4650Mean 0.7502RMS 3.227Underflow 2Overflow 4210210101011-60 -40 -20 0 20 40 60Difference in S1000 [percent]-60 -40 -20 0 20 40 60Difference in S1600 [percent]Figure 4.7: Deviations in S(1000) (left) and S(1600) (right) resulting from excluding individual stationsbefore <strong>the</strong> reconstruction.counts310Entries 1678Mean -0.5705RMS 7.437Underflow 10Overflow 1counts310Entries 1678Mean 0.8254RMS 3.631Underflow 0Overflow 2210210101011-60 -40 -20 0 20 40 60Difference in S1000 [percent]-60 -40 -20 0 20 40 60Difference in S1600 [percent]Figure 4.8: Deviations in S(1000) (left) and S(1600) (right) resulting from excluding individual stationsbefore <strong>the</strong> reconstruction from events with saturated <strong>detector</strong>s.
38 Stability <strong>of</strong> <strong>the</strong> reconstructionS(1800) are shown in steps <strong>of</strong> 50 m, each time leaving out <strong>the</strong> central station. For each groundparameter, <strong>the</strong> mean and <strong>the</strong> RMS <strong>of</strong> <strong>the</strong> histogram is calculated. The development <strong>of</strong> <strong>the</strong>se valueswith increasing ground parameter are shown in Figure 4.9.RMS values <strong>of</strong> energy difference distributions14121086421000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Mean values <strong>of</strong> energy difference distributions420-2-4-6-8-101000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Figure 4.9: RMS (left) and mean values (right) <strong>of</strong> <strong>the</strong> histograms shown in Figure 4.10.The mean becomes zero for S(1500) and <strong>the</strong> RMS becomes minimal at <strong>the</strong> same distanceto <strong>the</strong> core. The optimum ground parameter seems to be found, but <strong>the</strong> removal <strong>of</strong> <strong>the</strong> centralstations induces a systematic bias. The core position is calculated as <strong>the</strong> barycenter <strong>of</strong> <strong>the</strong> signals<strong>of</strong> <strong>the</strong> <strong>surface</strong> <strong>detector</strong> stations. The three stations, which measure <strong>the</strong> highest signals, form atriangle, which contains <strong>the</strong> shower core. The subtraction <strong>of</strong> a station, especially <strong>the</strong> one with <strong>the</strong>highest signal, leads to a displacement <strong>of</strong> <strong>the</strong> core (see Figure 4.11 left). The movement <strong>of</strong> <strong>the</strong>core changes <strong>the</strong> distances to <strong>the</strong> shower axis for all o<strong>the</strong>r stations. For <strong>the</strong> two stations, with <strong>the</strong>second and third highest signal, <strong>the</strong> core distances become smaller, for <strong>the</strong> o<strong>the</strong>r four stations <strong>of</strong><strong>the</strong> first crown, <strong>the</strong> core distances increase. The arrows in Figure 4.11 (right) illustrate <strong>the</strong> shifts.The LDF fit <strong>of</strong> <strong>the</strong> modified set <strong>of</strong> <strong>detector</strong> signals results in higher signals at small core distancesand smaller signals at larger distances. This is exactly <strong>the</strong> behavior, which can be seen in Figures4.10 and 4.9. An LDF fitted with all stations and one fitted without <strong>the</strong> central station are differentwith respect to <strong>the</strong> slope parameter. The differences between <strong>the</strong> reconstructions become minimalat <strong>the</strong> intersection point <strong>of</strong> <strong>the</strong> different LDFs, which is at a distance <strong>of</strong> ≈ 1500m.To reduce <strong>the</strong> impact <strong>of</strong> <strong>the</strong> movement <strong>of</strong> <strong>the</strong> core, <strong>the</strong> same test is performed <strong>by</strong> eliminatingstations from <strong>the</strong> first crown. For each event, <strong>the</strong> reconstruction is performed six times, each timeleaving out one station <strong>of</strong> <strong>the</strong> first crown. The movements <strong>of</strong> <strong>the</strong> cores are <strong>of</strong> <strong>the</strong> same order <strong>of</strong>magnitude as for <strong>the</strong> central stations (see Figure 4.4), but <strong>the</strong> six removals per event result in sixdislocations in different directions. It is no longer valid, that <strong>the</strong> core distances <strong>of</strong> <strong>the</strong> stations with<strong>the</strong> second and third highest signals always decrease.To check <strong>the</strong> statement, that <strong>the</strong> optimum ground parameter depends on <strong>the</strong> energy [58], <strong>the</strong> eventsare divided into three energy bins: 25EeV < E ≤ 30EeV, 30EeV < E ≤ 40EeV and E > 40EeV.The same type <strong>of</strong> histograms as in Figure 4.10 are plotted for <strong>the</strong>se energy bins leaving out <strong>the</strong>central station and stations <strong>of</strong> <strong>the</strong> first crown. Figure 4.12 shows <strong>the</strong> development <strong>of</strong> <strong>the</strong> RMS andmean values <strong>of</strong> <strong>the</strong> distributions.The points <strong>of</strong> interest (minimum RMS and mean value equal to zero) are shifted to smaller
4.2 Reconstruction without individual stations 392222Energy101010101111-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 602222101010101111-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 602222101010101111-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 602222101010101111-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60-60 -40 -20 0 20 40 60Figure 4.10: Deviations in S(r) <strong>by</strong> comparing <strong>the</strong> signals <strong>of</strong> <strong>the</strong> events above 25 EeV reconstructed withall stations and without <strong>the</strong> central station. In <strong>the</strong> left plot <strong>of</strong> <strong>the</strong> first line, r is equal to 1000 mand increases <strong>by</strong> 50 m with each histogram up to 1800 m in <strong>the</strong> last histogram on <strong>the</strong> right in<strong>the</strong> bottom row.
40 Stability <strong>of</strong> <strong>the</strong> reconstructionFigure 4.11: Direction <strong>of</strong> <strong>the</strong> core displacement after <strong>the</strong> removal <strong>of</strong> <strong>the</strong> central station (left) and <strong>the</strong>influence on <strong>the</strong> core distances for <strong>the</strong> o<strong>the</strong>r stations (right).distances for <strong>the</strong> removal <strong>of</strong> stations <strong>of</strong> <strong>the</strong> first crown. It has been explained, that <strong>the</strong> differencesin <strong>the</strong> minima are due to <strong>the</strong> shifts, caused <strong>by</strong> <strong>the</strong> displacements <strong>of</strong> <strong>the</strong> core positions, for <strong>the</strong> reconstructionsexcluding <strong>the</strong> central station. Fur<strong>the</strong>rmore, <strong>the</strong> choice <strong>of</strong> a ground parameter largerthan 1000 m improves <strong>the</strong> reconstruction for events with E > 25EeV. The optimum ground parameterincreases with increasing energy. Besides this qualitative results, <strong>the</strong> determination <strong>of</strong> <strong>the</strong>optimum ground parameter is difficult with this method. A clue is given <strong>by</strong> <strong>the</strong> mean values <strong>of</strong> <strong>the</strong>distributions, generated <strong>by</strong> alternatively leaving out <strong>the</strong> stations <strong>of</strong> <strong>the</strong> first crown. A mean value<strong>of</strong> zero implies that positive and negative deviations are <strong>of</strong> <strong>the</strong> same frequency. For <strong>the</strong> selectedenergy ranges this yields <strong>the</strong> optimum ground parameters listed in Table 4.7.Energy range25EeV < E < 30EeV30EeV < E < 40EeVE > 40EeVr opt1100 m1200 m1250 mTable 4.7: Optimum ground parameters determined <strong>by</strong> reconstructing events without individual stations<strong>of</strong> <strong>the</strong> first crown.4.3 Reconstruction without sets <strong>of</strong> <strong>detector</strong>s4.3.1 Reconstruction with <strong>the</strong> unitary cell onlyThe removal <strong>of</strong> individual stations <strong>of</strong> <strong>the</strong> second crown or far<strong>the</strong>r away changes <strong>the</strong> energy <strong>by</strong>less than 2% for events with energies above 57 EeV. For events with energies down to 25 EeV <strong>the</strong>differences remain in <strong>the</strong> same region. In an additional test, <strong>the</strong> results <strong>of</strong> <strong>the</strong> original reconstructionare compared with <strong>the</strong> values obtained <strong>by</strong> reconstructing <strong>the</strong> showers with <strong>the</strong> unitary cellonly. The test is performed for all events with energies above 57 EeV and all strict-T5 events withE > 25EeV as before. The results are shown in Figure 4.13. The deviations in energy as well asin arrival direction are smaller than <strong>the</strong> <strong>detector</strong> resolution.The deviations are <strong>of</strong> <strong>the</strong> same magnitude as for <strong>the</strong> removal <strong>of</strong> individual stations. These results
4.3 Reconstruction without sets <strong>of</strong> <strong>detector</strong>s 41RMS values <strong>of</strong> energy difference distributions14121086421000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Mean values <strong>of</strong> energy difference distributions420-2-4-6-8-10-12-141000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]RMS values <strong>of</strong> energy difference distributions121086421000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Mean values <strong>of</strong> energy difference distributions20-2-4-6-81000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]RMS values <strong>of</strong> energy difference distributions1086421000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Mean values <strong>of</strong> energy difference distributions210-1-2-3-4-5-61000 1100 1200 1300 1400 1500 1600 1700 1800Ground parameter [m]Figure 4.12: Analog plot to Figure 4.9, RMS values (left) and mean values (right): The circles are usedto illustrate <strong>the</strong> development <strong>of</strong> <strong>the</strong> histograms <strong>of</strong> <strong>the</strong> central stations, <strong>the</strong> rectangles for <strong>the</strong>histograms <strong>of</strong> <strong>the</strong> first crown stations. From top to bottom <strong>the</strong> energy range changes from25EeV < E ≤ 30EeV via 30EeV < E ≤ 40EeV to E > 40EeV.
42 Stability <strong>of</strong> <strong>the</strong> reconstructioncounts10Entries 32Mean -0.3065RMS 1.674Underflow 0countsEntries 32Mean 0.2427RMS 0.1821Underflow 0Overflow 1Overflow 111-20 -15 -10 -5 0 5 10 15 20Differences in energy [percent]0 0.2 0.4 0.6 0.8 1 1.2Differences in space angle [degree]counts102Entries 365Mean 0.706RMS 2.947Underflow 0Overflow 0counts210Entries 365Mean 0.2342RMS 0.2396Underflow 0Overflow 1101011-50 -40 -30 -20 -10 0 10 20 30 40 50Differences in energy [percent]0 0.5 1 1.5 2 2.5Differences in space angle [degree]Figure 4.13: Differences in energy in percent (left) and space angle in degrees (right) between <strong>the</strong> reconstructionwith all stations and <strong>the</strong> reconstruction with only <strong>the</strong> unitary cell for events withE > 57EeV (top) and E > 25EeV (bottom).
4.4 Less dense arrays 43show, that <strong>the</strong> signals <strong>of</strong> <strong>the</strong> seven highest signals suffice to guarantee a stable reconstruction. Itcan be concluded, that <strong>the</strong> reconstruction <strong>of</strong> strict-T5 events with E > 25EeV copes with <strong>the</strong> removal<strong>of</strong> all stations outside <strong>the</strong> unitary cell around <strong>the</strong> core. The accuracy for <strong>the</strong>se events ismuch higher than for <strong>the</strong> majority <strong>of</strong> events, as <strong>the</strong>y have only three or four stations with signals.4.3.2 Simulating borders <strong>of</strong> <strong>the</strong> arrayIn order to check, if <strong>the</strong> border <strong>of</strong> <strong>the</strong> array induces any bias in <strong>the</strong> reconstruction, <strong>the</strong> events arereconstructed leaving out sets <strong>of</strong> <strong>detector</strong>s located on one side <strong>of</strong> <strong>the</strong> core. The cut preserves <strong>the</strong>strict-T5 criterion and only stations from <strong>the</strong> second crown and far<strong>the</strong>r <strong>of</strong>f are erased. Figure 4.14Figure 4.14: Stations beyond <strong>the</strong> unitary cell on two sides <strong>of</strong> <strong>the</strong> central tank are left out in <strong>the</strong> reconstruction.These <strong>detector</strong>s are marked with a cross.shows <strong>the</strong> highest-signal station in <strong>the</strong> center surrounded <strong>by</strong> <strong>the</strong> stations <strong>of</strong> <strong>the</strong> different crowns.The stations not used in <strong>the</strong> reconstruction are marked with a cross. The test is performed fourtimes for each event, each time leaving out all <strong>detector</strong>s <strong>of</strong> two neighboring sides <strong>of</strong> <strong>the</strong> array,as shown in Figure 4.14. The deviations (see Figure 4.15) are similar to <strong>the</strong> ones obtained <strong>by</strong>reconstructing with <strong>the</strong> unitary cell only. The RMS values <strong>of</strong> <strong>the</strong> distributions are smaller than in<strong>the</strong> previous test. The asymmetric removal <strong>of</strong> <strong>detector</strong>s on one side <strong>of</strong> <strong>the</strong> core induces <strong>the</strong> largestdislocation <strong>of</strong> <strong>the</strong> core, as it is <strong>the</strong> barycenter <strong>of</strong> <strong>the</strong> signals <strong>of</strong> <strong>the</strong> stations. The small deviationsshow <strong>the</strong> robustness <strong>of</strong> <strong>the</strong> reconstruction algorithm. If an event passes <strong>the</strong> strict-T5 trigger, <strong>the</strong>effect <strong>of</strong> <strong>the</strong> border on <strong>the</strong> reconstructed energy and <strong>the</strong> arrival direction is not significant.4.4 Less dense arraysIt is planned, that <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory will be completed with <strong>the</strong> nor<strong>the</strong>rn side in <strong>the</strong>United States. The <strong>surface</strong> <strong>detector</strong> array will be similar to <strong>the</strong> one in <strong>the</strong> south, but with a widerspacing between <strong>the</strong> stations. With <strong>the</strong> <strong>data</strong> <strong>recorded</strong> <strong>by</strong> <strong>the</strong> existing array, <strong>the</strong> response <strong>of</strong> lessdense arrays can be simulated <strong>by</strong> using only <strong>the</strong> signals <strong>of</strong> sub-arrays in <strong>the</strong> reconstruction. Thereis no limitation in generating configurations with decreasing densities. One similar to <strong>the</strong> existingarray, is shown in Figure 4.16. The array is divided into three independent arrays (a, b, c), eachforming equilateral triangles <strong>of</strong> 2600 m (compare with results presented in [60]). The unitary cell(full hexagon) covers an area <strong>of</strong> 20.28km 2 and is <strong>by</strong> a factor <strong>of</strong> 3.5 bigger than in <strong>the</strong> regular array.For low multiplicity events, <strong>the</strong> distribution <strong>of</strong> tanks may cause <strong>the</strong> reconstruction to fail, even ifthree non-aligned stations are found. Consequently, <strong>the</strong> number <strong>of</strong> successful reconstructions is
44 Stability <strong>of</strong> <strong>the</strong> reconstructioncountsEntries 112Mean 0.04464RMS 1.209Underflow 0Overflow 0countsEntries 112Mean 0.1478RMS 0.1237Underflow 0Overflow 0101011-20 -15 -10 -5 0 5 10 15 20Differences in energy [percent]0 0.2 0.4 0.6 0.8 1 1.2Differences in space angle [degree]counts210Entries 1460Mean 0.1327RMS 2.4Underflow 0Overflow 1counts210Entries 1460Mean 0.1745RMS 0.2171Underflow 0Overflow 3101011-50 -40 -30 -20 -10 0 10 20 30 40 50Differences in energy [percent]0 0.5 1 1.5 2 2.5Differences in space angle [degree]Figure 4.15: Differences in energy in percent (left) and space angle in degrees (right) between <strong>the</strong> reconstructionwith all stations and modified sets <strong>of</strong> <strong>detector</strong>s simulating <strong>the</strong> border <strong>of</strong> <strong>the</strong> arrayfor events with E > 57EeV (top) and E > 25EeV (bottom).Figure 4.16: Triangle sub-array configurations.
4.5 Summary 45below 3·N, for N events. The reconstruction algorithm does not need to be modified. For <strong>the</strong> test,only strict-T5 events with E > 25EeV are used. In Figure 4.17, <strong>the</strong> deviations in energy and spaceangle are illustrated for different energy ranges.The deviations depend strongly on <strong>the</strong> energy. For events with E > 55EeV, most deviationsin energy are below 20% and in arrival direction <strong>the</strong>y are large and have values up to 4 ◦ . Therequest <strong>of</strong> two working crowns around <strong>the</strong> central station does not enhance <strong>the</strong> stability <strong>of</strong> <strong>the</strong>reconstruction noticeable (see Figure 4.18).Using <strong>the</strong> sub-arrays for a less dense configuration, <strong>the</strong> quality <strong>of</strong> <strong>the</strong> shower reconstruction <strong>of</strong>an <strong>Auger</strong> North-like array has been studied. For extensive air showers with high multiplicity andenergies above 35 EeV, <strong>the</strong> deviations in energy are comparable to those obtained <strong>by</strong> leaving outone individual station <strong>of</strong> <strong>the</strong> unitary cell around <strong>the</strong> core. A new definition <strong>of</strong> <strong>the</strong> T5 trigger andan optimum ground parameter for <strong>the</strong> wider spacing will improve <strong>the</strong> stability fur<strong>the</strong>r.4.5 SummaryIn this chapter <strong>the</strong> stability <strong>of</strong> <strong>the</strong> CDAS reconstruction for events with energies above 25 EeV hasbeen analyzed. For <strong>the</strong>se events <strong>the</strong> sets <strong>of</strong> <strong>detector</strong>s taking part in <strong>the</strong> reconstruction have beenmodified <strong>by</strong> leaving out individual stations or sets <strong>of</strong> <strong>detector</strong>s. For every event <strong>the</strong> reconstructionis repeated as many times as <strong>the</strong>re are active <strong>detector</strong>s involved, each time leaving out ano<strong>the</strong>r<strong>detector</strong> station or set <strong>of</strong> stations in <strong>the</strong> reconstruction. The resulting energies and angles are <strong>the</strong>ncompared to <strong>the</strong> original values obtained with all <strong>detector</strong>s.The removal <strong>of</strong> <strong>the</strong> highest signal station or a station <strong>of</strong> <strong>the</strong> first crown, leads for strict-T5 eventsto deviations <strong>of</strong> 20% in energy and <strong>of</strong> 3 ◦ in arrival direction. Leaving out a station with a largerdistance to <strong>the</strong> shower axis, changes <strong>the</strong> energy <strong>by</strong> less than 3% and <strong>the</strong> arrival direction <strong>by</strong> lessthan 1 ◦ , with very few exceptions. The sizes <strong>of</strong> <strong>the</strong> deviations show no correlation with <strong>the</strong> energy<strong>of</strong> <strong>the</strong> primary cosmic ray, but depend strongly on <strong>the</strong> distance <strong>of</strong> <strong>the</strong> removed station to <strong>the</strong>shower axis.For <strong>the</strong> subset <strong>of</strong> events with E > 57EeV no removal <strong>of</strong> an individual station changes <strong>the</strong> energymore than 15% and <strong>the</strong> arrival direction more than 0.8 ◦ . Both <strong>the</strong> deviations in energy and inarrival direction are smaller than <strong>the</strong> resolutions <strong>of</strong> <strong>the</strong> <strong>surface</strong> <strong>detector</strong>. They are 22% and 1 ◦ forthis energy range. No removal <strong>of</strong> a station results in a failing reconstruction or an energy below57EeV. This is <strong>the</strong> current energy cut for <strong>the</strong> search for correlations with source candidates. In afur<strong>the</strong>r test using all events above 25 EeV <strong>the</strong> influence <strong>of</strong> removing stations from <strong>the</strong> early or latepart <strong>of</strong> a shower has been discussed. Nei<strong>the</strong>r <strong>the</strong> removal <strong>of</strong> early nor <strong>of</strong> late triggered stationsshifts <strong>the</strong> energy systematically in one direction. The correction implemented in <strong>the</strong> reconstructioncode, which corrects for <strong>the</strong> different signal sizes, seems to work well for <strong>the</strong> analyzed energyrange.In addition, it has been shown, that strict-T5 events detected near <strong>the</strong> border <strong>of</strong> <strong>the</strong> array are notbiased <strong>by</strong> <strong>the</strong> missing <strong>detector</strong>s in <strong>the</strong> second crown and far<strong>the</strong>r away. The removal <strong>of</strong> sets <strong>of</strong> <strong>detector</strong>s,which simulate <strong>the</strong> border <strong>of</strong> <strong>the</strong> array changes <strong>the</strong> energy up to 10% and <strong>the</strong> reconstructedarrival direction up to 1.5 ◦ . Leaving out all stations except <strong>the</strong> unitary cell leads to deviations in<strong>the</strong> same ranges.The results summarized so far are all obtained for strict-T5 events. A comparison with <strong>the</strong> ICRC-T5 events, all events without a T5 cut, and with E > 25EeV has shown, that <strong>the</strong> deviations caused<strong>by</strong> removing a station <strong>of</strong> <strong>the</strong> unitary cell around <strong>the</strong> core, grow up to 60% in energy and 10 ◦ in arrivaldirection. The largest deviations have been found for reconstructions, where <strong>the</strong> two missing<strong>detector</strong>s (<strong>the</strong> not active one and <strong>the</strong> removed one) have a distance <strong>of</strong> 1500 m from each o<strong>the</strong>r.
46 Stability <strong>of</strong> <strong>the</strong> reconstructionFigure 4.17: Deviations in energy (top) and space angle (bottom) between events reconstructed with all stations and reconstructed with only <strong>the</strong> signals <strong>of</strong> onethird <strong>of</strong> <strong>the</strong> stations. From <strong>the</strong> left to right <strong>the</strong> energy threshold changes from E > 25EeV, <strong>the</strong>n E > 35EeV, E > 45EeV and finally, E > 55EeVon <strong>the</strong> right. The filled histograms are used to display subsets with five or more stations.0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree111110101010210Overflow 26210Overflow 0Overflow 0Overflow 0countsUnderflow 0RMS 1.811countsUnderflow 0RMS 1.137countsUnderflow 0210RMS 0.9098countsUnderflow 0RMS 0.7183Mean 1.598Mean 1.137Mean 0.9758Mean 0.8459Entries 1044Entries 490Entries 259Entries 139-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]-50 -40 -30-20 -10 0 10 20 30 40 50Difference in Energy [EeV]000-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]Difference in Energy [EeV]0-50 -40 -30 -20 -10 0 10 20 30 40 5030201020151051056423040251510850352012Overflow 91Overflow 2Overflow 1Overflow 0counts60Underflow 0Underflow 0RMS 15.64counts40Underflow 0RMS 12.46countsUnderflow 025RMS 12.59counts1445RMS 9.451Mean 9.651Mean 3.327Mean 2.834Mean 2.835Entries 1044Entries 490Entries 259Entries 139
4.5 Summary 47Entries 564Entries 269Entries 145Entries 8840Mean 9.674RMS 15.33Underflow 0counts35302530Overflow 46 2520Mean 3.809RMS 11.82Underflow 014countsOverflow 21210Mean 3.259RMS 11.14Underflow 0countsOverflow 1Mean 3.597RMS 8.153Underflow 0counts108Overflow 020158661510410452520-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]0-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]0-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]0-50 -40 -30 -20 -10 0 10 20 30 40 50Difference in Energy [EeV]Entries 564Entries 269Entries 145Entries 88Mean 1.675RMS 2.024Underflow 02counts10Overflow 1010Mean 1.0832RMS 0.9529Underflow 0countsOverflow 0Mean 0.9124RMS 0.7942Underflow 0countsOverflow 0Mean 0.8651RMS 0.7508Underflow 0countsOverflow 01010101011110 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degree0 2 4 6 8 10 12 14 16 18 20Spaceangle in degreeFigure 4.18: Deviations in energy (top) and space angle (bottom) between T5+-events reconstructed with all stations and reconstructed with only <strong>the</strong> signals <strong>of</strong>one third <strong>of</strong> <strong>the</strong> stations. T5+-events are surrounded <strong>by</strong> two crowns <strong>of</strong> working stations. The energy threshold changes from <strong>the</strong> left to <strong>the</strong> right:E > 25EeV, E > 35EeV, E > 45EeV and E > 55EeV. The filled histogramms are used to display subsets with five or more stations.
48 Stability <strong>of</strong> <strong>the</strong> reconstructionIn addition to <strong>the</strong> checks <strong>of</strong> <strong>the</strong> stability <strong>of</strong> <strong>the</strong> reconstruction, <strong>the</strong> described method can give a hint<strong>of</strong> <strong>the</strong> optimum ground parameter. The analysis shows, that <strong>the</strong> distance <strong>of</strong> 1000 m is too smallfor cosmic rays with energies above 25 EeV. It has been demonstrated, that <strong>the</strong> optimum distanceincreases with <strong>the</strong> energy. The identification <strong>of</strong> <strong>the</strong> optimum distance with this method is difficult,as <strong>the</strong> shift <strong>of</strong> <strong>the</strong> core position induces a bias.In <strong>the</strong> last part, <strong>the</strong> method <strong>of</strong> reducing <strong>the</strong> number <strong>of</strong> <strong>detector</strong>s taking part in <strong>the</strong> reconstructionis used to generate less dense arrays. With a spacing <strong>of</strong> 2600 m between <strong>the</strong> stations in each subarray,<strong>the</strong> distances are in <strong>the</strong> range, which is beeing discussed for <strong>Auger</strong> North. The results show,that <strong>the</strong> accuracy <strong>of</strong> <strong>the</strong> reconstruction depends on <strong>the</strong> energy. For events with energies above55 EeV <strong>the</strong> angular deviations are below 4 ◦ for all reconstructions and in energy below 20% for135 <strong>of</strong> 139 reconstructions. For <strong>the</strong> rest see Figure 4.17.From <strong>the</strong> analysis presented in this chapter can be concluded, that <strong>the</strong> CDAS reconstruction <strong>of</strong> highenergy strict-T5 events is very robust. Excluding individual stations or sets <strong>of</strong> <strong>detector</strong>s changes<strong>the</strong> reconstructed energy <strong>by</strong> less than 10% and <strong>the</strong> arrival direction <strong>by</strong> less than 1.5 ◦ for eventswith E > 25EeV.
Chapter 5Azimuth angle distributionIn <strong>the</strong> studies presented in this chapter, <strong>the</strong> focus is on <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> properties <strong>of</strong> <strong>the</strong> azimuthangle distribution. Starting from <strong>the</strong> basic assumption <strong>of</strong> an isotropic particle flux from <strong>the</strong> cosmosfor events with energies below 57 EeV, <strong>the</strong> measured zenith and azimuth angle distributions areanalyzed in detail.In <strong>the</strong> first part <strong>of</strong> this chapter, <strong>the</strong> zenith angle and azimuth angle distributions are described.Then a model is developed to understand structures in <strong>the</strong> azimuth angle distribution for energiesbelow full acceptance. After this, <strong>the</strong> obtained asymmetry with a period <strong>of</strong> 2! in <strong>the</strong> azimuth angledistribution is analyzed and finally <strong>the</strong> search for <strong>the</strong> reason <strong>of</strong> this effect is presented.5.1 IntroductionThe analysis presented in this chapter is based on <strong>the</strong> Herald <strong>data</strong> [41] detected between 1. January2004 and 20. July 2008. The Herald file contains all reconstructed T4 events. The usual cuts for<strong>the</strong> Herald <strong>data</strong> are: " < 60 ◦ , flag 22 > 0 and flag 23 > 1. Flag 22 > 0 declares <strong>the</strong> reconstructedarrival direction <strong>of</strong> <strong>the</strong> shower compatible with <strong>the</strong> estimation, obtained from <strong>the</strong> seed <strong>of</strong> <strong>the</strong> threestations with <strong>the</strong> highest signal. Flag 23 > 1 marks events as strict-T5. If <strong>the</strong> energy for an eventis needed, <strong>the</strong> value <strong>of</strong> column 38 is used, as <strong>the</strong> file contains different energy values. For fur<strong>the</strong>rinformation see [41].Before <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> azimuth distribution is presented, a short discussion <strong>of</strong> <strong>the</strong> zenith angledistribution is performed. The " distribution for events detected above full acceptance <strong>of</strong> <strong>the</strong><strong>surface</strong> <strong>detector</strong> can be described <strong>by</strong> <strong>the</strong> functionf (")=a · sin" cos". (5.1)The variable a increases with <strong>the</strong> number <strong>of</strong> detected events and an event with " = 0 ◦ comesexactly from above. The sine term is due to <strong>the</strong> increasing spherical segment and <strong>the</strong> cosine termis due to <strong>the</strong> decreasing effective <strong>detector</strong> area, seen <strong>by</strong> an air shower, for increasing zenith angle.The distribution <strong>of</strong> all events above 3 EeV is shown in Figure 5.1 and it has its maximum at 45 ◦ .The distribution complies with Function 5.1 and systematic deviations are not visible. Themedian <strong>of</strong> <strong>the</strong> distribution given <strong>by</strong> Function 5.1 is at " = 37.76 ◦ and for <strong>the</strong> measured <strong>data</strong> it isat <strong>the</strong> same value. The agreement <strong>of</strong> <strong>the</strong> <strong>data</strong> with <strong>the</strong> <strong>the</strong>oretical expectation means that <strong>the</strong>re areno systematic deviations. " distributions, containing events at energies below <strong>the</strong> full acceptancethreshold <strong>of</strong> <strong>the</strong> <strong>detector</strong>, are shifted towards lower zenith angles (see Figure 3.9 right). Thereason is <strong>the</strong> higher absorption <strong>of</strong> energy for inclined showers on <strong>the</strong>ir longer way through <strong>the</strong>
50 Azimuth angle distributioncounts700600Entries 26539Mean 36.63RMS 14.1850040030020010000 10 20 30 40 50 60Figure 5.1: Measured zenith angle distribution up to 60 ◦ for events with E > 3EeV and <strong>the</strong> usual qualitycuts. The solid line is <strong>the</strong> sin" cos"-function."atmosphere. The particle density or <strong>the</strong> energy <strong>of</strong> <strong>the</strong> individual particles decreases, so showerswith large zenith angles drop below <strong>the</strong> trigger threshold and are not being detected.5.2 Azimuth angle distributionSince cosmic rays arrive isotropically from <strong>the</strong> cosmos, <strong>the</strong> azimuth angle distribution is expectedto be flat. Figure 5.2 shows <strong>the</strong> )-distribution for all events above full acceptance (E > 3EeV) andwith " < 60 ◦ . Zero degree points to <strong>the</strong> east, 90 ◦ to <strong>the</strong> north and −90 ◦ to <strong>the</strong> south. Taking <strong>the</strong>errors into account, <strong>the</strong> distribution is in agreement with a flat distribution.Below full acceptance (E < 3EeV), things become more complicated. The probability <strong>of</strong> detectinga shower depends on <strong>the</strong> core position, <strong>the</strong> energy, <strong>the</strong> zenith angle and <strong>the</strong> azimuth angle. Dueto <strong>the</strong> hexagonal structure <strong>of</strong> <strong>the</strong> array and <strong>the</strong> distribution <strong>of</strong> <strong>the</strong> 3 PMTs in <strong>the</strong> tanks, deviationsfrom <strong>the</strong> flat distribution are expected. The modulations for all events with " < 60 ◦ and for allevents with 37.76 ◦ < " < 60 ◦ , respectively, are shown in Figure 5.3. In both diagrams, deviationsfrom <strong>the</strong> flat distribution are visible. The dominating oscillation has a period <strong>of</strong> 2!/6 and is caused<strong>by</strong> <strong>the</strong> hexagonal structure <strong>of</strong> <strong>the</strong> array. For <strong>the</strong> events with " > 37.76 ◦ <strong>the</strong> hexagonal structure <strong>of</strong><strong>the</strong> array has a stronger impact. The effect is superimposed <strong>by</strong> an effect with a period <strong>of</strong> 2!. Thechallenge <strong>of</strong> this analysis is to identify <strong>the</strong> reason for <strong>the</strong> latter oscillation. In addition to <strong>the</strong>seoscillations, <strong>the</strong> three PMTs may induce a modulation with a period <strong>of</strong> 2!/3, as <strong>the</strong>y are arrangedin a plane with an angle <strong>of</strong> 2!/3 between each pair <strong>of</strong> PMTs.5.2.1 Hexagonal structure <strong>of</strong> <strong>the</strong> arrayIn this section, <strong>the</strong> reason for <strong>the</strong> oscillation with a period <strong>of</strong> 2!/6 is explained. It is a puregeometric effect, caused <strong>by</strong> <strong>the</strong> hexagonal structure <strong>of</strong> <strong>the</strong> array.Primary cosmic rays produce a cascade <strong>of</strong> secondary particles, which reach <strong>the</strong> earth in <strong>the</strong> form<strong>of</strong> a “pancake”. At <strong>the</strong> core, <strong>the</strong> particle density is very high, far<strong>the</strong>r away <strong>the</strong> density decreaseswith increasing distance. The signals are, except for fluctuations, constant on circles around <strong>the</strong>
Entries26539Mean -1.338RMS 104.25.2 Azimuth angle distribution 51hThetacounts200150100500-150 -100 -50 0 50 100 150)Figure 5.2: Measured azimuth angle distribution for events with E > 3EeV and " < 60 ◦ .counts640014000 Entries 1169971 Entries 4945026200counts600013500580013000125005600540052005000120004800-150 -100 -50 0 50 100 150)-150 -100 -50 0 50 100 150)Figure 5.3: Measured azimuth angle distribution for all events with " < 60 ◦ (left) and <strong>the</strong> events with37.76 ◦ < " < 60 ◦ (right).
52 Azimuth angle distributionshower axis. For a shower with " = 0 ◦ , <strong>the</strong> signal distribution on <strong>the</strong> ground is point symmetric to<strong>the</strong> core. For inclined showers with " > 0 ◦ <strong>the</strong> circles <strong>of</strong> constant signals are deformed to ellipses.The particle density on <strong>the</strong> ground decreases, as <strong>the</strong> same number <strong>of</strong> particles is distributed on alarger area. The relation between <strong>the</strong> major axis S M and <strong>the</strong> minor axis S m <strong>of</strong> an ellipse dependson <strong>the</strong> zenith angle only and can be written asS m = S M · cos". (5.2)The orientation <strong>of</strong> <strong>the</strong> ellipse is defined <strong>by</strong> <strong>the</strong> azimuth angle ), with <strong>the</strong> major axis parallel to<strong>the</strong> incoming direction <strong>of</strong> <strong>the</strong> shower. If <strong>the</strong> shower reaches <strong>the</strong> ground, its spread depends on <strong>the</strong>energy <strong>of</strong> <strong>the</strong> primary particle. In addition, <strong>the</strong> asymmetry between <strong>the</strong> signals <strong>of</strong> early and latetriggered stations has to be considered for inclined showers (see Chapter 3.3.3).Neglecting all fluctuations, <strong>the</strong>re is one ellipse around <strong>the</strong> core which encircles all positions, wherea station would be triggered, whereas for all positions outside <strong>the</strong> signals are to small to trigger astation. A shower is detected, if at least three stations are located inside this ellipse. For showerswith energies above full acceptance <strong>the</strong> ellipse sizes are sufficiently large to enclose more thantwo stations, independent <strong>of</strong> <strong>the</strong> core position. For showers with energies below 3 EeV, <strong>the</strong> ellipsesizes become so small, that <strong>the</strong> fact, whe<strong>the</strong>r three or less stations are located inside, depends on<strong>the</strong> core position and <strong>the</strong> arrival direction <strong>of</strong> <strong>the</strong> shower. For small zenith angles, <strong>the</strong> major andminor axes <strong>of</strong> <strong>the</strong> ellipse have similar length and <strong>the</strong> probability to detect a shower depends <strong>of</strong> <strong>the</strong>distance <strong>of</strong> <strong>the</strong> core to <strong>the</strong> closest station, only. With increasing zenith angle a dependency on <strong>the</strong>azimuth angle emerges. The array consists <strong>of</strong> equilateral triangles <strong>of</strong> <strong>detector</strong> stations. Since <strong>the</strong>height h <strong>of</strong> an equilateral triangle is smaller than <strong>the</strong> length <strong>of</strong> one side, showers with <strong>the</strong> minoraxis parallel to <strong>the</strong> height can be triggered for smaller ellipses, than showers perpendicular to it(see Figure 5.4). This results in a sine variation <strong>of</strong> <strong>the</strong> number <strong>of</strong> events detected in <strong>the</strong> azimuthhFigure 5.4: Schematic view <strong>of</strong> two showers with <strong>the</strong> same energy and <strong>the</strong> same core position. The onewith ) = 0 ◦ (solid line) would be detected, as three stations are enclosed <strong>by</strong> <strong>the</strong> ellipses, <strong>the</strong>o<strong>the</strong>r one, with ) = 90 ◦ , would not be detected.angle distribution. The period <strong>of</strong> this hexagonal effect is 2!/6, due to <strong>the</strong> structure <strong>of</strong> <strong>the</strong> array.To achieve a better understanding <strong>of</strong> this geometric effect, it is interesting to examine not only<strong>the</strong> question, if an event is triggered or not, but also to determine <strong>the</strong> ratio between <strong>the</strong> number <strong>of</strong>events that trigger three stations and <strong>the</strong> number <strong>of</strong> events that trigger four or more stations. To dothis, <strong>the</strong> different configurations <strong>of</strong> triggered <strong>surface</strong> <strong>detector</strong> stations have to be determined for
5.2 Azimuth angle distribution 533-fold an 4-fold events. For 3-fold events two configurations <strong>of</strong> stations are possible: equilateraltriangles with <strong>the</strong> apex to <strong>the</strong> north or to <strong>the</strong> south and six isosceles triangles, as shown in Figure5.5 (left). For <strong>the</strong> isosceles triangles <strong>the</strong> azimuth angles are indicated, for which <strong>the</strong> maxima areexpected. At zero degree <strong>the</strong> )-distribution should have a minimum. In case <strong>of</strong> <strong>the</strong> equilateraltriangles, <strong>the</strong>re is a difference in <strong>the</strong> trigger probability between showers arriving parallel to <strong>the</strong>direct connecting line <strong>of</strong> two stations, with a length <strong>of</strong> 1500m, and showers arriving perpendicularto it (height <strong>of</strong> triangles ≈ 1300m). The maxima are expected to occur for ) = 0 ◦ ±60 ◦ , exactly at<strong>the</strong> positions <strong>of</strong> <strong>the</strong> minima <strong>of</strong> <strong>the</strong> isosceles triangles. The maxima in <strong>the</strong> ) distribution are defined<strong>by</strong> <strong>the</strong> appearance frequency <strong>of</strong> <strong>the</strong> different types <strong>of</strong> triangles. Due to <strong>the</strong> structure <strong>of</strong> <strong>the</strong> array<strong>the</strong> extrema recur every 60 ◦ , with an angle <strong>of</strong> 30 ◦ between each maximum and <strong>the</strong> neighboringminima.The 4-fold events are dominated <strong>by</strong> <strong>the</strong> three compact configurations <strong>of</strong> triggered stations shownmaxmaxmaxFigure 5.5: Left: The six possible isosceles triangles for 3-fold events and <strong>the</strong> expected maxima in <strong>the</strong>azimuth angle distribution. The only difference between <strong>the</strong> triangles with solid lines and <strong>the</strong>ones with dashed lines, are that <strong>the</strong>y are rotated <strong>by</strong> 60 ◦ . Right: The dominating configurations<strong>of</strong> stations for 4-fold events.in Figure 5.5 (right). All three have <strong>the</strong> same attributes, as <strong>the</strong>y can be converted into each o<strong>the</strong>r,<strong>by</strong> rotating <strong>the</strong>m <strong>by</strong> an angle <strong>of</strong> 60 ◦ . Therefore, <strong>the</strong> maxima and minima occur every 60 ◦ , witha minimum at 0 ◦ . The second possibility for 4-fold events are <strong>the</strong> twelve possibilities shown inFigure 5.6.It is not necessary to investigate <strong>the</strong> possible configurations <strong>of</strong> triggered stations for events withFigure 5.6: The twelve possible configurations for <strong>the</strong> non-compact adjustment <strong>of</strong> stations for 4-foldevents. The three stations <strong>of</strong> <strong>the</strong> solid triangle and one at <strong>the</strong> end <strong>of</strong> one dashed line aretriggered.more triggered stations. On <strong>the</strong> one hand <strong>the</strong>se events are detected independently <strong>of</strong> <strong>the</strong>ir arrival
54 Azimuth angle distributiondirection and distance between <strong>the</strong> core and <strong>the</strong> shower axis and on <strong>the</strong> o<strong>the</strong>r hand all events withmore than four triggered stations amount to 7.2% <strong>of</strong> all detected events, only. The frequencies<strong>of</strong> occurrence for all events determined from <strong>the</strong> <strong>data</strong> are listed in Table 5.1. The azimuth angle3-fold 4-fold 5-fold 6-fold > 6-fold77.0% 15.8% 4.3% 1.5% 1.3%Table 5.1: Fractions <strong>of</strong> events, which trigger three, four or more stations.distributions for 3-fold, 4-fold and 5-fold events are shown in Figure 5.7. Inclined showers exhibitdistinctive maxima with distances <strong>of</strong> 60 ◦ for <strong>the</strong> 3-fold and 4-fold events. For events with moretriggered stations, <strong>the</strong> distribution is flat, as shown in Figure 5.2.5.2.2 Direct light in inclined showersThree photomultipliers collect <strong>the</strong> Cherenkov light produced in <strong>the</strong> water <strong>of</strong> each <strong>surface</strong> <strong>detector</strong>station. In <strong>the</strong> CDAS reconstruction code, <strong>the</strong> signal <strong>of</strong> a station is calculated as <strong>the</strong> average <strong>of</strong><strong>the</strong> signals, collected <strong>by</strong> its working PMTs. This is not correct, as <strong>the</strong> signal measured <strong>by</strong> <strong>the</strong>individual PMTs depends on <strong>the</strong> azimuth angle <strong>of</strong> <strong>the</strong> extensive air shower. The Cherenkov lightis emitted <strong>by</strong> <strong>the</strong> secondary particles, which cross <strong>the</strong> station and propagate in <strong>the</strong> water. In <strong>the</strong>first 50 ns, <strong>the</strong> light is not completely diffusely distributed and <strong>the</strong> PMTs collect different amounts<strong>of</strong> direct light (without any reflection) and semi-direct light (after a small number <strong>of</strong> reflections).It is a completely geometrical effect, due to <strong>the</strong> overlapping areas between <strong>the</strong> PMTs’ field <strong>of</strong> viewand <strong>the</strong> Cherenkov cone [61, 62]. After a few reflections, <strong>the</strong> light is distributed uniformly, as <strong>the</strong>water is enclosed <strong>by</strong> a sealed liner with a diffusively reflecting inner <strong>surface</strong>. Since all stationsare oriented in <strong>the</strong> same way, <strong>the</strong> signal <strong>of</strong> <strong>the</strong> individual PMTs correlate with <strong>the</strong> azimuth angle(see Figure 5.8). This figure is generated <strong>by</strong> adding <strong>the</strong> signals <strong>of</strong> all stations with three workingPMTs, <strong>of</strong> all detected events <strong>of</strong> 2007 for each PMT, in " bins <strong>of</strong> 20 ◦ . The sine structure is clearlyvisible and <strong>the</strong> average signals <strong>of</strong> <strong>the</strong> PMTs are equal.5.2.3 Determination <strong>of</strong> amplitudes and phasesBoth effects described above result in sine structures in <strong>the</strong> azimuth angle distribution. At firstsight, <strong>the</strong> effect with a period <strong>of</strong> 360 ◦ seems to show a sine structure as well (compare Figure 5.2).In this part <strong>of</strong> <strong>the</strong> analysis, <strong>the</strong> <strong>data</strong> is fitted with a sine function, in Chapter 5.4.3 this assumptionis checked. The function fitted to <strong>the</strong> azimuth angle distribution is given <strong>by</strong>:N( )=c + a 6 · sin( 6!180 · ) + b 6)+ a 3 · sin( 3!180 · ) + b 3)( !)+ a 1 · sin180 · ) + b 1 . (5.3)It has seven free parameters, <strong>the</strong> absolute term c, <strong>the</strong> amplitudes a 6 , a 3 , a 1 <strong>of</strong> <strong>the</strong> three sine functionsand <strong>the</strong>ir phases b 6 , b 3 , b 1 . The function is fitted to all 3-fold events, all 4-fold events andall events without a cut on <strong>the</strong> number <strong>of</strong> triggered stations, respectively. In all three cases, onlyevents, which fulfill <strong>the</strong> strict-T5 and <strong>the</strong> usual cuts, are used. The selection <strong>of</strong> strict-T5 events isnecessary in order to use only events with a well defined multiplicity.The parameters <strong>of</strong> <strong>the</strong> fits are shown in Table 5.2. From <strong>the</strong> fit parameters <strong>the</strong> relative differencebetween <strong>the</strong> maxima and minima can be determined withp = 2 · ac . (5.4)
5.2 Azimuth angle distribution 55counts90008800860084008200Entries 756608 Entries 2631223400counts320030002800800026007800-150 -100 -50 0 50 100 150)-150 -100 -50 0 50 100 150)counts21002000Entries 156927 1400 Entries 96866counts130019001200180011001700100016009001500800-150 -100 -50 0 50 100 150)-150 -100 -50 0 50 100 150)counts600550500450400Entries 43094500 Entries 31930counts450400350300250350-150 -100 -50 0 50 100 150)200-150 -100 -50 0 50 100 150)Figure 5.7: Measured azimuth angle distributions for strict-T5 events with (left) " < 60 ◦ and strict-T5events with 37.76 ◦ < " < 60 ◦ (right); top: 3-fold events, middle: 4-fold events, bottom: 5-fold events.c a 6 b 6 a 3 b 3 a 1 b 13-fold 8408.7 ± 5.8 49 ± 14 −80.5 ◦ 11 ± 14 −88.5 ◦ 133 ± 14 −133.5 ◦4-fold 1743.9 ± 4.5 73.6 ± 6.4 −93.0 ◦ 5.3 ± 6.3 180.4 ◦ 21.2 ± 6.2 −165.3 ◦all 10951 ± 12 113 ± 16 −87.1 ◦ 12 ± 16 −74.6 ◦ 155 ± 16 −143.3 ◦Table 5.2: Parameters <strong>of</strong> <strong>the</strong> fits with Function 5.3 shown in Figure 5.9.
56 Azimuth angle distributionSignal in %0.380.360.340.320.30.28-150 -100 -50 0 50 100 150)Figure 5.8: Fraction <strong>of</strong> <strong>the</strong> total signal as a function <strong>of</strong> ) detected <strong>by</strong> <strong>the</strong> three PMTs. The errors are sosmall, that <strong>the</strong>y are not visible. The plot is generated <strong>by</strong> taking <strong>the</strong> siganls <strong>of</strong> all PMTs, usedfor <strong>the</strong> reconstruction <strong>of</strong> <strong>the</strong> T4 events, which have been detected in 2007.The error results from error propagation:√ √ (/ ) p 2 ( ) / p 2 ((a ) 2 ( ) a · (c 2( p =/a · (a +/c · (c = +c c 2 . (5.5)The differences in <strong>the</strong> number <strong>of</strong> detected events between <strong>the</strong> maxima and minima, for <strong>the</strong> differentcuts, are listed in Table 5.3.The fits show very clearly, that <strong>the</strong> influence <strong>of</strong> <strong>the</strong> different signals <strong>of</strong> <strong>the</strong> three PMTs in eachp 6 p 3 p 13-fold (1.17 ± 0.17)% (0.27 ± 0.17)% (3.15 ± 0.16)%4-fold (8.44 ± 0.37)% (0.61 ± 0.36)% (2.43 ± 0.36)%all (2.07 ± 0.15)% (0.22 ± 0.14)% (2.83 ± 0.14)%Table 5.3: Relative differences p 6 , p 3 and p 1 between <strong>the</strong> maxima and <strong>the</strong> minima <strong>of</strong> <strong>the</strong> oscillations withperiods <strong>of</strong> 2!/6, 2!/3 and 2!, in <strong>the</strong> )-distribution.station is not significant for <strong>the</strong> azimuth angle distribution. Therefore, in <strong>the</strong> following <strong>the</strong> focus<strong>of</strong> <strong>the</strong> analysis is put on <strong>the</strong> effects with periods <strong>of</strong> 2! and 2!/6.5.3 Model for <strong>the</strong> hexagonal effect5.3.1 LayoutTo study <strong>the</strong> effect <strong>of</strong> <strong>the</strong> hexagonal structure <strong>of</strong> <strong>the</strong> array, a model has been developed. Theunitary cell <strong>of</strong> <strong>the</strong> array is a hexagon, composed <strong>of</strong> seven stations. They form six triangles, threewith an apex pointing to <strong>the</strong> north and three with an apex to <strong>the</strong> south. The smallest unit, whichrepresents <strong>the</strong> whole array is formed <strong>by</strong> two triangles, one with <strong>the</strong> apex pointing to <strong>the</strong> northand one with an apex to <strong>the</strong> south. By dividing one triangle, a rectangular unitary cell can beconstructed, whose size is one third <strong>of</strong> <strong>the</strong> common unitary cell. In <strong>the</strong> rectangle (shown in Figure
5.3 Model for <strong>the</strong> hexagonal effect 57counts9200 Entries 75660890008800860084008200800078007600-150 -100 -50 0 50 100 150)counts220021002000Entries 1569271900180017001600150014001300-150 -100 -50 0 50 100 150)counts11800 Entries 9853671160011400112001100010800106001040010200-150 -100 -50 0 50 100 150)Figure 5.9: Azimuth distributions for <strong>the</strong> 3-fold (top), 4-fold events (middle) and all events (bottom),which fulfill <strong>the</strong> usual cuts. For <strong>the</strong> fits Equation 5.3 is used.
58 Azimuth angle distribution5.10) with edge lengths <strong>of</strong> 1500 m and 1300 m, a shower core is placed every ten meters in <strong>the</strong> x-y-plane, which adds up to 19500 core positions. Around each core position an ellipse is drawn. IfFigure 5.10: Model for <strong>the</strong> 2!/6-effect: The left picture shows <strong>the</strong> stations (dots) and <strong>the</strong> area (littlesquares), where <strong>the</strong> showers are simulated with a core positions on a ten meter grid. In <strong>the</strong>right picture, two ellipses are shown, one would trigger <strong>the</strong> <strong>surface</strong> <strong>detector</strong>, one would not,as only two stations, located at <strong>the</strong> apexes <strong>of</strong> <strong>the</strong> triangle, are inside <strong>the</strong> ellipse.three non-aligned stations (in <strong>the</strong> figure illustrated <strong>by</strong> little squares) are located inside <strong>the</strong> ellipse,<strong>the</strong> shower can be reconstructed, o<strong>the</strong>rwise it cannot. In this model, stations inside <strong>the</strong> ellipseshave a trigger probability <strong>of</strong> one, stations outside have a probability <strong>of</strong> zero. Around <strong>the</strong> rectangleone row <strong>of</strong> stations is inserted. No fur<strong>the</strong>r stations can be triggered <strong>by</strong> 3-fold and 4-fold events,since <strong>the</strong> ellipses are to small to encircle stations far<strong>the</strong>r away.The model developed so far has two free parameters, <strong>the</strong> lengths <strong>of</strong> <strong>the</strong> semi-major axis S M and <strong>the</strong>semi-minor axis S m <strong>of</strong> <strong>the</strong> ellipse. These two variables depend on <strong>the</strong> energy and <strong>the</strong> zenith angle<strong>of</strong> <strong>the</strong> simulated shower. For a given energy, <strong>the</strong> minor axis can be extracted from <strong>the</strong> LDF and<strong>the</strong> major axis is given <strong>by</strong> Equation 5.2. By simulating showers with all energies and zenith anglesoccurring, normalized <strong>by</strong> <strong>the</strong> frequency <strong>of</strong> <strong>the</strong>ir appearance, it is possible to compare <strong>the</strong> number<strong>of</strong> showers detected with two ellipses perpendicular to each o<strong>the</strong>r. One has its major axis parallelto <strong>the</strong> x-axis and corresponds to extensive air showers with ) = 0 ◦ ± n · 60 ◦ , <strong>the</strong> o<strong>the</strong>r one has itsmajor axis parallel to <strong>the</strong> y-axis and represents showers with ) = 30 ◦ ± n · 60 ◦ (see Figure 5.4.The orientations coincide with <strong>the</strong> maxima and minima determined from <strong>the</strong> fits for <strong>the</strong> hexagonaleffect.In <strong>the</strong> next steps, firstly, <strong>the</strong> connection between S(1000) and <strong>the</strong> semi-minor axis <strong>of</strong> <strong>the</strong> ellipsewill be described, <strong>the</strong>n, secondly, <strong>the</strong> frequency <strong>of</strong> occurrence <strong>of</strong> <strong>the</strong> showers is presented, independency on <strong>the</strong>ir zenith angles and energies and, finally, asymmetries <strong>of</strong> <strong>the</strong> footprint <strong>of</strong> <strong>the</strong>showers and fluctuations will be figured out.For <strong>the</strong> reconstruction <strong>of</strong> <strong>the</strong> energy, different types <strong>of</strong> LDFs can be selected. For this model, apower-law function [63] is used, as this is <strong>the</strong> standard LDF in <strong>the</strong> CDAS reconstruction code.The signal S depends on <strong>the</strong> distance r from <strong>the</strong> shower core:(r) −-S(r)=S(1000) ·, (5.6)1000mwith <strong>the</strong> slope parameter -- = 2.24 − 0.98(sec " − 1). (5.7)By transposing Equation 5.6, <strong>the</strong> distance to <strong>the</strong> core can be calculated, for a given S(1000) anda given signal S(r)=2.6VEM (TOT trigger condition: signal above 0.2 VEM in at least 13 time
5.3 Model for <strong>the</strong> hexagonal effect 59bins, see also Figure 3.4):( ) 2.6VEM − 1-r = 1000m ·. (5.8)S(1000) · cos"It is also possible to use a NKG-like function, which is <strong>the</strong> standard LDF in <strong>the</strong> <strong>of</strong>fline reconstructions<strong>of</strong>tware. The respective equations are[( r) (S(r)=S(1000) · 3.47 - · · 1 + r )] −-(5.9)700m 700mandr = − 700m2√ (700m ) 2 ( S(1000) · 3.47- · cos"++2S(r)) 1-(5.10)with <strong>the</strong> same slope parameter -.The cos"-term in Equations 5.8 and 5.10 is included to account for <strong>the</strong> fact, that <strong>the</strong> secondaryparticles <strong>of</strong> extensive air shower with large zenith angles are distributed on a wider area than <strong>the</strong>particles <strong>of</strong> showers with small zenith angles. The sizes <strong>of</strong> <strong>the</strong> ellipses increase for a constantsemi-minor axis proportional to 1/cos ". With this correction, <strong>the</strong> signal S(r)/cos " is selected in<strong>the</strong> LDF to have a signal <strong>of</strong> <strong>the</strong> same size on <strong>the</strong> ground as for vertical showers.To determine <strong>the</strong> ellipse, which encircles all triggered stations and leaves out all not triggeredstations, <strong>the</strong> threshold for triggering a station is needed. On <strong>the</strong> station level, two independenttrigger conditions are implemented. The single threshold trigger requires a signal <strong>of</strong> 3.2 VEM inone bin and for <strong>the</strong> time-over-threshold trigger, <strong>the</strong> signals in 13 time bins <strong>of</strong> 25 ns in an interval <strong>of</strong>3 µs have to be above 0.2 VEM each (see Chapter 3.1). This results in a signal <strong>of</strong> 2.6 VEM, whichis implemented in <strong>the</strong> model. This assumption is a very rough estimation and its consequenceswill be discussed in Chapter 5.3.5.For any given signal, <strong>the</strong> size <strong>of</strong> <strong>the</strong> corresponding ellipse can be calculated as a function <strong>of</strong>S(1000) and ". The semi-minor axis has a length <strong>of</strong> S m = r and <strong>the</strong> semi-major axis can becalculated from Equation 5.2. For each configuration (" and S(1000) fixed) a map can be drawn,which illustrates <strong>the</strong> core positions (x,y) that would trigger an event. Such a map for S m = 1000and " = 40 ◦ can be seen in Figure 5.11. The ellipses with <strong>the</strong> major axis parallel to <strong>the</strong> x-axiswould trigger 5875 showers, <strong>the</strong> ones with <strong>the</strong> major axis parallel to <strong>the</strong> y-axis only 5806. Thesemaps are generated for all zenith angles up to 60 ◦ and for all occurring ellipse sizes.In <strong>the</strong> next step, <strong>the</strong> normalization factors for <strong>the</strong> showers with different S(1000) and " have to becalculated. With respect to ", <strong>the</strong> events arrive proportional to sin" cos". The scale factor isN(")=a · sin" cos ". (5.11)To obtain <strong>the</strong> distribution <strong>of</strong> <strong>the</strong> occurring ellipse sizes, <strong>the</strong> starting point is <strong>the</strong> energy spectrum.From <strong>the</strong> energy spectrum first <strong>the</strong> S 38 and <strong>the</strong>n <strong>the</strong> S(1000) spectrum are calculated:N(E) ∼ E −# , (5.12)[N (S 38 ) ∼ a · (S 38 ) b] −#, (5.13)[ ( ) ]S(1000)b−#N (S(1000)) ∼ a(5.14)CICwith # = −3.0, a = 0.149 and b = 1.08 [50]. The CIC function used isCIC (")=1 + 0.94 ( cos 2 " − cos 2 38 ◦) − 0.48 ( cos 2 " − cos 2 38 ◦) 2. (5.15)
histEntries 5876Mean x 1493Mean y 649.9RMS x 441.4RMS y 189.50 0 01 5875 00 0 0hist2Entries 5807Mean x 1489Mean y 647.8RMS x 468.9RMS y 378.10 0 01 5806 00 0 060 Azimuth angle distributionsouth - north1200100050454035south - north120010005045403580030800306002520600252040015400152001052001050800 1000 1200 1400 1600 1800 2000 2200east -west00800 1000 1200 1400 1600 1800 2000 2200east - west0Figure 5.11: Number <strong>of</strong> triggered showers per bin for ellipses with <strong>the</strong> major axis parallel to <strong>the</strong> x-axis(left) and parallel to <strong>the</strong> y-axis (right) for showers with S m = 1000 and " = 40 ◦ .For a given shower size and a given zenith angle, 19500 ellipses are generated with <strong>the</strong> majoraxisparallel to <strong>the</strong> x-axis and <strong>the</strong> same number <strong>of</strong> ellipses with <strong>the</strong> major-axis parallel to <strong>the</strong>y-axis. If <strong>the</strong> positions <strong>of</strong> <strong>the</strong> required number <strong>of</strong> stations are located inside <strong>the</strong> ellipse, a counteris incremented. After all possible positions are tested, <strong>the</strong> number <strong>of</strong> triggered events is multipliedwith <strong>the</strong> two scale factors N(") and N(E). For <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> relative difference <strong>of</strong> triggeredevents with <strong>the</strong> two ellipses, 200 shower sizes are created, covering <strong>the</strong> whole spectrum, from <strong>the</strong>point where <strong>the</strong> triggering <strong>of</strong> three stations becomes possible for <strong>the</strong> first time, up to <strong>the</strong> energy,where 3 (4 for <strong>the</strong> 4-fold test) stations are triggered, independent <strong>of</strong> <strong>the</strong> core position. For eachshower size, showers for every zenith angle up to 60 ◦ are created in steps <strong>of</strong> 1 ◦ . In total19500 × 200 × 60 = 2.34 · 10 8 showersare simulated for both ellipses. For each shower size and zenith angle, <strong>the</strong> number <strong>of</strong> detectedshowers is counted and normalized with N (S(1000)). Finally, <strong>the</strong> number <strong>of</strong> showers N x with) = 0 ◦ (major axis parallel to x-axis) and N y with ) = 90 ◦ are calculated. The relative differenceis determined fromD = 2 · (N x − N y )N x + N y· 100. (5.16)5.3.2 Asymmetry correctionThe footprints <strong>of</strong> inclined showers are ellipses. As <strong>the</strong> <strong>detector</strong> level is below <strong>the</strong> shower maximum,<strong>the</strong> number <strong>of</strong> particles decreases, before <strong>the</strong> shower reaches <strong>the</strong> ground. In a first approximation,this can be taken into account <strong>by</strong> an inverted cone reaching <strong>the</strong> <strong>detector</strong> level. Theintersection is an ellipse, which is not centered around <strong>the</strong> core (see Figure 5.12). For a givencone, <strong>the</strong> half angle 0, <strong>the</strong> semi-major axis and <strong>the</strong> <strong>of</strong>fset <strong>of</strong> <strong>the</strong> elliptical center from <strong>the</strong> cone axiscan be calculated. The distances from <strong>the</strong> conical axis to <strong>the</strong> edges <strong>of</strong> <strong>the</strong> ellipse along <strong>the</strong> major
5.3 Model for <strong>the</strong> hexagonal effect 61Figure 5.12: The intersection <strong>of</strong> a vertical cylinder, an inclined cylinder, and an inclined (inverted) conewith <strong>the</strong> ground plane [46].and minor axis areThe semi-major axis adds isr 1 = S msin(90 − 0)sin(90 + 0 − ") and r 2 = S msin(90 + 0)sin(90 − 0 − ") . (5.17)S M = r 1 + r 22and <strong>the</strong> <strong>of</strong>fset d <strong>of</strong> <strong>the</strong> elliptic center is= S mcos"(5.18)d = r 2 − r 1. (5.19)2In order to consider this in <strong>the</strong> model, <strong>the</strong> core positions are shifted <strong>by</strong> d and <strong>the</strong> ellipses are drawnaround <strong>the</strong> new positions. After moving all cores <strong>by</strong> a constant term, <strong>the</strong> whole rectangle <strong>of</strong> corepositions is moved <strong>by</strong> this value and due to <strong>the</strong> regular shape <strong>of</strong> <strong>the</strong> array, this does not change <strong>the</strong>number <strong>of</strong> detected events. In <strong>the</strong> model, <strong>the</strong> influence has been tested for cone half angles up to10 ◦ and <strong>the</strong> number <strong>of</strong> events has not been affected.5.3.3 Signal fluctuationsIn studies dealing with trigger probabilities, it is essential to analyze signal fluctuations in detail.In <strong>the</strong> analysis presented here, <strong>the</strong> impact <strong>of</strong> fluctuations is small, since <strong>the</strong> comparison <strong>of</strong> <strong>the</strong>two orientations <strong>of</strong> <strong>the</strong> same ellipse guarantees that <strong>the</strong> fluctuations almost cancel each o<strong>the</strong>r.Never<strong>the</strong>less, a test has been performed to check <strong>the</strong> assumption.Without fluctuations, <strong>the</strong> trigger efficiency is one inside <strong>the</strong> ellipse and zero outside. In Chapter3.2, <strong>the</strong> trigger probability <strong>of</strong> individual <strong>surface</strong> <strong>detector</strong>s has been described. The continuousincrease <strong>of</strong> <strong>the</strong> trigger probability is simulated <strong>by</strong> s<strong>of</strong>tening <strong>the</strong> sharp transition from one to zero<strong>by</strong> a Gaussian smearing (see Figure 5.13). At <strong>the</strong> former edge <strong>of</strong> <strong>the</strong> ellipse <strong>the</strong> trigger probabilityis 0.5. Up to 0.9r, <strong>the</strong> probability stays at one and for distances larger than 1.4r it becomes zero. Inbetween, a random number between 0 and 1 is picked from a uniform distribution and comparedto <strong>the</strong> value <strong>of</strong> <strong>the</strong> Gaussian distribution at this distance r. If <strong>the</strong> randomly chosen value is smallerthan <strong>the</strong> value <strong>of</strong> <strong>the</strong> Gauss smeared edge, <strong>the</strong> station has been triggered, o<strong>the</strong>rwise not.In <strong>the</strong> next section, <strong>the</strong> results obtained with and without fluctuations are presented.
62 Azimuth angle distribution110.5r0.9r rFigure 5.13: Model with binary trigger probability (left) and with a continuously developing trigger probability(right).5.3.4 ResultsJust like for <strong>the</strong> <strong>data</strong>, <strong>the</strong> simulation is performed for all events and for <strong>the</strong> 3-fold and 4-fold events,separately. Table 5.4 lists <strong>the</strong> results. Figure 5.14 illustrates <strong>the</strong> number <strong>of</strong> showers triggering <strong>the</strong>ModelDataD D f luc % <strong>of</strong> events D % <strong>of</strong> events3-fold 1.32% 1.20% 72.5 −1.17% 77.04-fold −14.23% −13.7% 20.6 −8.44% 15.8all −0.51% −0.52% 100 −2.07% 100Table 5.4: Oscillations with amplitude D/2 in <strong>the</strong> azimuth angle distribution with a period <strong>of</strong> 2!/6.<strong>detector</strong>, plotted against S(1000) and ". In <strong>the</strong> zenith angle plots, <strong>the</strong> measured " distributions areadded. The " distributions obtained from <strong>the</strong> <strong>data</strong> are normalized, so that <strong>the</strong> maxima <strong>of</strong> <strong>the</strong> zenithangle distributions have <strong>the</strong> same amplitude. As shown in Table 5.4, <strong>the</strong>re are differences between<strong>the</strong> values <strong>of</strong> <strong>the</strong> model and <strong>the</strong> <strong>data</strong>. For all events, <strong>the</strong> model and <strong>the</strong> <strong>data</strong> show a minimum at) = 0 ◦ , but with different amplitudes. In <strong>the</strong> <strong>data</strong>, <strong>the</strong> effect is four times larger. In <strong>the</strong> subset <strong>of</strong><strong>the</strong> 3-fold events, <strong>the</strong> amplitudes are similar but <strong>the</strong> maxima <strong>of</strong> <strong>the</strong> model are at <strong>the</strong> positions <strong>of</strong><strong>the</strong> minima in <strong>the</strong> <strong>data</strong>. For <strong>the</strong> 4-fold events, <strong>the</strong> minima are at <strong>the</strong> same azimuth angles (90 ◦ ) for<strong>the</strong> model and <strong>the</strong> <strong>data</strong>, but <strong>the</strong> amplitude <strong>of</strong> <strong>the</strong> model is almost three times higher. At first view<strong>the</strong> model does not describe <strong>the</strong> <strong>data</strong> at all.3-fold events can trigger two types <strong>of</strong> triangle configurations, equilateral and stretched ones (seeChapter 5.2.1). In <strong>the</strong> model, <strong>the</strong> major part <strong>of</strong> <strong>the</strong> triggered triangles are equilateral triangles and,<strong>the</strong>refore, <strong>the</strong> minima are at 0 ◦ ± n · 60 ◦ , with n = 0,1,2,3. This compact configuration dominatesespecially for small zenith angles, as <strong>the</strong> footprints <strong>of</strong> <strong>the</strong>showers on <strong>the</strong> ground are ellipses, where<strong>the</strong> differences between S M and S m are small. For inclined showers <strong>the</strong> ellipses are more stretchedand <strong>the</strong> stations at <strong>the</strong> corners <strong>of</strong> isosceles triangles are triggered more <strong>of</strong>ten. The " distribution<strong>of</strong> <strong>the</strong> model is shifted towards lower zenith angles and, <strong>the</strong>refore, <strong>the</strong> equilateral triangles occurwith a higher probability than in <strong>the</strong> <strong>data</strong>.Fur<strong>the</strong>rmore, <strong>the</strong> fraction <strong>of</strong> 3-fold events in <strong>the</strong> model is lower and <strong>the</strong> fraction <strong>of</strong> 4-fold eventsis higher than in <strong>the</strong> <strong>data</strong>. 5% <strong>of</strong> <strong>the</strong> events, which are 3-folds in <strong>the</strong> <strong>data</strong>, trigger four stations in<strong>the</strong> model. The azimuth distribution <strong>of</strong> <strong>the</strong>se events has a minimum at ) = 0 ◦ . They reduce <strong>the</strong>amplitude <strong>of</strong> <strong>the</strong> oscillation for <strong>the</strong> 4-fold events in <strong>the</strong> <strong>data</strong>, as <strong>the</strong>y are measured as 3-fold events.Besides, <strong>the</strong>ir maxima are at <strong>the</strong> positions <strong>of</strong> <strong>the</strong> minima in <strong>the</strong> 3-fold " distribution. In <strong>the</strong> <strong>data</strong><strong>the</strong>y reverse <strong>the</strong> direction <strong>of</strong> <strong>the</strong> effect.In <strong>the</strong> ) distribution <strong>of</strong> all events, <strong>the</strong> amplitudes in <strong>the</strong> <strong>data</strong> are four times more distinctive than
5.3 Model for <strong>the</strong> hexagonal effect 63N(S1000)120010003110counts10008003110DataModel ellipse 1Model ellipse 280060040060040020020000 20 40 60 80 100 120s0 10 20 30 40 50 60"N(S1000)1109008007006003counts7006005003110DataModel ellipse 1Model ellipse 25004003002001004003002001000 20 40 60 80 100 120s00 10 20 30 40 50 60"N(S1000)1108007006005003counts1801601401203110200DataModel ellipse 1Model ellipse 2400300200100100806040200 20 40 60 80 100 120s0 10 20 30 40 50 60"Figure 5.14: The number <strong>of</strong> triggered showers as a function <strong>of</strong> S(1000) (left) and <strong>the</strong> " distributions <strong>of</strong><strong>the</strong> two ellipses and <strong>the</strong> measured events. The plot at <strong>the</strong> top is for all events, <strong>the</strong> one in <strong>the</strong>middle for 3-fold events and <strong>the</strong> one at <strong>the</strong> bottom for 4-fold events. The major axis <strong>of</strong> ellipse1 is parallel to <strong>the</strong> east-west axis and <strong>the</strong> major axis <strong>of</strong> ellipse 2 is perpendicular.
64 Azimuth angle distributionin <strong>the</strong> model (see Table 5.4). The shift <strong>of</strong> <strong>the</strong> " distribution in <strong>the</strong> model enlarges <strong>the</strong> fraction <strong>of</strong>triggered equilateral triangles. They reduce <strong>the</strong> amplitude <strong>of</strong> <strong>the</strong> hexagonal effect.5.3.5 Limits <strong>of</strong> <strong>the</strong> modelIt is important to remark, that creating this simple model helps to understand and visualize <strong>the</strong>effect <strong>of</strong> <strong>the</strong> hexagonal structure <strong>of</strong> <strong>the</strong> array, but due to <strong>the</strong> simplifications a perfect agreementis not possible. The displacements <strong>of</strong> <strong>surface</strong> <strong>detector</strong> stations, <strong>the</strong> differences in <strong>the</strong> trigger ratesfor individual stations or <strong>the</strong> influences <strong>of</strong> not working stations are all not taken into account. TheLDF implemented in <strong>the</strong> CDAS code (see Equation 3.3) is simplified, as <strong>the</strong> entire LDF dependson <strong>the</strong> distance <strong>of</strong> <strong>the</strong> core to <strong>the</strong> nearest station and contains a second slope parameter #. All <strong>the</strong>sesimplifications could be implemented in <strong>the</strong> model, but <strong>the</strong>ir impact is small in comparison to <strong>the</strong>severest simplification, which has been made for <strong>the</strong> trigger condition.In <strong>the</strong> <strong>surface</strong> <strong>detector</strong> stations, two different local triggers are implemented, <strong>the</strong> single thresholdtrigger, which requires a signal <strong>of</strong> more than 3.2 VEM in one signal bin, and <strong>the</strong> time-overthresholdtrigger (ToT), which requires signals above 0.2 VEM in 13 time bins <strong>of</strong> 25 ns in aninterval <strong>of</strong> 3µs. The minimum signal for <strong>the</strong> ToT is <strong>the</strong>refore only 2.6 VEM. These two signalscorrespond to two different ellipse sizes for <strong>the</strong> trigger threshold. Since <strong>the</strong> time-over-thresholdtrigger condition is <strong>the</strong> most frequent one and <strong>the</strong> single threshold trigger only contributes a smallfraction (see Figure 3.2), only ToT events are considered in <strong>the</strong> model. Since it is not possibleto implement a condition to distinguish between <strong>the</strong>se two trigger criteria, this is <strong>the</strong> limit <strong>of</strong> <strong>the</strong>model. For fur<strong>the</strong>r analyses Monte Carlo simulations are essential. With <strong>the</strong>m, <strong>the</strong> fractions <strong>of</strong>single threshold and time-over-threshold triggered stations can be determined and <strong>the</strong> shift <strong>of</strong> <strong>the</strong>maximum in <strong>the</strong> zenith angle distribution for events with E < 3EeV can be analyzed in moredetail.5.4 Description <strong>of</strong> <strong>the</strong> asymmetry in 2!The azimuth angle distribution shows an oscillation with a period <strong>of</strong> 360 ◦ . The results <strong>of</strong> <strong>the</strong>fits, performed in Chapter 5.2.3, are summarized in Table 5.5. Nei<strong>the</strong>r in <strong>the</strong> amplitude nor inp ) min3-fold (3.15 ± 0.16)% 43.5 ◦4-fold (2.43 ± 0.36)% 75.3 ◦all (2.83 ± 0.14)% 53.3 ◦Table 5.5: Azimuth angles ) min and amplitudes p <strong>of</strong> <strong>the</strong> minima, obtained <strong>by</strong> <strong>the</strong> sine fits to <strong>the</strong> azimuthdistributions (see Section 5.2.3).<strong>the</strong> phase, <strong>the</strong> fits <strong>of</strong> <strong>the</strong> subsets agree with <strong>the</strong> values obtained for <strong>the</strong> whole <strong>data</strong> set. Whe<strong>the</strong>r<strong>the</strong> oscillation in 360 ◦ depends on <strong>the</strong> multiplicity <strong>of</strong> <strong>the</strong> events, is discussed as well as, whe<strong>the</strong>r<strong>the</strong> strength <strong>of</strong> <strong>the</strong> effect depends on <strong>the</strong> energy or <strong>the</strong> zenith angle. Afterwards possible timedependencies are analyzed.
5.4 Description <strong>of</strong> <strong>the</strong> asymmetry in 2! 655.4.1 RatiosIt has been shown, that <strong>the</strong> three PMTs induce no oscillation, or an oscillation with a very smallamplitude. From now on oscillations with a period <strong>of</strong> 120 ◦ are ignored and <strong>the</strong> focus is only on<strong>the</strong> superposition <strong>of</strong> <strong>the</strong> two oscillations with periods <strong>of</strong> 360 ◦ and 60 ◦ , respectively. To determine<strong>the</strong> amplitude and <strong>the</strong> phase <strong>of</strong> <strong>the</strong> 360 ◦ effect, ratios are calculated.The azimuth angle distribution is divided into equally sized bins <strong>of</strong> 60 ◦ . Each bin includes onefull period <strong>of</strong> <strong>the</strong> oscillation in 60 ◦ and, <strong>the</strong>refore, <strong>the</strong> number <strong>of</strong> entries in each bin is independent<strong>of</strong> <strong>the</strong> hexagonal effect. By comparing <strong>the</strong> two bins with mean values <strong>of</strong> ) and ) + 180 ◦ , for all) angles, <strong>the</strong> phase and <strong>the</strong> amplitude <strong>of</strong> <strong>the</strong> 360 ◦ effect can be determined. The ratio r i ( ) iscalculated as <strong>the</strong> fraction <strong>of</strong> <strong>the</strong> number <strong>of</strong> entries in <strong>the</strong> bins N 1i ∈ [) − 30 ◦ ,) + 30 ◦ ] and N 2i ∈[) + 180 ◦ − 30 ◦ ,) + 180 ◦ + 30 ◦ ]:The error is calculated <strong>by</strong> applying error propagationr i = N 1iN 2i. (5.20)(r i ==√ ( ) 2 ( ) 2 /ri/ri(N 1i + (N 2i (5.21)/N 1i /N 2i√ ( ) 1 √ 2 (N1i + − N )1i √ 2N2iN 2i N2i2 .(5.22)Figure 5.15 shows <strong>the</strong> ratio r i as a function <strong>of</strong> <strong>the</strong> azimuth angle. Although one half <strong>of</strong> <strong>the</strong> graphcontains <strong>the</strong> complete information, since r( ) is equal to 1/r() +180 ◦ ), <strong>the</strong> whole range is plottedto illustrate <strong>the</strong> sine structure. In <strong>the</strong> graph at <strong>the</strong> bottom <strong>of</strong> Figure 5.15 <strong>the</strong> ratios for <strong>the</strong> 3-fold and4-fold events are compared to <strong>the</strong> ratio for all events. For most azimuth angles <strong>the</strong> <strong>data</strong> points agreewithin 1,. A significant dependency on <strong>the</strong> number <strong>of</strong> triggered stations can not be confirmed.The sine behavior is clearly visible for all subsets <strong>of</strong> events. The amplitude and <strong>the</strong> phase areobtained <strong>by</strong> a sine-fit. The result for all events is( ))r( )=1.0 + 0.026 · sin180 − 144.38 . (5.23)As <strong>the</strong> ratios are determined <strong>by</strong> integrations, <strong>the</strong>y have to be normalized, to be comparable with<strong>the</strong> relative deviations obtained <strong>by</strong> <strong>the</strong> sine-fits (see Table 5.5). In this case, <strong>the</strong> scale factor is one,as <strong>the</strong> area below <strong>the</strong> integrated function is equal to one:∫ 2!3!3sinxdx = −cosx| 2! 3 !3= −[−0.5 − 0.5]=1. (5.24)The minimum for <strong>the</strong> plot with all events is at ) min = 54.4 ◦ and <strong>the</strong> amplitude is p = 2.64%. Thevalues are in agreement with <strong>the</strong> ones listed in Table 5.5.In order to analyze, up to which energy <strong>the</strong> effect is significant, a Rayleigh analysis is performed.With this method, it is possible to quantify <strong>the</strong> probability <strong>of</strong> an asymmetry, to be due to randomfluctuations. This is especially important for <strong>the</strong> energy range above full acceptance. All searchesfor large scale anisotropies and correlations with point sources start with <strong>the</strong> basic assumption <strong>of</strong>a flat azimuth distribution for events with E > 3EeV.
0.02643p0 ±0.0002399p1 0.01745 ±0p2 -2.524 ±0.009115p3 1 ±066 Azimuth angle distributionratio1.041.031.021.0110.990.980.97all events0.96-150 -100 -50 0 50 100 150)ratio1.041.031.021.0110.990.980.970.96all events3-fold events4-fold events-150 -100 -50 0 50 100 150)Figure 5.15: Top: Ratios between all events measured in N 1i ∈ [) − 30 ◦ ,) + 30 ◦ ] and N 2i ∈[) + 180 ◦ − 30 ◦ ,) + 180 ◦ + 30 ◦ ]. Bottom: Comparison <strong>of</strong> <strong>the</strong> ratios <strong>of</strong> events with differentnumbers <strong>of</strong> triggered stations.5.4.2 Rayleigh analysisA Rayleigh analysis [64, 65] is a harmonic analysis, where <strong>the</strong> m-th order fits <strong>the</strong> distribution <strong>of</strong>azimuths . i <strong>of</strong> <strong>the</strong> N events to a sine wave with period 2!/m. The amplitude r and <strong>the</strong> phase . r <strong>of</strong><strong>the</strong> sine fit are given <strong>by</strong>√r = a 2 + b 2 and tan. r = b (5.25)awitha = 2 NN+i=1cos(m. i ) and b = 2 NN+i=1sin(m. i ). (5.26)The chance probability, for obtaining an amplitude larger than r for a uniform distribution, is given<strong>by</strong>P(≥ r)=exp(−k) (5.27)with k = Nr 2 /4. For <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> oscillation with a period <strong>of</strong> 2! in <strong>the</strong> azimuth distribution,first order Rayleigh tests (m = 1) are performed. The first analysis (see Figure 5.16 left) isperformed <strong>by</strong> determining <strong>the</strong> amplitude, phase and probability for T5 events with energies abovegiven values, as a function <strong>of</strong> <strong>the</strong> threshold energy. The Rayleigh amplitude, phase and probabilityare calculated as a function <strong>of</strong> <strong>the</strong> threshold energy. The phase corresponds to <strong>the</strong> location <strong>of</strong>
5.4 Description <strong>of</strong> <strong>the</strong> asymmetry in 2! 67Rayleigh amplitude1-110Rayleigh amplitude-110-210-210-3-11010 1 10210E [EeV]10-3-110 1 10E [EeV]Rayleigh phase20015010050Rayleigh phase2001501005000-50-50-100-100-150-150-200-110 1 10210E [EeV]-200-110 1 10210E [EeV]Rayleigh probability-210-410-610-81010101-10-12-1410-1610-1810-2010-22-11010 1 10210E [EeV]Rayleigh probability-210-410-610-810-101010-12-1410-1610-1810-201010 -22-24-11010 1 10210E [EeV]Figure 5.16: Rayleigh amplitude, phase and probability for T5 events with " < 60 ◦ above a given energy(left) and below a given energy (right).
68 Azimuth angle distribution<strong>the</strong> minimum <strong>of</strong> <strong>the</strong> sine wave, that fits <strong>the</strong> distribution best. For <strong>the</strong> <strong>data</strong> points up to an energy<strong>of</strong> 1 EeV, <strong>the</strong> amplitude is nearly constant at a value close to 10 −2 , <strong>the</strong> phase is constant at 55 ◦and <strong>the</strong> probability increases from 10 −21 to 10 −4 with increasing energy. The probability, that <strong>the</strong>asymmetry in <strong>the</strong> <strong>data</strong> is accidental is 10 −21 , if all events are taken. The decrease <strong>of</strong> <strong>the</strong> probabilityis due to <strong>the</strong> fact, that <strong>the</strong> number <strong>of</strong> events decreases with increasing energy threshold. For <strong>the</strong>events above 1 EeV, <strong>the</strong> probability to measure such an effect <strong>by</strong> chance is still 10 −4 . For eventsabove 3 EeV, <strong>the</strong> Rayleigh probability is above 10 −2 , as <strong>the</strong> number <strong>of</strong> events decreases. Never<strong>the</strong>less,<strong>the</strong> phase remains at about 55 ◦ , except for a few <strong>data</strong> points, up to 20 EeV.In <strong>the</strong> second test (see Figure 5.16 right), <strong>the</strong> amplitude, phase and probability are calculated for<strong>the</strong> events with energies below given values, again as a function <strong>of</strong> <strong>the</strong> threshold energy. The <strong>data</strong>point at <strong>the</strong> highest energy corresponds to <strong>the</strong> point at <strong>the</strong> lowest energy in <strong>the</strong> previous analysis.Both points are calculated using <strong>the</strong> whole <strong>data</strong> set. With decreasing energy threshold, <strong>the</strong>number <strong>of</strong> events is reduced. Down to an energy <strong>of</strong> 1 EeV, <strong>the</strong> amplitude (≈ 10 −2 ) , phase (55 ◦ )and probability (< 10 −22 ) are almost constant. Below 0.5 EeV, <strong>the</strong> phase is no longer constantand <strong>the</strong> probability reaches zero. The reason for this can be seen from Figure 5.16. In <strong>the</strong> regionaround 0.2 EeV, a few bins have a Rayleigh phase <strong>of</strong> −80 ◦ . The probability is close to zero, but itis sufficient to cause <strong>the</strong> dip in <strong>the</strong> phase diagram in Figure 5.16 (right).Two fur<strong>the</strong>r Rayleigh tests have been performed. The events are once divided into seven separateenergy ranges, and once into energy bins <strong>of</strong> varying sizes, with <strong>the</strong> bin center changed from smallto high energies. The entries <strong>of</strong> bin i are in <strong>the</strong> energy range <strong>of</strong>(−1 + 0.01 · i) < log 10 E i ≤ (−1 + 0.01 · (i + 10)).The result for <strong>the</strong> test with <strong>the</strong> seven bins is displayed in Table 5.6, whereas Figure 5.17 shows <strong>the</strong>result for <strong>the</strong> analysis with <strong>the</strong> bins <strong>of</strong> varying size.E [EeV] Entries Amplitude [%] Phase Probability< 0.5 396219 1.6 42.0 4.41 · 10 −110.5 − 1 366669 1.4 60.9 2.72 · 10 −81 − 2 165983 1.0 70.3 1.56 · 10 −22 − 3 32094 1.9 72.3 5.12 · 10 −23 − 5 14908 1.4 -74.8 5.05 · 10 −15 − 10 6605 2.6 58.8 3.31 · 10 −1> 10 2889 5.3 63.6 1.33 · 10 −1Table 5.6: Rayleigh amplitudes, phases and probabilities <strong>of</strong> T5 events, subdivided in six independentenergy bins. The phase corresponds to <strong>the</strong> location <strong>of</strong> <strong>the</strong> minimum <strong>of</strong> a sine wave.The plot in <strong>the</strong> middle <strong>of</strong> Figure 5.17 shows only small changes in <strong>the</strong> phase for <strong>the</strong> bins witha bin center less than 1 EeV. This energy range contains <strong>the</strong> majority <strong>of</strong> all detected events. Forabout 30 bins, <strong>the</strong> probability is below 10 −3 . For all bins with phases very different from 55 ◦ , <strong>the</strong>probabilities are close to zero. Table 5.6 shows <strong>the</strong> phases, amplitudes and probabilities for sevennon-overlapping bins and <strong>the</strong> number <strong>of</strong> entries in <strong>the</strong> bins. Here, again <strong>the</strong> phase is close to 55 ◦for most bins.The Rayleigh analyses have established, that <strong>the</strong> azimuth asymmetry is not accidental. TheRayleigh probability for all events is 10 −21 with a phase <strong>of</strong> 55 ◦ . These results are in perfectagreement with <strong>the</strong> phase <strong>of</strong> 55 ◦ and <strong>the</strong> amplitude <strong>of</strong> 2.66% obtained <strong>by</strong> <strong>the</strong> ratio method.
5.4 Description <strong>of</strong> <strong>the</strong> asymmetry in 2! 69Rayleigh amplitude-11010-2Rayleigh phaseRayleigh probability-310 -110 1 10200150100500-50-100-150-200-110 1 10101-110-210-310-4-510-610-710-110 1 10210E [EeV]210E [EeV]210E [EeV]Figure 5.17: Rayleigh amplitude, phase and probability for T5 events with " < 60 ◦ in logarithmic energybins.
70 Azimuth angle distribution5.4.3 Energy and " dependencyUp to now, a sine structure <strong>of</strong> <strong>the</strong> asymmetry in <strong>the</strong> azimuth distribution has been assumed, as <strong>the</strong>form <strong>of</strong> <strong>the</strong> oscillation looks like a sine. By modifying <strong>the</strong> method presented in Chapter 5.4.1, ananalysis independent <strong>of</strong> this assumption is performed. The number <strong>of</strong> events detected in a 60 ◦ binin ) is compared to <strong>the</strong> total number <strong>of</strong> events. For a flat distribution, 1/6 <strong>of</strong> all events is expectedto be found in each bin, independent <strong>of</strong> its position. The bin size <strong>of</strong> 60 ◦ is chosen again to excludeany inpact from <strong>the</strong> hexagonal effect.With this method <strong>the</strong> same plot as in Figure 5.15 is generated. It is shown in Figure 5.18. Theratio0.030.02all events0.010-0.01-0.02-0.03-150 -100 -50 0 50 100 150)Figure 5.18: Relative deviations <strong>of</strong> <strong>the</strong> number <strong>of</strong> events detected in 60 ◦ bins, from a flat distribution.azimuth angle distribution has a defined maximum at ) =(−130 ± 5) ◦ , with an excess <strong>of</strong> (1.7 ±0.3)% and a minimum between 0 ◦ and 100 ◦ , with a deficit <strong>of</strong> (−1.0 ± 0.3)% in <strong>the</strong> number <strong>of</strong>detected events. The deviations are in agreement with <strong>the</strong> results obtained with <strong>the</strong> sine fit (seeFigure 5.15). The amplitude <strong>of</strong> 2.64% at ) max = −126.4 ◦ is calculated as <strong>the</strong> difference between<strong>the</strong> number <strong>of</strong> events in <strong>the</strong> bin centered around ) max and <strong>the</strong> bin centered around ) min = ) max +180 ◦ and is <strong>the</strong>refore larger.Now, a two dimensional map in " and ) is created to find <strong>the</strong> maximum and minimum in ) andto figure out, if <strong>the</strong> strength or <strong>the</strong> location <strong>of</strong> <strong>the</strong> maximum depends on <strong>the</strong> zenith angle. At eachpoint (", ) in Figure 5.19 (upper left) <strong>the</strong> ratio between <strong>the</strong> events detected in [) − 30 ◦ ,) + 30 ◦ ]and [" − 5 ◦ ," + 5 ◦ ] and all events detected in [" − 5 ◦ ," + 5 ◦ ] for all azimuth angles, is calculated.These relative deviations p are <strong>by</strong> a factor <strong>of</strong> two smaller for a sine oscillation, compared to <strong>the</strong>ones calculated in Chapter 5.4.1, where <strong>the</strong> difference between <strong>the</strong> maximum and minimum iscalculated.With respect to ", <strong>the</strong> plot is limited to a range from 5 ◦ to 55 ◦ , to use only events below 60 ◦ . Thechoice <strong>of</strong> <strong>the</strong> interval size in " is motivated <strong>by</strong> a compromise between having enough statistics anda not to large overlap between <strong>the</strong> individual bins.The obtained ratios are multiplied <strong>by</strong> a factor <strong>of</strong> six and afterwards a value <strong>of</strong> one is subtracted. Thenumerical values represent <strong>the</strong> differences in <strong>the</strong> number <strong>of</strong> detected events from a flat distributionin percent. The upper left plot in Figure 5.19 shows <strong>the</strong>ses relative differences p and in <strong>the</strong> upperright plot <strong>the</strong> absolute errors ( p <strong>of</strong> <strong>the</strong> relative differences are shown. Their sizes depend on <strong>the</strong>number <strong>of</strong> <strong>the</strong> events in <strong>the</strong> bins. The plot on <strong>the</strong> bottom left shows <strong>the</strong> significance t = p/( p,
5.4 Description <strong>of</strong> <strong>the</strong> asymmetry in 2! 710.030.0130.030.020.010-0.01-0.02555045403530252015105-150 -100 -50 050100 1500.020.010-0.01-0.020.0140.0130.0120.0110.010.0090.0080.0070.0060.005555045403530252015105-150 -100 -50 050100 1500.0120.0110.010.0090.0080.0070.00640.06543210-1-2-35055 -445403530252015105-150 -100 -50 050100 1503210-1-2-30.080.060.040.020-0.02-0.04-0.06555045403530252015105-150 -100 -50 050100 1500.040.020-0.02-0.04Figure 5.19: Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): Relative deviations from a flat azimuth distribution (top left), errors <strong>of</strong> <strong>the</strong>se values (topright), significances (bottom left) and fluctuated map <strong>of</strong> deviations (bottom right).
72 Azimuth angle distributioncalculated from <strong>the</strong> two plots in <strong>the</strong> upper row. The plot on <strong>the</strong> bottom right is <strong>the</strong> same map as in<strong>the</strong> upper left, with each point (", ) fluctuated <strong>by</strong> its error. Every point in <strong>the</strong> map is obtained asa random value from a Gaussian distribution with <strong>the</strong> mean value p and <strong>the</strong> width ( p.Figure 5.19 shows, that <strong>the</strong> assumption <strong>of</strong> a sine structure might be incorrect and has to be analyzedin more detail. For <strong>the</strong> zenith angle region with <strong>the</strong> highest significances (" ≈ 50 ◦ ), <strong>the</strong> differencebetween <strong>the</strong> maximum ) max ≈−120 ◦ and <strong>the</strong> minimum ) min ≈ +100 ◦ is only 140 ◦ , not 180 ◦ .In addition to this, it seems that <strong>the</strong> position <strong>of</strong> largest negative deviation varies with <strong>the</strong> zenithangle. For " = 55 ◦ it is located at ) min ≈ 100 ◦ and shifts to ) min ≈−40 ◦ for " = 0 ◦ . As <strong>the</strong>statistics are small for vertical showers, <strong>the</strong> significances are small for bins with bin centers below25 ◦ . Within its errors, it is also possible that <strong>the</strong> minimum is at ) ≈ 70 ◦ for all zenith angles. T<strong>of</strong>igure this out and to determine any possible energy dependencies, <strong>the</strong> events are divided into sixenergy and six " bins, delimitated <strong>by</strong> <strong>the</strong> edges listed in Table 5.4.3. The bin edges are chosenin a way, that each bin contains <strong>the</strong> same number <strong>of</strong> events. The dependence <strong>of</strong> <strong>the</strong> variationsbin 1 2 3 4 5 6" [ ◦ ] < 20.5 20.5 − 28.5 28.5 − 35.0 35.0 − 41.0 41.0 − 47.5 > 47.5E [EeV] < 0.34 0.34 − 0.45 0.45 − 0.59 0.59 − 0.8 0.8 − 1.2 > 1.2Table 5.7: Borders <strong>of</strong> <strong>the</strong> " and energy bins.on <strong>the</strong> energy and on " are analyzed for bins around four selected azimuth angles: one at <strong>the</strong>position <strong>of</strong> <strong>the</strong> maximum () = −120 ◦ ) and three in <strong>the</strong> region <strong>of</strong> <strong>the</strong> minimum () = 5 ◦ , ) = 55 ◦ ,) = 105 ◦ ). Figure 5.20 shows <strong>the</strong> results for ) = −120 ◦ . Nei<strong>the</strong>r an explicit zenith angle, norRatio0.050.04Ratio0.050.040.030.030.020.020.010.01-0-0-0.011 2 3 4 5 6"-0.011 2 3 4 5 6EnergyFigure 5.20: Relative differences in <strong>the</strong> number <strong>of</strong> events detected in a 60 ◦ bin around ) = −120 ◦ incomparison to a flat distribution. The left plot shows <strong>the</strong> zenith angle dependence, <strong>the</strong> rightplot <strong>the</strong> energy dependence.an explicite energy dependence can be ga<strong>the</strong>red from <strong>the</strong> plots. Both graphs are compatible witha flat distribution. In <strong>the</strong> map in Figure 5.19, it seems that <strong>the</strong> strength <strong>of</strong> <strong>the</strong> effect increaseswith <strong>the</strong> zenith angle increasing. This apparent difference between <strong>the</strong> plots <strong>of</strong> Figures 5.19 and5.20 is caused <strong>by</strong> <strong>the</strong> fact, that <strong>the</strong> bins in <strong>the</strong> map at small zenith angles contain a relative small
5.4 Description <strong>of</strong> <strong>the</strong> asymmetry in 2! 73number <strong>of</strong> events. The significances are small and give <strong>the</strong> impression <strong>of</strong> a positive fluctuation. Itis possible, that <strong>the</strong> first <strong>data</strong> point in Figure 5.20 is in fact caused <strong>by</strong> a positive fluctuation, butthis has to be confirmed, when more events are detected.In <strong>the</strong> energy plot, no significant deviations from a flat distribution are found. As <strong>the</strong> first five binscontain only events with energies below 1.2 EeV and <strong>the</strong> last bin comprises <strong>the</strong> events with higherenergies, all events above full acceptance are included in this bin. The number <strong>of</strong> events is notsufficient to analyze <strong>the</strong> strength <strong>of</strong> <strong>the</strong> effect above full acceptance separately. The size <strong>of</strong> <strong>the</strong>errors make every value compatible with zero.Figure 5.21 shows <strong>the</strong> same plots for bins around various azimuth angles in <strong>the</strong> range <strong>of</strong> <strong>the</strong>minimum. For <strong>the</strong> energy plot, it is not possible to make a statement, besides, that <strong>the</strong> three ratiosRatio0.01Ratio0.01Bin around 5àBin around 55àBin around 105à00-0.01-0.01-0.02-0.02-0.03-0.031 2 3 4 5 6"1 2 3 4 5 6EnergyFigure 5.21: Same as Figure 5.20 with 60 ◦ bins around ) = 5 ◦ , ) = 55 ◦ and ) = 105 ◦ .<strong>of</strong> <strong>the</strong> three positions agree with each o<strong>the</strong>r within <strong>the</strong>ir errors. For zenith angles above 40 ◦ <strong>the</strong>rations do not agree within <strong>the</strong>ir errors. As for none <strong>of</strong> <strong>the</strong> three azimuth angles a tendency can bestated, nei<strong>the</strong>r a constant minimum nor a minimum varying with <strong>the</strong> zenith angle can be excluded.5.4.4 Different areas <strong>of</strong> <strong>the</strong> arrayIn this part, <strong>the</strong> array is divided into four spatial parts, north-west, north-east, south-west andsouth-east. The two cuts in north-south and east-west direction are such, that each quarter containsone fourth <strong>of</strong> <strong>the</strong> <strong>recorded</strong> events. In Figure 5.22, <strong>the</strong> deviations from an isotropic distribution andin Figure 5.23 <strong>the</strong>ir significances are plotted for each <strong>of</strong> <strong>the</strong> four parts. The ratios in <strong>the</strong> upperplots are again calculated for <strong>the</strong> events detected in [) − 30 ◦ ,) + 30 ◦ ] and [" − 5 ◦ ," + 5 ◦ ] andfor all events detected in [" − 5 ◦ ," + 5 ◦ ] with all azimuth angles. The significances represent <strong>the</strong>discrepancies in units <strong>of</strong> ,. All four ratio and significance plots are normalized, so <strong>the</strong>y can becompared <strong>by</strong> eye.The south-west part <strong>of</strong> <strong>the</strong> array shows less distinct deviations from a flat distribution than <strong>the</strong> o<strong>the</strong>rparts. This is <strong>the</strong> oldest part <strong>of</strong> <strong>the</strong> array. In this quarter, <strong>the</strong> deviations for small zenith angles arenot significant, due to <strong>the</strong> small number <strong>of</strong> detected extensive air showers and <strong>the</strong> distribution iscompatible with a flat distribution. In <strong>the</strong> adjacent part in <strong>the</strong> east, <strong>the</strong> minimum and maximumare much more distinctive. In <strong>the</strong> region around ) = −120 ◦ , <strong>the</strong> strength <strong>of</strong> <strong>the</strong> effect is up to 4%
74 Azimuth angle distribution0.040.040.040.020.020.040.020.02-0-0-0.02-0-0-0.02-0.04-0.065040302010-150 -100 -50 0 50100 150-0.02-0.04-0.06-0.04-0.065040302010-150 -100 -50 0 50100 150-0.02-0.04-0.060.040.040.040.020.020.040.020.02-0-0.02-0.04-0-0.02-0-0.02-0.04-0-0.02-0.065040302010-150 -100 -50 0 50100 150-0.04-0.06-0.065040302010-150 -100 -50 0 50100 150-0.04-0.06Figure 5.22: Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): The four plots show <strong>the</strong> relative differences from an isotropic distribution. The plots arearranged according to <strong>the</strong> positions <strong>of</strong> <strong>the</strong> parts in <strong>the</strong> array <strong>the</strong>y represent (north-west, north-east, south-west and south-east).
5.4 Description <strong>of</strong> <strong>the</strong> asymmetry in 2! 754404321-1-2-3-4-55040302010-150 -100 -50 0 50100 1503210-1-2-3-4-504321-1-2-3-4-55040302010-150 -100 -50 0 50100 1503210-1-2-3-4-54443210-1-2-3-4-55040302010-150-100 -50 0 50 100 1503210-1-2-3-4-543210-1-2-3-4-55040302010-150-100 -50 0 50 100 1503210-1-2-3-4-5Figure 5.23: Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): The four plots show <strong>the</strong> significances <strong>of</strong> <strong>the</strong> deviations shown in Figure 5.23. The plots arearranged according to <strong>the</strong> positions <strong>of</strong> <strong>the</strong> parts in <strong>the</strong> array <strong>the</strong>y represent (north-west, north-east, south-west and south-east).
76 Azimuth angle distributionwith significances between 2.5 and 4. In <strong>the</strong> north-east part, <strong>the</strong> relative deviations have a similarsize, as in <strong>the</strong> south-east, with slightly smaller significances. In <strong>the</strong> north-west part, <strong>the</strong> maximaare less distinctive than in <strong>the</strong> eastern parts.5.4.5 Time dependenceTo find <strong>the</strong> reason for <strong>the</strong> asymmetry in <strong>the</strong> azimuth angle distribution, it is important to know, if<strong>the</strong> strength or <strong>the</strong> location <strong>of</strong> <strong>the</strong> maximum, respectively <strong>the</strong> minimum, varies with time. Variationsare conceivable on different time scales. In this part, it is restricted to <strong>the</strong> obvious oneswith a periode <strong>of</strong> a day and a year. The time scan in hours is sensitive to influences <strong>of</strong> <strong>the</strong> sunand all o<strong>the</strong>r variations with a daily periodicity. By sorting <strong>the</strong> events into time bins <strong>of</strong> months,<strong>the</strong> influence <strong>of</strong> <strong>the</strong> seasons can be determined. In addition both studies give hints for possibletemperature dependencies.For each <strong>of</strong> <strong>the</strong> two tests, <strong>the</strong> events are sorted into six time bins. For <strong>the</strong> analysis on a daily basis,each bin includes <strong>the</strong> events <strong>of</strong> a four hour period, for <strong>the</strong> second analysis each bins includes <strong>the</strong><strong>data</strong> <strong>of</strong> two months <strong>of</strong> <strong>the</strong> year. Each point in Figure 5.24, respectively 5.25, shows <strong>the</strong> relativedeviation in <strong>the</strong> number <strong>of</strong> events detected in a 60 ◦ bin centered around <strong>the</strong> plotted azimuth angleand all measured events, both in <strong>the</strong> denoted time bins.In <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> daily variations (see Figure 5.24), <strong>the</strong>re is a difference in <strong>the</strong> locations <strong>of</strong> <strong>the</strong>maxima, between <strong>the</strong> evens detected in <strong>the</strong> morning and those, detected in <strong>the</strong> afternoon. The plot<strong>of</strong> <strong>the</strong> events detected between 8 h and 12 h has <strong>the</strong> maximum at ) ≈−140 ◦ and for <strong>the</strong> followingfour hours, it is at ) ≈−70 ◦ . The <strong>data</strong> points from <strong>the</strong> o<strong>the</strong>r time bins show no distinctive featuresand in <strong>the</strong> region <strong>of</strong> <strong>the</strong> minimum <strong>the</strong> values <strong>of</strong> all time bins are all compatible with each o<strong>the</strong>r.In Figure 5.25 <strong>the</strong> differences form a flat distribution are plotted dependent <strong>of</strong> <strong>the</strong> month, in which<strong>the</strong>y have been detected. There is no difference between summer and winter in <strong>the</strong> <strong>data</strong>. All valuesagree with each o<strong>the</strong>r, within <strong>the</strong>ir errors. This suggests that <strong>the</strong> effect does not vary with <strong>the</strong> temperatureor any o<strong>the</strong>r effects, like atmospheric conditions, which exhibit modulations in periods <strong>of</strong>years.5.4.6 Events with less strict cutsFor <strong>the</strong> analyses presented here, <strong>the</strong> number <strong>of</strong> detected events is too low to make explicit statements<strong>of</strong> dependencies on o<strong>the</strong>r parameters. This will change, when more events will be <strong>recorded</strong>in <strong>the</strong> future. At <strong>the</strong> moment, it is only possible to increase <strong>the</strong> number <strong>of</strong> events <strong>by</strong> s<strong>of</strong>tening <strong>the</strong>quality cuts. Two possibilities are discussed here: taking into account events with " > 60 ◦ andevents, which do not fulfill <strong>the</strong> T5 trigger, respectively.Cosmic rays with zenith angles well above 60 ◦ have to penetrate more air, as <strong>the</strong> path through<strong>the</strong> atmosphere increases with ". The muon content increases and, <strong>the</strong>refore, <strong>the</strong> reconstructionalgorithm is changed at " = 70 ◦ . The angular reconstruction becomes challenging, as <strong>the</strong> timedifferences between <strong>the</strong> stations increases and <strong>the</strong> influence <strong>of</strong> <strong>the</strong> hexagonal structure is morepronounced. The reconstruction is not as accurate as for events with " < 60 ◦ . Never<strong>the</strong>less, <strong>the</strong>reis no obvious reason, why this should effect <strong>the</strong> number <strong>of</strong> events detected in 60 ◦ bins, as eachbin includes one period <strong>of</strong> <strong>the</strong> oscillation, caused <strong>by</strong> <strong>the</strong> hexagonal structure <strong>of</strong> <strong>the</strong> array and reconstructionuncertainties should be distributed randomly. The ratio and <strong>the</strong> significance plot areexpanded and exhibited in Figure 5.26.Up to 70 ◦ , <strong>the</strong> map confirms <strong>the</strong> tendencies <strong>of</strong> increasing amplitudes and significances with increasing". The maximum stays constant at ) ≈−120 ◦ and <strong>the</strong> minimum seems to shift fur<strong>the</strong>rwith increasing " towards higher azimuth angles. Above 70 ◦ , <strong>the</strong> significances as well as <strong>the</strong>
5.4 Description <strong>of</strong> <strong>the</strong> asymmetry in 2! 77ratio0.040.030h - 4hratio0.040.034h - 8h0.020.020.010.0100-0.01-0.01-0.02-0.02-0.03-0.03-0.04-200 -150 -100 -50 0 50 100 150)-0.04-200 -150 -100 -50 0 50 100 150)ratio0.040.038h - 12hratio0.040.0312h - 16h0.020.020.010.0100-0.01-0.01-0.02-0.02-0.03-0.03-0.04-200 -150 -100 -50 0 50 100 150)-0.04-200 -150 -100 -50 0 50 100 150)ratio0.040.0316h - 20hratio0.040.0320h - 24h0.020.020.010.0100-0.01-0.01-0.02-0.02-0.03-0.03-0.04-200 -150 -100 -50 0 50 100 150)-0.04-200 -150 -100 -50 0 50 100 150)Figure 5.24: Relative deviations from a flat azimuth distribution in dependence on <strong>the</strong> time <strong>of</strong> <strong>the</strong> day,when <strong>the</strong> events were <strong>recorded</strong>.
78 Azimuth angle distributionratio0.040.030.020.010-0.01-0.02-0.03-0.04Month01 - 0203 - 0405 - 0607 - 0809 - 1011 - 12-150 -100 -50 0 50 100 150)Figure 5.25: Relative deviations from a flat azimuth distribution in dependence on <strong>the</strong> month, when <strong>the</strong>events were <strong>recorded</strong>.relative differences grow. Above 75 ◦ , <strong>the</strong> azimuth angle distribution has two maxima and twominima. The minimum obtained below 60 ◦ moves fur<strong>the</strong>r to higher azimuth angles. At " = 90 ◦ ,it is located at ) ≈ 180 ◦ . At " = 90 ◦ almost all measured events come from <strong>the</strong> north or <strong>the</strong> southand almost none form <strong>the</strong> east or <strong>the</strong> west. Although <strong>the</strong> significances are up to 11 respectively−10, <strong>the</strong> use <strong>of</strong> <strong>the</strong>se events needs a very detailed knowledge <strong>of</strong> <strong>the</strong> modified reconstruction and<strong>the</strong> trigger efficiencies. Within <strong>the</strong> scope <strong>of</strong> this <strong>the</strong>sis, it is not possible to perform such a comprehensiveanalysis.Ano<strong>the</strong>r method to increase <strong>the</strong> number <strong>of</strong> events, is to repeat <strong>the</strong> analysis without <strong>the</strong> T5 qualitytrigger requirement. The trigger requires, that <strong>the</strong> station with <strong>the</strong> highest signal is surrounded <strong>by</strong>a crown <strong>of</strong> six active stations during <strong>the</strong> time <strong>of</strong> <strong>the</strong> detection <strong>of</strong> <strong>the</strong> event. Just like for <strong>the</strong> cut at" = 60 ◦ , <strong>the</strong>re is no obvious reason, why <strong>the</strong> events should be biased without that cut, with respectto <strong>the</strong> occurrence in bins <strong>of</strong> 60 ◦ . The results for all events are shown in Figure 5.27. The result isqualitatively exactly <strong>the</strong> same as for <strong>the</strong> events, which fulfill <strong>the</strong> T5 trigger. The only differenceis, that higher significance can be obtained. The maximum in <strong>the</strong> azimuth angle distribution isat ) = −120 ◦ for all zenith angles. The largest excess <strong>of</strong> events (+3%) and a significance <strong>of</strong> 5is observed at ) ≈−120 ◦ and " = 55 ◦ ). The location <strong>of</strong> <strong>the</strong> minimum can not be specified asprecise as <strong>by</strong> <strong>the</strong> maximum. It is less pronounced and changes with <strong>the</strong> zenith angle. The absoluteminimum is at ) ≈ 100 ◦ and " = 55 ◦ with a deficit <strong>of</strong> events <strong>of</strong> −3% and a significance <strong>of</strong> 4.5.4.7 Attributes <strong>of</strong> <strong>the</strong> effectIn this section, <strong>the</strong> results <strong>of</strong> <strong>the</strong> tests performed to characterize <strong>the</strong> asymmetry in <strong>the</strong> azimuthangle distribution are summarized. In addition to <strong>the</strong> oscillation with a period <strong>of</strong> 60 ◦ a significantdeviation from a flat azimuth angle distribution has been found. The probability, that <strong>the</strong> azimuthangle distribution <strong>of</strong> all detected events with " < 60 ◦ , which fulfill <strong>the</strong> T5 trigger, is compatiblewith a flat distribution, is calculated as 10 −21 with a Rayleigh analysis. The effect has been
5.4 Description <strong>of</strong> <strong>the</strong> asymmetry in 2! 7911.210.80.60.40.20-0.2-0.4-0.68070605040302010-150 -100 -500501001500.80.60.40.20-0.2-0.4-0.61010550-50-10-58070605040302010-150 -100 -50050100150-10Figure 5.26: Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 85 ◦ ): Relative deviations from a flat distribution(top) and significance plot (bottom) for T5 events.
80 Azimuth angle distribution0.030.040.030.020.010.020.010-0.01-0.02-0.030-0.015040302010-150 -100 -50050100150-0.02-0.03564204321-20-4-15040302010-150 -100 -50 050100 150-2-3-4Figure 5.27: Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): Relative deviations from a flat distribution(top) and significance plot (bottom) for events, which fulfill <strong>the</strong> T5 requirement andthose which do not, for zenith angles up to 60 ◦ .
5.5 Origin <strong>of</strong> <strong>the</strong> asymmetry 81analyzed with and without <strong>the</strong> assumption <strong>of</strong> a sine behavior.With <strong>the</strong> assumption, <strong>the</strong> maximum is obtained at ) max = −125.6 ◦ and <strong>the</strong> difference between <strong>the</strong>maximum and minimum is 2.64%. Without <strong>the</strong> assumption <strong>the</strong> maximum is at ) =(−130 ± 5) ◦ ,with an excess <strong>of</strong> (1.7 ± 0.3)% and <strong>the</strong> minimum is located between 0 ◦ and 100 ◦ , with a deficit <strong>of</strong>(−1.0 ± 0.3)% in <strong>the</strong> number <strong>of</strong> detected events. Therefore, it is not clear, if <strong>the</strong> effect has a sinestructure, or not and will <strong>the</strong>refore be subject <strong>of</strong> fur<strong>the</strong>r investigations.By creating bins in " and ), <strong>the</strong> absolut maximum is found at ) ≈−120 ◦ and " = 55 ◦ and <strong>the</strong>absolute minimum is located at ) ≈ 100 ◦ and " = 55 ◦ , which complies with a phase difference<strong>of</strong> 140 ◦ , and not 180 ◦ , as expected for a sine. At <strong>the</strong> maximum, <strong>the</strong> excess <strong>of</strong> particles amountsto +3% with a significance <strong>of</strong> 4 and at <strong>the</strong> absolute minimum, <strong>the</strong> deficit is around −2.5% witha significance <strong>of</strong> 3. The position <strong>of</strong> <strong>the</strong> maximum is constant in ) for all zenith angles ". For <strong>the</strong>minimum, <strong>the</strong> " dependence remains unclear. Within <strong>the</strong> <strong>recorded</strong> statistics, a variation in ) from) = 0 ◦ at " = 5 ◦ to ) = 100 ◦ at " = 55 ◦ is as well possible as a constant value.A correlation with <strong>the</strong> energy could nei<strong>the</strong>r be obtained for <strong>the</strong> maximum nor for <strong>the</strong> minimumand an explicit time dependence is not visible. The only distinctive feature is a differene in <strong>the</strong>location <strong>of</strong> <strong>the</strong> maximum for events measured between 8 h and 12h() max ≈−140 ◦ ) and and eventsmeasured in <strong>the</strong> following four hours () max ≈−70 ◦ ).By splitting <strong>the</strong> array into four areas, a variation in <strong>the</strong> strength is determined. In <strong>the</strong> east, <strong>the</strong>extrema are more distinctive than in <strong>the</strong> west. In <strong>the</strong> south-west, <strong>the</strong> significances <strong>of</strong> <strong>the</strong> deviationsfrom a flat ) distribution are below 2.5, for all extrema in <strong>the</strong> " − )−map.5.5 Origin <strong>of</strong> <strong>the</strong> asymmetryNow, as <strong>the</strong> extent <strong>of</strong> <strong>the</strong> effect and <strong>the</strong> locations <strong>of</strong> <strong>the</strong> maximum and <strong>the</strong> minimum have beenpresented, <strong>the</strong> next step is to find <strong>the</strong> origin <strong>of</strong> <strong>the</strong> effect. In <strong>the</strong> search for <strong>the</strong> reason, it is importantto consider, that <strong>the</strong> asymmetry has been found in <strong>the</strong> local coordinate system <strong>of</strong> <strong>the</strong> <strong>detector</strong>and not in galactic coordinates. The causes are <strong>the</strong>refore limited to terrestrial impacts, <strong>detector</strong>effects and problems <strong>of</strong> <strong>the</strong> reconstruction algorithm. By assuming an isotropic flux for particles(with E < 57EeV) from outer space, <strong>the</strong> terrestrial effects could induce an asymmetry, <strong>by</strong>biasing <strong>the</strong> development <strong>of</strong> extensive air shower in <strong>the</strong> atmosphere. Possible reasons are varyingatmospheric conditions above <strong>the</strong> <strong>surface</strong> <strong>detector</strong> array or <strong>the</strong> influence <strong>of</strong> <strong>the</strong> geomagnetic field,which deflects <strong>the</strong> particles. Here, a comparison with <strong>the</strong> azimuth distribution <strong>of</strong> <strong>the</strong> fluorescence<strong>detector</strong> would be a useful tool. Unfortunately <strong>the</strong> <strong>recorded</strong> statistics <strong>of</strong> <strong>the</strong> telescopes are muchsmaller than for <strong>the</strong> <strong>surface</strong> <strong>detector</strong> and <strong>the</strong> ) distribution is influenced <strong>by</strong> many systematic effects.Therefore a comparison is <strong>of</strong> no help.It is only possible to stick to <strong>the</strong> <strong>data</strong> <strong>recorded</strong> <strong>by</strong> <strong>the</strong> <strong>surface</strong> <strong>detector</strong> or to compare it with MonteCarlo simulations. Monte Carlo simulation was not part <strong>of</strong> this <strong>the</strong>sis, so <strong>the</strong> search is limited totests <strong>of</strong> <strong>the</strong> measured events.5.5.1 CDAS reconstruction algorithmThe first test is to check, if <strong>the</strong> effect is also visible, if <strong>the</strong> events are reconstructed with <strong>the</strong> <strong>Auger</strong>Offline reconstruction s<strong>of</strong>tware instead <strong>of</strong> <strong>the</strong> CDAS code. For individual events, <strong>the</strong> differencesin <strong>the</strong> reconstructed arrival direction are less than three degrees [39]. The reconstructed S(1000)value is in average about 5% larger, if an event is reconstructed with <strong>the</strong> CDAS code, than in areconstruction with <strong>the</strong> Offline algorithm. The azimuth angle distributions <strong>of</strong> both reconstructionsare displayed in Figure 5.28. In both distributions, <strong>the</strong> oscillations in 2! and 2!/6 are clearly
82 Azimuth angle distributioncounts960094009600Entries 1079166 Entries 1079166counts9400920092009000900088008800860086008400-150 -100 -50 0 50 100 150)8400-150 -100 -50 0 50 100 150)Figure 5.28: The azimuth angle distributions <strong>of</strong> all events reconstructed with <strong>the</strong> CDAS algorithm (left)and <strong>the</strong> Offline algorithm (right).visible. The agreement <strong>of</strong> <strong>the</strong> distributions does not exclude an error in <strong>the</strong> reconstruction s<strong>of</strong>tware,but <strong>the</strong>n <strong>the</strong> same error is in <strong>the</strong> two independent algorithms. E.g. such an error could be a wrongdefinition <strong>of</strong> <strong>the</strong> coordinate system, which is implemented in both algorithms.5.5.2 Border effectsDuring <strong>the</strong> construction phase <strong>the</strong> array took sometimes complicated shapes (see Figure 5.29).The influence <strong>of</strong> <strong>the</strong> form and <strong>the</strong> border is excluded <strong>by</strong> using only <strong>the</strong> <strong>data</strong> <strong>of</strong> events, where <strong>the</strong>Figure 5.29: Status <strong>of</strong> <strong>the</strong> <strong>surface</strong> <strong>detector</strong> array in November 2005: 1031 tanks are deployed (shadedregion), 1012 filled with water and 898 with electronics [66].station with <strong>the</strong> highest signal is surrounded <strong>by</strong> two crowns <strong>of</strong> active stations. The requirement <strong>of</strong><strong>the</strong> T5+ trigger decreases <strong>the</strong> number <strong>of</strong> detected events from 985367 for <strong>the</strong> T5 trigger to 546140.The azimuth angle distribution shows still <strong>the</strong> same oscillations in 2! and 2!/6 as <strong>the</strong> plot <strong>of</strong> <strong>the</strong>events, that conformed to <strong>the</strong> T5 trigger only. An influence <strong>of</strong> <strong>the</strong> border can thus be excludedfor <strong>the</strong> <strong>data</strong> taking period with a growing array size, as well as for <strong>the</strong> time afterwards, when <strong>the</strong>installation <strong>of</strong> stations has been finished.
5.5 Origin <strong>of</strong> <strong>the</strong> asymmetry 835.5.3 Tilt <strong>of</strong> <strong>the</strong> arrayThe stations <strong>of</strong> <strong>the</strong> <strong>surface</strong> <strong>detector</strong> cover an area <strong>of</strong> 3000km 2 . Although <strong>the</strong> region in <strong>the</strong> PampaAmarilla is ra<strong>the</strong>r flat, variations <strong>of</strong> <strong>the</strong> ground level <strong>of</strong> up to 300 m occur. The stations with <strong>the</strong>highest altitudes are located in <strong>the</strong> west, <strong>the</strong> ones with <strong>the</strong> lowest altitudes in <strong>the</strong> north-east and<strong>the</strong> south (see Figure 3.11). The tilt <strong>of</strong> <strong>the</strong> array is determined <strong>by</strong> calculating <strong>the</strong> normal vector <strong>of</strong>each equilateral triangle, formed <strong>by</strong> three stations, and adding <strong>the</strong>m to an average normal vectorfor <strong>the</strong> whole array. This normal vector has changed, each time a new station has been deployed.In February 2008, 1547 stations <strong>of</strong> <strong>the</strong> regular grid were installed and <strong>the</strong> array was tilted <strong>by</strong> 0.16 ◦towards <strong>the</strong> south-east () = −22.2 ◦ ). This tilt influences <strong>the</strong> azimuth angle distribution, as <strong>the</strong>probability to detect events with ) = −22.2 ◦ is higher than <strong>the</strong> probability to detect events from<strong>the</strong> opposite direction. From <strong>the</strong> measured zenith angle distribution <strong>the</strong> size <strong>of</strong> this asymmetry canbe calculated. The estimated difference in <strong>the</strong> number <strong>of</strong> events between <strong>the</strong> minimum and <strong>the</strong>maximum is 0.18%.As <strong>the</strong> size <strong>of</strong> <strong>the</strong> effect is <strong>by</strong> a factor <strong>of</strong> 10 too small and <strong>the</strong> positions <strong>of</strong> <strong>the</strong> extrema are displaced<strong>by</strong> ≈ 100 ◦ , <strong>the</strong> tilt <strong>of</strong> <strong>the</strong> array is not <strong>the</strong> cause <strong>of</strong> <strong>the</strong> asymmetry in <strong>the</strong> azimuth angle distribution.5.5.4 PMT effectsWhen an extensive air shower deposits energy in a station, <strong>the</strong> signal <strong>of</strong> <strong>the</strong> station is calculatedas <strong>the</strong> average <strong>of</strong> <strong>the</strong> signals detected <strong>by</strong> <strong>the</strong> working PMTs. The fraction <strong>of</strong> <strong>the</strong> signal <strong>of</strong> <strong>the</strong> individualPMTs depends on <strong>the</strong> azimuth angle (see Chapter 5.2.2). The performed fits <strong>of</strong> <strong>the</strong> azimuthangle distribution have shown no significant oscillation with a period <strong>of</strong> 120 ◦ , induced <strong>by</strong> <strong>the</strong> threePMTs. Never<strong>the</strong>less, it is checked, if <strong>the</strong> PMTs can induce an oscillation with a period <strong>of</strong> 2!.A difference between <strong>the</strong> three PMTs is <strong>the</strong>ir temperature. The electronics <strong>of</strong> <strong>the</strong> stations is locatedbelow an aluminum enclosure above PMT1 and heats <strong>the</strong> PMT. The development <strong>of</strong> <strong>the</strong> temperaturesmeasured <strong>by</strong> <strong>the</strong>rmometers at <strong>the</strong> three PMTs and <strong>the</strong> electronics are plotted in Figure 5.30left. The temperature <strong>of</strong> <strong>the</strong> electronics is 10 ◦ higher across <strong>the</strong> day. To identify <strong>the</strong> temperaturetemp [degree]4035302520PMT 1PMT 2PMT 3Electronicstemp [degree]3210PMT 1 - PMT 2PMT 1 -PMT 3PMT 2 - PMT 315-110-250 2 4 6 8 10 12 14 16 18 20 22 24time [h]-30 2 4 6 8 10 12 14 16 18 20 22 24time [h]Figure 5.30: Temperatures <strong>of</strong> <strong>the</strong> electronics and <strong>the</strong> PMTs for one day (left) and differences betweenpairs <strong>of</strong> PMTs (right).
84 Azimuth angle distribution<strong>of</strong>fsets between <strong>the</strong> PMTs, <strong>the</strong>ir differences are calculated (see Figure 5.30 right). PMT 2 andPMT3 behave similar and have maximal differences <strong>of</strong> 1 ◦ . The temperature differences betweenPMT1 and <strong>the</strong> o<strong>the</strong>r two PMTs cover a range <strong>of</strong> 4 ◦ .In Chapter 5.4.5 <strong>the</strong> maxima obtained between 8 h and 16 h are a bit more distinctive <strong>the</strong>n in <strong>the</strong>o<strong>the</strong>r hours <strong>of</strong> <strong>the</strong> day. This is <strong>the</strong> region, where <strong>the</strong> temperature differences between <strong>the</strong> PMTs isminimal, but more events have to be detected to demonstrate a definite dependenceAno<strong>the</strong>r possible reason might be <strong>the</strong> raining behavior <strong>of</strong> many PMTs (see Chapter 3.4.2). Tocheck, if <strong>the</strong> raining PMTs are responsible for <strong>the</strong> asymmetry, <strong>the</strong> events are sorted into bins accordingto <strong>the</strong> number <strong>of</strong> triggered raining PMTs. Nei<strong>the</strong>r <strong>the</strong> amplitude, nor <strong>the</strong> phase <strong>of</strong> <strong>the</strong>asymmetry shows any correlation with <strong>the</strong> number <strong>of</strong> raining PMTs.The reconstruction algorithm is modified such, that <strong>the</strong> reconstruction is only performed with <strong>the</strong>signal <strong>of</strong> one PMT. To achieve this, <strong>the</strong> signal <strong>of</strong> one PMT is copied to <strong>the</strong> o<strong>the</strong>r two PMTs priorto reconstruction. By applying this to all stations, three modified HERALD files are generated,one for each PMT. The three azimuth distributions from <strong>the</strong> modified reconstruction are shown inFigure 5.31. All three distributions show <strong>the</strong> oscillations with periods <strong>of</strong> 2! and 2!/6 and agreecounts100009800Entries 1137358counts100009800Entries 1112948960096009400940092009200900090008800-150 -100 -50 0 50 100 150)8800-150 -100 -50 0 50 100 150)counts100009800Entries 1116668960021solar panel9400920090003north8800-150 -100 -50 0 50 100 150)Figure 5.31: Azimuth angle distributions, obtained <strong>by</strong> reconstructing <strong>the</strong> events with <strong>the</strong> signals <strong>of</strong> onlyone <strong>of</strong> <strong>the</strong> three PMTs per station. The plot in <strong>the</strong> upper left corner is for PMT 2, <strong>the</strong> upperright for PMT 1 and <strong>the</strong> plot at <strong>the</strong> bottom right is for PMT 3. The drawing illustrates <strong>the</strong>positions <strong>of</strong> <strong>the</strong> PMTs in <strong>the</strong> station.with each o<strong>the</strong>r. This check provides no fur<strong>the</strong>r information about <strong>the</strong> cause <strong>of</strong> <strong>the</strong> asymmetry.All tests performed with respect to <strong>the</strong> PMTs provide no indication <strong>of</strong> <strong>the</strong> reason <strong>of</strong> <strong>the</strong> asymmetry.
5.5 Origin <strong>of</strong> <strong>the</strong> asymmetry 855.5.5 Terrestrial magnetic fieldPrimary cosmic rays are mainly positively charged. They are deflected systematically <strong>by</strong> <strong>the</strong> terrestrialmagnetic field. Especially at low geomagnetic latitudes, this leads to an enhancement <strong>of</strong>cosmic rays hitting <strong>the</strong> atmosphere from <strong>the</strong> west. This so called east-west effect [67, 68] is aconsequence <strong>of</strong> <strong>the</strong> fact, that not all trajectories can reach <strong>the</strong> atmosphere from outside <strong>the</strong> geomagneticfield. To see, which trajectories are allowed, a standard procedure is to inject positivelyand negatively charged particles near <strong>the</strong> top <strong>of</strong> <strong>the</strong> atmosphere in various directions and simulate<strong>the</strong>ir paths back outward to <strong>the</strong>ir incoming directions. If <strong>the</strong>ir paths intersect with <strong>the</strong> <strong>surface</strong> <strong>of</strong><strong>the</strong> earth, <strong>the</strong> respective directions are impossible.The magnitude <strong>of</strong> <strong>the</strong> deflection <strong>of</strong> charged particles in magnetic fields decreases with <strong>the</strong> energies<strong>of</strong> <strong>the</strong> particles increasing. The horizontal component <strong>of</strong> <strong>the</strong> geomagnetic field at <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong>observatory in Malargüe is B ≈ 20 µT. A proton at an energy E = 3 · 10 18 eV has a momentum <strong>of</strong>|⃗p| ≈ E/c = 1 · 1010 eV·s. The Lorentz force forces <strong>the</strong> particles to move on a circular path with<strong>the</strong> radiusmr =peV·sq · B = 1 · 1010m1e· 20 · 10 −6 T = 5 · 1014 m. (5.28)The strength <strong>of</strong> <strong>the</strong> magnetic field decreases as <strong>the</strong> distance to <strong>the</strong> earth increases and in an altitude<strong>of</strong> 100 km above ground <strong>the</strong> strength is reduced <strong>by</strong> 98%. As <strong>the</strong> radius <strong>of</strong> <strong>the</strong> circle, which wouldbe described <strong>by</strong> a particle deflected <strong>by</strong> <strong>the</strong> geomagnetic field, is about nine orders <strong>of</strong> magnitudelarger, than <strong>the</strong> region, where <strong>the</strong> geomagnetic field deflects <strong>the</strong> cosmic rays, <strong>the</strong> impact is verysmall. This rough calculation illustrates that <strong>the</strong> east-west effect is negligible for <strong>the</strong> energy rangecovered <strong>by</strong> <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory. The deflection <strong>of</strong> <strong>the</strong> secondary particles is not studiedand can be subject <strong>of</strong> fur<strong>the</strong>r investigations.5.5.6 Solar panelThe power for <strong>the</strong> electronics is provided <strong>by</strong> a solar photovoltaic system, installed on top <strong>of</strong> eachstation. To optimize <strong>the</strong> exposure to sunlight in winter time, <strong>the</strong> solar panels are installed such, that<strong>the</strong>y face north, at an inclination <strong>of</strong> 55 ◦ with respect to <strong>the</strong> upward-looking position [15]. Eachstation has two panels, with a total size <strong>of</strong> 1.26m 2 [69]. As <strong>the</strong> minimum in <strong>the</strong> ) distributionis located almost in <strong>the</strong> north, <strong>the</strong> question, if it could be caused <strong>by</strong> <strong>the</strong> absorption <strong>of</strong> secondaryparticles in <strong>the</strong> solar panel, has to be considered.Each <strong>surface</strong> <strong>detector</strong> station covers an area <strong>of</strong> 10m 2 , which is about eight times <strong>the</strong> size <strong>of</strong> <strong>the</strong>solar panel. In a geometrical model, <strong>the</strong> effective area <strong>of</strong> a station, which is masked <strong>by</strong> <strong>the</strong> solarpanel, is calculated. Therefore, <strong>the</strong> scalar product <strong>of</strong> <strong>the</strong> normal vector <strong>of</strong> <strong>the</strong> solar panel and <strong>the</strong>vector <strong>of</strong> <strong>the</strong> incoming cosmic ray, is calculated. The result in dependency on " and ) is shownin Figure 5.32. The region, where <strong>the</strong> masked area is largest, coincides with <strong>the</strong> minimum in <strong>the</strong>map <strong>of</strong> <strong>the</strong> relative deviations from a flat distribution (see Figure 5.19). For cosmic rays comingfrom <strong>the</strong> position <strong>of</strong> <strong>the</strong> maximum, <strong>the</strong> masked area is zero. From this geometrical consideration,absorption <strong>of</strong> secondary particles in <strong>the</strong> solar panel could be <strong>the</strong> reason for <strong>the</strong> asymmetry in <strong>the</strong><strong>data</strong>.Solar panels are made <strong>of</strong> silicon, which has a radiation length <strong>of</strong> 9.4 cm. The installed solar panelshave a thickness <strong>of</strong> 3.2 cm, which is one third <strong>of</strong> a radiation length. The question is, whe<strong>the</strong>r thisis enough to absorb so much energy <strong>of</strong> <strong>the</strong> secondary particles <strong>of</strong> showers coming from <strong>the</strong> north,such that ≈ 2.5% <strong>of</strong> <strong>the</strong> events do not fulfill <strong>the</strong> event trigger conditions any longer. But this isbeyond <strong>the</strong> scope <strong>of</strong> this <strong>the</strong>sis. The best way to do this, is to simulate <strong>the</strong> signals, measured <strong>by</strong><strong>the</strong> <strong>surface</strong> <strong>detector</strong> stations with and without solar panels, if <strong>the</strong> secondary particles <strong>of</strong> extensive
86 Azimuth angle distribution0.910.80.80.70.60.60.40.50.20.460 050403020100-150-100-500501001500.30.20.10Figure 5.32: Area <strong>of</strong> a <strong>surface</strong> <strong>detector</strong> station masked <strong>by</strong> <strong>the</strong> solar panel as a function <strong>of</strong> " and ) andnormalized to one for <strong>the</strong> maximal masking.air showers reach <strong>the</strong> ground. If <strong>the</strong> number <strong>of</strong> triggered events, detected with <strong>the</strong> solar panelis <strong>by</strong> about 2.5% smaller than without, <strong>the</strong> solar panel would be identified as <strong>the</strong> cause <strong>of</strong> <strong>the</strong>asymmetry. Without this simulation, <strong>the</strong> hypo<strong>the</strong>sis can nei<strong>the</strong>r be confirmed nor rejected.5.6 SummaryIn this chapter, <strong>the</strong> azimuth angle distribution has been analyzed in detail. For events with energiesbelow full acceptance <strong>of</strong> <strong>the</strong> array (3 EeV), <strong>the</strong> hexagonal structure leads to an oscillationin <strong>the</strong> number <strong>of</strong> detected events, with a period <strong>of</strong> 60 ◦ . The difference between <strong>the</strong> extrema is(2.07 ± 0.15)% with a minimum at ) = 0 ◦ , which corresponds to <strong>the</strong> east (see Section 5.2.3).The amplitude <strong>of</strong> <strong>the</strong> oscillation increases with zenith angle increasing. In a model, <strong>the</strong> effect issimulated (see Section 5.3), <strong>by</strong> comparing <strong>the</strong> number <strong>of</strong> events triggering <strong>the</strong> array for showerscoming from <strong>the</strong> directions <strong>of</strong> <strong>the</strong> extrema. With <strong>the</strong> model, <strong>the</strong> effect <strong>of</strong> <strong>the</strong> hexagonal structurecan be reproduced. The amplidude <strong>of</strong> <strong>the</strong> oscillation is in <strong>the</strong> model (0.51%) <strong>by</strong> a factor <strong>of</strong> foursmaller, than in <strong>the</strong> <strong>data</strong>. This is a result <strong>of</strong> <strong>the</strong> fact, that <strong>the</strong> model has only one fixed triggerthreshold, whereas <strong>the</strong> stations can be triggered, if one <strong>of</strong> two trigger conditions is met, <strong>the</strong> singlethreshold trigger or <strong>the</strong> time-over-threshold trigger. Since it is not possible to implement two triggercriteria in this kind <strong>of</strong> model, a detailed Monte Carlo study is necessary to analyze <strong>the</strong> effectin more detail.A possible oscillation in <strong>the</strong> ) distribution with a period <strong>of</strong> 120 ◦ , caused <strong>by</strong> <strong>the</strong> dependence <strong>of</strong> <strong>the</strong>PMT signals on ), could not be stated. Ei<strong>the</strong>r <strong>the</strong>re is no oscillation at all, or <strong>the</strong> amplitude is sosmall, that it is not observable (see Sections 5.2.2, 5.2.3 and 5.5.4).In Section 5.4, <strong>the</strong> asymmetry, found with a period <strong>of</strong> 360 ◦ in <strong>the</strong> azimuth angle distribution <strong>of</strong><strong>the</strong> T5 events, is analyzed in detail. Firstly, <strong>the</strong> amplitude and <strong>the</strong> phase are calculated under <strong>the</strong>assumption <strong>of</strong> a sine structure <strong>of</strong> <strong>the</strong> asymmetry. The difference in <strong>the</strong> number <strong>of</strong> events is calculated<strong>by</strong> comparing <strong>the</strong> number <strong>of</strong> events in 60 ◦ bins to exclude any influence <strong>of</strong> <strong>the</strong> oscillationwith a period <strong>of</strong> 60 ◦ . The difference between <strong>the</strong> minimum () min = 54.4 ◦ ) and <strong>the</strong> maximum
5.6 Summary 87() max = −125.6 ◦ ) is 2.64%. By comparing <strong>the</strong> number <strong>of</strong> events measured in a 60 ◦ bin, with <strong>the</strong>average <strong>of</strong> all azimuth angles, <strong>the</strong> maximum is at ) =(−130±5) ◦ , with an excess <strong>of</strong> (1.7±0.3)%and <strong>the</strong> minimum is located between 0 ◦ and 100 ◦ , with a deficit <strong>of</strong> (−1.0 ± 0.3)% in <strong>the</strong> number<strong>of</strong> detected events (see Figure 5.18.In Rayleigh tests, <strong>the</strong> amplitude and phase were confirmed and <strong>the</strong> probability, that <strong>the</strong> <strong>recorded</strong>azimuth angle distribution is compatible with a flat distribution, is calculated, as 10 −21 . Fur<strong>the</strong>rmore,<strong>the</strong> method shows, that <strong>the</strong> phase sticks to ≈ 55 ◦ for all events above a given energythreshold, up to 10 EeV. Above 10 EeV, <strong>the</strong> phase is no longer constant.Secondly, <strong>the</strong> energy and " dependences are analyzed. The minimum and <strong>the</strong> maximum valuesare determined without <strong>the</strong> assumption <strong>of</strong> a sine behavior <strong>of</strong> <strong>the</strong> effect, <strong>by</strong> calculating <strong>the</strong> fraction<strong>of</strong> events, which are measured in 60 ◦ bins in ). The absolute maximum is found at ) ≈−120 ◦and " = 55 ◦ and <strong>the</strong> absolute minimum is located at ) ≈ 100 ◦ and " = 55 ◦ , which complies with aphase difference <strong>of</strong> 140 ◦ , and not 180 ◦ , as expected for a sine. At <strong>the</strong> maximum, <strong>the</strong> excess <strong>of</strong> particlesamounts to +3% with a significance <strong>of</strong> 4 and at <strong>the</strong> absolute minimum, <strong>the</strong> deficit is around−2.5% with a significance <strong>of</strong> 3. The position <strong>of</strong> <strong>the</strong> maximum is constant in ) for all zenith angles.For <strong>the</strong> minimum, <strong>the</strong> " dependence remains unclear. Within <strong>the</strong> <strong>recorded</strong> statistics, a variationin ) is as well possible as a constant value. The attempt to solve this question <strong>by</strong> increasing <strong>the</strong>statistics <strong>by</strong> using also events, which do not fulfill <strong>the</strong> T5 trigger, provides no fur<strong>the</strong>r information.A correlation with <strong>the</strong> energy could nei<strong>the</strong>r be obtained for <strong>the</strong> maximum nor for <strong>the</strong> minimum.By splitting <strong>the</strong> array into four areas, a variation in <strong>the</strong> strength is determined. In <strong>the</strong> east, <strong>the</strong>extrema are more distinctive than in <strong>the</strong> west. In <strong>the</strong> south-west, <strong>the</strong> significances <strong>of</strong> <strong>the</strong> deviationsfrom a flat ) distribution are below 2.5, for all extrema in <strong>the</strong> " − )−map. An explicit timedependence is not visible. The shift <strong>of</strong> <strong>the</strong> maximum between 8h and 16 h in <strong>the</strong> analysis <strong>of</strong> dailyvariations has to be analyzed with more statistics to judge, if this is a random fluctuation, or caused<strong>by</strong> a real dependency.Finally, in Section 5.5, several possible reasons are analyzed. A comparison <strong>of</strong> <strong>the</strong> results, obtained<strong>by</strong> reconstructing <strong>the</strong> events with <strong>the</strong> two common reconstruction algorithms, CDAS andOffline, shows, that <strong>the</strong> azimuth angle distributions are similar. In fur<strong>the</strong>r tests, border effects, <strong>the</strong>tilt <strong>of</strong> <strong>the</strong> array, effects <strong>of</strong> <strong>the</strong> individual PMTs and <strong>the</strong> influence <strong>of</strong> <strong>the</strong> geomagnetic field couldbe excluded as major causes. The solar panel could be a possible cause, since <strong>the</strong> position <strong>of</strong> <strong>the</strong>minimum agrees with <strong>the</strong> direction, where its absorption <strong>of</strong> secondary particles has a maximum.This might be <strong>by</strong> chance and has to be checked with Monte Carlo simulations. It has not beendiscussed, if <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> panel is sufficient, to cause an effect <strong>of</strong> 2.5%. It is, fur<strong>the</strong>rmore,unclear, which effect could cause <strong>the</strong> maximum in this case, as <strong>the</strong> solar panel would only decrease<strong>the</strong> energy <strong>of</strong> <strong>the</strong> secondary particles <strong>of</strong> extensive air showers coming from nor<strong>the</strong>rn directions.This would reduce <strong>the</strong> number <strong>of</strong> detected events coming from <strong>the</strong> north, as some fall below <strong>the</strong>trigger threshold <strong>of</strong> <strong>the</strong> <strong>surface</strong> <strong>detector</strong> stations.
Summary and outlookChapter 6Summary and outlookThe aim <strong>of</strong> this <strong>the</strong>sis was to analyze <strong>the</strong> properties <strong>of</strong> <strong>the</strong> <strong>surface</strong> <strong>detector</strong> <strong>data</strong> <strong>of</strong> <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong>observatory. Two different aspects have been discussed, <strong>the</strong> stability <strong>of</strong> <strong>the</strong> CDAS online reconstructionalgorithm and <strong>the</strong> features <strong>of</strong> <strong>the</strong> azimuth angle distribution.In Chapter 4, events with reconstructed energies above 25 EeV and " < 60 ◦ are analyzed. For eachevent <strong>the</strong> set <strong>of</strong> <strong>detector</strong>s taking part in <strong>the</strong> reconstruction is modified <strong>by</strong> leaving out individualstations, or sets <strong>of</strong> <strong>detector</strong>s. The resulting energies and angles are <strong>the</strong>n compared to <strong>the</strong> originalvalues, obtained with all <strong>detector</strong>s. For events, which fulfill <strong>the</strong> strict-T5 trigger condition, <strong>the</strong>exclusion <strong>of</strong> individual stations or sets <strong>of</strong> <strong>detector</strong>s changes <strong>the</strong> reconstructed energy <strong>by</strong> less than10% and <strong>the</strong> arrival direction <strong>by</strong> less than 1.5 ◦ . Fur<strong>the</strong>rmore, it has been shown, that strict-T5events, <strong>recorded</strong> near <strong>the</strong> border <strong>of</strong> <strong>the</strong> array, are not biased <strong>by</strong> <strong>the</strong> missing <strong>detector</strong>s in <strong>the</strong> secondcrown or far<strong>the</strong>r away. It has also been shown, that <strong>the</strong> uncertainties <strong>of</strong> <strong>the</strong> signal at a distance <strong>of</strong>1000 m from <strong>the</strong> core are larger than for more distant core distances. The reconstruction <strong>of</strong> cosmicrays with E > 25EeV can be improved, <strong>by</strong> determining S(r > 1000m) instead <strong>of</strong> S(1000m)from <strong>the</strong> signals <strong>of</strong> <strong>the</strong> triggered stations and calculating <strong>the</strong> energy from this S(r > 1000m). Todetermine <strong>the</strong> optimum distance from <strong>the</strong> shower core, Monte Carlo simulation is an appropriatetool, but it is beyond <strong>the</strong> scope <strong>of</strong> this <strong>the</strong>sis. In <strong>the</strong> analysis presented here, it has been shown,that <strong>detector</strong>s <strong>of</strong> <strong>the</strong> second crown and far<strong>the</strong>r away have almost no influence on <strong>the</strong> reconstructedproperties <strong>of</strong> <strong>the</strong> events. In addition, it has been evidenced, that <strong>the</strong> influence <strong>of</strong> one single failing<strong>detector</strong> is negligible for <strong>the</strong> detection <strong>of</strong> high energy cosmic rays (see also [70]).In Chapter 5 an asymmetry in <strong>the</strong> azimuth angle distribution has been obtained. It has been shown,that <strong>the</strong> three PMTs in each station induce no significant oscillation in <strong>the</strong> zenith angle distribution.In addition to an oscillation with a period <strong>of</strong> 60 ◦ , which is purely due to <strong>the</strong> hexagonal structure <strong>of</strong><strong>the</strong> array, a maximum and a minimum are found in <strong>the</strong> ) distribution, with a difference in phase<strong>of</strong> approximatly 180 ◦ . In a two dimensional search in " and ), <strong>the</strong> absolute maximum is foundat () ≈−120 ◦ ," ≈ 55 ◦ ) with an excess <strong>of</strong> detected events <strong>of</strong> +3% and a significance <strong>of</strong> 4. Theabsolute minimum is located at () ≈ 100 ◦ ," ≈ 55 ◦ ), where <strong>the</strong> deficit <strong>of</strong> events amounts to −2.5%with a significance <strong>of</strong> 3. In an analysis independent <strong>of</strong> <strong>the</strong> zenith angle, <strong>the</strong> extrema are obtainedat ) min = 54.4 ◦ (north-east) and ) max = −125.6 ◦ (south-west) with a difference in <strong>the</strong> number <strong>of</strong>detected events <strong>of</strong> 2.64%. For <strong>the</strong> 985000 strict-T5 events, detected up to August 2008, <strong>the</strong>se2.64% correspond to an excess <strong>of</strong> about 4300 detected events in a 60 ◦ bin in ), centered around<strong>the</strong> maximum, compared to <strong>the</strong> showers in a bin <strong>of</strong> <strong>the</strong> same size, centered around <strong>the</strong> minimum.The reason for <strong>the</strong> effect is not found yet. Never<strong>the</strong>less, border effects, <strong>the</strong> tilt <strong>of</strong> <strong>the</strong> array, effects<strong>of</strong> <strong>the</strong> individual PMTs and <strong>the</strong> influence <strong>of</strong> <strong>the</strong> geomagnetic field could be excluded as majorcauses. The effect might be caused <strong>by</strong> absorption <strong>of</strong> secondary particles in <strong>the</strong> solar panel. Due
to lack <strong>of</strong> time, <strong>the</strong> absolut absorption factor is not calculated in this <strong>the</strong>sis and will <strong>the</strong>refore besubject <strong>of</strong> fur<strong>the</strong>r investigations.89
LIST OF FIGURESList <strong>of</strong> Figures1.1 Primary cosmic ray spectrum [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Schematic drawing <strong>of</strong> <strong>the</strong> longitudinal development <strong>of</strong> an extensive air shower [8]. 31.3 Schematic views <strong>of</strong> an extensive air shower [9]. . . . . . . . . . . . . . . . . . . 41.4 Schematic view <strong>of</strong> <strong>the</strong> measurement <strong>of</strong> an extensive air shower <strong>by</strong> a fluorescencetelescope and <strong>surface</strong> <strong>detector</strong> stations [12]. . . . . . . . . . . . . . . . . . . . . 62.1 The <strong>Pierre</strong> <strong>Auger</strong> observatory near <strong>the</strong> city <strong>of</strong> Malargüe. The circles illustrate<strong>the</strong> positions <strong>of</strong> <strong>the</strong> 1600 water Cherenkov <strong>detector</strong>s forming <strong>the</strong> <strong>surface</strong> <strong>detector</strong>array. The array is over-looked <strong>by</strong> 24 fluorescence telescopes, situated in 4buildings. The fields <strong>of</strong> view <strong>of</strong> <strong>the</strong> individual telescopes are indicated <strong>by</strong> lines [14]. 82.2 Schematic view <strong>of</strong> a <strong>surface</strong> <strong>detector</strong> station [17]. . . . . . . . . . . . . . . . . . 92.3 Histograms <strong>of</strong> charge (left) and pulse height (right) for a single SD station, triggered<strong>by</strong> a 3-fold coincidence from all 3 PMTs (solid line). The histogram with<strong>the</strong> dashed line shows <strong>the</strong> spectrum <strong>of</strong> an external muon telescope for <strong>the</strong> sameevents. The first hump is due to <strong>the</strong> triggering <strong>of</strong> low-energy particles from EASand shows <strong>the</strong> typical exponential slope. The second hump is caused <strong>by</strong> <strong>the</strong> atmosphericmuons [19]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 The extensions near <strong>the</strong> Coihueco building: The dots illustrate <strong>the</strong> <strong>surface</strong> stationsand <strong>the</strong> lines indicate <strong>the</strong> field <strong>of</strong> view <strong>of</strong> <strong>the</strong> HEAT and <strong>the</strong> former installed fluorescencetelescopes. All stations indicated with a name belong to <strong>the</strong> 1.5 km grid,<strong>the</strong> o<strong>the</strong>rs are spaced 750 m and 433 m apart. All stations inside <strong>the</strong> huge hexagonwill have in addition a 30m 2 buried muon counter, after AMIGA is completed [24]. 122.5 Schematic view <strong>of</strong> a fluorescence telescope unit [25]. . . . . . . . . . . . . . . . 132.6 Sky map <strong>of</strong> <strong>the</strong> celestial sphere in galactic coordinates. The asterisks illustrate<strong>the</strong> positions <strong>of</strong> <strong>the</strong> 442 AGN (318 within <strong>the</strong> field <strong>of</strong> view <strong>of</strong> <strong>the</strong> observatory)with redshift z ≤ 0.017 (D ≤ 71Mpc) from <strong>the</strong> 12th edition <strong>of</strong> <strong>the</strong> Véron-Cettyand Véron catalog [32]. The black circles <strong>of</strong> 3.1 ◦ in diameter are centered around<strong>the</strong> reconstructed arrival directions <strong>of</strong> <strong>the</strong> 27 events with a reconstructed energyabove 57 EeV. Darker colors indicate higher relative exposure and <strong>the</strong> solid lineshows <strong>the</strong> limit <strong>of</strong> <strong>the</strong> field <strong>of</strong> view, for " < 60 ◦ . The dashed line displays <strong>the</strong>super-galactic plane [31]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
92 LIST OF FIGURES3.1 Raw histograms <strong>of</strong> station 1640, with an integrated signal <strong>of</strong> 10.3 VEM. The <strong>data</strong>belongs to event 200821400018 and is a randomly picked example. Top: baselinehistograms for all three dynode channels; middle: charge histograms <strong>of</strong> <strong>the</strong>three PMTs; bottom left: summed charge histogram; bottom middle: pulse height(peak) histograms <strong>of</strong> <strong>the</strong> three PMTs; bottom right: average pulse shape <strong>of</strong> <strong>the</strong>three PMTs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Zenith angle (left) and energy (right) distribution for events passing <strong>the</strong> T4 trigger.Events passing <strong>the</strong> 3ToT are displayed in <strong>the</strong> red shaded area and 4C1 events in<strong>the</strong> blue dashed area. Events fulfilling both criteria are counted as 3ToT events [34]. 183.3 The ICRCT5 (left) requires five <strong>of</strong> six active stations in <strong>the</strong> first crown and a reconstructedcore position in an active triangle <strong>of</strong> <strong>detector</strong>s. Core positions inside<strong>the</strong> right triangle satisfy <strong>the</strong> ICRCT5, core positions inside <strong>the</strong> left triangle not.The right picture shows <strong>the</strong> condition for <strong>the</strong> strict-T5, an active unitary cell. . . . 193.4 Left: Comparison between <strong>the</strong> experimental (symbols) and unbiased (solid line)trigger probability for " = 45 ◦ and S 1000 = 4.5VEM. Right: Lateral trigger probabilityfor three different values <strong>of</strong> S 1000 (3 (boxes), 10 (circles) and 30 VEM (triangles))and zenith angles <strong>of</strong> 0 ◦ and 45 ◦ (closed and open symbols) [37]. . . . . . 203.5 The distances d <strong>of</strong> <strong>the</strong> stations to <strong>the</strong> shower axis or shower core and <strong>the</strong> distancesD to <strong>the</strong> point, where <strong>the</strong> shower core hits <strong>the</strong> ground. The left station is an early<strong>detector</strong>, as <strong>the</strong> station is triggered before <strong>the</strong> core reaches <strong>the</strong> ground, whereas <strong>the</strong>right station is a late <strong>detector</strong>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.6 Pictures from <strong>the</strong> CDAS Event Display: event 200821400018, E = 12.03EeV," = 51.5 ◦ . The left plot shows <strong>the</strong> signals <strong>of</strong> <strong>the</strong> triggered stations (rectangles),<strong>the</strong> silent stations (triangles) and <strong>the</strong> LDF with <strong>the</strong> error band. The right showsa top view <strong>of</strong> <strong>the</strong> triggered stations. The size <strong>of</strong> <strong>the</strong> circles is proportional to <strong>the</strong>logarithm <strong>of</strong> <strong>the</strong> detected signal. The stations marked with a cross, are flagged asaccidental and <strong>the</strong> two black stations at <strong>the</strong> right were not active, at <strong>the</strong> time <strong>the</strong>event was detected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.7 - (left) and # (right) as a function <strong>of</strong> <strong>the</strong> zenith angle. The light line represent <strong>the</strong>parameterization <strong>of</strong> -. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.8 Correlation between lgS 38 and lgE FD for <strong>the</strong> 661 hybrid events used in <strong>the</strong> fit. Thesolid line is <strong>the</strong> best fit to <strong>the</strong> <strong>data</strong> [49]. . . . . . . . . . . . . . . . . . . . . . . . 243.9 Azimuth angle distribution (left) for all events with " < 60 ◦ and zenith angle distribution(right) without any cuts. . . . . . . . . . . . . . . . . . . . . . . . . . . 253.10 The left plot demonstrates <strong>the</strong> development <strong>of</strong> <strong>the</strong> ToT rate <strong>of</strong> <strong>the</strong> Piuquen <strong>detector</strong>since its deployment. The right graph shows <strong>the</strong> decreasing T5 rate <strong>of</strong> <strong>the</strong> subarray,which is operating since December 2004 [52]. . . . . . . . . . . . . . . . 263.11 Left: The altitude <strong>of</strong> <strong>the</strong> stations in meter in reference to <strong>the</strong> center <strong>of</strong> <strong>the</strong> array.Right: Stations, which had one or more raining PMTs in March 2008, are visualizedwith asterisks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.12 Histogram <strong>of</strong> <strong>the</strong> triangle sizes for <strong>the</strong> <strong>surface</strong> <strong>detector</strong>. The deviations in percentare caused <strong>by</strong> displaced stations. . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1 The station with <strong>the</strong> highest signal is called central tank. It is surrounded <strong>by</strong> <strong>the</strong>six stations <strong>of</strong> <strong>the</strong> first crown. The second crown consists <strong>of</strong> <strong>the</strong> twelve stationssurrounding <strong>the</strong> first crown. Crown n is formed <strong>by</strong> 6 · n stations. . . . . . . . . . 29
LIST OF FIGURES 934.2 Differences in energy (left) and space angle (right) between <strong>the</strong> original and modifiedreconstructions for events with E > 57EeV. . . . . . . . . . . . . . . . . . 304.3 (S(1000) (left) and space angle between (),") and () + ()," + (") (right) forT5 trigger events with E > 57EeV. . . . . . . . . . . . . . . . . . . . . . . . . . 304.4 Shifts <strong>of</strong> <strong>the</strong> reconstructed core position between original and modified reconstructionfor events with E > 57EeV . . . . . . . . . . . . . . . . . . . . . . . . . . 324.5 Differences in energy (left) and space angle (right) for all events above 25 EeV(top), ICRCT5 events (middle) and strict-T5 events (bottom). . . . . . . . . . . . 344.6 Deviations in energy resulting from excluding individual stations <strong>of</strong> <strong>the</strong> first crown(left) and far<strong>the</strong>r <strong>of</strong>f (right) for <strong>the</strong> early (top) and late part (bottom) <strong>of</strong> <strong>the</strong> showers. 364.7 Deviations in S(1000) (left) and S(1600) (right) resulting from excluding individualstations before <strong>the</strong> reconstruction. . . . . . . . . . . . . . . . . . . . . . . . 374.8 Deviations in S(1000) (left) and S(1600) (right) resulting from excluding individualstations before <strong>the</strong> reconstruction from events with saturated <strong>detector</strong>s. . . . . 374.9 RMS (left) and mean values (right) <strong>of</strong> <strong>the</strong> histograms shown in Figure 4.10. . . . 384.10 Deviations in S(r) <strong>by</strong> comparing <strong>the</strong> signals <strong>of</strong> <strong>the</strong> events above 25 EeV reconstructedwith all stations and without <strong>the</strong> central station. In <strong>the</strong> left plot <strong>of</strong> <strong>the</strong> firstline, r is equal to 1000 m and increases <strong>by</strong> 50 m with each histogram up to 1800 min <strong>the</strong> last histogram on <strong>the</strong> right in <strong>the</strong> bottom row. . . . . . . . . . . . . . . . . 394.11 Direction <strong>of</strong> <strong>the</strong> core displacement after <strong>the</strong> removal <strong>of</strong> <strong>the</strong> central station (left)and <strong>the</strong> influence on <strong>the</strong> core distances for <strong>the</strong> o<strong>the</strong>r stations (right). . . . . . . . 404.12 Analog plot to Figure 4.9, RMS values (left) and mean values (right): The circlesare used to illustrate <strong>the</strong> development <strong>of</strong> <strong>the</strong> histograms <strong>of</strong> <strong>the</strong> central stations, <strong>the</strong>rectangles for <strong>the</strong> histograms <strong>of</strong> <strong>the</strong> first crown stations. From top to bottom <strong>the</strong>energy range changes from 25EeV < E ≤ 30EeV via 30EeV < E ≤ 40EeV toE > 40EeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.13 Differences in energy in percent (left) and space angle in degrees (right) between<strong>the</strong> reconstruction with all stations and <strong>the</strong> reconstruction with only <strong>the</strong> unitarycell for events with E > 57EeV (top) and E > 25EeV (bottom). . . . . . . . . . 424.14 Stations beyond <strong>the</strong> unitary cell on two sides <strong>of</strong> <strong>the</strong> central tank are left out in <strong>the</strong>reconstruction. These <strong>detector</strong>s are marked with a cross. . . . . . . . . . . . . . 434.15 Differences in energy in percent (left) and space angle in degrees (right) between<strong>the</strong> reconstruction with all stations and modified sets <strong>of</strong> <strong>detector</strong>s simulating <strong>the</strong>border <strong>of</strong> <strong>the</strong> array for events with E > 57EeV (top) and E > 25EeV (bottom). . 444.16 Triangle sub-array configurations. . . . . . . . . . . . . . . . . . . . . . . . . . 444.17 Deviations in energy (top) and space angle (bottom) between events reconstructedwith all stations and reconstructed with only <strong>the</strong> signals <strong>of</strong> one third <strong>of</strong> <strong>the</strong> stations.From <strong>the</strong> left to right <strong>the</strong> energy threshold changes from E > 25EeV, <strong>the</strong>n E >35EeV, E > 45EeV and finally, E > 55EeV on <strong>the</strong> right. The filled histogramsare used to display subsets with five or more stations. . . . . . . . . . . . . . . . 464.18 Deviations in energy (top) and space angle (bottom) between T5+-events reconstructedwith all stations and reconstructed with only <strong>the</strong> signals <strong>of</strong> one third <strong>of</strong><strong>the</strong> stations. T5+-events are surrounded <strong>by</strong> two crowns <strong>of</strong> working stations. Theenergy threshold changes from <strong>the</strong> left to <strong>the</strong> right: E > 25EeV, E > 35EeV,E > 45EeV and E > 55EeV. The filled histogramms are used to display subsetswith five or more stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
94 LIST OF FIGURES5.1 Measured zenith angle distribution up to 60 ◦ for events with E > 3EeV and <strong>the</strong>usual quality cuts. The solid line is <strong>the</strong> sin" cos"-function. . . . . . . . . . . . . 505.2 Measured azimuth angle distribution for events with E > 3EeV and " < 60 ◦ . . . 515.3 Measured azimuth angle distribution for all events with " < 60 ◦ (left) and <strong>the</strong>events with 37.76 ◦ < " < 60 ◦ (right). . . . . . . . . . . . . . . . . . . . . . . . 515.4 Schematic view <strong>of</strong> two showers with <strong>the</strong> same energy and <strong>the</strong> same core position.The one with ) = 0 ◦ (solid line) would be detected, as three stations are enclosed<strong>by</strong> <strong>the</strong> ellipses, <strong>the</strong> o<strong>the</strong>r one, with ) = 90 ◦ , would not be detected. . . . . . . . . 525.5 Left: The six possible isosceles triangles for 3-fold events and <strong>the</strong> expected maximain <strong>the</strong> azimuth angle distribution. The only difference between <strong>the</strong> triangleswith solid lines and <strong>the</strong> ones with dashed lines, are that <strong>the</strong>y are rotated <strong>by</strong> 60 ◦ .Right: The dominating configurations <strong>of</strong> stations for 4-fold events. . . . . . . . . 535.6 The twelve possible configurations for <strong>the</strong> non-compact adjustment <strong>of</strong> stations for4-fold events. The three stations <strong>of</strong> <strong>the</strong> solid triangle and one at <strong>the</strong> end <strong>of</strong> onedashed line are triggered. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.7 Measured azimuth angle distributions for strict-T5 events with (left) " < 60 ◦ andstrict-T5 events with 37.76 ◦ < " < 60 ◦ (right); top: 3-fold events, middle: 4-foldevents, bottom: 5-fold events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.8 Fraction <strong>of</strong> <strong>the</strong> total signal as a function <strong>of</strong> ) detected <strong>by</strong> <strong>the</strong> three PMTs. Theerrors are so small, that <strong>the</strong>y are not visible. The plot is generated <strong>by</strong> taking <strong>the</strong>siganls <strong>of</strong> all PMTs, used for <strong>the</strong> reconstruction <strong>of</strong> <strong>the</strong> T4 events, which have beendetected in 2007. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.9 Azimuth distributions for <strong>the</strong> 3-fold (top), 4-fold events (middle) and all events(bottom), which fulfill <strong>the</strong> usual cuts. For <strong>the</strong> fits Equation 5.3 is used. . . . . . . 575.10 Model for <strong>the</strong> 2!/6-effect: The left picture shows <strong>the</strong> stations (dots) and <strong>the</strong> area(little squares), where <strong>the</strong> showers are simulated with a core positions on a tenmeter grid. In <strong>the</strong> right picture, two ellipses are shown, one would trigger <strong>the</strong><strong>surface</strong> <strong>detector</strong>, one would not, as only two stations, located at <strong>the</strong> apexes <strong>of</strong> <strong>the</strong>triangle, are inside <strong>the</strong> ellipse. . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.11 Number <strong>of</strong> triggered showers per bin for ellipses with <strong>the</strong> major axis parallel to<strong>the</strong> x-axis (left) and parallel to <strong>the</strong> y-axis (right) for showers with S m = 1000 and" = 40 ◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.12 The intersection <strong>of</strong> a vertical cylinder, an inclined cylinder, and an inclined (inverted)cone with <strong>the</strong> ground plane [46]. . . . . . . . . . . . . . . . . . . . . . . 615.13 Model with binary trigger probability (left) and with a continuously developingtrigger probability (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.14 The number <strong>of</strong> triggered showers as a function <strong>of</strong> S(1000) (left) and <strong>the</strong> " distributions<strong>of</strong> <strong>the</strong> two ellipses and <strong>the</strong> measured events. The plot at <strong>the</strong> top is for allevents, <strong>the</strong> one in <strong>the</strong> middle for 3-fold events and <strong>the</strong> one at <strong>the</strong> bottom for 4-foldevents. The major axis <strong>of</strong> ellipse 1 is parallel to <strong>the</strong> east-west axis and <strong>the</strong> majoraxis <strong>of</strong> ellipse 2 is perpendicular. . . . . . . . . . . . . . . . . . . . . . . . . . . 635.15 Top: Ratios between all events measured in N 1i ∈ [) − 30 ◦ ,) + 30 ◦ ] and N 2i ∈[) + 180 ◦ − 30 ◦ ,) + 180 ◦ + 30 ◦ ]. Bottom: Comparison <strong>of</strong> <strong>the</strong> ratios <strong>of</strong> events withdifferent numbers <strong>of</strong> triggered stations. . . . . . . . . . . . . . . . . . . . . . . . 665.16 Rayleigh amplitude, phase and probability for T5 events with " < 60 ◦ above agiven energy (left) and below a given energy (right). . . . . . . . . . . . . . . . . 67
LIST OF FIGURES 955.17 Rayleigh amplitude, phase and probability for T5 events with " < 60 ◦ in logarithmicenergy bins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.18 Relative deviations <strong>of</strong> <strong>the</strong> number <strong>of</strong> events detected in 60 ◦ bins, from a flat distribution.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.19 Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): Relative deviations from aflat azimuth distribution (top left), errors <strong>of</strong> <strong>the</strong>se values (top right), significances(bottom left) and fluctuated map <strong>of</strong> deviations (bottom right). . . . . . . . . . . . 715.20 Relative differences in <strong>the</strong> number <strong>of</strong> events detected in a 60 ◦ bin around ) =−120 ◦ in comparison to a flat distribution. The left plot shows <strong>the</strong> zenith angledependence, <strong>the</strong> right plot <strong>the</strong> energy dependence. . . . . . . . . . . . . . . . . . 725.21 Same as Figure 5.20 with 60 ◦ bins around ) = 5 ◦ , ) = 55 ◦ and ) = 105 ◦ . . . . . 735.22 Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): The four plots show <strong>the</strong>relative differences from an isotropic distribution. The plots are arranged accordingto <strong>the</strong> positions <strong>of</strong> <strong>the</strong> parts in <strong>the</strong> array <strong>the</strong>y represent (north-west, north-east,south-west and south-east). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.23 Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): The four plots show <strong>the</strong> significances<strong>of</strong> <strong>the</strong> deviations shown in Figure 5.23. The plots are arranged accordingto <strong>the</strong> positions <strong>of</strong> <strong>the</strong> parts in <strong>the</strong> array <strong>the</strong>y represent (north-west, north-east,south-west and south-east). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.24 Relative deviations from a flat azimuth distribution in dependence on <strong>the</strong> time <strong>of</strong><strong>the</strong> day, when <strong>the</strong> events were <strong>recorded</strong>. . . . . . . . . . . . . . . . . . . . . . . 775.25 Relative deviations from a flat azimuth distribution in dependence on <strong>the</strong> month,when <strong>the</strong> events were <strong>recorded</strong>. . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.26 Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 85 ◦ ): Relative deviations from aflat distribution (top) and significance plot (bottom) for T5 events. . . . . . . . . 795.27 Maps in ) (−180 ◦ ≤ ) < 180 ◦ ) and " (5 ◦ ≤ ) ≤ 55 ◦ ): Relative deviations froma flat distribution (top) and significance plot (bottom) for events, which fulfill <strong>the</strong>T5 requirement and those which do not, for zenith angles up to 60 ◦ . . . . . . . . 805.28 The azimuth angle distributions <strong>of</strong> all events reconstructed with <strong>the</strong> CDAS algorithm(left) and <strong>the</strong> Offline algorithm (right). . . . . . . . . . . . . . . . . . . . . 825.29 Status <strong>of</strong> <strong>the</strong> <strong>surface</strong> <strong>detector</strong> array in November 2005: 1031 tanks are deployed(shaded region), 1012 filled with water and 898 with electronics [66]. . . . . . . 825.30 Temperatures <strong>of</strong> <strong>the</strong> electronics and <strong>the</strong> PMTs for one day (left) and differencesbetween pairs <strong>of</strong> PMTs (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.31 Azimuth angle distributions, obtained <strong>by</strong> reconstructing <strong>the</strong> events with <strong>the</strong> signals<strong>of</strong> only one <strong>of</strong> <strong>the</strong> three PMTs per station. The plot in <strong>the</strong> upper left corner is forPMT 2, <strong>the</strong> upper right for PMT 1 and <strong>the</strong> plot at <strong>the</strong> bottom right is for PMT 3.The drawing illustrates <strong>the</strong> positions <strong>of</strong> <strong>the</strong> PMTs in <strong>the</strong> station. . . . . . . . . . 845.32 Area <strong>of</strong> a <strong>surface</strong> <strong>detector</strong> station masked <strong>by</strong> <strong>the</strong> solar panel as a function <strong>of</strong> " and) and normalized to one for <strong>the</strong> maximal masking. . . . . . . . . . . . . . . . . 86
LIST OF TABLESList <strong>of</strong> Tables2.1 Expected number <strong>of</strong> events per year with <strong>the</strong> completely installed AMIGA [22]. . 114.1 <strong>Properties</strong> <strong>of</strong> <strong>the</strong> energy and space angle distributions shown in Figure 4.2. . . . 314.2 Deviation in energy between <strong>the</strong> original and <strong>the</strong> modified reconstruction. Allevents for which <strong>the</strong> modification leads to a deviation in energy larger than 10%are listed. The number after <strong>the</strong> hyphen denotes <strong>the</strong> crown (0 = central station). . 314.3 Angular deviation between <strong>the</strong> original and <strong>the</strong> modified reconstruction. Allevents, for which <strong>the</strong> modification leads to a deviation larger than 0.6 ◦ , are listed. 314.4 RMS values <strong>of</strong> <strong>the</strong> energy and space angle distributions shown in figure 4.5. . . . 334.5 Values <strong>of</strong> <strong>the</strong> Gaussian fits to <strong>the</strong> energy histograms. . . . . . . . . . . . . . . . 354.6 Values <strong>of</strong> <strong>the</strong> fits to <strong>the</strong> distributions for <strong>the</strong> early and late part <strong>of</strong> <strong>the</strong> shower. . . . 354.7 Optimum ground parameters determined <strong>by</strong> reconstructing events without individualstations <strong>of</strong> <strong>the</strong> first crown. . . . . . . . . . . . . . . . . . . . . . . . . . . 405.1 Fractions <strong>of</strong> events, which trigger three, four or more stations. . . . . . . . . . . 545.2 Parameters <strong>of</strong> <strong>the</strong> fits with Function 5.3 shown in Figure 5.9. . . . . . . . . . . . 555.3 Relative differences p 6 , p 3 and p 1 between <strong>the</strong> maxima and <strong>the</strong> minima <strong>of</strong> <strong>the</strong>oscillations with periods <strong>of</strong> 2!/6, 2!/3 and 2!, in <strong>the</strong> )-distribution. . . . . . . . 565.4 Oscillations with amplitude D/2 in <strong>the</strong> azimuth angle distribution with a period <strong>of</strong>2!/6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.5 Azimuth angles ) min and amplitudes p <strong>of</strong> <strong>the</strong> minima, obtained <strong>by</strong> <strong>the</strong> sine fits to<strong>the</strong> azimuth distributions (see Section 5.2.3). . . . . . . . . . . . . . . . . . . . . 645.6 Rayleigh amplitudes, phases and probabilities <strong>of</strong> T5 events, subdivided in six independentenergy bins. The phase corresponds to <strong>the</strong> location <strong>of</strong> <strong>the</strong> minimum <strong>of</strong>a sine wave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.7 Borders <strong>of</strong> <strong>the</strong> " and energy bins. . . . . . . . . . . . . . . . . . . . . . . . . . . 72
List <strong>of</strong> AcronymsAcronymAGNAMIGACDASCICCLFCREASFADCFDGPSHEATLIDARLDFLTPMCPAOPMTRMSSDSTTOTUHECRVEMExplanationActive Galactic Nucleus<strong>Auger</strong> Muons and Infill for <strong>the</strong> Ground ArrayCentral Data Acquisition SystemConstant Intensity CutCentral Laser FacilityCosmic RayExtensive Air ShowerFlash Analog-to-Digital ConverterFluorescence DetectorGlobal Positioning SystemHigh Elevation <strong>Auger</strong> TelescopesLIght Detection And RangingsLateral Distribution FunctionLateral Trigger ProbabilityMonte Carlo<strong>Pierre</strong> <strong>Auger</strong> ObservatoryPhoto Multiplier TubeRoot Mean SquareSurface DetectorSingle Threshold (first level trigger)Time Over Threshold (first level trigger)Ultra High Energy Cosmic RayVertical Equivalent Muon
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AcknowledgmentMy gratitude goes out to all those, who made this <strong>the</strong>sis possible.Firstly I would like to thank Isabell Steinseifer and Daniel Eiteneuer. You two kept me fromquitting my studies in <strong>the</strong> first semesters.Then I would like to thank Pr<strong>of</strong>. Dr. Peter Buchholz for <strong>the</strong> opportunity to take part in <strong>the</strong> researchfor <strong>the</strong> <strong>Pierre</strong> <strong>Auger</strong> observatory and <strong>the</strong> support to spend half a year abroad.My thanks goes to all my friends in Bariloche, Argentina. It was a wonderful experience to staywith you. Thank you for your continuous support and especially for your warm hospitality. Iwould like to thank namely Hernán Asorey and Dr. Xavier Bertou. My special thanks goes toPr<strong>of</strong>. Dr. Ingomar Allekotte for agreeing to revise this <strong>the</strong>sis and for being more a friend, than asupervisor.In addition, my gratitude goes to <strong>the</strong> members <strong>of</strong> <strong>the</strong> Siegen group, especially to ThomasBäcker and Dr. Dirk Kickelbick. I am indebted to you, for pro<strong>of</strong>reading my <strong>the</strong>sis, sharing yourknowledge with me and for <strong>the</strong> many funny conversations, i.e. during lunch.Der größte Dank von allen, geht jedoch ohne Zweifel an meine gesamte Familie. Ich dankevor allem meiner Freundin Isabell: für deine Liebe, deine Unterstützung und dafür, dass du immerda warst. Genauso möchte ich meinen Eltern und meiner Schwester Nadine danken. Ihr habt michmeinen ganzen Lebensweg begleitet und mich immer unterstützt. Danke!
ErklärungHiermit erkläre ich, dass ich die vorliegende Masterarbeit selbstständig verfasst und keineanderen als die angegebenen Quellen und Hilfsmittel benutzt, sowie Zitate und ErgebnisseAnderer kenntlich gemacht habe.(Ort) (Datum) Stefan Grebe