The Pennsylvania State University. The Graduate School. Department of Physics A STUDY OF THE ELONGATION RATE AND AIR SHOWER PROPERTIES

Transcription

1 The Pennsylvania State University The Graduate School Department of Physics A STUDY OF THE ELONGATION RATE AND AIR SHOWER PROPERTIES OF ULTRA HIGH ENERGY COSMIC RAYS FROM THE SOUTHERN PIERRE AUGER OBSERVATORY A Thesis in Physics by Buddhika Sanjeevi Kumari Atulugama 2007 Buddhika Sanjeevi Kumari Atulugama Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2007

2 The thesis of Buddhika Sanjeevi Kumari Atulugama was reviewed and approved* by the following: Stephane Coutu Associate Professor of Physics, Astronomy and Astrophysics Thesis Advisor Chair of Committee Paul Sommers Professor of Physics, Astronomy and Astrophysics Richard Robinett Professor of Physics Jane Charlton Professor of Astronomy and Astrophysics Jayanth R.Banavar Distinguished Professor of Physics Head of the Department of Physics *Signatures are on file in the Graduate School

3 ABSTRACT ii The Southern Pierre Auger Observatory is the largest hybrid cosmic ray detector in operation, consisting of a 3000km 2 array of surface detectors as well as air fluorescence detectors. It is designed to measure the properties such as mass, energy, and arrival direction of the incident ultra high energy cosmic rays with an outstanding statistical precision in order to improve our understanding of their cosmological origins. Here I demonstrate the use of statistical analysis in determining the optimal parameters for Auger event reconstruction, selection of air shower modeling tools, and identification of the mass composition of cosmic rays. I use Monte Carlo simulations of air shower events to investigate the dependence of the mean particle density at 1000m from the air shower core, S(1000), on several different variables associated with air shower parameters. Using the same simulations, I investigate how calculating this mean particle density at distances other than 1000m from the core affects the uncertainties in the reconstructed parameters. Furthermore, I explore the differences between hadronic interaction models used in air shower simulations, and I demonstrate crucial deviations between simulated showers and real Auger data. Finally, I present a preliminary analysis of the primary mass composition of ultra high energy cosmic rays. After introducing novel anti-bias cuts, I find that, based on two years' worth of Auger data, the mass composition changes from heavy primaries to light primaries at energy of about ev.

4 TABLE OF CONTENTS iii LIST OF FIGURES...vi LIST OF TABLES...xiv ACKNOWLEDGEMENTS...xv Chapter 1 Introduction...1 Bibliography...5 Chapter 2 Science of Ultra High Energy Cosmic Rays Origins and Propagation Acceleration Top-Down Models Diffusion GZK cut-off Known Properties of Cosmic Rays Extensive Air Showers Anatomy Detection: Surface Arrays Reconstruction Detection: Fluorescence Reconstruction...19 Bibliography...21 Chapter 3 The Pierre Auger Observatory The Surface Detector Layout of a Pierre Auger Water Cherenkov Detector Calibration of the Surface Detector Trigger Levels of the Surface Detector Fluorescence Detector Fluorescence Detector Triggering Calibration and Atmospheric Monitoring...40 Bibliography...44 Chapter 4 Auger Surface Detector Analysis Event Generation Procedure Signal Fluctuations Event Reconstruction...54

5 4.2.1 Dependence of S(1000) on β and the Distance to the Closest Detector, r min Saturation Level and S(1000) Best Parameter S(r) The Correlation between S(r) and β...85 Bibliography...91 Chapter 5 Comparison between different Hadronic Interaction Models Monte Carlo Simulations The Risetime Sensitivity of the Ground Parameter S(1000) Constant Intensity Cut Method Comparison with Auger Surface Detector Data Event Selection Results Bibliography Chapter 6 A Measurement of the Elongation Rate using Auger Hybrid Data Introduction Event Selection The Quality Cuts The Z Parameter The Field of View and X low and X up Anti-bias Cuts Elongation Rate Results Comparison with Pure Proton and Iron Distributions Comparison with HiRes Experimental Results Conclusions Tables of Statistics Bibliography Chapter 7 Discussion and Conclusions Bibliography Appendix A Afterpulsing of Surface Detector Photonis XP1805 Photomultiplier Tubes A.1 Abstract A.2 Introduction A.3 Procedure A.4 Results and Discussion A.5 Discussion iv

6 Bibliography Appendix B Auger High Energy Events B.1 Event B.2 Event Bibliography v

7 LIST OF FIGURES vi Figure 2.1: Magnetic field as a function of characteristic length scale of several candidate cosmic ray sources. Diagonal lines indicate the conditions required to accelerate protons or iron nuclei to ev. The solid green line and broken blue line respectively indicate the minimal requirements for acceleration of iron and protons to ev, provided β=1 in Equation 2.1. The solid blue line shows the more realistic situation for protons, in which β=1/300. Only those astrophysical sources above the diagonals are capable of accelerating the associated particles to ultra-high energies [8]....8 Figure 2.2: Energy as a function of propagation distance for protons in the 2.7K cosmic microwave background radiation field. The highest energy protons have their energy degraded by interactions with the CMBR, placing a limit on the distance traveled by UHECRs [13]...11 Figure 2.3: Cosmic ray energy spectrum [18] Figure 2.4: Cartoon of an extensive air shower. The central red line indicates the incident axis of the primary cosmic ray, which triggers the EAS by interacting with an atmospheric nucleus. The green scattered points to the left of the shower axis indicate the particle density of the shower as a function of atmospheric depth. At the point indicated by X max, the number of particles in the shower is maximized. To the right of the axis is a schematic of typical interactions in the EAS. High-energy nucleons in the shower produce pions, which can decay into muons if they are charged, or gamma rays otherwise. The muons travel mostly unhindered to the ground, whereas the electrons and positrons scatter multiple times before arriving at the ground, also generating bremsstrahlung gamma rays in the process Figure 3.1: The deployment status of the array as of June Each circle represents an individual surface detector. The green circles represent detectors filled with water and with electronics. The blue circles represent detectors filled with water but without electronics. The gray circles represent detectors without water. Detectors with a red square in the array map have been removed from the acquisition due to missing differential global positioning system coordinates. The position of the observatory main campus and the locations of four fluorescence buildings are indicated by small arrows. The field of view of each telescope in each fluorescence detector is indicated by the dotted lines [1]...25 Figure 3.2: A surface detector deployed at the Pierre Auger Observatory [2] and a schematic layout ([3]) of the PMT positioning and few other components....27

8 Figure 3.3: Charge histogram from a surface detector station in integrated FADC channels. The trigger is set to fulfill the requirement that a peak signal be greater than 5 channels above the baseline, in each of the three PMTs in the detector. The first peak in this histogram is a trigger effect. The second peak is due to vertical throughgoing muons (Q VEM peak ) [7] Figure 3.4: Two possible 3C1 configurations [15] for zenith angle up to 60 o [15]...33 Figure 3.5: The alternative T3 requirement, 4C1: four detectors with T2 threshold or TOT for larger zenith angles (>60 o ) [15]. See text below for more details Figure 3.6: The FD building located at Los Leones with the external shutters in the open position [2]. The bottom left picture is a top view of the building and the bottom right picture is a schematic layout of the six telescopes...36 Figure 3.7: Schematic layout of a fluorescence detector telescope Figure 3.8: Layout of the FD camera. The PMTs are mounted at the focal surface of the telescope mirror in a hexagonal array as shown. A single PMT covers an area with 1.5 degrees diameter in the sky. To maximize the quantity of fluorescence light detected by the camera, and to encourage sharp transitions between pixels, each PMT is surrounded by six reflective mercedes stars, one at each vertex (inset). The shaded region illustrates the second level trigger algorithm described in Section The trigger reads camera data as a 5 by 22 pixel submatrix that sweeps over the entire camera surface. It searches for the 5 patterns indicated in red, as well as variations of these due to rotations and reflections. If at least 4 PMTs in a pattern have passed the first level trigger, the second level trigger is flagged Figure 4.1: Array of detectors used in this study. Detector spacing is set to 1500m so that it is similar to that of the Auger SD array spacing...49 Figure 4.2: Lateral distribution function of the form given in equation 4.1 fitted to a set of detector signals. The slope β varies between and in increments of 0.1 and illustrates how the variation effects the determination of the signal at a given distance from the core when the normalization constant, k, is fixed Figure 4.3: Distributions of Frac S(1000) for the primary energies 10, 25, 50 and 100EeV, respectively...55 Figure 4.4: Width σ of the Frac S(1000) distribution as a function of generated β for different primary energies. β is fixed to its mean value at the particular zenith angle θ=0 o vii

9 Figure 4.5: Width σ of the Frac S(1000) distribution as a function of r min for different primary energies...59 Figure 4.6: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 10EeV. The value of β is fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure Figure 4.7: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 25EeV. The value of β is fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure Figure 4.8: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 50EeV. The value of β is fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure Figure 4.9: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 100EeV. The value of β is set fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure Figure 4.10: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 125EeV. The value of β is set fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure Figure 4.11: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 150EeV. The value of β is fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure Figure 4.12: Variation of β with secθ viii

10 Figure 4.13: xcore of S(r) and the width σ of the distributions of xcore as a function of secθ for the primary energy 10EeV Figure 4.14: ycore of S(r) and the width σ of the distributions of ycore as a function of secθ for the primary energy 10EeV Figure 4.15: xcore of S(r) (first five panels) and the width σ of the distributions of xcore as a function of secθ (last panel) for the primary energy 100EeV Figure 4.16: ycore of S(r) (first five panels) and the width σ of the distributions of ycore as a function of secθ (last panel) for the primary energy 100EeV...76 Figure 4.17: An illustration of how geometric asymmetry is created by an inclined shower. Particles leaving the shower axis from the vertical shower (left) reach the ground symmetrically and creates no geometric asymmetry. Particles leaving the shower axis from the inclined shower, on the other hand, create geometric asymmetry on the ground causing less reconstruction accuracy of the core position Figure 4.18: Width σ of the distribution of shifts S(r) as a function of secθ for the primary energy E=10EeV Figure 4.19: Width σ of the distribution of shifts S(r) as a function of secθ for the primary energy E=100EeV Figure 4.20: Average shift < S(r)> as a function of secθ for the primary energy E=10EeV...80 Figure 4.21: Average shift < S(r)> as a function of secθ for the primary energy E=100EeV...81 Figure 4.22: Correlation between S(r) and r min for an energy E=10EeV and two zenith angles θ=15 o (top two rows), or θ=53 o (bottom two rows). β is set free in the reconstruction regardless of the multiplicity. See text for more details Figure 4.23: Correlation between S(r) and r min for an energy E=100EeV and two zenith angles θ=15 0 (top two rows), or θ=53 0 (bottom two rows). β is set free in the reconstruction regardless of the multiplicity. See text for more details Figure 4.24: Correlation between S(r) and β reconstructed for E=10EeV. The rest of the features are the same as in Figure Figure 4.25: Correlation between S(r) and β for energy E=100EeV. The rest of the features are the same as in Figure ix

11 Figure 4.26: δβ as a function of multiplicity for multiplicities 5. The primary energy is E=10EeV...89 x Figure 4.27: δβ as a function of multiplicity for multiplicities 5. The primary energy is E=100EeV...90 Figure 5.1: Illustration of how rise time is related to deep penetrating showers [6]. The dashed red lines indicate the path of the muons and green curved lines indicate the path of the EM particles. A light primary, such as a proton, that penetrates deep into the atmosphere will produce muons over a long length of its track. The difference in path lengths between these muons and the SD results in a longer rise time. The vertical scale here is tremendously compressed compared to the horizontal scale. In reality, the muons would appear essentially collinear with the primary track Figure 5.2: Illustration of how risetime is related to shallow penetrating showers [6]...99 Figure 5.3: Risetime as a function of secθ for AIRES (Sibyll and QGSJetI) and CORSIKA (Sibyll and QGSJetII) showers Figure 5.4: Risetime difference between Sibyll and QGSJet as a function of secθ, for the two incarnations of QGSJet studied and for proton and iron primaries Figure 5.5: The EM, Muonic and EM+Muonic components of S(1000) plotted as a function of secθ Figure 5.6: Average S(1000)/Energy 0.95 as a function of sin 2 θ for 10EeV showers Figure 5.7: The ratio of the quantity S(1000) between AIRES and CORSIKA as a function of sin 2 θ Figure 5.8: The ratio of the quantity S(1000) between Sibyll and QGSJet for AIRES and CORSIKA showers as a function of sin 2 θ Figure 5.9: S(1000)/E 0.95 as a function of θ for all the hadronic interaction models considered here in studying the CIC(θ) method Figure 5.10: Distributions of reconstructed values of S(1000), zenith angle θ and S(1000)/E 0.95 as a function of θ for the initial data set (top 3 panels) and for the final data set obtained after applying the quality cuts (bottom 3 panels) Figure 5.11: The sin 2 θ distributions of SD events. The red histogram in each panel corresponds to the sin 2 θ distributions obtained using the limit given in Equation This particular red histogram is same in all 4 panels as the

12 limit given in Equation 5.15 is the same everywhere. The black histograms are the sin 2 θ distributions for the different limits obtained from Equation 5.15 after substituting the fit parameters obtained from CORSIKA showers and given in Table Figure 5.12: The sin 2 θ distributions of SD events. The black histograms are the sin 2 θ distributions for the different limits obtained from Equation 5.15 after substituting the fit parameters obtained from AIRES showers and given in Table 5.2. The description of the red histograms is the same in Figure Figure 6.1: Distributions of FD energy and X max before and after (top and bottom) applying the quality cuts, respectively Figure 6.2: Z max obtained for each energy bin as a function of energy. The error in Z max is taken as [(δµ) 2 +(δσ) 2 ] where δµ and δσ are the uncertainties of µ and σ, respectively. The error bars are smaller than the size of the symbols, therefore they are not visible Figure 6.3: Distributions of Z at X max in different energy bins. The red area indicates where Z Xmax is greater than Z max in each energy bin. Events with Z Xmax > Z max will be rejected because of the low light level of these showers Figure 6.4: Illustration of the possible geometric relationship between the atmospheric shower profile and the FD field of view for a low-energy (left) or high-energy (right) event. Here, X max is underestimated (overestimated) for the low-energy (high-energy) event Figure 6.5: X low and X up limits in the FD field of view Figure 6.6: Distributions of X max as a function of X low for different energy bins. The blue arrows identify the maximum tolerated X low values to minimize reconstruction biases Figure 6.7: Distributions of X max as a function of X up after applying the X low cut. The blue arrows identify the minimum tolerated X up values to minimize reconstruction biases Figure 6.8: Mean X max as a function of energy. The number of events in each energy bin is indicated above each data point Figure 6.9: Mean X max as a function of energy with the two elongation rate fits to the data Figure 6.10: Comparison between Monte Carlo simulations of the elongation rate curve and the one determined from the data in the present analysis. The red and blue distributions correspond to the elongation rate curve predicted for xi

13 proton and iron showers, respectively, as simulated with the Conex/QGSJetI software packages. The mean X max values plotted here are obtained after applying similar quality cuts and anti-bias cuts mentioned in sections and Figure 6.11: Simulated elongation rate distribution for proton induced showers. The black points represent the pure simulated information. The red points represent the parameters reconstructed after processing of the simulation information through the detector simulation and response algorithms. The blue points represent the analyzed response including all quality and anti-bias selections Figure 6.12: Simulated elongation rate distribution for iron induced showers. The black points represent the pure simulated information. The red points represent the parameters reconstructed after processing of the simulation information through the detector simulation and response algorithms. The blue points represent the analyzed response including all quality and anti-bias selections Figure 6.13: Comparison between the HiRes experimental elongation rate and the one determined in the present analysis of Auger data. The blue distribution corresponds to the elongation rate obtained by HiRes-1 at energies between ev and ev, and the red distribution corresponds to the elongation rate obtained by HiRes-2 at energies between ev and ev, respectively Figure A.1: An actual FADC trace of a clean muon pulse Figure A.2: An actual FADC trace of an electromagnetic pulse Figure A.3: An actual FADC trace of a coincident muon pulse Figure A.4: Actual FADC traces of a late activity in an event observed by the station Bastille Figure A.5: The number of events observed by all the PMTs Figure A.6: Average afterpulse-to-signal ratio of all the PMTs in the study (red) and the total afterpulsing from the Malargue test facility (blue) Figure A.7: Average afterpulse-to-signal ratio of the 36 PMTs with more than 0.5% afterpulsing probability Figure A.8: The afterpulse-to-signal ratio of the noisier PMTs Figure A.9: The afterpulse-to-signal ratio of the noisier PMTs xii

14 Figure A.10: The afterpulse-to-signal ratio of the noisier PMTs Figure A11: The afterpulse-to-signal ratio of the noisier PMTs Figure A.12: The afterpulse-to-signal ratio of the noisier PMTs Figure A.13: The afterpulse-to-signal ratio of the noisier PMTs Figure B.1: Screenshot of the surface detector event display obtained from CDAS. According to the station color code, yellow circles are additional stations with signal, and the green triangle indicates the stations with trigger T3. Blue circles correspond to the silent stations, and pink crosses are the stations deleted. (For further information regarding station color code and details, please refer to [1] and [2].) Figure B.2: The array layout (panel 1), time to the plane front (panel 2), the standard fit to the lateral distribution of the integrated water Cherenkov signal (panel 3) and the values of reconstructed shower parameters (panel 4) obtained from the hybrid reconstruction of Auger Offline version 2.0. Impact position is denoted by a red arrow with a circle in panel 1. Only the x and y coordinates in the site coordinate system are used in plotting the station positions. The green triangle represents the TOT trigger. The fitted LDF corresponds to Equation 4.1 in Chapter Figure B.3: The longitudinal profile distribution of the event Figure B.4: The reconstructed light flux of the high energy event Figure B.5: Screenshot of the surface detector event display obtained from CDAS. The station color code is the same as in Figure B Figure B.6: Calibrated FADC traces of the SD stations. The color code represents the different PMTs by PMT1 = green, PMT2 = blue, PMT3 = red Figure B.7: The array layout (panel 1), time to the plane front (panel 2), the standard fit to the lateral distribution of the integrated water Cherenkov signal (panel 3) and the values of reconstructed shower parameters (panel 4) obtained from the hybrid reconstruction of Auger Offline version xiii

15 LIST OF TABLES xiv Table 4.1: The correlation factors between the width σ of the Frac S(1000) distribution and the β obtained for bins of r min from each graph in Figure Table 4.2: The correlation factors between the width σ of the Frac S(1000) distribution and r min obtained for bins of β from each graph in Figure Table 4.3: Summary of the various event reconstruction parameters studied and the optimal S(r) for each parameter...88 Table 5.1: Fit parameters for CORSIKA (Sibyll and QGSJetII) proton and iron showers Table 5.2: Fit parameters for AIRES (Sibyll and QGSJetI) proton and iron showers Table 6.1: Slopes of the distributions in Figures 6.11 and The color coding is explained in the text Table 6.2: List of quality and anti-bias cuts applied to the data, and the number of events remaining after each cut is applied successively and the efficiency Table 6.3: log 10 E, mean X max, the number of events in each energy bin and the error obtained for the final data set Table A.1: The afterpulse-to-signal ratio in this study and the Malargue test results of total after pulsing of the suspected 36 PMTs Type Caption Here...169

16 ACKNOWLEDGEMENTS xv First and foremost, I am deeply indebted to my academic advisor, Prof. Stephane Coutu, for his constant support and unwavering guidance. Prof. Coutu has shown me uncommon patience and understanding without which I never could have advanced to this level. I also owe many thanks to Prof. Paul Sommers, whose expertise and support have been invaluable assets in the final years of my studies. Prof. Sommers has clarified for me many of the finer points of the Auger project, and he has been the source of many ideas for my later research. For financial support in the early years of my graduate career, I am very grateful to Prof. James Beatty. I am also very thankful to my thesis committee members Prof. Richard Robinett and Prof. Jane Charlton for their careful academic evaluation of my work. I am indebted to Auger collaborators Denis Allard and Jose Bellido for answering my unlimited questions related to research, and to Bruce Dawson and Mike Roberts for educating me on the nuances of Auger hybrid data. Many thanks to Auger collaborators Maximo Ave, Michael Unger, Fabian Schüssler and Matt Healy for their assistance with data handling, and to Tom Paul and Sergio Barraso for their technical support. Many thanks also to Stephanie Jaminion, Ryan Nichols, and Steve Minnick for their support and assistance in early years of my graduate career. I would also like to thank Nick Conklin and Nathan Urban for their computer support and to Isaac Mognet for the conversations, both colorful and not.

17 Finally, thanks to the custodial staff of the 2 nd and 3 rd floors of Osmond Laboratory for keeping my work place clean. xvi

18 Chapter 1 Introduction On the evening of 15 October, 1991, the most energetic particle ever observed collided with the air high above the Utah sky, initiating a cascade of particle interactions and emitting a streak of fluorescent light that was seen by the Fly's Eye observatory far below [1]. The origins of this and other ultra high energy cosmic rays (UHECRs) remain shrouded in mystery, and modern theories of astronomical particle acceleration are strained to account for their existence. The most recent step in the decades-long search for the origins of cosmic rays is the Pierre Auger Observatory (PAO), an enormous detector designed specifically for the study of cosmic rays with energies exceeding ev. The PAO, which is already partially operational, promises to shed new light upon some of the most powerful processes in the cosmos. Near the dawn of the 20 th century, shortly after the discoveries of x-rays and radioactivity, serious efforts were underway to explain spontaneous ionization in the atmosphere. Simple gold-leaf electroscopes verified that around 10 ionic pairs per cm 3 per second are produced in even an isolated sample of air at ground level, but the source of the ionization remained mysterious. To test the dominant view at the time, that the ionization was the result of radiation emitted from heavy elements in the ground, Theodor Wulf measured the ionization rate at both the base and the top of the Eiffel Tower [2, 3, 4]. He found that the decrease in the ionization rate was much less than would be expected due to atmospheric attenuation, suggesting that the ionizing source may not be

19 2 the ground. Inspired by Wulf's attempt, Victor Hess launched a series of balloon experiments to measure ionization rates at altitudes up to 5350m. He found that the ionization rate increases at high altitudes, and he correctly concluded that the ionization was due to an extra-terrestrial source of penetrating radiation [3, 4]. For this he was awarded the 1936 Nobel Prize for Physics. After an initial period of intense skepticism about the interpretation of Hess' results, his explanation was eventually accepted by the physics community, and interest in what Robert Millikan called cosmic rays swelled [5, 6]. By measuring the ionization intensity at different latitudes along the route from Holland to the East Indies, J. Clay demonstrated that the cosmic ray flux is affected by the earth's magnetic field, and the rays are therefore of charged particles [6]. Using Geiger counters horizontally separated by several hundred meters, Pierre Auger demonstrated that the cosmic ray particles observed at ground level were not, in fact, strictly extra-terrestrial in origin, but were secondary particles produced from a cascade of interactions initiated by the impact of the primary cosmic ray with the earth's atmosphere [6, 7]. Through energy measurements of the secondary particles at ground level, Auger estimated the energy of primary cosmic rays to be on the order of ev, well beyond the energy of any particle seen before. The study of cosmic rays dominated particle physics experiments for the first half of the 20 th century, and the analysis of cosmic ray tracks left in cloud chambers led to the discovery of the positron, muon and pion. Cosmic rays remain a valuable source of data on cosmological processes, and a wide variety of cosmic ray experiments are in operation today. Some of these, such as CREAM and ANITA, are in the spirit of Hess, using balloon- or satellite-mounted

20 3 detectors to study cosmic ray primaries; others, like AGASA, follow the lead of Auger by using ground-based arrays of detectors to study cosmic rays through the air showers they generate. Despite the vast quantity of cosmic ray data amassed over the years, there are many outstanding questions in cosmic ray research, particularly as they pertain to UHECRs. The most energetic cosmic rays observed to date have energies of many joules, which is well beyond the range of energies that are produced with modern particle accelerators. Furthermore, the distribution of UHECR sources appears to be isotropic; no bias of UHECR incidence direction toward the galactic plane, the supergalactic plane, or individual point sources has been soundly established [6]. The physical processes that generate UHECRs remain unknown, but several theories about their cosmological origins exist. Experimental verification of any such theories is hindered by the low flux of UHECRs particles with energy ev impact the earth at a rate of about 1 per square kilometer per century. The study of these particles thus requires very large detectors and long exposure times. The PAO was designed for just this task [8]. With a surface array spanning 3000km 2 in Argentina, the completed southern observatory will be the largest fully-operational detector ever built. It is a hybrid detector that will rely not only on its surface array, but also on fluorescence measurements to determine the mass, energy, and arrival direction of the incident cosmic ray. In this thesis, I demonstrate how analysis of data from simulated and observed UHE cosmic rays assists in determining the physical parameters used in reconstructing events from the PAO. I also present an analysis of the chemical composition of the UHE

21 4 cosmic ray events detected by PAO and its possible change with primary energy. In Chapter 2, I review some of the science of UHECRs, including their known properties, atmospheric interactions, and methods of air shower observation. Chapter 3 focuses on the layout and operation of the PAO. An analysis of surface detector data appears in Chapter 4. This analysis uses Monte Carlo simulations of air shower events to investigate the dependence of the shower parameter S(1000) (mean particle density at 1000m from the air shower core) on several different variables associated with air shower parameters. In Chapter 5, I compare three hadronic interaction models that are widely used in air shower simulations, and I study their agreement with the constant intensity cut method often used in analyzing Auger Surface Detector data. Chapter 6 contains a composition analysis of hybrid data from the PAO. This chapter studies the distribution of the atmospheric depth of maximum shower development X max, and in particular the elongation rate (the variation of mean X max with energy) to determine the chemical composition of real UHE cosmic rays. Conclusions and directions for future study are discussed in Chapter 7. Appendix A is a technical discussion of a study I conducted of afterpulsing of the PAO surface detector photomultiplier tubes (PMTs). This appendix details a process for identifying PMTs possibly contaminated with gas such as helium, based on the photomultiplier tube traces that can evolve over time from the moment they are first deployed. Appendix B contains the reconstructed data on two high-energy cosmic ray events detected by the PAO.

22 Bibliography 5 1. F.Halzen, Astroparticle Physics, Proceedings of the First NCST Workshop, 3-22 (2001). 2. M.S.Longair, High Energy Astrophysics; vol. 1 Particles, photons and their detection (Cambridge University Press, 1992). 3. M.A Pomerantz, Cosmic Rays. Van Nostrand Reinhold Co., New York (1971). 4. C.Grupen, Astroparticle Physics; Springer-Verlag Berlin Heidelberg (2005). 5. P.Murdin et.al, The New Astronomy, International Publishers Ltd. (1978). 6. R.Clay, and B.Dawson, Cosmic Bullets. Addison-Wesley, Reading MA (1997). 7. P.Auger, Extensive Cosmic-Ray Showers, Rev. Mod. Phys. Vol. 11 (1939). 8. The Auger Collaboration. The Pierre Auger Observatory Design Report. 2 nd Edition(1997).

23 Chapter 2 Science of Ultra High Energy Cosmic Rays 2.1 Origins and Propagation Acceleration Direct measurements show that the cosmic rays with energy up to ev that hit the Earth are ionized particles consisting of almost 90% protons, 9% alpha particles and about 1% electrons. The exact sources of cosmic rays are unknown, but several powerful astrophysical processes are candidates. The most widely accepted paradigm for astrophysical acceleration is through the stochastic process proposed by Fermi [1], in which charged particles randomly interacting with moving magnetic fields gradually gain energy over time. Such Fermi acceleration requires particles to interact with large magnetic fields for long periods of time, and there is some doubt as to the existence of sufficiently strong and vast magnetic fields to stochastically accelerate particles to the observed upper energetic limits. According to simple models [2, 3], the maximum energy E max reached by the Fermi shock acceleration process is approximately given by: E max β Ze B L, 2.1 where βc is the shock velocity, Ze is the particle charge, B is the magnetic field and L is the characteristic size of the acceleration region. See Figure 2.1 for more details. Some of the most likely candidates for Fermi acceleration to ultra-high energies are the lobes of

24 7 radio galaxies, which are large enough to permit gradual acceleration over time. Supernova shock waves are also potential accelerators; however, these only exist for a few thousand years, which may not be long enough to generate the energies observed in UHECRs. Because of their strong magnetic fields, compact objects such as neutron stars have been proposed to produce cosmic rays from Fermi acceleration; however, radiation in the vicinity of neutron stars attenuates UHE particles, so compact objects are unlikely candidates for UHE cosmic ray sources Top-Down Models Contrary to bottom-up acceleration and propagation of charged particles mentioned above, top-down models describe more exotic sources where the cosmic rays are created at extremely high energies. Super heavy dark matter, topological defects such as magnetic monopoles and domain walls are examples of top-down models [4, 5]. Topological defects, especially, are capable of producing particles with ultra high energies beyond ev [6]. A common characteristic of these non-acceleration models is that they result in high fluxes of UHE photons and neutrinos and a much lower flux of protons. Some of these top-down models predict an isotropic arrival direction distribution, while others predict an anisotropy towards the direction of the Galactic center [7].

25 Figure 2.1: Magnetic field as a function of characteristic length scale of several candidate cosmic ray sources. Diagonal lines indicate the conditions required to accelerate protons or iron nuclei to ev. The solid green line and broken blue line respectively indicate the minimal requirements for acceleration of iron and protons to ev, provided β=1 in Equation 2.1. The solid blue line shows the more realistic situation for protons, in which β=1/300. Only those astrophysical sources above the diagonals are capable of accelerating the associated particles to ultra-high energies [8]. 8

26 2.1.3 Diffusion 9 The mass composition of cosmic rays with energies below ev reveals a larger fraction of light nuclei, such as lithium, beryllium and boron, than is present in the distribution for the Universe at large. These light nuclei are not readily produced in large quantities by stellar fusion, but are commonly produced as spallation products of heavier elements, suggesting that the cosmic ray mass composition is enhanced by secondary particles produced during cosmic-ray propagation through the Galaxy. The abundance of light nuclei can be accounted for if the average cosmic ray traverses about 10g/cm 2 of matter between its origin and Earth; however, a particle traveling in a straight line through the galactic disc will only encounter 10-3 g/cm 2 of matter [2]. It is therefore likely that sub-pev particles do not escape directly from the galaxy, but gradually diffuse through it. This idea is supported by the experimentally observed isotropic distribution of PeV-scale cosmic rays: should there be no diffusion, one would expect the incident cosmic rays to reflect the mass distribution in the galaxy. Several models of intra-galactic cosmic ray propagation have been proposed to account for the observed energy spectrum and mass composition [9], and the physical bases of the diffusive interactions in each of these models are particle interactions with other particles and with magnetic fields. In an order-of-magnitude calculation [10], one might consider the Larmor radius for a particle traveling through a magnetic field, R L = E/(300HZ), where Z is the particle's charge, R L is in cm, E is in ev and H is in gauss. For a 1 PeV proton traversing a typical galactic magnetic field of around 2 microgauss, R L ~1.6x10 18 cm, whereas the thickness of the galactic disk is about 5x10 20 cm. Even in

27 10 this highly simplified model, it can be seen how particles in this energy range can be subject to diffusion through the galaxy. On the other hand, particles with energies around ev are deflected only slightly by galactic magnetic fields and can pass through the galaxy without diffusion. Because the intergalactic magnetic field is thought to be only about 1/100 of the galactic magnetic field, UHECRs are also deflected minimally in intergalactic space, facilitating identification of their sources GZK cut-off The second phenomenon that makes UHE cosmic rays a valuable source of astrophysical data is the so-called GZK cut-off. Greisen [11], as well as Zatsepin and Kuzmin [12], proposed that UHE particles will interact with the 2.7K Cosmic Microwave Background Radiation (CMBR). In the rest frame of a proton with energy above about 5x10 19 ev, the CMBR is blue-shifted far enough to interact with the proton through pion photoproduction. Each such interaction removes about 20% of the particle's energy, and particles above ev energy are expected to have attenuation lengths of only about 50Mpc, resulting in an effective cut-off of the spectrum at Earth of the UHE cosmic rays. (See Figure 2.2). Thus, any UHECR incident at Earth is local in origin, traveling not much more than 50Mpc total. One important corollary of the GZK cut-off is that it eliminates many exotic and distant candidate sources for UHECRs, facilitating identification of sources. A second corollary is that the GZK cut-off distance is much less than the expected Larmor radius of UHE particles in the intergalactic medium, meaning that the direction of incidence of a UHE particle indicates its origin to within a few

28 degrees. Neutrinos, of course, would be immune to any possible GZK cut-off, and could in fact be produced as a result of GZK interactions of UHECRs. 11 Figure 2.2: Energy as a function of propagation distance for protons in the 2.7K cosmic microwave background radiation field. The highest energy protons have their energy degraded by interactions with the CMBR, placing a limit on the distance traveled by UHECRs [13]. 2.2 Known Properties of Cosmic Rays The effort put forth toward cosmic ray research has taught us a great deal about their nature through their energy and spectra and mass composition, as well as through their directions of approach. These particles have energies between 10 9 and ev, with an energy spectrum that follows a power-law distribution (Figure 2.3). The exponent of this spectrum is not uniform, but changes in two different places first at the spectrum's

29 12 knee around ev, and then at the ankle around ev. The knee results most likely from a combination of two effects: 1) the supernova shock acceleration mechanism reaches an effective limit at around ev, and 2) the magnetic diffusion of primary particles through the galaxy results in possible escape beyond about ev. The ankle can be accounted for by the appearance of an extra-galactic component, coupled with energy losses due to electron-positron pair production. The mass composition of cosmic ray primaries generally resembles that of the universe at large, but with slight energy-dependent variations. At energies below about ev, the mass composition exhibits an abundance of light elements. This abundance is largely in line with the abundance of light elements from stellar nucleosynthesis, with the important difference that some rare elements are over-represented in cosmic rays due to spallation reactions of heavier nuclei. Near the knee at ev the excess of light elements is expected to diminish and the bias to shift toward an excess of heavy elements, although this has yet to be observed directly experimentally. This would be a consequence of any cosmic ray acceleration model, such as supernova shock Fermi acceleration, that yields a maximum energy that is a function of the magnetic rigidity R=p/Ze of the particle; in such models, a more highly charged nucleus can be accelerated to a higher energy than a proton, say. Possible propagation effects including galactic escape would similarly include a dependence on the particle s magnetic rigidity. Beyond the ankle, in some models primaries could be dominated by an abundance of light elements, although again there is no direct experimental measurement of this effect.

30 13 Figure 2.3: Cosmic ray energy spectrum [14]. The incident directions of cosmic rays appear to be distributed isotropically at all energies. At low energies, this observation is accounted for by diffusion; however, one might expect sufficiently high-energy cosmic rays to more faithfully reveal their source

31 14 directions and therefore display some anisotropy. Because UHECRs are expected to deflect only by a few degrees due to galactic and intergalactic magnetic fields, there is hope that sufficient data will permit their sources to be discerned. As of yet, there are not enough data on UHECR arrival directions to convincingly substantiate arguments either for or against anisotropic distribution of their sources, although some weak claims of possible sources have been made by SUGAR [15, 16] and AGASA [17, 18]. The PAO is expected to remedy this paucity of data. 2.3 Extensive Air Showers Anatomy A cosmic ray that is incident upon the earth's atmosphere will interact with upper atmospheric molecules, producing secondary particles and triggering a cascade of interactions, or an extensive air shower (EAS). The shower front advances as a slightly curved, radially symmetric disk that is perpendicular to the shower axis. A typical air shower is composed of hadronic, muonic and electromagnetic channels. The hadronic channel, which is tightly concentrated about the shower axis, carries the hadronic products of the atmospheric interactions of the parent cosmic ray. The muonic and electromagnetic components are the products of pion decay. Charged pions produced in the EAS can decay into muons and neutrinos, which travel largely unimpeded to the ground (Figure 2.4), or can also further interact, continuing to feed the hadronic core of the shower. The concentration of muons in an EAS depends upon the mass of the primary

32 15 particle; heavy primaries produce more muons than do light primaries because the hadronic energy is more quickly put into low energy pions and not dissipated into the electromagnetic (EM) channel. The electromagnetic channel is initiated by the decay of neutral pions into high energy gamma rays, which produce electron/positron pairs, which in turn contribute additional gamma radiation to the shower via bremsstrahlung. Each neutral pion decay transfers about 30% of its energy to the electromagnetic cascade, which dissipates the shower's energy through atmospheric ionization. This in turn results in the production of fluorescent light along the cascade path. The amount of fluorescent light emitted from the shower is therefore a good indication of the shower's total energy. As the shower passes deeper into the atmosphere, its total number of particles increases until, at the depth of maximum, or X max, the rate of particle disappearance from the shower (either via decay or by particle energies being depleted below threshold) outpaces the rate of production. The value of X max indicates both the mass and energy of the primary particle. Further, because the heavier primaries such as iron can be approximated as superpositions of nucleons, they tend to be less penetrating in the atmosphere, causing small X max values, whereas lighter primaries such as protons penetrate deeper in the atmosphere, causing larger X max values.

33 16 Figure 2.4: Cartoon of an extensive air shower. The central red line indicates the incident axis of the primary cosmic ray, which triggers the EAS by interacting with an atmospheric nucleus. The green scattered points to the left of the shower axis indicate the particle density of the shower as a function of atmospheric depth. At the point indicated by X max, the number of particles in the shower is maximized. To the right of the axis is a schematic of typical interactions in the EAS. High-energy nucleons in the shower produce pions, which can decay into muons if they are charged, or gamma rays otherwise. The muons travel mostly unhindered to the ground, whereas the electrons and positrons scatter multiple times before arriving at the ground, also generating bremsstrahlung gamma rays in the process. The temporal span of the shower front also indicates the mass and energy of the primary particle. The shower front is slightly convex, and particles near the shower axis tend to arrive at the ground first. Because they tend not to scatter, muons generally arrive

34 17 before the EM and gamma components, which are delayed by multiple scatterings. The EM component therefore tends to have the most spread in the lateral and temporal distributions of the three channels Detection: Surface Arrays Because the EAS extends over a large area at the earth's surface, it is conveniently observed with an array of detectors spread over the ground [19]. Each detector in the array registers the passing of high-energy charged particles, and the combined measurements of the detectors are used to reconstruct the full event. Generally the detectors are either scintillating plastic plates, such as those used in the AGASA experiment, or water Cherenkov tanks, as in the Haverah Park and PAO arrays. The position of each detector is carefully specified, and all detectors in the array must be precisely synchronized in order to accurately measure and compare pulse arrival times and durations. By using well-designed surface arrays, one can accurately reconstruct air showers to reveal arrival direction as well as the mass and energy of the primary particle Reconstruction To reconstruct the EAS axis from Surface Detector (SD) data, one starts by approximating the intersection of the axis with the ground as roughly the center of mass of the shower as measured by particle counts in the surface detectors. Using timing information such as the order in which the shower front passed through the detectors and

35 18 the temporal span of the signal in each detector one can estimate the arrival direction of the shower. Reconstruction in this manner can identify the primary arrival direction to within 2 degrees of angular resolution for vertical showers with energy ev [13], but the reliance of this reconstruction technique on shower front geometry makes it dependent on EAS models and simulations. Primary energy is similarly reconstructed from SD data using the signal at a particular distance from the core. In this case, the data are interpolated to a single quantity that correlates well with the total shower energy, such as the signal, S(r), at a specified distance r from the shower axis. The value of r is of the order of the detector spacing, and the optimal value of r which minimizes dependence on modeling is found through simulations. The mass of the primary is largely calculated from the muon content of the EAS. Owing to the superposition principle, heavier primaries tend to produce showers with higher muon content than the showers produced by light nuclei. This difference is rather modest we expect about 30% more muons in an EAS from an iron primary than there are in an EAS from a proton primary of the same total energy [13]. The statistical uncertainty in EAS muon content prevents one from using this measure to accurately identify the primary mass for a single event, but it is nonetheless useful for determining the UHE cosmic ray mass composition from multiple events.

36 2.3.4 Detection: Fluorescence 19 As an EAS develops, it loses energy to the ionization and excitation of atmospheric molecules, and a fraction of this energy is re-emitted as near-uv nitrogen fluorescence. The atmospheric fluorescence yield is largely independent of temperature and pressure, and the amount of fluorescent light emitted by an air shower is therefore a good measure of the shower's energy. Sensitive earth-bound fluorescence detectors (FDs) are capable of measuring the light emitted by an EAS, and the event can be reconstructed from this data and that of atmospheric conditions during the event. A FD is an array of light collectors trained on a fixed portion of the sky. Each collector registers light only from a narrow solid angle, so that a shower passing through the line of sight of a FD will trigger several of the sensors in series. Because they effectively record the EAS in progress, FDs are useful for studying event dynamics; however, their use is limited to only clear moonless nights and locations with very low ambient light Reconstruction The EAS axis can be accurately reconstructed from FD data. An air shower registers as a line of activated photomultiplier tubes in the FD, allowing one to define the plane containing both the axis of the shower and the FD. In the absence of any other data, the primary arrival direction can be estimated within the shower-detector plane through timing information provided by the FD. This method of mono viewing is modestly accurate, but it is desirable to supplement the FD data with data from a surface array or another FD in order to better pinpoint the arrival direction. A monocular data analysis

37 20 done using a time fit in [20] with HiRes-I data shows an angular resolution of 5 o. Stereo reconstruction using two FDs offers more reliable reconstruction [21, 22]. When a pair of FDs each has data on the same event, the shower-detector plane can be constructed for each, and the shower axis is simply the intersection of the two planes. The exact angular resolution of stereo reconstruction depends on the geometry of the position and orientation of the shower axis with respect to the FDs. The HiRes detector results show a geometrical stereo reconstruction accuracy of a median space angle error of 0.4 o with errors less than 0.9 o for 95% of the reconstructed events with energy above ev [23, 24]. Even more accurate hybrid reconstruction can be obtained using a single FD in conjunction with timing data from a surface array. The studies in [24 (Figure 2)] indicate an angular resolution of 0.3 o of the hybrid events recorded at the Pierre Auger Observatory. After determining the shower axis, one can reconstruct the development of the shower and find the energy and mass of the primary particle. Each FD Photomultiplier Tube (PMT) collects light from only a segment of the shower's full path, and the length of the segment viewed by any PMT depends on the orientation of the shower axis relative to the FD. Knowing the quantity of light collected by the PMT, the length of and distance to the segment of the shower axis viewed by the PMT, and the atmospheric conditions at the time the shower is recorded, one can calculate the fluorescence light produce by the shower and therefore its total energy. By combining data from all PMTs that registered the event, one can construct a profile of the fluorescence energy emitted by the shower as a function of atmospheric depth. If the data are fitted to the appropriate functional form,

38 one can estimate the depth of maximum, and the number of particles at the depth of maximum. These values are all known to depend on primary energy and mass. 21 Bibliography 1. E. Fermi, On the origin of the cosmic radiation. Phys. Rev. 75: (1949). 2. T.K.Gaisser, Cosmic Rays and Particle Physics. Cambridge University Press, Cambridge (1990). 3. R.J.Protheroe, Origin and Propagation of The Highest Energy Cosmic Rays, astro-ph/ v1. 4. M.Risse, Upper Limit on the Photon Fraction in Highest-Energy Cosmic Rays from AGASA Data, Phys. Rev. Let. 95, (2005). 5. V.Berezinsky, Ultra High Energy Cosmic Rays, Nucl. Phys. B (Proc. Suppl.), 81: (2000). 6. V.Berezinsky et al., Cosmic Necklaces and Ultra High Energy Cosmic Rays, astro-ph/ S.Yoshida, Extremely High Energy Neutrinos, Neutrino Hot Dark Matter, and the Highest Energy Cosmic Rays, Phys. Rev. Let. Vol.81, 25 (1998). 8. P.Bhattacharjee et al., Origin and propagation of extremely high-energy cosmic rays, Phys. Rept., 327: , C.J.Cesarsky, Cosmic-ray confinement in the galaxy. Ann. Rev. Astron.

39 Astrophys. 18: (1980) P.Sokolsky, Introduction to Ultrahigh Energy Cosmic Ray Physics. Westview Press, Boulder CO (2004). 11. K.Greisen, End to the cosmic-ray spectrum? Phys. Rev. Lett. 16: (1966). 12. G.T.Zatsepin, and V.A.Kuz'min, Upper limit of the spectrum of cosmic rays. JETP Lett. 4:78-80 (1966). 13. The Auger Collaboration. The Pierre Auger Observatory Design Report. 2 nd Edition. (1997). 14. M.M.Winn et al., The cosmic-ray energy spectrum above ev, J.Phys. G:Nucl. Phys. 12(1986) C.B.A.McCusker et al., The arrival directions of cosmic-rays above ev, J.Phys. G:Nucl.Phys. 12(1986) M.Takeda et al., Extension of the Cosmic-Ray Energy Spectrum beyond the Predicted Greisen-Zatsepin-Kuz'min Cutoff, Phys. Rev. Let. Vol.81 (1998) K.Honda et al., Small-scale Anisotropy of Cosmic Rays above ev Observed with Akeno Giant Air Shower Array, The Astrophysical Journal, 522: (1999). 18. F.A.Aharonian, and J.W.Cronin, Influence of the universal microwave background radiation on the extragalactic cosmic-ray spectrum. Phys. Rev. D 50: (1994). 19. M.S.Longair, High Energy Astrophysics; vol.1 Particles, photons and their detection (Cambridge University Press, 1992).

40 T.Abu-Zayyad at al. A search for arrival direction clustering in the HiRes-I monocular data above ev, Astroparticle Phys. 22: (2004). 21. P.Sommers, Extensive air showers and measurement techniques. C. R. Physique 5: (2004). 22. R.U.Abbasi et al., Study of Small Scale Anisotropy of UHECRs Observed in Stereo by HiRes, Astrophys. J., 610, L73 (2004). 23. C.R.Wilkinson et al., Geometrical Reconstruction with the High Resolution Fly s Eye Prototype Cosmic Ray Detector, Astroparticle Phys., 12: (1999). 24. Bruce Dawson, Private Communication. 25. C.Bonifazi, Angular Resolution of the Pierre Auger Observatory, brabonifazi-c-abs1-he14-oral.

41 Chapter 3 The Pierre Auger Observatory Situated on a high plateau near the city of Malargue in the province of Mendoza, Argentina, the southern Pierre Auger Observatory (PAO) is specifically designed for measuring UHE cosmic ray events. The observatory is hybrid by design, utilizing both surface detector (SD) and fluorescence detector (FD) methods for data collection. The key advantage of this design is that, because they are measured independently by two separate instruments, hybrid events have significantly lower systematic errors than do events measured by either SD or FD instruments in isolation. However, because of the limited duty cycle of the FD, which is operational only on clear moonless nights, only about 10% of PAO events are expected to be hybrid. Nonetheless, the PAO promises to provide a wealth of UHE cosmic ray data, and although it is not yet completed, it has already surpassed all of its predecessors in cumulative exposure. A possible Northern PAO site is the subject of ongoing discussions within the international scientific collaboration and with various funding agencies. 3.1 The Surface Detector The surface detector of the Pierre Auger Observatory is an array of 1600 Water Cherenkov Detectors (WCD), deployed on a grid with a spacing of 1500m between detectors. The surface array operates with nearly 100% duty cycle and a response that is

42 25 highly independent of weather conditions. Once all the detectors in the array are deployed it will cover an area of 3000km 2. As of June, 2007 there are 1417 detectors deployed, 1367 with water and 1316 with electronics [1]. Figure 3.1 shows the present deployment status (June, 2007) of the surface array. Figure 3.1: The deployment status of the array as of June Each circle represents an individual surface detector. The green circles represent detectors filled with water and with electronics. The blue circles represent detectors filled with water but without electronics. The gray circles represent detectors without water. Detectors with a red square in the array map have been removed from the acquisition due to missing differential global positioning system coordinates. The position of the observatory main campus and the locations of four fluorescence buildings are indicated by small arrows. The field of view of each telescope in each fluorescence detector is indicated by the dotted lines [1].

43 Layout of a Pierre Auger Water Cherenkov Detector Figure 3.2 gives a picture of a WCD deployed in the surface array. Each detector is a cylindrical tank with a top area of 10m 2 and a height of 1.5m, and filled with purified water to a height of 1.2m. The water is contained within a bag that has a diffuse reflective white interior with three windows at 120 o intervals at the top [3]. Three photomultiplier tubes (PMTs) with a bulb diameter of 200mm are arranged in the windows looking downward from the top surface of the tank. Each of the three PMTs provides two signals: a high gain signal from an amplified dynode and a low gain signal from the anode, which are read out by a flash analog to digital converter (FADC) in time slots of 25ns [4]. The outputs of the 6 FADCs are then fed to a programmable logic device that performs trigger decisions on the signal. The performance of these triggers will be described in the following sections. Electric power is supplied to the detector by solar panels and is stored in two 12V batteries connected in series. Each detector in the array is completely independent from all other detectors and communicates with a central data acquisition system (CDAS) via a wireless communication system. Thus, when the deployment of a detector is completed in the array, it is able to take data and transfer them to the CDAS regardless of the status of the other detectors in the array.

44 27 Figure 3.2: A surface detector deployed at the Pierre Auger Observatory [2] and a schemac layout ([3]) of the PMT positioning and few other components Calibration of the Surface Detector The surface detectors are designed to be sensitive to signal sizes varying from a few photoelectrons to as many as about 10 5 photoelectrons. This dynamic range enables the calibration of the detector using single particles, as well as the measurement of thousands of particles in the detector without saturation. There are four surface detector calibration tasks, namely; 1) setting the PMT high voltages, 2) allocating the detector trigger levels to measure only signals above a prescribed signal size, 3) providing an established measurement for different signals from different detectors, and 4) determining the ratio between the low gain anode and the high gain dynode [5]. The first

45 28 task is carried out in the surface detector by setting the PMT voltages to a preliminary value at the time of deployment, while rest of the calibration tasks are performed on a timely basis depending on the signal characteristics of the air showers seen by the detectors [4, 6]. The Vertical Equivalent Muon (VEM) Units Due to certain factors such as differences in PMT gains or in water quality in the surface detectors, the same amount of light deposited by particles vertically crossing the water in different surface detectors, or the same surface detector at different times, does not in general yield the same FADC count. Therefore, it is necessary to have a standard measure of the surface detector signal. In the PAO, the signals are measured in units of the charge deposited by a vertical and central muon (i.e., a muon entering at the center of the top surface of the detector vertically, or a vertical throughgoing muon), termed a Vertical Equivalent Muon (VEM or Q VEM ). A vertical throughgoing muon is convenient in obtaining a standard unit because atmospheric muons passing through a detector produce a peak in a charge histogram which can be used to measure the value of 1 VEM. Since the particles enter a detector from arbitrary directions, the calibration is done by setting a low threshold, three PMT coincidence trigger for the detector and by studying the histogram of charge deposited (Figure 3.3) [7]. The peak in the charge histogram is called Q peak VEM, and the relationship between Q peak VEM and the charge deposited by a vertical and central muon Q VEM is given by: Q peak VEM = 1.05Q VEM, 3.1

46 29 measured in a single reference detector as described in [8]. This relationship is obtained by considering vertical throughgoing muons, muons that enter from the top or the bottom of the detector and exit through sides and muons that enter through the side of the detector and exit through the side. The shift observed in the relationship is due to the contribution from the second and third types of muons while the first type, the vertical throughgoing muons are clearly the VEMs. Figure 3.3: Charge histogram from a surface detector station in integrated FADC channels. The trigger is set to fulfill the requirement that a peak signal be greater than 5 channels above the baseline, in each of the three PMTs in the detector. The first peak in this histogram is a trigger effect. The second peak is due to vertical throughgoing muons (Q VEM peak ) [7].

47 30 The measurements of the channels in the FADC indicate the PMT photocurrent. Using the atmospheric muon baseline and a procedure similar to that for determining the relationship between Q peak VEM and Q VEM, one can obtain the relationship between the peak photocurrent produced by a vertical throughgoing muon, I VEM peak and the average maximum photocurrent I VEM as: I peak VEM = 1.05I VEM 3.2 The detector trigger is fixed with respect to I VEM. It is also, necessary to maintain a comparable trigger level for all the detectors in the surface detector array because of the possible drifts in the PMT gains, although the high voltages of the PMTs are set to a preliminary value at deployment. A rate-based calibration method is used to obtain a comparable trigger level [4, 8]. This particular calibration method involves identifying the PMT high voltage at which the event rates with a peak signal above an established baseline are comparable. The target rate of a PMT at 150 channels above the muon baseline is 100Hz. The measurements done in [7] using a single reference detector show that a 100Hz rate at 150 channels above baseline corresponds to a trigger point of roughly 3I VEM. This allows the setting up each of the three PMTs in a detector to a target of 50 channels/i peak VEM. The high voltages of each of the three PMTs are adjusted until the above requirement is fulfilled Trigger Levels of the Surface Detector The PAO surface detector trigger system has been designed to operate over a wide range of primary energies and maximize the efficiency of triggering on UHECRs

48 31 over a range from vertical to very inclined arrival directions. It should select the candidate cosmic ray events and reject any background events while fulfilling the data acquisition and communication event rate requirements. In this section we discuss the two types of triggers, namely the low level triggers and the high level triggers associated with the surface detector. Low Level Triggers There are three different low level local triggers for an individual surface detector. They are T1, T2 threshold and T2 TOT (time over threshold). The T1 and T2 threshold triggers are used for calibration purposes as described in the previous section. The T2 TOT trigger is implemented to retrieve physical signals. The T2 TOT trigger has a high cosmic ray detection power and has been used widely in higher-level trigger (T4 and T5 descriptions of these triggers will follow) selections [9]. The low level trigger T1 requires that in all three PMTs, at least one FADC bin should have a signal above 1.75I VEM [7]. This trigger rate is maintained to about 100Hz by the calibration method described in the previous section. Although this trigger is noisy, it is required to detect fast signals (<200ns) corresponding to the muonic component generated by inclined showers. The T2 threshold trigger requires that in all three PMTs, at least one FADC bin should have a signal above 3.2I VEM. The T2 threshold trigger rate is maintained to about 20Hz. The last low level trigger, T2 TOT requires that at least 13 FADC bins (325ns) in a window of 120 bins should have a signal above 0.2I VEM in coincidence between any two PMTs out of three. The charge of the signal depends on the quality of water in a detector. The T2 TOT rate is sensitive to this charge.

49 32 After deployment, the decay time of detectors gradually decreases, and stabilizes after a few months of deployment. Once the detectors are stable, the average T2 TOT rate is about 2Hz over the array [10, 11, 12]. High Level Triggers Apart from the above mentioned local triggers T1 and T2, three higher level triggers T3, T4 and T5 are designed to distinguish random coincidence events from cosmic ray shower events. Trigger T3 incorporates the locations and timing of all level 2 triggers. The triggers T4 and T5 are known as physics trigger and quality trigger, respectively. The T4 trigger enables us to select cosmic ray events partially contaminated by chance coincidences between neighboring detectors, and the trigger T5 ensures nominal reconstruction accuracy [13]. The T3 trigger checks whether the configuration of tanks simultaneously triggering T2 is consistent with the geometry of an EAS front. The notation used to describe the trigger refers to crowns, or degrees of separation, between T2 triggered detectors. The first crown of a surface detector contains its six first neighbors; the second crown consists of the 12 detectors that lie on the next largest hexagon concentric with and enclosing the first crown; the n th crown consists of the 6n detectors on the hexagon that is concentric with and enclosing the first n-1 crowns. A configuration of m detectors contained within n crowns is denoted mcn [14]. The basic T3 trigger can be satisfied in two different ways. In the first case, three detectors trigger T2 TOT such that one detector has both of the others within its second crown (3C2) and at least one within its first crown (2C1) as illustrated in Figure 3.4.

50 33 Combining the T2 TOT triggers and compact detector geometry in this way makes the T3 trigger efficient at selecting near-vertical events, but not those with a large zenith angle (i.e., zenith angle >60 o ). The alternative T3 requirement is four detectors triggering either T2 TOT or T2 Threshold meeting 2C1, 3C2 and 4C4. These criteria effectively select near-horizontal events that are discarded by the other T3 requirements [6, 15]. Figure 3.4: Two possible 3C1 configurations for zenith angle up to 60 o [15]. The T4 trigger uses a more stringent set of criteria to filter out unphysical T3 events. As with T3, this is a dual trigger that is satisfied with either of two sets of conditions. The first case consists of three detectors triggering T2 TOT and in the 3C1 configuration, whereas the second scenario involves four detectors triggering T2 and in the 4C1 configuration as illustrated in Figure 3.5. In both cases, the detectors must trigger T2 within a time window that is consistent with the transition of the EAS front through

51 34 the array. The front is quickly reconstructed as follows: Triangles consisting of three T2 triggered detectors in non-colinear 3C1 configurations are constructed. That triangle with the highest total signal is taken to be nearest the shower axis, and the trigger times of these three detectors are used to calculate the plane of the shower front. Detectors are then removed from the event if their trigger times do not coincide with the estimated passing of the shower front [15]. Figure 3.5: The alternative T3 requirement, 4C1: four detectors with T2 threshold or TOT for larger zenith angles (>60 o ) [15]. See text below for more details. The T5 quality trigger is in place to eliminate T4 events that occur on the edge of the array. If an event's greatest signal comes from a detector at the edge of the array, then it is possible that the shower axis intersects the ground outside of the array, in which case the event will be improperly reconstructed. The trigger requires T4 events in which either all six neighbors of the detector with the highest signal are operational, or at least five of its six neighbors are operational and the core is inside a working triangle [12, 15].

52 3.2 Fluorescence Detector 35 The surface array is flanked by four fluorescence detector (FD) buildings that look out over the array. Each FD building houses six telescopes for detecting atmospheric fluorescence from air showers (see Figure 3.6). The telescopes each cover 28.6 degrees of elevation and 30 degrees of azimuth, and they are positioned adjacent to each other such that the viewing area of a single FD building covers a continuous 180 degree azimuth angle. Each telescope occupies its own bay within the FD building. To protect their sensitive optics from ambient light, the telescopes each are positioned behind a glass UV filter that permits the transmission only of near-uv light peaked around 350nm [16]. External shutters over the UV filters are closed during daylight hours. Light entering a telescope passes through Schmidt optics [16, 17], reflects off the concave surface of a 3.5m by 3.5m spherical segmented mirror and focuses onto a camera composed of an array of 440 PMTs (see Figure 3.7). Each PMT is a hexagon approximately 45mm across and covers about an area with 1.5 degrees in diameter in the sky. The PMTs are arranged in a honeycomb fashion (see Figure 3.8) consisting of 22 rows and 20 columns and are mounted on a spherical aluminum manifold at the focal surface of the spherical mirror [18, 19]. To ensure that light incident at the edge of a pixel will also be counted without losing the information, each PMT is surrounded by a reflective wall that scatters light from its edge towards its center (see Figure 3.8). The PMTs are sampled at a rate of 10MHz, and their signals are digitized via ADC.

53 Figure 3.6: The FD building located at Los Leones with the external shutters in the open position [2]. The bottom left picture is a top view of the building and the bottom right picture is a schematic layout of the six telescopes. 36

54 Figure 3.7: Schematic layout of a fluorescence detector telescope. 37

55 Figure 3.8: Layout of the FD camera. The PMTs are mounted at the focal surface of the telescope mirror in a hexagonal array as shown. A single PMT covers an area with 1.5 degrees diameter in the sky. To maximize the quantity of fluorescence light detected by the camera, and to encourage sharp transitions between pixels, each PMT is surrounded by six reflective mercedes stars, one at each vertex (inset). The shaded region illustrates the second level trigger algorithm described in Section The trigger reads camera data as a 5 by 22 pixel submatrix that sweeps over the entire camera surface. It searches for the 5 patterns indicated in red, as well as variations of these due to rotations and reflections. If at least 4 PMTs in a pattern have passed the first level trigger, the second level trigger is flagged. 38

56 3.2.1 Fluorescence Detector Triggering 39 Prior to sending data to the CDAS, the FD filters candidate cosmic ray events from the background noise with a series of triggers. The first level trigger, which operates at the level of the PMT, identifies illuminated pixels. This trigger compares the sum of the digital PMT signal over the last 10 ADC cycles to a pre-set threshold [6, 20]. Owing to daily fluctuations in the level of background light, this threshold is allowed to float such that the first level trigger rate remains close to 100Hz, regardless of atmospheric conditions. When several PMTs trigger within a coincidence time of 20 microseconds, the second level trigger algorithm is initiated. This trigger is in place to identify patterns of illuminated pixels that indicate an air shower. The trigger operates under the assumption that an air shower should extend across at least 5 pixels. There are 5 basic patterns that can be formed by drawing a line through 5 contiguous cells of a hexagonal array. Taking rotations and reflections into account, the number of patterns increases to 39. Accounting for the possibility that one of the 5 contiguous PMTs triggered at a level that was just under the threshold, the acceptance criterion is relaxed such that if any 4 out of 5 PMTs in a straight line are illuminated, the event is flagged. This leaves 108 possible patterns of illuminated pixels that indicate an air shower [20]. The second level trigger algorithm sweeps a 5-column window across the camera data, searching for any of the 108 signaling patterns in each 5 by 22 submatrix. It takes about 1µs to sweep over the full camera. If a pattern match is found, the event is flagged and sent to the next level.

57 40 The third level trigger uses timing data to accept only events that may offer useful cosmic ray data. Simulations suggest that the lifetime of an air shower ranges between 400ns and 100µs, so events with duration outside of this range are rejected. An example of a fast event is a particle that passes very near the FD and provides an abundance of air Cherenkov light to the FD. Such a shower will have a very fast track on the FD camera and will be rejected. Slow phenomena, such as meteors or aircraft, will similarly be rejected by the upper cutoff. Recent studies [21, 22, 23] suggest improvements to the third level trigger algorithm to increase its efficiency. Beyond the third level trigger, a final algorithm, called T3, is implemented prior to sending data to the CDAS [24]. The T3 algorithm combines data from multiple cameras within the FD that register the same event. It reconstructs the shower and estimates X max as well as the point of primary impact with the earth's surface. Finally, the algorithm removes pixels which contribute significantly to the reconstruction χ 2. Events with four or more triggered pixels after T3 are sent to CDAS, with the information related to shower detector plane and the shower arrival time at ground Calibration and Atmospheric Monitoring The purpose of the FD is to gather data on the EAS from atmospheric fluorescence. In addition to identifying the path of the shower core, the FD is capable of determining the shower's energy and depth of maximum. Calculating these quantities reduces to estimating the number of photons produced by the EAS as it descends through the atmosphere. The two key factors that influence the precision to which the photon

58 41 yield is recovered are the precision of the instrument itself and the atmospheric conditions during the air shower. It is therefore necessary to maintain proper calibration of the FD, as well as to continuously monitor atmospheric conditions. The most thorough telescope calibration is the absolute, or dome, calibration [25] that is performed around three times per year. In this calibration, a cylindrical drum of 2.5m diameter is placed over the telescope diaphragm. The drum interior is coated with a diffusive material and is illuminated with a pulsed LED of about 375nm wavelength. A NIST-calibrated photodiode is used to measure the absolute flux of light at the diaphragm opening, and this known flux is compared to the FADC output of each PMT in the camera. This type of calibration allows one to directly relate the FADC output to the number of photons incident on the telescope. A daily calibration is used to monitor fluctuations in PMT performance [26]. This calibration uses optical fibers to direct light from xenon flash lamps to three different sources in the telescope, referred to as sources A, B and C. Source A is located at the spherical mirror and directed at the camera; source B is next to the camera, directed toward the mirror; source C is outside the telescope aperture, directed at diffusively reflective material mounted on the inside of the telescope shutters. The integrated charge induced on each PMT from sources A, B and C is compared to reference measurements taken at the time of absolute calibration. This way, any drift in gain of individual PMTs, any change in mirror reflectivity and window transmisivity can be monitored between absolute calibrations. Just as important as proper calibration of the FD is accurate data on the transmitting properties of the atmosphere. Fluorescence light intensity is affected both by

59 42 Rayleigh scattering due to atmospheric molecules and by Mie scattering by aerosols. It is therefore essential to closely monitor the atmospheric properties in the vicinity of the observatory. Because it is molecular in nature, the Rayleigh component of atmospheric attenuation can be calculated from the thermodynamic properties of the atmosphere. These are measured through balloon-based radiosonde measurements [27]. Temperature and pressure measurements are taken at 20m intervals to an altitude of 25km, and these are used to estimate the atmospheric depth. A local model of the molecular atmosphere for Malargue now exists for each month. Atmospheric aerosol content varies by a larger margin and on a shorter time scale than do pressure and temperature, and atmospheric aerosols must be continuously monitored. There are currently six distinct atmospheric monitoring systems used at PAO: LIDAR, CLF, HAM, APF, cloud cameras and star monitors [28]. Each of these is discussed briefly below. LIDAR: Each FD building is equipped with a steerable pulsed UV laser that can be used to detect atmospheric aerosols at various depths. The laser is pointed in some direction in the sky, and a nearby PMT measures the backscattered light from aerosols. Timing data are used to determine the scattering profile as a function of distance, and this is used in event reconstruction. The FD LIDARs (Light Detector and Ranging) are generally used to monitor the atmosphere above and behind the FD, but when a T3 event is detected, the LIDAR monitors the shower-detector plane so that the event can be correctly reconstructed.

60 43 CLF: The central laser facility (CLF) is a pulsed UV laser located near the geometrical center of the array [29]. Laser pulses of known energy are fired into the atmosphere by the CLF and detected by the FDs, providing information on the amount of scattering experienced by the beam, as well as the attenuation between the CLF and each FD. The CLF fires several pulses each hour on nights when the FDs are operating. It is also used for monitoring timing between the SD and FD: an optical cable diverts some of the light from the CLF into the nearby surface detector Celeste, which triggers each time a CLF pulse is fired. HAM: The horizontal attenuation monitors (HAMs) measure light attenuation at the level of the FDs. The FDs are equipped with DC light sources and corresponding light collectors. Light emitted from the source of one FD is detected by another FD, providing a measure of the horizontal light attenuation. These measurements occur about once an hour during FD operation. APF: The aerosol phase function (APF) monitors are used to measure the scattering properties of aerosols near the FDs. A beam of collimated UV light is pulsed horizontally across a FD, and the signal detected by the FD contains information on the differential scattering cross section of atmospheric aerosol particles. These data are then used to estimate the component of the light detected by the FD that is due to Cherenkov radiation. Cloud cameras and star monitors: Additional atmospheric properties can be discerned from direct observations of clouds and stars. Infrared cameras that can distinguish between clear skies and clouds are mounted at the FDs and scan the sky approximately every 5 minutes. The cloud camera information can then be combined

61 44 with LIDAR or CLF data to more accurately detail cloud conditions. Additionally, star intensities indicate the total amount of aerosol between the ground and the edge of the atmosphere. By comparing the measured intensity of a star with its known absolute magnitude, one can calculate the total attenuation due to atmospheric aerosols. Fixed and steerable CCD cameras are deployed at the PAO to supplement the atmospheric aerosol data with star intensity data [28]. Bibliography F.Nerling, Description of Cherenkov Light Production in Extensive Air Showers, GAP D.Barnhill, Composition Analysis of UHECRs using the PAO Surface Detector, GAP T.Suomijarvi, Surface Detector Electronics for the Pierre Auger Observatory, GAP N.Busca, The UHECR Flux from the Southern Pierre Auger Observatory Data, GAP P.Allison et al., In Proceedings of the 29 th ICRC (2005), usa-allison-ps-abs1- he14-poster. 8. M.Aglietta et al., In Proceedings of the 29 th ICRC (2005), fra-suomijarvi-tabs1-he14-poster.

62 45 9. P.Allison, Origin of the TOT trigger rate dependence on water quality and the TOT background, GAP P.L.Ghia et al., An empirical approach to the T2-T3 SD trigger optimization, GAP I.Allekotte et al., In Proceedings of the 29 th ICRC (2005), usa-arisaka-kabs1-he15-poster. 12.D.Allard et al. In Proceedings of the 29 th ICRC (2005), usa-bauleo-pm-abs1- he14-poster. 13.E.Parizot et al., In Proceedings of the 29 th ICRC (2005), fra-parizote-abs1- he14-poster. 14.S.Dagret-Campagne, The Central Trigger User Guide and Reference Manual, GAP M.Roth et al., Offline Reference Manual SD Reconstruction, GAP G.Matthiae, Optics and mechanics of the Auger fluorescence detector. Proc. ICRC (2001). 17.G.Matthiae G. and P.Privitera, The Schmidt telescope with corrector plate. GAP (1998). 18.C.Aramo, et al. The camera of the Auger fluorescence detector. GAP (1999). 19.S.Argiro, Performance of the Pierre Auger fluorescence detector and analysis of well reconstructed events. In Proceedings of 28 th ICRC (2003). 20.H.Gemmeke, The Auger fluorescence detector electronics. In Proceedings of

63 27 th ICRC (2001) T.Asch et al, Proposal for a new third level trigger for the fluorescence telescopes. GAP (2005). 22.S.Petrera et al, FD trigger and aperture revised. GAP (2006). 23.Y.Guardincerri et al., A method for rejecting lightning and other noise events from the Auger fluorescence detector data. GAP (2007). 24.J.Abraham, et al. Properties and performance of the prototype instrument for the Pierre Auger Observatory. Nuc. Inst. Meth. A. 523:50-95 (2004). 25.P.Sommers, Dome calibration of Auger telescopes. GAP (1999). 26.C.Aramo C. et al. Optical relative calibration and stability monitoring for the Auger fluorescence detector. In Proceedings of. 29 th ICRC (2005), ita-insolia- A-abs1-he15-poster. 27.J.A.Bellido, Performance of the fluorescence detectors of the Pierre Auger Observatory. In Proceedings of 29 th ICRC (2005), aus-bellido-j-abs1-he14- oral. 28.R.Cester, et al. Atmospheric aerosol monitoring at the Pierre Auger Observatory. In Proceedings of 29 th ICRC (2005), usa-roberts-m-abs1-he15- poster. 29.F.Arqueros, et al., The central laser facility at the Pierre Auger Observatory. In Proceedings of 29 th ICRC (2005), usa-malek-m-abs1-he15-poster.

64 Chapter 4 Auger Surface Detector Analysis The response of the surface detector to an Extensive Air Shower (EAS) allows an estimation of the energy of the primary cosmic ray. This is obtained through the computation of the average signal at a given distance from the axis. In Auger data analysis we choose this distance from the axis to be 1000m. The signal at 1000m from the axis, S(1000) is obtained through a fit to the particle lateral distribution at ground level. This particular fit is called the lateral distribution function (LDF). The parameter S(1000) plays a major role in determining the energy of a cosmic ray using surface detectors. Therefore it is important to understand the behavior of this parameter as a function of zenith angle, core position, and the LDF slope parameter β (defined below). Furthermore, one also needs to understand the random and systematic errors present in estimating S(1000) from the data obtained from single events. These errors may occur due to uncertainties in the estimated parameters such as core position and shower axis, uncertainties in how any saturated signals should be handled, uncertainties from signal fluctuations, and incorrect methods of modeling muonic and electromagnetic components of the shower. The aim of this work is to investigate how these parameters affect the determination of S(1000), which is so important in inferring the primary energy of the air showers. In this study we develop a Toy Monte Carlo (MC) method where by Toy we mean that features such as the particle interaction model, primary composition, and weighting in commonly used simulation packages are not used fully, but rather

65 48 approximated with suitable simplified parameterizations. In this particular Toy MC approach the attention is focused mainly on possible biases in the reconstruction of S(1000), and understanding of any random and systematic uncertainties that are present. 4.1 Event Generation Procedure As a first step we generate a hexagonal array with only 43 stations, which is sufficient to highlight the major features of S(1000) reconstructions, since the highest energy events trigger at most about 2 dozen stations. The detector spacing is set to 1500m, matching the actual spacing between the detectors in the Auger SD array. For the rest of this study we use this array of 43 stations. Figure 4.1 shows the layout of the 43 detectors used in this study. The shape of the lateral distribution function depends mainly on the nature of the primary particle, on the zenith angle θ of the shower, and on the altitude of the ground [1]. A lateral distribution function of the so-called NKG (Nishimura-Kamata-Greisen) form [2, 3] β r r S ( r) = k r0 r0 β is chosen where r is the core distance and r 0 =700m. The NKG-type lateral distribution function is initially developed for purely electromagnetic showers and is simple, robust and describes the Auger data reasonably well. Simulation results together with the data obtained from the Haverah Park array [4] and other studies [5, 6, 7] show that on average, 700m is roughly the transition region between the muonic and electromagnetic

66 component. Since we cannot fix r 0 and β in Equation 4.1 at the same time, we fix r 0 to be 700m. The parameter k is the normalization constant. The same studies [5, 6, 7] have shown that considering the elevation and other geometrical factors of the Auger site, the signal at a given distance can be best estimated with a β of the form: β = a + bsecθ Figure 4.1: Array of detectors used in this study. Detector spacing is set to 1500m so that it is similar to that of the Auger SD array spacing. Figure 4.2 shows the lateral distribution function fitted with a fixed k value but with different β values to a set of detector signals. From this figure we clearly see how

67 the slope β affects the measurement of the signal at a specific core distance r, when the normalization constant is fixed. 50 Signal 2 10 β=-2.14 β=-2.24 β=-2.34 β=-2.44 β= r(m) Figure 4.2: Lateral distribution function of the form given in equation 4.1 fitted to a set of detector signals. The slope β varies between and in increments of 0.1 and illustrates how the variation affects the determination of the signal at a given distance from the core when the normalization constant, k, is fixed. In this particular case, to generate events, we take a=-3.75 and b=1.05, following Ave and Yamamoto [5, 7]. In [5], it is shown that there is an offset of 0.2 in the mean value of β between the data obtained from the Haverah Park array and data obtained from Auger surface detectors. Moreover, constant composition studies show that the difference in the mean value of β between proton and iron is ~0.12, and the spread in β is 0.15 due to experimental reconstruction uncertainties, with a further spread of 0.2 due to error in

68 51 the core location estimate using arrival time of the showers. Therefore, in order to account for this β variance in analyzing Auger data, the value of β in our Toy Monte Carlo model is sampled from a Gaussian distribution with the mean value given by Equation 4.2 and an RMS of 0.2. At r=1000m the signal S(1000) can be obtained using Equation 4.1. Various studies done with air shower simulations in [1, 8] by Pierre Billoir et al. show that the S(1000) distribution plotted as a function of secθ varies according to E 0.95, where E is the primary energy. This preliminary estimate of the relationship between S(1000) and energy leads us to correlate S(1000) to the primary energy according to [5]: 7.8 S (1000) = E (sec 1) + θ Signal Fluctuations The fluctuations in the signal detected by the WCDs directly affect the reconstructions of the parameters such as primary energy, arrival direction and core position of the extensive air showers [9]. Any incorrect assumptions regarding signal fluctuations within the detector may generate systematic errors in the above mentioned reconstructed parameters. The signal in a WCD includes contributions from both the muonic and electromagnetic (EM) parts of the air showers, each of which is subject to its own fluctuations. We use basic parameterizations in order to get the ratio M of muonic to

69 total signal and then to obtain the separate electromagnetic and muonic signals in the detector. For a given zenith angle θ and core distance r, M can be written as [7]; secθ r /1000 for r < 1800 / secθ M = for r 1800 / secθ If S(r) is the total signal (in VEM) in the detector at a distance r, given by Equation 4.1, then the electromagnetic component S EM and the muonic component S µ can be written as [7]; S EM = S(r) (1-M) 4.5 S µ = S(r) M. 4.6 A vertical throughgoing muon in a detector will deposit energy of about 240MeV, which is 1 in units of VEM, while an EM particle will deposit a maximum energy of about 10MeV on average, which is 1/24 in units of VEM. Therefore in order to accommodate the electromagnetic signal to the standard VEM unit, we multiply the electromagnetic signal by 24. The number of 10MeV (on average) electromagnetic particles (N em ) is given by [7]; N EM = S(r) (1-M) Fluctuations in the electromagnetic component S EM are generated randomly from a Poisson distribution with a mean N EM and fluctuations of the muonic component S µ are generated also randomly using a Poisson distribution with a mean S µ. The values returned from the Poisson distributions in each case are added directly to obtain the total fluctuated signal S given by, S = S EM,P /24 + S µ,p 4.8

70 53 where S EM,P and S µ,p are EM and muonic signals returned by Poisson distributions, respectively. Different studies [10, 11, 12] have shown that when the observed signals from the LDF are fitted against the predicted signals via a maximum likelihood method, the station with a large signal (>15VEM) yields a relative uncertainty of about 8%. On the other hand, for detectors with small signals (<15VEM), the number of effective particles in the detector is required as Poisson fluctuations dominate the uncertainty of the detector signal. Especially for muons, a Poisson statistics on this effective number of particles at the detector level gives a good approximation for the fluctuation of the Cherenkov yield [13]. Roughly, 1VEM corresponds to 0.64 particles in the Poisson fluctuations [14]. Therefore, the total signal fluctuation can then be written as, 2 2 σ = ( S 0.08) + ( S 0.8) 4.9 where S is the total fluctuated signal obtained from Equation 4.8. Moreover, a core position for each shower is randomly generated inside a unit cell within the coordinates (- 750,-650), (750,-650), (0,650). The detector trigger threshold is considered to be 3.2VEM (corresponding to the experimental setting as described in Section 3.1.3). The shower zenith angle is taken as 0 o giving β=-2.7.

71 4.2 Event Reconstruction 54 In the event reconstruction, the same NKG-type LDF as in Equation 4.1 is fitted to the simulated signals in the detector, from which we extract S(1000). The zenith angle θ is taken to be the same as the generated zenith angle, and the value of β is fixed to its mean value at this particular zenith angle using Equation 4.2. Many high energy air showers have a detector located quite close to the core position, causing that particular detector to saturate. The signal detected by this closest detector is partly lost due to the maxing out of the FADC response, and also due to nonlinearities in the PMTs response at higher signal amplitudes. Ignoring these saturated signals in the event reconstruction could cause systematic shifts in the reconstructed core position, leading to possible biases in the reconstructed value of the parameter S(1000), and thereby in the primary energy [15]. Therefore, it is important to take the saturation level into account in event reconstruction. In this study we require that any signal greater than 1000VEM be considered to be saturated. Equation 4.9 is used again in the treatment of signal fluctuations Dependence of S(1000) on β and the Distance to the Closest Detector, r min Using the event generation procedure described in section 4.1, events for each energy setting are generated for the primary energies 10, 25, 50 and 100EeV. In this analysis our goal is to check the sensitivity of the estimated S(1000) parameter to the steepness of the LDF β and the distance r min from the shower core to the closest detector hit.

72 Figure 4.2 gives the distributions of the residuals Frac S(1000) defined by 55 Frac S (1000) S( 1000) Re c S(1000) Gen = 4.10 S(1000) Gen for the four different primary energies E=10, 25, 50, 100EeV, respectively. Here, S(1000) Gen is the generated S(1000) from Equation 4.3 and S(1000) Rec is the reconstructed S(1000). We see from Figure 4.3 that the RMS of these distributions is roughly constant until the highest energy bin, where the S(1000) reconstruction becomes slightly more uncertain. That is, the RMS of the Frac S(1000) distribution is around 0.12 in first three panels, although the RMS of the Frac S(1000) distribution is slightly higher in the last panel, which is for 100EeV. It can also be seen that the mean of the Frac S(1000) distribution is around 0.05 in all four panels. For each of the four energies, S(1000) is reconstructed with a 5% offset, on average. Figure 4.3: Distributions of Frac S(1000) for the primary energies 10, 25, 50 and 100EeV, respectively.

73 56 It is also instructive to study how the residuals depend on the distance to the nearest detector hit. Therefore, we also study the distribution of Frac S(1000) for different bins of r min in slices of 100m between 0 and 800m, and in different bins of β in slices of 0.05 between and We stop at r min =800m because this corresponds roughly to the half-way point between detectors, so that beyond this a shower core is closest to the next detector. For each of these histograms (not shown) a Gaussian is fitted to determine the width σ of the distribution. Then, this width σ is plotted as a function of β for the same set of bins of r min defined above. This is done in Figure 4.4, which gives the width σ of the Frac S(1000) distribution as a function of generated β for each primary energy considered. The correlation factors obtained for each graph are given in Table 4.1. It is readily apparent that at lower energies the resolution of the S(1000) reconstruction is strongly dependent on how far the shower strikes the ground from the nearest detector. When the core hits too close, in all likelihood the detector is saturated and effectively not useful for the reconstruction, leaving only few detectors available for the lateral distribution profile fit. At higher energies this is not a problem, because there are enough detectors with signals that the loss of effective detectors to saturation does not significantly affect the reconstruction. An alternative way of displaying the information is to plot the width σ of the Frac S(1000) distribution as a function of r min in various β slices of 0.05 between and These distributions are given in Figure 4.5. Table 4.2 indicates the correlation factors obtained from each graph. We will comment in detail on these figures and tables below.

74 57 σ E=10EeV σ E=25EeV σ β E=50EeV β σ β 0<r <100 min 100<r <200 min 200<r <300 min 300<r <400 min 400<r <500 min 500<r <600 min 600<r <700 min 700<r <800 min E=100EeV β Figure 4.4: Width σ of the Frac S(1000) distribution as a function of generated β for different primary energies. β is fixed to its mean value at the particular zenith angle θ=0 o. Figure 4.4 indicates in detail the width σ of the reduced S(1000) distribution as a function of generated β. In each panel are given curves obtained for the various r min bins, where r min is the distance from the shower core point of impact to the nearest detector. There is a strong correlation between the σ of the reduced S(1000) distribution and β (The correlation factors are given in Table 4.1). This correlation is particularly important for small values of r min. It can be seen from these distributions that when values of β larger than the mean value of -2.7 (used in generation) are used in reconstruction, the width of the reduced S(1000) distribution increases. The reason for this is that, as β increases, the slope of S(r) becomes steeper near r = 1000m, increasing the uncertainty in the reconstructed S(1000). It can also be seen that for energies 10 and 25EeV, when r min

75 is sufficiently large (600m or higher) the change in σ is not significant at all. This is because, when the closest detector hit is further away from the core it is very unlikely that the detector would saturate. Thus, there are more detectors available for the lateral distribution profile fit at these two energies, 10, 25EeV. At 10EeV, for r min between 0 and 500m, σ varies between 7% and 13% for β up to -2.6, and at β=-2.65 all the graphs seem to have a σ close to 10%. We observe a similar behavior in the plots for 25EeV where at β=-2.6 and r min between 0 and 600m, σ is around 6.5%, and in the case of E=50EeV all the plots seem to have σ around 5%. However, we observe that the cross-over β value at which all the plots seem to have the same width σ changes from -2.6 to for E=100EeV, which is not quite significant. Overall, at 10EeV we see large dispersions in σ of the reduced S(1000) values mainly due to the smaller number of detectors in the lateral distribution profile fit. These dispersions get smaller with increasing energy. This is expected from the effect of the threshold of the local detectors. r min E=10EeV E=25EeV E=50EeV E=100EeV 0<r min < <r min < <r min < <r min < <r min < <r min < <r min < <r min Table 4.1: The correlation factors between the width σ of the Frac S(1000) distribution and the β obtained for bins of r min from each graph in Figure 4.4.

76 59 σ E=10EeV σ E=25EeV r min (m) r min (m) σ E=50EeV σ <β <-2.86 Gen -2.86<β <-2.81 Gen -2.81<β <-2.76 Gen -2.76<β <-2.71 Gen -2.71<β <-2.66 Gen -2.66<β <-2.61 Gen -2.61<β <-2.56 Gen -2.56<β <-2.51 Gen E=100EeV r min (m) r min (m) Figure 4.5: Width σ of the Frac S(1000) distribution as a function of r min for different primary energies. Figure 4.5 indicates in detail the width σ of the reduced S(1000) distribution as a function of the distance from the shower core point of impact to the nearest detector, r min. In each panel are given curves obtained for the various β bins sampled from a Gaussian during the shower development. It can be seen that there is a strong dependence of the reduced S(1000) width on r min (the correlation factors are given in Table 4.2), which changes with the primary energy. At 10EeV all the curves show saturation effects around 540m and at 25EeV this occurs around 640m. In the distributions for 50EeV and 100EeV these saturation effects are not so drastic as there are more detectors used in the fit. However, the variation of σ at large r min is more pronounced in the distributions for 50EeV and 100EeV than it is for 10EeV and 25EeV for all the β ranges.

77 60 Β E=10EeV E=25EeV E=50EeV E=100EeV -2.91<β< <β< <β< <β< <β< <β< <β< <β< Table 4.2: The correlation factors between the width σ of the Frac S(1000) distribution and r min obtained for bins of β from each graph in Figure Saturation Level and S(1000) Experimentally, the Auger surface detector response saturates at very large light levels, corresponding roughly to 1000VEMs. A series of events are run with different saturation levels other than 1000VEM to check the behavior of S(1000) with each level. The events are generated using the same LDF of Equation 4.1. The zenith angle θ and the azimuth angle φ are set to 0 o. β is taken to be same as in Equation 4.2 and is sampled from a Gaussian distribution with this mean value and with an RMS of 0.2 considering the fluctuations of β explained in Section 4.1 [5]. The rest of the parameters such as core location, the detector trigger threshold are considered to be the same as in Section 4.2. In the event reconstruction, β is fixed to regardless of the multiplicity. The saturation levels considered are 600VEM and 1500VEM. The primary energies considered are 10, 25, 50, 100, 125 and 150EeV. The parameter Frac S(1000) given in Equation 4.10 is plotted in different bins of r min in slices of 100m between 0 and 800m

78 61 and in different bins of β in slices of 0.05 between and For each of these histograms a Gaussian is fitted to find out the width σ and mean of the distribution. Then, the mean and width of the Frac S(1000) distribution are plotted as a function of r min for the same set of bins in β for all six different primary energies mentioned above. Figures 4.6, 4.7 and 4.8 show these distributions for 10EeV, 25EeV and 50EeV showers, with a β fixed to 2.70 in the reconstruction, with the saturation levels set either to 600VEM or to 1500VEM. At 10EeV (Figure 4.6), all the curves show saturation effects around 600m when the saturation level is 600VEM and around 520m when the saturation level is 1500VEM. The mean value of β used in event generation is As can be seen from the figures, S(1000) is reconstructed correctly within the range <β Gen <-2.66 (blue triangles), but as β fluctuates up or down by as much as 0.2, the mean of the Frac S(1000) parameter changes by as much as 18% (14%) for the 600VEM saturation level (1500VEM). At 25EeV (Figure 4.7), the saturation effect is clearly seen around 620m only for the 1500VEM saturation level. Here also, S(1000) is reconstructed correctly within the range -2.71<β Gen <-2.66 and the mean of the Frac S(1000) parameter changes by at least 10% when β fluctuates up or down from its mean value, for either saturation level considered here. The reconstruction accuracy increases within the range <β Gen <-2.61 (σ changes from 8% to about 5% when going from r min =50m to r min =750m) for 600VEM saturation, and for all β ranges σ changes from 12% to about 4% at all r min for 1500VEM. Furthermore, in Figure 4.6, we observe a flip-flop in the plots of the mean of the Frac S(1000) distribution as a function of r min, for both saturation levels. This happens

79 62 because of the different β values used in the LDF. For a given shower, when the value of β used in shower generation is larger than the value of β used in shower reconstruction, the LDF associated with the shower generation is steeper at lower distances and eventually crosses with the LDF associated with the shower reconstruction. This cross over point happens to be around 600m (520m) when the saturation level is 600VEM (1500VEM). Before the cross over point the LDF associated with the shower generation lies above the LDF associated with shower reconstruction, and after the cross over point (i.e., after 600m for the 600VEM saturation level, and after 520m for the 1500m saturation level) it lies below the LDF associated with shower reconstruction. Therefore, the Frac S(1000) calculated before the cross over point is negative (positive) and after the cross over point is positive (negative) depending on the values of β used in the shower generation. The mean and σ of the Farc S(1000) distribution become small after this cross over point as a result of there being no saturated detectors in the fit.

80 63 mean β = -2.70, Saturation at 600VEM Rec E=10EeV mean β = -2.70, Saturation at 1500VEM Rec r min (m) r min (m) σ 0.16 β = -2.70, Saturation at 600VEM Rec σ 0.16 β = -2.70, Saturation at 1500VEM Rec r min (m) r min (m) Figure 4.6: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 10EeV. The value of β is fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure 4.5.

81 64 mean β = -2.70, Saturation at 600VEM Rec E=25EeV mean β = -2.70, Saturation at 1500VEM Rec r min (m) r min (m) σ 0.16 β = -2.70, Saturation at 600VEM Rec σ 0.16 β = -2.70, Saturation at 1500VEM Rec r min (m) r min (m) Figure 4.7: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 25EeV. The value of β is fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure 4.5.

82 65 mean β = -2.70, Saturation at 600VEM Rec E=50EeV mean β = -2.70, Saturation at 1500VEM Rec r mon (m) r min (m) σ 0.16 β = -2.70, Saturation at 600VEM Rec σ 0.16 β = -2.70, Saturation at 1500VEM Rec r min (m) r min (m) Figure 4.8: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 50EeV. The value of β is fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure 4.5.

83 Figures 4.9, 4.10 and 4.11 are for 100EeV, 125EeV and 150EeV showers, respectively, with a fixed β of 2.70 used in reconstruction. Here again, we consider the two saturation levels 600VEM and 1500VEM. In these figures the saturation effects for each level are not so drastic as there are more detectors used in the fit. Again we see that in the plots of mean of the Frac S(1000) parameter distribution, S(1000) is reconstructed correctly within the range -2.71<β Gen <-2.66 at all three energies. Also in all 3 figures the mean of the Frac S(1000) behavior is more pronounced with a variation as much as 10%- 15% when β fluctuates up or down by as much as 0.2 at larger r min values compared to that of Figures 4.6, 4.7 and 4.8. The mean of the Frac S(1000) distribution changes from about 12% when β is shifted 0.2 from the mean value when r min < 350m at all three energies. One would expect to have a mean close to zero at these high energies as there are more detectors in the fit. Although the saturation effects are not as strong as they are for the low energies, we still observe the deviations of the mean of the Frac S(1000) distribution to be more than 10%. The reason is the fixed β in shower reconstruction. By fixing β in shower reconstruction, we impose a constraint on the slope of the LDF although there are enough signals in the fit for β to be a free parameter, and thereby the data are not accurately described (This effect is clearly seen in Figures 4.19 and 4.21). In all three energies, the width σ of the Frac S(1000) distribution is equal to or less than 4% at lower r min values (r min up to about 250m) for both 600VEM and 1500VEM saturation levels. The width σ of the Frac S(1000) distribution increases from about 1% at higher r min values regardless of the saturation level at all three energies.

84 67 mean β = -2.70, Saturation at 600VEM Rec E=100EeV mean β = -2.70, Saturation at 1500VEM Rec r min (m) r min (m) σ 0.16 β = -2.70, Saturation at 600VEM Rec σ 0.16 β = -2.70, Saturation at 1500VEM Rec r min (m) r min (m) Figure 4.9: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 100EeV. The value of β is fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure 4.5.

85 68 mean β = -2.70, Saturation at 600VEM Rec E=125EeV mean β = -2.70, Saturation at 1500VEM Rec r min (m) r min (m) σ 0.16 β = -2.70, Saturation at 600VEM Rec σ 0.16 β = -2.70, Saturation at 1500VEM Rec r min (m) r min (m) Figure 4.10: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 125EeV. The value of β is set fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure 4.5.

86 69 > S(1000) <Frac β = -2.70, Saturation at 600VEM Rec E=150EeV > S(1000) <Frac β = -2.70, Saturation at 1500VEM Rec r min (m) r min (m) ) S(1000) β = -2.70, Saturation at 600VEM Rec ) S(1000) β = -2.70, Saturation at 1500VEM Rec σ(frac σ(frac r min (m) r min (m) Figure 4.11: <Frac S(1000) > as a function of r min for the two saturation levels 600VEM and 1500VEM (top two distributions) and σ of Frac S(1000) as a function of r min for the same saturation levels (bottom two distributions) at the primary energy 150EeV. The value of β is fixed to in the event reconstruction. The 8 different graphs in each box are plotted for different bins of β. The color coding is the same as in Figure Best Parameter S(r) The measurement of the primary energy of a cosmic ray particle using the WCDs mainly involves calculating the detector signal at a particular core distance and linking this signal to the energy of the air shower initiator. The distance at which this expected signal should be measured depends on the procedure implemented in the event reconstruction [16, 17]. When reconstructing the size of the shower, a lateral distribution

87 70 function (LDF) is used and any inaccuracies in the function can lead to inaccuracies in the location of the shower core and the particle density at the distance at which we measure S(r). The effect of such uncertainties can be minimized by choosing the appropriate core distance at which to do this procedure. In this study, the parameter S(r) is studied for r=600m, 800m, 1000m, 1200m and 1400m for zenith angles 0 o, 15 o, 36 o, 45 o, 53 o, 60 o and for the primary energies 10EeV and 100EeV, respectively, to determine the best distance to use in the LDF. In the process of event generation, the azimuth angle φ is generated randomly between 0 o and 360 o. The core location is randomly distributed inside the unit cell within the coordinates (-750,- 650), (750,-650) and (0,650). The detector threshold is considered to be 3.2VEM. In this study we use the saturation level to be as follows [7, 18]: Sat VEM = 600 ( area / peak) 4.11 where area/peak = 1 + r ( (secθ-1))/1000, and r is the core distance. In the event reconstruction for this study, the LDF given in Equation 4.1 is used to calculate the signal. The slope parameter β is a free parameter regardless of the multiplicity (in reality, for the event reconstruction in Auger, this is not always possible, especially at lower energies, when there may not be enough detector signals to allow β to be a free fit parameter; we will return to this later in Section 4.4.1). The zenith angle and the azimuth angle are taken directly from the event generation. The signal fluctuation is the same as in Equation 4.9.

88 We define 71 S( r) S( r) S( r) = 4.12 S( r) where S ( r) is the reconstructed value and S (r) is the generated value at r for the values of 600m, 800m, 1000, 1200m and 1400m. We also define xcore = xcore - xcore and ycore = ycore - ycore where xcore' and ycore' are the reconstructed core coordinates along x and y, respectively, and xcore and ycore are the generated core coordinates along x and y, respectively. Figure 4.12 shows the variation of β with secθ where β = secθ. As can be seen, the values assigned for a and b in this particular study are somewhat different from the values assigned for a and b in Equation 4.2. The motivation for this change is that here we consider different distances to determine the optimal energy estimator S(r), and r is not fixed to 1000m as in the previous case [19, 20]. Figure 4.12: Variation of β with secθ.

89 72 In Figures 4.13and 4.14 the first 5 panels give the xcore and ycore distributions of S(r) for E=10EeV and the sixth panel at the bottom right hand corner of each figure gives the variation of σ as a function of secθ for xcore and ycore respectively. Figures 4.15 and 4.16 are the same distributions for E=100EeV. In the distributions for E=10EeV, it is clearly seen that the spread is narrower for angles 0 o, 15 o, 36 o and the spread becomes wider for 45 o, 53 o and 60 o. In the distributions for E=100EeV, the spread is narrower for angles 0 o, 15 o, 36 o and 45 o and after that it becomes wider in all cases of S(r). This is also seen in the σ as a function of secθ plots given in each figure. The value of σ increases abruptly after secθ=1.414 for E=10EeV and the increase is not so sharp for E=100EeV. This reconstruction effect can be explained using Figure 4.17 In a vertical shower, the particles going away from the shower axis at an angle α reach the ground symmetrically, and therefore the shower fluctuations are minimized. Several studies [21, 22] have shown that these geometric asymmetries are minimized in showers with up to about 40 o of zenith angle. Therefore, the reconstruction accuracy of the core positions is higher. This is what we see in Figures 4.13, 4.14, 4.15 and The observed σ values are quite a bit smaller for zenith angles up to about 36 o, regardless of the distance from the core at which we calculate the energy estimator. On the other hand, in an inclined shower, the particles going away from the shower axis reach the ground at different times, creating an asymmetry on the ground. This enhances the shower fluctuations, and the reconstruction of core position is done with less accuracy. We therefore observe a drastic increase in σ after 40 o regardless of the distance used in the energy estimator, S(r). However, these geometrical asymmetries present in inclined showers are more important

90 73 for larger distances from the core (>2000m). In this study, the ground parameters are obtained for a distance less than 1500m from the core. Therefore, although the core coordinates are reconstructed with less accuracy, the impact on size reconstruction by the geometric asymmetry is less. Figure 4.13: xcore of S(r) and the width σ of the distributions of xcore as a function of secθ for the primary energy 10EeV.

91 Figure 4.14: ycore of S(r) and the width σ of the distributions of ycore as a function of secθ for the primary energy 10EeV. 74

92 Figure 4.15: xcore of S(r) (first five panels) and the width σ of the distributions of xcore as a function of secθ (last panel) for the primary energy 100EeV. 75

93 Figure 4.16: ycore of S(r) (first five panels) and the width σ of the distributions of ycore as a function of secθ (last panel) for the primary energy 100EeV. 76

94 77 Figure 4.17: An illustration of how geometric asymmetry is created by an inclined shower. Particles leaving the shower axis from the vertical shower (left) reach the ground symmetrically and creates no geometric asymmetry. Particles leaving the shower axis from the inclined shower, on the other hand, create geometric asymmetry on the ground causing less reconstruction accuracy of the core position. Figures 4.18 and 4.19 give the reconstruction accuracy of S(r) for the primary energies 10EeV and 100EeV, respectively. In the reconstructions of S(r) for both E=10EeV and E=100EeV, we can clearly see that the value of σ is higher for θ=0 o, 15 o (i.e.,secθ=1.00,1.04) than that for θ=36 o, 45 o (secθ=1.23,1.41) and again increases for θ=53 o, 60 o (secθ=1.66, 2.00). The lower values of σ around θ=36 o, 45 o (secθ=1.23, 1.41) are clearly visible in all the distributions. The reason for this is that the generated muonic signal increases and the generated EM signal decreases with increasing zenith angle. Within the zenith angle range where we see the lowest values of σ, the combined muonic and EM components cause the total signal to be nearly a constant. The signal fluctuations are minimized, and hence the reconstruction is obtained with a large accuracy regardless

95 78 of the values of r. By looking at the spreads in Figures 4.18 and 4.19, we can conclude that distributions of S(1000) are a reasonable compromise for use in the LDF reconstruction. At 1000m from the core, the distance is large enough that fluctuations are reduced, and at the same time the signal is still large enough that the statistical power of the signal is sufficient. The optimal value of 1000m is comparable to the Auger interdetector spacing of 1500m, not surprisingly. Figure 4.18: Width σ of the distribution of shifts S(r) as a function of secθ for the primary energy E=10EeV.

96 79 Figure 4.19: Width σ of the distribution of shifts S(r) as a function of secθ for the primary energy E=100EeV. Figures 4.20 and 4.21 show the mean shifts of S(r) as a function of secθ for energies E=10EeV and E=100EeV, respectively. In the distributions for S(600), S(1200) and S(1400) the mean values are quite offset from zero for all zenith angles at both E=10EeV and E=100EeV. In the distributions for S(800), the shift varies between and 0.08 for E=10EeV, and and for E=100EeV. In the distributions for S(1000), the mean value varies between 0.02 and 0.27 for E=10EeV and and 0.17 for E=100EeV. When we look at all the distributions of mean values, S(800) seems to give the best distribution among all, with least shift from the true value.

97 Figure 4.20: Average shift < S(r)> as a function of secθ for the primary energy E=10EeV. 80

98 81 Figure 4.21: Average shift < S(r)> as a function of secθ for the primary energy E=100EeV. Figures 4.22 and 4.23 give the correlation between S(r) and r min for energies E=10EeV and E=100EeV, respectively, for zenith angles θ =15 o, 53 o. The black points correspond to events with no saturated stations and red points correspond to events with at least one saturated station. β is set free in the reconstruction. In Figure 4.22, clearly in S(600), S(800) and S(1000) for θ=15 o and E=10EeV, there is a larger dispersion of saturated stations whereas for S(1200) and S(1400) the dispersions are not as wide as the previous cases. This is somewhat different for θ=53 o, in which the greatest dispersion is for S(600). Although the rest of the distributions do not have such large dispersions, the ranges of their S(r)'s vary, i.e., S(800) varies between -0.6 and 0.4, S(1000) varies

99 82 between -0.4 and 0.5, S(1200) varies between -0.2 and 0.8 and S(1400) varies between -0.2 and 0.8 (in some cases it is beyond 0.8 for S(1400) ). In this case, for θ=15 o, S(1200) seems to give the best distribution whereas for θ=53 o, S(1000) gives the best distribution among all, with least dispersion. In Figure 4.23, which is for E=100EeV, we do not notice such large dispersions in S(r), but we can clearly identify the value of r min at which the saturation becomes large regardless of S(r). For θ=15 o, this value of r min is ~550m and for θ=53 o, it is ~350m. For θ=15 o, the distributions from S(800) to S(1400) are all fine and for θ=53 o, S(1000) yields the optimal distribution.

100 Figure 4.22: Correlation between S(r) and r min for an energy E=10EeV and two zenith angles θ=15 o (top two rows), or θ=53 o (bottom two rows). β is set free in the reconstruction regardless of the multiplicity. See text for more details. 83

101 Figure 4.23: Correlation between S(r) and r min for an energy E=100EeV and two zenith angles θ=15 0 (top two rows), or θ=53 0 (bottom two rows). β is set free in the reconstruction regardless of the multiplicity. See text for more details. 84

102 4.4.1 The Correlation between S(r) and β 85 In the next several figures we investigate the correlation between S(r) and β. β is one of the most important parameters that affect the estimation of core location, S(r) and the primary energy and its uncertainty. This is true especially when there are saturated events as is shown in Figures 4.22 and A shallower slope used in the LDF makes S(r) larger and thereby the primary energy may be overestimated. On the other hand, wrong values assigned to β will lead to poor estimation of S(r) causing long tails in the S(r) distributions [14]. Figures 4.24 and 4.25 show the correlation between S(r) and β for energies E=10EeV and E=100EeV, respectively, for θ=15 o and 53 o. According to these distributions we can see that there are large dispersions in the distributions for E=10EeV whereas all the black and red points overlap in the distributions for E=100EeV. Here also, in event reconstruction β is set as a free parameter regardless of the multiplicity. At this point it is clear that we cannot always set β as a free parameter in the reconstruction. As is clearly seen in Figure 4.24, depending on the number unsaturated stations used in the fit or the number of saturated stations, the S(r) distributions can have large dispersions. To overcome the problem of poor estimation of S(r), and thereby other parameters such as core location, primary energy and their uncertainties, one can either set β free at a fixed station multiplicity, or set it free when there is no saturated detector. In Figures 4.10 and 4.11, we observe that even at higher energies (125EeV and 150EeV), when β is fixed in shower reconstruction regardless of the multiplicity and the number of saturated

103 detectors, S(1000) is reconstructed with a higher uncertainty. Therefore, it is important to consider at which multiplicities β should be fixed. 86 S(600) 0 E=10EeV,θ=15 S(600) 0.8 N sat = N sat >0 S(800) S(800) S(1000) S(1000) S(1200) β S(1200) β S(1400) β S(1400) β β S(600) E=10EeV,θ=53 S(600) N sat =0 N sat >0 S(800) S(800) S(1000) S(1000) S(1200) β S(1200) β S(1400) β S(1400) β β Figure 4.24: Correlation between S(r) and β reconstructed for E=10EeV. The rest of the features are the same as in Figure 4.22.

104 87 S(600) 0 E=100EeV,θ=15 N =0 0.8 S(600) sat N sat > β S(800) S(800) β S(1000) S(1000) β S(1200) S(1200) S(1400) S(1400) S(600) S(1200) β 0 E=100EeV,θ=53 S(600) β S(1200) β -0.8 S(800) S(1400) β S(800) β S(1400) β S(1000) S(1000) β Figure 4.25: Correlation between S(r) and β for energy E=100EeV. The rest of the features are the same as in Figure 4.23.

105 88 Table 4.3 illustrates the outcome of these studies by summarizing the apparent best parameter to use in the event reconstruction, ranging from S(800) to S(1400), depending on which aspect of the reconstruction is optimized. We can see that the parameter S(1000) is optimal for the distribution width σ of S(r) as a function of secθ in both 10EeV and 100EeV cases. It is encouraging to see that even with a free β in the reconstruction, regardless of the multiplicity, S(1000) can be reconstructed with a higher accuracy than it can be for any other S(r) parameter. Moreover, in the distributions of S(r) as a function of r min, S(1000) is the optimal parameter for θ=53 o for both 10EeV and 100EeV. Therefore, it appears overall that S(1000) offers the best compromise as the parameter to use in reconstructing Auger SD data. Distribution σ of S(r) as a function of secθ Mean of S(r) as a function of secθ Best Parameter S(1000) S(800) S(r) as a function of r min E=10EeV,θ=15 o E=10EeV,θ=53 o E=100EeV,θ=15 o E=100EeV,θ=53 o S(1200) S(1000) S(800) to S(1400) look fine S(1000) Table 4.3: Summary of the various event reconstruction parameters studied and the optimal S(r) for each parameter. Given the conclusion that S(1000) is the optimal parameter, in the next step we investigate how the multiplicity and β vary against each other for the parameter S(1000). In this analysis we require that the multiplicity be 5 for each distribution. The

106 89 considered zenith angles are 0 o, 15 o, 36 o, 45 o, 53 o and 60 o and the primary energies are 10EeV and 100EeV, respectively. Figure 4.26 and 4.27 show the distributions of δβ as a function of multiplicity for each zenith angle and primary energy, where δβ is defined as β generated -β reconstructed. The black points correspond to events with no saturated stations and the red points correspond to events with at least one saturated station. Figure 4.26: δβ as a function of multiplicity for multiplicities 5. The primary energy is E=10EeV.

107 90 Figure 4.27: δβ as a function of multiplicity for multiplicities 5. The primary energy is E=100EeV. In Figure 4.26 the quantity δβ is widely dispersed over a range between -0.3 and 0.3 for smaller zenith angles 0 o and 15 o, whereas for θ = 36 o it is limited to the range between -0.2 and 0.1 for either events with at least one saturated station or events with no saturated stations. The δβ distribution is biased towards negative values when going from θ = 45 o to 60 o. Then in Figure 4.27, the δβ values are mostly distributed between 0 and for all zenith angles. The δβ difference between events with at least one saturated station and events with no saturated stations is quite small compared to that for 10EeV. It is seen that for E=10EeV, if we do not use a condition that multiplicity be greater than or equal to 5 then we would see larger dispersions in δβ distributions. Therefore, setting β as a free parameter irrespective of the multiplicity may lead to poor reconstruction in

108 91 S(1000), the energy and its systematic error at this energy, and lower zenith angles. On the other hand, as can be seen in Figure 4.27, at 100EeV the lowest multiplicity recorded is close to 10. Therefore, it is safer to set β as a free parameter in event reconstruction with the proper handling of saturated events with higher multiplicity (n 5). Bibliography 1. P.Billoir, P. Da Silva: Towards a Parameterization of the Lateral Distribution Function and its Asymmetries in the Surface Detector, GAP K.Kamata and J.Nishimura, Prog. Theoret. Phys. Suppl. 6 (1958) K.Greisen, Progress in Cosmic Ray Physics Vol.III (1956) North Holland Publishing Company M.Ave and T.Yamamoto, The Reconstruction of 6 months of data recorded by the EA, GAP M.Roth, The Lateral Distribution Function of Shower Signals in the Surface Detector of the PAO, In Proceedings of the 29 th ICRC (2003) P.Billoir, Parameterization of the Relation between Primary Energy and S(1000) in Surface Detector, GAP M.Ave, P.Bauleo, T.Yamomoto: Signal Fluctuation in the Auger Surface Detector Array, GAP

109 A.Chou et al. Signal Fluctuation in the Auger Surface Detector Array: New Result using the Preproduction Array, GAP P.L.Ghia, Statistical and systematic uncertainties in the event reconstruction and S(1000) determination by the Pierre Auger surface detector, In Proceedings of the 29 th ICRC (2005). 12. D.Barnhill et al., In Proceedings of the 29 th ICRC (2005), usa-bauleo-pmabs2-he14-poster. 13. P.Billoir, Natural and Artificial Fluctuations in the Auger Surface Detector, GAP D.Allard et.al, A Guide Line to the Auger Surface Detector Analysis, GAP M.Roth et al., A Phenomenological Method to Recover the Signal from Saturated Stations, GAP J.Knapp et al., The Optimum Ground Parameter, S(r opt ), GAP D.Newton et al., The Optimum Distance at which to Determine the Size of a Giant Air Shower, GAP M.Ave, Private Communication. 19. M.Roth et al. Offline Reference Manual SD Reconstruction, GAP M.Roth, Private Communication. 21. X.Bertou et al., On the origin of asymmetry of ground densities in inclined showers, GAP P.Billoir et al., Checking the origin of the Asymmetry of the Surface Detector.

110 Chapter 5 Comparison between different Hadronic Interaction Models The analysis of UHE cosmic rays by means of extensive air shower techniques relies strongly upon a detailed understanding of the shower development in the earth s atmosphere. Simulation tools are used to model the propagation of particles through the atmosphere, their interactions with atmospheric nuclei, the production of secondary particles and particle interactions in the ground detectors. Many extensive air shower experiments have been using such simulations to determine the primary energy and to derive conclusions about the cosmic ray composition and its possible variation with primary energy. However, studies throughout the years have shown that simulation programs with different particle interaction models can sporadically give different results when applied to the same data [1]. This leads to a considerable systematic uncertainty in both the model used and in the properties of the UHE cosmic rays. By comparing simulations of air showers using different particle interaction models, one is able to identify key differences in the models predictions and to select the model that most realistically captures the physics of the EAS [2, 3]. An air shower simulation tool must be able to simulate not only the gross features of the shower development, such as particle mean free path lengths and interaction probabilities, but also the details of the exchanges between individual particles. A major source of uncertainty in EAS simulation is the choice of hadronic interaction model, which is responsible for calculating the outcomes of interactions involving nucleons or

111 94 nuclei. Variations in these models affect the values of such shower parameters as primary energy, composition, the change of composition with primary energy, the optimal slope parameter for the LDF and the ground parameter S(1000). Because hadronic interaction models are calibrated at the energies of ground-based accelerator experiments for which copious data are readily available, they work well for low-energy hadronic interactions; however, there is considerable uncertainty in extrapolating their behavior to energies of UHE cosmic rays that are of interest to the Auger collaboration [3]. To assess the suitability of hadronic interaction models for simulating UHE air showers, here we evaluate UHE cosmic ray air showers simulated using the Sibyll [4], QGSJetI [5, 6] and QGSJetII [2, 7] hadronic interaction models described below. We compare the risetime and S(1000) parameters for both proton and iron primaries simulated using the Sibyll and QGSJetII interaction models in the CORSIKA [8] shower program, described below, with similar results for simulations using Sibyll and QGSJetI in the AIRES [9] shower program, also described below. We find that the CORSIKA and AIRES shower programs give similar results for the S(1000) parameter and both types of primaries using the Sibyll interaction model. Although the hadronic interaction models generally agree for intermediate zenith angles, their results differ at both high and low zenith angles. In the second part of this analysis we investigate the differences between the behavior of S(1000) as a function of zenith angle θ, the so-called attenuation curve, obtained from the above mentioned Monte Carlo events. The attenuation curve parameters obtained separately from each simulation program and the attenuation curve parameters given in [10] are applied to a set of real SD data to study the distribution of

112 95 sin 2 θ. We observe that the sin 2 θ distributions obtained by applying fit parameters in [10] correspond to a constant flux with increasing zenith angle, while the sin 2 θ distributions obtained by applying the MC attenuation curve fit parameters correspond to an increase in flux with increasing zenith angle. 5.1 Monte Carlo Simulations The two most widely used EAS simulation packages are CORSIKA (COsmic Ray SImulation for KAscade) and AIRES (AIR shower Extended Simulation). Both packages simulate the EAS development from the primary interaction to the ground. Each package uses its own tools for simulating the EM component of the EAS, as well as low-energy hadronic interactions, and both packages can use a variety of high-energy hadronic interaction models. In general, the CORSIKA program is more versatile than AIRES. It incorporates more details of the shower and provides the user with greater freedom to define the shower parameters than does AIRES. On the other hand, the AIRES program runs more quickly than CORSIKA, completing simulations at about 4 times the rate of CORSIKA [11]. The total number of particles in an EAS can exceed 10 11, making all-particle EAS simulation impossible on present-day computers. Instead, shower simulation packages rely on statistical thinning to reduce the number of particles tracked during the simulation. Thinning the shower involves retaining only a small, randomly selected set of representative particles throughout the simulation, as follows: Define a threshold energy, E Th, and throughout the simulation retain all secondary particles with energy

113 96 E i >E Th. When a particle with energy E i >E Th decays, retain each of its secondary particles of energy E j <E Th with probability P j =E j /E Th. When a particle with energy E i <E Th decays, retain only one of its secondary particles with a probability proportional to its energy. Each retained particle is assigned a weight that indicates the number of discarded particles that it represents. The thinning level, ε T =E Th /E primary, refers to the ratio of the threshold energy to the primary energy and roughly indicates the reciprocal number of particles retained in the simulation. Typical thinning levels range from 10-7 to The hadronic interaction models that we are interested in here are QGSJet (Quark- Gluon String Jet) I and II, as well as Sibyll. The QGSJet models have been developed directly from quantum chromodynamic theory, whereas the Sibyll model also incorporates parameterizations taken from accelerator experiments. For further details on these and other hadronic interaction models, see Knapp et al. [11] and references therein. We have chosen to compare CORSIKA (Sibyll and QGSJetII) and AIRES (Sibyll and QGSJetI) proton and iron of primary energy 10EeV showers. The CORSIKA (Sibyll and QGSJetII) shower library was created by the Auger group at the University of Chicago and is available at the official Auger server in Lyon for downloading. The showers were generated with a thinning level of 10-6 and had already passed through the detector simulation. The zenith angles considered are 0 o, 12 o, 25 o, 36 o, 45 o, 53 o and 60 o. There are about 750 events generated for each zenith angle. The AIRES (Sibyll and QGSJetI) shower library was obtained directly from the Auger group at UCLA. The showers were generated with a thinning level of The zenith angles considered are 0 o, 25 o, 36 o, 45 o, 53 o and 60 o. There are about 20 events generated for each zenith angle. The

114 simulated showers were reconstructed using the Offline 2.0 software package of the Data Processing and Analysis framework [12] The Risetime The risetime is defined as the time an event takes to rise from 10% to 50% of the total signal amplitude in an Auger surface detector [13]. This rise time is directly related to the muon and electromagnetic components of the shower. The muons in a shower go through fewer interactions in the atmosphere compared to EM particles. They travel in straight lines and their trajectories are more direct than those of EM particles, while EM particles scatter multiple times and, on average, arrive later than the muons in a surface detector. Therefore, muons dominate the early signal (up to about 1microsecond [14]) in a surface detector while the EM particles dominate the later signal. Deep penetrating primaries such as protons will create muons along a longer path in the atmosphere causing the muons to spread out in time on their arrival and thereby resulting in larger rise times as illustrated in Figure 5.1. On the other hand, iron nuclei interact sooner than protons, so their first interaction takes place at a higher altitude and therefore they are not as deeply penetrating. At the same total nucleus energy as a proton, each nucleon in an iron nucleus has less energy. This has the effect of superimposing several lower energy showers, each of which develops more quickly and is therefore less penetrating than the proton shower of the same total energy. Iron nuclei will create muons along a shorter path, causing the muons to be grouped together tightly and thereby resulting in a smaller risetime, as illustrated in Figure 5.2 below.

115 Figure 5.1: Illustration of how rise time is related to deep penetrating showers [6]. The dashed red lines indicate the path of the muons and green curved lines indicate the path of the EM particles. A light primary, such as a proton, that penetrates deep into the atmosphere will produce muons over a long length of its track. The difference in path lengths between these muons and the SD results in a longer risetime. The vertical scale here is tremendously compressed compared to the horizontal scale. In reality, the muons would appear essentially collinear with the primary track. 98

116 99 Figure 5.2: Illustration of how risetime is related to shallow penetrating showers [6]. Figure 5.3 indicates the risetime as a function of secθ plotted for AIRES (Sibyll and QGSJetI) and CORSIKA (Sibyll and QGSJetII) proton and iron showers. It is clear that for both AIRES and CORSIKA, the risetime for iron showers is small compared to that of proton showers. At low zenith angles, even near the core of the shower, muons arrive first although the EM component dominates, resulting in the shorter risetime for iron showers mentioned above. At higher zenith angles we detect mostly muons (since the EM component is attenuated by the atmosphere) and hence a smaller risetime regardless of the primary.

117 100 Risetime (ns) 450 Corsika/Sibyll/Proton Corsika/QGSJetII/Proton Aires/Sibyll/Proton 400 Aires/QGSJetI/Proton Corsika/Sibyll/Iron 350 Corsika/QGSJetII/Iron Aires/Sibyll/Iron Aires/QgsJetI/Iron Secθ Figure 5.3: Risetime as a function of secθ for AIRES (Sibyll and QGSJetI) and CORSIKA (Sibyll and QGSJetII) showers. It is instructive to study whether there are systematic differences in the risetime between the two hadronic interaction models. Figure 5.4 shows the risetime difference between Sibyll and QGSJet for AIRES and CORSIKA showers.

118 101 (ns) 60 Sibyll-QGSJetI:Proton Risetime Sibyll -Risetime QgsJet Sibyll-QGSJetI:Iron Sibyll-QGSJetII:Iron Sibyll-QGSJetII:Proton Secθ Figure 5.4: Risetime difference between Sibyll and QGSJet as a function of secθ, for the two incarnations of QGSJet studied and for iron and proton primaries. The blue curve in Figure 5.4 represents the risetime difference between Sibyll and QGSJetI for AIRES/Proton showers as given in Equation 5.1. The subscript in each risetime refers to the particular shower category. Difference = Risetime AIRES/Sibyll/Proton Risetime AIRES/QGSJetI/Proton 5.1 The red curve represents the same difference as above but for AIRES/Iron showers. Similarly the brown curve represents the risetime difference between Sibyll and QGSJetII for CORSIKA/Proton showers as given in Equation 5.2. Difference = Risetime CORSIKA/Sibyll/Proton Risetime CORSIKA/QGSJetI/Proton 5.2 The green curve represents the same difference as above but for CORSIKA/Iron showers.

119 102 In Figure 5.4, the difference in risetime between Sibyll and QGSJetI for AIRES/Proton showers (blue curve) over the zenith angle range from θ=0 o to 60 o varies from ~36ns to ~10ns whereas it only changes from ~ 22ns to ~ 4ns between Sibyll and QGSJetII for CORSIKA/Proton showers in the same zenith angle range (brown curve). The difference between Sibyll and QGSJetI for AIRES/Iron showers for θ=0 o to 60 o varies from ~ -6ns to ~ 31ns (red curve) whereas the difference between Sibyll and QGSJetII for CORSIKA/Iron showers varies between ~0 and 8ns (green curve) in the same zenith angle range. We observe that the spread of the risetime difference between Sibyll and QGSJetII for iron showers (green curve) is noticeably smaller compared to the risetime difference between Sibyll and QGSJetI (red curve). Moreover, the spread of the risetime difference between Sibyll and QGSJetII for proton showers (brown curve) is also smaller than the difference between Sibyll and QGSJetI (blue curve). Thus we notice a better agreement between the predictions of Sibyll and QGSJetII. 5.3 Sensitivity of the Ground Parameter S(1000) Here, the detector signal at 1000m from the shower axis, S(1000), is studied as a function of zenith angle θ for the above mentioned hadronic interaction models. In the shower generation process, the average value of S(1000) is a combination of both the muonic component and the EM component, given by [15]: S ( 1000) = S µ (1000) + S EM (1000) 5.3 In ground based UHECR detectors, the contribution from the muons to the total signal is significant. The studies in [16, 17, 18] show that in an extensive air shower, for

120 103 particles entering the WCDs vertically, a muon will deposit about 240MeV in the water when traveling 1.2m vertically whereas an electromagnetic particle will deposit almost all of its energy, 1-10MeV. Due to this characteristic of muons, the detector signal is enriched by the muonic component. This behavior is even more striking for inclined particles entering the detector as the particles travel a longer distance inside the detector. The EM-to-muon signal ratio is about 1 to 1 for vertical showers, whereas the muonic component clearly dominates for inclined showers. This effect can be seen clearly in Figure 5.5. The true S(1000) components (EM, Muonic, EM+Muonic) obtained from the truth files (as generated absolutely in the Monte Carlo calculations) are averaged in each zenith angle bin and then plotted as a function of secθ. Each plot is then fitted with a third degree polynomial over the entire secθ range, resulting in the curves in Figure 5.5 intended to guide the eye only.

121 104 Figure 5.5: The EM, Muonic and EM+Muonic components of true S(1000) plotted as a function of secθ. Panel 1 in Figure 5.5 gives the electromagnetic component of iron and proton initiated showers from QGSJetII and Sibyll and panel 2 gives the muonic component of the same showers. All the distributions of EM components in panel 1 are bunched together regardless of their primary and hadronic interaction model. However, the muonic components in panel 2 are clearly different for proton and iron showers, with iron showers yielding the greater muon harvest. As explained above, at lower zenith angles the ratio of EM to muonic components is almost 1 whereas at higher zenith angles the muonic component dominates regardless of the hadronic interaction model. Although it is not clearly seen in EM component in panel 1, in muonic and EM+muonic components in panels 2 and 3, we notice a disagreement between Sibyll and QGSJetII, outside the error

122 105 bars. The hadronic interaction model QGSJetII produces a larger muonic component compared to Sibyll regardless of the primary particle. The ground parameter S(1000) is related to the energy of the air shower through Equation 4.3 and is used to calculate the energy. This ground parameter varies from primary to primary and also with different hadronic interaction models. To quantify the behavior of S(1000) with different primaries and hadronic models we have plotted S(1000)/Energy 0.95 as a function of sin 2 θ in Figure 5.6 where Energy=10EeV S(1000)/Energy Aires/QGSJet1/Iron Corsika/QGSJet11/Iron Aires/Sibyll/Iron Corsika/Sibyll/Iron Aires/Sibyll/Proton Aires/QGSJet1/Proton Corsika/QGSJet11/Proton Corsika/Sibyll/Proton sin θ Figure 5.6: Average S(1000)/Energy 0.95 as a function of sin 2 θ for 10EeV showers. The shower event files obtained from the University of Chicago shower library at Lyon contain about 750 showers per zenith angle whereas the shower event files obtained from the UCLA shower library only contain about showers per zenith angle. Therefore, the error bars in the UCLA distributions are significantly larger than those of

123 106 the Chicago set when averaging at each zenith angle. At sin 2 θ=0 (θ=0 o ), the distribution of S(1000)/Energy 0.95 ranges between 3.6 for CORSIKA/Sibyll/Proton and 5.6 for AIRES/QGSJetI/Iron, with the other models falling in-between. As zenith angle is increased, the spread in S(1000)/Energy 0.95 decreases; for instance, at sin 2 θ =0.75 (θ=60 o ), it varies roughly between 1.3 and 1.9. What is more informative than the absolute spread in this value is the fractional difference between the extremes in S(1000)/Energy 0.95 at different zenith angles. The fractional difference does not vary significantly with zenith angle: at sin 2 θ=0 it is 2 ( )/( )=0.43, whereas it is 2 ( )/( )=0.38 at sin 2 θ=0.75. Thus, the differences between the various air shower and hadronic interaction models do not at first glance appear to be greatly dependent on zenith angle. To further study the systematic differences between the two MC simulation packages and the two hadronic interaction models, we define the systematic difference between AIRES/Sibyll/Proton and CORSIKA/Sibyll/Proton showers is defined as: Ratio = S(1000) S(1000) Aires / Sibyll / proton Aires / Sibyll / proton S(1000) + S(1000) Corsika / Sibyll / proton Corsika / Sibyll / proton 5.4 Similarly, the systematic difference between AIRES/Sibyll/Iron and CORSIKA/Sibyll/Iron showers can be defined as: Ratio = S(1000) S(1000) Aires / Sibyll / Iron Aires / Sibyll / Iron S(1000) + S(1000) Corsika / Sibyll / Iron Corsika / Sibyll / Iron 5.5 For AIRES/QGSJetI/Proton and CORSIKA/QGSJetII/Proton showers we use:

124 107 Ratio = S(1000) S(1000) Aires / QGSJetI / proton Aires / QGSJetI / proton S(1000) + S(1000) Corsika / QGSJetII / proton Corsika / QGSJetII / proton 5.6 and for AIRES/QGSJetI/Iron and CORSIKA/QGSJetII/Iron showers: Ratio = S(1000) S(1000) Aires / QGSJetI / Iron Aires / QGSJetI / Iron S(1000) + S(1000) Corsika / QGSJetII / Iron Corsika / QGSJetII / Iron 5.7 The ratio values calculated according to the above equations are plotted as a function of sin 2 θ and given in Figure 5.7. This figure shows the differences between S(1000) values reconstructed by AIRES and CORSIKA shower simulations. The two packages agree well only with Sibyll/Iron, in which the systematic difference between reconstructed S(1000) values is roughly constant across zenith angles. We notice that the spread of the systematic differences is higher for large and small zenith angles and smaller for intermediate angles. It is minimized around sin 2 θ=0.64 (θ=53 o ). Also, the difference between AIRES and CORSIKA is noticeably small for sin 2 θ between 0.34 and 0.50 (θ between 36 o and 45 o ) for both primaries. To check this effect further, we take the difference of S(1000) between Sibyll and QGSJet separately for each MC package AIRES and CORSIKA. Figure 5.8 indicates the ratio of the quantity S(1000) between Sibyll and QGSJet for AIRES and CORSIKA showers separately plotted as a function of zenith angle θ.

125 108 +S(1000) Corsika Aires Sibyll/Proton QGSJet/Iron Sibyll/Iron QGSJet/Proton /S(1000) -S(1000) Corsika Aires S(1000) sin θ Figure 5.7: The ratio of the quantity S(1000) between AIRES and CORSIKA showers as a function of sin 2 θ. written as: For AIRES/Sibyll/Proton and AIRES/QGSJetI/Proton showers the ratio can be Ratio = S(1000) S(1000) Aires / Sibyll / proton Aires / Sibyll / proton S(1000) + S(1000) Aires / QGSJetI / proton Aires / QGSJetI / proton 5.8 Similarly, for AIRE/Syll/Iron and AIRESQGSJetI/Iron showers the ratio can be written as: Ratio = S(1000) S(1000) Aires / Sibyll / Iron Aires / Sibyll / Iron S(1000) + S(1000) Aires / QGSJetI / Iron Aires / QGSJetI / Iron 5.9 and for CORSIKA/Sibyll/Proton and CORSIKA/QGSJetII/Proton showers:

126 109 Ratio = S(1000) S(1000) Corsika / Sibyll / proton Corsika / Sibyll / proton S(1000) + S(1000) Corsika / QGSJetII / proton Corsika / QGSJetII / proton 5.10 Finally, for CORSIKA/Sibyll/Iron and CORSIKA/QGSJetII/Iron showers: Ratio = S(1000) S(1000) Corsika / Sibyll / Iron Corsika / Sibyll / Iron S(1000) + S(1000) Corsika / QGSJetII / Iron Corsika / QGSJetII / Iron 5.11 Sibyll-QGSJetI:Proton +S(1000) QGSJet Sibyll Sibyll-QGSJetI:Iron Sibyll-QGSJetII:Iron Sibyll-QGSJetII:Proton /S(1000) -S(1000) S(1000) QGSJet Sibyll sin θ Figure 5.8: The ratio of the quantity S(1000) between Sibyll and QGSJet for AIRES and CORSIKA showers as a function of sin 2 θ. In Figure 5.8 we also observe the same behavior as in Figure 5.7. In this plot, the ratio varies noticeably for the blue curve, which is for the difference between Sibyll and QGSJetI for AIRES/Proton showers from sin 2 θ=0 (θ=0 o ) to sin 2 θ=0.75 (θ=60 o ), varying from ~0.02 to ~ The ratio varies between to for the brown curve, which is for the difference between Sibyll and QGSJetII for CORSIKA/Proton showers in the

127 110 same zenith angle range. The variation in the red curve for the difference between Sibyll and QGSJetI for AIRES/Iron showers between sin 2 θ=0 (θ=0 o ) and sin 2 θ=0.75 (60 o ) ranges from ~ to ~ -0.02, whereas it varies between ~ and ~ for the green curve for the difference between Sibyll and QGSJetII for CORSIKA/Iron showers in the same zenith angle range. Here also again we notice that the difference is noticeably small for sin 2 θ between 0.34 and 0.50 (θ between 36 o and 45 o ) for both primaries, as was the case in Figure 5.7. The change in the ratio of electromagnetic signal to muon signal causes this small systematic difference between the models. The muonic fraction of the total signal increases with the increasing zenith angle while the electromagnetic fraction decreases. Within the zenith angle range where we see a small spread in the difference between models and primaries, the combined signal of the electromagnetic and muonic components is such that the total signal deposited is nearly a constant regardless of the primary particle and the hadronic interaction model. In Figures 5.3 and 5.6 we can not see a significant difference between Sibyll and QGSJetI or Sibyll and QGSJetII. But in Figures 5.4 and 5.8 the spreads of the difference between Sibyll and QGSJetII for the S(1000) ratio and the risetime are clearly noticeable for iron and proton showers. The spread from θ=0 o to 60 o between Sibyll and QGSJetII for iron is significantly less compared to that between Sibyll and QGSJetI for both protons and irons. From this analysis it can be concluded that, in terms of S(1000) and risetime, the agreement between QGSJetII and Sibyll is better than the agreement between QGSJetI and Sibyll.

128 Constant Intensity Cut Method For a given energy of a UHE cosmic ray the value of S(1000) decreases with increasing zenith angle due to the attenuation of the shower particles and geometric effects such as slant depth. The shape of this attenuation curve can be directly obtained from the data. In deriving the attenuation curve it is assumed that the cosmic rays arrive isotropically and hence the flux of the cosmic rays above a given energy should be independent of the zenith angle of arrival. This particular Constant Intensity Cut (CIC) method has been widely adopted in analysis of air shower data in the surface detectors at PAO. The attenuation curve was parameterized for Auger data by plotting S(1000) as a function of shower zenith angle, θ where θ is in degrees, as [10]: 2 CIC ( θ ) = θ θ Here we study the sensitivity of the MC-inferred attenuation factor to the different hadronic interaction models, and we compare this with the results of the CIC(θ) method. In Figure 5.9, the computed S(1000)/E 0.95 is plotted as a function of zenith angle θ for proton and iron showers simulated with CORSIKA (Sibyll and QGSJetII) and AIRES (Sibyll and QGSJetI). The fitted line for each distribution is the CIC(θ) MC parameter, where the functional form used is CIC(θ) MC = a 0 + a 1 θ + a 2 θ 2. The fit parameters for CORSIKA and AIRES showers are given in Tables 5.1 and 5.2, respectively. In Section 5.5 below we conduct an extensive comparison of the Monte Carlo derived CIC technique with the experimental one.

129 S(1000)/Energy Aires/QGSJetI/Iron Corsika/QGSJetII/Iron Aires/Sibyll/Iron Corsika/Sibyll/Iron Aires/Sibyll/Proton Aires/QGSJetI/Proton Corsika/QGSJetII/Proton Corsika/Sibyll/Proton θ Figure 5.9: S(1000)/E 0.95 as a function of θ for all the hadronic interaction models considered in the CIC(θ) method. CORSIKA a 0 ±δa 0 a 1 ±δa 1 a 2 ±δa 2 Prot/Sibyll 3.59± ± ± Prot/QGSJet ± ± ± Iron/Sibyll 4.96± ± ± Iron/QGSJet ± ± ± Table 5.1: Fit parameters for CORSIKA (Sibyll and QGSJetII) proton and iron showers.

130 113 AIRES a 0 ±δa 0 a 1 ±δa 1 a 2 ±δa 2 Prot/Sibyll 4.4± ± ± Prot/QGSJet1 4.2± ± ± Iron/Sibyll 5.1± ± ± Iron/QGSJet1 5.59± ± ± Table 5.2: Fit parameters for Aires (Sibyll and QGSJetI) proton and iron showers. 5.5 Comparison with Auger Surface Detector Data To compare the Monte Carlo derived CIC curves with the experimental one, data collected by the Auger surface detectors during the period from January 2004 to March 2006 were obtained from the Auger Observer database [19]. There are events in this original data set. To ensure the optimal quality, several selections are applied to this data set as described below Event Selection Since the CIC(θ) method [10] of interest in this work is developed for the showers with zenith angles between 0 o and 60 o, we require here that for a given event the zenith angle θ be less than 60 degrees. As described in Chapter 3, the higher level triggers are imposed to distinguish between random coincidence events and UHE cosmic ray events. Out of the trigger levels T3, T4 and T5, T5 ensures a quality reconstruction of SD data. Therefore, here we require a non-zero T5 trigger so that all events selected are well contained inside the SD.

131 114 Furthermore, in order to enhance the quality of reconstruction and to obtain a data set within a given uncertainty level, the following two selections are applied to the data [20]: Uncertainty of S(1000)/S(1000) < 10% Uncertainty of SD Energy/SD Energy < 10% Results After these quality selections there were events in the data set. The distributions of S(1000), zenith angle θ and S(1000)/E 0.95 as a function of θ for the initial data set with events and the data set obtained after applying the quality selection cuts are plotted in Figure The quality cuts increase the mean value of S(1000) from 4.84 to 16.58, rejecting poorly reconstructed events. The mean of the zenith angle θ is less affected by the imposed cuts.

132 115 Figure 5.10: Distributions of reconstructed values of S(1000), zenith angle θ, and S(1000)/E 0.95 as a function of θ for the initial data set (top 3 panels) and for the final data set obtained after applying the quality cuts (bottom 3 panels). To check the above mentioned discrepancy between the CIC(θ) inferred dependence of S(1000) on zenith angle and MC inferred attenuations, we have taken the fit parameters from Table 5.1 and Table 5.2 and applied them to the above SD data set of events obtained after the quality selection along with the CIC(θ) parameters from Equation That is, for any given MC shower category given in Figure 5.9, we obtain a CIC(θ) MC where CIC(θ) MC is the attenuation curve for the particular MC shower category (CORSIKA/Sibyll/Iron or AIRES/QGSJetI/Proton and so on) of 10EeV: CIC( θ ) MC θ + θ 2 = a 0+ a1 a where a 0, a 1 and a 2 for all the shower categories are given in Tables 5.1 and 5.2. Then we set a lower limit for S(1000) as follows:

133 116 2 ( a + a θ + a ) b S(1000) LIMIT > / θ where b is a normalization constant. The normalization constant used in Equation 5.14 is determined such that the limits given in Equations 5.14 and 5.15 are comparable when applying to the same SD data set. According to the parameterization we get 8 such limits for all the parameters given in Tables 5.1 and 5.2. The second limit is: 2 ( θ 0. ) S ( 1000) LIMIT 2 > θ Then these two limits are applied for the final SD data set and sin 2 θ is plotted for each limit. Figure 5.11 gives the sin 2 θ distributions of SD events plotted using the CORSIKA MC shower parameters obtained from Table 5.1 along with the S(1000) lower limit obtained from Equation Figure 5.12 gives the same distribution but for AIRES MC shower parameters obtained from Table 5.2 along with the S(1000) lower limit obtained from Equation 5.15.

134 117 2 S1000>15.0*( θ θ )/ S1000>15.0*( θ θ )/ Corsika/Sibyll/Iron 120 Corsika/QGSJetII/Iron Entries 6292 Entries 6437 Mean Mean RMS RMS Sin θ 40 Entries 6423 Mean RMS Sin θ S1000>15.0*( θ θ )/3.312 Corsika/Sibyll/Proton S1000>15.0*( θ θ )/3.521 Corsika/QGSJetII/Proton Entries 6696 Mean RMS Sin θ Entries 6612 Mean RMS Sin 0.8 θ Figure 5.11: The sin 2 θ distributions of SD events. The red histogram in each panel corresponds to the sin 2 θ distributions obtained using the limit given in Equation This particular red histogram is same in all 4 panels as the limit given in Equation 5.15 is the same everywhere. The black histograms are the sin 2 θ distributions for the different limits obtained from Equation 5.15 after substituting the fit parameters obtained from CORSIKA showers and given in Table 5.1.

135 S1000>15.0*( θ θ )/4.083 Aires/Sibyll/Iron Entries 6292 Mean RMS Entries 7054 Mean RMS Sin θ S1000>15.0*( θ θ )/3.521 Aires/Sibyll/Proton Entries 6776 Mean RMS Sin θ S1000>15.0*( θ θ )/ Aires/QGSJetI/Iron Entries 6399 Mean RMS Sin θ S1000>15.0*( θ θ )/3.812 Aires/QGSJetI/Proton Entries 7024 Mean RMS Sin θ Figure 5.12: The sin 2 θ distributions of SD events. The black histograms are the sin 2 θ distributions for the different limits obtained from Equation 5.15 after substituting the fit parameters obtained from AIRES showers and given in Table 5.2. The description of the red histograms is the same as in Figure As can be seen, in both Figures 5.11 and 5.12 the sin 2 θ distribution (the red histogram) obtained from Equation 5.12 is flat. In Figure 5.11, the black distributions have low flux in the limit sin 2 θ 0.3 (θ ~ 33 o ) and a higher flux above sin 2 θ 0.5 (θ~45 o ). The red and black distributions overlap within the region 0.3 < sin 2 θ < 0.5. We notice this two histograms overlap behavior only in panel 2 of Figure In this panel the black distribution corresponds to the limit obtained from AIRES/QGSJetI/Iron showers. As mentioned earlier, within the region 0.3<sin 2 θ< 0.5 where the two distributions overlap, the combined electromagnetic and muonic signal deposited is nearly a constant. Therefore, regardless of the hadronic interaction model, the curves overlap in this region.

136 119 We also see a similar behavior in [21] where the attenuation curves plotted with CIC(θ) and MC data meet each other between sin 2 θ~0.3 and sin 2 θ~0.4. From this study we observe that the sin 2 θ distributions obtained from MC parameters behave differently from CIC(θ) distributions, giving lower fluxes at lower zenith angles and higher fluxes at higher zenith angles. Although CIC(θ) gives a constant flux with SD data used in this analysis throughout the zenith angle region considered, it does not clearly explain why energies based on MC simulations lead to lower fluxes at smaller zenith angles and higher fluxes at higher zenith angles. On the other hand, CIC(θ) is derived [10] by equalizing the observed event count above the theta-dependent S(1000) cut. The shower to shower fluctuations, uncertainties in event reconstruction, composition issues may cause fluctuations in the ground parameter S(1000). This analysis, however, is limited by the selection of MC simulations and also by the quality of the SD reconstructed events. The PAO is still under construction but collecting data actively. Therefore, in the near future we will have more statistics to work with for further analysis. On the other hand, this study is carried out only with CORSIKA and AIRES events and we observe similar behavior in sin 2 θ plotted for the number of events in both simulation tools that is different from [10]. It is important to verify that the discrepancy observed in this study did not occur due to the MC shower simulation framework. It is also important to study what the results would be with other frameworks such as CONEX, COSMOS or SENECA.

137 120 Bibliography 1. J.Knapp et al., Comparison of Hadronic Interaction Models Used in EAS Simulations, Nucl. Phys. Proc. Suppl. 52B, (1997). 2. S.Ostapchenko and D.Heck Hadronic Interactions in QGSJet-II: Physics and Results, 29 th ICRC, Pune (2005) 00, D.Heck et al., Comparison of hadronic interaction models at Auger energies, Nucl. Proc. Supp. 122, (2003). 4. R. S. Fletcher, T. K. Gaisser, P. Lipari and T. Stanev. SIBYLL: An event generator for simulation of high energy cosmic ray cascades. Phys. Rev. D (1994). 5. N. N. Kalmykov, S. S. Ostapchenko. The nucleus-nucleus interaction, nuclear fragmentation, and fluctuations of extensive air showers. Phys. Atom. Nucl (1993). 6. N. N. Kalmykov, S. S. Ostapchenko and A. I. Pavlov. Quark-Gluon-String model and EAS simulation problems at ultra-high energies. Nucl. Phys. B (Proc. Suppl.) 52B (1997). 7. S. Ostapchenko. QGSJET-II: towards reliable description of very high energy hadronic interactions. Nucl. Phys. B (Proc. Suppl.) (2006). 8. D. Heck, J. Knapp, J.N. Capdevielle, G. Schatz and T. Thouw. CORSIKA: A Monte Carlo Code to Simulate Extensive Air Showers. Forschungszentrum Karlsruhe Report FZKA 6019 (1998). 9. S. J. Sciutto. AIRES: A system for air shower simulations user's guide and

138 121 reference manual (2002) P.Sommers for the Pierre Auger Collaboration, usa-sommers-p-he14- oral, Proc. 29 th ICRC (Pune), 00, 101(2005). 11. J. Knapp, D. Heck, S. J. Sciutto, M. T. Dova and M. Risse. Extensive air shower simulations at the highest energies. Astropart. Phys. 19, (2003) M.Healy et al. A Study of Composition Trends Using Rise Time and Curvature Data - GAP X.Bertou et. al., Observing muon decays in water Cherenkov detectors at the Pierre Auger Observatory, use-busca-n-abs-he15-poster 15. Alvarez-Muñiz et al. An Alternative Method for Tank Signal Response and S(1000) Calculation GAP Ranchon et al., Response of a Pierre Auger Observatory surface detector to a few MeV electrons, GAP T.Suomijarvi et al., Response of the Pierre Auger Observatory Water Cherenkov Detectors to Muons, fra-suomivi-t-abs1-he14-poster, Proc. 29 th ICRC (Pune), 00, (2005). 18. M.Urban et al., Muon decay and water level determination in the preproduction tanks, GAP Mike Roberts and Paul Sommers Private Communication 21. P.Sommers, Talk given at the Auger South Analysis Meeting, Chicago, Sept.

139 Chapter 6 A Measurement of the Elongation Rate using Auger Hybrid Data 6.1 Introduction A high energy particle entering the atmosphere collides with a nucleus and produces a shower. The longitudinal development of the air showers can be used to identify the primary mass composition and its possible change with the primary energy. The atmospheric depth X max, at which the air shower reaches the maximum number of charged particles, allows one to determine the chemical composition of the incident cosmic rays, on average. The lighter primaries such as protons penetrate deeper in the atmosphere, resulting in a larger X max, while heavier primaries such as iron develop earlier in the atmosphere. Therefore, according to MC simulations, on average the X max of iron and proton primary nuclei differ by about g/cm 2 [1]. The evolution of the mean X max (<X max >) per decade in primary energy is the elongation rate. Another important feature of shower sensitivity to composition is that the fluctuations of X max for showers generated by heavy nuclei are smaller than for light nuclei [2]. The MC simulations associated with different hadronic interaction models show that the Root- Mean-Square (RMS) width of the pure proton distribution is 66g/cm 2, whereas the RMS width of the pure iron distribution is 22g/cm 2 [3].

140 123 In this study, the Auger Observer Hybrid data are used to determine the X max of air showers as a function of the primary energy E, and to investigate the implications for the cosmic ray composition and its possible change with primary energy. First, some basic quality cuts are applied to this original data set in order to get rid of poorly reconstructed events. Also steps are taken to account for the fact that the limited field of view of the detector can restrict the detection of shallow and deep showers: additional cuts are applied to eliminate X max values that are poorly reconstructed due to the finite acceptance of the detector. 6.2 Event Selection For the elongation rate analysis presented in this work we have used the Auger Observer Hybrid data from January 2004 to December 2006 [4]. We use the events from Los Leones, Los Morados and Coihueco with reconstructed FD energy between ev and ev. Before applying any geometrical and quality cuts, the initial data sample consists of events within the energy range mentioned above. Due to reasons such as accidental trigger, possible Cherenkov light contamination and low quality shower profiles, some of these events may be poorly reconstructed. Therefore, we need to obtain a set of genuine hybrid events and reject any poorly reconstructed events.

141 6.2.1 The Quality Cuts 124 First, the following quality cuts are applied to the data to obtain a data set with higher quality reconstruction parameters [5]: Number of pixels 6, where a pixel is a FD PMT hit; χ 2 of GH fit/ndf < 6 (GH is the Gaisser-Hillas function fitted to the shower profile in the atmosphere); Angle of shower in the SDP χ 0 is between 0 o and 180 o, where SDP is the shower detector plane; Distance between FD and the closest point in the shower axis to FD (R p ) > 0; XTrackMin+30 < X max < XTrackMax-30, where XTrackMin is the first slant depth (the shallowest depth along the track of the shower within the field of view) of the track and XTrackMax is the last slant depth (the deepest depth along the track of the shower within the field of view) of the track (this cut is also called X max bracket cut); Cherenkov Light Fraction < 50%. After applying the above quality cuts events are obtained from the initial data set. The most effective cut is the X max bracket cut which eliminates about 50% of the data. The effectiveness of these cuts are discussed in section 6.5. Then, a requirement that the viewed grammage be at least 300g/cm 2 is applied to this data set: XTrackMax XTrackMin > 300g/cm 2.

142 125 The viewed grammage of 300g/cm 2 is enough to reconstruct the X max with an uncertainty of about 40g/cm 2. This brings down the data set to The hybrid data set used in this study requires only one triggered surface detector which is closest to the shower core and one fluorescence detector. The timing and location of the surface detector is necessary in order to obtain the shower geometry. Therefore, in addition to the above quality cuts, we apply several geometric cuts to the parameters that are sensitive to the reconstructed geometry. In other words, for a successful hybrid geometry reconstruction, the following three conditions have to be satisfied [6]: SD/FD time offset <200ns (the time offset between SD and FD after the minimization); χ 2 of axis fit (FD)/ndf < 5 where χ 2 of axis fit is the χ 2 component obtained from the timing fit (TimeChi2FD); Distance between the shower axis and the hottest station (AxisDist) < 2000m. These quality selections allow us to obtain a data set that contains measured X max values with high quality reconstructed geometry. Figure 6.1 shows the distributions of FD energy and X max before applying the quality cuts (top two distributions) and after applying the quality cuts (bottom two distributions), respectively. The distribution of X max after applying the quality cuts spans a range of g/cm 2. This agrees with the physical range of X max observed in various studies [7, 8].

143 126 Figure 6.1: Distributions of FD energy and X max before and after (top and bottom) applying the quality cuts, respectively The Z Parameter The light flux F emitted isotropically by a source and observed by a detector at a distance R is given by F/R 2. In Auger Observer data parameterization, if T is the transmission factor after Mie and Rayleigh attenuation from X max to the eye at 370nm are taken into account, and R is the distance to the shower maximum, then the intensity of the shower light that reaches the detector should be proportional to T/R 2. Then we define the parameter Z calculated at X max as Z Xmax = -log 10 (T/R 2 ). We take log for our convenience as T/R 2 values are rather small [9]. The value of Z gives an idea of whether the signal emitted by a particular segment of the shower will trigger the detector. Larger Z values mean the signal will be less likely to reach the detector.

144 127 Since larger Z values indicate a lower percentage of the shower signal seen by the telescope, we set a cut off value for Z in order to ensure the quality of the data and to maintain a better resolution of the signal detected by the telescope. In order to optimize the cut off value for Z Xmax, the distributions of the Z parameter calculated at X max (Z Xmax ) were plotted for each energy bin, after the application of all quality cuts mentioned above. To obtain the maximum effective value Z max of this Z Xmax parameter, a simple Gaussian function is fitted to each distribution of Z Xmax from ev to ev. The value µ+σ where µ is the mean of the distribution and σ is the width of the distribution, is taken as the Z max for each energy bin. The Z max values are plotted as a function of E and extrapolated to determine Z max values above ev. Figure 6.2 shows the Z max distribution as a function of energy. The fitted line in Figure 6.2 is given by Z max = ( 0.611± 0.008) log10 E 8.1±

145 128 Figure 6.2: Z max obtained for each energy bin as a function of energy. The error in Z max is taken as [(δµ) 2 + (δσ) 2 ] where δµ and δσ are the uncertainties of µ and σ, respectively. The error bars are smaller than the size of the symbols, and therefore they are not visible. The distributions of Z Xmax are given in Figure 6.3 for various energy bins. The red area in each distribution indicates where Z Xmax is greater than Z max, such that at most only 17% of the data are rejected. The chosen value of Z max increases with the increasing energy of the air showers. In principle, the value of Z does not depend on energy, but depends only on the shower geometry and the atmospheric conditions. However, in a given energy range the detected showers have different mean values of R that depend on energy. The mean value of R increases at higher energies. Therefore, the mean value of Z also evolves with energy, and Z max is set to increase accordingly.

146 129 Figure 6.3: Distributions of Z at X max in different energy bins. The red area indicates where Z Xmax is greater than Z max in each energy bin. Events with Z Xmax > Z max will be rejected because of the low light level of these showers The Field of View and X low and X up In a high energy event, the shower X max can be below the ground; this can cause the FD reconstruction to underestimate the true X max value, as illustrated in Figure 6.4. On the other hand, a low energy event can have already developed past X max before it even enters the field of view of the FD, and therefore cause the FD reconstruction to overestimate the true X max (also illustrated in Figure 6.4). Therefore, the X max of such events can be poorly reconstructed. In the process of event selection it is important that we not include such biased events. In order to identify a set of events with X max located

147 within the FD field of view, we calculate two parameters X low and X up along the shower axis, as defined below. 130 Figure 6.4: Illustration of the possible geometric relationship between the atmospheric shower profile and the FD field of view for a low-energy (left) or high-energy (right) event. Here, X max is underestimated (overestimated) for the low-energy (high-energy) event. In Figure 6.5, X low and X up represent the effective FD viewable range along the shower axis. The values of Z max for each energy bin from Figure 6.2 are used to determine X low and X up along the shower axis. For each shower we scan along the axis to calculate a set of Z i values, where Z i is the value of Z in the i th depth bin along the shower axis. The first condition in calculating X low and X up is that for any given point on the shower axis Z i has to be less than the corresponding Z max. Then, X up is taken as the

148 131 deepest slant depth along shower axis that has a Z i value less than the corresponding Z max, and X low is taken as the shallowest slant depth along the shower axis that has a Z i value less than the corresponding Z max. Once the positions of X low and X up are located we impose another condition, namely that X low and X up have to be inside the field of view of the detector. This way we get a data set with X max located within the FD viewable range. Figure 6.5: X low and X up limits in the FD field of view Anti-bias Cuts After rejecting any events with Z i >Z max we are left with events. In order to retain only events with a measured X max that is not biased by the range of atmospheric depth that is well within the detector s field of view, several other so-called anti-bias

149 132 cuts are applied to these events, based on the calculated X low and X up values. With further requirements of zenith angle θ 60 o and uncertainty of measured X max <40g/cm 2, we also apply the following basic anti-bias cut: X low > 0 and X low < X max < X up After this requirement we are left with events. In Figure 6.6, X max is plotted as a function of X low for different energy bins in an attempt to optimize the maximum X low requirements. Beyond a certain plateau, it appears that X max starts increasing with increasing X low ; in other words, if the shallowest effective slant depth is too great, the resulting X max value becomes increasingly biased. We strive to remove this bias by requiring an X low value on the insensitive plateau regions of Figure 6.6. The blue arrows in three energy bins between and ev in Figure 6.6 show where we choose the X low cuts. Based on the energy dependence of the X low cuts in Figure 6.6, for the three energy bins where a plateau is well defined, we use the following extrapolation in setting the maximum allowed X low value as a function of energy: Xlow LIMIT = (log10 E 18) for log10 E < Xlow LIMIT = 600 for log10 E

150 133 Figure 6.6: Distributions of X max as a function of X low for different energy bins. The blue arrows identify the maximum tolerated X low values to minimize reconstruction biases. Events with a X low value greater (deeper) than the limits from Equations (2) and (3) are rejected. At low energies the increase in X max with deeper X low is steeper than at higher energies. Therefore, the X low cuts we apply for events with energies less than ev are tighter and remove the more strongly biased X max values. At higher energies, X max does not increase with X low very significantly, such that the X low cuts we use are much less restrictive. After these X low cuts we are left with 6699 events. In Figure 6.7, X max is plotted as a function of X up for different energy bins after applying the X low cut. The following procedure is used to determine the minimum (shallowest) allowable X up. The distributions of X max are studied for different energy bins, and a Gaussian function is

151 134 fitted to each distribution, with a mean µ and width σ. The distribution of X max is studied again as a function of X up, with the condition that X max µ-2σ to determine the limit of X up. The blue arrows in Figure 6.7 indicate where the minimum limit of X up is set in each energy bin. Events with a X up parameter shallower than this limit are rejected as being potentially biased. It is observed that with the condition X max µ-2σ, a fixed limit of 800g/cm 2 works well for each distribution regardless of the energy of the events. Figure 6.7: Distributions of X max as a function of X up after applying the X low cut. The blue arrows identify the minimum tolerated X up values to minimize reconstruction biases.

152 6.3 Elongation Rate Results After applying the X low and X up cuts we are left with 6683 events. Figure 6.8 is a profile histogram of <X max > as a function of energy for these 6683 events, where the number of events in each energy bin is indicated above each point. A single elongation rate fit over the entire energy range yields an elongation rate of 60±2 g/cm 2 /decade with a χ 2 /ndf of 103.7/24 and with X max = 690 g/cm 2 at ev. However, close inspection of Figure 6.8 indicates that the data can be best described with two distinct elongation rates. Figure 6.9 shows the results of a fit to the distribution that assumes a change in the elongation rate beyond a certain energy. The fits yield a break point at log 10 E = 18.45±0.05 at a depth of 726±1g/cm 2. The elongation rate below this break point is 80±3 g/cm 2 /decade and above this break point is 35±4 g/cm 2 /decade with a χ 2 /ndf of 31.62/22. (The highest energy point in the distribution beyond ev is not taken into account when fitting the lines.) It can be seen that the elongation rate obtained between ev and ev is greater than what is expected for any constant composition (see section for more details). The difference between the slope of a constant composition and the slope of this study is statistically significant. Near ev there is clear evidence for a reduction in the elongation rate. The measured elongation rate above ev is too low to be consistent with a constant composition. However, since the anti-bias cuts are based on data, there remain concerns, especially in the higher energy regions of low statistics. So, even though 35±4 g/cm 2 /decade seems statistically inconsistent with the 45-

153 56 g/cm 2 /decade expected for any constant composition (see section for more details), there could still be significant systematic uncertainties present. 136 Figure 6.8: Mean X max as a function of energy. The number of events in each energy bin is indicated above each data point.

154 137 Figure 6.9: Mean X max as a function of energy with the two elongation rate fits to the data Comparison with Pure Proton and Iron Distributions Figure 6.10 compares the elongation rate distributions obtained from simulations and the measurements obtained from the data this study. The red and blue distributions indicate the elongation rates from CONEX (CONEX is another simulation package very similar to CORSIKA but with a capability of simulating hadronic interactions not only of nearly vertical showers but also of very inclined showers [10]) simulated proton and iron hybrid events, respectively, at primary energy between ev and ev and with a zenith angle θ 60 o [8]. We have applied all the basic quality cuts stated in section and the anti-bias cuts of Field of View Min (equivalent to X low ) and Field of View Max (equivalent to X up ) in plotting the pure proton and iron distributions from

155 138 simulations. The slopes of the red and blue distributions are 49±1 g/cm 2 /decade and 56.9±0.4 g/cm 2 /decade, respectively. As can be seen, the slope recorded for data below the break point is significantly steeper than that of either proton or iron showers, while the experimental slope above the break point is too low compared to that of proton or iron showers. Figure 6.10: Comparison between Monte Carlo simulations of the elongation rate curve and the one determined from the data in the present analysis. The red and blue distributions correspond to the elongation rate curve predicted for proton and iron showers, respectively, as simulated with the Conex/QGSJetI software packages. The mean X max values plotted here are obtained after applying similar quality cuts and antibias cuts mentioned in sections and

156 139 Figures 6.11 and 6.12 indicate the elongation rate distributions for the same proton and iron showers obtained from [8]. In each figure, the black points represent the pure simulated information. The red points represent the parameters reconstructed after processing of the simulation information through the Auger detector simulation and response algorithms. The blue points represent the analyzed response including all quality and anti-bias selections. The slopes of the various distributions are given in Table 6.1. As can be seen, the slope for pure proton showers (black points) increases by about 7% after applying the quality cuts and anti-bias cuts (blue points), whereas the slope for iron showers is compatible with that obtained after applying the quality cuts and anti-bias cuts (blue points). Primary Black Red Blue Proton 45.8± ±0.7 49±1 Iron 56.4± ± ±0.4 Table 6.1: Slopes of the distributions in Figures 6.11 and The color coding is explained in the text.

157 140 Figure 6.11: Simulated elongation rate distribution for proton induced showers. The black points represent the pure simulated information. The red points represent the parameters reconstructed after processing of the simulation information through the detector simulation and response algorithms. The blue points represent the analyzed response including all quality and anti-bias selections.

158 141 Figure 6.12: Simulated elongation rate distribution for iron induced showers. The black points represent the pure simulated information. The red points represent the parameters reconstructed after processing of the simulation information through the detector simulation and response algorithms. The blue points represent the analyzed response including all quality and anti-bias selections Comparison with HiRes Experimental Results Figure 6.13 compares the elongation rate distributions obtained from the HiRes-I and HiRes-II experiments and the measurements obtained from the Auger data in this study. The blue distribution indicates the elongation rate result (93.0±8.5g/cm 2 /decade) from the HiRes-1 experiment at primary energies between ev and ev and the red distribution indicates the elongation rate result (54.5±6.5 g/cm 2 /decade) from the HiRes-2 experiment at primary energies between ev and ev. As can be seen, the slope obtained in this study below the break point is quite comparable with the slope

159 142 obtained by HiRes-1 within errors. Above the break point, the mean X max distributions obtained from this study and for HiRes-2 are also comparable up to ev. Overall, the three distributions are in reasonably good agreement. Figure 6.13: Comparison between the HiRes experimental elongation rate and the one determined in the present analysis of Auger data. The blue distribution corresponds to the elongation rate obtained by HiRes-1 at energies between ev and ev, and the red distribution corresponds to the elongation rate obtained by HiRes-2 at energies between ev and ev, respectively. 6.4 Conclusions A single elongation rate fit gives a poor χ 2 /ndf value and it is clear that the composition is not constant over the entire energy range considered in Figure 6.8. If the ankle in the cosmic ray energy spectrum is explained as a transition from Galactic to Extra-Galactic sources of cosmic rays, then a transition in the composition from a protoniron mixture to probably a pure proton composition is expected. Therefore, above

160 ev, we would expect to have a pure proton composition. However, at very high energies, the hadronic models are uncertain. When comparing the observed data with the current interaction models, the elongation rate below ev is greater than what is expected from contemporary models. The mean X max values lie in the allowed range between proton and iron. So, there is a natural interpretation that the large elongation rate implies that the composition is getting lighter in that range. Above the break point, the elongation rate is less than what is predicted for a constant composition from hadronic models. This difference is statistically significant. No systematic error has been identified that would affect the energy range above the break point differently than the energy range below the break point. A soft conclusion is that the composition is becoming heavier, which is unexpected, or that the hadronic models are incorrect in predicting an elongation rate that is greater than what is measured for any constant composition. 6.4 Tables of Statistics Table 6.2 gives the quality and anti-bias cuts applied to the data (the details of these cuts are given in sections and 6.2.3, respectively). The cuts appear in the table in the order in which they are applied to the data. The second column indicates the number of events remaining after application of a cut, and the efficiency listed in the third column indicates the percentage of events that pass the cut. The efficiency is calculated below:

161 144 If the number of events remaining before applying a given quality (or anti-bias) cut is N 1, and the number of events remaining after applying that particular quality (or ant-bias) cut is N 2, then: Efficiency = N N % 6.6 Cut Events Efficiency % # of events (17.25 log 10 E 20.5 ) Npix < 6 χ 2 of GH fit/degrees of freedom< 6 0 < χ 0 < 180 degrees R p > 0 X max bracket cut Che. Frac. < 50% Grammage>300g/cm 2 SD/FDdT 0 & SD/FD<200 TimeChi2FD 0 & TimeChi2FD /ndf< 5 AxisDist <2000m θ 60 o X max < 40 g/cm X low > 0 and X low < X max < X up X low cut X up cut Table 6.2: List of quality and anti-bias cuts applied to the data, and the number of events remaining after each cut is applied successively and the efficiency. Table 6.3 indicates the mean energy for energy bins between ev and ev, the mean X max obtained for each energy bin, the number of events in each energy bin and the parameter RMS/ (number of events) obtained from the final data set of 6683 events.

162 145 log 10 E <X max (g/cm 2 )> Events RMS/ Events Table 6.3: log 10 E, mean X max, the number of events in each energy bin and the error obtained for the final data set.

163 Bibliography Heiko Geenen X max Resolution and Mass Composition Studies with the Auger FD Detectors GAP Thomas K. Gaisser - Cosmic Rays and Particle Physics, Cambridge University Press, Pierre Billoir et.al.- Identification of the Primary Cosmic Ray, C. R. Acad. Sci. Paris,t.4, Série IV, p.1-??, Mike Roberts Private Communication D.R Bergman - UHECR Composition Measurements Using the HiResII Detector, astro-ph/ J.Bellido, Measuring the Mean X max as a Function of the Shower Energy Using the Hybrid Data, GAP R. Engle, Very High Energy Cosmic Rays and Their Interactions, Nucl. Proc. Sup. B, 151 (2006),

164 Chapter 7 Discussion and Conclusions The PAO has the potential to teach us about the sources of the most energetic particles in the universe, but only if we know how to properly analyze the data that it produces. In a project of this magnitude, correct data analysis is a multi-step process. First the fundamental physics of the EAS must be understood and incorporated into realistic simulation tools. These tools can then be applied to model the operation of the PAO under various simulated event scenarios, and the results used to determine the parameters of event reconstruction and analysis. Finally, these parameters can be applied to real event data from the observatory. In this thesis, I used Monte Carlo simulations to study how event reconstruction depends on specific shower parameters, I compared the behavior of different hadronic interaction models, and I analyzed the mass composition of Auger events. Chapter 4 is dedicated to Auger surface detector analysis using a toy Monte Carlo method that uses a simplified parameterization to investigate the behavior of the signal calculated at 1000m from the core, S(1000), with the slope β of the lateral distribution function and the distance to the closest detector hit, r min. I found that the width σ of the reduced S(1000) distribution correlates strongly with both β and r min. Small errors in β values assigned in shower reconstruction lead to significant increases in the uncertainties of the reconstructed S(1000) parameter. This effect is particularly

165 148 noticeable for events with r min value less than 500m and with primary energy around 10EeV. Only a few stations are triggered in these events, and removing saturated stations significantly changes the lateral distribution profile fit. For energies around 25EeV and higher, this effect is not so drastic at lower r min values, but we observe larger dispersions in σ at these energies when r min values are larger than 500m. These uncertainties emerge because the slope β of the lateral distribution function is fixed in my analysis of the event reconstruction regardless of the detector multiplicity. Clearly, at higher energies there are enough triggered stations to fit the lateral distribution profile using β as a free parameter, even if we ignore the saturated stations in the fit. This effect is independent of the saturation level considered, and I found that it is best to set β as a free parameter in shower reconstruction when the detector multiplicity is greater than or equal to five. To reconstruct an event from SD data, one seeks to determine the event signal at a specified distance from the shower core, and then to use that signal in reconstruction. In order to minimize errors, it is important that we correctly choose the distance at which the signal is to be determined. In Chapter 4, I reconstructed simulated events by calculating their signals at 600m, 800m, 1000m, 1200m and 1400m. I found that the best parameter for reconstructing events from PAO SD data is the signal, S(1000), at 1000m. This parameter provides minimal uncertainty in reconstruction and is robust against changes in energy and incident zenith angle. Just as important as identifying the correct parameters to use for data analysis is understanding the differences between the simulation programs that are used to model Auger events. In Chapter 5, I investigated the risetime and S(1000) behavior of simulated

166 149 showers generated using proton and iron primaries and different hadronic interaction models. The hadronic interaction models used are Sibyll, QGSJetI and QGSJetII; and the simulation programs are CORSIKA and AIRES. As expected, the risetime for pure iron showers is smaller than that for pure proton showers in both CORSIKA and AIRES. Regardless of the primary, the risetime agreement between QGSJetII and Sibyll is better than that between QGSJetI and Sibyll. The curves for S(1000)/Energy 0.95 plotted as a function of sin 2 θ are qualitatively similar for all hadronic interaction models and shower simulation tools (Figure 5.6). The systematic differences between CORSIKA and AIRES are small for intermediate angles of 36 o and 45 o. I observed a similar behavior in systematic differences between Sibyll and QGSJetI, as well as between Sibyll and QGSJetII for both proton and iron primaries. This is because the total signal deposited, which is a combination of EM and muonic signal components, is almost a constant in this zenith angle range, regardless of the hadronic model and the primary particle. Furthermore, the systematic difference between Sibyll and QGSJetII is smaller than that between Sibyll and QGSJetI. Therefore, I conclude that there is in general a better agreement between Sibyll and QGSJetII than the agreement between Sibyll and QGSJetI. The constant intensity cut (CIC) method was developed to account for the attenuation of signals received by the SD from events with large zenith angles, θ. The method involves using real data to determine a set of empirical parameters that can be used to reject events that bias the flux toward low zenith angles. When the CIC method is employed, the observed cosmic ray flux does not vary with sin 2 θ. However, similar cuts obtained from Monte Carlo simulations did not give a constant flux for the same data set

167 150 through the entire zenith angle range. The obtained flux was lower at smaller zenith angles and higher at larger zenith angles. At this point, we can not clearly explain why MC inferred attenuation curves behave differently from that obtained from the constant intensity cut method. This is an area of ongoing investigation within the Auger collaboration. The field of view of a single PAO FD covers an elevation between 2 and 30 degrees in the atmosphere. Because event reconstruction from FD data is limited to only that segment of the shower that is visible to the FD, several quality cuts must be employed to ensure proper event reconstruction. For example, events with X max values outside of the FD field of view may not be accurately reconstructed. This happens both for low energy events, in which X max may be too shallow to occur within the field of view, and for high energy events with X max deeper than the field of view. Another concern in FD data quality comes from Cherenkov light. The signals from showers with axes pointed toward the FD may be contaminated with direct or scattered Cherenkov radiation, hindering reconstruction. Furthermore, the limited field of view of the FD results in a detection bias toward events that occur within a certain slant depth range: events that occur largely within the field of view are more readily detected by the FD, skewing the statistics of the data collected. To accurately measure any quantity associated with a set of showers, we must first filter the data to obtain a clean and unbiased set. Quality cuts are introduced to get rid of poorly reconstructed events, and anti-bias cuts based on the FD geometry are developed to filter out events that are accepted only because of the FD bias. In Chapter 6, I introduced novel anti-bias cuts that filter out events that are only accepted because of

168 151 their specific geometry with respect to the FD. These cuts, which depend on the energy of the primary, can be readily applied to any Auger hybrid data with an FD detection bias. They remove nearly 62% of the events that remain after quality cuts, but the remaining events can be used in producing clean, unbiased analyses of distributions such as the elongation rate. I employed these anti-bias cuts in an analysis of the elongation rate of PAO hybrid data obtained between January 2004 and December Figures 6.8 and 6.9 show that, after application of quality cuts and anti-bias cuts, the data are best described with two elongation rates. Events with energies below the break point of log 10 E=18.45±0.05 fit an elongation rate of 80±3 g/cm 2 per decade, whereas those with energies above the break point best fit an elongation rate of 35±4 g/cm 2 per decade. I compared these rates to simulated showers generated using both proton and iron primaries. In each case, I employed the same quality cuts as were used to filter the hybrid data, as well as a set of anti-bias cuts corresponding to the primary used in the simulation. I found that the quality and anti-bias cuts give better results with iron than with protons. With iron primaries, the reconstructed X max distribution varies significantly from the generated distribution at lower energies (log 10 E 17.5) when no filtering is employed, whereas the overall reconstructed distribution is much closer to the generated distribution when both quality cuts and anti-bias cuts are used. Thus, with a pure iron composition, the correct X max fluctuations can be estimated with an optimum set of anti-bias cuts. On the other hand, for proton primaries the reconstructed elongation rate obtained from unfiltered data is nearly equal to that of the generated data, which is 45.8 g/cm 2 per

169 decade; however, the elongation rate obtained after applying the quality cuts and anti-bias cuts is about 7% greater than that of the generated showers. 152 The calculated elongation rate for the real data below the break point does not agree with either of the constant composition elongation rates from the Monte Carlo runs, and the elongation rate above the break point is also significantly less than that of proton showers. According to the interaction models, the evidence from data in this study suggests a transition from heavy to a lighter composition from ev to about ev and another transition from light to a heavier composition above ev with shallower mean X max values, but more data are required to more accurately identify the typical primary mass on both sides of the break point assuming that we fully trust the particle interaction models at these high energies. Future Directions Work continues on the PAO, and further study is required to fully understand the data from the observatory. Here, I present some possible directions for future study. The earlier described discrepancy between the empirically determined CIC and its MC analogue needs to be better understood. Does the observed result that the MC filter favors events with larger sin 2 θ values depend on the data set that is used to compare the filters? Or is this a robust difference that indicates a deviation of the simulation programs from real data? It is possible that the observed differences in the behavior of the filters result from the particular SD data set that was used in the analysis

170 153 of Chapter 5. It would be interesting to compare the two cuts using different data sets. It might also now be possible to determine directly whether the discrepancy is an artifact of the AIRES and CORSIKA simulation tools, especially at higher energies (10 19 ev or above). The newly developed EPOS simulation tool, which is claimed to produce a higher concentration of muons than other simulation packages, can also be used to calculate attenuation curve parameters for filtering data. If these agree with the CIC, then it is likely that the discrepancy is caused by some error in the current shower simulation tools. Measurements of elongation rates might also be improved. Data are sparse above the break point, introducing a modest amount of statistical error into the calculated elongation rate in that region. However, this error will be reduced now that the fourth FD has begun taking data. Not only will the additional data provide a better measure of the elongation rate by increasing the quantity of events that pass the anti-bias cuts, it will also directly affect the anti-bias cuts themselves. Because these cuts are based on real events, they will continue to change and improve as data are collected. Additionally, it was recently suggested by Jose Bellido [1] that the Cherenkov Light Fraction quality cut employed in Chapter 6 should be replaced with a minimum viewing angle cut. It would be interesting to see whether this alternative cut affects the calculated elongation rates.

171 154 It is desirable to have anti-bias cuts that are independent of primary energy. Currently a method is being developed to incorporate energy dependence into the anti-bias cuts discussed in Chapter 6. The composition analysis study of Chapter 6 is based on the variation of mean X max per decade of energy; however, measuring the width of the X max distributions might also prove useful in analyzing the mass composition of UHE cosmic rays. It would be interesting to compare PAO data to MC showers to see what the spread in X max distributions reveals about the primary mass composition. When the southern Pierre Auger Observatory is completed later this year, it will provide a window to a universe that has so far remained almost entirely invisible to us. Although the PAO is certain to elucidate many properties of UHE cosmic rays in the coming years, perhaps its greatest power lies in its potential to identify their sources. Knowledge of the astronomical processes that spawn these most energetic particles will open up doors to new branches of fundamental astrophysics. Bibliography 1. J.Bellido, MC Studies of the Quality and Anti-bias Cuts for Elongation Rates, GAP

172 Appendix A Afterpulsing of Surface Detector Photonis XP1805 Photomultiplier Tubes This is a slightly modified version of the article Afterpulsing of Surface Detector Photonis XP1805 Photomultiplier Tubes by Sanjeevi Atulugama and Stephane Coutu, published in PAO GAP note archives as GAP A.1 Abstract Photomultiplier tubes (PMTs) often suffer from "afterpulsing", wherein PMT pulses are followed by small pulses, which are proportional to the amount of charge in the initial pulse, and which in the Auger surface detectors represent a contamination of the true cosmic-ray induced signals. We would like to identify any "suspicious" PMTs which produce a significant amount of such afterpulses, contaminating the data. In this study we describe a procedure used to identify such PMTs and then we find that out of 1971 PMTs operating during the month of February, 2005, 50 PMTs exhibited some afterpulsing between 0.5% and 2.0% per incident photoelectron. Out of these 50, only 36 PMTs recorded a sufficiently large sample of events with afterpulsing activity to make a reliable afterpulsing assessment. We present the afterpulsing activity of all those 36 PMTs. All of the PMTs considered have an afterpulse-to-signal ratio within the nominal 5% specification.

173 A.2 Introduction 156 Afterpulsing in a PMT can result from a variety of mechanisms [1]. These include light feedback to the photocathode from the anode or a dynode in the tube, typically occurring ns after the incident pulse. Another mechanism is due to the ionization of contamination gas in the tube, typically hydrogen, helium or nitrogen, yielding afterpulses hundreds of ns after the incident pulse. In both cases, the total amount of afterpulsing activity is proportional to the amount of current, or charge in the initial pulse. The Photonis XP1805 PMT was chosen for the Auger surface detectors for a variety of performance characteristics. In particular, a specification was made for the PMT selection process that the tubes not exhibit more than 5% afterpulse probability per incident photoelectron in the range from 200 ns to 5 µs after the incident pulse [2]. The PMTs are routinely tested for afterpulsing at the Malargue test facility prior to deployment [3]. In an early set of pre-production and production PMT tests [4], it was found that on average the first 270 XP1805 PMTs did exhibit some afterpulsing, but acceptably within the 5% specification. Here, we investigate the afterpulsing activity of production PMTs that have been deployed in the field for some months or years. The method used in this study in identifying suspicious PMTs (producing significant afterpulsing activity) is to estimate the fraction of deposited energy recorded in FADC traces which are due to afterpulses; if this fraction is equal to or greater than 0.5% of the total incident pulse, the PMT is flagged as suspect. Most traces contain a record of only one event, but some may contain more than one event. Signals found in the traces may be either muonic or electromagnetic in origin. Muon signals lead to

174 157 narrow peaks in the trace, decaying from a sharp peak over a period of usually up to about 500 ns, or sometimes a few hundreds of ns beyond that. Electromagnetic events typically lead to "messier" traces, spanning over 500 to several thousand ns, often with multiple largish peaks. A.3 Procedure For this analysis 5921 real events recorded during the month of February, 2005 were obtained from the Lyon database with each event observed by 8 or more stations. At that time, 657 stations were in operation, so that there are 1971 PMTs active for this study. The software used was CDAS version v3r4p3. To cleanly estimate the extent to which a PMT produces afterpulses, we analyze only traces that consist of a single muon event, plus (potentially) afterpulses. With traces that consist of multiple muon events, or messy electromagnetic pulses, it is too difficult to distinguish the event(s) from the afterpulses, so such traces are rejected here (as explained in detail below). Once only clean muon traces (plus possibly afterpulsing) have been selected for further analysis, we divide traces into two time periods, the first representing the event signal, and the second, late-time afterpulses if any. The first period of time is the time before1500 ns and the second period is after 1500 ns, with respect to a t = 0 origin, which we define as the leading edge of the first pulse of the FADC trace. The first period of time may include some afterpulses as well as the muon event, but the integrated total energy measured in that period is dominated by the contribution from the muon event

175 158 itself. The second period of time should consist solely of afterpulses, if they are present, since we have rejected traces that contain other events. Accordingly, we compute the "afterpulse to signal" ratio of the integrated activity in the two regions: total activity (charge) in the afterpulse period, divided by total activity in the muon-event period. We average this quantity over a number of singlemuon traces produced by the same PMT, in order to investigate the typical operating behavior of that PMT. Over the 5921 event data set, each PMT has between 0 and 100 events, or about 54 events on average, from which to calculate this mean afterpulse-tosignal ratio. If its average "afterpulse to signal ratio" exceeds 0.005, the PMT producing these traces is deemed "suspect". As mentioned above, in judging the quality of a PMT, we select only FADC traces that contain a clean single muon event (with afterpulses if present), because only in such traces is it possible to cleanly separate cosmic-ray signals from afterpulse noise. The trace selection process is thus complicated by the need to determine whether signal peaks in the trace represent single muon events, multi-muon events, electromagnetic events, muon + electromagnetic events, etc. Any of these traces may also contain afterpulses. The type of event (single-muonic, multi-muonic, electromagnetic, etc.) is analyzed solely from the behavior of the peaks in the trace, where a "peak" is a local maximum (a bin where VEM[t]>VEM[t-1] and VEM[t]>=VEM[t+1], where VEM[t] represents the PMT FADC signal in the bin at time t.). Though theoretically a smooth unimodal curve with a fast rise followed by a slower decay, a muon event trace may contain multiple peaks due to noise Thus, a trace

176 159 with a single muon event can typically consist of a few closely-spaced "big" peaks (roughly decreasing in amplitude with time), possibly followed by some small afterpulse peaks. Because muon events are shorter and "cleaner" than electromagnetic events, any trace with more than 7 peaks is rejected as being an electromagnetic event (though, in principle, it could be a "messy" muon event, with or without afterpulses). In addition, any disconnected "big" peak in a trace which occurs sufficiently long (100 ns) after the first peak is considered to be part of an accidental second event, and such traces are also rejected. (A "big" peak is one that is at least 20% the height of the highest peak in the trace.) Figures A.1, A.2 and A.3 illustrate the actual traces of a single clean muon pulse, an electromagnetic pulse, and coincident accidental muon pulses, respectively. According to the rejection process, the electromagnetic and coincident muon pulses are rejected and what remains are the single muon and muon + afterpulse traces, whose average afterpulse-to-signal ratio is used to identify suspect PMTs, as described previously. Before rejecting any FADC trace there are traces and after the rejection process there are traces left for analysis. This is 62% of the initial total FADC traces.

177 160 Figure A.1: An actual FADC trace of a clean muon pulse. Figure A.2: An actual FADC trace of an electromagnetic pulse.

178 161 Figure A.3: An actual FADC trace of a coincident muon pulse. A.4 Results and Discussion We analyzed 5921 cosmic ray events recorded in February, There were 657 stations for which all three PMTs observed at least one single-muon event, with a total of 1971 PMTs. Only these stations' observations were included in this analysis. After the rejection process, all three PMTs in 12 stations recorded events with afterpulses as shown in Figure A.4. In such cases, the apparent afterpulses are considered to be real late activity in the tank (e.g., an accidental muon), rather than afterpulses, as all three PMTs recorded the same late signal. (Random afterpulses are unlikely to coincide by chance in all three PMTs, but true event signals do.) Such FADC traces are not taken into account for afterpulsing. However, in the 5921 events we observe only 19 such events with real late activities. The stations Dhue and Rulan observed 3 such late activity events and stations Irini, Mina Los Castanos and Guadalupe observed 2 such events. In

179 the rest of the 7 stations, all three PMTs recorded only one event with real late activity each. 162 Figure A.4: Actual FADC traces of a late activity in an event observed by the station Bastille.

180 163 Figure A.5 is a distribution of how many PMTs observed a given number of single-muon events (i.e., events passing the selection/rejection procedure discussed in Section 2). According to this histogram, out of 5921 events, the PMTs used in this analysis observed 54 clean single muon events on average. In Figure A.6, the red line gives a distribution of the average afterpulse-to-signal ratio of the 1971 PMTs in this study and the blue line gives the total afterpulsing results of the Malargue test facility. Of the 1971 PMTs, 50 PMTs had an average afterpulse-to-signal ratio exceeding 0.5%, but all PMTs showed less than 2.0% afterpulsing activity. Of those 50 "noisier" PMTs, only 36 (about 1.8% of the original 1971) recorded a sufficiently large sample of afterpulsing activity to deserve being flagged and looked at more closely. The population of entries with negative afterpulsing measurements from the Malargue test facility is apparently an artifact of the data acquisition equipment used at the test facility. It would seem that the events within the negative tail of the Malargue test facility distribution (blue histogram) pile up within the central peak of our measured distribution (red histogram). Figure A.7 indicates the average afterpulse-to-signal ratio for these 36 PMTs only. Figures A.8, A.9, A.10, A11, A.12 and A.13 are distributions of the afterpulse-to-signal ratio, for each of the 36 PMTs. Finally, Table A.1 gives the afterpulse-to-signal ratio in this study and the Malargue test results of total after pulsing of the suspected 36 PMTs. According to this table, in the Malargue test facility, the PMTs in stations Huenu Huerquenlu(261), Quintana(412), Harry Potter(435), Tato(440), Boby(522), Pichi-peni-hue(556), Barbi(543), Seis Meses(596) have been tested 3 times or more. Although our afterpulsing-to-noise ratios are not very close to the Malargue test results except for PMT

181 1 in station Chapa(574), in both cases there is no significant indication of afterpulsing in any of the tested PMTs Entries Mean RMS # of events Figure A.5: The number of events observed by all the PMTs.

182 Entries= Mean RMS Mean= RMS= Entries= Mean= RMS= <afterpulsing> Figure A.6: Average afterpulse-to-signal ratio of all the PMTs in the study (red) and the total afterpulsing from the Malargue test facility (blue). 12 Entries Mean RMS <ratio> Figure A.7: Average afterpulse-to-signal ratio of the 36 PMTs with more than 0.5% afterpulsing probability.

183 166 Karl Jansky(114)-pmt 1 El Cortaderal(123)-pmt 3 Rene Favaloro(143)-pmt 1 9 Entries Entries Entries Mean Mean Mean RMS RMS RMS ratio Rene Favaloro(143)-pmt 2 10 Entries ratio Franco(146)-pmt 1 25 Entries ratio Quechubil(157)-pmt 2 30 Entries 37 8 Mean Mean Mean RMS RMS RMS ratio ratio ratio Figure A.8: The afterpulse-to-signal ratio of the noisier PMTs. Irini(169)-pmt 2 Montmartre(196)-pmt 1 Celeste(203)-pmt 1 50 Entries Entries Entries 48 Mean Mean Mean RMS RMS RMS ratio Fernanda(226)-pmt ratio Ezra(230)-pmt ratio Deborah(234)-pmt 1 40 Entries Entries Entries Mean RMS Mean RMS Mean RMS ratio ratio ratio Figure A.9: The afterpulse-to-signal ratio of the noisier PMTs.

184 167 Mina Los Castanos(258)-pmt 3 50 Entries 60 Mean RMS Huenu-Huerquenlu(261)-pmt 1 50 Entries Mean RMS Dhue(279)-pmt 2 60 Entries Mean RMS ratio Ines(350)-pmt ratio Alda(363)-pmt ratio Quintana(412)-pmt Entries 57 Mean RMS Entries 53 Mean RMS Entries Mean RMS ratio ratio ratio Figure A.10: The afterpulse-to-signal ratio of the noisier PMTs. Oso(418)-pmt 3 Harry Potter(435)-pmt 2 Tato(440)-pmt 1 30 Entries 44 Mean Entries Mean Entries Mean RMS RMS RMS ratio Pamperito(482)-pmt ratio Rulan(519)-pmt ratio Boby(543)-pmt 1 40 Entries Entries Entries Mean Mean Mean RMS RMS RMS ratio ratio ratio Figure A11: The afterpulse-to-signal ratio of the noisier PMTs.

185 168 Arnold(537)-pmt Entries 47 Mean RMS Barbi(543)-pmt 3 50 Entries 68 Mean RMS Pichi-peni-hue(556)-pmt Entries 57 Mean RMS ratio Pichi-peni-hue(556)-pmt 3 45 Entries Mean RMS ratio Mauri(572)-pmt 2 50 Entries 57 Mean RMS ratio Chapa(574)-pmt 1 22 Entries Mean RMS ratio ratio ratio Figure A.12: The afterpulse-to-signal ratio of the noisier PMTs. Seis Meses(596)-pmt Entries 57 Mean RMS La Salinilla(651)-pmt 2 50 Entries 54 Mean RMS Guadalupe(657)-pmt Entries 57 Mean RMS ratio El Cenizo(660)-pmt 2 Entries Mean RMS ratio Kerberos(723)-pmt 2 50 Entries 54 Mean RMS ratio Tolhiun(758)-pmt 2 50 Entries Mean RMS ratio ratio ratio Figure A.13: The afterpulse-to-signal ratio of the noisier PMTs.

186 Station PMT serial # Afterpulse -to-noise ratio Total afterpulsing Malargue test results Karl Jansky(114) SET El Cortaderal(123) setphoto_900_00635-c Rene Favaloro(143) SET Rene Favaloro(143) SET Franco(146) SET Quechubil(157) SET Irini(169) SET A Montmartre(196) SET Celeste(203) SET Fernanda(226) SET Ezra(230) SET CF Deborah(234) SET B Mina Los Castanos (258) SET B Huenu Huerquenlu(261) SET ,-0.012,0.003, Dhue(279) SET , Ines(350) SET Alda(363) SET DB , Quintana(412) SET E ,0.012, Oso(418) SET FC Harry Potter(435) SET , 0.008, Tato(440) SET B , 0.014, Pamperito(482) SET E Rulan(519) SET DF Boby(522) SET E ,-0.010, Arnold(537) SET F , Barbi(543) SET ,0.02, 0.023,0.025 Pichi-peni-hue(556) SET C ,0.005,0.005,0.002 Pichi-peni-hue(556) SET ,-0.004,0.01, 0.009,0.015,0.008,0.013 Mauri(572) SET , Chapa(574) SET C , 0.029, Seis Meses(596) SET F ,0.002, ,0.004 La Salinilla(651) SET Guadalupe(657) SET El Cenizo(660) SET CD Kerberos(723) SET FF Tolhuin(758) SET EE Table A.1: The afterpulse-to-signal ratio in this study and the Malargue test results of total after pulsing of the suspected 36 PMTs.

187 A.5 Discussion 170 In this study we have analyzed the afterpulsing of the Photonis XP1805 surface detector PMTs. After observing FADC traces of individual PMTs of 5921 real events observed during the month of February 2005, we found that out of 1971 PMTs only 36 had significant afterpulsing activity. Out of these 36 PMTs only 3 PMTs (PMT 2 of Rene Favaloro, PMT 2 of Pamperito and PMT1 of Chapa) have an average afterpulse-to-signal probability between 1 % and 2%, whereas the total afterpulsing measured prior to deployment for PMT 2 of Rene Favaloro was -2%, and 0% for PMT 2 of Pamperito, according to the database of the Malargue testing facility [3]. In three different tests PMT 1 of the station Chapa has a total afterpulsing of 2.9%, 1.9% and 1.7%, respectively in [3], with which our results are comparable. The rest of the suspected PMTs have an average afterpulse-to-signal probability of less than 1%. All of the 1971 PMTs studied here have an afterpulse-to-signal ratio within the nominal 5% specification. Therefore we conclude that afterpulsing activity does not represent at present a significant contamination of the signals in the Auger surface detector stations. This study should be repeated in the future after the PMTs have been in operation for some years in the field to determine the extent of any contamination due to slowly diffusing gas (such as helium) into their evacuated volume.

188 Bibliography Burle Photomultiplier Handbook (TP-136), Lancaster, PA (1989) D. Barnhill et al., Results of Testing Pre-Production and Production PMTs for the Surface Detector in the New PMT Test Facility in Malargue, GAP Stephane Coutu et al., Surface Detector PMT Tests, GAP Arun Tripathi, Chris DiPasquale, David Barnhill, Chris Jillings, et al., Study of 8" PMTs at UCLA for Pierre Auger Surface Detectors, GAP

189 Appendix B Auger High Energy Events Here I present the reconstructed results of two events detected by Auger Observatory surface detectors alone (an SD event) and by both surface and fluorescence detectors (a Hybrid event). B.1 Event The hybrid event was recorded on July 04, 2006 with 22 active stations. The SD event display obtained from the CDAS Event Display configuration is given in Figure B.1. Figure B.1: Screenshot of the surface detector event display obtained from CDAS. According to the station color code, yellow circles are additional stations with signal, and the green triangle indicates the stations with trigger T3. Blue circles correspond to silent stations, and pink crosses are the stations deleted. (For further information regarding station color code and details, please refer to [1].)

190 173 Figure B.2 gives the array layout (panel 1), time to the plane front (panel 2), the standard fit to the lateral distribution of the integrated water Cherenkov signal (panel 3) and the values of reconstructed shower parameters (panel 4) obtained from the hybrid reconstruction of Auger Offline version 2.0. Figure B.2: The array layout (panel 1), time to the plane front (panel 2), the standard fit to the lateral distribution of the integrated water Cherenkov signal (panel 3) and the values of reconstructed shower parameters (panel 4) obtained from the hybrid reconstruction of Auger Offline version 2.0. Impact position is denoted by a red arrow with a circle in panel 1. Only the x and y coordinates in the site coordinate system are used in plotting the station positions. The green triangle represents the TOT trigger. The fitted LDF corresponds to Equation 4.1 in Chapter 4.

191 X max = N max = 4.7e e+08 X 0 = χ 2 /dof 376 / 346 Log(E ) = em Log(E ) = tot 174 The particular event (SD information) is merged with event (FD information for the same event) and can be found at the Lyon shower library [2]. Figures B.3 and B.4 give the distributions of longitudinal profile and the light flux of the event , respectively. The X max obtained from the reconstruction is 745.5g/cm 2 and the maximum number of particles N max is n_e 9 10 LongProfile_ _EyeId_ X [g/cm2] Figure B.3: The longitudinal profile distribution of the event When the shower passes through the atmosphere, the telescopes map development of the shower. The longitudinal profile plotted here indicates the number of particles the telescopes detects at different slant depth. In the above figure, the fitted red line is the Gaisser-Hillas energy deposit function [3] which can be used to obtain the shower maximum, X max, and the energy deposited, de/dx max.

192 175 Light_Flux_ _EyeId_4 Photons/m^ time slots [ns] Figure B.4: The reconstructed light flux of the high energy event Figure B.4 indicates the number of photons detected by each PMT in the telescope camera per square meter, plotted as a function of time. B.2 Event This SD event was recorded on January 14, 2007 with energy of 166.7EeV and a zenith angle of 14.5 degrees and seen by 13 active stations. This is one of the highest energy events detected by PAO at the beginning of this year. A screenshot of the surface detector event display obtained from CDAS is given in Figure B.5.

193 176 Figure B.5: Screenshot of the surface detector event display obtained from CDAS. The station color code is the same as in Figure B.1. The calibrated FADC traces of the SD stations are given in Figure B.6. There were 4 accidentals out of the 13 active stations. Then in Figure B.7 we have plotted the array layout (panel 1), time to the plane front (panel 2), the standard fit to the lateral distribution of the integrated water Cherenkov signal (panel 3) and the values of reconstructed shower parameters (panel 4) obtained from the hybrid reconstruction of Auger Offline version 2.0.

194 Figure B.6: Calibrated FADC traces of the SD stations. The color code represents the different PMTs by PMT1 = green, PMT2 = blue, PMT3 = red. 177