University of Alberta Library Release Form Name of Author: Andrew Hamilton Title of Thesis: ALTA: Alberta Large Area Time Coincidence Array Degree: Master of Science Year this Degree Granted: 2006 Permission is hereby granted to the University of Alberta Library to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatever without the author's prior written permission. Andrew Hamilton 208-10636 120 St. Edmonton, AB Canada T5H 4L5 Date: University of Alberta ALTA: Alberta Large Area Time Coincidence Array by Andrew Hamilton A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science. Department of Physics Edmonton, Alberta Fall 2002 University of Alberta Faculty of Graduate Studies and Research The undersigned certify that they have read, and recommend to the Faculty of Graduate Studies and Research for acceptance, a thesis entitled ALTA: Alberta Large Area Time Coincidence Array submitted by Andrew Hamilton in partial fulfillment of the requirements for the degree of Master of Science. Dr. John W. McDonald (Supervisor) Dr. Roger Toogood (External) Dr. James Pinfold Dr. Sharon Morsink Date: To Kelleigh, Thank-you for your support - I love you Abstract The Alberta Large Area Time Coincidence Array (ALTA) is a joint collaboration between the University of Alberta and area high schools to study some fundamental properties of high energy cosmic rays. Scintillating air shower detectors are mounted on the roofs of Alberta high schools and connected to a data acquisition system that is controlled by a computer in the classroom. The primary objective of the ALTA project is to find correlations in the arrival times of air showers over large distances and to find non-random arrival times in showers arriving at a single site. This thesis contains a review of cosmic ray physics, a detailed description of the ALTA experiment, and an overview of the analysis routines and techniques that will be used. Acknowledgements I would like to thank Professor John W. McDonald of the University of Alberta for his support, advice, insight, and excellent guidance since January of 2001. You are an inspiration to me. Without the work, ingenuity, and perseverance of the electronics shop; Len Wampler, Lars Holms, Bill Burris, Drew Price, Jan Schaapman, John Hewlett, and Pat Wong the ALTA project would not be possible. My thanks to everyone in the electronics shop for the work they've done and for putting up with all my questions. Thank-you Dr. Richard Soluk for all the hard work you've put into the ALTA project and all the help you have given me. My thanks to my supervisory committee: Dr. John W. McDonald, Dr. James Pinfold, Dr. Sharon Morsink, Dr. Roger Toogood I would also like to recognize and thank the undergraduate summer students that assisted me; Justin Stedman and Doug Gish. The funding and support of the University of Alberta, ISRIP, IONC-MASTE, Saint-Gobain Crystals and Detectors, Life Members Organization of the Engineering Institute of Canada, and CMASTE, are all gratefully acknowledged. Finally, I am sincerely grateful to my friends, colleagues and family for their advice and support. Contents 0.1 Introduction............................ 12 0.1.1 Objectives of Experiment ................ 12 0.1.2 Objectives of Thesis ................... 12 0.1.3 Summary of Chapters .................. 12 1 Cosmic Rays 1 1.1 Cosmic Ray Basics........................ 1 1.1.1 The Energy Spectrum .................. 3 1.1.2 The Composition Spectrum............... 7 1.1.3 A Question of Origin................... 10 1.2 Extensive Air Showers...................... 12 1.2.1 Electromagnetic Showers................. 12 1.2.2 Hadronic Showers..................... 14 1.2.3 Other Shower Phenomena................ 16 1.3 Non-Random Cosmic Rays.................... 17 1.3.1 Cosmic Ray Bursts.................... 18 1.3.2 Correlated Cosmic Rays................. 20 1.4 Cosmic Ray Experiments..................... 24 2 ALTA Systems 28 2.1 Overview.............................. 28 2.2 The Detectors........................... 33 2.2.1 The Bicron Detectors................... 33 2.2.2 The OPAL Detectors................... 36 2.2.3 The U of A Detectors................... 36 2.3 Global Positioning System.................... 37 2.3.1 How does GPS work?................... 37 2.3.2 What does ALTA do with GPS?............. 41 2.4 The Electronics Crate ...................... 42 2.4.1 The Coincidence Module................. 44 2.4.2 The Time Tag Module.................. 46 2.4.3 The Analog Module.................... 48 2.4.4 The Calibration Module................. 49 2.4.5 The Temperature Module ................ 49 2.4.6 High Voltage Control Module.............. 50 2.4.7 The Crate Controller Module .............. 50 2.5 The Software ........................... 50 3 System Calibrations and Uncertainties 57 3.1 Deposited Energy......................... 57 3.2 Primary Energy.......................... 61 3.3 Global Timing........................... 64 3.4 Local Timing........................... 64 3.5 Uncertainties in Arrival Angle.................. 71 4 Analysis 74 4.1 Data Structure and Organization................ 74 4.2 Coordinate Systems........................ 75 4.2.1 Site Coordinates ..................... 75 4.2.2 The Earth's Coordinate System............. 78 4.2.3 Astronomical Coordinate Systems............ 80 4.2.4 Converting Local Timing To Horizon.......... 83 4.2.5 Converting Horizon to Celestial............. 86 4.2.6 Converting Celestial to Galactic............. 86 4.3 Analysis Routines......................... 87 4.3.1 Correlation Routine.................... 87 4.3.2 Burst Find Routine.................... 91 4.3.3 Skyplot .......................... 92 5 Conclusion 93 A Analysis Code 95 A.l The Summary Routine...................... 95 A.2 The Correlation Routine..................... 100 A.3 The Burstfind Routine...................... 104 Bibliography 95 Glossary 105 List of Tables 3.1 Result of signal delay test at MacDonald site.......... 70 4.1 Word structure of ALTA binary data. (1 word = 32 bits) ... 75 4.2 Block structure of ALTA database................ 76 4.3 WGS84 parameter values..................... 79 4.4 Summary of astronomical coordinate systems ......... 83 List of Figures 1.1 Simplified diagram of an air shower............... 2 1.2 Cosmic ray flux as a function of primary energy (left) [?], cosmic ray fluxxE3 as a function of energy to emphesis knee and ankle (right) [?].............................. 3 1.3 Cosmic Microwave Background (CMB) frequency spectrum . . 5 1.4 Attenuation length of protons in CMB, showing the GZK limit at about 50 Mpc. The three lines represent three different initial energies: 1020, 1021, and 1022 eV................. 6 1.5 The ultra-high energy cosmic ray spectrum reported by the AGASA experiment at the 1999 ICRC. The dotted line is the flux predicted with the GZK limit................ 7 1.6 The abundances of cosmic rays compared to galactic abundances (normalized to 100 at Si)................. 8 1.7 Simplified schematic of an electromagnetic shower....... 13 1.8 Simplified schematic of a hadronic shower ........... 15 1.9 Schematic of a sonic boom or Cerenkov radiation....... 16 1.10 Hypothetical event creating correlated showers......... 21 1.11 Fraction of GZ events for Fe nuclei at 6 x 1017 eV in ecliptic coordinates with the direction of the sun at the center of the plot. 23 1.12 Photograph of the STACEE (left) and HEGRA (right) facilities 25 1.13 Diagram of a high energy cosmic ray event at HiRes...... 26 2.1 Basic schematic of ALTA system components ......... 29 2.2 Map of ALTA sites currently in operation and under construction 30 2.3 Schematic of determining shower arrival direction in 2 dimensions 31 2.4 Basic schematic of bicron detectors................ 34 2.5 (a) Emission spectra of Bicron BC-408 plastic scintillator and (b) spectral sensitivity of Philips XP2262B PMT........ 34 2.6 Experimental setup to test the efficiency of Bicron detectors . 35 2.7 Typical results of the dependence of efficiency with position on the Bicron detectors ....................... 35 2.8 Diagram of an OPAL detector. Detection area is 0.16 square meters............................... 36 2.9 Plot of spectral sensitivity of Electrontubes 9902 PMT .... 37 2.10 Diagram of U of A detectors................... 37 2.11 Determining location in two dimensions with uncertain timing using (a) two satellites (b) three satellites............ 40 2.12 Schematic of GPS system at an ALTA site........... 41 2.13 Photograph of ALTA electronics crate.............. 43 2.14 Schematic of ALTA electronics crate .............. 43 2.15 Block diagram of coincidence module.............. 44 2.16 Block diagram of ALTA time tag module............ 47 2.17 Block diagram of ALTA analog module............. 48 2.18 ALTA software main display................... 51 3.1 A typical MIP peak and ADC pedestal.............. 58 3.2 Angle of arrival of secondary particles from 100 vertical showers 61 3.3 Distance from shower core that density reaches 2.8 particles per m2 as a function of shower energy. The curve represents a fit to a quadratic............................. 63 3.4 Time distribution of particles arriving at 700 m detector altitude within annulus of 4 m and 5 m from shower core........ 65 3.5 Detector Size Test (a) test detector at center (b) test detector at corner.............................. 66 3.6 Detector size test results..................... 67 3.7 A plot showing the dependence of voltage on the timing of the reference detector at 30 mV threshold. The linear fit has a slope of 0.66 TDC counts per Volt................... 68 3.8 Histograms comparing the timing of the reference detector as it is oriented north-south and east-west............... 69 3.9 A typical display of a TDC calibration............. 71 3.10 Plot of uncertainty in altitude angle as a function of altitude angle (crosses are data points, dotted curve is fit)....... 72 3.11 Plots of uncertainty in azimuth angle as a function of azimuth angle for varying TDC values in detectors 0, 1, and 2..... 73 4.1 Coordinate system used to describe the positions of the detectors at a site............................ 77 4.2 WGS84 parameter definitions................... 78 4.3 Horizon coordinate system.................... 81 4.4 Celestial coordinate system.................... 82 4.5 Galactic coordinate system.................... 82 4.6 Hypothetical, perfectly correlated, air shower events...... 87 4.7 Burstfind routine would find a burst of 5 events ending at t6 . 92 4.8 An example of 3 hypothetical events displayed with skyplot . . 92 List of Symbols Acronyms ADC Analog to Digital Converter ALTA Alberta Large Area Time Coincidence Array CFPHT Constant Fraction Pulse Height Trigger EAS Extensive Air Shower eV electron Volt FIFO First In First Out memory device FPGA Field Programable Gate Array GPS Global Positioning System HA Hour Angle HV High Voltage ICRC International Cosmic Ray Conference LST Local Sidereal Time Mpc Megaparsec PC Personal Computer RMS Root Mean Square TAC Time to Analog Converter TDC Time to Digital Converter UTC Universal Coordinated Time Symbols a Right Ascension angle of celestial coordinates 5 Declination angle of celestial coordinates / Galactic longitude of galactic coordinates b Galactic latitude of galactic coordinates 9 Altitude angle of horizon coordinates (f> Azimuth angle of horizon coordinates p Longitude on Earth Ac Geocentric latitude on Earth A9 Geographic latitude on Earth /3 Vertical incidence angle of correlated showers (see Figure 4.6) £ Exponential slope of primary cosmic ray energy spectrum 0.1 Introduction 0.1.1 Objectives of Experiment The Alberta Large Area Time Coincidence Array (ALTA) was first conceived by Jim Pinfold in the mid 90's. The concept is to create a sparse, but very large area, cosmic ray detector to study some intriguing properties of cosmic ray air showers that have been hinted at, but never fully explored. Properties such as correlations between showers separated by very large distances [?] [?] [?], as well as non-random and chaotic series in the arrival times of showers [?] [?] [?] are currently unexplained. The primary objective of the ALTA experiment to gather more data to help unravel these mysteries. ALTA also has an interest in promoting outreach at the high school level. The experiment's detection equipment is housed at high schools throughout Alberta, giving high school students the opportunity to observe and participate in fundamental scientific research. For more information on the outreach aspects of ALTA visit [?]. ALTA is part of a larger network of experiments called NALTA (North American Large Area Time Coincidence Array). Each experiment in NALTA has objectives similar to ALTA; some placing primary interest in outreach, others placing primary interest in research, all participating actively in both. For more information on NALTA visit [?]. 0.1.2 Objectives of Thesis This thesis has a two-fold objective; the primary goal is to explain work that I have participated in for the ALTA project, the secondary goal is to act as a guide and information manual to the high school teachers involved in the experiment. To this end the material is presented with the intention of being understood by someone with a limited background in physics research, while still exploring the fundamental concepts of cosmic ray research. Due to the nature of the requirements of a Masters thesis, this work will focus on the scientific aspects of the ALTA project, not the outreach aspects. 0.1.3 Summary of Chapters Chapter 1 is a review of cosmic ray physics and includes a description of the current understanding of the cosmic ray spectrum, the possible origins of cosmic rays, and a brief outline of the current experimental situation of cosmic ray physics. The possibility of correlated and non-random cosmic ray showers is also discussed. Chapter 2 includes a description of the ALTA experiment. The system and its components are outlined. Chapter 3 contains a description of the calibration processes and the uncertainties involved in the ALTA system. In Chapter 4 is the data analysis routines are described. The body of the chapter includes the processes of the routines, while the source code is written in an appendix. The structure and organization of the ALTA data is also included in this chapter. Chapter 5 contains a conclusion with an overview of what has been accomplished and what still needs to be done to complete the ALTA experiment. Chapter 1 Cosmic Rays The purpose of this chapter is to introduce the basic physics of cosmic rays, to present some of the questions of interest to cosmic ray researchers, and to outline some of the experimental attempts currently being applied to answer those questions. 1.1 Cosmic Ray Basics Cosmic rays were first discovered by Victor Hess in 1912, a discovery which earned him the 1936 Nobel Prize. In a balloon flight up to an altitude of 5350 m, Hess discovered that radiation in the atmosphere increases with altitude. He explained this observation in his 1912 paper: The results of the present observations seem to be most readily explained by the assumption that a radiation of very high penetrating power enters our atmosphere from above, and still produces in the lowest layers a part of the ionization observed in closed vessels. - Victor Hess[?] Naturally, with this discovery there came many questions about cosmic rays. What are they? Where do they come from? How do they get here? How many are there? How much energy do they carry? Ninety years have passed and, while much has been learned, some important questions still remain. So what do we know about cosmic rays? Cosmic rays are subatomic particles from space constantly bombarding the Earth's atmosphere. It is estimated 1 that roughly 90% of cosmic rays are hydrogen nuclei (protons) and helium nuclei, about 9% heavier nuclei, and the remaining 1% are electrons and positrons [?]. Traditionally, photons and neutrinos were not considered to be cosmic rays because they do not carry any charge. We know today that photons (and even neutrinos) can produce a cosmic ray phenomena known as an air shower, a very important phenomena in modern day cosmic ray research. Figure 1.1: Simplified diagram of an air shower Figure 1.1 is an extraordinarily simplified diagram of a cosmic ray air shower. Air showers occur when a high energy cosmic ray collides with an atmospheric nucleus. The high energy subatomic collision produces additional high energy particles, which then collide with other nuclei in the atmosphere, and so on. This process causes a cascade, or shower, of particles streaming through the atmosphere. The cosmic ray that initiates the shower is referred to as the primary cosmic ray, and the shower of particles produced are called secondary cosmic rays, or secondaries. The secondaries all travel very close to the speed of light, so almost all of them stay in a roughly planar shower front. When an air shower is large enough that the secondaries reach the ground it is called an extensive air shower (EAS). Extensive air showers will be discussed in more detail in Section 1.2. 2 The following sections contain an outline of the essential features of primary cosmic rays. The first sections will deal with the energy and composition spectra, and the latter sections will discuss questions about the origin of cosmic rays and what the energy and composition spectra could be telling us about the origin question. 1.1.1 The Energy Spectrum Cosmic rays have a very wide range of energies. The lowest energy cosmic rays to produce an effect in the Earth's atmosphere are around 108 eV. Less energetic particles are deflected by the solar wind and the Earth's magnetic field. The highest energy cosmic rays yet observed are around 1020 eV. log(ENERG¥ In eV> Figure 1.2: Cosmic ray flux as a function of primary energy (left) [?], cosmic ray fluxxE3 as a function of energy to emphesis knee and ankle (right) [?]. Figure 1.2 is a plot of the measured cosmic ray energy spectrum. The first part of the spectrum, below roughly 1010 eV, is relatively well understood because the flux is high enough that significant statistics can be achieved by direct measurement of the cosmic ray itself, and not the air shower that it produces. The rest of the spectrum shows an approximately exponential dependence of the form: dF , - The value of the exponential slope, £, remains almost constant over 10 orders of magnitude. The section between 1010 eV and 1015 eV satisfies £ = 2.7, while the section between 1015 eV and 1018 eV satisfies £ = 3.1. The change in the power law at 1015 eV is called the 'knee' of the spectrum. Why the spectrum changes at 1015 eV is not yet understood. The spectrum then flattens out slightly to £ ~ 2.3 [?] at approximately 1018 eV. This kink is called the 'ankle' of the spectrum. Its cause is also unknown. So, not far into our discussion of cosmic rays, we are already faced with some puzzling, yet fundamental, unanswered questions. And what is there past the ankle? One of the most intriguing mysteries in cosmic ray physics today is the question of where, or if, the spectrum will end. The question seemed to have a theoretical answer in 1966, but comparison with recent experiments simply makes the problem more puzzling than before. In 1966 Kenneth Greisen published a paper [?] titled "End to the Cosmic-Ray Spectrum?" explaining that we should observe a very sharp cut-off of the spectrum at about 5 x 1019 eV. This expected cut-off in the spectrum is now called the Greisen-Zatsepin-Kuz'min (or GZK) limit. The Zatsepin-Kuz'min part of the name comes because G.T. Zatsepin and V.A. Kuz'min published a similar paper [?] at the same time as Greisen. At the time of publication of Greisen's paper there had been one observation of a cosmic ray with an energy of 1.0 x 1019 eV by John Linsley of the Volcano Ranch experiment [?]. Greisen called this event "quite remarkable" [?], due to the very low probability he had calculated for such high energy events. Since then there has been an interestingly large number of even less probable events. What causes the GZK limit? In 1965 Arno Penzias and Robert Wilson of Bell labs discovered an unexpected source of microwave electromagnetic radiation coming from all directions. The radiation was characteristic of the Planckian black body radiation that would be emitted from a source at 2.73 K, as shown in Figure 1.3 [?]. This radiation is now called the cosmic microwave background (CMB), and seems to permeate all space. The CMB is now interpreted to be the cosmic background radiation (CBR) predicted by the standard Big Bang model. 4 Wavelength (cm) Frequency (GHz) Figure 1.3: Cosmic Microwave Background (CMB) frequency spectrum Extremely high energy protons are expected to collide with one of these CMB photons roughly once every 20 million years. If the proton has more than 5 x 1019 eV, than a collision with a CMB photon has enough center of mass energy to be above the threshold for the p + 7 =>• p + n reaction. The creation of the pion takes energy away from the proton, degrading its energy. So, the CMB reduces the distances over which protons can carry energies greater than 5 x 1019 eV. The net result is that protons with more than 5 x 1019 eV cannot travel more than about 160 million light years (or 50 Mpc) through the CMB, without their energy being degraded below 5 x 1019 eV. But, if the proton has less than 5 x 1019 eV then the collisions with CMB photons are elastic, and the CMB is essentially invisible. Figure 1.4 (adapted from [?]) is a plot of the attuation length of protons travelling in the CMB. Notice that the energy of any proton above 5 x 1019 eV will be degraded as the distance it travels increases. So what does the GZK limit tell us? Basically, it says that if we observe cosmic ray protons above 5 x 1019 eV then they must have come from a source 5 22 50 Mpc 10 22 ---10 21 CD C 10 20 LLI 10 21 10 20 s 1 10 Figure 1.4: Attenuation length of protons in CMB, showing the GZK limit at about 50 Mpc. The three lines represent three different initial energies: 1020, 1021, and 1022 eV. less than 50 Mpc away1. Therein lies the conundrum; events above 5 x 1019 eV have been observed, but there doesn't seem to be any nearby astronomical objects that could accelerate particles to such a high energy. At the 26th International Cosmic Ray Conference (ICRC) a total of 14 events above 1020 eV were reported [?] [?]. The two highest energy events were observed by the Akeno Giant Air Shower Array (AGASA) in Japan, and the HiRes experiment in Utah. They had energies of 2 x 1020 eV and 3 x 1020 eV, respectively. Figure 1.5 [?] shows a plot of the spectrum of AGASA's data. 1.1.2 The Composition Spectrum At the beginning of this chapter I mentioned that roughly 90% of cosmic rays are believed to be hydrogen and helium nuclei, about 9% heavier nuclei, 1 Proton collisions with the CMB is a statistical process, so there is a chance that a proton could retain its energy for more than 50 Mpc, but it is very unlikely 6 „26 10 CD CO o CD CO 1015 eV) Fermi acceleration is still a possibility, but the magnetic fields making up the mirror must be either much larger, or much stronger, than those that a supernova can create. Pulsars could have strong enough magnetic fields to accelerate cosmic rays past 1015 eV and even up to 1020 eV [?]. A pulsar is a highly magnetized neutron star with a radius of typically about 10 km and density roughly a 1012 times that of the sun. There are pulsars in our Milky Way galaxy, so the cosmic rays accelerated by pulsars could avoid the GZK limit. What about other theories explaining observations of cosmic rays past the GZK limit? Torres et. al. [?] have recently examined the correlation between 7 events above 1020 eV and 12 quasar remnants. Quasars are very active galaxies; quasar remnants are dead quasars containing super-massive black holes. Torres discovered a weak correlation between three of the events and some of the quasar remnants. All of the quasar remnants compared were within the 160 million light year threshold of the GZK limit. Another possible theory recently re-examined by Fodor et.al. is the possibility that ultra-high energy neutrinos annihilate with relic anti-neutrinos creating Z bosons. The 11 Z bosons would then decay to fermion anti-fermion pairs which then produce showers of ultra-high energy protons and photons [?] [?]. Relic anti-neutrinos are a predicted result of the Big Bang, similar to the photon CMB. Unlike the CMB, relic anti-neutrinos have not yet been observed. For this theory to predict the flux of ultra-high energy protons observed, the flux of high energy neutrinos needs to be at the present upper limit. Fodor et. al. do not present a possible source for the flux of high energy neutrinos. 1.2 Extensive Air Showers As discussed at the beginning of this chapter extensive air showers (EASs) are cosmic ray air showers that are large enough for the secondary particles to reach the ground. When the secondaries do reach the ground the area and density of the shower front can give a good estimate of the energy of the primary. Higher energy primary particles will produce larger area, higher density, shower fronts. Since the relationship is not a simple one, Monte Carlo simulations are normally used to determine the primary energy from a measured density distribution. The form of an EAS depends greatly on the type of primary which created it. The two main types of showers are hadronic showers and electromagnetic showers. Hadronic showers are initiated by hadrons (protons and nuclei) while electromagnetic showers are initiated by photons. In principle, electromagnetic showers can also be initiated by electrons and neutrinos, but the flux of primary electrons is very low and the probability of a neutrino interacting in the atmosphere is extremely small. The following two sections will outline some of the basic features of electromagnetic and hadronic showers. 1.2.1 Electromagnetic Showers The dominant energy loss mechanism for high energy (>10 MeV) photons (7) is pair production. The process of pair production is the conversion of a photon to an electron-positron pair in the presence of a nucleus, such as an atmospheric nucleus, 7 + 7 —>• e+ + e~. The nucleus is required in the 12 interaction to conserve momentum; it provides the second 7 in the equation. The electron and the positron each get half of the incident photon's energy. The dominant energy loss mechanism for high energy (>100 MeV) electrons and positrons is Bremsstrahlung radiation loss. In a Bremsstrahlung loss, the electron, or positron, decelerating in the electric field of an atomic nucleus of the medium (air) emits a photon, e=l= —>• e± + 7. The emitted photon will then pair produce, the products of that pair production will then Bremsstrahlung, and so on, creating a cascade of electrons, positrons, and photons as shown in Figure 1.7. 'y Primary Photon Atmospheric Nucleus <£gfc + e~ e \ I y y /I A A l\ e+ Y e+ e~ e+ e~ Y e~ Figure 1.7: Simplified schematic of an electromagnetic shower The cascade will continue until the pair produced electrons fall below the critical energy. The critical energy is the energy at which collision with atoms begin to be the dominant source of energy loss. When this occurs the number of particles in the shower will decrease rapidly, until the shower eventually stops. Some muons are created in the electromagnetic showers. They are created from the e+ + e~ —>• /A + \i~ interaction when a high energy positron from pair production interacts with an electron of an atmospheric nucleus. 13 1.2.2 Hadronic Showers Showers produced by protons, neutrons, and nuclei are called hadronic showers. When a high energy hadronic primary interacts with an atmospheric nucleus it produces a more complex shower than the electromagnetic case. Hadronic showers produce many types of high energy particles including: pi-ons, protons, neutrons, kaons, and nuclear fragments. The stable particles go on to have more hadronic interactions, while the unstable particles either decay or undergo more hadronic interactions. The most common unstable particles produced are kaons and pions. The mean lifetime of a kaon is rK = 1.2 x 10~8 sec. The principal kaon decays produce either pions or muons: n± + v (64%) K± TT* + 7T° (21%) The number in brackets is the branching ratio of the decay. Charged pions decay into muons ~100% of the time: TT* ft* + V„ (~ 100%) while neutral pions predominantly decay into photons; 7T° ->• 7 + 7 (99%) Pions also decay very quickly, rw± = 2.6 x 10~8 sec and rwo = 8.4 x 10~17 sec, so neither pions nor kaons are observed in showers near sea level. All of this means that almost all of the pions and kaons produced in the shower will decay to muons before reaching the ground. You can see that hadronic showers make lots of muons. Relativistic muons can live long enough to reach the ground. Even though traveling through 10 km of atmosphere at c requires 3.3 x 10~6 sec (longer than their mean lifetime = 2.2 x 10~6 sec), relativistic time dilation allows the muons to live longer in the Earth's rest frame than their own. Muons do not interact via the strong force (the force that holds a nucleus together). When they pass 14 through matter, the dominant interactions are electromagnetic interactions with electrons. Since muons are 200 times heavier than electrons, the situation is similar to throwing a baseball into a room full of house flies; the flies don't do much to slow the baseball down. Muons are very penetrating, they will pass several kilometers into the Earth without slowing very much. Muons predominantly decay to an electron and some neutrinos; The electrons and photons produced by the decay of muons, pions, and kaons, will go on to create small electromagnetic sub-showers within the hadronic shower. Since the products of hadronic interactions are much heavier than the electromagnetic components of the shower, there will be a hadronic core in the center of a hadronic shower with electromagnetic sub-showers spreading out from the core, as shown in Figure 1.8. By the time the shower gets to ground level there is usually very little hadronic matter left in the shower as it has all interacted to produce photons, electrons, and muons. A very significant difference between hadronic showers and electromagnetic showers is the ratio of muons to other particles. Hadronic showers have a much higher ratio of muons than electromagnetic showers. This IT ->• e± + ve + Vlk (98.6%) Hadronic Primary Atmospheric Nucleus Hadronic Shower Core Figure 1.8: Simplified schematic of a hadronic shower 15 detail will come up in the next section when we talk about non-random cosmic ray phenomena. 1.2.3 Other Shower Phenomena Apart from the secondary particles of the air shower itself, there are two other physical processes that can be useful in the detection of cosmic ray air showers: Cerenkov radiation and nitrogen fluorescence. Cerenkov Radiation When charged particles pass through a medium faster than the speed of light in that medium, Cerenkov radiation is produced. Cerenkov radiation is the light equivalent of a sonic boom. When a jet flies through the air it causes the surrounding air molecules to oscillate. If the jet is moving faster than the speed of sound (the speed that those oscillations can propagate in air) then the oscillations will be able to constructively interfere, causing huge oscillations of the air molecules; a sonic boom. When a charged particle passes Constructive Interference Figure 1.9: Schematic of a sonic boom or Cerenkov radiation through a medium it polarizes the atoms as it passes them. The atom then quickly depolarizes, producing an electromagnetic wave. If the next atom in the path of the charged particle is polarized and depolarized before the wave from the previous atom reaches it then the two electromagnetic waves will be able to constructively interfere. Since the electromagnetic wave travels at the speed of light in the medium (c/n), if the charged particle travels faster than c/n than the next atom will be polarized and depolarized before the 16 electromagnetic wave reaches it. The constructive interference produces an observable electromagnetic wave which is the Cerenkov radiation, as shown in Figure 1.9. When high energy charged particles of a shower pass through the atmosphere they produce Cerenkov radiation. Observing the Cerenkov radiation is one way of detecting air showers; even if the shower does not reach the ground, the Cerenkov photons might. So, Cerenkov radiation is a good way to detect air showers in the lower end of the energy spectrum. Nitrogen Fluorescence When an electron passes through a gas it excites atoms along the way, which then de-excite, emitting photons. This is the phenomena behind Cathode ray tubes, neon lighting, and the Aurora Borealis2. Nitrogen fluorescence is the same physical process. In the context of cosmic ray air showers it happens when a high energy secondary charged particle passes through the atmosphere exciting atmospheric atoms and molecules along the way. Since nitrogen is the most abundant element in the atmosphere, the phenomenon is called nitrogen fluorescence. The amount of nitrogen fluorescence is proportional to the number of charged particles in the air shower. If you can observe the amount of nitrogen fluorescence along the path of the shower then you can determine where the shower reached its maximum number of secondaries. This is useful because heavier primaries penetrate deeper into the atmosphere before reaching their shower maximum, so the mass of the primary cosmic ray can be estimated. 1.3 Non-Random Cosmic Rays It is generally believed that cosmic rays arrive at Earth randomly in time. However, there have been several experiments which show that there could be components of the cosmic ray spectrum that have non-random arrival times. 2 The Aurora Borealis is created when solar wind electrons enter the ionosphere. They emit most commonly in the oxygen spectra at high altitude, but nitrogen emission lines can be seen if the electrons penetrate deep enough into the atomosphere. 17 Several different patterns have been observed, but none have been consistent enough to draw any definitive conclusions about their cause. The following sections describe two different, but possibly related, non-random phenomena that have been observed. 1.3.1 Cosmic Ray Bursts During the analysis of a Cerenkov telescope experiment in 1980 Bhat et. al. [?] found an overall excess of events with time separations < 40 s. A histogram of the time difference between sequential showers required two exponential functions to fit; not one, as expected. One experiment, Badino et. al. [?], found a similar excess, while two other experiments, Smith et. al. [?] and Fegan et. al. [?], could not detect any such excess of showers < 40 s apart in the overall air shower arrival time spectrum. In 1983 Fegan and Smith each published papers observing a slightly different phenomena. They both observed short term increases in the rate of the cosmic ray flux; cosmic ray bursts. Smith [?] observed a burst which occurred on January 20, 1981 at the Manitoba Air Shower Array. The array was composed of three 1 m2 scintillator detectors in a triangle with 12 m sides. The array operated from October 1980 until April 1982, observing a total of roughly 150 000 showers with an estimated mean energy of 3 x 1015 eV. The average count rate being about 0.2 events/min. Beginning at 17:25 (local sidereal time) on January 20 a series of 32 showers were detected in a 5 minute interval. With an average event rate of 6.4 events/min (that's over 30 times the average count rate) the burst had a statistical probability of approximately 10~32. This was the only burst observed in the lifetime of the experiment. The Fegan [?] burst published in 1983, observed on February 25 1975, was observed at two stations simultaneously. The two stations were 250 km apart (in Dublin and Cork Ireland) and had relative timing accuracy of 1 ms. Each station consisted of four 1 m2 scintillation counters, positioned to produce a lower limit on shower energy of 1014 eV. The system was operational from January 1975 until December 1977, a total of 807 days. The event of February 25 lasted 20 seconds. There was a 1.7-fold increase in the rate over the 20 18 second period. It was the only event of its kind observed in the 807 days of operation and had a calculated probability of 2.7 x 10~5 of being a statistical fluctuation. The authors of both papers speculated on the possibility of these bursts being initiated by very high energy photons in a 7-ray burst (GRB). However, there is no definitive evidence that GRBs contain photons with enough energy to create an electromagnetic extensive air shower. GRBs are bursts of gamma-rays lasting anywhere from milliseconds to tens of minutes. The sources of GRBs are not yet known, as their arrival directions seem to be completely isotropic. For a review of present GRB knowledge see [?]. The biggest piece of evidence contradicting the GRB hypothesis was that the Vela satellite system did not detect a GRB at the time of either burst. The Vela satellite system was a U.S. military constellation of 4 satellites used to detect the 7 emissions from nuclear detonations so that they could monitor nuclear testing and activity around the world. Nobody knew that GRBs existed when the millitary launched the constellation. They discovered that all 4 satellites would simultaneously detect 7-rays for no apparent reason. The Vela satellite system had accidentally discovered GRBs. While the Vela satellites were only capable of detecting gamma-rays up to 1.5 MeV, one could expect a high energy gamma-ray burst to be accompanied by a low energy tail. More evidence suggesting that these cosmic ray bursts were not caused by GRBs came in 1998 from the Mitsuishi air shower array, Katayose et al [?]. The Mitsuishi air shower array is an array of 16 lm2 scintillation detectors and an underground muon detector located near Mitshuishi, Japan. The muon detector has four layers of proportional chambers, so muon direction can be determined. The array covers approximately 2000 m2 and has been in operation since 1961. 3.6 million events with estimated mean energy of 1.1 x 1015 eV were collected from January 1989 to October 1996 and were examined for periods of elevated count rates. Five such periods were found with probabilities less than 5 x 10~2. The elevation in count rate occurred for different lengths of time, between 20 minutes and 40 hours, for each period. The evidence against the theory that GRBs caused these bursts is that there 19 was no decrease in the muon component of the burst showers, when compared to the 'ordinary' showers. As discussed in Section 1.2 a significant decrease in the density of muons is expected for showers produced by photons. Recently, the LAAS (Large Area Air Shower) group in Japan analysed the arrival direction of roughly 1 million successive air showers [?] [?]. They seemed to see that the higher the rate of successive events the more the arrival directions correlated to the galactic plane. If there is a correlation pointing to the galactic plane, that would mean that the primaries causing the successive air showers could not have any charge. If they were charged, their paths would have been deflected by the galactic magnetic field. The cause of these rarely observed cosmic ray bursts is still unknown. Even the question of their existence remains debated. Have the observations been simply random chance? With the low probability of the Fegan event and the very low probability of the Smith event, it seems very unlikely that the events are random chance. However, the only way to find out for sure is to perform additional observations using as many experiments and techniques as possible. 1.3.2 Correlated Cosmic Rays Another non-random phenomenon in question is correlated cosmic ray air showers. The search for correlated cosmic ray showers is the primary objective of the ALTA experiment. A correlated air shower event could be created by the same processes that provide non-random events, or possibly a cosmic ray interaction that occurred far outside the Earth's atmosphere and produced a shower of particles hitting the atmosphere, as shown in Figure 1.10. We've already seen one possible example of a pair of correlated events - the burst observed by Fegan et al [?] was observed at two stations simultaneously, 250 km apart. Unfortunately, the Fegan et. al. experiment did not have the directional information to determine if the events were arriving from the same direction. The only directional information they had was the field of view of the detectors at the time of the event. In 1994 Carrel and Martin [?] published an observation of another possible correlated cosmic ray event. Carrel and Martin's detector consisted of four 20 Interaction creating correlated primaries Figure 1.10: Hypothetical event creating correlated showers sites, between 50 and 186 km apart, with 3 units of 3 stacked scintillators at each site. There was a 10 cm layer of lead between two of the scintillators to distinguish between muon and electron events. The potentially correlated event occurred between December 15th and December 22nd 1991, and consisted of a 4.8cr excess of quadruple electron hits over the expected random coincidences. A quadruple electron hit was defined as a signal in all four sites in the electron component of the detectors within 0.62 ms (0.62 ms is the light travel time for 186 km). The event was not observed in the muon component of the detectors. This implies that it was most likely caused by a photon primary. The probability of this excess being a statistical fluctuation was calculated to be less than 10~4. The Carrel and Martin detector was not able to determine the direction of a shower incident on a site. This information could have provided valuable insight into the nature of the observed excess, and would have been instrumental in determining if the showers at the different sites were actually correlated. Inspired by the Carrel and Martin observation, the LA AS group analysed 4 years of data for possible correlated showers [?]. Of the 2.6 million events analysed one pair of events produced a possible correlation. The two events 21 had a time difference of only 195 /j,s and occurred in stations 153 km apart. The arrival angles of the events matched within the angular accuracy of the arrays. The chance probability of this event was 0.16. Because the Crab Nebula was within the angular accuracy of the events, the LA AS group hypothesized that the event was caused by ultra-high energy gamma-rays from the Crab. Other physical processes that could create correlated showers include the disintegration of cosmic dust grains and a process known as the GZ effect. GZ Effect The GZ effect was first proposed by Gerasimova and Zatsepin [?], [?] in the 1950's. The effect was re-examined in a paper by A.A. Watson and G.A. Medina-Tanco in 1999 [?]. The GZ effect is the process of a heavy cosmic ray nucleus colliding with a solar photon and fragmenting, or photodistingrating, thereby producing fragments that could initiate extensive air showers on Earth. The most probable fragmentation is to a single nucleon and remainder of the nucleus. The fragments would be separated by the interplanetary magnetic field due to their difference in charge and mass. If both fragments hit the Earth, the air showers would be correlated in time and arrival angle. Figure 1.11 [?] shows some of the results of the Watson and Medina-Tanco work. In the figure the contour lines are the logarithm of the median separation of the air showers on Earth (in km), the shaded regions show the ratio of GZ events to unperturbed cosmic ray flux of Fe nuclei at 6 x 1017 eV, and the plot at the bottom shows a cross-section of the shaded regions with (j)=0 being the direction of the sun. It is clear from the figure that the highest flux of GZ events come from the direction of the sun with a flux ratio of 10~32. Unfortunately, these are also the most widely spaced showers with a median separation of around 1000 km. A median separation of about 100 km is found on the night side of the Earth, but here the flux ratio has gone down to 10~48. To make an estimate of the flux of GZ events Watson and Medina-Tanco used an incident Fe flux of 3.8 x 10~12m~2s~1sr~1. Flux ratios of 10~32 and 10~48 would produce fluxes 22 0 -3.0 I..........i......t................. ~^ -3.5 - /x a — n -^.j _______.__— -----_________ bo -5.0 r Ti ......t........i .....i...J I i I i 1=3 — 180 450 -120 -90 -60 -30 0 30 60 90 120 150 ISO Figure 1.11: Fraction of GZ events for Fe nuclei at 6 x 1017 eV in ecliptic coordinates with the direction of the sun at the center of the plot. of approximately 1500 and 40 GZ showers per year on 100 km2. These seem like measurable fluxes, but remember, to detect a GZ event the experiment must detect both showers that are around 100 to 1000 km apart. Another complication in the detection of the showers is the relative shower size. The most probable products of photodisintegration are a single nucleon and a nucleus with the remaining nucleons. So, if a 6 x 1017 eV Fe nucleus were to photodisintegrate into two fragments, the resulting showers would most likely carry 1/56 and 55/56 of the original energy, with the smaller shower being on the order of 1 x 1016 eV. For an array like the Pierre Auger Project (see Section 1.4), with an area of 3000 km2 and a detector spacing of 1.5 km, the smaller shower would probably not even be detected as a shower, since it would not be large enough to hit more than one of the detectors. Dust Grain Disintegration Cosmic dust grains have long been considered a remote candidate for the originators of the largest air showers. Even recent studies show that there is a small possibility that the observed showers above 1019 are relativistic dust grains [?]. Berezinskiy [?] showed that as relativistic dust grains propagate 23 through the CMB and solar photon fields they gain charge as electrons are stripped from their surface. The dust grain will eventually disintegrate due to the large electrostatic forces caused by the build-up of charge. Dust grains with Lorentz factors greater than 30 disintegrate "especially effectively" [?] on solar photons within the solar system. If a relativistic dust grain were to disintegrate in the solar photosphere it would cause a shower of smaller dust grains that could be the originator of correlated cosmic ray air showers. 1.4 Cosmic Ray Experiments In the century that physicists have been trying to unravel the cosmic ray mystery they have devised many different techniques to detect cosmic rays. The purpose of this section is to describe the basic techniques that are used today and present some of the experiments currently employing these techniques. There are two basic types of experiments; direct detection experiments and ground based experiments. Direct detection experiments are high altitude balloon and space craft experiments that depend on the primary cosmic ray interacting directly with their detector. These experiments can determine the energy and composition of the primary cosmic ray with high accuracy. The disadvantage of these experiments is their size limit (they need to fit on a space shuttle or high altitude balloon). Since the flux drops exponentially with increasing energy, this small size (and mass) prevents them from detecting a significant number of high energy cosmic rays. Balloon experiments like JACEE are exploring cosmic rays with energies up to 1016 eV [?]. Ground based experiments3 do not directly detect the primary cosmic ray, they detect some component of the air shower that was initiated by the primary. The three major components currently exploited are; Cerenkov radiation, nitrogen fluorescence, and the secondary particles of the air shower (see Section 1.2 for more about these processes). 31 use the term 'ground based' loosely to mean any experiment whose apparatus is located near the surface of the Earth. They could be underground or underwater. 24 Detectors that use Cerenkov radiation are called Cerenkov telescopes and Cerenkov arrays. STACEE [?] (Solar Tower Atmospheric Cerenkov Effect Experiment) is a Cerenkov array that uses a solar power testing facility in New Mexico. The solar power facility is an array of mirrors which can be controlled to focus to a point on top of a large tower nearby. A Cerenkov telescope like HEGRA [?] (High Energy Gamma-Ray Astronomy) images the Cerenkov light in a light collecting dish. Pictures of both experiments are shown in Figure 1.12. Figure 1.12: Photograph of the STACEE (left) and HEGRA (right) facilities On clear moonless nights Cerenkov detectors can point toward sources of interest and gather information about the cosmic rays they produce. Cerenkov detectors excel at detecting photon primaries in the GeV and TeV energy range. Experiments like HiRes (also known as Fly's Eye) look for streaks of nitrogen fluorescence in the night sky. The HiRes detector is basically a pair of hemispherical structures covered with mirrors that point outward, to the sky. Each mirror is monitored by several PMTs. The two 'eyes' of the HiRes detector allow for position resolution of the shower, as shown in figure 1.13. The biggest advantages of a detector like HiRes is the huge area monitored and the ability to produce a plot of the longitudinal development (number of particles in shower as a function of depth in atmosphere). A plot of the longitudinal development can be used to estimate the mass of the primary 25 Figure 1.13: Diagram of a high energy cosmic ray event at HiRes particle because heavier particles develop deeper in the atmosphere. Fly's Eye lays claim to the highest energy cosmic ray ever observed at 3 x 1020 eV [?]. A third type of ground based detector uses the distribution of secondary particles in the air shower to extrapolate primary particle information. In general, the larger the area covered by the footprint of the shower front, the larger the energy of the primary. By putting particle detectors in large arrays on and under the ground the size and density distribution of a shower front can be measured. With detectors placed underground, or under thick lead shields, the fraction of muons in the air shower can be determined. The muon fraction information can distinguish electromagnetic showers from hadronic showers. AGASA (Akeno Giant Air Shower Array) is currently the largest air shower array. The array covers an area of 100 km2 with 111 scintillator electromagnetic detectors and 27 shielded scintillator muon detectors. On December 3, 1993 they observed the second highest energy cosmic ray ever observed at 2 x 1020 eV [?]. The next generation in the evolution of the ground based cosmic ray detector is a hybrid detector called the Auger project [?]. The experiment is named in honour of Pierre Auger who discovered extensive air showers back in 1939 [?]. The Auger project will have two sites, one in the northern hemisphere (Utah) and one in the southern hemisphere (Argentina). Each site will have an area of 3000 km2 and contain an array of 1600 Cerenkov water tanks and a nitrogen fluorescence detector. The site in Argentina is currently under 26 construction. A cosmic ray experiment that is actively searching for correlated cosmic rays and non-random arrival time series is the Large Area Air Shower (LAAS) group in Japan [?]. The LAAS group consists of 9 stations of scintillator arrays. The stations vary primarily in the number of scintillation detectors, but most stations have about 5 detectors, (50x50x5 cm3) each. The estimated mean energy of observed air showers is (3-5) xlO14 eV. Most stations are roughly 100 - 200 km apart and equipped with GPS for relative timing. At the 2001 ICRC Villasenor et. al. [?] presented a plan for an international collaboration of cosmic ray detectors to search for time correlations and GRBs in cosmic ray air showers on an international scale. The plan includes the Chacaltaya (Bolivia), Cerro la Negra (Mexico), Auger (Argentina), and Milagro (USA) air shower arrays. The Cerro la Negra and Auger arrays are still under construction, while the Chacaltaya and Milagro arrays are currently in operation. While the LAAS group's objectives are similar to the ALTA project, this new proposal's objectives are complimentary to the objectives of the NALTA (North American Large Area Time Coincidence Array) [?] collaboration. The NALTA collaboration is a group of ALTA-type experiments spread throughout North America. The NALTA collaboration currently includes: ALTA (Alberta, Canada), CHICOS (California, USA), CROP (Nebraska, USA), SALTA (Colorado, USA), and WALTA (Washington, USA). Locations in the development and planning stages include: Boston (USA), Mexico City (Mexico), Montreal (Canada), Morelia (Mexico), Ottawa (Canada), Puebla (Mexico), Vancouver (Canada). 27 Chapter 2 ALTA Systems The purpose of this chapter is to discuss the apparatus of the ALTA experiment. Section 2.1 contains an overview of the system and its components, and the remainder of the chapter contains details of those components. 2.1 Overview The goal of ALTA is to look for correlations and non-random time series in cosmic ray air showers. To accomplish this broad goal the experiment must be flexible and adaptable. The ALTA experiment is composed of many self-contained sites, spread throughout Alberta. Each site contains three scintillation detectors placed in the corners of an equilateral triangle of 10 m per side, an electronics crate to determine coincidences and energy loss information, a GPS antenna and receiver, and a PC with a software program to operate the electronics and temporarily store data from that site. Figure 2.1 is a basic schematic of the components of an ALTA site. Much of ALTA's flexibility comes from the fact that each site operates independently. There are presently 6 operational sites. Figure 2.2 is a map of the sites in operation and those currently under construction. The sites are referred to by their name and/or site number, both of which are listed in the legend of Figure 2.2. Each site is capable of detecting an Extensive Air Shower (EAS) with a minimum energy of about 1014 eV, pointing to the arrival direction of that shower within roughly ±5°, and timing the event relative to other ALTA sites 28 Site Building Electronics ALTA 4. PC Figure 2.1: Basic schematic of ALTA system components within about 16 ns (see Chapter 3 for more details on the energy, angle, and time resolution). Events from each site are recorded on the local site PC until they are downloaded, every night, to the central database at the University of Alberta. Each event contains the information necessary to determine when the event occurred, the arrival angle of the event, and a rough estimate of the density of the shower front. 29 scal« / Echeiic 75 0 75 1S0 km L Figure 2.2: Map of ALTA sites currently in operation and under construction 30 The remainder of this section contains a synopsis of how the system attains all this information about an air shower. To simplify the explanation of how the arrival direction of the shower is determined in 3 dimensions, I'll use a 2-dimensional example. The 2-dimensional case is shown in Figure 2.3. If an air Shower Front Detector 1 Detector 2 Figure 2.3: Schematic of determining shower arrival direction in 2 dimensions shower hits a detector At seconds after hitting a detector d meters away, then the arrival angle can be calculated simply with the definition of the cosine. cosO = d This requires three assumptions: 1. the shower front is planar 2. the shower front is traveling at c 3. the shower front is perpendicular to the shower axis The electronics crate determines the relative arrival time of the shower front and the location of the detectors relative to each other is easily measured. In 3 dimensions the process is called triangulation, and 3 detectors are required. The details of the triangulation calculation are slightly more complex than the 2-dimensional case and are explained in Section 4.2.4. 31 Next, to determine the absolute arrival time of an event the GPS receiver and antenna are used. The GPS system is also used to determine the positions of the ALTA sites relative to each other. Details of the GPS system are discussed in Section 2.3. You may have noticed that there are two time scales in this experiment; the relative time of arrival of the shower front on the detector triangle, and the absolute time reference used to compare sites to each other. To keep these clear, the term local timing will be used when referring to the relative timing in the detector triangle, and global timing when referring to the GPS timing between different sites. The last major piece of information is the energy of the shower. To determine the shower energy with a ground based scintillation detector you need to determine the density of secondary particles as a function of distance from the shower axis. To get an estimate of how many particles passed through the detector (and hence an estimate of the particle density) the ALTA electronics crate determines the energy deposited in the scintillation detectors (see Section 3.1). But there are only three detectors at each site. This seriously limits the sample area for determining the shower's density distribution and means that all we can do is put a lower limit on the shower's energy. The lower limit of the shower energy is determined by finding the smallest energy that could reasonably fire all three detectors in the 10 m equilateral triangle using computer simulations. The energy limit for an ALTA detector is shown to be 1014 eV in Section 3.2. Correlations between sites by analysis of the GPS global times would indicate a much higher minimum energy or a physical process that generates correlated air showers. So, in summary, the ALTA experiment is composed of many independent cosmic ray air shower detectors, each capable of determining the shower's arrival time and direction. The data will be searched in an effort to find non-random phenomena in the arrival of cosmic rays at different sites. The rest of this chapter contains the details of each of the components making up an ALTA site. 32 2.2 The Detectors All of the ALTA detectors are composed of plastic scintillator viewed by a photomultiplier tube (PMT). A scintillator emits a small flash of light when a secondary cosmic ray passes through it and the PMT turns that flash of light into an electrical signal. The PMT signal is then sent to the electronics crate. The scintillator and PMT are both sensitive to their external environment so they need to be weather-proofed for operation on the roof of a building. To weather-proof the detectors we enclose them in water-tight, insulated wooden boxes that we call 'doghouses'. Inside each doghouse there is a temperature sensor, a temperature controller, and a strip of heater tape. The sensor turns the heater tape on when the temperature inside the doghouse drops below 0°C. The tape is turned off when the temperature rises above 10°C. This prevents the temperature in the doghouse from going below approximately -10°C. The detectors are also equipped with an LED (Light Emitting Diode) to make sure that the PMTs are still working properly. The LED is glued into the scintillator plastic and can be pulsed at intervals that are controlled by the user via the calibration module in the electronics crate. On the scale of most present day cosmic ray research ALTA is a fairly low cost experiment. We have benefitted greatly from the generosity of companies and other experiments. This has resulted in three different types of detector. All of the detectors installed thus far, except the one on the University of Alberta campus, are Bicron BC-408 plastic scintillator. The OPAL experiment (at CERN) has also donated 78 scintillator tiles and 48 photomultiplier tubes that will be used when all of the BC-408 scintillator has been used. Each of these detectors will be discussed in the following sections. 2.2.1 The Bicron Detectors The ALTA detectors made from the Bicron donation are sheets of plastic scintillator that are 60 cm x 60 cm x 1 cm (detection area = 0.36 m2). Figure 2.4 is a diagram of one of the Bicron detectors. Bicron's BC-408 plastic scintillator is designed for fast counting, large area 33 *-60 cm-►»«-50 cm-► Figure 2.4: Basic schematic of bicron detectors. detectors. With a signal rise time of 0.9 ns, and an attenuation length of 2.1 m [?], the BC-408 has timing and attenuation characteristics suitable for the experiment. The scintillators are connected to 2" Philips XP2262B photomul-tiplier tubes (PMT) via a triangular acrylic light guide. The XP2262B tubes are 12 stage tubes with a suggested maximum operating voltage of 2500 V. The tubes are operated between 1900 and 2100 V, a gain of about 10r. The emission spectra of the scintillator and the spectral sensitivity plot of the Philips PMT are shown in Figure 2.5 [?] [?]. You can see the emission spectra maxima matches the spectral sensitivity maxima at about 425 nm, the blue part of the spectrum. 36D 3S0 -100 420 «0 *SD JSC 500 £10 ™ 2°o 300 400 500 600 700 800 Wavelength, nm 1 !nm) Figure 2.5: (a) Emission spectra of Bicron BC-408 plastic scintillator and (b) spectral sensitivity of Philips XP2262B PMT. The efficiency of the Bicron detectors was examined with the setup shown in Figure 2.6. The trigger detectors used were made of 1 cm x 5 cm x 5 cm pieces of BC-408 scintillator coupled by optical grease to the face of a Philips 34 Trigger Detectors \ Triples Doubles Counter Counter Figure 2.6: Experimental setup to test the efficiency of Bicron detectors XP2262B PMT. The efficiency of the ALTA detector was determined by requiring a double coincidence between the trigger detectors and then comparing to see if a triple coincidence was also observed. The number of triples observed in the time that 100 doubles are observed is the efficiency that is shown in Figure 2.7. Percent Efficiency | | 90-95 | | 95-96 | | 97-98 | | 99-100 Figure 2.7: Typical results of the dependence of efficiency with position on the Bicron detectors The Bicron detectors are currently installed at O'Leary, MacDonald, Drayton Valley, Holy Trinity, and O'Brien high schools. Bicron detectors are planned for installation at high schools in Grand Prairie, and Thorhild. 35 2.2.2 The OPAL Detectors The OPAL detectors are composed of plastic scintillators with embedded wave-shifting fibers. Optical fibers are used to couple the wave-shifting fibers to the PMT. Figure 2.8 is a diagram of an OPAL scintillator. -*-93 cm -► Figure 2.8: Diagram of an OPAL detector. Detection area is 0.16 square meters Along with the scintillator tiles the OPAL experiment also donated 56 ElectronTubes 9902 PMTs. The 9902 series PMTs are 10 stage tubes with a maximum 1800 V recommended operating voltage. They are smaller than those used with the Bicron detectors, with a 1.5" diameter window. The OPAL PMTs were chosen by the OPAL collaboration to match the light output of the wave-shifting optical fibres. The fibers emit in the green part of the visible spectrum and the 9902 series PMTs are produced for green sensitivity. Figure 2.9 [?] shows a plot of the quantum efficiency of the PMT as a function of wavelength. While you can see the peak is not in the green part of the spectrum, the quantum efficiency is still around 15-20% at 500 nm. The OPAL detectors have roughly half the detection area (0.16 m2) of the Bicron detectors, so two OPAL detectors will be coupled to one PMT. Efficiency tests for the OPAL detectors have not yet been completed. 2.2.3 The U of A Detectors The site on the U of A campus has detectors that were donated by the National Research Council. Figure 2.10 is a diagram of the U of A detectors. The U of A scintillators are roughly 100 cm x 100 cm x 2 cm. They are diffusing scintillators with light attenuators placed on top of them. The inside 36 Figure 2.9: Plot of spectral sensitivity of Electrontubes 9902 PMT Light Tight Box Scintillator 5" RCA PMT Figure 2.10: Diagram of U of A detectors of the box is painted with reflecting paint. We do get a larger count rate and better energy loss resolution at the U of A site due to the larger size of the detector. 2.3 Global Positioning System The purpose of this section is to review the basics of how the Global Positioning System (GPS), Section 2.3.1, works and to describe how the ALTA project uses GPS, Section 2.3.2. GPS is a common enough technology that almost everyone knows its basic purpose - to tell you where you are on the Earth. Something that many people don't know about GPS is that it can also give you timing precision on the order of billionths of a second! It needs this sort of timing precision to determine 2.3.1 How does GPS work? 37 position accurately. GPS is composed of a constellation of 24 satellites, 5 ground stations, and millions of GPS receivers. The satellites and ground stations are operated by the United States Department of Defense (DoD), while the receivers are operated by whoever wants to purchase one. The satellites orbit the Earth once every 11 hours 58 minutes at an altitude of 20,200 km (well above the Earth's atmosphere) in a pattern such that there are always at least five satellites visible from every point on Earth. Each satellite has an atomic clock on board so that it can maintain very accurate timing. How do the satellites, ground stations, and receivers work together to tell you your location on the Earth and what time it is? The basic premise of GPS is triangulation - the same concept as ALTA's arrival angle calculation, just applied a little differently. If you know that the distance from you to one of the GPS satellites was 22,000 km, you would know that your position was somewhere on the surface of the sphere of radius 22,000 km that was centered on the GPS satellite. If you also know that you are 24,000 km away from a different satellite, you would have to be on that sphere too. In order for you to be on the surface of both of these spheres you would need to be somewhere on the circle that defined the intersection of those two spheres. Now, if you know the distance to just one more satellite you would narrow your position down to just two points on that circle. Generally, one of these points lies somewhere on, or near, the Earth's surface and the other lies somewhere very far away from the Earth's surface. Consumer GPS systems assume that you are near the Earth's surface, so you now know your position. This is all based on knowing the distance from you to one of the GPS satellites. How does GPS figure that out? For now, let's assume that radio signals always travel at c = 299, 792,458 m/s. Then if you could determine the time it took for a signal to travel from the satellite to your position, you would know the distance between the satellite and your position. To determine the travel time of the radio signal the GPS satellites transmit something called a pseudo-random signal. To explain how this works I'm going to use an analogy from a very good GPS website [?]. Say 38 the satellite and receiver both started singing the "Oh Canada" at exactly the same time. When the receiver gets the satellite's anthem it will be slightly delayed because it had to travel from the satellite to the receiver. The amount of delay will be the travel time from the satellite to the receiver. In the analogy, "Oh Canada" plays the part of the pseudo-random signal. The signal is called pseudo-random because it is very close to being random, but it is not absolutely random because it is reproduced by both the satellite and the receiver. So, the receiver just figures out how much delay there is between its pseudo-random signal and the satellite's pseudo-random signal, and BINGO you've got the travel time from satellite to receiver. All of this hinges on the fact that the receiver's signal starts at the same time as the satellite's signal. To ensure that the receiver and satellite are synchronized GPS simply requires one extra satellite. To explain how it works I'm going to use 2 dimensions, instead of 3, to make the explanation easier to convey. If your receiver tells you that you are 5 seconds away from satellite A and 7 seconds away from satellite B, as shown in Figure 2.11, you would think that you were at point x'. In the figure the grey lines are your actual distance from the satellite, while the black lines are the distances that your receiver calculates before corrections. But what if your receiver was 1 second fast? That would mean that you are actually only 4 seconds from satellite A and 6 seconds from satellite B, at point x. With a third satellite, satellite C, your receiver can figure out how far out of sync it is. If your receiver tells you that you are 9 seconds away from satellite C, that would put you at three places at once: x', y', and z' - not a very likely scenario. The grey lines are our actual distances from the satellites, which all join at one point. Since all the satellites are in sync (with their on board atomic clocks), there is only one timing error: your receiver's. That means that there must also be just one timing correction that will make all three circles intersect at one position, point x. The receiver calculates this correction and applies it to the measurements, putting you finally where you actually are, at point x. In the 2-dimensional case you needed three satellites to get timing and position, so in 3-dimensions you will need four satellites to 39 (a) (b) Figure 2.11: Determining location in two dimensions with uncertain timing using (a) two satellites (b) three satellites do the same thing. So that's the basics of how GPS works. Unfortunately, we have made some incorrect assumptions that simplify the matter quite considerably. The most obvious assumption being that the signal is not going to travel at c all the way from the satellite to the receiver, it must pass through the atmosphere. This is called propagation uncertainty. The most significant sources of propagation uncertainty are the ionosphere and the troposphere. The ionosphere is a layer of ionized gas 50 km to 500 km above the Earth. The ions alter the path and propagation speed of the electromagnetic signal. The troposphere is where most of our weather comes from, and so the density and moisture content of the air changes significantly with time. Changes in density and moisture content will change the index of refraction of the atmosphere. Both the ionosphere and troposphere are monitored and modeled to calculate these effects and then corrections are made in the signals via communication between the 5 ground stations and the satellites. The accuracy of the modeling is the limiting factor in the corrections. Another source of error in the signal propagation is multipath error. Mul-tipath error is caused by a GPS signal reflecting off of some structure on the 40 Earth's surface, like a building or a mountain. This would make the travel time of the signal not equal to the shortest path length from the satellite to the receiver. In the ALTA experiment multipath errors are minimized by installing all of our antennas on the roofs of buildings. There are many more sources of uncertainty, each varying in magnitude and complexity, some being easier to fix than others. For more information I will refer the curious reader to [?], and an interesting paper explaining the need to account for both special and general relativity in GPS technology [?]. 2.3.2 What does ALTA do with GPS? ALTA uses GPS to determine each site's longitude, latitude, and altitude, and to determine each event's arrival time, or time tag. Since the time tag is generated in the electronics crate it will be discussed in Section 2.4. This section contains an outline of what the GPS system needs to send in order for the electronics crate to generate the time tag. Figure 2.12 is a schematic of the GPS system at an ALTA site. GPS Antenna (mounted on site roof) Coaxial Cable (Max. 60 ft) GPS Receiver Data Link (to serial port) Power Supply PC 1 PPS to Time Tag Module Figure 2.12: Schematic of GPS system at an ALTA site The antennae are Micropulse (now a division of Andrew Corp.) models 19300 and 2640NW. All of the sites currently in operation have model 19300 antennae, while all new sites will have model 2640NW antennae. The change in antennae model was forced by lack of supply. The receivers are all Motorola UT+ Oncore receivers. The receiver sends a pulse every second to the time tag module in the 41 electronics crate. This pulse, called the PPS (pulse per second) pulse, is one of the pieces of information used to time tag an event. The receiver also communicates with the computer via a bi-directional data link to the serial port. The computer can run one of two programs to communicate with the receiver; the ALTA program, or a program called TAC32 (Totally Accurate Clock, produced by CNS Systems Inc. [?]). TAC32 is used primarily to initialize the reference location of the antenna. TAC32 is operated in navigation mode for an extended period of time (on the order of days) to determine the location of the ALTA site. The TAC32 program is also used to initialize some receiver parameters and to diagnose suspected problems in the GPS system. After the TAC32 program has been stopped the ALTA program can initialize the receiver to run in precision timing mode. In precision timing mode all of the satellites are used to maximize timing accuracy. No satellites are 'wasted' on position measurements, since the position is already known. The ALTA program then reads the date, time, and something called the sawtooth correction from the receiver once every second. The sawtooth correction is a timing correction for the PPS pulse. The sawtooth correction ranges from -50 ns to +50 ns since the receiver sends the PPS on the edge of an internal oscillator that is not synchronized with the satellites. During the summer of 2001 GPS tests were completed to determine the resolution of the GPS timing system. A resolution of 16 ns is achieved when comparing two sites that are observing the same satellites (at least ~4). This same satellite approximation is valid for sites up to about 2000 km apart. These tests are discussed in detail in [?]. 2.4 The Electronics Crate This section contains a description of the major components and functions of the ALTA electronics crate. The electronics crate contains seven modules, plus high and low voltage power supplies. Each module has a specific function that will be discussed in detail in this chapter. All the modules were designed 42 and constructed in the physics electronics shop at the U of A. The crate housing is a 6U Eurocrate (6U refers to the height of the crate). Figure 2.13 is a picture of an ALTA electronics crate. Figure 2.14 is a schematic of the crate and its components. Figure 2.13: Photograph of ALTA electronics crate PC- o o ~ cd o_ čď~ to LEDs S O O 0) If CD a O 3 backplane o o c_ O CD oj CD n CD from PMTs: o 3 o. 9L c o cď" 1000 MeV for protons and > 100 MeV for muons. Other heavy subatomic particles have minimum ionization thresholds in the same order of magnitude as protons and 57 muons. The important thing about MIPs is that they lose about the same amount of energy per amount of material that they pass through (^f )■ For MIPs ~ 2 MeV/(g/cm2) (the unit g/cm2 is a measure of the amount of material a particle passes through, derived from density x length). So, for example, a MIP passing through 1 cm of material with a density of 1 g/cm3 would lose about 2 MeV. It is important to note that the amount of energy lost is not dependent on the energy of the MIP. Considering the ALTA detectors, if only one particle passes through the energy deposited will depend on the path length of the particle in the detector. This means that particles that arrive vertically will deposit the least energy. Since a majority of cosmic ray showers detected are roughly vertical, the majority of events will have pulses which correspond to the energy deposited by a MIP traveling through the vertical thickness of the detectors. The detectors (except for the U of A detectors) are 1 cm thick and have a density of approximately 1 g/cm3, so most events will deposit 2 MeV in the detector, producing ~ 20,000 photons1. A typical MIP peak in an ADC histogram is shown in Figure 3.1, along with the ADC pedestal, which is discussed below. The horizontal axis of this histogram is the ADC value of the channel, which is of course proportional to the energy deposited in the detector. Figure 3.1: A typical MIP peak and ADC pedestal. To determine the amount of energy deposited at any point other than the MIP peak, the ADC value corresponding to zero energy deposited must be known. Then, a linear correlation between energy loss and ADC value can 1 While 20,000 photons are produced, only about 25 photons are actually converted to photo-electrons at the PMT face. 58 be derived. This is called energy loss calibration. To determine the ADC value that corresponds to zero energy (called the ADC pedestal) we simply run the analog module with no input in one of the channels. The detectors are run in normal operating mode (triple coincidence) to get a MIP peak. Figure 3.1 shows an ADC pedestal along with the corresponding MIP peak for that channel. A user would not see the ADC pedestal in normal operation since it is cut out by the triple coincidence requirement. To get the MIP peak and ADC pedestal on the same histogram the detectors were run in normal operating mode and then the input for channel 0 (the channel displayed in the histogram) was disconnected and the input was disabled in the 'Coincidence' pop-up window. The largest adjustable factor in the energy loss calibration is the PMT voltage. Changing the voltage changes the gain (number of electrons produced at the anode per incident photon) of the PMT. Changing the gain changes the proportionality constant between light produced in the scintillator and size of PMT pulse, which therefore changes the proportionality between energy loss and ADC value. All PMTs have slightly different gains, even if they are the same model from the same manufacturer. So, the gain of the PMT is a very important part of the energy loss calibration. When setting the gain of the PMT you want to be sure to set it so that you can see as much of your energy loss spectrum as possible. If your gain is too low then events will fall into the pedestal, and if your gain is too high events will overflow the ADC. The gain of the ALTA PMTs is set to the voltage that places the MIP peak at 100 ADC counts above the pedestal. Since each channel has a different pedestal, each MIP peak should have a different value. However, the linear relationship between energy and ADC count should be the same with the exception of an additive constant (equal to the difference in the ADC pedestals). As you can see in Figure 3.1 the MIP peak is very broad. This makes the position of the MIP peak the major source of uncertainty in the energy/ADC linearization. Typical pedestals and MIP peaks are around 30 and 130 ADC 59 counts, respectively, so a typical energy loss calibration equation would be [Energy Loss (in MeV)} = 0.02[(ADC Value)] - 0.6 (3.1) A conservative estimate of the uncertainty in the MIP peak determination would be about 30 ADC counts, the uncertainty in determining the ADC pedestal is then negligible. A 30 count uncertainty in the MIP peak would result in a 30% uncertainty in the slope of the energy loss calibration. But what does all this tell us about the density of particles in the shower front? After all, that is why the energy loss calibration is being done. A very rough approximation of the number of particles can be easily attained by simply dividing the energy calculated from Equation 3.1 by 2 MeV. This approximation is very rough for several reasons. Firstly, the ADC distribution is very wide. This is due to the statistical fluctuations in the number of photo-electrons created in the PMT. Secondly, the ADC distribution is also asymmetrical. The asymmetry is due to secondaries arriving at non-vertical angles - therefore having a path length longer than 1 cm in the detector. Figure 3.2 shows the results of a CORSIKA [?] (see Section 3.2 for a brief description of CORSIKA) study of the incident angles of secondary particles as they hit the detector level; using vertical, 1014 eV, proton primaries. The figure shows that the incident angle of most of the secondaries is confined to a roughly 10° of the shower axis. If primaries with zenith angles up to 30deg are considered, then the path length of the secondaries will be up to 1.3 times as long. This would produce a tail on the high energy side of the ADC distribution, making an asymmetry on the order of 1.3 x MIP peak in the high energy direction. This asymmetry can be seen in Figure 3.1. So, there's a calibration equation that is uncertain to about 30%, an ADC distribution whose width is larger than the average energy deposited by one particle, and an asymmetry in the ADC distribution on the order of 30%. All these uncertainties combined make the calculation of the number of particles passing through the detector a very rough approximation. What the ADC information will tell us is the order of magnitude of the density of particles passing through the detector. An energy loss near 2 MeV means that roughly 60 ffi 70000 — 50000 — 40000 — 30000 — Incident Angle at Detector Figure 3.2: Angle of arrival of secondary particles from 100 vertical showers one particle passed through, while an energy loss of roughly 20 MeV means that roughly 10 particles passed through the detector. It is also important to look at the energy of each channel in an event. If a large shower hit the site, then a large energy loss would be expected in every channel. If a small shower hit the detector and, for example, one particle happened to stop in one of the detectors is very high when particles stop in a detector), then that would create a large energy loss in one channel with small energy loss in the others. 3.2 Primary Energy The primary energy calibration is the process of determining the energy of the primary cosmic ray by sampling the density distribution of the secondary particles. To figure out the density of particles that would hit the ALTA detectors for different shower energies we have used the Monte Carlo air shower simulation program CORSIKA [?] (version 6.016 using the QGSJET hadronic interaction model). The goal of this simulation is to determine the minimum energy shower that our sites can reasonably detect. The simulation consisted of 10 runs of 100 showers each. The showers had proton primaries with energies ranging from 1 x 1014 eV to 1 x 1015 eV in 61 Angle Nent = 296369 Mean = 85.79 RMS = 5.258 10 eV increments. The showers were all dropped vertically directly above the detector. The showers were sampled at 700 m above sea level, the altitude of Edmonton. The first interaction altitude of each shower was determined by CORSIKA. CORSIKA gives the user the ability to set the kinetic energy cuts for hadrons, muons, electrons, and photons. As discussed in the previous section our secondary energy loss distribution is well defined by a MIP peak near the low end of the spectrum with a long tail following at the high end. I've defined the energy cuts for the CORSIKA simulations to be the MIP energy (2 MeV) of the corresponding particle. For protons MIP energy is greater than 1000 MeV, and for muons MIP energy is greater than 100 MeV [?], so the energy cuts used for hadrons and muons were set at 1000 and 100 MeV, respectively. The energy cut for electrons and photons is slightly more complicated than for hadrons and muons. To determine the energy cut for electrons I assumed that the electrons were highly relativistic. Low energy electrons incident on the scintillator can deposit 2 MeV, or more, in the detector since the ^ for collision loss increases at low energy, but they are not likely to be part of the shower front in a cosmic ray air shower. So, on the assumption that we only want to see the shower front, I can use the exponential radiation loss relationship: E = E0e-x/xo where E is the energy of the electron after passing through x thickness of material of radiation length xq, and E0 was the initial energy of the electron. Using the above formula, for an electron to deposit 2 MeV into 1 g/cm2 of scintillator (x0 = 43 ll GPS time (hours, minutes, seconds) 12 GPS sawtooth correction 13 number of b-latch values in the second, (i) 14 number of analog values in the second, (J) 15 number of coincidence values in the second, (k) 16 the a-latch value of the second 17^20 temperature readings (detO, detl, det2, crate) 21^21+i b-latch values of the second from Time Tag Board (21+»)->(21+»)+j analog values of the second from Analog Board (21+i+j)^(21+i+j)+A; coincidence values of the second Coincidence Board Table 4.1: Word structure of ALTA binary data. (1 word = 32 bits) by an event number which differentiates multiple events in a single second. Data will be retrieved from the database and calibration corrections applied during extraction. After the extraction a summary routine is run on the data to convert the data into a usable format. The summary routine converts A and B latch values to fractions of seconds, and converts TDC information to arrival angle in horizon, celestial, and galactic coordinate systems. The code for the summary routine is given in Appendix A. 4.2 Coordinate Systems In order to compare the data from one site to another we must define some meaningful coordinate systems. The first is the site coordinate system, how the detectors are oriented at the site. The next is the coordinate system to relate site to site, and the final step is the coordinate systems used to point in some direction in the sky and universe. 4.2.1 Site Coordinates The positions of the 3 detectors at a site must be clearly defined in order to derive any useful information from the local timing. As shown in Figure 75 Data Block Contents Raw Data sawtooth B-A frequency temperature [4] TDC[3] ADC [3] Timing Data TTAGflag DataType counter CalBits sawtooth temperature [3] ALatch BLatchCnt ADCCount TDCCount Calibration Data ADCPed[3] MIPpeak[3] SignalDelay[3] Settings Logfile StatusWord CoinLevel Threshold [3] HV[3] CalibOffset[3] Calib Voltage Coin(ADC-DAC)[3] HVScale[3] HV(ADC-DAC)[3] Static Input Latitude Longitude (A9) Altitude GPSOffset SiteX[3] SiteY[3] DAQVersion HVSupply PMTType ScintType CrateNumber BoardNumber[7] IOBoardNumber Dynamic Input StatusWord RunDescription Table 4.2: Block structure of ALTA database 4.1 the detector positions are described by their x and y coordinates in the frame with the GPS antenna at the origin, the y-axis pointing to celestial (or geographic) north and the x-axis pointing East. The GPS antennae are about 2 m above the plane of the detectors; this small correction is ignored. The most challenging part of determining the detector positions in this coordinate system is determining what direction is north. It seems like a very simple problem and to 4 or 5 degrees of accuracy it is. Unfortunately getting much more accuracy than that is a more difficult problem. A magnetic compass measurement depends on two factors; the local magnetic field, and the conversion from magnetic to geographic north. Since the sites are on top of buildings, the local magnetic field can vary by tens of degrees depending on your position on the roof. A measurement with the GPS system is not 76 y (North) □ □ Detector 1 Detector 0 (Xo. M>) (0,0) x (East) GPS 1 Antenna □ Detector 2 (x2, y2) Figure 4.1: Coordinate system used to describe the positions of the detectors very accurate because the uncertainty in our GPS position is on the order of meters, while the baseline to compare two measurements is restricted to the roof of the building on the order of tens of meters. So there's also a significant uncertainty in this measurement. The technique we have decided to use to determine the direction of geographic north is a solar compass. At local noon1 (half way between sunrise and sunset) the sun will be directly south. The shadow of a vertical pole or plumb line will then point toward geographic north at local noon. The disadvantage of this measurement is the short baseline of the shadow. This can be overcome by making the pole or plumb line very long or by marking the location of the shadow near sunrise and then again near sunset - giving you an East-West baseline rather than a north-south one. To use this second method correctly you must be sure to use the shadow from the same point on the pole each time and be sure that the two measurements are taken at equal lengths of time before and after local noon. 1The website http://aa.usno.navy.mil/data/docs/RS_OneDay.html will calculate local noon to the minute for any latitude and longitude at a site 77 Using the solar compass technique we can determine the direction of geographic north to within 2 degrees. The (x,y) positions of the detectors are determined to within 5 cm. 4.2.2 The Earth's Coordinate System In order to compare one site to another we obviously need to determine their relative positions. We use the Earth's coordinate system of longitude, p, latitude, A, and altitude to describe the sites' positions relative to each other. This seems easy enough, but there are some details that I would like to be sure are clear. Geodetics is the science of defining the shape of the Earth. GPS uses a convention known as the World Geodetic System - 1984 (WGS84) to define the basic shape of the planet. WGS84 defines the Earth as a spheroid, an ellipse rotated about its minor axis. Figure 4.2 is a schematic of the Earth with the relavent WGS84 parameters. Table 4.3 is an summary of the values of these parameters. You may noticed that Figure 4.2 also includes two angles Ac and A9. These angles are the geocentric and geographic latitudes, respectively. The geocentric latitude (Ac) is the latitude we normally think of when we think latitude - the angle between our position, the center of mass of the Earth, and the equatorial spheroid of Earth Figure 4.2: WGS84 parameter definitions. 78 Parameter Description Value GMe Earth Mass 3.986004418 x 1014m3/s w Earth Rotation Rate 7.292115 x 10-W/s a Equatorial Radius 6378137m f Flattening, f=(a-b)/a 1/298.257223560 Table 4.3: WGS84 parameter values plane. The geographic latitude (A9) is the angle between the line perpendicular to the Earth's surface at our position, and the equatorial plane. Why does geographic latitude exist? Because that is all that we can measure on the surface of the Earth. Think about it like this: If the Earth were a ball of water spinning in space with no currents or waves in the water (not too far from the truth), then the surface of the water would define a gravitational equipotential surface. If we are in an unknown location on the Earth and want to know our position we could drop a plum line to define vertical and then measure the angle between vertical and the north star. Which latitude would this give us? Well, it depends on where the plum line would point. Would it point to the center of mass of the Earth, Ac, or would it point to the focus of the spheroid, A9? The plum line would point to the focus of spheroid because, as we all know, field lines are always perpendicular to equipotentials, and so the plum line would give us geographic latitude. Geographic latitude is what appears on maps, and more importantly, is what GPS units display. We are going to use the site latitude to calculate the distance between two sites so we will need geocentric latitude. Thankfully the conversion is simple, and is as follows: tan\c = —tan\„ a2 The latitude quoted in the database is simply the geographic latitude determined by the GPS system. We convert to geocentric latitude whenever it is necessary in the analysis routines. Longitude is defined as usual, with zero longitude at Greenwich and positive defined to the east (therefore pEdmonton — —113°). Altitude is defined as the height above the surface of the spheroid. This definition of altitude is different 79 than altitude above mean sea level. The difference between the two definitions is usually on the order of 10's of meters and varies from place to place on the globe. 4.2.3 Astronomical Coordinate Systems Astronomers have many different coordinate systems that are convenient for describing and analysing various phenomena. There are three astronomical coordinate systems that lend well to the ALTA project which are descibed in this section. Each coordinate system is defined by a fundamental plane and a fundamental direction in that plane. For example, in the Earth's coordinate system the fundamental plane is the equatorial plane and the fundamental direction is the line from the centre of the Earth to the Greenwich meridian in the fundamental plane. The fundamental direction always defines the zero of the "around" angle, and the fundamental plane defines the zero of the "up/down" angle. An astronomical coordinate system does not define a distance to the astronomical object, it only gives the direction from the origin of the system to the object. So having said that, here are the astronomical coordinate systems that ALTA uses. Horizon Coordinate System A site's local timing allows us to point to the direction in the sky that a shower came from. This direction is most easily described in the horizon coordinate system. The horizon coordinate system's fundamental plane is the plane of the horizon that an observer on Earth would see if they spun around 360° (while standing vertically), and the fundamental direction is from the observer toward geographic north. The two angles of the horizon coordinate system are called altitude and azimuth. Figure 4.3, cf. [?], shows the coordinate system where X is the direction the shower came from, Z is the observers zenith (the point directly overhead), (j) is the azimuth angle, and 9 is the altitude angle. Some texts use the zenith angle instead of the altitude angle. The zenith angle is the angle between X and the observer's zenith (ie. 90° — 9) This coordinate system is useful because it allows us to analyse the data 80 Observer's Zenith Observer's Horizon Plane Figure 4.3: Horizon coordinate system from a local perspective. For example, most showers we observe will be close to vertical, but we know the cosmic ray flux is isotropic, so why don't we see showers from all over the sky? The answer is that showers at lower altitude angles will have more atmosphere to penetrate, and so we will not observe as many showers. The disadvantage of the horizon coordinate system is that it rotates with the Earth, it is an "Earth fixed" system. To see where in the universe an event pointed we need to know the horizon angles (altitude and azimuth) as well as the latitude, longitude, and time of the event. The next two coordinate systems do not have that drawback. Celestial Coordinate System The celestial (also known as the equatorial) coordinate system is Earth centered (origin at the center of the Earth), but not Earth fixed (does not rotate with the Earth). The fundamental plane is the equatorial plane of the Earth, and the fundamental direction is from the centre of the Earth to vernal equinox (also called the first point of Aries). A point in the celestial coordinate system is defined by the angles called right ascension and declination (RA, Dec) or (a,6). Figure 4.4 shows the celestial coordinate system where a is the right ascension angle, and 5 is the declination angle. 81 North Star Earth's Equitorial Plane Figure 4.4: Celestial coordinate system This is the most common coordinate system used to describe the location of stars. The celestial coordinate system will be the most commonly used system when looking for correlated cosmic ray pheneomena. The local timing information will be coverted to (RA, Dec) for comparison to other sites. Galactic Coordinate System The galactic coordinate system is often used when searching for phenomena originating in our galaxy. The two angles defining direction are galactic longitude, /, and galactic latitude, b. The fundamental plane is the plane of the galaxy, and the fundamental line is the line from our sun to the center of the galaxy, as shown in Figure 4.5. Galactic Plane Figure 4.5: Galactic coordinate system Table 4.4 is a summary of the astronomical coordinate systems used. 82 System Fund. Plane Fund. Line "Around" "Up/Down" Horizon observer's horizon observer to north azimuth (a) altitude (A) Celestial Earth's equa- Earth to first right ascen- declination torial plane point of Aries sion (a) Galactic galactic plane sun to galac- galactic longi- galactic lati- tic center tude (I) tude (b) Table 4.4: Summary of astronomical coordinate systems 4.2.4 Converting Local Timing To Horizon Converting the local timing (relative arrival time of the shower front in the scintillators) information to horizon coordinates is an important step in the handling of the ALTA data. The process is called triangulation. In the conversion it is assumed that; 1) the shower front is planar, 2) the shower front is perpendicular to the shower axis, 3) the shower front is travelling at the speed of light in vaccum, c. In order to be explain how the conversion is done I will first review some basic geometry. The equation of any plane which contains a point Po(xQ,y0, zq) is defined by: A(x - xQ) + B(y - yQ) + C(z - z0) = 0 A vector normal to that plane is then defined as ft = (A,B,C). The distance from some point pt(xi, yt, zi) to the plane can then be defined by: _ A(xj - xp) + B(yj - y0) + C(zj - z0) 1 1^1 where the sign of A{x{ — xq) + B(yi — y0) + C(zt — zq) determines if the point is above or below the plane. We will use these concepts in the following derivation of the conversion from the local timing to the azimuth and altitude angles. Using the site coordinate system defined in Section 4.2.1 label the positions of detectors 0,1, and 2 as p0, pi, p2: Po = (xQ,yQ,0) Pi = (zi, 2/i,0) 83 P2 = (^2,2/2,0) Now, imagine the shower plane as it is incident on detector 0. Let's call this plane II. II is therefore defined as: A(x - x0) + B(y - y0) + C(z) = 0 where A, B and C are the direction numbers of the plane. Since the plane is propagating at the speed of light (c), we can define c = (A,B,C) (note that this just makes A, B, and C velocities). Therefore distance from a point Xi,yi,Zi to II is: A(xi - x0) + B(yt - y0) + C(zi) di Therefore, d0 = 0 (4.1) d± = AiyXl ~ X°) + B(yVl ~ V^ (4 2) d2 = M^-xQ) + B(y2-yQ) (43) Solving for A and B using Equation 4.2 and Equation 4.3: d2 - yi -yo _ \ y2-yo (x2-xo) - (xi -xo)^^ d2 - rii^fi B = c_-_ X1~X0_ (A 5) (2/2-2/o)-(2/i-2/o)f^ 1 ' ^ Using the time signals of the detectors to, t\, and t2, and the approximation that the shower is traveling at the speed of light, the distance from the plane to the detectors will be: di = c(ti-t0) i = 0,1,2 (4.6) Substituting these distances into Equation 4.4 and Equation 4.5 will give the direction numbers of the shower in terms of the time signals of the detectors and the positions of the detectors. The direction numbers A and B can also be represented in horizon coordinates, azimuth ((f)) and altitude (9), by the equations: A = c cos 9 sin cj) 84 B = c cos 9 cos (j) To solve for the azimuth angle, take the fraction A/B: tan (j) \ (4.7) B Substitude Equations 4.4 and 4.5 for A and B to get (f) in terms of time and detector position. Notice that the arc tangent function will result in azimuth angles in the range (—7r/2,7r/2), while the azimuth angle requires a range of (0, 27r) to cover the whole sky. This is because taking the fraction A/B creates an ambiguity, note A/B = (—A)/(—B). To resolve this ambiguity we simply note the sequence of the coincidence and use logical arguments to resolve which quadrant the shower came from. This allows for the conversion of the range (—7r/2,7r/2) to the range (0, 2ir). To solve for the altitude angle, solve A2 + B2: Notice that if the square root is always assumed to be positive, then the altitude angle will be given from 0 to 7r/2, as desired. This ambiguity in the square root represents the fact that there is no way to tell if the shower came from above or below the detector. It is assumed that the shower comes from above. This solution uses a simple linear system of two equations and two unknowns. When solving a system of linear equations the condition number of the system should be checked. The condition number will indicate whether the system is sensitive to small perturbations. The condition number is defined as the norm of the matrix (a 2 x 2 matrix in this system) multiplied by the norm of the inverse of the matrix. In this system the matrix is defined by the Xj and yi values, so the condition number depends only on the positions of the detectors. The triangular positioning of the detectors optimizes the condition number. (4.8) 85 4.2.5 Converting Horizon to Celestial To convert from the horizon coordinate system to the celestial coordinate system we need to know the geographic latitude, A9, and longitude, p, of the detector array as well as the UTC (Coordinated Universal Time) and date of the event. To calculate the declination, 6, use Equation 4.9, from [?]: sin S = sin 9 sin A9 + cos 9 cos A9 cos 4> (4.9) Calculating the right ascension, a is only slightly more complex since we must first calculate the hour angle, HA, of the shower. The hour angle is the angular distance from the shower axis to the detector's meridian. sin 9 — sin A„ sin 8 cos HA = cos A9 cos 5 To convert from hour angle to right ascension use Equation 4.10: a = LST - HA (4.10) Where the hour angle is measured in hours, minutes, and seconds, and west is defined as the positive angular direction. LST is called Local Sidereal Time. Sidereal time is the time referenced from the stars, as opposed to universal time which uses the sun as a reference. There is a series of time conversions to go from UTC to LST which are detailed in Reference [?]. 4.2.6 Converting Celestial to Galactic The equations for converting celestial coordinates to galactic coordinates are [?1 b = sin-1{cos(6)cos(27A°)cos(a - 192.25°) + sin(6)sin(27A°)} I = tan-' { °!niS)r gW^27-4°) \ + 33° cos(5)sin(a - 192.25°)cos(27.4°) where a is right ascension and S is declination 86 4.3 Analysis Routines There are several different analysis routines, each looking for different phenomena. The routines are written in C. The important parts of the code are written in Appendix A. Here I will describe the steps of the routines. 4.3.1 Correlation Routine The correlation routine, called correlation.c, searches for correlations in air showers between ALTA sites. When a correlation is found it could mean that correlated cosmic showers have been observed or that a very large shower covering several detectors has been observed. Figure 4.6 shows a schematic of a pair of hypothetical, perfectly correlated, cosmic ray air showers. Figure 4.6: Hypothetical, perfectly correlated, air shower events The correlation routine has two basic functions: to search for strictly correlated and very high energy air showers, and to search for angular correlations between air showers over large time intervals. A pair of strictly correlated air showers would be like those shown in Figure 4.6, while a very high energy air shower would be an air shower that was large enough to trigger more than one site. To differentiate these two possibilities we will need to look at the 87 particle density information from both sites and consider the distance between the sites. This can be done on an event by event basis. Searching for angular correlations over large time intervals is motivated by the possibility of a source that produces uncharged cosmic rays that would arrive at the Earth close in time, but not stricly correlated as defined by Figure 4.6. If the production or acceleration of these cosmic rays were to fluctuate with time a fluctuation in the total number of showers arriving from the direction of the source could potentially be observed. The correlation routine has 3 basic steps, or cuts; 1. Determine if At is less than a specified time 2. Determine if the difference between the two arrival angles is less than a specified angle, e 3. Determine if cAt ~ dcos(/3) (only used to search for strictly correlated and very high energy air showers) To accomplish the first of the basic functions the first cut requires that At < l.lr, where tau is the light travel time between the two sites being compared. The extra 10% (the multiplication by 1.1) is given to account for potential experimental error and shower fluctuations. Pairs of showers that pass the first cut progress to the second cut. To pass the second cut, the angle between the two shower axes must be less than 10° (that's roughly 2 times the uncertainty in the arrival angles). For the third cut the cAt — dcos(/3) is required to be less than 0.2d. These cuts have been chosen to be loose cuts, since there will be few events that pass all three cuts. The events that do pass all of the cuts can then be examined closely, one at a time, to determine if they are a pair correlated showers or a single very high energy shower. A rough estimate of the number of events that are expected to pass all three triggers can be attained by estimating the event rate for showers large enough to trigger two sites and adding the estimated event rate for correlated phenomena. The set of operational and in-planning sites: Ross Sheppard, MacDonald, Odysseum, and U of A cover an area of approximately 10 km2 88 (Figure 2.2), so approximately 10 showers above the ankle (~ 10185 eV) can be expected to be incident on this area each year (Figure 1.2). Placing more sites within 5 to 10 km of each other would increase the expected rate. Placing sites south-east of U of A, connecting the O'Brien, W.P. Wagner, and Harry Ainlay group (Figure 2.2) with the U of A group, would be an efficient way of increasing effective detection area for high energy events. Using the Carrel [?] and Fegan [?] observations versus run time as very rough approximations an event rate of around 0.5 per year can be estimated. The second basic function of the correlation routine is accomplished by setting the At cut to be less than the desired time interval, on the order of hours to days, and then applying the second cut. This produces a list of showers that arrived within 10°, and within the specified time interval, in both sites being examined. This list can then be compared to other site pairs. Correlation Routine Details The following contains the details of how each cut is executed using the data given by the ALTA data acquisition system. Determining r To determine r (the light travel time between sites) the straight line distance between two sites, d, must be known. To determine d use the longitude, latitude, and altitude of the site. It is easiest to find the distance between two points in a Cartesian coordinate system, so convert to a right handed Cartesian system with the origin at centre of Earth, z-axis toward north pole, and y-axis toward Greenwich. Writing x, y, and z in terms of longitude,p, latitude,Ac, and altitude: where R(XC) = Radius of Spheroid Earth at Ac + Altitude. The radius of the WGS84 spheroid at any latitude can be calculated from the equation of an x y : R(\c)cos(\c) sin(p) R(Xc)cos(Xc)cos(p) R(\c)sin(\c) (4.11) (4.12) (4.13) 89 ellipse: 1 _ cos2 (Ac) sin2 (Ac) r2 a2 62 Then simply calculate the distance (of) between points 1 and 2 with the Pythagorean Theorem: d = \J(x2 - xi)2 + (y2 - 2/i)2 + (z2 - zi)2 Truncation errors in cos and sin are not a factor for distances greater than 1 meter if you use double values for Ac and p in the code. With the straight line distance between the sites known, r = dc, where c=299792458 m/s. Determining e The next cut in the analysis is the relative arrival angles of the showers. To calculate the angle between the shower axes (e), the dot product is the simplest method. To take the dot product, the celestial coordinates must be projected onto a unit sphere in right handed Cartesian coordinates. In this projection y is pointing toward a=0, z pointing to 5=90 degrees: %i = cos(Si)sin(ai) (4-14) yi = cos(6i)cos(ai) (4-15) Zi = sin(Si) (4.16) So, using the dot product, the angle between shower axes 1 and 2, e, is: cos(e) = (xix2 + y±y2 + z±z2); e can now be compared to the desired cut. Determining dcos(/3) The final cut in the analysis is comparing the correlated shower front with the global timing difference between showers, the cAt = dcos(/3) test. dcos(/3) is basically the same as the 2 dimensional triangulation in 2.1. The only complication is that there are two coordinate systems; the positions of the sites in latitude and longitude, and the shower axes in celestial coordinates. 90 So, consider a right-handed Cartesian coordinate system with its origin at the centre of the Earth, z-axis pointing toward north, and y-axis pointing toward Vernal Equinox (the zero of right ascension). To get the sites' coordinates in this system Equations 4.11 are used, just with p replaced by the angle Greenwich mean Sidereal Time (GST) + p. This angle is called 'Celestial Longitude' in the analysis code. It takes into account the rotation of the Earth in the non-Earth fixed coordinate system being used here. With the positions of the two sites known in this coordinate system; create a vector, d, with a magnitude equal to the distance between the sites and a direction from the second site hit to the first site hit. Create another vector, cr, this time a unit vector in the direction of the right ascension and declination of the showers (the average of two angles is used in the code). The dot product of these two vectors is then equal to dcos(/3) (see Figure 4.6 for definition of /3). dcos(/3) can be calculated with the statement of the two vectors in the Cartesian coordinate system: Now, dcos{j3) can be compared to cAt. 4.3.2 Burst Find Routine The burst find routine, burstfind.c, is designed to locate time periods of elevated count rate at a site. The routine simply reads sequentially through the data and searches for consecutive pairs of events that have a time difference, At, that is less than a user defined time, ta. When a sequence of consecutive pairs with At < ta is found, it is recorded as a burst with the number of events in the burst and the end time of the burst. The end of the burst is defined when one consecutive pair has At > ta, as shown in Figure 4.7. The routine is based on analysis by Katayose of the LAAS group [?], the code can be found in the Appendix A. Therefore: dcos((3) = xdxcr + ydycr + zdz( 'cr 91 At1 At2 At3 At4 At5 At6 tl t2 t3 t4 ts t6 t_1 At3 ..... At6 < ta At7 t7 Figure 4.7: Burstfind routine would find a burst of 5 events ending at t6 When a burst is found data from all other sites will be examined closely to look for bursts that occured at and around the same time. 4.3.3 Skyplot There is another analysis tool, called skyplot, that plots the locations of events in a Hammer-Aitoff plot of the celestial or galactic coordinate systems. Figure 4.8 is an example plot of three hypothetical events with skyplot. Skyplot was written with ROOT by Doug Gish. Figure 4.8: An example of 3 hypothetical events displayed with skyplot 92 Chapter 5 Conclusion The Alberta Large Area Time Coincidence Array (ALTA) is almost ready to search for cosmic ray phenomena that could be vital to unravelling some of the mysteries surrounding cosmic rays. The possibility that cosmic ray showers can be correlated over large distances has been glimpsed at, but never fully explored. The existence of correlated showers could point the proverbial finger at interactions and processes that could give valuable insight into the nature of our universe. It is generally accepted that cosmic rays arrive at the Earth randomly in time, but several experiments have shown that this might not be the case. The presence of a component of the cosmic ray spectrum with some structure in the arrival time could indicate possible sources of cosmic rays and help solve the mystery of where cosmic rays come from. ALTA currently has 6 sites in operation, each of them capable of determining the arrival time and direction of air showers with energies > 1014 eV. The arrival time can be determined to about 16 ns, while the arrival angle can determined to within 5° (for showers arriving at least 45° above the horizon). In the near future the arrival angle uncertainty will be examined in more detail by overlapping two sites and completing more extensive Monte Carlo simulations. The overlapping arrays will on the roof of physics building at the U of A. The current U of A site is already on the west roof of the physics building, so a second site will be installed overlapping the existing site. This overlapping site will be temporary. A permanent site will be installed on the east roof of the physics building (~100 m away) to look for rates of larger air 93 showers. ALTA is envisioned to have approximately 30 sites spread throughout the province of Alberta. Within the next 12 months at least 5 more sites are expected to be operational, with several more under construction. ALTA and NALTA will be able to search for correlations in cosmic ray phenomena that will not be observable by the largest air shower arrays under construction today. 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B (Proc. Suppl), 52B:17, 1997. [61] Triumf kinematic handbook, 1987. [62] Geant web page, http://wwwinfo.cern.ch/asd/geant/. [63] Peter Duffet-Smith. Practical Astronomy with Your Calculator, 3rd Ed. Cambridge University Press, 1998. 98 Appendix A Analysis Code This appendix contains the code for the analysis routines described in Chapter 4.3. The code is written in C. In an effort to save space all of the code is not written here, only the important function calls and 'main' routines are written. A.l The Summary Routine The summary routine is used before each of the other analysis routines to convert the TDC and Time Tag information into arrival angles (in horizon, celestial, and galactic coordinates) and arrival times. main Program //read through the input file with while loop while( !feof(fpinput) ) { //call conversion functions timeconvert( sawtooth, delta, frequency, fetime ); horizon( coin, fesite, feangle ); celestiaK fesite, fetime, feangle ); galactic( feangle ); //write ouput file } timeconvert Function struct TIME *timeconvert( int sawtooth, long delta, double frequency, struct TIME *time ) { double fracsecond; fracsecond = delta/frequency + sawtooth/pow(10,9); 99 time->second = time->second + fracsecond; return( time ); horizon Function struct ANGLE *horizon( int *coin, struct SITE *site, struct ANGLE *angle ) { double time[3], A, B; float xl, x2, yl, y2; int c = 299792458; // Converting TDC value to seconds time[0] = 0.000000000025*coin[0]; time[l] = 0.000000000025*coin[l]; time[2] = 0.000000000025*coin[2]; // Calculating A and B values for azi and alt calculations xl = site->x[l] - site->x[0]; yl = site->y[l] - site->y[0]; x2 = site->x[2] - site->x[0]; y2 = site->y[2] - site->y[0]; A = c*( ( time[2]-time[0] )-( time[1]-time[0] )*( y2 / yl ) ) / ( x2 - xl * ( y2 / yl ) ); B = c*( ( time[2]-time[0] )-( time[1]-time[0] )*( x2 / xl ) ) / ( y2 - yl * ( x2 / xl ) ); // Calculate azi and convert from [-pi/2, pi/2] to [0, 2*pi] angle->azi = atan( A/B ); // azi in rad [-pi/2 to pi/2] if ( angle->azi < 0 && angle->azi >= -pi/2 ) { angle->azi = angle->azi + pi; } if ( time[l] > time[2] ) /* DEPENDS ON SITE GEOMETRY */ { angle->azi = angle->azi + pi; } // Calculate of alt angle angle->alt = acos( sqrt(A*A+B*B) ); // alt in rad [0 to pi/2] // Algorithm fails for alt = pi/2 (since then azi is undefined) 100 // so this is the correction if( coin[0] == coin[l] && coin[l] == coin[2] ) { angle->alt = pi/2; angle->azi = 0; } return angle; } celestial Function struct ANGLE *celestial( struct SITE *site, struct TIME *time, struct ANGLE *angle ) { // Convert the time from hour, min, sec to decimals decimalUTC = time->hour + ( time->minute )/60.0 + time->second/3600.0; // Convert lat to radians and Ion to hours lat = (pi/180) * lat; Ion = Ion / 15.0; // Calculations for ra and dec (ha is hour angle) angle->dec = asin( sin(angle->alt) * sin(lat) + cos(angle->alt) * cos(lat) * cos(angle->azi) ); ha = acos( ( sin(angle->alt) - sin(lat) * sin(angle->dec) ) / ( cos(lat)*cos(angle->dec) ) ); ha = ( ha / (pi/180) ); if ( sin(angle->azi) > 0) { ha = 360 - ha; } ha = ha / 15; 1st = GST(decimalUTC, time) + Ion; if ( 1st < 0 ) { 1st = 1st + 24; } if ( 1st > 24 ) { 1st = 1st - 24; } angle->ra = 1st - ha; //ra in decimal hours 101 if ( angle->ra < 0 ) { angle->ra = angle->ra +24; } if ( angle->ra > 24 ) { angle->ra = angle->ra - 24; } angle->ra = (pi/12)*angle->ra; //convert hours to radians return angle; } galactic Function struct ANGLE *galactic( struct ANGLE *angle ) { angle->b = asin( 0.8878*cos(angle->dec) *cos(angle->ra-192.25*(pi/180)) + 0.4602*sin(angle->dec) ); angle->l = atan2((sin(angle->dec)-0.460199784*sin(angle->b)), (0.887815385*cos(angle->dec) *sin(angle->ra-192.25*(pi/180)))) + 33*(pi/180); if( angle->l < 0 ) { angle->l = angle->l + 2*pi; } return angle; } GST Fuction double GST( double decimalUTC, struct TIME *time ) { double t, T, gst; t = ( JDate( time ) - 2451545.0 ) / 36525.0; T = 6.697374558 + 2400.051336*t + 0.000025862*t*t; if ( T < 0) { while ( T < 0 ) { T = T + 24; } } else { while ( T > 24 ) { T = T - 24; } } decimalUTC = 1.002737909 * decimalUTC; 102 gst = decimalUTC + T; if ( gst < 0 ) { gst = gst + 24; } if ( gst > 24 ) { gst = gst - 24; } return (gst); } JDate Function double JDate ( struct TIME *time ) { int year, month, day, A, B, C, D; float Date; year = time->year; month = time->month; day = time->day; if ( month <= 2 ) { year = year - 1; month = month + 12; } A = (year) / 100; B = 2 - A + A/4; C = 365.25 * ( year); D = 30.6001 * ( month + 1); Date = B + C + D + day + 1720994.5; return(Date); } 103 A.2 The Correlation Routine This program finds correlations in cosmic ray showers between two sites. Constant Variable Definitions #define pi 3.1415926535897932384626433832795 #define a 6378137 // Earth's equitorial radius (WGS84) #define b 6356752.314 // Earth's polar radius (WGS84) #define c 299792458 // Speed of light in vaccum main Program //convert longitude and latitude to radians sitel.lon = (pi/180) * sitel.lon; site2.1on = (pi/180) * site2.1on; sitel.lat = (pi/180) * sitel.lat; site2.1at = (pi/180) * site2.1at; //calculate tau (the light travel time between the sites) tau = make_tau( fesitel, &site2 ); //read through file 1 with while loop while( !feof( fpldst ) ) { //read event from file 1 //for each event in file 1, compare to event in file 2 while( !feof( fp2dst ) ) { //read event from file 2 //sequence of if statements to make the comparisons if( comparetime( fetimel, &time2, tau ) == 1 ) { if( make_epsilon( feanglel, &angle2 ) <= delta ) { if( fabs( time1.second - time2.second ) -fabs( dcosbeta( ... ) / c ) <= DELTA ) { fprintf( fpoutput,"to output file" ); } } } } 104 rewind( fp2dst ); } comparetime Function int comparetime( struct TIME *timel, struct TIME *time2, double tau ) { if( timel->year == time2->year ) { if( timel->month == time2->month ) { if( timel->day == time2->day ) { if( timel->hour == time2->hour ) { if( timel->minute == time2->minute ) { if( fabs( time2->second - timel->second ) <= tau ) { return(1); } else { return(O); } } else { return(O); } } else { return(O); } } else { return(O); } } else { return(O); } } else { return(O); } } make_epsilon Function double make_epsilon(struct ANGLE *anglel, struct ANGLE *angle2) { double epsilon; double ral, ra2, decl, dec2; double xl, yl, zl, x2, y2, z2; // x, y, z on a unit circle, // y is pointing in ra=0, z pointing to dec=90 degrees xl = cos(decl)*sin(ral); yl = cos(decl)*cos(ral); zl = sin(decl); x2 = cos(dec2)*sin(ra2); y2 = cos(dec2)*cos(ra2); 105 z2 = sin(dec2); // 1 dot 2 = cos(epsilon) epsilon = acos( xl*x2 + yl*y2 + zl*z2 ); return( epsilon ); } make_tau Function double make_tau( struct SITE *sitel, struct SITE *site2 ) { double tau; double xl, yl, zl, x2, y2, z2; double gclatl, gclat2; /* gclat is GeoCentric LATitude */ gclatl = atan( pow( b/a, 2 ) * tan( sitel->lat ) ); gclat2 = atan( pow( b/a, 2 ) * tan( site2->lat ) ); xl=(radius(gclatl)+sitel->alt)*cos(gclatl)*sin(sitel->lon); yl=(radius(gclatl)+sitel->alt)*cos(gclatl)*cos(sitel->lon); zl=(radius(gclatl)+sitel->alt)*sin(gclatl); x2=(radius(gclat2)+site2->alt)*cos(gclat2)*sin(site2->lon); y2=(radius(gclat2)+site2->alt)*cos(gclat2)*cos(site2->lon); z2=(radius(gclat2)+site2->alt)*sin(gclat2); tau=sqrt(pow(x2-xl,2) + pow(y2-yl,2) + pow(z2-zl,2) )/c; return( tau ); } radius Function double radius( double lat ) { double radius; radius = l/sqrt( pow(cos(lat)/a,2) + pow(sin(lat)/b,2)); return( radius ); } dcosbeta Function double dcosbeta( ... ) { double xl, yl, zl, x2, y2, z2, xCR, yCR, zCR; double gclatl, gclat2; double cstlonl, cstlon2; double dcosbeta, dec, ra; 106 // convert geographic to geocentric latitude gclatl = atan( pow( b/a, 2 ) * tan( sitel->lat ) ); gclat2 = atan( pow( b/a, 2 ) * tan( site2->lat ) ); // calculate cstlon "Celestial Longitude" cstlonl = (pi/180)*(15)*GST( timel ) + sitel->lon; cstlon2 = (pi/180)*(15)*GST( time2 ) + site2->lon; // calculate x, y, z and make site2 the last site hit if( time2 > timel ) { xl=(radius(gclatl)+sitel->alt)*cos(gclatl)*sin(cstlonl); yl=(radius(gclatl)+sitel->alt)*cos(gclatl)*cos(cstlonl); zl=(radius(gclatl)+sitel->alt)*sin(gclatl); x2=(radius(gclat2)+site2->alt)*cos(gclat2)*sin(cstlon2); y2=(radius(gclat2)+site2->alt)*cos(gclat2)*cos(cstlon2); z2=(radius(gclat2)+site2->alt)*sin(gclat2); } if( time2 < timel ) { x2 = (radius(gclatl)+sitel->alt)*cos(gclatl)*sin(cstlonl); y2 = (radius(gclatl)+sitel->alt)*cos(gclatl)*cos(cstlonl); z2 = (radius(gclatl)+sitel->alt)*sin(gclatl); xl = (radius(gclat2)+site2->alt)*cos(gclat2)*sin(cstlon2); yl = (radius(gclat2)+site2->alt)*cos(gclat2)*cos(cstlon2); zl = (radius(gclat2)+site2->alt)*sin(gclat2); } if( time2 == timel ) // if timel=time2 then dcosbeta=0 { return( 0 ); } // taking average of ra and dec dec = ( anglel->dec + angle2->dec ) / 2; ra = ( anglel->ra + angle2->ra ) / 2; //calculate xCR, yCR, zCR xCR = cos( (pi/180)*dec ) * sin( (pi/180)*15*ra ); yCR = cos( (pi/180)*dec ) * cos( (pi/180)*15*ra ); zCR = sin( (pi/180)*dec ); dcosbeta = (x2-xl)*xCR + (y2-yl)*yCR +(z2-zl)*zCR; return( dcosbeta ); 107 A.3 The Burstfind Routine This program takes output of summary.c program and searchs for a non-random time series. main Program //read the first event //read sequential events with while loop while( !feof( fpinput ) ) { previous_event = current_event; //read event delta_t = get_delta_t( ¤t_event, &previous_event ); if( delta_t < time_interval ) //can be > for "anti-bursts" { if( index_check+l == index ) { burst_counter[n] ++; burst_event[n]=current_event; } index_check = index; } index++; if( index_check+2 == index ) //go to next burst_counter { n++; } } get_delta_t Function double get_delta_t( struct EVENT *current_event, struct EVENT *previous_event ) { double delta; double current_time, previous_time; current_time = 3600*current_event->hour + 60*current_event->minute + current_event->second; previous_time = 3600*previous_event->hour + 60*previous_event->minute + previous_event->second; delta = current_time - previous_time; return(deIta); } 108 Glossary ADC Pedestal The value of the ADC that corresponds to zero energy being deposited in the detector., page 59 ADC An Analog to Digital Converter is an electronic device that converts the amount of charge in (the size of) an electronic signal to a digital value., page 49 AGASA Akeno Giant Air Shower Array is a 100 km2 ground based air shower array near Akeno Japan, page 26 Air Shower The cascade of particles produced when a high energy cosmic ray enters the atmosphere., page 2 Ankle The kink in the cosmic ray energy spectrum at ~ 1018 eV is called the ankle., page 4 Auger The Pierre Auger project is a pair of 3000 km2 air shower arrays being built in Argentina and the United States, page 26 Cerenkov Radiation Light created by a charged particle traveling faster than the local speed of light in a medium., page 16 CMB The Cosmic Microwave Background is electromagnetic radiation (photons) that seem to permeate the entire universe, page 4 Correlated Cosmic Rays Cosmic rays coming from some common origin creating air showers that would tend to point in similar directions. The cosmic rays could be stricly correlated, meaning that the primaries were all contained in a plane; or roughly correlated, meaning the primaries would all have come from the same direction, but not necessarily in a plane., page 20 Cosmic Ray Burst An increase in the rate of air showers over time intervals from seconds to hours., page 18 Cosmic Ray A high energy subatomic particle of extra-terrestrial origin. Electromagnetic Shower An air shower initiated by a photon, page 12 eV An electron volt is a unit of energy: 1 eV = 1.602 x 10~19 J Extensive Air Shower An air shower large enough to reach the ground., page 12 Flux The amount of something passing through some specified area in some specified time 109 Global Timing The relative timing between sites; the GPS time., page 32 GZK Limit The Greisen-Zatsepin-Kuz'min limit is a restriction on the distance protons with energy greater than 5 x 1019 eV are likely to travel due to pion production with the photons of the CMB, page 4 Hadronic Shower An air shower initiated by a hadron, page 14 Hadron A class of subatomic particles containing 3 quarks, protons and neutrons are the most common hadrons. HiRes The High Resultion Fly's Eye experiment is a nitrogen fluorescence detector in Utah, USA; an upgraded version of the former Fly's Eye experiment, page 25 ICRC The International Cosmic Ray Conference is a gathering of cosmic ray researchers every two years to discuss progress and future goals in cosmic ray physics. Knee The kink in the cosmic ray energy spectrum at ~ 1015 eV is called the knee., page 4 LAAS Large Area Air Shower group is a group of 9 small air shower arrays in Japan., page 26 Local Timing The relative timing between the detectors at a site., page 32 MIP A Minimum Ionizing Particle is a particle that deposits ~2 MeV of energy in every g/cm2 of material it passes through., page 57 Mpc A unit of distance equal to 1 million parsecs: 1 parsec ~ 3.2 light years Nitrogen Fluorescence Light created by an electron exciting atoms as it propagates through nitrogen gas, page 17 Nucleon A proton or neutron. PMT A PhotoMultiplier Tube is a device that detects small amounts of light and converts it to a measurable electric signal., page 33 Primary Cosmic Ray The cosmic ray that initiates an air shower., page 2 Scintillator A material that emits a small flash of light when a charged particle passes through it., page 33 Secondary Cosmic Ray A particle produced in an air shower., page 2 Shower Front The roughly planar region that contains the secondary particles of an air shower., page 2 Spallation Spallation is the process of a heavy nucleus splitting appart, or fragmenting, when it interacts with a lighter nucleus TDC A Time to Digital Converter is an electronic device that converts the time between two electronic signals to a digital value., page 45 110