Enrico Fermi Institute the University of Chicago

COMPOSITION AND SPECTRUM OF COSMIC RAYS AT THE K. EE MEASURED BY THE CASA-BLANCA EXPERIMENT

BY JOSEPH WESTBROOK FO\VLER

MARCH 2000

Enrico Fermi Institute The University of Chicago

Dissertation THE UNIVERSITY OF CHICAGO

COMPOSITION AND SPECTRUM OF COSMIC RAYS AT THE KNEE MEASURED BY THE CASA-BLANCA EXPERIMENT

A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF PHYSICS.

BY JOSEPH WESTBROOK FOWLER

CHICAGO, ILLINOIS MARCH 2000 To my family ABSTRACT

The energy spectrum and primary composition of cosmic rays with energy between 3 x 10 14 and 3 x 10 16 eV have been studied using the CASA-BLANCA detector. In this energy range, a "knee" in the spectrum has been recognized for over 40 years. The astrophysical origins of the knee remain unknown. Various models propose that the knee indicates an inherent feature of cosmic ray sources, a new type of source, or a change in the propagation of cosmic rays through the Galaxy. Measuring the spectrum and elemental composition of cosmic rays near the knee can help to address the problem. The favored model of acceleration in supernova shock waves predicts that cosmic rays with energy above,....., 1016 eV consist entirely of heavy nuclei. The measurements were made by BLANCA, a new array of 144 angle-integrating Cherenkov light detectors located at the CASA-MIA site in Utah. CASA data on particle density are used to find the core and direction of air showers, while BLANCA measures the lateral distribution of Cherenkov light about the core. The Cherenkov detectors receive light emitted throughout the air shower rather than relying only on the few particles which reach the ground. This advantage over air shower arrays makes it possible for BLANCA to measure shower energy with little composition bias and to estimate accurately the depth of shower maximum. The differential flux of cosmic rays measured by BLANCA exhibits a knee in the range of 2-3 Pe V with a width of approximately 0.5 decades in primary energy. The power law indices of the differential flux above and below the knee are - 2. 72 ± 0. 02 and -2.95 ± 0.02. The data on mean shower depth indicate that the composition is lighter at 3 Pe V than below the knee and that it becomes heavier with increasing energy above 3 PeV. Cherenkov measurements are interpreted using the predictions of the CORSIKA Monte Carlo air shower simulation coupled with each of four hadronic interaction codes (QGSJET, VENUS, SIBYLL, and HDPM). The distribution of air shower depths can be reproduced well at all energies by the QGSJET and VENUS models, and these distributions suggest the same composition trends exhibited by the mean shower depth.

lll ACKNOWLEDGMENTS

CASA-BLANCA was a small project compared to many particle astrophysics experiments, and it was possible only because of the dedicated efforts of a small core group of researchers. I have been fortunate to work on an experiment from its design through construction, operation, and analysis. Three physicists above all guided me through the project and shared the myriad duties. Without them, BLANCA would not have happened. Clem Pryke steered me through the calibration and analysis of the instrument and led the enormous CORSIKA-for-BLANCA simulation effort. My advisor Rene Ong offered me a hard and exciting thesis topic and led me wisely through the minefields but always gave me the independence to decide issues both big and small. His larger view of astrophysics has kept me anchored, while his excellent example as a writer and spea~er (along with hours and hours worth of detailed suggestions) has led me to make huge improvements in this thesis. Crucially, Lucy Fortson dared to take on a huge project nearly alone with the full-time help of only one green graduate student. Her leadership, hard work, and friendship over the past four years have made BLANCA not only possible but also exceptionally fun. I am grateful to the entire CASA-MIA collaboration for supporting the BLANCA effort always and for their invaluable assistance in the design and construction of BLANCA. The combined knowledge of the CASA group was staggering and inspiring. Many members of the High Resolution Fly's Eye (HiRes) group also shared their expertise, their tools, camaraderie, the A-1 steak sauce out of their refrigerator, and above all the complete set of old Fly's Eye PMTs, without which BLANCA would have been too expensive to build. Stan Thomas was especially helpful in suggesting simple solutions to our weirdest design problems. We tested optics in the Utah labs of Werner Gellermann and Di Li. Michigan's Ande Glasmacher wrote the first CASA-MIA thesis on cosmic ray composition. I thank her for the guidance it provided (and for teaching me to drive the CASA four-wheel ATVs). I also thank the command and staff of the U.S. Army Dugway Proving Ground for their cooperation. Many people helped to build BLANCA in 1996. They include Matt Pritchard and Katherine Riley, who sweated in the desert in August. Jeremy Meyer aluminized 150

lV v

Winston cones in Salt Lake City. A great many physicists from the CASA, STACEE, and HiRes groups volunteered their time to construct and install detectors in the field, including Jim Cronin, Mark Chantell, Scott Oser, Charlie Jui, Dave Kieda, Jon Matthews, and Paul Sommers. In addition, Kevin Green, Ken Gibbs, Brian Fick and Brian Newport spent desert days "swapping lead" to prepare CASA for the addition of BLANCA. Megan McClellan and Caleb Cassidy helped in 1997 to get ready for the second season. Clara Eberhardy patiently pioneered the BLANCA laboratory measurements, using a beautiful dark box and computer-controlled neutral density filter graciously loaned us by Kelby Anderson. Above all, our talented on-site tech- nician Mike Cassidy made BLANCA materialize. His practical knowledge turned the BLANCA concept into an huge array of sturdy, water-tight, baby blue detectors. He kept the trailers cool in the summer, warm in the winter, and always friendly. For making life in Chicago fun (even in Hyde Park) I thank the friends who did problem sets, studied for the candidacy exam, threw the frisbee, watched Bulls games, and went to the Pub with me so many nights, especially Jeff Berryhill, James Geddes, Jordan Koss, and Ted Quinn. Life in the CASA/STACEE group was fun and stimulating thanks to folks like Corbin Covault, Richard Scalzo, Dan Schuette, Jaci Conrad, and especially my long-time fellow student Scott Oser. I am grateful ... to Barbara Schubert for her superb orchestra program and for conducting Strauss, Stravinsky, Bruckner, and Mahler; to my other conductor, Antoinette Arnold; and to my musician pals Sylvie Anglin and Martin Pergler. Nobuko McNeill, Aspasia Sotir-Plutis, and Marty Dippel helped my stay in Chicago be as swift and painless as they could conveniently make it. I thank the National Science Foundation and the McCormick and Grainger Foundations for my financial support at Chicago. Like anyone who completes the 22nd grade, I have been blessed with many won- derful teachers and mentors over the years. Dozens prepared me for this thesis and more generally for a life of the mind. I am grateful to them all but especially to the two most inspiring, Carolyn Huff and Pat Freeman. Finally, I thank my parents, my sister Amy, and my wife Jennifer for their love, patience, and faith in me over many years. They made this worthwhile. TABLE OF CONTENTS

ABSTRACT lll

ACKNOWLEDGMENTS IV

LIST OF FIGURES IX

LIST OF TABLES XI

1 COSMIC RAY PHYSICS 1 1.1 What we do know about cosmic rays ...... 1 1.1.1 The discovery of cosmic rays and air showers . 2 1.1.2 The cosmic ray energy spectrum ...... 4 1.1.3 The age of cosmic rays and other observations 7 1.2 How cosmic rays are created and transported. 8 1.2.1 Supernovae ...... 8 1.2.2 Fermi acceleration ...... 9 1.2.3 Propagation and escape from the Galaxy 11 1.2.4 Current models of composition ..... 12 1.3 Existing measurements of the cosmic ray composition 17 1.3.1 Direct measurements at energies below the knee 17 1.3.2 Indirect measurements at the knee 17 1.3.3 Ultra-high energy composition . 19

2 EXTENSIVE AIR SHOWERS 20 2.1 The anatomy of an air shower 20 2.2 The Cherenkov effect ..... 23 2.3 Composition and air showers . 26 2.3.1 Atmospheric depth of shower maximum . 27 2.3.2 Cherenkov light ...... 31 2.3.3 Other composition-dependent properties 34

3 THE CHICAGO AIR SHOWER ARRAY 36 3.1 The CASA Instrument ...... 37 3.1.1 The array trigger ...... 40 3.1.2 Measuring particle densities 41 3.1.3 Surface array timing . 41 3.2 CASA Offiine Reconstruction . . 43 3.2.1 Detector calibration .... 43 3.2.2 Fitting the air shower core 46 3.2.3 Fitting the air shower direction 47

VI Vll

4 THE BLANCA CHERENKOV ARRAY 49 4.1 Array overview ...... 49 4.1.1 Use of the CASA trigger .. 51 4.1. 2 Operating the Cherenkov array 51 4.2 BLANCA detectors ...... 52 4.2.1 Optical design ...... 55 4.2.2 Simulations of the optics ... . 59 4.2.3 Laboratory studies of the optics 61 4.3 BLANCA electronics . . . 64 4.3.1 Preamplifiers . . . 64 4.3.2 Station electronics 66 4.4 Operating BLANCA 68

5 BLANCA CALIBRATION 71 5.1 Determining the BLANCA constants 71 5.1.1 Pedestals ...... 71 5.1.2 Preamplifier gain ratio ... . 74 5.1.3 Relative gains ...... 75 5.2 LED measurements of relative gains . 78 5.2.l The portable calibration device 78 5.2.2 LED relative gain results . . . . 80 5.3 Detector saturation ...... 80 5.3.1 Causes of photomultiplier saturation 81 5.3.2 Laboratory measurements of the BLANCA linearity . 82 5.3.3 Nonlinearity correction to the BLAN<:::A data 85 5.4 Absolute light intensity calibration ...... 86 5.4.1 Calibration of the LED source ..... 86 5.4.2 Calibration of two BLANCA detectors 90 5.5 Nightly variations of the array gain . . . . 91 5.6 Detector alignment ...... 94 5. 7 Eliminating bad detectors and bad events . 97 5.7.1 Detector quality cuts 97 5. 7.2 Weather requirements ...... 98

6 AIR SHOWER SIMULATIONS FOR BLANCA 100 6.1 The CORSIKA simulation program ...... 101 6.1.1 How CORSIKA simulates air showers ...... 102 6.1.2 High energy hadronic models used in CORSIKA . 103 6.1.3 Thinned air shower computations 105 6.2 Atmospheric scattering of Cherenkov light ...... 108 6.2.1 Rayleigh and Mie scattering ...... 109 6.2.2 Effect of scattering on the Cherenkov distribution 112 Vlll

6.3 Using CORSIKA for BLANCA ...... 114 6.3.1 Preserving angular information . . 114 6.3.2 The BLANCA detector simulation 117 6.3.3 CASA-BLANCA Monte Carlo shower library. 118

7 CHERENKOV FITTING AND SHOWER ENERGY 120 7.1 Fitting the Cherenkov lateral distribution. 120 7.1.1 Event selection ...... 120 7.1.2 The lateral distribution fit ...... 122 7.1.3 Interpretation of the Cherenkov fit parameters 125 7.2 Cherenkov event energies ...... 127 7.2.l Simple energy function ...... 127 7.2.2 Reducing the composition bias of the energy function 129 7.3 The cosmic ray energy spectrum ...... 133 7.3.1 The BLANCA cosmic ray exposure 133 7.3.2 Spectrum results . . . . . 135 7.3.3 The knee in the spectrum . . . . . 135

8 COSMIC RAY COMPOSITION 144 8.1 Depth of shower maximum ...... 144 8.1.1 Estimating Xmax from the Cherenkov lateral distribution 145 8.1.2 Results: Mean depth of maximum versus primary energy 148 8.2 Mean primary mass ...... 152 8.2.1 Estimating ln(A) from the Cherenkov lateral distribution 153 8.2.2 Results: ln(A) versus primary energy 156 8.3 A multi-species fit to the Cherenkov slopes . 156 8.3.1 Procedure ...... ·...... 156 8.3.2 Results of the multi-species analysis . 158 8.4 Summary of composition results ...... 162

A FITTING THE DETECTOR RELATIVE GAINS 167

B THE CORSIKA MODEL ATMOSPHERE 170

C TABLES OF RESULTS 172 C. l Cosmic ray energy spectrum ...... 172 C.2 Shower depth of maximum and derived primary mass 173

BIBLIOGRAPHY 177 LIST OF FIGURES

1.1 The all-particle spectrum of primary cosmic ray energies. 5 1.2 Combining two power law sources to create a spectral knee .. 6 1.3 A schematic spectrum with rigidity-dependent cutoffs .. 13

2.1 The principal components of an extensive air shower. 22 2.2 Example air shower development curves...... 23 2.3 Diagram of the Cherenkov radiation shock front. . . . 25 2.4 Simplified picture of Cherenkov emission in a vertical shower. . 32 2.5 The BLANCA concept: example Cherenkov light lateral distributions. 33

3.1 Map of the Dugway site...... 38 3.2 Exploded diagram of one CASA detector station. 39 3.3 Timing diagram of an air shower front...... 42 3.4 Calibration distributions for one CASA scintillation counter. 44

4.1 Diagram of a BLANCA detector...... 53 4.2 Photograph of a BLANCA detector...... 54 4.3 The shape of several possible Winston cones with rout= 3.6cm. 56 4.4 Wavelength response of the complete BLANCA detector. . 58 4.5 Simulated BLANCA cone response as a function of angle. . . 60 4.6 Apparatus used to measure BLANCA angular response. . . . 62 4. 7 Laboratory measurements of the detector angular response. . 63 4.8 Block circuit diagram of the BLANCA preamplifiers. . 65 4.9 Cherenkov observation start and end times "'each night. . . . 69

5.1 How raw ADC data are converted to Cherenkov photon densities. 72 5.2 Preamplifier high/low gain ratio calibration...... 74 5.3 Calibration of the BLANCA detector relative gains...... 77 5.4 The portable flasher used for calibrating detector gains in the field. 79 5.5 Comparison of relative gains measured using the external LED calibrator with those extracted from cosmic ray data. 81 5.6 Measuring the BLANCA linearity. . 83 5. 7 The absolute calibration method...... 88 5.8 Nightly array gain variation...... 93 5.9 The concept behind the BLANCA alignment estimates. 95 5.10 Detector pointing angles...... 96 2 5.11 Rate of events during one run with C120 > 1 photon cm- . . 99

6.1 Comparison of shower parameters from the four hadronic models. 106 6.2 Consistency of air shower quantities at several thinning levels. 107 6.3 Atmosphrric scattering models...... 111

lX x

6.4 The effect of atmospheric scattering on an example 1 PeV shower. . . 113 6.5 Emission height of atmospheric Cherenkov light...... 114 6.6 The Cherenkov angular distribution reconstructed from the BLANCA geometry histograms...... 116

7.1 Mean number of BLANCA stations alerted versus primary energy. 121 7.2 Two Cherenkov lateral distributions measured by BLANCA. . . . 123 7.3 Reduced x2 distribution of the Cherenkov lateral fit...... 124 7.4 The species discrimination power of the Cherenkov lateral technique. 126 7.5 Cosmic ray energy as a function of the Cherenkov intensity C 120. . 129 7.6 Error on the simple energy fit versus Cherenkov slope. 131 7.7 Energy reconstruction errors as a function of energy...... 132 7.8 BLANCA sky exposure, in relative units...... 134 7.9 The all-particle differential cosmic ray flux measured by BLANCA. 136 7.10 The three functions used to fit the cosmic ray spectrum...... 137 7.11 Choosing the transition width w in fitting the knee...... 138 7.12 The knee region of the spectrum along with the smooth power law fit. 140 7.13 The BLANCA cosmic ray"'spectrum compared with other measurements.142

8.1 Air shower depth of maximum (Xmax) versus the Cherenkov slopes .. 146 8.2 Xmax reconstruction errors as a function of energy. . . . 147 8.3 Mean Xmax versus energy in BLANCA data...... 149 8.4 Systematic uncertainties on BLANCA Xmax estimates. 151 8.5 The magnitude of the reconstruction errors on ln(A). . 154 8.6 The inherent mass resolution of Xmax and of BLANCA. . 155 8.7 The mean logarithmic mass (ln(A)) measured by BLANCA. 157 8.8 A demonstration of the multi-species fitting procedure 159 8.9 Results of the multi-species fit to the BLANCA data. . . . . 160 8.10 The BLANCA measurement of Xmax compared with other results. 163

B.1 The density profile of the U.S. standard atmosphere used in CORSIKA.171 B.2 The overburden of the U. S. standard atmosphere used in CORSIKA. 171 LIST OF TABLES

1.1 Models of the knee composition...... 16 1.2 Cosmic ray composition at 100 TeV per nucleus...... 17 1.3 Several recent measurements of cosmic ray composition near the knee. 18

3.1 CASA characteristics during the 1997-98 BLANCA observations. 37

4.1 Summary of average BLANCA detector characteristics. 50

6.1 Features of the interaction models used in CORSIKA. . 105 6.2 Comparison of the two atmospheric scattering processes. 110 6.3 Elements of the BLANCA detector simulation. . . . 119

7.1 Parameters of the quadratic fits of log E to log C120 . 130 7.2 Results of fitting double power-laws to the energy spectrum. 139 7.3 Correlation coefficients for the QGSJET smooth knee fit. . . 141

8.1 The best-fit parameters of the inner slope to Xmax transfer function .. 147 8.2 Results of the multi-species fits to the BLANCA data...... 161

B.l The five-layer parameterization of the U. S. standard atmosphere. 170

C.l Relationships among the cosmic ray energy spectrum variables. . . 173 C.2 The primary cosmic ray energy spectrum measured by BLANCA. 174 C.3 Mean Cherenkov slope and mean Xmax measured by BLANCA. 175 C.4 Mean ln(A) measured by BLANCA...... 176

Xl CHAPTER 1 COSMIC RAY PHYSICS

A swarm of charged particles fills our Galaxy. Electrons, protons, and bare nuclei spiral for millions of years among interstellar magnetic fields, eventually colliding with other matter or escaping into intergalactic space. On their winding path, some enter our Solar System. A few of these particles produce a steady rain of secondary particles striking the Earth's surface. These particles from outer space are called cosmic rays, and 87 years after their discovery, we do not know what creates them.

1.1 What we do know about cosmic rays

Cosmic rays arrive at Earth's atmosphere as a hail of ionizing radiation. In the 3 interstellar medium, they carry an energy density of approximately 1 eV cm - , comparable to the energy density in starlight, in Galactic magnetic fields, and in the cosmic microwave background radiation [l]. Because cosmic rays are charged particles, their paths are bent by magnetic fields. The interstellar magnetic fields of our Galaxy distort cosmic ray trajectories so much that astronomy with cosmic rays below 1018 eV is impossible. A proton of energy 3 x 10 15 eV in a typical Galactic field of,...... , lµG, for example, has a radius of curvature (Larmour radius) of one parsec, less than the distance to the nearest stars. Any sources of cosmic rays much further away (for example,...... , 104 pc, the distance to the center of the Galaxy) would produce a nearly isotropic distribution of particles reaching the Earth. The arrival direction of a cosmic ray striking the atmosphere tells us practically nothing about its point of origin. Only trajectories of the most energetic particles (;::, 1019 eV) could point back to their sources [2, for example]. Cosmic rays are observed with an enormous range of energies, from ,...... , 109 eV up to 3 x 1020 eV. Very few of these particles, regardless of energy, penetrate the atmosphere completely. Instead, almost all suffer collisions with nuclei of oxygen and nitrogen molecules in the air. The collisions can create penetrating product particles which carry energy deeper into the atmosphere before interacting. Cosmic rays with 1 2 energies1 2: 100 TeV can in this way produce a cascade of particles so energetic that detectable numbers reach the ground. The cascade is known as an extensive air shower. The term primary cosmic rays refers to particles entering the atmosphere, while secondary cosmic rays are the charged particles produced in the air showers of the primary cosmic rays. Direct measurements on low energy primary cosmic rays show that approximately 2% are electrons and positrons. The remainder consist of fully ionized nuclei. Most are protons (hydrogen), but helium, carbon, oxygen, and iron are prominent components of cosmic rays. In fact, nearly all chemical elements up to lead (Z = 82) have been observed [1]. There is little controversy about the origin of the least energetic particles (:S 109 eV), whose intensity rises with Solar activity. They are part of the Solar Wind and largely come from the Sun. 1\1.ost cosmic rays of intermediate energy come from beyond our Solar System but apparently from within the Galaxy (as discussed in Section 1.1.3). The origin of cosmic rays above ~ 1016 eV remains a mystery. This thesis describes a study of cosmic rays in the PeV energy range, in search of clues to their origin.

1.1.1 The discovery of cosmic rays and air showers

Cosmic rays were first noticed one hundred years ago, when slowly discharging elec- troscopes revealed the presence of ionizing radiation in air. Natural radioactivity of the Earth seemed a plausible explanation. In 1910, Wulf carried an electroscope up the Eiffel tower and found that the ionization rate fell only slightly with increasing altitude [1]. If the radiation originated in the Earth, then it had remarkable penetrating power through air. To extend these measurements, Victor Hess in 1911-1912 made a series of dangerous flights in open hot air balloons to 5 km altitude. Hess reported that the ionization rate decreased initially but rose quickly above 1.5 km, reaching a value two to three times higher than the sea level ionization rate [3]. Hess

1 Although the electron volt (e V) is the preferred unit of energy in cosmic ray physics, it is often more convenient to use multiples of the eV. This thesis uses both TeV and PeV units, where 1TeV=1012 eV and 1 PeV = 1015 eV. 3 concluded that the radiation must originate above the atmosphere. Flights up to 9 km by Kolhorster in 1914 confirmed the extraterrestrial nature of the cosmic rays.

Later investigations showed that the cosmic radiation does not consist of gamma rays as originally supposed. In the late 1920's, Bothe and Kolhorster found that cosmic rays at ground level produced many more coincidences between Geiger counters than one would expect from neutral particles. This observation established that the secondary cosmic rays consist of charged particles [1]. The primary radiation was found to be charged as well, when Clay (and later Compton) surveyed the rate of cosmic rays at sea level around the world. They found that secondary cosmic rays are less common near the magnetic equator. The rate rises with geomagnetic latitude, suggesting that charged primary cosmic rays are deflected from the mid-latitudes by the Earth's magnetic field [4]. The slight excess of secondary particles arriving from the west established that the primary cosmic rays carried a positive charge.

Until the invention of modern particle accelerators after World War II, cosmic rays were a fertile source of high energy interactions which could be studied for their own sake. After Chadwick's discovery of the neutron in 1932 [5], all new particles discovered over the following two decades were found in products of cosmic ray interactions. The positron [6], the muon [7], the t>ion [8], the kaon [9], and the 0 A , L;±, and 3- hyperons [10] were all first detected in cloud chambers studying cosmic ray interactions. The age of particle discovery at accelerators began only in 1955 with the first convincing evidence for the anti proton [11], created at the Bevatron. Cosmic rays, however, remain the only accessible source of extremely energetic particles (> 1 TeV). Ultra high energy cosmic rays may teach us still more about high energy nuclear interactions.

Auger and his colleagues discovered extensive air showers in 1938. Before this time, cosmic rays were known to have energies as high as 10 10 eV, and localized showers induced by muon decay had been observed. Auger's team used a system of two and three particle counters and a 1 µs coincidence circuit to reduce the accidental background. They found that the coincidence rate fell as the counters were separated, but it did not cut off rapidly at ~ 30 m separations as predicted for local cascades 4

initiated low in the atmosphere. Instead, the coincidence rate exceeded one per hour even when the detectors were 300 m apart. Auger measured the particle density, estimating that a total energy of 1014 e V reached the ground. Accounting for energy lost in the atmosphere, he further estimated that the energy of the primary particle was probably 1015 e V. Suddenly, the cosmic ray energy scale had grown by a full five orders of magnitude. In a contemporary summary of his studies, Auger concluded:

One of the consequences of the extension of the energy spectrum of cosmic rays up to 10 15 eV is that it is actually impossible to imagine a single process able to give to a particle such an energy. It seems much more likely that the charged particles which constitute the primary cosmic radiation acquire their energy along electric fields of a very great extension [12].

Auger may have underestimated the imagination of future generations of physicists, but in fact the modern picture is"similar to his suggestion. Cosmic rays are now thought to be accelerated by a repeated process of incremental energy gains, although Auger's "fields of great extension" are magnetic, not electric fields.

1.1. 2 The cosmic ray energy spectrum

The energy spectrum of cosmic rays appears in Figure 1.1. Cosmic rays span eleven decades in particle energy, and measurements at the highest energies show no sign of an end to the spectrum. The particle flux falls steeply with energy. While satellite 14 payloads can study lower energy cosmic rays, the total flux above rv 10 eV is only one particle per m2 per hour, so small that only extremely large, ground-based detectors can measure an appreciable number of cosmic rays. A few features are visible in the spectrum of Figure 1.1 besides the steady decline. Below approximately 1 Ge V, the spectrum shows a pronounced reduction from the power law shape of higher energies. The attenuation of Ge V cosmic rays, known as solar modulation, varies with the solar cycle. In periods of high solar activity the attenuation is more severe, as low energy cosmic rays have trouble diffusing into the solar system through the strong Solar Wind [1]. Solar modulation has a negligible 11 effect on cosmic rays above rv 10 eV. 5

~66 sGI CJ 6~ Fluxes of Cosmic Rays Ill 102 "6 Ill... 66 "'.s >< ,6 :I -1 2 ii: 10 6, (1 particle per m -second)

-4 '<> 10

-7 10 '0 'o ' f> ,() -10 10 ,o Knee 2 (1 particle per m -year)

-13 10 'f!.~ "'> ~ 105 '7 UI ** -16 '7._ 10 UI ':' §. ~ 'W -19 x 10 >< :I ii:

-22 10

-25 10 14 10 15 10 16 17 Ankle 10 10 Energy (eV) 2 (1 particle per km -year)

-28 '\tt 10 GeV TeV PeV EeV

109 10 10 10 11 10 12 10 13 10 14 10 15 10 16 10 17 10 18 10 19 1020 Energy (eV)

Figure 1.1: The all-particle spectrum of primary cosmic ray energies. Cosmic rays are observed by a variety of techniques over eleven orders of magnitude in energy. 2 75 The inset multiplies the spectrum by a factor of E · to highlight the "knee" feature near 1 PeV. The knee is the subject of this thesis. (Figure adapted from [13]) 6

2-Knee

1-Ankle

-- .. '------... _... _::. :::: ~ --- -

log( Energy) log(Energy)

3 4

A ," ' , ' ' ' ' '

log(l!nergy) log( Energy)

Figure 1.2: Combining two power law sources to create a spectral knee. Two sources with unequal power laws can easily combine to form an "ankle" in a spectrum like that observed near 3 x 1018 eV (panel #1). Creating a knee from two power law spectra requires that the harder source cut off at approximately the same energy as the softer source begins ( #2). The smooth knee is lost if the two energies are unequal (#3) or if the energies match but the fluxes do not (#4).

Above the region of solar modulation, the cosmic ray spectrum has approximately a smooth power law shape up to the highest measured energies. At a few PeV, however, lies a feature called the "knee." The differential flux J appears to steepen 2 7 from the form J ex E- · to J ex E-3.o. The knee was first noted in measurements of electromagnetic shower particle size in 1958 [14] and has been verified many times since in a variety of air shower measurements. A softening of the spectrum (an "ankle") appears near 3 x 1018 eV. This thesis describes a study of cosmic rays near the knee. One possibility is that the knee results from two separate cosmic ray sources, each with a characteristic power-law index. As discussed below in Section 1.2, a fairly broad class of phenomena can accelerate particles to produce a non-thermal, 7 power-law spectrum. It is considerably harder to see how two distinct sources, or types of sources, can combine to produce a broken power-law spectrum with a knee (Figure 1.2). One source would have to cut off above the knee energy, while the other must turn on at nearly the same energy. Furthermore, the cosmic ray intensity due to the two hypothetical sources would have to be similar at the transition energy. While not impossible, such a double coincidence in energy and intensity would be surprising. This argument suggests that cosmic rays below and above the knee come from not from two distinct source classes but from one. The knee would thus result from an inherent change in the cosmic ray acceleration process itself, in the propagation of cosmic rays, or in the physics of nuclear interactions through which the particles are detected.

1.1.3 The age of cosmic rays and other observations

Detailed observations of Ge V-energy cosmic rays offer a number of clues as to their origins. During their journey through the Galaxy, cosmic rays interact with the cold gas of the interstellar medium. In the more violent collisions, the cosmic ray nucleus can fragment. The partial loss of protons and neutrons from a nucleus is called spallation. Spallation of carbon or oxygen cosmic rays can produce the rare L-nuclei: lithium, beryllium, and boron. Because of this process, the L-nuclei are thousands of times more abundant in cosmic rays than in stars, where thermal equilibrium conditions destroy the light nuclei as quickly as they are produced. The abundance of the L-nuclei relative to carbon and oxygen therefore acts as a Galactic odometer, indicating the path length of cosmic rays through the interstellar gas. The average path length traversed by cosmic rays is approximately 5 g cm-2 of material, decreasing at higher energies. Other spallation products, such as the nuclei with Z = 21 to Z = 25, just lighter than iron (Z = 26) support this conclusion [4]. 3 Assuming a gas density of one particle per cm , the column density suggests a travel distance of 1 Mpc, thirty times the diameter of the Galaxy. Cosmic rays must follow quite twisted paths to travel so far and remain within the Galaxy.

Another abundance comparison of spallation products serves as ;:i cosmic ray clock. The radioactive isotope 10 Be decays with a 2. 7 million year half-life. Since 8

nearly all beryllium originates in the spallation of carbon and oxygen, we can calculate that 10% of beryllium is produced in the 10 Be isotope. The observation at Earth of a 10 Be fraction of 2.8% leads to an estimate of the mean cosmic ray propagation time of 107 years. This measurement can be used to refine our estimate of the mean gas density along cosmic ray paths [15]. The age and path length measurements establish the Galactic origin of the lower energy cosmic rays ("' 1014 e V), as the particles do not have time to reach us from any extragalactic sources. The arrival direction of cosmic rays at our Solar System is highly isotropic. The dipole anisotropy is less than 10-3 for energies below the knee and is of order "' 1% at 10 PeV. This result shows that the net velocity of cosmic rays streaming through the interstellar medium is quite small. The small anisotropy helps constrain models of cosmic ray diffusion and escape from the Galaxy [l]. From these and other similar observations emerges the modern t>icture of cosmic rays.

1.2 How cosmic rays are created and transported

The origin of cosmic rays is a difficult problem. Without directional information, acceleration sites cannot be identified directly. The generally accepted model of cosmic rays is that strong hydrodynamic shock waves ionize and accelerate atoms from the interstellar medium. A supernova explosion creates a shock wave of sufficient energy and lifetime to accelerate nuclei to energies of order 100 Te V. Astrophysical sources of stronger, longer duration shocks are possible, but it is unclear whether any exist in our Galaxy. If so, then cosmic rays above the knee could be created by the reacceleration of particles initially accelerated in supernovae. Otherwise, the highest energy cosmic rays must be extragalactic.

1. 2.1 Supernovae

In the evolution of some stars, the stellar core can become so dense that the electrons and protons in the central plasma fuse into neutrons through inverse ,8-decay (p + e- --+ n + ve)· Once this reaction starts to deplete the electron population, 9 electron degeneracy pressure can no longer prevent the gravitational collapse of the star. The explosive release of gravitational binding energy in the sudden collapse is called a supernova.2 A white dwarf can collapse in this way as it accretes matter from a companion star, as can an isolated, very massive star (;:;: 8M0 ). These two cases are possible explanations for the distinct Type I and Type II supernovae, respectively [15]. The explosion heats the surrounding stellar material, and energy propagates outward from the star in a spherical shock wave. The energy released in a supernova explosion can be on the order of 1052 erg [15]. A simple argument shows that supernovae could supply the energy stored in cosmic rays, assuming that particle acceleration occurs efficiently. If cosmic rays fill the 3 disk but not the halo of the Galaxy with an energy density of 1 eV cm- , then their stored energy is ,...., 1055 erg. With a cosmic ray lifetime of 107 years, the power 40 1 required to maintain cosmic rays is ,...., 3 x 10 erg s- . The Galactic supernova 43 1 rate is thought to be approximately three per century [15], releasing ,...., 10 erg s- . Supernova explosions would have to convert a surprising 1% of their energy to high energy particles in order to maintain a steady cosmic ray energy density. The Galaxy contains no other known sources of such power. Supernovae are thus possible cosmic ray accelerators, but proof remains elusive. The Whipple.. Observatory has searched for evidence by seeking 300 GeV gamma-rays from supernova remnants [17]; the flux limits they 5et contradict the predictions of a recent model for supernova gamma- ray emission [18]. And even if supernova do power cosmic rays, a highly efficient mechanism must still be identified for transferring energy to individual nuclei in the vicinity of the explosion.

1. 2. 2 Fermi acceleration

The characteristic non-thermal power law spectrum of cosmic rays can be explained by an incremental, repetitive acceleration process [19]. Fermi presented a model in 1949 in which a particle's energy increases by a fixed fraction ~ at each step, and

2 The name supernova was introduced by Baade and Zwicky in 1934, who suggested in the same pair of papers that supernovae might power the cosmic rays [16]. 10

the probability per step of escaping the acceleration region Pesc is independent of energy [20]. Under these assumptions, Fermi writes, "It is gratifying to find that the theory leads naturally to the conclusion that the spectrum of the cosmic radiation obeys an inverse power law [20]." The differential fiux 3 of particles with energy E will be ex: E-1 where / ~ 1 + Pesc/f,. The power law index thus depends on the relative time scales for encounters and for escape, as well as the energy gain per encounter. The repetitive acceleration process takes longer to produce particles of higher energy. The maximum possible energy increases exponentially with time, but a source with a limited lifetime will have a characteristic cutoff energy above which it produces no particles. Fermi's original model supposed that the accelerating encounters occur between energetic charged particles and "wandering magnetic fields which, according to Alf- ven, occupy the interstellar spaces r20] ." Particles enter a cloud of magnetized plasma more dense than average which has a net velocity relative to the interstellar medium 4 Vc1oud l"V 10- c. Diffusing in the cloud, a particle's direction is randomized before it emerges, as if the particle had bounced off the cloud .. A particle could gain or lose energy in such a process, depending on the angles at which it enters and exits the cloud. Energy gain is slightly more probable, however. In this situation, the average 2 gain per encounter would be f, ~ (4/3)/3 , where f3 Vczoud/c. The wandering plasma cloud picture has several problems [15]. Although the typical gain or loss per encounter is of order f3, the mean energy gain is of order 2 (3 . For this reason, it is called second order Fermi acceleration. Given clouds 4 with f3 l"V 10- , at a reasonable separation in interstellar space ( l"V 1 pc, or 3 light years), Fermi acceleration is an extremely slow and inefficient process. To accelerate a particle from 100 Me V to 100 PeV by increments of 10-s every three years would require several billion years, the age of most structures in our Galaxy. Particle energy loss by ionization, in addition to lengthening the acceleration time even further,

3 Here the symbol J is used for the differential flux, the cosmic ray rate per unit area per unit solid angle per unit energy range. The integral flux of particles above some minimum energy I(E) =J:O dE' J(E') is also commonly used. If the differential flux is a power law spectrum with 2 7 an index of -1, then the integral flux is also a power law with an index of 1 - 'Y· Thus Jex E- · corresponds to I ex E-i.7 _ 11 reqmres that particles be injected into the accelerator with energy 2: 100 MeV if ionization losses are not to dominate. Finally, the cloud model gives no explanation why the power law index r should be close to -2.7, as r depends on the the gain per encounter and the relative time for encounters compared with escape. Although the basic idea of Fermi acceleration has merits, acceleration does not appear to take place in plasma clouds. The modern picture of cosmic ray acceleration requires a strong hydrodynamic shock front [15, Ch. 21], such as that produced by a supernova explosion. A shock front replaces the random motions of clouds with a highly ordered system. Ener- getic particles moving in the shocked or unshocked gas come to equilibrium4 in the irregular magnetic fields and randomly cross the shock front. Regardless of which direction the particle crosses the front, the shock and the plasma beyond it appear to be approaching. All collisions are head-on in this scenario. Although the typical energy change per encounter is again of order /3, the particle crossing the front gains energy with each encounter. The mean gain is ~ ~ (4/3)/3 for strong shocks. This results in much faster particle acceleration and is called first order Fermi acceleration. In addition, the strong shock model predicts the probability for escaping the acceleration region and thus constrains the spectral index r ,...., -2, independent of "' the shock environment [21]. Although this index does not match the observed cosmic ray spectrum with r ~ -2.7, models of propagation through the Galaxy can explain the discrepancy [19].

1.2.3 Propagation and escape from the Galaxy

The 10Be clock (Section 1.1.3) shows that cosmic rays have a characteristic lifetime in the Galaxy of 10 million years. Since the light travel time across the galactic diameter is a factor of 100 shorter, cosmic rays must be confined in the Galaxy by magnetic fields. Comparing the 10Be measurements with the light element production, we find 3 that cosmic rays traverse material with an average density of ,...., 0.3 atoms per cm ,

4 In this context, equilibrium means isotropy in the local rest frame rather than full thermal equilibrium. 12 three times lower than the density of the Galactic disk. This observation suggests that the cosmic ray confinement volume extends significantly beyond the plane of the disk [19]. Naturally, the Galactic confinement is imperfect. Cosmic rays can diffuse out of the confining magnetic fields, a process usually framed in terms of the "leaky box" model. Particles with a higher magnetic rigidity ( R =p / Z) escape from the Galaxy more quickly because the magnetic fields bend their trajectories less. This observation explains why the boron to carbon ratio falls with increasing energy: the higher energy carbon cosmic rays escape faster and produce less boron through spallation. Fitting the B/C ratio with energy suggests that the escape time scale falls 0 6 as Tesc ex R- · [19]. The energy-dependent escape probability effects a steepening of the power law energy spectrum, as well. If the source spectrum has the J ex E-2 characteristic of first order Fermi' acceleration, then the observed spectrum after 2 diffusion from the Galaxy should be J ex E- ·6 . Thus the observed index of the cosmic ray power law spectrum can be reasonably explained by the production and propagation models.

1.2.4 Current models of composition

The combination of supernova shock acceleration and Galactic escape provides the starting point for current debate about the origin of cosmic rays. It is generally 11 14 agreed that most or all cosmic rays between ,...... , 10 - 10 eV originate in the explosions of Galactic supernovae. The question is whether the same sources explain higher energy cosmic rays and the knee in the spectrum. The knee is suspiciously close to the energy above which supernova acceleration is impossible (due to the finite lifetime of the supernova shock wave). If the knee represents a cutoff in the shock acceleration, the knee should occur at a fixed rigidity (p / Z) for each element. The maximum energy expected from supernova shocks is approximately Z x 1014 eV [22]. Therefore the composition is expected to become slowly heavier through the knee (Figure 1.3). The simplest supernova models cannot explain the origin and composition of cosmic rays far above the knee. 13

~ ..; w x )( ::I ii: Total

-1 10 ' ' ------~ ,- --...... - ---- _.... .,,., ':---- ', ',, -2 10 H \ H~\ CNO,\ Fe ' ' ' ' ' ' \ ' ' ' -3 \ 10 '-----'-'--'-'--'--'--'-~~'---'-----'---.1-"--JC..L.L-'---~-'-----'--'--"--'--'-'--'-'-~-'--'---'--'--'-L-'-'-'L.L.L..~--'--'----.J -1 10 1 10 Energy (PeV)

Figure 1.3: A schematic spectrum with rigidity-dependent cutoffs. Four cosmic ray species (dashed) are shown each with a cutoff at a fixed rigidity Re = p/ Z of 2 x 10 14 V. The solid curve is the sum of the four component spectra. Regardless of the relative abundances below the knee, the composition becomes heavier smoothly through the knee region in any scenario where the cutoff depends only on magnetic rigidity.

Below are several models that try to explain the existence of cosmic rays above the knee (or of the knee itself) and which predict the cosmic ray composition in this energy range. This list is not exhaustive, nor are these models all exclusive of one another. In particular, all models assume some form of Galactic escape. Galactic escape: In this model, diffusion out of the Galaxy occurs at all energies, but it changes fundamentally at some critical energy. The knee thus results from the propagation rather than the acceleration of cosmic rays. This type of explanation was put forward in 1958 by the discoverers of the knee [14]. Diffusion is determined by the magnetic irregularities in the Galaxy. Particles with a gyroradius smaller than the size of the irregularities will be confined in the Galaxy, while the more energetic cosmic rays cannot easily be trapped and will escape more readily. Since the confinement depends on a particle's magnetic gyroradius, the change in the 14 spectrum occurs at a fixed magnetic rigidity for all species. That is, the knee appears at an energy 26 times higher for iron nuclei than for protons. The model predicts a very wide knee in the spectrum, over a 1.5 decade range, with a composition that becomes much heavier above the knee than below [23].

Reacceleration: The reacceleration of cosmic rays by interstellar turbulence could operate in conjunction with supernova shock acceleration to power cosmic rays [24]. Since the turbulence is an essential feature of the Galaxy rather than being short-lived like supernovae, reacceleration models do not limit the maximum possible cosmic ray energy to ,....., 1 Pe V. But explaining all cosmic rays above the knee by reacceleration is problematic, as the observed secondary abundances (the B/C ratio for example) are too low. In a model of supernovae plus reacceleration, the knee would depend only on rigidity.

Compact sources: In contrast, the compact source model attributes the knee to effects at the acceleration sites, which are assumed to be pulsars rather than supernova shock waves. The pulsar environment is filled with X-rays, which interact with the high energy cosmic rays. Nuclei tend to disintegrate when struck by energetic photons. The main photonuclear reactions are those at the giant resonance region, where the photon has energy 20 Me V in the nucleus rest frame. The cosmic ray energy required to reach this threshold is proportional to nuclear mass, so the knee that results from photonuclear reactions would occur at a fixed energy per nucleon E /A. This prediction would be similar to the Galactic escape prediction of a knee at fixed rigidity (p/ Z), except that protons cannot disintegrate. The energy threshold for photopion production by protons is approximately 150 MeV in the proton rest frame. Thus protons should survive to higher values of E /A than compound nuclei. The expected composition changes are complicated, but the mean mass is expected to stay roughly constant up to the energy at which even the iron nuclei disintegrate. Above this energy, the composition at the source becomes very light, purely protons and neutrons [25].

Extragalactic sources: According to Protheroe and Szabo, cosmic rays above the knee could have an extragalactic origin [26]. Specifically, most cosmic rays up to at 15 least 10 16 e V, or even 10 19 e V, could originate in the central regions of active galactic nuclei (AGN). Depending on diffusion in intergalactic magnetic fields, cosmic rays from rv 500 AGN might have reached us in the a,ge of the Universe. Remarkably, the predicted flux of AGN cosmic rays is of the same order of magnitude as the observed flux at the knee and higher energies. In this model, the knee appears because the supernova acceleration cutoff coincides with the arrival of extragalactic cosmic rays above the knee (as in the upper right panel of Figure 1.2). The photonuclear disintegration discussed above would also operate in AGN. Heavy nuclei would be accelerated in AG N, but only protons would survive the intense X-ray flux of the dense central region. The extragalactic component of cosmic rays should therefore be entirely protons, predicting a light composition above the knee.

Three site model: Biermann and others advocate a model that uses three mechanisms to explain the cosmic ray origin [27]. Below the knee, cosmic rays come from supernovae shock acceleration of the normal interstellar medium. Far above the knee, extragalactic sources dominate. Cosmic rays at the knee itself are attributed to supernovae exploding into an unusually dense medium, the former stellar wind of the supernova progenitor. Wolf Rayet stars are excellent candidates, as they shed mass prodigiously before becoming supernovae [15].eThe acceleration of stellar wind particles produces a change in spectral index because the acceleration efficiency drops rapidly when particles reach a certain rigidity. The authors claim that the expected spectral index (including Galactic escape effects) is -2.67 below the knee and -2.97 above it. The predicted composition is quite heavy at and above the knee. Far above the knee (E?:: 3 x 10 18 eV) the composition becomes lighter again when extragalactic protons begin to dominate the faltering heavy cosmic rays from Wolf Rayet supernova.

Single source: Wolfendale and Erlykin propose that all cosmic rays near the knee come from "a single local, recent supernova" that exploded in the last 105 years within rv 100 pc of Earth [28]. Other models, in which cosmic rays are accelerated by many distinct sources with different cutoff energies, predict a smooth knee. The single source suggestion is based on the claim of "fine structure" in the cosmic ray 16

Model Reference Prediction Supernova cutoff [15] Heavier through a very wide knee Galactic escape [23] Heavier through a very wide knee Reacceleration [24] Heavier through a very wide knee Compact source [25] Constant through the knee, protons above it AG N (extragalactic) [26] Protons above the knee Three sites [27] Heavy at the knee, becoming heavier Single source [28] CNO at the knee, Fe above it Interaction [23] Unconstrained

Table 1.1: Models of the knee composition.

energy spectrum which would not be expected in the aggregate spectra of multiple supernova sources. In this model, the knee corresponds to the single source's cutoff energy for acceleration of oxygen. A second knee, or bump, in the spectrum is predicted at the same rigidity for iron nuclei, i. e. at an energy 26/8 times higher. Although the authors see the purported bumps in existing data [29], convincing observations of the peaks would require rather better energy resolution than is likely to be achieved in the near future. The single source model predicts that the cosmic ray composition becomes heavier through the knee, with most particles at the knee being oxygen and most above it being iron.

Interaction model: Some workers attribute the apparent knee in the cosmic ray spectrum to changes in high energy physics rather than in the astrophysics of particle acceleration or propagation. The knee is thus a measurement artifact. Yet observations of electromagnetic particles, muons, and Cherenkov light in air showers all exhibit a knee. The interaction models must therefore postulate hidden particles which divert energy from the traditionally observable air shower components. Such models tend to predict a sharp knee at the onset of the new interaction physics, but they leave open the question of composition [23]. 17

Fractional abundance Nucleus Mass A JACEE RUN JOB H 1 0.24 0.28 He 4 0.31 0.21 C-N-0 14 0.21 0.35 Ne-Si 24 0.12 0.04 Fe 56 0.12 0.12

Table 1.2: Cosmic ray composition at 100 TeV per nucleus, as reported at the 1997 ICRC from two high altitude balloon groups [30].

1.3 Existing measurements of the cosmic ray composition

Measurements of cosmic ray composition at and above the energy of the knee all rely on observations of extensive air showers. Their interpretation depends on the assumed physics of high energy interactions in the atmosphere. This section summarizes the published measurements of high energy composition. Watson gives more detail in his excellent overview of results from the 1997 International Cosmic Ray Conference [30].

1. 3.1 Direct measurements at energies below the knee

Below ,...., 10 14 e V, cosmic rays can be studied directly by satellite or balloon payloads. The instruments contain wire chambers, transition radiation detectors, Cherenkov counters, or other detectors typical of high energy physics. Currently, the direct detections with the highest energy reach use photographic emulsions, for example the JACEE balloon payload [31]. Table 1.2 summarizes the measured composition just below the knee, which slightly favors the light elements.

1. 3. 2 Indirect measurements at the knee

The cosmic ray flux falls quickly with energy, and above ,...., 1014 eV cosmic rays are inaccessible to balloons of reasonable size and flight duration. For this reason, higher energy particles must be studied indirectly by observing their air showers. The 18

Experiment Reference Technique Result DICE [32] Cher. imaging mixed-t light AIROBICC [33] Cher. lat. dist., Ne mixed throughout VULCAN [34] Cher. lat. dist. mixed-theavy CASA-MIA [35] Ne and Nµ mixed-theavy EAS-TOP [36] µlat. dist., Ne mixed-t heavy MSU [37] 10 GeV µlat. dist. light-theavy Frejus [38] Deep (Te V) muons light KASCADE [39] Hadrons mixed-t heavy KASCADE [39] Ne and Nµ light-tmixed

Table 1.3: Several recent measurements of cosmic ray composition near the knee (1-10 PeV). Results give the trend with increasing energy through the knee. The conclusions differ widely among different experiments, reflecting the difficult and simulation-dependent nature of the problem.

large fluctuations inherent in the showering process largely obscure the differences between primary cosmic rays of different mass (see Chapter 2). Furthermore, working backwards from observed shower properties to the energy and mass of the primary cosmic ray requires simulations. The interaction physics of energetic cosmic rays with air nuclei requires substantial extrapolations from accelerator data, leaving the simulations open to unknown systematic errors. Composition measurements at and above the knee are therefore extremely difficult and provide at best a rather crude mass resolution.

A qualitative summary of current composition measurements near the knee appears in Table 1.3. Most were reported recently, between 1997 and 1999. Even this simple comparison of the conclusions shows striking disagreement. Many results are consistent with the expected heavier composition above a rigidity-dependent cutoff, but in many cases the conclusion is weak and the data are also consistent with very different interpretations. Different experiments measure different components of an air shower, and the simulations used for interpreting the data vary. Some combination of these differences is probably responsible for the disparate conclusions. 19 1.3.3 Ultra-high energy composition

Above the knee, the cosmic ray flux becomes so small that huge detectors of many square kilometers are required to gather a useful sample of cosmic rays. Giant air shower arrays have detector separations on the order of rv 1 km. At such high energies, the interaction physics becomes quite uncertain, and the interpretation of particle density measurements is increasingly difficult. The air shower fluorescence technique is an interesting alternative. As implemented by the Fly's Eye experiment, the technique reveals the development of air showers throughout the atmosphere rather than at the ground only. The Fly's Eye group finds that the cosmic ray composition is consistent with very heavy nuclei at 1017 eV but becomes much lighter over the next two decades of primary energy [40]. CHAPTER 2 EXTENSIVE AIR SHOWERS

When a cosmic ray reaches the Earth, it collides high in the atmosphere with the nucleus of an air molecule, producing a spray of nuclear material. If the primary cosmic ray is energetic enough, then the secondary particles themselves can also interact with other nuclei. A particle cascade then develops through the atmosphere, as a growing number of particles share the energy of the original cosmic ray. This cascade is called an extensive air shower. This chapter describes the development of a particle air shower and the emission of Cherenkov radiation and discusses how the mass of the primary cosmic ray affects the particles and Cherenkov light produced in the air shower.

2 .1 The anatomy of an air shower

A high energy cosmic ray entering the Earth's atmosphere first interacts with an air nucleus, either nitrogen or oxygen, at a typical altitude of 15-30 km. The outcome of this collision can vary widely even for primaries of identical energy and mass. Generally, the first interaction produces one or more large nuclear fragments along with many pions. The nuclear fragments carry roughly half of the collision energy deeper into the atmosphere, where they interact repeatedly with air nuclei. At each successive generation, the nucleonic cascade loses half of its energy through the production of more pions. Each high energy hadronic interaction produces positive, negative, and neutral pions in approximately equal numbers. 1 Charged pions have a proper lifetime of 26 ns. Because of relativistic time dilation, the energetic charged pions in an air shower are more likely to interact with air nuclei than to decay. The pion-nucleus collisions create yet more pions, again with a two to one charged to neutral ratio. Since the interactions produce approximately 10-20 pions each, the energy per particle falls rapidly, one order of magnitude per interaction length (>.int~ 90 gcm-2 [41]). After

1 Charge is of course conserved. 20 21 only a few generations, the charged pions reach an energy sufficiently low that they tend to decay before interacting. At this point, the charged pions decay into muons and muon neutrinos, and the pion cascade quickly evaporates.

The neutral pions produced at each stage of the nucleonic and pion cascades have a proper lifetime of only 8 x 10-17 s. Even with an energy of 10 16 eV, a Ho has a mean decay length of less than 2 m, while the nuclear interaction length at the bottom of the atmosphere is 1000 m. Nuclear interactions of neutral pions are therefore irrelevant for cosmic ray air showers with energies near the knee. Instead, the Ho decays immediately into two gamma rays (or with 1% probability by the Dalitz decay Ho ~ 1e+e-). The result of either decay is to channel energy from strongly interacting shower hadrons into electromagnetic particles.

Air shower gamma rays convert in the atmosphere to electrons and positrons. These particles in turn emit energetic bremsstrahlung gamma rays, which produce more electrons and positrons. The growing population of photons, electrons, and positrons constitute the electromagnetic cascade. At some point, the particles in the cascade no longer have enough energy to multiply, and below this level the shower begins to attenuate through ionization energy loss. The quantity Xmax labels the atmospheric depth at which the number of charged particles is highest. Electrons and photons rarely produce new nuclear particles, so energy flows from the pion cascade into electromagnetic particles but not in the other direction. Thus the electromagnetic cascade quickly dominates the air shower. For cosmic rays at the knee, the electromagnetic particles carry as much as 80-90% of the primary energy at the peak of the shower. The remaining energy is shared among the muons, neutrinos, and those few nuclear fragments that penetrate to the ground level. Ultimately, most of the primary energy is dissipated by heating the atmosphere, and only ,...., 10% reaches the ground in the form of energetic particles. Figure 2.1 shows in schematic form the main components of an air shower.

Figure 2.2 shows how the number of shower particles (mostly electrons) rises then falls with increasing depth in the atmosphere. The curves shown here are idealized, based on the parameterization by Gaisser and Hillas [42]. The left panel 22

Primary Cosmic Ray

Electromagnetic shower

Figure 2.1: The principal components of an extensive air shower. Unlike this diagram, an actual shower's hadronic, pion, and electromagnetic components overlap in time and space. Although the number of pions grows with each generation, the total energy carried by pions falls, as 7ro -t 'Yr decays transfer energy from the pions to the electromagnetic cascade. 23

20km 10 km Skm 3km 1.5 km co~ 7 _; 10 7 0 u ... t: ..:!... 10 PeV Iron 10 PeV Proton 111 en 6 6 GI ~ 10 Q 0 :;:::;...... GI 111 5 ..a ll. E 10 5 :I z 4 10 4 3

10 3 2

10 2 1 ' '

0 0 200 400 600 800 1000 0 200 400 600 800 1000 2 2 Atm Depth (g cm" ) Atm Depth (g cm- )

Figure 2.2: Example air shower development curves based on the Gaisser-Hillas parameterization [42]. The vertical dotted lines indicate the atmospheric depth at 2 the Dugway observation site, 870 g cm- . Left: Protons of different primary energies. Right: Two 10 PeV nuclei of different mass (solid lines) and the same two species with 5 PeV primary energy (dashed). Charged particle measurements at a single shower depth could not distinguish a 10 PeV iron primary from a 5 PeV proton.

compares proton showers of different primary energy. The right panel shows the difference between primaries of the same energy but unequal mass, a topic which Section 2.3 discusses further. Actual air showers are the aggregate result of many random processes (collision and decay). While the figure presents only an average shower development curve, a single real shower can differ substantially from the average, particularly in the depth of shower maximum.

2. 2 The Cherenkov effect

A charged particle moving through a dielectric medium radiates when its velocity exceeds the local speed of light. The emission is called Cherenkov radiatirm, after its 24 discoverer Pavel Cherenkov (1904-1990). Because the particle velocity exceeds the phase velocity of electromagnetic waves in the medium, the particle's Coulomb field produces a coherent "shock wave" behind the particle (Figure 2.3). The wave front propagates away from the particle path at a fixed angle Be, the Cherenkov angle, which depends only on the relative velocities of the radiation and the particle:

cos Be = vq,/v = l/n{3 where v and vq, are the particle and electromagnetic phase velocities, n is the refractive index of the medium, and {3 =v/c. The charged particle produces no Cherenkov light unless its velocity exceeds the threshold velocity f3t = 1/n. Equivalently, the particle radiates only if the cosine of the Cherenkov angle Be is less than one [l]. The particle cascade produced by air showers of 100 Te V or higher energy can "' be studied at ground level. But the ground particles provide only a "snapshot" of the air shower at one instant. The atmosphere is thick enough that even 1016 eV showers detected at the ground are well past their level of maximum particle density (Figure 2.2), which leaves ground observations susceptible to large fluctuations that depend on unobservable details such as the height of the first interaction. Optical Cherenkov radiation provides an alternative to direct particle detection. Since energetic particles at all levels in an air shower produce Cherenkov light, its detection offers an integral over the complete history of the shower.2 Cherenkov light emission is strongest at short wavelengths, appearing primarily in the blue and ultraviolet. For a singly charged particle, the number of photons emitted per unit length per unit wavelength interval is

2 d Ny 27ra . 2 27ra ( 1 ) dx d>. = --:,\2 sm Be(>.) = --:,\2 1 - (32n2(>.) where a= 1/137 is the fine structure constant [41]. The l/>.2 dependence of the Cherenkov spectrum means that most emitted photons have short wavelengths. An

2 Scintillation, or fluorescence, of the atmosphere is another method for observing a shower throughout its development. Production of a detectable optical signal, however, requires primary cosmic ray energies of at least 1017 e V. 25

Figure 2.3: Diagram of the Cherenkov radiation shock front. Spherical wavefronts emanate from a moving charged particle at the phase velocity of light, c/n. The particle on the left is moving at half the phase veloci ';y; the one on the right moves at l.33c/n and thus emits Cherenkov light. The Cherenkov angle shown here ( 41°) corresponds to the case of highly relativistic particles in water. Figure based on [43].

equivalent expression for photon emission per unit interval of photon energy is

d2 N __'Y = 370 sin2 (} (E) eV- 1 cm-1 dxdE c

If integrated over all photon wavelengths or energies, the expressions given above for the Cherenkov photon emission would seem to diverge in the ultraviolet. This apparent problem is resolved by noting that the refractive index (and thus the Cher- enkov angle) is not constant over all wavelengths. Any real medium is dispersive and has wavelength bands of resonant absorption. Below the absorption bands, the phase velocity of light is greater than c, and thus particles produce no Cherenkov light at short wavelengths [43]. In air, ultraviolet absorption provides a short-wavelength cutoff to the Cherenkov emission at approximately 270 nm. The index of refraction of the atmosphere is only slightly larger than 1.0, so the Cherenkov threshold velocity is quite high. At standard temperature and pres- 26

4 sure, nair ~ 1 + 2.93 x 10- • This refractive index fixes the energy threshold for positrons and electrons, the most important Cherenkov radiators in an air shower, at 21 MeV. The atmospheric Cherenkov emission angle ~s Oc ~ 1.4° for particles well above threshold, smaller for particles closer to the Cherenkov threshold velocity. Higher in the atmosphere, the air density falls exponentially with a scale height of approximately 9 km. The index of refraction in a gas follows the approximate rule ( n - 1) ex p. Consequently, the Cherenkov threshold energy rises as Ethresh ex Jn=-I ex -JP, which is also exponential but with an 18 km scale height. The radiation emitted per unit length of particle track falls with increasing altitude, in proportion to the gas density. These changes with altitude combine to increase the Cherenkov emission from particles lower in an air shower relative to the yield of particles at higher altitudes. This effect governs the relationship between air shower longitudinal development and the, distribution of Cherenkov light on the ground.

2.3 Composition and air showers

Interpreting air shower measurements requires a detailed model describing the interactions and decays of many types of fundamental particles and nuclei. The model must track the millions of energetic particles produced in a shower and their spatial and angular divergence from the central shower axis. The modern approach to these calculations relies on computer Monte Carlo simulations. Monte Carlo programs track individual shower particles, producing interactions and decays by random sampling of the relevant distributions. The technique is especially useful for predicting how the showers produced by a primary of a given energy and mass can fluctuate due to the inherent randomness of the cascade. Many features of an air shower, however, can be derived from analytic calculations on a simple model. In particular, such a model can explain how showers change with primary energy as well as some of the effects of primary mass. Although the BLANCA data set is ultimately analyzed by comparing it with full Monte Carlo calculations, the simple model presented in this section anticipates many predictions made by the detailed simulations. Nuclear superposition is the most important assumption in this argument. Su- perposition approximates a nucleus of mass A as a bundle of A separate but identical 27

nucleons. In this simplification, an iron primary cosmic ray with energy E produces an air shower equivalent to 56 simultaneous proton showers, each having primary energy E /56. The assumption is justified partly because the kinetic energy in a PeV primary is much larger than the binding energy, so the nucleons behave approximately as free particles. Superposition is only approximate, as the presence of other nucleons does affect the nuclear interactions, and shadowing causes cross sections to rise less than linearly with A [45]. Superposition is the simplest case of the more general wounded nucleon picture [19], in which nucleus-nucleus collisions are conceptually reduced to a series of nucleon-nucleon collisions. The superposition model predicts mean shower development parameters well, but it tends to underestimate fluctuations. One result that follows immediately from superposition is that heavy primaries produce air showers with smaller inherent fluctuations than those found in a proton- induced shower. An iron-initiated air shower consists of an average over many nuclear collisions, suggesting that the resulting fluctuations in longitudinal development should be a factor of ,....., -/56 smaller than the inherent proton shower fluctuations. Monte Carlo calculations verify this conclusion qualitatively.

2. 3.1 Atmospheric depth of shower maximum

Air showers consist mainly of electromagnetic particles, e± and photons. The shower is therefore dominated by the development of the electromagnetic cascade. A simple cascade model, suggested by Beitler [47, §24], illustrates several features of air showers. Although the model describes electromagnetic cascades specifically, it serves as a model for the similar but more complex hadronic air showers. Consider a shower initiated by a high energy electron or photon with energy E 0 . The cascade multiplies through two mechanisms, pair production by gamma rays and bremsstrahlung radiation by electrons. Either process converts one electromagnetic particle into two, which share the original energy in roughly equal proportion. Assume the parent particle energy is divided exactly in two and that the interactions take place after the parent particle traverses a column density of exactly ..\. For an electromagnetic 28 cascade, the relevant length is the radiation length of air (X0 ), the column density in which a high energy electron loses all but 1/e of its energy to bremsstrahlung. The mean free path for high energy photons to produce an e+e- pair is tXo, so A= X 0 is the characteristic length scale in this model. Thus the number of particles in the cascade doubles with each increase in depth of ;\:

x N(X) = 2~ (2.1)

and each of the N particles has energy E 0 / N.

After the energy per particle falls below some critical value Ee, the shower stops growing. For electrons, the critical energy is the energy below which ionization energy loss exceeds the loss by bremsstrahlung. For gamma rays, it the energy below which Compton scattering is morn. important than pair production [46]. The critical energy for electrons or gamma rays in air is approximately 80 Me V [41 J. In the simple cascade model, the shower achieves its maximum size when each particle has exactly the critical energy, Nmax = E0 / E 0 where E0 is the primary particle energy. Below shower maximum, particles are attenuated by ionization and Compton scattering. Solving Equation 2.1 for the depth of maximum,

Xmax = ln2,\ ln (Eo)Ee (2.2)

The depth of shower maximum increases logarithmically with the primary energy.

Suppose instead that a heavy primary initiates an electromagnetic cascade of energy E0 . For a compound nucleus of A nucleons, the number of particles at maximum is unchanged, but the formula for the depth of maximum is modified because each of the A subshowers has an energy of E0 / A.

Xmax = In,\ 2 In (AEe Eo) (2.3)

From the simple cascade model, we find that showers produced by heavy nuclei reach maximum higher in the atmosphere than proton showers do (Figure 2.2). 29

Another important point is that the depth of maximum varies as the logarithm of the primary mass instead of linearly with mass. The BLANCA shower simulations (Chapters 7 and 8) support this result. Setting,,\= 36gcm-2 we find that at any given primary energy, the Xmax of proton showers exceeds that of iron showers by 2 .A(lnA)/(ln2) ~ 200gcm- . Detailed shower calculations show that this simple model overestimates the proton- iron difference by 50%. There are many factors that modify the predictions of the basic cascade model. One problem is that the model assumes the fraction of energy entering the electromagnetic cascade E 0 / Eprimary is independent of primary mass. The electromagnetic energy fraction is higher for light primaries, a fact which follows only when the pion and nuclear cascades are considered in addition to the electromagnetic component of the shower. Furthermore, the model ignores the changing production of hadronic secondary particles with energy. The multiplicity increases with energy, which has the effect of dividing proton showers into more subshowers at the first interaction, pulling Xmax(P) higher in the atmosphere and reducing the proton-iron difference. But the main problem with the simple cascade model is that it ignores the inherent randomness of a cascade, both in the interaction lengths of individual shower particles and in the energy distribution of the products at each & interaction.

The most important random variable is X 1, the depth of the first interaction between the primary and the air.3 The simple model of the air shower assumes that the first interaction takes place at an atmospheric depth of .A. Instead, the atmospheric depth of the first interaction is distributed exponentially according to

where NA is Avagadro's number, aint is the interaction cross section for the primary, 1 and mair is the average atomic weight of air in g mo1- . The cross section depends on both the type and energy of the cosmic ray. For primary protons and iron with PeV energies, the mean nucleus-air cross sections are approximately 0.35 and 1.5

3 The depth of first interaction X 1 is not to be confused with X 0 , the radiation length in air. 30 barns [46], which correspond to mean interaction lengths of approximately 70 g cm-2 2 and 15 g cm- , respectively. The cross sections rise slowly with primary energy. It is apparent that iron showers begin higher in the atmosphere on average than proton showers and furthermore that the depth of their first interaction will vary less from one shower to another. This deeper first interaction is in addition to the greater distance required for the full development of proton showers, both effects causing proton Xmax to be larger than iron Xmax on average. Chapter 8 shows the results of a full Monte Carlo simulation of hadronic air showers, including how the depth of maximum changes with primary energy. There is a middle ground between the simple model given above and a full shower Monte Carlo, however. Analytic cascade theory, developed in the 1940s by Rossi, Greisen, and others [44], can predict longitudinal profiles of shower particles, lateral distributions, and size spectra. The analytic calculations involve solving the transport , equations, which are integro-differential equations for the flux N(E, X) of particles with a certain energy at a certain depth. In the simplest case of a single particle species, the equation has the form

00 dN N(E,X) 1, dE' N(E',X) I dX (E, X) = - >..(E) + E E >..(E') Pint(E -+ E) where).. is the interaction length and Pint(E' -+ E) is the probability per unit length of a particle with energy E' interacting and having energy E after the collision [19]. Thus the first term represents the loss of energy E particles through interactions, and the second accounts for the creation of new ones due to the interactions of higher energy particles. In a complete cascade calculation, the above equation becomes a set of coupled transport equations, in which the integrals contain multiple source terms to account for particles of one type interacting and producing other types. Analytic cascade theory generally has been replaced by Monte Carlo calculations, but with simplifying approximations it can still be used to check the results of more complicated models.

To summarize the discussion of Xmax, proton primaries initiate air showers that reach maximum deeper in the atmosphere than heavy nucleus air showers, for several 31 reasons. Proton primaries tend to begin showering later in the atmosphere than heavy primaries, and they produce showers which require more generations before the electromagnetic particles reach the critical ener5y of 80 MeV. The variation of Xmax at a fixed energy is much larger in a set of proton showers than in heavier showers, primarily because the multiple nucleons allow the composite shower to behave like a superposition of smaller showers, tending to average away fluctuations. For any species, Xmax grows deeper with increasing energy but only logarithmically.

The change in Xmax per decade, dXmax/d(log10 E) is called the elongation rate. The elongation rate is sometimes preferred, as it can often be measured and predicted with less systematic error than Xmax can.

2.3.2 Cherenkov light

The lateral distribution of Cherenkov light is sensitive to the primary cosmic ray composition almost entirely because Xmax depends on mass. Showers of a given energy and depth of maximum produce very similar Cherenkov distributions, regardless of the primary mass. The Xmax dependence appears in the slope of the Cherenkov lateral distribution near the shower core. The distribution is approximately exponential there, c (r) ex e-sr' and the inner slope s can be used as an indicator of shower depth. Steeper slopes correspond to deeper developing showers. The reasons for the variation of the Cherenkov lateral distribution with energy and Xmax are complicated, involving the changing Cherenkov angle with atmospheric density and the increasing angular spread of electromagnetic shower particles. A simplified model of the Cherenkov emission in a vertical air shower appears in Figure 2.4, using the U. S. standard atmospheric model (Appendix B). The left panel shows that the maximum Cherenkov angle falls with altitude, having an approximate scale height of 18 km (as discussed in Section 2.2). The center panel shows the radius on the ground of a Cherenkov cone emitted at various heights, which a diagram in the last panel illustrates. All Cherenkov light emitted above 6 km (500 g cm-2 depth) lands in a ring between 110 and 150 m from the point where the emitting particle's path intersects the ground. If all particles in an air shower were to travel parallel 32

UI 14 Cll 140 e Cll 1.4 g ~ ... Ill Cl :I 12 Cll .s::. Cl ~ 1.2 =g 120 - a; Cll ... Cll .s::. 10 '61 c: c: 1 y - 1000 5 100 0 Ill u ·u; > > Ill 8 0 0 .I<: 0.8 .I<: 80 c: c: ·ew Cll Cll 6 ...Cll 0.6 ...Cll 60 .s::. y:100 .s::. 0 0 0.4 40 4

0.2 20 2

0 0 0 10 20 0 10 20 -50 50 150 Emission height (km) Emission height (km) Ground distance (m)

Figure 2.4: Simplified picture ot Cherenkov em1ss10n in a vertical shower. Left: 2 Cherenkov angle for particles with relativistic I= E/(mc ) of 100 and 1000. The angle is nearly the same for all particles with / ~ 1000. Center: Cherenkov ring radius at ground as a function of emission height. Right: Diagram of Cherenkov rings in the absence of particle scattering. to the primary, then Cherenkov light would never be found more than 150 m from the shower core, and light closer than 100 m to the core would be produced only by 2 particles below a depth of 500 g cm- . Electron multiple scattering in a real air shower smears the expected Cherenkov ring at 120-150 m, but it does not eliminate it because the scattering distribution is peaked at small angles [46]. At lower shower energies, a "shoulder" remains in the Cherenkov lateral distribution. At PeV energies, the shoulder disappears, but 120 m remains a transition point in the Cherenkov lateral distribution. One approach to improving this simple Cherenkov model and determining the effects of multiple scattering is to use the subshower model [48]. In this picture, an air shower consists of a superposition of independent electromagnetic subshowers arising at different atmospheric depths, which can be simulated by Monte Carlo methods. Very deep subshowers are found to produce Cherenkov light very near to 33

~ 10 6 10 6 ':'s ':'s i!' i!' "iii "iii c: «-- Cherenkov Inner Slope c: Cll Cll "C "C .sc: .sc: 0 10 5 0 10 5 .s:: .s:: Q. Q. > > 0 0 .II: .II: c: c: ...Cll Cll Cll Qi .s:: .s:: 0 0

10 4 104

0 100 200 300 0 100 200 300 Core distance (m) Core distance (m)

Figure 2.5: The BLANCA concept: example Cherenkov light lateral distributions. Left: Two showers of the same energy but reaching different depths. The steeper inner slope corresponds to deeper Xmax· Right: Two showers with equal Xmax but a factor of three difference in primary energy. By measuring the Cherenkov lateral distribution, BLANCA finds the primary energy and shower depth. the core, falling quickly with increased core distance. Subshowers beginning higher in the atmosphere tend to produce more light in the 120-300 m core distance range than the lower subshowers, and less light within 100 m. Consequently, the main determinant of the inner exponential slope s is the proportion of light emitted close to the observation level. The inner slope is sensitive to the overall depth of Cherenkov emission in the shower, increasing with Xmax· The Cherenkov lateral distribution at radii beyond 150 m depends less on shower development than the inner region does. Instead, the outer part of the Cherenkov distribution indicates the total path length of charged particles in the showers. This result suggests the BLANCA strategy (Figure 2.5): sample the Cherenkov light pool, use the distant regions to find the energy, and convert the inner slope into an estimate of Xmax and thus the composition [49]. The critical radial distance of 120m is determined entirely by the density and scale height of the atmosphere. 34 2. 3. 3 Other composition-dependent properties

The present work determines the cosmic ray composition through Cherenkov measurements alone. A number of other air shower parameters, however, also depend on the composition of primary cosmic rays. The number of electrons at ground level, for example, depends on the primary mass as well as energy, with proton showers providing more electrons. As shown in Figure 2.2, iron showers reach maximum higher in the atmosphere and are therefore attenuated more before the observation level than proton showers are. The number of muons produced in a shower also depends on the primary species. At Pe V energies, the electron number rises faster than the primary energy because of the competition in the pion cascade between decay and interaction. Each pion generation transfers energy to the electromagnetic cascade through 7ro --+ 2"( decays . ... Since the number of pion generations increases with energy, the fraction of hadronic energy which eventually ends up in the electrons and photons also increases. For the same reason, a smaller fraction of the primary energy remains in charged pions after the final generation of the pion cascade, leaving fewer 7r± and thus fewer decay 1 muons. If (Nµ) ex (E0 ) -€, then the superposition model suggests that for a mass 1 A nucleus, (Nµ) ex A(E0 /A) -€ or for a fixed energy, (Nµ) ex A€. At PeV energies,

E ~ 0.13, so the iron showers have approximately 1.7 times as many muons as proton showers of the same primary energy [35]. Other shower parameters can also help to distinguish primary composition, such as the particle lateral distributions and arrival times. The electron lateral distribution falls more slowly with core distance for heavier primaries [35]. In terms of the standard NKG parameterization [50], the shower "age" is larger for iron showers than for protons. The lateral spread of muons likewise carries information about the early nuclear interactions and hence the primary mass, as muons are more widely spread at ground level when produced in early developing showers [51]. For geometrical reasons, the arrival time of electromagnetic shower particles depends on the depth of shower maximum. The delay of the shower front at a point, relative to the arrival time at the core, is larger when the location of shower maximum is nearer to the 35 detector (i.e. when Xmax is larger). The Haverah Park giant air shower array has measured the arrival time spread of the shower front and finds that the time spread is larger for showers that develop deeper in the atmosphere [52]. Cherenkov pulse time profiles measured 200 m or further from the core are also wider for showers that develop close to the ground [53]. Many of these composition-sensitive shower parameters are difficult to measure. Arrival time and pulse width effects are significant only at large distances from the core, where particle or Cherenkov densities are quite low. Electron and muon density measurements present their own difficulties, including sampling and saturation effects. The Cherenkov intensity is in many ways the most accessible of the potential composition-dependent measurements. Showers at PeV energies generate copious numbers of photons. Furthermore, the photon lateral distribution is less steep than the particle distributions, so sampling and saturation are less serious problems in Cherenkov measurements than in particle detection. The Cherenkov light beyond 120 m fluctuates much less than the particles size does for showers of a given energy. Furthermore, the Cherenkov slope is primarily of geometric origin, and unlike the particle counts or distributions, it has a clear, model-independent interpretation in terms of Xmax· This thesis describes a detector array which measures the lateral dis- ., tribution of Cherenkov light and uses it to estimate the primary cosmic ray energy spectrum and composition. CHAPTER 3

THE CHICAGO AIR SHOWER ARRAY

The Chicago Air Shower Array (CASA) was designed to search for astrophysical point sources of gamma-rays. During its seven years of operation, it was the world's largest observatory for 100 Te V cosmic rays. CASA consists of an array of nearly 1000 charged particle detectors connected to a central trigger system. Using fast (nanosecond) timing among the individual detectors, the array measures the shape of the air shower front and thus determines the direction of the primary particle. CASA also uses the Michigan Muon Array (MIA) to select muon-poor events, reducing the background of hadronic primary.. cosmic rays. MIA consists of sixteen patches of buried scintillator detectors, spread around the CASA site. Gamma-ray searches by CASA-MIA from 1990-1996 produced flux limits of unprec~dented sensitivity for candidate sources such as the Crab Nebula [54], Hercules X-1 and Cygnus X-3 [55], dozens of AGN [56], and diffuse emission from the Galaxy [57]. However, CASA-MIA did not positively detect any gamma-ray source.

The Broad Lateral Non-imaging Cherenkov Array (BLANCA) relies on CASA to identify air showers. BLANCA measures the spatial distribution of Cherenkov light on the ground, but Cherenkov data are recorded only in coincidence with a CASA air shower event trigger. The Cherenkov light distribution is circularly symmetric about the air shower core. Combining the CASA core location with the BLANCA data produces a Cherenkov lateral distribution, which is the fundamental BLANCA measurement, used to determine both the energy and mass of the primary cosmic ray. The primary direction measured hy CASA is also important in BLANCA analysis, because it identifies the usable subset of cosmic rays arriving from near the zenith. This chapter briefly describes the CASA detector components and operation. It discusses the calibration and fitting procedures that convert raw CASA data into the shower parameters required by BLANCA: the core location, direction, and shower size. More detailed descriptions of CASA appear in [58] and [59]. 36 37 Enclosed area 215,000 m2 (until Sept. 1997) 200,000 m2 (after Sept. 1997) Total number of detectors 957, later 891 Area of each detector 1.5m2 Detector array spacing 15m Cosmic ray trigger rate 9s-1 Angular reconstruction error ( rms) ;s 10 Core location error (rms) :S 3m

Table 3.1: CASA characteristics during the 1997-98 BLANCA observations.

3.1 The CASA Instrument

CASA observes cosmic rays from a site on the U.S. Army Dugway Proving Ground in the Great Salt Lake Desert, Utah (40.2°N, 112.8°W). The site sits 1460m above 2 sea level at an average atmospheric depth of 870 g cm- , although the depth varies with air pressure. The climate is hot and dry in the summer and fall, but winter snowstorms and spring rains are not unusual. A wire grid above the array, erected after a 1991 lightning strike, protects CASA from electrical damage. Several mobile home trailers near the center of the array serve as living quarters, a repair shop, and the array control and data recording center. The vigilant Cygnus, a small black cat, keeps the trailers free of desert rodents. When first built in 1991, the array consisted of 1089 separate detectors on a square grid with 15 m spacing. Over time, many stations at the array edges were removed to provide spare parts for maintenance of the remaining detectors. During the first several months of BLANCA operation, CASA had 957 detector stations, but 66 were removed during the summer of 1997 for further array repairs. Figure 3.1 is a map of the Dugway site as of January 1997, including the surface array, the Cherenkov array, and the muon detectors. The CASA detectors sample the density of charged particles in an air shower. The active area covers approximately 0.63 of the total array area. Table 3.1 lists some important characteristics of the array, including the resolution in reconstructed air shower direction and core location. CASA's ability to determine both of these parameters improves with increasing shower size. The 38

...... 15 m .... Iii ...... •...... , .....• ...... ·• ...... ·•·• ...... CASA ...... 9:4-t . ~: ...... • BLANCA • ...... _. • MIA ..... :tt.: ~ ...... -...... •• ...... ·• ...... :.:;...... • ....••• ......

Figure 3.1: Map of the Dugway site. CASA is the surface array, BLANCA is the Cherenkov array, and MIA is the buried muon system. 39

Figure 3.2: Exploded diagram of one CASA detector station. values given are representative of showers observed by BLANCA in the range of several hundred Te V. Each detector station contains four identical scintillation counters sensitive to the passage of charged particles (Figure 3.2). A counter consists of a sheet of acrylic scintillator, 61 cm x 61 cm and 1.3 cm thick, with a.. photomultiplier tube glued to the center. Each counter is sealed in a lightproof black styrene tray so that only scintillation light reaches the photomultiplier. A plastic box and canvas cover protect the four counters from rain and snow. Inside this box, a single circuit board provides analog and digital electronics for the station and supplies high voltage to the photomultipliers. The CASA stations were originally covered with lead sheets to lower the array's energy threshold for gamma-ray observations; the lead was removed during the construction of BLANCA in 1996, however, and it does not affect the measurements described in the present work. Unlike many other air shower arrays, CASA employs a distributed electronics system. The central electronics are used only to make global triggering decisions, to control the array, and to merge and store data. The global trigger requires at least three detector stations to satisfy a local coincidence requirement within each 40

station. The layered trigger system uses the local requirements to reduce the rate of random array triggers and the resulting array-wide dead time. The local electronics also digitize the counter signals, and they perform the relative timing measurements used to determine the arrival direction of the air shower.

3.1.1 The array trigger

Discriminator circuits on the CASA station board monitor the signals from each counter. The station registers an "alert" when any two of the four counters fire simultaneously (within 30 ns). Only alerted detectors are recorded as part of a shower. When a station alerts, photomultiplier charges are stored in a sample-and-hold circuit for 10 µs so they can be digitized if necessary. Meanwhile, the station waits for a possible signal from the central trigger, box to declare a full array trigger. A typical station meets the alert requirement only 3-10 times per second. If an alerted station has a three-of-four coincidence among its counters, then the station "triggers." That is, the station sends a trigger request signal to the central trigger box on a dedicated cable network. Stations typically request a trigger fewer than 0.5 times per second. The array-wide trigger circuit determines whether air shower events are recorded. The local coincidence requirement drastically reduces the burden on the central trigger logic, which has to handle 891 stations making requests at 0.5 Hz rather than rv 3600 individual counters each registering thousands of hits per second. The central trigger box declares an array trigger if at least three detector stations send trigger requests within the same 10 µs period. The trigger acknowledgment is sent to every CASA station via a separate network. On receiving a trigger acknowledge signal, every alerted station digitizes the stored charge from its four photomultipliers. These four charges are held locally in memory for later readout by the central data acquisition (DAQ) computer.

The CASA event rate is generally ~ 9 Hz, and events on average contain data from 20 alerted stations. The DAQ computer polls each CASA station individually for its digital data, repeating the full poll cycle 2.5 times per minute. The central computer then sorts the data so that all alerts from a single air shower trigger are 41 stored together, and it writes the data to magnetic tape for later analysis. The combined CASA-BLANCA data require approximately 50 MB of storage space per hour of observation.

3.1. 2 Measuring particle densities

A CASA counter is designed to measure the number of charged particles passing through the scintillator. The photomultiplier collects the scintillation light, and the station electronics digitize the resulting charge pulse. Most air shower particles produce roughly the same amount of scintillation light because they are highly relativistic-even at ground level-and are therefore minimum ionizing particles. In this simple picture, CASA counters measure particle density by counting the individual particles. Two major factors complicate the CASA density measurement, however. Al- though all particles produce similar scintillation yields, the photomultiplier light collection efficiency depends strongly on where a given particle passes through the scintillator. An electron striking the center of the counter can produce 30 times as much photomultiplier charge as one that hits a corner of the scintillator. CASA measures only the total photomultiplier charge froi;n each counter. In later data processing, the charge is compared to the mean charge left by a minimum ionizing particle to determine a number of equivalent particles. A second complication to the density measurement is that the analog-to-digital converters (ADCs) saturate at the level of 30 equivalent particles, so densities above ,...., 80 particles cm-2 cannot be measured. Despite these limitations, CASA can determine the center of the electromagnetic particle distribution by sampling it at many locations, particularly in high energy showers. This center, the shower core, is required in the BLANCA analysis.

3.1.3 Surface array timing

The surface array uses precision timing of the shower particles to determine the arrival direction of an air shower. At any given detector, most particles arrive in a very narrow time window called the shower front. The shape of this front is approximately 42

c ~t=(l5m) sin 8

Figure 3.3: Timi'1g diagram of an air shower front. a plane perpendicular to the shower axis. By measuring the relative arrival time of the front at separated detectors, CASA finds the orientation of the shower front and thus the shower axis (Figure 3.3). With a detector separation of 15 m, a 1° change in the shower axis changes the relative arrival time by approximately 1 ns (or less, for showers steeply inclined from zenith). Therefore CASA requires approximately 1 ns timing resolution to achieve directional accuracy of 1°. Smaller air shower arrays typically run cables from each counter to a central timing system to determine the shower direction. Having nearly 1000 detector stations, with some over 300 m from the center, CASA instead uses local timing circuits to measure the relative times between stations. When a station alerts (2 of 4 counters hit), it sends a signal to each of its four nearest neighbors over dedicated twisted-pair cables. The station also starts four timing clocks and waits for alert signals from each of its neighbors, which stop the clocks. The timers have a full range of 300 ns and a least count resolution of 0.3 ns. A single link between neighboring stations thus produces two "cross times,'' one measured at each station. If the two stations alert simultaneously, then the cross times will be equal to one another and to the signal propagation time in the cable. If one station alerts first, then it will measure 43 the longer cross time, as it waits for the neighbor to send an alert signal. The sum of the two cross times is constant for any link, as it depends only on the length of the cables and other intrinsic delays. The difference between the cross times is a direct measurement of the angle the shower axis makes with the vertical. A single link can estimate only a shower's north-south or east-west direction; several links of each type are required to make a full two-dimensional direction estimate. Four other clocks measure the relative firing times of the four counters within each detector. These local times are used to correct for the time difference between the first hit in a station and the second, at which time the alert actually forms and the clocks start. In practice, several timing offsets must be determined for each counter and each link to achieve an accurate measurement of shower direction, as described in the next section.

3.2 CASA Offiine Reconstruction

The raw CASA data consist of the digitized photomultiplier charges, cross times, and local times. Offiine reconstruction programs process these data in several passes for each shower to find the optimum core location, primary direction, and electron • size (the total number of electrons which reach the ground). The first processing stage finds the electronic pedestals, gains, and timing offsets. Collectively, these quantities are called "constants," although they vary from run to run. Temperature changes are the main reason that the constants are not actually constant, but the counter gains are also affected by changes in the high voltage. Equipment failure is another source of changing constants. The second processing stage corrects the raw data for these effects, producing a set of physical measurements: pulse heights become particle densities, and raw TDC data become times in nanoseconds. Finally, each event is fit to find the shower direction, core position, and size.

3. 2.1 Detector calibration

Determining the pedestal and gain of each channel is the first step in calibrating the 3600 CASA counters. The discriminator threshold for each counter is set to ,....., 24 m V, 44

1200 Entries 1733 225 Entries 1819 Mean 71.61 Mean 81.14 1000 RMS 0.5410 200 RMS 9.140 175 800 150

125 600 100

400 75

50 200 25

0 0 65 70 75 80 80 100 120

Pedestal ADC Counts Gain ADC Counts

Figure 3.4: Calibration charge distributions for one CASA scintillation counter: events used to calculate the pedestal (left) and gain (right). This counter has a pedestal of 71.6 counts and a gain of 7. 7. or 10% of the average particle pulse height. Therefore, the counter fires nearly every time a particle passes through it. When a counter is not hit in a given event, it is almost certain that no particle struck that counter and that no scintillation light was produced. Counters not hit can be easily recognized because the corresponding local timer does not stop ("times out"). A channel's pedestal is thus the mean pulse height in cases where the counter times out.

Gain calibration means determining how many ADC counts the average particle produces in a counter. Ideally, gains would be found by averaging pulses that result when only one particle strikes a counter. Such events cannot be selected perfectly, however. The gain calculation instead uses events in which only the minimum two out of four counters in the station is hit. This cut preferentially selects events with low particle densities, which are more likely to produce a single particle in each counter. Even minimally alerted stations can observe more than one particle per detector, however, so a correction factor of 0.81 is applied to account for multiple 45

particle hits. 1 Further event cuts on the gain calculation require ADC values to be significantly above the pedestal and below the value that typically corresponds to 10 particles. The resulting truncated and corrected mean pulse height gives the gain, which is the average ADC value due to a single minimum-ionizing charged particle. Figure 3.4 gives an example of the charge distributions used to find the pedestal and gain of a single counter. All other calibrations involve timing, including the conversion of the time-to- digital converter (TDC) values into nanoseconds, as well as the various timing offsets. The TDC constants are measured with a dedicated timing calibration circuit on each station electronics board. This circuit contains a precise 50 MHz crystal oscillator. For five minutes, several times a day, normal cosmic ray observations stop and the oscillator feeds pairs of test signals to each TDC on the board. The first signal in a pair starts all TDC clocks, and the second stops them. The time differences range from 40 ns to 240 ns, in several discrete steps. Offiine analysis procedures use these timing calibration runs to determine the constants for each TDC in the array, both a slope (typically 0.3 ns per count) and an intercept. The procedure also verifies the linearity of each TDC. Experience shows that the time to height conversion depends on the temperature of the timing circuit. ..CASA stations record the box temperature with each event. Therefore timing calibrations taken over a period of days are combined, permitting the slope and intercept of each TDC to be fit as a quadratic function of temperature. Using the six parameters of the two fits, any TDC value can be converted into a time in nanoseconds, given the station temperature. Timing offsets are derived from the data, taking advantage of the fact that air shower arrival directions are azimuthally symmetric and peak at zenith. Internal offsets are used to correct the local clock on each counter. The offsets result from differences in cable length and electronic delays in individual local timing circuits. Likewise, each link between neighboring stations has a unique external offset due to different cable and electronic delays. External offsets are found by noting that the physical time difference between neighbors should average to zero over a large

1 This correction factor was determined through laboratory studies of the CASA counter response to isolated vertical muons [58). 46 number of symmetrically distributed air showers. Any residual difference gives the external offset of the link. The calibration software completes its job by applying the correction constants to the raw data. The program converts all pulse heights into particle densities using the pedestal and gain constants. It also converts every pair of cross times into a single time difference in nanoseconds by correcting the calibrated TDC data for the internal and external offset times, as well as for the relative height of the stations (which can differ by as much as 2 m). Finally, stations or links for which accurate constants cannot be found are flagged so that the fitting procedures can ignore them.

3. 2. 2 Fitting the air shower core

The air shower core is defined as the place where the shower axis intersects the Earth's surface. The core location can be estimated from particle density measurements, because it coincides with both the point of highest particle density and the center of symmetry. CASA uses each of these methods in different situations. The point of peak particle density can be found even in quite small air shower events. The center of symmetry can be determined only in relatively large showers, but it has the advantage that it can sometimes be found accurately even when the core falls outside the detector array. Several effects complicate the core-finding procedure. CASA detectors saturate at 80 particles m-2 and cannot accurately record the particle density near the center of larger showers. Furthermore, broken detectors cause gaps in the density map. The edges of the array also leave showers incompletely sampled.2 Occasionally an accidental coincidence between two air showers can produce an event with multiple cores. 3 A clustering algorithm attempts to identify accidental coincidences by search- ing an event for distinct clusters in either space or shower arrival direction. Events thus tagged as multi-cored or multi-directional are ignored in the analysis. The core-finding routines, however, must handle the saturation and sampling problems.

2 Unfortunately, "Most of the array is near the edge." 3The accidental rate is approximately one per 11,000 events-every twenty minutes-during BLANCA operation (assuming a trigger rate of 9 Hz and a coincidence window of 10 µs). 47 The High5 routine determines the peak of the particle density distribution by taking the weighted average position of the five detectors with the highest density. A saturated detector is given a weight equal to that detector's saturation density. By using only five stations near the core, this method is less affected by the array edge than an average over all alerted stations would be. The stations measuring the highest density are also least susceptible to density fluctuations. However, detector saturation weakens the High5 method, making it impossible to find the highest density point in large showers. High5 is also strongly influenced by the presence of dead stations near the core. The Circlecore algorithm complements High5, because it works best on large showers. Circlecore interpolates between the sampled densities to construct several 2 contours of equal particle density between 5 and 50 particles m- . The highest density contour with at least five interpolated points is fit to a circle, and the center of the circle is used as the core location. Unlike High5, the Circlecore result can place cores outside the array boundaries, When it succeeds, the Circlecore method is used in preference to the High5 method. The Circlecore fit is used for 20% of all CASA showers, and for more than 50% of large showers. Together, the core reconstruction methods have an average error of less than 3 m ... for small events, reaching 1 m for larger events. Near the array edge, core errors can be much larger, as some events apparently close to the edge are actually centered outside CASA. The BLANCA analysis uses only events with reconstructed cores at least 30 m from the physical edge of the array in order to avoid these poorly reconstructed events.

3. 2. 3 Fitting the air shower direction

BLANCA analysis uses the reconstructed air shower direction only for event selection, to determine whether the limited optical field of view permits accurate Cheren- kov measurements of the shower. Good direction fits require the careful temperature- compensated timing calibrations and timing offsets (Section 3.2.1) and as many good cross-time measurements as possible. 48 The CASA cross-times are first fit to a planar shower front. A large sample of showers shows that the residual delay relative to a plane increases linearly with distance from the core. Therefore, a revised fit is performed assuming a cone-shaped shower front. The cone has a fixed apex angle of 1°, producing a delay of 0.07 ns per meter from the core. The axis of the best-fit cone is taken to be the air shower direction. The conical correction is especially important for showers landing near the array edge. Such events are sampled only on one "side" of the cone, and fitting a mere plane to one side of a cone would distort the shower direction by about 1°. Like the core location error, angular resolution improves with increasing shower size. Three separate methods are used to check the CASA angular resolution. First, the array is divided conceptually into two overlaid sub-arrays, and the two sets of cross-times are fit separately to find two directions for each event. The difference between the directions indicates the.. random error (after correcting for the reduced statistics in the split arrays). The systematic pointing error of the array is found to be less than 0.2° by studying the cosmic ray shadow of the Moon. The lunar shadow acts approximately as a "point sink" in the cosmic ray distribution because its apparent size of 0.25° is smaller than the angular resolution of CASA. Five tracking Cherenkov telescopes which operated in coincidence with CASA during 1993 provide a third test of CASA's direction reconstruction. The telescopes used a separate timing system to find the direction of each shower independently from CASA. Together, the three techniques establish that the angular resolution averaged over the entire data set is 1.2°. BLANCA analysis uses only larger than average showers, for which the resolution is better than 1°. CHAPTER 4 THE BLANCA CHERENKOV ARRAY

BLANCA, the Broad Lateral Non-imaging Cherenkov Array, consists of 144 angle- integrating Cherenkov light detectors. The array operates only on dark, moonless nights. Each detector views the sky within approximately 12° of zenith and records optical flashes coinciding with the cosmic ray air showers detected by the CASA surface array. Measuring the spatial distribution of air Cherenkov light at ground level allows us to determine the energy and mass of the primary cosmic ray. Construction of the BLANCA array began in June 1996. At that time, 99 of the 1056 existing CASA surface detectors were permanently decommissioned and their electronics and cables collected to be reused in BLANCA. The first eight Cherenkov units were installed in September. Construction continued through the autumn, and the last detectors were completed in January 1997. The data presented in this thesis were taken in two separate periods, mainly during the autumn and winter months when the nights are longest. The first campaign ran from January to May, 1997; the second began in October, 1997 and ended on May 1, 1998. Between these periods, the two columns.. of CASA detectors on the east and west edges of the array were shut off. The decommissioned electronics were used to instrument the 72 "holes" left in the CASA array during the construction of BLANCA. Therefore, the 1998 data have a smaller cosmic ray rate because of the smaller array, but these data also have superior core reconstruction because the filled surface array samples air showers more completely.

4.1 Array overview

Each BLANCA detector contains a Winston cone light concentrator, a photomultiplier tube, and associated electronics. The concentrator views ,...., 100 square degrees centered around the zenith. The photomultiplier converts light from this patch of sky into an electrical charge. If the tube should detect Cherenkov light from a shower that also triggers the CASA surface array, its charge pulse is amplified, digitized, and 49 50 Total number of detectors 144 Characteristic detector spacing 35m Cone entrance area 880cm2 Cone cutoff half-angle 12.5° Least count sensitivity 300 blue photons m-2 Minimum detector threshold 7500 blue photons m-2 Saturation level 6 x 106 blue photons m-2 Winston cone alignment (rms) lo

Table 4.1: Summary of average BLANCA detector characteristics. stored. The digitized signal is later sorted with the signals from other Cherenkov and particle detectors recorded during the same shower. This information is used to reconstruct the geometry and Cherenkov light density profile of the shower. The 144 BLANCA detectors are arranged as uniformly as possible, subject to • several constraints. First, the detectors all stand within 10 to 20 cm of a CASA station in order to use its spare 120 volt AC power outlet. Each detector is paired with another one 30 meters away, with a single digitizing station halfway between them to record the Cherenkov light signal from both units. The 72 digitizing stations sit inside normal CASA enclosures. Signal and high voltage power cables connect each station with its two detectors, 15 meters to the west and 15 meters to the east. Finally, detectors could not be installed on steep sand dunes or below overhanging mesquite trees. Figure 3.1 shows the final map of BLANCA detectors along with the other instruments at the Dugway site. The number of BLANCA detectors was chosen to keep the characteristic spacing between them small (35-40 meters), which ensures that any air shower landing in the array is sampled at several places near its core. Accurate measurements of Cherenkov intensity near the core are necessary to provide information about the depth of shower maximum (see Figure 2.5). On average, there are 20 detectors within 100 meters of the core and five detectors within 50 meters. The collecting area of each detector is as large as possible so that Cherenkov light intensities as low as one photon per cm2 can be observed. This allows BLANCA detectors to measure low energy showers more than 200 meters from the core. BLANCA detectors saturate at a level of 51

2 approximately 600 photons per cm . Table 4 .1 summarizes the characteristics of the individual detectors.

4.1.1 Use of the CASA trigger

The BLANCA Cherenkov array relies entirely on the surface array to recognize the arrival of an air shower. Light intensities are recorded only in coincidence with a CASA trigger for several reasons. Providing a separate trigger system for the Cherenkov array and integrating the two types of detectors into a single trigger would have required more time and resources than were available. Furthermore, the optical detectors are very susceptible to accidental events resulting from normal night sky light. Recording Cherenkov events only in coincidence with particle arrival prevents the accidental events from overwhelming the real air showers. 'A CASA event requires that three surface stations request an event trigger within a 10 µs period, as described in Section 3.1.l. Monte Carlo simulations of air showers and the array response show that the CASA trigger is 90% efficient for proton- induced showers above 150TeV and equally efficient for iron showers above 250TeV. These energies are lower than the 300 Te V minimum energy for showers used in the BLANCA analysis, so the standard CASA trigger is fully efficient for showers of interest here.

4.1. 2 Operating the Cherenkov array

The CASA-MIA air shower arrays are operated from a central electronics trailer. The control room contains the MicroVAX III data acquisition (DAQ) computer and three other computers to monitor the data for potential problems before writing it to tape. The CASA run procedures have long been automated, so the operator can begin a data run using a simple menu-driven control program. The main data acquisition computer also controls the BLANCA units. The computer can open and close the shutters that protect the detectors during daylight hours. It also sets the high voltages on the photomultiplier tubes, up to 3000 volts. 52

The shutters on each BLANCA unit operate independently, but the high voltages must be set to a single value for each pair of detectors. Because of the computer automation, CASA-BLANCA can run without an operator on the site. The operator need only connect to the data acquisition computer cluster through the Internet. This feature was sometimes used to run the experiment remotely from the rental house in Dugway's English Village. Only a few data runs were taken without an operator in Dugway at all, however, and they came in the final two months of BLANCA's observations. Until then, it was considered too dangerous to risk destroying the BLANCA photomultipliers, which could happen if a computer failure were to leave the high voltage on until dawn.

4.2 BLANCA detectors

The 144 BLANCA detectors are angle-integrating Cherenkov sensors, or "light buck- ets" that record the total amount of Cherenkov light arriving i:i an air shower. In practice, however, they must have a limited field of view to reduce the noise from background sources of light such as starlight and the glow from Salt Lake City and

Wendover, Nevada. The BLANCA detectors are sensitive to light from within rv 12° of zenith. Each detector stands in a cylindrical enclosure 130 cm tall and 40 cm in diameter. The enclosure, made of PVC pipe, protects the optics and electronics from rain, snow, and other moisture. It also allows light to enter the detectors only through the main aperture at the top of the cylinder. The aperture itself is protected from the elements by a circular piece of UV-transmitting Borofloat (Pyrex) glass 3 mm thick. The glass window is sloped by 8° from horizontal, allowing rainwater and melted snow to drain easily. To prevent frost formation, a 6 m length of Nichrome heating wire runs back and forth below the glass. Continuously supplied with 12 VDC, this wire generates 8 W of heat and helps to speed snow melting, as well as eliminating frost. Inside the enclosure, the main optical element is a hollow compound parabolic concentrator (Winston cone), which collects light from an entrance aperture of 33 cm diameter into a smaller exit aperture of 7.5 cm diameter. A piece of 1/2" plywood 53

~---- 40 cm ----~

Figure 4.1: Diagram of a BLANCA detector. Left: Side view of a detector. The window at the top is sloped slightly so that water can run off. The motor beside the PMT rotates the protective shutter. Right: A detail of the protective shutter between the cone and PMT, seen from above. The two notches and switches allow the control electronics to know the shutter's position. 54

Figure 4.2: Photograph of a BLANCA detector, removed from its enclosure for maintenance. hangs from the bottom of the cone and supports the other apparatus in the enclosure. The most important item is the photomultiplier tube, held in a metal can just below the bottom of the cone. The tube is wrapped with several layers of thin sheet metal with a high magnetic permeability. This "mu metal" shields the photomultiplier from external magnetic fields which can affect its gain and increase its high frequency noise. The shielded photomultiplier emerges through a hole in the plywood disk so that its face-flush with the top of the plywood-nearly touches the cone output aperture. The average gap between tube window and cone output plane is 9 mm. Figure 4.1 is a diagram of a single BLANCA detector. Figure 4.2 shows a detector sitting on top of its enclosure. A mechanical shutter fits in the small gap between the Winston cone and the photomultiplier. The shutter is an aluminum disk 2 mm thick, with a hole the size of the photomultiplier (Figure 4.1, right). By rotating the shutter with a 1 RPM motor, 55 the aluminum disc can expose the photomultiplier to the night sky for observations, and it can cover the tube to protect it during the day. Notches in the edge of the disk control the two switches that indicate when the shutter has reached its fully closed or fully open position.

4.2.1 Optical design

To collect light from an area as large as possible, BLANCA detectors employ compound parabolic concentrators. This optical element, also known as a Winston cone, is a non-imaging device that collects light from a large surface into a smaller area [60]. The cone concentrates light only from a restricted angular range. In designing Win- ston cones, there are only two free parameters among the following: the input and output radii (rin and rout), the cone length (£), and the field of view angle (0). One of these free parameters is an overall size scale; the other is constrained by the two equations • D Tout Slnu = - (4.1) Tin

rin+rout tan e =--£--. (4.2)

For BLANCA, the 7.8 cm diameter photomultiplier window fixes the cone output size. The actual cone output radius is 3.6 cm, slightly smaller than the photomultiplier window in order to concentrate light on the most sensitive and uniform section of the photocathode. Equation 4.1 shows that with rout fixed, increasing the input radius reduces the cutoff angle. Thus the remaining parameter is selected by balanc- ing the need for maximum light collection (large input area) against a wide angular field of view for observing cosmic rays from a large solid angle on the sky. We chose cones with an angle of 0 = 12.5°, which have an ideal concentration ratio (ratio of input to output aperture areas) of 21.3. The actual concentration ratio is reduced by reflection losses, imperfect light collection at the output, and other effects. In practice, the concentration ratio of the BLANCA cones is smaller than ideal for several reasons. The complete Winston cone with half-angle 12.5° and output radius of 3.6 cm would be 92 cm long. To reduce the size (and thus the cost) of 56

e 20 ~ Ill ::I 15 =tiIll a: 10

40° 30° 12.5° 12.5° 0 Truncated Complete

-5

-10

-15

-20 0 20 40 60 80 100 Length (cm)

Figure 4.3: The shape of several possible Winston cones with rout = 3.6 cm, including the full-length and the truncated 12.5° cone. the detectors, BLANCA uses truncated Winston cones. These cones have the same shape as full cones, but only the bottom 60 cm are produced. Figure 4.3 shows the shape of the ideal 12.5° cone and the shortened version used in BLANCA. The truncation reduces the length by 403 and cuts the surface area in half, but retains 903 of the input area. The more serious limitation of the truncated cones is that they transmit more light from outside the nominal field of view. This extra light unfortunately increases the night sky background noise relative to the Cherenkov signal strength. Plastic Fabricating, Incorporated of Salt Lake City produced the BLANCA cones. Each cone was vacuum-formed in two identical halves from sheets of ABS plastic, and the halves were bolted together along two flanges. The exact shape of the cone was controlled using a wooden form cut on a computerized lathe to match the required surface. The wooden mold shape was then transferred to the custom fiberglass mold used in the vacuum forming. ABS is a clear plastic, so the inner surfaces were 57 aluminized at the University of Utah by vacuum deposition to make them highly reflective. A photomultiplier tube sits at the output end of each Winston cone, converting optical photons into electrical signals. The EMI Corporation produced the tubes for the Fly's Eye cosmic ray telescopes [61], which operated from 1986-1994. The photomultipliers are ten-stage tubes with a bialkalai photocathode material and a UV-transmitting glass window. Fly's Eye observed atmospheric nitrogen fluorescence, a very slow light pulse compared with Cherenkov radiation. Therefore, the EMI photomultipliers are not optimized for this application. The BLANCA tube

response to a Cherenkov light pulse ( f'V 10 ns) is an electrical pulse lasting typically 30 ns (FWHM). Decommissioning the Fly's Eye I telescope made nearly 500 photomultiplier tubes available for BLANCA. Due to their age and previous use, many had very low sensitivity. To select the 144 most suitable tubes, we measured the gain of all 500 tubes. The photomultipliers were placed four at a time in a large light-tight dark box at the University of Utah. A helium-cadmium laser (325 nm wavelength) and a double Teflon plate diffuser provided continuous and uniform illumination of the four photomultiplier windows, while a calibrated photodiode.. monitored the light intensity. The anode current divided by the light intensity estimates the tube gain (actually, the product of quantum efficiency and the dynode gain). The measurement was repeated with four different high voltages to determine how the gain increased with voltage. In a typical tube, the gain varies as the fifth power of voltage. BLANCA was built using the 160 photomultipliers having the highest measured gains. 1 Since BLANCA has only 72 separate high voltage supplies for 144 detectors, tubes with similar gains were paired and used in adjacent detectors. The BLANCA photomultipliers are most sensitive to wavelengths between 280 and 500 nm. This sensitivity in the UV and blue range is ideal because the Cherenkov 2 light spectrum falls quickly with increasing wavelength ( dN/ dA. ex A.- ). The Philips Corporation measured the quantum efficiency of four sample photomultipliers at

1Sixteen of these tubes were reserved for later use as replacements. 58

c 0 "iii Ill 0.9 ...... W.i llct.C>V'I. gl_a_!;!; ·e Illc 0.8 as ·-cc>ii"e.retlecHvity· I-.. 0.7 0.6 0.5 . . 0.4 .. ······-···-··-- -·--·-·- . . 0.3 . . . . . -...... - -- .- -. --. - . . . 0.2 0.1 0 250 300 350 400 450 500 550 600 650 700 Wavelength (nm)

Figure 4.4: Wavelength response of the complete BLANCA detector. The measured quantum efficiency of the photomultiplier, the transmission of the protective glass, and the reflectivity of the aluminum surface inside the concentrator combine to give the effective response. The reflectivity curve shown assumes an average of 1.4 reflections per transmitted light ray, a robust value independent of incident angle.

a range of wavelengths. Figure 4.4 shows the average of the four measurements, but all four photomultipliers have similar sensitivity curves and differ only in the peak value. In the 300-450 nm wavelength range, the average quantum efficiency is between 10% and 15%. Although the Borofloat glass at the top of the BLANCA detector transmits near-ultraviolet light better than standard glass, it still has a sharp cutoff for light below 290 nm. The window transmission was measured at the University of Utah. Aluminum reflectivity depends very weakly on wavelength in the optical range [62], so the mirrored interior surface of the cones has little effect on the detectors' wavelength sensitivity. The product of the glass transmission, cone reflectivity, and quantum efficiency gives BLANCA's sensitivity to light of different wavelengths. This estimate of the spectral sensitivity of BLANCA is used in the detector simulation programs described in Chapter 6. 59 4.2.2 Simulations of the optics

The properties of the ideal Winston cone described in Section 4.2.1 can be calculated exactly only in two dimensions. In that case, the concentration ratio is constant for angles below the critical angle and exactly zero at larger angles. To understand the three-dimensional BLANCA cone, with its truncated top and other effects, we employ a computer ray-tracing simulation. The simulation follows several thousand parallel rays of light entering the cone on a uniform grid of points. Assuming geometric optics and the cone's known shape, the program calculates how many rays reach the output aperture and how many are reflected back out the input aperture. The fraction of rays transmitted through the cone times the ratio of input to output areas gives the cone's concentration ratio. By repeating this calculation using light from different directions, we compute the concentration ratio as a function of angle from the optical axis. The concentration versus angle curve, together with the angular distribution of Cherenkov light, determines how much light is measured in a given observation. This study shows that the concentration is almost independent of angle for light near the optical axis but that it falls quickly beyond 10°. Several differences between ideal Winston cones and the BLANCA ones produce changes in the angular response of the detectors. Through the ray-tracing simulation, the differences can be examined separately. First, BLANCA detectors use truncated Winston cones to limit construction costs. Figure 4.5 shows that the truncated cones have a concentration ratio for on-axis light reduced by about 10% relative to the ideal cone. The truncated cones also transmit some light out to 18°, while the full cone transmits almost no light beyond 14°. This change occurs because the material omitted from a truncated cone serves primarily as a baffie against off-axis light. Absorption in the aluminum reflecting surface also reduces the transmission of the Winston cones. The simulation uses the simplifying assumption that the surface has reflectivity of 87% at all wavelengths and incident angles. Consequently, the concentration ratio falls by 17% relative to a cone with ideal mirror surfaces. The reduction is nearly independent of incident angle, because the transmitted rays reflect 60

.2 .2 a:iii 20 a:iii 20 c ------~ ' c ~ 17.5 . ~ 17.5 la .. la :: ······································.•.. .. ------w:..·:,;=.·~····· .. 15 · ~ 15 ·. (,)5i (,) . c c ~, .... 8 12.5 8 12.5

10 10

7.5 7.5 - ldealCPC ...... CPC ... 5 - - - . Truncated 5 ---· + 9 mm gap ...... + 87% refl - + Fresnel refl 2.5 2.5 ·. ··...... 0 0 0 5 10 15 20 0 5 10 15 20 Angle (degrees) Angle (degrees)

Figure 4.5: Simulated BLANCA cone response as a function of angle from the optical axis. Left: Ideal cone and the effects of truncation and partial reflectivity. Right: The additional effects of the gap between cone and photomultiplier and reflections off the photomultiplier window. from the cone surface an average of 1.4 times regardless of incident angle.

In addition to the cone itself, the positioning and sensitivity of the photomultiplier tube also affects the optical performance of a BLANCA detector. A 9 mm gap separates the output aperture of the Winston cone and the photomultiplier window in order to accommodate the shutter described in Section 4.2. The simulation shows that this gap does not affect the near-axis concentration ratio. Its main effect instead is to reduce the cutoff angle (defined as the angle of half-maximum transmission, 81;2), from 12.5° to 11.2°. Finally, incoming light can reflect off the glass window at the top of the photomulti plier instead of passing through and striking the photocathode material. We model this process using the Fresnel equation for reflection of unpolarized light at an optical interface [43], assuming that the window glass has an index of refrac- 61

tion of 1.5. Fresnel reflection reduces the overall concentration ratio by 6% without changing the cutoff angle of the optics. The ray-tracing simulation shows that the BLANCA detector concentration ratio is 15.1 for angles up to 8° from the axis. The ratio falls to half the peak value at 01;2 = 11.2° and falls below 1.0 at 15°.

4.2.3 Laboratory studies of the optics

The ray-tracing simulation allows us to examine several optical effects separately, but laboratory measurements verifies the composite concentration ratio curve predicted by simulation. Measuring the transmission as a function of angle requires a source of parallel light shining on a BLANCA detector from an adjustable direction. In addition, the source has to illuminate the entrance aperture of the cone as uniformly as possible, like realistic Cherenkov light. A Panasonic gallium nitride LED serves as a light source for several types of calibration, including the angular response measurement. It mimics Cherenkov light in many ways, including a very fast light pulse ("' 10 ns). The GaN LED emission spectrum peaks at a wavelength of 430 nm with a full width at half maximum of 60 nm. The LED is bright enough that the full systefh can produce a photon density much higher than that in most Cherenkov events observed by BLANCA. The light source is rigidly supported on an optical bench in a 50 cm x 50 cm x 200 cm dark box. An optical fiber 3 mm in diameter carries the LED light to a second dark box, a closet large enough to hold a complete BLANCA detector. Inside the second dark box, the end of the optical fiber is fixed at the focal point of a 40 cm diameter Fresnel lens. This plastic lens collimates the light emitted from the fiber. An aluminum support structure holds the fiber and lens rigidly in place above the detector. Two bolts attach the support to the top of the Winston cone assembly so that the lens and the fiber can rotate, illuminating the detector with collimated light as much as 30° from its optical axis (see Figure 4.6). Using the rotating light source, we measured the BLANCA tube response to collimated light from different angles, in 1° increments. For this test, photomultiplier 62

----- BLANCA cone /e\

Figure 4.6: Apparatus used to measure BLANCA angular response. pulses were amplified and digitized by the same electronics used in the field. The results of two such measurements are shown in Figure 4. 7 and compared with the predictions from ray-tracing simulations. The measured response does not cut off as sharply as predicted, probably because of limitations in the measurement itself. The Fresnel lens does not perfectly collimate the light it transmits because of scattering at the surface ridges and imperfections. Therefore, not all of the light entering the BLANCA detector comes from the indicated angle. This effect makes the measured angular response curves artificially smooth. In principle, the measurement could be improved by using a highly polished converging lens in place of the inexpensive but scuffed Fresnel lens. The measured and predicted curves are consistent except for the smoothing. To test the azimuthal symmetry of the BLANCA detectors, the angular response was measured four times. In each trial, the light source was rotated about a different horizontal axis. The white plastic housing that holds the glass top at an angle caused a detectable asymmetry. In the configuration shown in Figure 4.6, diffuse reflection from the inside of the housing slightly increased the total light collected at the photomultiplier. The enhancement was noted only in a small range of incident angles (6°-9°), however, and amounted to less than 33 of the total light collected. 63

II> 18 II> 18 Ill Ill c c Measurements : 0 -fr- Measurement 0 Q. 16 Q. 16 ---tr- 9 mm gap Ill - Ill ..II> Simulation ..II> ---8- Nogap II> 14 II> 14 .::: :;:;> ia Ill "iii 12 "iii 12 a: a: 10 10

8 8

6 6

4 4

2 2

0 0 0 5 10 15 20 0 5 10 15 20 Angle (degrees) Angle (degrees)

Figure 4.7: Laboratory measurements of the detector angular response. The results are relative, not absolute measurements, so they are normalized to the ray tracing results (Figure 4.5). Left: Measured response (6), compared with the simulation (smooth curve). Right: The previous measurement in normal configuration ( 6) and with the gap artificially removed (D). This comparison confirms a key prediction of the ray-tracing simulation.

This effect is smaller than the other uncertainties contributing to each Cherenkov measurement (such as gain calibration), so this analysis ignores the enhancement and assumes that the detectors are azimuthally symmetric. Another comparison between the simulated and measured angular response curves helps to confirm the ray-tracing predictions. Figure 4.5 shows the response predicted under several different physical conditions. Many conditions cannot be controlled, such as the cone length or the reflectivity of the mirrored surface. However, we can remove the rotating shutter and close the 9 mm gap separating the Winston cone from the photomultiplier. Simulations predict that the main effect of this gap is to reduce the angle of half-maximum transmission, 01; 2 , by 1.3°. The right panel of Figure 4.7 shows that the detector has 01; 2 = 10.8° in its normal arrangement, while the angle becomes 01; 2 = 12.2° when the tube is placed flush against the end 64 of the cone. The agreement between simulation and measurement establishes the soundness of the ray-tracing code. A detector simulation is used to study the relationship between measured Cher- enkov light properties and the initiating primary cosmic ray. The angular response of the BLANCA detectors is an important component of the simulation. Knowing how the detector response falls off with increasing angle is necessary to predict how BLANCA measurements deteriorate for showers several degrees from zenith. This analysis makes a cut and considers only showers within 9° of the zenith, reducing the need for a careful estimate of this deterioration.

4.3 BLANCA electronics

The electrical signal from a BL4NCA photomultiplier is digitized by a circuit 15 meters away, allowing a single electronics board to serve two detectors separated by 30 meters. Each detector contains a preamplifier to increase the photomultiplier signal before sending it down a 22 m twisted-pair cable. The 144 preamps and 72 digitizing stations comprise the BLANCA electronics.

4.3.1 Preamplifiers

BLANCA requires preamplifiers to boost the photomultiplier signal into a useful range. The necessary gain follows from the collection area and efficiency of the Winston cones, the gain and quantum efficiency of the photomultipliers, and the sensitivity of the analog-to-digital converters (ADCs). A rough lower limit to the required sensitivity is given by the light intensity 200 m from the core of a 300 Te V proton shower. Simulations predict an average yield of ,..,_, 1 photon cm-2 at that distance. A preamp charge gain of 50 was chosen in order to convert this intensity into 30 digital counts. BLANCA attempts to record the complete lateral distribution of Cherenkov light for showers over two orders of magnitude in primary energy. This ambitious goal requires substantial dynamic range, ideally a factor of 1000 or better. The 10-bit 65

In >------.----+----;---1 -----+High

Cl 0 Vi LM6365 AD 8042

Figure 4.8: Block circuit diagram of the BLANCA preamplifiers.

ADCs, however, saturate at 1023 counts, a factor of only 34 above the minimum light level. To prevent the ADCs from saturating and losing all high intensity information, the preamp actually creates two separate signals differing by a factor of 27. The reconstruction program uses the lower gain signal whenever the high gain signal exceeds the range of its ADC. The exact ratio of the high to low gain is measured for each preamp from the cosmic ray data itself, by comparing the two signals in their range of overlap (see Section 5.1.2). Each two-gain charge amplifier is an inexpensive custom circuit board built specifically for BLANCA. It contains two 8-pin DIP operational amplifiers. The LM 6365 contains a single amplifier to produce the high gain signal. The other chip, an AD 8042, provides the high current capacity required to drive pulses onto the low impedance (50 D) twisted-pair signal cables. The output signals pass through a pair of high-speed signal transformers (BH 500-1425) to break the ground loops that would otherwise result. These transformers greatly reduce the radio frequency noise on the signal lines in the Dugway environment. The preamps are placed in small aluminum boxes for further shielding from RF noise. The BLANCA preamplifiers were tested extensively to determine their gain and check their linearity. The test input signal was roughly 30 ns in duration, matching 66

the response time of the photomultipliers. With this input, the charge gains of the high and low gain channels are approximately 40 and 1.6. Loss in the 22 m signal cables reduces the effective charge gains to 26 and 1. The amplified pulses are approximately 100 ns long (FWHM), limited by the bandwidth of the high current op-amps. The digitizing circuit has a gate time of over 200 ns, so even the relatively slow 100 ns preamplifier pulse is fast enough for this system. Tests demonstrate that both channels are linear charge amplifiers at least to the level that saturates the AD Cs.

4.3.2 Station electronics

A single electronics station handles a variety of functions for each pair of BLANCA detectors. The station: • Receives commands and sends data using an Ethernet network,

• Provides the high voltage to operate the photomultiplier tubes and the power to rotate the protective shutters,

• Enforces the requirement of coincidence between the local Cherenkov detectors and the CASA particle array,

• Digitizes both the high and low-gain signals from each detector, and

• Records the digital results in a memory buffer for later use.

Fortunately, the particle array stations require almost exactly the same functions, so CASA circuit boards can serve as BLANCA boards with surprisingly few modifi- cations. BLANCA stations communicate with the central data acquisition (DAQ) computer through the same Ethernet network that the CASA stations use. This central computer issues commands to control the shutters and high voltage of BLANCA detectors, and it also receives data from the BLANCA stations. Each station has a unique address, so the DAQ system can request data from the stations one at a time in a process called the "polling cycle." A poll of the complete BLANCA and CASA arrays takes about six seconds and is repeated every 24 seconds. 67

The BLANCA station board controls the high voltage power supplied to its two detectors. A separate "pod" containing a 12 -+ 3000 Volt DC-to-DC converter circuit plugs into the board to provide the actual high voltage. The removable pods greatly simplify replacement, which is often necessary because of the hot desert environment. The station board contains the high-current power transistors that supply the pod, along with a feedback circuit to stabilize the high voltage at the desired level. An on-board digital-to-analog converter chip allows the operator to set this voltage level. The original CASA design for the feedback circuit actually prevented the output voltage from falling below 250 V, which presents no problems for the light-proof CASA counters. To protect the BLANCA photomultipliers during daylight, however, the voltage control circuit was modified to bring the minimum supply voltage below 10 V. Together, the board and pod can supply up to 1 mA of current at up to 3000 V. The BLANCA photomultipliers actually operate between 1000-1500 V during observations and draw about 0.5 mA apiece. The station board also controls the shutters that close after each run to protect the photomultipliers from direct sunlight. The shutter control circuit decides whether to turn or stop the motor based on the position of the two sensing switches (Figure 4.1) and whether the operator has commanded.. the shutter to be open or closed. Shutter control is the only completely new function not available on the original CASA boards. With extensive rewiring, spare open collector TTL logic gates on the board are used to control the motors, turning the shutters at roughly 1 RPM. Starlight, light pollution, and low energy air showers in the Dugway sky con- stantly subject BLANCA detectors to accidental pulses. The BLANCA board employs comparators with programmable thresholds to reject pulses smaller than some minimum amplitude (12 m Vin standard operation). When any one of the four amplified photomultiplier signals reaching the board exceeds this threshold, the station alerts.2 The board temporarily stores the charge from each of its four analog inputs as a DC voltage to wait for an array trigger. The Cherenkov array does not form a separate trigger but rather relies on the particle array, whose trigger conditions

2 Unlike CASA stations, which require a 2-of-4 coincidence to alert. 68 are described in Section 3.1.1. When the BLANCA station board receives a trigger pulse, it digitizes the stored DC voltages. If no trigger arrives within 10 µs, the voltages are reset and the board waits for the next alert. The BLANCA board contains four identical analog sections which convert charge to voltage and a single analog-to-digital converter (ADC). The charge-to-voltage circuits integrate the four Cherenkov signal charges on capacitors and amplify the capacitor voltages by a factor of 25. These voltages enter a sample-and-hold circuit to wait for a possible array trigger. If a trigger does arrive, a multiplexer sends the four voltages, one at a time, to the 10-bit ADC chip. One bit corresponds to approximately 3 pC of charge. The ADC also digitally records the temperature of the board, the comparator threshold, and the photomultiplier voltage. The BLANCA station stores the digitized photomultiplier signals in the memory of a specialized on-board COIIlputer, an Intel 80186 with a math co-processor. The computer communicates with the central DAQ computer through its Ethernet transceiver. In addition to storing the ADC values, each local coL1puter must count the triggers received in each polling cycle. Storing the trigger number with the local data allows the DAQ computer to sort data from separate CASA and BLANCA detectors properly into a single event after it has polled both arrays. The sorted data is written to disk and to magnetic tape for later calibration and analysis.

4.4 Operating BLANCA

BLANCA observes Cherenkov light only during clear, moonless nights, when background light is at a minimum. Even the longest nights in summer offer only five hours of darkness, so the experiment was not operated from May to August, 1997. Observations in the winter, however, last up to eleven hours. Runs are longest within several days of the new moon. On other nights, the observations are cut short by the rising or setting of the moon. BLANCA does not operate during the two weeks around the date of a full moon. The moon is very bright during this period and is above the horizon most of the night. Cherenkov light reaching the ground must pass through many kilometers of atmosphere, and clouds and precipitation can drastically change the Cherenkov distribu- 69

I=' 14 :::> 1997 1998 en ..:I 12 0 ==->- 111 10 '1J 0 GI E 8 i= Summer 6

2 (I) (I) ..,. CIC! co LO 0 M CIC! ... en en "? 0 ~ tD C>i C>i c-; C>i c-; ...... (I) ...... LO M M ..,. LO LO ..,...... ,. 0 '° '° 0 50 100 150 200 250 300 350 400 450 500 Days into experiment

Figure 4.9: Cherenkov observation start and end times each night, after removing periods of bad weather. Numbers give the hours of good data recorded each month. tion on the ground through light absorption and scattering. Even the highest clouds float near the typical altitude of maximum air shower development and can therefore affect the light pool measured by BLANCA. For this teason, Cherenkov observations are made only during completely clear weather. Section 5.7.2 describes the checks used to identify cloudy periods which the on-site operator overlooks. These periods are removed from the final data set, leaving the remainder of the night's data intact. Figure 4.9 shows the start and end time of the observations that meet the stan- dards for good weather. The midline of this figure, 7:00 UT, corresponds to Dug- way local time of midnight during the winter, or 1:00 A.M. during daylight savings months. The observations are bunched into two-week periods surrounding the date of the new moon. The slow variation in typical start and end times is due to the changing time of sunrise and sunset. Weather, the rising and setting of the crescent moon, and maintenance problems produce the irregular pattern seen in the figure. BLANCA almost always observes with an operator at the array site, although the procedure is highly automated and can be controlled from a remote computer. The 70

operator monitors the weather and ends the observing run if heavy cloud cover, rain, or snow begins. Because of the glass covers on BLANCA detectors, precipitation does not physically threaten the detectors, but it obscures Cherenkov light. The operator's other main duty is to keep the temperamental data acquisition computer working through the run. In the worst case of complete computer failure (never realized), the operator can use the array circuit breakers to cut power to the photomultipliers manually before sunrise. An observing run begins half an hour before complete darkness, which arrives roughly 90 minutes after sunset or immediately after moonset. The operator first runs a CASA timing calibration and then starts a normal CASA data run. Once the surface array is operating and its trigger rate is verified to be 8-10 Hz, the BLANCA photomultipliers are raised to their operating voltage and given five minutes to equili- brate. At the end of twilight, the vrotective shutters are rotated to the open position, allowing the photomultipliers to view the Winston cones and the night sky. Shutters are opened in two stages to collect pedestal calibration data (see Section 5.1.1). The BLANCA array requires no further attention: CASA triggers, sorts, and records data automatically through the end of the night. To end the observing run at the start of morning twilight (or at moonrise), the operator simply reverses the startup procedure. The protective shutters are closed (again in two stages), the photomultiplier high voltage is turned off, the CASA data run is halted, and the timing calibration is repeated. To ensure the safe execution of the shutdown procedure,3 an automatic safeguard was added to the data acquisition program. At the start of a run, the operator is required to enter the intended shutdown time. The DAQ computer then completes the end-of-run procedure without supervision at the specified time (typically 5:00 A.M. local time). The operator uses the daylight hours for array maintenance and repairs.

3 And to guard against the operator forgetting to set an alarm clock. CHAPTER 5 BLANCA CALIBRATION

The BLANCA detectors are designed to measure the lateral distribution of air shower Cherenkov light. Converting the raw data into photon density measurements requires several instrumental response quantities. Some quantities are extracted from the data itself, for example the gain ratio of each two-channel preamplifier. Other instrumental parameters can be determined only though laboratory studies of the BLANCA detectors, in particular the array's absolute sensitivity to Cherenkov light. This chapter describes the BLANCA calibration process, which turns raw observations into estimates of the Cherenkov photon density at each working detector.

5.1 Determining the BLANCA constants

The BLANCA detector properties that can be estimated from the data itself on a run-by-run basis are called the array "constants." The constants do change from night to night; the name refers to the fact that they are assumed not to vary during a single run. BLANCA constants are determined using detector redundancies or symmetry properties of air showers. A single Chereukov detector's set of constants consists of a pedestal for each of the two ADC channels, a preamplifier high/low gain ratio, and a detector relative gain. Applying these four constants to correct the data compensates for detector differences, revealing the shape of the Cherenkov 2 distribution. Determining its scale (in units of photons cm- ) requires an absolute calibration of the array, described in Section 5.4. Figure 5.1 indicates the procedure by which all the corrections are applied to an example pair of raw ADC data. The BLANCA constants also serve to identify detectors with unreliable data or with no data at all. In a typical run, ten to twenty detectors are not working properly.

5.1.1 Pedestals

Each of the charge digitizers (two per detector) has an offset from zero called the pedestal. The pedestal is the average ADC value recorded when no net charge enters 71 72

;························: High ADC i Saturated:! (1023) :..~?.~.?.~~--!

-Pedest H/L ratio Low ADC (68.3) (108) (26.3) §5.1.1 §5.1.2

-;-BLANCA sensitivity 49.5 photons 2 2 per cm (27.8 ADC cm ) §5.4

Figure 5.1: How raw ADC data are converted to Cherenkov photon densities. Num- bers in parentheses give hypothetical constants for a detector. Section numbers indicate where each correction is discussed in this thesis.

the ADC. The BLANCA photomunipliers are AC-coupled to the preamplifiers, so the fluctuating night sky background can create pulses of positive or negative charge. The blocking capacitor ensures that the night sky produces zero average charge. Thus in the absence of Cherenkov light, the mean ADC value is the electronic pedestal itself. To determine the charge contained in a signal pulse, the relevant channel's pedestal must be subtracted from the raw ADC data. The difference includes an unknown contribution from night sky background light, but this background component is zero on average. The ground array determines the CASA pedestals by averaging the signal values when a counter is not hit (see Section 3.1.1). This method assumes that if a single particle hits the scintillator, then the signal would exceed CASA's relatively low alert threshold. This assumption does not apply to BLANCA, however; a BLANCA detector can receive many Cherenkov photons before registering an alert. Because even unalerted BLANCA detectors can record Cherenkov as well as background light, the cosmic ray data cannot be used to determine the pedestals. One way to ensure that no Cherenkov light interferes with BLANCA pedestal measurements is to close the detectors. An alert requires a signal from only one member of a detector pair, so a digitizing station with one detector closed digitizes 73

charge from both detectors when Cherenkov light alerts the open one. The pedestal is thus defined as the average ADC value recorded in a channel with the corresponding detector shutter closed. The pedestals are measured each night before and after the period of complete darkness, to maximize the time spent observing with all detectors. To collect a full set of pedestal estimates, BLANCA shutters are opened in two stages at the start of each run: first the west member of each pair, followed five minutes later by the 72 remaining detectors. The process is reversed at the end of a run, when the 72 west detectors close five minutes earlier than their partners.

A typical detector records ,..,_, 100-150 events during a 5 minute pedestal period. The mean pedestal is 69 counts, with an RMS variation of ±1 among the 288 channels. Since the digitizers have a 10-bit range, they saturate approximately 954 counts above the pedestal. The pedestal distribution for any given channel is less than one or two counts wide, so 100 events are more than adequate to estimate each pedestal to within a few tenths of a count. Pedestal values vary with the air temperature, having a full range of 2-3 counts in any given channel. Aside from their temperature dependence, the pedestals exhibit no systematic rise or fall over the life of the experiment.

If a detector fails for any reason, then it is impossible to record pedestal data from the other member of the pair. The pair never alerts when its only working detector is closed. For this reason, pedestals cannot be found for some otherwise good detectors. In such a case, the pedestals are assumed to equal that channel's mean pedestal during the entire 1997-98 observation period. This assumption ignores the temperature dependence and can bias the detector's measurements but only by a negligible amount.

This method measures only the electronics pedestals. Because the photomultipliers are shielded from the night sky during the measurement, the average ADC value is never actually measured in the presence of night sky noise. The AC-coupling of the photomultiplier signal ensures that the time-averaged current is zero even when a constant light source illuminates the tube. Therefore, the mean pedestal should not 74

20 g 1200 Entries 133 <( c 18 Mean 25.88 RMS 1.002 "ii1000 16 .c Cl :i: 14 800 12 10 600 Linear fit: 8 ; ~l()p(! ~7.1 400 Intercept 69.4 6 x2lndf =29.2 / 2.6 4 200 ...... ·······' 2 0 0 80 90 100 110 15 20 25 30 35 Low gain ADC B2,B8 east High-Low profile, High/Low ratios, Run 22725

Figure 5.2: Preamplifier high/low gain ratio calibration. Left: Comparison of the two output signals from a single preamp in one night of Cherenkov observations. The line is a fit to the data. Right: Distribution of the high/low ratios for the 133 good detectors in a single night's run. depend on the presence of night sky background light. 1 Tests of BLANCA detectors triggered randomly (i.e. not in coincidence with air showers) demonstrate that the pedestal is in fact the same regardless of whether the photomultiplier is exposed to the sky. The process of opening and closing shutters in two phases was therefore a standard part of the nightly operating procedure throughout the experiment.

5.1. 2 Preamplifier gain ratio

A two-gain preamplifier (Section 4.3.1) boosts each BLANCA photomultiplier signal and sends two correlated pulses to separate digitizers. This design extends the dynamic range of the detectors beyond the 10-bit limit imposed by the ADCs. Very small pulses do not register in the low-gain channel and very large ones saturate

1 The width of the pedestal will increase when the tubes are illuminated by starlight 75 the high-gain channel. The calibration takes advantage of those pulses between the extremes, which both channels record simultaneously. Because the preamplifier outputs are linear, the relationship between the two digitized values is also linear. Figure 5.2 (left) shows this relationship for a single detector during one night of observing. For each detector, a line is fit to the corresponding graph using only points with high-gain ADC values between 130 and 900. This range avoids both the noisy small signal region and saturation of the high-gain channel. The slope of the best-fit line gives the ratio of the preamplifier's high and low gains. The fitted line generally intercepts the point where both channels equal their pedestal values and confirms the previous pedestal estimate to better than one digital count. The mean high/low gain ratio found by the linear fit is 26, very close to the design value of 27. The RMS spread about the average is ±1, although two unusual preamplifiers had ratios of 19 and 38. Figure 5.2 (right) shows the range of high/low ratios in a single run. During the 16-months of observations, detector high/low ratios did not vary appreciably, except in a few cases where the preamplifier was replaced. Once the pedestal and high/low gain ratio are determined for each detector, all data are corrected using these constants. The process converts each pair of preamplifier signals into a single number. Normally, the low-gain data are ignored. However, if a raw high-gain value exceeds 900 (of a '"possible 1023 counts), the low- gain channel is used instead.2 The relevant channel's pedestal value is subtracted, and if the low-gain channel is being used, the result is multiplied by the high/low gain ratio. This process renders Cherenkov light measurements in equivalent high- gain counts above pedestal and effectively extends the dynamic range of the detector well beyond the actual limit of the high-gain channel. The corrected data are used in determining the detector relative gains.

5.1. 3 Relative gains

The detector relative gains are the most important constants, because they vary the most among the 144 BLANCA units. In this context, the term "gain" refers

2 Approximately 1.4% of all Cherenkov measurements use the low-gain data. 76

to a detector's total sensitivity to Cherenkov light, the digital output per unit photon density. Photomultiplier tube gains are one component, but optical transmission, preamplifier gain, cable losses, and ADC charge sensitivity also contribute. Although a portable flasher was used to check the gain inter-calibration in April 1998 (Sec- tion 5.2), it is critical to determine the relative gains on a nightly basis. Therefore, we use the cosmic ray data itself to estimate the detector relative gains from each night's data.

The method relies on the observation that the Cherenkov pool of a vertical air shower is circularly symmetric about the shower core location. 3 The circular symmetry means that any two detectors equidistant from the shower core receive equal Cherenkov photon densities. The two detectors should therefore register the same digital signals, after the pedestal and high/low gain ratio corrections. Any remaining discrepancies, when averaged .. over many showers, must be due to detector gain differences. Events with a zenith angle of less than 7° are used in determining the relative gains if they also alert at least 10 BLANCA detectors and if their cores are at least 20 m inside the physical edge of the array. Beyond 7° zenith angle, the circular symmetry assumption begins to fail. The Cherenkov lateral distribution itself remains symmetric well past 7°, but BLANCA's ability to measure the light degrades asym- metrically because of the Winston cone optical characteristics and the Cherenkov angular distribution. The minimum detector cut selects larger showers. The edge distance cut eliminates showers with biased core positions. Together, these requirements ensure that the selected events have the necessary circular symmetry. Within a selected event, individual detectors are ignored if they register fewer than 20 counts above pedestal. The relative gain determination uses BLANCA data in the form of charge ratios. When any two detectors i and j are the same distance from a shower core, the ratio of their Cherenkov measurements gives an estimate of the ratio Gif G1 of the detector

3 Air showers inclined from the zenith actually exhibit elliptical symmetry. Since BLANCA uses only showers observed within Bzen < 9°, we ignore this complication. 77

350 20 300 133 detectors 250 18 RMS=0.444 200 150 16 100 50 14 0 -2 -1 0 2 12 Raw log-ratios, Run 22715 10

1600 8 1400 RMS:0.068 1200 6 1000 800 4 600 400 2 200 0 -2 -1 0 1 2 -1 0 2 Corrected log-ratios, Run 22715 loge(Detector rel. gains), Run 22715

Figure 5.3: Calibration of the BLANCA detector relative gains. Left: The "log- ratios" before and after correcting for the relative gains. Right: The distribution of relative gains in a single run.

gains. 4 After applying the pedestal, high-low ratio. and core distance corrections, the remaining intensity ratio is the final estimator of the gain ratio. This ratio is subject to several multiplicative uncertainties, so we assume that it is log-normally distributed and therefore examine logarithms of ratios. The mean log-ratio and its variance are calculated for each possible detector pair over a single run. The relative gains consist of a value for each detector, all but one of which are independent (as it uses only ratios, the method is insensitive to the overall gain). The relative gains are over-constrained by the large number of pairwise estimators. Assuming that the log-ratios are normally distributed, maximizing the log-likelihood finds the set of relative gains in a run that are most consistent with the measured

4 A small correction is made for the shape of the average Cherenkov lateral distribution, so that detector pairs can be used even if their core distances differ somewhat. Studies of the cosmic ray data show that the optimum correction assumes an average Cherenkov profile with exponential shape and a scale length of 89 m. Even with this correction, ratios are not used if the core distances differ by more than 30m. That is, we require Ir; - ril < 30m. 78 log-ratios. This log-likelihood fit requires solving a linear system of 144 coupled equations. Fortunately, an iterative procedure converges rapidly to the solution and inverting a large matrix is not necessary. Appendix A gives the log-likelihood function and describes the mathematical details of the relative gain procedure. Figure 5.3 (left) shows the distribution of log-ratios from an example run. The upper plot represents the raw log-ratios and the lower one shows the same data after the relative gains are found and the corrections are applied. The corrections reduce the width of the log-ratio distribution by a factor of nine, which shows that the relative gains are indeed mostly responsible for the apparent departures from azimuthal symmetry. The right panel of Figure 5.3 shows the distribution of derived relative gains during the same run. Relative gains are scaled to make their geometric mean exactly one. The natural logarithm of the detector relativ~ gains has an RMS between 0.40 and 0.45 in all runs, and 703 of the gains lie between 0.6 and 1.5. For most detectors, the relative gain varies by less than 10% from one night to the next, with no appreciable change over time. A few detectors, however, show a gain decline of 30-40% during the final observing season. In other cases, the gain jumps significantly following replacement of the photomultiplier or another element of the detector.

5.2 LED measurements of relative gains

During the 1998 BLANCA observing season, a portable flashing light was employed as a reference source to calibrate the Cherenkov detector array. The flasher provided an external confirmation of the method described in the previous section by which relative detector gains are extracted from the cosmic ray data.

5.2.1 The portable calibration device

The portable flasher uses the same blue GaN LED that served as a light source in laboratory tests (see Section 4.2.3). Figure 5.4 shows the apparatus. The portable flasher is fixed in a vertical orientation, unlike the rotating lab apparatus (Figure 4.6). 79

Figure 5.4: The portable flasher used for calibrating detector gains in the field.

The LED is held at the focus of a 14 inch Fresnel lens and illuminates the BLANCA detector with vertical, collimated light. A small battery-operated circuit controls the timing of the flashes and regulates the LED voltage to keep the flash intensity stable. The portable device also carries a small GPS receiver, which provides trigger pulses exactly once per second. During the calibration survey, CASA's dedicated GPS receiver triggers the CASA and BLANCA arrays exactly on the second as well. Using separate but synchronized timing signals allows the portable device to flash a few microseconds before an array trigger, without requiring the flasher to connect physically into the array trigger network. A single 12 V battery supplies both the portable GPS device and the LED circuit. The flasher was tested in March 1998 and a complete survey of all detectors was performed over six consecutive nights in April 1998. The survey began well after twilight each night during the course of normal data runs. Surveying required an operator in the control room to verify that the calibration data were being recorded 80 and a second person to carry the device and place it on top of the BLANCA detectors. The flasher sat for only two minutes above most detectors. It was left on one detector (B7B4 west) for several hours each night to verify that the light intensity was stable throughout the night. The final BLANCA data set uses the Cherenkov data collected during the calibration survey because only one detector was affected at a time. The data do exclude the B7B4 west detector during the week of the survey, however.

5. 2. 2 LED relative gain results

The external calibration survey provides an independent test of the detector relative gains and helps to verify the complicated algorithm described above (Section 5.1.3). Unfortunately, surveying the entire array took nearly a week, so the results cannot be compared directly with any single. night's relative gains. Instead, the LED results are compared with the detector relative gains averaged over the April 1998 observing period. Figure 5.5 compares the relative gains determined using the two methods. Each set of gains is re-scaled so that their geometric mean is exactly 1.0. The histogram shows the ratio of LED to data gains, which demonstrates that the results differ by about 133 (RMS). The two gain estimates agree as well as can be expected, given that the estimate based on the Cherenkov data varies by nearly 103 from one night to the next. A further complication is that the bright LED flasher typically produced 1000 equivalent high-gain counts (saturating the high-gain channel) and reached the nonlinear domain of the BLANCA photomultipliers.

5.3 Detector saturation

At the highest Cherenkov light densities, the BLANCA photomultiplier tubes collect 20,000 photoelectrons or more. This pulse size strains the physical limits of the photomultipliers, and they no longer produce output charge in proportion to the incident light intensity. For BLANCA to measure the Cherenkov lateral distribution of high energy ( > 5 Pe V) showers, the nonlinear behavior of the detectors must be corrected. 81

c: 35 'ia Entries 124 Cll QI Mean 1.001 > ..,. 30 :;::; 2 . RMS 0.1258 ca .._. .i Qi , ... . 25 0 w ;~ . ..J 1 . 0.9 20 0.8 ..1!·. . 0.7 .. • • 0.6 . . 15 .•"' . . 0.5 10 0.4

0.3 5

0.2 0 1 0 0.5 1 1.5 2 Data relative gain Ratio of LED to data gain

Figure 5.5: Comparison of relative gains measured using the external LED calibrator with those extracted from cosmic ray data. Data are averaged over the April 1998 run period.

Fortunately, laboratory studies establish that the B~ANCA photomultipliers all saturate in a similar manner, which can be approximated by a one-parameter function.

5.3.1 Causes of photomultiplier saturation

The lab measurements of BLANCA detector saturation test the complete detector system. In principle, the preamplifier or the digitizing circuit could be nonlinear in addition to the photomultiplier. Separate studies, however, confirmed that the combined preamplifier and ADC circuit have good charge linearity up to the input pulse charge (,....., 2000 pC) that saturates both channels. Therefore, the photomultiplier must be responsible for the observed nonlinearity. Photomultiplier linearity can be compromised when large pulses draw enough current to reduce the tube's interelectrode voltages [63]. The electrons ejected from a photomultiplier dynode are supplied by the voltage divider circuit that fixes the 82 dynode voltages. The voltage divider cannot maintain the required voltage if the pulse itself diverts too much current from the divider. Generally speaking, sagging dynode voltages become a problem when the instantaneous pulse current between any two electrodes exceeds a few percent of the usual voltage divider current between those stages. The BLANCA photomultiplier base was designed with a high divider current (500 µA) for this reason. Furthermore, the divider circuit bypasses the last two interelectrode resistors with .01 µF capacitors. These capacitors can supply the charge for a pulse large enough to saturate both ADC channels without their voltage dropping by more than 50 m V. Because of the high divider current and the blocking capacitors, the BLANCA photomultiplier power supply circuit has a high capacity for continuous current and pulsed charge and is probably not responsible for the observed nonlinearity. High space charge in the viciq,ity of the last dynode is a more likely cause of the BLANCA photomultiplier saturation. The amount of charge striking the last dynode in a large pulse can distort the nearby electric field, even if the voltage divider itself is capable of supplying the charge without sagging. Changing the electric field causes collection losses at the last dynode or anode and briefly reduces the overall tube gain. A nonlinearity due to space charge becomes more serious for increasing numbers of photoelectrons as the focusing electric field becomes progressively more distorted by the pulse charge. This sort of under-linearity lasts only during the large pulse itself, on the order of 10 ns, so subsequent Cherenkov measurements are not affected.

5.3.2 Laboratory measurements of the BLANCA linearity

The BLANCA detector nonlinearity was measured with an apparatus similar to the one used to test the Winston cone angular response (Section 4.2.3 and Figure 4.6). The same LED light source, fiber optic, and Fresnel lens collimator were used, but the rotating support was fixed in the vertical position for this study. The intensity was varied rather than the incident direction of the light. A variable neutral density filter provided fine control over the photon density of the LED flashes. The circular filter (Reynard Corporation #4412) was placed between the LED and the input end 83

~ ai .e ·u;~ c: ,S! -1 .51Q .c.... :::;Cl

-2 10

2 150 200 250 300 350 400 10 · 10 -l 1 10 2 Wheel angle (degrees) Light intensity (p.e. per 31 mm )

Figure 5.6: Measuring the BLANCA linearity. Left: Calibration of the neutral density wheel. Right: Measured charge vs. light intensity for three BLANCA photomultipliers.

of the optical fiber. The nominal optical density ~panned the range from 0 to 4, or four orders of magnitude in transmission. The neutral density filter consisted of absorbing material deposited on a 5 cm diametef glass disk. One quadrant was uncoated, and the optical density varied linearly with angle along the remainder of the disk at a nominal rate of one decade change in transmission per 67.5°. A high- precision stepper motor moved the filter to the desired position under computer control so that a series of intensities could be observed without human intervention. Because the filter wheel was used specifically to test the nonlinearity of the BLANCA detectors, it was important to calibrate carefully the actual optical density of the filter as a function of angular position, measuring both small-scale variations and the endpoint optical densities. For this calibration, a Hamamatsu R2154-UV photomultiplier detected the light, and a CAMAC module (LeCroy #2249A) digitized its signals. Two LeCroy #612 fixed gain preamplifiers increased the signal size 84

7 by a factor of 100. The Hamamatsu tube was run with a high charge gain ('"" 10 ) and with most of its photocathode masked off. The tube thus worked as a single photoelectron counting system (described further in Section 5.4). In the counting mode, the Hamamatsu was linear over a wide range of light intensities, from '"" 10-2 to '"" 10 photoelectrons per pulse. Figure 5.6 (left) shows the intensity of the LED flasher as a function of the neutral density wheel angle as measured with the Hama- matsu/CAMAC system. To confirm that the system accurately measured the higher intensities, the wheel scan was repeated with an additional fixed neutral density filter (optical density 1.0) and the results scaled up by a factor of 10 for comparison. The results were identical.

The important features of the transmission curve were also verified using the BLANCA detectors and digitizers. To avoid the intensity range in which BLANCA detectors are known to be nonlinear, the scan was repeated several times with additional fixed neutral density filters in place. No single scan accurately measured the transmission of the entire variable filter wheel, but the six scans did measure overlapping segments of the wheel. Together the measurements confirmed the slow curvature of the transmission function T( ¢>) as well as the feature near ¢> = 370°, both of which appear in the left panel of Figure 5.6.

With the neutral density filter calibrated, the linearity of fourteen photomultipliers was measured. The tubes were selected at random from the 144 used in the BLANCA array. All measurements used the same Winston cone and preamplifier; only the photomultiplier was replaced. Each tube was supplied with the same high voltage it used during BLANCA cosmic ray observing runs. The filter wheel was scanned in 1° steps, corresponding approximately to a 4% increase in intensity with each step. For each tube, 1000 flashes were recorded at each light intensity. The flash rate was 50-100 Hz. The photomultiplier gain was shown not to depend on flash rate unless the rate exceeded 105 Hz. Three representative scans appear in Figure 5.6 (right). The charge versus intensity curves are linear below some critical charge value and then curve downward (signifying under-linear behavior) above this charge. 85 5.3.3 Nonlinearity correction to the BLANCA data

It was unfortunately not possible to measure the nonlinearity of each photomultiplier used in the BLANCA Cherenkov array. Since a sample of only 10% of the tubes was studied, the data must be corrected based on the average characteristics of the sample. Unique corrections for each detector are impossible. Nevertheless, we assume that the properties of the random tube sample accurately characterize both the average nonlinearity and its variation within the full set of 144 photomultipliers. The fourteen measured intensity/ charge relationships were fit to a function with three parameters: the tube gain, g, the critical charge, q0 , and a curvature parameter, a. The intensity is proportional to charge below q0 and adds a smooth logarithmic curvature above q0 :

q, gxl= 2 { q X 10-a[log10(q/qo)] , q > Qo

The gains found in these fits are highly correlated with the detector relative gains measured using both the data and the LED methods. Complete correlation is not expected, because the photomultipliers are only one component of the gains measured in the field.

In all fourteen fits, q0 was very similar~nonlinearity begins at roughly the same charge in all photomultipliers. The average fit value of q0 was 285 ADC units, which corresponds to an anode pulse charge of approximately 40 pC. Therefore, the curves were refit with only the gain and a allowed to vary and with q0 fixed at 285 ADC counts. The resulting set of fitted curvature parameters has a mean of (a) = 0.203. With this curvature, a measured charge of 1000 ADC units would indicate an actual charge of 1130 units. The 1-CT range of the curvature parameter is 0.203 ± 0.050, and the error on the mean is 0.013. All BLANCA observations are corrected for the detector nonlinearity using the average values of q0 and a. The observed range of a values and the error on the mean are used to study the systematic errors resulting from this correction. 86 5.4 Absolute light intensity calibration

Converting raw data to photon density measurements requires an absolute calibration of the BLANCA detectors. For this purpose, the output of a stable flashing LED source was calibrated by photoelectron counting. Then BLANCA detectors were calibrated using the known photon density produced by the LED.

5.4.1 Calibration of the LED source

None of the light sources or detectors used in BLANCA were previously calibrated to an absolute standard. The discrete photon nature of light, however, provides a reference by which to calibrate a photomultiplier tube. Using a high-quality tube, it is

possible to count individual photoelectrons, ejected by the photocathode and thereby infer the light intensity. This section describes the BLANCA implementation of the photoelectron counting method of calibration. The absolute calibration employs the same blue LED flasher used to study the photomultiplier nonlinearities (Section 5.3.2). This LED is very stable from pulse to pulse as well as over a period of days, at least in the controlled conditions of the laboratory. Bright flashes of ,....., 10 ns duration pass through a variable neutral density filter and 4 m of optical fiber and are collimated by a large Fresnel lens. The entire system acts as a simulated Cherenkov light source with adjustable intensity. "Calibrating" the source means measuring the photon density immediately below the lens, where the light enters the glass cover of the BLANCA detector. This density can be compared directly with photon densities reported by air shower simulations. A Hamamatsu photomultiplier (part #R2154-UV) was used instead of a BLANCA unit for the LED calibration because of its excellent sensitivity to single photoelectrons. The Hamamatsu tube was operated at its maximum rated voltage (-1400 V) and its pulses were passed through a LeCroy #612 x 10 preamplifier. The high gain ensured that pulses due to a single photoelectron could easily be distinguished from the pedestal. A LeCroy #2249A CAMAC module digitized the signals with a nominal charge sensitivity of 0.25 pC per count. Most of the photomultiplier window was 87 covered with an opaque mask to reduce the number of photoelectrons created. A single hole of 6.3 mm diameter was drilled into the aluminum mask, exposing only 31±3 mm2 of the window to incident light. Photocathode material can have nonuniform efficiency, particularly near its edges. By covering all but the center of the tube window, the mask exposed only the most reliable section of the photocathode.

For the Hamamatsu tube to count single photoelectrons, even with the mask in place, the flasher intensity had to be attenuated with variable and fixed neutral density filters. The photon density was reduced so that on average much less than one photon entered the 31 mm2 aperture per flash, and a charge spectrum of 25,000 flashes was recorded. The spectrum features a narrow pedestal peak and a distinct wider peak resulting from the flashes that produce one or more photoelectrons (Fig- ure 5.7, top panel). For very low light intensities, the mean photoelectron density could be estimated by counting the fraction of events that produced no photoelectrons, i.e. those in the pedestal peak. Assuming that the number of photoelectrons is governed by Poisson statistics, then the mean number per pulse (µ) follows from Nped/ Ntot = e-µ. The method of counting pedestal event works as long as many events produce no photoelectrons, i.e. for µ ~ 1.5. Photoelectrons produce approximately 70 ADC counts (18 pC) on average.

The numberµ is found to be proportional to the mean pedestal-subtracted ADC charge, a strong argument that µdoes indeed count individual photoelectrons. Only a Poisson process of discrete events can account for the fact that the mean charge scales with the logarithm of the pedestal fraction. However, an even stronger test [64] helps to confirm this claim. If single photoelectrons are observed, then Monte Carlo sampling of their charge spectrum can predict the charge distribution produced by any number of photoelectrons. At increasing photon densities, the prediction should match not only the mean of the measured distributions, but the width and shape as well.

Figure 5. 7 (top) shows the single photoelectron charge spectrum. This spectrum is then used to predict the charge spectrum expected for various light intensities. The lower six frames of Figure 5. 7 compare the predicted and measured spectra at 88

102 Single photoelectron charge spectrum

0 20 40 60 80 100 120 Charge (pC) 10 6 10 6 10 6

10 5 5.0 pC 10 5 10.2 pC 10 5 20.0 pC 0.26 p.e.s 0.54 p.e.s 1.07 p.e.s 104 10 4 10 4

10 3 10 3 10 3

102 10 2 10 2

10 10 10

0 100 200 0 100 200 0 100 200 Charge (pC) Charge (pC) Charge (pC)

10 5 27.0 pC 10 5 35.5 pC 10 5 1.47 p.e.s 1.95 p.e.s 10 4 104 104

103 10 3 10 3

102 10 2 10 2

10 10 10

0 100 200 0 100 200 0 100 200 Charge (pC) Charge (pC) Charge (pC)

Figure 5.7: The absolute calibration method. Top: The estimated Hamamatsu single photoelectron charge spectrum. Middle and bottom: Predicted (solid) and measured (dots) charge spectra at several different light intensities. The mean charge is given for the measured distributions, as well as the number of photoelectrons used in the predictions. 89 six different photon densities. The distributions each contain 1.4 x 106 events. The number of photoelectrons assumed in each simulation was determined by requiring the mean charge to match the corresponding measured distribution. The predicted distributions match the measured ones very well, even out to the high-charge tails. This result confirms the assumed single photoelectron charge spectrum and verifies that the Hamamatsu photomultiplier apparatus produces 18 pC per photoelectron. A measured charge distribution can be converted to a mean number of photoelectrons using the mean charge alone. The conversion fails if more than a few events produce enough charge to saturate the ADC module, which constitutes an upper limit of rv 6 photoelectrons per pulse. This limit extends the range of the pedestal-counting method, which works only below µ ~ 1.5. To convert from photoelectrons to photons, the number of photoelectrons is divided by the tube's quantum efficiency. According to the manufacturer, the Hama- matsu photomultiplier has a very flat quantum efficiency of 0.25 ± .04 in the wavelength range of the blue LED ( 400-4 70 nm). In terms of t 1 ie photoelectron count µ, the photon density at the Hamamatsu window is

µ p'Y = 0.25(31mm2 ) ·,

The method described so far calibrates the LED flasher at a range of light densities but only at a single location: the center of the Fresnel lens. The BLANCA 2 detector has an aperture of approximately 800 cm , which is 2500 times larger than the hole drilled into the Hamamatsu tube mask. Because of the geometry of the optical fiber and the Fresnel lens, the LED apparatus does not produce a perfectly uniform light intensity at the BLANCA detector. By moving the small Hamamatsu tube to 20 different locations below the lens, a two-dimensional map was made of the light intensity in the BLANCA entrance plane. This map was circularly symmetric about a point very near the center of the Fresnel lens. Initially, the intensity was very non-uniform; it fell by a factor of three from the center to the edge of the BLANCA aperture. To make the illumination more uniform across the aperture, an opal-coated glass diffusing flat (Edmund Scientific H43717) was placed against the 90 output of the optical fiber. The diffuser reduced the peak intensity by almost half, but it made the spatial distribution of light much more uniform. With the diffuser in place, the intensity 13 cm from the center of the aperture was a full 803 of the peak value. The intensity profile was approximately a two-dimensional Gaussian. By integrating the best-fit Gaussian, we find that the flasher's average intensity in the BLANCA aperture was 0.83 ± 0.05 times the intensity at the center. A completely uniform light distribution would be ideal for calibrating a BLANCA detector, but the flasher with diffusing glass is nearly as uniform as the geometry of the apparatus allows (unfortunately, both the diffuser and collimating lens are fiat instead of spherical). Including a 17% correction for nonuniform light distribution, a photon density of 10.6 cm-2 (averaged over the BLANCA aperture) produces on average one photoelectron in the Hamamatsu tube.

5.4.2 Calibration of two BLANCA detectors

With a known source of simulated Cherenkov light, it is possible to calibrate BLANCA detectors for their absolute light sensitivity. The flasher intensity was determined at a wide range of settings for the variable neutral density wheel, although absolute calibration in principle requires only a single light intensity. A pair of BLANCA detectors and their shared digitizing board were shipped from the Dugway site to Chicago for laboratory calibration. These detectors had very similar gains according to LED flasher measurements in the field. After the flasher itself was calibrated using the Hamamatsu photomultiplier, the BLANCA detectors were illuminated with light 2 densities ranging from 0.2-100 blue photons cm- . The detectors were operated at the same high voltage used in the field (+1140V), and their pulses were digitized by the same station board. The signal cables connecting the preamplifier to the board were the only component different from those used in the field. The cables used in the lab were the same type and length, however, as those in the Dugway array. As expected, the two detectors gave matching results (differing by less than 103). 2 Above 10 photons cm- , the photomultiplier non-linearity was observed. At lower intensities, however, the BLANCA ADC value was linear with the photon density. 91

The BLANCA detectors are calibrated at only one color, the color of the GaN LED (.A ~ 400-470 nm). Their response at other colors is estimated using the quantum efficiency versus wavelength curves for the EMI photomultipliers. The Philips Cor- poration measured these curves for four sample BLANCA photomultipliers. The average of the four measurements appears in Figure 4.4. The two calibrated BLANCA detectors record 33 ADC counts given a Cheren- 2 kov photon density of 1 cm- . The relative gains determined for these detectors in the field were 13% higher than average. Thus the conversion factor to physical quantities is 1 photon cm-2 per 27.8 ADC counts. This factor is subject to several uncertainties. It is in direct proportion to the area of the mask aperture and to the quantum efficiency of the Hamamatsu tube in the blue wavelengths. These independent quantities are known only to 10% and 15%, respectively. The correction for nonuniform light intensity also contributes to the calibration error. The possibility that the detectors measured in the lab somehow changed during or after shipping to Chicago cannot be dismissed, but neither can it be quantified. We estimate that the absolute calibration has a systematic uncertainty of 20%.

5.5 Nightly variations of the. array gain Calibrating BLANCA detector gains is a complicated procedure that combines several kinds of data. Section 5.1.3 and Appendix A describe the intercalibration of detector relative gains, a procedure confirmed by a portable flasher (Section 5.2). Section 5.4 explains the laboratory measurement of the absolute detector sensitivity. But the absolute calibration was performed only once, after the end of the BLANCA observation period in 1998. The intercalibration cannot determine how much the average detector gain changes from night to night, if indeed it drifts at all. The constant nature of the cosmic ray spectrum suggests a method for estimating night- to-night variations in the average gain. Assuming the energy spectrum is constant, any shifts in the measured spectrum must be the result of gain variations or changing weather conditions. 92

Rather than comparing the nightly cosmic ray energy spectra, however, we use the distribution of the fitted Cherenkov parameter C120 . Section 7.1.2 describes in detail the procedure for fitting the Cherenkov lateral distributions. The relevant point for the present argument is that C120 characterizes the photon density of the Cherenkov light pool and is an approximate indication of the shower energy. Although its distribution may differ slightly from the energy spectrum,5 if the energy spectrum and composition are both constant over time, then the C120 spectrum should be constant as well. Departures from a constant C120 spectrum indicate detector gain variations. The reason for working with C120 is that the detector gains affect intensity measurements directly, while they only indirectly affect the energy estimates.

For each night of BLANCA observation, we find the spectrum of the C120 Cher- enkov intensity values. Integrating this distribution produces the total flux of cosmic rays with C 120 above any given "'1Jue. Figure 5.8 (left) shows the C120 integral flux for four example runs in 1997. The C120 value at which each curve crosses any particular test flux gives the relative gain for the run. With a higher gain, the C120 that corresponds to any particular cosmic ray flux also increases. We choose as a standard the integral flux 5 x 10-6 events per (m2 sr s), which corresponds to 500-1000 events in most runs. This flux is high enough to include adequate statistics in each run yet low enough to avoid the low energy region in which BLANCA may not be fully efficient. Within these constraints, the gain results do not depend on the choice of test flux. The spectrum-matching method of finding the gains could be performed instead using a point on the differential spectrum of C 120 , but the integral flux is more robust and confers a statistical advantage simply by counting more events each night. Figure 5.8 (right) shows the average detector gain in each of the 80 good BLANCA runs. At day 40 (February 10, 1997) the high voltages on all photomultipliers were changed. The voltage change was intended primarily to bring all the detectors to the same gain, but it also raised the mean gain by ,....., 50%, as figure shows. The voltages were adjusted again in March 1997. As the detectors aged, the gain fell steadily

5 C120 is not quite a linear indication of the shower energy. 93

c 1.6 ... 2 0 c 1.5 c;; Cl CD 1.4 /I' > i,, I ~ ii 1.3 ,1 a:

1.2 i ( I 'I 1.1 I ~ I I 11 1 J ...... J( .. 1. l1l ...... J.. 1···~··

0.9

0.8

0.7 105 106 0 50 100 150 200 250 300 350 400 450 500

c120 (photons m·') Days after Jan 1, 1997

Figure 5.8: Nightly gain variation. Left: Integral flux as a function of C120 on four nights. The gains were intentionally raised after the February 10 run and lowered slightly before the March 8 run. The gain is given by the C120 value at which each curve crosses the test flux. Right: BLANCA gain history during 1997-1998. through the summer of 1997. The reflectivity of the Winston cones is probably responsible for the reduced gain, as many cones had small areas damaged by sunlight. The average gain was remarkably constant for the final 9 months of operation. The BLANCA analysis uses the nightly average gains found with this method to correct the data; Cherenkov data for a given night are divided by the gain shown in Figure 5.8. The absolute scale of the run gain correction is fixed by setting the mean gain during the final month of operation (April 1998) to be 1.0. April 1998 serves as the reference month for connecting the laboratory absolute calibration with the nightly in situ calibration because the absolute calibration was performed immediately following the end of the BLANCA observing period.

It may be that the "gain" found using the C120 spectrum depends on conditions which do not strictly reflect the sensitivity of the detector. Atmospheric changes, in particular, can affect the measured C120 values. It does not follow that this definition of gain is flawed, as we want to correct for minor atmospheric variations which change the observed C120 . Major changes are of course eliminated by the weather quality 94 cuts (Section 5. 7.2). In fact, the weather cuts have a clear interpretation in terms of the run gains: time periods are cut whenever the array-wide average gain is too low.

5.6 Detector alignment

The BLANCA detectors are intended to point vertically. Given their narrow field of view ("' 10° half-angle), it is important to align the detectors with 1° pointing accuracy. A wider range of pointing directions would require severe zenith angle cuts on the data to eliminate air showers that would be poorly measured by tilted BLANCA units. The detectors sit securely in their PVC housing, so the Winston cone optical axis is well aligned with the PVC pipe axis. The more difficult problem is pointing the pipe itself accurately and securing it. Initially, the pipes were placed on cinder blocks, and their top surfaces were made level by wedging wooden shims • between the pipe and the concrete blocks. To keep it standing on its shims, each pipe was tied to a single stake planted in the ground. In September 1997, however, a more stable support mechanism was installed on all 144 detector housings. Three metal stakes were bolted to each pipe and driven into the earth. Pipe alignment was adjusted by hammering one or more stakes further into the ground. The Cherenkov data offer an indication of each BLANCA detector's alignment because of the sudden drop in sensitivity outside the detector field of view. Cosmic rays strike the array in equal numbers from east and west or from north and south; CASA verifies that the reconstructed arrival directions are symmetric in azimuth. But a BLANCA detector pointed slightly to the east will show a bias in favor of showers arriving from the east. The mean direction of the showers that exceed some threshold number of counts at a detector indicates the optical axis of that detector. The term "direction" here refers to the two direction cosines for the angles a shower axis makes with axes pointing west and south. This correspondence between detector axis and mean shower direction would be exact if Cherenkov light were perfectly collimated parallel to the air shower axis. However, Cherenkov light generally strikes a detector from the direction of the shower maximum, not necessarily parallel to the shower arrival direction, as shown in Fig- 95

--E-Shower Maximum

.,, ~I \.BLANCA/ ti \ FOY 61 \ t51 I I 0 n

4 4 CiCl) CiCl) ~ :!::!. Cl) 3 Cl) 3 "61 "61 c c Ill Ill x 2 > 2 c c Ill Ill Cl) Cl) 1 == == 0 0

-1 -1

-2 -2

-3 -3

-4 -4 -100 0 100 -100 0 100 Core X distance (meters) Core Y distance (meters)

Figure 5.9: The concept behind the BLANCA alignment estimates. Top: Why angular bias depends on detector position relative to the core. Two shower cores land an equal distance to the east of a detector. Depending on the shower direction, the Cherenkov emitting region may or may not be in the detector field of view. Bottom: Average angle versus relative core location in the X and Y directions, for one detector in a single run. The intercept of the fit gives the alignment angle. 96

45 Mean -0.8103 Mean -0.1763 40 -- RMS 1.013 50 RMS 0.5346

35 40 30

25 30

20 20 15

10 10 5

0 -2 0 2 4 -4 -2 0 2 4 Pointing angle (deg) Pointing angle (deg)

Figure 5.10: Detector pointing angles. Left: Run 22715, before detectors were staked down. Right: Run 23703, after the realignment. ure 5.9 (top). Showers landing to the east of a vertical detector might be visible coming from as much as 10° west of zenith but begin to slip from view if they arrive from a mere 5° or more east of zenith. The lower panels of Figure 5.9 demonstrate this effect. The average east-west direction of detected showers correlates negatively with the east-west core location. Because of this correlation, averaging the direction cosines of all showers reaching a detector produces a biased alignment estimate for detectors near the array edges. Instead, the average direction is fit as a linear function of core location. The intercept of this fit gives the average direction of showers after accounting for the core-direction correlation. The slope is a consequence of the geometry of the air shower and to the angular distribution of Cherenkov light at various distances from the shower core. For each run, an x (east-west) and a y (north-south) fit are made for each detector. The directions determined by this method show that most detectors did not move substantially during the September 1997 installation of the new three-stake support structures. A few detectors were realigned by as much as 2-3°, however. The RMS of 97 the set of x and y angles was 1.0° before the realignment; afterwards it was reduced to 0.5° (Figure 5.10). The RMS zenith angle is a factor of v'2 higher than the individual x and y angles, meaning the detectors were aligned with the zenith to a 0.7° tolerance for the 1997-98 observing season. The BLANCA analysis does not use the detector pointing directions in the Cherenkov distribution fits, even though it is possible in principle to reduce some measurement errors by compensating for the effects of misaligned detectors. Instead, the measured distribution of pointing angles is used to simulate the effects of imperfect alignment. These simulations determine the zenith angle cut used in selecting "good" Cherenkov air showers.

5. 7 Eliminating bad detectors and bad events

The extensive calibrations described in this chapter attempt to correct for small differences among the BLANCA detectors. Detectors fail from time to time and in various ways, however, and no amount of correcting can render their data useful. It is therefore important to recognize and eliminate bad detectors from the data. Hazy or cloudy weather can also disrupt Cherenkov measurements. This section describes the criteria used to identify working BLANCA detectors and periods of good weather.

5. 7.1 Detector quality cuts

For many detectors, it is impossible to determine the two pedestal constants using the usual method. That method requires a good detector to alert a station while the other detector in the pair is shuttered. Often a detector has no good pedestal events simply because its partner detector has failed. Therefore, no detector is cut from the data solely due to undetermined pedestals. The unknown pedestals are instead assumed to equal the mean pedestal for that channel averaged over the remainder of the BLANCA campaign (Section 5.1.1). This compromise never affects the raw data by more than three ADC counts, which is less than the noise due to the night sky background. 98

Failing to determine a detector's preamplifier high/low gain ratio is more serious. A high/low ratio is considered good if at least 50 events are recorded in the range of 2 overlap between the two channels, if the linear fit has a low x , and if the resulting ratio falls between the extremes of 15 and 40. If a detector does not meet all of these criteria, its low-gain channel cannot be converted to equivalent high-gain ADC counts. Therefore, its data are not used when the high-gain channel saturates, although it can still provide useful Cherenkov measurements below the saturation level. Unlike the high/low gain ratios, the detector relative gain constants (Section 5.1.3) are used to correct every single Cherenkov observation. Detectors are ignored for an entire run if their relative gains cannot be determined from the data. Mechanical or electronics problems are usually responsible for the failure of the relative gain determination. This cut eliminaies approximately 5-15 detectors from each run. Detectors are also cut if their relative gain is less than 0.25 or greater than 4 times the average gain, although this restriction rarely eliminates any detectors.

5. 7.2 Weather requirements

Only BLANCA observations made on clear nights are used for Cherenkov analysis. Any significant change in the transparency of the atmosphere affects the measurements. The on-site operator begins taking data only if the weather is clear and ends a run when obvious bad weather arrives. In the absence of snow or rain, however, it is possible for the operator to overlook partial cloud cover. The entire BLANCA data set was checked offiine for periods of bad weather, to eliminate previously unnoticed cloudy periods. Two related quantities are used to track the transmission of the atmosphere. One atmospheric indicator is the rate of events with at least five BLANCA stations alerted, typically 80 min-1 in clear weather. The other indicator uses the Cherenkov lateral distribution fit described in Section 7.1.2, which finds the photon density 120 m from the shower core ( C120). The rate of events with C120 exceeding 1 photon cm-2 was typically "'"' 40 min-1 during good weather. Both rates fall dra- 99

c 70 §. 60 .l!lc Q) > w so

0 4 6 8 10 12 Time (hours UT) 2 Rate of events with C120 > 1 phot cm·

2 Figure 5.11: Rate of events during one run with C 120 > 1 photon cm _ _ The arrival of clouds is apparent at 10:30 UT as is a short break in the clouds an hour later.

matically when clouds obscure the sky near the zenith. Figure 5.11 gives the C120 indicator during a January 1997 run as an example'." For most of the night, the rate was constant, but it fell quickly when the weather deteriorated after 10:15 UT. A plot of the 5-alert event rate has similar features. Using these two rates, the atmospheric transmission is followed over the course of each run. Periods of good transmission are identified during a manual scan of the rates. At most one continuous period of good data is selected from each night, because using disjoint intervals in a single run could easily include by mistake data taken under intermittent cloud cover. The C 120 event rate during the good period should be Poisson-distributed, unless partial cloud cover lowers the rate. This ex- pectation provides a simple test of the good period selected in the manual scan. Of the 87 runs, 80 have a period of good data, for a total of 457 hours of usable cosmic ray observations. CHAPTER 6 AIR SHOWER SIMULATIONS FOR BLANCA

Extensive air showers are complicated processes. Determining the energy and mass of a primary cosmic ray from air shower measurements requires a detailed model of the millions of particle interactions that take place in a shower. Analytic models can predict many important features, but air showers change with energy and primary mass in ways that depend on the interplay of many competing factors. The sheer number of particles and possible interactions calls for a Monte Carlo1 approach to shower modeling. A Monte Carlo computation simulates air showers by generating a series of pseudo-random numbers. For each particle, the random numbers determine such variables as a particle's decay and interaction lengths, as well as the number, type, and momentum of the procJ.uct particles in each interaction. These quantities are chosen according to measured or theoretical probability distributions. Computers make it possible to create large libraries of simi1lated air showers for interpreting cosmic ray experiments. Unfortunately, there are large inherent uncertainties in the particle physics at the highest energies. Modeling the interactions of Pe V cosmic rays requires significant extrapolation from measurements made at accelerator experiments. In the collision of a 5 PeV proton with an air nucleus, for example, the proton-nucleon center of mass energy is 3 TeV, beyond the reach of the Tevatron and other existing particle colliders. Interactions after the first one take place at lower energies, of course, but even these are difficult to model based on experimental results. One problem is that most interactions involve relatively little momentum transfer, while collider detectors are primarily equipped to study those rare collisions with high momentum transfer (i.e. high Pr in the collider). Products of the more common interactions are lost down the beam pipe. Furthermore, cosmic rays probably consist of many nuclear species, not just protons, and their targets are air nuclei rather than single nucleons. The heavy ion collisions that take place in an air shower have not been studied directly at the relevant energies. The

1 This statistical method for performing complicated numerical integrations was named and developed by von Neumann and Ulam during the U. S. fusion bomb project [65]. 100 101 high energies and compound nuclei involved in air showers make their simulation a difficult and uncertain task. The cross sections, inelastic scattering products, and angular distributions for the highest energy interactions in a shower must be estimated by extrapolating from accelerator results. These extrapolations may be entirely empirical or motivated by theory. Several methods of either type exist in the high energy physics and air shower communities. Four different models are used in this work. Like any air shower study, the BLANCA analysis relies on comparisons between measured showers and simulated showers of known origin. The philosophy adopted here is that the simulation should be as complete as possible. The detector, with all its imperfections, should be modeled in addition to the shower itself. We simulate air showers and the detector array in separate stages so each Monte Carlo shower can be studied more than once. The two-stage arrangement also makes it possible to continue developing the detector simulation after creating the finished air shower library. The shower and detector simulations produce "fake data," which is then studied to find the correlations between Cherenkov lateral density distributions and primary energy and mass. We compare BLANCA measurements with the results of simulations using four different interaction models. The multiple interpretations of BLANCA data show which conclusions depend on tlie choice of hadronic interaction model and which are insensitive to the model. 5 The BLANCA analysis uses a large number ( ,..._., 10 ) of simulated showers to determine how observable properties depend on the primary cosmic ray. This chapter describes the air shower and detector simulation programs. The following two chapters explain the procedure for extracting primary cosmic ray energy and mass from Cherenkov measurements.

6.1 The CORSIKA simulation program

This work uses the CORSIKA ("Cosmic Ray Simulations for KASCADE") Monte Carlo program [66, 67, 68] to simulate extensive air showers. CORSIKA was developed by the KASCADE collaboration [69], which operates an air shower array 102 in Karlsruhe, Germany to study the cosmic ray composition between 0.3 PeV and 50 PeV. The KASCADE detectors measure the electromagnetic, hadronic, and muon components of air showers, so the original program simulated only these particles. CORSIKA has since been extended to produce neutrinos and Cherenkov light, making the program useful to a wide range of air shower experiments. CORSIKA was chosen for the BLANCA analysis instead of the bider MOCCA Monte Carlo [70] for the same reasons that it is becoming a de facto standard in the air shower commu- nity. CORSIKA is extremely well supported and documented, it supports a choice of hadronic interaction models in the high energy regime, and it uses standard codes from the high energy and nuclear physics communities for the lower energy regime, where exact calculation is possible.

6.1.1 How CORSIKA simulates air showers

The CORSIKA program consists of four main components. The program frame tracks the primary and all secondary particles in the shower and stores the results on disk. The second program component handles the interactions of shower nuclei and other hadrons with air nuclei for lab-frame energies above 80 GeV. A separate section treats the lower energy nuclear interactions. The final CORSIKA component handles the electromagnetic interactions of leptons and photons. Apart from the program frame, the other three sections of the program are interchangeable, allowing the user to select any desired combination of the two electromagnetic shower codes, the two low energy nuclear codes, and five high energy hadronic models. For BLANCA analysis, EGS4 ("Electron Gamma Shower version 4") computes the electromagnetic component of the shower, and the GHEISHA code handles the low energy hadronic interactions. Both of these models are slower but more rigorous than the alterna- tives [66]. BLANCA uses all but one of the available high energy hadronic models for the sake of comparison. CORSIKA simulates air showers by following the paths of millions of particles from their production to decay or interaction. Along each particle track, the program accounts for ionization energy losses and deflections due to low-angle multiple 103

scattering and to the Earth's magnetic field. Interaction lengths are generated using measured or theoretical cross sections, combined with a model of the atmospheric density (described in Appendix B). Unstable particles are allowed to decay before interacting. In either case, the interaction or decay products are placed on the stack of particles to be tracked. If a particle penetrates to the observation altitude without decaying, interacting, or ranging out by ionization energy loss, it is recorded in an output file as a ground particle, i.e. one that an air shower array could observe. The data for each particle consist of its type, energy, direction, location, and arrival time. Every charged particle in the simulated air shower can produce Cherenkov light if its velocity exceeds the Cherenkov threshold in air. Depending on the atmospheric depth, Cherenkov production can be as high as 40 photons per meter for a highly relativistic particle. The Cherenkov photons outnumber the massive particles by several orders of magnitude, so they cannot easily be tracked and listed individually like the particles. To reduce the computational burden of the Cherenkov light calculations, CORSIKA produces the photons in "bunches" of approximately 40. Only one photon in a bunch is actually tracked, and it is assigned a weight to compensate for the discarded photons. This technique makes the simulated Cherenkov light distribution less smooth that it should be, but the bunch sizes are small enough and • the number of bunches is large enough that the exaggerated lumpiness presents no problems.

6.1.2 High energy hadronic models used in CORSIKA

The choice of hadronic interaction model has small but important effects on the simulated air showers. Unfortunately, all models rely on extrapolations from accelerator data. It is not possible to know a priori which one, if any, of the current models accurately describes real air shower interactions. CORSIKA offers a choice of five models: QGSJET, SIBYLL, VENUS, HDPM, and DPMJET. All of the models are used in this analysis except DPMJET, which requires prohibitive computing time. The other four models take different approaches to hadronic interactions: 104

• The QGSJET model (Quark Gluon String model with Jets) [71] treats single and multiple Pomeron exchange as the fundamental process in high energy hadron scattering. A quark gluon string model describes the hadronization process. Minijets are also produced in hard interactions.

• VENUS (Very Energetic Nuclear Scattering) [72] was developed for the study of relativistic heavy ion collisions in accelerators. Like QGSJET, it uses Pomeron exchange to compute scattering amplitudes. VENUS simulates particle creation through the interaction and fragmentation of color strings between hadrons. Unlike QGSJET, however, VENUS does not produce jets, which become important at very high energies. For this reason, the authors of CORSIKA recommend that VENUS not be used for primaries with energies exceeding 20 PeV per nucleon [66]. BLANCA pushes that limit, simulating protons up to 32 PeV.

• The SIBYLL event generator [73] was developed specifically for high energy air shower simulations. It emphasizes the production of QCD color strings and minijets. SIBYLL treats nucleus-nucleus collisions approximately as a semi- superposition of nucleon-nucleus interactions, with the number of interacting nucleons determined by Glauber theory. SIBYLL allows the production and decay of strange baryons and many flavors of mesons, but only nucleons, anti- nucleons, pions, and kaons are actually allow2d to interact with air nuclei. The other hadrons can only decay in this model.

• The HDPM model [66] is empirically motivated, adjusted wherever possible to experimental results. As a parameterization of laboratory data, HDPM is simpler and faster than the other models, but it oversimplifies nucleus-nucleus collisions by assuming simple superposition. The authors of CORSIKA state that HDPM is less realistic than the other models when comparing the air showers produced by different primary nuclei [67].

All CORSIKA hadronic models calculate the interaction cross sections separately from the product particle types and momentum distributions, which allows the user 105 QGSJET VENUS SIBYLL HDPM Gribov-Regge * * * Minijets * * * Secondary interactions * N-N interaction * * Superposition * * Table 6.1: Features of the interaction models used in CORSIKA. to combine the cross sections of one model with the interactions from another. The BLANCA analysis does not take advantage of this feature. Figure 6.1 shows smoothed distributions of several air shower parameters as computed by the different hadronic models. The comparison sets each consist of 1000 protons at 1 PeV. The top row shows properties of the electromagnetic shower component: the depth of maximum and the total numbers of electrons and muons. The middle row shows properties of the first hadronic interaction. The lower row shows Cherenkov lateral density fit parameters. The observable quantities (top and bottom rows) are in good agreement. Nevertheless, the small dif:erences become important when interpreting air shower measurements, as the following chapters will demonstrate. Without direct measurements of the relevant collisions,.. it is difficult to choose a favorite hadronic model. However, their handling of nucleus-nucleus collisions suggests that SIBYLL and HDPM are likely to be less realistic than the other two models. On the experimental side, the multi-component KASCADE detector has measured air shower hadrons [74] and muons [75], finding that the data slightly favor the predictions of QGSJET, followed by VENUS. The hadron measurements do not agree well with the predictions of SIBYLL. Therefore, BLANCA analysis uses QGSJET as its preferred model, but the measurements will be interpreted using each of the four models.

6.1. 3 Thinned air shower computations

Computing time for an extensive air shower simulation is approximately proportional to the number of secondary particles in the shower, which rises linearly with the primary energy. Simulating a single 10 Pe V air shower can take several hours, even 106

100 557.2 Q 5.33 Q 150 150 572.9 v 80 5.34 v 585.6 s 5.41 s 602.4 H 5.41 H 100 60 100 40 50 50 20

0 0 0 0 500 1000 4.5 5 5.5 6 3.5 4 4.5

) Xmax log10(N 9 log10(N) 250 250 80 61.08 Q 105.2 Q 0.383 Q 200 70.01 v 200 112.8 v 0.385 v 60.56 s 83.6 s 60 0.442 s 150 66.73 H 150 101.7 H 0.535 H 40 100 100 .. ' 20 "· r: 50 50 I; ---- 0 0 0 0 250 500 0 500 1000 0 0.5 First Interaction Depth Multiplicity Elasticity 200 150 250 0.0154 Q -2.14 Q 0.0161 v 200 -2.16 v 150 0.0167 s -2.19 s 100 0.0171 H 150 -2.17 H 100 100 50 50 50

0 0 0 0 10 20 0 0.02 0.04 -3 -2 -1 C120 (y cm -2) Inner Slope Power Index

QGSJET

------VENUS

.. ·-····--. SI BY LL

HDPM

Figure 6.1: Comparison of several shower parameters from the four hadronic models QGSJET, VENUS, SIBYLL, and HDPM using 1 PeV protons (1000 per model). The numbers indicate the mean value of the distributions for each model. 107

35 >- iii 1 ~ :c= ___ {-"-'~ .! Ill . 30 ..Q -1 . .5 c ------~ 0 10 i---~~~~-=-::., ____ ~ ...Q. -- E 25 > : "'- u 0 -2 g '. Cl 0 10 !!m \, Xmax 0 20 Cl :?:'.:. 0 GI ... E -3 a: 41 10 Q. 0 15 ~ UI -4 ...41 :i:: 10 0 10 .r:. -5 "' 5 10 N. -6 0 10 400 600 800 1000 -5 -4 -3 -2

xmax (g cm -2) Thinning energy fraction log10(E1 /EP)

Figure 6.2: Consistency of air shower quantities at several thinning levels. Left: 5 5 2 Distribution of Xmax for 500 showers at thinning levels from 10- . to 10- . Right: Probability that Xmaxi Ne, Nµ, C120 and s distributions at each thinning level are 5 5 compatible with the 10- - reference set. on the fastest computers readily available. The "thinning" technique can reduce • dramatically the computer time required to simulate an air shower. The idea of thinning is that the less energetic particles in a shower are so numerous that any measurable average property can be determined by studying a random sample of the full population. With the CORSIKA thinning option, the user specifies a minimum particle energy. When the products of a collision have less than this threshold energy, CORSIKA follows only one particle produced in the interaction and ignores the others. The tracked particle is given an appropriate weight to compensate for the lost particles, in analogy to the Cherenkov bunching described above. 2 The thinning threshold energy is usually specified as a fraction of the primary energy. The BLANCA analysis uses simulated air showers thinned at 10-4 times the primary energy. To select the optimum thinning level, 500 1 PeV proton showers

2 0f course, this means that Cherenkov photons are doubly thinned; they have both a bunch size and a weight inherited from the radiating particle. 108

5 5 were produced at each of eight thinning levels (every half decade from 10- . to 2 10- , inclusive). The distributions of bulk shower properties were compared. Fig- ure 6.2 (left) shows the eight distributions of shower maximum depth (Xmax) as an example. The most unusual distribution in this plot corresponds to the most heav- 2 ily thinned shower set (10- ). Although the distributions are not shown, the total number of muons (Nµ), total number of electromagnetic particles (Ne), Cherenkov intensity (C120 ), and Cherenkov slope (s) were also compared. Taking the least 5 5 thinned shower set (10- · ) as a reference for each distribution, the more heavily thinned sets were checked for consistency with the reference set. The Kolmogorov test was used to compare distributions. This test is used in preference to the x2 test because it is sensitive to a series of small deviations of the same sign in successive bins [76]. The right panel of Figure 6.2 shows the Kolmogorov probability of the thinned distributions being cons~tent with the reference distributions. For most bulk shower properties, even 10-3 thinning produces the proper distribution. The property most sensitive to thinning is the number of electromagnetic particles Ne, which can be reproduced accurately only with thinning of 10-4 times the primary energy or lower. Therefore, the BLANCA analysis uses showers with 10-4 thinning. Note that this test compares only bulk shower properties and Cherenkov lateral distributions. To accurately reproduce the lateral distribution of ground particles and its fluctuations, for example, would require significantly less thinning. Fortunately, the lateral distribution of Cherenkov light is found to be sufficiently smooth even with 10-4 thinning. This novel method3 for determining the optimal thinning level empirically is a unique strength of this analysis.

6.2 Atmospheric scattering of Cherenkov light

The standard version of CORSIKA does not consider interactions between Cherenkov photons and the atmosphere. Light absorption and scattering are ignored, and all photons produced in standard CORSIKA reach the observation level. To account for these effects, a special version of CORSIKA was prepared for this analysis. The

3 Due to C. Pryke. 109

modified CORSIKA models both molecular and aerosol scattering phenomena and deflects photon paths accordingly, producing the most realistic Cherenkov lateral distributions possible. Atmospheric absorption of ultraviolet light is also considered, but its effects are small and are not added to the simulation.

6. 2.1 Rayleigh and Mie scattering

Rayleigh scattering refers to the elastic scattering of light by neutral gas molecules in the atmosphere. The probability per meter of Rayleigh scattering is proportional to the gas density, so the path length increases with altitude as the density falls. The CORSIKA atmospheric density profile is approximately exponential with a scale height of '"'"' 10 km (Appendix B gives details of the density model). The scattering cross section depends on the photon wavelength, so CORSIKA assigns each photon bunch a random wavelength between 290 nm and 650 nm drawn from the P(>..) ex ;..- 2 distribution characteristic of Cherenkov emission. The detector has no sensitivity outside this wavelength range. Light with a wavelength of 400 nm 2 has a mean Rayleigh scattering path length of 2900 g cm- , which corresponds to 22 horizontal km at Dugway altitude [62]. This mean free path is greater than 2 the observation depth at Dugway (870 gcm- ) yet st'ill short enough that 10 - 15% of Cherenkov photons scatter. The path length increases rapidly with wavelength 4 (as >. ), so Rayleigh scattering is important primarily for the shorter blue and UV wavelengths. The angular distribution of Rayleigh scattered light is symmetric forwards and 2 backwards, with d(c:B) ex (1 + cos e). Light generally scatters through large angles. A scattered photon has a 50% chance of emerging from an encounter heading upward, regardless of its incident direction. Since a second scatter is unlikely, scattered photons do not usually reach the detector array. The BLANCA version of CORSIKA also models the Mie scattering process, which results from dust particles suspended in the atmosphere. Aerosol concentration varies substantially at different locations and times, as does the distribution of dust grain sizes. For the sake of simplicity, we use an empirical model for Mie scattering that 110 Rayleigh Mie Scattering centers Air molecules Suspended dust grains Path length at ground (..\ = 400 nm) 27km 14km Wavelength dependence of path length ,\ 4 ,\ 1.3 Scale height lOkm l.2km 2 Angular distribution of scattered light 1 + cos () exp(-B/27°)

Table 6.2: Comparison of the two atmospheric scattering processes. represents typical conditions at BLANCA's desert site [46]. Since the Rayleigh process actually dominates the scattering of Cherenkov light, this simple aerosol model suffices. The scale height of aerosol particles (1.2 km in this model) is much shorter than that of the atmosphere itself ( 10 km in the lowest layer), so Mie scattering generally occurs closer to the ground than Rayleigh scattering does. The model assumes that the Mie scattering path length at the ground is 14 horizontal km for 400 nm 3 wavelength light and that it increases weakly with wavelength, as /!. ex: ,\ i. [62]. For all wavelengths, the mean free path increases with altitude as eh/ho, where the scale height h0 = 1.2 km. Aerosol scattering is highly peaked in the forward direction, unlike molecular 0 270 scattering, and we assume an angular distribution of the form d(cd:So) ex: e- 1 [46]. Table 6.2 summarizes the differences between the two components of the scattering model, and Figure 6.3 shows them graphically.

The modified CORSIKA tracks photons even after they scatter, assigning them random new directions governed by the angular distributions listed in Table 6.2. Molecular scattering generally redirects photons out of the detector area entirely, both because it is almost isotropic and because it happens several kilometers above the detector array. The dust layer hugs the ground, however, so Mie scattering occurs only near the observation level. The low altitude combined with the forward- peaked angular distribution means that photons scattered by aerosols can still land in the main pool of Cherenkov light. These displaced photons are the reason that tracking the scattered light is necessary. The code permits multiple scattering, but 111

80 .s:;. E' ...Cl 1.6 11 1 ~ 70 ,' c ·c: .s:;. Mie .!! :I 1.4 CD '5i 60 Cl 0.8 c c 1.2 :;::> ' ·;: la ' .!! 50 CD - ' Cl ::: 1 ii 0.6 ' c 40 la .:. ·c: Rayleigh u 0.8 CD Ill enIll ::: 30 CD 0.4 la 0.6 0 > (,) u 20 :;:: en la 0.4 =ti' ii 0 0.2 10 a: 0.2 - "C 0 0 0 2.5 5 7.5 300 350 400 450 0 100 Altitude (km MSL) Wavelength /... (nm) Scatt. Angle e (deg)

Figure 6.3: Atmospheric scattering model. The increasing scattering length as a function of altitude above sea level (left), wavelength dependence (center), and angular distribution (right). the optical depth of the atmosphere is so small that this effect has little impact on the final Cherenkov distributions. In addition to molecular scattering, the atmosphere can affect Cherenkov observations by absorbing ultraviolet light. Molecular oxygen is an important absorber for wavelengths shorter than 270 nm [77], which is well below the BLANCA detector UV cutoff (see Figure 4.4). Ozone absorbs wavelengths as long as 340 nm, but it also has very little effect on BLANCA observations for two reasons. First, the shape of the absorption curve due to atmospheric ozone is quite similar to that of the combined BLANCA window and photomultiplier tube. Ozone primarily absorbs the short wavelength light that the two glass surfaces would have filtered out anyway.4 Fur- thermore, ozone is not distributed uniformly in the atmosphere but instead resides primarily in the troposphere (12-50 km) and in a thin layer near the ground [62]. Most Cherenkov light in Pe V air showers is produced below the troposphere, so the ozone layer cannot affect it. Cherenkov light must penetrate the ground ozone to

4 This is no accident. The ozone cutoff at ~ 300 nm fixed the window glass cutoff at a similar value. Glass with a longer wavelength cutoff would waste photons; a shorter cutoff would waste money. 112 reach BLANCA, but this layer is relatively thin far from urban areas. Even if shower Cherenkov light were to pass through a full atmosphere of ozone, the glass cutoff at 300 nm would limit the effect of ozone absorption to a decrease of approximately 43 in the Cherenkov light at ground level. Therefore, atmospheric absorption was not incorporated into the BLANCA version of CORSIKA.

6. 2. 2 Effect of scattering on the Cherenkov distribution

The effect of atmospheric scattering on Cherenkov measurements is small for showers in BLANCA's energy and zenith angle range. On average, only 203 of the photons scatter in a vertical 1 PeV air shower. Scattering would be a more important effect for cosmic rays of lower energy or those arriving from steeper zenith angles. Such showers develop further from the... observation site, and their Cherenkov light must pass through more intervening atmosphere. Photons that reach the ground in a 1 PeV shower scatter an average of 0.24 times. Most photons that scatter one or more times land at least 500 m from the shower core. The Rayleigh process scatters twice as many photons as aerosols do, according to the CORSIKA/BLANCA model. By reducing the number of Cherenkov photons reaching the detectors, atmospheric scattering changes the absolute energy calibration. Figure 6.4 shows that the two scattering processes together reduce the Cherenkov intensity uniformly by 203 (except near the shower core). If scattering were ignored, BLANCA would systematically underestimate primary energies by a similar amount. The light loss due to scattering changes very slowly with shower energy. Higher energy primaries produce showers that penetrate deeper into the atmosphere, so slightly less of their Cherenkov light is lost to scattering. In addition to reducing the total amount of light, atmospheric scattering changes the shape of the observed Cherenkov lateral distribution. This happens because light at different core distances traverses different amounts of atmosphere, as shown in Figure 6.5. Most light that lands more than 100 meters from the shower core is emitted 2 to 6 km above the surface, i.e. near shower maximum. Cherenkov light observed exactly at the shower core is emitted much nearer to the observation level, 113

~ Cl ":' c E 10 6 Ill "5i 0.95 c I'll 0 =u 0.9 ..0 Ill .s::. S: lii 0.85 ::- I'll 0.8 "iii =c c 0 Cl) 0.75 Rayleigh + Aerosol 5 fj "E 10 I'll -=::- 0.7 -~ 0.65 Cl) .E.. 0.6 0.55 0.5 0 100 200 300 0 100 200 300 Core distance (m) Core distance (m)

Figure 6.4: The effect of atmospheric scattering on an example 1 PeV shower. Left: The Cherenkov lateral distribution with no scattering, Rayleigh only, and Rayleigh and Mie. Right: The fraction of Cherenkov light remaining after scattering, as a function of core distance.

most of it less than 2 km above the ground. This difference makes scattering loss less severe near the core, which steepens the observed slope in the Cherenkov lateral distribution (as seen in Figure 6.4).

The Cherenkov lateral distribution shape is used to find the primary mass (discussed further in Chapter 8). In particular, its exponential slope within 120 meters of the core (the "inner slope") is an approximately linear indicator of the depth of shower maximum. The combined effects of the two types of atmospheric scattering 1 increase the inner slope by approximately 0. 8 km- . Scattering thus makes all showers appear to have deeper Xmax and seem more proton-like. At any given energy, however, the slope change due to scattering is still much smaller than the average 1 slope difference between protons and iron, which is typically 5 km- . Accounting for scattering will therefore increase the inferred primary mass, but only slightly. 114

::J c (/) 14 0.12 '150 m :8u == ...IU 100-150 m 12 LL. .!. ! 0.1 200-250 m .c.. .2' 10 .!. GI :c 0.08 c 0 8 ·u; 0.06 Ill ·e 6 w 0.04 4

2 0.02

0 0 0 100 200 300 400 0 2.5 5 7.5 10 Core Distance (m) Emission Height (km MSL)

Figure 6.5: Emission height of atmospheric Cherenkov light. Left: The intensity of Cherenkov light reaching the ground, as a function of both core distance and emission height. Light nearer the core is generally emitted lower in the atmosphere. The logarithmic intensity scale spans a factor of 200. Right: The relative contribution of Cherenkov light from different altitudes observed at 0-50 m, 100-150 m, and 200- 250 m from the core. Distributions are normalized to 1.0 for comparison.

6.3 Using CORSIKA for BLANCA

The BLANCA version of CORSIKA differs slightly from the standard release. Be- sides adding atmospheric scattering code, the BLANCA edition changes the format for recording Cherenkov data in order to reduce data storage requirements. The resulting Monte Carlo data are then passed to a full detector simulation to produce fake data. The fake data, in turn, can be fit by the same procedures used to fit the real Cherenkov lateral distributions.

6. 3.1 Preserving angular information

The standard edition of CORSIKA records Cherenkov photons in a list, giving the locations where they reach the ground and their directions and arrival times. Each 115 entry in the list can signify many hundreds of actual photons because of the Cher- enkov bunching techniques and particle thinning described in Section 6.1.3. Even when both methods are employed to reduce the output lists, however, the resulting data files for 1015 eV showers are uncomfortably large. The authors of CORSIKA provide one more method for paring down the output: recording only photons that land near a limited grid of points. This selection process emulates a sampling array. Unfortunately, the method compresses the Cherenkov data by discarding most of it. The BLANCA solution instead depends on several symmetries of air showers to eliminate redundant information. Taking advantage of these symmetries, the Cherenkov photons can be accumulated in two arrays which store their angular distribution. As vertical primary cosmic rays produce Cherenkov light pools with circular symmetry, two-dimensional detector positions can be reduced to a single core distance number. Near-vertical primaries also produce circularly symmetric showers, although their axis of symmetry is the shower axis rather than the vertical. Therefore, the histograms divide photon bunches according to their distance from the shower axis, in 5 m wide rings. The spatial distribution of Cherenkov light is smooth enough (over scales the size of BLANCA detectors) that adding up the photons within 5 m annuli does not obscure any important fluctuations. These assumptions • have been checked for a sample of CORSIKA showers. For near-zenith primaries ((}z .S 10°), the simplifications introduce errors much smaller than the expected BLANCA measurement precision of 5-10%. The BLANCA code uses a coordinate rotation to transform photon bunch arrival directions into a new coordinate system aligned with the shower axis. The three important parameters of a bunch are the distance of the observer from the axis, the altitude of the photon in the observer-shower axis plane, and the angle between the photon and that plane. The in-plane angle is typically 1-2 degrees below zenith and has a range of a few degrees, as most Cherenkov light comes from an extended region near shower maximum, rather than from infinitely far away long the axis. The out-of-plane angle is less than one degree for most photons, because most Cherenkov radiation reaching the observer originates at a point very near the shower axis. The CORSIKA/BLANCA program further reduces the three-parameter data for each 116

Ci Oi Cll 4 50-55 m Cll 4 200-205 m ~ ~ Cll 2 Cll 2 c c ftl ftl ii 0 ii 0 Cll.. ..Cll := -2 := -2 0 0 .:::; -4 .:::; -4 11 UI UI .5 -6 .5 -6 Cll Cll Ci Ci c -8 c: -8 < < -10 -10 -12 -12 -14 -14 -10 -5 0 5 10 -10 -5 0 5 10 Angle out of plane (deg) Angle out of plane (deg)

Figure 6.6: The Cherenkov angular distribution reconstructed from the BLANCA geometry histograms for an example shower, as observed at core distances of 50 m (left) and 200m (right). The intensity scale is logarithmic, so the black central regions contain most of the photons. photon bunch by accumulating them in a pair of two dimensional arrays. The arrays record the correlation between core distance and each of the two angles. Correlations between in-plane and out-of-plane angles are not recorded because they are found to be unimportant. From these two histograms, the angular distribution of Cherenkov light at any core distance can be reconstructed. Figure 6.6 shows the distributions as seen on the sky at two observation points for one example Monte Carlo shower. The observer nearer the shower axis (left panel) sees the Cherenkov light arriving from higher along the shower axis. The scattering code assigns each photon bunch a wavelength between 290 and 650 nm to determine the scattering cross sections. Ideally, this wavelength would be recorded along with the geometrical information. To conserve storage space, however, photon bunches are instead assigned a weight that indicates the sensitivity of the BLANCA detector to photons of that wavelength, shown in Figure 4.4. The Cherenkov histograms therefore accumulate the product of photon bunch size, the 117 thinning weight of the emitting particle, and the detector wavelength response. This procedure accounts for the full correlation of wavelength with core distance and arrival direction, at the cost of making the CORSIKA output file specific to the BLANCA experiment.5

6.3.2 The BLANCA detector simulation

The BLANCA detector simulation program cor_to_bl reads the angular distributions from the CORSIKA output data and converts them into BLANCA digital signal values. The program simulates as many of the detector properties as possible. The body of CORSIKA handles the first step of simulating the detectors' wavelength dependence. The next task is geometrical: converting the Cherenkov intensity map from a coordinate system centered on the shower axis into one centered on a particular detector. The rotation must be repeated for each of the 144 BLANCA units. This new coordinate system is aligned with the detector's Winston cone axis, which is not necessarily vertical. The cone axes are assigned randomly to each unit; they are normally distributed about the vertical in two perpendicular directions, with a 1° RMS variation in each direction (suggested by the study described in Section 5.6). BLANCA detectors are assumed to be rotationally.symmetric, so the only relevant angle is that between the Winston cone axis and the photon direction. The simulation then considers each pixel in the Cherenkov map (Figure 6.6) and finds the cone-photon angle for the pixel. The program multiplies the Winston cone transmission at that angle (Figure 4.5) by the number of photons in the pixel, and it sums over all directions to find the total amount of light reaching each photomultiplier. This procedure carefully combines the angular distribution of Cherenkov light with the angular response of BLANCA detectors. Given the expected Cherenkov photon density, the detector simulation next models several fluctuations expected in the real data. A constant level of night sky background light is added to the Cherenkov signal itself, and the actual number of

5The wavelength-angle and wavelength-distance correlations are quite small, however, so the shower libraries could probably be used for other detectors with minimal error. 118 photoelectrons is drawn from a Poisson distribution. The mean background level is then subtracted because the photomultipliers are AC-coupled to the digitizing circuitry. The detectors do not count photoelectrons, however; they measure a total charge. The simulation also models the range of possible charge due to each photoelectron, assuming that the charge is drawn from an exponential distribution. The effect of this wide single photoelectron charge distribution is remarkably similar to the shot noise of discrete photoelectrons. In the limit of many photoelectrons, the fractional charge fluctuation becomes J2/Npe, rather than the J1/Npe expected from photoelectron counting statistics alone. The resulting quantity has units of BLANCA photomultiplier charge. Next, the detector simulation converts this charge to a simulated ADC output. The real BLANCA detectors have a range of gains and other properties. In the simulation, each unit is randomly a~igned values for these detector constants. Elec- tronics pedestals and the relative gains of the two-gain preamplifiers are normally distributed, while the photomultiplier relative gains are log-normal. The central values and widths of all distributions are identical to those measured for the actual BLANCA array. The most important variation is in the tube gains; In G has an RMS value of 0.4. The fake data are later processed using the standard method for finding constants (Section 5.1). Comparing the randomly generated detector parameters with the reconstructed values provides a test of the constants algorithms. We find that the relative gains are reconstructed with a 53 random error. The errors on the other constants are somewhat smaller. Besides the Cherenkov measurement fluctuations, the core location and shower arrival direction are also given a random error based on the performance of the CASA surface array [59]. Table 6.3 summarizes the elements that constitute the detector simulation program.

6.3.3 CASA-BLANCA Monte Carlo shower library

The Monte Carlo showers produced by CORSIKA for the BLANCA analysis consist of four shower libraries, each the product of a different high energy hadronic interaction model. Each library consists of 40,000 simulated air showers, with proton, 119 • The measured detector response as a function of wavelength. • Imperfect detector alignment towards zenith (1° RMS in both directions). • The measured Winston cone transmission as a function of incident direction. • Fluctuations due to the night sky background light. • Shot noise in the Cherenkov signal. • Wide single photoelectron charge spectrum in photomultipliers. • Random detector pedestals and gains. • Variation in detector saturation values. • CASA core location and direction errors.

Table 6.3: Elements of the BLANCA detector simulation that contribute to the fake signals generated for the detector array.

helium, nitrogen, and iron primaries in equal numbers. These four nuclei were chosen because species-dependent air shower parameters tend to vary with the logarithm of the primary mass A, and hydrogen (A= 1), helium (A= 4), nitrogen (A= 14), and iron (A = 56) nuclei are equally spaced in log A. We select nitrogen as a representative of carbon and oxygen, which are abundant in lower energy cosmic rays. Thus these four elements are some of the most abundant species in lower energy cosmic rays, whose composition is directly measured by bailoon and satellite detectors [1].

Each shower has a random energy, with log 10 (E/1 eV) uniformly distributed between 14 and 16.5, and a random arrival direction with the zenith angle ()z < 13°. The shower libraries, processed through the detector simulation, are used to determine the optimal methods for extracting the energy and mass from the Cherenkov data. A realistic, steeply falling power-law energy spectrum is necessary in some studies, for example to test methods of extracting calibration constants from the data. The CORSIKA-BLANCA shower libraries contain a uniform distribution in log E, however. We simulate a falling spectrum by sampling from this distribution according to the desired power-law. Therefore, lower energy events are sampled many times while only a small fraction of the most energetic events are used. CHAPTER 7 CHERENKOV FITTING AND SHOWER ENERGY

The lateral distribution of Cherenkov light in air showers is largely symmetric around the shower axis. The primary BLANCA measurement is the radial dependence of the Cherenkov light in each event. After calibrating each observation with the methods described in Chapter 5, we fit the Cherenkov distribution to a simple function using three parameters. These parameters can be combined to form an energy estimate that is relatively independent of the unknown primary cosmic ray mass. Using the energy determined for each event, we measure the all-particle cosmic ray spectrum. In Chapter 8, we use the Cherenkov fits to study the cosmic ray mass composition.

7.1 Fitting the Cherenkov lateral distribution

7.1.1 Event selection

Before the Cherenkov data are fit, the events must be checked to confirm that BLANCA and CASA were working properly and capable of measuring each event accurately. Above all, Cherenkov measurements require good weather. Section 5. 7.2 explains how the rate of events above a certain Cherenkov size indicates the atmospheric transparency, on the assumption that the primary cosmic ray rate and spectrum remain constant. By scanning the rate of medium-sized Cherenkov events and comparing it against the operator's weather observations, we select a single continuous period of good conditions in each run for use in this analysis. Seven runs out of the 87 have poor weather throughout and are not used at all. The weather selection criterion selects events in long periods at once, but other criteria consider air shower events one at a time. Individual events are used only if they include data from at least five working BLANCA detectors. Smaller events do not adequately constrain the three-parameter fit. Simulations show that events which fail to alert five detectors always have less than the minimum energy reported in this analysis (200 Te V) even in the presence of a realistic number of dead BLANCA 120 121

tn 140 t: Cl) Ci: <( 120 0z <( ...I 100 m c Ill Cl) 80 :ii

0 14.4 14.6 14.8 15 15.2 15.4 15.6 15.8 16 16.2

log10(Energy/1 eV)

Figure 7.1: Mean number of BLANCA stations alerted versus primary energy in a real data run.

stations (see Figure 7.1). Therefore, the event size requirement does not bias the spectrum or composition results at low energies. • BLANCA analysis of the Cherenkov lateral distribution requires a good measurement of the air shower core position. The CASA electromagnetic particle detectors determine the core location, with limitations discussed in Section 3.2.2. The circular symmetry of the Cherenkov pool suggests that BLANCA measurements could also fix the core position. In practice, it is difficult to find the shower center of symmetry using Cherenkov light alone. The closer spacing of the CASA detectors and the steeper lateral distribution of particles make the ground array much better suited to core determination than the Cherenkov array. Simulations confirm this superiority, showing that BLANCA alone would have a core error of approximately 10 m for the largest showers and worse for lower energies. CASA's mean core error of less than 3 m makes it the obvious choice for core determination, but it also has limits. The CASA High5 core algorithm can only reconstruct a core to be inside the physical ar- 122 ray boundary, even though many showers with cores outside the array trigger CASA. The Circlecore method can reconstruct cores outside the array boundary, but it also has a bias that tends to pull cores inside. Therefore, BLANCA uses events only if their CASA reconstructed core location is inside the array and at least 30 m from the edge. For this purpose, the west edge is defined as the line passing through the centers of the westernmost active CASA detector stations. Rejecting all events with cores near the edge does not eliminate the problem of core errors, but it does remove the events with drastically wrong core locations. Unfortunately, the edge cut also eliminates many good events, reducing the usable array area by approximately 25%. Finally, events can be used only if the shower axis is close enough to the vertical. The BLANCA Winston cone response (Figure 4.5) limits the experiment's angular field of view. The detectors lose collection efficiency for light more than "" 10° off axis. Simulation and the cosmi~ ray data both show that BLANCA's ability to fit Cherenkov distributions degrades rapidly above 10°; this analysis considers only showers with ()z < 9°. Even so, the zenith angle must be taken into account when interpreting shower measurements. The energy in particular must be corrected for Cherenkov collection efficiency in the 7°-9° zenith angle range.

7.1. 2 The lateral distribution fit

BLANCA samples the Cherenkov pool at up to 144 separate locations, depending on the light intensity and the number of working detectors (typically 125-135). The Cherenkov light distribution is fit assuming circular symmetry about the shower axis. Figure 7.2 shows two sample events from the BLANCA data, plotting the light density (with all corrections and calibrations from Chapter 5 applied) against the distance of each detector from the shower core. The fitting function used in this analysis falls exponentially with increasing distance to a maximum of 120 m from the core. Beyond this point it falls as a power of core distance. The two sections of the function are continuous and are given by:

C es(l20m-r) 30m

Run 022725 Event · 82523 Run 022725. Event 79948 ----~--·,--

c ~ 10t. 0 ~ ~

~ c m u 3 ~ 10 j u

10 10

100 200 300 400 500 0 100 200 300 400 500 Core Distance (meters) Core Distance (meters)

Figure 7.2: Two Cherenkov lateral distributions measured by BLANCA: one steep, one flat. Both have primary energy ~ 3 PeV.

The three parameters to be fit are the intensity at 120 m, C120 ; the inner exponential slope, s; and the outer power-law slope, (3. This function is empirically motivated and is derived from experience with the shape of measured and simulated Cherenkov distributions rather than from first prino!ples. Nevertheless, it describes both the real and fake data well, to within the measurement precision (Figure 7.3). Some groups use the Cherenkov distribution suggested by Protheroe and Turver [78], 0 C[l + (R/50 m)J- . We find that the CORSIKA simulations, with scattering and detector effects, agree better with the mixed exponential-power law function as long as the fit is not carried too close to the shower core.

The Cherenkov lateral distribution is fit only in the limited range of 30-350 m, because air shower simulations show that the empirical function (Equation 7.1) works well only in this range. According to CORSIKA, the Cherenkov distribution has a very sharp peak near the core location. Although core measurement errors tend to smooth out this peak in real data, BLANCA data within 30 m of the core are excluded from the fit as a precaution. Otherwise, the occasional event with a Cherenkov measurement very near the core would be assigned an inner slope steeper than other 124

Entries 11315 1000 Mean 1.346 RMS 0.6658 800

600

400

200

0 0 1 2 3 4 5 6 7 8 9 10 2 Reduced x

Figure 7.3: Reduced x2 distribution of the Cherenkov lateral fit for real data showers in a single run. similar events would get. Simulations also establish that the power law decline at large distances continues only to 300 or 400 m. Further from the core, scattered light and other effects make the expected distribution flatter than a power law. Because of these limitations, the Cherenkov fit uses only detectors between 30 and 350 m from the core. The event fitting is actually performed in log space. The procedure fits the logarithm of the measured Cherenkov photon density to the logarithm of Equation 7.1. The log fit is used because the measurement errors consist of many multiplicative uncertainties and are therefore distributed log-normally. The fit minimizes

_ Ndet [ln Ci - ln C(r)l 2 2 (7.2) x = t; ln(l + O"(Ci)) where Ci are the Cherenkov measurements, C(r) is the Cherenkov fitting function given by Equation 7.1 and the fractional error O"(Ci) is a positive quantity which depends on the measurement itself. 125

For this analysis, we assume a fractional error of 12% on each data point, added in quadrature to a fixed error of 11 ADC counts. The fixed term accounts for night sky noise and electronic jitter, which tend to increase the fractional error at low Cherenkov intensities. The 12% random error is derived from the BLANCA data by finding the residuals about the Cherenkov fits to each event. Although the typical size of the residuals varies with zenith angle and core distance, the variation is small and we ignore it. The assumed error function derived from real data also agrees with the fake data generated by the air shower and detector simulations. For small showers, there can be few or no reliable Cherenkov samples outside the 120 m break point in the fitting function. Such events leave the power law index f3 entirely unconstrained. Therefore, a two-parameter fit is made for events with fewer than five valid detections in the r > 120 m region, using only the exponential section of Equation 7.1. Because the present analysis ignores the index (3, small showers with at least five detections inside 120 m can still be used.

7.1. 3 Interpretation of the Cherenkov fit parameters

In this chapter and the following one, we explore in detail the relationships of the measured quantities C120 and s with the fundamental shower parameters, primary energy, depth of maximum, and primary mass. An approximate interpretation is that the Cherenkov intensity 120 m from the shower core, C120 , provides a good estimate of the primary cosmic ray energy; the two are approximately proportional to one another. The inner exponential slope, s, is a nearly linear function of the depth of shower maximum Xmax and hence connects directly with the primary mass. For sufficiently large showers, the outer slope f3 is highly correlated with the inner slope s. For smaller showers, f3 is poorly constrained or unconstrained by the data. In either case, the outer slope seems to add little information to the combined intensity and inner slope parameters and f3 is therefore not used in this analysis. It is nevertheless important to fit the Cherenkov distribution in the outer region in order to get the best possible value for the intensity C120. 124

Entries 11315 1000 Mean 1.346 RMS 0.6658 800

600

400

200

0 0 1 2 3 4 5 6 7 8 9 10 2 Reduced x

2 Ndet [lnCi - lnC(r)l x2 = (7.2) - ~ ln(l + a(Ci)) where Ci are the Cherenkov measurements, C(r) is the Cherenkov fitting function given by Equation 7.1 and the fractional error a(Ci) is a positive quantity which depends on the measurement itself. 126

..-- 800 --;"""' 30 E E -a. ~ --:. 700 8. 25 ~ 0 >< iii.. ~ 20 600 .5

15 500

10 400

5 300 0 14.5 15 15.5 16 4.5 5 5.5 6 2 ) log10(Energy/1 eV) log10(C121/1 phot m"

Figure 7.4: The species discrimination power of the Cherenkov lateral technique. Left: The 1-o- range of Xmax as a function of energy for the extreme species. Right: The equivalent plot comparing measured quantities, including detector resolution effects.

Figure 7.4 demonstrates how the limitations of a realistic sampling Cherenkov detector affect the shower measurement. The left panel shows the range of Xmax in 0.1-decade bins of primary energy, where range means the one standard deviation above and below the mean. The data come from CORSIKA/QGSJET simulations of pure proton and pure iron samples. The right panel shows the range of the analogous measured quantities for the same set of showers: inner slope binned by C120 . The first plot makes it clear that even perfect knowledge of the shower properties Xmax and energy would provide good, but imperfect, separation between the extreme species of protons and iron. Intermediate species such as helium and the CNO elements obviously could not be identified on an event by event basis even if Xmax and energy were known. The second panel shows that BLANCA measurements, in spite of the sampling and detector resolution, can distinguish the two species almost as well 127 above 300 TeV. Together, the plots demonstrate that BLANCA should be able to determine the primary composition nearly as well as the inherent air shower differences and fluctuations permit.

7.2 Cherenkov event energies

The Cherenkov light intensity in an air shower is an excellent indication of the primary cosmic ray energy, with better intrinsic resolution than that obtained from particle measurements. The absolute energy scale is difficult to establish, however, because of detector calibration issues and uncertain Monte Carlo Cherenkov production. Despite these problems, this analysis uses the BLANCA Cherenkov measurements alone to determine the energy of each event. A more sophisticated energy estimate incorporating both Cherenkov and muon or electron measurements might be able to improve the resolution, systematic error, or composition bias, but such a measurement was not done.

'l.2.1 Simple energy function

The Cherenkov photon density is closely related to .. primary energy, because an air shower emits Cherenkov light continuously throughout its development. While the electromagnetic particle density at ground level offers only a snapshot of the shower at one depth (a depth well below Xmax), the intensity of Cherenkov light gives an integral of the charged particle tracks over the entire life of the shower. The Cherenkov intensity thus serves as a calorimeter for air shower energies.

Specifically, we use the value of C120 to estimate the primary energy rather than the intensity at other distances. The photon density at core distances less than 120 m suffers from with increasing bias at smaller core distances, because the inner region of the lateral distribution depends on Xmax and thus on primary mass. At more than 150 m from the core, the Cherenkov intensity correlates well with energy and depends only weakly on primary mass. The BLANCA detector simulation shows that in low energy showers, however, measurement error degrades the resolution 128 for intensities measured too far from the core. Use of the C 120 parameter balances the goals of limiting the correlation with mass and reducing the effects of detector resolution. The C120 parameter also has the advantage that its energy dependence is more nearly linear than is the Cherenkov intensity at larger core distances, according to shower Monte Carlos.

The CORSIKA simulation libraries and the full detector simulation are used to determine a transfer function for converting a measured C120 to primary energy. The detector simulation uses each CORSIKA shower three times to produce three fake events with different core locations, arrival directions, 1 and Cherenkov fluctuations. The libraries consist of an equal mix of proton, helium, nitrogen, and iron primary cosmic rays, with approximately 21,000 showers per primary species in each hadronic interaction model. The shower energies are uniformly distributed in log10 (E/1 eV) between 14 and 16.5.

In all four hadronic models, the Cherenkov intensity C120 grows approximately as Ei.o7 . The intensity rises faster than primary energy because the fraction of primary energy directed into the electromagnetic component of the cascade increases with energy. On careful inspection, a slight curvature appears in the C120-energy relationship. Figure 7.5 shows a scatter plot of this relationship, according to the QGSJET hadronic model. The data are fit taking log E to be a quadratic function of logC120 . 2 logE = logE5 + Alog(C120 ) + B [log(C120)]

5 2 where C120 is expressed in units of 10 photons m- , A is the slope, and B is the curvature. Table 7.1 gives the resulting parameters for each model. The models disagree by as much as 153 on the absolute energy or light intensity scales; they agree well on the slope of the log E-log C120 relationship. The performance of this simple quadratic transfer function is discussed in the next section and displayed in the top panels of Figure 7. 7.

1 Only the azimuth angle is randomized. The CORSIKA shower's zenith angle is not changed, because shower development depends slightly on zenith angle. 129

CORSIKA/QGSJET Energy-C120 Relation

>Cll ~ 16.5 Qi c w ~ a; .2 16

15.5

14.5

3 3.5 4 4.5 5 5.5 6 6.5 7

Figure 7.5: Cosmic ray energy as a function of the Cherenkov intensity C120 predicted by Monte Carlo (CORSIKA/QGSJET). The dashed.line is a quadratic fit of log E to log C120 . Points to ~he left of the fit are mostly iron; points to the right are generally protons; nitrogen and helium showers lie between.

7.2.2 Reducing the composition bias of the energy function

The simple log E = f (C 120 ) function works well, but it still depends somewhat on the primary mass. Protons direct more energy into the electromagnetic part of an air shower than the typical iron primary. Therefore, protons of any given energy produce more Cherenkov light than heavier cosmic rays of the same energy. Inverting the argument, a given C120 measurement tends to overestimate the energy of a proton and underestimate the energy of an iron nucleus. On the other hand, proton showers occasionally begin unusually deep in atmosphere and reach the ground before the cascades develop fully. Such showers produce much less Cherenkov light per unit 130 Hadronic Energy Es to produce Power law A of Curvature B 2 model 10s phot/m at 120 m E vs C1 20 (decadet1 QGSJET 1.15PeV 0.934 .006 VENUS 1.23PeV 0.940 .001 SIBYLL 1.11 PeV 0.944 .005 HDPM 1.28 PeV 0.941 .012

Table 7.1: Parameters of the quadratic fits oflogE to logC120 in each of the hadronic models. The energy value Es and slope A parameters are given for the case of 2 C120 = 10s !' /m .

energy than most; they are visible in Figure 7.5 to the left of the bulk of the simulated data points. Both effects can bias the simple energy estimate of the previous section. Fortunately, BLANCA also measures a composition-sensitive parameter, the inner slope s. A small adjustment., to the simple energy estimating function can reduce its mass dependence by incorporating the slope information. In fact, the inner slope can help eliminate both of the biases mentioned above. Flatter slopes suggest heavy nuclei and an upward correction to the first energy estimate; steep inner slopes suggest light nuclei and a negative correction. And especially steep slopes (s 2: 0.022m-1) indicate the very deep protons, which require a large positive correction to the energy. Figure 7.6 shows the necessary logarithmic energy correction to the simple log E = !simp( C120 ) function for simulated showers, plotted against the inner slope. Both Cherenkov fit parameters in the figure (s and C120 ) come from Monte Carlo showers with all detector resolution effects included. The data clearly indicate an additive correction to log E with a curving dependence on s. We find that the best relatively simple correction function is linear below some critical value of inner slope and quadratic above it. This function has four parameters: the three parameters of the parabola (c1, c2 , and c3 ), plus the slope value s* at which the parabolic and linear sections connect. The function is continuous and smooth at the joining point:

(7.3) 131

CORSIKA/QGSJET Inner Slope Correction to Energy w 0.7 Lil

0 -0.1 -0.2 -0.3 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 1 Inner Slope (m" )

Figure 7.6: Error on the simple energy fit (from the previous figure) versus Cherenkov slope. The line is one example of the slope-dependent correction function.

The best-fit correction function varies slightly with energy, or equivalently with C120 . This variation arises because the typical slope of an·iron or proton shower increases slightly with increasing energy (as higher energy showers can penetrate deeper into the atmosphere). Likewise, the best energy correction also depends weakly on the air shower zenith angle because of the limited Winston cone field of view. Therefore, we divide the data into five half-decade ranges in the C120 parameter and four equal ranges of cos ez, find the best correction in each of the ranges, and interpolate linearly among the twenty correction functions. The C120 dependence of the energy correction is rather complicated, but the correction is approximately proportional to cos4 ez. The energy correction resulting from this procedure is less than a factor of 1.26 in either direction (0.1 decades) for 99% of the real BLANCA events. For the central 84% of events, the correction is smaller than ±10% (0.04 decades). Although the correction is small, it reduces the mass dependence of the energy estimation function. Figure 7. 7 shows the mean energy error for each species versus 132

... 25 ... 25 ...~ ...0 w 20 w 22.5 ti< 15 ti< 20 u E ..Ill 0 10 "O 17.5 E c Ill sIll 5 a: 15 >- Ill 0 12.5 -5 10 -10 7.5 -15 5 -20 2.5 -25 0 14.5 15 15.5 16, 16.5 14.5 15 15.5 16 16.5

log10(Energy/1 eV) log10(Energy/1 eV)

... 25 ... 25 ...0 ...0 w 20 w 22.5 ti< ti< 15 20 u E Ill 0 .. 10 "O 17.5 E c Ill sIll 5 a: 15 >- Ill 0 12.5 -5 10 -10 7.5 -15 5 -20 2.5 -25 0 14.5 15 15.5 16 16.5 14.5 15 15.5 16 16.5

log10(Energy/1 eV) log10(Energy/1 eV)

Figure 7.7: Energy reconstruction errors as a function of energy. Monte Carlo data are shown for the QGSJET hadronic model. Top: Mean and RMS errors about the mean for the simple function E = lsimp(C120 ). Bottom: Mean and RMS of the slope-corrected function E = J(C120, s, Bz). 133

energy using the simple function (top left) and using the corrected function (lower left). The slope-dependent correction reduces the proton and iron shower energy bias at lower energies. As expected, the intermediate species are affected less by the correction. At high energies, the mass bias increases slightly but is still much less

than the random error. Nevertheless, the energy bias that depends on Xmax (not shown) is greatly reduced, which improves the results described in Section 8.1. The top and bottom right panels of the figure show the RMS spread about the mean energy error for the simple and corrected energy functions. The figure shows the random energy errors caused by the combination of measurement error and inherent shower fluctuations. The slope correction reduces the large random error on proton energies, primarily by accounting for deep, incompletely developed air showers. The energy error distribution is thus a complicated function of the primary composition and energy spectrum. In general, the random errors are comparable to the systematic errors. Assuming a mixed cosmic ray composition, the BLANCA energy resolution for a single event is approximately 12% for a 200TeV shower, falling to 8% at the top of the energy range.

7.3 The cosmic ray energy spectrum

Each BLANCA event that passes the selection cuts is assigned an energy using the reduced-bias energy function described above. By computing the total exposure of the Cherenkov array, we can convert the distribution of event energies into an energy spectrum of the primary cosmic rays.

7.3.1 The BLANCA cosmic ray exposure

The BLANCA exposure to cosmic rays is simply the product of the solid angle, the sensitive area, and the operating time. BLANCA's angular aperture is limited by the zenith angle cut of 9°, which the 11° Winston cone field of view imposes. The angle cut leads to a solid angle of n = 0.077 sr. The array area changed in the summer of 1997, when 66 CASA stations at the edges of the array were turned off to 134

o; ! 80 1500 ...... : ....: ...... Q) "C 1000 .... :.·················,·················•.·...... :E 60 ~:~500 ft(=~m~··1. . ' ...... ···~···· ...... ·- -; ..J 0 30 35 40 45 50 ~ 40 ~ Declination (degrees) "iii <.? 20

-20

-10 -5 0 5 10 -100 0 100 Right Ascension (hours) Galactic Longitude (deg)

Figure 7.8: BLANCA sky exposure, in relative units. Left: Distributions in ecliptic coordinates. Right: Equal-area map in galactic coordinates. provide spare parts for repairs. The 29 x 33 station CASA array became a 27 x 33 station array. Since BLANCA analysis uses only events with cores reconstructed to be at least 30 m from any edge of the array, the sensitive area was 151,200 m2 during the first season and 138,600 m2 during the second. BLANCA observations total 457 hours, 40% recorded in the first year. The total exposure is thus 1.83 x 10 10 m2 sr s. The CASA array trigger is fully efficient for showers with primary energy exceeding 300TeV. Likewise, the BLANCA event requirement of at least five Cherenkov detections only affects showers of 150TeV energy or lower (Figure 7.1). While the measurement errors are larger at the lowest energies, neither the Cherenkov data nor the CASA trigger have significant trigger losses in the energy range of this analysis. For the range 0.3-30PeV, the BLANCA exposure is given by the argument above, without any efficiency corrections required. Figure 7.8 shows the BLANCA exposure as a function of position, both in ecliptic and in galactic coordinates. The narrow declination band results because BLANCA 135 observes only within 9° of zenith. The observing schedule produces the complicated structure of the exposure in right ascension. In particular, the gap at a = 19h occurs because this part of the sky passes zenith at night only during midsummer, when BLANCA never operated. Unfortunately, BLANCA observes a narrow swath of sky near 6 = 40°, so its data cannot be used to measure the large-scale anisotropy of cosmic rays at knee energies.

7. 3. 2 Spectrum results

Figure 7.9 shows the differential energy flux determined from BLANCA data, using the QGSJET and other energy transfer functions. Each data point is scaled up by 2 75 a factor of (E/l GeV) · in order to emphasize the structure, particularly the knee itself. The cosmic ray spectrum depends somewhat on the hadronic model used for interpreting the data, but the unequal Cherenkov intensity scales fully account for the differences in the spectra. For example, HDPM predicts the least Cherenkov light and thus takes showers of a given C120 value to be higher in energy than VENUS, QGSJET, and SIBYLL do. Appendix C gives the complete spectrum results in tabular form, along with further discussion of the exact method for "flattening" and binning the data. In this figure, the error bars represent only the .JN Poisson contribution. The BLANCA energy resolution has very little effect on the figure. Energy resolution could smooth out small features in the spectrum, except that the bin width of 0.1 decades used in this figures is larger than the array's resolution. And, of course, the absolute Cherenkov intensity scale is uncertain to 20%, as discussed in Section 5.4. 0 93 As E ex: (C120 ) · (Table 7.1), the absolute calibration error causes an overall 183 systematic error in the energy scale.

7. 3. 3 The knee in the spectrum

Figure 7.9 clearly demonstrates the presence of a knee in the BLANCA cosmic ray spectrum at approximately 3 PeV. Below the knee, the flux appears to fall as a power law with an index close to -2.7. 136

105 ..,"'- ~> Cl> (.!) ' ' ':' II) l' ·"'·'··-,.-·····T:···T.. ':' ...II) • • • • ,. • • • • ~ • • E ··' . .... ,,;"'- w x ,. >< ::J :;::: ·----·-······---·---·-··t··-. Cl> u:;::::; ...cu a. . ' ' . ' Systematic energy error (18%) . . ' .

BLANCA Data; e QGSJET ' ' ' • VENUS A. SIBYLL : ··· -. HDPl\ll

10 15 10 16 Energy (eV)

Figure 7.9: The all-particle differential cosmic ray flux measured by BLANCA, scaled 2 75 up by a factor of (E/1 GeV) · to emphasize the knee. The spectrum depends on the model used to interpret the data, but only the energy scale differs noticeably (not the shape). Statistical errors are shown on the QGSJET results but are smaller than the data points below 2 PeV; they are similar in all four interpretations. The energy calibration error of 183 is common to all data. Because the vertical axis is 2 75 J x E · , the systematic energy error appears as a diagonal shift. 137

Broken

Separate

Smooth, w=.25

Smooth, w=.75

10 15 17 10 14 10 16 10 log10(Energy/1 eV)

Figure 7.10: The three functions used to fit the cosmic; ray spectrum as described in the text. The smooth function is shown with two different values of the transition width parameter w. All are power law functions in the limit of high or low energy, and all have four independent parameters: the knee energy, the two power law indices, and an overall normalization. The examples shown here all have a= -1.75, {3 = -2.00, and Ek= 3.16 PeV.

In order to compare the BLANCA results with measurements made by other experiments, we fit the spectrum to determine the position (energy) of the knee and the power law indices above and below the knee energy. Three different functional forms were investigated (Figure 7.10). The broken power law consists of two distinct power laws joined at a sharp knee. The broken power law form generally describes the data well, but the errors on its parameters tend to be asymmetric and highly correlated. A similar function, a separated power law, is fit to the spectrum only at high and low energies and disregards the shape of the data around the knee itself 15 15 (i.e. between 10 ·1-10 ·5 eV). 138

'6" 0 0 0 :5 -0.5 Qi E!! -1 gbi -1.5

-2

-2.5

-3

-3.5

-4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 w=Half-width of knee (decades)

Figure 7.11: Choosing the transition width w in fitting the knee. Equation 7.4 is fit by maximizing the log-likelihood function with fixed w and variable Jk, Ek, a, and /3. The log-likelihood (shown here with arbitrary additive offset) is largest for w = 0.25. Assuming a smooth knee, the data favor a knee one-half decade wide.

The third function is a smooth knee, which ·seems to be the most robust and which agrees well with the data. This function features a smooth transition region connecting two asymptotic power laws:

(7.4)

Ek is the energy at the center of the transition, i.e. the knee energy. For E ~ Eki the function is a power law with index a, while the spectral index becomes j3 for E »Ek· Jk sets the normalization at the knee. The fifth parameter, w, is the half- width of the transition region in decades. Although the data could be fit to find all five parameters, the fit is quite insensitive to the transition width. Instead, we fix w at several values and vary only Jk, Ek, a, and /3. Figure 7.11 shows the dependence 139

Model Eknee (PeV) Low index o: High index /3 loglO ]knee Smooth (w = 0.25): 0 QGSJET 2 .0+ -0.2.4 -2.72 ± 0.01 -2.95 ± 0.02 2.44 ± 0.01 VENUS 2 . 4+0.3-0.2 -2.71±0.01 -2.97 ± 0.02 2.35 ± 0.01 SIBYLL 2 .5+0.3 -0.2 -2.72 ± 0.01 -2.99 ± 0.03 2.21±0.01 HDPM 2 .4+0.5 -0.3 -2.73 ± 0.01 -2.95 ± 0.02 2.36 ± 0.01 Brok<-m: QGSJET 1 .5+0.2 -0.1 -2.72 ± 0.01 -2.91±0.03 Separate: QGSJET 2 .o+o.3 -0.2 -2.72 ± 0.01 -2.96 ± 0.04

Table 7.2: Results of fitting double power-laws to the energy spectrum. The half- width is fixed at w = 0.25 in the smooth fit. The smooth function and the separated knee fit the data better than the broken knee function does. on w of the log-likelihood function (which the fit maximizes). The best fit to the observed spectrum has a value of w = 0.25, so the full width of the smoothly curving region is half a decade, or a factor of 3.2. The spectrum fitting procedure employs a log-likelihood maximization. This algorithm properly accounts for the Poisson nature of discrete events in a binned energy distribution (see Appendix C for more details). Figure 7.12 shows the measured cosmic ray spectrum in the vicinity of the knee as well ..as the smooth power law fits to the spectrum derived from the QGSJET hadronic model. Table 7.2 lists the results of fitting the BLANCA data to the functions described above. The smooth function with w = 0.25 best matches the BLANCA data, with x2 = 201 for 213 degrees of freedom. 2 Assuming the QGSJET energy function, we find a spectral index below the knee of -2.72 ± 0.01; above the knee, the index is -2.95 ± 0.02. BLANCA's exposure of 1.83 x 10 10 m2 sr s limits the amount of data above the knee and thus our ability to determine the spectral index at high energies (> 10 16 eV). The knee energies differ depending on the hadronic model used to build the BLANCA energy spectrum, as expected, but the indices of the two power laws are consistent among the models. The separate knee function gives results very similar to the smooth

2 2 Note that the fit does not minimize x , but instead maximizes (log£). Nevertheless, x2 serves to indicate the quality of the fit. 140

~10 5 ~~~~~~~~~~~~~~..---.---, le -> ------·------·- Cl> 0 ...... : ....• ... ; .. . . -. ~- ...... ; . -. .... UI ':' ~~.:.~~.-....., ••, ~ -t - - ....s t .... Nw ------.. ++++ . x >< QGSJET j :E tf1t . Cl> 0 t: . f T ff ca D.

10 15 10 16 Energy (eV)

Figure 7.12: The knee region of the spectrum along with the smooth power law fit. According to the QGSJET energy parameterization, the best-fit power law indices are -2.72 ± 0.01 and -2.95 ± 0.02, with the knee centered at 2.0 ± 0.3 PeV. The fit has x2 = 201 with 213 degrees of freedom. fit. The broken knee was less consistent with the data than the smooth function. Figure 7.11 shows why, since the broken knee is the limit as w --+ 0 of the smooth knee. The broken fit requires a knee at lower energy than the other fits do.

The log-likelihood fit is performed by the MINUIT package [79], which reports errors on the parameters. To confirm the soundness of the stated errors, we test the fitting procedure on a large number of artificial distributions. The artificial spectra are generated from a known smooth power law distribution with the same shape and normalization as the BLANCA data. The log-likelihood fit is performed on each artificial spectrum, and the fit parameters can be compared with those of the known parent distribution. The parameter errors determined in this manner agree with the MINUIT errors. Table 7.3 shows the correlations among the fit parameters. 141

log10 (Jk) 0: {3 log10 (Ek) log10 (Jk) 1.000 -0.823 0.560 -0.968 0: -0.823 1.000 -0.684 0.933 {3 0.560 -0.684 1.000 -0.645

log10 (Ek) -0.968 0.933 -0.645 1.000

Table 7.3: Correlation coefficients for the QGSJET smooth knee fit.

When measuring a falling power law distribution such as the cosmic ray energy spectrum, random errors on the data can bias the distribution. Although the errors on measured shower energies can be positive or negative with equal probability, the upward fluctuations are more important because they push events into a relatively less populated energy bin. In the case of a simple power law distribution (i.e. with no knee), the effect does not bias the measured power law index, but it does systematically shift the normalization to higher values. Assuming that the measurement errors are log-normally distributed, then the apparent flux normalization increases 2 2 2 by a factor of ea u / ~ 1+2o.2 in the case of an o: = -2 cosmic ray spectrum. The BLANCA random energy error is approximately a = 10%, so this bias amounts to an increase in the apparent flux of only 2%. The data reported here are not corrected for this small effect, but an experiment with poorer i'iitrinsic energy resolution would need to account for it because the discrepancy grows as the square of the resolution.

In Figure 7.13, the BLANCA cosmic ray flux is compared with that reported by other groups which have studied the knee in the spectrum. The BLANCA flux is quite similar to most other measurements, given that a 15-20% systematic energy error is typical of Cherenkov experiments, while most particle arrays report an even larger uncertainty. The most serious disagreement (between BLANCA and Tibet) amounts to only a 30% difference in energy assignment. Tibet data were taken 2 at a very high altitude (4300m, or 606gcm- ), so direct comparison between the Tibet results and other measurements taken nearer to sea level relies heavily on air shower models. Note that although the BLANCA, DICE, and CASA-MIA data were taken at the same Dugway site, the three data sets are entirely independent and use completely different analysis techniques. 142

It) ":- ~> Q) (!) ";" (/) ~ ~ ~ ! ~ " " : ";" 105 T • T • ;;-· ··T··---T .• -T ' T ...(/) ········...... ·····•····-·····-···---·······················-· ')' ._.E ....It) .,; w x ., . >< : T ::I ;:

Q) .... , ..... '. .. ; .. 0 ~ 0."' System~tic en¢rgy error p ~%) • . . ' ...... ' ' ' . .' . ' . . ••• • ••• ' ••• • • • • • ' • • ••• r ••••.: • • • • ;. • • • ~ • ~ • .~ • • • • • • • • •

: : : : : : : • : BLANCA (this work) : ••DICE • : • -'. • CASA-MIA • . •* •Akeno · ' "' : Tibet

10 15 10 16 Energy (eV)

Figure 7.13: The BLANCA cosmic ray spectrum compared with measurements by DICE [32], CASA-MIA [80], Akeno [81], and Tibet AS/' [82]. CASA-BLANCA and DICE are Cherenkov experiments; CASA-MIA and Akeno measure electrons and muons; Tibet measures only electrons. 143

Results differ on whether the knee is found in the 2-3 PeV range, as suggested by BLANCA, CASA-MIA, and Tibet, or the 4-5 PeV range, as reported by DICE, Tibet, and KASCADE (not shown) [39]. In general, the "position" of the knee can depend on the function chosen to fit the spectrum. Indeed, a glance at the BLANCA spectrum in Figure 7.9 suggests that the knee is not at 2 PeV but at 4 PeV. It is important to keep this issue of definition in mind when comparing the knee position reported by different experiments, particularly since the knee is a smooth rather than a sharp feature. CHAPTER 8 COSMIC RAY COMPOSITION

The BLANCA measurements of air shower Cherenkov lateral distributions offer insight into the primary cosmic ray mass. The Cherenkov inner slope s, discussed in the previous chapter, correlates with an air shower's depth of maximum and thus indirectly with the primary mass. We present results on the averagE shower depth as a function of energy, the derived logarithmic mass (In A) versus energy, and a multi-component model which compares the measured distribution of s with that predicted by Monte Carlo simulation.

8.1 Depth of shower maximum

The depth of shower maximum (Xmax) is an important characterization of air shower development. The mean Xmax for a given primary type grows logarithmically with energy at an approximate elongation rate of 80 g cm-2 per decade. The expected Xmax is similar for two primaries of different mass if they have equal energy per nucleon E /A. By imaging the Cherenkov emission or fluorescence light from a shower and identifying the depth of brightest emission, experiments such as DICE [32] or the Fly's Eye [61] measure Xmax more directly than BLANCA does. Nevertheless, the step from BLANCA measurements of the Cherenkov lateral distribution back to an estimate of Xmax requires only known physics: electromagnetic cascades, atmospheric scattering and absorption, and Cherenkov emission by energetic charged particles. Imaging detectors must also account for these effects. Converting the Cher- enkov inner slopes to Xmax does not depend on the high energy hadronic interaction models. Therefore the BLANCA determination of Xmax is a robust measurement which has the added benefit of allowing us to compare BLANCA results with other experiments. Unfortunately, interpreting a measured value of Xmax as a primary mass does depend strongly on the chosen interaction model. Thus we present results on the depth of shower maximum and on the primary mass separately. 144 145

8.1.1 Estimating Xmax from the Cherenkov lateral distribution

The Cherenkov lateral distribution is fit to the function described in Section 7.1.2. For data recorded less than 120 m from the shower core, the fit function is exponential with a slopes. The CORSIKA shower Monte Carlo and BLANCA detector simulation demonstrate that this inner slope is linearly related to Xmax except for the deepest developing showers.

To determine the optimum transfer function for converting measured s into Xmax, we study the same set of simulated showers used to derive the primary energy function (Section 7.2). The fake data libraries use each of the four hadronic interaction models processed through the BLANCA detector simulation. Proton, helium, nitrogen, and iron primaries are produced in equal numbers with an energy distribution 14 16 5 uniform in log E between 10 and 10 · eV.

The relation between inner slope and Xmax is shown in Figure 8.1. This figure uses the QGSJET hadronic model in CORSIKA, but equivalent scatter plots for the other three models look very similar. Although the interaction models predict different air shower development, they all agree on the correspondence between s and Xmax· This consensus allows us to extract Xmax from the BLANCA data in a model-independent way. The agreement occurs beoouse electromagnetic showering and multiple Coulomb scattering are the main determinants of the Cherenkov lateral distribution shape. The transfer function which fits the data is linear with an 1 additional quadratic term for slopes exceeding s* = 0.018 m- :

(8.1)

The value X1, slope"(, and curvature r5 are fit to the Monte Carlo results for each of the four interaction models. Table 8.1 lists the best-fit parameters.

The systematic and random errors of the Xmax transfer function (Equation 8.1) are shown in Figure 8.2 for the QGSJET case. The errors are derived entirely from the simulation. We compare the known depth of shower maximum with the Xmax estimated by entering slopes s from fake data into Equation 8.1. The mean difference 146

CORSIKA/QGSJET Xmax - Inner slope Relation ~-- 1200 E u s )

1000

BLANCA observation depth ~

800

600

400

200~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 1 Inner Slope (m" )

Figure 8.1: Air shower depth of maximum (Xmax) versus the Cherenkov inner slopes predicted by CORSIKA. The slope is derived from Monte Carlo with the full detector simulation applied. The solid line is the best-fit transfer function, Equation 8.1. 2 The text shows the atmospheric depth at Dugway, 870 gcm- . BLANCA's ability 2 to estimate Xmax from slope measurements degrades for Xmax 2: 800 g cm- , because Cherenkov lateral distributions cannot indicate the depth of a shower which reaches maximum near or below the observation level. 147

Model QGSJET 586 19400 570000 VENUS 590 20300 570000 SIBYLL 589 20400 480000 HDPM 596 21800 720000

Table 8.1: The best-fit parameters of the inner slope to Xmax transfer function. X f is 1 the derived value of Xmax at s* = O.Ol8m- , 'Y is the slope of the linear relation, and b is the coefficient of the quadratic term (see Equation 8.1). The typical uncertainties on the parameters are 1, 50, and 104 in these units.

"t~ 25 cf' 50 E E u 20 u 45 !:!! ~ .. 15 40 ..0 ..0 w 10 w.. 35 ~" ~ x 5 x 30 u :;: E I'll 0 0 "C 25 E c: -Si I'll Ill -5 a: 20 >- (/) -10 15

-15 10

-20 5

-25 0 14.5 15 15.5 16 16.5 14.5 15 15.5 16 16.5

log10(Energy/1 eV) log10(Energy/1 eV)

Figure 8.2: Xmax reconstruction errors as a function of energy in the QGSJET model. Left: The mean error. Positive values mean that BLANCA overestimates atmospheric depth. Right: The RMS spread about the mean error. 148 between the actual and derived Xmax produces the systematic error (left panel), while the RMS spread about the mean produces the random error (right panel). The transfer function has only a small mass bias. The function tends to overestimate the depth of iron-induced showers and underestimate Xmax for proton showers. This bias is approximately 5 g cm-2 or less at all energies. The right panel shows that the random Xmax reconstruction error is between 20 and 40 g cm - 2 depending on energy and primary mass.

The Xmax resolution degrades above a few PeV primary energy in spite of the increasing Cherenkov intensities. The reason is not primarily instrumental, but rather that the Cherenkov lateral profile loses its power to measure Xmax for the deepest showers. The scatter plot in Figure 8.1 shows that showers with maximum deeper 2 than rv 800 g cm- cannot be distinguished through the inner slope alone. Raw CORSIKA air showers show the same effect even when the BLANCA detector simulation is not applied to the Monte Carlo data. An addition problem is the difficulty in estimating the "actual" Xmax for a simulated shower which strikes the ground 2 (Xground = 870 g cm- ) before reaching maximum development. We determine the value of Xmax for Monte Carlo showers by fitting the longitudinal profile of charged particles to the standard Gaisser-Hillas development curve [19]. The assumed profile has four parameters which correspond to the size and depth of the shower at maximum, the effective depth of the first interaction, and a shower development scale length. The fit miaimizes x2 assuming VN errors on the census of charged particles at each 10 g cm-2 step. This procedure cannot find Xmax with good precision for late developing showers, because the simulation stops at the observation level of 2 870 g cm- . Fortunately, very few showers in the data appear to reach maximum 2 below 700gcm- , so this loss of Xmax information has little effect on the mean Xmax measurements.

8.1.2 Results: Mean depth of maximum versus primary energy

The measured Cherenkov slope can be converted by the procedure outlined above to an estimate of Xmax that depends only weakly on the choice of interaction model. 149

~ 750~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ·e u -9 700 ".,. ..E ~ 650

600

550

500

450 e BLANCA (Stat. + Sys. Errors shown)

400 QGSJET VENUS 350 SIBYLL HDPM

10 15 10 16 Energy (eV)

Figure 8.3: Mean Xmax versus energy in BLANCA data. Points with error bars are the mean Xmax and the error on the mean. The thick error bars represent statistical uncertainties only, while the thin errors include the systematic errors (added in quadrature) as well. The lines show the mean Xmax predicted by CORSIKA using each of the four interaction models. Interpreting Xmax as a primary composition depends on the model chosen. 150

The mean Xmax is shown in Figure 8.3 as a function of energy, both quantities derived from the BLANCA data using the CORSIKA/QGSJET Monte Carlo results. The value of Xmax derived for each shower is similar for all four hadronic models, however. The thick error bars represent the statistical uncertainty on finding (Xmax), while the thin errors include the systematic uncertainties discussed below. Statistical errors are important only above 10 PeV.

Figure 8.3 also shows the mean Xmax expected for pure samples of proton primaries and iron primaries. The superposition approximation (that compound nuclei behave as independent nucleons, discussed in Section 2.3) is approximately valid in all models, which can be seen by shifting the predicted Xmax curves for iron by a factor of 1/56 in energy. SIBYLL generally predicts deeper shower maximum than other models, while HDPM exhibits a steeper elongation rate than the others (""' 90 g cm-2 per decade compared with 70-75 gcm-2 typical of the other models). The BLANCA results are clearly consistent with a mixed composition throughout the energy range, regardless of the hadronic interaction model. The data suggest tha~ the composition becomes lighter approaching the knee and then becomes heavier.

A few systematic errors have the potential to bias the BLANCA Xmax estimates (Figure 8.4). One possible bias in the Xmax or slope data results from the CASA core position error. Random core error can produce a systematic effect in the Cherenkov inner slope measurement. Any offset from the center of symmetry tends to flatten the apparent Cherenkov distribution. The core error is largest for low energy showers, in which the CASA measurement consists of only a few particle density samples. The effect biases the Cherenkov mass in favor of heavy primaries, but the bias is quite small. We model the core error using the results of an earlier study which gives the core error as a function of the number of detected charged particles [59], but we double the expected error to account for degradation in the CASA array over time. The effect of dead CASA stations (typically 8-10% of the array) is modeled by assigning a much larger core error (""' 15 m) to the events with cores which land nearest to a dead station. The resulting mean core errors range from 7 m to 3 m over the BLANCA energy range, with consequent systematic errors on Xmax of 3.5 gcm-2 151

~ "'I E 14 u ~ )( 12 > (/) 4

------2 ------Core error statistics~_ 0 10 15 10 16 Energy (eV)

Figure 8.4: Systematic uncertainties on BLANCA Xmax estimates. At low energies, the dominant error comes from the s to Xmax conversion function and its dependence on composition. At high energies, the uncertain photomultiplier linearity is more important (see Section 5.3). For comparison, the statistical error on the BLANCA mean Xmax measurements is also shown (dashed line). Statistical error is important only above 10 Pe V.

2 to 1.5 g cm- . Since the CASA core error becomes smaller for high energy showers,

the Xmax systematic follows the curve shown in Figure 8.4. This conservative model probably overestimates core errors and their effect. At the opposite end of the energy range, photomultiplier saturation (Section 5.3) also poses a potential systematic problem. A nonlinear detector with reduced output at high light intensities would make the measured Cherenkov slope artificially flat and the derived Xmax too small. This is a particular concern, because Figure 8.3 shows a smaller elongation rate at the highest energy, exactly the effect that uncorrected detector nonlinearity would produce. However, the saturation has been characterized in laboratory studies. The 1-a uncertainty on the nonlinearity parameter a is small.

A Monte Carlo study shows that it leads to a systematic error on Xmax which is only 152

10 g cm-2 at the highest energies, as shown in Figure 8.4. The uncertainty resulting from nonlinear photomultipliers is thus too small an effect to produce the flattening found in the BLANCA mean Xmax measurements.

The third systematic error dominates at energies below 1 Pe V: the limitations of the function that converts Cherenkov slope to an Xmax estimate. The function tends to overestimate the depth of showers at the extreme ends of the BLANCA energy range. It is difficult to overcome this weakness without introducing at the same time a much larger bias which varies strongly with Xmax itself. Instead, we take the apparent systematic error found in Monte Carlo studies as a systematic error on the measured Xmax· This error is increased somewhat because of the unknown cosmic ray composition.

Figure 8.4 depicts the size 0£: the various systematic uncertainties on Xmax in BLANCA measurements. The three errors are added in quadrature to create the total systematic error that enters into Figure 8.3. These errors are important only below 10 PeV. At high energy, statistical errors are the more important limitation on measuring mean Xmax·

8.2 Mean primary mass

The Cherenkov inner slope can be used to find primary mass directly, although the derived mass depends much more on the hadronic interaction model than Xmax does. Figure 8.3 suggests this problem by showing the wide disparity in the (Xmax) predicted by each model. At fixed primary energy, Xmax and Cherenkov slope both depend linearly on ln(A) (as do most composition-sensitive air shower measurements), so the BLANCA measurements are best converted to a mean logarithmic mass rather than to a mean mass. 153 8.2.1 Estimating ln(A) from the Cherenkov lateral distribution

The linear relation between Xmax and ln(A) suggests that the primary mass could be estimated using the formula:

ln(A) ~ [ Xmax - (Xmax)p (ln(56) - ln(l)) (8.2) (Xmax)Fe - (Xmax)p l where (Xmax)p and (Xmax) Fe are the mean depths predicted by Monte Carlo for protons and iron. The value of Xmax for each data event, however, would be subject to the errors and distortions inherent in the slope-to-Xmax transformation. The derived ln(A) would also depend on the event energy estimate, since the mean values in Equation 8.2 would change with energy. Instead, we create a new transfer function which converts C120 ands directly into a ln(A) estimate without using primary energy or Xmax as an intermediate quantity. The best estimate of ln(A) is linear with the Cherenkov slope s, but the strength of the relationship weakens at higher energies for two reasons. One is that the superposition model for the primary cosmic ray interactions is incomplete. The difference in Xmax between protons and iron actually decreases slightly at high energy (see QGSJET predictions in Figure 8.3). The weakff correlation between measured slope and shower Xmax for the deepest showers (Figure 8.1) also flattens the ln(A)-s relationship at high energy. We convert the Cherenkov fit values C120 and s into an estimate of ln(A) using a function which is linear in s. The function's slope and intercept are fit to the Monte Carlo in six separate bands of C120 . The ln(A) estimate for each shower interpolates between the appropriate C120 bands. This method for converting the Cherenkov measurements to an estimate of the primary mass has very small bias. The mean reconstructed ln(A) for a pure sample of each simulated primary species is accurate to 0.2 (i.e. to 20%) over the BLANCA energy range. Only helium shows a bias across all energies, its mass being systematically underestimated on average. On the other hand, the random error is large on a single measurement of ln(A). Shower-by-shower estimates of primary mass cannot be made with any accuracy-the fluctuations inherent in the air shower process en- 154

1 5 ..0 ..0 w.. 0.8 w.. 4.5 < < :E 0.6 :E 4 u :;::; E CIJ 0.4 0 3.5 E '1Jc: Proton Cl) 0.2 CIJ 3 ..Ill a: ------I >- I/) 0 2.5 Helium -0.2 2 Nitrogen -0.4 1.5

-0.6 1 Iron

-0.8 0.5

-1 0 14.5 15 15.5 16 16.5 14.5 15 15.5 16 16.5

log10(Energy/1 eV) log10(Energy/1 eV)

Figure 8.5: The magnitude of the reconstruction errors on ln(A), according to Monte Carlo (CORSIKA/QGSJET). Left: The mean error is less than 0.2 for each species. The function systematically underestimates the ln(A) of helium because the linear relation between ln(A) and s is not exact. Right: The random error on ln(A) is large, especially for the lighter nuclei, because of intrinsic shower fluctuations. sure this. Nevertheless, averaging the derived ln(A) for enough showers produces a good indication of the cosmic ray composition. Figure 8.6 illustrates the mass separation of individual showers and of the av- erages. The top panels show the distributions of Xmax for simulated shnwers of different primary species (in the 1-3 Pe V and 10-30 PeV energy ranges). The variation in air shower development smears out Xmax even for a single species and fixed energy. The lower panels show the distribution of reconstructed ln(A) for the same sets of simulated showers. The mass resolution for single events is poor, but the mean ln(A) of each species matches the actual ln(A) well (as shown by the arrows).

The Xmax fluctuations are primarily responsible for the large uncertainties in reconstructed ln(A). As in Figure 7.4, BLANCA is seen to separate primary species nearly as well as the enormous intrinsic fluctuations allow. 155

400 400

350 1-3 PeV 350 10-30 PeV

300 7-lron 300

250 250

200

150 150

100 100

50 50

0 0 400 600 800 1000 400 600 800 1000

350 250 HHeN Fe HHeN Fe 225 300 tttt 200 250 175

200 150 125 150 100 100 75 50 50 25 0 0 -15 -10 -5 0 5 10 -15 -10 -5 0 5 10 Estimated ln(A) Estimated ln(A)

Figure 8.6: The inherent mass resolution of Xmax and of BLANCA. Top: The distribution of Xmax expected for each primary type in the indicated energy ranges (CORSIKA/QGSJET). The curves assume perfect knowledge of Xmax· Bottom: The distribution of the ln(A) reconstructed on the basis of Cherenkov measurements (with detector effects simulated). The arrows indicate the actual values of ln(A) for the four species. The energy ranges are the same as the upper panels. BLANCA distinguishes primary species (bottom) as well as the intrinsic fluctuations (top) allow. 156 8. 2. 2 Results: In( A) versus primary energy

The derived mean ln(A) is shown as a function of primary energy in Figure 8.7. The four symbols show the BLANCA data interpreted according to the predictions of CORSIKA with the four hadronic models. The dependence on interaction model is clear: the models set the overall mass scale differently, but they all indicate the same changes with energy. The mean mass becomes lighter with increasing energy through the knee, then becomes heavier above ,,_.., 3 PeV. The ln(A) method finds the same trends observed in the Xmax results (Section 8.1).

8.3 A multi-species fit to the Cherenkov slopes

The lower panels of Figure 8.6 suggest another method for extracting composition information from the BLANCA data. The techniques described in the two previous sections involve estimating Xmax or ln(A) for each shower and then taking the average over all showers in a given energy range. By considering only the average value, we lose the most of the information contained in the decidedly non-Gaussian shape of the composite Xmax distribution. This section explains how the full distribution of measured Xmax values can be compared with the distributions predicted for each of the four primary species hydrogen, helium, nitrogen, and iron.

8. 3.1 Procedure

Comparing measured and simulated distributions requires high statistics samples, both for the data and Monte Carlo sets. The steep cosmic ray energy spectrum ensures that only the highest energy range suffers from limited numbers of showers. 1

We separate the data into five logarithmic energy bins between 10 14 ·5 and 1016·5 eV. This bin choice is a compromise between the need to include many showers in each range and the wish to examine trends on an energy scale as fine as possible. Since no radical change is expected in the composition with energy, bins of 0.4 decades are reasonable. The CORSIKA showers are grouped into the same energy ranges.

1 Unfortunately, the high energies are exactly where the composition is most interesting. 157

/\ 4.5 ,------~ < c -v 4 .. , .. Fe

3.5 ··-·-·-··--·-·-·····

3 .... A. ....'!' ..

N 2.5 ···············-··.... ---- ····-······ .. .. : " ' 2 " ...... ,...... ·········••••••...... •.• " ~ • I .._ .;. I . . . . I • 1.5 He

1 ...... :T -HOP~

A SIBYLL

0.5 •• VENLIS •• QGSjET

o ~~~~~~~~~~~~~~~~~~~~~~~~~H 14.5 14.75 15 15.25 15.5 15.75 16 16.25 16.5

log10(Energy/1 eV)

Figure 8.7: The mean logarithmic mass (ln(A)) measured by BLANCA over the sensitive energy range. Each symbol corresponds to the predictions of CORSIKA paired with a different hadronic model. Error bars are statistical only and shown only on the QGSJET results. Errors on the other points are comparable in size. The differences among the four interpretations give an indication of the systematic uncertainty on (ln( A)). 158 Within each range, we find the distribution of the Cherenkov inner slope (s) for the BLANCA data and for pure samples of each species in the Monte Carlo library (protons, He, N, and Fe). The simulated distributions of s (with detector effects) are smoothed by a multiquadric smoothing algorithm [76]. To preserve information about their limited statistics, the data distribution are not smoothed. The multi-species fit in each energy range finds the linear combination of the four simulated distributions which reproduces the data distribution best. Since each primary species has a characteristic signature in its s distribution, this fit uses more information than simply the mean or even the width of s. We do not constrain a priori the fractional contribution of each primary type to lie in the physical range of 0-100%, nor is the sum of the fractions constrained to equal 1.0. Nevertheless, in practice the sum is always in the range 100 ± 0.5%. 14 9 As an example, Figure 8.8 shq,ws the multi-species fit in the energy range 10 · -

1015·3 eV. The lower right panel (#4) displays the full fit using all four available primary types. The other panels show the best fits that can be made when helium (#2), nitrogen (#3), or both (#1) are omitted. The Monte Carlo predictions cannot match the data using protons and iron alone; the intermediate mass nitrogen species is also required. Panel #2 shows that the best fit of p, N, and Fe to the data is very close but fails to match the shape at the peak and in the long tail to high values of s. The data strongly suggest that at least the four primary types considered here contribute to the cosmic rays just below the knee. Although other species may be present, the data do not require them at the current level of precision. Extrapolations of lower energy cosmic ray measurements (Chapter 1) suggest that CNO, helium, and protons are likely to be far more abundant that the L-nuclei (Li, Be, B). Therefore, additional species would probably lie between nitrogen and iron in mass and would affect the shape of the peak in the s distribution.

8.3.2 Results of the multi-species analysis

The fits demonstrated in Figure 8.8 (lower right) are performed for all five energy ranges and using the predictions of all four high energy hadronic interaction models. 159

Multi-Species Fit Exampl~

~~~~~~~~~~~~~ ~~~~~~~~~~~~------,

#1 0.732 Proton #2 0.556 Proton 2500 2500

2000 2000 0.287 Nitrogen 0.268 Iron 0.158 Iron 1500 1500

1000 1000

500 500

0 0 0 0.01 0.02 0.03 0.04 0 0.01 0.02 0.03 0.04 1 1 Cherenkov Slope (m" ) Cherenkov Slope (m" ) (p,Fe) (p,N,Fe)

#3 0.352 Proton #4 0.417 Proton 2500 2500 0.412 Helium 0.214 Helium

2000 2000 0.190 Nitrogen 0.236 Iron 0.178 Iron 1500 1500

1000 1000 "'

500 500

0 0 0 0.01 0.02 0.03 0.04 0 0.01 0.02 0.03 0.04 1 1 Cherenkov Slope (m" ) Cherenkov Slope (m" ) (p,He,Fe) (p,He,N,Fe)

Figure 8.8: A demonstration of the multi-species fitting procedure, in this case the 14 energy range 10 ·9 - 10 15·3 eV. The solid histogram gives the distribution of Cher- enkov slope s for all BLANCA data in that energy range and is the same in all four panels. The solid curves show the combination of Monte Carlo ( QGSJET) showers which best reproduce the measured distribution. Panels 1-4 correspond to different allowed combinations of primary species, as indicated. Clearly a nitrogen component is needed to match the data, but a helium component is also important. 160

c: c: .2 .2 (j QGSJET (j VENUS E E LI.. * Fe LI.. Fe Cl) Cl) * .~ () i) .~ () i) ~ 0.8 ~ 0.8 * E * E :s :s 0 ~. /~,' 0 0.6 0.6 \ \ * He \ * 0 0.4 0.4

0.2 * 0.2 * p p 0 0 14 15 16 14 15 16

Log10(Energy/1 eV) Log10(Energy/1 eV)

Figure 8.9: Results of the multi-~pecies fit to the BLANCA data. The line graphs indicate the mixture of proton, helium, nitrogen, and iron primaries which best reproduces the Cherenkov slope distributions of the data. The lines show cumulative fractions (i.e. the lowest line gives the proton fraction, while the next line gives the combined proton and helium fraction). QGSJET (left) and VENUS (right) are shown. The other two interaction models show similar trends but with heavier overall composition. The stars ( *) at 10 14 e V show the results of direct measurements from the JACEE balloon-borne emulsion experiment [83, 30]. JACEE Ne-Si data have been divided evenly into the N and Fe groups for comparison with BLANCA.

Table 8.2 lists the results. The fit uses the MINUIT log-likelihood maximization procedure [79], which accounts properly for the non-Gaussian probability distribution of data events in the bins with low statistics. As a rough indicator of the fit quality, the reduced x2 value for each fit is also provided in the table. In the lowest energy range, the number of data events is so large that no combination of the four cosmic ray species can reproduce the data adequately. Conversely, the high energy ranges have too few events to constrain the abundances tightly. The results of the multi-species fit to the BLANCA Cherenkov slope data are shown graphically in Figure 8.9 for the QGSJET and VENUS models. The SIBYLL and HDPM models show similar trends but a heavier overall composition. Since these the models give an unphysical negative helium abundance in a middle energy 161

Energy Range ...... Abundance (%) ...... x2 of log 10 (E /1 eV) p He N Fe Fit QGSJET 14.5 - 14.9 21.8 ± 0.4 40.1±0.7 23.4 ± 0.7 14.6 ± 0.3 38.1 14.9 - 15.3 41.7 ± 1.3 21.4 ± 1.8 19.0 ± 1.3 17.8 ± 0.6 4.5 15.3 - 15.7 51.0 ± 2.7 32.7 ± 4.0 3.2 ± 2.9 13.1±1.1 1.9 15.7 - 16.1 53.3 ± 7.6 14.3 ± 9.5 22.8 ± 6.4 9.6 ± 3.0 0.7 16.1 - 16.5 30.7 ± 12. 12.1±18. 35.4±17. 21.9 ± 8.2 1.9 VENUS 14.5 - 14.9 23.9 ± 0.4 27.6 ± 0.7 31.8 ± 0.5 16.7 ± 0.3 47.8 14.9 - 15.3 29.1±1.1 29.3 ± 1.9 18.9 ± 1.4 22.6 ± 0.6 5.9 15.3 - 15.7 46.3 ± 2.4 22.8 ± 3.8 15.2 ± 2.7 15.7 ± 1.1 1.7 15.7 - 16.1 46.0 ± 5.8 5.9 ± 9.4 33.3 ± 7.0 14.8 ± 2.6 0.8 16.1 - 16.5 15.5 ± 8.9 33.1±14. 22.6 ± 13. 28.8 ± 7.8 1.8 SIBYLL 14.5 - 14.9 16.8 ± 0.4 20.9 ± 0.7 24.8 ± 0.7 37.4 ± 0.3 49.4 14.9 - 15.3 35.0 ± 1.0 -6.9 ± 1.7 38.9 ± 1.4 33.0 ± 0.7 21.6 15.3 - 15.7 36.7 ± 2.9 21.3 ± 4.8 9.2 ± 3.6 32.7 ± 1.5 4.8 15.7 - 16.1 31.3 ± 5.5 19.4 ± 9.5 8.6 ± 8.0 40.7 ± 3.8 1.2 16.1 - 16.5 8.6 ± 9.0 31.4 ± 17. 7.5.;I:: 19. 52.5 ± 11. 2.6 HDPM 14.5 - 14.9 19.9 ± 0.3 17.9 ± 0.5 31.4 ± 0.5 30.7 ± 0.2 90.0 14.9 - 15.3 18.6 ± 0.6 23.2 ± 1.1 24.3 ± 0.9 34.0 ± 0.5 11.5 15.3 - 15.7 31.7 ± 1.5 16.3 ± 2.5 26.4 ± 2.1 25.6 ± 1.0 3.2 15.7 - 16.1 36.7 ± 3.9 -3.0 ± 6.4 43.4 ± 5.5 22.9 ± 2.5 1.2 16.1 - 16.5 11.9 ± 5.8 21.2 ± 12. 18.0 ± 12. 48.9 ± 7.7 1.5

Table 8.2: Results of the multi-species fits to the BLANCA data. Statistical errors on each fraction are strongly correlated. The errors increase with energy due to limited statistics. The number of data showers in the lowest energy range is large enough that no combination of species fits well in any model (indicated by high x2). 162 range, the SIBYLL and HDPM results are not shown. At 100 TeV, data are shown from the JACEE balloon direct measurements [83, 30] for comparison.2 The direct composition at lOOTeV agrees surprisingly well with the BLANCA data at 400TeV.

The results of the multi-species fit also agree with the mean Xmax and mean ln(A) derived in the previous two sections. All three studies indicate that the cosmic ray composition is lighter near 3 PeV than it is at either 300 TeV or 30 PeV.

8.4 Summary of composition results

Figure 8.10 compares the BLANCA measurement of Xmax with other results over more than five decades of primary energy. Extrapolations of the BLANCA data to lower and higher energy give reasonable agreement with the Xmax expected based on direct low energy measurements [S2] and with the high energy Fly's Eye results [40].

The smooth continuation of composition indicators like Xmax over large energy ranges is expected on physical grounds, but it has been confirmed only with the latest generation of Cherenkov experiments. Oddly, there is considerable disagreement among the Cherenkov experiments themselves in measuring Xmax near the knee. It is possible that the discrepancies arise from the different air shower simulations chosen to interpret the data. Our CORSIKA study with four hadronic interaction models suggests that the conversion of Cherenkov slope into Xmax depends very little on hadronic model. Nevertheless, other factors in the simulations (such as atmospheric scattering of Cherenkov light) could be important. The BLANCA measurements of Cherenkov slope are converted directly to an estimate of the cosmic ray mean logarithmic mass. The trend in mean logarithmic mass is from mixed to lighter composition at the knee, becoming heavier again above the knee. The mean ln(A) indicates a mixed rather than an extreme composition at all energies, even at several tens of PeV. The multi-species fit, which compares the full distribution of the measured slope with Monte Carlo simulations, shows the same behavior. In both techniques, the inferred mass depends on the choice of hadronic interaction model, but the trends are the same regardless of model.

2The JACEE composition at lOOTeV is similar to that measured by the Spacelab CRN experiment [84], which studied only heavy nuclei (Z;::: 6). 163

.-.850~------, ~ E u .9 800

x""' e v 750 t t t • t 700

650 • • • t •• 600 ;;c Direct

550 e BLANCA .A HEGRA/AIROBICC

500 ' SPASENULCAN • DICE

450 'Y Flys Eye

-- QGSJET 400

350 10 14 17 10 15 10 16 10 10 18 10 19 Energy (eV)

Figure 8.10: The BLANCA measurement of Xmax compared with other results. All experiments operating near the knee use atmospheric Cherenkov light, including DICE [32], the AIROBICC array at HEGRA [33], and the VULCAN array at SPACE-2 [34]. The high energy measurements (> 10 17 eV) by Fly's Eye use the atmospheric fluorescence technique [40]. The "direct" point estimates the (Xmax) that would be expected on the basis of direct balloon measurements [32]. The Monte Carlo lines use CORSIKA with QGSJET [85]. 164

That the cosmic ray composition becomes heavy above the knee is widely, though not universally, expected. Cosmic ray models which place the origin in our Galaxy generally explain the knee as the result of one or more rigidity-dependent effects (Section 1.2.4). Thus iron and other heavy nuclei should become more abundant above the knee than below. The BLANCA data generally agree with this prediction, showing a trend to heavy composition above the knee. The simplest models of supernova acceleration predict that the composition becomes heavier starting not at 3 PeV (as BLANCA finds) but an order of magnitude lower in energy. The 0.5- decade wide knee which BLANCA observes in the cosmic ray flux is also narrower than simple rigidity effects would predict. The current observations agree generally but not in all details with the expectations of the supernova acceleration and Galactic escape picture.

Few current models of cosmic ,.ays predict a light composition at the knee itself, as Figure 8. 7 indicates. One possible explanation is due to Swordy, who argues for a modification of the Galactic leaky box model which would produce a light composition just below the knee [86]. This modification is motivated by the need to explain why ultra high energy cosmic rays are not observed with a large dipole anisotropy as they stream quickly out of the Galaxy.

Models in which PeV cosmic rays are accelerated in AGN or pulsars predict that a high flux of X-ray photons breaks up compound nuclei at the source and allows only protons to escape. The BLANCA results are inconsistent with such models, as the data show a clear trend towards heavy or at least mixed cosmic ray composition even at 10 PeV. At this energy, extragalactic and pulsar source models predict pure proton compositions.

The CASA-BLANCA data described in this thesis were analyzed using only the Cherenkov lateral distribution to determine the primary energy and composition. Nevertheless, the BLANCA data were recorded along with the electron and muon distribution in each shower as measured by the CASA and MIA arrays. The surface array was used to find the shower core and direction, but the electron and muon number in each shower were ignored. As argued in Section 2.3.3, electrons and 165 muons provide additional power to discriminate among cosmic ray species. Heavier primaries produce more muons and fewer electrons at ground level than light primaries of the same energy. Incorporating the electron and muon measurements is one possible way to extend this analysis in the near future.

The future of the field as a whole is harder to predict. One possible improvement is to make the BLANCA Cherenkov lateral measurements simultaneously with an imaging Cherenkov detector such as DICE. Unfortunately, bo~h instruments have probably reached the end of their useful life. Another goal is to join the high energy measurements of Xmax from fluorescence detectors with the knee results from Cherenkov experiments. The energy range of 30-100 Pe V would be accessible to a large instrument such as BLANCA if it observed a wide enough angular region on the sky to collect an adequate sample of showers. One could, for example, build a BLANCA in which half the detectors have a much larger Winston cone angle but a reduced collection area. These smaller detectors could be used for measuring high Cherenkov photon densities from a larger section of sky. An array of this sort could conceivably study composition through the entire energy range of 0.3-100 PeV.

Another approach is that of the multi-component air shower array, such as KAS- CADE [69], which measures shower cores with a hadronic calorimeter in addition to the usual electron and muon detectors. KASCADE has provided exciting results in its first few years of operation. Like any air shower array, however, KASCADE can only produce composition measurements under assumptions that depend on high energy hadronic interaction models. One strength of the array is its partial ability to discriminate among the available models [74]. A BLANCA-like detector at KAS- CADE would be an attractive prospect, allowing us to combine the energy resolution of Cherenkov arrays with measurements of many types of air shower particles.

In the next decade, measurements at the knee such as the one presented here should make contact at least at the lower energies with results from improved direct detectors. The ACCESS spacecraft [87] has been proposed to fly on the International Space Station in 2005. Its goal is to measure directly the abundances of all elements between protons and iron up to energies of 1 PeV. Such a measurement would 166

provide us with a much better picture of cosmic ray acceleration sites and propagation through the Galaxy. With its wide energy coverage, extrapolations of individual element spectra through the knee should become possible. The knee itself, however, will remain out of reach of high statistics direct measurements for the foreseeable future. The atmospheric Cherenkov technique will certainly continue to be a valuable tool for studying the origin of cosmic rays. APPENDIX A FITTING THE DETECTOR RELATIVE GAINS

The BLANCA detector relative gains are determined for each run using the cosmic ray Cherenkov showers recorded in the run. The gains are assumed to be constant throughout the night. Section 5.1.3 describes the event selection and the assumptions. The main concept is that the Cherenkov distribution has circular symmetry about the shower core and that measured departures from symmetry arise from differences in detector gains. Thus the Cherenkov data allow us to estimate the relative gain of any possible pair of detectors. This Appendix explains the procedure for combining the estimates of the gain ratios to determine the relative gains. The relative gains are those which maximize the joint likelihood of the measured ratios. The observed log-ratios for each detector pair are assumed to be drawn from a normal distribution (i.e. the ratios themselves are log-normally distributed). The parent distribution is assumed to have a mean equal to the log of the detector gain ratio and a variance equal to the variance of the data. Therefore, ignoring the prefactors, the likelihood Lij of observing a single log-ratio Lij with a corresponding uncertainty of aij is

2 Lij ex exp --1 (Lij - ln(Gi/Gj)) ] . [ . 2 a ~

Gi is the relative gain of station i, and a& is the estimated variance of the mean Lij· The combined likelihood of all observations is the product of the individual like- lihoods:

where the additional factor of 1/2 accounts for the summation over both ln Lij and ln Lji 1 even though the terms are identical. It is simpler to calculate the logarithms of the gains gi ln Gi rather than the relative gains themselves. The set of log-gains which maximizes the likelihood is

167 168 found by requiring &(ln£)/&gk = 0 for all k, which produces 144 coupled linear equations for the set of unknowns {gk}:

Performing one of the sums,

Lij is antisymmetric in its indices, and O"ij is symmetric, so the terms can be combined:

This set of equations is not linearly independent. In fact, the sum of the left sides of all equations (that is, the sum over k) is identically zero, leaving only 143 independent equations. If the set of log-gains gi solves the maximum likelihood equation, then so does the set g: = gi + c. This degeneracy reflects the nature of the method: it determines only the relative gains of the BLANCA detectors. We define the arbitrary constant so that the sum Li gi = CJ. This choice is equivalent to scaling the relative gains Gi to make their geometric mean unity.

The equations can be expressed more compactly by defining the vector A and matrix M: 169 Notice that A and M depend only on the observations and not on the (as yet) undetermined values of 9i· The equations for 9i become

or in vector notation X+Mg= 0.

The vector A and matrix M depend only on measured quantities: Lij, the mean log-ratios, and ai1, the uncertainties on the means. Notice that we now have an exact equation for the relative gains. The quantity ln [, has been maximized without requiring numerical fit procedures. This result is a consequence of ln [, being quadratic in each of the unknowns. Solving this vector equation for g in general requires inverting the matrix M. In practice, however, the gains can be found to arbitrary precision with an iterative procedure. Let ffn represent the nth iteration of the SJlution, starting with g0 = 0. The equation for the gains is rewritten

§=(M+l)ff+A and iterated according to

The limit (limn-+oo ffn), if it exists, is a solution to the maximum likelihood equation for the relative gains. In this application, the procedure converges rapidly, usually requiring only 20-40 iterations. After the log-gain vector converges, a constant offset is added to each log-gain to make their sum zero. Because of the degeneracy of the equations, this new vector is also a solution. The relative gains are then Ci =exp 9i· Data from any BLANCA detector are scaled down by the appropriate relative gain, thereby correcting for gain variations among the detectors. APPENDIX B THE CORSIKA MODEL ATMOSPHERE

The density of the atmosphere as a function of altitude is an important component of any air shower simulation. The atmosphere controls both the development of the particle cascade and the Cherenkov angle and intensity. The CORSIKA program provides eight choices of atmospheric density profiles. This analysis uses the U. S. standard atmosphere as parameterized by Lindley [88]. The parameterization divides the atmosphere into five layers. In the lower four, the density p falls exponentially with increasing altitude. In the highest layer, the density is assumed to be constant up to a sharp cutoff height. The density is continuous at all layer boundaries. The mass overburden, or thickness T ( h), is the integral column density above a given height: "'

00 T(h) = l dh' p(h')

This layered atmospheric model leads to a thickness which is also an exponential (with the same scale height) plus a constant in the lower layers. Thickness decreases linearly with height in the top layer. Table B.l gives the scale heights and range of altitudes and overburdens for the layers of the model. Figures B.l and B.2 show the density and thickness as a function of altitude.

Altitude Overburden at bottom Density scale 2 Layer range (km) of layer ( g cm- ) height (km) 1 0-4 1036 9.94 2 4-10 631 8.78 3 10-40 272 6.36 4 40-100 3 7.72 5 100-112.8 1.28 x 10-3 constant

Table B.l: The five-layer parameterization of the U. S. standard atmosphere used 9 in CORSIKA. The density in layer 5 is a constant 10- gcm-3 . This approximation has a negligible effect on extensive air showers, all of which begin in layer 3 or 4.

170 171

.,~ ., -3 E E 10 () 1.2 () Cl .., .!:!! -4 0 ....- ~ 10 ~ rn c: ~ Q) "iii c -5 c: 0.8 Q) 10 c 0.6 -6 10 0.4 -7 10 0.2

-8 0 10 0 5 10 15 20 0 20 40 60 80 Altitude (km MSL) Altitude (km MSL)

Figure B.1: The density profile of the U. S. standard atmosphere used in CORSIKA. Both plots show the air density as a function of height above mean sea level.

~ ~ '1 '1 10 3 E E ; 1000 () .!:!! rn rn 10 2 rn rn Q) Q) c: 800 c: ..lO: ..lO: () .!::! :c .c 10 I- 600 I-

400

-1 200 10

-2 0 10 0 5 10 15 20 0 20 40 60 80 Altitude (km MSL) Altitude (km MSL)

Figure B.2: The overburden of the U. S. standard atmosphere used in CORSIKA. Both plots show the overburden (thickness) as a function of height above mean sea level. APPENDIX C TABLES OF RESULTS

Careful comparison of results from different experiments can be difficult when various groups report their measurements only in graphical form. This appendix contains tables of the CASA-BLANCA physics results, including the cosmic ray spectrum, the mean Xmax as a function of energy, and the mean ln(A) versus energy.

C.1 Cosmic ray energy spectrum

The cosmic ray spectrum is shown in Figures 7.9 and 7.13 interpreted according to the QGSJET hadronic model. We clarify here what is meant by a "differential flux spectrum" of primary cosmic • rays. In a steeply falling power law spectrum such as this one, data binning presents two problems. If the bins are too narrow, then the high energy end of the spectrum will contain too few cosmic rays to be meaningful. But if the bins are too wide, then the difference between a bin's center and the mean energy in that bin can become large. A number of biases can result. We avoid the latter problem by performing all calculations on a spectrum with extremely narrow bin widths, and we rebin the data into wider groupings for presentation only. In particular, the spectral index fits described in Section 7.3.3 use the narrow bins. Fluxes are computed from the number distribution of cosmic ray energies. Data are binned into histograms with a bin width of 0.01 decades, which is much smaller than the energy resolution of the detector. Fits are performed at this first stage, using the raw number of counts per bin as the basis for a full log-likelihood fit to a model spectrum. The fit accounts for the fact that the number of events in each bin is Poisson-distributed rather than being Gaussian [76]. At the high energy end of the spectrum, where the event counts are low, the approximation of normal errors would introduce significant biases to the fitted results. To convert the distribution of primary energies into a spectrum, we divide each count by the bin width (fj_E =Emax - Emin) to produce dN/dE. The original his- 172 173 Name Quantity Events in bin N Bin width 6.E = Emax - Emin ~ 0.023Emin Number spectrum dN/dE = N/6.E Differential flux J(E) = (AOT)- 1dN/dE Flattened differential flux E2.15 J(E) Integral flux I(E) = fif dE' J(E')

Table C.l: Relationships among the cosmic ray energy spectrum variables. Table C.2 below gives the differential ft ux dJ / dE, while Figures 7. 9 through 7 .12 show the flattened differential flux. The integral flux is not used in this analysis, but it appears occasionally in the literature.

togram has bins uniformly spaced in log10 E, so the bin width 6.E rises in proportion to the energy of the bin. Dividing by the cosmic ray exposure of 1.83 x 10 10 m2 sr s converts dN/ dE into the differential ft ux J (E). Table C. 2 lists these data. The differential flux can be "flattened," a procedure for highlighting features besides the dominant falling power law. To flatten, the differential flux J(E) in each bin is 2 75 multiplied by (Emid) · , where Emid is the energy at the middle of the bin (i.e. the geometric mean of the energies at the top and bottom of the bin). Finally, the data are re-binned by combining the 0.01 decade-wide bins into new bins of the desired width. The flux in the composite bin is the average flux in its component bins. Table C.2 gives the average flux J(E) measured by BLANCA. 2 75 For the flattened spectrum plots, we multiply by the E · factor before averaging. 15 8 Figure 7.9 uses bins 0.1 decades wide at lower energies (below 10 · eV) and twice as wide at high energies. The bins in Figure 7.12 are 0.05 decades wide, because the figure is intended to show the shape of the spectrum near the knee.

C.2 Shower depth of maximum and derived primary mass

Table C.3 lists the mean Cherenkov inner slope and the mean depth of maximum for showers in each 0.1 decade range of primary energy. The first column of errors given in the table is statistical, the width of the Xmax distribution divided by VN. The second error is a systematic error consisting of contributions from core location error, photomultiplier saturation, and reconstruction bias (Figure 8.4, left). Reconstruction 174 Energy range Differential flux J(E) in each bin 2 1 1 1) log 10 (E /1 eV) (m- sr- s- Gev- 14.3 - 14.4 1.21 x 10-10 ± 3.60 x 10-13 14.4 - 14.5 6.68 x 10-11 ± 2.39 x 10-13 14.5 - 14.6 3.58 x 10-11 ± 1.56 x 10-13 14.6 - 14.7 1.91 x 10-11 ± 1.01 x 10-13 14.7 - 14.8 1.03 x 10-11 ± 6.64 x 10-14 14.8 - 14.9 5.42 x 10-12 ± 4.29 x 10-14 14.9 - 15.0 2.90 x 10-12 ± 2.80 x 10-14 15.0 - 15.1 1.57 x 10-12 ± 1.83 x 10-14 15.1 - 15.2 8.18 x 10-13 ± 1.18 x 10-14 15.2 - 15.3 4.36 x 10-13 ± 7.69 x 10-15 15.3 - 15.4 2.21 x 10-13 ± 4.88 x 10-15 15.4 - 15.5 1.22 x 10-13 ± 3.23 x 10-15 15.5 - 15.6 6.19 x 10-14 ± 2.05 x 10-15 15.6 - 15.7 2.86 x 10-14 ± 1.24 x 10-15 15.7 - 15.8 1.51 x 10-14 ± 8.02 x 10-15 15.8 - 15.9 7.68 x 10-15 ± 5.10 x 10-15 15.9 - 16.l 2.95 x 10-15 ± 1.92 x 10-15 16.1 - 16.3 8.14 x 10-15 ± 8.08 x 10-17 16.3 - 16.5 2.12 x 10-15 ± 3.26 x 10-17 16.5 - 16.7 3.12 x 10-17 ± 9.97 x 10-18 16.7 - 16.9 2.31 x 10-17 ± 6.97 x 10-18

Table C.2: The primary cosmic ray energy spectrum measured by BLANCA. Bin widths rise with increasing energy so that Emax/ Emin = 10°·1 up to 10°·9 = 7.94 PeV. 2 For the seven highest bins Emax/ Emin = 10°· . Only results using the QGSJET energy model are listed here. Errors represent the Poisson uncertainty in each bin. bias and saturation are important primarily at low and high energies, respectively. The core error bias is small at all energies. Figure 8.2 (right panel) shows the Xmax resolution for a single shower, depending on energy. Table C.4 shows the mean logarithmic mass derived from BLANCA measurements (Figure 8.7). The same 0.1 decade binning is used as in the Xmax table. The four hadronic interaction models give different interpretations of the same data, so all are shown in the table. The variation provides some insight into the model- dependent systematic errors. The trend is the same in all cases: the composition is lighter at the knee than above or below it. 175

Energy range 1 2 log10 (E /1 eV) Means( m- ) (Xmax) ±stat.± sys.(gcm- ) 14.3 - 14.4 0.0114 ± 0.0000 458.4 ± 0.3 ± 11.8 14.4 - 14.5 0.0119 ± 0.0000 469.0 ± 0.3 ± 9.8 14.5 - 14.6 0.0125 ± 0.0000 478.9 ± 0.4 ± 9.2 14.6 - 14.7 0.0129 ± 0.0000 487.9 ± 0.4 ± 9.1 14.7 - 14.8 0.0134 ± 0.0000 497.3 ± 0.5 ± 8.9 14.8 - 14.9 0.0137 ± 0.0000 503.8 ± 0.6 ± 8.6 14.9 - 15.0 0.0141 ± 0.0000 511.3 ± 0.8 ± 8.1 15.0 - 15.1 0.0147 ± 0.0000 522.8 ± 1.0 ± 7.4 15.1 - 15.2 0.0152 ± 0.0001 532.2 ± 1.2 ± 7.0 15.2 - 15.3 0.0156 ± 0.0001 541.5 ± 1.4 ± 7.0 15.3 - 15.4 0.0163 ± 0.0001 555.2 ± 1.9 ± 7.1 15.4 - 15.5 0.0168 ± 0.0001 564.9 ± 2.1 ± 7.2 15.5 - 15.6 0.0172 ± 0.0001 572.6 ± 2.6 ± 7.4 15.6 - 15.7 0.0173 ± 0.0002 576.3 ± 3.6 ± 7.7 15.7 - 15.8 0.0174 ± 0.0002 577.9 ± 4.3 ± 7.9 15.8 - 15.9 0.0175 ± 0.0002 578.Q ± 5.0 ± 8.3 15.9 - 16.0 0.0179 ± 0.0003 588.2 ± 6.1 ± 8.6 16.0 - 16.1 0.0170 ± 0.0004 570.3 ± 7.8 ± 9.0 16.1 - 16.2 0.0175 ± 0.0004 579.0 ± 9.7 ± 9.4 16.2 - 16.3 0.0174 ± 0.0006 575.9 ± 12.3 ± 10.0 16.3 - 16.4 0.0181 ± 0.0005 588.9 ± 11.4 ± 10. 7 16.4 - 16.5 0.0185 ± 0.0008 600.5 ± 18.7 ± 11.3 16.5 - 16.6 0.0172 ± 0.0015 572.0 ± 30.8 ± 11.7

Table C.3: Mean Cherenkov slope and mean Xmax measured by BLANCA. 176

Energy range Mean ln(A)

log10 (E /1 eV) QGSJET VENUS SIBYLL HDPM 14.3 - 14.4 1.71±0.01 1.58 2.27 1.99 14.4 - 14.5 1.67 ± 0.01 1.63 2.24 2.06 14.5 - 14.6 1.63 ± 0.01 1.69 2.28 2.14 14.6 - 14.7 1.61±0.01 1. 71 2.29 2.18 14.7 - 14.8 1.60 ± 0.02 1.74 2.35 2.20 14.8 - 14.9 1.69 ± 0.02 1.80 2.47 2.26 14.9 - 15.0 1.65 ± 0.03 1.85 2.45 2.32 15.0 - 15.l 1.49 ± 0.03 1.78 2.34 2.32 15.1 - 15.2 1.39 ± 0.04 1.69 2.29 2.18 15.2 - 15.3 1.28 ±: 0.05 1.61 2.16 2.10 15.3 - 15.4 1.07 ± 0.06 1.36 1.99 2.01 15.4 - 15.5 0.90 ± 0.07 1.28 1.78 1.83 15.5 - 15.6 0.86 ± 0.09 1.06 1.68 1.59 15.6 - 15.7 0.95 ± 0.12 1.25 1.81 1.85 15.7 - 15.8 1.11±0.14 1.22 2.00 1.67 15.8 - 15.9 1.18 ± 0.19 1.57 2.02 2.01 15.9 - 16.0 1.01±0.24 1.28 2.13 2.13 16.0 - 16.1 1.96 ± 0.30 2.31 2.89 2.54 16.1 - 16.2 1.79 ± 0.38 2.09 2.76 2.69 16.2 - 16.3 2.13 ± 0.52 2.32 2.59 2.93 16.3 - 16.4 1.70 ± 0.50 1.93 3.11 2.44 16.4 - 16.5 1.43 ± 0.75 2.25 2.91 3.21 16.5 - 16.6 2.92 ± 1.38 3.18 2.82 2.40

Table C.4: Mean ln(A) measured by BLANCA for each 0.1 decade energy range. The four columns show ln(A) interpreted according to each hadronic interaction model. Statistical errors shown on the QGSJET points are similar for all four models. BIBLIOGRAPHY

[1] M. Longair, High Energy Astrophysics, Vol. I, 2nd Ed., Cambridge University Press, Cambridge, 1992.

[2] E. J. Ahn et al., "The origin of the highest energy cosmic rays: Do all roads lead back to Virgo?" submitted to Phys. Rev. Lett. (1999). Preprint astro- ph/9911123.

[3] V. F. Hess, Physik. Zeit., 13, 1084 (1912).

[4] M. Friedlander, Cosmic Rays, Harvard University Press, Cambridge, 1989.

[5] J. Chadwick, Nature, 129, 312 (1932). Reprinted in [10].

[6] C. D. Anderson, Phys. Rev., 43, 491 (1933). Reprinted in [10].

[7] S. H. Neddermeyer and C. D. Anderson, Phys. Rev., 51, 884 (1937). J.C. Street and E. C. Stevenson, Phys. Rev., 52, 1003 (1937). Reprinted in [10].

[8] C. M. G. Lattes et al., Nature, 160, 453 (1947). Reprinted in [10].

[9] L. Leprince-Ringuet and M. L'heritier, Comptes Rendus Acad. Sciences de Paris, seance du 13 Dec. 1944, 618. G. D. Rochester and C. C. Butler, Nature, 160, 855 (1947). Reprinted in [10].

[10] R. N. Cahn and G. Goldhaber, The Experimental Foundations of Particle Physics, Cambridge University Press, New Yofk, 1989.

[11] 0. Chamberlain et al., Phys. Rev., 100, 947 (1955). Reprinted in [10].

[12] P. Auger et al., Rev. Modern Phys., 11, 288 (1939).

[13] J. Cronin, T.K. Gaisser, and S.P. Swordy, Sci. Amer. 276, 44 (1997).

[14] G. V. Kulikov and G. B. Khristiansen, J. Exptl. Theoret. Phys. (USSR), 35, 635 (1958). Appears in English translation as Soviet Phys. JETP, 8, 441 (1959).

[15] M. Longair, High Energy Astrophysics, Vol. II, 2nd Ed., Cambridge University Press, Cambridge, 1994.

[16] W. Baade and F. Zwicky, Proc. Nat. Acad. Sci. U. S., 20, 254 and 259 (1934).

[17] J. H. Buckley et al., Astron. Astrophys., 329, 639 (1998).

[18] L. O'C. Drury, F. A. Aharonian, and H. J. Volk, Astron. Astrophys., 287, 959 (1994). 177 178

[19] T. K. Gaisser, Cosmic Rays and Particle Physics, Cambridge University Press, Cambridge, 1990.

[20] E. Fermi, Phys. Rev., 75, 1169 (1949).

[21] R. D. Blandford and J. P. Ostriker, Astrophys. J., 221, 129 (1978).

[22] P. 0. Lagage and C. J. Cesarsky, Astron. Astrophys., 118, 223 (1983) and 125, 249 (1983).

[23] A. D. Erlykin, Nucl. Phys. B (Proc. Suppl.), 39A, 215 (1995).

[24] E. S. Seo and V. S. Ptuskin, Astrophys. J., 431 705 (1994).

[25] A. M. Hillas, Proc. 16th Int. Cosmic Ray Conj., Kyoto, 8, 7 (1979).

[26] R. J. Protheroe and A. P. Szabo, Phys. Rev. Lett., 69, 2885 (1992).

[27] T. Stanev, P. L. Biermann, and T. K. Gaisser, Astron. Astrophys., 274, 902 (1993). This paper is the conelusion of a series which also includes: P. L. Biermann, Astron. Astrophys., 271, 649 (1993). P. L. Biermann and J. P. Cassinelli, Astron. Astrophys., 277, 691 (1993). P. L. Biermann and R. G. Strom, Astron. Astrophys., 275, 659 (1993).

[28] A. D. Erlykin and A. W. Wolfendale, J. Phys. G, 23, 979 (1997).

[29] A. D. Erlykin and A. W. Wolfendale, Astron. Astrophys., 350, Ll (1999).

[30] A. A. Watson, Proc. 25th Int. Cosmic Ray Conj., Durban, 8, 257 (1997).

[31] Burnett et al., Astrophys. J., 349, 125 (1990).

[32] S. P. Swordy and D. B. Kieda, "Elemental Composition of Cosmic Rays near the Knee by Multiparameter Measurement of Air Showers," accepted in As- troparticle Phys. (1999). Preprint astro-ph/9909381. See also K. Boothby et al., Astrophys. J., 491, 135 (1997).

[33] F. Arqueros et al., accepted in Astron. Astrophys. (1999). Preprint astro- ph/9908202.

[34] J.E. Dickinson et al., Proc. 26th Int. Cosmic Ray Conj., Salt Lake City, session OG 1.2.05 (1999).

[35] M. A. K. Glasmacher et al., Astroparticle Phys., 12, 1 (1999).

[36] EAS-TOP Collaboration, Proc. 25th Int. Cosmic Ray Conj., Durban, 4, 13 and 41 (1997). 179

[37] Y. A. Fomin et al., Proc. 25th Int. Cosmic Ray Conj., Durban, 4, 17 (1997).

[38] T. K. Gaisser et al., Seventh Int. Symposium on Very High Energy Cosmic Ray Interactions, Ann Arbor, 1992.

[39] K. Kampert et al., Proc. 26th Int. Cosmic Ray Conf., Salt Lake City, OG 1.2.11, 1999.

[40] D. Bird et al., Phys. Rev. Lett., 71 3401 (1993).

[41] R. M. Barnett et al., "Review of Particle Properties,'' Phys. Rev. D, 54, 1 (1996).

[42] T. K. Gaisser and A. M. Hillas, Proc. 15th Int. Cosmic Ray Conj., Plovdiv, 8, 353 (1977).

[43] J. D. Jackson, Classical Electrodynamics, 2nd Ed., Wiley & Sons, New York, 1975.

[44] B. Rossi and K. Greisen, Rev. Modern Phys., 13, 240, (1941).

[45] S. S. M. Wong, Introductory Nuclear Physics, P T R Prentice-Hall, Englewood Cliffs, New Jersey, 1990.

[46] P. Sokolsky, Introduction to Ultrahigh Energy Cosmic Ray Physics, Addison- Wesley, Redwood City, California, 1988.

[47] W. Heitler, Quantum Theory of Radiation, -2nd Edition, Oxford University Press, London, 1944.

[48] J. R. Patterson and A. M. Hillas, J. Phys. G, 9, 1433 (1983).

[49] B. R. Dawson, R. vV. Clay, J. R. Patterson and J. R. Prescott, J. Phys. G, 15, 893 (1989).

[50] K. Greisen, Ann. Rev. Nucl. Sci., 10, 63 (1960).

[51 J M. V. S. Rao and B. V. Sreekantan, Extensive Air Showers, World Scientific, River Edge, New Jersey, 1998.

[52] R. Walker and A. A. Watson, J. Phys. G, 7, 1297 (1981).

[53] J. R. Patterson and A. M. Hillas, J. Phys. G, 9, 323 (1983).

[54] A. Borione et al., Astrophys. J., 481, 313 (1997).

[55] A. Borione et al., Phys. Rev. D, 55, 1714 (1997). 180

[56] M. Catanese et al., Astrophys. J., 469, 572 (1996).

[57] A. Borione et al., Astrophys. J., 493, 175 (1998).

[58] A. Borione et al., Nucl. Instr. and Meth. A, 346, 329 (1994).

[59] T. McKay, A Search for 100 Te V Gamma Ray Point Sources, unpublished Ph.D. Thesis, University of Chicago, 1992.

[60] W. T. Welford and R. Winston, High Collection Non-imaging Optics, Academic Press, San Diego, 1989.

[61] R. M. Baltrusaitis et al., Nucl. Instr. and Meth. A 240, 410 (1985).

[62] C. W. Allen, Astrophysical Quantities, Third Edition, Athlone Press, London, 1973.

[63] Philips Photonics product manual, Photomultiplier Tubes: Principles and Ap- plications, Brive, France, 1994. ~ [64] C. Pryke and T. Kutter, "Measurements of R1408 photomultiplier performance," Pierre Auger project technical note GAP-96-041, FNAL, 1996.

[65] R. Rhodes, Dark Sun: the Making of the Hydrogen Bomb, Simon & Schuster, New York, 1995.

[66] D. Heck et al., "CORSIKA: A Monte Carlo Code to Simulate Extensive Air Showers," technical report FZKA 6019, Institut fiir Kernphysik, Forschungs- zentrum Karlsruhe, 1998.

[67] J. Knapp and D. Heck, "Extensive Air Shower Simulation with CORSIKA: A User's Guide (Version 5.20),'' Institut fiir Kernphysik, Forschungszentrum Karlsruhe, 1997.

[69] G. Schatz et al., Nucl. Phys. B Proc. Suppl., 60, 151 (1998).

[70] A. M. Hillas, Proc. 19th Int. Cosmic Ray Conj., La Jolla, l, 155 (1985).

[71] N. N. Kalmykov, S. S. Ostapchenko, and A. I. Pavlov, Bull. Russ. Acad. Sci. (Physics), 58, 1966 (1994).

[72] K. Werner, Phys. Reports, 232, 87 (1993).

[73] R. S. Fletcher et al., Phys. Rev. D, 50, 5710 (1994). 181

[74] T. Antoni et al., J. Phys. G, 25, 2161 (1999).

[75] M. Risse et al., Proc. 26th Int. Cosmic Ray Conf., Salt Lake City, HE 1.3.02, 1999.

[76] F. James, "HBOOK Reference Manual, Version 4.24," CERN Program Library Long Writeup Y250, Geneva, 1995.

[77] K. Bernlohr, "Impact of atmospheric parameters on the atmospheric Cher- enkov technique," submitted to Astroparticle Phys. (1999). Preprint astro- ph/9908093.

[78] R. Protheroe and K. E. Turver, Nuovo Cimento, 51A, 277 (1979).

[79] F. James, "MINUIT Reference Manual," CERN Program Library Long Writeup D506, Geneva, 1994.

[80] M. A. K. Glasmacher, et al., Astroparticle Phys., 10, 291 (1999).

[81] M. Nagano et al., J. Phys. G, 10, 1295 (1984).

[82] M. Amenomori et al., Astrophys. J., 461, 408 (1996).

[83] M. L. Cherry et al., Proc. 25th Int. Cosmic Ray Conj., Durban, 4, 1 (1997).

[84] D. Muller et al., Astrophys. J., 374, 356 (1991).

[85] C. Pryke, "Shower Model Comparison I: Longitudinal Profile," Pierre Auger project technical note GAP-98-035, FNAL, 1998.

[86] S. P. Swordy, Proc. 24th Int. Cosmic Ray Conj., Rome, ,2 697 (1995).

[87] J. P. Wefel and T. L. Wilson, Proc. 26th Int. Cosmic Ray Conj., Salt Lake City, ,5 84 (1999).

[88] J. Lindsey, cited in [66] by private communication.