xtzmd _ £. 1 “T I - (a 7A “it (3 \o LIBRARY MiChigan State University This is to certify that the thesis entitled A MONTE CARLO STUDY OF DIFFERENT DETECTOR GEOMETRIES FOR HAWC presented by IRIS GEBAUER has been accepted towards fulfillment of the requirements for the MS. degree in Physics and Astronomy Ma'or Professor’s Signature ”/29: 2005"” Date U MSU is an Affirmative Action/Equal Opportunity Institution PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 2/05 www.m-ms A MONTE CARLO STUDY OF DIFFERENT DETECTOR GEOMETRIES FOR HAWC By Iris Gebauer A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department. of Physics and Astronomy 2005 '10,..: if- ABSTRACT A MONTE CARLO STUDY OF DIFFERENT DETECTOR GEOMETRIES FOR HAWC By Iris Gebauer Compared to other parts of astronomy the study of the universe at energies above 100GeV is a relatively new field. Pointed instruments presently achieve the highest sensitivities. They have detected gamma-rays from at least 10 sources, but they are only able to monitor a relatively small fraction of the sky. The detection of exciting phenomena such as Gamma-ray Bursts (GRBS) requires a highly sensitive detector capable of continuously monitoring the entire overhead sky. Such an instrument could make an unbiased study of the entire field of view. With sufficient sensitivity it could detect short transients (~ 15 minutes) and study the time structure of Active galac- tic nuclei (AGN) flares at energies unattainable to space-based instruments. This thesis describes the design and performance of the next generation water Cherenkov detector HAWC (High Altitude Water Cherenkov). Focussing on the performance in background-rejection and sensitivity to point sources. two possible detector geome- tries, different in the way the photomultipliers (PMTs) are separated from each other, are compared. ACKNOWLEDGEMENTS I would like to thank Brenda Dingus for mentoring and assisting me during my time in Los Alamos, as well as Gus Sinnis and Curtis Lansdell for their constant input and support. Aous Abdo deserves special thanks for keeping me warm in Lansing. I also would like to acknowledge a scholarship and further financial support of the German National Academic Foundation (Studienstiftung des deutschen Volkes). iii TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES Introduction 1.1 Motivation for '7—Ray Astronomy .................... 1.2 Cosmic Rays ................................ 1.3 Hadronic and Electromagnetic Air Showers ............... 1.4 Detection Technique ........................... Air Shower Simulations vi vii abut—‘1‘ 14 2.1 The Propagation of Air Showers through the Atmosphere with CORSIKA 14 2.2 The Detector Simulation with Geant .................. 2.2.1 The HAWC-detector ....................... 2.2.2 The curtained geometry: GeomO4 . . . .- ............ 2.2.3 The baffled geometry: Geom05 ................. 2.2.4 Data sample ............................ Binning Analysis Angular Reconstruction with HAWC 4.1 Angular Resolution in HAWC ...................... Gamma / hadron-Separation 5.1 Background Rejection in Milagro .................... 5.1.1 Compactness parameter ..................... 5.1.2 AX 4 ................................ 5.2 Background Rejection in HAWC ..................... 5.2.1 The new Compactness-parameter ................ 5.2.2 AX 3 ................................ 5.2.3 Comparison and energy-spectrum ................ Effective area iv 15 15 16 16 17 18 25 25 28 28 28 30 31 32 36 42 44 7 Sensitivity to point sources 7.1 Crab-like sources ............................. 7.2 Gamma-Ray-Bursts ............................ 8 Conclusion References 50 52 61 70 72 LIST OF TABLES Gamma-ray shower parameters as a function of energy. The variables are explained in the text. Values taken from [30]. ........... 9 Angular resolution and optimal bin size of the two geometries . . . . 26 The most successful cuts in both geometries ............... 42 vi 10 11 12 13 14 LIST OF FIGURES The spectrum of cosmic rays. Taken from [27] .............. The simulated development of a 1 PeV air-shower. Only a small frac- tion of particles is shown. The right hand plot shows the evolution of the total particle number with depth. The lower figure shows the distribution of particles at ground level. Taken from [23]. ...... A) The ‘toy model’ picture of a cascade. B) A more realistic model of an electromagnetic cascade assuming AW, z gAbrem, Taken from [23]. Development of the cascades of three different primaries through the atmospherezgreen: muons, red: leptons, black: hadronsTaken from [27]. 11 Top: The fraction of gammas kept after a cut in bin size for different cuts in N fit for geom04. Bottom: The corresponding Q-factors. Top: The fraction of gammas kept after a cut in bin size for different cuts in N fit for geomOS. Bottom: The corresponding Q-factors. Maximum relative Q-factor (Q-factor corresponding to the optimal bin size) versus N fit. ............................. Normalized Aangze distribution for both geometries. .......... Three gamma-ray induced events (left) and proton induced events (right) as observed in geom04. The PMTs in top- and bottom-layer are superimposed: bottom-layer: color-scale, top-layer: black boxes. The size of the boxes and the color corresponds to the number of PBS in the PMT ................................. The normalized event distribution for both geometries in parameter space: a) for geom04 and both primaries, b) for geom05 and both primaries, c) for gamma-MC and both geometries, d) for proton-MC and both geometries ............................ The efficiency distribution for both geometries in parameter-space: a.) for geom04 and both primaries, b) for geom05 and both primaries, c) for gamma-MC and both geometries, d) for proton-MC and both geometries ................................. Q-factor versus CH for both geometries ........ . ......... The normalized event distribution for both geometries in parameter- space, z-axis is logarithmic: a.) y-MC for geomO4, b) '7-MC for geomOS, c) proton-MC for geomO4, d) proton-MC for geom05. ......... The efficiency-distribution for both geometries in parameter—space: a) 7-MC for geomO4, b) '7-MC for geomO5, c) proton-MC for geomO4, (l) proton-MC for geomOS ........................... vii 21 22 26 29 33 34 35 37 38 16 17 18 19 20 21 22 23 24 26 27 28 29 30 31 The Q-factor distribution for both geometries in parameter space: a) side view for geomO4. b) side view for geomOS. c) top view for geomO4, d) top view for geomOS. ......................... Q-factor Versus AX 3 for both geometries ................. The triggered energy-spectrum without and with cuts, full lines: geomO4, dotted lines: geom05. No y/p—separation—cuts means that only cuts in bin size and N fit are applied. For each geometry the spectra are nor: malized with respect to the case of no ’y/p-separation-cuts. ...... Effective area for both geometries and the most successful cuts given in table 1. geom04: full lines, geom05: dotted lines. .......... ’7 efficiency for the most successful 7/p—separation cuts ......... Effective area versus zenith angle. Only cuts in bin size and N fit are applied. .................................. A view into the center of the Crab-Nebula (F igure:STScI /NASA). Number of events expected from the Crab—Nebula per day and decli- nation for HAWC-MC. a) geomO4, b) geom05. ............. The scaling-factor k. ........................... Sensitivity of both geometries for a Crab-like source versus declination for the most successful cuts in AX3, 0X2 and CH ............ Sensitivity of both geometries for a source similar to the Crab-nebula versus declination for different spectral indices .............. Sensitivity of both geometries for a Crab-like source versus declination for different cutoff-energies. Geom04: full lines, geom05: dotted lines. Time duration distribution as recorded by BATSE. The duration used here is T90 which is the interval time between the points in which the GRB has emitted 5% and 95% of its energy. Taken from [7]. ..... Complete spectrum of GRB990123 as measured by BATSE, OSSE, COMPTEL and EGRET on CGRO. Taken from [11]. ........ Distribution of the arrival directions of the 2074 GRBs detected by BATSE in galactic coordinates. Taken from [7]. ............ Flux required for a 50—observation of a 603 GRB versus cutoff-energy for different zenith-angle ranges for both HAWC-geometries. ..... Flux required for a 50-observation of a 60 second GRB for both ge- ometries: blue: geomO4, red: ge011105. Summary of detected GRBs provided by Gus Sinnis, localizing instruments taken from [20]. . . . . Images in this thesis are presented in color. viii 39 41 43 45 46 47 51 55 56 57 58 60 63 64 67 68 1 Introduction 1.1 Motivation for y-Ray Astronomy Before experiments could detect gamma rays emitted by cosmic sources, it was known that the universe should be producing these photons. Work by Feenberg and Pri- makoff in 1948, Hayakawa and Hutchinson in 1952, and, especially, Morrison in 1958 had led to the belief that a number of different processes would result in gamma- ray emission. These processes included cosmic ray interactions with interstellar gas, supernova explosions, and interactions of energetic electrons with magnetic fields. Balloon-borne hard X-ray and gamma-ray imaging telescopes provided the first im- ages of the sky in the energy range 20-1000 keV. They discovered black hole candidate sources in the galactic center region, first imaged the cobalt-decay gamma-rays from the supernova SN 1987A, and provided the first capability to localize high—energy sources for comparison with more detailed lower-energy X-ray observations. Significant gamma-ray emission from our galaxy was first detected in 1967 by the gamma-ray detector aboard the OSO-3 satellite. It detected 621 events attributable to cosmic gamma-rays. The satellites SAS-2 (1972) and the COS-B (1975-1982) con- firmed earlier findings of a galactic gamma-ray background, produced the first detailed map of the sky at gamma-ray wavelengths, and detected a number of point sources. However. the poor resolution of the instruments made it impossible to'identify most of these point sources with known objects. Perhaps the most spectacular discovery in gamma-ray astronomy came in the late 19605 and early 19708 from a constellation of defense satellites which were put into orbit for a completely different reason. Detectors on board the Vela satellite series, designed to detect flashes of gamma-rays from nuclear bomb blasts, began to record bursts of gamma-rays —— not from the vicinity of the Earth, but from deep space. Today, these gamma-ray bursts are seen to last for fractions of a second to minutes. Studied for over 25 years now with instruments on board a variety of satellites and space probes, and ground—based instruments, the sources of these high-energy flashes remain unknown. They appear to be of extragalactic origin, and currently the most likely theory seems to be that at least some of them come from so-called hypernova explosions - supernovas creating black holes rather than neutron stars. T he Swift spacecraft was launched in November, 2004. It is designed to provide rapid location and follow-up for a large sample of gamma-ray bursts. For the most energetic part of the gamma-ray spectrum, ground-based experi- ments are suitable. The Imaging Atmospheric Cherenkov Telescope technique cur- rently achieves the highest sensitivity. The Crab Nebula, a steady source of TeV gamma-rays, was first detected in 1989 by the Whipple Observatory (Az, USA) and later confirmed by seven ground-based telescopes, including the water-Cherenkov— detector Milagro. Modern Cherenkov telescope experiments like H.E.S.S., VERITAS, MAGIC, and CANGAROO 111 can detect the Crab Nebula in a few minutes. The most energetic photons (up to 16 TeV) observed from an extragalactic object origi- nate from the blazar Markarian 501 (Mrk 501). These measurements were done by the High-Energy-Gamma—Ray Astronomy (HEGRA) air Cherenkov telescopes. Gamma—ray astronomy is mostly dominated by the number of photons that can be detected. Larger area detectors and better background suppression are essential for progress in the field (see section 5). The observation of the universe in gamma-rays opens a window to some of the most extreme environments which are invisible to ordinary telescopes. Some specific targets include: Gamma-ray Bursts, Black Holes and Neutron Stars, Supernovae, Pulsars, Diffuse Emission, Active Galaxies and Unidentified Sources. 1.2 Cosmic Rays Figure 1 shows the cosmic ray energy spectrum. Below 10‘6eV the spectrum can be fitted with a. power law with spectral index -2.7, above this value the energy- dependence becomes 13—3-0. The turning-point. known as the knee, has a flux of about 1 particle per square meter and year. A second change in the gradient of the curve occurs at 1019 eV, known as the ankle, where the spectrum becomes less steep once again. Cosmic ray particles are most likely accelerated by diffusive shock acceleration in strong shock fronts of supernova remnants. The model first introduced by Fermi [16] (”2nd order Fermi-acceleration”) has been extended and modified by many authors (see, e.g. [8], [9], [14], [15] and [10]). In these models particles are deflected by moving magnetized clouds. Particles cross the shock front several times and thereby gain energy up to the PeV region. Fermi acceleration at strong shocks leads to a power—law spectrum close to the observed one. However, there must be a limiting energy that can be achieved in this process: when a particle’s energy reaches the value at which its gyro-radius in the magnetic field is greater than the dimensions of the accelerating regions, it will inevitably escape. The presence of the knee in the spectrum could be caused by different effects. First, it could indicate that that two distinct sources are responsible for the accel- eration of particles below and above it. The lower energy part might be described by the supernova acceleration, the origin of the higher energetic part of the spectrum is unknown, although many theories exist. The most accepted of these is acceleration in active galactic nuclei (AGN). Second, energy dependent losses occurring during the propagation through the interstellar medium could be responsible for the change of the spectral index. Pro- cesses like spallation, leakage from he galaxy, nuclear decay, ionization losses and, for low energies. solar modulation can modify the energy spectrum during the diffuse Grog m mac—25 hon 3.55— : A: S A: acm ”A: ecu ea: mcfi can mam fifi _____ _____fi_—‘ ______.~_ _::_dd_ _::____ _::_.d L Juddqq_. _________ m w 1.1: I; oh - _ . . l 4 :io o n O I ++++. m a. . _ I 2...... . {.1 9mm— mbh O 8%: «i=8... 3 Semi—Eco o .. 3 nu) ”a a. (an Z (“A33 .18 s Figure 1: The spectrum of cosmic rays. Taken from [27]. propagation of the particles through the galaxy. Third, a change in the elemental composition of the cosmic rays could cause the steepening [4] . Fourth, new interaction characteristics owing to new particle physics at energies 81/2 above 1TeV nucleon.‘l [4]. And fifth, an observational bias related to the change in the experimental tech- niques from direct particle-by—particle balloon and spacecraft experiments below ~ 101’1 eV to indirect ground-based air shower measurements above 1015 eV [4]. Below 1019 eV it is not possible to trace particles back to their sources. even if the arrival direction on earth is known. The trajectories of these particles are completely scrambled by the galactic magnetic field, since, even at these energies, the gyro-radius in the galactic field is smaller than the size of the galaxy. Assuming a magnetic field of 1G and a galactic radius of 50.000Ly the gyro—radius of a proton becomes comparable to the radius of the Milky Way at energies above 1019eV. No phenomenon in the neighborhood of our galaxy can account for cosmic rays with energies up to 1019, yet their sources may not lie much further away, because otherwise the Greisen-Zatsepin-Ku’zmin (GZK)-cutoff needs to be taken into account: Space is filled with the cosmic microwave background (CMB) radiation, a relic of the epoch of recombination when the first hydrogen-atoms formed. There are about 109 of these photons in a cubic meter of space, yet normally a cosmic ray particle will be oblivious to their presence. Things change however when a cosmic ray proton has so much energy that in its own reference frame the CMB photon’s energy is sufficient to cause the A-excitation: + n + 7T+ mpm7r p+’yCMB—+A +X——>{ ,forEp-p-c0302—, p+7r0 q with Ep: energy of the proton in center-of—mass system, p: absolute value of the pro- ton’s momentum in center-of-mass system, 6: angle under which the proton hits the photon, , q: absolute value of the photons momentum in center—of—mass system, mp: proton-mass, m“: pion-mass. The universe becomes opaque for cosmic-ray protons when this resonant reaction with comic microwave background radiation photons becomes energetically allowed. The excited state then decays by the two channels shown. Naturally the resulting particles will have to share the energy, thus none will have an energy as great as the original one. This is called the GZK cutoff. The reaction above is possible when the proton’s energy is greater than 5 - 1019 eV. Such a proton is expected to be reduced to an energy below the cutoff over a distance of 50 Mpc. Note that cosmic ray nuclei will be broken up by interactions with CMB at lower energies. Particles with energies above the cutoff have been detected none the less. despite the lack of known sources within range. At low energies the cosmic ray spectrum mainly consists of protons and light ele- ments. The fraction of heavier elements increases with increasing energy significantly. At around 100GeV protons make up about 56% of the cosmic rays, helium 24% and heavier elements 20%. At 1PeV the spectrum consists of about 15% protons, 33% helium and 52% heavier elements [26]. 1.3 Hadronic and Electromagnetic Air Showers When cosmic rays arrive at earth, they interact in the atmosphere, provided that the cosmic ray-particles are not deflected or captured by the Earth’s magnetic field. The latter occurs if the energy of a charged particle exceeds ~ 10 GeV. A cosmic ray particle will interact with a nucleus in the atmosphere (primarily oxygen and nitrogen). This is referred to as the primary interaction and typically occurs at an altitude of about 15-20km. The primary interaction causes both the nucleus and the cosmic ray particle to fragment into a number of hadrons such as kaons, pions, neutrons and protons and light nuclei as well as a number of more exotic: particles. Due to the conservation of momentum these particles continue along the path of the original particle, with a small spread in the transverse direction. Some will fragment further and others will decay. Both charged pions and kaons decay into a. muon and a neutrino, while neutral pions decay into a pair of photons. The photons can initiate electromagnetic cascades: they produce electron-positron pairs, which in turn can produce more photons through bremsstrahlung. The process continues as long as there is enough energy to create more particles. Figure 2 shows a simulation of a hadronic cascade. Photon-initiated cascades, on the other hand, are completely electromagnetic, thus showing a significantly different appearance of the shower front at sea level. For a gamma ray of energy larger than 10 MeV the dominant interaction as it enters the atmosphere is pair production. On the average this will occur after it traverses one radiation length of atmosphere, i. e. at an altitude of 29km. The resulting electron positron pair will share the energy of the primary gamma ray and will be emitted in forward direction [17]. After another radiation length these secondary particles may also pair produce (see figure 3). On the average the number of particles doubles after each radiation length, leading to an average energy of 27”} per particle in the Nth generation, with E: the energy of the primary (0th generation). m The angle of emission in all these processes will be cc 7:55 rad, where E is the energy of the electron and me is the rest mass of the electron [30]. Consequently the electromagnetic cascade will be strongly concentrated around the shower core. This process continues until the ionization energy losses and radiation energy losses are equal. At this point the cascade reaches the ’shower maximum’. Pion —— Muon — Electron —7 Panlcle Density at Ground I 3000 I 1200 I 450 I 170 I I I 9 partldestmz Figure 2: The simulated development of a 1 PeV air-shower. Only a. small fraction of particles is shown. The right hand plot shows the evolution of the total particle number with depth. The lower figure shows the distribution of particles at ground level. Taken from [23]. A) E B) l"; ,1”- f“\ l '\ N 8"! e? A. f *"K/ ] ,/ \e" / s. / “ E92 7.\ x 1x, ’6 I": ’ / \ / ‘2- ./<' ” e7": I, ". ‘7'““5kw-r’ /' .x (>\ E134 ,r' .‘. ’ I, Y, .\ [1. \\_ \e [y I 316' x .' \h i a I /’.\~ .‘I‘\ .I/gx a". "1 E18 e\ 'I 18‘” x ./ x. x \ /~ ‘1 I“ r /e- '.'l‘ r'e‘r Figure 3: A) The 'toy model" picture of a cascade. B) A more realistic model of an electromagnetic cascade assuming Ami, z gigem, Taken from [23]. From here on the number of particles gradually decreases and the cascade dies away. The altitude at which the shower maximum occurs depends on the energy of the primary particle. The observation altitude therefore changes the observed energy—range. Energy E7 X,,,a,(g - 6771—2) hmax(km) NW”, N81 NW 10 GeV 175 12.8 1.6 x 101 4 x 10-4 2 x 10-2 100 GeV 261 10.3 1.3 x 102 4 x 10-2 1.4 x 100 1 TeV 346 8.4 1.1 x 103 3 x 100 6 x 101 10 TeV 431 6.8 1.0 x 104 1.3 x 102 1.7 x 103 100 TeV 517 5.5 9.3 x 104 4.5 x 103 3.6 x 104 Table 1: Gamma-ray shower parameters as a function of energy. explained in the text. Values taken from [30]. The variables are Table 1 shows the values N,,,,,,.=maximum number of electrons, X muzshower thickness traversed in g - (rm-2. h,,,,u=elevation of shower maximum, Nslznumber of surviving particles at sea level and NW: number of surviving particles at mountain altitude (2300111) for typical gamma-ray primaries. The development of an electro- magnetic cascade in comparison with a hadronic cascade is shown in figure 4. The particles in an air shower travel through the atmosphere at a velocity close to the speed of light. At a given moment or altitude the shower front can be visualized as a segment of a sphere (a disk with curvature), while the density of the particles in the center of the disk (shower core) is far greater than at large radii. As the shower propagates through the atmosphere the shower front expands. At ground level an electromagnetic shower is composed primarily of electrons, positrons and photons. The total number of particles in a gamma-ray-induced shower is approximately equal to the the energy of the primary one, expressed in GeV [30]. A 1019 eV shower involves on the order of 10 billion particles. These particles will be spread over an area that for the largest extensive air showers is tens of square-kilometers. Over the energy range of interest the charged cosmic radiation is 103 — 104 times as numerous as the diffuse gamma-ray background. This means that, in the field of view of a simple telescope whose solid angle is optimized for gamma ray detection, the background of cosmic: ray events is 103 times as numerous as the strongest steady gamma-ray source thus far detected. The arrival directions of the charged cosmic rays are isotropic, because of interstellar magnetic fields, therefore a discrete gamma-ray-source can only be de- tected as an anisotropy in an otherwise isotropic distribution of air showers. In order to detect a gamma-ray source in this way, it would have to be very strong (a few per- cent of the cosmic radiation). Fortunately there are a number of factors concerning the properties of hadronic showers and purely electromagnetic cascades that enable us to differentiate between hadronic and electromagnetic cascades and make the ground based study of cosmic sources of VHE gamma rays with air- and water-Cherenkov telescopes possible. The electromagnetic cascade consists almost entirely of electrons, positrons and photons. The hadronic cascade is initiated by a charged ion and the core of the cascade consists of the products of hadronic interactions. These feed lesser 10 .33 fl ' i l]. 35 - ‘\‘ i ll) 1" r « ll‘l\\\l “ '1. {l‘\\\‘ : 5* [I < °35 " 3 35 . 35 3 35 ' 3‘llill'35 5 .5 1 (km) Figure 4: Development of the cascades of three different primaries through the atmo- spherezgreen: muons, red: leptons, black: hadrons.Taken from [27]. 11 electromagnetic cascades whose products are largely responsible for the emission of Cherenkov light. Because a greater proportion of the energy in an electromagnetic cas- cade goes into particles that emit Cherenkov light, the typical Cherenkov light yield is two to three times that of a primary cosmic ray of the same energy. The hadron interactions in the core emit their secondary products at wider angles of emission than their electromagnetic counterparts, so that the hadronic cascade is broader and more scattered. The resulting Cherenkov light distribution in the focal plane of a detector is broader than for a gamma ray initiated air-shower and provides a simple method differentiating between the two. Some of the secondary particles emitted from the core are penetrating particles which can reach ground level. These, as well as the larger fluctuations in the development of the hadron shower, have the effect of increasing the fluctuations in the Cherenkov shower image. Cosmic electrons also produce electromagnetic cascades. They constitute a small, but virtually irreducible, background. The background due to cosmic electrons is 100-1000 times smaller than the background due to protons. 1.4 Detection Technique The Milagro observatory was the first water Cherenkov detector used for the detection of extensive air showers. In addition to the atmosphere the water acts as a large calorimeter which, because of its higher refractive index compared to air, lowers the threshold energy and raises the photon yield and the Cherenkov angle significantly. At ground level the diffraction index in air is n. = 1.00029 and 6mm. is 1.30. The threshold energy for electrons is 21MeV and the light yield in the visible range is about 30 photons 17271. In water, where n = 1.33, 6mm. is about 410 and the threshold energy for electrons is lowered to 260 keV, the Cherenkov photon yield is about 2500 l photons m— , an increase by a factor of more than 80 compared to air [30]. Unlike 12 pointed instruments, an extensive air shower array (EAS) can monitor nearly the complete overhead sky continuously. Since it detects particles that penetrate to the ground level from each direction in the overhead sky it has a field of view that nearly covers the entire overhead sky. The observation of the Crab nebula and the active galaxies Mrk 421 and Mrk 501 by the first-generation-experiment Milagro proved, that the technique is sufficient to detect sources [6] and the influence and importance of high altitude has been demonstrated by the Tibet group [3]. A natural next step is the combination of both these properties: the all—sky and high-duty factor capabilities of Milagro, a lower energy threshold (due to high alti- tude) and an increased sensitivity (due to large area). As formulated in [29] reasonable design goals for such an experiment are: -Ability to detect gamma-ray bursts to a red-shift of 1.0 «Ability to detect AGN to a red-shift beyond 0.3 -Ability to resolve AGN flare at the intensities and durations observed by the current generation of ACTs -Ability to detect the Crab nebula in a single transit This thesis describes two slightly different designs for a next generation all-sky VHE gamma-ray telescope, the HAWC (High Altitude Water Cherenkov) array, that sat- isfies the above requirements. The required sensitivity demands a large area detector (~ 105 m2). Because of the desired low energy threshold the detector needs to be placed at extreme altitude (above 4500m). At present two different sites for the HAWC-detector are discussed: A site at 4572 m in Yanbajing,Tibet and a site at 5200m in the Atacama desert in Chile. In this thesis only the Chile-altitude is dis- cussed. For the simulations Milagro's latitude of about 35" 5’ north is used in order to enable comparison (see e.g section 7.1). 13 2 Air Shower Simulations The analysis presented in this thesis is entirely based on Monte-Carlo (MC)-simulations. Two different programs are used: The program CORSIKA for the propagation of the cascade through the atmosphere and the program Geant for the propagation of the shower particles through the detector. 2. 1 The Propagation of Air Showers through the Atmosphere with CORSIKA CORSIKA (COsmic Ray SImulations for KAskade) is a program for simulation of extensive air showers initiated by high energy cosmic ray particles [21]. Possible pri- maries are protons, light nuclei up to iron, photons and other particles. For this analysis only photons and protons are considered as primaries. Since protons make up a large fraction of the cosmic rays this is a reasonable estimate of the cosmic ray background. Starting with the first interaction the particles are tracked through the atmosphere until they undergo reactions with the air nuclei or decay. The hadronic interactions at high energies can be described by five different interaction models. For this Monte Carlo simulation the VENUS option has been used, which is based on the Gribov-Regge-theory. In order to obtain enough statistics for a reasonable analysis millions of air showers have been thrown with the following parameters for proton and gamma primaries: Energy-spectrum: Energy-Range: 10GeV to 100TeV Spectral index: -2.7 for protons and -2.4 for photons 14 Geometry of thrown range: Thrown azimuth-anglerange: 0° — 3600 Thrown zenith—angle-range: 0° — 45" Observation-level: 5200111 2.2 The Detector Simulation with Geant The program Geant [18] is used in order to simulate the penetration of the shower particles through pond-cover and water. Input for Geant are the CORSIKA showers. The core positions are distributed randomly over a circle with radius 1km centered on the pond. The output of Geant includes, for each PMT that was hit by at least one photon, the number of photoelectrons (PBS) and their arrival times, it is therefore very similar to the calibrated data format of Milagro. 2.2. 1 The HAWC-detector The HAWC—detector consists of 11250 photomultiplier tubes (PMTs) arranged in a grid of 75x75 PMTs in a top- and 75x75 PMTs in a bottom—layer. With a horizontal PMT-spacing of 4m, a height of 1.5m of the bottom-layer above the ground, a distance of 4m between top- and bottom-layer and 2m of covering water above the top-layer the pond has a volume of 675,000 m3, with a length and width of 300m and a depth of 7.5 111. As in the Milagro detector, tubes are planned to be aligned at sand filled PVC-tubes giving each tube only a small variation in height and horizontal direction. In order to prevent scattering of Cherenkov light by particles in the water, the water in the pond needs to be constantly cleaned by filters. The concrete on the ground and side-walls of the pond is modelled as a metal with 5% reflectivity, the pond cover is also assumed to have 5% reflectivity. 2.2.2 The curtained geometry: Geom04 In this geometry half-height curtains, consisting of a material with 5% reflectivity, surrounding each PMT are added to the detector design. The curtains go from shortly above the top layer to the center of the pond. The aim is to prevent photons emitted from one particle from reaching two different PMTs thus causing a “shifted” image of the particle. In addition photons can be reflected from the PMT-case or the glass surface, the concrete floor and walls or the cover. Compared to baffles (see section 2.2.3) curtains are expected to lower the number of triggered events. The PMTs are modelled by a volume with a diameter of 20.32cm and a height of 35cm. The glass is assumed to be 0.20m thick with a diameter of 16.76cm. The performance of curtained PMTs will be tested at the Milagro detector prob- ably in fall 2005. 2.2.3 The baffled geometry: Geom05 In this detector setup cone—shaped baffles of 16.54cm height and a radius of 26.67cm at the top and 8.38cm at the bottom are added to each PMT. The material of the baffles is assumed to have an absorbtion probability of 95% on the outside and 2% on the inside. Similarly to the curtains, the main purpose of this adjustment is the prevention of multiple PMT hits and the detection of photons that have been reflected at other PMTs or concrete and cover. Baffles similar to the ones described above are currently in use in the Milagro-detector. 16 2.2.4 Data sample With a trigger—condition of at least 55 PMTs hit in HAWC’s top layer and at least 20 PMTs participating in the fit, the 4,294,285 thrown gamma—ray initiated showers led to 9300 triggered events and the 13,118,625 thrown proton-initiated showers led to 3,667 triggered events for geomO4. For geom05 2,387,719 gamma-ray initiated show- ers where thrown, leading to 12,933 triggered events and 4,331,657 proton-initiated showers where thrown, leading to 4,277 triggered events. 17 3 Binning Analysis Due to the high number of cosmic ray events, the analysis for HAWC consists of looking for an excess of gamma-ray events above the hadronic background. For a point source the presence of the large background and the finite angular resolution of the HAWC detector (028" for geom04 and 0.350 for geom05, see section 4.1) makes it necessary to subdivide the data into bins. An infinitely large bin would on the one hand include the excess from other possible point sources as well and on the other hand the signal would disappear in the large background. Without any background an infinitely large bin would keep all the signal events. An optimal bin size that, when centered directly on a point source, keeps as little background events and as much signal events from the source as possible, needs to be determined. The angular resolution of HAWC is a function of the number of tubes participating in the fit, N fit. A higher N fit‘cut would throw away more poorly reconstructed events and therefore improve the angular resolution. Since most of the poorly reconstructed events would not have fallen into the signal bin an N fit‘Cllt leads to an increase in sensitivity as an N fit'Cut reduces the number of background events. The angular resolution in Milagro is usually quantified by two parameters out of which one can be considered as a theoretical” parameter which only applies to MC—data. This parameter, Aangle, is the space angle difference between the true direction of the shower front and the fitted direction of the shower front: Aangle : the '_ int- (1) The second parameter, Ago, does not depend on the true direction of the shower front. This parameter compares the the fitted directions of the shower front that are provided by two different parts of the detector: the detector is subdivided into a set of squares (each square centered around a PMT like the white and black squares of a 18 chessboard), of which the white fraction is used for one fit and the black fraction is used for another fit. Ago is now the difference between the fit directions from from the two subset-fits. Since systematic errors are expected to affect both fits in the same way the difference between the two fits, A30. should be widely independent of the systematics. In the absence of systematic errors Ago is expected to be about twice the angular resolution of the detector [2]. Because the angular resolution depends on the number of tubes participating in the fit, the optimal bins size and N {it cannot be determined independently. The background spectrum can be assumed to be isotropic. so that the effect of a change in bin size is purely geometric: 5% = 523;, for a circular bin, where p,- is the number of protons in a bin of size n. For this analysis only circular bins are used. Square bins are easier to implement and only slightly inferior [2]. A decrease in bin size leads to a gain in sensitivity, since more background events are excluded until a point is reached where too many signal events are thrown out. The improvement in sensitivity is given by the relative Q-factor, defined as: Q = _f_“£“’_ 4 (2) V (background with c,- is the fraction of events of type i kept after a. certain cut (or set of cuts). This definition leads to n,,,-,,,,a,(cuts) "bgf’refl Q = : ~ (3) rzbg(cut.s) ”Signal(ref) where n,(cut.s) is the number of events of type i kept after a certain set of cuts and n.,-(re f ) is the number of events of type i kept after a set of reference cuts. In the case of ’7/proton-separation (see section 5) this is the total number of triggerrxl events that pass an N [it cut. 19 In this case, where cuts in N f.“ and 7' are applied the Q-factor can be written as _ n'signal(Nfit~ 7.) . 711,9(7'8f) __ nsignal(Nfitw 7’) . C n'bg(1Vfit~ T‘) n‘signal(ref) . nbg(Nf,t, 7") (4) where c is a constant factor that only depends on the reference point. The number 72.,(NN, r) is the number of events of type i which have at least N M tubes participating in the fit and Amyle < r. The assumption of a flat background immediately leads to "by = "ngNfitl ' 723 (5) where ngg(Nf,-t) is the number of background events in a bin with radius 1 for a given N fit cut. Substituting eq. 5 into eq. 4 leads to: -: nsignaI(Nfitsr) . C. (6) Wharf/Vial ° 7" The absolute value of Q is arbitrary, it depends on the set of reference cuts. In order to find the optimal bin size only the position of the maximum of the Q-factor distribution is of interest. Figures 5 and 6 show the relative Q-factors versus bin radius for different N [it cuts. The optimal bin sizes r=0.45 for geom04 and r=0.55 for geomO5 and N fit = 20 have been chosen as reference points. A higher N fit cut leads to a smaller bin radius thus resulting in an improvement in angular resolution. In the range of 0 S N fit S 50, the variations of the relative Q-factor and of the fraction of photons kept are small, the value 20 was chosen for the analysis. This choice on the one hand eliminates the events with the poorest reconstruction, but on the other hand keeps a reasonable fraction of photons. h’laximization of the Q-factor leads to an optimal bin size of 20 Fraction of Photons versus Bin Size, geom04 * 0.9:— ; : —— >0 2 osi Nm :9 ' t 5: 0.7"— ——Nfit>20 0- .; ‘5 I 0.6— : n— 2 : _ >50 3 0.5:— NI" “ 0.4g- _Nfit>80 0.35— 03:— ———Nfit>100 0.1:— o—llllllllllLllLlllllllllllJllAJlllllllJlllJ 0 0.2 0.4 0.6 0.8 1 1 .2 1 .4 1 .6 1.8 2 Din Radius in degrees Relative Q-Factor versus Bin Size, geom04 I 3 : g 15— ;A\ _ Nfit>0 0.9:— 3 E \. _ Nm>20 § 0.3:— ‘ C l- 0.7 5— _ Nfit>50 06;— —~..>eo 0.5L “‘ E - Nfi3100 0.4:— 0.3,§[- — Nfit>150 FillljlllllllLALlLlnllllllll'llllllllllllLJ—L J 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.0 2 Bin Radius in degrees Figure 5: Top: The fraction of gammas kept after a cut in bin size for different cuts in N fit for geom04. Bottom: The corresponding Q-factors. 21 [ Fraction of Photons versus Bin Size, m05 ‘5- : § : 0.7:- ; 5 _ N,,,>2o .. 0.6:- 0 : c I— 2 0.55— — Nflt>50 g : u. 0.4:- 0.3 :— 0.2 E— _ Nfit>100 o:lllllllllllllllllllllllllllllllllllllLllll 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Bin Radius In degrees Relative Q-Factor versus Bin Size, eom05 3 : g 1.2 5. _ Nfit>0 IL : <5 1.1 :— 3 1 5 ‘ _ Nfit>20 0.8 E- 5 — Nfit>80 0'7 :— \ 0.6 :— f E - - Nfit>1 00 0.5 : 0.4 : — Nfit>1 5O ' ELI...1...I...I...1...I...I...1...I.111... 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Bin Radius in degrees Figure 6: Top: The fraction of gammas kept after a cut. in bin size for different cuts in N fit for geomO5. Bottom: The corresponding Q-factors. Maximum Q-factor versus Mm] in d Ls "I Relative G-iactor at optimal bin size 1 .05 Figure 7: Maximum relative Q-factor (Q-factor corresponding to the optimal bin size) versus N f... 23 0.45 for geomO4 and 0.55 for geomO5. These values are. expected to optimize the significance of a point source for the two geometries. As one can see from figure 5 and 6 these values keep about 44% of the signal events while throwing away about 18% of the background for geomO4 and 35% of the signal events while throwing away about 19% of the background for geom05. The difference in the detector geometries leads to a significantly different depen- dence of the maximum relative Q-factor on N fit cuts. Figure 7 shows the maximum relative Q-factor versus N fit- For geomO4 the maximum relative Q-factor is maximal for an N fit out of 80. Higher and lower values of N fit lead to lower Q—factors. For geom05 the maximum relative Q-factor rises with rising N fit cut. Figure 7 suggests an N [a cut of 80 for geomO4 and 150 or higher for geom05. As discussed before such high N fit cuts reduce the number of photons kept significantly. 24 4 Angular Reconstruction with HAWC The relative arrival times at which the different PMTs in the detector are struck are used to reconstruct the direction of the incident shower. The fir includes a correction for curvature of the shower front and a so-called sampling-correction which takes into account that the shower front has a finite thickness the incident direction of the shower is determined by a. weighted least squares fit. It should be noted that the curvature corrections used in this analysis are the curvature corrections that have been optimized for the Milagro site, i.e. for Milagro’s altitude and the size of the detector. Due to the higher altitude of the HAWC-detector and due to the larger area the detector covers, a different curvature of the shower front can be expected: Assuming the shower to cover a cone-shaped volume as it propagates through the atmosphere, the higher altitude and the larger detector cause HAWC to ”see” a larger fraction of the shower in a different state of development, thus possibly leading to a different curvature. 4.1 Angular Resolution in HAWC Under the assumption of a flat background spectrum the angular resolution can be estimated through 1" 1 .58 = a, (7) where r is the optimal bin size [2].Thus, the expected angular resolution for the two geometries is 0.28 degrees for geomO4 and 0.35 degrees for geon105. Table 2 shows the optimal bin size and the resulting angular resolution for the two geometries. Figure 8 shows the 1'1(‘)rmalized Aangle distributions for both geometries. The full lines correspond to an N ,5. cut of 20. For comparison the distributions for an N fit cut of 100 are also shown (dotted lines). For both N [it cuts the distribution for geomO4 I] parameter: geomO4 geom05 I] I] optimal bin size 1‘ 0.45 0.55 [I I] angular resolution a 0.28 0.35 I] Table 2: Angular resolution and optimal bin size of the two geometries Normalized Aan awe-distribution I €0.07: , —— Nm>20, geomO4 > t .5.. gm; g ————-—- Nm>20, geom05 g E 5.3 --------- N,,,>100, geomO4 £0.05}; Nm>100, geom05 0.04 :7, .1 0.03 E'; ' I‘ 0.023? 0.01 :1 f --'. -"'. ........ _ '-3- “.l_-'- -. Pi i l l I l I I I lJ_IJ 11 l 1 11 l LLLLI 1 LiLiI.f.-IILfLIJ1-Lf': 1.2 1.4 1.6 0° 0.2 0.4 0.6 0.8 1 1.8 2 A Figure 8: Normalized Aangle distribution for both geometries. 26 is shifted towards lower values in Amy), compared to geomO5. The fraction of events at high values of Aangle is lower for geomO4 than for geom05, thus leading to a better angular resolution for geomO4. As discussed before (see section 3), a higher N w cut increases the angular resolution by reducing the number of poorly reconstructed events. 27 5 Gamma / hadron-Separation 5.1 Background Rejection in Milagro Hadrons entering the atmosphere interact with nucleons in the air thus producing charged pions which then can decay into muons and neutrinos. Also high-energetic hadronic particles can reach ground—level. Gamma-rays in contrast interact with the nuclei in the air almost purely electromagnetic, leading to an air shower with mostly lower-energetic electrons, positrons and gamma rays. Because of their high mass compared to electrons, muons have great penetrating power, e. g. muons with energies above 1.2GeV (at observation level) reach the bottom layer of Milagro [6]. Muons that reach the bottom layer illuminate a small number of PMTs thus leading to a clustered image. Figure 9 shows six Monte-Carlo events imaged in the top- and bottom layer of HAWC. During the 5 years of operation of the Milagro-Gamma—Ray-Observatory the Milagro—Collaboration has introduced several variables in order to differentiate be- tween gamma and proton induced air showers. The additional wa.ter-calorimeter and the two separate layers of PMTs enable the detector to differentiate between the two possible shower types by looking at the number of muons in the shower. Addi- tional information about the clumpiness and the physical size of the image has been implemented in different variables. 5.1.1 Compactness parameter As described in the beginning of this section hadronic air showers lead to a number of hits in the bottom layer in a relatively confined region with a high number of photoelectrons in the PMTs. Electromagnetic cascades on the other hand lead to a more homogeneous distribution of hits with a lower number of PBS in the tubes. In 28 Proton 80.1 GOV Figure 9: Three gamma-ray induced events (left) and proton induced events (right) as observed in geomO4. The PMTs in top- and bottom-layer are superimposed: bottom- layer: color—scale. top—layer: black boxes. The size of the boxes and the color corre— sponds to the number of PBS in the PMT. 29 2003 the so called compactness parameter was introduced [6], a variable that combines these two properties in order to differentiate between hadronic and electromagnetic cascades. The compactness parameter C is defined as the number of PMTs in the bottom layer with a pulse height above a fixed PE threShold divided by the number of PBS in the PMT with the largest number of PBS in the bottom layer: 7262 C — mzPE’ (8) The compactness parameter summarizes information about the number of tubes in the bottom layer with more than two hits (n62) and the number of PBS in the tube in the bottom layer with the most PEs (mrPE) thus, using the size and the relative inhomogeneity of hadron-initiated events in the bottom layer in order to differentiate between gamma and proton induce air showers. At present a compactness cut of 2.5 in Milagro rejects about 90% of the back- ground while keeping more than 50% of the signal events, leading to a Q-factor of about 1.7. 5.1.2 AX4 The variables AX4 and (IX; have been introduced in 2005 by A.Abdo [1]./1X4 is a new type of variable in two different aspects: On the one hand this variable -unlike C - includes information from top - and bottom-layer and from the outriggers. The outriggers have been added in 2003 to the Milagro detector in order to increase the angular resolution through a better core fit. On the other hand AX 4 is not a ’physical’ variable in the sense that it has not been found by trying to implement the air showers properties in the variable. Instead a set of different variables was examined and their 30 performance in gamma/ hadron separation compared. AX 4 is defined as: Naut ' Nf-it ' Ntop A X4 : (..1‘ PE ’ with Now: the number of outriggers hit, N fit: the number of PMTs entered in the fit, Map: the number of PMTs hit in the top layer and cxPE: the number of PBS in the muon layer tube with the highest number of PBS where a region of 10m around the fitted shower core is excluded from consideration. CX2 is defined as n62 X« = . 1 C 2 chE (0) Two dimensional cuts in AX4 and 0X2 have been applied, leading to Q—factors of 2.5 and more. The application of AX4 and 0X2 to the Crab nebula increased the signal by a factor of 1.4 from 3.650 (with a C-cut) to 5.050. 5.2 Background Rejection in HAWC In the following I will compare the performance of the two parameters C and AX4 in the two HAWC geometries. AX 4 has to be modified for the HAWC detector, because of the different detector geometry. The parameter C does not depend on the actual detector geometry, but in preliminary studies for different HAWC geometries a. slight modification appeared to be more successful. 31 5.2.1 The new Compactness-parameter The compactmess-parameter for HAWC is defined as CH = ——_— (11) with Ntop as the number of struck PMTs in the top layer. Unlike C, this parameter now includes information from top and bottom layer. Figure 10 shows the CH-distribution for gamma and proton induced showers for the two geometries. For both geometries the proton events are mostly confined to a region CH < 10, this region includes more than 90% of the events (see figure 11). The region including 90% of the gamma-events spreads out until OH x 25. Figure 11 shows the fraction of Monte Carlo gamma primaries and Monte Carlo proton primaries with CH-values larger than the x-axis-value. While the normalized gamma- distribution is very similar for both geometries, the proton-distribution spreads out further for geom05. Thus, for a 0;; cut a better background rejection can be expected from geomO4. Figure 11 shows the fraction of Monte Carlo gamma primaries and Monte Carlo proton primaries with CH-values larger than the x-axis-value. Figure 12 shows the Q—factor as a function of CH. For geomO4 with a CH-cut of 8, 65.5% of the signal events are kept while excluding 97.2% of the proton events, thus leading to a Q-factor of 3.344. For geom05 with an CH—cut of 6.1, 79.0% of the signal events are kept while excluding 83.4% of the proton events, thus leading to a Q-factor of 1.94115. 32 I6) Proton- snd Gem-MC (neutralized), gsomtq 0.05 _, Y‘M C °'°‘ — proton-MC 0.03 0.02 0.01 Cram/w“ fifiamma MC (normalized) I — y-MC, geom05 — y-MC, geomO4 0.008 0.008 0.004 we‘re-cps 10152025303640“50 I b)Proton-sndGsmms—IIC(nonnsllzsd).gsomos I 0.035 _ ’Y-MC 0.03 i — proton-MC 0.026 ' - 0061016202630 60 Gnu-NulcxPE B) Proton MC (normalizedi 0.06 a — proton-MC, geomO4 0.04 0.03 _- pfOtOfl-MC, 96011105 0.0 °0 6101520253036404550 ”Nu/“PE Figure 10: The normalized event distribution for both geometries in parameter space: a) for geomO4 and both primaries, b) for geom05 and both primaries, c) for gamma- MC and both geometries, d) for proton-MC and both geometries. b) Proton- and Gamma-MC, geomO4 I Ib) Proton- and Gamma-MC, geomosI 3- 1 § 1 g — y-MC g _ Y'MC $0.8 80. .5 — proton-MC '5 — proton-MC $05 $0. .5 - .2 0.4 O b 051M202535404550 °06101620263035404660 CH-NwlcxPE cu=NwIGXPE lc) Gamma MCI Id) Proton MC] '5‘ 1 '5' 1 .8 .8 3 —7-MC. geom05 3 —— proton-MC, geomO4 C C O C 30.01. 30,. .5 —Y'MC. geomO4 '5 -— proton-MC, geom05 5 . .5 150.6L 130.6 ' 8 . 8 IL IL .° ‘ I .° . I 1 02 02ff 0 0 ....-55- 06101620263036404560 051015202530 CulflhplcxPE 35 40 45 50 CuanlcxPE Figure 11: The efficiency distribution for both geometries in parameter-space: a) for geomO4 and both primaries, b) for geom05 and both primaries, c) for gamma-MC and both geometries, d) for proton-MC and both geometries 34 Q-factor Q-factor versus CH ] — geomO4 , — geom05 9" or 00 flIIIIIIIIIjIIIIIII 2.5 1.5 1L C 0.5:- o—lLlJlllllllLlllllllIlllllllllilll ILUlllllllUiJ 0 5 1015 20253035404550 CH=NmplcxPE Figure 12: Q-factor versus CH for both geometries 35 5.2.2 AX3 The parameter AX4 includes information about the outriggers. The HAWC geome- tries do not include such outriggers, the parameter AX 4‘ therefore cannot be applied to HAWC. However a slight modification which simply excludes the outrigger infor- mation can be used for HAWC. The new parameter AX 3 includes only the variables Ntop, N fit and cxPE, thus keeping AX4’S character as a variable that compares top to bottom layer and weights it with the fit information. AX 3 is defined as _ Ntop ' Nfit AX 3 chE (12) In analogy to Milagro one and two dimensional cuts in AX 3 and CK; can be applied. Figure 13 shows the normalized event-distribution for gamma and proton pri- maries for the two geometries in parameter space. The left side shows geomO4, the right side shows geom05. For both geometries the proton events are confined to a relatively small area in parameter space compared to the 7 events. Note that for both geometries there are a few proton events at relatively high values of 0X2 and AX3. Fig 14 shows the two-dimensional efficiency distribution. A point in this plot shows the fraction of events kept after a cut at the corresponding AX3- and 0X;- values, keeping only events with AX 3 and 0X2 larger than the cut-values. For geomO4 a fraction of less than 10% of the protons is at values AX3 > 2000 and 0X2 > 2, for geom05 a comparable fraction of the protons in confined to the region AX 3 > 3000 and CX2 > 3. Figure 15 shows the two—dimensional Q-factor distribution for both geometries. The upper row shows a side view, the lower row the top view of the distribution. For geomO4 Q-factors of more than 5 are possible, but only for very high values of 36 Gamma MC normsllnd Gamma MC normalized -som05 2:“ ' :._. .._.: - 4 3:” é _: #6- F5 10 § .3”; 15000 10000 10‘ 10'1 10'2 10'2 10*1 10" 10* Figure 13: The normalized event distribution for both geometries in parameter-space, z-axis is logarithmic: a) ’7-MC for geomO4, b) 'y-MC for geom05, c.) proton-MC for geomO4, d) proton-MC for geom05. 37 1 20000 0) 0.0 § 0.0 15000 0.7 0.6 0.5 0.4 0.3 5000 5000 0.2 0.1 ; la 1 2 4 6 8 10 12 14 CX2 S “3% 3 g NU‘UIO‘IOO d d Proton MC gumos 2000 Figure 14: The efficiency-distribution for both geometries in parameter-space: a) 7— MC for geomO4, b) v-MC for geom05, c) proton-MC for geomO4, d) proton—MC for geom05. 38 Ia) Two-dimensional O-fsctor, geom04I fir) Two-dimensional Q-tactor, geomOSI O Q-Fscior E) Two-dimensional Q-factor, 900mg 15000 O-Fsctor Figure 15: The Q-factor distribution for both geometries in parameter space: a) side view for geomO4, b) side view for geom05. c) top view for geomO4, d) top view for geom05. 39 AX3 and (1sz (a cut at AX3 = 8100 and 0X2 2 4.2 e.g. leads to C2255). As mentioned before for very high values of AX3 and CX2 we run out of proton—events, consequently the peaks in the Q—factor-distribution for high values of AX 3 and CX2 have to be considered as statistical fluctuations. Safe values for the Q-factor can be obtained from the plateau-like structure for 0X2 < 3.5. Here the proton statistics should be sufficient. In the area 0 S AX3 S 6000’ and 0 3 (1X2 3 4 Q—factors above 3 are achievable, e.g. a cut in AX3 = 4000 and 0X2 = 4 leads to (223.4, while keeping about 12.3% of the gammas and 0.13% of the protons. The percentage of gammas passing this cut is very low, so that for the following analysis a softer cut at AX3 = 2000 and CX2 = 2.5 is chosen. This cut leads to a Q-factor of 3.2 while keeping 31.8% of the gammas and 1% of the protons. The cut values lie in the middle of a very smooth plateau, so that fluctuations due to the low proton statistic can be excluded. For geom05 there are very few proton-events at AX 3-values around 11000. These events cause the striking peak in the Q-factor distribution for 0X2 < 6 and AX3 x 11000. Excluding the region with AX3 > 8000 and CX2 > 7 the Q-factor distribution is a broad plateau that, with growing AX 3 and 0X2, rises relatively smoothly. Q-factors above 3 can be achieved in the region AX3 > 3000 and 0X2 > 3. In order to not decrease the percentage of gammas kept too much the values AX3 = 4000 and CX2 = 5 are chosen. Such a cut leads to a Q-factor of 4.07 while keeping 25% of the gammas and 0.4% of the protons. As can be seen from figure 16 a. one dimensional cut only in AX3 leads to Q- factors not above 3 for geomO4 and not above 4 for geom05. The peak around AX3 = 11000 for geom05 corresponds to the peak in two-dimensional parameter— space described earlier. In order to exclude statistical variations a one-dimensional cut in AX3 should be softer than 7000, thus leading to Q-factors between two and three for both geometries. 40 Q-factor versus Ax,| — geomO4 — geom05 I I I I Q-factor IIIrI b Futllrlllr Figure 16: Q-factor versus AX 3 for both geometries. 41 5.2.3 Comparison and energy-spectrum Since GRBs and steady sources like the Crab-nebula are some of the most interesting sources for HAWC it is necessary to look at the influence of these cuts on the energy- spectrum. ]IGeometry [I AX3 CX2 Q-factor [I CH Q I] geomO4 I] 2000 2.5 3.2 I] 8 3.3 || geom05 [] 4000 5 4.07 I] 6.1 1.9 Table 3: The most successful cuts in both geometries. Table 3 shows an overview over the most successful cuts in both geometries. Figure 17 shows the fraction of triggered gamma and primaries as a function of energy that are retained after these cuts. A trigger condition of at least 55 tubes in the top layer are struck and at least 20 tubes are participating in the fit is applied. In addition to the cuts in AX3, 0X2 and CH the N w-cut of 20 and the corresponding cuts in Aangle have been applied. Without cuts in AX3, 0X2 and CH geom05 triggers more lower-energetic events compared to geomO4. The median of the distribution for no 7/p—separation-cuts is at about 2102 GeV for geom05 and at about 3-102 GeV for geomO4. For both geometries the cuts in CH have comparable effects: They reduce the number of triggered events in the low-energy part significantly more than in the high energy part, the medians are shifted to about 3- 102 GeV for geom05 and about 4 - 102 GeV for geomO4 after the cuts in CH. With the softer CH-cut for geomO5 the total number of events thrown away is less than for geomO4: about 65.5% of the events are kept after the CH-cut in geomO4 while about 78.4% of the events are kept after the cut in geom05. The comparably hard cuts in AX 3 and 0X2 reduce the number of events passing the cut even more significantly: about 36.6% are kept in geomO4 and only 22.3% in geom05. As for CH the cuts in these two variables reduce the number of lower-energetic events more than the number of higher-energetic events. The medians 42 are shifted to about 4 - 102 GeV for geomO5 and about 5- 102 GeV for geomO4. For very high energies, above 2TeV the cuts in AX3 and 0X2 and the CH-cut perform similarly, i.e. they keep a. similar fraction of events. For energies larger than 10TeV the AX 3 and CXz-cut keeps more events then the CH-‘cut for geomO4. Energy-spectrum for different cute in AX,,,CX2 and c" (y-MC), normalized I 0.35 — geom042no y/p-sep.-cuts : —— geomO4zAX3>2000 81 CX2>2.5 0 3: geomO4:CH>8 ' _ ----------------- geom05:no y/p-sep.-cuts I --------- geom052AX3>4000 & CX2>5 035 L --------- geom05:CH>6.1 0.2L ‘ r— } ..... 0.15:— 5 ------ 0.1} ‘ '- ----- _ ,........: 0.055— I " """ 3' """ E' """" '5 "...-nun] 03"."..1“ 1 1 11411l ind-'LL 10 103triggered «1ng in GeV Figure 17: The triggered energy-spectrum without. and with cuts, full lines: geomO4. dotted lines: geomO5. No y/p-separation-cuts means that only cuts in bin size and N [it are applied. For each geometry the spectra are normalized with respect to the case of no 7/p-separation-cuts. 43 6 Effective area The effective area is the thrown area scaled by the fraction of events that are detected, therefore it can be interpreted as a measure for the detector’s efficiency. The effective area A8” is defined as Npass N thrown Aeff = ° Athrowns (13) where Nthmwn is the number of thrown events, Athrown is the area over which the showers where thrown (normal to incident direction, Athrm = 7r - 1km2, see section 2.2) and Np”, is a number of events that are successfully reconstructed and pass certain cuts (see section 5)] Figure 18 shows the effective area as a function of primary energy. for different cuts in AX3 and 0X2 as well as CH. Only events that fulfill the following conditions are considered in NW”: -at least 55 tubes in the top-layer are struck and at least 20 tubes are participating in the fit (trigger-condition) -cuts in Aangze according to the optimal values for each geometry (see table 2) -additional cuts in AX 3, 0X2 or CH as indicated In the following the term “no '7/proton-separation-cuts” is used in order to express that the trigger condition is fulfilled and that for gamma primaries the corresponding Aangze cut is applied. No further cuts in AX3 and 0X2 or CH are applied. The effective area increases for both geometries up to about 2 - 10477124057712 at 1TeV. From 1TeV to 10TeV the effective area is essentially constant and starts drop- ping around 10TeV. Without 7/p-separation—cuts the effective area at low energies is significantly larger for geom05 than for geomO4. With rising energy the effective area for geomO4 grows faster than for geom05, so that geomO4 reaches an effective area of 5 - 104m2 at an energy of 3 TeV and geomO5 reaches 7 - 104m2 at 1.5 TeV. In figure 44 18 this effect is stressed by the logarithmic scale on the y-axis. The decrease of the effective area due to cuts in AX 3 and 0X2 is more drastic for lower-energetic events for both geometries. As discussed in section 5.2.3 the cuts in AX3 and 0X; reduce the number of lower-energy events more significantly than the number of higher energetic events. A9,, for different cuts in AX3 and (2H (y-MC) me E v I I IIITII ofl < 0‘ -L I I IIIIIII 3. 102 E— I ...... : E _______ ' .___. g '” """" geomO4: no y/p-sep.-cuts 10 ”? geom04: AX3>2000 & CX2>2.5 5 E geomO4: CH>8 5 : ------------ geom05: no y/p-sep.-cuts 5 --------- geom05: AX3>4OOO & CX2>5 5 1 :— --------- geom05: CH>6.1 E11 lllll l lllllill A llllllll ii 10 1 02 1 03triggered 91163534131 GeV Figure 18: Effective area for both geometries and the most successful cuts given in table 1, geomO4: full lines, geomO5: dotted lines. 45 For geomO5 these cuts also throw away a large portion of the higher-energetic events, while for geomO4 the AX 3 and 0X2 cuts perform even better than the softer CH cut. The Cu cut reduces the effective area of geomO4 in a similar way the softer 0;; cut of geom05 does it. At energies larger than 2TeV the decrease in effective area due to the CH-cut in geomO4 is less drastic than the decrease due to the softer cut in geom05. y efficiency for different cuts in A)(:,,CX2 and CH g geomO4:AX3>2000 & cx,>2.5 3 geomO4:CH>8 G g ........... geom05:AX3>4000 81 CX2>5 ~05 1 _ ----------- geom05:CH>6.1 C .2 ii .3: I 5 L L llillli J llllllll 1 11111111 10 102 10“t J riggered ene’g‘ln GeV Figure 19: 7 efficiency for the most successful 'y/p-separation cuts. 46 Figure 19 shows the '37 efficiency for the most successful y/p-separation cuts. The ratio of the number of 7 events that pass the 'y/p-separation cuts in addition to the cuts in N fit and bin size and the number of 7 events that pass only the cuts in N fit and bin size is plotted on the y-axis. For both geometries the cuts in AX 3 and 0X2 reduce the number of low energy events significantly more than the number of high energy events. The reduction of high energy events is more drastically for geom05. Effective area versus zenith-angle (y-MC)I .r‘ g I —geom04 62000 I < _ —geom05 “0°:- —l—- 1._.mm Qua—swig wcqfim +®o Jew/.11... .mmxgl!‘ Nléflu .. ...eeassp .. .. ...... a assesses. 8-. 8-. 35:8. mo-woo xm< Amam 0:3 Figure 29: Distribution of the arrival directions of the 2074 GRBs detected by BATSE in galactic coordinates. Taken from [7]. 65 probability for a GRB to occur in one of these bins. For this analysis an exposure of 605 has been chosen. A spectrum with spectral index of -2.0 models the source and a flux of 10‘4m"2 - sec‘1 - TeV‘l is assumed and cutoff—energies in the range from 100GeV to 1TeV are taken into account. The background is modelled by the cosmic ray background: a spectral index of -2.7 was chosen for the proton-spectrum, the flux observed from the Crab-nebula (3.2- 10‘7m'2 - sec‘1 ~TeV‘1) has been used in order to be able to scale the MC event rate with the scale factor obtained from Milagro MC and Milagro data. No energy cuts are applied to the proton spectrum. For different zenith angle ranges A0 = 5" the expected sensitivity of the tWo detector geometries to this kind of source has been estimated, the results are presented in figure 30. Since the Milagro observatory does not have an energy-scale, i.e. for data the energy of the primary is unknown, the scaling-factor It cannot be calculated for each energy bin. As an estimate the mean of 3.244 for geomO4 and 4.846 for geom05 of the k-distribution calculated in subsection 7.1 has been taken. As expected, both geometries gain sensitivity with smaller zenith angles. For all zenith angle-bands geom05 achieves higher sensitivities than geomO4 at low cutoff energies. For cutoff energies larger than 400GeV, however, the behavior changes. Here geomO4 leads to higher sensitivities. For geom05 the higher effective area at lower energies leads to an increase in sensitivity to sources with an energy cutoff at low energies. For high cutoff energies the higher effective area of geomO4 and the smaller bin size lead to higher sensitivities. For the lowest zenith angles, however, where both geometries have their maximal effective areas, the difference in sensitivity becomes less significant and the behavior even flips for zenith angles out of the range 10° 3 0 S 35° and cutoff-energies higher than 400GeV. With decreasing zenith angle and increasing cutoff-energy the performance of the two geometries becomes more and more similar. For an overhead source with a low energy-cutoff at 100GeV the flux required for a 50—observation around 9- 10’Sergs - cm‘2 for geom05 and less than 66 3- 10‘7e'rgs ' cm‘2 for geomO4. An overhead source with high energy-cutoff at 1TeV 2 requires only less than 3 - 10‘sergs - cm‘ in both geometries. Sensitivity to 60s GRB with energy-cutoff "It; — 0-5 degrees -. — 10-15 degrees : — 20-25 degrees _ - — 30-35 degrees _ " ' . - -- 40-45 degrees ' - . —-geom04 “Ir-10‘ E 0 on E’ 0 2161 'O'U N “107$ 10'. IIIIII|llIlll[III]IIIIIIIIIIIIIIIIIIIIlIllI 100 200 300 400 500 600 700 800 9001000 Ecm(GeV) Figure 30: Flux required for a 5a-observation of a 603 GRB versus cutoff-energy for different zenith—angle ranges for both HAWC-geometries. GRBS have been measured in a redshift-range from z=0.008 to 223.4. Distant sources are detected with a lower flux at earth, because on the one hand the density of photons originating from the source decreases with -r2 and on the other hand interactions with the interstellar medium lead to absorbtion. The redshift dependence of HAWCs sensitivity for a 603 GRB up to redshifts of 1.8 is shown in figure 31. 67 I Sensitivity to 60 Second GRBI r1“: 5 1 a * , e x x 5 10“ A 1 . x m x '0 av ox * t O 2 A X o q “a A O In 10.6 X e O O - A x 0 § 0 ‘ a. * A * xv § v O K v O O 3.; ¥ * ¥ 0 3K x 1‘ O 3" f 10'7 8 ' Q "‘ * IIIJJIILIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII 10‘ 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.3 Redshift , Legend I Detected 6883: x 30-40 degrees, geomO4 ‘ SAX’WFC 0 20-30 degrees, geomO4 ... HETE are 10-20 degrees, geomO4 ' SWIFT, + 0-10 degrees, geomO4 x 30-40 degrees, geom05 ' 'NTEGRAL 0 20-30 degrees, geom05 A Uly/Ko/NE x 10-20 degrees, geom05 o RXTE/ASM + 0-10 degrees, geom05 e BAT/PCA * Uly/MO/SAX Figure 31: Flux required for a 50-observation of a 60 second GRB for both geometries: blue: geomO4, red: geomO5. Summary of detected GRBs provided by Gus Sinnis, localizing instruments taken from [20]. 68 The two lowest zenith angle-bands 0" S 0 g 100 and 10" S 0 S 20" perform nearly identical for low redshifts: For a local source (z=()) a flux of about 5.4 - 10‘8ergs - (317172 is required in order to observe the source at the 50-level for geomO5 and 7.2- 10461118.cm‘2 are required for geomO4. With growing distance the difference in sensitivity between the declination bands becomes more significant, for redshifts higher than 0.8 the sensitivity in the highest zenith-angle band starts decreasing rapidly for geomO4. leading to a difference in fluxes required for a 50 observation of two orders of magnitude at a redshift of 1.8. For a 50 observation of an overhead source at a redshift of 1 a. flux of less than 3- 10‘7ergs - cm‘2 is required for geomO5 and a flux of 1.6 - 10‘Gergs - cm.“2 is required for geomO4. Apart from one GRB at z=0.2 all detected GRBs shown in figure 31 with redshifts lower than 1.8 could have been observed by geom05 at the 50—1evel assuming they occured at zenith angles lower than 20°. Including all zenith angles up to 40° a fraction of 71% could have been observed at the same level in this geometry. 69 8 Conclusion I have compared the performance of two possible HAWC-geometries with respect to angular resolution and optimal bin size, backgroundrejection-capabilities and sensi- tivity to point sources. Compared to baffles, curtains decrease the optimal bin size by a factor of 0.8, thus leading to an improvement in angular resolution by the same factor. Two different variables for 7/hadron-separation, CH and the combination of AX3 and CX2 have been examined. With baffles, Q-factors above 4 are achievable for cuts in AX3 and 0X2, while the curtained geometry still leads to Q-factors of more than 3. Cuts in CH lead to a Q-factor of less than 2 in the baffled geometry and above 3 in the curtained geometry. Cuts in both variables and geometries reduce the number of lower energetic events significantly more than the number of higher energetic events, thus shifting the trig- gered energy spectrum towards higher energies. Similarly, the effective area is reduced mainly for lower energies due to these cuts. Despite the different cut values the baffled geometry leads to higher effective areas in nearly all energy-ranges and for all 7/ p cuts. Crab-like sources with fluxes of less than 26.2mCrab per year are observed at the 5a—level with the baffle geometry. while curtains instead of baffles increase this sensitivity to about 23.6mCrab per year. The 7/p—separation-cuts lead to a further increase by a factor of 2.7 for geomO4 and the CH cut and a factor of 3.7 for geomO5 and the AX 3 and 0X2 cut. For the curtained geometry the comparably hard CH cut performs as good as the AX 3 and 0X2 cut in terms of sensitivity to point sources. Despite the higher effective area of geom05 baffles lead to a higher sensitivity to a Crab-like source with spectral index —2.3 2 a 2 -2.6. For a source spectrum with a hard cutoff above a certain energy the effect of the increase in sensitivity due to curtains instead of baffles becomes even more significant: a cutoff at 10 TeV leads to 70 an increase in sensitivity by a factor of less than 1.1 due to curtains instead of baffles, while a cutoff at 100 GeV leads to an increase in sensitivity by a factor of about 2.5. Local GRBS with a duration of 608 and fluxes as low as 5.4 ~ 10‘8ergs - (an-2 are observed at the 5a-level with the baffled geometry while the curtained geometry requires a flux of at least 7 - 10—887'98 - CIR—2 for the same significance. For redshifts around one fluxes between 3 - 10‘7ergs - cm’2 and 1.7 - 10—667‘98 - ("m—2 are required to observe a GRB at the 50-level with geom05 while geomO4 requires fluxes between 1.6 - 10‘667‘93 - cm‘2 for overhead sources and 3.8 - 10‘sergs - era-2 for high zenith angles. Curtains decrease the sensitivity to GRBS for redshifts larger than 0.8 and high zenith angles dramatically, for all redshifts up to 1.8 and all zenith angles baffles lead to higher sensitivities. Curtains compared to baffles improve the background rejection capability with the variable CH, but higher Q-factors can be achieved through cuts in AX3 and 0X2 with baffles. Baffles lead to a higher detector efficiency, but the smaller bin size for curtains makes geomO4 more sensitive to Crab-like sources. Compared to baffles, curtains improve the angular resolution, but lead to a significantly worse sensitivity to GRBs, especially for high zenith angles. 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