Gamma-ray/Hadron Separation Techniques for
the HAWC Observatory
Samuel Thomas Flynn
University of Wisconsin - Madison
Dept. of Engineering Physics
Research Mentor: Prof. Teresa Montaruli
December 18, 2010
Abstract
The anticipated High Altitude Water Cherenkov (HAWC) Observatory is an important addition to the field of gamma ray astronomy. It will surpass its predecessor experiment Milagro
by about a factor of 10 − 15 in sensitivity thanks to a larger collecting area and a modular structure that improves the discrimination of the background. It also will have a lower
energy threshold since it will be located at a higher altitude (4100 m a.s.l. compared to
2650 m a.s.l.). Like Milagro, HAWC is an extensive air shower (EAS) array detector that
uses photomultiplier tubes (PMTs) situated in pools of water to detect Cherenkov radiation from secondary particles that were created from gamma ray interactions at the top of
the atmosphere. These improvements will give HAWC a greater potential for discovering
high energy gamma ray sources, detecting gamma ray bursts, mapping diffuse gamma ray
emission above 1 TeV from within the galaxy, as well as make it suitable for monitoring the
behavior of Active Galactic Nuclei. However, among other challenges the success of HAWC
rests on its ability to separate the cosmic ray background from the gamma ray signal. In
this thesis, I investigate several variables used for separating gamma rays from cosmic ray
background at the time of data collection (also known as the trigger level1 ). Out of the
variables studied, the Compactness Parameter that was borrowed from Milagro appears to
be the best discriminator, but its definition should be changed to reflect the differences in
HAWC’s detector design and scientific goals.
1
Although my thesis is primarily concerned with implementing discrimination at the trigger level using
a FPGA-based digital trigger thereby reducing the amount of collected data, the methods of discrimination
described herein could also be used after collecting all data, by using a computing farm for filtering.
1
Executive Summary
Due to the similarities in the secondary showers created by gamma and cosmic rays, it can
be difficult to distinguish the two. This leads to difficulties when researchers want to study
purely gamma ray data. My project aims to reduce the cosmic ray background through
optimizing a variable known as the Compactness Parameter (or C = nPMT/CxPE), where
nPMT is the number of photomultiplier tubes hit in an event and CxPE (“C cross PE”)
is the number of photoelectrons in the ”hottest” tank outside of a 40m radius from the
reconstructed shower core 2 . This parameter was borrowed from the Milagro, so it may need
to be changed to work effectively with HAWC. In addition, I want to attempt to discover
new variables for gamma/hadron (g/h) discrimination. Modifying the event display program
will be an essential part of this work.
For the CxPE variable, I have looked at 5 different modifications of the standard definition. I have tried to summarize the output of the 5 modifications in order to determine the
optimal definition of CxPE. My results show that a 30m radius is best.
For the second aspect of my research, I wanted to find a new g/h discriminator variable.
To achieve this, I thought it first necessary to modify the event display (evd) GUI in order
to gauge the size of the events and understand their topology. By modifying the source
code, I added new buttons and functions on the evd. For instance, now users can jump to a
specific event number in a simulation file instead of clicking their way through it. The new
changes make file navigation easy and greatly speed up topological trigger variable analysis
(TTV). Before other users can benefit, the code should be submitted to SVN and properly
documented.
Finally, since the whole of my study depends on the quality of HAWC’s simulation, I
took initial steps to make HAWC’s simulation more comprehensive. Specifically, I worked to
improve the simulation of PMT pulses traveling in electrical cable to the front end boards
of the data acquisition (DAQ) system by properly adding in thermal noise effects due to
Johnson Noise. While I did not get to fully conclude this portion of my research, I have laid
the groundwork for further investigation.
2
shower core The point of impact of the primary particle that generated the shower of particles on the
plane of the detector.
2
List of Figures
1.1
Artist’s Conception of GRB from Collapsar . . . . . . . . . . . . . . . . . . .
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
The Electromagnetic Spectrum . . . . . . . . . . . . . .
Schematic of Cosmic Ray Spectrum . . . . . . . . . . .
Longitudinal Development of an EAS . . . . . . . . . .
EAS Differences . . . . . . . . . . . . . . . . . . . . . . .
Topological Differences with the Compactness Parameter
HAWC Layout . . . . . . . . . . . . . . . . . . . . . . .
HAWC Photo . . . . . . . . . . . . . . . . . . . . . . . .
HAWC Layout . . . . . . . . . . . . . . . . . . . . . . .
PMT Schematic . . . . . . . . . . . . . . . . . . . . . .
TOT Method . . . . . . . . . . . . . . . . . . . . . . . .
ROOT Command Line Interface . . . . . . . . . . . . . .
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10
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3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
The CxPE Distribution, 40m Radius . . . . . . . . . . . . . . . .
The Gamma and Hadron Efficiencies for CxPE, 40m Radius . . .
The Quality Factor of a CxPE Cut, 40m Radius . . . . . . . . .
Comparing CxPE Quality Factors . . . . . . . . . . . . . . . . . .
Statistical Influence in High nPMT CXPE Distributions . . . . .
Optimizing CxPE Radius . . . . . . . . . . . . . . . . . . . . . .
Efficiencies vs Energy . . . . . . . . . . . . . . . . . . . . . . . . .
HAWCEye Display Variables . . . . . . . . . . . . . . . . . . . . .
Modified HAWCEye . . . . . . . . . . . . . . . . . . . . . . . . .
Homepage - Gamma Events Displaying nPE . . . . . . . . . . . .
Bin Contents - Gamma Events Displaying nPE . . . . . . . . . .
Example nPE Topology for Gammas . . . . . . . . . . . . . . . .
RMS of nPE/nPMT radial distribution, 0 < log10 < 2, 0 < θ < 10
Weighted Average Distance to Rec Core . . . . . . . . . . . . . .
The Effect of Johnson Noise on PMT Signal . . . . . . . . . . . .
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23
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4.1
4.2
Construction of Tanks for HAWC . . . . . . . . . . . . . . . . . . . . . . . .
Efficiencies, large nPMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
44
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7
LIST OF FIGURES
4.3
4.4
4.5
4.6
4.7
Efficiencies, small nPMT . . .
Tank Simulation . . . . . . .
CxPE Distribution, Efficiency,
Detailed Layout . . . . . . . .
Scale of Johnson Noise . . . .
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and Quality
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Factors, nPMT=100
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4
45
45
46
47
48
Contents
Abstract
1
Executive Summary
2
List of Figures
3
1 Introduction to Gamma-ray Astronomy
1.1 Complications of Background . . . . . . . . . . . . . . . . . . . . . . . . . .
7
8
2 Literature Review
2.1 Definition of Gamma-rays . .
2.2 Definition of Cosmic rays . . .
2.3 Atmospheric Interactions . . .
2.3.1 Shower Characteristics
2.4 HAWC Site . . . . . . . . . .
2.4.1 The Location . . . . .
2.4.2 The Layout . . . . . .
2.5 Detector and Electronics . . .
2.6 Simulation . . . . . . . . . . .
2.7 Programming Aspect . . . . .
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9
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34
4 Conclusion
4.1 HAWC’s Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
38
38
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3 Topological Trigger Variables for HAWC
3.1 Finding an Optimal CxPE Radius . . . . .
3.2 HAWCEye as a Tool for Discovery . . . .
3.2.1 Modifying HAWCEye . . . . . . . .
3.2.2 Searching for New Cut Variables .
3.3 Radial Distribution of TTVs . . . . . . . .
3.3.1 Thermal Noise in Electrical Cables
5
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0.0
CONTENTS
6
References
39
Appendix
List of Abbreviations .
Table of Particles . . .
Biographical Sketch . .
Best Practice Analysis
Additional Figures . .
41
41
42
42
43
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Chapter
1
Introduction to Gamma-ray Astronomy
Gamma-ray astronomy is the study of the universe with the highest energy electromagnetic
radiation. Being produced by amazing astronomical events, gamma rays carry information
about intriguing phenomena at the frontier of our knowledge. Two major topics that stand
out in gamma astronomy are Gamma-ray Bursts (GRBs) and the origins of cosmic rays.
GRBs are short bursts of intense electromagnetic radiation primarily in the gamma-ray
wavelength, but also consisting of a lower wavelength afterglow. The so-called ’long lived’
GRBs have a direct correlation with the death of massive stars, and are thought to originate
from regions of low metallicity at cosmological distances1, 2 . Long lived GRBs can therefore
give us a clue on the gradual change in composition of stars from light to heavy nuclei,
solidifying our theories on the evolution of the universe1, 3, 4 .
According to Enrico Ramirez-Ruiz from
UC Santa Cruz, while not the total mysteries they were 40 years ago, short lived GRBs
remain an important topic in astronomy: no
specific progenitor has been linked to them,
and no specific type of host galaxy has been
identified6 .
When it comes to the origins of cosmic
rays, gamma-ray astronomy is essential. Cosmic rays are highly energetic particles (mostly
protons) that come from powerful phenomena Figure 1.1: Artist’s Conception of GRB from
irreproducible on earth7 . Even our most pow- Collapsar Some GRBs are thought to originate from
erful particle accelerator experiments cannot Collapsar events. When a supermassive rotating star
match the energy of cosmic rays by a factor collapses to form a Black Hole, the Black Hole can
it emits a
of 10 million. Therefore, our only option for draw in material until a critical state when
GRB explosion similar to a Supernova.5
studying these interesting cosmic particle accelerators is by observation.
The cosmic rays that reach the earth inform us of their mysterious presence, but do little
to explain their origins. This is due to deflections in the cosmic ray’s trajectory by magnetic
fields in space. However cosmic ray sources are also sources of gamma rays, which can be
produced directly in sources by electrons gyrating in magnetic fields (synchrotron radiation)
7
1.1
COMPLICATIONS OF BACKGROUND
8
and up-scattering 1 from photon interactions with electrons (Inverse Compton scattering).
Cosmic rays may also produce high energy gamma rays when protons or hadrons interact
(eg. p − γ → δ + → π 0 + p, π 0 → 2γ), but these processes are not substantial contributers
to gamma emission from sources. These high energy gamma ray producing processes are
important because the gamma’s lack of charge preserves directional information and hence
make them a good target for cosmic ray studies.
1.1
Complications of Background
A major complication in the study of gamma-rays is background radiation. There are two
types of background with different effects: low-level noise that triggers random photomultiplier tubes (PMTs), and high-level background from cosmic rays.
To be more specific, low-level noise is attributed to radiation from the nearby environment, or the equipment and detector itself (ex: the photomultiplier tubes (PMTs) or water
inside the tanks). In order to prevent the system from acquiring this noise that would keep
the electronics busy, a low threshold of 0.25 PEs is set on the PMTS. However, it is estimated that HAWC will see noise above this discriminator at a rate of 20 kHz. Additional
thresholds can be set on the minimum number of PMTs hit and maximum time window in
which they are hit. These sets of conditions are referred to as a Simple Multiplicity Trigger
(SMT) and can greatly reduce noise.
Dealing with the cosmic ray background is a little more difficult. In most cases, the
background can be removed by analysis after experimental data has been collected. This
requires a beforehand knowledge of the different characteristics of gammas and cosmic rays
in the data. Performing background analysis on simulation data is a way to justify the
separation to be performed on the experimental data.
While separating the background after collecting data is a reasonable approach, HAWC
will have to investigate g/h discrimination at the time of data collection. The high altitude
of HAWC extends the detection capabilities to lower energies, but doing so may likely put
strains on the electronics. Collecting too much information will overload equipment (such
as the Time-to-Digital-Converters, or TDCs) and therefore requires cosmic ray background
reduction at the time of collection (known as the ’trigger level’).
HAWC is currently pursuing a solution to this problem by investigating Field Programmable Gate Arrays (FPGAs). By incorporating a FPGAs in to the design, more
complex trigger decisions can be made that take into account pattern recognition2 . It is
therefore possible to explore topological triggers that discriminate based on the different
patterns cosmic rays make when transversing the detector. One such trigger variable is
known as the Compactness Parameter (C) and is being borrowed from Milagro due to it’s
success.
In this thesis, I will explore incorporating C into HAWC and the search for other topological trigger variables as a way to reject cosmic rays at the time of data collection. In the
next chapter, more detailed background information is given.
1
up-scattering The increase in wavelength and hence energy of radiation scattered by an electron.
A look back table can be built into the FPGA that allows for diagnosis of the PMT that are hit and
participate to the trigger by decoding them into a matrix of 1s and 0s. (1 when hit)
2
Chapter
2
Literature Review
2.1
Definition of Gamma-rays
Gamma-rays are a form of electromagnetic (E-M) radiation similar to visible light. Like all
forms of E-M radiation, gamma-rays have both particle and wave-like properties.
When light is described as a particle, each particle, or photon, carries an energy in discrete
amounts according to the Plank-Einstein equation
E = hf
(2.1)
where f is frequency of the light and h is Planck’s constant8 .
The particle nature of light explains the Photoelectric Effect, without which water
Cherenkov detectors like HAWC would not be possible. When visible light hits certain
metals, electrons are ejected from the metal’s surface with energy proportional to the frequency of the light8 . The PMTs that HAWC uses take advantage of this phenomenon to
generate an electric signal from the Cherenkov radiation of extensive air showers.
Under the wave model, light is characterized by a frequency f and wavelength λ which
are related by
v = fλ
(2.2)
where v is the speed of the wave. Often for first order calculations the speed of light is
taken to be the speed of light in a vacuum (c ≈ 3 · 108 m/s), but when light travels in
different mediums such as the atmosphere, its speed (vphase ) is less than c and depends on
the refractive index of the medium (n):
vphase =
c
,
n
n = 1 vaccuum, n > 1 medium
(2.3)
In these other mediums, it is possible for particles to travel faster than light.
Whereas the wavelength of visible light is in the range of 400 − 700 nm, gamma-rays
can have wavelengths from .001 nm (or 1 pm) to much smaller lengths (Fig 2.1). In fact,
gamma-rays have the smallest wavelengths of all E-M radiation and consequently have the
highest energy (Eqs 2.1,2.2).
9
2.2
DEFINITION OF COSMIC RAYS
10
Figure 2.1: The Electromagnetic Spectrum Gamma-rays have the smallest wavelengths, and highest energies of all E-M radiation. 9
Despite being the most energetic form of E-M radiation, gamma-rays do not penetrate
the earth’s atmosphere like visible light does (Fig 2.1). Many gamma-ray detectors are on
board satellites to compensate for this fact. However, satellites only view a limited energy
range of gammas from 1 GeV - 300 GeV. Understanding atmospheric interactions is key to
studying higher energy gamma rays on Earth.
2.2
Definition of Cosmic rays
According to NASA, cosmic rays are highly energetic particles that bombard earth from
anywhere beyond its atmosphere10 . About 90% of cosmic rays are protons and nearly 9% are
alpha particles.11 Electrons and light to heavy elements make up the remainder. Although
these elements make up a small percentage of the composition of cosmic rays, they are in fact
more abundant than normally found in matter. Medium elements in cosmic rays, such as
carbon and nitrogen, are roughly 10 times more abundant than in normal matter.11 Heavy
elements are found about 100 times more often as well. Cosmic rays are therefore thought to
originate where there is an enrichment of medium to heavy elements (ex: after the explosion
of a star).
The origins of cosmic rays are associated frequently with their energies. At low energies,
the cosmic rays seen on Earth are generally from within the solar system. They are associated
with the Sun’s activity and are greatly influenced by solar winds. The Earth’s magnetic
field tends to deflect these charged particles and limit the number reaching Earth.12 This
geomagnetic suppression on the intensity can be seen at energies lower than 109 eV in the
cosmic ray spectrum (Fig 2.2).
From 109 eV to ≈ 1015.5 eV, the spectrum of cosmic rays follows an E −2.7 power law12 .
These cosmic rays are thought to be of galactic origin and produced by supernovae remnants.
When cosmic rays collide with matter in the galaxy, they produce gamma-rays. Observations
with gamma ray detectors such as HAWC provide a way to measure the cosmic ray flux and
2.3
ATMOSPHERIC INTERACTIONS
Figure 2.2: Schematic of Cosmic Ray Spectrum
11
12
strengthen existing ideas about galactic sources.
The highest energy cosmic rays come from extragalactic origins. While the sources of
these particles is unknown, likely candidates do exist.13 One possible source are Active
Galactic Nuclei (AGN). These exotic objects are supermassive black holes (≈ 8 solar masses)
with relativistic jets spewing material. The gravitational potential is believed to be great
enough to accelerate cosmic rays to extreme energies. During this process, gamma rays are
produced from shocks of the accelerated material in the jets. By studying the variation in
gamma ray signal from flaring AGN, HAWC can test the theories of extragalactic cosmic
rays.
2.3
Atmospheric Interactions
Gamma-rays can carry information about our universe from distances up to ≈ 10 Mpc.
Their interaction length depends on energy1 . They travel in a straight trajectory due to their
neutral charge. As soon as they reach the earth’s atmosphere, they undergo interactions with
matter based on their energy creating secondary particles that suffer energy losses mostly
in the form of bremsstrahlung radiation14 . Cosmic rays, on the other hand, are deflected
regularly by magnetic fields in space (including the Earth’s magnetic field).
Whether it is a gamma-ray or cosmic ray, the primary particle develops into an extensive
air shower (EAS) once it interacts at a shallow depth in the atmosphere. The number of
1
The highest energy gamma-rays coming from cosmological distances interact with the Extragalactic
Background Light (EBL) and are therefore not seen on Earth.15
2.3
ATMOSPHERIC INTERACTIONS
12
Figure 2.3: Longitudinal Development of an EAS ”The longitudinal development of an EAS as given by approximation B for several different primary gamma-ray
energies. The x-axis is the atmospheric depth expressed as the number of radiation
lengths. The y-axis gives the number of electromagnetic particles in the air shower.
Sea level is 28 radiation lengths of atmosphere, 2600m above sea level is 20 radiation
lengths, 4300m above sea level is 16.5 radiation lengths, and 5200m above sea level
is 14.7 radiation lengths.” 16
secondary particles in this cascade continues to grow as the shower advances towards the
surface of the earth. When the average energy of the secondary particles, that is lost primarily through bremsstrahlung radiation, drops below a critical value of roughly 84 MeV16 ,
ionization dominates over other interactions and particles are absorbed in the atmosphere.
The number of particles continues to decrease, reaching zero at the surface of the earth
in many cases. However, if the primary has enough energy, the secondaries can reach the
ground. In any event, having an EAS array detector at a high altitude close to the shower
maximum will improve detection capabilities. Figure 2.3 illustrates the relationship between energy, altitude, and number of secondary particles for a gamma-ray. At 4300m, or
about 16.5 radiation lengths 2 , HAWC can detect an impressive amount of secondaries with
energies ranging from 100 GeV to 100 TeV.
When it comes to detecting secondary shower particles, there are two main ground based
methods that both rely on Cherenkov radiation from the fast moving charged particles. The
first method uses mirrors to reflect this faint blue light onto an array of PMTs. Since the
Cherenkov radiation was made from secondaries traveling in the atmosphere, this method
is called the Imaging Atmospheric Cherenkov Technique (IACT). The second method is
called the Water Cherenkov technique because it detects Cherenkov radiation from charged
particles in a pool of water.
Having the PMTs submerged in water greatly aids the detection process7 . First, consider
that 1 or more meters of water depth will convert gamma rays into electrons and positrons
2
radiation length The average length in a specific material in which a relativistic charged particle will lose
67% of its energy by bremsstrahlung17 . The radiation length in the atmosphere is 36 g/cm2
2.3
ATMOSPHERIC INTERACTIONS
13
(via pair production) which in turn release Cherenkov radiation. Since there are much more
protons than electrons in EASs, a great deal more shower particles are sampled than with
the IACT. In addition, with a sufficient amount of PMTs, the entire detector area is sensitive
to showers. To understand this more, recall that the blue Cherenkov light is emitted at an
angle specific to the medium the particle is in:
cos θ =
1
nβ
(2.4)
where θ is the half angle of the cone, n is the index of refraction of the medium, and β = vc .
The higher refractive index of water over air widens the Cherenkov radiation angle from
≈ 1° to roughly 41°. A cover on top of the water pools provides darkness so that the faint
Cherenkov radiation is detectable. This means that Water Cherenkov detectors can operate
continuously while IACTs are limited to the nighttime when light pollution is lowest.
Although I’ve highlighted some of the benefits of the Water Cherenkov technique, both
methods have advantages and disadvantages. For a more comprehensive comparison, read
the works of G. Sinnis16 . Regardless of the detection technique, both detector types have to
deal with the high cosmic ray background. Understanding the different shower characteristics is the key for developing topological discrimination methods.
2.3.1
Shower Characteristics
Although PMTs cannot distinguish between the EASs of gamma-rays and cosmic rays, researchers can. The different types of primary interactions in the atmosphere produce EASs
of different compositions. Knowing this, topological triggers can be implemented to separate
the cosmic ray background (Section 3).
At HAWC’s altitude (4300m), most of the gammas are in the 50 GeV−100 TeV energy
range and pair production is the most common gamma interaction16 . This process produces
an electron and positron as long as the gamma-ray has energy greater than the rest mass of
the two products (≈1.02 MeV).14 The most significant source of energy loss for these electrons and positrons is through bremsstrahlung radiation. These processes continue as the
number of secondary particles grow, forming a purely electromagnetic extensive air shower
(EAS) (Fig 2.4). The secondary particles may also annihilating with their corresponding
antiparticle, releasing lower energy gamma-rays. When the average energy of the secondary
particles is low, other modes of gamma interaction occur more frequently (Compton Scattering dominates for gamma rays with E < 5 MeV14, 18 ) and secondary electrons lose energy
primarily through ionization interactions 3 .
Cosmic ray induced EASs are more complicated. For each type of cosmic ray particle
(proton, alpha, light nuclei, etc.) there are a variety of interactions that can take place. Pions
3
ionization interactions with electrons happen when an energetic electron collides with a quasi-free atomic
electron, removing it from the atom, other atomic electrons in high orbitals drop to lower orbitals for stability,
releasing a low energy photon with energy related to the potential difference.
2.3
ATMOSPHERIC INTERACTIONS
(a) gamma-ray
14
(b) cosmic ray
Figure 2.4: EAS Differences Fig 2.4a shows a simplified scheme of gamma-ray
interactions that start high in the atmosphere. Fig 2.4b shows an EAS originating
from a cosmic ray and its various components.
and kaons are frequently produced, which can decay to produce muons11 . Unlike gamma
induced EASs, cosmic ray induced EASs include muonic and hadronic components as well
as an electromagnetic component (See Appendix 4.2 for a classification of particles).
Ultimately, the different EAS characteristics means a different charge distribution. Figure 2.5 highlights some of the differences in this topology. While the charge is concentrated
near the shower core and drops smoothly for gammas (top), there are pockets of high energy
at large distances from the shower core for hadrons (bottom).
2.4
HAWC SITE
15
Figure 2.5: Topological Differences with the Compactness Parameter Events
are viewed in terms of nPMT/nPE with the color scheme inverted to make PMTs detecting a lot of charge appear in red. Noting that hadron primaries produced irregular
clusters of PMTs with high charge outside of a 40m radius from the reconstructed
shower core (red circle) more often gamma primaries was the motivation for developing the Compactness Parameter C = nPMT/CxPE, where CxPE is the highest
amount of PEs in a PMT outside the core radius. The size of the collecting pool of
Milagro is shown to emphasize the increased area of HAWC.19
2.4
HAWC Site
2.4.1
The Location
Located inside the Parque Nacional Pico de Orizaba of Mexico, HAWC will rest at 4100
meters above sea level on a plateau between the peak Pico de Orizaba and the volcano
Sierra Negra 7 . The site will be close to the Large Millimeter Telescope (LMT) experiment,
which is situated at the top of Sierra Negra, 4600 meters above sea level (Figure 2.7). The
infrastructure needed for HAWC will be an extension on the current construction plans for
the LMT. Figure 2.6, taken from the HAWC website20 , shows how much the roadway and
electrical infrastructure will need to be augmented.
2.4
HAWC SITE
Figure 2.6: HAWC Layout At left, Google Earth image of the Parque Nacional
Pico de Orizaba showing the Citaltepetl, with snow, and Sierra Negra SW of it. At
right we show a map from INEGI, with 20 topographic contours and the UTM grid
indicated in blue. The blue square indicates the predetermined location of HAWC
and its dimensions, with the dotted rectangle covering 90,000m2 . The red dot is the
nearest point to the LMT road, electricity and Internet.
Figure 2.7: HAWC Photo Actual photo of the Pico de Orizaba with an artist’s
conception of the HAWC array and annotations. 21
16
2.5
HAWC SITE
2.4.2
17
The Layout
The HAWC observatory will feature water-filled tanks housing PMTs, arranged in a square
array comprising 150m x 105m instrumented area7 . The plastic tanks will be 5.0m deep and
have a diameter of 7.3m22 . In a preliminary engineering study 7 , the tank design was shown
to be less expensive, quicker to operate, easier to repair, and more flexible for changing
scientific goals than the reservoir model of Milagro. (See Figure 2.8)
In addition, the tank layout will reduce the number of events that are detected twice,
known as multiplicity7 . This is because the tanks optically isolate the PMTs. To understand
this, consider one charged secondary particle transversing MILAGRO at a near-horizontal
angle. When the PMTs are triggered at one side of the detector, an event is registered. As
the Cherenkov radiation continues to travel to the other side of the detector, another PMT
may be hit signaling an additional event, although in reality there was only one event that
was recorded twice.
(a) Tank Array
(b) Sim. Tank
Figure 2.8: HAWC Layout Fig 2.8a Artist’s conception of the 300 tank array.
Fig 2.8b HAWC will reuse MILAGRO’s 900 8” Hamamatsu R5912 PMTs, placing
one in each tank7 . This simulation with GEANT4 shows how a vertical traveling
muon might look if the number of photons were reduced by a factor of 5020 .
Instead of a dual layer PMT system like Milagro, the choice was made for a single deep
layer design that incorporates a topological g/h discriminator in the trigger. The current
analog trigger cannot perform such a task because no information is stored about the location of the PMTs.
2.5
2.5
DETECTOR AND ELECTRONICS
18
Detector and Electronics
When a charged particle enters the detector, it emits Cherenkov radiation which the PMTs
detect. The basic principle of a PMT relies on the Photoelectric Effect and Secondary
Emission. Light entering the PMT first hits the metal photocathode which releases a photoelectron. The PMTs for HAWC were chosen so that the photocathode is sensitive to
wavelengths of light corresponding to blue Cherenkov radiation7 . The photoelectron then
collides on the surface of a target electrode (known as a dynode) to induce emission of multiple electrons. A series of these dynodes are setup so many electrons are collected at the
anode (Figure 2.9). A voltage across the dynodes ensures the electrons reach the anode,
where an electron current is outputted to an external circuit23 .
Figure 2.9: PMT Schematic A circular-cage type PMT is shown courtesy of
Hamamatsu23 as an example of a dynode system.
The current is converted to a voltage to function with other devices23 in the circuit such
as the Time-to-Digital-Converter (TDC). Two typical signals are shown on the top portion
of Figure 2.10. The TDC digitalizes these analog signals producing a square wave when
the PMT voltage crosses a certain energy level, preserving the time at which this occurs. A
threshold energy level of about .25 PE (photoelectrons) is set so that noise does not trigger
the PMT to register a ’hit’. A second threshold energy level of 4 PE is also set to indicate
large pulses.
When we talk about EAS arrays, we often talk about the charge deposited in the detector.
Since the primary gamma is converted to charged secondary particles, knowing the charge
distribution in the detector will give insight into the gamma’s energy.
As it turns out, the charge can be computed only knowing the time difference between
the rising and falling edges of a digitalized square wave output from the PMT. A low pulse
signal will consist of 2 ”edges” because it has crossed one energy threshold twice, whereas
a large pulse will have 4 edges due to crossing 2 thresholds twice. In a similar manner as
with small pulses,the charge for large pulses can also be easily calculated. This method for
calculating charge is known as the Time-Over-Threshold (TOT) method. For 4-edged pulses,
it can be unclear whether there was indeed one large pulse or two smaller pulses crossing
2.6
SIMULATION
19
the lower threshold within the same time frame. Luckily, for every large pulse, the timing
information of the 4 edges is proportional so a distinction can be made.
In energy reconstruction, all of the PMTs are read and the charge from the TOT method
is used in a weighted average to find the center of charge (cog) coordinates Xi , Yi
N
X
Xi =
N
X
nP Ei · xi
i=1
N
X
i=1
Yi =
nP Ei
nP Ei · yi
i=1
N
X
(2.5)
nP Ei
i=1
The cog represents the location of the shower core, and is necessary for the angular reconstruction process as well as the CxPE cut on background. After energy reconstruction, if
the event satisfies the SMT it is acquired by the DAQ.
For angular reconstruction, the leading edge times at the low threshold from the TDCs
are used as the ”Hit Times” of the PMTs. Knowing the cog and when all the PMTs detected
secondary particles, it is possible to reconstruct a track that the primary particle most likely
took.
Figure 2.10: TOT Method A low intensity and high intensity event are shown
above. The TOT method extracts the time at which the PMT’s voltage crosses an
energy threshold, then uses that to calculate the charge by the relation ∆t ∝ charge.
2.6
Simulation
Simulation in HAWC depends on 3 main programs: CORSIKA, GEANT4, and MILINDA.
The first program is the standard in almost all cosmic ray experiments. It models the different
types of atmospheric particles and the electromagnetic showers they produce. GEANT4 is
used by many types of particle experiments. Its purpose is modeling the passage of the
particles through detectors. The final program is meant to account for all the other aspects
2.7
PROGRAMMING ASPECT
20
of the detector24 . Since MILINDA was optimized for MILAGRO, updates are needed to
reflect HAWC’s differences.
Once the simulation files are made, the task becomes analyzing data. HAWC has created
a beta version of a software package known as AERIE (”Analysis and Event Reconstruction
Integrated Environment”), offering a suite of tools for reconstruction and analysis. Among
the tools is the software framework HAWCNest and modules for reading simulated data.
A framework provides a uniform way of writing code and greater clarity because the
implementation is hidden from users. It is a highly object orientated paradigm where the
logical steps of code are revealed more easily. When physicists are writing a program, they
can add and configure ’services’ to perform certain tasks. If the physicist wants to use a
random number, he may add a service for random numbers and specify which instance of the
random number service he wishes to use. One instance of the service may generate random
numbers according to the standard C++ library, while another may use ROOT’s libraries
(see Section 2.7). Regardless of which instance of the service is used, the physicist can use
virtual base class methods without needing to think about their implementation.
2.7
Programming Aspect
For most of the work in this thesis, I used a combination of C++ and ROOT. ROOT was
used to make histograms pertaining to gamma/hadron discrimination. Developed by CERN,
ROOT is a software package for analyzing large amounts of data and is ubiquitous in the
physics community. Its framework provides specialized data structures and histogramming
methods among other things. An important feature is the C-like interpreter CINT, which
covers most4 of ANSI-C and ISO C++ 2003 and makes prototyping programs fast (Figure 2.11).
While having an interactive tool can be very useful, ROOT’s error messages can be
quite cryptic at times. In addition, for much faster program execution, it is better to use
a compiled language. For these reasons, I started writing C++ code for compilation and
linking against ROOT for graphing and i/o with ROOT formatted data structures. I found
the C++ compiler to have much more instructive error messages which made up for the time
lost compiling/linking.
When it was convenient, I used Python with the MatPlotLib library to produce pretty
plots like Figure 3.4b. Python is an interpreted language like ROOT, but provides more
helpful support and superior aesthetics.
Lastly, the HAWCNest framework is built upon the C++ standard and boost libraries.
For the final part of my project, I started to improve a software module that simulates signal
propagation in electical cables by adding thermal noise. C++ was used for this task, but
the plotting was done with Python.
4
covers 85-95% of the C++,ANSI-C, and K&R-C language constructs, according to CERN.
2.7
PROGRAMMING ASPECT
Figure 2.11: ROOT Command Line Interface For quickly developing a program
or making a simple histogram, ROOT can be very useful.
21
Chapter
3
Topological Trigger Variables for HAWC
3.1
Finding an Optimal CxPE Radius
In Milagro, CxPE was defined as the number of PEs in the hottest tank outside of a 40m
radius from the reconstructed shower core. A change in the size of the radius may be needed
to reflect the different altitude, area, and geometry from Milagro to HAWC. Initial analysis
showed that a 60m radius has a higher gamma efficiency than 40m throughout the energy
spectrum of the primary particle for the most part (Figure 3.7b). Having a high gamma
efficiency alone does not make 60m the best core radius. In fact, one of HAWC’s top goals
is to push the spectrum to lower energies, yet at the same time, reducing background rates
is very important. A radius may be optimal for collecting low energy gamma rays but not
be optimal in the sense that there are a lot of protons in the data. In general, HAWC will
look to have high gamma efficiency at low energies, and maximize the ratio of signal to noise
throughout. As will be explained later, we can define a quality factor (Q) that encompasses
this signal to noise attribute for determining an optimal core radius.
To begin the analysis, a set of simulation files was produced for gammas, protons, and
other hadrons (e.g. Helium) which had CxPE calculated for radii of 30m, 40m, 50m, and
60m. All of the simulation data had the true information with which the primary particle
was generated as well as the reconstructed data.
For each of the radius lengths tested, the distribution of CxPE was plotted for gammas
and hadrons (includes proton and other hadron data). The objective was to find an optimal
value of CxPE which separated the two populations of primaries.
As in Figure 3.1, the gamma population had lower values of CxPE than protons, in
agreement with (Figure 2.5). Therefore, the decision of the cut would be to only keep data
with values of CxPE lower than the cut value, or to the left of the cut value in Figure 3.1,
because it is more gamma-like.
22
3.1
FINDING AN OPTIMAL CXPE RADIUS
23
Figure 3.1: The CxPE Distribution, 40m Radius The distribution of CxPE is shown with a
log scale. Most of the gammas have lower values of CxPE than hadrons do, so events should be
kept if their CxPE is below the cut value. For this data, it looks like the cut will be around 1.55 on
the log scale of CxPE, or 35.48 PEs (superimposed). The number of events of each primary particle
tested with nPMT= 30 is shown upper-right box
Figure 3.2: The Gamma and Hadron Efficiencies for CxPE, 40m Radius Selection of a
cut on CxPE should consider a high gamma efficiency and low proton efficiency. The superimposed
line at 1.55 on the log10 CxPE scale shows when this ratio is the highest.
Figure 3.3: The Quality Factor of a CxPE Cut, 40m Radius The largest quality factor for
this particular set of data is at 1.55 on the log scale of CxPE, or 35.48 PEs.
In order to find the best value of CxPE on which to cut, the quality factor of the cut
value was plotted (Figure 3.3). The quality factor is a rating of the cut value, so whichever
cut value had the highest quality factor would be chosen.
Since the underlying idea of CxPE cut is to keep as√much gamma and few proton events
as possible, the quality factor was defined as Q = eg / eh where eg and ep are the gamma
3.1
FINDING AN OPTIMAL CXPE RADIUS
24
and hadron efficiencies, or the percent of the corresponding data that is kept after cuts are
applied. A cut value with 0% gamma efficiency would be all the way to the left on the scale
of Figure 3.2. None of the gamma data would be kept because all events have CxPE higher
than the cut value. Conversely, for a cut with 100% gamma efficiency, all of the data would
be kept. A good cut value should have a high gamma efficiency and low proton efficiency.
The location on the x-axis of these distribution, efficiency, and quality factor histograms
represents the value of CXPE that will maximize the number of gamma primaries to the root
of proton primaries. The simple approach to determining the optimal core radius would be
to compare the quality factor curves for each radius. Figure 3.4a shows that a 30m radius
has a higher quality factor than the standard definition of 40m and slightly overpowers a
20m radius for nPMT= 30. What effect does the nPMT have on the quality factor though?
Physically, the more energy a primary has the more PMTs it will hit in an event. Raising
nPMT will filter out lower energy events. Mathematically, when nPMT is increased in
Figure 3.4b, the general trend is for smaller radii to vastly improve their maximum quality
factor over other radii as the minimum number of PMTs in an event is increased. Intuitively
the opposite effect is expected: large radii will be best suited for events with a large nPMT.
(a) nPMT=30
(b) small nPMT
Figure 3.4: Comparing CxPE Quality Factors Fig 3.4aFor CxPE with nPMT= 30, the radius
with the highest ratio of gamma efficiency to the root of proton efficiency is 30m. This is achieved
when the cut is at 1.6 on the log10 E scale. Fig 3.4b As the number of required PMTs in an event
goes up, the optimal quality factor for a 20m radius skyrockets.
If we look that the distribution and quality factor histograms with large nPMT and
small radii, we see that these extremely high maximum quality factors have little meaning.
In Figure 3.5, we see that although the quality factor for nPMT= 400 is close to 30, an
unacceptably low amount of gammas would be kept after applying that cut (10%). In other
3.1
FINDING AN OPTIMAL CXPE RADIUS
25
Figure 3.5: Statistical Influence for High nPMT CXPE Distributions At high
values of nPMT, the gamma and proton populations distinguish themselves enough to
effect the quality factor’s importance. Normally, a cut on CXPE would be determined
from the location of the maximum quality factor. If the same were done here, there
would be a gamma efficiency of less that 10%. The figure above is for nPMT= 400,
radius= 20m.
words, while maximizing the quality factor for a cut is extremely important, it is not the
only aspect involved in choosing an optimal radius.
To summarize thus far, we have found that using the maximum quality factor for a
basis in choosing the optimal radius is acceptable for small cuts on nPMT. The results in
Figure 3.4a show that a 30m radius is best for small nPMT.
Another method for choosing an optimal radius is to pick a particular acceptable gamma
efficiency and find the lowest proton efficiency. Milagro used this method for nPMT=
400, 500, 600 instead of 30, 50, 100 (Figure 3.6). Notice the comments next to the legend relating the nPMT with the energy of the primary. The minimum value for nPMT=
400, 500, 600 is at 40m, 45m, and 50m respectively. For Milagro’s purposes, having an efficient radius for selecting middle range energy primaries was important, and ultimately this
method helped Milagro select a 40m radius.
If one wants to properly ensure that a certain energy range of primary particles has a
3.1
FINDING AN OPTIMAL CXPE RADIUS
26
Figure 3.6: Optimizing CxPE Radius A 40m radius was found to be best suited
for the Milagro detector for having a small proton efficiency at 0.5 gamma efficiency.
high gamma efficiency, they can use their optimal cut on CXPE, however they determine
it, to plot gamma efficiency versus energy as in Figure 3.7b. This figure shows that for
primary particle energies above 2.2 log10 E, a 60m radius with a CXPE cut found from the
maximum quality factor has the highest gamma efficiency. In the lower energy range, 50m,
40m, and 30m radii take turn for highest gamma efficiency.
Since the HAWC is focused on lowering the energy threshold for primaries, and smaller
radii have both higher gamma efficiency and lower proton efficiency in low energies, I recommend HAWC doesn’t increase its standard reconstructed core distance. Furthermore,
because a 30m radius had the maximum quality factor for small nPMT1 , I support the
option of lowering the core radius to 30m.
1
For nPMT= 30. For nPMT= 100, the maximum quality factor was not a useful metric for evaluating
radii lengths because it yielded a very small gamma efficiency. (See Figure 4.5). For nPMT= 50, 20m has
a slightly higher maximum quality factor than 30m (See Figure 3.4b). Somewhere between nPMT= 50
and nPMT= 100, the maximum quality factor becomes unreliable . To be conservative, I recommend 30m .
3.1
FINDING AN OPTIMAL CXPE RADIUS
(a) Proton Efficiency
(b) Gamma Efficiency
Figure 3.7: Efficiencies vs Energy Fig 3.7a The 60m radius has the highest
proton efficiency, and may therefore not be the ideal radius length. Since lower
proton efficiency is desired, a 20m radius appears the best by this metric Fig 3.7b
The gamma efficiency after taking the optimal CXPE cut for each core radius length
reveals a 60m core radius as superior from 2.5 > log10 Eγ > 6 . The figure is made
with a nPMT cut of 30, and no core containment requirement. A time window cut
was also ignored.
27
3.2
HAWCEYE AS A TOOL FOR DISCOVERY
3.2
28
HAWCEye as a Tool for Discovery
In order to understand and compare the different topologies of gamma and proton events,
using an event display (evd) program was necessary. HAWC has a prototype evd program
aptly named ”HAWCEye” which shows a top view of the array of tanks with event information overlaid in a color scheme. For instance, Figure 3.8a shows the number of PEs of
each PMT in an event. The timing information is also available as well (Figure 3.8b).
Through studying the different patterns on the evd, a new topological trigger variable
(TTV) was hoped to be found that would be an even better discriminator than CxPE.
However, before this could be done, some improvements to the program had to be made.
(a) nPE
(b) Hit Times
Figure 3.8: HAWCEye Display Variables The original event display program
allowed users to visualize the variables nPE and Hit Times. Although the legend
was removed from Figure 3.8a, both figures show the same event with different
information visualized.
3.2.1
Modifying HAWCEye
The main drawback of the program was its limited ability to search files for specific events.
On the right panel of the evd, as shown in Figure 3.9, there are a list of options, known
individually as modules. The top module lets the user pick which variable to visualize in the
left display. Below this are modules that limit the events that are shown if the corresponding
check box is checked. For instance, with the Energy Cut module checked and set from 0 to
100 GeV, only events with Monte Carlo (MC) simulated energy in that range will be shown
when the Next or Previous buttons are pressed (the left and right arrows in Figure 3.9).
3.2
HAWCEYE AS A TOOL FOR DISCOVERY
29
Figure 3.9:
Modified HAWCEye This updated version of HAWCEye includes a Zenith Cut
and an Event Number module for better file navigation (Shown in red).
Originally, HAWCEye only included modules for limiting the search based on energy
(Energy Cut), number of PMTs hit (NHit Cut), and whether the MC core was inside the
detector or not (Containment Cut). However, users often times wanted to search files based
on the MC zenith angle of the primary, so a Zenith Cut module was added.
Just by adding this one module, the search time for users with specific events in mind
has been reduced drastically. Another module that greatly helped speed up search time was
the module for searching a specific event number (Event Number).
If users are browsing through a large file and see an interesting event, they can choose to
only write down the event number and file name instead of energy, zenith angle, containment
cut and/or other information. When entering the event number, users can jump straight to
the event, rather than clicking through the events that agree with the specifications given in
the right panel.
The final modification of HAWCEye was the addition of the Play & Save button just below the display. When clicking this button, the evd would automatically browse through the
events with matching criteria in the right panel and save the display image. The functionality of the button is essentially the same as the Play button, but for analysis that require
events to be additionally saved, it is extremely useful.
Using the Play & Save button is faster than clicking the Next button and saving the
image. For users who do not have HAWCEye installed on their personal computer and are
connecting remotely to HAWC’s network, the Play & Save button is especially recommended
if possible. Remote connections can be slow, and if a user is saving a display image and clicks
3.2
HAWCEYE AS A TOOL FOR DISCOVERY
30
to view the next event too soon, the next event will be saved instead of the desired one. There
is no risk of this occurring with the Play & Save button.
3.2.2
Searching for New Cut Variables
In the quest for a new topological trigger variable, the Play & Save button of the evd was used
to quickly sort gamma and proton events in categories of energy and zenith angle ranges. A
website was created to store the images and allow for easy navigation between bins of energy
and zenith. The task of finding a new variable was more difficult than expected.
Figure 3.10 is an example of a homepage for a particular primary type and display
variable. On each homepage, there is a title at the top informing visitors which images they
are looking at and a grid of display images based on primary energy and zenith angle. The
bins of energy were in powers of ten using a GeV as a base unit staring from 0 − 100 GeV
for the first bin and 105 − 106 GeV for the last. The bins of zenith angles went from 0 − 10 ◦
to 50 − 60 ◦ .
Figure 3.10:
Homepage - Gamma Events Displaying nPE In a web browser each image
appears as an animation displaying the series of events in the same zenith and energy bin. When
the highlighted bin is clicked, the visitor sees Fig 3.11.
Since there are many saved images from HAWCEye available, organization can be a
challenge. On each homepage, the grid of display images is actually a series of animated
GIF files that show the bin contents. The goal of the homepage is to allow visitors to quickly
get an overall sense of the different topological distributions when changing energy or zenith
angle. Rapidly viewing images of a bin in succession will hopefully spark the imagination
3.2
HAWCEYE AS A TOOL FOR DISCOVERY
31
quicker than viewing all images in a bin all at once. If a visitor has an intuition of a pattern
that could be used as a cut variable, they may click on the bin GIF and see the contents all
at once (Figure 3.11).
Inside each bin, the user can click on links to change the display variable or switch
primary particle type. The bins are organized in descending energy so switching back and
forth between gammas and protons will show events with nearly the same attributes. If more
interaction is wanted, the visitor can view the webpage of the description and see instructions
for how to run and/or modify HAWCEye.
Figure 3.11: Bin Contents - Gamma Events Displaying nPE The events with
MC energy and zenith angles corresponding to the bin are displayed as a gallery.
After the website was in place, the events were compared in each bin. It was difficult
to derive another cut variable based off of the nPE visualization. In fact, it was even hard
to believe that CxPE was a reliable cut variable judging from the events in the simulation
files used. In particular, the gamma topology was not well behaved at lower energies as
in Figure 2.5. Instead of charge centered around the core, smoothly decreasing energy as
the radial distance increased, there were many images showing clumps of charge in irregular
patterns, with pockets of high energy (Figure 3.12). To my surprise, the gammas were more
3.2
HAWCEYE AS A TOOL FOR DISCOVERY
32
Figure 3.12: Example nPE Topology for Gammas This event display image is
of a gamma event in the 2 <log10(E) < 3, 20 ◦ < Z < 30 ◦ category. For many
events that were used in this analysis, the topological distribution of PEs for gammas
was irregular and similar to that of hadrons.
spread out than proton events in general, having many low energy PMTs. Proton primaries
with the same energy and zenith generally had fewer PMTs hit, but they had higher PEs
per PMT.
While finding distinguishing features using the nPE display variable was difficult, there
were other variables that revealed subtle features more easily. Viewing an event with the
log of nPE highlighted the small changes in nPE per PMT, and was therefore more useful
for viewing energies with more uniform charge distributions.The variable nPE/nPMT was
probably an even better display variable that revealed more complicated patterns.
Due to the difficulty in developing a new TTV with the event display program, I decided
to investigate another way of visualizing the same data.
3.3
3.3
RADIAL DISTRIBUTION OF TTVS
33
Radial Distribution of TTVs
After looking for patterns in the topology of the nPE variable for quite some time without
success, another approach was taken. Instead of a ”top-view,” a ”side-view” was used to
study the distribution of the display variables.
For each event, the distribution of the display variable from the reconstructed core was
plotted. The average profile of the display variables nPE, log10 nPE, and nPE/nPMT revealed
a smooth quick drop for gammas and slightly bumpy gradual decent for protons. In short,
the gammas appeared to have higher values of the display variable closer to the core. In
order to quantify this, several graphs were made comparing the root-mean square (RMS) of
gammas and protons. For each of the bins in energy and zenith as seen in (Figure 3.10,
the RMSs were studied. As the RMS summary plot in Figure 3.13 indicates, there is a
clear variation in the radial distribution of nPE/nPMT. Radial histograms were also made
for the Hit Times and Hit Time Residual display variables, but there was little to discern
gammas from protons.
Figure 3.13: RMS of nPE/nPMT radial distribution, 0 < log10 < 2, 0 < θ < 10 The RMS
of the radial distribution of nPE/nPMT is higher for protons than for gamma rays. In this figure,
the numbers along the X-axis represent 0 < log10 E < 2, 2 < log10 E < 3, . . . , 5 < log10 E < 6.
The radial distribution of nPE/nPMT for gammas was clearly distinguishable from protons. Recalling that nPE/nPMT was also a relatively good TTV from using HAWCEye, I
decided to start a similar analysis as in Section 3.1 to study the average distance of the
PMTs to the reconstructed core weighted with the nPE/nPMT per event. Instead of making a distribution of CXPE, I would make the distribution for this new variable and would
calculate the efficiencies and quality factors of cuts just the same.
3.3
RADIAL DISTRIBUTION OF TTVS
34
Figure 3.14: Weighted Average Distance to Rec Core The average distance
between PMTs and the reconstructed core was weighted with the nPE/nPMT. Here
the cut on nPMT= 30 and the result is shown for a radius of 40m.
Unfortunately, the average does not make a good cut variable. In Figure 3.14 the
gamma distribution looks nearly identical to the proton distribution. This weighted average
convolutes many effects that may depend on the zenith angle and energy of the primary
particle. Although no use can become of this new variable as it is, if more constraints are
placed on the events then perhaps the background hadrons will stand out.
3.3.1
Thermal Noise in Electrical Cables
The last part of my work was orientated towards creating a more accurate simulation of the
signal in the electrical cables by adding Johnson noise. First observed by J.B. Johnson in
the late 1920s, Johnson noise2 describes the random fluctuations in voltages across electrical
resistors due to thermal agitation25 , and can be written as:
hV 2 i = 4kT RB
(3.1)
3.3
RADIAL DISTRIBUTION OF TTVS
35
where k is the Boltzmann constant, T is the temperature of the cable, R is the cable resistance, and B is the bandwidth (For a derivation, See 26 ).
The part of AERIE that takes care of the signal simulation is in the electronics-simulator
module, which defines the CoaxialCable and FEBoard classes, representing the coaxial cable
and front end board respectively. Inside these classes, there is a method for each stage of
signal simulation, characterized in Table 3.1.
Table 3.1: Stages of Simulation Previously, the simulation of the PMT signal
was broken up into 4 stages. The addition of Johnson noise adds another stage in
the process. (Right column) The corresponding methods are shown for anyone who
would like to look into this further. (Left column) For the sake of brevity, the full
method declaration has been omitted.
Important methods in electronics-simulator
TestElectronicsService::ConvertPEsToPMTSignal convert PEs of PMTs into a signal (voltage)
CoaxialCable::PropagateSignal
attenuate signal
CoaxialCable::JohnsonNoise
cable thermal noise
FEBoard::TerminateSignal
simulate front end board
FEBoard::IntegrateSignal
amplification & integration
To account for the Johnson noise, I created a method in the CoaxialCable class to
modify the PMT pulse in the time domain. In order to replicate the random nature of
Johnson noise, I defined a noise power term PN that is drawn from a Gaussian with mean
= 0 and width = KT B. I then found the voltage of the Johnson noise VN by
p
(3.2)
VN = 4PN R
taking special care to preserve the sign of the PN term from the Gaussian.
For a first analysis, I took the temperature of the cable to be room temperature, a
resistance of 75 ohm, and a bandwidth of 3 GHz. After running through the modified code,
the noise was on the order of 2 mV and shown not to have too much of an impact on the
signal. For instance, TOT from Figure 3.15 didn’t change much from Figure 3.15. (To
see the Johnson noise before it is added to the signal, see Appendix 4.7).
2
Sometimes referred to as Nyquist noise from H. Nyquist who published a theoretical analysis of Johnson’s
observation a year later25
3.3
RADIAL DISTRIBUTION OF TTVS
(a) Without Noise
36
(b) With Noise
Figure 3.15: The Effect of Johnson Noise on PMT Signal The Time-overThreshold is not effected much by the addition of Johnson noise on the order of 2
mV. Fig 3.15a shows the original PMT signal, the low level threshold (-6.6 mV),
and the signal after passing two stages of simulation. Fig 3.15b shows the result
of adding a Johnson noise in the simulation. In both figures, the stage for simulating
the effect of the front end board (green) has little effect so it overdraws itself on the
signal from the previous stage.
With the changes to the CoaxialCable in place, continuing this study will in the future
will be easy. I highly recommend measuring the properties of the rg11 cable as a way
to confirm the accuracy of the variables that I used. This is especially important for the
bandwidth term, as the 3 Ghz number was a theoretical upper limit and more realistic values
may be around 100 Mhz. In addition, more complex noise models could be added to the
CoaxialCable class using the JohnsonNoise method I created as a template.
Chapter
4
Conclusion
Finding an optimal radius for CxPE is less about finding, and more about choosing. Priorities
must be set and research goals defined before choosing a reconstructed core radius because
it has so much of an effect on what sample is chosen.
While some results show that a 60m radius has a better gamma efficiency than the
standard 40m radius for high energies, it also has the highest proton efficiency in overall
energy. A 30m radius had high gamma efficiencies and low proton efficiency for low energy
primaries, which falls in line with HAWC’s research goals. Since 30m was also shown to have
the highest maximum quality factor for cuts on CXPE, I endorse lowering the core radius
to 30m. Since the effects from 40m to 30m weren’t very drastic in my study and in lieu of
more support, I don’t believe a switch is fully necessary however.
The modifications to HAWCEye have been extremely convenient to my research. Navigating files has become a lot quicker and the Play & Save button has speed up the time it
took to gather large sets of images. Before more users can benefit from the improvements,
the code for the evd must be submitted to SVN and documented.
All of the groundwork has been laid for future TTV studies. The new weighted averages
that I started exploring in Section 3.3 can be looked at in greater detail, and the old
variables from Section 3.1 can be revisited easily with the programs I have made. I tried
really hard to comment my code so that it is understandable, but if there are any questions,
I am also putting examples on my HAWC website.
Lastly, I didn’t have as much time as I wanted to explore noise in the electrical cables.
While I believe the Johnson noise is the same magnitude as expected, it would be great to
actually measure properties of the cables in a laboratory to confirm this. In the future, it
would be good to see other noise models added to the electronics-simulator module.
37
4.2
4.1
HAWC’S FUTURE
38
HAWC’s Future
The future for HAWC is looking bright. The National Science Foundation (NSF), Department of Energy (DOE) and Mexican institution known as CONACyT have all sponsored the
experiment. Just recently, the first construction phase, known as VAMOS, was completed,
getting the first 7 tanks ready to test equipment. Within no time, HAWC will be searching
the cosmos for powerful gamma rays.
Figure 4.1: Construction of Tanks for HAWC
4.2
Acknowledgments
I would like to thank my adviser Prof. Teresa Montaruli for giving me this great opportunity
and helping me understand HAWC through useful discussions. I acknowledge Prof. Wendy
Crone for teaching me the skills necessary for conducting research. Lots of thanks to Juan
A. Aguilar for helping me answer many questions and helping me with the next step. There
are too many others to thank completely, but I would not want to leave out Ian Wisher,
Dan Fiorino, and Zig Hampel-Arias. A special thanks to Chris Weaver for helping me in the
fight against ROOT – we will win someday!
References
[1] R. Salvaterra, M. D. Valle, S. Campana, G. Chincarini, S. Covino, P. D/’Avanzo,
A. Fernandez-Soto, C. Guidorzi, F. Mannucci, R. Margutti, C. C. Thone, L. A. Antonelli, S. D. Barthelmy, M. De Pasquale, V. D/’Elia, F. Fiore, D. Fugazza, L. K.
Hunt, E. Maiorano, S. Marinoni, F. E. Marshall, E. Molinari, J. Nousek, E. Pian, J. L.
Racusin, L. Stella, L. Amati, G. Andreuzzi, G. Cusumano, E. E. Fenimore, P. Ferrero,
P. Giommi, D. Guetta, S. T. Holland, K. Hurley, G. L. Israel, J. Mao, C. B. Markwardt,
N. Masetti, C. Pagani, E. Palazzi, D. M. Palmer, S. Piranomonte, G. Tagliaferri, and
V. Testa. Grb 090423 at a redshift of z ≈ 8.1. Nature, 461(7268):1258–1260, 10/29
2009. M3: 10.1038/nature08445; 10.1038/nature08445. 7
[2] Neil Gehrels and Lynn Cominsky. Gamma-ray bursts, Friday, 28-Mar-2008 09:12:51
PDT. 2008. 7
[3] Bing Zhang. Astrophysics: Most distant cosmic blast seen. Nature, 461(7268):1221–
1223, 10/29 2009. M3: 10.1038/4611221a; 10.1038/4611221a. 7
[4] N. R. Tanvir, D. B. Fox, A. J. Levan, E. Berger, K. Wiersema, J. P. U. Fynbo, A. Cucchiara, T. Kruhler, N. Gehrels, J. S. Bloom, J. Greiner, P. A. Evans, E. Rol, F. Olivares, J. Hjorth, P. Jakobsson, J. Farihi, R. Willingale, R. L. C. Starling, S. B. Cenko,
D. Perley, J. R. Maund, J. Duke, R. A. M. J. Wijers, A. J. Adamson, A. Allan, M. N.
Bremer, D. N. Burrows, A. Castro-Tirado, B. Cavanagh, Ugarte Postigo de, M. A. Dopita, T. A. Fatkhullin, A. S. Fruchter, R. J. Foley, J. Gorosabel, J. Kennea, T. Kerr,
S. Klose, H. A. Krimm, V. N. Komarova, S. R. Kulkarni, A. S. Moskvitin, C. G. Mundell,
T. Naylor, K. Page, B. E. Penprase, M. Perri, P. Podsiadlowski, K. Roth, R. E. Rutledge, T. Sakamoto, P. Schady, B. P. Schmidt, A. M. Soderberg, J. Sollerman, A. W.
Stephens, G. Stratta, T. N. Ukwatta, D. Watson, E. Westra, T. Wold, and C. Wolf.
A γ-ray burst at a redshift of z ≈ 8.2. Nature, 461(7268):1254–1257, 10/29 2009. M3:
10.1038/nature08459; 10.1038/nature08459. 7
[5] Sr Short Nicholas M. Novae, supernovae; neutron stars and pulsars; quasars and black
holes; gamma ray bursts; and star collisions. 7
39
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[6] Enrico Ramirez-Ruiz and William Lee. Gamma-ray bursts: Maybe not so old after all.
Nature, 460(7259):1091–1092, 08/27 2009. M3: 10.1038/4601091a; 10.1038/4601091a.
7
[7] Hawc project summary. Technical report. 7, 12, 15, 17, 18
[8] R. Nave. Waveparticle duality. 9
[9] Dr Lin Chambers and Penny Oats. Electromagnetic spectrum, 2010. 10
[10] Beth Barbier and SP Systems. Cosmic rays, 2010. 10
[11] Carl R. Nave. Cosmic rays. 10, 14
[12] Yoshiki Tsunesada. The extreme energy cosmic rays. 10, 11
[13] Hawc university of wisconsin - madison, 7/30/2010 2010. 11
[14] CNSC. Candu fundamentals. 11, 13
[15] The VERITAS Collaboration. Veritas education website. 11
[16] G. Sinnis. Air shower detectors in gamma-ray astronomy. New Journal of Physics,
11:055007, May 2009 2009. 12, 13
[17] Photonics dictionary. 12
[18] Glenn F. Knoll. Radiation Detection and Measurement. John Wiley amd Sons, Inc.,
third edition, 2000. 13
[19] Hawc project proposal. Technical report. 15
[20] Hawc techincal design, 5/21/2009 12:50:22. 2009. 15, 17
[21] Hawc observatory. Technical report. 16
[22] Jordan A. Goodman HAWC Milagro Collaborations. Physics with hawc. volume 1085,
pages 809–812. AIP, 2008. 17
[23] Editorial Committee Hamamatsu Photonics K.K. Photomultiplier tubes – basics and
applications, 2006. 18
[24] Juan A. Aguilar. In HAWC meeting, Nov 4 2009. 20
[25] Jim Lesurf. Sources of noise: Johnson and shot noise. 34, 35
[26] Johnson noise. Technical report. 35
[27] Miguel Mostafa. Requirements and baseline design: Wbs 3.1 - tank design, 2010. 43
[28] Hawc internal report. Technical report. 45
[29] David Orozco Andres Sandoval. personal communication. 47
Appendix
List of Abbreviations
AGN – Active Galactic Nuclei
C – Compactness Parameter; C = nPMT/CxPE
cog – center of charge
CxPE – C cross PE; the number of PEs in the hottest tank outside of a 40m radius from
the reconstructed shower core
EAS – Extensive Air Shower
eV, Mev, Tev – electron volts, mega-electron volts, tetra-electron volts
E-M – Electromagnetic
FPGA – Field Programmable Gate Array
GRB – Gamma-ray Burst
HAWC – High Altitude Water Cherenkov
LMT – Large Millimeter Telescope
MC – Monte Carlo
nPE – number of PEs
PE – Photoelectron
PMT – Photomultiplier Tube
SMT – Simple Multiplicity Trigger
TDC – Time-to-Digital-Converter
TOT – Time-Over-Threshold
41
REFERENCES
42
Table of Particles
Table 4.1: Fundamental Particles There are 2 main categories of fundamental
particles according to the Standard Model: fermions that are the most basic matter
and bosons that carry force. 12 types of fermions exists along with their antimatter
counterparts, not shown in the table below. Hadrons are composite particles split
into two families based on the number of constituent quarks: baryons (3 quarks) and
mesons (1 quark and 1 antiquark). (Adapted from CPEP)
Biographical Sketch
I was born March 29, 1988 and grew up in Milwaukee, WI. I attended Greendale High School
and was involved in many after school programs, both athletic(Wrestling, Football, Track
& Field) and academic (Debate, Math Team). After high school, I began studying at the
University of Wisconsin - Madison. I was active in the student residential communities as a
resident my freshman and sophomore years, and then eventually as a staff member, serving
as a Peer Mentor for the Bradley Learning Community.
My major is Engineering Physics with a focus on scientific computation. I also have a
strong interest in Spanish and am working towards a Certificate in International Engineering.
During the 2008-2009 academic year, I was fortunate enough to be able to study abroad at
the Universidad Politécnica de Valencia in Valencia, Spain. My courses were all engineering
courses taught in Spanish, and I feel that unique experience has prepared me for and fueled
my interest in an international career.
REFERENCES
43
The summer after my freshman year, I started research with Project IceCube in the
Physics Department under the tutelage of Prof. Teresa Montaruli. I investigated the effective
area of the neutrino detector and later created a small program to display depth verses time
information for events that triggered the detector. Needless to say, the skills I gained with
IceCube will prove invaluable when working with HAWC.
I have additional research experience in related areas, having participated in a Math
and Physics based REU program at the University of Central Florida the summer of 2008.
Under the guidance of Prof. Roy Choudhury, I examined bifurcations and chaos in population
dynamics, specifically predator-prey models with delayed effects.
Best Practice Analysis
Although HAWC has received funding from 3 agencies, the funding is limited. In order
for HAWC to keep within budget, financial aspects must be considered and weighed with
scientific goals.
HAWC has demonstrated best practice by finding ways to stay within the budget and
not sacrifice scientifically. For instance, several materials for the tank were envisioned, but
ultimately steel was used.27 A steel design not only can provide the proper structure,
but the relatively low cost of steel for high commodities can allow the diameter of the
tanks to increase. In turn, a larger spacing between PMTs can be advantageous because it
increases the total detector area.27 Also, the low weight of steel helps in transportation and
construction.
Using steel has additional benefits provided by the manufacturer. All tanks are prefabricated and come with kits that include the fasteners and other hardware. All holes are
pre-drilled to speed up assembly time.
As another example of best practice, take the PMTs into consideration. The cost of refurbishing the PMTs is smaller than purchasing new ones. By reusing the PMTs from Milagro,
HAWC has used their resources wisely to extend the budget. In addition, being located in
a national park of Mexico carries some environmental responsibilities. By reusing PMTs,
HAWC has made strides to lower the impact of astronomy experiments on the environment.
As a final example, even HAWC’s construction plan follows best practice. Instead of
building the entire 300 tank array of HAWC all at once, the construction plan calls for incremental deployment and testing (7, 30, 100, 300). This allows for flexibility and unforeseen
problems to be fixed early on. If cost becomes an overwhelming issue, the number of tanks
can be adjusted and later readjusted due to the scalability of the design27 .
REFERENCES
Additional Figures
Additional Efficiency Figures
(a) Proton Efficiency
(b) Gamma Efficiency
Figure 4.2: Efficiencies, large nPMT Fig 4.2a shows the proton efficiency for
a fixed gamma efficiency of 50%. The optimal radius according to this metric will
have the lowest proton efficiency. Notice how the optimal radius increases with nPMT
similar to Figure 3.6 Fig 4.2b the gamma efficiency for a low proton efficiency fixed
at 10%. The optimal radius remains at 60m (and may be possibly higher) regardless
of how nPMT increases.
44
REFERENCES
(a) Proton Efficiency
(b) Gamma Efficiency
Figure 4.3: Efficiencies, small nPMT Fig 4.3a shows the proton efficiency for
a fixed gamma efficiency of 50%. A 20m radius performs the best with the lowest
proton efficiency for all nPMT shown. Fig 4.3b the gamma efficiency for a low
proton efficiency fixed at 10%. As nPMT increases, the optimal radius according to
this metric increases from 20m to 30m and finally 40m.
Additional Simulation Figures
Figure 4.4: Tank Simulation The current simulation is set up for VAMOS, the
first stage of operation that features 7 tanks with 3 PMTs each. 28
45
REFERENCES
Additional CxPE Distribution Figures
Figure 4.5: CxPE Distribution, Efficiency, and Quality Factors, nPMT=100
Even at nPMT= 100, the maximum quality factor is not a good indicator of g/h
discrimination because there is an extremely low gamma efficiency.
46
47
REFERENCES
B'
C
16.742
6.842
16.742
9.900
6.842
E'
F
F'
G
G'
H
H'
I
I'
J
J'
cota general plataforma
60.442
6.842
9.900
6.842
16.742
9.900
6.842
16.742
9.900
6.842
11.192
9.900
cotas a ejes principales
6.842
cotas a ejes totales
026
013
070
055
027
071
056
042
1.0
014
087
057
043
137
089
139
156
122
106
090
140
157
123
107
141
124
6.566
155
121
105
074
154
138
158
28.521
280
266
251
236
45.440
148.640
139.940
43.150
308
295
281
267
252
307
294
309
296
282
310
Figure 4.6: Detailed Layout HAWC will closely resemble the design above. Current
simulations are based off of the specified dimensions29 .
cota general ejes
101.079
166.216
cotas a ejes totales
65.137
250
220
293
279
265
235
203
186
249
219
185
172
278
264
234
202
306
263
248
218
184
171
292
233
217
4
305
247
232
201
304
291
277
216
183
170
276
231
200
303
290
120.119
246
214
182
169
275
262
199
302
289
261
197
215
168
4.350
4.350
245
198
153
120
088
058
136
104
073
152
119
103
072
00
028
102
086
041
135
118
274
260
230
301
288
4'
cota general plataforma
040
101
085
273
244
213
151
300
287
259
229
3
51.350
012
069
054
134
117
243
212
196
00
039
025
100
084
181
150
272
258
228
299
286
4.350
068
053
133
116
1.0
011
099
083
242
211
195
271
257
227
298
285
00
038
024
115
180
167
270
241
210
194
297
284
256
226
00
067
052
149
098
082
179
166
240
209
193
283
269
255
225
1.0
066
037
010
081
051
148
239
208
178
268
254
224
192
165
132
207
177
147
131
114
065
050
023
113
097
223
191
164
253
238
1.0
080
190
163
130
206
176
146
112
096
049
036
129
237
222
4.350
4.0
079
189
162
145
221
205
175
144
111
188
174
161
128
095
064
160
1
204
00
00
078
048
022
110
187
173
143
127
094
063
035
009
093
062
047
126
109
077
034
008
092
159
142
6.0
046
021
53.424
9.900
125
108
076
061
032
007
47.400
6.842
16.742
00
017
091
060
031
020
cotas lados plataforma
9.900
16.742
6.0
003
006
28.831
6.842
075
045
019
cota general plataforma
cotas lados plataforma
cota general ejes
16.742
CASETA
6X20 m
030
005
119.809
9.900
059
044
033
5
6.842
16.742
00
36.900
9.900
029
018
2
16.742
4.0
001
004
6.566
E
4.350
016
137.724
D'
157.516
002
148.640
D
4.350
015
5'
C'
166.216
4.350
4.350
B
105.774
4.350
1
A'
cotas lados plataforma
cotas a ejes totales
A
cota general ejes
cotas lados plataforma
cota general plataforma
Additional Site Figures
REFERENCES
Additional Thermal Noise Figures
Figure 4.7: Scale of Johnson Noise For HAWC’s setup, the noise in the cable due
to Johnson Noise is on the order of 2 mV.
48