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DISCOVERY OF LOCALIZED TEV GAMMA-RAY SOURCES
AND DIFFUSE TEV GAMMA-RAY EMISSION FROM THE
GALACTIC PLANE WITH MILAGRO USING A NEW
BACKGROUND REJECTION TECHNIQUE

presented by

Aws Ahmad Abdo

has been accepted towards fulfillment
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6/07 p:/ClRC/DaIeDue.indd-p.1

DISCOVERY OF LOCALIZED TEV GAMMA-RAY SOURCES AND
DIFFUSE TEV GAMMA-RAY EMISSION FROM THE GALACTIC
PLANE WITH MILAGRO USING A NEW BACKGROUND
REJECTION TECHNIQUE

By
Aws Ahmad Abdo

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department. of Physics and Astronmny

2007

ABSTRACT

DISCOVERY OF LOCALIZED TEV GAMMA-RAY SOURCES AND
DIFFUSE TEV GAMMA-RAY EMISSION FROM THE GALACTIC
PLANE WITH MILAGRO USING A NEW BACKGROUND
REJECTION TECHNIQUE

By
Aws Ahmad Abdo

Very high energy gamma-rz-tys can be used to probe some of the most powerful
astrophysical objects in the universe, such as active. galactic nuclei, supernova rein-
nants and pulsar-powered nelmlae. The diffuse. gamma radiation arising from the
interaction of cosmic-ray particles with matter and radiation in the Galaxy is one
of the few probes available to study the origin of cosmic-rays. Milagro is a water
Cherenkov detector that continuously views the entire overl‘iead sky. The large field-
of—view combined with the long observation time makes l\’lilagro the. most sensitive
instrument available for the study of large, low surface brightness sources such as the
diffuse gamma radiation arising from interactions of cosmic radiation with interstellar
matter. In this thesis I present a new backgrount‘l rejection technique for the Milagro
detector through the development. of a new gamma hadron separation variable. The
Abdo variable, A4, coupled with the weighting analysis technique significantly im-
proves the sensitivity of the Milagro detector. This new analysis technique resulted
in the first discoveries in lN'Iilagro. Four localized sources of TeV gamma-ray emission
have been discovered, three of which are in the Cygnus region of the Galaxy and one
closer to the Galactic center. In addition to these localized sources, a diffuse emission
of TeV gamma-rays has been dismvered from the Cygnus region of the. Galaxy as
well. However, the TeV gamma—ray flux as measured at ~12 TeV from the Cygnus
region exceeds that predicted from a conventional model of cosmic-ray production

and propagation. This observation indicates the existence of either hard-spectrann

cosmic—ray sources and/or other sources of TeV gannna rays in the region. Other
TeV gannna—ray source candidates with post-trial statistical significances of > 40

have also been observed in the Galactic plane.

© Copyright by
AWS AHMAD ABDO
2007

I dedicate this work to my mother Muna Al-Qaisi and to the memory of my father

Ahmad Abdo

ACKNOWLEDGMENTS

First of all I would like to thank my parents, Ahmad Abdo and Muna Al—Qaisi.
Their continuous caring, support, and encouragentent to me all my life made me the
man I am today and helped me face all obstacles in my life with ease and determina-
tion.

I would like to thank my wife, Callista, for her continuous and limitless support

during my days at grad school. Without her my life would have been much harder.

As a student on Milagro, I was lucky to have more than one advisor, each an
expert in his field. I would like to thank my l\rlichigan State University advisor,
Professor James Linnemann, for offering me the opportunity to work on Milagro, for
his kindness, and for his continuous support. I would like to thank my advisor from
Los Alamos National Laboratory, Dr. Gus Sinnis, for all his support and kindness,
for believing in me, and for helping me. become the scientist that I am today. His
invaluable comments, ideas, and guidance helped shape this thesis in the best way
possible. Dr. Andrew Smith of the University of Maryland (ileserves very special
thanks. I won’t be exaggerating when saying that I owe most of what I learned
while working on Milagro to him. I would like to thank him for his patience and for
answering many of my endless questions about Milagro and about the field in general.
I am also grateful for all the long hours we spent in his office in Maryland working
on this analysis. I would like to thank Dr. Brenda Dingus of Los Alamos National
Laboratory for all her invaluable inputs and comments on my work. I would also
like to thank the Maryland group, Prof. Jordan Goodman, Prof. Robert Ellsworth,
and Prof. David Barely for their comments on my work and for their support. I
would like to thank Dr. Curtis Lansdell for helping me during my first days at Los
Alamos and for being a good friend. I would like to thank the. Los Alamos postdocs

Dr. Gary Walker, Dr. Sabrina Casanova, and Dr. Petra Huentenuiéyer for their help

vi

and kindness.

My Milagro friends deserve special thanks for making my life as a grad student
much more enjoyable. I would like to thank Dr. David Noyes for all the intellectual
conversations I had with him. I would like to thank him for being open minded, for
being interested in my culture, and for all the good vegan food he cooked for me.
He is a great friend. My fellow student and friend, Vlasios Vasileiou, deserves all
the thanks for creating all the Monte Carlo simulations needed for the completion of
this work. The times I spent with him and David in Maryland make one of the best
memories I have. Iris Gebauer deserves special thanks for her continuous support and
for being such a good friend.

I am grateful to l\-'Iic.hael Schneider for his kindness, support, and for being a good
friend. I am also grateful to Scott Delay for helping me while on shift and for all the
interesting conversations I had with him. I am grateful to Prof. Allen h'liticer from
NYU for all the intellectual conversations I had with him.

I am sincerely grateful to Brenda W’enzlick the HEP secretary at MSU for her help
and kindness. I am also grateful to Pam l\'Iarteniz from Los Alamos for her kindness

and for helping me in all the paper work needed there.

vii

Contents

LIST OF FIGURES .............................

1 Introduction To Very High Energy Gamma-Ray AstrOphysics
1.1 The Relativistic Universe .........................
1.2 Gamma-Ray Astronomy .........................
1.3 Gamma-Ray Detection ..........................
1.3.1 Space-based Detectors ......................
1.3.2 Ground-based Detectors .....................
1.3.3 Extensive Air Showers ......................
1.3.4 Imaging Air Cherenkov Telescopes ...............
1.3.5 Extensive. Air Slmwer Arrays ...................
1.3.6 Water Cherenkov T(‘('lllll(lll(-’, ...................
2 Galactic Gamma-Ray Emission ....................
2.1 Cosmic-Rays ................................
2.2 Basic. Processes of Gamma-Ray Production ...............
2.2.1 Pion Decay ............................
2.2.2 Bremsstrahlung ..........................
2.2.3 Inverse Compton S('i-tlt(‘1‘111g ...................
2.3 Galactic Structure ............................
2.3.1 Interstellar Gas ..........................
2.3.2 Interstellar Radiation Field ...................
3 The Milagro Detector ..........................
3.1 Detector Description ...........................
3.1.1 Location ..............................
3.1.2 The Pond .............................
3.1.3 The Outrigger Arrz-iy .......................
3.2 Water System ...............................
3.3 Pond Cover ................................
3.4 Electronic System .............................

viii

xii

COOKIJKCOMHH

r—‘r—‘h—I’
Obi-Li

20
23
23
24
26

28
28
29

31
31
34
36
37
37
38

3.4.1 Signal Extraction ......................... 38
3.4.2 Triggering ............................. 39
3.5 Data Acquisition System ......................... 42
3.6 Calibration ................................ 44
3.7 Event Reconstruction ........................... 45
3.7.1 Core Position Reconstrur-tion .................. 45
3.7.2 Shower Front Sampling Correctimi ............... 48
3.7.3 Shower Front Curvature Correction ............... 51
3.7.4 Direction Reconstruction ..................... 52
3.8 Energk Dependence ............................ 54
3.9 Effective Area ............................... 54
3.10 Simulations ................................ 60
3.10.1 Monte Carlo Simulations of Extensive Air Showers ...... 60
3.10.2 Monte. Carlo Simulations of Detector Response ......... 61
Data Analysis Techniques ........................ 62
4.1 Coordinate Systems on the Celestial Sphere .............. 62
4.1.1 Equatorial Coordinate System .................. 62
4.1.2 .12000 Reference .......................... 63
4.1.3 Julian Date and Modified Julian Date ............. 65
4.1.4 Galactic Coordinate System ................... 65
4.2 Background Estimation .......................... 69
4.3 Significance of a h’Ieasurement ....................... 71
New Gamma-Hadron Separation Technique and Variable ..... 74
5.1 Gamma-Hadron Separation In Milagro ................. 74
5.1.1 The Compactness Parameter ................... 75
5.2 A4, Milagro’s New Camma—Hadron Separation Variable ........ 81
5.3 Properties of A4 .............................. 82
5.3.1 Energy Dependence. ........................ 82
5.3.2 Core Location Dependence .................... 87
5.3.3 Zenith Angle Dependence .................... 88
5.4 Observations of the Crab Nebula Using A4 ............... 90
A4 Weighted Analysis Technique ................... 100
6.1 Motivations for Weighted Analysis Technique ............. 100
6.2 Determining the Garmna-Hz—rdrrm “fights ............... 101
6.3 Determining the PSF Fits ........................ 103
6.4 Median Energy For the W’eighted Analysis Technique ......... 106
6.5 Results on the Crab Nebula ....................... 108

7 All-Sky Survey .............................. 109

7.1 Data Set .................................. 109
7.1.1 Event Selection Cuts ....................... 109
7.1.2 Excluded Data Runs ....................... 110

7.2 Epochs in Milagro ............................. 1.10
7.2.1 Dead PMTs ............................ 111

7.3 Determining the Gamma—Hadron \Veights ............... 113
7.3.1 Relative Epoch \Veighting .................... 117

7.4 Determining the PSF Fits ........................ 118

7.5 Flux Calculation ............................. 125
7.5.1 Flux Calculation for the A4 \N-"eighted Analysis Technique . . 126

7.6 All-Sky Map ................................ 127
7.6.1 Observations of the Crab Nebula ................ 129
7.6.2 Observations of the Active Galaxy Mrk421 ........... 130

8 Discovery of Localized TeV Gamma-Ray Sources in the Galactic
Plane .................................... 134
8.1 Discovery of the TeV Gamma-Ray Source.
MGRO .I'20l9+37 ............................. 137
8.1.1 Location of MGRO .I2019+37 .................. 137
8.1.2 Spatial Morphology of MGRO .I'2019+37 ............ 139
8.1.3 Flux from MGRO J2019+37 ................... 141

8.2 Discovery of the TeV Gamma-Ray Sources
MGRO J2033+42 & MGRO J2031+41 ................. 143

8.3 Discovery of the TeV Gamma-Ray Source.

MGRO J1909+06 ............................. 144

8.4 The TeV Gamma—Ray Source. Candidate
MGRO J2032+37 ............................. 147

8.5 The TeV Gamma-Ray Source Candidate
MGRO J2043+36 ............................. 147

8.6 The TeV Gamma-Ray Source Candidates
MGRO .11852+01 and MGRO J1859+03 ................ 147

8.7 The TeV Gan'una-Ray Source Candidate
MGRO J2233+60 ............................. 150

8.8 Milagro TeV Gamma—Ray Source Catalog ............... 153

9 Discovery of Diffuse TeV Gamma—Ray Emission From the Cygnus

Region ................................... 154

9.1 The GALPROP Model .......................... 156

9.2 Interpretation of Results ......................... 158

10 Conclusions ................................ 161

10.1 Summary ................................. 161

10.2 Future Directions ............................. 162

Appendices ..................................

A Spectral Index Analysis Technique .................. 163
A.1 Energy Dependence on A4 ........................ 164
A2 Spectral Index Determination Technique ................ 164
A3 Crab Nebula Spectral Index Estimation ................. 165
A.4 Cosmic Rays Spectral Index EstiIm-ition ................. 166

B Detailed Plots ............................... 171
13.1 Aangle Distributions for Different Epochs ................ 171
B2 Anny“, Distributions for Different Spectral Indices ........... 186

C

8.3 A4 Distributions as a function of “Dead” PMTs for different epochs . 191

Detailed Tables .............................. 199

Bibliography ................................. 207

xi

List of Figures

1.1

1.2

1.3

2.1
2.2

3.1

3.2

3.3

3.4
3.5

Third EGRET source catalog, shown in Galactic coordinates. The
size of each symbol is proportional to the highest intensity seen for the
corresponding source. Out of the 271 sources 170 have not yet been
identified with known objects. Taken from [73]. Images in this thesis
are presented in colors ...........................

Simulated development of a 1 PeV hadronic 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 [36] .......
Development of the cascades of three different primaries through the.
atmosphere. Taken fron'1[74] .......................

The HESS telescope array in Namibia. .................

The Tibet air shower array ........................

EGRET all-sky q-ray map above 100 MeV in Galactic coordinates[75].

The average spectrum of diffuse ’7-rays detected by EGRET from the
inner galaxy (Galactic Longitude, 300° < l < 60°, and Galactic Lati-
tude, [b] S 10°). Contributions from point sources detected with more
than 50 significance have been removed. The data are represented by
the points and the solid line represents the prediction of the diffuse
'y-ray model. The model incorporates electron brernsstrahlung (EB),
inverse Compton (IC), and nucleon-nucleon (N N) processes, as indi-
cated by the various lines. ........................

An aerial view of the Milagro detector. The pond is visible in the
center of the photo. The red circles mark locations of the outrigger
tanks. ...................................

A schematic diagram of the Milagro pond (not. to scale). Figure. taken
from [45] ..................................

Schematic of PMT placement. in the pond (not to scale). Figure taken
from [34]. .................................

An inside view of the Milagro pond ....................
Tin1e-over-threshold (TOT) method. ..................

xii

11

12
14
16

21

32

3.6

3.8

3.9

3.1

3.1

3.1

3.1

3.1

3.1

4.1
4.2
4.3

4.4

4.6

0

1

2

3

4

O

Distributions of the risetime parameter [33]. From top to bottom: data
events that could be fit, data events that. failed the fit, and simulated
gamma-ray showers.

Conceptual diagram of the primary particle direction reconstruction in
Milagro.

RNeconstruc ted core positions for simulated gamma-ray events that trig-
gered the detector using the current 2-D Gaussian fitter. In the figure,
the y- and x-axes point north and east, respectively. The Milagro pond
is inclined by angle of 244° from the north—south direction. .
Reconstructed (fit) core position versus true core position for simulated
gamma—ray events.

Distribution of error in core location for the simulated gamma—ray
events shown in figure 3.9.

Distribution of Amy“. for triggered garnma-ray events that. passed the
Nfit _>_ 40 cut. The median of the Amy)“ distribution of ~ 085° is
roughly the angular resolution of the detector for this N fit cut.

Distribution of gamma-ray events that triggered the detector for a
power law spectrum of dN/tlly' oc 111—2'4. The median energy (3.5
TeV) is indicated by the middle. dotted line. The two other dotted
lines indicate the energies above which 95% and 5 Vt of the detected
gamma-rays fall.

Median triggered energy as a function of zenith angle for simulated
gamma—ray events with a power law spectrum of dN/dE oc 111—2'4
The effective area as a function of energy for three different zenith angle
ranges for an [2"2'4 spectrum. The horizontal dashed line represents
the physical area of the detector (4.8 ><103 mg).

The effective area as a function of zenith angle for an E ‘24 spectrum.

Equatorial coordinates on the celestial sphere. Image taken from [76]
Galactic coordinate system. Figure taken from [77].

Optical view of our Galaxy in Galactic coordinates. The Galactic
center (I = 0) is in the middle of the map. Galactic longitude increases
to the left of the center and decreases to the right. .

Artist conception of the Milky \\ 11y Galaxy as seen from the North
Galactic Pole. . . . . . . . .
An all- sky rate. for one day. As (an be seen .the rate1 varies 111th time
of the day. For a two hour period, 7200 seconds, the rate is essentially
constant.

Distribution of excess (or deficit) signific ances. The distribution' 1s well

fitted to a Gaussian distribution 111th a mean of 0.0005 and sigma of
0.997.

Gamma-ray (top row) and proton (bottom row) events imaged in the
rnuon layer of IVIilagro. The area of each square is proportional to the
number of photoelectrons (PEs) registered in the corresponding PMT,
and the area is saturated at 300 PEs.

xiii

43

46

48

49

50

53

59

64
67

68

70

73

76

U!
[\D

5.3

5.6

C}!
x]

5.8

5.9

5.10

5.12

The compactness distribution for Monte Carlo y-ray showers, l\"Ionte
Carlo cosmic-ray showers, and data. All of the histograms have. been
normalized to have unit area. . . . . . . . . . . . . . . . . . .
Fraction of data, cosmic-ray Monte Carlo, and y—ray Monte Carlo show-
ers with a compactness value that is greater than the X-axis value.

Quality factor Q as a function of the minimum value of C required to
retain an event. The red line compares Monte Carlo y-rays to Monte
Carlo cosmitit—rays, and the black line compares Monte Carlo 'y-rays to
data.
A4 distribution for Monte Carlo '11-ra3' showers, Monte Carlo cosmic-
ray showers, and data. All of the histograms have been normalized to
haveunitarea.
Fraction of data, ('( 1s111ic-ra3' Monte Carlo, and Tray Monte Carlo show—
ers with an A4 value that is greater than the x—axis value.

Quality factor Q as a function of the minimum value of A4 required to
retain an event. The red line compares Monte Carlo y-rays to Monte
Carlo cos111ic-ra11's, and the black line compares Monte Carlo 'y-rays to
Fraction of gamma-rays and cosmic-rays retained by the cut A4 2 3.0
as a function of the primary energy. Gamma-ray in blue, cosmic—ray
inred.
Median energies of gamma-ray—initiated air showers as a function of
A4. Each point represents the median energy for gamma-ray events
with an A4 value greater than the 1.1-axis value.

A4 distribution for Monte Carlo '11-ray showers, Monte Carlo cosmic-
ray showers, and data for events with their core on the. pond. All of
the histograms have been normalized to have unit area.

A4 distribution for Monte Carlo y-ray showers, Monte Carlo cosmic-
ray showers, and data for events with their core off the pond. All of
the histograms have been normalized to have unit area.

Quality factor Q for events with their core on and off the pond. In

both cases Monte Carlo 1.1-rays are compared to Monte Carlo cos111ic-rays

Quality factor Q for events with their core on and off the pond. In
both cases Monte Carlo Trays are compared to data . .

A4 distribution for Monte Carlo 11-ray showers, Monte Carlo cosmic-
ray showers, and data for the zenith angle range 0° g 0 3 15°. All of
the histograms have been normalized to have unit area. . . . .

A4 distribution for Monte Carlo “pray showers, Monte. Carlo cosmic-
ray showers, and data for the zenith angle range 15° 3 6 S 30°. All of
the histograms have been normalized to have unit area. . . . .
A4 distribution for Monte Carlo y-ray showers, Monte Carlo cosmic—

ray showers, and data for the zenith angle range 30° 3 0 S 45°. All of
the histograms have been normalized to have unit area. . . . .

Quality factor as a function of the A4 cut for three different zenith
angle ranges. In all three cases Monte Carlo 111-rays is compared to
cosmic-rays.

Quality factor as a function of the A4 cut for three. different zenith

angle ranges. In all three cases Monte Carlo 1.1-rays is compared to data.

xiv

“J

Kl

80

83

84

86

a}
\J

89

90

91

92

93

94

95

96

97

5.19

5.20

6.1

6.2

6.3

6.4

6.5

fl
p—a

7.2
7.3

7.4

7.5

“\I
O)

7.7
7.8

Map of the statistical significance around the Crab Nebula with the
A4 2 3.0 and Affit 2 40 cuts applied ...................

Map of the statistical significance around the Crab Nebula with the,
C 2 2.5 and Nf-z’t Z 20 cuts applied. ..................

Map of the statistical significance around the Crab Nebula with the
A4 2 12.0 and .Nfit 2 40 cuts applied. .................
Distribution of Anna“. for triggered gamma-ray events that. passed the
N fit 2 40 cut. The median of the distribution is ~ 085° ........

Distribution of Aangle for triggered gamma-ray events that passed the
A4 2 3.0 (top) and A4 2 12.0 cuts (bottom) ...............

Energy distribution for gamma-ray events with a power law spectrum
of dN/dE or E ‘2'°. The blue line. represents the energy distribution
for the A4 weighted analysis technique, while the green line represents
the energy distribution for triggered events. The 111edian of the distri-
butions are 12 and 3.2 TeV, respectively. ................
Map of the statistical significance around the Crab Nebula with the
weighting analysis method applied. ...................

Distributions of A4 for the different 1.1crccntage of “dead” PMTs for
cosmic-ray Monte Carlo, data, and ganuna—ray Monte Carlo for the
eighth epoch. ...............................

Same distributions as in figure 7.] but with log-scale on the y-axis.

Aangle distributions and the corresponding PSF fits for the first six
slices in A4 for the eighth epoch for a Crab-like spectrum. ......

Adm)“, distributions and the corresponding PSF fits for the 111st six
slices in A4 for the eighth epoch for a Crab-like spectrum. ......

The effective Anny]? distributions and the corresponding PSF fits for
the weighted analysis for four different source spectra ..........

Same distributions as in figure 7.5 overlaid on the same plot. The lines
represent in each case the fit to a double 2D Gaussian function.

Distribution of significanccs ........................

A TeV gamma-ray image of the northern hemisphere. The brightest
extended region in the entire northern sky is the Cygnus Region of the
Galactic plane located at roughly 300 degrees in Right Ascension and
35 degrees in Declination. The white lines show a i5 degree region
around the Galactic plane. At each point the statistical significance of
the observed excess (or deficit) is plotted. The most significant TeV
gamma-ray source in the map is the Crab Nebula located at a Right
Ascension of 83.6 and a Declination of 22 degrees and visible at 15.2
standard deviations. ...........................

XV

98

99

102

104

105

107

108

114
115

120

121

122

123
128

7.9

7.10

8.1

8.2

8.3

8.4

8.5

8.6

8.7

A TeV gamma-ray image of the region around the Crab nebula for the
six-year data set. The color scale is the statistical significance of the
TeV gamma-ray excess at each point. The significance at the location
of the Crab nebula is 15.2 standard deviations. This significance is less
than what one might expect by scaling the significance from the 1.7
years data set. reported in section 5.4, namely 10.55 x «6.0/1.7 = 19.8
standard deviations. This is due to the fact that the larger data set
contains data with lower quality (no outriggers) than the 1.7 years data
set ......................................

A TeV gamma-r2 y image of the region around the active Galaxy Mrk421
for the six- -year data set. The color scale is the statistical significance
of the TeV gamma-ray excess at each point. The significance at the
location of Mik421 is 7. 3 standard deviations. .............

A TeV gamma-ray image of the northern hemisphere in Galactic coor-
dinates. The large grey region is the part of the Galaxy that. is obscured
by the earth at. the location of Milagro. The small grey region to the
upper left of the figure is near the Zenith. ...............

A TeV gamma-ray image of the Inner Galaxy visible to Milagro. The
Galactic Center is toward the right. The Galactic Center is not visible
from the location of Milagro ........................

The Cygnus Region of the Galaxy as seen in TeV gamma rays. The
color sc ale. is the statistical signific 2111(2) of the TeV gamma-ray excess at
each location. Since the Milagro exposure and sensitivity are roughly
constant over the region in the figure the statistical significance is
nearly proportional to the flux from each point. The crosses show the
location of EGRET sources and their corresponding location errors.

A TeV gamma-ray image of the area around the new source MGRO
J2019+372 The location and location error of the source is marked
by the wlute circle. Locations and location errors of the two EGRET

source (3EGJ2016+3657 and 3EG J2021+3716) are marked by blue
and black circles, respectively. The location and location error of the
GeV source GeV J2020+3658 is marked by the red ellipse. This GeV
source is associated with the PW'N G75.2+0.1 shown in this map as a
yellow dot ..................................

The radial distribution of excess exents from the location around the

Crab Nebula (blue) and MGRO J2019+37 (led) The extent of IVIGRO
J2019+37 18 clearly visible here 1n comparison to the Crab Nebula [1].

A TeV gamma—ray image of the area around the new sources MGRO
J2033+42 and MGRO J2031+41. The location and location error of
MGRO J2033+42 is marked by the white ellipse and the location and
location error of MGRO J2031+41 is marked by the yellow circle. The
Location of the EGRET source (3EG .l2033+4118) is marked by the
red circle, while the location of the HEGRA source (TeV J 2032+4130)
is marked by the green circle. ......................

A TeV gamma-ray image of the area around the new source MGRO
.11909+06. The. location and location error of the source is marked by

the white _circle. The location and location error of the GeV source
GeV .1190! +0557 1s marked by the black ellipse .............

xvi

132

133

138

140

142

146

8.8

8.9

8.10

8.11

9.1

9.2

A.1

A.2
A.3

A.4

8.1

B2

B3

A TeV gamma-ray image of the area around the new source candidate
MGRO I2032+37. The location and location error of the source is
marked by the black ellipse. The black spot in the middle of the map
is MGRO J2019+37. ...........................

A TeV ganuua-rav image of the are 21 around the new source candidate

MGRO J2043+36. The location and location error of the source is
marked by the bl211k circle. . . . . ...................

A TeV gamma-ray image of the area around the new source candi—
date IVIGRO .I1852+01. The location and location error of MGRO
J1852+01 is marked by the white ellipse. The location and location
error of MGRO J1859+03 is marked by the red circle. The black circle
in the middle of the map marks the location and location error of the
GeV sources GeV .I1856+0115 [43] .................

A TeV gamma-1211 image of the a1ea alound the new sour1 e (audidate
MGRO .I2033+60 The lo1ation of the soiuc e is 111211 k1d by the white
cross. . . . . ..........................

The same TeV image, of the. Cygnus re rion as in floure 8.3 but. with the

addition of contours showing the matter density in the region[42, 23, 46].

Gamma-ray spectrum of the diffuse emission from the Cygnus region of
the Galactic plane. The red bars are the EGRET data, and the purple
bar is the Milagro measurement with the statistical error shown as a
broad line and with the systematic error shown as a narrow line. The
solid lines represent the “convent.ional”, and the dotted lines represent

the “optimized" GALI’ROP model of Strong ct a1. [51]. The dark

blue lines represent the total diffuse flux, the red lines represent the 710
component, the green lines represent the inverse Compton component,
the light blue lines are due to bremsstrahlung, and the black lines are
due. to the extragalactic background. The Milagro analysis is insen-
sitive to isotropic emission due to the background subtraction, so the
extragalactic. background is not included in the Milagro energy range.

Median energies of gamma-ray-initiated air showers as a function of
A4. Each point r1'2presents the median energy for gamma-ray events
with an A4 value greater than the ar—axis value. . . . . ........
Differential excess from the Crab Nebula as 21 function of A4

A4 differential distribution of four gamma. Monte Carlo sets with spec-
tral indices -2.1, -2.3, -2.6, and -2.9. For comparison, the differential
excess from the Crab is shown on each of the plots. .........

Distribution of the >12 values of the fits of the different gamma Monte
Carlo sets to the Crab data as a. function of the spectral index 11.

Aanglc distributions and the corresponding PSF fits for the first. six
slices in A4 for the first epoch. .

Aangle distributions and the correspmiding PSF fits for the last. six
slices in A4 for the first. epoch. .

Amwle distributions and the corresp1)nding PSF fits for the first. six
slices in A4 for the second epoch. . . . . . . . . . . ......

xvii

149

152

167

168

169

170

172

173

174

B.4 Anny“, distributions and the corresponding PSF fits for the last six

slices in A4 for the second epoch. .................... 175
B5 Aangle distributions and the correspon1'ling PSF fits for the first six
slices in A4 for the third epoch. ..................... 176
B6 Amgle distributions and the correspcmding PSF fits for the last six
slices in A4 for the third epoch. ..................... 177
8.7 Aangle distributions and the corresponding PSF fits for the first six
slices in A4 for the fourth epoch. .................... 178
B8 Amyle distributions and the corresponding PSF fits for the last six
slices in A4 for the fourth epoch. .................... 179
13.9 Amyle distributions and the corresponding PSF fits for the first. six
slices in A4 for the fifth epoch ....................... 180
B.10 Aangh. distributions and the corresponding PSF fits for the last. six
slices in A4 for the fifth epoch ....................... 181
8.11 Amy]? distributions and the corresponding PSF fits for the first six
slices in A4 for the sixth epoch. ..................... 182
8.12 Aangle distributicms and the corresponding PSF fits for the last six
slices in A4 for the sixth epoch. ..................... 183
B.13 Aangle distributions and the corresponding PSF fits for the first six
slices in A4 for the seventh epoch ..................... 184
13.14 Aangle distributions and the corresponding PSF fits for the last six
slices in A4 for the seventh epoch ..................... 185
B.15 Aangle distributions and the corresponding PSF fits for the first six
slices in A4 for the eighth epoch for a -2.2 spectrum. ......... 187
B.16 Aangle distributions and the corresponding PSF fits for the last six
slices in A4 for the eighth epoch for a —2.2 spectrum. ......... 188
B.17 Amy“. distributions and the corresponding PSF fits for the first six
slices in A4 for the eighth epoch for a -3.0 spectrum. ......... 189
318 Aangle distributions and the corresponding PSF fits for the last six
slices in A4 for the eighth epoch for a -3.0 spectrum. ......... 190

8.19 Distributions of A4 for different percentages of “dead” PMTs for cosmic-
ray Monte Carlo, data, and gamma-ray Monte Carlo for the first epoch. 192

B.20 Distributions of A4 for different percentages of “dead” PMTs for cosmic-
ray Monte Carlo, data, and gamma-ray I\'Ionte Carlo for the second
epoch. ................................... 193

B.21 Dist.ri1;)utions of A4 for different percentages of “dead” PMTs for cosmic-
ray Monte Carlo, data, and gamma-ray Monte Carlo for the third epoch. 194

B22 Distributions of A4 for different percentages of “dead” PMTs for cosmic-
ray Monte Carlo, data, and gamma-ray lVIonte Carlo for the fourth epoch. 195

B.23 Distributions of A4 for different percentages of “dead” PMTs for cosmic-
ray Monte Carlo, data, and gamma-ray Monte Carlo for the fifth epoch.196

8.24 Distributions of A4 for different. percentages of “dead” PMTs for cosmic.-
ray Monte Carlo, data, and gamn‘ia-ray IVIonte Carlo for the sixth epoch. 197

xviii

B25 Distributions of A4 for different p1—2rceutages of “dead” PMTs for cosmic-
ray Monte Carlo, data, and gamma—ray I\lonte Carlo for the seventh
epoch. 198

xix

Chapter 1

Introduction To Very High Energy

Gamma—Ray Astrophysics

1.1 The Relativistic Universe

Our knowledge of the universe comes from the study of the radiation we detect from
different sources in the sky. Most of this radiation is emitted by thermal processes.
Such processes include the Cosmic Microwave Bwrkground (CMB), thermal emissions
from the stars, or from the accretion disks around neutron stars and other massive
objects. Beyond this Ordinary Universe there exists a non—thermal relativistic uni-
verse. This universe is of particular interest to particle physicists, this is because it
involves physical 1.)ro1-.esses that are impossible. to emulate in our laboratories. One
example of these non—thermal processes is the cosmic radiation, whose origin, after 90
years of its discovery. is still largely a 11'1ystery. cosmic-rays are rem2u‘kable for many

I'B‘clSOIlSZ

o cosmic-ray particles represents the largest source of material reaching Earth
from outside our Solar System. The chemical composition of these particles

reflects the nuclcosynthetic process1s occurring at. their origin.

o (":osmic-rays span a very large range of energies. from 1 MeV (100 eV) to 100
r ‘) ,v o . . .
EeV (10“0 eV). The very high energles involved are ev1dence for powerful as-
trophysical accelerators.
o cos111ic-r2—1ys are abundant and serve an important role in the energy balance of
the Galaxy. Their cncrg 1 density ~ 1 eV cm"; is comparable to that contained

in the CRIB.

The study of sources of very high energy cosmic radiation involves the study of
astrophysical situations in which conv >11tional physics operates under extreme condi-
tions (e.g. intense magnetic 21nd gravitational fields). It may also involve new physical
phenomena (cg. annihilation of Dark Matter (DM) particles.)

Observing the non-thermal universe is difficult. One reason for this is the domi-
nance of the radiati1m from thermal pr1‘2cesses. This can be overcome by making use
of the hard power-law spectrum of many of the non-thermal emissions by using the
highest radiation detectors to probe such processes. Thus, hard x-ray and gamma-ray

observational techni1mes are widely used to study this non-thermal universe.

1 .2 Gamma-Ray Astronomy

Ganuna-ray astronomy is relatively a new field compared to other branches of as-
tronomy. The energy domain of gamma-ray astronomy spans from approximately
E = mpc2 2 0.5 X 106 eV to 2 10'20 eVl. C1jivering more than 14 decades in fre—
quency, this is more than the rest of the observe1‘l elect1'1‘111‘1agnetic spectrum. It is
thus not surprising that a wide variety of different. objects and phenomena can be
studied using 'y—rays. The lower bound of this range characterizes the region of nuclear
7eray lines, as well as electron-positr1)n annihilation lines. The higher bound charac-

terizes the energy of the highest energy cosmic-ray particles detected. This enormous

 

lGamma rays have been detected with energies 11p to 10H eV. However. gamma rays with higher
energies are possible.

range in energies is divided in bands according to the interaction phenomena and
detection techniques [72]. Table 1.1 lists these ’7-ray bands.

Gamma-ray photons represent the most energetic part of the, electromagnetic spec-
trum. They therefore Inevide information about the most. energetic processes and
phenomena in the universe.

Unlike cosmic—rays, gamma-rays are. neutrally charged particles and thus will not.
be deflected in the. interstellar magnetic fields and will point. back to their sources of
origin.

Ganuna—rays are emitted from the most compact and energetic objects in the
universe: neutron stars, stellar and massive black holes, supernova remnants, and
cosmic-rays via the interactions with matter and fields. Gamma-ray astronomy has
become an integral part of astronomy and astrophysics. It is now recognized that
objects exist in the universe. such as pulsars, quasars, blazars, and ’y-ray burst sources,
which have their peak luminosities at y-ray energies. It is impossible to understand

these objects witlimit knowing and understanding their ’7-rays properties.

 

 

 

 

Band Low / 1\=Iedium High Very High Ultra High
Shorthand LE / ME HE V HE UHE

Range 01-30 MeV 0.3—100 GeV 0.1-100 TeV >100 TeV
Environment. Space Space Ground-based Ground-based

 

 

Table. 1.1: Gamma-Ray Bands[72]

1 .3 Gamma-Ray Detection

There are. two broad categories of cosmic. “prays detectors: space-based, and ground-

based, each of which uses different. detection techniques.

1.3.1 Space-based Detectors

Space-based detectors are flown on satellites and high altitude l,)all(‘)ons. Space-based
detectors have. three basic cmnponents: a tracking chamber, a calorimeter, and an
anti-coincidence counter. The tracking chamber is used to record the path of charged
particles in the detector. The tracks are used to reconstruct the direction of the.
incident 'y-ray photon through the identification of the electron positron pair that
resulted from. the. amiil’iilation of this y—ray photon. The calorin'ieter determines the
energy of the incident photon by measuring the integrated path length of particles in
the electromagnetic cascade produced by the incident photon. The anti—coincidence
counter rejects triggers caused by charged particles which are usually protons, heav-
ier nuclei, and electrons. Space-based detectors have excellent background rejection
which allows them to unambiguously identify '7-1'ays. They also have high duty cycle
which allows continuous monitoring of transient sources all year around. One more
advantage of space-based detectors over ground—based ones is the high exposure. They
can View the whole sky in matter of hours unlike groum'l-l;)ased detectors that can only
view half of the sky since the other half is always obscured by earth. Despite all these
advantages, satellite detectors have limited angular resolution, usually on the order
of a degree. This made it hard to correlate observed sources with satellite detectors
to those observed in other wavelengths. Unlike ground-based detectors, space-based
detectors have small detection area, on the. order of 0.1 1112. This limits the energy
range of these detectors to be. in the range of several l\='IeV to several GeV. This is
because the flux of q'-1‘a_\«*s from a 7-I'ay source follows a rapidly falling power-law

spectrum in energy and is given by:

 

(1N fi_
(1F (X 12 0’ (11)

where o- is the ('lifferential spectral index of the energy spectrum. That is, the. higher
the energy, the lower the flux. requiring very large detection area for VHE and UHE
observations. A typical range of a is 2.0—3.0.

The most successful satellite experiment to date was the Compton Gamma Ray
Observatory (CGRO) project. It oj.)erate,d from 1991 to 2000. CGRO had four instru-
ments that covered an unprecmlented six decades of the electromagnetic. spectrum,
from 30 keV to 30 GeV. In order of increasing spectral energy, coverage, these instru-
ments were the Burst And Transient. Smirce Experiment (BATSE), the Oriented Scin-
tillation Spectrometer Experiment (OSSE), the Imaging Compton Telescope (COMP-
TEL), and the Energetic Galmna Ray Experiment. Telescope (EGRET).

EGRET covered an energy range between ‘20 MeV to 30 GeV. One of EGRET’S
major an-hievements was the production of the third EGRET catakig. This catalog
contained 271 new e,'-ray sources with energies above 100 MeV [32]. Figure 1.1 shows
the third EGRET source catalog in galactic coordinates. The 271 sources in the
catalog include the single 1991 solar flare, the. Large Magellanic. Cloud, five pulsars,
one radio galaxy, and (56 high-confidence identifications of blazars. In addition, '27
l(;)wer confidence potential blazar identificatitms are noted. The rest of the sources,
170 out of ‘271, have. not yet been it'lentified with known objects. Many of these.
unidentified sources are located near the galactic plane which suggests a galactic
origin of these smirces. The spectra of the identified sources are. flat (a N 2.0) with
luminosities that peak in the high-energy region of the spectrum which indicate that
they may be. scmrces of VHE photons.

A next-generation telescope, the Gamma. Ray Large Area Space. Telescope (GLAST),
is scheduled for launch in fall of 2007. GLAST is a major space mission to explore
the high energy 7-1‘ay universe. There are two instruments on board. The primary
instrument is the GLAST Large Area Telescope (LAT), which is sensitive at. energies

from '20 MeV to 300 GeV. The secondary instrument. is the GLAST Burst l\'lonitor

Cf!

Third EGRET Catalog

E> |00 MeV
+90
. Q .1 a. 8.0,
' ‘ * V o o L x; . ~ _ -
e z . *3 ',
.' O ,
. '- .' o' o. . ° ’ ° . , .
O ,1. . o g . . .. O. .
.. ’ O 0
. o .0 . 0:0 , ‘u. :0 . . .
so... .00. .....O.... ° 0 .
O a .
use . .0 ‘0 O o. .G.:Uo‘f. 0‘ Q ’ . g . .180
‘0‘. o 0 T ’. . .f’. o. . ' .3. 0 fl . .
O O 0 a
" O o . O O 0". 3 . . O .t.
O. a \ .0... . o ' ' .O':Ar’f.;:g
I ,
.. ‘ o X ‘ O .
o .o - ,, o, x r ,
C O " ’
I I
9 Active Galactic Nuclei I Pulsars
. Unidentified EGRET Sources . LMC

0 Solar FLare

Figure 1.1: Third EGRET source catalog, shown in Galactic coordinates. The size of
each symbol is proportional to the highest intensity seen for the corresponding source.
Out of the 271 sources 170 have not yet been identified with known objects. Taken
from [73]. Images in this thesis are presented in colors.

(GBM) to detect y-ray bursts and provide broad band spectral coverage of this im-
portant phenomenon. The LAT instrument will have many advantages over EGRET.
The improvement in its angular resolution (< 0.150 for E > 1 GeV) is expected to
reduce the source location error box by as much as a factor of 100 depending on the
energy spectrum of photons detected and the local y-ray backgr01111d[49]. The large
collection area of LAT , ~ 1 1112, will allow for the galactic 7-rav spectra to be derived
for much smaller area bins than was possible with EGRET[49]. The extension of
the energy reach from 30 GeV for EGRET to 300 GeV for LAT will allow for direct
comparisons with results from ground based y-r'ay detectors that operate at energies

above 100 GeV, like Milagro.

1.3.2 Ground-based Detectors

The flux of y-rays from celestial y-ray sources is low and decreases rapidly with energy.
As a result, very large detector area is required to do VHE 7—ray astronomy. The
large detector area required limits the detection of VHE photons to be done from
the ground. Howwer, the atmosphere is opaque to VHE photons. Therefore the
by-products2 of the interaction of the VHE photon with the atmosphere are used
to determine the direction and energy of the initial photon. This is done by either
detecting the secondary particles in the Extensive Air Shower (EAS) that reaches the
ground or by detecting the Cherenkov light produced by these secondary particles as
they propagate through the atmosphere. One main disadvantage for ground based
'y-ray detectors is the large background from cosmic-rays. Cosmic-rays, consisting
of protons and heavier nuclei, are constantly striking the atmosphere. These cosmic
rays produce EAS that are superficially similar to those produced by photons, and
are ~ 10,000 more numerous for a given incident photon energy. This large hadronic

background limits the sensitivity of ground based detectors and makes it very hard to

 

28cc next section

observe a statistically significant signal from a celestial 7-ray source. To minimize the
effect of this large hadronic background, differences in the EAS initiated by hadronic

particles and photons have to be detected.

1.3.3 Extensive Air Showers

The development of an EAS begins with the interaction of the primary particle in the
upper atmosphere. The physics of the interaction of the primary qv-ray photon with
the earth’s atnmsphere is fairly well understood. The. total cross section for photon-
proton collisions has been measured for center-of—mass energies up to “200 GeV [8],
which is equivalent to a ‘20-TeV photon colliding with a proton at rest. VHE '7—ray
photons interact with the molecules in the atmosphere through ele(‘:tromagnetic and
hadronic interactions.

In the electronragnetic case, VHE *y-ray photons interact with the electromagnetic
field of a nitrogen or oxygen nucleus and produces an electron-positron pair moving
at ultra-relativistic speeds. This first interaction typically occurs after the photon
has traversed one radiation length of the atmosphere, i.e. at an altitude of about
20 km. The resultant electron and positron form more high energy photons via
bremsstrahlung radiation which in turn form more electron-positron pairs, and so on.
The resulting electromagnetic cascade grows nearly exponentially as it propagates
through the atmosphere. The energy of the primary particle is divided among more
and more particles until the mean energy of the electrons and positrons approaches
the critical energy for bremsstrahlung interactirm (80 MeV in air). At this point
energy loss through ionization mechanism, which does not produce additional shower
particles, becomes more important than bremsstrahlung, while Compton scattering
and photoelectric absorption begin to dominate over pair prmluction for the yrays.
This point in the shower development is referred to as the shower maximum since

this is when the shower contains the greatest number of particles. After the slmwer

maximum is reached, energy is lost from the shower and the number of particles
in the shower decreases rapidly as the shower continues to propagate. This makes it
important for ground-based detectors to be located at high altitude with the exception
of Air Cherenkov Telescopes (IACTs)3 which detect Cherenkov light in the shower,
and since the attenuation length of light in the atmosphere is large, ACTs are not
required to be placed at high altitudes.

The cross sections for the production of hadrons and muon pairs are several or-
ders of magnitude lmver than that for pair production and thus the predominant
interaction for a ’7-1‘ay primary is electrr)magnetic.

Since the particles in the EAS are ultra-relativistic and the dominant 1.)hysical
processes are. sharply peaked forward, the EAS arrives at ground level in a thin front
only a few meters thick. \Vhile the. front is only a few meters thick, the lateral extent
of the showers, primarily the result of multiple Coulomb scattering of the electrons
and positrons in the EAS, is of order one hundred meters.

The passage of cosmic—rays through the atmosphere follows similar, but more com-
plicated process. The interaction of the primary cosmic particle with the molecules in
the atmosphere generz-rtes a hadronic cascade. This hadronic cascade includes neutral
and charged pions. The neutrz-rl pious decay into two ql-rays, which in turn pro-
duce electroniagnetic cascades. The charged pious decay into muons and neutrinos.
The low energy muons can decay into electrons and positrons, while the high energy
muons typically reach ground level. As a result, particles reaching the ground level
in a hadronically initiated air shower are mostly muons, electrons, positrons, neutri-
nos, and photons. Figure 1.2 shows a simulated development of a 1 PeV (1000 TeV)
hadronic air shower. Only a small fraction of particles is slmwn. 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.

 

3See. next section

Except. for the 11)rcseuce of muons, a cosmic-ray shower at ground level is not very
dissimilar to a ’7-ray' shower. The nmon lateral distribution is considerably wider
than that of the electn)magnetic particles. There are roughly ‘20 times more muons
in a hadron-initiated EAS than in a photou-initiated EAS of the same energy. Figure
1.3 shows the development of the cascades of three different primaries through the

atmosphere [74].

1.3.4 Imaging Air Cherenkov Telescopes

In addition to shower particles in an EAS, Cherenkov photons are. also produced.
C herenkov light is produced in a medium when a charged particle is traveling faster
than the speed of light in that medium. This emission is governed by the refractive
index of the medium, 72. For air, the refractive index is proportional to the atmo-
spheric density which decreases exponentially with height, with a scale height4 of ~
8 km. The radiation is emitted by atoms and molecules polarized by the moving
charged particle. This radiatitm is emitted as a light cone. with a fixed angle with

respect to the direction of the particle’s motion, this angle. is given by:

(.
(1)8 ()(f : _— (1.2)
no
where c is the speed of light in vacuum, and c is the speed of the charged particle in
the medium.

The condition for this radiation to occur is "(7 < 1, which can be expressed in

terms of the particle’s energy:

1,10 ('2

N"

4Scale height is the vertical distance upwards. over which the pressure of the atn'iosphere dwreases
by a factor of c

I'jth : (1.3)

 

10

iPrimary Ne
. —>
1st Interaction

 

 

 

 

 

 

 

 

 

Pion
— Muon
— Electron
Y
" ’ , 3f
. 3 “
xmax ‘‘‘‘‘‘ f'3 ,3, “" ““““ Nmax
1’}, ,_
. i
f L:
,h‘;
#5,: x
" r L". V
Particle Density 100 m
at Ground ‘—"——>
I 3000
I i200
I 450
I .70
I 65
I 25
D 9
particles/m2

 

 

 

 

 

Figure 1.2: Simulated development of a l PeV hadronic 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 lowr-r figure shows the distribution of particles at
ground level. Taken from [36]

11

 

 

   

\ \\\\\\5
.\ Ikluwilh 3

ll.‘\l\‘\‘\t\‘\
liliilllll \‘i l lli‘llll
. \ltlllotllltlullhul‘

3 i E ill I 3 II-
i ilIII. iuIIrI

 

 

 

 

 

l.
r.

 

x(km)

Figure 1.3: Development of the east-axles of three different primaries through the
12

atmosphere. Taken from[74]

'here mo is the rest mass of the particle. For example, at sea level, the threshold
nergy for Cherenkov emission to occur is 21 MeV for electrons [or 35 MeV at 8 km
hove sea level (a.s.l.)], 4.4 GeV for muons, and 39 GeV for protons. The maximum
ngle of Cherenkov emission is 1.30 at sea level, or 10 at 8 km a.s.l., independent of
he mass of the emitting particle.

Observations with Imaging Air Cherenkov Telescopes (IACTs) are done through
he detection of the Cherenkov light produced in an EAS [72]. One or more mirrors
re used to concentrate the Cherenkov light onto a camera of photomultiplier tubes
PMTs). Observations with IACTs faces two problems; the night-sky background
nd the large isotropic background from cosmic—ray showers. Cherenkov light in an
AS is very faint compared to moonlight or even bright stars within the field of
iew. Observations can only be made on clear, moonless nights. This limits the
uty cycle of these detectors to ~l()% and restricts them to viewing sources for the
art of the year that they are above the horizon at. night. An effective background
"ject ion teclmique has been (,leveloped which is based on the image characteristics of
he Cherenkov light cone. cosmic-ray showers are more chaotic than v-ray showers,
ince their development is governed by a relatively small number of particles in the
adronic core. The larger transverse momentum of hadronic interactions gives a
reader lateral distrilgmtion. Therefore, ineasurei‘nents of the angular distribution
f the Cherenkov light cone on the sky for each shower allow for the separation
etween hadronic showers and 7-ray showers. In addition to this imaging technique,
ccurate measurement of the shower arrival direction improves the separation between
-ray showers from point sources and isotropic cosmic-ray showers. The imaging
:échnique can achieve high angular resolution (< 0.10), especially when individual
E‘ICSCODGS are combined into arrays. In addition to the low duty cycle, IACTs are
ointed instruments and this make it inefficient to use them as survey instruments.

‘he Whipple 10m "y-ray telescope made. the. first successful detection of a TeV “3-

13

 

 

Figure 1.4: The HESS telescope array in Namibia.

ray source, the Crab Nebula. A next generation of IACTs arrays are already making
significant progress in the field of TeV v-ray astronomy. The High Energy Stereoscopic
System (H.E.S.S) telescope in Namibia had detected point sources of TeV 'y—rays from
the galactic plane. The Very Energetic Radiation Imaging Telescope Array System
(VERITAS) is currently under construction in Arizona. Figure 1.4 shows the H.E.S.S

telescope array.

1.3.5 Extensive Air Shower Arrays

Another way to detect EAS is to directly detect secondary charged particles in the
shower that reach the ground at the detector level. Extensive Air Shower Arrays
(EASA) are used to detect EASS produced by UHE primaries. Fluxes of UHE 'y-rays
are expected to be small, so a large detection area in excess of 104 m2 is neededl37].
The cost of having a uniformly sensitive detector over such large areas is prohibitive.
However, one doesn’t need to observe all the particles in an EAS to make a successful
detection of this shower, this is because the number of particles in an EAS that reaches
the ground is large. A typical EAS initiated by a IOU—TeV photon has roughly 50,000
electrons and positrons and about five times as many 'y-rays, spread out over an area
in excess of 104 m2 at mountain altitudeslii'r’]. Because there are so many particles

reaching the ground, an EASA need to sample only a relatively small fraction of these

14

 

particles to make a successful detection of the. shower. However, this partial sampling
of the shower causes the energy threshold of these instruments to be large, on the
order of 50 TeV. A typical EASA has between 50 and 1000 scintillaticm counters, each
with an area of ~ 1 1112. These are usually spread over an area of 104 -— 105 1112 and
cover only 1% of the total area of the array. The performance of the array can be
improved by placing lead, roughly one radiatioi’i-length thick, above each counter to
convert the more plentiful shower photons into charged particles.

The individual scintillation counters in the array are used to measure the rela-
tive arrival times of charged particles in the shower. These times are then used to
reconstruct the dirwtion of the shower. The angular resolution resulting from this
method of reconstruction is ~ 0.50. This angular resolution depends upon proper-
ties of both the EAS and the detector. To obtain good angular resolution with an
EASA, one must perform a fit to a shower front that is curved by an amount that is
a function of position from the shower core. To se},)aratc 'y-ray-initiated air showers
from cosmic-ray-initiatcd air showers, EASA use muon detectors to look for muons
which are mostly presented in cosmic-ray-initiated showers. These muon detectors
are usually placed around the scintillation counters. This technique is limited by the,
partial sampling of the shower. Scintillation counters measure the energy deposited
by charged particles in the. shower.

EASA have two advantages over IACTs: large duty cycle (> 90%), and large field
of View (~ ‘2 sr). These. two factors provide. the ability for continuously monitoring
the over-head sky, study of transient sources, and performing sky surveys. Despite all
of this, no new y-ray sources have been discovered and only upper limits exist using

EAS arrays. Figure 1.5 shows the Tibet air slum-er array.

 

Figure 1.5: The Tibet air shower array

1.3.6 Water Cherenkov Technique

The large field of view and large duty cycle of an EAS array make it an ideal survey
instrument. However, the low sensitivity, high energy threshold (> 50 TeV), and
the difficulty of discriminating v-ray showers from hadron showers limited the results
from these instruments to only setting upper limits and no new er-ray sources have
been discovered using these instruments.

The Milagro gamma—ray detector near Los Alamos, New Mexico is a new type of
detectors that uses the water Cherenkov technique to detect extensive air showers.
The water Cherenkov technique is widely used in particle physics experiments but is
new to air shower detection. The use of water as a detection medium has the advan-
tage of lowering the energy threshold of the detector to energies comparable to those
of IACT’s. The lower energy threshold is achieved through the detection of nearly
every relativistic particle in an extensive air shower. At ground level, gamma-rays in
an EAS outnumber electrons and positrons by a factor of ~ 5. In a conventional air

shower array these photons are undetected. Upon their entrance into the water, these

16

gamma-ray photons convert to electron-positn)n pair or Compton scatter electrons
which will in turn produce Cherenkov radiation that can be detected.
A detailed description of the water Cherenkov technique and the Milagro detectm

and its performance are given in chapter 3.

17

Chapter 2

Galactic Gamma-Ray Emission

The Milky W'ay Galaxy is a bright, diffuse source. of high energy y-rays. About
90% of the total luminosity of the galaxy at high energies (>1 GeV) comes from
processes in the interstellar medium (ISl\t-'I)[52]. Diffuse 7-rays are. produced in the
galaxy via the interaction of Cosmic-Rays (CR) with the interstellar gas and with
the interstellar radiation field. Therefore, the study of this emission may provide
information about the properties of CR. and their production sites. The main part
in this diffuse emission is believed to originate by CR, processes but some part is
certainly contributed to by two other components; the extragalactic background, and
the contribution from unresolved and faint Galactic point sources.

Observations of the diffuse ”yr-ray emission by the Energetic. Gamma Ray Experi-
ment Telescope (EGRET), with its high sensitivity and spatial and energy resolution,
resulted in high quality data over three decades of energy in *y-rays (Figure 2.1). The
first detailed analysis of this diffuse emission for Galactic latitudes |b| S 100 came in

1997 [39]. The basic assumptions of this analysis were :

1. cosmic—rays are Galactic in origin.

2. cosmic-ray density is related to the gas column density of the interstellar medium.

18

3. The spectra of cosmic-rays are the same in all parts of the Galaxy and are equal

to those measured locally.

Gamma-rays are produced in the galaxy through hadronic and leptonic interac-
tions (sec. 2.2). These different types of interactions will give different ’y-ray spectra.
The fact that the overall observed spectrum of y-rays does not significantly vary
as a function of Galactic longitude and latitude, indicates that the cosmic ray elec-
tron / proton ratio is more or less constant throughout the galaxy.

In their analysis Hunter et. a1. [39] used a three dimensional model to describe the
spatial and spectral distribution of the diffuse ey-ray emission. This analysis revealed
an excess above model predictions in the diffuse y-ray emission for energies > 1 GeV
in all directions of the sky as shown in Figure “2.2. Although many explanations for
this GeV excess have been proposed[67. 223’, 15, 12], there. is still no definitive answer
for this observed excess. These explz‘mations include. a varying CR spectrum and
intensity across the. galaxy[(jT, ‘28], a. hard electron injection spectrum leading to an
increase in the ICS componentlfii’], the existence of unresolved point sources with
hard spectra[‘20], the annihilation of relic dark matter part.i("les[24l, inverse Compton
scattering of cosmic microwave background (CMB) and star light. photons by the CR
electrons produced in our galaxy and in external galaxies[1'2], and a miscalibration of
the. EGRET telescope[53].

In an attempt to solve. this “GeV Excess“ puzzle, attempts had been made to
re-evaluate the reaction of 7r0-1‘n'oduction in prtm)n-proton-interactir)ns. However,
a calculation made using modern Monte Carlo went generators to simulate high
energy proton-pronm-(-()llisir)ns has shown[50] that the Tray flux agrees rather well

with previous calculatirms.

 

Figure 2.1: EGRET all-sky 'y-ray map above 100 MeV in Galactic coordinates[75].

2.1 Cosmic-Rays

Cosmic—Rays are observed with energies from a few MeV up to more than 1020 eV.
Electrons in the MeV—TeV energy range and protons and u particles in the GeV-TeV
energy range are relevant to the production of the diffuse *y-ray emission. The spectra
of CR are measured using balloons and satellites. These measured spectra represent
the spectra of CR in the local region of the galaxy. For energies below ~ 10 GeV, the
heliospheric modulation 1 is large. This heliospheric modulation hinders the study
of the truly interstellar spectrum and the locally measured CR spectra may not be
representative of the CR spectra in the rest of the Galaxy.

Galactic CR are an important part of the interstellar medium. The average energy
density of GR is about 1 eV cur—3 and is comparable to the energy density of the
interstellar radiation and magnetic fields. Thus, CR are one of the essential factors

determining the dynamics and processes in the interstellar medium. The EGRET

 

1Helimzpheric modulation is the interaction of cosmic-rays with protons from the sun. This may
alter the spmtra of the wsmic—rays observed at Earth.

20

 

V'Utiv‘l r YTV'IIV' ‘ I UTY'U‘I V Vi

10'5

t
E 10'8
TL—
0)
'm
“3
E
o
.c
-10
3 1o

 

 

 

10.12 1 l .1111 L l l l Lllll l l l 1 I‘ll] \ 1"\. .l ‘

100 1000 10000
Energy [MeV]

Figure 2.2: The average spectrum of diffuse e,I-rays detected by EGRET from the
inner galaxy (Galactic Longitude, 300° < l < 60°, and Galactic Latitude, |b| S 10°).
Contributions from point sources detected with more than 50 significance have. been
removed. The data are represented by the points and the solid line represents the pre-
diction of the diffuse 'y-ray model. The model incorporates electron bremsstrahlung
(EB), inverse Compton (IC), and nucleon-nucleon (NN) processes, as indicated by
the various lines.

21

obscrvatirms of the Small l\lagcllanic Cloud [(35] have shown that. CR. are a Galactic
and not. a extra galactic phenomenon. The. flux of gamma-ray emission (> 100 MeV)

_ 4) _ . . _ — _~
measured was 0.5 x 1() 7 cm. r .s 1, a third of the expected value of (2.4:t:().o) x 10 ‘

2 5’1 if cosmic-rays were universal in origin.

cm-

Sources of CR are not yet known but. are believed to be s111:)ernov-(w, supernova
remnants, pulsars, compact ob jccts in close binary systems, and stellar wind. To
sustain the observed CR density of 1 eV cur—3, the total power of Galactic CR
sources needed is of the order ~ 10“10 erg s—l. If the supernova rate. in the Galaxy is
1 every 30 years, a release of energy in the form of CR. of 1049 erg per supernovae is
required. This value comes to about 500 of the kinetic energy of the ejecta, which is in
agreement with the prediction of the theory of diffusive shock acceleration [41]. These
shock accelerated CR propagate further in the Galaxy where they are contained for
at least 10 million years before escaping into intergalactic space. Before escaping
into the intergalactic space, CR. spend most of the time in a region several kpc wide
around the Galactic disk. Direct evidence for this wide confinement region comes
from observations of synchrotron emission from CR. electrons, which indicates a scale
height that is much larger than that of the Galactic disc [22].

During their propagation, the initial spectra and composition of CR. change due
to energy gain and loss processes. These processes include the production of sec—
ondary particles and y-rays. Secondary nuclei and isotopes that are. rare in nature
are produced in spallation processes ( e. g. 12C —*11B). Because secondary antiprotons,
positrons, and diffuse ”yr—rays are all products of the same proton-proton-interactnins,
accurate measurements of the antiproton and positron fluxes, especially at. high ener-

gies, could provide a diagnostic of the interstellar nucleon spectrum ('(')IIlI)l(‘IIl(‘.IltaI‘y

to that provided by "ja-rays [51, (56]

2‘2

2.2 Basic Processes of Gamma-Ray Production
Gannna—rays are produced in the galaxy through three main processes:

1. Decay of a0 mesons produced through the interaction of CR nucleons with the

interstellar gas.

2. Brcmsstrahlung from relativistic CR electrons interacting with the. interstellar

gas.

3. Inverse Compton scattering from relativistic CR. electrons with the interstellar

optical, infrared, and microwave radiation field.

2.2.1 Pion Decay

The interaction of CR nucleons, predominantly protmis and 0 particles, produce

(ii-0)

neutral and charged pions via N + N —> 7r + X. Neutral pions in turn decay into

0 —* ’7 + 7). The production spectrum of secondary 'y-rays can be obtained if

i-r'vws (7r
one knows the distribution of pions FTO(( ,0 , (p) from a collision of a proton of energy

6p, and the distribution of ’7'-I"d_\’S [537, (fig) from the decay of a pion of energy (7:0:

 

(U7 -3c x . p ‘
do, znil/($11,“(1(P.1p((pl<I/(T7r0((p)>["8"(194113072(W())Fn0((7r0, (p) (2.1)
7T

where 7) H is the. atomic hydrogen number density, ./p((p) is the proton flux, (yang (61,»
is the inclusive cross section of 7r(J production, and (28“ = c», + "IND/407 is the
1.
minimum energy a pion should have to contribute to the production of y-ravs with
energy (7.
For elements heavier than hydrogen, the inclusive cross section of 7r0 production

. . 3/8 3’8 - .
should be scaled wrth a factor ~ (."ll’ + 519/ —— 1)2, where :112 are the atomic

23

numbers of the target and CR nuclei. Besides hydrogen, the main contributor is
helium, with a ratio in the. interstellar medium of He/ H ~ 0.1 by number.

The distribution of 'y—rays from 770 decay is given by:

 

2
I" (. «(-0) = —— <22)
7 7 “ ‘mfiolfinudno
with
Info 7”..0 . . .7
i2“ Fnoll —i1,,()l S (7 S —2“—11,,()(1 + 5,0) (2'3)

where TWO and 137,0 are the pion Lorentz factor and velocity.

The 'y-ray spectrum (equation 2.1) obtained after integration over the CR nucleon
spectrum peaks at 70 MeV and is symmetric about the maximum on a logarith—
mic energy scale. For CRs with a. power law spectral distribution of index a”, the
spectral distribution for high energy y-rays will also be a power law spectrum with

(Y7 = 41/301”. — 1/27)[T2].

2.2.2 Bremsstrahlung

Bremsstrahlung, or braking radiation, happens when a charged particle is deflected in
the electric field of another charged particle. In the interstellar medium consisting of
atomic hydrogen, helium. and the ionized medium, electron-mu~leon bremsstrahlung
is the most important.

In the case of a nucleus as a. target, the nucleus is screened by the bound electrons.
The screening factor“2 is defined as[()'(i]:

622:? (as

 

 

2For units h. = c = m. = '1.

where 5,, is the energy of the emitted photon, Po and F are the initial and final Lorentz
factor of the electron in the collision. In the case where 6 —i 0, the distance between
the electron and the atom is large compared to the atomic radius. In this case the
screening of the nucleus by the bound electrons is important. For low-energy electrons
only the contribution of the nucleus is significant, while at high energies the atomic
electrons can be treated as unbound targets in the same way as the nucleus[66].

The contribution to the. Galactic diffuse emission from bremsstrahlung is impor-
tant for energies < 200 MeV. For electron energies 2 2 MeV, the producticm cross
section is given by:

do],

9 1 1‘2 , 2 I‘
: , T . 1 —_ J, _ —— ('6‘ 205
“(1‘7 reflf; < + F3) ()1 3 P002 ( l

where 1",; is the classical electron radius, of is the fine structure constant, and for an

unshielded charge, 651 :— 02 = (Du which is given by:

 

. 2M“ 1
¢,,=4z-2 ln< _ ——)] (2.6)

where Z is the nucleus (i-harge.
Approximate expressimis for 0,, have been derived for different energy ranges of

T, the kinetic energy of the. electron:

o Non—relativistic case; T < “met-2:

16
0b = 700:2 (2.7)
3
0 Highly relativistic case; T > 777,12:
‘2 T + m .c2 1 -
0b = 40012 III <—(—n'I——(—2—(—)) —' 3] (2.8)
1(J

0 Extreme relativistic case; T > 137*III.(.(:2Z_1/3:
01. -—- 40022 [111(1532—1/:3)] (2.9)

i F7 9 9 r) f - '
where (10 = 4(1/131)(e“/n'1,.c“)“z2 = 0.58 nulhbarn/ nucleus.
To obtain the. production spectrum of electron bremsstrahlung for a distribution
of electrons we integrate over the spectrum of CR electrons and sum over the species

of the ISM:

 

(If, . (10' .
' - Z (.‘Tl.,''/\(1’l>/.€(All)d(aI (2.10)

(1‘7 ir—H.HI.HII.He :1”
where c is the. speed of light, 72,- is the number density of the corresponding species,
and f(.(e;') is the spectrum of CR. electrons.
The y-rays that result. from bremsstrahlung have energies that are comparable to
those of the incident electron. Thus, if the population of the electrons is characterized
by a power law with spectral index (re, the resulting ’7-ray spectrum has an index

017 z (re [72].

2.2.3 Inverse Compton Scattering

Inverse Compton scattering is a process in which a high energy electron interacts with
a low energy photon, transferring some of its energy to the photon.

For photons with energies. in the electron rest frame system (ERS), (CPU —
,3 cos fl) << 772,42, where (o is the energr of the background photon, f) is the angle
between the momenta of the electron and the photon, and F is the Lorentz factor of.
the electron in the rest. frame of the. photon, the. scattering cross section is that given

by the clz‘issical Thmnson cross section:

0r = 27'? (2.11)

3
where n. is the classical electron radius. In this nonrelativistic region, the cross section
is independent of the photon energy. As soon as the energy of the electron is high
enough that the lip-scattered photon has an ERS energy that is comparable with the

electron rest mass, the cross section is given by the Klein-Nishina formula:

. 1+ (1 2(1+(“r) 1 1 , . (1+ 30)
=2.»~% . ——————1 1 2 —1 1 21——— 2.12
a 77‘ [ 02 ((1 + 2”) (r n( + 0)) + 20 n( + a) (1+ 2”)? ( )

 

where (r = 60/77’mf2.

The average energy of the scz-Lttered photons is given by:

((1,) N r260 (2.13)

This allows for the estimate of the contribution of different background radiation
fields to the resulting spectrum of v-rays.

If the electron is energetic enough, the incoming photons can be considered as a
unidirectional beam in the ERS since the angular distribution of the photons in that
system is confined to angles ~ 1/P radians. In this case, for an isotropic distribution
of monoenergetic electrons and photons the. spectrum of the up-scattered photons is

given by:

mr .0 2 '2. , 401“ 2
Li_ m6 ‘2qlnq+(l+2q)(1—q)+ (( (I)

1 .
— -———- 1— 2.14
do, for 2 (1 + 4(OF(1)( q) ( )

 

where (7 is the energy of the photon after scattc—rring, q : 6.7/[4601—12(1 — co/l‘)] and

1/41‘2 < q s 1.

27

The. resulting spectrum for a distribution of electrons can be. obtained by integrat-

ing over the spectra of electrons and the background radiation:

(”1 — —c /(l(o / (1')- f,,( ((0) )fm )(—1——'——H(r (o) (2.15)

 

(1(7 do

where flu, are the spectra of the interstellar radiaticm field and the CR electrons.

2.3 Galactic Structure

The Galaxy is a barred spiral with a radius of ~ 30 kpc. For the o,’-ray diffuse emission
the important components are the interstellar gas and the interstellar radiation field

[22].

2.3.1 Interstellar Gas

The gas content in the Galaxy is dominated by atomic (HI) and molecular (H2)
hydrogen. Although present. in approximately equal amounts in the inner Galaxy
(~ 1()9 Mg), atomic and molecular hydrogen have very different radial distributions.
In addition, low density ionizml hydrogen (H11) and heavier elements make a small
fraction of the interstellar gas. Helium has a ratio of 10 ~ ‘70 by number relative to
hydrogen. This makes it an important. cmrtributor to the gas-related ’y-ray emission.

Atomic hydrogen extends out to 30 kpc, with a rather uniform density and a
scale height of 200 pc [(51]. The atomic. hydrogen disk is asymmetric, with warping
in the outer disk, and it extends to about 1.5 kpc almve the Galactic plane in the
northern hemisphere and down to about 1 kpc in the southern hemisphere [22]. The
gas density is roughly uniform at 1 atom ('111-3. HI gas is mapped directly via its
21 cm radio line, which gives both distance (from the. Doppler-shifted velocity and
Galactic. rotation models) and density information.

Molecular hydrogen is concentrated within R. < 10 kpc, with a peak around 5

28

kpc and a scale height of 70 pc. It. is mainly concentrated in dense clouds of typical
density of 104 atom cm’3. Unlike atomic hydrogen, H2 cannot. be detected directly
on large scales. However, the 115 GHZ emission of the abundant molecule 12C0 is
a good tracer, since it. forms in the dense clouds where the H2 resides. Molecular
hydrogen column densities N512 have. been found to be approximately proportional
to Ill/"CO, the integrated density of CO line, where the. constant of proportionality is
X E N H2/ 11270. A recent result of the H2 density obtained from a complete CO
survey and infrared and HI maps gives an average X E- NH2/1'VC0 = 1.8 x 1020
cm;2 K‘1 km“1 s [23]. Observations of particular local clouds [25, 26, 27, 38] yield
somewhat lower values X = (0.9 — 1.65) x 10‘20 cm"2 K'—1 km—1 s (with error bars
of l5—20%), but still close to the awrage.

Ionized hydrogen is present in the interstellar medium at lower densities ~ 10—3
atom cm“3 and has a large scale height of 1 kpc. Although this gas makes a small
contribution to the y-ray emission, it is of interest because it produces a much broader

latitude distribution than the neutral gas.

2.3.2 Interstellar Radiation Field

The interstellar radiation field (ISRF) is made up of contributions from starlight,
cosmic microwave. background (CMB), and emission from dust [22]. It is important
for y-ray production through inverse Compton scattering of CR electrons.

Stellar emission dominates from 0.1 ,um to 10 um, and emission from very small
dust grains contributes from 10 pm to 30 um. Emission from dust. at T ~20 K
dominates from 20 11m to 300 nm. The 2.7 K microwave background is the main
radiation field above 1000 pm. The ISRF has a vertical extent of several kpc., where
the Galaxy acts as a disk-like source of radius ~10 kpc. The radial distribution of the
stellar component is also centrally peaked, since the stellar density increases expo-

nentially inwau‘ds with a scale—length of ~25 kpc until the bar is reached. The dust

29

cmnponent is related to that. of the atomic. and molecular hydrogen and is therefore

distributed more uniformly in radius than the stellar component.

30

Chapter 3

The Milagro Detector

The hililagro observatory is a ground-based TeV detector that utilizes a large water
Cherenkov detector to observe extensive. air showers produced by high energy particles
impacting the Earth’s atmosphere. Milagro‘s distinct advantage compared to other
ground-based TeV gamma-ray detectors is its wide. field of view (2 steradian over-
head sky) and its high duty cycle (> 90% live time). These factors give Milagro the
potential for discovery of new sources with unknown positions and times, such as
gamma-ray bursts, flaring AGNs, and (')l')servation of diffuse extended sources like the
Galactic plane or large supernova remnants.

The l\~Iilagro detector configuration, its electronics and data acquisition system,
trigger conditions, event reconstruction algorithms, and simulations are described in

this chapter.

3.1 Detector Description

3.1.1 Location

The lVIilagro detector is located near Los Alamos, NM, in the .Iernez mountains at

latitude 350 52’ 45” and longitude 1000 40‘ 37” “est. Since. the number of particles

4" I , . 25,-, a." vie-e“ 1'
t .l . N;.~ «.
,- “r -x ,, Vac- g7 .
" .I _ . : . ,.
rim—a me" ~ Hit?” 1». . 1.
, s. v. ..' \' ‘I L '

~ "1.3!?"

- ..- .3...~

 

Figure 3.1: An aerial view of the Milagro detector. The pond is visible in the center
of the photo. The red circles mark locations of the outrigger tanks.

in an EAS decreases after a height known as shower maximum (~ 7—10 km above sea
level) is reached, the detector is located at high altitude in order to sample as many
particles as possible. The altitude of the detector is 2630 m which translates into 750
g cm‘2 of atmospheric overburden. The detector consist of a 24 million liters artificial
pond sealed with a light tight cover and instrumented with 723 photomultiplier tubes
(PMTs) arranged in two layers. The pond has dimensions of 80 m x 60 m x 8
m (depth). The sides of the. pond are sloping, leading to an area of 30x50 1112 on
the bottom. A schematic diagram of the pond is shown in Figure 3.2. In addition
to the central pond, Milagro is surrounded by an outrigger array of 175 tanks, each
containing a single PMT. The outrigger array extends the physical area of the detector
from 5,000 m2 to 40,000 7112. Figure 3.1 shows an aerial view of Milagro. The pond
is visible in the center of the photo. The red circles mark locations of the. outrigger

tanks.

32

5; 50¢ :33 aroma .Aflmom 3 ~05 ESQ Ewe—:4 of we EEwEt 3.383% < ”mam Emma

F— Om

 

 

33

r
L

 

Eco

 

 

 

Eow

3.1.2 The Pond

The pond PMTs are arranged in two layers. The. top layer, called the air shower
(AS) layer, consists of 450 PMTs and is under 1.5 m of water. This layer is used
primarily for triggering and event reconstruction. The bottom layer, called the muon
layer (MU), consists of 273 PMTs and is placed under 6 m of water. It is used
for background rejection and energy imaging. In each of these layers the PMTs are
arranged on a 2.8 m x 2.8 m grid. The MU layer PMTs are horizontally offset from
the AS layer PMTs by half the grid spacing. Figure 3.3 shows a schematic diagram
of the PMT placement in the pond [34]. Figure 3.4 shows the inside of the pond. The
AS layer PMTs can be seen attached to the grid crossing, while the MU layer PMTs
are tied between grid crossing. This photo was taken with the cover inflated during
one of the tube repair operations.

The pond densely samples the EAS particles that reach the detector level. Since
the Cherenkov angle in water is ~ 41°, the AS layer PMTs detects the Cherenkov
radiation from the relativistic, charged particles in the air shower with high efficiency.
Roughly 50% of all electnnnagnetic particles that enter the pond are detected. In
addition, at ground level gaImna—rays in an EAS outnumber electrons and positrons
by a far-tor of ~ 5. Since the AS PMTs are placed under 4 radiation lengths of water,
these gamma-rays convert to electrons and positrons before reaching this layer. These
electrons and positrons in turn Cherenkov radiate in water and will be detected. The
depth of the Muon layer corresponds to 16 radiation lengths of water. This means
that all electromagnetic particles in an air shower will be absorbed before reaching
this layer and that only muons and hadrons can penetrate and shower near this layer.
Thus, the MU layer is used to detect muons and hadrons which are mostly present
in hadronic showers. Muons of energies as low as 1.2 GeV reach the muon layer
in Milagro. l\='lonte Carlo simulations estimate that 80 ‘70 of ctismic-ray-initiated air

showers and 6 % of gamma-ray-initiated air showers that trigger Milagro contain a

 

 

 

 

e'FMrs‘

‘

 

 

" Hadro ‘;

 

 

 

 

lat—91...— at
Air Shower Layer 5'

 

 

 

Figure 3.3:
from [34].

Schematic of PMT

Figure 3.4: An inside View of the Milagro pond.

 

 

 

muon or a hadron that enters the pond].

The combination of high altitude and high particle detection efficiency gives Mila-
gro a lower energy threshold compared to other air shower arrays. Milagro is sensitive
to gamma-rays with energies above ~ 1.00 GeV.

The PMTs used in he'lilagro are 20 cm in diameter (Hamamatsu #R5912SEL). A
waterproof polyvinyl chloride (PVC) casing protects the electronic base. of each PMT.
A single RG-59 coaxial cable carries the high voltage to the tube and the AC signal
from the tube back to the electronic system. The initial high—voltage Fisher connector
used when all of the PMTs were installed had a. high failure rate when submerged
in water. This was the cause of many PMT failures and led to the development of
an improved connector which had reduced strain and was sealed in heat shrink and
glue. Each PMT is surrounded by a conical collar baffle. These baffles were installed
for two reasons: blocking out. light traveling horizontally (from muons at large zenith
angles) and increasing the collection area of each PMT. The baffles were originally
made of anodized aluminum on the inside with black polypropylene on the outside.
Aluminum was originally chosen because its good reflectivity increases the. collection
area of the PMT. However. due to corrosion of the aluminum in water, the aluminum
baffles were. replaced by new baffles made of polyprt)pylene with a white interior and

black exterior.

3.1.3 The Outrigger Array

The outrigger array covers a 40,000 m2 area around the central Milagro pond (Figure
3.1). An outrigger is an individual Cherenkov counter that consists of a 5,680 liter
tank of water, measuring 2.4 m in diameter and 1 m. in height. Each outrigger is

instrun‘iented with a single PMT facing the. bottmn of the tank. The inside of each

 

1The rate of production of muons and hadrons in a gamma—ray initiated air shower is much
less than this. However muons and hadrons generated in the shower have. a much higher survival
probability than electrons and positrons and can reach the ground level.

tank is lined with Tyvek to reflect light inside. the tank.

By extending the physical area of the detector from 5,000 m2 to 40,000 112,2, the
outrigger array allows a more. accurate determination of the location of the shower
core. It also irii]_)ro\-'es the angular reconstruction of the air shower by providing a

. e z 1' ' ,ss , ( s )v o . o is. '. s )I‘ "gr-Tc.
longer l‘ver an arm“ th" ‘l1(\ er fr nt t I‘(‘(()I "trurt the ‘hcwcr (l11((i1)11

3.2 Water System

The central Milagro pond holds 24 million liter of water. The water is constantly
recirculated at a rate of 200 GPM. During recirculation the water is filtered through
a charcoal filter, a 10 pm filter, a 1 mn filter , a carbon filter, and a 0.2 pm filter 2
to maintain transparency. In addition, the. water passes through a UV filter before
returning to the pond to prevent any biological growth. To ensure good quality of the
water, measurenrents of the attenuation length of the water are made periodically.
Recent tests have shmvn an attenuation length of 17 m at 325 nm. The bottom of

the pond is lined to keep contaminants out of the filtered water.

3.3 Pond Cover

In order to keep external light out. of the pond, the pond is covered with a 1 mm thick
p(:)lyprol,)ylene cover. The top of the cover is painted with highly reflective roofing
paint in order to reduce the temperature inside the pond. The cover is normally kept
in contact with the water by adjustable nylon straps as seen in figure 3.1. During
repair operations, the cover is inflated through vents and fans that are placed in the
pond utility building (PUB). W" hen fully inflated the. internal pressure keeps the cover

approximately 20 feet from the. surface of the water. This allows people to enter the

 

2The 0.2 pm. filters have been removed due to clogging with the aluminum oxide from corroding

baffles.

37

pond and («induct repair operations.

3.4 Electronic System

The main function of the electronic system is to provide timing and pulse height
information from each PMT. In addition, selection of showers for digitization must
be made using a trigger decision. The accurate. time-of—arrival of the. selected showers
must be recorded. Custom made. electronics boards distribute high voltage to the
PMTs and processes the PMT signals prior to readout using conmiercial FASTBUS

modules.

3.4. 1 Signal Extraction

The PMTs are divided into patches of sixteen tubes that operate at the same high
voltage level. Each patch is first processed by a custom 16 channel front end board
(FEB). The FEB reads in the AC signal from each PMT, and distributes the high
voltage (HV) to each tube. The FEB then processes the signal from each PMT and
sends it to the digital boards where timing and pulse height information is prepared
for digitization.

To determine the arrival time and charge of a signal in a PMT, the time-over-
threshold (TOT) technique is used. A more straight-forward way of doing this would
be to employ analog-to-digital converters (ADCs), but due to high cost and high
event rate in Milagro the TOT method was used instead.

In the FEB, the signal from each PMT is split and sent to high gain (~ X 7) and
low gain (~ x 1) amplifiers [13]. The amplified signals are then sent to a discriminator
with a preset plrote-electron (PE) thresholds. The signal from the high gain amplifier
is sent to a low threshold discriminator with a N 1/4 PE threshold. The signal from

the low gain amplifier is split. in two, one part goes to a high threshold discriminator

38

with a ~ 5 PE threshold, while the other goes to an output which can be cmmected
to an external ADC for calibratirm purposes. Whenever the PMT pulse crosses either
of the low or high thresholds, an edge. is generated as illustrated in fig 3.5. For a small
pulse which crosses only the. low threshold, two edges are generated. For a pulse that
crosses both the low and high thresholds, four edges are generated. The time spent
over the threshold can then be calibrated to get the charge, under the assumption
that all signals have the same shape.

The output. of the low and high threshoh'l discrin‘iinators are sent to the digital
boards. The digital boards multiplex the. signaLs from the low and high threshold dis-
criminators, and also provide triggering and monitoring information. The edges are
then digitized in LeCroy FASTBUS time-to-digital converters (TDCs). The FAST-
BUS TDCs can record up to 16 edges per event with a 0.5 113 resolution. A FASTBUS

latch connected to a GPS clock encodes the common stop time for each event.

3.4.2 Triggering

Over the course of running l\inlagro, different trigger conditions have been used. From
the time h'lilagro began taking data in January 1999 until March 2002, the Milagro
trigger consisted of a simple multiplicity count of the number of PMTs hit in the AS
12- yer (Map). A threshold on this number was set to be between 50 and 70 PMTs hit
within a 200 ns time window. The threshold was set by the maximum data rate the
data acquisition system (DAQ) could handle (~ 2000 Hz). A lower trigger threshold
would increase the number of low energy (hundreds of GeV) showers detected. This
would increase h-lilagro’s sensitivity to gan‘una-rays at these energies. One obstacle to
doing so are events gemrated by single. muons traveling nearly horizontally across the
pond. A muon entering the pond at high angle and crossing the pond horizontally
causes a cone. of light that produces signals in a large number of PMTs. Such an event.

can satisfy the multiplicity trigger condition. On the other hand, these events have

39

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(’lifferent time profiles in the PMT arrival times than that of an air shower. While
particles in an air shower travel nearly at the speed of light, c, the light cone from
a horizontal muon travels at the speed of light in water, e/n, where n is the index
of refraction of light in water. Thus, hits from a high angle muon will occur over a
longer period of time than those from an air shower, and by making a cut on the
time development of the event, it is possible to reject these muon events. Although
such events can be removed after the angle reconstruction, since the resulting angles
are unphysical, removing these events at the trigger level will allow for the trigger
threshold to be lowered without a large increase. in the event rate.

The arrival time profile of an event is characterized by the risetime parameter.
The risetime. of an event is defined as the time interval within which 10% to 90% of
the hits occur in that event. The risetime distributions for data events which were
fit, data events which failed the fit, and simulated gamma—ray showers are shown in
Figure 3.6 ['33]. It is clear from this figure that data events that failed the fit have
longer risetimes. The. risetin'ie is calculated and applied at the. trigger level to bias
triggers at low multiplicities toward gan‘ima-ray showers while. keeping the trigger rate
below the 2000 Hz limit of the DAQ system.

A custom made. VME (Versa Module Europa) trigger card was built. that allowed
the risetime of the event to be included in the trigger decision. In addition, the card
is reprogramniable allowing the implen‘ientation of multiple trigger conditions and
external triggering. These trigger conditions could be changed to keep the trigger
rate. below the maximum the DAQ system could handle. The set of trigger conditions

that were. used when the VME trigger was first installed are. as follows:
1. Ntop > 20 8; risetime < .50 ns.
2. N10}, > 53 8: risetime < 87.5 ns.

3. lefop > 74 .

These values were selected to maximize. the number of low energy showers, while
keeping the trigger rate at a manageable level of ~ 1800 Hz with ~ 8% dead time.
The trigger conditions have been modified over time to keep the trigger rate below
the DAQ limit. The simple multiplicity trigger was brought back online on April 1st,

‘2006 after the VME trigger card failure on the same, day.

3.5 Data Acquisition System

W’hen a. trigger condition is met, information from the TDCs is read out using a
FASTBUS Smart Crate Controller (FSCC). A CPS clock is used to determine the
time of the event. The TDC information from all the channels are transferred to a
VME memory module. This data are then read and processed by the DAQ computer.
The DAQ computer system COIlSlStS of a master PC and several PC workers. The
DAQ system operates using a client-server architecture in which the. master controls
the assignments of data blocks to workers on several PCs.

The raw data are broken into runs and subruns. A new subrun is started every 5
minutes. A new run started at 0:00 UT every day and will last for a whole day unless
the DAQ system is shut down by a user, for maintenance, or by external factors like
power outage. The raw data consists of the TOT information from each tube and
the time of the event. Storing all the raw data would be prohibitively expensive since
in one day it will require more than 230 GB of disk space which translates into ~
8‘2 TB / year. Instead raw data are saved only for selected sources, such as the Crab
Nebula, the active galaxies Mrk 4‘21 and Mrk 501 when. they are flaring, the sun,
and the moon. The raw data are also saved when there is a notification, by other
experiments, of a GRB that occurred in the field of view of Milagro. All the raw data
are calibrated and reconstructed in real time. All of these reconstructed data are

saved. The reconstructed (lata contain information about each reconstructed event

42

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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3500? Mean = 116.1
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160

140

120

100

 

o8888

 

 

Figure 3.6: Distributions of the risetime parameter [33]. From top to bottom: data
events that could be fit, data events that failed the fit, and simulated gamma-ray
showers.

43

which include, the reconstructed direction of the event, core position, event. time, the
modified Julian date (MJD) (see section 4.1.3), and timing error information from the
CPS clock. The. size of disk space required to store all the reconstructed data for one
day is ~ 5 GB. The recmistructed data are stored on a DLT (Digital Linear Tape)
tapes at the site , and more recently on portable disk arrays, which are then physically
transferred for storage in Los Alamos National Laboratory. The reconstructed data
are also piped through the network to large redundant disks arrays (RAID) in Los

Alamos National Laboratory and University of l\rlaryland.

3.6 Calibration

As was discussed above, the raw data from Milagro consist of a series of edge times.
This raw edge information must be ccmverted to relative arrival times of the Cherenkov
photons at the PMTs and to the number of PBS in each hit PMT. Although the hit
time of each PMT is known, it must be corrected for two effects. The first correction
involves timing corrections. This correction is required because the analog PMT
pulses have finite risetime. A large pulse will cross a threshold more quickly than a
smaller pulse. This correction is referred to as electronic slewing and is corrected for
by measuring the change in start time as a function of TOT. The second correction
applied accounts for differences in travel times of the PMT pulses through the signal
cables and electronics. These corrections are done with a laser calibration system
which consists of a pulsed laser, a filter wheel, and optical fibers that carry the light
to a system of diffusing balls placed throughout the pond. The laser fires a set number
of pulses of fixed amplitude through a filter wheel which go through optical fiber that
connects to an optical switch, allowing the light to be sent to any of the thirty laser
balls in the pond. A laser ball is an Optical fiber with a sphere of epoxy at. the end

which diffuses the. light. out isotropic-ally from the fiber. The filter wheel allows the

44

intensity of the light. sent to the pond to be varied. Laser calibration data are taken
periodically to produce new calibration constants [34].

In addition to the timing calibrations, the calibration of the PMT charge is carried
out. As discussed above, in the TOT method an edge is generated whenever the
PMT signal crosses one of the high or low discriminator thresholds. The TOT is
proportional to the logarithm of the number of photo-electrons. This relation is
determined using the occupancy method, which is based on the fact that, at low
light levels, the number of photon-electrons created by the PMT obeys a Poisson
distribution. This produces a logarithmic relation between TOT and the number of

PBS. The exact relation is determined by the laser ('talibration.

3.7 Event Reconstruction

Next, each event has to be re(onstructed to (‘letermine the direction of the incident
primary particle and the core location of the air slmwer on the ground. During the
development of an air shower, the swarm of particles spreads out laterally forming
what is known as the shower front. The relative arrival times of the shower particles in
the pond are used to reconstruct the direction of the. incident primary particle. Figure
3.7 shows a crmceptual drawing of the primary particle direction reconstruction in

l\"Iilagro. The reconstruction of an event proceeds in the following steps:

3.7.1 Core Position Reconstruction

The core position of an EAS is the point on the ground at which the primary particle
would hit if it were to experiem‘te no interaction in the atmosphere. Over the course
of running lV’Iilagro, different algorithms have been used to determine the location of
the shower core. The core of an air shower contains the highest energy particles in

the shower. The. particle density near the shower core is also at its maximum. Thus,

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the shower core should be associated with the largest number of PBS detected and
with the location of the largest number of PMTs hit in an event.

The first core fitter used in Milagro was a simple center of mass fitter which put
all the cores on the pond. This algorithm used a weighted sum of the locations of all

the hit PMTs in the AS layer. The core location in this case is given by:

 

(3.1)

M

ZEN/Ply,- x m,-
il7("(.rr'e =
i V 1 Bi
21 Di X M

(DIP I'm:

 

M

where. PE,- is the number of PEs detected by the PMT with coordinates 1‘, and yi.
The weight assigned for each hit PMT was taken as \fpf—l to keep the. big hits from
completely dominating the fit.

To improve the core fitter, several methods were used to to determine if the shower
core was likely to be located off the. pond. If the core. was likely to be on the pond, the
center of mass core fitter was used; otherwise the. reconstructed core location is placed
50 meters from the center of the pond in the direction determined by the center of
mass fitter. The value of 50 meters was used because l\~Ionte Carlo simulations indicate,
that this value results in the. best agreement, on average, with the true core location.

After the installation of the (mtriggers, they were used in the core fitter to deter-
mine if the core was located on or off the pond. The ratio of the number of outriggers
hit. to the number of the AS layer PMTs hit. provides a. goml measure of whether the
core was on or off the. pond. If the core. was determined to be off the pond, the center
of mass of the outriggers was used to determine the location of the shower core. If
the core was determined to be on the pond, the center of mass of the AS layer tubes
was used to determine the location of the shower core.

The current core. fitter algorithm performs a least square fit to a. 2-D Gaussian

47

 

2200
2000
1800
1600
1400
1200
1000

  

 

   

 

_L
50
X Core Position (m)

Figure 3.8: Reconstructed core positions for simulated gamma—ray events that trig-
gered the detector using the current ‘2-D Gaussian fitter. In the figure, the y- and

x—axes point north and east, respectively. The h‘lilagro pond is inclined by angle of
24.40 from the mu'th—scmth direction.

using the AS layer PMTs and the outriggers. Figure 3.8 shows the distribution of core
locations for simulated gamma-ray events that triggered the detector using this core
fitter. Figure 3.9 shows the fit core location versus true core location for simulated
gamma ray events. The core resolution, the distribution of the. errors in the fitted
core location, is shown in figure 3.10. The error is determined by comparing the fitted

core location to the true core. location from the Monte Carlo simulations.

3.7.2 Shower Front Sampling Correction

The shower front of an extensive. air shower has a finite thickness. It is thinner near

the shower core and thicker near the edge of the shower (Figure 3.7). This thickness

48

 

[ Fit Core Distance vs. True Core Distance I

 

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1O 20 30 40 5O 60 7O 80 90 100
True Core Distance (m)

Figure 3.9: Reconstructed (fit) core position versus true core position for simulated
gamma-ray events.

49

 

Distribution of Error in Core Location for Simulated Gamma Ray Events I

 

 

 

—

1200

1000

800

600

400

200

l—rjlilllllll

 

 

 

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Figure 3.10: Distribution of error in core. location for the simulated gamma-ray events
shown in figure 3.9.

in the shower front is due to the lower energy secondary particles, which are present
near the shower edge, suffering more. scattering than the higher energy ones that
are present near the shower core. Since the arrival time of the first photoelectron is
measured by the TDC, the larger the number of particles (and thus more PE’S), the
earlier the measured arrival time, therefore a correction must be applied. Sampling
correction corrects for the. time difference between PMTs hit by one photon as opposed
to many photons and is determined as a function of PES from Monte Carlo simulations
and data optimization. The sampling correction is relatively smaller around the core
position, where each PMT collects more photons, and bigger away from the core,

where. each PMT collects fewer photons.

3.7.3 Shower Front Curvature Correction

For an extensive air shower, the shower front is actually not a plane, but is approx-
imately a apherical cap with apex at the primary interaction location as shown in
figure 3.7. One could fit a parabola to the shower front but the equations to be solved
in such a fit. are not of closed form and the algorithms to solve such equations will be
slow and hard to implement in the reconstruction code. Therefore, instead of fitting
the shower front to a parabola, a curvature correction is applied to the shower front
and the resulting shower front is fit to a plane. The curvature of the shower front
is defined as the slope of the cmie I’neasured from the slmwer core. The curvature
correction accounts for this shower curvature and is 0.07 ns per meter from the core.
The time information of each PMT used in the core. reconstruction is corrected by
this amount. The value. of the curvature correction is found using Monte Carlo sim-
ulations. Monte Carlo simulations show an improvement in the. angular resolution of

l\/Iilz~i.gro when using this correction [l3].

3.7.4 Direction Reconstruction

To reconstruct the direction of the primary particle, the shower front is fit to a plane
using an iterative least squares (\2) fit. (figure 3.7). These iterative fits are applied
after the sampling and curvature cm‘rections have. been applied. Each hit PMT is
assigned a weight depending on its pulse height. In each of these iterations, PMTs
with poor residuals are removed from the fit, and the PE threshold cut is relaxed to
allow more PMTs to enter in the fit in the next iteraticm. This process is repeated five
times. Using this method ~ 90% of triggered data is successfully fit. The remaining
10% of the triggers are due to single muons passing through the detector at nearly
horizontal angles and single hadrons.

Originally, only the AS layer was used in the angular recrmstruction but after
the addition of the outriggers they were used as well. The. addition of the outrig-
gers improved the angular resolution of the detector by giving a longer lever arm to
rectmstruct the shower.

A measure of the angular resolution of the detector is given by the A0,, 916., variable.
Amy“ is defined as the. space angle difference. between the true direction of an air

shower (from Monte Carlo simulations) and the reconstructed direction:

Aangle 2 thI‘lu’ _ intl (33)

If in represents a normal vector in the. true direction of the air shower, from the
l\'lonte Carlo. and 'flf represents a. normal vector in the fitted air shower direction,

then fit and fif are given by:

ii; = sin I), cos (f), :i.‘ + sin 0f sin (1'), y + cos 0t 5. (3.4)
73f = sin/)f cos (if .it + sin 0f sinof g) + cos (if z‘ (3.5)

 

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600

500

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400

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300

200

100

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Figure 3.11: Distribution of Amwl“ for triggered gamma-ray events that passed the
Nfit _>_ 40 cut. The. median of the Aangle distribution of ~ 0.850 is roughly the
angular resolution of the detector for this Nfit cut.

The Amy“ 1s then given by:

Amelie : ““03 [Sill ”t Si“ 0 f Sill (£91, + of) + cos 0t cos 6f] (3(3)

where 6 and (,b are the zenith and azimuth angles. respectively.

The distribution of Aging”. is shown in figure 3.11 for triggered gamma-ray events
with 40 or more PMTs participating in the fit (Nfit 2 40). The median of the
Amy]? distribution of ~ 0.850 is roughly the angular resolution of the detector for
this N fit cut. In general the angular resolution improves with increasing the N fit
cut. The angular resolutimi is also a function of the. background rejection cut applied.
Angular resolutions as good as 0.30 can be achieved. More detailed discussions of the

angular resolution and its dependencies are given in chapter 6.

3.8 Energy Dependence

l\lilagro has a rather broad energy response as can be seen in figure 3.1‘2 3. This
figure shows the distribution of detected gamma-ray events as a function of energy
for a power law spectrum of (1\/(1 [5 oc £7-24. Air showers initiated by low energy
primaries are hard to detect since fewer particles in the air shower will survive to the
ground. At higher primary particle energies there are simply fewer primary particles
(for a power law spectrum). Milagro has no well defined energy threshold below
which no events are. detected. The median triggered energy is useful as it usually
illustrates the peak of the energr distribution, in logarithmic space, and above which
fluxes and upper limits are usually quoted. The median energy for gamma-ray events
that trigger Milagro is N 3.5 TeV. For triggered gamma-ray events, 90% of the events
from a source with this spectrum fall between ~ 400 GeV and ~ 70 TeV.

The median energy is a function of the zenith angle. At larger zenith angles
particles in the shower have to traverse more. of the atmosphere and hence fewer
shower particles survive to ground level. This means that higher energy showers have
a higher chance of triggering the detector at larger zenith angles than lower energy
ones. This is illustrated in figure 3.13 which shows the relation between the median
energy of detected gannna-ray events as a function of the zenith angle of the shower.
The median energy is roughly constant. for small zenith angles (< 20°), but increases
for larger zenith angles. For evens with zenith angles greater than 40°, the median

crim‘gv is roughly :3 times that for events with small zenith angles.

3.9 Effective Area

The. effective area is a parameter used to characterize the energy response of a detec-

tor. The effective arca is a measure of the efficiency for the successful detection of a

 

3Figure for epoch 7. see section 7.2 for details.

54

 

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Figure 3.12: Distribution of gamma-ray events that triggered the detector for a power
law spectrum of dN/(IE oc 13—2'4. The median energy (3.5 TeV) is indicated by the
middle dotted line. The two other dotted lines indicate the energies above which 95%
and 5 % of the detected gamma-rays fall.

55

 

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gamma-ray events with a power law spectrum of (1N / (I F} (X 127—2'4

gamma-ray-induced air shower based on the energy and zenith angle of the primary

particle. The. effective area is defined as:

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where N,,.,-g(E,()) is the number of events that triggered the detector at. a given
energy and zenith angle, NH,.,.0,L,(I.~J,()) is the number of events that were thrown,
from the Monte. Carlo, at that energy and zenith angle, and Ath-rou.‘ is the area over
which the simulatml gamma-rays were thrown. This area is equal to 1 km2 (see next
section).

Figure 3.14 shows the effective area as a function of energy for three. different. zenith
angle ranges. As can be seen the. effective area increases dramatically, from almost
zero at 30 GeV, to about 10,000 m2 at 10 TeV. The physical area of the detector
is marked by the dashed horizontal line and is equal to (4.8 x103 m2). For energies
above several TeVs, the effective area exceeds the physical area of the detector. This is
be(’-.ause a successful detection of a gamn’ia-ray shower does not. require that the initial
trajectory of the 1')rimary gamnna-ray intersects the physical area of the. detector. All
that is needed for a successful detection is the satisfaction of the trigger condition
and direction reconstruction which may be achieved by high energy primaries landing
off the detector.

The effective area as a function of zenith angle is given by:

I'Emar AefffE» 0) %%:(1E

 

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ranges for an [3‘24 spectrum. The horizontal dashed line represents the physical
‘ 9

area of the (‘letector (4.8 x10" 1n“).

 

[ Effective Area vs Zenith Angle |

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

450 ____| ............... a ...................................
...
400 :_.. ......................................................................................................
b 5
350 :_............. ..................
oT‘ - i
E ~—
vaa oo_
0 I
b _
(250?» ...........................................................................................................................................
0 _
> -
3200”
o p—_. ................................................................................................................................................
0 _
in:
150;— .........................................................................................
100..—_.. ......................................................................................................
_
_
50 —_, ............... . '
LLLllllJlllLlllIllllllllllllllllLlllllllllLl

 

 

 

0 5 10 15 20 25 30 35 40 45
Zenith Angle (deg)

Figure 3.15: The effective area. as a function of zenith angle for an [5‘24 spectrum.

3.10 Simulations

3.10.1 Monte Carlo Simulations of Extensive Air Showers

The first stage in simulating the response of the hrlilagro detector to EAS is the sim-
ulation of the production and propagation of EAS through the atmosphere. This is
done using the CORSIKA (Cosmic—Ray Simulations for KAskade) v6.50'21 software
package [78]. For hadronic air shmvers, only the ones created by proton or helium
primaries were simulated. Low energy (< 80 GeV) hadronic interactions were simu-
lated with F LUKA v2005.0, higher energr hadronic interactions were simulated with
NEXUS V3975. Electrmnagnetic interactitms were simulated with EGS4[4].

The simulation of an EAS with CORSIKA begins with the first interaction of the
primary particle in the atmosphere, followed by the subsequent interactions of the.
secondary particles in the shower down to ground level. In order to obtain enough
statistics, especially at high energies, hundreds of millions of CORSIKA showers were
generated. The primaries that were thrown were proton and helium, to simulate the
cosn'iic-ray background, and gannna—ray primaries to simulate cosmic. gamma—rays.
The gamn'ia-ray slmwers were thrown over a zenith angle range of 00 to 45°, while
the helium and proton slmwers were thrown over a zenith angle range of 0° to 70°.
All the showers had an energy in the range 30 GeV to 100 TeV. The showers were
thrown with a falling power law spectrum of (IN/(1E oc 1340. Later, at the analysis
stage, the events were properly re-weighted so that the spectral indices for hadrons
were a = —2.75 for proton and o = —‘2.68 for helium showers. For the Monte Carlo
cosmic-ray sample, the helium flux is about 35% of the total flux. These values are

the ones measured by the. BESS balloon experiment[30].

(if)

3.10.2 Monte Carlo Simulations of Detector Response

The simulation of the. detectors response to EAS is done using the GEANT4 (GEom-
etry AN (1 Tracking) software package [79]. The input for this stage of the simulation
are the information about the shower particles reaching the ground (from CORSIKA).
The GENAT s<,)ftwarc takes these particles and propagates them through a model of
the Milagro detector. The interactions of the secondary particles in the shower, such
as Cherenkov light pnxlucticm by relativistically charged particles traveling in water,
pair production of electron-1xisitron pairs from gamma—rays, hadronic interactions,
and other interactions are simulated with GEANT4. The GEANT4 software redis-
tributes the core positions of the CORSIKA showers randomly over a circle of 1000
m radius centered on the pond. For each PMT hit, the GEANT4 output includes the
number of PEs, their arrival times, and the position of detection on the face of the

1:)hotocatlunle.

(31

Chapter 4

Data Analysis Techniques

4.1 Coordinate Systems on the Celestial Sphere

The (fifelestial sphere is an imaginary sphere with an infinite radius centered on the
earth. Stars, galaxies, and other extraterrestrial objects appear to lie on this celestial
sphere. Astronomers use different coordinate systems to describe the positions of
objects on the celestial sphere. The most commonly used coordinate system is the

equatorial coordinate system.

4.1.1 Equatorial Coordinate System

The earth rotates eastward on its axis once a day, as a consequence, the sky appears
to rotate westward about the earth. The extension of the earth’s rotation axis to
the celestial sphere defines the north and south celestial poles (NCP and SCP). The
extension of the earth’s equatorial plane to the celestial sphere defines the celestial
equator (see figure. 4.1).

For an observer on the earth’s surface, the direction of gravity fixes the direction
of the local vertical. The point at which the local vertical intersects the celestial

sphere is the zenith for that observer. The. great circle passing tln'cmgh the celestial

6‘2

poles and the zenith is the meridian. The horizon is the great circle whose pole is the
zenith.

As the earth revolves annually around the sun, the. sun appears to move from west
to east around the celestial sphere on a path called the ecliptic. The earth's rotation
axis is inclined from the normal to its orbit by an angle of 23.5 0, hence the ecliptic
is also inclined to the celestial equator by the same angle. This angle is called the
obliquity of the. ecli1.)tic. The celestial equator and the ecliptic intersect at two points
separated by 180°, these two points are called the vernal and autumnal equinoxes.
The sun passes by through the vernal equinox around l\-'Iarch 21 each year. About six
months later it passes by the autumnal equinox.

The great circle. through the celestial poles (NCP and SCP) and a star’s position is
that star’s hour circle. The star’s hour angle is the angle around the celestial equator
between the meridian and its hour circle. The star’s right ascension a is the arc of the
celestial equator from the vernal equinox to the star’s hour circle. Right ascension
increases from west to east, thus stars with large right ascension rise later than those
with small ones. A star’s declination 6 is the angular distance measured from the
celestial equator along the star’s hour circle to the star. A declination is positive
northward and negative southward. For example the NCP is at 6 = +900, the SCP
is at (5 = —90°, and the celestial equator is at 6 = 0°. In this system a and 6 on the

celestial sphere are equivalent to longitude and latitude 011 the earth’s surface.

4.1.2 J 2000 Reference

The earth is not spherical but flattened near the. equator. This flattening allows the
sun and the moon to exert torques on the earth, and, since the earth spins like a top,
its axis of rotation processes about the ecliptic pole. The period of this precession
is about. 26 000 years. In addition to this precession, the shape and orientation of

the earth’s orbit around the sun is changing on a time scale of millions of years in

(i3

(N . north celestial pole

 
   
   
     
 
 
   

celestnat equator
. r

. p.
I I5 )

 

- north poie .

     

x ‘ declination \“ .

I

2, Eqaazor

 

echptsc
south pote -‘—'

3
fight asceesson

 
   
 

sour. retest .i' 0019 \J

 

Figure 4.1: Equatorial coordinates on the celestial sphere. Image taken from [76]

64

response to the. forces applied by the planets. Since the vernal equinox is defined
as the interscxttion on the celestial sphere of the great circles of the equator and the
ecliptic, any change in the direction of the ecliptic will result in a change in the vernal
equinox and hence a change in the equatorial coordinate system. It is, thus, essential
to specify an epoch at which the right ascension and declination were measured.
Each of these epochs last for 50 years and the current epoch is defined with respect
to the position of the earth at noon on January 1, 2000. The reference epoch for all
equatorial coordinates in this dissertation is J2000. For example, if a source has the
coordinates a: J 2019 and 6: 37 in the J 2000 epoch, then this means that the source

has a right. ascension of 20 hours and 19 I‘ninutes, and a declination of 37 degrees.

4.1.3 Julian Date and Modified Julian Date

The Julian day (JD) is the integer number of days that passed since noon on January
1, 4713 BC. Almost. 2.5 million days have transpired since this date. The use of Julian
day omits any depemlence on months and years when used as a calendar, thus Julian
dates are widely used in astronomy. For reference, Julian day 2450000 began at noon
on 1995 October 9. Because Julian dates are so large, astronomers often make use of

a “modified Julian date”; MJD 2 JD - 24000005.

4.1.4 Galactic Coordinate System

The Galactic coordinate system is most useful for consi('lerations of objects beyond
the solar system, especially for considerations of objects of our Milky Way Galaxy.
The reference for the Galactic coordinate system is the disk of our Galaxy. The
intersection of this plane with the celestial sphere is known as the Galactic equator
and is inclined by 62.870 with respect. to the celestial equator. The north pole of the
Galactic coordinate system is located at (o0 p, (56 p) : (19286027130). T he. Galactic.

latltude I) ()f a star is the angle from the Galactic equator to the star along the great

C:
CH

circle through the start and the Galactic poles. For example, the north Galactic
pole (NC?) is at b 2 +900, and the south Galactic pole (SGP) is at b = —90°.
The Galactic longitude l of a star is measured with respect to the direction to the
Galactic. centerl. The Galactic Center position in the equatr‘n‘ial coordinate system
' a ‘ _ . ' ' O . 'i ( 0
IS ((igc,dgc) — (200.4 ,-2b..)4 ).

Transfi)rmations between the equatorial coordinates and Galactic coordinates are

given by [40]:

sin b = sin (lap sin (5 + cos 60]) cos (5 cos (a — 0019) (4.1)
cos bcos (le — I) = cos 66p sin 6 - sin (50p cos (5 cos (a — (I'Gp) (4.2)
cos bsin (le — l) = coso'sin (o - (rap) (4.3)

The inverse traiisformation is given by:

sin (5 = sin 60p sin b + cos 6GP cos 1) cos (le — l) (4.4)
cosdcos (o — (1GP) = cos (56p sin I) — sin (56p cos b cos (le — l) (4.5)
cosdsin (o — (16p) 2 cos bsin (lcp — I) (4.6)

where. le : 123.930 is the longitude of the NCP.

The Galactic coordinate system is shown in figure. 4.2. An optical View of the
Milky \Vay Galaxy in Galactic coordinates is slmwn in figure 4.3. In this figure, the
Gale—rctic center (I = 0) is in the. middle. of the map. Galactic longitude increases to
the left. of the center and decreases to the right. Figure 4.4 shows an artist drawing

of what the Milky “’ay Galaxy might look like from the North Galactic Pole.

 

lThe Galactic Center (GC) lies in the constellation of the Sagittarius. The compact radio source.
Sgr A" believed to mark the location of the GC is actually 0.0MQ away from the GC.

(50

North Galactic Pole
90° lat

    

180° long

North Galacfic Pole

Figure 4.2: Galactic coordinate system. Figure taken from [77].

67

 

Figure 4.3: Optical View of our Galaxy in Galactic coordinates. The Galactic center
(I = 0) is in the middle of the map. Galactic longitude increases to the left of the
center and decreases to the right.

68

 

F igurc 4.4: Artist conception of the Milky Way Galaxy as seen from the North
Galactic Pole.

69

 

4.2 Background Estimation

For ground-based gamma-ray detectors, the search for a gamma-rayr signal from a
celestial gamma-ray source is obscured by a large isotropic background that is due
to hadronic-initiated EAS. A crucial step in searching for a gamma-ray signal is the
correct estimation of this hadronic background. If the background is overestimated,
a real gamma-ray signal could be washed out by this overestimation and could be
lost. If the background is underestimated, a fluctuation in the estimation of the
background could appear as a signal.

The method used in this analysis for background estimation is the direct integra-
tion method [14]. This technique assumes that the efficiency for detecting events is
a function of the local coordinates and is independent of the trigger rate for short.
periods of time. Figure 4.5 shows the all-sky rate for one day. From this figure we
see a clear variation of the trigger rate over an entire day. This variation is mainly
due to atmospheric effects. For this analysis, an integration period of two hours was
selected. This integration time of two hours was selected because the duration needs
to be long enough that the source transits a large enough distance so that the back-
ground can be well measured, and not so long that the assumption that the local
coordinate (.‘fficiency is crmstant is not. violated.

In this method the number of background events is obtained by the numerical

integration:

:N’B(o,6)= / / («11.40)») mi) ((Hxl(l),(ir,l.) (11, (19. (4.7)

where N 301,6) is the background estimate within a bin in equatorial coordinates
((1.6), [RH/1(1), (5) is the efficiency or acceptance of the detector at local coordinate.
( H A(t),6) and is simply the probability that an event comes from the differential

angular bin (10 = (1(H."i(())d(6). The event rate of the detector as a function of time

70

 

 

 

..a
8
O
0

Rate (Hz)
1

 

1850

 

 

1800 . L

1750

 

l

TT1

1700

 

 

 

 

 

 

 

 

 

 

 

llll ILll llll llll lllJ llll Ill! 1111 L1

o1oooozoooosoooo¢oooosoooosoooo7ooooaoooo
UTseconds

 

Figure 4.5: An all-sky rate for one day. As can be. seen ,the rate varies with time of
the day. For a two hour periml. 7200 seconds. the rate is essentially constant.

is given by the [{(1) term. The ((1/ AU). (1'. I ) term is equal to 1 if an event falls in the
(a, (i) bin at sidereal time2 t and zero otherwise. The hour angle, HA(t), is a function

of the sidereal time and is given by:

1mm :1, —o (4.8)

The hour angle provides the conversion from the local coordinates to the equatorial
coordinates.

To estimate the detector acceptance HUI/1(1). (5). events in the sky are binned in
0.10 x 0.10 bins. The number of events in each of these bins is then normalized by
dividing it by the total number of events observed in that integration period. The.

resulting map is -alled the efficiency map. Events in the efficiency map have. to pass

 

2Sidereal time literally means "star time". A sidcreal day is the time it takes for the earth to
complete a full revolution around its axis. 3600 with respect to distant stars. and is equal to 23 hours
and 56 minutes.

 

any cuts applied on the data. At the end of the two hours background integration
period, the. efficiency map is converted into background map in equatorial coordinates
by multiplying the rate of events collected for each 24 seconds of time by the efficiency
for each bin. The size of the time bin is selected to eliminate any appreciable motion
of the sky within the angular bin of 0.10. This ensures that the background events
have the same time distribution as the collected data.

The presence of a signal from a gamma-ray source will conteuninate the back—
ground. This means that the background estimate will be higher in the presence. of
a gamma-ray signal since these signal events will be included in the efficiency map.
This effect is removed by excluding a 3° >< 3° region around known sources like the
Crab nel’mla and the active Galaxy Mrk421 from the background estimate. For the
Galactic plane, the region defined by |b| < 2.5 is also excluded from the background
estimate. It should be noticed that. a truly diffuse isotropic gamma—ray emission will
not be detected, using this background estin’iation method, and will be counted as
background. However, gamma-ray sources with sizes smaller than the integration
scale (30 degrees for ‘2 hours) are. detectable.

After the estimation of the backgroimd the map is smoothed by the point spread

function (PSF) of h‘IiIagro. See section 6.3 for more details.

4.3 Significance of a Measurement

The next. step in searching for a gamma-ray signal is the calculatirm of the statistical
significance of an excess (or deficit) for each point in the sky. To calculate the statis-
tical significance the method of Li and Ma [47] is used. This method of calculating
the significance is based on the likelihood ratio test. In this method the statistical

significance, 3, of a measurmnent is given by:

72

 

(1 + (i) No”
(I (TN/r07) + fvoff)

1V0]: f
(Non. + No f f)
(4.9)

 

 

S = fl N0” ll] + Noff ln (1 + (1')

where N0.” is the number of events in the signal bin, Noff is the number of events
in the background bin. and a is the ratio of signal to background exposures and is

given by:

- B 1
0(6) :2 (m) (TX—13) (4.10)

where B is the. bin size, 0.10 in this case, 6 is the declination of the bin at which the
significance is to be calculated, and T is the integration time in hours, 2 hours in this
case. The first part. on the left. gives the signal exposure in degrees, while the second
part gives the rmiprocal of the background exposure in degrees. The. number 15 in
the numerator is the number of degrees the earth rotates in one hour.

Equation 4.9 is valid in the case that the observed counts are not too few (N07, 2
10, Noff 2 10). The significance distrilmtions obtained with this method are consis-
tent. with the Gaussian probabilities [47].

The distribution of significance provides a check of the background estimation.
This distribution for the background, in the absence of any signals, should follow a
Gaussian distribution with zero mean and sigma of 1.0. Divergence from the back-
ground expectation indicates a signal. or a bias in the calculation of significance or
of the background estimate. Figure 4.6 shows the distribution of excess (or deficit)
significances for the whole sky. The distribution follows a Gaussian distribution with
a mean of 0.0005 and sigma of 0.997. T hose values are very close to that 1')redieted

in the absence of a signal.

‘1
C»?

 

I Distribution of Excesses on Sky I

 

 

10‘

T1 lllllfl

103

1o2

IITIUITI 1 TI Illlll

10

T l Willi]

T [Tlllll

lJJllllle_L lllllllLlllL4l

-15 -10 -5 0 5 10 15 20
Standard Deviations(o)

F
)-

 

 

 

-2

D

Figure 4.6: Distrilnition of excess (or deficit) significances. The distribution is well
fitted to a Gaussian (.liStl‘il)llti(.)Il with a mean of 0.0005 and sigma of 0.997.

Chapter 5

New Gamma-Hadron Separation

Technique and Variable

5.1 Gamma-Hadron Separation In Milagro

W’hen a '7'-ray enters the atmosphere, its interactions with the nuclei in the air are
almost purely electromagnetic, resulting in an air shower that. contains mostly lower
energy electrons, positrons, and *y—rays. Hadronic cosmic-rays, on the other hand,
will undergo hadronic interactions with the nuclei in the air. This will give rise to
charged pions that can decay into muons and neutrinos. In addition, multi-GeV
hadronic particles may also reach the ground.

A y-ray initiated EAS at ground level is composed primzu‘ily of electrons, positrons,
and low-energy Trays. The air-rays outnumber the electrons and positrons in the air
slmwer by a factor of ~ 5. The Top layer in l\‘lilagro is placed under ~ 4 radiation
lengths (X of) and ~ ‘2 interaction lengths (A1). This means that the bulk of the 7-rays
that enter the pond will be converted to electron-positron pairs. These relativistic

charged particles will Cherenkov radiate in the water and will illuminate the PMTs

in the Top layer. Roughly 50% of all electronragnetic particles that enter the pond

 

are detected.

The muon layer in Milagro is located under 6111 of water (c(.)rresp(mding to 17 more
radiation lengths and 7.2 interaction lengths). This means that most EM charged
particles that enter the pond get absorbed before. reaching this layer, although their
Cherenkov light does reach the muon layer. On the other hand, muons with energies
as low as 1.2 GeV can penetrate and shower near the PMTs of the muon layer. These
penetrating muons and hadrons will result in bright compact clusters of light in this
12 yer. This is clearly seen in figure. 5.1 which shows images from the muon layer
of six Monte Carlo events. The top three events are '7-ray—indueed events, and the
bottom three. are proton-induced events. The area of each square is proportional to
the number of pliotoelectrons (PEs) registered in the corresponding PMT, and the
area is saturatml at 300 PEs. It can be seen from this figure that the y-ray events have
relatively smooth PE distributions in the muon layer while the. hadronic events have
well-defined clumps of high intensity regions. Using Monte Carlo simulations it is
estimated that. 79% of all proton showers that trigger Milagro contain a muon and / or
a hadron that enters the pond. while only 6% of gamma ray induced air showers

contain a muon and/or a hadron that enters the pond.

5.1.1 The Compactness Parameter

A simple algorithm has been developed [14] to distinguish ”y-ray initiated air showers
from the overwhelming background of hadron initiated air showers. The compactness

pz-irameter [14] is defined as:

(, _ AFbotZ‘ZPEs (r 1)
I 75771an

where. M0122 p E8 is the number of PMTs in the bottom layer with more than ‘2 PBS,

and 179,7,”er is the number of PBS in the bottom layer tube with the maximum

Kl
CE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K. ' " r""" .... ‘ —"' "" 1
\\ / ‘2 / \. /
\\ / \ / "\ '/
[ t
||
.,. :. ‘ F
o ..... 4
DI!.|:. :(:
‘ F I v v v : . ' “t-r-o-W'r-I-r- <l‘
/ ...... \ 4" ------------ \ ‘I/ ' \
t \ 2’ /" ~
*/ ‘\ ’ \ - “
"l v—/
\, \ f
'\ / \
.,‘-—_—-'—-..,- _ 1’-
'.I v. on. ' b
t"':‘ 2:; .. '::_
?. no- I I I an.
_t . 1. :t'. .i-. . I .
P " . I I... ----- I . .o .. .
'f - v1. .pi-ll- ‘I- - -i
‘9 v u- 1. I col-oo- - I u - In
I; IOI I. l 9"... a- can. -. .
P .. :. ‘. .[szz'z ‘. :L':::;.
. .l' . -:-:-I ‘ i . .
x" 73'7‘.""“\ :t'xt :' r" " \, r‘fl" “r ' :'*.\
/ ‘. -' "x ’ ‘s.
\r .’ \ -/ \

 

 

 

 

 

 

 

 

F igurc 5.1: Gamma-ray (top row) and proton (bottom row) events imaged in the
muon layer of Milagro. The area of each square is proportional to the number of
1‘)hotoelectrons (PEs) registered in the correspomling PMT, and the area is saturated
at. 300 PEs.

number of PEs. The cmnpactness parameter should yield small values for events
where few PMTs in the bottom layer are struck with a large amount of light (large
P EmamB) and large values for events where few PMT s are struck with a small amount
of light (large .Av’rbofzngs ). Therefore, hadronically initiated showers typically have.
small values of C, while >7—ray initiated showers typically have large values of C.
Figure 5.2 slmws the compactness distribution for Monte Carlo 'y-ray showers,
Monte Carlo cosmic-ray showers, and datal. An event selection is made on the

Monte Carlo events identical to that made on data: the number of PMTs used in the

angular fit must. be greater that ‘20, and, for '71-ray Monte Carlo, the events must be

 

lEpoch 7 is used throughout this chapter. The Monte Carlo gamma-ray sample was thrown with
a Crab-like spectrum of E ‘2'”.

77

_
/ '__

 

reconstructed within 1.20 of their true direction. As can be seen in this figure, there
is a clear difference between the l\r’lonte Carlo 'y-ray showers and the Monte Carlo
comic-ray showers. Further, there is a reasonable agreement between the data and
the Monte Carlo cosmic-ray showers, as expected, since the data consist mainly of

cosmic-ray initiated showers.

 

 

Compactness distribution

 

 

 

 

 

 

 

 

 

 

 

 

0-05 _ — MC Gamma Rays
: — MC Cosmic Rays
0 05 — Data
0.04
0.03
0.02
0.01 .
: ll Il
o—llllllllllLlLllLJll. 2:; L-h-IAJ ”.11
0 1 2 3 4 5 6 7 8 9 10

C

Figure 5.2: The compactness distribution for Monte Carlo c;-'-ray showers, Monte Carlo
cosmic-ray showers. and data. All of the histograms have been normalized to have
unit area.

Figure 5.3 Sl‘1(_)WS the efficiencies for retaining data, cosmic—ray Monte Carlo, and
Tray Monte Carlo showers as a function of the compactness cut.
The relative increase in sensitivity for a given selection criterion is given by the

Quality factor (Q) of the cut. F(,)r a large number of events, Q is given by:

 

Fraction of events retained as a function of the Compactness cut

 

 

 

 

 

 

 

 

 

 

1 — MC Gamma Rays
_ — MC Cosmic Rays
_ — Data
0.8L -
0.6—
0.4—
0.2—
_IUIlLlllllllllllll ._ ‘lllllllLlllll __
00 1 2 3 4 6 7 a 9 1o

5
C

Figure 5.3: Fraction of data, cosmic—ray Monte Carlo. and y-ray Monte Carlo showers
with a compactness value that is greater than the x-axis value.

 

Q = '7 (5.2)

where (8 and q, are the efficiencies for retaining the signal and background, respec-
tively.

Figure 5.4 shows the Q factor as a function of the minimum value of C required
to retain an event. Requiring events to have. C 2 2.5 rejects 89.0 ‘70 of the simulated
cosmic-ray-induced air showers that trigger Milagro and 90.0 % of the data (for this

data sample), and retains 39.0 ‘70 of the Tray-induced air showers. This results in

a predicted Q-factor of 1.18 comparing Monte Carlo ’)’-I“d_V events to Monte Carlo
cosmic-ray events, and 1.23 comparing Monte Czu'lo y—ray events to data. In a pre-
vious publication by the Milagro collaborathin [14], a different set of Monte Carlo
simulations was used to study the compactness parameter which gives a quality fac-
tor of 1.6 comparing Monte. Carlo qr-ray events to Monte Carlo proton events, and 1.7
comparing Monte Carlo “,u-ray events to data. These simulations used GRANT 3.0 to
simulate the detectors response to extensive air showers and had different values for
the quantum efficiency of the PMTs than the one used in this thesis. The current
PMT efficiency adopted in the current. simulations were performed at the University
of Maryland and seems to give a better agreement with the data [70].

The compactness parameter does not carry information about the size of the air
shower, it also does not carry information about how well the shower was fit. Air
Cherenkov telescopes, for example, make use of their excellent angular resolution to
improve their backgrmind rejection. As will be. shown in the coming sections, the
inclusion of the information about the shower size and how well the shower was fit in
a new gannna—hadron separation variable in Milagro lead to a significant increase in

the sensitivity of the detector.

80

 

I Q-Factor as a function of C I

O —— MC Cosmic Rays
0.8

-'— Data

0.6

0.4

0.2

 

0012345678910

C
Figure 5.4: Quality factor Q as a function of the minimum value of C required to
retain an event. The red line compares Monte Carlo arrays to Monte Carlo cosmic-
rays, and the black line compares Monte Carlo '7-rays to data.

81

5.2 A4, Milagro’s New Gamma-Hadron Separation

Variable

The denomilmtor of the con'ipactness para-uneter (equation 5.1) carries the proper
information about the (‘-lumpiness in the muon layer that is caused by the penetrating
muons and hadrons that are mostly present in cosmic-ray-induced air showers. This
parameter, howwer, does not carry information about the size of the air shower or
how well this shower was fit.

A4 is a new V-llzuiil'on sepzu'ation variable that makes use of the information about

the SllOW'il‘ size and how well the. shower was fit [‘2, 3]. A4 is defined as:

(ftop + font) X Nf'it
P EmarB

 

A4 =
where
o fmp is the fraction of the air shower layer PMTs hit in an event.
0 font is the fraction of the. outriggers hit in an event.
0 N fit is the number of PMTs that entered in the angle fit.

The “A” in A4 stands for “Abdo” and the “4” stands for the number of parameters
that make up A4. Originally A4 included Ntop and Nam instead of [mp and font,
respectively. The reason for using the fraction of the air shower layer and outriggers
hit and not the actual numbers of the tubes hit is to give a higher weight for the.
outriggers in this variable. This is done. for many reasons. One of these reasons is
that events with cores on the pond seem to be more hadron like, while events with
cores off the pond seems to be more fia—ray like. Also, events with large number of

outriggers hit have better angular and core resolutions.

The first part in the riunierattu' of A4 carries information about the size of the

 

 

slmwer, while Nfit carries information about how well the. shower was reconstructed.
I’linmj. B carries information about the clumpiness in the Muon layer that is due
to the penetrating Muons and hadrons which are. mostly presented in hadronic air
showers.

F igure 5.5 shows the. A4 distribution for v-ray Monte Carlo, cosmic-ray Monte
Carlo, and data. Figure 5.6 shows the efficiencies for retaining data, cosmic-ray
Monte Carlo, and y-ray Monte Carlo as a function of A4. In both figures we see a clear
difference between the Monte Carlo 7-ray showers and the Monte Carlo cosmic-ray
showers, while there. is a good agreement between the data. and the cosmic-ray Monte.
Carlo showers. Figure 5.7 shows the Q-factor as a function of the minimum value of
A4 required to retain an event. Requiring events to have A4 2 3.0 rejects 97.4% of
the simulated cosniic-ray-indiu-ed air showers that. trigger hvlilagro and 97.2% of the
data (for this data sample), and retains 270/0 of the Tray-induced air showers. This
results in a. predicted Q-factor of 1.62 comparing l\fI(_>nte Carlo cosmic—ray events to
Monte Carlo y-ray events, and 1.59 comparing the data to l\~’Ionte Carlo y-ray events.
Thus the Monte Carlo predicts an improvement in significance over all triggered data
of 1.62. or a factor of 1.62/ 1.18 = 1.4 over the present compactness cut.

It can be. noted from figures 5.2 through 5.7 that the A4 distribution for cosmic-ray
shmvers matches the data better than does the con‘lpactness distribution of cosmic-ray

showers. This is clearly evident in figures 5.4 and 5.7.

5.3 Properties of A4

5.3.1 Energy Dependence

The efficiency of the. A4 parameter is a. function of the energy of the primary gamma-
ray. At low gamma—ray energies, few PMTs are hit in the. air shower layer and the

outrigger array (low (fml, + f(-,,,t)). This will also mean that few PMTs entered in the

83

 

 

A4 distribution

 

 

 

 

—— MC Gamma Rays
—— MC Cosmic Rays
— Data

0.14

l

 

   

0.12

0.1

0.08

0.06

lllllllillllll

0.04

0.02

llllll

 

 

Ollldillllillll
0 1 2 3 4 5 6 7 8

A4

Figure. 5.5: A4 distribution for h’Ionte Carlo 'y—ray slmwers, Monte Carlo cosmic—ray
showers, and data. All of the histogrz—uns have. been normalized to have unit area.

84

 

Fraction of events retained as a function of A4 cut I

 

 

 

 

 

 

 

 

 

 

1 —— MC Gamma Rays
—— MC Cosmic Rays
_ —-—Data
0.8
0.6-
t—
0.4L-
0.2——
o—LJJLLIIIIIJJLI1L41i11r21‘lllllllthgLJ
0 1 2 3 4 5 6 7 8

A4

Figure 5.6: Fraction of data, cosmic-ray Monte Carlo, and ”y-ray Monte Carlo showers
with an A4 value that is greater than the x-axis value.

angular fitter (low Alf”). As a result, events with a low value of P 1')",th may have
low values of A4. In addition, low energy gamma-ray events tend to have their cores
on the. pond. These on—pond events will again have low values of (ftop + font) and
Nfit and high values of PEmaJ'B which will result in smaller values of A4. Figure
5.8 shows the efficiency of the A4 2 3.0 cut as a function of the primary energy for
gamma-ray and cosmic-ray showers. From this figure it is seen that the efficiency of
gan'una-ray-initiated events is dependent on the energy of the primary gamma-ray,
while for cosniic-ra},~'s the efficiency is nearly independent of energy. It is also noticed
that. for the A4 2 3.0 cut we don’t. expect to see. any ganuna-ray-initiate<l events

with primary energy less than 400 GeV, and that the median energy for gamma-ray-

85

 

 

l Q-Factor as a function of A4 I

 

— MC Cosmic Rays

—°— Data

 

Figure 5.7: Quality factor Q as a function of the minimum value of A4 required to
retain an event. The red line compares Monte Carlo 7—rays to Monte Carlo cosmic-
rays, and the black line compeu‘es Monte Carlo 'y—ravs to data.

initiated events passing this cut is around 10 TeV.

The energy of the primary gamma-ray is also a function of the A4 cut applied.
Figure 5.9 shows the median energies as a function of an A4 cut. Each point represents
the median energy for gamma-ray events with an A4 value greater than the sc-axis
value. As can be seen from this figure, there is a good correlation between the median
energy for a given A4 value and that value of A4. One can use this dependence to

estimate the energy spectrum of a gamma-ray source. See Appendix A for details.

86

I Energy Efficiency I

 

0.25

0.2

0.15

0.1

0.05

 

 

 

l L l l I I J

E'

 

”_Illllfrillllllllfilrlllllllll

N
cn
o:
S”
01
4:.

4.5 5
Log 1 oE(GeV)

Figure 5.8: Fraction of gamma-rays and cosmic-rays retained by the cut A4 2 3.0 as
a function of the primary energy. Gamma-ray in blue, cosmic-ray in red.

87

 

 

Median Energy vs A‘1

 

 

35

 

3O

 

25

 

 

20

IIITITFFIITIITT111111

15

Median Energy (TeV)

1O

lllllll]

_f._

 

 

 

Q
~:—
“E—
m;-
m;-
.1
O.—
_.:
..

Figure 5.9: Median energies of gamma-ray-initiated air showers as a function of A4.
Each point represents the median energy for ganuna—ray events with an A4 value
greater than the 117-axis value.

5.3.2 Core Location Dependence

A4 is a function of the location of the. core of the air shower. Events that land on the
pond tend to have. smaller values of A4 (i.e. more. hadron like) than events with cores
off the pond. This is because these events tend to have higher values of PEmax B and
lower values of ((ftop + font) x N fit) which will result in smaller values of A4. Low
energy events are more likely to trigger the detector if they land on the pond, because
a low energy event landing off the pond will have less chance of satisfying the trigger
criteria. High energy events, on the other hand, have. a good chance of triggering the
detector whether they land on or off the pond.

Figures 5.10 and 5.11 show the A4 distributions for q—I'ay Monte Carlo, cosmic-

88

ray Monte Carlo, and data for on and off the pond showers, respectively. As can be
seen from these two figures, there. is a clear difference in the A4 distribution for 7—ray
showers in the two cases. More. events have. lower values of A4 for on-pond events
mmpared to off-pond events, while. more events have higher values of A4 for off-pond
events compared to on-pond events. This will make. it. harder to distinguish between
y-ray-induced air showers and cosmic-ray—induce(l air showers when their cores land
on the pond. This is clear from figures 5.12 and 5.13 which show the Quality factor
distribution for on and off the pond events, respectively. Figure 5.12 compares Monte
Carlo Trays to Monte Carlo cosmic-rays and figure 5.13 compares Monte Carlo y-rays
to data. The quality factor for events with cores off the pond is > 50% higher than
for the events with cores on the pond. In figures 5.10 through 5.13 there is a. good

agreement between the data and the cosmic-ray Monte Carlo.

5.3.3 Zenith Angle Dependence

Since the. energy threshold of the detector is a function of the zenith angle, and the
number of muons generated in a. cosmic-ray shower rises with primary energy, it is
expected that the performance of A4, as a background rrjection variable, will improve
with larger zenith angles. Figures 5.14 through 5.16 show the A4 distribution for ”y-
ray Monte Carlo, cosmic—ray Monte Carlo, and data for three different zenith angle
ranges, Figure 5.14 shows the A4 distribution for zenith angles less than 15°, Figure
5.15 for zenith angles between 15° and 30°, and Figure 5.15 for cwents between 30°
and 45°. The distributions look relatively similar. The quality factor as a function
of the A4 cut is shown in Figures 5.17 and 5.18 for the three zenith angle ranges.
Figure 5.17 cmnpares Monte Carlo y-rays to Monte Carlo cosmic-rays and figure 5.18
compares Monte Carlo Trays to data. Although in general the higher zenith angle
ranges give higher quality factors than lower zenith angle ranges, these differences are

insignificant and the three zenith angle ranges give similar quality factors. In figures

80

 

 

A4 distribution for on-pond events

 

 

 

 

 

 

 

0'18 i — MC Gamma Rays
e — MC Cosmic Rays
0.16 W
: — Data 1
0.14 E-
o.12 E—
0.1}
0.08 E

   
     

 

 

 

0.06_
0.04:—
0.02:—
O:1111 LJll ‘ gL—l—JJJ+I_IJ_1_I_JJ_I
o 1 2 3 4 5 6 7 8

Figure 5.10: A4 distribution for Monte Carlo "pray sh(‘)wers, Monte Carlo cosmic-ray
showers, and data for events with their core on the pond. All of the histograms have
been normalized to have unit. area.

5.14 through 5.18 there is a good agreement between the data and the cosmic-rayr

Monte Carlo.

90

5.4 Observations of the Crab Nebula Using A4

The Crab Nebula acts as a standard candle for gannna-ray astronomy due. to its long-
term, unchanging energy emission though many wavelengths. A new technique in the
field of TeV gamma-ray astronomy is best verified on this source.

To verify the performance of the A4 parameter a data set of 1.7 years of off-line
reconstructed data was searched for gamma-ray signals from the location of the Crab
Nebula using A4. This data set. extends from September 2003 to l\'Iay 2005. Figure
5.10 shows a map of the statistical significance around the Crab Nebula with the

A4 2 3.0 and .Nfit 2 40 cuts applied. In this map the Crab Nebula is seen at 8.02

 

A4 distribution for off-pond events

 

 

 

 

 

 

 

 

 

 

 

 

F — MC Gamma Rays
_ — MC Cosmic Rays
01:” -— Data
0.08 "—
0.06 —
- I
- I
0.04 ~— I.
0.02 1:“
I'_| I
E -— q I-
0 lLlllllllllLlJll _ '_..._-; —_l—A_nni in:
0 1 2 3 4 5 6 7 8

Figure 5.11: A4 distribution for Monte Carlo array showers, Monte Carlo cosmic-ray
showers, and data for events with their core off the pond. All of the histograms have
been normalized to have unit area.

91

 

Q-Factor as a function of A, and core location I

 

-°- Cores In

— Cores out

 

1 2 3 4 5 6 7 8
A4

Figure 5.12: Quality factor Q for events with their core on and off the pond. In both
cases Monte Carlo y-rays are compared to Monte Carlo cosmic-rays

a 2. To compare the performance of the A4 parameter to that of the compactness
parameter, the same data set was searched using the compactness parameter. Figure
5.20 shows the map of the statistical significance around the Crab Nebula with the
C 2 2.5 and N fit 2 20 cuts applied. In this map the statistical significance in the
location of the Crab Nebula is 5.34 a.

The improvement in the detection of a gamma—ray signal from the Crab Nebula
using A4 over the compactness parameter (Q : 8.02 / 5.34 = 1.5) is in good agreement
with that predicted by the Monte. Carlo (Q = 1.4).

Another improvement is the sigiizil-to-background ratio in both cases. The signal-

 

2Changing the. cut on NI” from 40 to ‘20 improves the quality factor for the A4 2 3.0 cut by
“410%.

92

 

Q-Factor as a function of A 4 and core location I

 

-°- Cores In

3.5

— Cores out

2.5

1.5

0.5

 

0 1 2 3 4 5 6 7 8

Figure 5.13: Quality factor Q for events with their core on and off the pond. In both
cases Monte Carlo 'y-rays are compared to data

to—background ratio in the case of A4 is roughly 7 times that for the compactness.

As will be discussed in the next chapter, signal—to—background ratios as high as 60%

are achievable with high A4 cuts.

93

 

 

A4 distribution for 00 s 9 s 150

 

 

 

— MC Gamma Rays
— MC Cosmic Rays

0.14 _ Data

0.16

 

0.12

0.1

0.08

0.06

0.04

0.02

 

 

 

 

o 1 2 5 6 7 8

Figure 5.14: A4 distribution for h-"Ionte Carlo ’7-ray showers, Monte Carlo cosmic-ray
showers, and data for the zenith angle range 0° 5 0 S 15°. All of the histograms
have been normalized to have unit area.

94

 

 

A4 distribution for 150 s G s 30°

 

 

 

0.14 — MC Gamma Rays
—— MC Cosmic Rays

0.12 Data _

 

0.1

0.08

0.06

TjIIIIIIITIIII

0.04

0.02

 

 

 

 

00 1 2 3 ‘4‘ 5 6 7 8

Figure 5.15: A4 distribution for Monte Carlo y—ray showers, Monte Carlo cosmic-ray
showers, and data for the zenith angle range 15° g 9 S 30°. All of the histograms
have been normalized to have unit area.

95

 

 

A 4 distribution for 300 S 6 s 450

 

 

 

0-14 — MC Gamma Rays
— MC Cosmic Rays

—— Data

 

0.12

ll—fr—L—l—Ld I

 

0.1

0.08

0.06

lllllIIlllllll
—

0.04 I-

0.02

5+1-

llll

 

 

 

_-
oiniiliimuliiiil” 1" Let U

o 1 2 3 4 5 6 7 8
A4

Figure 5.16: A4 distribution for Monte Carlo nil-ray showers, Monte Carlo cosmic-ray
showers, and data. for the zenith angle range 300 S 0 g 450. All of the histograms
have been normalized to have unit area.

96

 

Q-Factor as a function of A4 for different zenith angle ranges J
4.5

 

—0° 59315°
—15°sesso°
3-5 — 30° 5 e 3 45°
3
2.5
o

1.5

0.5

 

1 2 3 4 5 6 7 8

Figure 5.17: Quality factor as a fimction of the A4 cut for three different zenith angle
ranges. In all three cases Monte Carlo 7-rays is compared to cosmic-rays.

97

 

Quality factor as a function of A 4 for different zenith angle ranges I

 

—o°ses15°
—15°ses30°
~3o°ses45°

 

1 2 3 4 5 6 7 8
A4

Figure 5.18: Quality factor as a function of the A4 cut for three different zenith angle
ranges. In all three cases Monte Carlo v—I'ays is compared to data.

98

 

I Map of Significances |

92..

   
  
 
 
 
 
 
   

M
Q

Declination (de
M
O)

M
A

-2

14

74 76 78 80 82 84 86 88 90
RA (deg)

Figure 5.19: Map of the statistical significance around the Crab Nebula with the
A4 2 3.0 and N fit 2 40 cuts applied.

99

 

| Map of Significances ]
’OT'BO

 

 
  
 
 
 
 

Declination (de
M N
at on

N
b

22
20
-1
-2
-3
14
76 78 so a2 84 as ea 90 92
RA (deg)

Figure 5.20: Map of the statistical significance around the Crab Nebula with the
(7 2 2.5 and N fit 2 20 cuts applied.

100

Chapter 6

A4 Weighted Analysis Technique

6.1 Motivations for Weighted Analysis Technique

As can be seen from figures 5.5 through 5.7, the Monte Carlo predicts an improvement
in the performance of the A4 parameter when higher values of this parameter are
applied. The signal-tti-background ratio (S / B) increases with increasing A4.

Harder A4 cuts were applied on the same data set as the one used in section 5.4.
Figure (5.1 slmws the map of statistical significance around the Crab Nebula with the
A4 2 12.0 and Nfif 2 410 applied on this data set. In this map the Crab Nebula
is seen at 5.58 (7. Although there was a z 30% loss in statistical significance of the
Crab Nebula. when the harder A4 cut. was applied, the. main advantage of applying
the hard A4 cut is the higher S / l3 ratio (60.0%) achieved with this cut compared to
that with the. softer A4 2 3.0 cut. (3.4‘76). An increase by a factor of ~ 18.

The. fact that one can achieve a higher S /B ratios with no major loss in statistical
significance when applying harder A4 cuts, and the fact that a single cut applied on
the A4 parameter would result. in retaining a. small fraction of the gamma-ray signal
led to the developn'ient of the weighting analysis technique. This technique weights

events based on the relative probability that. the. event was due to a gamma-ray, rather

101

than a cosmic-ray[0J3]. Events in an angular bin are. not counted equally. Instead a
weighted sum of events is used where events with higher values of A4 are assigned
higher weights. The same technique was applied to the estimation of the background.
Rather than the background event count, a sum of the weights of the background
sample was used for the background estimate in the bin.

Because there is a correlation between the gamma-ray energgr and the value of
A4 of an event (figure 5.9), this weighting technique enhances the contribution of
high energy ganuna—rays and increases the median energy of detected events relative
to previously published analyses. A source with a Crab-like spectrum will have a
median energy of 12 TeV as compared to 3 TeV using a compactness cut[14].

The weighting analysis technique is equivalent to a likelihood ratio method esti—

mation in the limit that the background is large, which is true. for the lVlilagro data.

6.2 Determining the Gamma-Hadron Weights

In order to determine the weights for different values of A4, the. data set is binned in
12 bins in A4. In each of these bins, (wealts with A4 value greater than or equal to
the. lower end of the bin and smaller than the upper end of the bin are kept in that

bin. i.e.. for the. i’th A. bin, only events that satisfy the criteria
-1 . .
m 1' n. m. or

are kept in that bin (with the exception of the. last bin, for which the upper end is

(Iii!)

00), b, ”u” be

and 1),- ing the bins lower and upper limits, res1,)ectively.

Table 6.1 lists the set of cuts applied for each A4 bin along with the number of

Monte. Carlo gamma-ray events1 expected in that bin (Si): the number of measured

 

1The Monte Carlo gamma-ray sample, was generated with a Crab-Like spectrum (E716)

102

 

I Map of Significances I

92.

    
  
 
 
 
 

N
on

Declination (de
M
a:

N
A

14

74 76 78 80 82 84 86 88 90
RA (deg)

Figure 6.1: Map of the statistical significance around the Crab Nebula with the
A4 2 12.0 and N fit 2 40 cuts applied.

background events in the same bin (8,), and the weight assigned for that bin w. The

weight assigned for the i’th bin is equal to [63, 48]:

 

All weights have been normalized to that of the first bin.

103

 

 

 

Bin N0 Cuts \f‘l’ \glwa x10“) Weight
1 13 A4 < 2 1202.5 109.311 1.00
2 23 A4 < 3 700.3 120.831 1.79
3 33 A4 < 4 410.1 50.100 2.05
4 43 A4 < 5 2.54.1 23.001 3.49
5 53 A4 < 0 152.4 13.055 4.53
0 03 A4 < 7 102.2 3.404 0.20
7 7_<_ A4 < 3 101.4 0.130 3.40
s 33 A4 < 9 19.5 1.335 12.03
9 93 A4 < 10 32.2 0.713 14.03
10 103 A4 < 11 27.9 0.479 13.90
11 11_<_ A4 < 12 7.1 0.275 20.93
12 123 A4 5.1 0.159 32.01

 

Table 6.1: List of the set of cuts applied for each A4 bin along with the number of
gamma Monte Carlo events expected in that bin, the number of measured background
events in the same bin, and the weight assigned for each bin. All weights have been
normalized to that of the first. bin.

6.3 Determining the PSF Fits

For Milagro, the point spread function (angular response) is determined from simula-
tions of the detector response to gz-unma-ray-initiated air showers, and is given by the
distribution of the space angle difference between the simulated primary directionand
the reconstructed direction ($01,916). The point spread function can be characterized

by a double 2D Gaussian function of the form:

.‘2. 2 ,2. 2
19(7):.17-(«H WI) + ml" ””2’) (0.3)

where A is the amplitude, 11’ is the ratio between the two parts of the 2D Gaussian,
and r is AWN/1,. Figure 6.2 shows the Anny/V distributicm of triggered gamma—ray
events that passed the 1an Z 40 cut. ()11 the same plot the fit to equation 6.3 is
shown (black line). The box on the right side. of the figure. lists the fit parameters.
The. median of the distribution is N 0.850.

The PSF of Milagro is a function of the A4 cut applied. It is expected that the

angular resolution of the detector will improve with harder A4 cuts. This is clearly

104

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Distribution of Aangle lendf 266.7/72
* Prob 0
700 : ...- ............ . ...... A 235.1 i 15.9
3 H 7.592 i 0.536
500 ,__‘ .. .......... .............. ...... 0'1 1.071 1'. 0.016
: i 5 1 i . 02 0.5050: 0.0058
500 E... 1 ............................. , ........................................................ E
400:
300:
200 ',
100
0
0 1 2 3 4 5 6 7 8 9 10
Aangle(deg)

Fi rure (5.2: Distribution of A for trivn‘cl‘e(l rannna—ray events that )assed the
angle cm .
A'fit Z 40 cut. The median of the distribution. is ~ 0.850.

seen in Figure (5.3 which shows the AWE/1., distribution for triggered gamma-ray events
that passed the A4 2 3.0 (top) and A4 2 12.0 cuts (bottom). In the first. case. the
angular response is essentially a 2D Gaussian with (7 = 0.44 and a median of 0.750,
while for the second case the angular response is essentially a 2D Gaussian with
0 = 0.36 and a median of 0.50.

Since the PSF of Milagro is a. function of the A4 cut applied, it. is necessary
to determine the PSF for each bin in A4. The distrilmtion of Anny/e for triggered
gamma—ray events in each bin in A4 was fitted to a function of the form given in
equation 6.3. The fit parameters are. given in Table 6.2. Each event in an A4 bin is

smoothed by the PSF of the detector for that. A4 bin [9].

105

 

     
 

Bistribution of A for A4 2 3.0 72.11 42
62.32 i 9.30
10.72 i 1.65

0.9679 i 0.0344

angle

 

    

     
    
  

 

  

Distribution ofA for A4212.0 l 22.90/19

angle

   
 
 

 

  
    

A 5.1 :t 5.7
35 R 27.24 : 24.75
01 0.8114:r 0.1899

    
 
 
 

30

  

25

Figure 6.3: Distribution of Aangh. for triggered gamma-ray events that passed the
A4 2 3.0 (top) and A4 2 12.0 cuts (bottom).

10G

 

 

 

Bin N9 Cuts Amplitude (A) Ratio (R) (71 (72
l 13 A4 < 2 594$ 7.2 5.39:l:0.73 1.06i0.03 0.54i0.0l
‘2 2: A4 < 3 33.42i 8.09 6.06:l:1.64 l.04:l:0.05 0.54i0.02
3 3S A4 < 4 37.64i 8.63 3.32i0.95 0.85zt0.03 0.48:l:0.03
4 43 A4 < 5 15.4%: 3.58 6.37i1.60 0.93:l:0.05 0.431002
5 5S A4 < 6 7.18i 3.29 10.33;}:551 0.92i0.09 0.47:l:0.02
6 63 A4 < 7 4.39:l: 3.49 12.49i10.‘24 0.91:l:0.16 0.43i0.03
7 73 A4 < 8 0.98i 1.99 42.55i86.05 l.‘28:l:1.24 0.48:l:0.04
8 83 A4 < 9 0.86:}: 0.76 46.62i53.l3 l.23i0.59 0443:0012
9 93 A4 < 10 0.562l: 0.38 72.40:l:56.2 1.652t1.25 0.41i0.0‘2
10 103 A4 < 11 0.3‘2i 0.20 106.60i9l.4 —‘2.32:l:5.20 0.38:l:0.0‘2
11 113 A4 < 12 0.3'2i 0.57 68.18i10896 -1.7l:l:2.12 0.442t0.02
1‘2 123 A4 5.103: 5.70 27.24i2475 0.8li0.‘20 0.36:l:0.02

 

 

Table 6.2: A list of the fit ])itl‘&iIIl(,‘i.(‘I‘S for Milagro’s PSF for the different A4 bins used
in this analysis.

6.4 Median Energy For the Weighted Analysis Tech-
nique

Since the weighting analysis technique assigns higher weights for events with higher
values of A4 and since events with higher values of A4 have, on average, higher
median energies (see Figure 5.9), it. is expected that the median energy for gamma-ray
mrents using this technique will be higher than the one for triggered events (Figure

3.12 . This is clearlv shown in ti “ure. 6.4 which shows the ener0 r distribution for
. ., 41').

2'6. The blue line

ganuna—ray events with a power law spectrum of dN/dE (x E-
represents the energy (ilistribution for the A4 weighted analysis technique, while the
green line represents the energy distribution for triggered events. The median of
the distributions are 12 and 3.2 TeV, respectively. Changing the spectrum of the
simulated gamma—ray events from [5‘20 to 1'3"“) changes the median energies from

~ 19 TeV to ~ 8 TeV. Table 6.3 lists the median energies for different spectra.

107

 

 

(1' Median energxr (TeV)
- 2.0 19.0
- 2.2 15.9
- 2.4 14.2
- 2.6 12.0
- 2.8 11.1
- 3.0 8.0

 

 

 

Table 6.3: A list of the. fit parameters for Milagro‘s PSF for the different. A4 bins used
in this analysis.

 

| Energy Distribution I

 

 

 

 

 

 

 

 

0045 ...— ................................. . . - - . . ...............................
c - ----- A 4 Weighted Analysns . ; ._ _.l 4';
. 4 — ..... . ...........E............i..:..:..;..g..:f..:....;.:........f. ....................
O 0 : ------ Triggered Events 33-2; - .
— : . I I t! t E
0035 :_... ....... ..... fi....£l..l.:: ............ E........'. ....................
E Mar-.1. f
__.. .................... .r. .3 ...... .-.'.....‘..'. .. 1.3.2! ........ i .............. :......i ....................
°-°3 : .z' eta-1" t-
0.025 :_.. ............... , .................... ¢ .......... _.-:."-i_‘" ..... :,1 .......... ..- ........................
002 __ ................. 1:3 ............ .......... -, .............. ;.......§ ................... l ....................
: s -:; ;:;-.
_ E ’ E f E ' E 'i - ‘;
0.015 r... .................. E.‘ ..................... '. ....... r. ...... ....: ................... 'x.‘_‘: ..............
0.01:-..3 ................... *.. ...... '. 2-..: .........
: .z _:‘-- 5 ‘-g
0005 __. ....... "5L. ...... --f- ..................... .............. .-.:j. ................ I...
:1"; .1. 1-.l1--Ar1-"1-'1'..l 1 1 L 1 l 1 1 1 1 l 1 1 1 1 l 4 1 L 1 l J .:1.'1"
9 5 2 2.5 3 3.5 4 4.5 5

Log(Energy/GeV)

Figure 6.4: Energy distribution for gamma-ray events with a power law spectrum of
dN /dE or E ’2'6 . The blue line represents the energy distribution for the A4 weighted
analysis technique, while the. green line represents the energv distribution for triggered
events. The median of the distributions are 12 and 3.2 TeV, respectively.

108

 

I Map of Significances I

Declination (deg)
N N 00
c» on o

N
A

22

 

14

74 76 78 80 82 84 86 88 90
RA (deg)

Figure 6.5: Map of the statistical significance around the Crab Nebula with the
weighting analysis method applied.

6.5 Results on the Crab Nebula

To test the new weighting analysis technique, this technique was applied to the same
data set as the one used in sections 5.4 and 6.1 with the gamma-hadron weights as
those given in table 6.1 and PSF weights given by the fit parameters in table 6.2.
Figure 6.5 shows the map of statistical significance around the Crab Nebula with
the A4 weighted analysis applied. The significance at the location of the Crab is
10.55 a. An increase by 32% over the significance achieved with the standard A4 cut

(A4 2 3.0).

109

Chapter 7

All-Sky Survey

7.1 Data Set

After the confirmation of the new A4 weighting analysis method on the. Crab neb-
ula, the next logical step was to apply this analysis method to a bigger data set in
search for new TeV gamma—ray sources in the sky. This all-sky survey revered online-
rcciinstructed data collected between l\l.lD5174.’3(.luly ‘20, 2000) and MJD54102(Ja1‘iuary

1, 2007). A total of 23-58 days of ('oll(".('te(l data.

7.1.1 Event Selection Cuts

In performing this analysis two event selection cuts were applied on the whole. data

set:
2. Zenith angle (I < 45°

The. Nfz’t cut was applied to ensure the selection of good fit slmwers. The. zenith
angle cut applied was selected to match the cut applied on the simulated gamma-ray

Monte Carlo events generated for this analysis (see section 3.10).

110

7 .1.2 Excluded Data Runs

1

Some of the runs in the online-reconstructed data set were taken under special

conditions such as calibration runs. Some runs show sudden change in the trigger
rate and /or zenith angle distribution. Other runs have corrupted data due to buffers

with overwrites. Other runs were taken with deep water on cover. These runs make

up a small fractimi of the entire data set and are excluded from this analysisQ.

. O
7 .2 Epochs 1n Milagro
Milagro is a very dynamic experiment. It is dynamic in, at least, two ways:
1. Human controlled variations. Those include:

(a) Installation of Outriggers.

(b) Different reconstri1ction algorithms.
(c) Different calibration software.

((1) Trigger type used.

(e) Trigger conditions.
‘2. W'mther related variations. Those include:

(a) \Vater on top of the cover.

(b) Snow and ice on top of the cover.

((1’) Air under cover.

((1) Freezing of a layer of water under the cover.

(e) Change of atmospheric properties due to daily and seasonal changes.

 

1At 0 UT each day a new run is started by the DAQ system. Each run consists of smaller subruns
of 5 minutes each. A new run will also be started if the DAQ system is restarted for any reason.

2A full list of all the excluded data runs is available in the Bad Run List file under Milinda. the
Milagro software.

111

Variations due to weather changes have much less effect on the detector than
those due to human controlled variations. Although weather variations are hard to
keep track of and wmild require many different sets of Monte Carlo simulations, such
weather effects can be I‘ninimized by excluding runs with big fluctuations due to
weather as mentioned in section 7.1.2.

To take into account. the human controlled variations, the data set was split into
epochs. Table 7.1 lists epochs in Milagro. For each epoch, the detector was simulated

with the exact (-onfigi_1rations.

7.2.1 Dead PMTs

During the operation of Milagro, some. of the PMTs leak water through their con-
nectors and stop working. An annual repair operation is performed in which these
“dead” PMTs are taken out. of the pond and are. either fixed or replaced with new
ones. The percentage of PMTs that are dead can have an effect on the performance
of the detector and. thus, should be. taken into account in any analysis. The number
of “dead” PMTs changes from small numbers after each repair to bigger numbers be—
fore the next repair is performed. To study the effect of dead PMTs on the. behavior
of A4. three different runs from each epoch were used to compare the A4 distribu-
tions in each case. These runs correspond to the minimum, average, and maximum
percentages of “dead” PMTs for the given epoch. In addition to using these data
runs, IVIonte Carlo sin‘iulatimis of the detector for the. different percentag is of “dear ”
PMTs, minimum, averz-ige, and maximum, were used to study the effect of “dear ”
PMTs in the IVIcnite Carlo. Figure 7.1 show distrilnitions of A4 for the. different per-
centage of “dead” PMTs for cosmic-ray Monte. Carlo, data, and gamma-ray h-"Ionte
Carlo for the eighth epoch. It can be seen that the distributions, in all three cases,
are indistinguishable. The same. distributions are shown in figure 7.2 on a log-scale

for the y—axis. Similar l’)eha\-'ior is seen in the rest of the epochs. Similar figures for

112

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113

 

 

Epoch No Exposure (days) ‘X. AS Dead % l\IU Dead % OU Dead

 

1 131.6 5 5 100
'2 382.5 5 5 100
3 4.30.1 5 5 100
4 471.8 5 5 3
5 169.8 8 5 2
6 164.6 10 5 2
T 174.3 ‘2 4 4
8 280.4 3 6 ‘2

 

 

Table 7.2: Percentage of “dead” PMTs in each layer for the. different epochs. The
second column shows the number of dead PMTs for the air shower layer, the third
column for the muon layer, and the fourth column for the outrigger array. For the
first three epochs the outrigger array was not yet installed and thus 100% of the
outrigger array PMTs were simulated as dead PMTs.

the. other epochs are shown in Appendix B.

.A more sensitive analysis to the effect. of “dead” PMTs was performedl64]. This
analysis estimated the number of events from the Crab Nebula per day for different.
percentage of “dead“ PMTs. Again, there were no significant. differences in this
number for the (‘lifferent percentages.

Since there were no significant differences in the A4 distributions for the different
percentages of "dead” PMTs, the average number of “dead“ PMTs in each epoch
was taken as input for the simulations. These mnnbers are shown in table 7.2. For
the first three epochs the mitrigger array was not yet. installed and thus 100% of the

outrigger array PMTs were simulated as dead PMTs.

7 .3 Determining the Gamma-Hadron Weights

1“ Order to calculate the gamma—hadron weights, the same method used in section
6-2 Was applied to each epoch. The. only difference is that. for the pre outrigger data
the A4 bins were different. Table 7.3 lists the A4 bins used for the pre outrigger and
Post outrigger data sets. On average; the contribution from the [0“, term in A4,

(‘rpiation 5.3, is equal to that. from the. term fTUp. So in the absence of this term. for

114

 

 

IA4 distributiofl

1 Cosmic-Ray MC

— High % dead PMTs
Avg. "/0 dead PMTs
— LOW °/o dead PMTS

 

 

0.8

 

 

0.6

0.4

0.2

erlI—l—Tll—I—TT—TT

  
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 _ ‘ I A ._k l l
0 2 4 6 8 10 12
[A4 distribution]
1 Data
— High % dead PMTs
0-8 Avg. % dead PMTs
E —— Low % dead PMTs
0.6 _-
E
L.
0.4 f
P
0.2 _—
0 .- . ‘ l A ._ l ._L l
O 2 4 6 8 1O 12
[A1 distributionI
1 Gamma-Ray MC
2 — High % dead PMTs
0.8 _— Avg. % dead PMTs
I —- Low % dead PMTs
0.6 _—
o.4 :—
o.2 :—
: A l . l . l 4 4 l 1 l 1 4 l .
0 2 4 6 8 10 12

Flgure 7.1: Distributions of A4 for the. different percentage of “dead” PMTs for
cosnncsray Monte Carlo. data, and gamma-ray Monte Carlo for the eighth epoch.

 

[14 distribution]

1 Cosmic-Ray MC
— High % dead PMTs
Avg. % dead PMTs

 

 

 
 
      

 

 

 

 

 

 

 

10" — Low % dead PMTs
10"2
10‘3
o 4 6 I 8 10 12
[A4 distribution]
1 Data

— High °/o dead PMTs
Avg. % dead PMTs

 

 

 

 

 

10‘1 — Low % dead PMTs
10'2
10‘3
0 2 4 6 A 8 i 10 12
[T4 distribution |

 

 

Gamma-Ray MC
—— High % dead PMTs
Avg. % dead PMTs
— Low % dead PMTs

 

 

llllfl

T

10"

I llllll

 

 

 

O
N
b
O)
m .
_i.
O
_s
N

Figure 7.2: Same distributions as in figure 7.1 but; with log-scale on the y-axis.

116

 

 

Pre Outrigger. Epochs 1-3

 

 

 

 

 

 

 

 

13in Numberti) 1 2 3 4 5 6 7 8 9 10 11 12
5;“ 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
62"” 1.0 1 5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 00

Post Outrigger. Epochs 4-8

Bin Nuinberfi) 1 2 3 4 5 6 7 8 9 10 11 12
57"" 1 2 3 4 5 6 7 8 9 10 11 12
I)?“ 2 3 4 5 6 7 8 9 10 11 12 00

Table 7.3: A4 Bins. 1):.” i ” and fig-"M represent the lower and upper edges of the A4
bin, respectively (see section 6.2 and equation 6.1).
\Veights
Bin Ng E1 E2 E3 E4 E5 E6 E7 E8
1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
2 2.38 2.25 1.87 2.10 2.07 1.83 1.34 1.47
3 4.60 4.08 2.82 3.69 3.43 2.70 1.62 1.72
4 8.26 7.1] 4.12 5.96 5.11 3.98 1.64 2.22
5 13.08 11.23 5.51 10.72 7.17 5.26 2.01 2.43
6 20.28 16.25 6.78 15.32 9.45 6.92 2.08 2.91
7 29.27 22.04 7.76 17.25 15.93 11.13 2.81 3.70
8 42.12 27.18 7.96 21.74 20.15 14.81 3.47 4.88
9 49.72 37.51 8.92 23.88 30.90 20.72 4.56 5.67
10 51.83 35.34 6.66 22.44 45.75 30.91 5.48 6.50
11 72.23 55.35 8.02 23.95 62.71 45.31 6.87 8.54
12 116.17 97.32 10.50 44.22 100.33 116.02 8.24 10.25

 

 

Table 7.4: Gamina-hadnin weights for the different. epochs. In each epoch, the weights
have. been nornnilized to that of the first A4 bin.

the pre outrigger data, A4 is roughly half that for the. post. outrigger data, hence the
different binning for the pre outrigger data.

Equation 6.2 was used to estimate the gainma—hadron weights for each epoch. As
in SP-(ftion 6.2, the simulated gannna—ray Monte Carlo events were. used to estimate,
the. OXIHK‘UKl number of signal events in an A4 bin ((3,1)), while the data were used
to estimate the number of lmckground events in the same bin ((131)). Table 7.4 lists

the galinna—liadrtin weights for the eight epochs used in this analysis.

117

 

 

Epoch E1 E2 E3 E4 E5 E6 E7 E8
Relative weight. 1.00 1.05 1.04 2.38 2.24 2.33 2.23 2.22

 

 

Table 7.5: Relative epoch weights. The weights have. been normalized to that of the
first epoch (E1). For (waniple, the. eighth epoch gets 2.22 times more weight. than the
first epoch in this analysis.

7 .3.1 Relative Epoch Weighting

The efficiency for detecting a gannna—ray event varies from one epoch to another. This
efficiency depends on the rectinstruction algorithms used, the detector configuration
(number of dead PMTs). and the outriggers. It is thus necessary to take this into
account when combining the different epochs. To account for this, the. gan'lma-hadron
weights in the first A 4 bin for each epoch were calculated and then normalized to that

) .ie 'rs.e)oc1.' iis'ssiowiii tie 1.5
(ftl iii} 1 T1 ll iitrll'”

118

7 .4 Determining the PSF Fits

For each A4 bin in each epoch the PSF fits were calculated using the metlmd described
in section 6.3. Figures 7.3 and 7.4 show the (laugh. distribution for the 12 A4 slices
for the last epoch for a Crab-like s1.)ectrum. The. fit function is shown in black and
the. fit parameters are shown for each case. Table 7.7 shows the fit. parameters for
this epoch. Similar plots and tables for the other epochs are shown in Appendices B
and C, respectively. For some of the bins in the earlier epochs the fit to a double. 2D
Gaussian function of the form given in equation 6.3 resulted in a poor fit and thus a

one 2D Gaussian function was used:

2/2n2)

rm 2 .1 r x 8*" (7.1)

where xi is the amplitude, It is the ratio between the two parts of the 2D Gaussian,
and r is Anny“. Although the error on the ratio It in some cases is of the same order
as If. itself, the fit to the function given is good as can be seen in the last column
(\Q/IIdf) in each table.

To study the effect of different. source spectra on the PSF of Milagro, different
‘3ngqu distributions as a function of A4 for different spectral indices were generated
and compared. Such distributions are shown in Appendix B for a -2.2 and -3.0
SIN‘K'tr-a. As can be seen from these plots, the Anna“ distributions are similar in both

(Wises and the fit parameters to a double 2D-Gaussian are very similar. Table 7.6 lists

the fit. parameters of Milagro‘s PSF for the two different. source. spectra (a = —2.2
and (r : —3.0) for the different A4 bins for the eighth epoch. The effective angular

resolution of Milagro for the weighted analysis takes into account the (.lifferent weights
for different. A4 slices, and since different s}.)ectra will have different A4 distributions,
the effective angular resolution of the detector should be studied for different. spectra

to determine any changes. This has been done for four different. source spectra,

119

 

 

 

 

o' = —2.2 (r = —3.0
Bin N9 (71 (.72 R (71 (72 R.
1 1.05 :t: 0.03 0.52 :t: 0.02 ~ ."5 1.05 :t 0.03 0.56 :l: 0.02 5.24
2 1.05 :l: 0.04 0.51 i 0.02 5.18 1.04 :t 0.07 0.57 :i: 0.02 7.86
3 0.88 :1: 0.04 0.49 :i: 0.03 3.53 0.82 i 0.03 0.48 :l: 0.03 3.20
4 0.88 i 0.04 0.37 :l: 0.02 4.17 0.91 :1: 0.06 0.45 :l: 0.03 7.42
5 0.86 :t 0.07 0.43 :l: 0.03 5.80 0.99 :1: 0.14 0.49 :l: 0.02 19.2
6 0.73 :1: 0.06 0.37 i 0.04 3.58 1.39 :l: 0.29 0.45 :1: 0.02 58.2

 

 

Table 7.6: A list. of the fit parameters of Milagro’s PSF for two (’lifferent source spectra
for the different A4 bins for the eighth epoch.

a :— —2.0, —2.4, —2.6, and — 3.0. The. effmrtive angular resolutions for these spectra
are shown in figure 7.5 and 7.6. As can be seen, the distributions look very similar and
the fit paranu-tms to a. 2D Gaussian function are. very similar in all cases. Therefore,

the PSF of Milagro is independent of the spectral shape of the source for the A4

weighted analysis.

120

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Weighted Aangle distributions for different source spectra]

 

 

 

 

 

 

 

 

 

 

0.14
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:_ .A — (I = ‘2.0
0.12 _ g \\ —— a = -2,4
: \x — (1 = -2.6
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represent. in each case the fit. to a double 2D Gaussian function.

124

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125

7 .5 Flux Calculation

Fluxes from VHE gamma—ray sources typically have a power law spectrum (equation
1.1). The difi‘erential gamma—ray flux for a given source. is defined as the number of
photons from that souue per unit area per unit ener< gv per unit. time. For a power

law spectrum this is given by:

 

 

(1N , l'} —('
(IE 2 00 E0) (7.2)

where 950 is the differential flux normalization, Eo is the energy at which the flux is
normalized, and o is the spectral index of the source.

It is customary to report. the integral fluxes above some. threshold energv, wl‘iich
is usually the median energy. The integral flux from a gamma-ray source is defined
as the number of photons per unit area per unit time from that source, and is given

by:

        

E‘ (IN
Q /Et (1E ( )

E( ‘ _O
= /¢') 0(4: ) (IE (7.4)
Et [)0
1—0' 1 1—0
(90 30 .156 by
: — 7.5
(1(1) Lo) (E0) ( )

where, In} is the threshold energy, and In}. is some cut off energy in the spectrum of

 

 

the source. 111 this analysis, all the. fluxes are reported as integral fluxes above the.
111edian energy of this analysis which is 12 TeV, i.e. [th = 12 TeV, and EC is assumed
to be 100 TeV.

To calculate the flux from a source it is I'1(‘.("essal‘y to take. the effective area of the

detector in consideration (see section 3.9). The number of events is given by:

126

‘E(' 1" —0
N 2 / .1. (E.0)g’>o<—f—) (11; (7.6)
7 '51 ff I'

40

7.5.1 Flux Calculation for the A4 Weighted Analysis Tech-
nique

To determine the. flux from a gamma-ray source, the simulations are used to determine
the number of Monte Carlo gamma-ray events per day as a function of declination.
These numbers were obtained assuming a Crab-like spectrum of dN/dl‘} o< [bl—2'62
and a flux at 1 TeV of 2.83 X 10“5 TeV—1111_2s_1. This is done. for all the A4 bins
in all eight epochs. This number is then multiplied by the gamma-hadron weights

'o‘eaci )i1an( 1e 111m )e'o (avsiieacie oc 1' " 11' 1e, .‘unne( ,o )‘i7 ' ' 2
f1 llI it] I lIfl. 1 1115ailtlnsri it gxeafmtl

total number of weighted events as a function of declination:

8 1‘2
we) = Z 2 Wife) x we) x am» (

i=1j=1

f]
~J
v

The first summation is over the number of epochs while the second summation
is over the number of A4 bins in each epoch, N47) ((5) is the number of gammas per
day as a function of declination for the j’th A4 bin in the i’th epoch. w’j(’7) is the
gamma-hadron weight for the j‘th A4 bin in the i’th epoch, and 1N"day(i.) is the number
of days in the i’tli epoch.

This (.leclination dependent weighted number of events. 01(6), is used to remove
the declination dependence of the data excess map to give map in units of Crab flux:

(QC =

(7.8)

where (fir is the flux in units of the Crab flux, and 13(6) is the excess as a function of

 

3To correct. for the instrumental dead time of ~ 10%. the number of days in each epoch is
multiplied by a factor of 0.5).

127

declination. To get the flux in units of TeV—Infzs-lsr-l, a. further normalization
factor is needed:
(1le
[no (7 -9)

( 'J

 

e = o. X

The (IQ term is to give the flux in units of per steradian.

7 .6 All-Sky Map

The A4 weighted analysis technique was applied to six years of data (same as the
data set mentioned in section 7.1). Figure 7.8 shows a TeV gamma-ray image. of
the northern hemisphere. The brightest. extended region in the entire northern sky
is the Cygnus Region of the Galactic plane located at roughly 300 degrees in Right
Ascension and 35 degrees in Declination. The white lines show a :tS degree region
around the Galactic plane. At each point the statistical significance of the observed
excess (or deficit) is plotted.

Figure 7.7 shows the distribution of Significances for the all sky map (in blue). The
distribution of significanccs with the Crab Nebula, Markarian 4‘21, and the Galactic
Plane renmved is shown in red. This distrilfimtion follows a. Gaussian with a width of
0.997 and a mean of 0.001.

In the. rest of this Chapter observations of known TeV gamma-ray sources will
be presented. New sources that have been discovered will be discussed in the next

Chapters.

 

| Significance Distribution

 

 

 

 

 

 

 

 

  

.
— AllSky
4..
10 5 Crab, Mrk421,&GP removed
103';—
:
102g"
10;,-
E ;
’11 ...11141.||| ll! ....

 

 

 

 

-5 0 5 1 0 15 20
Standard Deviations(o)

Figure 7.7: Distribution of significances.

1‘29

7.6.1 Observations of the Crab Nebula

The most significant TeV gamma-ray smirce seen in figure 7.8 is the Crab Nebula,
located at. a Right Ascension of 83.63 degrees and a Declination of 22.01 degrees and
visible at 15.2 standard (leviatimis. Figure 7.9 shows a close. up at the region around
the. Crab Nebula. The significance of the. Crab in this data set is less than what
one might expect by scaling the significance from the 1.7 years data set reported in
section 5.4, namely 10.55 x «6.0/1.7 = 19.8 standan‘l deviations. This is due to the
fact that the larger data set contains data with lower quality ( no outriggers) than the
1.7 years data set.

The best. fit. lmation of the excess from the Crab Nebula is RA 2 83.60000063mt,
Dec = 22.100 :l: 0.05:,at, with a Gaussian width of a = 0.380 i 0.04gmt. This is in
very good agreement with the true location of the Crab Nebula[80], RA 2 83.630,
Dec 2 22.010.

The flux from the Crab Nebula. at 12 TeV is (4.680047'5mti1.43%) ><10—14 TeV—1
111—‘2s_1 assuming a power law spectrum with spectral index a = —2.62. This
is consistent with the HEGRA flux at 12 TeV of [7'] (4.21 :l: 0.04,,mt i 0.503%) x
10‘14 TeV’1ni“2s_1.

Altlmugh h’lilagro‘s estimate for the flux from the crab Nebula is corisistmlt with
those measured by ACTs to less than 3000, the cosmic-ray rate. measured in hr’lilagro
is about 30°/o less than that measured by balloon experiments [30]. A conservative
value of 30% for the. systematic error on the flux is thus being applied in this analysis.

Table 7.8 lists the significances of the Crab Nebula for the different epochs. The
first. row gives the 111easured significance (Z) the second row gives the expected sig—
nificance (ZE), and the last row gives the (:leviation from the expected significance.
As can be seen, there is a good agreement between the expected and measured sig-

nificances in each case.

130

 

 

Epoch N9 1 2 3 4 5 6 7 8

 

Significance (Z) 2.1 5.2 5.3 9.2 5.1 6.6 6.3 6.3
Expected Significance (ZE) 2.4 4.7 4.9 8.9 4.9 6.5 6.3 6.0
IZE — Z /ZE 0.12 0.10 0.08 0.04 0.04 0.02 0.0 0.05

 

 

 

Table 7.8: Statistical Significances of the Crab Nebula. for the different epochs. The
first row gives the measured significance (Z), the second row gives the expected
significance (Z E), and the last row gives the deviation from the expected significance.

7.6.2 Observations of the Active Galaxy Mrk421

One extragalactic source has been observed in this analysis. The active. Galaxy
Mrk421 has been observed at the level of 7.3 standard deviations in this analy-
sis. Figure 7.10 shows a TeV gamma-ray image of the region around the active
Galaxy Mrk421 for the six-year data set. The color scale. is the statistical significance.
of the TeV gamma—ray excess at each point. The flux from Mrk421 at 12 TeV is
(3.9 3: 0.85,”, i 1.25%) x 10‘14 TeV—1111_2.s_1 assuming a power law spectrum with
spectral index (i = —2.62. This amounts for 0.83 in Crab flux units. If a power law
spectrum with spectral index a = —1.9 is assumed, the flux from Mrk421 changes by
~ 2500 to (2.9:t0.63mt :l:0.8sys) x 10‘14 TEV—1111—25—1. This is the first observation

of Mrk421 at such high energies.

131

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132

   

(959)
3‘

Declination
0)
d
0

RA (deg)

Figure 7.9: A TeV gamma-ray image of the region around the Crab nebula for the
six-year data set. The color scale is the statistical significance of the TeV gamma-
ray excess at each point. The significance at the location of the Crab nebula is
15.2 standard deviations. This significance is less than what one might expect by
sealing the significance from the 1.7 years data set reported in section 5.4, namely
10.55 x «6.0/1.7 = 19.8 standard deviations. This is due to the fact that the larger
data set contains data with lower quality (no outriggers) than the 1.7 years data set.

133

  
 
 
 
  

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Decilnatign (deg)

40 .

l. 3
38

' 2
36 ‘-
34 o
32 _1

‘V‘ ,_ .. gt ‘. ,,'....£!;. 3
3° 155 160 165 170 175 2
RA (deg)

Figure 7.10: A TeV gamma-ray image of the region around the active Galaxy Mrk421
for the six-year data set. The color scale is the statistical significance of the TeV
gamma-ray excess at each point. The significance at the location of Mrk421 is 7.3
standard deviations.

134

Chapter 8

Discovery of Localized TeV
Gamma-Ray Sources in the

Galactic Plane

As mentione(‘l in the previous Chapter, the most prominent feature in the. all-sky
TeV gamma-ray map obtained in this analysis is the Galactic plane, which is clearly
visible on the right side of figure 7.8. The same map is shown in Galactic coordinates
in figure 8.1. Figure 8.2 shows a close up at the inner Galaxy visible to i\-‘lilagro.
This map shows a TeV gamma-ray emission from the Galactic plane in the region
I E [300,850] and IM < 5°. The significance of the TeV gamma-ray emission from
this region ranges from 4.0 to 11.3 standard deviations. The brightest TeV emission
comes from within the Cygnus region of the Gala‘qr defined by l E [650,850] and
|b| < 30. Moving to regions further away from the. Galactic plane shmvs no significant
TeV gannna-ray emission.

Emissions of TeV gannna—rays from nine regions in the Galactic plane have been
observed in this work. Sources with a post-trials significance 2 5 standard deviatimls

are considered as new sources. Sources with a post-trials significance < 5 and > 4

sass 2:

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137

standard deviations are considered as candidate sources.

8.1 Discovery of the TeV Gamma-Ray Source
MGRO J2019+37

Figure 8.3 shows a close. up at the Cygnus region of the Galaxy. The brightest TeV
gamma-ray emission comes from Galactic Longitude 75 ('legrees and Galactic latitude
0.3 degrees. Observed at 11.3 standard deviations (10.2 post-trials 1), this new TeV
gamma—ray source is the second brightest source of TeV gamma-ray emission (after the
Crab nebula) in the northern hemisphere. The statistical significance of this source
is ~ 6 standard deviatirms above the diffuse TeV gamma-ray emission in the region.
The new source is given the. name MGRO J 2019+37, where MGRO is for Milagro,
the rest of the. name gives the location of the source in equatorial coordinates; J 2019
is the right ascension of the. source in hour angle with reference to the J 2000 epoch,
and 37' is the (‘lcclination of the source. This naming convention will be applied for

all the newly discovered sources which will be presented in the coming sections.

8.1.1 Location of MGRO J2019+37

The hication of MGRO .I2t)10+37 is R.A.= 304.83 i: 0.1451(1) :i: 0.35.0.5- degrees and
Dec: 30.83 i 0.083,,” :t 0.33,”. which. in Galactic coordinates, is equal to l = 75.0 i
0.18m) :t 0.33%, degrees and b = 0.39 :1: 0.15)”) :i: ()'33.1/3 degrees. The systematic error
is a eon'ibination of the 0.07 degree uncertainty in the location of the Crab Nebula as
seen in this analysis, the uncertainties due to the unknown source morphology, and

the uncertainties due to the diffuse. background in the Cygnus region. The uncertainty

 

l The post—trials significance was calculated from the significance measured ( pre-trials) by convert-
ing this pre-trials significance into a probability (1)0). recalculating the probability of the occurrence
of one or more such events given the number of trials IV}. ([2 2 p0 x N,). and converting this proba—
bility back into a significance. The number of trials for the scanned region of the Galactic plane is
953000 trials.

Galactlc Latitude (dog)
Slgnlflcance

 

Figure 8.3: The Cygnus Region of the Galaxy as seen in TeV gamma rays. The color
scale is the statistical significance of the TeV gamma—ray excess at each location.
Since the Milagro exposure and sensitivity are roughly constant over the region in
the figure, the statistical significance is nearly proportional to the flux from each
point. The crosses show the location of EGRET sources and their corresponding
location errors.

139

in the location of the Crab is used to adjust. the absolute pointing of Milagro in this
analysis [1].

A (:lefinitive umlerstanding of this new TeV source requires further multi—wavelength
observations of this source. The location of MGRO J2019+37 is consistent (within
the cmnbined location errors of EGRET and Milagro) with 2 EGRET sources (black
and blue circles in figure 8.4). One of the EGRET sources (3EG J2016+3657) is coin-
cident with the blazar-like source of unknown redshift.[55], B‘2013+370. The location
of MGRO J2019+37 is also coincident with the GeV source GeV J2()‘20+3658 [43]
which is associated with the young pulsar wind nebula [35](PWN) G75.2+0.1. An
analysis of the highest energy photons (>1 GeV) observed by EGRET from this region
indicates that the two EGRET sources were. not resolved by EGRET. This analysis
gives a median energy of 12 TeV. Given this, a blazar-like source is less likely since
such high energy gannna-rays are attenuated by interactions with the extragalactic

infrared background light.

8.1.2 Spatial Morphology of MGRO J2019+37

To study the spatial morphology of the newly discovered sources a subset of the
data. which contains the highest energy events was used. In this “high energy” data
set, a cut. on Nfit of 1.30 was applied. In addition. only events with A4 > 3.0 were
included. Using these data, the l\vlonte Carlo predicts an angular resolution of 0.30.
An exan’iination of the arrival directions of the higher-energy photons shows that
MGRO J 2019+37 is most. likely an extended source or multiple unresolved sources of
TeV gannna rays as seen in figures 8.4 and 8.5. Fitting the excess from the. source to
a circular ‘2-D Gaussian gives a width 2 of (7 = 0.32 :l: 0.12 degrees[7l]. If an elliptical
2-D Gaussian fit is used instead, the extent in the RA. direction is ~ 2 times large

than the extent. in the Dec. direction. Figure 8.5 shows the radial distribution of

 

2After accounting for the width of the Crab nebula which is a point source in our PSF.

140

Galactic Latitude (deg)
Significance

 

76 J 74
Galactic Longitude (deg)

Figure 8.4: A TeV gamma-ray image of the area around the new source MGRO
.12019+37. The. location and location error of the source is marked by the white
circle. Locations and location errors of the two EGRET source (3EGJ2016+3657 and
3EG .12021+3716) are marked by blue and black circles. respectively. The location
and location error of the GeV source GeV J2020+3658 is marked by the red ellipse.
This GeV source is associated with the PWN G75.2+0.1 shown in this map as a
yellow dot.

141

excess events from the location around the Crab Nebula and MGRO .l‘2019+37. The
extent. of MGRO J‘2()19+37 is clearly visible here in cmnparison to the Crab Nebula.

To detern‘iine the source radius, the distance to the source should be determined.
Unfi)rtunately, Milagro’s current capabilities don‘t allow for such a measurement and
some assumptions have to be made about the source. distance. The. Cygnus Region
lies at a distance of 1-2 kpc from the solar system. If MGRO J2019+37 lies within
this region, it would have a source radius of 4-15 pc. If, on the other hand, MGRO
.l2()19+37 is associated with the PWN G75.‘2+O.1, which is at a distance of 8-12 pc

[(30]. then this source would have a source radius of 330-90 pc.

8.1.3 Flux from MGRO J2019+37

To estimate the flux from this source, the excess from a 3 x 3 square degree bin
centered at the location of MGRO J2019+37 is used. Assuming a differential source
spectrum" of F."2'(’, the flux from this region is given by EZdN/(IE- = (3.492l:().47s,m:t

1.05,, ,.,f x 10'12 TeV cm‘2 s_1 at the Iiimliaii (.letected energv of 12 TeV.
./

 

3At the present time. an assumption has to be made about the spectral shape of a source. A new
technique for measuring the spectral shape of a source in Milagro is being developed. See Appendix
A for more details.

142

 

I Radial Event Distribution I

Normalized Excess

 

Radial Distance (degrees)
Figure 8.5: The radial distribution of excess events from the location around the Crab

Nebula (blue) and MGRO .l2()19+37 (red). The extent of MGRO J2019+37 is clearly
visible here in comparison to the Crab Nebula [1].

143

8.2 Discovery of the TeV Gamma-Ray Sources
MGRO J2033+42 & MGRO J2031+41

Another TeV gannm-L-ray source has also been discovered in the Cygnus region.
MGRO .l‘2()33+-1-‘2 is the next brightest source. in the Cygnus region after MGRO
.l‘2()19+37. At 7.1 standard deviations (5.2 post-trials), this is a new source of TeV
gamma-rays in this region. This source. is located at l = 80-4i0-4smt i033!” degrees
and I) : 1-2i0-3smt itljltm; degrees. MGRO .l‘2()33+42 is coincident with an EGRET
source (3EG J'2()33+4118) and the HEGRA source TeV J2()3‘2+4130. In addition to
this source, there appears to be another source at l = 79.7 :t 0.33“” :t: 0.33ng degrees
and b = ().7 i 0.33,“ :t 0.38.03. This source, MGRO .12031+41 is not coincident with
any of the sources in the region including MGRO J‘2t)33+4‘2. At 6.82 standard devi-
ations (5.0 post—trials). this appears to be a separate source. Further detailed studies
will be required to determine if this is an independent source.

Figure 8.6 shows a TeV gamma-ray image of the area around these. sources. The
flux from a region of 3 x 3 degrees centered at MGRO J 2033+4‘2 (which include MGRO
J2t)31+41) is given by 1272(1N/(1E = (2.5:i:0.65faf2i10.83y3) x 10'12 TeV cm—2 s-1 at
the median detected energy of 1‘2 TeV and assuming a (‘lifl'erential source spectrum
of 194-“.

The HEGRA source was detected in the energy range of 1-10 TeV with a dif-
ferential photon spectral index of —1.9 :t 0.15m) :t 0.33118 [(5]. When extrapolated
to energies at 12 TeV. the flux from this source is given by EQdAUdE = (7.9 i
2-73tat) x 10‘” TeV mil—2 s—l. The flux from a 3 x 3 square degrees area centered
at the HEGRA source as measured by Milagro at 12 TeV and assuming a differen-
tial source spectrum of E‘l'g is given by la‘QJN/(HC = (1.73 :1: 0.43m) i 0.5233,,g) x
10“12 TeV cm—2 s—1 which is higher than the HEGRA flux for this source This

may be due to the additional contribution from the diffuse emission to the flux in this

144

region.

8.3 Discovery of the TeV Gamma-Ray Source
MGRO J1909+06

Another source that has been discovered in the Galactic plane. is the new TeV gamma-
ray smirce MGRO .11900+06. This source is located outside the Cygnus region and is
closer to the Galactic center. The location of this source is l = 40.5 :i: 0.13“” :i: 0.38113
degrees and b = — 1.0 3: 0.15,”, :l: 0.35113 degrees. At 8.2 standard deviations (6.7 post-
trials), this new source is the second brightest source in the part of the inner Galaxy
that is visible to Milagro after MGRO J2019+37. Figure 8.7 shows a TeV image of
the area around this source. The location and location error of the source is marked
by the white circle. The black circle shown in the same figure marks the location and
location error of the GeV source GeV J 1907+0557 is marked by the black ellipse[43].

The flux from a region of 3 x 3 degrees around this source is given by (IN/(1E =
(4.1 :l: 0.95,“) i: 1283/3) x 10‘14 TeV‘1 (Tu—2 s‘1 at the median detected energy of
12 TeV and assuming a differential source spectrum of E"2'6.

In addition to the four discovered sources, TeV gamma-ray emission from four
more sources in the Galactic plane are. observed with pre-trials significances above
4.5 standard dex-iations. The location and the flux estimates for these sources are

given in the next sections.

145

 

4

Galactic Latitude (deg)
w
Significance

 

78

80 ..
Galactic Longitude (deg)

Figure 8.6: A TeV gamma-ray image of the. area around the new sources MGRO
J2033+42 and MGRO J2031+4l. The location and location error of MGRO
.12033 +42 is marked by the. white ellipse and the location and location error of MGRO
J2031+41 is marked by the. yellow circle. The Location of the EGRET source (BEG
J2033+4118) is marked by the red circle, while the location of the HEGRA source
(TeV J2032+4130) is marked by the green circle.

146

 

0'!

.5
Significance

Galactic Latitude (deg)
u

 

 

 

40
Galactic Longitude (deg)

Figure 8.7: A TeV gamma—ray image of the area around the new source MGRO
J1909+06. The. location and location error of the source is marked by the white
circle. The location and location error of the GeV source GeV .11907+0557 is marked
by the black ellipse.

147

8.4 The TeV Gamma-Ray Source Candidate

MGRO J2032+37

This TeV gaunna—ray source candidate is observed at the level of 5.8 standard devia-
tions pre-trials. A TeV gamma—ray image of the area around this source is shown
in figure 8.3. The location of this source is I = 76.3 :t 0.18m) :l: 0.35.113 degrees
and b = —1.9 fl: 02mm :l: 03.9113 degrees. The. flux from this source is given by
(IN/(Hf; = (0.9 :1: 02mm :l: 0.38%.) x 10‘14 TeV“1 cm‘2 s‘1 at the median detected

energy of 12 TeV and assuming a differential source spectrum of [fl—2‘6.

8.5 The TeV Gamma-Ray Source Candidate

MGRO J 2043+36

This TeV gamma-ray source candidate is observed at the level of 5.6 standard devia-
tions pre—trials. A TeV gamma—ray image. of the area around this source is shown
in figure 8.9. The location of this source is l = 77.2 i 0-23tat :1: 0.33%,- degrees
and h = —4.0 :l: 0.23)“ :t 0.35!” degrees. The flux from this source is given by
(IN/(1E = (1.2 :l: 0.25mi i 0.43.113) x 10‘14 TeV—1 cm"2 s‘1 at the median detected

energy of 12 TeV and assuming a differential source spectrum of Isl—2'6.

8.6 The TeV Gamma-Ray Source Candidates

MGRO J1852+01 and MGRO J1859+O3

This TeV gannm-L—ray source candidate is (iibserved at the. level of 5.1 standard devi-
ations pre-trials. A TeV gamma-ray image of the area around this source is shown
in figure. 8.10. The location of this source is l :— 335 :l: 0-3smt :i: ”-3803 degrees and

b 7- U-OiO-Qsmt i:0.33ys degrees and is marked by the white ellipse. The black circle. in

148

6

.h
Significance

Galactic Latitude (deg)
N

 

76 74
Galactic Longitude (deg)

Figure 8.8: A TeV gannna-ray image of the area around the new source candidate
MGRO J2032+37. The location and location error of the source is marked by the
black ellipse. The black spot in the middle of the map is MGRO J2019+37.

149

Galactic Latitude (deg)
Significance

 

 

74

78 76
Galactic Longitude (deg)

Figure 8.9: A TeV gamma-ray image of the area around the new source candidate
MGRO J2043+36. The location and location error of the source is marked by the
black circle.

150

the middle of the. map marks the location and location error of the GeV sources GeV
.11856+()115 [43]. In addition to MGRO J1852+01 there is another source candidate
that is seen at he level of 4.1 standard deviations (pre—trials). This source. candidate is
given the. name MGRO .11859+()3 and is located at l = 36.4 :i: 0.23“” :1: 0.33113 degrees
and b = —().45 :l: 0.25,”; i 0.35,”.

The flux from a 3 x 3 squared degrees region around MGRO Jl85‘2+01 is given by
(1:\"'/(ll'} = (5.7 i 1.53,,” :1: 1.9395) x 10’14 TeV‘1 cm—2 s"1 at. the median detected
energy of 12 TeV and assuming a differential source spectrum of Fl—Q'G. While the. flux
from a. 3 x 3 squared degrees region around MGRO J1859+03 is given by (IN/(1E =
(4.6 i 1.23;.” :1: 1.4.9.03) x 10”14 TeV"1 cm“2 s’1 at the same median energy and

assuming the same. spectrum.

8.7 The TeV Gamma-Ray Source Candidate
MGRO J 2233+60

This TeV gamma-ray source candidate is observed at the level of 5.1 standard devi-
ations pre-trials. A TeV gamma-ray image of the area around this source is shown
in figure 8.11. The location of this source is l = 106.4 :t 0.53“” i 0.3qu degrees
and I) : 1.7 :l: (l-Ssmt :l: 0333/3 degrees. The flux from this source is given by
(IN/(115’ : (1.0 :1: 0.45,”; i 0.38.115.) x 10’14 TeV—1 cm—2 s—1 at the median detected

energy of 12 TeV and assuming a differential source spectrum of E‘_2'(’.

 

Galactic Latitude (deg)
Significance

 

' 36 34
Galactic Longitude (deg)

Figure 8.10: A TeV gamma—ray image of the area around the new source candidate
MGRO .11852+01. The location and location error of MGRO J1852+01 is marked
by the white ellipse. The location and location error of MGRO J1859+03 is marked
by the red circle. The black circle in the middle of the map marks the location and
location error of the GeV sources GeV .ll856+0115 [43]

 

O

Galactic Latitude (deg)
O .5

I
_A

M
[Illllllllllllllllllrlrrl‘

 

 

Figure 8.11: A TeV gamma-ray image of the area around the new source candidate
MGRO J2033+60. The location of the. source is marked by the white cross.

153

8.8 Milagro TeV Gamma-Ray Source Catalog

The newly (.liscovered TeV gamma-ray sources and the candidate sources are cataloged
in Table 8.1. Listed in this catalog are the names, l(_)cati(.ms (in Galactic coordinates),
pl'tf-tl'ltllh‘ significances, and fluxes for all the sources that have been observed with pre—
trials significance > 4.5 standard deviations. ()nly sources with post-trial significant-es
> 5.0 standard deviations are. considered as sources while sources with post-trial

significances < 5.0 standard deviations are considered source candidates.

 

 

 

()l)j(‘('t- Location Significance Flux (x 10"”)
(1,1)) (std. dev.) (TeV—1 cur? s-l)

MGRO J2019+37 (75.1i0.1,0.3 i: 0.1) 11.3 2.4 :l: 0.4 :l: 0.8
MGRO J1909+06 (40.5 i 0.1, —1.0 :l: 0.1) 8.2 4.2 :l: 0.9 i1.2
MGRO J2033+42 (80.4 i 0.4, 1.0 :l: 0.3) 7.1 1 7 :l: 0 4 :l: 0 5
MGRO J2031+41 (79.7 :t 0.3, 0.7 :t 0.3) 6.8 ' ° '
MGRO J2032+37 (76.3 :l: 0.1, —1.9 :l: 0.2) 5.8 0.9 :l: 0.2 :t 0.3
MGRO J2043+36 (77.2 :1: 0.2, —4.0 i 032) 5.6 1.2 :l: 0.2 i: 0.4
MGRO J1852+01 (336i 0.3.0.0102) 5.1 5.7:}: 1.5i 1.9
MGRO J2233+60 (106.4 :t0.5,1.7 i 0.8) 4.5 1.0 :t 0.4 :t 0.3

 

 

Table 8.1: Milagro TeV gamma—ray source catalog. A 0.3 degrees systematic error
applies to the location of each source. The Significances reported are pre-trials sig-
nificances. The fluxes are. given at the median energy of this analysis, 12 TeV and
assuming a differentiz—tl source spectrum of Iii—2'6.

Chapter 9

Discovery of Diffuse TeV
Gamma-Ray Emission From the

Cygnus Region

It can be seen in figure 9.1, that in addition to the newly discovered sources in the
Cygnus region, there exists a diffuse TeV gamma-ray emission from this part of the
Galaxy as well. The contours in the figure show the matter density in the region. The
TeV emission is cm‘related with the matter density with the exceptiim of a significant
('lt‘V'iz-lihill near the new MGRO J2019+37. This region of the Galaxy is a natural
laboratory for the study of cosmic-ray origins. It contains a large column density
of interstellar gas that should lead to strong emission of diffuse gamma rays. It is
also the. home. of potential cosmic-ray acceleration sites—7W'()lf-Rayet stars [69], OB
associations [18]. and supernova. remnants ['29]. The. Tibet Air Shower detector also
recently reported an excess in the cosmic-ray flux from this region [11].

To study the diffuse emission from the Cygnus regirm, the contribution from the
h‘Iilagro sources in the same region must first be subtracted. To do this, a 3 x 3 square.

degrees area centered at the two Milagro smlrces in this region. MGRO J2019+37

Galactic Latitude (dog)
Slgnlfleanco

 

Figure 9.1: The same TeV image of the Cygnus region as in figure 8.3 but with the
addition of contours showing the matter density in the region[42, 23, 46].

156

and MGRO J2033+42, is excluded from the flux calculations for the region defined by
Galactic latitude. -30 to 3.0 degrees and Galactic longitude 65 to 85 degrees. The flux
from the remaining region at. 12 TeV and assuming a differential power law spectrum
of E726 is given by (IN/(1E = (8.3 i 1.33th i 2.73313) x 10“14 TeV—1 cur—2 s—1
which accmmts for twice the flux from the Crab nebula. A change in the assun‘ied
spectral index from -2.4 to -2.8 changes the quoted flux at 12 TeV by < 10 ‘70. In
this measured flux, it is assumed that the source has no cut off in its spectrum up
to 100 TeV. If there exists a cutoff in the spectrum of the source, the flux estimate
will go down. The maximum factor by which the flux will go down is the case that.
the source has a cutoff at 12 TeV, in this case the flux will go down by a factor of
1 / 2. However, this is unlikely since the significance of the gamma-ray emission from
this region improves when the weighted analysis is used. Taking into account that
the weighting analysis gives higher weights for events with energies higher than 12
TeV (see figure. 5.9), gamma-ray emission from this source is most likely to extend
well beyond this energy.

In order to compare the flux value measured for the diffuse TeV gamma-ray emis-

sion from the Cygnus region, the. GALPROP model is used.

9.1 The GALPROP Model

GALPROP is a computer code that is used for the (i-alculati(')n of Galactic cosmic-ray
propagation [51] . Primary and secondary nucleons, primary and secondary electrons,
secondary positrons and antiprotons, as well as gamma-rays and synchrotron radia-
tion are included. The GALPROP model calculates the gamma-ray emissivities in
every spatial grid point using the. propagated spectra of cosmic-ray species, leptons
and nucleons, the interstellar radiation field, and the gas densities. The gas-related

comprments (7rU and ln‘emsstrahlung) of the gamma-ray sky maps are calculated us-

ing ‘21 cm line survey data [23] for HI and CO J = 1 to .120 survey data for H2, in
the form of colunm densities for Gahurtocentric rings, using velocity information and
a rotation curve. The msnii<_:-ray source distribution is based on SNR/ pulsars and
a variable C('.)-to—H2 conversion factor. In this way, details of Galactic structure are
included. Full details of the GALPROP model are given in [51].

GALPROP has two models for the propagation of cosmic—ray in the Galaxy; the
“conventional” model, and the “optimized” model. The “(.r()11ve11tional” model is
tuned to have. the propagated cosmic-ray particle spectra and intensities match the
lmiral direct. measurenrents [.51]. This model yields a deficit of diffuse gamma—ray
emission above. 1 GeV, a so-called GeV excess, observed in all directions on the
sky (see Chapter ‘2). The “optimized” model [67"] is tuned to match the EGRET
diffuse emission data. for the whole sky and reproduces the GeV excess by relaxing
the constraints on matching the local cosmic-ray proton and electron measurements.
This “optimized” model is instead based upon the secondary antiprotons in cosmic-
rz‘ws and EG RET diffuse gamma—ray data. In this model the cosmic-ray intensities are
significantly higher than those measured locally and the electron spectrum has been
assumed to extend to well beyond 10 TeV to produce garmna rays in the Milagro
energy range. The. “optimized” model thus has a much larger contribution from
inverse Compton scattering.

The Cygnus region is in a ('lirection tangential to our spiral arm located at. approx-
imately the same distance from the Galactic center as the solar system. This direction
is the most accurate to determine the gas distribution based on velocity information
and the Galactic rotation curve. Therefore, the uncertainty in the determination of

the gas distributitm in this direction. is minimal.

158

9.2 Interpretation of Results

Figure 9.2 shows the GALPROP models for the diffuse emission from the Cygnus
region along with the. EGRET and Milagro measurenuants for the same region. The
Milagro measurennint of the diffuse flux in the Cygnus region is a factor of ~7 above
predictirms of the “conventional” model. The Milagro flux also exceeds the predic-
tion of the “optimized” model, which incorporates higher c(_:)smic-ray intensities to
fit the EGRET data. Increasing the gas column density to agree with the Milagro
data would violate the restrictions imposed by the EGRET data, and increasing the
cosmic-ray flux at higher energies would violate constraints such as antiproton flux
Incasurenwnts unless the increase in cosn’iic—rays was local to the Cygnus region. Both
the. parameters of the GALPROP model and the Milagro flux measurement have large
systematic uncertainties; howrwer, the discrepancy between the model and the data
likely implies the existence of an additional gamma—ray component. The spectrum
of this component must be hard (for example, a differential photon spectral index of
-2.3 to —2.4) in order to agree with fluxes measured by both EGRET and Milagro.
There are several possible explanations for this component: unresolved sources
of TeV gamma rays, a population of higl‘i-energy electrons in the region producing
an inverse Comptmi flux at. TeV energies, or a population of cosmic-ray accelerators
which is dark because the hadrons do not. interact near their sources but instead
with the local matter distribution. The correlation of the observed emission with the
matter density can be. consistent with all of these explanations if the sources are co-
located with the matter. If the. excess is due to inverse Compton scattered photons,
then this component must be a factor of ~20 higher at 12 TeV than the prediction
of the conventional model. Given typical diffusion and energy-loss times of such high
energy elrwtrons, the source of these. electrons must reside within the Cygnus region.
Also, the prrumsed explanation of the GeV excess due to neutralino annihilation

[24] cannot explain the Milagro high energy flux, because such a massive neutralino

159

 

 

 

 

 

10“:
> I
Q) _
2 _ I I
IV!
:1
IE 10'2
U
rd
'0
\
Z
‘O
N|-|.|
10‘3
104
10-5 l llllllll J lJllllll lllllllll 1 1111111] lLlllllLi‘i l lllllll
102 103 10“ 105 10" 10’ 108

Energy, MeV

Figure 9.2: Gamma-ray spectrum of the diffuse emission from the Cygnus region
of the Galactic plane. The red bars are the EGRET data, and the purple bar is
the Milagro measurement with the statistical error shown as a broad line and With
the systematic error shown as a narrow line. The solid lines represent the “conven—
tional", and the. dotted lines represent the “optimized” GALPROP model of Strong
et al. [51]. The dark blue lines represent. the total diffuse flux, the red lines represent
the 7r0 component. the green lines represent the inverse Compton component, the
light blue lines are due to bremsstrahlung, and the black lines are due to the extra-
galactic background. The Milagro analysis is insensitive to isotropic emission due to
the background subtraction, so the extragalactic background is not included in the

l\«"li1agro energy range.

160

wouhl have a, nun-11 sumllur number dmlsity and hence lower flux. Therefore, this
I\Iilagro nl‘mervnti<_nl suggests that. the Cygnus region contains hard-spectrum, cosmic-

ray proton ()1‘ (‘1(¥(‘t1‘(’1)11 au'Ccle‘ators.

Chapter 10

Conclusions

10. 1 Summary

The development of the. new gamnia—l‘iadron separation variable, A4, along with the
weighted analysis teclmique developed elsewhere, has significantly improved the sen-
sitivity of the Milagro (’lete("t(,)r. This new analysis resulted in the first discoveries in
Milagro. Four localized sources of TeV gamma-ray emission have been discovered,
three of which are in the Cygnus regimi of the. Galaxy and one closer to the Galactic
center. In addition to these localized sources, a diffuse emission of TeV gamma-rays
has been discovered from the Cygnus regiml of the Galaxy. The localized sources
haw no obvious counterparts in other wavelengths and thus remain as unidentified
sources. The most interesting of these localized sources is the new source MGRO
J‘2()19+37 which is the brightest TeV gann'na—ray source seen by Milagro after the
Crab Nebula. Unlike. the other sources, MGRO J2019+37 is located at a region of
low-matter density. The diffuse. TeV gamma-ray emission from the Cygnus region ac-
counts for twice that of the Crab Nebula. The flux of the diffuse emission measured
by l\'Iilagro from this region exceeds predictions from the “(:01iventional” GALPROP

1110(ch by a factor of ~ 7. It also exceeds predictions from the “optimized” GALPROP

16‘2

model by a factor of ~ 5. This Milagro observation suggests that the Cygnus region
contains hard—spectrum proton or electron accelerators and / or unresolved sources of

TeV ganuna-rays in the region.

10.2 Future Directions

The obvious continuation of this work would be the. addition of more data to increase
the number of discovered sources. What is more important are more detailed studies
of each of the discovered sources in this thesis. This includes observations at other
wavelengths especially at. GeV gamma-rays, X-rays, radio, and optical wave bands.
()l)S(‘I‘V?ttl(’)IlS of these. sources with ACTs should increase our understanding of these
smirces. The excellent angular resolution of ACTs, < 0.10, should allow for better
nior1‘)hological studies of these sources. The VERITAS telescope array in Arizona is
the best ACT telescope suited for such studies. The fact that it is at a latitude similar
to that of l\rlilagro, ~ 370, gives similar exposures for these sources. It also gives it the
maxin'unn exposure for the Cygnus region which is located at similar declinations in
the sky. At the (uncut time, Milagro is unable to determine the spectral shape of a
gamma—ray source. The determination of the spectral shape of each of the discovered
sources will substantiz-illy increase our understanding of the nature of these sources.
The. develt)Innent of such a technique has been explored which gave results for the
Crab Nebula and the (_-.(.')smic-r2;iy spectra which agree with those measured by other
experiments (see Appendix A). The perfection and implementation of the spectral
index analysis technique given in Appendix A seems to be a natural and a necessary
continuation of the. work done in this thesis. One other possible continuation of this
thesis work is the study of the time variability of the gannna-ray emission from the

discovered sources.

163

Appendix A

Spectral Index Analysis Technique

()ne of the important parameters that should be determined for a gamma-ray air
shower is its energn A11 algorithm that determines the energy of an air shower based
on some shower parameters like the zenith angle of the shower and the distance of the
shower core from the center of the pond (core. distance) is being developed. As has
been mentioned earlier, the flux from celestial gamma-ray sources follows a rapidly

falling power law spectrum given by:

(IN I; ‘0
—= '0 — A.1
(113 (p (1:70) ( )

where (5)0 is the differential flux nmmalizaticm, E0 is the energy at which the. flux is
normalized, and o- is the spectral index of the source.

The spectral index, a of a source is a characteristic of this sources. Sources with
smaller as will emit more photons at higher energies. In this sense, the energy
spectrum of a source is proportional to its spectral index a. One way to quantify the
energy spectrum of a gamma—ray source will be. to determine its spectral index.

In this appendix a new technique for measuring the spectral index of a v-ray source
in Milagro using A4 is introduced. This technique makes use of the energy dependence

on A4. The spectral index of the Crab Nebula obtained with this technique is o’ =

164

—'2.57+(().12—().11)“"mf. This value agrees with those measured by other experiments

in the same energy range as Milagro.

A.1 Energy Dependence on A4

In order to be able to measure the spectral index of a ”y-ray source one needs to have

a variable that is well correlated with energy, A; is such a variable. Figure A.1 shows

the relation between the energy and A4 for gamma Monte Carlol. As can be seen in

this figure, there is a very good correlation between the energy of a y—ray event and

the A4 value of that event. in the energv range ‘2-‘20 TeV.

A.2 Spectral Index Determination Technique

In order to determine. the spectral index of a Tray source, the following steps were

(l()11(>:

Eleven different gamma Monte Carlo sets were created. These data sets were
simulated with different spectral indices ranging from -2.0 to -3.0 in increment

of 0.1.
Excess from the data were binned in A4, differentially.
Gamma MC sets were binned in A 4, differentially.

The different gamma MC differential distributions were fit. to the differential

excess from the data.
X2 for each of these eleven fits were (u—ilculated.

A plot of these \2 values as a function of spectral index was generated.

 

lEpoch 5 is used throughout this Appendix.

0 Minimum of this plot corresponds to spectral index of the source.

A.3 Crab Nebula Spectral Index Estimation

The Crab Nebula serves as a standard candle in ’7-171)’ astronomy and a new technique
is best tested on this steady source. In addition to this, the fact that this smirce has
been well studied by many experiments in the same energy range as Milagro helps
test the new technitnie by cross checking the results of this new technique with those

of the other experiments.

Figure A.‘2 shows the distribution of differential excess from the Crab Nebula as a
function of A4 . The last bin in this figure contains all excess events with A4 2 12.0,
this is the reason why this bin has more events than the two previous bins. Figure A.3
shows the A4 differential distributions of four gamma Monte Carlo sets with spectral
indices -‘2.1, -‘2.3, -2.(i, and -2.9. For comparison, the differential excess from the Crab
(figure A.‘2) is shown on each of the plots.

Figure A4 shows the distribution of the \2 values of the fits of the different gamma
Monte Carlo sets to the Crab data as a function of the spectral index a. From this

plot we see that the minimum \2 corresponds to a spectral index of:
on“), = —2.57 + (0.12 — Ollie-rm

The statistical errors were obtained by fitting the distributi<m in figure A.4 to a
quadratic function and then going up one unit. in x2 from the minimum. As can be
seen from this figure, the distribution is not synnnetric around the minimum, this
is why the statistical errors are not equal. In total there are 12 degrees of freedom
(ndf). After the subtracticm of one degree of freedom for the. minimization of X2 with

r(:*s1:)ect to a and another one for the minimization of \2 with respect to the scaling

166

factorQ, one ends up with 10 degrees of freedom. y; at the minimum is equal to 13.9

this corresponds to chance probability of :2: 18%

The value of o for the Crab obtained in this analysis is in good agreement. with
results form other experiments. Table A.1 lists Measurements of the Crab spectral

index by other experiments in the same energyr range as l\r‘lilagro.

 

 

Tibet -—'2.62 :l: 0.17““;
HEGRA —'2.59 :l: 0.033mt :t 0.0531,;-
Vll'hipple —‘2.49 i 0.063th :i: 0.045313

 

Table A.1: l\Ieasurements of the Crab spectral index by other experiments in the
same energy range as Milagro

A.4 Cosmic Rays Spectral Index Estimation

The same technique was applied to measure the s1;)ectral index of cosmic rays. To
do this, eleven different proton and helium Monte Carlo sets with different spectral
indices were created. These data sets were simulated with different spectral indices
ranging from -‘2.0 to -3.0 in increment of 0.1. The data used to measure the spectral
index is the Crab off source data. The analysis 1')roceeds in the same steps as in the

one previous section.

The result for the measurement. of the cosmic rays spectral index is:

 

2Thc scaling factor of the i‘th gamma MC distribution. 3, is defined as:

where A, and A, are the areas under Crab differmrtial excess and the i‘th gamma MC differential
distribution. rcspectivdy. and (5, is a correction applied to S,- to minimize X“) of the fit of the i‘th
gamma MC distril'mtion to the Crab data.

167

 

Median Energy vs A4

 

 

 

 

 

 

35E-
L—
305— ~
€25:
b :
3 t
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m :
.315:— +
3 E
210;- l
5ri
p
Ohgl I l L L l L LLJ I #11 L L 111 1 1J
2 4 6 8 1o 12
A4

Figure A.1: lVIedian energies of gamma-ray-initiated air showers as a function of A4.
Each point represents the median energy’ for gamma-ray events with an A4 value
greater than the :r-axis value.

This is in good agreement. with BESS measurements in the energyr range 30—540 GeV:

("rproton 1': _2.732 i ().()113t(1t :t ()-()193y3

”helium : _2.699 It 0.04stat It 0.0443113

r2 at. the minimum is equal to 7.54 this corresponds to chance probability of z 67%

168

 

L Crab Differential Excess vs. A4

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure A.‘2: Differential excess from the Crab Nebula as a function of A4

169

     

 

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Figure A.3: A4 differential distribution of four gamma Monte Carlo sets with spectral
indices -2.1, —2.3, -2.6, and -2.9. For comparison, the differential excess from the Crab
is shown on each of the plots.

170

 

 

 

342 vs. Spectral Index a

 

 

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Spectral Index a

Figure A4: Distributirm of the \2 values of the fits of the different gamma. Monte
Carlo sets to the Crab data as a function of the spectral index a.

171

Appendix B

Detailed Plots

B.1 Aunyzu Distributions for Different Epochs

In this section, distributions of A” ,1 (1k, for different A4 slices for each epoch are shown

with the correspomling fit parameters to a 2D Gaussian function.

172

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191

B.13 A4 Distributions as a function of “Dead” PMTs
for different epochs

In this swtion. (listl‘iinltions of A for different. )(srcelltadcs of “dead“ PMTs for
. 4 b

(11:).91niv-ray Monte Carlo, (121m. and gamma-1713' Monte Carlo for each epoch are shown.

1‘)?

 

FA, distributionl

1 ' Cosmic-Ray MC

-— High % dead PMTs
Avg. % dead PMTs
— Low % dead PMTs

 

 

1

0.8

 

 

0.6

 
    

0.4

0.2

 

IIIIIII

 

 

 

 

 

o l A P. L+ l . A . l . L A I A A l A
o 2 4 6 8 1o 12
[A4 distribution]
Data

— High % dead PMTs
Avg. % dead PMTs

— Low °/o dead PMTs

 

 

 

 

b
p
p-
p
r
r
p-
L
h
b
r

 

 

 

 

 

 

 

 

  

 

 

 

 

4 6 8 1o 12
[A4 distribution |
1 Gamma-Ray MC
— High % dead PMTs
0-3 _ Avg. % dead PMTs
: — Low % dead PMTs
0.6 :-
0.4 E-
02 :—
0— .L . l---1+LLILL.1
o 2 4 6 8 10 12

Figure 8.19: Distributions of A4 for different percentages of “dead” PMTs for cosmic-
ray Monte Carlo, data, and gan‘nna-ray 1\"Ionte Carlo for the first epoch.

193

 

[A4 distribution]

1 .— Cosmic-Ray MC
' High % dead PMTs

 

 

 

 

 

 

 

 

 

 

 

 

 

0-3 Avg. % dead PMTs
— Low % dead PMTs
0.6
0.4 P
n
0.2
0 A_ l A . A l . A #1 A A L l L J J l A
0 4 6 8 1O 12
[A4 distribution]
Data

— High % dead PMTs
Avg. °/o dead PMTs
— Low % dead PMTs

 

 

 

 

 

 

 

 

 

 

 

 

[A] distribution]
1 Gamma-Ray MC
— High % dead PMTs
0-8 Avg. % dead PMTs
E — Low % dead PMTs
0.6 r
t
0.4 :-
o.2 :—

 

  

 

 

 

OD

Figure. B20: Distributions of A4 for different percentages of “dead” PMTs for cosmic-
ray Monte Carlo, data, and gamma-ray [\Ionte Carlo for the. second epoch.

194

 

[A4 distribution]

 

Cosmic-Ray MC

High % dead PMTs
Avg. % dead PMTs
-—- Low % dead PMTs

 

 

 

 

 

F
i-

1 I A L .A l

 

 

 

 

Data
— High % dead PMTs

Avg. °/o dead PMTs
— Low % dead PMTs

 

 

 

 

i
i
i
P
r

 

 

4 6 8 1O 12

 

 

 

 

 

 

 

 

  

 

 

Lil4 distribution]
1 Gamma-Ray MC
— High % dead PMTs
0-3 _ Avg. % dead PMTs
: — LOW °/o dead PMTS
0.6 :-
o.4 :—
C
0.2 E—
0... 1...]--LL#+.1A
0 2 4 6 8 10 12

Figure 8.21: Distributions of A4 for different percentages of “dead” PMTs for cosmic—
ray Monte Carlo, data, and gamma-ray Monte Carlo for the third epoch.

 

[A4 distribution]

 

 

 

1 .— Cosmic-Ray MC
‘ — High °/o dead PMTs
0-8 :' Avg. % dead PMTs
” — Low % dead PMTs

 

 

0.6

      

 

 

 

 

 

 

0.4;—
0.2;
.
1..
OF; A IHA41H-HI. 214;.l.
o 2 4 6 3 10 12
[A4 distribution]
Data

— High % dead PMTs
Avg. % dead PMTs
— Low % dead PMTs

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 A i i . l L 4 . l A A . l . L A l . . . J .
0 2 4 6 8 1O 12
|AI distribution]
1 Gamma-Ray MC
— High % dead PMTs
0.8 _ Avg. % dead PMTs
I Low % dead PMTs
0.6 _—
o.4 :—
o.2 :-
.
n
i- 1 1
0 A n -
0 2 4 6 8 10 12

Figure [3.22: Distributions of A4 for different. percentages of “dead” PMTs for cosmic-
ray Monte Carlo, data, and gallium-ray Monte Carlo for the fourth epoeh.

 

[A4 distribution]

 

 

 

 

 

 

 

 

 

 

 

 

1 T Cosmic-Ray MC
’ — High % dead PMTs
0132' Avg. % dead PMTs
— Low % dead PMTs
0.6
0.4
0.2
O L L L L J L A l L l
0 6 8 10 12
[A] distribution]
1 ." Data

 

 

— High % dead PMTs

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0-8 Avg. % dead PMTs
— Low % dead PMTs
0.6
0.4
0.2
o . I l . I _A__. _I j.
0 2 6 8 10 12
|AI distribution ]
1 Gamma-Ray MC
— High % dead PMTs
0.8 _ Avg. % dead PMTs
I — Low % dead PMTs
0.6 :-
0.4 E—
02 :—
0 - L L L l A l L l l I A L A L 4 A l I
0 2 6 8 10 12

Figure B23: Distributions of A4 for different percentages of “dead” PMTs for cosmic-
ray Monte Carlo, data, and gamma-ray Monte Carlo for the fifth epoch.

197

 

 

[A4 distributiofi

 

 

 

 

 

 

 

 
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 ,— Cosmic-Ray MC
' — High % dead PMTs
0-3 :i Avg. % dead PMTs
— Low °/o dead PMTs
0.6 _
0.4 é—
0.2 E
0 ‘ 1 . . . 1 . 1 . 1 . 1 .
0 2 4 6 8 1O 12
[A] distribution]
1 7' Data
I — High % dead PMTs
0-8 :' Avg. % dead PMTs
I — Low "/6 dead PMTs
0.6 :
0.4 E—
02 :—
01—4 1 l LL111LLLLL..1L
0 2 4 6 8 10 12
[A4 distribution]
1 Gamma-Ray MC
— High % dead PMTs
0-8 _ Avg. % dead PMTs
: —— Low °/o dead PMTs
0.6 _—
o.4 :—
o.2 :—
0 _ L 1 1 1 r . 1 1 L 1 1 1
0 2 4 6 8 10 12

Figure 13.24: Distributions of A4 for different. percentages of “dead” PMTs for cosmic.-
ray Monte Carlo, data, and gamma-ratr Monte Carlo for the sixth epoch.

198

 

A, distribution]

1 CosmioRay MC
— High % dead PMTs

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0-8 Avg. % dead PMTs
Low % dead PMTs
0.6 _
0.4 :-
o.2 :—
0 - L 1 1 1 1 1 1 1 1
o 8 10 12
A4 distribution]
1 Data
— High % dead PMTs
0-8 _ Avg. % dead PMTs
I Low °/o dead PMTs
0.6 :-
o.4 :—
i.
0.2 _—
E
o l LLI ‘ A L H 1 1 L1. 1 L
0 2 4 6 8 1o 12
[A]1 distribution]
1 Gamma-Ray MC
: — High % dead PMTs
0.8 :- Avg. % dead PMTs
2 Low % dead PMTs
0.6 :-
o.4 :—
o.2 _—
C
*‘ 1 1 L 1 1 1 1 1 1 1 1 1 1 1 1 1
o 2 4 6 8 1o 12

Figure 13.25: Distl‘il’iutions of A] for different percentages of “dead“ PMTs for cosmic.-
ray Monte Carlo, data. and gannna—rz-iy Monte Carlo for the seventh epoch.

199

Appendix C

Detailed Tables

In this Appendix are detailed tables of the. PSF fit. parameters for different A4 slices

in each epoch.

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