LEVERAGING MULTI-MESSENGER ASTROPHYSICS FOR DARK MATTER SEARCHES

By

Daniel Nicolas Salazar-Gallegos

A DISSERTATION

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

Physics—Doctor of Philosophy
Computational Mathematics, Science, and Engineering—Dual Major

2024

ABSTRACT

This dissertation enhances the search for dark matter (DM) through a multi-wavelength and multi-

messenger approach by combining data from leading gamma-ray and neutrino observatories. The

first analysis combines data across five gamma-ray observatories, including the High Altitude

Water Cherenkov (HAWC) Observatory and four others. This foundational study probed the largest

DM mass space that spans from 5 GeV up to 100 TeV. This collaboration achieved a threefold

improvement in sensitivity to DM annihilation from dwarf galaxies. The collaborative framework

developed among these five experiments also set a goal for including neutrino observatories in DM

searches. Though no significant dark matter signals were detected, more stringent upper limits

were set on the velocity-weighted annihilation cross-section, ⟨𝜎v⟩.

A pivotal aspect of the research involved developing new analytical methods within the IceCube

Neutrino Observatory that achieved an order of magnitude increase in sensitivity for heavy dark

matter annihilation. These improvements set the stage for multi-messenger dark matter searches

with IceCube and gamma-ray observations.

Within HAWC, computational methods were optimized to speed up the analysis pipeline by an

order of magnitude. HAWC is therefore able to take on more ambitious DM searches and observe

many more potential DM sources.

The combined efforts from HAWC and IceCube form the basis for a novel multi-messenger

strategy to probe dark matter annihilation searches. The research culminates in a preliminary

mock limit from HAWC data and IceCube simulation. These analyses showcase the enhanced

capability of detecting dark matter in the mass region above 1 PeV. With these two instruments

alone, we could see two to threefold improvement to our sensitivity to heavy dark matter compared

to these observatories searching for DM independently. This dissertation presents a comprehensive

multi-instrument and multi-wavelength approach that provides a robust framework for future dark

matter research. This work will be the foundation for a multi-messenger approach in the pursuit of

unveiling the universe’s dark sector.

ACKNOWLEDGMENTS

This dissertation was ambitious and benefited greatly from support and love of my friends, family,

and mentors. These people believed in me at times when I found it hard to believe in myself.

Thank you so much, all of you, for encouraging me to follow my ambition and achieve great things.

Several of you come to mind and below I thank you individually in no particular order.

My mentors

Ben Hooberman, my undergraduate mentor who took a risk on an inexperienced undergraduate

researcher. He gave me the opportunities in physics I was craving and exposed me to the world of

research. The first of many doors opened when I started with Ben, and I am tremendously grateful.

Kirsten Tollefson, my graduate advisor and chair to my thesis committee. She guided my

ambitious program and kept me grounded. Her direction and training taught me a lot about

successful research and building strong, collaborative teams. I will miss the days of gaming out

research and project plans. Thanks a ton for making graduate school a pleasant experience for me.

Pat Harding, member on my committee and mentor at Los Alamos National Lab. I learned

ways of thinking pragmatically towards solving problems with Pat. He helped me lower the stakes

and focused on the core goals in research. Thanks for taking a chance on me and introducing me

to Los Alamos, truly an enchanting place.

Mehr Nisa, previously a MSU postdoc, now faculty. We arrived at MSU at about the same

time and was the only postdoc/peer who was also working on both HAWC and IceCube. Her

expertise and guidance was critical in developing the ambitious research of this dissertation. It’s

also been inspiring and a source of community to grow in our careers in parallel. Thanks a ton for

the mentorship, and supporting my many questions.

Jim Linnemann, faculty at MSU in HAWC and rigorous physics mentor. Jim has been a role

model of scientific rigor who has guided my physics skill set since arriving at MSU. He is among

the most exposed to my research and has similarly enabled my ambition. It’s been a pleasure to

work with Jim and I thank you tremendously for your input to my research.

Thank you to Kendall Mahn, who saw my potential from the moment of application to MSU.

iii

You cultivated the fight in me that’s been exercised in leadership positions at MSU.

Thank you to the remaining members of my thesis committee: Claudio Kopper, Brian O’Shae,

and Filomena Nunes. You have been a great committee providing constructive feedback on this

dissertation.

Thank you to the MSU postdocs Hans Niederhausen, Brian Clark, and Rob Halliday who

provided substantial intellectual training and were great people to work with.

Thank you to the Los Alamos HAWC cast, Andrea Albert, Brenda Dingus, Kelly Malone and

Mora Durocher for holding space for me and creating a second research home. My experience at

LANL was invaluable and left a positive, indelible mark on my experience as a grad student.

Thank you to grad students, Allison Peisker, Joe Lundeen, Jessie Micallef, and Minjin Jeong

who showed me the ropes on research with HAWC and IceCube. You provided a strong foundation

for me to build on with my research.

My Family

Familia is core principle and social support within the Mexican culture, and I am no exception.

Thank you to my mom, and brothers, Miguel and Chris, especially who have kept me grounded

through my Ph.D. and came to my rescue at my lowest points in it. Thank you to my extended family

in Texas and Mexico who have always had a door open for me and supported me as I redefined who

I am.

We came from simple means, lives, and beginnings. I hope that this effort and title inspires

those within the family of the great things we are capable of.

My Friends

Thank you to the friends I made at Los Alamos and being the first to accept me as my authentic

self. You were among the first to show me to embrace myself. Thank you specifically to Eames

Bennet and Jeremy Monroe who opened their homes to me and did not ask for repayment. A place

to stay was invaluable for enabling my visits to LANL.

Thank you to the climbing belaytionships that are the backbone to my sanity through the

COVID-19 pandemic and grad school. David Shane, Jon Fleck, and Alex Harnisch, thank y’all for

iv

belaying me on so many routes and motivating me to push hard. The grit and adventures we’ve had

are cherished memories.

Thank you to Tristan Wells. It’s crazy that I met someone so chill and easy to get along with

by accident. I’m so happy to have grown in my Ph.D. with you and would not have chosen another

roommate. Thank you for being along for the ride and being a part of my life for these six years.

Thank you to Jenny and her late child Kaydince. I only got to know you for a short amount of

time, but you made a big splash. I wish the best for you and that you are successful in your pursuit

to cure the blind.

Thank you to my partner Corey Snyder. You came at the best time to see me under the most

stress and loved me nonetheless. Your support and love propped me up through the roughest

moment of my dissertation. Quite literally, this work would not have been completed without your

support. Thank you for your kindness, motivation, love, laughs, safety, adventure, and thoughtful

conversation.

Institutions

Thank you to the National Science Foundation for funding me for three years of my Ph.D.

Thank you to MSU for funding another two through their fellowship program. Thank you to GEM

for their fellowship program in partnership with LANL. Thank you to LANL for always leaving a

desk for me after my first summer in 2019. Thank you to HAWC and IceCube for providing me

with the resources and expertise to thrive.

v

TABLE OF CONTENTS

CHAPTER 1

. .

1
DARK MATTER IN THE COSMOS . . . . . . . . . . . . . . . . . . .
1
1.1
.
Introduction . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Dark Matter Basics .
1.3 Evidence for Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.4 Searching for Dark Matter: Particle DM . . . . . . . . . . . . . . . . . . . . . 10
1.5 Sources for Indirect Dark Matter Searches . . . . . . . . . . . . . . . . . . . . 17
. . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.6 Multi-Messenger Dark Matter

CHAPTER 2

HIGH ALTITUDE WATER CHERENKOV (HAWC) OBSERVATORY . 22
. 22
2.1 The Detector
2.2 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3 Background Estimation: Direct Integration . . . . . . . . . . . . . . . . . . . . 36

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

.

.

.

CHAPTER 3

.
.

.
.

.
.

.
.

GLORY DUCK: MULTI-WAVELENGTH SEARCH FOR DARK MAT-
TER ANNIHILATION TOWARDS DWARF SPHEROIDAL GALAX-
IES .

.
Introduction .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 37
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1
. 39
3.2 Dataset and Background . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 41
3.3 Analysis . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Likelihood Methods .
3.5 HAWC Results
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.6 Glory Duck Combined Results . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.7 HAWC Systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
𝐽-factor distributions
3.8
. . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.9 Discussion and Conclusions

. .

. .

.

.

.

CHAPTER 4

.

.

.

Introduction .

MULTITHREADING HAWC ANALYSES FOR DARK MATTER
SEARCHES .
.

. 73
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1
. 73
4.2 Dataset and Background . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 75
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Analysis . .
4.4 Likelihood Methods .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.5 Computational Methods: Multithreading . . . . . . . . . . . . . . . . . . . . . 79
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.6 Analysis Results .
4.7 Systematics .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
. .
4.8 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

.
. .

. .

. .

CHAPTER 5

ICECUBE NEUTRINO OBSERVATORY . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 93
5.1 The Detector
. 94
5.2 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
. 104
5.3 Background . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .

. .

.

CHAPTER 6

HEAVY DARK MATTER ANNIHILATION SEARCH WITH ICE-
CUBE’S NORTH SKY TRACK DATA . . . . . . . . . . . . . . . . . . 106

vi

.

.

.

.

.

.

. .

Introduction . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.1
. 106
6.2 Dataset and Background . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
. 108
6.3 Analysis .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
6.4 Likelihood Methods .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.5 Background Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.6 Signal Recovery per Channel
. . . . . . . . . . . . . . . . . . . . . . . . . . . 118
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
.
6.7 Sensitivities .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
.
6.8 Systematics .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.9 Conclusions . .

.
.
.
.
. .

.
.
.

CHAPTER 7

7.1 Future Directions: Multi-Messenger Dark Matter Search . . . . . . . . . . .
7.2 Conclusions . .

NU DUCK: CONCLUSIONS AND FUTURE DIRECTIONS . . . . . . 153
. 153
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

. .

.

BIBLIOGRAPHY . .

. .

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

APPENDIX A

MULTI-EXPERIMENT SUPPLEMENTARY FIGURES . . . . . . . . 170

APPENDIX B

REMAINING SPECTRAL MODELS . . . . . . . . . . . . . . . . .

. 171

APPENDIX C

MPU_ANALYSIS.PY . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

APPENDIX D

COMPARISON WITH GLORY DUCK . . . . . . . . . . . . . . . .

. 181

APPENDIX E

DOCKER IMAGE FOR OSCILLATING NEUTRINO SPECTRA . . . 184

APPENDIX F

SPLINE FITTING STATUSES . . . . . . . . . . . . . . . . . . . . . . 187

APPENDIX G

NEUTRINO COMPOSITE SPECTRA . . . . . . . . . . . . . . . . . . 188

APPENDIX H

SEGUE 1 AND URSA MAJOR II SIGNAL RECOVERY . . . . . . . . 189

APPENDIX I

SIGNAL NEUTRINO SENSITIVITIES . . . . . . . . . . . . . . . .

. 195

vii

CHAPTER 1

DARK MATTER IN THE COSMOS

1.1

Introduction

The dark matter problem can be summarized in part by the following thought experiment.

Let us say you are the teacher for an elementary school classroom. You take them on a field

trip to your local science museum and among the exhibits is one for mass and weight. The exhibit

has a gigantic scale, and you come up with a fun problem for your class.

You ask your class, "What is the total weight of the classroom? Give your best estimation to

me in 30 minutes, and then we’ll check your guess on the scale. If your guess is within 10% of the

right answer, we will stop for ice cream on the way back."

The students are ecstatic to hear this, and they get to work. The solution is some variation of

the following strategy. The students should give each other their weight or best guess if they do

not know. Then, all they need to do is add each student’s weight and get a grand total for the class.

The measurement on the giant scale should show the true weight of the class. When comparing

the measured weight to your estimation, multiply the measurement by 1.0 ± 0.1 to get the ±10%

tolerances for your estimation.

Two of your students, Sandra and Mario, return to you with a solution.

They say, "We weren’t sure of everyone’s weight. We used 65 lbs for the people we didn’t know

and added everyone who does know. There are 30 of us, and we got 2,000 lbs! That’s a ton!"

You estimated 1,900 lbs. assuming the average weight of a student in your class was 60 lbs. So,

you are pleased with Sandra’s and Mario’s answer. You instruct your students to all gather on the

giant scale and read off the weight together. To all your surprise, the scale reads 10,000 lbs! 10,000,

in technical terms, is significantly more than a 10% error from 2,000. In fact, it is approximately 5

times more massive than either your or your students’ estimates. You think to yourself and conclude

there must be something wrong with the scale. You ask an employee to check the scale and verify it

is well calibrated. They confirm that the scale is in working order. You weigh a couple of students

individually to assess for yourself that the scale is well calibrated. Sandra weighs 59 lbs, and Mario

1

weighs 62 lbs, typical weights for their age. You then weigh each student individually and see that

their weights individually do not deviate greatly from 60 lbs. So, where does all the extra weight

come from? This dilemma is what we are faced with when weighing the cosmos.

This thought experiment serves as an analogy to the Dark Matter problem. The important

substitution to make however is to replace the students with stars and the classroom with a galaxy,

say the Milky Way. Individually the mass of stars is well measured and defined with the Sun as our

nearest test case. However, when we set out to measure the mass of a collection of stars as large as

galaxies, our well-motivated estimation is wildly incorrect. There simply is no way to account for

this discrepancy except without some unseen, or dark, contribution to mass and matter in galaxies.

I set out in my thesis to narrow the possibilities of what this Dark Matter could be.

1.2 Dark Matter Basics

Presently, a compelling theory of cosmology that includes Dark Matter (DM) in order to explain

a variety of observations is Λ Cold Dark Matter, or ΛCDM. I present the evidence supporting

ΛCDM in Section 1.3 yet discuss the conclusions of the ΛCDM model here. According to

ΛCDM fits to observations on the Cosmic Microwave Background (CMB), DM is 26.8% of the

universe’s current energy budget. Baryonic matter, stuff like atoms, gas, and stars, contributes to

4.9% of the universe’s current energy budget [1, 2, 3].

DM is dark; it does not interact readily with light at any wavelength. DM also does not interact

noticeably with the other standard model forces (Strong and Weak) at a rate that is readily observed

[3]. DM is cold, which is to say that the average velocity of DM is below relativistic speeds [1].

‘Hot’ DM would not likely manifest the dense structures we observe like galaxies, and instead

would produce much more diffuse galaxies than what is observed [3, 1]. DM is old; it played a

critical role in the formation of the universe and the structures within it [1, 2].

Observations of DM have so far been only gravitational. The parameter space available to what

DM could be is therefore extremely broad. The broad DM parameter space is iteratively tested in

DM searches by supposing a hypothesis that has not yet been ruled out and performing observations

to test them. When the observations yield a null result, the parameter space is constrained further.

2

I present some approaches for DM searches in Section 1.4.

1.3 Evidence for Dark Matter

Dark Matter (DM) has been a looming problem in physics for almost 100 years. Anomalies

have been observed by astrophysicists in galactic dynamics as early as 1933 when Fritz Zwicky

noticed unusually large velocity dispersion in the Coma cluster. Zwicky’s measurement was the

first recorded to use the Virial theorem to measure the mass fraction of visible and invisible matter

in celestial bodies [4]. From Zwicky in [5], "If this would be confirmed, we would get the surprising

result that dark matter is present in much greater amount than luminous matter." Zwicky’s and

others’ observation did not instigate a crisis in astrophysics because the measurements did not

entirely conflict with their understanding of galaxies [4].

In 1978, Rubin, Ford, and Norbert

measured rotation curves for ten spiral galaxies [6]. Rubin et al.’s 1978 publication presented a

major challenge to the conventional understanding of galaxies that could no longer be dismissed by

measurement uncertainties. Evidence has been mounting ever since for this exotic form of matter.

The following subsections provide three compelling pieces of evidence in support of the existence

of DM.

1.3.1 First Clues: Stellar Velocities

Zwicky, and later Rubin, measured the stellar velocities of various galaxies to estimate their

virial mass. The Virial Theorem upon which these observations are interpreted is written as

2𝑇 + 𝑉 = 0.

(1.1)

Where T is the kinetic energy and V is the potential energy in a self-gravitating system. The classical

Newton’s law of gravity from stars and gas was used for the gravitational potential modeled in the

observed galaxies:

𝑉 = −

∑︁

∑︁

1
2

𝑚𝑖𝑚 𝑗
𝑟𝑖 𝑗

.

(1.2)

𝑖
Here 𝑚𝑖, 𝑗 are the ith or jth masses of the 𝑖th or 𝑗th star in the cluster. 𝑟𝑖 𝑗 is the distance between

𝑗≠1

these two stars. Zwicky et al. measured just apparent velocities of stars apparent from optical

observations which provides a measure for 𝑇 [5]. Rubin et al. added to this by measuring the

3

Figure 1.1 Stellar velocity curve fit to NGC 6503 from [7]. Dashed line is the contribution from
visible matter. Dotted curves are from gas. Dash-dot curves are from dark matter (DM). Solid line
is the composite contribution from all matter and DM sources. Data are indicated with bold dots
with error bars. Data agree strongly with a matter + DM composite prediction.

velocity of the hydrogen gas via the 21 cm emission line of Hydrogen [6]. The velocities of the

stars and gas are used to infer the total mass of galaxies and galaxy clusters via Equation (1.1).

An inferred mass is obtained from the luminosity of the selected sources. The two inferences are

compared to each other as a luminosity (𝐿) to virial mass (𝑀) ratio which typically yielded [1]

𝑀
𝐿

∼ 400

𝑀⊙
𝐿⊙

(1.3)

with 𝑀⊙ and 𝐿⊙ referring to stellar mass and stellar luminosity, respectively. These observations

clearly indicate a discrepancy in mass from apparent light and mass inferred from the velocity of

stars and gas.

Rubin et al. [6] demonstrated that the discrepancy was unlikely to be an underestimation of

the mass of the stars and gas. The inferred "dark" mass was up to 5 times more than the luminous

mass. This dark mass also needed to extend well beyond the extent of the luminous matter.

Figure 1.1 features one of many rotation curves plotted from the stellar velocities within galaxies.

The measured rotation curves mostly feature a flattening of velocities at larder radii which is not

4

expected if the gravity was only coming from luminous matter. The extension of the flat velocity

region also indicates that the DM is distributed far from the center of the galaxy. Modern velocity

measurements include significantly larger objects, galactic clusters, and smaller objects, dwarf

galaxies. Yet, measurements along this regime are leveraging the Virial theorem with Newtonian

potential energies. However, we know Newtonian gravity is not a comprehensive description of

gravity. New observational techniques have been developed since 1978, and those are discussed in

the following sections.

1.3.2 Evidence for Dark Matter: Gravitational Lensing

Modern evidence for dark matter comes from new avenues beyond stellar velocities. Gravita-

tional lensing from DM is one of these channels from general relativity. General relativity predicts

aberrations in light caused by massive objects. In recent decades we have been able to measure

the lensing effects from compact objects and DM halos. Figure 1.2 shows how different massive

objects change the final image of a faraway galaxy resulting from gravitational lensing.

Gravitational lensing provides additional compelling evidence for DM. The observation of two

merging galactic clusters in 2006, shown in Figure 1.3, provided a compelling argument for DM

outside the Standard Model. These clusters merged recently in astrophysical time scales. Galaxies

and star cluster have mostly passed by each other as the likelihood of stars colliding within them

is low. Therefore, these massive objects will mostly track the highest mass, dark and/or baryonic,

density. Yet, the intergalactic gas is responsible for the majority of the baryonic mass in the systems

[4]. These gas bodies will not phase through so heat up and compress as they collide together.

The hot gas is located via x-ray emission from the cluster. Two observations of the clusters were

performed independently of each other.

The first was the lensing of light around the galaxies due to their gravitational influences.

When celestial bodies are large enough, the gravity they exert bends space and time itself. The

warped space-time lenses light and will deflect in an analogous way to how glass lenses will bend

light, see Figure 1.2. With a sufficient understanding of light sources behind a massive object, we

can reconstruct the contours of the gravitational lenses. The gradient of the contours shown in

5

Figure 1.2 Light from a distant galaxy is bent in unique ways depending on the distribution of
mass between the galaxy and Earth. Yellow dashed lines indicate where the light would have gone
if the matter were not present. Solid yellow is the path the light actually traverses [8]. Spherical
densities deform the light to creates a halo around the originating source. Ellipsoidal densities
will create nodes in the image. Clumpy aggregations will manifest as complex light streams and
aberrations in an image.

6

Figure 1.3 (left) Optical image of galactic cluster 1E0657-558. (right) X-ray image of the cluster
with redder meaning hotter and higher baryon density. (both) Green contours are the
reconstructed gravity contours from weak lensing. White rings are the best fit mass maxima at
68.3%, 95.5%, and 99.7% confidence. The matter maxima of the clusters are clearly separated
from x-ray maxima. [9]

Figure 1.3 then indicates how dense the matter is and where it is. In the absence of DM, it should

also map out where the majority of the mass is.

The x-ray emission is then be observed from the clusters. Since these galaxies are mostly gas

and are merging, the gas should be getting hotter. If they are merging, the x-ray emissions should

be the strongest where the gas is mostly moving through each other. Hence, X-ray emission maps

out where the gas is in the merging galaxy cluster.

The lensing and x-ray observations were done on the Bullet cluster which are featured on Fig. 1.3

[9]. The x-ray emissions do not at all align with the gravitational contours. The incongruence

in mass density and baryon density suggests that there is a lot of matter somewhere that does not

interact with light. Moreover, this DM cannot be baryonic [9]. The Bullet Cluster measurement

did not really tell us what DM is exactly, but it did give the clue that DM also does not interact with

itself very strongly. If DM did interact strongly with itself, then it would have been more aligned

with the x-ray emission [9]. There have been follow-up studies of galaxy clusters with similar

results. The Bullet Cluster and others like it provide a persuasive case against something possibly

amiss in our gravitational theories.

7

Figure 1.4 Plank CMB sky. Sky map features small variations in temperature in primordial light.
These anisotropies are used to make inferences about the universe’s energy budget and
developmental history. [10]

1.3.3 Evidence for Dark Matter: Cosmic Microwave Background

The Cosmic Microwave Background (CMB) is the primordial light from the early universe

when Hydrogen atoms formed from the combination of free electron and proton soup in the early

universe. Prior to this recombination, the universe was too hot to form atoms and was opaque

to light. The CMB is the earliest light we can observe; released when the universe was about

380,000 years old. Then we look at how the simulated universes look like compared to what we

see. Figure 1.4 is the most recent CMB image from the Plank satellite after subtracting the average

value and masking the galactic plane [10]. Redder regions indicate a slightly hotter region in the

CMB, and blue indicates colder. The intensity variations are on the order of 1 in 1000 with respect

to the average value.

The Cosmic Microwave Background shows that the universe had DM in it from an incredibly

early stage. To measure the DM, Dark Energy, and matter fractions of the universe from the CMB,

the image is analyzed into a power spectrum, which shows the amplitude of the fluctuations as a

function of spherical multipole moments (𝑙). ΛCDM provides the best fit to the power spectra

of the CMB as shown in Fig. 1.5. The CMB power spectrum is quite sensitive to the fraction

8

Figure 1.5 Observed Cosmic Microwave Background power spectrum as a function of multipole
moment from Plank observatory [10]. Blue line is the best fit model from ΛCDM. Red points and
lines are data and error, respectively.

of each energy contribution in the early universe. Low l modes are dominated by variations in

gravitational potential. Intermediate l emerge from oscillations in the photon-baryon fluid from

competing baryon pressures and gravity. High l is a damped region from the diffusion of photons

during electron-proton recombination. [1]

Figure 1.6 Predicted power spectra of CMB for different Ω𝑚 ℎ2 values for fixed baryon density
from [11]. (left) Low Ω𝑚 ℎ2 increases the prominence of first and second peaks. (middle) Ω𝑚 ℎ2 is
most similar to the observed power spectrum. The second and third peaks are similar in height.
(right) Ω𝑚 ℎ2 is large which suppresses the first peak and raises the prominence of the third peak.

The harmonics would look quite different for a universe with less DM. Figure 1.6 demonstrates

the effect Ω𝑚 ℎ2, the mass fraction, has on the expected power spectrum for fixed baryon matter

density. [11] Sweeping Ω𝑚 ℎ2 while keeping the baryon mass fraction fixed clearly shows the effect

dark matter has on the CMB power spectrum. The observations fit well with the ΛCDM model,

9

and the derived fractions are as follows. The matter fraction: Ω𝑚 = 0.3153; and the baryon

fraction: Ω𝑏 = 0.04936 [10]. Plank’s observations also provide a measure of the Hubble constant,

𝐻0. 𝐻0 especially has seen a growing tension in the past decade that continues to deepened with

observations from instruments like the James Webb Telescope [12, 13]. As Hubble tensions deepen,

we may find that perhaps ΛCDM, despite its successes, is missing some critical physics.

Overall, the Newtonian motion of stars in galaxies, weak lensing from galactic clusters, and

power spectra from primordial light form a compelling body of research in favor of dark matter.

It takes another leap of theory and experimentation to make observations of DM that are non-

gravitational in nature. In Section 1.3, the evidence for DM implies strongly that the DM is matter

and not a lost parameter in the gravitational fields between massive objects. In there was a failure in

our gravitational modeling, we would not see lensing at the strength observed by Fig. 1.3 [9] so far

from the baryons mass. Additionally, the multipole peaks corresponding to the matter fraction, see

Fig. 1.6 occur with DM as matter. The peaks would soften significantly if DM were a shortfall in

gravitational modeling. Finally, if we take one axiom: that this matter has quantum behavior, such

as being described by some Bohr wavelength and abiding by some fermion or boson statistics; then

we arrive at particle dark matter. One particle DM hypothesis is the Weakly Interacting Massive

Particle (WIMP). This DM candidate theory is discussed further in the next section and is the focus

of this thesis.

1.4 Searching for Dark Matter: Particle DM

Figure 1.7 shows the Standard Model (SM) of particle physics, that is currently the most accurate

model for the dynamics of fundamental particles like electrons and photons. The current status

of the SM does not have a viable DM candidate. When looking at the standard model, we can

immediately exclude any charged particle because charged particles interact strongly with light.

Specifically, this will rule out the following charged, fundamental particles: 𝑒, 𝜇, 𝜏, 𝑊, 𝑢, 𝑑, 𝑠, 𝑐, 𝑡, 𝑏

and their corresponding antiparticles. Recalling from Section 1.2 that DM must be long-lived and

stable over the age of the universe, we exclude all SM particles with decay half-lives at or shorter

than the age of the universe. The lifetime constraint additionally eliminates the 𝑍 and 𝐻 bosons.

10

Figure 1.7 The Standard Model (SM) of particle physics. Figure taken from [14]

Finally, the candidate DM needs to be somewhat massive. Recall from Section 1.2 that DM is cold

or not relativistic through the universe. This eliminates the remaining SM particles: 𝜈𝑒,𝜇,𝜏, 𝑔, 𝛾 as

DM candidates. Because there are no DM candidates within the SM, the DM problem strongly

hints to physics Beyond the SM (BSM).

As we are in a BSM regime, the parameter space for DM is vast. Unconstrained particle

models include large de Broglie wavelengths at macroscopic scale and is referred to as fuzzy dark

matter [15, 16]. Models also range up to very heavy models such as primordial black holes (PBH)

[17]. Beyond particle models there also exists a zoo of gravitational alternatives or corrections to

Newtonian or Einsteinian gravity [18], however these models are increasingly less favored [16].

The particle DM models considered in this thesis correspond to heavy Weakly Interacting Massive

Particles (WIMPs) whose experimental signatures are explored below [19, 16].

11

1.4.1 Shake it, Break it, Make it

Figure 1.8 Simplified Feynman diagram demonstrating the different ways DM can interact with
SM particles. The ’X’s refer to the DM particles whereas the SM refer to fundamental particles in
the SM. The large circle in the center indicates the vertex of interaction and is purposely left
vague. The colored arrows refer to different directions of time as well as their respective labels.

When considering DM that couples in some way with the SM, the interactions are roughly

demonstrated by the interactions shown in Figure 1.8. The figure is a simplified Feynman diagram

where the arrow of time represents the interaction modes of: Shake it, Break it, Make it.

Shake it refers to the direct detection of dark matter. Direct detection interactions start with

a free DM particle and a SM particle. The DM and SM particle interact via elastic or inelastic

collision and recoil away from each other. The DM remains in the dark sector and imparts some

momentum to the SM particle. The hope is that the momentum imparted onto the SM particle is

sufficiently high enough to be picked up with extremely sensitive instruments. A direct detection

experiment must wait until DM is incident on the detector. Most direct detection experiments are

therefore placed in low-background environments with inert detection media like the noble gas,

Xenon. [20]

Make it refers to the production of DM from SM initial states. The experiment starts with SM

particles that are accelerated to incredibly high energies and then collided with each other. In the

12

confluence of energy, DM hopefully emerges as a byproduct of the SM annihilation. Often it is the

collider experiments that are energetic enough to hypothetically produce DM. These experiments

include the world-wide collaborations, ATLAS and CMS at CERN, where protons collide together

at extreme energies. DM likely does not interact with the detectors and lives long enough to escape

their detection apparatus. This means any DM production experiment searches for an excess of

events with missing momentum or energy in the events. An example event with missing transverse

momentum is shown in Figure 1.9. The missing momentum with no particle tracks implies a

weakly interacting particle carried the energy out of the detector. However, there are other neutral

particles in the SM, like neutrons or neutrinos, so any analysis has to account for SM signatures of

missing momentum. [21]

Figure 1.9 A single jet event in the ATLAS detector from 2017 [22]. Total transverse momentum
was observed to be 1.9 TeV where it should be 0. Missing transverse momentum is inferred to be
opposite the observed transverse momentum in order to preserve overall momentum in the event.

13

1.4.2 Break it: Standard Model Signatures of Dark Matter through Indirect Searches

Break it refers to the creation of SM particles from the dark sector, and it is the primary focus

of this thesis. The interaction begins with DM in the dark sector. The hypothesis is that this

DM will either annihilate with itself or decay and produce SM byproducts. This method is often

referred to as the Indirect Detection of DM because we have no lab to directly control or manipulate

the DM. Therefore, most indirect DM searches are performed using observations of known DM

densities among astrophysical sources. A strength is that we have the whole of the universe and its

13.6-billion-year lifespan to use as a detector and particle accelerator. Additionally, locations of

dark matter are well cataloged since it was astrophysical observations that presented the problem

of DM in the first place.

Figure 1.10 More detailed pseudo-Feynman diagram of particle cascade from dark matter
annihilation into 2 quarks. The quarks hadronize down to stable particles like photons (𝛾) or the
anti-proton (𝑝−). Diagram pulled from ICRC 2021 presentation on DM annihilation search [23].

However, anything can happen in the universe. There are many difficult to deconvolve back-

grounds when searching for DM. One prominent example is the galactic center. We know the

galactic center has a large DM content because of stellar kinematics in our Milky Way and DM halo

simulations. Yet, any signal from the galactic center is challenging to parse apart from the extreme

environment of our supermassive black hole, unresolved sources, and diffuse emission from the

14

interstellar medium [24]. Despite the challenges, any DM model that yields evidence in the other

two observation methods, Shake it or Make it must be corroborated with indirect observations of

the known DM sources. Without corroborating evidence, DM observation in the lab is hard-pressed

to demonstrate that it is the model contributing to the DM seen at the universal scale.

In the case of Weakly Interacting Massive Particle (WIMP) DM, signals are described in terms

of primary SM particles produced from DM decay or annihilation. The SM initial state particles

are then simulated down to stable final states such as the 𝛾, 𝜈, 𝑝, or 𝑒 which can traverse galactic

lengths to reach the Earth.

Figure 1.10 shows the quagmire of SM particles that emerges from SM initial states that are not

stable [23]. There are many SM particles with varying energies that can be produced in such an

interaction. For any arbitrary DM source and stable SM particle, the SM flux from DM annihilating

to a neutral particle in the SM, 𝜙, from a region in the sky is described by the following.

𝑑Φ𝜙
𝑑𝐸𝜙

=

⟨𝜎v⟩
8𝜋𝑚2
𝜒

𝑑𝑁𝜙
𝑑𝐸𝜙

×

∫

source

𝑑Ω

∫

𝑙.𝑜.𝑠

𝜌2
𝜒𝑑𝑙 (𝑟, 𝜃′)

(1.4)

In Eq. (1.4), ⟨𝜎v⟩ is the velocity-weighted annihilation cross-section of DM to the SM. 𝑚 𝜒 refers
to the mass of DM, noted with Greek letter 𝜒. 𝑑𝑁 𝜙
𝑑𝐸 𝜙
energy. Example spectra are provided in Fig. 1.11 for the 𝜒 𝜒 → 𝑏𝑏 → 𝛾 final state. The integrated

is the N particle flux weighted by the particle

terms are performed over the solid angle, 𝑑Ω, and line of sight, l.o.s. 𝜌 is the density of DM for

a location (𝑟, 𝜃′) in the sky. The terms left of the ’×’ are often referred to as the particle physics

component. The terms on the right are referred to as the astrophysical component. For decaying

DM, the equation changes to. . .

𝑑Φ𝜙
𝑑𝐸𝜙

=

1
4𝜋𝜏𝑚 𝜒

𝑑𝑁𝜙
𝑑𝐸𝜙

×

∫

source

𝑑Ω

∫

𝑙.𝑜.𝑠

𝜌 𝜒𝑑𝑙 (𝑟, 𝜃′)

(1.5)

In Equation (1.5), 𝜏 is the decay lifetime of the DM. Just as in Eq. (1.4), the left and right terms are

the particle physics and the astrophysical components respectively. The integrated astrophysical

component of Eq. (3.1) is often called the J-Factor. Whereas the integrated astrophysical component

of Eq. (1.5) is often called the D-Factor.

15

Figure 1.11 Dark Matter (DM) decay spectrum for 𝑏 ¯𝑏 initial state and 𝛾 final state. Redder spectra
are for larger DM masses. Bluer spectra are light DM masses. 𝑥 is a unitless factor defined as the
ratio of the mass of DM, 𝑚 𝜒, and the final state particle energy 𝐸𝛾. Figure from [25].

The DM annihilation branching ratios in the SM are not known, so it is usually assumed that

DM annihilates 100% of the time into a given SM particle/anti-particle pair. Transformations on

the best fit physics parameters in an indirect dark matter search can be done as shown by [26, 27].

Any transformation will come with some assumptions intrinsic in the selected model. Therefore,

indirect limits are show with 100% BRs as a generic and useful limit that can be recomputed

for more specific DM models. For an analysis with more specific BRs, the 𝑑𝑁/𝑑𝐸 would be a

summation of the fractional components. For example, a model with

𝜒 𝜒 → 𝑏 ¯𝑏

50%

→ 𝜏+𝜏−

50%

(1.6)

will change Eq. (1.4) and Eq. (1.5) only by changing the 𝑑𝑁𝜙/𝑑𝐸𝜙 term to (0.5 × (𝑑𝑁𝜙/𝑑𝐸𝜙)𝑏 ¯𝑏 +

0.5 × (𝑑𝑁𝜙/𝑑𝐸𝜙)𝜏+𝜏− ). For most composite models, the limits will be dominated by the hardest

spectra as these are typically most distinct from the backgrounds.

When a DM annihilation or decay produces one of the long-lived, neutral SM particles (neutrinos

16

Figure 1.12 Different dark matter density profiles compared. Each model accommodates different
assumptions about how a galaxy formed. The Navaro-Frenko-White [28] profile is among the
more popular models used for dwarf galaxies. Some models produce exceptionally large densities
at small radii (𝑟) [29].

or photons), the particle can be traced back to the DM source. For DM above GeV energies, there

are very few SM processes that can produce particles with such a high energy. Seeing such a signal

would almost certainly be an indication of the presence of dark matter. Fortunately, the universe

provides us with the largest volume and lifetime ever for a particle physics experiment.

1.5 Sources for Indirect Dark Matter Searches

The first detection of DM relied on optical observations. Since then, we have developed new

techniques to find DM dense regions. As described in Section 1.3.1, many DM dense regions were

discovered through observing galactic rotation curves. Our Milky Way galaxy is among the known

DM dense regions discovered, and it is the largest nearby DM dense region to look at. Additionally,

the DM halo surrounding the Milky Way is clumpy [24]. There are regions in the DM halo of

the Milky Way that have more DM than others that have captured gas over time. These sub-halos

were dense enough to collapse gas and form stars. These apparent sub galaxies are known as dwarf

spheroidal galaxies (dSphs) and are the main sources studied in this thesis. Each source type comes

with different trade-offs. Galactic Center studies will be very sensitive to the assumed distribution

17

of DM. The central DM density can vary substantially as demonstrated in Fig. 1.12. At distances

close to the center of the galaxy, or small r, the differences in DM densities can be 3-4 orders of

magnitude. Searches toward the galactic center will therefore be quite sensitive to the assumed DM

distribution.

Searches dSphs suffer less from uncertainties in the DM density than the galactic center studies.

This is mostly from their diminutive size being smaller than the angular resolution of most high

energy astrophysical observatories [24]. The DM content of dSphs are typically determined with the

Virial theorem, Eq. (1.1), and are usually mostly DM [24] in mass. DSph’s tend to be ideal sources

to look at for DM searches. Their environments are quiet with little astrophysical background.

Unlike the galactic center, the most energetic components of dSph’s are the stars within them versus

a violent accretion disc around a black hole. All this together means that dSph’s are among the best

sources to look at for indirect DM searches. dSph’s are the targets of focus for this thesis.

1.6 Multi-Messenger Dark Matter

Astrophysics entered a new phase in the past few decades that leverages our increasing sensitivity

to SM channels and general relativity (GR). Up until the 21st century, astrophysical observations

were performed with photons (𝛾) only. Astrophysics with this ’messenger’ is fairly mature now.

Novel observations of the universe have since only adjusted the sensitivity of the wavelength of light

that is observed except at MeV energies. Gems like the CMB [10], and more have ultimately been

observations of different wavelengths of light. Multi-messenger astrophysics proposes using other

SM particles such the 𝑝+/−, neutrinos (𝜈), or gravitational waves predicted by general relativity.

Figure 1.13 provides a graphic of what kinds of paths stable particles in SM will take on their way

to Earth.

The experiment LIGO had a revolutionary discovery in 2016 with the first detection of a binary

black hole merger [31]. This opened the collective imagination to observing the universe through

gravitational waves. There has also been a surge of interest in the neutrino (𝜈) sector. The IceCube

Neutrino Observatory demonstrated that we are sensitive to neutrinos in regions that correlate with

significant photon emission like the galactic plane [32]. Neutrinos, like gravitational waves and

18

Figure 1.13 Stable SM Particles from astrophysical sources are deflected in different ways because
of their intrinsic properties. Charged particles like cosmic rays (𝑝) are charged and will be bent by
magnetic fields as they traverse the universe. Neutrinos (𝜈) and photons (𝛾) are neutral and can
traverse almost unimpeded. Photons however can be occluded by dust and other massive objects.
Figure from [30].

light, travel mostly unimpeded from their source to our observatories. This makes pointing to the

originating source of these messengers much easier than it is for cosmic rays which are deflected

from their source by magnetic fields.

The IceCube collaboration recently published a groundbreaking result of the Milky Way in

neutrinos. The recent result from IceCube, shown in Figure 1.14, proves that we can make

observations under different messenger regimes. The top two panels show the appearance of the

galactic plane to different wavelengths of light. Some sources are more apparent in some panels,

while others are not. This new channel is powerful because neutrinos are readily able to penetrate

through gas and dust in the Milky Way. This new image also refines our understanding of how high

energy particles are produced. For example, the fit to IceCube data prefers neutrino production

19

Earthair showerGamma raysThey point to their sources, but they can be absorbed and are created by multiple emission mechanisms.NeutrinosThey are weak, neutral  particles that point to their sources and carry information from deep within their origins.Cosmic raysThey are charged particles and are deflected by magnetic fields.AGNs, SNRs, GRBs...black holesνννppγγγννFigure 1.14 The Milky Way Galaxy in photons (𝛾) and neutrinos (𝜈) [32]. The Galactic center is
at l = 0°and is the brightest region in all panels. (top) An Optical color image of the Milky Way
galaxy seen from Earth. Clouds of gas and dust obscure some light from stars. (2nd down)
Integrated flux of 𝛾-rays observed by the Fermi-LAT telescope [33]. (middle) Expected neutrino
emission that corresponds with Fermi-LAT observations. (2nd up) Expected neutrino emission
profile after considering detector systematics of IceCube. (bottom) Observed neutrino emission
from region of the galactic plane. Substantial neutrino emission was detected.

from the decay of 𝜋0 [32].

Exposing our observations to more cosmic messengers greatly increases our sensitivity to

rare processes.

In the case of DM, Figure 1.15, there are many SM particles produced in DM

annihilation. Among the final state fluxes are gammas and neutrinos. Charged particles are also

produced however they would not likely make it to Earth since they will be deflected by magnetic

fields between the source and Earth. This means observatories that can see the neutral messengers

are especially good for DM searches and for combining data for a multi-messenger DM search.

20

Figure 1.15 Dark Matter annihilation spectra for different final state particles and standard model
annihilation channels [34]. Photons, 𝛾, (red), electrons, 𝑒±, (green), protons, ¯𝑝, (blue), neutrinos,
𝜈 (black).

21

CHAPTER 2

HIGH ALTITUDE WATER CHERENKOV (HAWC) OBSERVATORY

2.1 The Detector

Figure 2.1 Photo of the HAWC detector that I took on May 17, 2023. Main array is centered in the
photo and comprised of the larger tanks. Outriggers are the smaller tanks around the main array.

The High Altitude Water Cherenkov (HAWC) Observatory is a specialized instrument designed

for the observation of high energy gamma-rays and cosmic rays [35]. Located on the Sierra

Negra volcano in Mexico, HAWC observes gamma rays and cosmic rays in the energy range of

approximately 100 GeV to 100’s of TeV. At an elevation of 4,100 meters, it monitors about two-

thirds of the sky every day with an uptime above 90%. This capability is essential for studying

high-energy astrophysical phenomena.

HAWC consists of 300 water Cherenkov detectors (WCDs) spread over 22,000 𝑚2. Each main

array detector is filled with purified water and equipped with four, upward-facing photomultiplier

tubes (PMTs). See Fig. 2.4 for a schematic of WCDs. These PMTs detect Cherenkov radiation from

charged particles passing through the tanks. These charged particles are generated when a high

energy gamma or cosmic ray collides with gas in the atmosphere to create a charged particle shower,

22

Figure 2.2 Geometry of Cherenkov radiation. This occurs when a charged particle traverses a
medium faster than the speed of light within the medium. The particle, red arrow, when traversing
through water, will create an optical shockwave that emits blue light. The angle of the Cherenkov
cone will depend on the speed of the particle (𝛽𝑐) and the index of refraction (𝑛) in the media.
Figure from [36].

as shown in Fig. 2.3. Cherenkov radiation occurs when a charged particle traverse a medium faster

than the speed of light withing the medium. An electromagnetic shockwave is formed, akin to an

optic boom, that corresponds with the velocity of the particle, see Fig. 2.2.

The observatory includes a separate tank configuration which are referred to as the outriggers.

They are a secondary array of 345 smaller WCD’s. Surrounding the main array, each outrigger

tank measures 1.55 meters in diameter and height and contain a single upward-facing 8-inch PMT.

This add-on increases the instrumented footprint fourfold. The outriggers are meant to improve

the reconstruction of showers extending beyond the main array, especially for events above 10

TeV. However, at the time of writing this thesis, the outriggers have not been fully integrated into

HAWC’s reconstruction software.

2.1.1 Construction and Hardware

Each main array WCD, see Fig. 2.4, is a cylindrical tank with dimensions of 7.3 m in diameter

and 5.4 m in height and filled with 180,000 L of water [35]. The metal shell of these tanks is

made from corrugated, galvanized steel panels bolted together. The interior of each tank is lined

with a black, low-density polyethylene bladder, designed to be impermeable to external light and to

23

Figure 2.3 A particle physics illustration of high energy particle showers. Left shower is an
electromagnetic shower from a high energy gamma-ray. Most particles in the shower will be a
combination of photons and charged leptons, in this case electrons and positrons (𝑒±). Right
figure shows a cosmic ray particle shower. The cosmic ray will produce many more types of
particles including pions (𝜋), neutrinos (𝜈), and other charged leptons. Figured pulled from [37].

Figure 2.4 The WCDs. Left image features several WCDs looking from within the main array of
HAWC. Right image shows a schematic of a WCD pulled from [35].

24

Figure 2.5 Overview of HAWC control and data electronics. The LoToT and HiToT threshold
signals are discussed in Section 2.1.2. Figure from [35]

prevent reflection of Cherenkov light within the tank. This bladder is approximately 0.4 mm thick of

low-density polyethylene. To further minimize light penetration, a black agricultural foil covers the

bladder. The ground and walls inside the tank are protected with felt and sand to safeguard against

punctures. The tanks are filled 4.5 m deep of purified water, achieving a photon attenuation length

for Cherenkov photons that exceeds the tank’s dimensions [35]. This purification level ensures the

optimal detection environment for the photons generated by traversing charged particles.

At the base of each tank, four photomultiplier tubes (PMTs) are installed to detect the Cherenkov

radiation emitted by charged particles in water. Three 8-inch diameter PMTs surround a larger 10-

inch PMT from Hamamatsu [38]. The variation in PMT response is carefully accounted for in event

reconstruction algorithms. Signals from the PMTs traverse 610 ft cables to the counting house,

where they are processed by Front-End Boards (FEBs), see Figs. 2.5 and 2.6. These FEBs, along

with Time to Digital Converters (TDCs), digitize the signals and manage the high voltage supply

to the PMTs.

25

Figure 2.6 Schematic of data flow in HAWC data acquisition and online processing system. Pulled
from [39].

Figure 2.7 How HAWC FEB initially processes analog PMT signals. Signals are split through an
amplifier and discriminator circuit. Each path is designated for either the HIGH or LOW threshold
for the signal. The 2-edge event corresponds to LOW, while the 4 edge corresponds to HIGH.
Figure from [39].

2.1.2 Data Acquisition and Signal Processing

The HAWC data acquisition (DAQ) and signal processing systems convert the physical detection

of particles into analyzable data. This process involves a series of steps from initial signal detection

by PMTs to digital conversion and preliminary analysis, see Figs. 2.6 and 2.7.

Once the signal from the PMTs arrive at the counting house, they enter the Front-End Boards

26

(FEBs). The FEBs are responsible for the initial processing of these signals, which includes

amplification and integration [40]. Each PMT signal is compared against preset LOW/HIGH

voltage thresholds in the FEBs, see Fig. 2.7, identifying signals that correspond to about 1/4 and

4 photoelectrons, respectively. This differentiation allows the system to gauge the strength of

the detected Cherenkov radiation. The processed signals are then digitized by Time to Digital

Converters (TDCs). These converters measure the time over threshold (ToT) for each signal, a

parameter that reflects both the duration and amplitude of the signal. This digitization facilitates

reconstruction of the original event for translating the physical interactions within the detectors into

data [35, 39, 40].

Synchronization across the HAWC observatory is maintained by a central GPS Timing and

Control (GTC) system, which achieves a timing resolution of 98 ps. This high-resolution timing

is vital for accurately reconstructing the timing and location of air showers initiated by cosmic

and gamma rays. The GTC system ensures that all components of the DAQ operate in unison to

preserve the temporal integrity of the detected events [35, 41].

Once digitized, the data are transferred to an online event reconstruction system. This system

runs the Reconstruction Client, which utilizes the raw PMT data to reconstruct the characteristics

of the air showers, such as their direction and energy [39]. The capacity for real-time analysis

allows HAWC to promptly respond to astrophysical phenomena like Gamma Ray Bursts (GRBs)

and to participate in multi-messenger astronomy by following up on alerts from other observatories.

This real-time processing system is designed to handle high data throughput, using ZeroMQ [42]

for efficient data transfer between software components. Analysis Clients perform specific online

analyses that require immediate data, including monitoring for GRBs, solar flare activity, and

participation in global efforts to track gravitational waves and neutrinos [35].

The DAQ system is overseen by an Experiment Control system and crew that manage the

operational aspects of data collection. This includes initiating and terminating data collection

runs and monitoring the experiment for errors. In the event of a system crash, often caused by

environmental factors such as lightning, the Experiment Control system is designed to automatically

27

restart the experiment and minimize downtime [35, 39].

2.2 Event Reconstruction

Event reconstruction at the HAWC Observatory is a critical procedure that converts the raw data

from the observatory’s WCDs into a coherent framework for understanding cosmic and gamma-

ray events. This process includes several distinct steps. Core Fitting determines the geometric

center of the air shower on the detector plane. Angle Reconstruction assesses the trajectory of the

incoming particle, revealing its origin in the sky. Energy Estimation is performed using both f -hit

and Neural Network (NN) methods to quantify the energy of the detected events. Gamma/Hadron

discrimination differentiates between gamma-ray and hadronic cosmic ray initiated showers, a

vital step for astrophysical interpretations. Each of these steps is described in more details in the

following sections.

2.2.1 Core Fitting

Figure 2.8 A particle shower incident on WCDs. Secondary particles of an air shower travel in a
cone centered on primary incident particle. Reconstruction of the initial angle is possible with
arrival time of hits in PMTs inside WCDs. Figure from [43].

In the study of air showers, accurately determining the location of the air shower core on the

28

Figure 2.9 Charge deposition in each PMT for a reconstructed gamma-ray event. WCDs are
outlined in black surrounding the 4 smaller circles that represent PMTs. The color scale indicates
the charge deposition in each PMT. The best shower core fit from Super Fast Core Fit (SFCF) is
noted with a red star in the center of the dashed circle [44].

ground is crucial for reconstructing the direction of the originating primary particle. An illustration

of this can be seen in a HAWC event plot, Figs. 2.8 and 2.12, where the lateral charge distribution

across the array is displayed. The core is identified and marked with a red star in Fig. 2.8,

reconstructed using a predetermined functional form, Eq. (2.1). We model the signal, 𝑆𝑖, from the

ith PMT by following the equation

𝑆𝑖 = 𝑆( 𝐴, ˜𝑥, ˜𝑥𝑖) = 𝐴

(cid:18) 1
2𝜋𝜎2

𝑒− | −→𝑥 𝑖 −−→𝑥 |

2
2𝜎2 +

𝑁
(0.5 + |−→𝑥 𝑖 − −→𝑥 |/𝑅𝑚)3

(cid:19)

(2.1)

In this model, ˜𝑥 represents the core location and ˜𝑥𝑖 is the position of the ith PMT. 𝑅𝑚 stands for

the Molière radius, which is approximately 120 meters at the altitude of HAWC. 𝜎 is the standard

deviation of the Gaussian distribution. 𝑁 is the normalization factor for the tail of the distribution.

The equation incorporates fixed values of 𝜎 = 10 m and 𝑁 = 5.10−5. This leaves the core location

and overall amplitude 𝐴 as the free parameters to be determined during fitting.

29

The chosen functional form for the Super Fast Core Fit (SFCF) algorithm is a simplified version

of a modified Nishimura-Kamata-Greisen (NKG) function [45], selected for its computational

efficiency which is essential for rapid fitting of air shower cores. The SFCF form allows numerical

minimization to converge more quickly due to the function’s simplicity, the analytical computation

of its derivatives, and the absence of a pole at the core location [44]. Figure 2.9 provides a

visualization of a recorded event, with the plot depicting the charge recorded by each PMT as a

function of the distance to the reconstructed shower core. Through the application of the SFCF,

core locations can be identified with a median error of approximately 2 m for large events and about

4 m for smaller ones, assuming the gamma-ray event core impacts directly upon the HAWC detector

array [44]. It is noted that as the core’s distance from the main array increases, the precision in

locating the core diminishes [44], highlighting the importance of proximity in the accuracy of core

reconstruction.

2.2.2 Angle Reconstruction

After establishing the core position, the next step is angle reconstruction. This process deter-

mines the primary particle’s trajectory. The angle of arrival is indicative of the originating gamma

ray’s direction. It correlates to the cosmic source of the gamma-ray. We deduce this angle using

the timing of PMT hits [44].

The air shower’s front is conically shaped, not flat. This shape arises from the travel patterns

of secondary particles. An event example is illustrated in Fig. 2.8. Far from the core, secondary

particles undergo multiple scattering. They also travel longer distances [46]. Particle sampling

decreases with distance from the core. This decrease results in measurable delays in arrival times

[46, 44]. Simulations provide a corrective measure for these effects. The correction is a function

of shower parameters [44]. The distance from the shower core and the charge recorded by PMTs

are crucial to this correction.

Corrections lead to the 𝜒2 minimization step. This technique fits a plane to the timing data of

the PMTs. It then calculates the shower’s angle of arrival. The zenith and azimuth angles are the

results of this fit [46]. The local angles are converted to celestial coordinates. These coordinates

30

Figure 2.10 Simulated normalized energy distribution of each 𝑓hit bin defined in Tab. 2.1. Monte
Carlo simulation of gamma-rays with 𝐸 −2.63 spectral shape and simulated source at 20◦
declination. Figure from [44].

allow correlation with gamma-ray sources. Right ascension (RA) and declination (Dec) are used

for this purpose. RA is akin to longitude, and Dec to latitude.

The reconstructed angle’s resolution ranges from 0.1° to 1°. This range depends on the incoming

particle’s energy and zenith angle [46]. The analysis uses a curvature/sampling correction. This

correction applies a quadratic function based on distance from the core [44]. The adjustment

improves angular resolution. However, discrepancies between simulation and observation persist.

These discrepancies introduce systematic errors into HAWC analyses [44].

2.2.3

𝑓hit Energy Estimation

The HAWC Observatory quantifies the primary particle energy of air showers using a metric

known as 𝑓hit. This ratio compares the count of PMTs involved in the event reconstruction to the

total number of functional PMTs at the time [44]. The main array consists of about 1200 PMTs,

31

Bin Lower Edge % Upper Edge % Θ68 (◦)
1.05
1
0.69
2
0.50
3
0.39
4
0.30
5
0.28
6
0.22
7
0.20
8
0.17
9

10.5
16.2
24.7
35.6
48.5
61.8
74.0
84.0
100

6.7
10.5
16.2
24.7
35.6
48.5
61.8
74.0
84.0

Table 2.1 Definitions of 𝑓hit energy estimator bins. Bins are defined by the fraction of available
PMTs that are triggered during an air shower event. The angular resolution, Θ68, is the bin
containing 68% of events [44].

but the count may vary due to maintenance or other operational factors.

Events are stratified into several 𝑓hit bins. Each bin corresponds to a specific range of angular

resolutions, enabling a structured approach to event analysis based on the extent of the shower

footprint, see Tab. 2.1.

The relationship between 𝑓hit and primary energy is complex; atmospheric attenuation can cause

high-energy showers to present a smaller footprint, misrepresenting their energy in the 𝑓hit metric.

This effect is captured in simulations that chart the actual energy distribution across 𝑓hit categories

[46]. Such distributions vary with the declination of the source and the theoretical energy spectrum

used in the model. The 𝑓hit metric, while effective, has several limitations.

It is dependent on

the zenith angle and the spectral characteristics presumed for the observed source. The variable

also reaches a saturation point around 10 TeV, after which the detector’s ability to discriminate

between higher energy levels diminishes [44]. Furthermore, the energy distribution for each 𝑓hit

bin is notably broad, see Fig. 2.10.

In response to these limitations, HAWC has developed more intricate algorithms for energy

estimation. These algorithms incorporate the zenith angle and the distribution of charge around

the shower core for a more accurate assessment of the primary particle’s energy, particularly at

energies surpassing 10 TeV [46]. The following section describes the improvements made in energy

estimation using a neutral network.

32

2.2.4 Neural Network Energy Estimation

The energy estimation for photon events at the HAWC Observatory is refined through an

artificial neural network (NN) algorithm. This method, based on the Toolkit for Multivariate

Analysis NN, adopts a multilayer-perceptron model with logistic activation functions across its

layers. The structure includes two hidden layers, the first with 15 nodes and the second with 14,

designed to process input variables through a neural network optimized to estimate primary particle

energies [47].

The NN is trained to minimize a specific error function that measures discrepancies between the

NN’s energy predictions and the actual energies from Monte Carlo simulations. This minimization

targets an error function that incorporates the relative importance of each event, weighting more an

𝐸 −2 power law spectrum. This approach helps achieve a uniform error rate across energies ranging

from 1 to 100 TeV. The optimization process leverages the Broyden-Fletcher-Goldfarb-Shanno

algorithm that calibrates the NN’s 479 weights [48].

The spectral analysis employs a binned likelihood method, using a forward-folding technique

to accommodate the energy estimate’s bias and resolution [48]. This establishes a 2D binning

scheme that categorizes events by both their 𝑓hit value and estimated energy. The decision to use

this scheme over a simple energy-based binning lies in the correlation between gamma/hadron

separation parameters and the angular resolution with both the size and energy of the event. The

spectrum of interest is partitioned into nine 𝑓hit bins, each further divided into 12 energy bins,

spanning from 0.316 TeV to 316 TeV, encompassing a total of 108 bins [48]. However, not all

bins contribute to the final estimate. Bins with low event populations or insufficient Monte Carlo

simulation are excluded. This approach focuses on the central 99% of events by estimated energy

within each 𝑓hit bin, effectively removing outliers [48].

Input variables for the NN are selected to capture key characteristics of the air shower: energy

deposition, containment, and atmospheric attenuation. The algorithm calculates energy deposition

using the fraction of PMTs and tanks activated, alongside the logarithm of the normalization from

the lateral distribution fit. Containment is inferred from the distance between the shower core and

33

Figure 2.11 Neural Network energy estimator performance compared to true energy. The dotted
line is the identity line where the estimator and injection agree. Gamma/hadron separation cuts
were applied with the energy estimation. Figure pulled from [48]

Figure 2.12 Lateral distribution functions (LDFs) for cosmic ray (left) and a photon candidate
from the Crab Nebula (right). Cosmic ray LDF has clearly isolated hits far from the reconstructed
shower core. Gamma-ray shower shows a more cuspy event [44].

the array’s center, while atmospheric attenuation is evaluated using the reconstructed zenith angle

and a detailed analysis of the shower’s lateral charge distribution [47, 48]. The performance on this

NN is shown in Fig. 2.11.

This refined NN energy estimation methodology is an integral component of HAWC’s toolkit,

enabling precise analysis of high-energy gamma-ray events. It represents a significant advancement

in the field by more accurately mapping observed shower characteristics to primary particle energies.

34

2.2.5 G/H Discrimination

At the HAWC Observatory, distinguishing between air showers initiated by gamma rays and

those by hadronic cosmic rays is fundamental for astrophysical data purity. The separation process

leverages differences in shower characteristics: electromagnetic showers from gamma rays typically

display fewer muons and a smoother lateral distribution, whereas hadronic showers are more chaotic

due to the abundance of muons and hadronic sub-showers.

Two primary parameters facilitate the identification of cosmic-ray events [44]:

1) Compactness (C): This parameter evaluates the charge captured by PMTs, particularly

focusing on the PMT with the highest effective charge beyond a 40-meter radius from the shower

core. Compactness is inversely proportional to this effective charge, as higher charges at extended

distances from the core are indicative of hadronic showers. It is mathematically expressed as:

𝐶 =

𝑁hit
𝐶𝑥𝑃𝐸40

(2.2)

where 𝑁hit is the number of PMTs hit and 𝐶𝑥𝑃𝐸40 is the effective charge measured outside a 40 m

radius from the shower cores [44].

2) PINCness (P): PINCness quantifies the "clumpiness" of a shower using the charges recorded

by PMTs and is short for Parameter for Identifying Nuclear Cosmic Rays. It is computed from the

logarithm of the effective charge, 𝑄eff,𝑖, of each PMT hit, 𝑖, compared to an expected average for

that annular region. A higher PINCness suggests a less smooth distribution, typical of hadronic

showers. The formula is:

𝑃 =

1
𝑁

𝑁
∑︁

𝑖=0

(𝜁𝑖 − ⟨𝜁𝑖⟩)2
𝜎2
𝜁𝑖

(2.3)

where 𝜁𝑖 = log10(𝑄eff,𝑖). The average, ⟨𝜁⟩ is the average over an annular region surrounding the

shower core. The errors, 𝜎𝜁𝑖 , are computed and allocated from gamma-ray candidates close to the

Crab.

These parameters are tested and modeled in simulations and with observational data near the

Crab Nebula. Figure 2.12 illustrates the lateral distributions for representative cosmic-ray and

photon candidate showers, and the Compactness and PINCness distributions [44].

35

The discrimination technique has remained consistent, but cut values have been reoptimized

for the 2D bins based on 𝑓hit and NN estimated energy. This refinement, referred to as Pass

5.F, enhances the selection of high-energy events. Each bin ensures at least 50% efficiency for

gamma-ray detection, with efficiencies extending up to 99% at the highest energy bins [44, 48].

2.3 Background Estimation: Direct Integration

The ratio of cosmic rays to gamma rays can be as high as 10,000 to 1, depending on the energy.

At HAWC, we confront a significant challenge even after gamma/hadron cuts: our gamma-ray data

is still inundated with cosmic-ray events. To tackle this, we rely on the direct integration method

developed by Milagro [49]. This method capitalizes on the cosmic rays’ isotropic nature resulting

from their deflection by interstellar magnetic fields.

The direct integration method estimates background events by integrating over a stable two-

hour period of detector operation. The expected number of background events at a particular sky

coordinate (𝜙, 𝜃) is determined by integrating the normalized detector’s efficiency with the all-sky

event rate:

𝑁exp(𝜙, 𝜃) =

∫ ∫

𝐸 (ha, 𝜃) · 𝑅(𝑡)𝑑𝑡

(2.4)

Here, 𝐸 (ha, 𝜃), represents the detector’s efficiency, which varies with local coordinates (hour angle

and declination). 𝑅(𝑡) is the event rate as a function of time [49].

Our background estimation is expected to falter in high-energy ranges where cosmic-ray events

are less frequent due to enhanced gamma/hadron discrimination. Sparsity in our background and

data also arise at the limits of HAWC’s sensitivity and during short-term analyses of transient events.

HAWC addresses these issues by using a pixel size of 0.5◦ in our direct integration to maintain

robustness in our estimation [44, 46]. In constructing the background model, it’s crucial to exclude

areas of the sky with known gamma-ray sources. Regions containing the Crab Nebula, Mrk 421,

Mrk 501, and the Galactic Plane are masked to prevent their significant gamma-ray signals from

biasing our background estimate [44].

36

CHAPTER 3

GLORY DUCK: MULTI-WAVELENGTH SEARCH FOR DARK MATTER
ANNIHILATION TOWARDS DWARF SPHEROIDAL GALAXIES

3.1

Introduction

Figure 3.1 Sensitivities of five gamma-ray experiments compared to percentages of the Crab
nebula’s emission and dark matter annihilation. Solid lines present estimated sensitivities to power
law spectra for each experiment. Green lines are Fermi-LAT sensitivities where lighter green is
the sensitivity to the galactic center and dark green is its sensitivity to higher declinations. Orange,
red, and purple solid lines represent the MAGIC, HESS, and VERITAS 50 hour sensitivities
respectively. The maroon and brown lines are the HAWC 1 year and 5 year sensitivities. Across
four decades of gamma-ray energy, these experiments have similar sensitivities on the order 10−12
erg cm−2s−1. The dotted lines are estimated dark matter fluxes assuming 𝑚 𝜒 = 5 TeV DM
annihilating to bottom quarks (red), tau leptons (blue), and W bosons (green). Faded gray lines
outline percentage flux of the Crab nebula. Figure is an augmented version of [50]

The field of astrophysics now has several instruments and observatories sensitive to high energy

gamma rays. The energy sensitivity for the modern gamma-ray program spans many orders

of magnitude. Figure 3.1 demonstrates these comparable sensitivities across energies for five

experiments: Fermi-LAT, HAWC, HESS, MAGIC, and VERITAS.

Each of the five experiments featured in Fig. 3.1 have independently searched for DM an-

nihilation from dwarf spheroidal galaxies (dSph) and set limits on annihilation cross-section of

WIMPs. Intriguingly, there are regions of substantial overlap in their energy sensitivities. This

37

clearly motivates an analysis that combines data from these five. Each experiment has unique

gamma-ray detection methods and their weaknesses and strengths can be leveraged with each other.

The HAWC gamma-ray observatory is extensively introduced in Sec. 2, so it is not introduced here.

A brief description of the remaining experiments are in the following paragraphs.

The Large Area Telescope (LAT) is a pair conversion telescope mounted on the NASA Fermi

satellite in orbit ∼550 km above the Earth [51]. LAT’s field of view covers about 20% of the sky

and sweeps the whole sky approximately every 3 hours. LAT’s energy sensitivity ranges from 20

MeV up to 1 TeV. Previous DM searches towards dSphs using Fermi-LAT are published in [52]

and [53].

The High Energy Spectroscopic System (HESS), Major Atmospheric Gamma Imaging

Cherenkov (MAGIC), and Very Energetic Radiation Imaging Telescope Array System (VERI-

TAS) are arrays of Imaging Atmospheric Cherenkov Telescopes (IACT). These telescopes observe

the Cherenkov light emitted from gamma-ray showers in the Earth’s atmosphere. The field of

view for these telescopes is no larger than 5° with energy sensitivities ranging from 30 GeV up

to 100 TeV [54, 55, 56]. IACTs are able to make precise observations in selected regions of the

sky, however can only be operated in ideal dark conditions. HESS’s observations of the dwarves

Sculptor and Carina were between January 2008 and December 2009. HESS’s observations of

Coma Berenices were taken from 2010 to 2013, and Fornax was observed in 2010 [57, 58, 59].

MAGIC provided deep observations of Segue1 between 2011 and 2013 [60]. MAGIC also provides

data for three additional dwarves: Coma Berenices, Draco, and Ursa Major II where observations

were made in: January - June 2019 [61], March - September 2018 [61], and 2014 - 2016 [62]

respectively. VERITAS provided data for Boötes I, Draco, Segue 1, and Ursa Minor from 2009 to

2016 [63].

This chapter presents the Glory Duck analysis, the name given for the search for dark matter

annihilation from dSph by combining data from the five gamma-ray observatories: Fermi-LAT,

HAWC, HESS, MAGIC, and VERITAS. Specifically, the methods in analysis and modeling are

presented for the HAWC gamma-ray observatory. This work will be published in the Journal of Cos-

38

mology and Astroparticle Physics and was presented at the International Cosmic Ray Conference

in 2019, 2021, and 2023 [64, 65, 66].

3.2 Dataset and Background

This section enumerates the data analysis and background estimation methods used for HAWC’s

study of dSphs. Sections 3.2.1 and 3.2.2 are most useful for fellow HAWC collaborators looking

to replicate the Glory Duck analysis.

3.2.1

Itemized HAWC files

These files are only available within HAWC’s internal documentation. They are not meant for

public access, and are presented here so that HAWC collaborators can reproduce results accurately.

• Detector Response: response_aerie_svn_27754_systematics_best_mc_test_nobroadpulse_1

0pctlogchargesmearing_0.63qe_25kHzNoise_run5481_curvature0_index3.root

• Data Map: maps-20180119/liff/maptree_1024.root

• Spectral Dictionary: DM_CirrelliSpectrum_dict_gammas.npy

• Analysis wiki: https://private.hawc-observatory.org/wiki/index.php/Glory_Duck_Multi-E

xperiment_Dark_Matter_Search

3.2.2 Software Tools and Development

This analysis was performed using HAL and 3ML [44, 67] in Python version 2. I built software

to implement the A Poor Particle Physicist Cookbook for Dark Matter Indirect Detection (PPPC)

[68] DM spectral model and dSphs spatial model from [69] for HAWC analysis. A NumPy version

of this dictionary was made for both Py2 and Py3. The code base for creating this dictionary is

linked on my GitLab sandbox:

• Py2: Dictionary Generator (Deprecated)

• Py3: PPPC2Dict

39

The analysis was performed using the 𝑓hit framework and described in the HAWC Crab paper

[44] and Section 2.2.3. The Python2 NumPy dictionary file for gamma-ray final states is dmCir-

SpecDict.npy. The corresponding Python3 file is DM_CirrelliSpectrum_dict_gammas.npy. These

files can also be used for decay channels and the PPPC describes how in [68]. All other software

used for data analysis, DM profile generation, and job submission to SLURM are also kept in my

sandbox for the Glory Duck project.

3.2.3 Data Set and Background Description

The HAWC data maps used for this analysis contain 1017 days of data between runs 2104

(2014-11-26) and 7476 (2017-12-20). They were generated from pass 4.0 reconstruction. The

analysis is performed using the 𝑓ℎ𝑖𝑡 energy binning scheme with bins (1-9) similar to what was done

for the Crab and previous HAWC dSph analysis [44, 70]. Bin 0 was excluded as it has substantial

hadronic contamination and poor angular resolution.

This analysis was done on dSphs because of their large DM mass content relative to baryonic

mass. We consider the following to estimate the background for this study.

• The dSphs’ angular extent are small relative to HAWC’s spatial resolution, so the analysis is

not sensitive to large or small scale anisotropies.

• The dSphs used in this analysis are off the galactic plane and therefore not contaminated by

diffuse emission from the galaxy.

• The dSphs are baryonically faint relative to their expected dark matter content and are not

expected to contain high energy gamma-ray sources.

Therefor we make no additional assumptions on the background from our sources and use

HAWC’s standard direct integration method for background estimation [44]. The largest background

under this consideration is from an isotropic flux of cosmic rays. The contamination of this hadronic

flux is worse at lower energies where HAWC’s gamma/hadron is discrimination worse. It is possible

for gamma rays from DM annihilation to scatter in transit to HAWC via Inverse Compton Scattering

40

(ICS). This was investigated and its impact on the flux is negligible. Supporting information on

this is in Section 3.7.1

3.3 Analysis

The expected differential photon flux from DM-DM annihilation to standard model particles,

𝑑Φ𝛾/𝑑𝐸𝛾 is described by the familiar equation.

𝑑Φ𝛾
𝑑𝐸𝛾

=

⟨𝜎v⟩
8𝜋𝑚2
𝜒

𝑑𝑁𝛾
𝑑𝐸𝛾

× 𝐽

(3.1)

Where ⟨𝜎v⟩ is the velocity weighted annihilation cross-section. 𝑑𝑁

𝑑𝐸 is the expected differential
number of photons produced at each energy per annihilation. 𝑚 𝜒 is the rest mass of the supposed

DM particle. 𝐽 is the astrophysical J-factor, over solid angle, Ω, and is defined as

∫

𝐽 =

𝑑Ω

∫

𝑙.𝑜.𝑠

𝑑𝑙 𝜌2

𝜒 (𝑟, 𝜃′)

(3.2)

𝜌 𝜒 is the DM density.

𝑙 is the distance to the source from Earth. 𝑟 is the radial distance from

the center of the source. 𝜃′ is the half angle defining a cone containing the DM source. How

each component is synthesized and considered for HAWC’s analysis is presented in the following

sections. Section 3.3.1 presents the particle physics model for DM annihilation. Section 3.3.2

presents the spatial distributions built for each dSph.

3.3.1

𝑑𝑁𝛾
𝑑𝐸𝛾 - Particle Physics Component

For these spectra, we import the PPPC with Electroweak (EW) corrections [68]. Public versions

of the imported tables are provided by the authors online. The spectrum is implemented as a model

script in astromodels for 3ML. The EW corrections were previously not considered for HAWC and

are significant for DM annihilating to EW coupled SM particles such as all leptons, and the 𝛾,

𝑍, and 𝑊 bosons [70]. Figure 3.2 demonstrates the significance of EW corrections for W boson

annihilation. Across EW SM channels, the gamma-ray spectra become harder than spectra without

EW corrections. Tables from the PPPC were reformatted into Python NumPy dictionaries for

collaboration-wide use. A class in astromodels was developed to include the EW correction from

the PPPC and is aptly named PPPCSpectra within DM_models.py.

41

Figure 3.2 Effect of Electroweak (EW) corrections on expected DM annihilation spectrum for
𝜒 𝜒 → 𝑊 −𝑊 +. Solid lines are spectral models that consider EW corrections. Dash-dot lines are
spectral models without EW corrections. Red lines are models for 𝑀𝜒 = 1 TeV. Blue lines
represent models for 𝑀𝜒 = 100 TeV. All models are sourced from the PPPC4DMID [68].

3.3.2

𝐽- Astrophysical Component

The J-factor profiles for each source are imported from Geringer-Sameth’s 2015 publication

(referred to with GS) [69]. GS fits the Zhao DM profile to the dSphs which has a DM density

described as [71]

𝜌(𝑟) =

𝜌0
(𝑟/𝑅𝑠)𝛾 (1 + (𝑟/𝑅𝑠)𝛼) (𝛽−𝛾)

.

(3.3)

𝑅𝑠 is the scale radius and free parameter in the model. 𝛾 is the logarithmic slope in the region

𝑟 << 𝑅𝑠. 𝛽 is the logarithmic slope in the region 𝑟 >> 𝑅𝑠. 𝛼 is known as the sharpness of transition

where 𝑟 ≈ 𝑅𝑆. The classic Navarro-Frenk-White DM distribution [28] (NFW) can be retrieved

from Zhao by fixing (𝛼, 𝛽, 𝛾) = (1, 3, 1).

GS best fits were pulled from the publication as 𝐽 (𝜃), where 𝜃 is the angular separation from

the center of the source. HAWC requires maps in terms of 𝑑𝐽
𝑑Ω

. The description on how this was

done follows.

42

First, convert the angular distances to solid angles

Ω = 2 · 𝜋(1 − cos(𝜃))

(3.4)

which reduces with a small angle approximation to 𝜋𝜃2. Next, the central difference for both the

Δ𝐽 and ΔΩ value were calculated from the discretized 𝐽 (𝜃) with the central difference stencil:

Δ𝜙𝑖 = 𝜙𝑖+1 − 𝜙𝑖−1

(3.5)

Where 𝜙 is either Ω or 𝐽. These were done separately in case the grid spacing in 𝜃 was not uniform.

Finally, these lists are divided so that we are left with an approximation of the 𝑑𝐽/𝑑Ω profile that

is a function of 𝜃. Admittedly, this is an approximation method for the map which introduces small

errors compared to the true profile estimate. This was checked as a systematic against the author’s

profiling of the spatial distribution and is documented in Section 3.8.1.

With 𝑑𝐽

𝑑Ω (𝜃, 𝜙), a map is generated, first by filling in the north-east quadrant of the map. This
quadrant is then reflected twice, vertically then horizontally, to fill the full map. Maps are then

normalized by dividing the discrete 2D integral of the map. The 2D integral was a simple height

of bins, Newton’s integral:

𝑝2 ·

𝑁,𝑀
∑︁

𝑖, 𝑗=0

𝑑𝐽
𝑑Ω

(𝜃𝑖, 𝑗 , 𝜙𝑖, 𝑗 )

(3.6)

Here, 𝑝 is the side length of a HEALpix pixel used for the map. 𝜃𝑖 and 𝜙𝑖 are the discrete coordinates

whose origin is the center of the modeled dSph. These maps are HEALpix maps with NSIDE

16384 and saved in the ".fits" format. The hyper fine resolution was selected to better preserve the

total expected counts after integrating Eq. (3.1) with the detector response.

Another DM spatial distribution model from Bonnivard (B) [72] was used for the Glory Duck

study. However, to save computational time, limits from GS were scaled to B instead of each

experiment performing a full study a second time. How these models compare is demonstrated for

each dSph in Figs. 3.17 and 3.18. Examples of the two most impactful dSphs derived from GS,

Segue1 and Coma Berenices are featured in Fig. 3.3

43

Figure 3.3 Dark Matter density ( 𝑑𝐽
𝑑Ω

) maps for Segue1 (top) and Coma Berenices (bottom). Origin

is centered on the specific dwarf spheroidal galaxies (dSph). X and Y axes are the angular
separation from the center of the dwarf. Profile is truncated at the scale radius. Plots of the
remaining 11 dSph HAWC studied are provided in Fig. A.1.

44

1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)01234log10(dJd/GeV2cm5sr)3.3.3 Source Selection and Annihilation Channels

Many of the dSphs presented in HAWC’s previous dSph DM search are used [70]. HAWC’s

sources for the Glory Duck analysis include Boötes I, Coma Berenices, Canes Venatici I + II,

Draco, Hercules, Leo I, II, + IV, Segue 1, Sextans, and Ursa Major I + II. A full description of all

sources used in Glory Duck are found in Table 3.2. Triangulum II was excluded from the Glory

Duck analysis because of large uncertainties in its 𝐽 factor. Ursa Minor was excluded from HAWC’s

contribution to the combination because the source extension model extended Ursa Minor beyond

HAWC’s field of view. Ursa Minor was not expected to contribute significantly to the combined

limit, so work was not invested in a solution to include Ursa Minor.

This analysis improves on the previous HAWC dSph paper [70] in the following ways. Pre-

viously, the dSphs were treated and implemented as point sources. For this analysis, dSphs are

modeled and treated as extended source. The impact of this change with respect to the upper limit

is source dependent and is explored in Section 3.7.2. Previously, the particle physics model used for

gamma-ray spectra from DM annihilation did not have EW corrections where the PPPC includes

them. Finally, the gamma-ray ray dataset is much larger. The study performed here analyzes over

1000 days of data compared to 507.

The SM annihilation channels probed for the Glory Duck combination include 𝑏 ¯𝑏, 𝑒 ¯𝑒, 𝜇 ¯𝜇, 𝜏 ¯𝜏,

𝑡 ¯𝑡, 𝑊 +𝑊 −, and 𝑍 𝑍. A summary of all sources, with a description of each experiments’ sensitivity

to the source, is provided in Table 3.1.

45

Table 3.1 Summary of dSph observations by each experiment used in this work. A ‘-’ indicates the experiment did not observe the dSph
for this study. For Fermi-LAT, the exposure at 1 GeV is given. For HAWC, |Δ𝜃| is the absolute difference between the source
declination and HAWC latitude. HAWC is more sensitive to sources with smaller |Δ𝜃|. For IACTs, we show the zenith angle range, the
total exposure, the energy range, the angular radius 𝜃 of the signal or ON region, the ratio of exposures between the background-control
(OFF) and signal (ON) regions (𝜏), and the significance of gamma-ray excess in standard deviations, 𝜎.

IACT

H.E.S.S, MAGIC, VERITAS
Zenith (°) Exposure (h) Energy range (GeV) 𝜃 (°)

Source name
Boötes I
Canes Venatici I
Canes Venatici II
Carina

Coma Berenices

Draco

Fornax
Hercules
Leo I
Leo II
Leo IV
Leo V
Leo T
Sculptor

Segue I

Segue II
Sextans
Ursa Major I
Ursa Major II
Ursa Minor

Fermi-LAT
Exposure (1011 s m2)
2.6
2.9
2.9
3.1

HAWC
|Δ𝜃| (°)
4.5
14.6
15.3
−

2.7

3.8

2.7
2.8
2.5
2.6
2.4
2.4
2.6
2.7

2.5

2.7
2.4
3.4
4.0
4.1

4.9

38.1

−
6.3
6.7
3.1
19.5
−
−
−

2.9

−
20.6
32.9
44.1
−

14.0
−
−
23.7
11.4
49.5
52.1
49.8
6.8
−
−
−
−
−
−
11.8
158.0
92.0
−
−
−
94.8
60.4

VERITAS 15 − 30

−
−
−
−
27 − 46
H.E.S.S.
47 − 49
H.E.S.S.
5 − 37
MAGIC
MAGIC
29 − 45
VERITAS 25 − 40
11 − 25
H.E.S.S.
−
−
−
−
−
−
−
−
−
−
−
−
10 − 46
H.E.S.S.
MAGIC
13 − 37
VERITAS 15 − 35

−
−
−
−
−
−
35 − 45
MAGIC
VERITAS 35 − 45

46

100-41000
−
−
310 − 70000
550 − 70000
60 − 10000
70 − 10000
120 − 70000
230 − 70000
−
−
−
−
−
−
200 − 70000
60 − 10000
80 − 50000
−
−
−
120 − 10000
160 − 93000

−
−

−
−

S (𝜎)
𝜏
0.10 8.6 −1.0
−
−
−
−
0.10 18.0 −0.3
0.10 14.4 −0.4
0.17 1.0
0.22 1.0
0.10 9.0 −1.0
0.10 45.5 −1.5
−
−
−
−
−
−
−
−
−
−
−
−
0.10 19.8 −2.2
0.12 1.0 −0.5
0.7
0.10 7.6
−
−
−
−
−
−
−
−
−
0.30 1.0 −2.1
0.10 8.4 −0.1

−
−
−
−
−
−

Table 3.2 Summary of the relevant properties of the dSphs used in the present work. Column 1
lists the dSphs. Columns 2 and 3 present their heliocentric distance and galactic coordinates,
respectively. Columns 4 and 5 report the 𝐽-factors of each source given from the GS and B
independent studies and their estimated ±1𝜎 uncertainties. The values log10 𝐽 (GS set) [69]
correspond to the mean 𝐽-factor values for a source extension truncated at the outermost observed
star. The values log10 𝐽 (B set) [72] are provided for a source extension at the tidal radius of each
dSph. Bolded sources are within HAWC’s field of view and provided to the Glory Duck
analysis.

Name

Boötes I

Canes Venatici I

Canes Venatici II
Carina

Coma Berenices

Draco
Fornax

Hercules

Leo I

Leo II

Leo IV
Leo V

Leo T

Sculptor

Segue I
Segue II

Sextans

Ursa Major I

Ursa Major II
Ursa Minor

Distance
(kpc)

𝑙, 𝑏
(°)

66

218

160

105

44

76

147

132

254

233

154

178

417

86

23

35

86

97

32

76

358.08, 69.62

74.31, 79.82

113.58, 82.70

260.11, −22.22
241.89, 83.61

86.37, 34.72

237.10, −65.65
28.73, 36.87

225.99, 49.11

220.17, 67.23

265.44, 56.51

261.86, 58.54

214.85, 43.66

287.53, −83.16
220.48, 50.43

149.43, −38.14
243.50, 42.27

159.43, 54.41

152.46, 37.44

104.97, 44.80

log10 𝐽 (GS set)
log10 (GeV2cm−5sr)
18.24+0.40
−0.37
17.44+0.37
−0.28
17.65+0.45
−0.43
17.92+0.19
−0.11
19.02+0.37
−0.41
19.05+0.22
−0.21
17.84+0.11
−0.06
16.86+0.74
−0.68
17.84+0.20
−0.16
17.97+0.20
−0.18
16.32+1.06
−1.70
16.37+0.94
−0.87
17.11+0.44
−0.39
18.57+0.07
−0.05
19.36+0.32
−0.35
16.21+1.06
−0.98
17.92+0.35
−0.29
17.87+0.56
−0.33
19.42+0.44
−0.42
18.95+0.26
−0.18

log10 𝐽 (B set)
log10 (GeV2cm−5sr)
18.85+1.10
−0.61
17.63+0.50
−0.20
18.67+1.54
−0.97
18.02+0.36
−0.15
20.13+1.56
−1.08
19.42+0.92
−0.47
17.85+0.11
−0.08
17.70+1.08
−0.73
17.93+0.65
−0.25
18.11+0.71
−0.25
16.36+1.44
−1.65
16.30+1.33
−1.16
17.67+1.01
−0.56
18.63+0.14
−0.08
17.52+2.54
−2.65
19.50+1.82
−1.48
18.04+0.50
−0.28
18.84+0.97
−0.43
20.60+1.46
−0.95
19.08+0.21
−0.13

47

3.4 Likelihood Methods

3.4.1 HAWC Likelihood

For every analysis bin in energy, 𝑓ℎ𝑖𝑡 bins (1-9), and location, we can expect 𝑁 signal events and

𝐵 background events. The expected number of excess signal events from dark matter annihilation,

𝑆, is estimated by convolving Equation (3.1) with HAWC’s energy response and pixel point spread

functions. The test statistic (TS) is computed with the log-likelihood ratio test,

TSmax = −2 ln

(cid:19)

(cid:18) L0
Lmax

(3.7)

where L0 is the null hypothesis, or no DM emission, likelihood. Lmax is the best fit signal

hypothesis where ⟨𝜎v⟩ maximizes the likelihood. We calculate the likelihood of each source and

model, assuming events are Poisson distributed, with

L =

(cid:214)

𝑖

(𝐵𝑖 + 𝑆𝑖) 𝑁𝑖 𝑒−(𝐵𝑖+𝑆𝑖)
𝑁𝑖!

(3.8)

where 𝑆𝑖 is the sum of expected number of signal counts. 𝐵𝑖 is the number of background counts

observed. 𝑁𝑖 is the total number of counts.

An upper limit on ⟨𝜎v⟩ is calculated using the 95% confidence level (CL). For the CL, we

define a parameter, 𝑇 𝑆95, as

TS95 ≡

(cid:20)

∑︁

bins

2𝑁 ln

(cid:18)

1 +

(cid:19)

𝜖 𝑆ref
𝐵

(cid:21)

− 2𝜖 𝑆ref

(3.9)

where the expected signal counts from a dSph is scaled by 𝜖. 𝑆ref is the expected number of excess

counts in a bin for DM emission from a dSph with a corresponding annihilation cross-section,

⟨𝜎v⟩. We scan 𝜖 such that

2.71 = TSmax − TS95

(3.10)

HAWC’s exclusive results are provided in Section 3.5.

48

3.4.2 Glory Duck Joint Likelihood

The joint likelihood for the 5-experiment combination was done similarly as Section 3.4.1. We

calculate upper limits on ⟨𝜎v⟩ from the TS, Eq. (3.7), and define the likelihood ratio more generally

𝜆 (cid:0)⟨𝜎v⟩ | DdSphs(cid:1) =

(cid:16)

(cid:16)

L

L

⟨𝜎v⟩; ˆˆν | DdSphs

(cid:154)⟨𝜎v⟩; ˆν | DdSphs

(cid:17)

(cid:17)

(3.11)

DdSphs is the totality of observations across experiments and dSphs. ν are the nuisance parameters

which are the 𝐽 factors in this study. (cid:154)⟨𝜎v⟩ and ˆν are the respective estimate that maximize L
globally. Finally, ˆˆν is the set of nuisance parameters that maximize L for a fixed value of ⟨𝜎v⟩.

The complete joint likelihood, L that encompasses all observations from all instruments and

dSphs can be factorized into partial functions for each dSph 𝑙 (with LdSph,𝑙) and its 𝐽 factor (J𝑙):

L (cid:0)⟨𝜎v⟩; ν | DdSphs

(cid:1) =

𝑁dSphs
(cid:214)

𝑙=1

LdSph,𝑙 (⟨𝜎v⟩; 𝐽𝑙, ν𝒍

| D𝒍) × J𝑙 (cid:0)𝐽𝑙 | 𝐽𝑙,obs, 𝜎log 𝐽𝑙

(cid:1) .

(3.12)

For this study, 𝑁dSphs = 20 is the number of dSphs studied. D𝒍 are the gamma-ray observations

of dSph, 𝑙. νl are the nuisance parameters modifying the gamma-ray observations of dSph, 𝑙, but

excludes J𝑙. J𝑙 is the 𝐽 factor for dSph, 𝑙, as defined in Eq. (3.2), and it is a nuisance parameter

whose value is unknown.

log10 𝐽𝑙,obs and 𝜎log 𝐽𝑙 are obtained by fitting a log-normal function of

𝐽𝑙,obs to the posterior distribution of 𝐽𝑙 [73]. log10 𝐽𝑙,obs and 𝜎log 𝐽𝑙 values are provided in Tab. 3.2.

The term J𝑙 constraining 𝐽𝑙 is written as:

J𝑙 (cid:0)𝐽𝑙 | 𝐽𝑙,obs, 𝜎log 𝐽𝑙

(cid:1) =

1
ln (10)𝐽𝑙,obs

√

2𝜋𝜎log 𝐽𝑙
Both the GS and B sets of 𝐽 factors, displayed in Tab. 3.2, are used in this analysis. Equation (3.13)

log 𝐽𝑙

(cid:32)

exp

−

(cid:0)log10 𝐽𝑙 − log10 𝐽𝑙,obs(cid:1) 2
2𝜎2

(cid:33)

.

(3.13)

is also normalized, so it can also be interpreted as a probability density function (PDF) for 𝐽𝑙,obs.

From Eq. (3.1), we can also see that ⟨𝜎v⟩ and 𝐽𝑙 are degenerate when computing LdSph,𝑙. Therefore,

as noted in [74], it is sufficient to compute LdSph,𝑙 versus ⟨𝜎v⟩ for a fixed value of 𝐽𝑙. We used

𝐽𝑙,obs(GS) reported in Tab. 3.2, in order to perform the profile of L with respect to 𝐽𝑙. The

degeneracy implies that for any 𝐽′

𝑙 ≠ 𝐽𝑙,obs (in practice in our case we used 𝐽′

𝑙 = 𝐽𝑙,obs(B) to compute

results from a different set of 𝐽 factors):

LdSph,𝑙 (cid:0)⟨𝜎v⟩; 𝐽′

𝑙 , νl | D𝒍

(cid:1) = LdSph,𝑙

(cid:18) 𝐽′
𝑙
𝐽𝑙,obs

⟨𝜎v⟩; 𝐽𝑙,obs, νl | D𝒍

(cid:19)

,

(3.14)

49

which is a straightforward rescaling operation that reduces the computational needs of the profiling

operation since:

L (cid:0)⟨𝜎v⟩; ˆν | DdSphs

(cid:1) =

(cid:20)

max𝐽𝑙

𝑁dSphs
(cid:214)

𝑙=1

LdSph,𝑙 (⟨𝜎v⟩; 𝐽𝑙, ˆν𝒍

| D𝒍) × J𝑙

(cid:16)

𝐽𝑙 | 𝐽𝑙,obs, 𝜎log𝐽𝑙

(cid:17) (cid:21)

.

(3.15)

In addition, Eq. (3.14) enables the combination of data from different gamma-ray instruments and

observed dSphs via tabulated values of LdSph,𝑙, or equivalently of 𝜆 from Eq. (3.11) as was done in

this work, versus ⟨𝜎v⟩. LdSph,𝑙 is computed for a fixed value of 𝐽𝑙 and profiled with respect to all

instrumental nuisance parameters νl, these nuisance parameters are discussed in more detail below.

These values are produced by each detector independently and therefore there is no need to share

sensitive low-level information used to produce them, such as event lists. Figure 3.4 illustrates the

multi-instrument combination technique used in this study with a comparison of the upper limit

on ⟨𝜎v⟩ obtained from the combination of the observations of four experiments towards one dSph

versus the upper limit from individual instruments.

It also shows graphically the effect of the

𝐽-factor uncertainty on the combined observations.

The partial joint likelihood function for gamma-ray observations of each dSph (LdSph,𝑙) is

written as the product of the likelihood terms describing the 𝑁exp,𝑙 observations performed with

any of our observatories:

LdSph,𝑙 (⟨𝜎v⟩; 𝐽𝑙, νl | D𝒍) =

𝑁exp,𝑙
(cid:214)

L𝑙 𝑘 (⟨𝜎v⟩; 𝐽𝑙, ν𝒍 𝒌 | D𝒍 𝒌) ,

(3.16)

𝑘=1
where each L𝑙 𝑘 term refers to an observation of the 𝑙-th dSph with associated 𝑘-th instrument

responses. 𝑁exp,𝑙 varies from dSph to dSph and can be inferred from Tab. 3.1.

Each collaboration separately analyzes their data for D𝒍 𝒌 corresponding to dSph 𝑙 and gamma-

ray detector 𝑘, using as many common assumptions as possible in the analysis. HAWC’s treatment

was described earlier in Section 3.4.1 whereas the specifics of the remaining experiments is left to

the publication. We compute the values for the likelihood functions L𝑙 𝑘 (see Eq. (3.16)) for a fixed

value of 𝐽𝑙 and profile over the rest of the nuisance parameters ν𝒍 𝒌. Then, values of 𝜆 from Eq. (3.11)

are computed as a function of ⟨𝜎v⟩, and shared using a common format. Results are computed for
seven annihilation channels, 𝑊 +𝑊 −, 𝑍 𝑍, 𝑏 ¯𝑏, 𝑡 ¯𝑡, 𝑒+𝑒−, 𝜇+𝜇−, and 𝜏+𝜏− over 62 𝑚 𝜒 values between

50

Figure 3.4 Illustration of the combination technique showing a comparison between −2 ln 𝜆
provided by four instruments (colored lines) from the observation of the same dSph without any 𝐽
nuisance and their sum, 𝑖.𝑒. the resulting combined likelihood (thin black line). According to the
test statistics of Eq. (3.7), the intersection of the likelihood profiles with the line −2 ln 𝜆 = 2.71
indicates the 95% C.L. upper limit on ⟨𝜎v⟩. The combined likelihood (thin black line) shows a
smaller value of upper limit on ⟨𝜎v⟩than those derived by individual instruments. We also show
how the uncertainties on the 𝐽 factor effects the combined likelihood and degrade the upper limit
on ⟨𝜎v⟩(thick black line). All likelihood profiles are normalized so that the global minimum (cid:154)⟨𝜎v⟩
is 0. We note that each profile depends on the observational conditions in which a target object
was observed. The sensitivity of a given instrument can be degraded and the upper limits less
constraining if the observations are performed in non-optimal conditions such as a high zenith
angle or a short exposure time.

5 GeV and 100 TeV provided in [68]. The ⟨𝜎v⟩range is defined between 10−28 and 10−18cm3 · s−1,

with 1001 logarithmically spaced values. The likelihood combination, i.e. Eq. (3.12), and profile

over the 𝐽-factor to compute the profile likelihood ratio 𝜆, Eq. (3.11), are carried out with two

different public analysis software packages, namely gLike [75] and LklCom [76], that provide the

same results [77].

As mentioned previously, each experiment computes the L𝑙 𝑘 from Eq. (3.11) differently. The

remainder of this section highlights the differences in this calculation across the experiments.

Four experiments, namely Fermi-LAT, H.E.S.S., HAWC and MAGIC, use a binned likelihood to

compute the L𝑙 𝑘 . For these experiments, for each observation D𝒍 𝒌 of a given dSph 𝑙 carried out

51

10251024102310221021v [cm3/s]0123452ln2.71 (95% C.L.)Instument 1 w/o J nuisanceInstument 2 w/o J nuisanceInstument 3 w/o J nuisanceInstrument 4 w/o J nuisanceCombination w/o J nuisanceCombination w/ J nuisanceusing a given gamma-ray detector 𝑘, the binned likelihood function is:

L𝑙𝑘 (⟨𝜎v⟩; 𝐽𝑙, ν𝒍𝒌 | D𝒍𝒌 ) =

𝑁E’
(cid:214)

𝑁P’
(cid:214)

(cid:104)

𝑖=1

𝑗=1

P (𝑠𝑙𝑘,𝑖 𝑗 (⟨𝜎v⟩, 𝐽𝑙, ν𝒍𝒌 ) + 𝑏𝑙𝑘,𝑖 𝑗 (ν𝒍𝒌 ) | 𝑁𝑙𝑘,𝑖 𝑗)

(cid:105)

× L𝑙𝑘,ν

(cid:0)ν𝒍𝒌 | D𝝂𝒍𝒌

(cid:1)

(3.17)

where 𝑁E’ and 𝑁P’ are the number of considered bins in reconstructed energy and arrival direction,

respectively; P represents a Poisson PDF for the number of gamma-ray candidate events 𝑁𝑙 𝑘,𝑖 𝑗

observed in the 𝑖-th bin in energy and 𝑗-th bin in arrival direction, when the expected number is

the sum of the expected mean number of signal events 𝑠𝑖 𝑗 (produced by DM annihilation) and of

background events 𝑏𝑖 𝑗 ; L𝑙 𝑘,ν is the likelihood term for the extra ν𝒍 𝒌 nuisance parameters that vary

from one instrument 𝑘 to another. The expected counts for signal events 𝑠𝑖 𝑗 for a given dSph 𝑙 and

detector 𝑘 is given by:

𝑠𝑖 𝑗 (⟨𝜎v⟩, 𝐽) =

∫ 𝐸′

max,𝑖

∫ 𝑃′

max, 𝑗

d𝐸 ′

𝐸′

min,𝑖

𝑃′

min, 𝑗

dΩ′

∫ ∞

∫

d𝐸

0

ΔΩ𝑡𝑜𝑡

dΩ

∫ 𝑇obs

0

d𝑡

d2Φ(⟨𝜎v⟩, 𝐽)
d𝐸dΩ

IRF (𝐸 ′, 𝑃′ | 𝐸, 𝑃, 𝑡)

(3.18)

where 𝐸′ and 𝐸 are the reconstructed and true energies, 𝑃′ and 𝑃 the reconstructed and true arrival

directions; 𝐸′

min,𝑖, 𝑃′

min, 𝑗 , 𝐸′

max,𝑖, and 𝑃′

max, 𝑗 are their lower and upper limits of the 𝑖-th energy bin

and the 𝑗-th arrival direction bin; 𝑇obs is the (dead-time corrected) total observation time; 𝑡 is the

time along the observations; d2Φ/d𝐸dΩ is the DM flux in the source region (see Eq. (3.1)); and

IRF (𝐸′, 𝑃′ | 𝐸, 𝑃, 𝑡) is the IRF, which can be factorized as the product of the effective collection

area of the detector 𝐴eff (𝐸, 𝑃, 𝑡), the PDFs for the energy estimator 𝑓𝐸 (𝐸′

| 𝐸, 𝑡), and arrival

direction 𝑓𝑃 (𝑃′ | 𝐸, 𝑃, 𝑡) estimators. Note that for Fermi-LAT, HAWC, MAGIC, and VERITAS

the effect of the finite angular resolution is taken into account through the convolution of 𝑑Φ/𝑑𝐸 𝑑Ω

with 𝑓𝑃 in Eq. (3.18), whereas in the cases of H.E.S.S. 𝑓𝑃 is approximated by a delta function.

This approximation has been made in order to maintain compatibility of the result with what

has been previously published. The difference introduced by this approximation is < 5% for

all considered dSphs. A more comprehensive review of the differences between the analyses of

different instruments can be found in [50].

52

Figure 3.5 HAWC 95% confidence limits on ⟨𝜎v⟩ versus DM mass for seven annihilation
channels with 𝐽-factors from GS. Limits are shown for each source individually as colored,
dashed lines. Combined limit represented with solid black line. The lower the limit, the stronger
the constraint. We can see the combined limit is lower than any source individually.

3.5 HAWC Results

Thirteen of the 20 dSphs considered for the Glory Duck analysis are within HAWC’s field of

view. These dSph are analyzed for emission from DM annihilation according to the likelihood

method described in Section 3.4. The 13 likelihood profiles are then stacked to synthesize a

53

100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]bbHAWC PreliminaryBootesISextansLeoILeoIICanesVenaticiIIUrsaMajorIHerculesLeoIVUrsaMajorIICanesVenaticiICombinedSegue1DracoComaBerenices100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]eeHAWC PreliminaryBootesISextansLeoILeoIICanesVenaticiIIUrsaMajorIHerculesLeoIVUrsaMajorIICanesVenaticiICombinedSegue1DracoComaBerenices100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]WWHAWC PreliminaryBootesISextansLeoILeoIICanesVenaticiIIUrsaMajorIHerculesLeoIVUrsaMajorIICanesVenaticiICombinedSegue1DracoComaBerenices100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]ZZHAWC PreliminaryBootesISextansLeoILeoIICanesVenaticiIIUrsaMajorIHerculesLeoIVUrsaMajorIICanesVenaticiICombinedSegue1DracoComaBerenices100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]HAWC PreliminaryBootesISextansLeoILeoIICanesVenaticiIIUrsaMajorIHerculesLeoIVUrsaMajorIICanesVenaticiICombinedSegue1DracoComaBerenices100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]HAWC PreliminaryBootesISextansLeoILeoIICanesVenaticiIIUrsaMajorIHerculesLeoIVUrsaMajorIICanesVenaticiICombinedSegue1DracoComaBerenices100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]ttHAWC PreliminaryBootesISextansLeoILeoIICanesVenaticiIIUrsaMajorIHerculesLeoIVUrsaMajorIICanesVenaticiICombinedSegue1DracoComaBerenicescombined limit on the dark matter cross-section, ⟨𝜎v⟩. This combination is done for the 7 SM

annihilation channels used in the Glory Duck analysis. Figure 3.5 shows the combined limit for

all annihilation channels with HAWC only observations. We also perform 300 studies of Poisson

trials on the background. These trials are used to produce HAWC sensitivities with ±1𝜎 and ±2𝜎

uncertainty bands which were shared with the other collaborators for combination. The results

on fitting to HAWC’s Poisson trials of the DM hypothesis is shown in Figure 3.7 for all the DM

annihilation channels studied for Glory Duck.

No DM was found in HAWC observations. HAWC’s limits are dominated by the dSphs Segue1

and Coma Berenices. The remaining 11 dSphs do not contribute significantly to the limit because

they are at high zenith and/or have much smaller 𝐽 factors. Even though some remaining dSphs

have large 𝐽 factors, they are towards the edge of HAWC’s field of view where HAWC analysis is

less sensitive.

54

Figure 3.6 HAWC TS values for best fit ⟨𝜎v⟩ versus 𝑚 𝜒 for seven SM annihilation channels with 𝐽
factors from GS. The solid black line shows the combined best fit TS values. The colored, dashed
lines are the TS values for each of the 13 sources HAWC studied. The lower the limit, the stronger
the constraint.

55

100101102M [TeV]02468101214TSbbHAWC PreliminaryCombined and per Source Best Fit TS for bbBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoIVSegue1SextansUrsaMajorIUrsaMajorIICombined100101102M [TeV]02468101214TSee+HAWC PreliminaryCombined and per Source Best Fit TS for ee+BootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoIVSegue1SextansUrsaMajorIUrsaMajorIICombined100101102M [TeV]02468101214TSHAWC PreliminaryCombined and per Source Best Fit TS for BootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoIVSegue1SextansUrsaMajorIUrsaMajorIICombined100101102M [TeV]02468101214TSHAWC PreliminaryCombined and per Source Best Fit TS for BootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoIVSegue1SextansUrsaMajorIUrsaMajorIICombined100101102M [TeV]02468101214TSWW+HAWC PreliminaryCombined and per Source Best Fit TS for WW+BootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoIVSegue1SextansUrsaMajorIUrsaMajorIICombined100101102M [TeV]02468101214TSZ0Z0HAWC PreliminaryCombined and per Source Best Fit TS for Z0Z0BootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoIVSegue1SextansUrsaMajorIUrsaMajorIICombined100101102M [TeV]02468101214TSttHAWC PreliminaryCombined and per Source Best Fit TS for ttBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoIVSegue1SextansUrsaMajorIUrsaMajorIICombinedFigure 3.7 HAWC Brazil bands at 95% confidence level on ⟨𝜎v⟩versus DM mass for seven
annihilation channels with 𝐽-factors from GS [78]. The solid line represents the combined limit
from 13 dSphs. The dashed line is the expected limit. The green band is the 68% containment.
The yellow band is the 95% containment.

56

100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]bbHAWC PreliminaryExpectedObserved95% containment68% containment100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]eeHAWC PreliminaryExpectedObserved95% containment68% containment100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]HAWC PreliminaryExpectedObserved95% containment68% containment100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]HAWC PreliminaryExpectedObserved95% containment68% containment100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]WWHAWC PreliminaryExpectedObserved95% containment68% containment100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]ZZHAWC PreliminaryExpectedObserved95% containment68% containment100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]ttHAWC PreliminaryExpectedObserved95% containment68% containment3.6 Glory Duck Combined Results

The crux of this analysis is that HAWC’s results are combined with 4 other gamma-ray observa-

tories: Fermi-LAT, H.E.S.S., MAGIC, and VERITAS. No significant DM emission was observed

by any of the five instruments. We present the upper limits on ⟨𝜎v⟩assuming seven independent
DM self annihilation channels, namely 𝑊 +𝑊 −, 𝑍 +𝑍 −, 𝑏 ¯𝑏, 𝑡 ¯𝑡, 𝑒+𝑒−, 𝜇+𝜇−, and 𝜏+𝜏−. The 68%

and 95% containment bands are produced from 300 Poisson realizations of the null hypothesis

corresponding to each of the combined datasets. These 300 realizations are combined identically

to dSph observations. The containment bands and the median are extracted from the distribution

of resulting limits on the null hypothesis. These 300 realizations are obtained either by fast simu-

lations of the OFF observations, for H.E.S.S., MAGIC, VERITAS, and HAWC, or taken from real

observations of empty fields of view in the case of Fermi-LAT [73, 79, 80].

The obtained limits are shown in Figure 3.8 for the GS set of 𝐽-factors [78] and in Figure 3.9

for the B set of 𝐽-factors [72, 81]. The combined limits are presented with their 68% and 95%

containment bands, and are expected to be close to the median limit when no signal is present.

We observe agreement with the null hypothesis for all channels, within 2𝜎 standard deviations,

between the observed limits and the expectations given by the median limits. Limits obtained from

each detector are also indicated in the figures, where limits for all dSphs observed by the specific

instrument have been combined.

Below ~300 GeV, the 𝐹𝑒𝑟𝑚𝑖-LAT dominates the DM limits for all annihilation channels. From

~300 GeV to ~2 TeV, 𝐹𝑒𝑟𝑚𝑖-LAT continues to dominate for the hadronic and bosonic DM channels,

yet the IACTs (H.E.S.S., MAGIC, and VERITAS) and 𝐹𝑒𝑟𝑚𝑖-LAT all contribute to the limit for

leptonic DM channels. For DM masses between ~2 TeV to ~10 TeV, the IACTs dominate leptonic

DM annihilation channels, whereas both the 𝐹𝑒𝑟𝑚𝑖-LAT and the IACTs dominate bosonic and

hadronic DM annihilation channels. From ~10 TeV to ~100 TeV, both the IACTs and HAWC

contribute significantly to the leptonic DM limit. For hadronic and bosonic DM, the IACTs and

𝐹𝑒𝑟𝑚𝑖-LAT both contribute strongly.

57

Figure 3.8 Upper limits at 95% confidence level on ⟨𝜎v⟩in function of the DM mass for eight
annihilation channels, using the set of 𝐽 factors from Ref. [78] (GS set in Table 3.2). The black
solid line represents the observed combined limit, the black dashed line is the median of the null
hypothesis corresponding to the expected limit, while the green and yellow bands show the 68%
and 95% containment bands. Combined upper limits for each individual detector are also
indicated as solid, colored lines. The value of the thermal relic cross-section in function of the
DM mass is given as the red dotted-dashed line [82]. Dropping below the thermal relic effectively
rules out the DM mass as a candidate for primordial DM.

58

 [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limit-W+W [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limitZZ [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limitbb [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limittt [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limit-e+e [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limit-m+m [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limit-t+tFigure 3.9 Same as Fig. 3.8, using the set of 𝐽 factors from Ref. [72, 81] (B set in Table 3.2).

59

 [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limit-W+W [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limitZZ [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limitbb [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limittt [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limit-e+e [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limit-m+m [GeV]DMm10210310410510/s]3 [cmUL v>s95% <30-1029-1028-1027-1026-1025-1024-1023-1022-1021-1020-10Combined limitFermi-LAT limit median0HHAWC limit 68% containment0HH.E.S.S. limit 95% containment0HMAGIC limitThermal relic cross sectionVERITAS limit-t+tFigure 3.10 Comparisons of the combined limits at 95% confidence level for each of the eight
annihilation channels when using the 𝐽 factors from Ref. [78] (GS set in Table 3.2), plain lines,
and the 𝐽 factor from Ref. [72, 81] (B set in Table 3.2), dashed lines. The cross-section given by
the thermal relic is also indicated [82].

60

 [GeV]DMm10210310410510/s]3 [cmUL v>s95% CL <28-1027-1026-1025-1024-1023-1022-1021-1020-1019-1018-1017-10- W+WThis work (GS)This work (B)Thermal relic cross section [GeV]DMm10210310410510/s]3 [cmUL v>s95% CL <28-1027-1026-1025-1024-1023-1022-1021-1020-1019-1018-1017-10ZZThis work (GS)This work (B)Thermal relic cross section [GeV]DMm10210310410510/s]3 [cmUL v>s95% CL <28-1027-1026-1025-1024-1023-1022-1021-1020-1019-1018-1017-10bb This work (GS)This work (B)Thermal relic cross section [GeV]DMm10210310410510/s]3 [cmUL v>s95% CL <28-1027-1026-1025-1024-1023-1022-1021-1020-1019-1018-1017-10tt This work (GS)This work (B)Thermal relic cross section [GeV]DMm10210310410510/s]3 [cmUL v>s95% CL <28-1027-1026-1025-1024-1023-1022-1021-1020-1019-1018-1017-10- e+eThis work (GS)This work (B)Thermal relic cross section [GeV]DMm10210310410510/s]3 [cmUL v>s95% CL <28-1027-1026-1025-1024-1023-1022-1021-1020-1019-1018-1017-10-m +mThis work (GS)This work (B)Thermal relic cross section [GeV]DMm10210310410510/s]3 [cmUL v>s95% CL <28-1027-1026-1025-1024-1023-1022-1021-1020-1019-1018-1017-10-t +tThis work (GS)This work (B)Thermal relic cross sectionWe notice that the limits computed using the B set of 𝐽-factor are always better compared to the
ones calculated with the GS set. For the 𝑊 +𝑊 −, 𝑍 +𝑍 −, 𝑏 ¯𝑏, and 𝑡 ¯𝑡 channels, the ratio between the

limits computed with the two sets of 𝐽-factor is varying between a factor of ~3 and ~5 depending

on the energy, with the largest ratio around 10 TeV. For the channels 𝑒+𝑒−, 𝜇+𝜇−, and 𝜏+𝜏−, the

ratio lies between ~2 to ~6, being maximum around 1 TeV. Examining Figure 3.17 and Figure 3.18

in Section 3.8, these differences are explained by the fact that the B set provides higher 𝐽-factors

for the majority of the studied dSphs, with the notable exception of Segue I. The variation on the

ratio of the limits for the two sets is due to different dSph dominating the limits depending on the

energy. One set, B, pushes the range of which thermal cross-section which can be excluded to

higher mass. This comparison demonstrates the magnitude of systematic uncertainties associated

with the choice of the 𝐽-factor calculation The GS and B sets present a difference in the limits for

all channels of about This difference is explained, see Figure 3.17 and Figure 3.18, by the fact that

the B set provides higher 𝐽-factors for all dSph except for Segue I.

3.7 HAWC Systematics

3.7.1

Inverse Compton Scattering

The DM-DM annihilation channels produce many high energy electrons regardless of the

primary annihilation channel. These high energy electrons can produce high energy gamma-rays

through Inverse Compton Scattering (ICS). If this effect is strong, it would change the morphology

of the source and increase the total expected gamma-ray counts from any source. The PPPC [68]

provides tools in Mathematica for calculating the impact of ICS for an arbitrary location in the

sky for a specified annihilation channel. We calculated the change in gamma-ray counts for DM

annihilation to primary 𝑒 ¯𝑒 for RA and Dec corresponding to Segue1 and Coma Berenices. These

dSphs were chosen because they are the strongest contributors to the limit. 𝑒 ¯𝑒 was selected because

it would have the largest number of high energy electrons. The effect was found to be on the order

of 10−7 on the gamma-ray spectrum. As a result, this systematic is not considered in our analysis.

61

3.7.2 Point Source Versus Extended Source Limits

The previous DM search toward dSph approximated the dSphs as point sources [70].

In

this analysis, the dSphs are implemented as extended with J-factor distributions following those

produced by [78]. The resolution of the cited map is much finer than HAWC’s angular resolution.

The vast majority of the J-factor distribution is represented on the central HAWC pixel of the dSph

spatial map. However, the neighboring 8 pixels are not negligible and contribute to our limit.

Figure 3.11 Comparisons of the combined limits at 95% confidence level for a point source
analysis and extended source using [78] GS J-factor distributions and PPPC [68] annihilation
spectra. Shown are the limits for Segue1 which will have the most significant impact on the
combined limit. 6 of the 7 DM annihilation channels are shown. Solid lines are extended source
studies. Dashed lines are point source studies. Overall, the extended source analysis improves the
limit by a factor of 2.

Figure 3.11 shows a substantial improvement to the limit for Segue1. Fig. 3.12 however showed

identical limits. These disparities are best explained by the relative difference in their J-Factors.

Both dSphs pass almost overhead of the HAWC detector, however Segue1 has the larger J-Factor

between the two. Adjacent pixels to the central pixel will therefor contribute to the limits. This is

the case for other dSph that are closer to the zenith of the HAWC detector.

62

100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]bbHAWC PreliminaryExtendedPoint100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]WWHAWC PreliminaryExtendedPoint100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]HAWC PreliminaryExtendedPoint100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]HAWC PreliminaryExtendedPoint100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]ZZHAWC PreliminaryExtendedPoint100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]eeHAWC PreliminaryExtendedPointFigure 3.12 Same as Fig. 3.11 on Coma Berenices. This dSph also contributes significantly to the
limit. The limits are identical in this case.

Figure 3.13 HAWC reconstructed declination minus HESS reconstructed declination plotted over
HAWC longitude. There is a clear correlation with longitude and disparity between catalogs. This
disparity is maximized the larger the zenith angle. Plot pulled from internal HAWC presentation.

Comparison plots for all sources and the combined limit can be found in the sandbox for the

Glory Duck project.

63

100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]bbHAWC PreliminaryExtendedPoint100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]WWHAWC PreliminaryExtendedPoint100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]HAWC PreliminaryExtendedPoint100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]HAWC PreliminaryExtendedPoint100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]ZZHAWC PreliminaryExtendedPoint100101102M [TeV]1027102610251024102310221021102010191018< v > [cm3s1]eeHAWC PreliminaryExtendedPoint3.7.3

Impact of Pointing Systematic

During the analysis it was discovered that directional reconstruction of gamma-rays had a

systematic bias at large zenith angles. Figure 3.13 demonstrates the disparity between HAWC’s

reconstructed declination versus the same sources reconstructed by HESS. Shown on the presenta-

tion is dependence on the pointing systematic on declination. New spatial profiles were generated

for every dSph and limits were computed for the adjusted declination.

Figure 3.14 demonstrates the impact of this systematic for all DM annihilation channels studied

by HAWC. The impact is a tiny improvement, yet mostly identical, to the combined limits.

3.8

𝐽-factor distributions

3.8.1 Numerical integration of GS maps

It was discovered well after the HAWC analysis was completed that the published tables from

GS [69] quoted median 𝐽-factors were computed in a non-trivial manner. The assumption had

been that the published tables represented the 𝐽-factor as a function of 𝜃 for the best global fit model

on a per-source basis. However, this is not the case. Instead, what is published are the best fit

model for each dwarf that only considers stars up to the angular separation 𝜃. Therefore, the model

is changing for each value of 𝜃 for each dwarf. Yet, the introduced features from unique models at

each 𝜃 are much smaller than the angular resolution of HAWC. It is not expected for these effects

to impact the limits and TS greatly as a result.

Median 𝐽-factor model profiles were provided by the authors. New maps were generated

and analyzed for Segue1 and Coma Berenices. Figure 3.15 shows the differential between maps

generated with the method from Section 3.8.1 and from the authors of [69]. These maps were

reanalyzed for all SM DM annihilation channels. Upper limits for these channels are shown in

Fig. 3.16

From Fig. 3.16, we can see that the impact of these model differences was not substantial.

The observed impact was a fractional effect which is much smaller than the impact from selecting

another DM spatial distribution model as was shown in Fig. 3.10.

64

Figure 3.14 Comparison of combined limits when correcting for HAWC’s pointing systematic.
All DM annihilation channels are shown. The solid black line is the ratio between published limit
to the declination corrected limit. The blue solid line or "Combined_og" represented the limits
computed for Glory Duck. The solid orange line or "Combined_ad" represented the limits
computed after correcting for the pointing systematic.

3.8.2 GS Versus B spatial models

In this is a comparison between the 𝐽-factors computed by Geringer-Sameth et al. [78] (the

GS set) and the ones computed by Bonnivard et al. [72, 81] (the B set). The GS 𝐽-factors are

computed through a Jeans analysis of the kinematic stellar data of the selected dSphs, assuming a

65

100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]bbHAWC PreliminaryPoint Systematic Comparison for Combined_ogCombined_ad0.000.250.500.751.001.251.501.752.00Ratio100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]eeHAWC PreliminaryPoint Systematic Comparison for Combined_ogCombined_ad0.000.250.500.751.001.251.501.752.00Ratio100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]HAWC PreliminaryPoint Systematic Comparison for Combined_ogCombined_ad0.000.250.500.751.001.251.501.752.00Ratio100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]HAWC PreliminaryPoint Systematic Comparison for Combined_ogCombined_ad0.000.250.500.751.001.251.501.752.00Ratio100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]ttHAWC PreliminaryPoint Systematic Comparison for Combined_ogCombined_ad0.000.250.500.751.001.251.501.752.00Ratio100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]WWHAWC PreliminaryPoint Systematic Comparison for Combined_ogCombined_ad0.000.250.500.751.001.251.501.752.00Ratio100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]ZZHAWC PreliminaryPoint Systematic Comparison for Combined_ogCombined_ad0.000.250.500.751.001.251.501.752.00RatioFigure 3.15 Differential map of 𝑑𝐽/Ω from model built in Section 3.8.1 and profiles provided
directly from authors. (Top) Differential from Segue1. (bottom) Differential from Coma
Berenices. Note that their scales are not the same. Segue1 shows the deepest discrepancies which
is congruent with its large uncertainties. Both models show anuli where unique models become
apparent.

66

Figure 3.16 HAWC limits for Coma Berenices (top) and Segue1 (bottom) for two different map
sets. Blue lines are limits calculated on maps with poor model representation. Orange lines are
limits calculated on spatial profiles provided by the authors of [69]. Black line is the ratio of the
poor spatial model limits to the corrected spatial models. The left y-axis measures ⟨𝜎v⟩for the
blue and orange lines. The right y-axis measures the ratio and is unitless.

67

100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]bbHAWC PreliminaryJ-Fac Model Systematic Comparison for ComaBerenicesComaBerenices poor dJ/dOComaBerenices correct dJ/dO0.000.250.500.751.001.251.501.752.00Ratio100101102M [TeV]102610251024102310221021102010191018v [cm3 s1]bbHAWC PreliminaryJ-Fac Model Systematic Comparison for Segue1Segue1 poor dJ/dOSegue1 correct dJ/dO0.000.250.500.751.001.251.501.752.00Ratiodynamic equilibrium and a spherical symmetry for the dSphs. They adopted the generalized DM

density distribution, known as Zhao-Hernquist, introduced by [71], carrying three additional index

parameters to describe the inner and outer slopes, and the break of the density profile. Such a

profile parametrization allows the reduction of the theoretical bias from the choice of a specific

radial dependency on the kinematic data. In other words, the increase of free parameters with the

use of the Zhao-Hernquist profile allows a better description of the mass density distribution of

dark matter.

In addition, a constant velocity anisotropy profile and a Plummer light profile [83] for the stellar

distribution were assumed. The velocity anisotropy profile depends on the radial and tangential

velocity dispersion. However, its determination remains challenging since only the line-of-sight

velocity dispersion can be derived from velocity measurements. Therefore, the parametrization of

the anisotropy profile is obtained from simulated halos (see [84] for more details). They provide the

values of the 𝐽-factors of regions extending to various angular radius up to the outermost member

star.

The B 𝐽-factors were computed through a Jeans analysis taking into account the systematic

uncertainties induced by the DM profile parametrization, the radial velocity anisotropy profile, and

the triaxiality of the halo of the dwarf galaxies. They performed a more complete study of the

dSph kinematics and dynamics than GS for the determination of the 𝐽-factor. Conservative values

of the 𝐽-factors where obtained using an Einasto DM density profile [85], a realistic anisotropy

profile known as the Baes & Van Hese profile [86] that takes into account the inner regions can be

significantly non-isotropic, and a Zhao-Hernquist light profile [71].

For both sets, 𝐽-factor values are provided for all dSphs as a function of the radius of the

integration region [78, 72, 81]. Table 3.2 shows the heliocentric distance and Galactic coordinates

of the twenty dSphs, together with the two sets of 𝐽-factor values integrated up to the outermost

observed star for GS and the tidal radius for B. Both 𝐽-factor sets were derived through a Jeans

analysis based on the same kinematic data, except for Draco where the measurements of [87] have

been adopted in the computation of the B value. The computations for producing the GS and B

68

samples differ in the choice of the DM density, velocity anisotropy, and light profiles, for which the

set B takes into account some sources of systematic uncertainties.

Figure 3.17 and Figure 3.18 show the comparisons for the 𝐽-factor versus the angular radius

for each of the 20 dSphs used in this study. The uncertainties provided by the authors are also

indicated in the figures. For the GS set, the computation stops at the angular radius corresponding

to the outermost observed star, while for the B set, the computation stops at the angular radius

corresponding to the tidal radius.

3.9 Discussion and Conclusions

In this multi-instrument analysis, we have used observations of 20 dSphs from the gamma-ray

telescopes Fermi-LAT, H.E.S.S., MAGIC, VERITAS, and HAWC to perform a collective DM

search annihilation signals. The data were combined across sources and detectors to significantly

increase the sensitivity of the search. We have observed no significant deviation from the null DM

hypothesis, and so present our results in terms of upper limits on the annihilation cross-section for

seven potential DM annihilation channels.

Fermi-LAT brings the most stringent constraints for continuum channels below approximately

1 TeV. The remaining detectors dominate at higher energies. Overall, for multi-TeV DM mass,

the combined DM constraints from all five telescopes are 2-3 times stronger than any individual

telescope for multi-TeV DM.

Derived from observations of many dSphs, our results produce robust limits given the DM

content of the dSphs is relatively well constrained. The obtained limits span the largest mass

range of any WIMP DM search. Our combined analysis improves the sensitivity over previously

published results from each detector which produces the most stringent limits on DM annihilation

from dSphs. These results are based on deep exposures of the most promising known dSphs with

the currently most sensitive gamma-ray instruments. Therefore, our results constitute a legacy of

a generation of gamma-ray instruments on WIMP DM searches towards dSphs. Our results will

remain the reference in the field until a new generation of more sensitive gamma-ray instruments

begin operations, or until new dSphs with higher 𝐽-factors are discovered.

69

Figure 3.17 Comparisons between the 𝐽-factors versus the angular radius for the computation of 𝐽
factors from Ref. [78] (GS set in Table 3.2) in blue and for the computation from Ref. [72, 81] (B
set in Tab. 3.2) in orange. The solid lines represent the central value of the 𝐽-factors while the
shaded regions correspond to the 1𝜎 standard deviation.

This analysis serves as a proof of concept for future multi-instrument and multi-messenger

combination analyses. With this collaborative effort, we have managed to sample over four orders

in magnitude in gamma-ray energies with distinct observational techniques. Determining the nature

of DM continues to be an elusive and difficult problem. Larger datasets with diverse measurement

techniques could be essential to tackling the DM problem. A future collaboration using similar

70

102101100101Angular radius (°)1617181920J factor (GeV2.cm5.sr)Bootes IGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)15.015.516.016.517.017.518.0J factor (GeV2.cm5.sr)Canes Venatici IGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)1617181920J factor (GeV2.cm5.sr)Canes Venatici IIGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)15.516.016.517.017.518.018.5J factor (GeV2.cm5.sr)CarinaGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)1718192021J factor (GeV2.cm5.sr)Coma BerenicesGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)1617181920J factor (GeV2.cm5.sr)DracoGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)15.516.016.517.017.518.0J factor (GeV2.cm5.sr)FornaxGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)1516171819J factor (GeV2.cm5.sr)HerculesGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)16.016.517.017.518.018.5J factor (GeV2.cm5.sr)Leo IGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)16.517.017.518.018.5J factor (GeV2.cm5.sr)Leo IIGeringer-Sameth etal.Bonnivard etal.Figure 3.18 Comparisons between the 𝐽-factors versus the angular radius for the computation of 𝐽
factors from Ref. [78] (GS set in Tab. 3.2) in blue and for the computation from Ref. [72, 81] (B
set in Tab. 3.2) in orange. The solid lines represent the central value of the 𝐽-factors while the
shaded regions correspond to the 1𝜎 standard deviation.

techniques as the ones described here could grow even beyond gamma rays. The models we used

for this study include annihilation channels with neutrinos in the final state. Advanced studies could

aim to merge our results with those from neutrino observatories with large data sets. Efforts with

IceCube have already started, and the groundwork is presented in Sec. 6.

From this work, a selection of the best candidates for observations, according to the latest

71

102101100101Angular radius (°)131415161718J factor (GeV2.cm5.sr)Leo IVGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)15.516.016.517.017.518.018.5J factor (GeV2.cm5.sr)Leo TGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)1314151617J factor (GeV2.cm5.sr)Leo VGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)16.517.017.518.018.5J factor (GeV2.cm5.sr)SculptorGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)1314151617181920J factor (GeV2.cm5.sr)Segue IGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)1415161718192021J factor (GeV2.cm5.sr)Segue IIGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)15161718J factor (GeV2.cm5.sr)SextansGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)151617181920J factor (GeV2.cm5.sr)Ursa Major IGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)171819202122J factor (GeV2.cm5.sr)Ursa Major IIGeringer-Sameth etal.Bonnivard etal.102101100101Angular radius (°)16.517.017.518.018.519.0J factor (GeV2.cm5.sr)Ursa MinorGeringer-Sameth etal.Bonnivard etal.knowledge on stellar dynamics and modelling techniques for the derivation of the 𝐽-factors on

the potential dSphs targets, is highly desirable at the time that new experiments are starting their

dark matter programs using dSphs. Given the systematic uncertainty inherent to the derivation of

the 𝐽-factors, an informed observational strategy would be to select both objects with the highest

𝐽-factors that could lead to DM signal detection, and objects with robust 𝐽-factor predictions, i.e.

with kinematic measurements on many bright stars, which would strengthen the DM interpretation

reliability of the observation outcome.

This analysis combines data from multiple telescopes to produce strong constraints on astro-

physical objects. From this perspective, these methods can be applied beyond just DM searches.

Almost every astrophysical study can benefit from multi-telescope, multi-wavelength gamma-ray

studies and is continued in this thesis. Moreover, HAWC and IceCube have made substantial leaps

in their analysis methods and merits a refreshed analysis on DM signals from dSph. In HAWC, the

updated 2D energy binning scheme, see Section 2.2.4 for description, split by 𝑓hit and estimated

energy from our Neural Network (NN) method in an effort to better estimate gamma-ray energy.

Whereas, IceCube’s previous DM search towards dSph was performed when it was an incomplete

detector. Leaps have also been made on the theoretical front for both the particle physics modeling

and DM density profiles. These broad improvements have been implemented and started on both

HAWC and IceCube. The improvements for HAWC are featured in Chapter 4 and IceCube’s are in

Chapter 6.

The results of the Glory Duck collaboration have gone through collaboration review for all

experiments involved. The final step of verifying and consolidating the author list is what remains

before sending the work to publication.

72

CHAPTER 4

MULTITHREADING HAWC ANALYSES FOR DARK MATTER SEARCHES

4.1

Introduction

HAWC’s current software suite, plugins to 3ML and HAL [77, 44], do not fully utilize compu-

tational advancements of recent decades. Said advancements include the proliferation of Graphical

Processing Units (GPUs), and multithreading on multicore processors. The analysis described in

Chapter 3 took up to 3 months of wall time waiting for the full gambit of data analysis and simulation

of background to compute. Additionally, with the updated 2D energy binning scheme split by 𝑓hit

and estimated energy from our Neural Network (NN) method, the time needed to compute was

expected to grow. Although excessive computing time was, in part, from an intense use of a shared

computing cluster, it was evident that there was room for improvement. In HAWC’s next generation

dSph DM search, I decided to develop codes that would utilize the multicore processors on modern

high performance computing clusters. The results of this work are featured in this chapter and

brought a human timing improvement to computation that scales approximately as 1/𝑁 where 𝑁

is the number of threads.

4.2 Dataset and Background

This section describes the data and background methods used for HAWC’s multithreaded study

of dSphs. Sections 4.2.1 and 4.2.2 are most useful for fellow HAWC collaborators looking to

replicate a multithreaded dSph DM search.

4.2.1

Itemized HAWC files

These files are only available within HAWC’s internal documentation and collaborators. They

are not meant for public access, and are presented here so that HAWC can reproduce results

accurately.

• Detector Resolution: refit-Pass5-Final-NN-detRes-zenith-dependent.root

• Data Map: Pass5-Final-NN-maptree-ch103-ch1349-zenith-dependent.root

• Spectral Dictionary: HDMSpectra_dict_gamma.npy

73

4.2.2 Software Tools and Development

This analysis was performed using HAL and 3ML [44, 67] in Python3.

I built software in

collaboration with Michael Martin and Letrell Harris to implement the Dark Matter Spectra from

the Electroweak to the Planck Scale (HDM) [25] and dSphs spatial model from [88] for HAWC

analysis. A NumPy dictionary of HDM, HDMSpectra_dict_gamma.npy, was made for portability

within the collaboration. These dictionaries were generated from the git repository [25]. The

analysis was performed using the Neural Network energy estimator for Pass 5.F. A description

of this estimator was provided in Section 2.2.4. Its key, relevant improvements are an improved

energy estimation and improved sensitivities at higher zenith angles. All other software used for

data analysis, DM profile generation, and job submission to SLURM are kept in my sandbox in

the Dark Matter HAWC project. The above repository also incorporates the model inputs used

previously in Glory Duck, described in Chapter 3, so Glory Duck remains compatible with modern

software.

4.2.3 Data Set and Background Description

The HAWC data maps used for this analysis contain 2565 days of data between runs 2104 and

7476. They were generated from pass 5.F reconstruction. The analysis is performed using the NN

energy estimator with nominal bin list:

B1C0Ea, B1C0Eb, B1C0Ec, B1C0Ed, B1C0Ee, B2C0Ea, B2C0Eb, B2C0Ec, B2C0Ed,

B2C0Ee, B3C0Ea, B3C0Eb, B3C0Ec, B3C0Ed, B3C0Ee, B3C0Ef, B4C0Eb, B4C0Ec,

B4C0Ed, B4C0Ee, B4C0Ef, B5C0Ec, B5C0Ed, B5C0Ee, B5C0Ef, B5C0Eg, B6C0Ed,

B6C0Ee, B6C0Ef, B6C0Eg, B6C0Eh, B7C0Ee, B7C0Ef, B7C0Eg, B7C0Eh, B7C0Ei,

B8C0Ee, B8C0Ef, B8C0Eg, B8C0Eh, B8C0Ei, B8C0Ej, B9C0Ef, B9C0Eg, B9C0Eh,

B9C0Ei, B9C0Ej, B10C0Eg, B10C0Eh, B10C0Ei, B10C0Ej, B10C0Ek, B10C0El

Bin 0 was excluded as it has substantial hadronic contamination and poor angular resolution. This

list was cut down depending on the declination of the source because the Point Spread Function

(PSF) of these bins were too large, or the statistics were too low.

74

Background considerations and source selection was identical to Section 3.2.3, and no additional

arguments are provided here. Many of the HAWC systematics explored in Section 3.7 also apply

for this DM search and are not discussed here.

4.3 Analysis

The analysis and its systematics are almost identical to Section 3.3.

Importantly, the same

Eqs. (3.1) and (3.2) for estimating the gamma-ray flux at HAWC from our sources are used here.

This analysis improves on Chapter 3 in the following ways. The particle physics model used for

gamma-ray spectra was updated to accommodate recent measurements and constraints in particle

physics. For this study, HAWC samples DM masses up to 10 PeV, where previously it stopped at 1

TeV. Additionally, we use a new DM density profile catalog. Finally, the gamma-ray ray dataset is

much larger, almost double the size of the data used in Chapter 3.

4.3.1

𝑑𝑁𝛾
𝑑𝐸𝛾 - Particle Physics Component

For these spectra, we import HDM with Electroweak (EW) corrections and additional correc-

tions for neutrinos above the EW scale [25]. The spectra are implemented as a model script in

astromodels for 3ML. A comprehensive description of EW corrections and neutrino considerations

are provided later in Sec. 7.

Figure 4.1 demonstrates the impact of changes implemented in HDM on DM annihilation to W

bosons. A class in astromodels was developed to include HDM and is aptly named HDMSpectra

within DM_models.py. The SM DM annihilation channels studied here are 𝜒 𝜒 →:

𝑒+𝑒−, 𝜇+𝜇−, 𝜏+𝜏−,𝑏 ¯𝑏, 𝑡 ¯𝑡, 𝑔𝑔, 𝑊 +𝑊 −, 𝑍 𝑍, 𝑐 ¯𝑐, 𝑢 ¯𝑢, 𝑑 ¯𝑑, 𝑠 ¯𝑠, 𝜈𝑒𝜈𝑒, 𝜈𝜇𝜈𝜇, 𝜈𝜏𝜈𝜏, 𝛾𝛾, ℎℎ.

For 𝛾𝛾 and 𝑍 𝑍, a substantial fraction of the signal photons are expected to have 𝐸𝛾 = 𝑚 𝜒 [25]. This

introduces a 𝛿-function in the tested spectra, referred to as a spectral line, that is much narrower than

the energy resolution of the HAWC detector. To ensure that this feature is not lost in the likelihood

fits, the ‘line’ feature is convolved with a Gaussian kernel with a 1𝜎 width of 0.05 · 𝑚 𝜒 and total

kernel window of ±4𝜎. The kernel width was chosen based on the choices made from HAWC’s

previous gamma-line study [89] and the observed energy resolution of the NN energy estimator

75

Figure 4.1 Spectral hypotheses from PPPC [68] and HDM [25] for DM annihilation:
𝜒 𝜒 → 𝑊 −𝑊 +. Solid lines are spectral models with EW corrections from the PPPC. Dash-dot
lines are spectral models from HDM. Red lines are models for 𝑀𝜒 = 1 TeV. Blue lines represent
models for 𝑀𝜒 = 100 TeV.

[48]. This differs from HAWC’s previous line study where 30% of HAWC’s energy resolution was

used for the kernel [89]. The NN energy estimator’s improved energy resolution compared to 𝑓hit at

low gamma-ray energy enables narrower kernels [25] (see Section 2.2.4). The annihilation spectra

after Gaussian smoothing for 𝜒 𝜒 → 𝛾𝛾 and 𝑍 𝑍 spectral hypotheses are shown in Fig. 4.2. We

did not explore how well we reconstruct injected signal events for various kernels widths. This is a

systematic that should be tested before publication in a journal. Spectral models for the remaining

annihilation channels are plotted for each 𝑚 𝜒 in Figure B.1.

4.3.2

𝐽 Astrophysical Components

The J-factor profiles for each source are imported from Louis Strigari et al. (referred to with

LS) [88]. The LS catalog fits a Navarro–Frenk–White (NFW) [28] spatial DM distributions to

the dSphs which has a DM density of

𝜌(𝑟) =

𝜌0
(cid:16)1 + 𝑟
𝑅𝑠

.

(cid:17) 2

𝑟
𝑅𝑠

76

(4.1)

Figure 4.2 Photon spectra for 𝜒 𝜒 → 𝛾𝛾 (left) and 𝜒 𝜒 → 𝑍 𝑍 (right) after Gaussian convolution of
line features. Both spectra have 𝛿-features at photon energies equal to the DM mass. Bluer lines
are annihilation spectra with lower DM mass. Redder lines are spectra from larger DM mass. All
spectral models are sourced from the Heavy Dark Matter models [25]. Axes are drawn roughly
according to the energy sensitivity of HAWC.

𝜌0 and the scale radius, 𝑅𝑠 are free parameters fit for each dSph. 𝑟 is the distance from the center of

the dSph. Because the LS catalog uses fewer parameters for the DM density fits, they are able to

fit on ultra-faint dSphs. This increases the number of available profiles to 43. The updated catalog

was considered useful for a future combination with the IceCube neutrino observatory, and is a

significant reason we selected this catalog.

Profiles in 𝑑𝐽

𝑑Ω (𝜃) up to an angular separation 𝜃 = 0.5◦ were provided directly by the authors.
Map generation from these profiles were almost identical to Section 3.3.2 except that a higher order

trapezoidal integral was used for the normalization of the square, uniformly-spaced map:

𝑝2 ·

𝑁
∑︁

𝑀
∑︁

𝑖=0

𝑗=0

𝑤𝑖, 𝑗

𝑑𝐽
𝑑Ω

(𝜃𝑖, 𝑗 , 𝜙𝑖, 𝑗 )

(4.2)

𝑝 is the angular side of one pixel in the map. 𝑤𝑖, 𝑗 is a weight assigned the following ways:

𝑤𝑖, 𝑗 = 1 if (𝜃𝑖, 𝑗 , 𝜙𝑖, 𝑗 ) is fully within the region of integration

𝑤𝑖, 𝑗 = 1/2 if (𝜃𝑖, 𝑗 , 𝜙𝑖, 𝑗 ) is on an edge of the region of integration

𝑤𝑖, 𝑗 = 1/4 if (𝜃𝑖, 𝑗 , 𝜙𝑖, 𝑗 ) is on a corner of the region of integration

Figure 4.3 shows the median and ±1𝜎 maps used as input for this DM annihilation study.

77

−1𝜎

Median

+1𝜎

s
e
c
i
n
e
r
e
B
a
m
o
C

1
e
u
g
e
S

s
n
a
t
x
e
S

Figure 4.3 𝑑𝐽
maps for Coma Berenices, Segue1, and Sextans. Columns are divided for the ±1𝜎
𝑑Ω
uncertainties in 𝑑𝐽/𝑑Ω around the mean value from LS [88]. Origin is centered on the specific
dwarf spheroidal galaxies (dSph). 𝜃 and 𝜙 axes are the angular separation from the center of the
dwarf. Profiles are truncated at 1◦ and flattened beyond.

4.3.3 Source Selection and Annihilation Channels

HAWC’s sources for this multithreaded analysis include Coma Berenices, Segue 1, and Sextans.

LS estimated the DM distributions of 43 sources in its publication, however only 4 of the best

fit profiles within HAWC’s field of view were provided at the time this thesis was written. A full

description of each source used in this analysis is found in Tab. 4.1.

This analysis improves on Chapter 3 in the following ways. Previously, the particle physics

model used for gamma-ray spectra from DM annihilation was from the PPPC [68] which missed

important considerations relevant for the neutrino sector. HDM is used to account for this shortfall

[25]. HDM also models DM to the Planck scale which permits HAWC to probe PeV scale DM. For

this study, we sample DM masses: 1 TeV - 10 PeV with 6 mass bins per decade in DM mass. In

the case of line spectra (𝜒 𝜒 → 𝛾𝛾, or 𝑍 𝑍), we double the mass binning to 12 DM mass bins per

78

1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)0123456log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)0123456log10(dJd/GeV2cm5sr)decade in DM mass.

LS published 25 sources’ 𝐽-factors within HAWC’s field of view. Additionally, NFW [28]

DM distributions have fewer parameters than Zhao [71], so LS fits ultra-faint dwarves which

expands the number of sources. However, all sources were not provided by the authors in time for

the completion of this dissertation. Draco was provided by the authors. However, Draco is not

included in this study as the PSF of the bins at its declination were wider than what is reasonable

for a point source analysis. Finally, the gamma-ray ray dataset is much larger. The study performed

here analyzes 2565 days of data compared to 1017 days analyzed in Chapter 3.

4.4 Likelihood Methods

These are identical to Section 3.4.1 and no additional changes are made to the likelihood. Bins

in this analysis are expanded to include HAWC’s NN energy estimator.

4.5 Computational Methods: Multithreading

Previously, as in Section 3.3, the likelihood was minimized for one model at a time. One

model in this case representing a DM annihilation channel (CHAN), DM mass (𝑚 𝜒), and dSph

((SOURCE)). In an effort to conserve human and CPU time, jobs submitted for high performance

computing contained a list of 𝑚 𝜒 to iterate over for likelihood fitting. Jobs were then trivially

parallelized for each permutation of the two lists: CHANS and SOURCES. The lists for CHANS

and SOURCES are found in Section 4.3.1 and Tab. 4.1, respectively. Initially, 11 𝑚 𝜒 were serially

Name

Distance
(kpc)

𝑙, 𝑏
(°)

Coma Berenices

Segue I

Sextans

44

23

86

241.89, 83.61

220.48, 50.43

243.50, 42.27

log10 𝐽 (LS set)
log10 (GeV2cm−5sr)
19.00+0.36
−0.35
19.12+0.49
−0.58
17.73+0.13
−0.12

Table 4.1 Summary of the relevant properties of the dSphs used in the present work. Column 1
lists the dSphs. Columns 2 and 3 present their heliocentric distance and galactic coordinates,
respectively. Column 4 reports the 𝐽-factors of each source given from the LS studies and
estimated ±1𝜎 uncertainties. The values log10 𝐽 (LS set) [88] correspond to the mean 𝐽-factor
values for a source extension truncated at 0.5◦.

79

sampled for one job defined by a [CHAN, SOURCE] tuple. Computing the likelihoods would

take between 1.5 to 2 hrs, stochastically, for a job. We expect to compute likelihoods for data and

300 Poisson background trials. The estimated CPU time based on the above for all CHAN (N =

17) and SOURCE (M = 25) was estimated to be 127, 925 jobs. In total, 1, 407, 175 likelihood fits

and profiles would be computed for the 11 mass bins we wished to study. The estimated CPU time

ranged between 8k CPU days to 10k CPU days. Human time is more challenging to estimate as job

allocation is stochastic and highly dependent on what other users are submitting. Yet, it is unlikely

that all jobs would run simultaneously. Therefore, we can expect human time to be about as long

as was seen in Chapter 3, which was on the order of months to fully compute a smaller analysis. A

visual aid to describe how jobs were organized is provided in Fig. 4.4.

Figure 4.4 Infographic on how jobs and DM computation was organized in Section 3.3. Jobs were
built for each permutation of CHANS and SOURCES shown by the left block in the figure. Each
job, which took on the order 2 hrs to compute, had the following work flow: 1. Import HAWC
analysis software, 2 min to run. 2. Load HAWC count maps, 5 min to run. 3. Load HAWC energy
and spatial resolutions, 4 min. 5. Load DM spatial source templates and spectral models, less than
1 s. 6. Perform likelihood fit on data and model, about 8 min per DM mass. 7. Write results to
file, less than 1s.

The computational needs for this next generation DM analysis are extreme and is unlike other

analyses performed on HAWC. It became clear that there was a lot to gain from optimizing how

80

the likelihoods are computed. This section discusses how multi-threading was applied to solve and

reduce HAWC’s computing of likelihoods for large parameter spaces like in DM searches.

4.5.1 Relevant Foundational Information

The profiling of the likelihood for HAWC is done via gradient descent where the normalization

of Equation (3.1) (linearly correlated with ⟨𝜎v⟩) is rescaled in the descent. Additionally, we sample

the likelihood space for a defined list of ⟨𝜎v⟩’s described in Section 3.4.2. The time to compute

these values is not predictable or consistent because many variables can change across the full

model-space. Comprehensively, these variables are:

• 𝑚 𝜒 : DM rest mass

• CHAN : DM annihilation channel in SM.

• SOURCE : dSph. Involves a spatial template AND coordinate in HAWC data.

• ⟨𝜎v⟩: Proportional to the flux normalization and free parameter in the likelihood fit.

Therefore, an asynchronous, functional-parallel coding pattern was developed. Asynchronous

means the instructions within a function are independent and permitted to be out of sync with

sibling computations. Functional-parallel means that instructions are the subject of parallelization

rather than threading the likelihood computation. This is close to trivial parallelization seen in

Fig. 4.4 except that jobs are joined in the loading stages (software, data, and detector resolution

loading). Multiple asynchronous threads are expected to reduce total serial processing time and

total overhead across the entire project in addition to saving human time.

A way to measure and compare the expected speedup and efficiency gain is needed for this

asynchronous coding pattern. Inspiration for timing measurement was pulled from [90] and used

Amdahl’s law with hybrid programming. Hybrid programming meaning that the computation is

a mix of distributed and shared memory programming. Assuming the code is fully parallelizable

over 𝑝 processors and 𝑐 threads, the ideal speedup is simply 𝑝𝑐, and ideal run-time is 𝑇1/( 𝑝𝑐). 𝑇1

is the total time for a parallel program to run if only 1 processor is allocated. However, the coding

81

Figure 4.5 Graphic of Gustafson parallel coding pattern. 𝑓𝑠 is the fraction of a program, in time,
spent on serial computation. 𝑓𝑝 is the fraction of computing time that is parallelizable. 𝑇𝑝 is the
total time for a parallel program to run. 𝑇1 is the total time for a parallel program to run if only 1
processor is allocated. 𝑃𝑁 is the 𝑁-th processor where it’s row is the computation the processor
performs. The Gustafson pattern is most similar to what is implemented for this analysis. Figure
is pulled from [90].

pattern contains some amount of unavoidable serial computation, as shown in Figure 4.5. In this

case, the run time, 𝑇𝑝,𝑐, is estimated to be

𝑇𝑝,𝑐 =

𝑇1
𝑝𝑐

(1 + 𝐹𝑠 (𝑐 − 1)) .

(4.3)

𝐹𝑠 is the fraction of CPU time dedicated to serial computation. The expected speedup, 𝑆 𝑝,𝑐, is

𝑆 𝑝,𝑐 ≡

𝑇1
𝑇𝑝,𝑐

=

𝑝𝑐
1 + 𝐹𝑠 (𝑐 − 1)

.

(4.4)

From Equation (4.4), we can see that the speed-up scales with 𝑝/𝐹𝑠. We are free to minimize 𝐹𝑠

asymptotically by enlarging the total models that are submitted to the thread pool, thereby shrinking

the CPU fraction dedicated to serial operation. We are also free to define exactly how many threads

and processors we utilize, yet eventually hit a hard cap at the hardware available on our computing

cluster. HAWC uses Intel Xeon™processors with 48 cores and 96 threads. We see that a successful

code will scale well as the expected speedup is inversely correlated with 𝐹𝑠. As the total number

of models sampled grows, the speedup will also.

82

Figure 4.6 Task chart for one multithreaded job developed for this project. Green blocks indicate a
shared resource across the threads AND computation performed serially. Red blocks indicate
functional parallel processing within each thread. 3 threads are represented here, yet many more
can be employed during the full analysis. Jobs are defined by the SOURCE as these require
unique maps to be loaded into the likelihood estimator. The 𝑚 𝜒, CHAN, and ⟨𝜎v⟩ variables are
entered into the thread pool and allocated as evenly as possible across the threads.

4.5.2

Implementation

The multithreaded code was written in Python3 and is documented in the dark_matter_hawc

repository within the script named mpu_analysis.py. A version of the script as of April 15 is also

provided in Chapter C. It has many dependencies including the HAWC analysis software. Figure 4.6

displays the workflow of a job with 3 threads. Within a job, SOURCE is kept fixed and CHANS

remains 17 elements long. More 𝑚 𝜒 are sampled from 11 bins up to 49 (for 𝛾𝛾 and 𝑍 𝑍) and 25

(for remaining CHANS) which amounts to 12 or 6 mass bins per decade. 𝑚 𝜒 and CHANS are

permuted into a 473 element list which is split evenly across N threads where N is [2, 8, 16]. For

each 𝑚 𝜒-CHAN tuple, 1001 ⟨𝜎v⟩ values are sampled in the likelihood, and the value of ⟨𝜎v⟩ that

maximizes the likelihood is found. Although rare, fits that failed are handled on a case by case

basis.

83

M Tasks
50
74
100
200
473

𝑇1,1
1:40:37.5
2:22:30.0
(3:07:51.9)
(6:02:20.6)
(13:58:40.3)

𝑇𝑝,𝑐 (hr:min:s)
𝑇1,2
0:52:43.7
1:15:00.6
1:40:10.5
-
-

𝑇1,8

𝑇1,16

0:19:13.8 0:13:44.0
0:25:21.3 0:15:49.8
0:20:01.4
0:30:44.4
0:30:35.0
1:00:32.0
1:07:53.2
2:01:41.4

Table 4.2 Timing summaries for analyses for serial and multithreaded processes. M tasks is the
number of functional-parallel tasks ran for the computation. 𝑇𝑝,𝑐 is a single run time in
hours:minutes:seconds for runs utilizing 𝑝 nodes and 𝑐 threads. Runs are run interactively on the
same computer to maximize consistency. Empty entries are indicated with ’-’. (·) entries are
estimated entries extrapolated from data earlier in the column.

4.5.3 Performance

A significant reduction to wall time is needed for the dSphs analysis to run. Table 4.2 shows

the timing summaries for analyses of different sizes and thread counts. Additionally, the efficiency

gained when consolidating the serial loading of data is also apparent in our ability to study many

more tasks in about the same amount of wall time as a smaller serial computation. Trials represented

in the table were run on an AMD Opteron® processor 6344 with 48 cores, 2 threads per core; 2.6

GHz clock. This is not the same architecture used for analysis on the HAWC computing cluster

however they are similar enough that results shown here are reasonably representative of computing

on the HAWC computing cluster. Table 4.2 is used for the inferences and conclusions made in the

following paragraphs.

First, we want to find 𝑇𝑠, the time of serial computation. From Fig. 4.5, the timing for our

coding pattern can be written as

𝑇𝑠 + 𝑀𝑡 𝑝 = 𝑇 𝑀
1,1.

(4.5)

𝑀 is the number of functional-parallel tasks (represented as column 1 of Tab. 4.2), and 𝑡 𝑝 is the

average time to complete a single parallel task. 𝑇 𝑀

1,1 is the total time for a parallel program to run if
only 1 processor is allocated for M parallel task. With two runs of different M (𝑀1 and 𝑀2), we

can use a system of equations to compute

𝑇𝑠 = 803.1s and 𝑡 𝑝 = 104.6s

(4.6)

84

Now, we have specific estimation for the fraction of serial computing time, 𝐹𝑠:

𝐹𝑠 =

803.1
803.1 + 104.6 · 𝑀

.

(4.7)

The maximum M for this study is 473 which evaluates to: 𝐹𝑠 = 0.016 or 1.6% of computing time.

Table 4.3 shows the resulting speedups.

M Tasks
50
74
100
200
473

𝐹𝑠
1.33 E-1
9.40 E-2
7.13 E-2
3.70 E-2
1.60 E-2

𝑆1,2
1.90 [1.76]
1.90 [1.83]
1.88 [1.87]
- [1.93]
- [1.97]

𝑆1,8
5.23 [4.14]
5.62 [4.82]
6.11 [5.34]
5.98 [6.36]
6.89 [7.20]

𝑆1,16
6.35 [5.34]
9.00 [6.64]
9.38 [7.73]
11.85 [10.29]
12.35 [12.91]

Table 4.3 Speed up summaries for analyses for serial and multithreaded processes. M tasks is the
number of functional-parallel tasks ran for the computation. 𝑆 𝑝,𝑐 is a single speedup comparison
for runs utilizing 𝑝 nodes and 𝑐 threads. [·] are the estimated speedups calculated from Tab. 4.2,
Eq. (4.7), and Eq. (4.4). Empty entries are indicated with ’-’.

A speedup that generally exceeds expectations from Eq. (4.4) is seen for real trail runs. There

are also diminishing returns as the number of threads increases. For small jobs with large 𝑐, both

the expected and observed speedup are significantly smaller than 𝑐. One thing not considered in

Eq. (4.4) is the time incurred via communication latency. Communication latency increases with

the number of threads and contributes to diminishing returns. Additionally, these values are for

single runs and do not consider the stochastic variation expected in a shared high performance

computing resource. Therefor, these results are not strictly conclusive, yet demonstrate the merits

of multi-threading. There is a lot to gain, and this new coding pattern will expand HAWC’s analysis

capabilities.

4.6 Analysis Results

Three of the 43 LS dSphs are considered for the multithreaded analysis. These dSph are

analyzed for emission from DM annihilation according to the likelihood method described in

Section 3.4. The three likelihood profiles are then stacked to synthesize a combined limit on

the dark matter annihilation cross-section, ⟨𝜎v⟩. This combination is done for each of the 17

SM annihilation channels. Figure 4.7 and Fig. 4.8 show the combined limits for all annihilation

85

channels with HAWC’s observations. Test statistics of the best fit ⟨𝜎v⟩ values for each 𝑚 𝜒 and

CHAN are shown in Fig. 4.9 and Fig. 4.10. These limits are compared to HAWC’s Glory Duck

limits from Section 3.5 and shown in Fig. 4.11 for all the DM annihilation channels studied for

Glory Duck. A full comparison is provided in Chapter D in Figs. D.1 to D.3. Here, we show

updated limits for 𝜒 𝜒 → 𝑏𝑏, 𝑒𝑒, 𝜇𝜇, 𝜏𝜏, 𝑡𝑡, 𝑊 +𝑊 −, 𝛾𝛾 and 𝑍 𝑍. For the first time ever, we show

limits for 𝜒 𝜒 → 𝑐𝑐, 𝑠𝑠, 𝑢𝑢, 𝑑𝑑, 𝜈𝑒𝜈𝑒, 𝜈𝜇𝜈𝜇, 𝜈𝜏𝜈𝜏, 𝑔𝑔, and ℎℎ.

No DM was found in HAWC observations. The largest excess found in HAWC data was for DM

annihilating to 𝑊-bosons or 𝜈𝑒𝜈𝑒 for 𝑚 𝜒 = 10 TeV at significance 2.11𝜎 and 2.14𝜎 respectively.

HAWC’s limits and excesses are dominated by Segue1. Coma Berenices shows excesses at higher

DM mass, yet no similar excesses were observed in Segue1 or Sextans. Sextans did not contribute

significantly to signal excesses or the combined limit as it is at high zenith. Draco is at a high zenith

for HAWC, so the effort required to include it was not justified by the benefits.

We did not generate background trials in time of writing this thesis. These are not shown and

are an immediate next step for this analysis before publication.

When comparing these results to Section 3.5, we see an overall decrease in the observed confi-

dence limits on ⟨𝜎v⟩, therefore improvement to HAWC’s expected sensitivity. This improvement

is generally stronger than a doubling of data, or a factor

√

2 decrease. The comparison is somewhat

complex and dependent on the dSph and SM annihilation channel. Figure 4.11 shows the com-

parisons of limits calculated for this analysis and Glory Duck (Section 3.5). Segue 1 and Coma

Berenices are sources at low zenith angles where improvements to HAWC’s analysis come almost

entirely from energy estimation. Differences between these two are dominantly from their differ-

ences in 𝐽-factor, half-light radii of the dSphs, and the particle physics inputs. Substantial gains

in HAWC’s analysis methods (pass 5.F) were made at high zenith which is important for sources

like Sextans. The HDM particle physics model produces almost identical spectra to the PPPC for

𝜒 𝜒 → 𝑒−𝑒+. This channel can be used to compare limits between dSph spatial models. Overhead

sources see modest improvement to the observed limits on ⟨𝜎v⟩, while high zenith sources see an

order of magnitude improvement for all DM masses. Softer SM annihilation channels see broad

86

Figure 4.7 HAWC upper limits at 95% confidence level on ⟨𝜎v⟩ versus 𝑚 𝜒 for 𝜒 𝜒 → 𝑏𝑏, 𝑡𝑡, 𝑢𝑢,
𝑑𝑑, 𝑠𝑠, 𝑐𝑐, 𝑔𝑔, 𝑊 +𝑊 −, and ℎℎ. Limits are with LS 𝐽-factors [88]. The solid line represents the
observed combined limit. Dashed lines represent limits from individual dSphs.

improvements to the limit compared to harder channels.

4.7 Systematics

Systematics to this analysis are identical to what was performed earlier in Glory Duck, Sec-

tion 3.7. We are also sensitive to the choice in spatial template, and this was explored in Section 3.7.2

and Section 3.8.2.

87

100101102103104M [TeV]1025102310211019v [cm3 s1]bbHAWC PreliminaryCombined and per Source 95% CL for bbComaBerenicesSegue1SextansCombined100101102103104M [TeV]1025102310211019v [cm3 s1]ttHAWC PreliminaryCombined and per Source 95% CL for ttComaBerenicesSegue1SextansCombined100101102103104M [TeV]1025102310211019v [cm3 s1]uuHAWC PreliminaryCombined and per Source 95% CL for uuComaBerenicesSegue1SextansCombined100101102103104M [TeV]1025102310211019v [cm3 s1]ddHAWC PreliminaryCombined and per Source 95% CL for ddComaBerenicesSegue1SextansCombined100101102103104M [TeV]1025102310211019v [cm3 s1]ssHAWC PreliminaryCombined and per Source 95% CL for ssComaBerenicesSegue1SextansCombined100101102103104M [TeV]1025102310211019v [cm3 s1]ccHAWC PreliminaryCombined and per Source 95% CL for ccComaBerenicesSegue1SextansCombined100101102103104M [TeV]1025102310211019v [cm3 s1]ggHAWC PreliminaryCombined and per Source 95% CL for ggComaBerenicesSegue1SextansCombined100101102103104M [TeV]10261024102210201018v [cm3 s1]WW+HAWC PreliminaryCombined and per Source 95% CL for WW+ComaBerenicesSegue1SextansCombined100101102103104M [TeV]1025102310211019v [cm3 s1]hhHAWC PreliminaryCombined and per Source 95% CL for hhComaBerenicesSegue1SextansCombinedFigure 4.8 HAWC upper limits at 95% confidence level on ⟨𝜎v⟩ versus 𝑚 𝜒 for 𝜒 𝜒 → 𝜈𝑒𝜈𝑒, 𝜈𝜇𝜈𝜇,
𝜈𝜏𝜈𝜏, 𝑒𝑒, 𝜇𝜇, 𝜏𝜏, 𝛾𝛾 and 𝑍 𝑍. Limits use LS 𝐽-factors [88]. The solid line represents the
observed combined limit. Dashed lines represent limits from individual dSphs.

4.8 Conclusion and Discussion

In this multithreaded analysis, we have used observations of 3 dSphs from HAWC to perform

a collective DM annihilation search towards dSphs. The data were combined across sources

to significantly increase the sensitivity of the search. Advanced computational techniques were

deployed to accelerate wall-time spent analyzing by an order of magnitude. We have observed

88

100101102103104M [TeV]1024102210201018v [cm3 s1]eeHAWC PreliminaryCombined and per Source 95% CL for eeComaBerenicesSegue1SextansCombined100101102103104M [TeV]1024102210201018v [cm3 s1]HAWC PreliminaryCombined and per Source 95% CL for ComaBerenicesSegue1SextansCombined100101102103104M [TeV]10251023102110191017v [cm3 s1]HAWC PreliminaryCombined and per Source 95% CL for ComaBerenicesSegue1SextansCombined100101102103104M [TeV]10261024102210201018v [cm3 s1]ee+HAWC PreliminaryCombined and per Source 95% CL for ee+ComaBerenicesSegue1SextansCombined100101102103104M [TeV]10251023102110191017v [cm3 s1]HAWC PreliminaryCombined and per Source 95% CL for ComaBerenicesSegue1SextansCombined100101102103104M [TeV]10261024102210201018v [cm3 s1]HAWC PreliminaryCombined and per Source 95% CL for ComaBerenicesSegue1SextansCombined100101102103104M [TeV]10251023102110191017v [cm3 s1]HAWC PreliminaryCombined and per Source 95% CL for ComaBerenicesSegue1SextansCombined100101102103104M [TeV]1025102310211019v [cm3 s1]Z0Z0HAWC PreliminaryCombined and per Source 95% CL for Z0Z0ComaBerenicesSegue1SextansCombinedFigure 4.9 HAWC TS values for best fit ⟨𝜎v⟩ versus 𝑚 𝜒 for SM annihilation channels: 𝜒 𝜒 → 𝑏𝑏,
𝑡𝑡, 𝑢𝑢, 𝑑𝑑, 𝑠𝑠, 𝑐𝑐, 𝑔𝑔, 𝑊 +𝑊 −, and ℎℎ. Limits use LS 𝐽-factors. The solid black line shows the
combined best fit TS values. The colored, dashed lines are the TS values from each dSph.

no significant deviation from the null DM hypothesis, and so present our results in terms of

upper limits on the velocity-weighted cross-section, ⟨𝜎v⟩, for seventeen potential DM annihilation

channels across four decades of DM mass.

This analysis serves as a proof of concept for multithreaded HAWC analyses with large parameter

spaces. Larger datasets with fast techniques will be essential to tackling the DM problem. The

89

100101102103104M [TeV]02468101214TSbbHAWC PreliminaryCombined and per Source Best Fit TS for bbComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSttHAWC PreliminaryCombined and per Source Best Fit TS for ttComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSuuHAWC PreliminaryCombined and per Source Best Fit TS for uuComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSddHAWC PreliminaryCombined and per Source Best Fit TS for ddComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSssHAWC PreliminaryCombined and per Source Best Fit TS for ssComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSccHAWC PreliminaryCombined and per Source Best Fit TS for ccComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSggHAWC PreliminaryCombined and per Source Best Fit TS for ggComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSWW+HAWC PreliminaryCombined and per Source Best Fit TS for WW+ComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TShhHAWC PreliminaryCombined and per Source Best Fit TS for hhComaBerenicesSegue1SextansCombinedFigure 4.10 HAWC TS values for best fit ⟨𝜎v⟩ versus 𝑚 𝜒 for SM annihilation channels: 𝜒 𝜒 →
𝜈𝑒𝜈𝑒, 𝜈𝜇𝜈𝜇, 𝜈𝜏𝜈𝜏, 𝑒𝑒, 𝜇𝜇, 𝜏𝜏, 𝛾𝛾 and 𝑍 𝑍. Limits use LS 𝐽-factors. The solid black line shows the
combined best fit TS values. The colored, dashed lines are the TS values from each dSph.

models we used for this study include annihilation channels with neutrinos in the final state.

Advanced studies could aim to merge our results with those from neutrino observatories with large

data sets.

A full HAWC analysis will include systematic studies of the 𝐽-factor distributions. Additionally,

because of the timing reduction, the study can be doubled in size to include DM decay. We have not

90

100101102103104M [TeV]02468101214TSeeHAWC PreliminaryCombined and per Source Best Fit TS for eeComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSHAWC PreliminaryCombined and per Source Best Fit TS for ComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSHAWC PreliminaryCombined and per Source Best Fit TS for ComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSee+HAWC PreliminaryCombined and per Source Best Fit TS for ee+ComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSHAWC PreliminaryCombined and per Source Best Fit TS for ComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSHAWC PreliminaryCombined and per Source Best Fit TS for ComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSHAWC PreliminaryCombined and per Source Best Fit TS for ComaBerenicesSegue1SextansCombined100101102103104M [TeV]02468101214TSZ0Z0HAWC PreliminaryCombined and per Source Best Fit TS for Z0Z0ComaBerenicesSegue1SextansCombinedyet received the remaining spatial profiles to the LS catalog, and limits can be quickly computed

once these are received. Finally, statistical studies with Poisson variation of HAWC’s background

are essential to a comprehensive understanding of our observed excesses.

91

Segue1

Coma Berenices

Sextans

¯𝑏
𝑏

→
𝜒
𝜒

𝜏
𝜏

→
𝜒
𝜒

+
𝑒
−
𝑒

→
𝜒
𝜒

Figure 4.11 Comparison of HAWC limits from this analysis to Glory Duck (Fig. 3.5) for 3 dSphs
and 3 DM annihilation channels: 𝑏𝑏, 𝜏𝜏, and 𝑒𝑒. Each sector shows the 95% confidence limit
from Glory Duck (blue line) and this analysis (orange line) in the top plot. The lower plot features
the ratio in log scale of Glory Duck to this analysis in a red solid line. Horizontal dashed lines are
2 (blue). Ratios larger than 1.0 are for limits smaller, or stricter, than
for ratios of 1.0 (black) and
Glory Duck. Ratios larger than
2 indicates limits are stricter than a simple doubling of the Glory

√

√

Duck data.

92

1024102310221021102010191018v [cm3 s1]bbHAWC PreliminarySystematic Comparison for New_duckComaBerenices Glory DuckComaBerenices New_duck100101102103104M [TeV]1006×1012×1003×1004×100GD/SysModel RatiosR=1.0R=2102410231022102110201019v [cm3 s1]bbHAWC PreliminarySystematic Comparison for New_duckSegue1 Glory DuckSegue1 New_duck100101102103104M [TeV]1006×1012×1003×100GD/SysModel RatiosR=1.0R=21023102210211020101910181017v [cm3 s1]bbHAWC PreliminarySystematic Comparison for New_duckSextans Glory DuckSextans New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=210241023102210211020101910181017v [cm3 s1]HAWC PreliminarySystematic Comparison for New_duckComaBerenices Glory DuckComaBerenices New_duck100101102103104M [TeV]1006×1012×1003×100GD/SysModel RatiosR=1.0R=210251024102310221021102010191018v [cm3 s1]HAWC PreliminarySystematic Comparison for New_duckSegue1 Glory DuckSegue1 New_duck100101102103104M [TeV]100GD/SysModel RatiosR=1.0R=210241023102210211020101910181017v [cm3 s1]HAWC PreliminarySystematic Comparison for New_duckSextans Glory DuckSextans New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=210241023102210211020101910181017v [cm3 s1]ee+HAWC PreliminarySystematic Comparison for New_duckComaBerenices Glory DuckComaBerenices New_duck100101102103104M [TeV]100GD/SysModel RatiosR=1.0R=210251024102310221021102010191018v [cm3 s1]ee+HAWC PreliminarySystematic Comparison for New_duckSegue1 Glory DuckSegue1 New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=210231022102110201019101810171016v [cm3 s1]ee+HAWC PreliminarySystematic Comparison for New_duckSextans Glory DuckSextans New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=2CHAPTER 5

ICECUBE NEUTRINO OBSERVATORY

Figure 5.1 IceCube Neutrino observatory and science center at the South Pole. Detector volume is
beneath glacial ice. Image from [30].

Located at the South Pole, the IceCube Neutrino Observatory is a pivotal instrument for neutrino

astronomy. The above and below ice components of the IceCube observatory are shown in Figs. 5.1

and 5.2. IceCube’s primary function is the detection and analysis of elusive, high-energy neutrinos.

These neutrinos carry information from the most energetic and distant cosmic phenomena. The

observatory uses thousands of digital optical modules embedded in a cubic kilometer of Antarctic

ice to detect Cherenkov radiation. This radiation occurs when neutrinos interact with the ice,

revealing their origin and energy.

IceCube is a critical component in the multi-messenger astrophysics toolkit, especially in the

search for dark matter and beyond standard model (BSM) astrophysical processes. The observa-

tory’s analysis of neutrino signals enhances our understanding of the universe by correlating these

93

Figure 5.2 Graphic of the full IceCube Neutrino Observatory. In-ice array is made up of 86 strings
with a total of 5160 optical sensors. Deepcore is a denser arrangement of optical sensors for
sensitivity to lower energy neutrinos. Figure from [30].

signals with other cosmic messengers, including electromagnetic, gravitational waves, and cosmic

rays. The following sections will discuss the observatory’s design, data acquisition, and event

reconstruction methodologies.

5.1 The Detector

The IceCube Neutrino Observatory is embedded within a cubic kilometer of Antarctic ice at

the South Pole. IceCube’s modules are designed to detect neutrinos through Cherenkov radiation

emitted after neutrino interactions within the ice.

It comprises 5160 Digital Optical Modules

(DOMs), arranged across 86 strings that span depths of 1450 m to 2450 m beneath the surface.

This arrangement allows IceCube to capture high-energy neutrinos across a broad neutrino energy

spectrum.

94

Figure 5.3 Composition of the Digital Optical Module (DOM). Left image is an illustration of the
mechanical layout. Right is a flow chart of functional connections. Figure from [91]

5.1.1 Hardware and Construction

Digital Optical Modules (DOMs) are at the core of IceCube’s detection technology. Figure 5.3

illustrates the construction and signal flow of a DOM. Each DOM is encased in a glass sphere

that can withstand deep-ice pressures. A DOM features a 10-inch PMT for Cherenkov light

detection, a high-voltage power supply for the PMT, and a Main Board for signal digitization and

timestamping. An LED Flasher Board is included for calibration purposes. They assist in verifying

DOM responses and measuring the glacial ice’s optical properties. The DOMs are deployed along

cables on strings in a hexagonal grid pattern that spans a cubic kilometer. Strings are placed with

125 m of horizontal spacing, and DOMs are vertically separated by 17 m on each string. This

detector geometry optimizes detection of TeV to PeV neutrinos.

DeepCore and IceTop, additional components of IceCube, extend its research capabilities.

DeepCore, with its denser array of DOMs, targets lower energy neutrinos for studies such as

neutrino oscillations. IceTop, situated at the ice surface, measures cosmic rays, contributing data

that complement the neutrino observations from below the ice. Figure 5.2 illustrates the full

detector volume and auxiliary systems.

The central hub for IceCube’s operations is the IceCube Laboratory (ICL) and is situated at

95

Figure 5.4 IceCube Laboratory (ICL) that houses the data acquisition systems. Picture from [30].

the surface at the center of the array (see Fig. 5.4). This facility houses the servers and computers

responsible for data acquisition and online filtering. ICL connects to the DOMs via cables routed

up from beneath the ice [91]. The ICL manages the data flow from the ice, ensuring continuous

operation and data integrity. It maintains optimal conditions for its electronic equipment, including

temperature control and protection against electromagnetic interference [91].

5.1.2 Data Acquisition

The data acquisition process in IceCube starts when a PMT within a DOM detects light

surpassing a threshold of 0.25 photoelectrons. The importance of the information transmitted to

the ICL depends on the detection of hits in neighboring DOMs within a microsecond window.

Isolated signals prompt a Soft Local Coincidence (SLC) response, transmitting only a timestamp

and a charge summary. In contrast, signals detected by neighboring DOMs initiate a Hard Local

Coincidence (HLC). The full waveform is compressed and sent along with the timestamp and

charge summary to the ICL [91]. Figure 5.5 shows a flow chart of PMT data within the DOMs

96

Figure 5.5 Data flow chart PMT waveforms from the DOMs. “Hit Records" are sent to the surface
DAQ computers in ICL. Full waveform data, represented with dashed arrows, are included when
neighboring DOMs are hit in coincidence above the SPE discriminator threshold.

before being sent to the ICL.

Achieving uniform timing across DOMs is essential for accurate event reconstruction. Each

DOM’s independent clock is finely calibrated and synchronized with the ICL’s clocks. Times are

translated to Universal Coordinated Time (UTC). This calibration is set by sending continuous

pulses between the DOMs and the ICL. The waveforms are adjusted by subtracting the common

baseline and applying the gain [91].

Within the ICL, the Data Acquisition (DAQ) system employs various trigger algorithms to

discern neutrino events from the vast majority of DOM hits caused by dark noise. One such

mechanism, the Simple Multiplicity Trigger (SMT), requires a specific number of HLC hits within

a brief timeframe to recognize a series of hits as an event [91].

Further, refining the observatory’s data, the Processing and Filtering (PnF) system, also housed

within the ICL, applies around 25 different filters after initial event detection. Each filter is designed

for specific physics analyses. The system employs filters such as: the Muon Track Filter to isolate

high-quality track events crucial for neutrino source identification, the Shower Event Filter to

97

select events with large energy deposits indicative of neutrino interactions, and the High-Charge

Filter to highlight events with extensive photoelectron deposits [91]. These filters ensure that

the data prepared for further analysis and transmission to researchers in the Northern Hemisphere

contains the most significant scientific insights [91].

The operational control of the observatory, maintained by the LiveControl system within the

ICL, oversees the DAQ and PnF systems. It handles the initiation and conclusion of data-taking runs

and maintains a database of operational parameters. LiveControl alerts operators to any deviations

from expected conditions. It is crucial for ensuring that the observatory operates within its optimal

parameters [91].

5.2 Event Reconstruction

Event Reconstruction within the IceCube Neutrino Observatory transforms signals captured

by DOMs into quantifiable scientific insights. The goal of event reconstruction is to ascertain

the origin, trajectory, and energy of interacting neutrinos. This process is pivotal for interpreting

signals as either originating from celestial neutrino sources or other phenomena. I will focus mostly

on how IceCube reconstructs track-like events as these are the most relevant for this dissertation.

5.2.1 Tracks and Cascades

Events in IceCube’s detector volume manifest primarily as either tracks or cascades. The

primary cause of the event topology are both the neutrino flavor and the nature of the primary

neutrino’s interaction with the ice. Figure 5.6 presents Feynman diagrams of typical neutrino

interactions with particles in the ice. Figure 5.7 illustrates the signatures from various topologies

of neutrino interactions in the ice.

Tracks emerge from charged-current (CC) interactions involving muon neutrinos (𝜈𝜇). These

events are characterized by the production of a high-energy muon (𝜇). These muons, due to its

relatively large mass compared to electrons, can traverse substantial distances through the ice,

exceeding kilometers. These long trajectories are obvious from their continuous, distinct, and

elongated track of Cherenkov light in the ice. See Fig. 5.8 for a simulated track event. The angular

deviation between the incoming 𝜈𝜇 and the secondary 𝜇 is notably slight, tapering to near 0.3◦

98

Figure 5.6 Feynman diagrams for W (a/b) and Z (c/d) boson mediated interactions between
neutrinos and light quarks. Charged current (CC) interactions are shown in panels a and b.
Neutral current (NC) interactions are shown in panels c and d. NC interactions occur between
neutrinos and quarks within atomic nuclei in the ice. CC interactions will exchange W bosons and
produce a lepton corresponding to the neutrino flavor and a hadronic cascade. NC interactions
will exchange a Z boson and produce a hadronic cascades. Figure from [92].

above TeV energies. Therefore, 𝜇 tracks closely approximate the primary neutrino’s path [92, 95].

Such precision affords angular resolutions finer than 1◦ for TeV neutrinos which facilitates the

determination of their cosmic origins [92].

Cascades are products of both neutral-current (NC) interactions across all neutrino flavors and

CC interactions involving electron or tau neutrinos, 𝜈𝑒 and 𝜈𝜏 respectively. Unlike tracks, cascades

result in a more localized burst of Cherenkov radiation. The burst imprints as a nearly spherical light

pattern from the rapid dissipation of energy by the produced particles. See Fig. 5.9 for a simulated

track event. This diffusion creates a distinct event signature with good energy estimation, but worse

directional clarity compared to track events. The isotropic nature of cascades leads to larger angular

uncertainties, typically around 15◦. Yet, cascades excel in providing energy measurements, with

resolutions reaching as tight as 15% from the contained nature of the energy deposition [92, 95].

99

Figure 5.7 Event topologies for high energy NC and CC neutrino interactions with ice. Signatures
can be split as either: hadronic and electromagnetic cascades; Cherenkov radiation from a charged,
long-lived particle. Cascades from 𝜏 decays will depend on its decay products. For energies below
1 PeV the double bang of the 𝜈𝜏 signature overlap and are indistinguishable. Figure from [93].

The double-bang event, posited for 𝜈𝜏 interacting via CC at energies above 1 PeV, would display

as two distinct cascades within the detector. These events start from an initial interaction and

subsequent decay of the 𝜏 lepton over a discernible distance. See Fig. 5.10 for a simulated track

event. The double-bang offers a unique marker for high-energy 𝜈𝜏 detection [92]. Preliminary

whispers of double-bang events have been observed in IceCube [96]. Yet, efforts are ongoing to

isolate such an event.

5.2.2 Reconstruction of Track Direction

Angular reconstruction for 𝜈𝜇 induced tracks in the IceCube detector volume starts with the

LineFit algorithm [97]. LineFit estimates the 𝜇’s trajectory through the least squares fit to the

Cherenkov light hits on the DOMs. LineFit assumes the muon propagates with constant velocity

and treats its path as linear in order to simplify the emission patterns of Cherenkov radiation. To

improve this approximation, the Huber penalty function [98] is applied which distinguishes between

signal and noise by considering the spatial distribution of hits relative to the track [99].

The reconstruction process is refined further by the Single Photoelectron (SPE) likelihood

100

Figure 5.8 A simulation of a track-like event in IceCube. Redder bubbles indicate earlier photon
arrival times. Greener bubbles occur later. The size of the DOM bubble illustrate the charge
deposition in the DOM. For this event, the CC neutrino interaction occurred by the red hits. There
is then a long muon track going to the left. Figure taken from [94].

method, which calculates the probability of photon arrival times at the DOMs [98]. It does so by

taking into account the earliest detected photons as they are least likely to have been scattered in

the ice:

𝐿(Θ) =

𝑁DOM
(cid:214)

𝑁hit
(cid:214)

𝑗=1

𝑖=1

𝑝 𝑗 (𝑡𝑖)𝑞𝑖

(5.1)

where 𝑁DOM is the number of DOMs involved in the event. 𝑁hit is the number of hits registered

[97]. 𝑝 𝑗 (𝑡𝑖) is the probability density function (PDF) of the photon arrival time. The charge

detected by each DOM, 𝑞𝑖, factors into the probability calculation, assuming that earlier photons

provide more reliable directional information.

An alternative to SPE, the Multi-Photoelectron (MPE) likelihood method accounts for all

101

Figure 5.9 Same as Fig. 5.8 but for a cascade-like event. Figure taken from [94].

Figure 5.10 Same as Fig. 5.8 but for a double-bang event. Two distinct cascades are visible if the
initial neutrino is very high energy. Figure taken from [94].

102

detected photons. MPE uses the total observed charge to weight the significance of each hit:

𝐿(Θ) =

𝑁DOM
(cid:214)

𝑗=1

(cid:104)

𝑝 𝑗 (𝑡1)𝑞1 · (cid:0)1 − 𝑃 𝑗 (𝑡1)(cid:1)𝑄 𝑗 −𝑞1 (cid:105)

,

(5.2)

where 𝑄 𝑗 is the sum of charges observed by the 𝑗th DOM, providing a more detailed picture of the

𝜇’s path [97].

SplineMPE, is the final step and employs a spline-based parameterization of the photon arrival

times. These spline fits encode a detailed understanding of the ice’s optical properties derived from

calibration data [97]. This approach yields the following likelihood function for improved angular

resolution:

𝐿 ( (cid:174)𝑟0, 𝑡0, 𝜃, 𝜙) =

(cid:214)

𝑘

𝐿DOM𝑘 ( (cid:174)𝑟0, 𝑡0, 𝜃, 𝜙),

(5.3)

where the parameters (cid:174)𝑟0, 𝑡0, 𝜃, and 𝜙 describe the reconstructed track within IceCube’s voluminous

array [97].

From the light weight LineFit to the complex SplineMPE, each step incorporates more detailed

physics to enhance the reconstruction’s accuracy. Each hones in on the 𝜇 track to reveal the 𝜇’s

cosmic origin. This multi-stepped tracking is crucial for IceCube’s mission to map the universe

through the lens of high-energy neutrino interactions.

5.2.3 Energy

After pinpointing the 𝜇 track’s direction, IceCube employs the MuEX algorithm to estimate the

energy deposited by the muon inside the detector. The MuEX algorithm uses a Poisson likelihood

model, comparing the observed photoelectrons 𝑘 to the expected light output, Λ, which is directly

related to the deposited energy 𝐸:

ln L = 𝑘 ln(Λ𝐸 + 𝜌) − (Λ𝐸 + 𝜌) − ln(𝑘!)

(5.4)

𝜌 is the number of expected noise photons, and Λ reflects the light yield per unit energy, taking into

account the optical properties of the ice and the detector response. The logarithm of the likelihood

is minimized with respect to the energy, resulting in a best-fit estimate [95].

For a more detailed energy reconstruction, the Millipede algorithm unfolds the muon’s energy

loss along its path by adapting the Poisson likelihood. This approach accounts for the stochastic

103

energy losses due to Bremstrahlung and pair production, treating the 𝜇 as a series of electromagnetic

cascades:

(cid:174)𝑘 − (cid:174)𝜌 = Λ · (cid:174)𝐸

(5.5)

where 𝑘 denotes the observed photons, 𝜌 the noise, 𝐸 the energy losses, and Λ the matrix of

predicted light yields throughout the detector. By fitting the muon’s position, direction, and the

vector of energy losses, Millipede achieves a resolution on total deposited energy along the muon

track of approximately 10-15% [95].

IceCube makes some approximations when estimating 𝜆 for the reduction of computational time.

Two important assumptions IceCube makes are that Cherenkov light from cascades is spherically

symmetric along the 𝜇 track and the Cherenkov emission is uniform [95]. The uncertainties in

these approximations is accounted for by convolving 𝜆 with a PDF, 𝐺, on the light yield. The

likelihood is then rewritten as:

L =

∫ ∞

(cid:214)

0

𝑗

𝑑𝜆 𝑗 𝐺 (𝜆𝑖, 𝜆 𝑗 )

𝜆𝑘𝑖
𝑗 𝑒−𝜆𝑖
𝑘𝑖!

,

(5.6)

The full description for the PDF, 𝐺 (𝜆𝑖, 𝜆 𝑗 ) is discussed in [95]. After considering the uncertainties,

the energy resolution was observed to be in the range of 30%-35% [95].

5.3 Background

In IceCube, the primary challenge in detecting astrophysical neutrinos is the background noise

from atmospheric neutrinos. These are produced from cosmic rays hitting the Earth’s atmosphere,

leading to a cascade that includes both neutrinos and muons (see Fig. 2.3). These particles

sometimes generate detector signals similar to those from astrophysical sources.

IceCube employs selective criteria to reduce this background. For instance, downward-moving

tracks are scrutinized more heavily, as these are more likely to be related to atmospheric events.

Upward-moving neutrinos, however, are less likely to be confused with this background because

the Earth filters out most other particles, including muons. The detector uses the Earth itself as a

filter to increase the purity of potential astrophysical neutrino signals. This differentiation between

104

up-going and down-going events helps IceCube focus on the neutrinos that are of most interest for

astronomical observations.

105

CHAPTER 6

HEAVY DARK MATTER ANNIHILATION SEARCH WITH ICECUBE’S NORTH SKY
TRACK DATA

6.1

Introduction

Neutrinos are another astrophysical messenger than can travel long distances without significant

attenuation or deflection. Additionally, neutrinos come in three flavors, all of which IceCube is

sensitive to. Uniquely, they interact less readily than photons especially above PeV energies.

Neutrinos therefore provide another window through which we can perform dark matter searches.

The last IceCube DM annihilation analysis towards dwarf galaxies was performed in 2013

[100] which, in technical terms, is more than a minute ago. This is in spite of IceCube’s crucial

sensitivity afforded from neutrino spectral lines [101]. A lot has changed in IceCube since its

previous DM annihilation search, such as additional strings (previously 59 versus presently 86),

more sophisticated analysis methods, and more accurate theoretical modeling. It has come time for

IceCube to make a DM dSph contribution.

IceCube is sensitive to annihilating DM with masses above 1 TeV. Additionally, IceCube’s

sensitivity is comparable to gamma-ray observatories in spectral models that produce hard neutrino

features where 𝐸𝜈 ≈ 𝑚 𝜒. The goal of this analysis is to perform a DM annihilation search using the

Northern Sky Tracks datasets, a standard IceCube analysis pipeline with superior angular resolution.

The search will only be towards dwarf spheroidal galaxies (dSph) for the strengths mentioned in

Section 3.3.3. These sources are treated as point sources for IceCube with little loss to sensitivity

or model dependence on how the DM is distributed. DM masses from 500 GeV to 100 PeV and

several DM annihilation channels available from the HDMSpectra [25] are studied in this analysis.

This chapter presents the analysis work for IceCube to update our DM searches toward dSphs.

6.2 Dataset and Background

This section specifies the data and background methods used for IceCube’s study of dSphs.

Section 6.2.1 and Section 6.2.2 are most useful for fellow IceCube collaborators looking to replicate

this analysis.

106

6.2.1

Itemized IceCube Dataset and Software

These files are only available within IceCube’s internal documentation and wikis. They are not

meant for public access, and are presented here so that IceCube collaborators can reproduce results

accurately.

• Software Environment: CVMFS Py3-v4.1.1

• Data Sample: Northern Tracks NY86v5p1

• Likelihood Software: csky (nu_dark_matter)

• Analysis wiki: Dark Matter Annihilation Search towards dwarf spheroidals with NST

• Project Repository: IceCube_dark_matter_dsph

6.2.2 Software Tools and Development

This analysis was performed inside IceCube’s CVMFS (3.4.1.1) software environment using

csky. Csky is an unbinned likelihood maximization software made for quick analyses typically

performed in IceCube [102]. It importantly has multi-threading capabilities which will be essential

as we set out to sample a large parameter space. Csky at first did not come with dark matter spectral

models nor could it accommodate custom flux models. We developed these capacities for single

source and stacked source studies for this analysis. The analysis code is held in a separate repository

from csky. The nu_dark_matter branch of csky manages the input of custom dark matter spectra

and accompanied DM astrophysical sources. Csky also enables the use of multithreading which

was shown to be crucial for DM searches (see Sec. 4). Csky then calculates the likelihood of a DM

signal from a location in the sky within a selected data sample. The IceCube Dark Matter dSph

repository manages the generation of spectral models for neutrinos, physics parameter extraction

from fitted 𝑛s, 𝐽-factor per source inputs, and bookkeeping for the large parameter space. The

project repository required a secondary software environment for neutrino oscillations. How to

launch and run those calculations are documented in the project repository and the Docker image

is additionally saved in Sec. E.

107

6.2.3 Data Set and Background Description

For this analysis, I use the Northern Sky Tracks (NST) Sample (Version V005-P01). The sample

contains up-going track-like events, usually from 𝜈𝜇 and 𝜈𝜏, with a superior angular resolution

compared to the cascade dataset. This sample covers 10.4 years of data (IC86_2011-2021). The

neutrino energy range accepted for this analysis is unique among most other IceCube searches

because DM spectra are hard with large contributions close to 𝐸𝜈 ≈ 𝑚 𝜒. Therefore, we fully utilize

the energy range of IceCube Monte Carlo with sampled energy range 1 < log(𝐸𝜈/GeV) < 9.51.

The strength of a dwarf analysis is that there are no additional background considerations beyond

nominal, baseline background estimations used in a typical points source search (see Section 3.2.3).

For NST, the nominal contributions come from atmospheric neutrinos and isotropic astrophysical

neutrinos. We estimate the background by scrambling NST data along right ascension [103, 104,

105].

6.3 Analysis

The expected differential neutrino flux from DM-DM annihilation to standard model particles,

𝑑Φ𝜈/𝑑𝐸𝜈, over solid angle, Ω is described by the familiar equation.

𝑑Φ𝜈
𝑑𝐸𝜈

=

⟨𝜎v⟩
8𝜋𝑚2
𝜒

𝑑𝑁𝜈
𝑑𝐸𝜈

×

∫

source

𝑑Ω

∫

𝑙.𝑜.𝑠

𝜌2
𝜒𝑑𝑙 (𝑟, 𝜃′)

(6.1)

This is identical to Eq. (3.1) except that there are three neutrino flavors, so there are a corresponding

3 flux equations. Section 3.3 has a complete description of each term in Eq. (6.1). Additionally,

neutrinos oscillate between flavors, which needs to be considered when calculating the expected

neutrino flux at Earth. Section 6.3.1 presents the particle physics model and processing for methods

DM annihilation. Section 6.3.2 presents the spatial distributions built for each dSph.

6.3.1

𝑑𝑁𝜈
𝑑𝐸𝜈 - Particle Physics Component

Neutrino spectra from heavy DM annihilation were generated using HDMSpectra [25] and

𝜒aro𝜈 [106]. HDMSpectra has tables for the decay and annihilation of heavy DM for different

dark DM and SM primary annihilation channels. The simulation includes electroweak or gluon

radiative corrections and higher order loop corrections from the 𝑊 and 𝑍 bosons (such as 𝑊𝑊 𝑍

108

and 𝑊𝑊 𝛾 loops). These corrections are especially important for accurately estimating the prompt

neutrino flux. This publication also pushes the simulated DM mass to the Plank scale (1 EeV),

however this study will not explore that high.

An important, new feature in the spectra is that channels with neutrino lines will be accompanied

by a low energy tail [25], see Fig. 6.1. These tails emerge from the higher order loops corrections

in the electroweak sector mentioned earlier. Thus, the Earth will not longer fully attenuate spectra

for 𝜒 𝜒 → 𝜈𝑒𝜈𝑒, 𝜈𝜇𝜈𝜇, or 𝜈𝜏𝜈𝜏 from high declination sources where the neutrino flux must first

traverse through the Earth. The DM annihilation channels that feature lines include all leptonic

channels: 𝜈𝑒,𝜇,𝜏, 𝑒, 𝜇, and 𝜏. We use the 𝜒aro𝜈 software to propagate and oscillate the neutrinos

from the source to Earth. Because these sources are large compared to the oscillation baseline,

and also far (order 10 kpc or more), the resulting flavor spectra are the averages of the transition

probabilities [106]:

𝑃(𝜈𝛼 → 𝜈𝛽) ≈

(6.2)













0.55 0.18 0.27



0.18 0.44 0.38



0.27 0.38 0.35




Examples of the spectra before and after propagation are shown in Fig. 6.1. We do not systematically

study the uncertainties on the terms in Eq. (6.2) as these are small compared to the theoretical

uncertainties in the 𝐽-factor.

When calculating the expected contribution to signal neutrinos, 𝑛𝑠, only 𝜈𝜇 and 𝜈𝜏 are considered

as NST’s effective area to 𝜈𝑒 is negligible [103] whereas its effective area to 𝜈𝜇 and 𝜈𝜏 is almost

identical. Therefore, the expected composite neutrino spectrum is the sum of the two flavors:

𝑑𝑁 𝜈𝜇
𝑑𝐸 𝜈𝜇

+ 𝑑𝑁 𝜈𝜏
𝑑𝐸 𝜈𝜏

. The spectral tables are then fitted with splines to condense information, enable

random sampling of the spectra, and reduce computing times. The spectral splines are finally

implemented as a DM class in csky.

109

𝜒 𝜒 → 𝑏𝑏

𝜒 𝜒 → 𝜏𝜏

𝜒 𝜒 → 𝜈𝜇𝜈𝜇

𝑀𝜒

V
e
T
1

V
e
P
1

V
e
E
1

1
1
0

Figure 6.1 Neutrino spectra at production (left panels) and after oscillation at Earth (right panels). Blue, orange, and green lines are the

𝜈𝑒, 𝜈𝜇, and 𝜈𝜏 spectra respectively. Top panels show the spectra in 𝑑𝑁

𝑑𝐸 . Lower panels plot the flavor ratio to 𝜈𝑒 + 𝜈𝜇 + 𝜈𝜏. SM

annihilation channels 𝑏𝑏, 𝜏𝜏, and 𝜈𝜇𝜈𝜇 are shown for 𝑀𝜒 = 1 Pev, TeV, and EeV.

105103101101103105dNdxFluxes at Productione105103101101103105Fluxes at Earthe101100X=(KM)0.00.51.0101100X=(KM)0.00.51.0Mass = 0.999999992572 TeV; Ann. channel = bb105103101101103105dNdxFluxes at Productione105103101101103105Fluxes at Earthe101100X=(KM)0.00.51.0101100X=(KM)0.00.51.0Mass = 0.999999992572 TeV; Ann. channel = 105103101101103105dNdxFluxes at Productione105103101101103105Fluxes at Earthe101100X=(KM)0.00.51.0101100X=(KM)0.00.51.0Mass = 0.999999992572 TeV; Ann. channel = 105103101101103105dNdxFluxes at Productione105103101101103105Fluxes at Earthe104103102101100X=(KM)0.00.51.0104103102101100X=(KM)0.00.51.0Mass = 999.999997029 TeV; Ann. channel = bb105103101101103105dNdxFluxes at Productione105103101101103105Fluxes at Earthe104103102101100X=(KM)0.00.51.0104103102101100X=(KM)0.00.51.0Mass = 999.999997029 TeV; Ann. channel = 105103101101103105dNdxFluxes at Productione105103101101103105Fluxes at Earthe104103102101100X=(KM)0.00.51.0104103102101100X=(KM)0.00.51.0Mass = 999.999997029 TeV; Ann. channel = 105103101101103105dNdxFluxes at Productione105103101101103105Fluxes at Earthe106105104103102101100X=(KM)0.00.51.0106105104103102101100X=(KM)0.00.51.0Mass = 100000.0 TeV; Ann. channel = bb105103101101103105dNdxFluxes at Productione105103101101103105Fluxes at Earthe106105104103102101100X=(KM)0.00.51.0106105104103102101100X=(KM)0.00.51.0Mass = 100000.0 TeV; Ann. channel = 105103101101103105dNdxFluxes at Productione105103101101103105Fluxes at Earthe106105104103102101100X=(KM)0.00.51.0106105104103102101100X=(KM)0.00.51.0Mass = 100000.0 TeV; Ann. channel = 6.3.1.1 Treatment of Neutrino Line Features

Figure 6.2 Signal recovery for 100 TeV DM annihilation into 𝜈𝜇𝜈𝜇 for a source at Dec = 16.06◦.
𝑛inj is the number of injected signal events in simulation. 𝑛𝑠 is the number of reconstructed signal
events from the simulated data. Although the uncertainties are small and tight, the reconstructed
𝑛𝑠 are systematically underestimated.

All DM annihilation channels into leptons 𝜒 𝜒 → [𝜈𝑒,𝜇,𝜏, 𝑒, 𝜇, 𝜏] develop a prominent and

narrow spectral line feature [25, 106]. For all neutrino flavors, this line is visible and prominent in

all 𝑚 𝜒 studied in this analysis. For charged leptons, the feature typically manifests at 𝑚 𝜒 > 10 TeV,

yet its prominence varies slightly between the flavors. Examples for lines in the annihilation spectra

with neutrinos or charged leptons are provided in Fig. 6.1.

The neutrino line feature is so narrow relative the sampled energy range that the random sampling

of the spectra and likelihood fitting rarely capture the line in computation. As a result, the best

fit to simulation of background will almost always bias downward and the analysis systematically

underestimates the signal (see Fig. 6.2).

To remedy this, we take a similar approach to the IceCube’s DM decay analysis [107] and my

previous gamma-ray study in Section 4.3.1. Two smoothing kernels were tested (Gaussian and

uniform) to widen the line feature. The widths were tuned such that the signal recovery approached

unity for DM masses from 100 TeV to 1 PeV for a source at Segue 1’s declination, 16.06◦. A source

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near the horizon was chosen in order to isolate loss in signal recovery from Earth’s attenuation

of very high energy neutrinos and atmospheric backgrounds. The kernel convolution needed to

closely preserve the integrated counts of neutrinos. The optimized kernel parameters for all lines

are summarized as:

• Gaussian kernel with 1𝜎 width = 1.75 × 10−3 · 𝑚 𝜒

• Minimum energy included in convolution = MIN[0.995 · 𝑚 𝜒, 𝐸 (𝜈line) − 4𝜎]

• Maximum energy included in convolution = MAX[1.005 · 𝑚 𝜒, 𝐸 (𝜈line) + 4𝜎]

where 𝐸 (𝜈line) is the neutrino energy where the neutrino line is at the maximum.

𝑁
𝑑

𝑋
𝑑

𝐸𝜈 (GeV)

Figure 6.3 Left panel shows the two kernels overlaying the original spectrum from 𝜒aro𝜈 after
propagation to Earth [106]. The vertical red line indicates where the original neutrino line is
maximized. Blue line is the output from 𝜒aro𝜈. Green line is the spectrum after convolution with
a flat kernel. Orange line is the spectrum after Gaussian convolution. Right panel shows the signal
recovery of the spectral model using the Gaussian kernel with parameters enumerated above.

These parameters broadly improved the signal recovery of the line spectra. An example is in

Fig. 6.3. Analysis level signal recovery studies are expanded upon in Section 6.6.

6.3.1.2 Spline Fitting

In an effort to reduce computational load and memory burden, and to align with point source

methods used for NGC1068 [105], spectral splines were created and adopted for estimating the

neutrino flux for the different spectral models. Software was written to generate, record, and

calculate values on the splines.

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When using splines, one has to be careful of the goodness of fit. The spline software used here,

Photospline [108], uses the penalized spline technique [109]. Through the penalized technique,

poor fits are penalized according to the accuracy of the nominal value and the smoothness of

the first and second derivatives. However, this construction does not conserve the integral of the

fitted distribution, which is critical in low signal studies such as DM searches. There are additional

caveats when testing the goodness of fit to the MC generated above for all DM annihilation channels.

• The splines must be logarithmic in energy and 𝑑𝑁/𝑑𝑥 to account for the exponential nature

of the flux.

• The fidelity of the fit matters more at 𝐸𝜈 ≈ 𝑚 𝜒 where the model uncertainties are minimal

and physical considerations (like the cut-off) are most important.

• The fidelity of the fit matters less at low 𝐸𝜈 as the model uncertainties are large AND

IceCube’s sensitivity diminishes significantly below 500 GeV.

• Total integrated counts should be well-preserved.

The resulting cost function was built to evaluate the goodness of spline fits to account for the above

considerations.

𝑒𝑖 = 𝑥𝑖 ·

(cid:18) 𝑑𝑁𝑖
𝑑𝑥𝑖

(cid:19)

− 10 ˆ𝑒𝑖

(6.3)

Here, 𝑒𝑖 is the weighted error between the spline and DM Monte Carlo for the 𝑖-th discrete sample.
ˆ𝑒𝑖 is the spline estimator’s value at 𝑥𝑖. 𝑥𝑖 = 𝐸𝜈𝑖 /𝑚 𝜒, and 𝑑𝑁𝑖
𝑑𝑥𝑖

is the flux value from MC. I then take

the RMS of the error distribution and the resulting value, err, is used to evaluate the fidelity of the

spectral spline.

√︄

err =

1
𝑥max − 𝑥min

∫ 𝑥max

𝑥min

e2𝑑𝑥

(6.4)

𝑥min and 𝑥max are the scope of the error evaluation and are provided in Tab. 6.1. e is the vector sum
of 𝑒𝑖: (cid:205)𝑖=0 𝑒𝑖 ˆ𝑖

Each SM channel had unique tolerances for ’err’. Channels with very hard cut-offs had looser

tolerance for err because a significant error would be generated from single counts over/under-

113

𝜒 𝜒 →

GOOD

𝑍 0𝑍 0, 𝑊 +𝑊 −

1.0 · 10−3

𝑡 ¯𝑡, ℎℎ

1.0 · 10−5

𝑏 ¯𝑏, 𝑑 ¯𝑑, 𝑢 ¯𝑢

9.0 · 10−7

𝜈 ¯𝜈𝑒,𝜇,𝜏

1.0 · 10−3

𝑒 ¯𝑒, 𝜇 ¯𝜇, 𝜏 ¯𝜏

1.0 · 10−3

OK
1.0 · 10−3,
1.0 · 10−2
1.0 · 10−5,
1.0 · 10−4
9.0 · 10−7,
9.0 · 10−6
1.0 · 10−3,
1.0 · 10−2
1.0 · 10−3,
1.0 · 10−2

FAIL

Limits of err calc [𝑋𝑚𝑖𝑛, 𝑋𝑚𝑎𝑥]

1.0 · 10−2 MAX[100GeV/𝑚 𝜒, 10−6], 1.0

1.0 · 10−4 MAX[100GeV/𝑚 𝜒, 10−6], 1.0

9.0 · 10−6 MAX[100GeV/𝑚 𝜒, 10−6], 1.0

1.0 · 10−2

1.0 · 10−2

MAX[100GeV/𝑚 𝜒, 10−6],
MIN[0.995, (𝐸𝜈𝑙𝑖𝑛𝑒) − 4𝜎)/𝑀𝜒]
MAX[100GeV/𝑚 𝜒, 10−6],
MIN[0.995, (𝐸𝜈𝑙𝑖𝑛𝑒) − 4𝜎)/𝑀𝜒]

Table 6.1 Spline err tolerances used for input in particle physics component to Eq. (3.1). Column
1 is the DM annihilation channel being fit. Columns 2, 3, and 4 are the tolerances for "GOOD"
(pass), "OK" requires inspection, and "FAIL" (tune and refit) respectively. Column 5 has the X
ranges over which the error is evaluated. MAX/MIN [·,·] takes the maximum or minumum of the
two enclosed values.

estimated at the cut-off. Soft channels do not share this issue, so the tolerance is much stricter.

All annihilation channels from HDM are modeled well below IceCube’s NST sensitivity, which

falls off substantially below 100 GeV [103]. We do not think it is necessary to evaluate the spline

fits below 100 GeV and use this value as the default lower cut-off.

In addition, HDM’s model

uncertainties at 𝐸𝜈 < 10−6 · 𝑚 𝜒 span an order of magnitude [25]. Therefore, we also choose not to

evaluate the splines below this critical value even if it is within IceCube’s sensitivity. Finally, the

smoothing of the spectral lines in leptonic annihilation channels are ignored for evaluating the fit.

This is because our fits are compared to Monte Carlo, which models these regions as delta functions

instead of Gaussian peaks. Additionally, the kernels selected in Section 6.3.1.1 already preserve

the integrated counts. We used the lower limit of the kernel mask as the upper limit of evaluation.

Table 6.1 summarizes the tolerances for the DM annihilation channels used for this analysis.

The errors are then assessed in two ways. First, fits evaluated as FAIL and OK are directly

plotted with e as a function of 𝑥 with the full spline and MC. An example of a single failure

is provided in Fig. 6.4. Second, a summary plot of all the splines is plotted and color coded.

Figure F.1 show the spline summaries as of writing this thesis. They may still be refined further as

other systematic studies are performed for the publication. The goal broadly is to eliminate all red

114

Figure 6.4 Example of a spline that failed the fit. Failed splines are corrected on a case by case
basis unless the SM channel has a systematic problem fitting the splines. In this case, I made a
bookkeeping error and loaded the incorrect spectral model

and inspect all yellow statuses.

The 𝜈𝑒 spectra at Earth are not considered in this analysis, so no work was done to refine the

spline fits for this flavor. Finally, I perform a visual inspection of the splines to verify that the spline

fitting did not introduce spurious features that would corrupt the likelihood fitting.

6.3.1.3 Composite Neutrino Spectra

With all the previously mentioned pieces, we are ready to fully assemble a comprehensive

description of the particle physics term 𝑑𝑁/𝑑𝐸 in Eq. (6.1).

𝑑𝑁𝜈
𝑑𝐸𝜈 ⊕

=

(cid:18) 𝑑𝑁𝜈𝑒
𝑑𝐸𝜈𝑒

+

𝑑𝑁𝜈𝜇
𝑑𝐸𝜈𝜇

+

(cid:19)

𝑑𝑁𝜈𝜏
𝑑𝐸𝜈𝜏

src

· P(𝜈𝛼 → 𝜈𝛽)

(6.5)

Figure 6.5 shows the spectral models that required Gaussian smoothing, the leptonic annihilation

channels. The remaining models where the only processing steps required were spline fitting and

neutrino oscillation are documented in Sec. G. Notice that the spectra of different neutrino flavors

are unique, especially in their low energy tails. Therefore, this analysis will be sensitive to DM

annihilating to the distinct neutrino flavors.

6.3.2

𝐽- Astrophysical Component

For this analysis, we re-adopt the GS model [69] used in Sec. 3 for dSphs. These models are

based on a Zhao DM density profile, see Eq. (4.1). The angular width of these sources is much

smaller than the angular resolution of IceCube NST [105]. We therefore treat these sources as point

115

sources in this analysis, and forgo generating maps. These sources and the GS model have already

been discussed at length in Section 3.3.2 and is not repeated here. IceCube uses identical sources

to Tab. 3.2 except we analyzed sources with declinations above 0.0◦.

6.3.3 Source Selection and Annihilation Channels

We use all the dSphs presented in IceCube’s previous dSph DM search [100] and expand beyond

it. IceCube’s sources for this analysis studies include Boötes I, Canes Venatici I, Canes Venatici II,

Coma Berenices, Draco, Hercules, Leo I, Leo II, Leo V, Leo T, Segue 1, Segue 2, Ursa Major I,

Ursa Major II, and Ursa Minor. A full description of all sources used is in Table 3.2. Sources with

declinations less than 0.0◦ are excluded from this analysis.

This analysis improves on the previous IceCube dSph paper [100] in the following ways. The

𝜒 𝜒 → 𝑒𝑒

𝜒 𝜒 → 𝜇𝜇

𝜒 𝜒 → 𝜏𝜏

𝜒 𝜒 → 𝜈𝑒𝜈𝑒

𝜒 𝜒 → 𝜈𝜇𝜈𝜇

𝜒 𝜒 → 𝜈𝜏𝜈𝜏

Figure 6.5 Summary of input spectral models that were smoothed with Gaussian kernels. Spectral
models are for 𝜒 𝜒 → 𝑒𝑒, 𝜇𝜇,𝜏𝜏, 𝜈𝑒𝜈𝑒, 𝜈𝜇𝜈𝜇, and 𝜈𝜏𝜈𝜏. These spectra are the composite (𝜈𝜇 + 𝜈𝜏)
of neutrino flavors. Every spectral model used for this analysis is featured as a colored solid line.
Bluer lines are for low 𝑚 𝜒 models. 𝑚 𝜒 ranges from 681 GeV to 100 PeV. HDM [25], 𝜒aro𝜈 [106],
and Photospline [108] are used to generate these spectra. Energy (x-axis) was chosen to roughly
represent the energy sensitivity of NST.

116

0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0122,=0.462100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.037[1e3]0.0112,=0.503100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0122,=0.495100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.038[1e3]0.0122,=0.483100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.039[1e3]0.0122,=0.474100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.037[1e3]0.0122,=0.462100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.035[1e3]0.0122,=0.434100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.034[1e3]0.0112,=0.415100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.030[1e3]0.0092,=0.381100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.027[1e3]0.0092,=0.345100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.024[1e3]0.0082,=0.311100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.022[1e3]0.0072,=0.280100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.020[1e3]0.0062,=0.257100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.018[1e3]0.0062,=0.232100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.015[1e3]0.0052,=0.210100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.014[1e3]0.0052,=0.181100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.014[1e3]0.0052,=0.174100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.014[1e3]0.0052,=0.169100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.014[1e3]0.0042,=0.166100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.012[1e3]0.0042,=0.136100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.010[1e3]0.0032,=0.114100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.012[1e3]0.0042,=0.134100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.011[1e3]0.0032,=0.139100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.009[1e3]0.0032,=0.113100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.012[1e3]0.0042,=0.146100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.011[1e3]0.0042,=0.127100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.014[1e3]0.0042,=0.159100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.014[1e3]0.0052,=0.166100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.013[1e3]0.0042,=0.156100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.013[1e3]0.0042,=0.160100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.014[1e3]0.0042,=0.167100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.014[1e3]0.0042,=0.162100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  ee0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0122,=0.519100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0122,=0.507100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0122,=0.497100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.039[1e3]0.0132,=0.483100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.038[1e3]0.0122,=0.479100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.038[1e3]0.0122,=0.473100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.037[1e3]0.0122,=0.459100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.035[1e3]0.0112,=0.438100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.033[1e3]0.0112,=0.415100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.031[1e3]0.0092,=0.385100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.029[1e3]0.0092,=0.355100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.025[1e3]0.0092,=0.324100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.023[1e3]0.0072,=0.294100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.021[1e3]0.0072,=0.266100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.017[1e3]0.0052,=0.244100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.016[1e3]0.0052,=0.220100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.015[1e3]0.0052,=0.198100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.014[1e3]0.0042,=0.181100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.014[1e3]0.0042,=0.169100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.013[1e3]0.0042,=0.151100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.011[1e3]0.0042,=0.134100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.011[1e3]0.0032,=0.127100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.010[1e3]0.0032,=0.123100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.009[1e3]0.0032,=0.107100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.009[1e3]0.0032,=0.107100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.008[1e3]0.0022,=0.100100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.008[1e3]0.0032,=0.104100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.008[1e3]0.0032,=0.102100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.008[1e3]0.0022,=0.100100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.008[1e3]0.0032,=0.105100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.009[1e3]0.0032,=0.110100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.010[1e3]0.0032,=0.114100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  mumu0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0132,=0.521100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0122,=0.509100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0122,=0.499100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.040[1e3]0.0122,=0.486100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.039[1e3]0.0132,=0.485100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.039[1e3]0.0122,=0.476100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.038[1e3]0.0112,=0.464100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.036[1e3]0.0112,=0.445100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.034[1e3]0.0112,=0.423100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.031[1e3]0.0102,=0.395100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.029[1e3]0.0092,=0.366100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.027[1e3]0.0092,=0.337100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.025[1e3]0.0082,=0.310100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.023[1e3]0.0082,=0.284100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.019[1e3]0.0062,=0.263100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.018[1e3]0.0052,=0.241100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.016[1e3]0.0052,=0.219100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.015[1e3]0.0052,=0.202100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.015[1e3]0.0052,=0.189100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.014[1e3]0.0042,=0.172100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.013[1e3]0.0042,=0.155100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.012[1e3]0.0042,=0.146100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.011[1e3]0.0042,=0.139100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.010[1e3]0.0032,=0.124100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.010[1e3]0.0032,=0.122100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.009[1e3]0.0032,=0.113100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.009[1e3]0.0032,=0.113100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.009[1e3]0.0032,=0.109100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.009[1e3]0.0032,=0.105100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.009[1e3]0.0032,=0.106100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.009[1e3]0.0032,=0.106100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.009[1e3]0.0032,=0.105100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  tautau0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.038[1e3]0.0132,=0.480100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.038[1e3]0.0122,=0.460100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.037[1e3]0.0122,=0.411100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.036[1e3]0.0112,=0.395100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.037[1e3]0.0122,=0.400100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.035[1e3]0.0112,=0.360100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.032[1e3]0.0102,=0.353100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.030[1e3]0.0102,=0.311100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.026[1e3]0.0082,=0.268100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.023[1e3]0.0072,=0.261100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.021[1e3]0.0072,=0.238100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.013[1e3]0.0042,=0.148100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.013[1e3]0.0042,=0.153100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.012[1e3]0.0042,=0.164100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.010[1e3]0.0032,=0.123100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.010[1e3]0.0032,=0.130100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.006[1e3]0.0022,=0.096100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.011[1e3]0.0042,=0.112100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.008[1e3]0.0032,=0.102100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.008[1e3]0.0032,=0.080100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.003[1e3]0.0012,=0.057100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.008[1e3]0.0022,=0.089100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.006[1e3]0.0022,=0.091100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.004[1e3]0.0012,=0.064100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.007[1e3]0.0022,=0.101100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.006[1e3]0.0022,=0.078100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.012[1e3]0.0042,=0.134100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.016[1e3]0.0052,=0.172100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.012[1e3]0.0042,=0.143100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.012[1e3]0.0042,=0.149100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.013[1e3]0.0042,=0.159100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.014[1e3]0.0042,=0.161100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  nuenue0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.038[1e3]0.0132,=0.480100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.038[1e3]0.0122,=0.460100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.037[1e3]0.0122,=0.411100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.036[1e3]0.0112,=0.395100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.036[1e3]0.0112,=0.388100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.035[1e3]0.0112,=0.361100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.032[1e3]0.0102,=0.355100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.030[1e3]0.0092,=0.314100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.026[1e3]0.0092,=0.272100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.022[1e3]0.0072,=0.265100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.021[1e3]0.0072,=0.243100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.014[1e3]0.0042,=0.156100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.014[1e3]0.0042,=0.162100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.012[1e3]0.0042,=0.172100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.011[1e3]0.0042,=0.136100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.011[1e3]0.0042,=0.139100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.007[1e3]0.0022,=0.105100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.012[1e3]0.0042,=0.123100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.010[1e3]0.0032,=0.118100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.008[1e3]0.0032,=0.094100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.004[1e3]0.0012,=0.068100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.007[1e3]0.0022,=0.093100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.007[1e3]0.0022,=0.095100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.004[1e3]0.0012,=0.068100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.007[1e3]0.0022,=0.093100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.004[1e3]0.0012,=0.072100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.008[1e3]0.0032,=0.105100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.012[1e3]0.0042,=0.128100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.010[1e3]0.0032,=0.111100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.009[1e3]0.0032,=0.126100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.011[1e3]0.0042,=0.131100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.012[1e3]0.0042,=0.139100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  numunumu0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.038[1e3]0.0132,=0.480100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.038[1e3]0.0122,=0.460100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.037[1e3]0.0122,=0.411100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.036[1e3]0.0112,=0.395100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.037[1e3]0.0122,=0.400100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.035[1e3]0.0112,=0.362100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.032[1e3]0.0102,=0.355100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.030[1e3]0.0092,=0.315100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.026[1e3]0.0082,=0.273100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.022[1e3]0.0072,=0.266100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.021[1e3]0.0072,=0.244100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.014[1e3]0.0042,=0.157100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.015[1e3]0.0052,=0.165100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.013[1e3]0.0042,=0.174100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.012[1e3]0.0042,=0.140100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.012[1e3]0.0042,=0.143100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.008[1e3]0.0022,=0.108100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.013[1e3]0.0042,=0.131100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.011[1e3]0.0032,=0.132100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.009[1e3]0.0032,=0.102100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.005[1e3]0.0022,=0.076100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.008[1e3]0.0032,=0.104100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.008[1e3]0.0032,=0.105100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.006[1e3]0.0022,=0.078100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.007[1e3]0.0022,=0.103100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.006[1e3]0.0022,=0.081100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.009[1e3]0.0032,=0.111100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.011[1e3]0.0042,=0.128100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.010[1e3]0.0032,=0.113100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.009[1e3]0.0032,=0.126100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.010[1e3]0.0032,=0.125100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.011[1e3]0.0032,=0.130100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  nutaunutaudata used in that study were taken when the IceCube detector was not yet completed to the 86

string configuration. Many more dSphs are observed, from 4 in the previous study to 15 here.

Previously, the particle physics model used for neutrino spectra from DM annihilation did not

have EW corrections, which are now included [25]. The spectral models also predict substantial

differences between the neutrino flavors, so this analysis will be the first DM dwarf analysis to

discriminate between primary neutrino flavors. The study performed here uses 10.4 years of data.

The SM annihilation channels probed for this study include 𝜒 𝜒 → 𝑏𝑏, 𝑡𝑡, 𝑢𝑢, 𝑑𝑑, 𝑒𝑒, 𝜇𝜇, 𝜏𝜏,

𝑍 𝑍, 𝑊 +𝑊 −, 𝜈𝑒𝜈𝑒, 𝜈𝜇𝜈𝜇, and 𝜈𝜏𝜈𝜏

6.4 Likelihood Methods

I use the point-source search likelihood generally used in IceCube analyses [105]. The likelihood

function is defined as the following:

𝐿(𝑛𝑠) =

𝑁
(cid:214)

𝑖=1

(cid:104) 𝑛𝑠
𝑁

𝑆𝑖 +

(cid:16)1 −

(cid:17)

(cid:105)

𝐵𝑖

𝑛𝑠
𝑁

(6.6)

where 𝑖 is an event index, 𝑆 and 𝐵 are the signal PDF and background PDF respectively. For a joint

analysis where the sources are stacked the likelihood is expanded to

𝑖=1
where 𝐿𝑖 is the likelihood, Eq. (6.6), from the i-th source in the stacked analysis. The Test Statistic

𝐿(𝑛𝑠) =

𝑁sources
(cid:214)

𝐿𝑖 (𝑛𝑠)

(6.7)

(TS) definition remains the same as Eq. (3.7)

6.5 Background Simulation

Before we look at data, we must first analyze background and simulated sky maps to validate

our analysis. We set out to characterize the TS distributions for each source, annihilation channel,

and 𝑚 𝜒. Previous IceCube DM searches [107, 110] showed TS distributions that did not behave

according to a 𝜒2 distribution with 1 degree of freedom. TS distributions can also vary significantly

between DM mass and annihilation models. Therefore, Wilks’ theorem may not be applicable to

the analysis. Instead, a critical value is defined from many background trials. We study the TS

distributions first for each source, then for the stacked analysis. The following sections show the

results of the likelihood fitting for a suite of background trials.

117

I assume that TS values are physical: TS ≥ 0. 𝜖 [𝑥] indicate the fraction of events where TS < 𝑥.

For TS plots shown here, the decimal values of x are 1.0 · 10−2 and 1.0 · 10−3. These values serve as

an additional sanity check to validate the likelihood is not systematically biased downward. Each

subplot represents a simulation of 100,000 scrambled-data background trials. Section 6.5.1 shows

the background TS distributions obtained for Segue 1, a source with little Earth attenuation and a

large 𝐽-factor, and Ursa Major II, which has a similarly large 𝐽-factor but significantly more Earth

attenuation. The select DM annihilation channels shown are 𝑏𝑏, 𝑒𝑒, 𝜇𝜇, 𝜏𝜏, 𝜈𝑒𝜈𝑒, 𝜈𝜇𝜈𝜇, and 𝜈𝜏𝜈𝜏.

I also show the TS distributions of a stacked study of 15 sources for all DM annihilation channels.

6.5.1 TS per Source

Figures 6.6 to 6.19 present some TS distributions for Segue 1 and Ursa Major II for 100,000

trials. More studies for all annihilation channels and remaining 13 sources were also performed

and are documented in IceCube’s internal wiki.

Almost every distribution produced follows a 𝜒2 distribution with 1 degree of freedom. This

is more true for low 𝑚 𝜒 than high 𝑚 𝜒 models. These observations are important for the future

assumptions made in Chapter 7 and may justify statistical calculations assuming our test statistics

follow a 𝜒2 with 1 degree of freedom, rather than time-consuming numeric determinations of

significance.

6.5.2 Stacked TS

Figures 6.20 to 6.31 present the TS distributions for a stacked study of 15 sources with GS

𝐽-factors on 100,000 trials. The presentation of these plots are identical to the single source

distributions in Section 6.5.1. We see similar behavior in the stacked TS distributions compared to

the single source studies.

6.6 Signal Recovery per Channel

We also wish to understand how well the analysis is able to reconstruct signal neutrinos across

all annihilation channels.

In order to test this, we inject neutrinos from our spectral models

randomly then attempt to discern the number of signal neutrinos in the simulated data. Figure 6.32

and Figure 6.33 show this study for 𝜒 𝜒 → 𝑏𝑏, 𝑡𝑡, and 𝜈𝜇𝜈𝜇 for a stacked analysis of 15 sources.

118

Figure 6.6 Test statistic (TS) distributions for Segue 1 and 𝜒 𝜒 → 𝑏𝑏. Each subplot, except the
final, is the TS distribution for a specific DM mass listed in the subplot. Orange dashed lines are
the traces for a 𝜒2 distribution with 1 degree of freedom. 𝜖 [·] is the fraction of trials smaller than
the bracketed value. The final subplot features the all DM spectral models, similar to Fig. 6.5,
used as input for the TS distributions.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0122,=0.486100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0122,=0.492100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0122,=0.495100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.038[1e3]0.0122,=0.485100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.039[1e3]0.0122,=0.489100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.039[1e3]0.0132,=0.489100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.040[1e3]0.0142,=0.490100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.039[1e3]0.0122,=0.486100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.039[1e3]0.0122,=0.481100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.039[1e3]0.0122,=0.470100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.038[1e3]0.0122,=0.460100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.036[1e3]0.0112,=0.445100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.035[1e3]0.0122,=0.429100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.034[1e3]0.0112,=0.413100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.032[1e3]0.0102,=0.394100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.030[1e3]0.0102,=0.378100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.029[1e3]0.0092,=0.361100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.028[1e3]0.0092,=0.344100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.026[1e3]0.0092,=0.328100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.025[1e3]0.0082,=0.311100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.023[1e3]0.0082,=0.295100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.022[1e3]0.0072,=0.278100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.020[1e3]0.0072,=0.263100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.019[1e3]0.0062,=0.249100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.018[1e3]0.0062,=0.236100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.018[1e3]0.0052,=0.224100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.017[1e3]0.0062,=0.212100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.015[1e3]0.0052,=0.201100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.015[1e3]0.0052,=0.191100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.014[1e3]0.0042,=0.182100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.014[1e3]0.0052,=0.174100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.014[1e3]0.0042,=0.166100k bg trials103104105106107108E (GeV)1011109107105103101dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  bbFigure 6.7 Same as Fig. 6.6 for Segue 1 𝜒 𝜒 → 𝑒𝑒.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0122,=0.462100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.037[1e3]0.0112,=0.503100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0122,=0.495100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.038[1e3]0.0122,=0.483100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.039[1e3]0.0122,=0.474100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.037[1e3]0.0122,=0.462100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.035[1e3]0.0122,=0.434100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.034[1e3]0.0112,=0.415100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.030[1e3]0.0092,=0.381100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.027[1e3]0.0092,=0.345100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.024[1e3]0.0082,=0.311100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.022[1e3]0.0072,=0.280100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.020[1e3]0.0062,=0.257100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.018[1e3]0.0062,=0.232100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.015[1e3]0.0052,=0.210100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.014[1e3]0.0052,=0.181100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.014[1e3]0.0052,=0.174100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.014[1e3]0.0052,=0.169100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.014[1e3]0.0042,=0.166100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.012[1e3]0.0042,=0.136100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.010[1e3]0.0032,=0.114100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.012[1e3]0.0042,=0.134100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.011[1e3]0.0032,=0.139100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.009[1e3]0.0032,=0.113100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.012[1e3]0.0042,=0.146100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.011[1e3]0.0042,=0.127100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.014[1e3]0.0042,=0.159100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.014[1e3]0.0052,=0.166100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.013[1e3]0.0042,=0.156100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.013[1e3]0.0042,=0.160100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.014[1e3]0.0042,=0.167100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.014[1e3]0.0042,=0.162100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  eeFigure 6.8 Same as Fig. 6.6 for Segue 1 𝜒 𝜒 → 𝜇𝜇.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0122,=0.519100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0122,=0.507100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0122,=0.497100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.039[1e3]0.0132,=0.483100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.038[1e3]0.0122,=0.479100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.038[1e3]0.0122,=0.473100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.037[1e3]0.0122,=0.459100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.035[1e3]0.0112,=0.438100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.033[1e3]0.0112,=0.415100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.031[1e3]0.0092,=0.385100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.029[1e3]0.0092,=0.355100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.025[1e3]0.0092,=0.324100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.023[1e3]0.0072,=0.294100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.021[1e3]0.0072,=0.266100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.017[1e3]0.0052,=0.244100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.016[1e3]0.0052,=0.220100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.015[1e3]0.0052,=0.198100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.014[1e3]0.0042,=0.181100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.014[1e3]0.0042,=0.169100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.013[1e3]0.0042,=0.151100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.011[1e3]0.0042,=0.134100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.011[1e3]0.0032,=0.127100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.010[1e3]0.0032,=0.123100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.009[1e3]0.0032,=0.107100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.009[1e3]0.0032,=0.107100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.008[1e3]0.0022,=0.100100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.008[1e3]0.0032,=0.104100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.008[1e3]0.0032,=0.102100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.008[1e3]0.0022,=0.100100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.008[1e3]0.0032,=0.105100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.009[1e3]0.0032,=0.110100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.010[1e3]0.0032,=0.114100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  mumuFigure 6.9 Same as Fig. 6.6 for Segue 1 𝜒 𝜒 → 𝜏𝜏.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0132,=0.521100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0122,=0.509100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0122,=0.499100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.040[1e3]0.0122,=0.486100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.039[1e3]0.0132,=0.485100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.039[1e3]0.0122,=0.476100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.038[1e3]0.0112,=0.464100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.036[1e3]0.0112,=0.445100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.034[1e3]0.0112,=0.423100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.031[1e3]0.0102,=0.395100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.029[1e3]0.0092,=0.366100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.027[1e3]0.0092,=0.337100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.025[1e3]0.0082,=0.310100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.023[1e3]0.0082,=0.284100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.019[1e3]0.0062,=0.263100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.018[1e3]0.0052,=0.241100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.016[1e3]0.0052,=0.219100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.015[1e3]0.0052,=0.202100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.015[1e3]0.0052,=0.189100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.014[1e3]0.0042,=0.172100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.013[1e3]0.0042,=0.155100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.012[1e3]0.0042,=0.146100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.011[1e3]0.0042,=0.139100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.010[1e3]0.0032,=0.124100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.010[1e3]0.0032,=0.122100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.009[1e3]0.0032,=0.113100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.009[1e3]0.0032,=0.113100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.009[1e3]0.0032,=0.109100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.009[1e3]0.0032,=0.105100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.009[1e3]0.0032,=0.106100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.009[1e3]0.0032,=0.106100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.009[1e3]0.0032,=0.105100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  tautauFigure 6.10 Same as Fig. 6.6 for Segue 1 𝜒 𝜒 → 𝜈𝑒𝜈𝑒.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.038[1e3]0.0132,=0.480100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.038[1e3]0.0122,=0.460100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.037[1e3]0.0122,=0.411100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.036[1e3]0.0112,=0.395100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.037[1e3]0.0122,=0.400100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.035[1e3]0.0112,=0.360100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.032[1e3]0.0102,=0.353100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.030[1e3]0.0102,=0.311100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.026[1e3]0.0082,=0.268100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.023[1e3]0.0072,=0.261100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.021[1e3]0.0072,=0.238100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.013[1e3]0.0042,=0.148100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.013[1e3]0.0042,=0.153100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.012[1e3]0.0042,=0.164100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.010[1e3]0.0032,=0.123100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.010[1e3]0.0032,=0.130100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.006[1e3]0.0022,=0.096100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.011[1e3]0.0042,=0.112100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.008[1e3]0.0032,=0.102100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.008[1e3]0.0032,=0.080100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.003[1e3]0.0012,=0.057100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.008[1e3]0.0022,=0.089100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.006[1e3]0.0022,=0.091100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.004[1e3]0.0012,=0.064100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.007[1e3]0.0022,=0.101100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.006[1e3]0.0022,=0.078100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.012[1e3]0.0042,=0.134100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.016[1e3]0.0052,=0.172100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.012[1e3]0.0042,=0.143100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.012[1e3]0.0042,=0.149100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.013[1e3]0.0042,=0.159100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.014[1e3]0.0042,=0.161100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  nuenueFigure 6.11 Same as Fig. 6.6 for Segue 1 𝜒 𝜒 → 𝜈𝜇𝜈𝜇.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.038[1e3]0.0132,=0.480100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.038[1e3]0.0122,=0.460100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.037[1e3]0.0122,=0.411100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.036[1e3]0.0112,=0.395100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.036[1e3]0.0112,=0.388100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.035[1e3]0.0112,=0.361100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.032[1e3]0.0102,=0.355100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.030[1e3]0.0092,=0.314100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.026[1e3]0.0092,=0.272100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.022[1e3]0.0072,=0.265100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.021[1e3]0.0072,=0.243100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.014[1e3]0.0042,=0.156100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.014[1e3]0.0042,=0.162100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.012[1e3]0.0042,=0.172100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.011[1e3]0.0042,=0.136100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.011[1e3]0.0042,=0.139100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.007[1e3]0.0022,=0.105100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.012[1e3]0.0042,=0.123100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.010[1e3]0.0032,=0.118100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.008[1e3]0.0032,=0.094100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.004[1e3]0.0012,=0.068100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.007[1e3]0.0022,=0.093100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.007[1e3]0.0022,=0.095100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.004[1e3]0.0012,=0.068100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.007[1e3]0.0022,=0.093100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.004[1e3]0.0012,=0.072100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.008[1e3]0.0032,=0.105100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.012[1e3]0.0042,=0.128100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.010[1e3]0.0032,=0.111100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.009[1e3]0.0032,=0.126100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.011[1e3]0.0042,=0.131100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.012[1e3]0.0042,=0.139100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  numunumuFigure 6.12 Same as Fig. 6.6 for Segue 1 𝜒 𝜒 → 𝜈𝜏𝜈𝜏.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.038[1e3]0.0132,=0.480100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.038[1e3]0.0122,=0.460100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.037[1e3]0.0122,=0.411100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.036[1e3]0.0112,=0.395100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.037[1e3]0.0122,=0.400100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.035[1e3]0.0112,=0.362100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.032[1e3]0.0102,=0.355100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.030[1e3]0.0092,=0.315100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.026[1e3]0.0082,=0.273100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.022[1e3]0.0072,=0.266100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.021[1e3]0.0072,=0.244100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.014[1e3]0.0042,=0.157100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.015[1e3]0.0052,=0.165100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.013[1e3]0.0042,=0.174100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.012[1e3]0.0042,=0.140100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.012[1e3]0.0042,=0.143100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.008[1e3]0.0022,=0.108100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.013[1e3]0.0042,=0.131100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.011[1e3]0.0032,=0.132100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.009[1e3]0.0032,=0.102100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.005[1e3]0.0022,=0.076100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.008[1e3]0.0032,=0.104100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.008[1e3]0.0032,=0.105100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.006[1e3]0.0022,=0.078100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.007[1e3]0.0022,=0.103100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.006[1e3]0.0022,=0.081100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.009[1e3]0.0032,=0.111100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.011[1e3]0.0042,=0.128100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.010[1e3]0.0032,=0.113100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.009[1e3]0.0032,=0.126100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.010[1e3]0.0032,=0.125100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.011[1e3]0.0032,=0.130100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  nutaunutauFigure 6.13 Same as Fig. 6.6 for Ursa Major II 𝜒 𝜒 → 𝑏𝑏.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0132,=0.487100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.038[1e3]0.0122,=0.493100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.038[1e3]0.0132,=0.469100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.037[1e3]0.0122,=0.466100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.038[1e3]0.0112,=0.464100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.038[1e3]0.0122,=0.465100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.037[1e3]0.0122,=0.465100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.036[1e3]0.0122,=0.466100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.036[1e3]0.0122,=0.465100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.035[1e3]0.0112,=0.460100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.033[1e3]0.0112,=0.449100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.032[1e3]0.0102,=0.434100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.031[1e3]0.0102,=0.417100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.030[1e3]0.0092,=0.401100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.030[1e3]0.0102,=0.384100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.028[1e3]0.0092,=0.365100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.028[1e3]0.0092,=0.347100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.026[1e3]0.0082,=0.329100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.025[1e3]0.0082,=0.313100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.024[1e3]0.0082,=0.298100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.023[1e3]0.0082,=0.283100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.022[1e3]0.0072,=0.269100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.021[1e3]0.0072,=0.256100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.021[1e3]0.0062,=0.244100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.020[1e3]0.0062,=0.233100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.020[1e3]0.0062,=0.223100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.019[1e3]0.0062,=0.213100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.017[1e3]0.0062,=0.205100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.017[1e3]0.0052,=0.197100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.016[1e3]0.0052,=0.191100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.017[1e3]0.0052,=0.185100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.017[1e3]0.0052,=0.180100k bg trials103104105106107108E (GeV)1011109107105103101dN/dE(GeV1)M=681 GeVM=100 PeVUrsaMajorII(J = 2.66e+19, Dec = 63.11) Chi2 for  bbFigure 6.14 Same as Fig. 6.6 for Ursa Major II 𝜒 𝜒 → 𝑒𝑒.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.037[1e3]0.0122,=0.470100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.037[1e3]0.0122,=0.466100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.036[1e3]0.0122,=0.446100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.035[1e3]0.0112,=0.449100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.035[1e3]0.0122,=0.452100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.034[1e3]0.0112,=0.447100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.031[1e3]0.0102,=0.428100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.029[1e3]0.0092,=0.401100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.026[1e3]0.0092,=0.357100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.024[1e3]0.0082,=0.320100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.023[1e3]0.0072,=0.283100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.021[1e3]0.0072,=0.250100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.018[1e3]0.0062,=0.204100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.017[1e3]0.0052,=0.186100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.016[1e3]0.0052,=0.166100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.015[1e3]0.0052,=0.149100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.015[1e3]0.0052,=0.154100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.013[1e3]0.0042,=0.137100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.017[1e3]0.0052,=0.187100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.017[1e3]0.0052,=0.173100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.019[1e3]0.0062,=0.214100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.020[1e3]0.0072,=0.226100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.020[1e3]0.0062,=0.223100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.021[1e3]0.0062,=0.232100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.019[1e3]0.0062,=0.225100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.020[1e3]0.0062,=0.218100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.019[1e3]0.0062,=0.216100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.018[1e3]0.0062,=0.203100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.017[1e3]0.0052,=0.199100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.017[1e3]0.0052,=0.193100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.017[1e3]0.0052,=0.187100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.017[1e3]0.0052,=0.182100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVUrsaMajorII(J = 2.66e+19, Dec = 63.11) Chi2 for  eeFigure 6.15 Same as Fig. 6.6 for Ursa Major II 𝜒 𝜒 → 𝜇𝜇.

128

0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.038[1e3]0.0122,=0.481100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.037[1e3]0.0112,=0.470100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.037[1e3]0.0122,=0.449100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.035[1e3]0.0112,=0.448100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.036[1e3]0.0112,=0.453100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.036[1e3]0.0122,=0.454100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.034[1e3]0.0112,=0.445100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.032[1e3]0.0102,=0.430100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.029[1e3]0.0092,=0.401100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.026[1e3]0.0082,=0.364100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.025[1e3]0.0082,=0.330100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.024[1e3]0.0082,=0.298100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.021[1e3]0.0072,=0.259100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.019[1e3]0.0062,=0.227100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.017[1e3]0.0052,=0.199100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.016[1e3]0.0052,=0.175100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.015[1e3]0.0052,=0.156100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.013[1e3]0.0042,=0.140100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.013[1e3]0.0042,=0.133100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.012[1e3]0.0042,=0.123100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.012[1e3]0.0042,=0.125100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.012[1e3]0.0042,=0.131100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.012[1e3]0.0042,=0.132100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.014[1e3]0.0042,=0.145100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.014[1e3]0.0052,=0.160100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.016[1e3]0.0052,=0.163100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.016[1e3]0.0052,=0.170100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.017[1e3]0.0052,=0.166100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.016[1e3]0.0052,=0.173100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.017[1e3]0.0052,=0.176100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.016[1e3]0.0062,=0.173100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.016[1e3]0.0052,=0.172100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVUrsaMajorII(J = 2.66e+19, Dec = 63.11) Chi2 for  mumuFigure 6.16 Same as Fig. 6.6 for Ursa Major II 𝜒 𝜒 → 𝜏𝜏.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.037[1e3]0.0122,=0.482100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.037[1e3]0.0122,=0.473100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.037[1e3]0.0122,=0.451100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.036[1e3]0.0112,=0.451100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.036[1e3]0.0122,=0.455100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.035[1e3]0.0112,=0.457100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.034[1e3]0.0102,=0.448100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.033[1e3]0.0102,=0.436100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.030[1e3]0.0092,=0.410100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.028[1e3]0.0092,=0.376100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.027[1e3]0.0092,=0.346100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.025[1e3]0.0082,=0.316100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.023[1e3]0.0072,=0.282100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.021[1e3]0.0072,=0.255100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.020[1e3]0.0072,=0.229100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.018[1e3]0.0062,=0.206100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.017[1e3]0.0052,=0.189100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.016[1e3]0.0052,=0.174100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.015[1e3]0.0052,=0.164100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.014[1e3]0.0052,=0.152100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.014[1e3]0.0042,=0.148100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.014[1e3]0.0042,=0.145100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.013[1e3]0.0042,=0.139100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.013[1e3]0.0042,=0.140100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.014[1e3]0.0042,=0.146100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.014[1e3]0.0052,=0.143100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.014[1e3]0.0042,=0.145100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.014[1e3]0.0052,=0.145100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.014[1e3]0.0052,=0.151100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.015[1e3]0.0052,=0.154100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.015[1e3]0.0052,=0.155100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.015[1e3]0.0052,=0.156100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVUrsaMajorII(J = 2.66e+19, Dec = 63.11) Chi2 for  tautauFigure 6.17 Same as Fig. 6.6 for Ursa Major II 𝜒 𝜒 → 𝜈𝑒𝜈𝑒.

130

0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.036[1e3]0.0112,=0.422100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.036[1e3]0.0122,=0.447100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.036[1e3]0.0112,=0.412100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.035[1e3]0.0112,=0.423100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.033[1e3]0.0112,=0.426100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.032[1e3]0.0112,=0.403100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.029[1e3]0.0092,=0.355100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.026[1e3]0.0082,=0.339100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.023[1e3]0.0072,=0.305100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.019[1e3]0.0062,=0.224100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.017[1e3]0.0052,=0.205100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.015[1e3]0.0052,=0.169100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.011[1e3]0.0032,=0.133100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.007[1e3]0.0022,=0.078100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.008[1e3]0.0022,=0.068100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.007[1e3]0.0022,=0.084100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.005[1e3]0.0022,=0.042100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.008[1e3]0.0022,=0.080100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.015[1e3]0.0052,=0.160100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.008[1e3]0.0032,=0.077100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.016[1e3]0.0052,=0.161100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.020[1e3]0.0062,=0.227100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.019[1e3]0.0062,=0.209100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.020[1e3]0.0062,=0.234100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.014[1e3]0.0042,=0.158100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.020[1e3]0.0062,=0.220100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.019[1e3]0.0062,=0.216100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.016[1e3]0.0052,=0.173100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.017[1e3]0.0052,=0.185100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.017[1e3]0.0052,=0.193100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.017[1e3]0.0052,=0.187100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.017[1e3]0.0052,=0.183100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVUrsaMajorII(J = 2.66e+19, Dec = 63.11) Chi2 for  nuenueFigure 6.18 Same as Fig. 6.6 for Ursa Major II 𝜒 𝜒 → 𝜈𝜇𝜈𝜇.

131

0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.036[1e3]0.0112,=0.421100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.036[1e3]0.0122,=0.447100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.036[1e3]0.0112,=0.412100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.035[1e3]0.0112,=0.423100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.032[1e3]0.0102,=0.347100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.032[1e3]0.0102,=0.404100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.029[1e3]0.0092,=0.357100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.026[1e3]0.0092,=0.341100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.023[1e3]0.0072,=0.307100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.019[1e3]0.0072,=0.230100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.018[1e3]0.0052,=0.212100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.016[1e3]0.0052,=0.178100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.013[1e3]0.0042,=0.145100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.008[1e3]0.0022,=0.089100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.009[1e3]0.0032,=0.091100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.009[1e3]0.0032,=0.097100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.007[1e3]0.0022,=0.060100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.009[1e3]0.0032,=0.094100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.013[1e3]0.0042,=0.136100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.007[1e3]0.0022,=0.071100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.013[1e3]0.0042,=0.123100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.015[1e3]0.0052,=0.174100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.015[1e3]0.0052,=0.161100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.018[1e3]0.0062,=0.193100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.012[1e3]0.0042,=0.131100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.018[1e3]0.0062,=0.197100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.018[1e3]0.0062,=0.200100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.014[1e3]0.0052,=0.144100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.016[1e3]0.0052,=0.168100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.017[1e3]0.0052,=0.188100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.017[1e3]0.0052,=0.183100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.016[1e3]0.0052,=0.181100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVUrsaMajorII(J = 2.66e+19, Dec = 63.11) Chi2 for  numunumuFigure 6.19 Same as Fig. 6.6 for Ursa Major II 𝜒 𝜒 → 𝜈𝜏𝜈𝜏.

132

0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.036[1e3]0.0112,=0.421100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.036[1e3]0.0122,=0.447100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.036[1e3]0.0112,=0.412100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.035[1e3]0.0112,=0.423100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.033[1e3]0.0112,=0.426100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.032[1e3]0.0102,=0.404100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.029[1e3]0.0092,=0.357100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.026[1e3]0.0092,=0.342100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.023[1e3]0.0072,=0.307100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.020[1e3]0.0062,=0.232100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.018[1e3]0.0062,=0.214100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.017[1e3]0.0062,=0.180100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.013[1e3]0.0042,=0.148100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.008[1e3]0.0022,=0.093100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.011[1e3]0.0042,=0.103100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.010[1e3]0.0042,=0.109100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.008[1e3]0.0032,=0.076100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.010[1e3]0.0032,=0.111100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.015[1e3]0.0052,=0.158100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.010[1e3]0.0032,=0.094100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.014[1e3]0.0042,=0.142100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.015[1e3]0.0052,=0.173100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.015[1e3]0.0052,=0.160100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.016[1e3]0.0052,=0.178100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.012[1e3]0.0042,=0.138100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.017[1e3]0.0052,=0.181100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.017[1e3]0.0052,=0.185100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.014[1e3]0.0052,=0.145100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.016[1e3]0.0052,=0.164100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.016[1e3]0.0052,=0.181100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.016[1e3]0.0062,=0.178100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.016[1e3]0.0052,=0.176100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVUrsaMajorII(J = 2.66e+19, Dec = 63.11) Chi2 for  nutaunutauFigure 6.20 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝑏𝑏.

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0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.039[1e3]=0.0122,=0.498100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.039[1e3]=0.0122,=0.512100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.039[1e3]=0.0122,=0.492100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.038[1e3]=0.0122,=0.487100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.038[1e3]=0.0122,=0.489100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.038[1e3]=0.0122,=0.491100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.039[1e3]=0.0122,=0.494100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.039[1e3]=0.0132,=0.495100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.039[1e3]=0.0132,=0.495100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.038[1e3]=0.0122,=0.488100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.037[1e3]=0.0112,=0.479100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.038[1e3]=0.0122,=0.469100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.036[1e3]=0.0112,=0.454100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.035[1e3]=0.0112,=0.440100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.035[1e3]=0.0112,=0.425100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.033[1e3]=0.0112,=0.408100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.032[1e3]=0.0102,=0.391100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.029[1e3]=0.0102,=0.374100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.028[1e3]=0.0092,=0.358100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.028[1e3]=0.0092,=0.341100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.026[1e3]=0.0082,=0.325100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.025[1e3]=0.0082,=0.309100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.024[1e3]=0.0082,=0.294100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.023[1e3]=0.0082,=0.279100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.021[1e3]=0.0072,=0.264100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.020[1e3]=0.0072,=0.251100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.018[1e3]=0.0062,=0.237100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.018[1e3]=0.0062,=0.226100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.017[1e3]=0.0052,=0.215100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.016[1e3]=0.0052,=0.205100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.016[1e3]=0.0052,=0.196100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.015[1e3]=0.0052,=0.187100k bg trials103104105106107108E (GeV)1011109107105103101dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15  bbFigure 6.21 Same as Fig. 6.6 for 15 stacked GS 𝐽-factor, sources and 𝜒 𝜒 → 𝑡𝑡.

134

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.040[1e3]=0.0122,=0.531100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.038[1e3]=0.0122,=0.514100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.037[1e3]=0.0122,=0.488100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.039[1e3]=0.0122,=0.482100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.039[1e3]=0.0132,=0.487100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.038[1e3]=0.0132,=0.491100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.037[1e3]=0.0122,=0.491100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.037[1e3]=0.0122,=0.485100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.037[1e3]=0.0122,=0.472100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.036[1e3]=0.0112,=0.451100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.034[1e3]=0.0112,=0.430100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.034[1e3]=0.0112,=0.414100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.033[1e3]=0.0102,=0.399100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.031[1e3]=0.0102,=0.384100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.030[1e3]=0.0102,=0.371100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.030[1e3]=0.0102,=0.362100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.029[1e3]=0.0102,=0.353100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.028[1e3]=0.0092,=0.344100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.028[1e3]=0.0092,=0.336100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.027[1e3]=0.0092,=0.327100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.027[1e3]=0.0092,=0.318100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.026[1e3]=0.0092,=0.308100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.025[1e3]=0.0082,=0.296100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.024[1e3]=0.0072,=0.285100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.022[1e3]=0.0072,=0.272100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.021[1e3]=0.0072,=0.260100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.020[1e3]=0.0072,=0.248100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.018[1e3]=0.0052,=0.235100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.018[1e3]=0.0062,=0.225100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.017[1e3]=0.0062,=0.214100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.016[1e3]=0.0052,=0.204100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.016[1e3]=0.0052,=0.195100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15  ttFigure 6.22 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝑢𝑢.

135

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.040[1e3]=0.0122,=0.502100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.039[1e3]=0.0122,=0.513100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.040[1e3]=0.0132,=0.495100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.040[1e3]=0.0132,=0.490100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.038[1e3]=0.0122,=0.490100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.038[1e3]=0.0122,=0.491100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.039[1e3]=0.0122,=0.491100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.039[1e3]=0.0132,=0.492100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.039[1e3]=0.0132,=0.492100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.039[1e3]=0.0132,=0.490100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.037[1e3]=0.0122,=0.485100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.037[1e3]=0.0112,=0.476100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.037[1e3]=0.0112,=0.463100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.035[1e3]=0.0112,=0.446100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.035[1e3]=0.0112,=0.430100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.034[1e3]=0.0112,=0.413100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.032[1e3]=0.0102,=0.394100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.030[1e3]=0.0102,=0.374100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.029[1e3]=0.0092,=0.356100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.027[1e3]=0.0092,=0.339100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.025[1e3]=0.0082,=0.322100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.024[1e3]=0.0082,=0.305100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.024[1e3]=0.0072,=0.290100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.022[1e3]=0.0072,=0.275100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.021[1e3]=0.0072,=0.261100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.020[1e3]=0.0072,=0.248100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.018[1e3]=0.0062,=0.236100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.018[1e3]=0.0062,=0.225100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.017[1e3]=0.0052,=0.215100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.016[1e3]=0.0052,=0.205100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.016[1e3]=0.0052,=0.197100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.015[1e3]=0.0052,=0.188100k bg trials103104105106107108E (GeV)1011109107105103101dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15   uuFigure 6.23 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝑑𝑑.

136

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.040[1e3]=0.0132,=0.477100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.039[1e3]=0.0122,=0.499100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.039[1e3]=0.0122,=0.487100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.040[1e3]=0.0132,=0.485100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.038[1e3]=0.0122,=0.486100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.038[1e3]=0.0122,=0.487100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.039[1e3]=0.0122,=0.487100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.039[1e3]=0.0132,=0.490100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.038[1e3]=0.0122,=0.491100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.039[1e3]=0.0132,=0.491100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.038[1e3]=0.0112,=0.486100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.037[1e3]=0.0122,=0.478100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.037[1e3]=0.0122,=0.465100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.036[1e3]=0.0112,=0.449100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.034[1e3]=0.0102,=0.431100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.034[1e3]=0.0112,=0.414100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.032[1e3]=0.0102,=0.395100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.029[1e3]=0.0092,=0.375100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.029[1e3]=0.0092,=0.357100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.028[1e3]=0.0092,=0.340100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.025[1e3]=0.0082,=0.322100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.024[1e3]=0.0082,=0.306100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.024[1e3]=0.0072,=0.290100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.022[1e3]=0.0072,=0.275100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.021[1e3]=0.0072,=0.261100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.020[1e3]=0.0072,=0.248100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.018[1e3]=0.0062,=0.235100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.018[1e3]=0.0062,=0.225100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.017[1e3]=0.0062,=0.215100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.016[1e3]=0.0052,=0.205100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.016[1e3]=0.0052,=0.196100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.015[1e3]=0.0052,=0.188100k bg trials103104105106107108E (GeV)1011109107105103101dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15   ddFigure 6.24 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝑒𝑒.

137

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.038[1e3]=0.0122,=0.478100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.039[1e3]=0.0132,=0.501100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.039[1e3]=0.0132,=0.479100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.038[1e3]=0.0122,=0.476100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.038[1e3]=0.0122,=0.480100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.037[1e3]=0.0122,=0.481100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.036[1e3]=0.0112,=0.464100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.034[1e3]=0.0102,=0.440101k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.032[1e3]=0.0102,=0.402100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.031[1e3]=0.0102,=0.367100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.027[1e3]=0.0092,=0.339100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.024[1e3]=0.0082,=0.313100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.021[1e3]=0.0072,=0.274100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.020[1e3]=0.0062,=0.253100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.018[1e3]=0.0062,=0.231100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.014[1e3]=0.0042,=0.201100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.015[1e3]=0.0052,=0.182100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.014[1e3]=0.0052,=0.166100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.016[1e3]=0.0052,=0.169100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.013[1e3]=0.0042,=0.144100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.012[1e3]=0.0042,=0.128100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.014[1e3]=0.0052,=0.156100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.015[1e3]=0.0052,=0.161100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.013[1e3]=0.0052,=0.145100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.016[1e3]=0.0052,=0.179100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.015[1e3]=0.0052,=0.161100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.016[1e3]=0.0052,=0.187100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.016[1e3]=0.0052,=0.191100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.015[1e3]=0.0052,=0.185100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.015[1e3]=0.0052,=0.187100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.016[1e3]=0.0052,=0.189100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.015[1e3]=0.0052,=0.183100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15  ee+Figure 6.25 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝜇𝜇.

138

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.039[1e3]=0.0122,=0.528100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.038[1e3]=0.0122,=0.508100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.039[1e3]=0.0122,=0.483100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.039[1e3]=0.0132,=0.475100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.038[1e3]=0.0122,=0.479100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.037[1e3]=0.0122,=0.483100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.037[1e3]=0.0122,=0.480100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.036[1e3]=0.0112,=0.466100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.035[1e3]=0.0112,=0.441100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.033[1e3]=0.0112,=0.410100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.031[1e3]=0.0102,=0.380100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.029[1e3]=0.0102,=0.356100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.025[1e3]=0.0082,=0.324100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.022[1e3]=0.0072,=0.295100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.021[1e3]=0.0072,=0.270100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.019[1e3]=0.0062,=0.245100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.017[1e3]=0.0052,=0.219100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.015[1e3]=0.0052,=0.196100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.014[1e3]=0.0042,=0.178100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.013[1e3]=0.0042,=0.159100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.013[1e3]=0.0042,=0.140100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.012[1e3]=0.0042,=0.130100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.011[1e3]=0.0042,=0.124100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.010[1e3]=0.0032,=0.114100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.010[1e3]=0.0032,=0.115100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.009[1e3]=0.0032,=0.107100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.009[1e3]=0.0032,=0.110100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.010[1e3]=0.0032,=0.109100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.010[1e3]=0.0032,=0.108100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.010[1e3]=0.0032,=0.113100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.011[1e3]=0.0042,=0.118100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.012[1e3]=0.0042,=0.123100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15  Figure 6.26 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝜏𝜏.

139

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.040[1e3]=0.0122,=0.531100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.038[1e3]=0.0122,=0.512100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.038[1e3]=0.0122,=0.486100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.039[1e3]=0.0132,=0.479100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.038[1e3]=0.0112,=0.483100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.038[1e3]=0.0122,=0.487100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.038[1e3]=0.0122,=0.483100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.036[1e3]=0.0112,=0.471100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.035[1e3]=0.0112,=0.448100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.033[1e3]=0.0112,=0.419100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.032[1e3]=0.0102,=0.393100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.029[1e3]=0.0092,=0.370100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.027[1e3]=0.0092,=0.341100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.025[1e3]=0.0082,=0.314100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.023[1e3]=0.0072,=0.290100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.020[1e3]=0.0062,=0.266100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.018[1e3]=0.0062,=0.243100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.017[1e3]=0.0052,=0.222100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.016[1e3]=0.0052,=0.206100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.015[1e3]=0.0052,=0.187100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.014[1e3]=0.0052,=0.170100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.014[1e3]=0.0042,=0.160100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.013[1e3]=0.0052,=0.150100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.013[1e3]=0.0042,=0.136100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.012[1e3]=0.0042,=0.132100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.011[1e3]=0.0042,=0.122100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.011[1e3]=0.0032,=0.119100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.011[1e3]=0.0032,=0.115100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.010[1e3]=0.0032,=0.111100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.010[1e3]=0.0032,=0.112100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.010[1e3]=0.0032,=0.111100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.010[1e3]=0.0032,=0.111100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15  Figure 6.27 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝑊 +𝑊 −.

140

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.039[1e3]=0.0122,=0.530100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.039[1e3]=0.0122,=0.511100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.039[1e3]=0.0122,=0.486100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.039[1e3]=0.0122,=0.482100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.038[1e3]=0.0122,=0.489100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.038[1e3]=0.0122,=0.489100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.036[1e3]=0.0112,=0.481100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.036[1e3]=0.0112,=0.465100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.035[1e3]=0.0112,=0.440100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.033[1e3]=0.0112,=0.413100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.032[1e3]=0.0102,=0.393100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.029[1e3]=0.0092,=0.374100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.028[1e3]=0.0092,=0.351100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.026[1e3]=0.0082,=0.333100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.026[1e3]=0.0082,=0.319100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.026[1e3]=0.0082,=0.307100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.025[1e3]=0.0092,=0.296100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.024[1e3]=0.0082,=0.286100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.024[1e3]=0.0082,=0.279100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.023[1e3]=0.0072,=0.273100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.022[1e3]=0.0072,=0.264100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.022[1e3]=0.0072,=0.257100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.020[1e3]=0.0072,=0.249100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.019[1e3]=0.0062,=0.239100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.018[1e3]=0.0062,=0.231100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.018[1e3]=0.0062,=0.222100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.017[1e3]=0.0052,=0.212100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.016[1e3]=0.0052,=0.202100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.016[1e3]=0.0052,=0.193100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.015[1e3]=0.0052,=0.183100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.014[1e3]=0.0052,=0.175100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.014[1e3]=0.0052,=0.166100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15  WW+Figure 6.28 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝑍 𝑍.

141

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.038[1e3]=0.0122,=0.528100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.039[1e3]=0.0122,=0.509100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.040[1e3]=0.0122,=0.484100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.038[1e3]=0.0122,=0.480100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.038[1e3]=0.0112,=0.487100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.038[1e3]=0.0122,=0.488100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.037[1e3]=0.0112,=0.479100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.036[1e3]=0.0112,=0.462100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.034[1e3]=0.0102,=0.435100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.033[1e3]=0.0112,=0.407100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.032[1e3]=0.0102,=0.386100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.029[1e3]=0.0092,=0.368100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.027[1e3]=0.0092,=0.342100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.026[1e3]=0.0082,=0.326100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.025[1e3]=0.0082,=0.312100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.025[1e3]=0.0082,=0.300100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.024[1e3]=0.0082,=0.289100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.024[1e3]=0.0082,=0.281100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.023[1e3]=0.0072,=0.275100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.022[1e3]=0.0072,=0.270100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.021[1e3]=0.0072,=0.262100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.021[1e3]=0.0072,=0.255100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.020[1e3]=0.0072,=0.248100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.019[1e3]=0.0062,=0.238100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.018[1e3]=0.0062,=0.230100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.018[1e3]=0.0062,=0.221100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.016[1e3]=0.0052,=0.211100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.016[1e3]=0.0052,=0.201100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.016[1e3]=0.0052,=0.191100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.014[1e3]=0.0042,=0.181100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.014[1e3]=0.0042,=0.173100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.014[1e3]=0.0042,=0.164100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15  Z0Z0Figure 6.29 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝜈𝑒𝜈𝑒.

142

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.038[1e3]=0.0122,=0.429100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.039[1e3]=0.0122,=0.430100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.036[1e3]=0.0122,=0.376100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.036[1e3]=0.0112,=0.353100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.036[1e3]=0.0122,=0.387100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.035[1e3]=0.0112,=0.351100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.031[1e3]=0.0102,=0.315100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.028[1e3]=0.0092,=0.282100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.027[1e3]=0.0092,=0.273100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.023[1e3]=0.0072,=0.233100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.021[1e3]=0.0072,=0.223100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.015[1e3]=0.0052,=0.172100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.014[1e3]=0.0052,=0.156100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.013[1e3]=0.0042,=0.136100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.011[1e3]=0.0042,=0.109100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.009[1e3]=0.0032,=0.101100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.007[1e3]=0.0022,=0.081100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.008[1e3]=0.0032,=0.102100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.008[1e3]=0.0032,=0.090100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.006[1e3]=0.0022,=0.073100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.004[1e3]=0.0012,=0.059100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.008[1e3]=0.0022,=0.082100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.007[1e3]=0.0022,=0.091100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.008[1e3]=0.0032,=0.085100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.011[1e3]=0.0042,=0.124100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.009[1e3]=0.0032,=0.089100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.014[1e3]=0.0052,=0.154100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.017[1e3]=0.0052,=0.182100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.015[1e3]=0.0042,=0.165100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.014[1e3]=0.0052,=0.171100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.015[1e3]=0.0052,=0.174100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.015[1e3]=0.0052,=0.180100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15  eeFigure 6.30 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝜈𝜇𝜈𝜇.

143

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.038[1e3]=0.0122,=0.428100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.039[1e3]=0.0122,=0.429100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.036[1e3]=0.0122,=0.377100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.036[1e3]=0.0112,=0.353100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.032[1e3]=0.0102,=0.302100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.034[1e3]=0.0112,=0.352100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.031[1e3]=0.0102,=0.319100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.029[1e3]=0.0092,=0.287100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.027[1e3]=0.0092,=0.278100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.023[1e3]=0.0072,=0.239100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.021[1e3]=0.0062,=0.231100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.016[1e3]=0.0052,=0.181100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.015[1e3]=0.0052,=0.169100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.015[1e3]=0.0052,=0.151100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.014[1e3]=0.0042,=0.130100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.011[1e3]=0.0032,=0.116100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.009[1e3]=0.0032,=0.096100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.010[1e3]=0.0032,=0.118100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.010[1e3]=0.0032,=0.111100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.008[1e3]=0.0032,=0.087100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.006[1e3]=0.0022,=0.072100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.007[1e3]=0.0022,=0.087100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.007[1e3]=0.0022,=0.093100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.007[1e3]=0.0022,=0.085100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.008[1e3]=0.0022,=0.106100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.007[1e3]=0.0022,=0.075100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.011[1e3]=0.0042,=0.112100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.013[1e3]=0.0042,=0.133100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.012[1e3]=0.0042,=0.124100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.012[1e3]=0.0042,=0.135100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.013[1e3]=0.0042,=0.139100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.014[1e3]=0.0042,=0.156100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15  Figure 6.31 Same as Fig. 6.6 for 15 stacked, GS 𝐽-factor sources and 𝜒 𝜒 → 𝜈𝜏𝜈𝜏.

144

0510152025100101102103104105trials per binM=0.68 TeV[1e2]=0.038[1e3]=0.0122,=0.428100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]=0.039[1e3]=0.0122,=0.429100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]=0.036[1e3]=0.0122,=0.377100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]=0.036[1e3]=0.0112,=0.353100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]=0.036[1e3]=0.0122,=0.388100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]=0.034[1e3]=0.0102,=0.352100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]=0.031[1e3]=0.0102,=0.318100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]=0.029[1e3]=0.0092,=0.288100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]=0.027[1e3]=0.0082,=0.279100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]=0.024[1e3]=0.0072,=0.243100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]=0.022[1e3]=0.0072,=0.232100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]=0.016[1e3]=0.0052,=0.182100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]=0.016[1e3]=0.0052,=0.171100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]=0.015[1e3]=0.0052,=0.154100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]=0.014[1e3]=0.0042,=0.135100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]=0.012[1e3]=0.0042,=0.122100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]=0.009[1e3]=0.0032,=0.102100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]=0.011[1e3]=0.0042,=0.129100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]=0.012[1e3]=0.0042,=0.127100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]=0.010[1e3]=0.0032,=0.099100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]=0.008[1e3]=0.0032,=0.087100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]=0.009[1e3]=0.0032,=0.104100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]=0.009[1e3]=0.0032,=0.106100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]=0.008[1e3]=0.0022,=0.097100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]=0.009[1e3]=0.0032,=0.119100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]=0.007[1e3]=0.0022,=0.089100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]=0.011[1e3]=0.0042,=0.120100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]=0.013[1e3]=0.0052,=0.135100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]=0.012[1e3]=0.0042,=0.126100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]=0.013[1e3]=0.0042,=0.136100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]=0.013[1e3]=0.0042,=0.134100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]=0.014[1e3]=0.0042,=0.146100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVStacked sources; Chi2 for Nsources=15  Figure 6.32 Signal Recovery study for an analysis with 15 stacked sources using the GS 𝐽-factors
[69]. The plots above show 14 studies for DM mass ranging between 1 TeV and 20 PeV for 𝜒 𝜒 →
𝜈𝜇𝜈𝜇. The bottom right subplot features every spectral model used as input for the remaining
subplots. The remaining subplots show 𝑛inj as the number of signal events injected into
background simulation. Whereas, 𝑛𝑠 is the number of signal events recovered from analyzing the
injected simulation. Blue line represents the median values of 100 simulations. Light blue bands
show the 1𝜎 statistical spread around the median.

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0204060801000255075100nsM=1 TeV0204060801000255075100M=2 TeV0204060801000255075100M=5 TeV0204060801000255075100nsM=10 TeV0204060801000255075100M=20 TeV0204060801000255075100M=50 TeV0204060801000255075100nsM=100 TeV0204060801000255075100M=200 TeV0204060801000255075100M=500 TeV0204060801000255075100nsM=1000 TeV0204060801000255075100M=2000 TeV0204060801000255075100M=5000 TeV020406080100ninj0255075100nsM=10000 TeV020406080100ninj0255075100M=20000 TeV103104105106107108E (GeV)108106104102dN/dE(GeV1)M=1 TeVM=20000 TeVSignal recovery for 15 stacked sources.  numunumuFigure 6.33 Same as Fig. 6.32 but for 𝜒 𝜒 → 𝑡𝑡 (top) and 𝑏𝑏 (bottom).

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0204060801000255075100nsM=1 TeV0204060801000255075100M=2 TeV0204060801000255075100M=5 TeV0204060801000255075100nsM=10 TeV0204060801000255075100M=20 TeV0204060801000255075100M=50 TeV0204060801000255075100nsM=100 TeV0204060801000255075100M=200 TeV0204060801000255075100M=500 TeV0204060801000255075100nsM=1000 TeV0204060801000255075100M=2000 TeV0204060801000255075100M=5000 TeV020406080100ninj0255075100nsM=10000 TeV020406080100ninj0255075100M=20000 TeV103104105106107108E (GeV)109107105103101dN/dE(GeV1)M=1 TeVM=20000 TeVSignal recovery for 15 stacked sources.  tt0204060801000255075100nsM=1 TeV0204060801000255075100M=2 TeV0204060801000255075100M=5 TeV0204060801000255075100nsM=10 TeV0204060801000255075100M=20 TeV0204060801000255075100M=50 TeV0204060801000255075100nsM=100 TeV0204060801000255075100M=200 TeV0204060801000255075100M=500 TeV0204060801000255075100nsM=1000 TeV0204060801000255075100M=2000 TeV0204060801000255075100M=5000 TeV020406080100ninj0255075100nsM=10000 TeV020406080100ninj0255075100M=20000 TeV103104105106107108E (GeV)1010107104101dN/dE(GeV1)M=1 TeVM=20000 TeVSignal recovery for 15 stacked sources.  bbFigure H.1 to Figure H.6 show identical studies for Segue 1 and Ursa Major II. We see that the

analysis is conservative at smaller 𝑚 𝜒, yet improves at larger 𝑚 𝜒. We also see that the uncertainty

is small for the neutrino annihilation spectra, and the uncertainty is larger for softer channels like

𝑏𝑏.

6.7 Sensitivities

In IceCube, we usually define the 90% confidence level (CL) sensitivities, as the minimum

number of expected signal events (𝑛𝑠) required to have a Type I error rate smaller than 0.5 and Type

II error rate of 0.1. Type I error occurs when the null hypothesis is erroneously rejected in flavor of

a signal hypothesis. Type II occurs in when we fail to reject the null when it is actually false. We

compute 𝑛𝑠 from the following equation

𝑛𝑠 = 𝑇live

∫ ΔΩ

0

𝑑Ω

∫ 𝐸max

𝐸min

𝑑𝐸𝜈 𝐴eff ( ˆ𝑛, 𝐸𝜈)

𝑑Φ𝜈
𝑑Ω𝑑𝐸𝜈

( ˆ𝑛, 𝐸𝜈),

(6.8)

to extract the sensitivity on the dark matter velocity-weighted annihilation cross-section, ⟨𝜎v⟩. 𝑇live

is the detector live time, 𝐴eff is the effective area of the detector, and 𝐸min, 𝐸max are the minimum,

maximum energies of the expected neutrinos, respectively.

Sensitivities are calculated for each source individually as if they were the only source and as

a stack over 1000 trials. From Eqs. (6.1) and (6.8) we can compute the ⟨𝜎v⟩ at a 90% confidence

level. Figures 6.34 and 6.35 show the sensitivities for the DM annihilation channels studied here.

147

6.8 Systematics

The current analysis plan is to compare these sensitivities to another 𝐽-factor catalog such as

LS [88], although this was not completed in time for this dissertation. Additionally, we set out

to perform a standard suite of IceCube detector related systematic studies which include: DOM

efficiency, hole ice, ice absorption, and photon scattering. We do study Earth attenuation, and

Section 6.8.1 enumerates the impact of the Earth on our hardest neutrino spectra.

6.8.1 Earth Effects

We look to quantify the impact of the Earth on our sensitivity to 𝜒 𝜒 → 𝜈𝜇𝜈𝜇. This channel is

expected to be among the significantly impacted annihilation channels because it has a significant

contribution at PeV energies for 𝑚 𝜒 ≥ 1PeV. The Earth is expected to attenuate these higher energy

neutrinos. However, these neutrino spectra have significant low energy contributions, so we do not

expect to entirely lose our sensitivity. This motivated a study examining our ⟨𝜎v⟩ sensitivity over

all DM masses sampled for a selection of declinations.

For this systematic study, I sample 6 DM masses per decade from 681 GeV to 100 PeV. I select

declinations that are shared with sources in the GS catalog: Boötes I, Canes Venatici II, Leo V,

Ursa Major I, and Ursa Minor. I study a fake source who’s 𝐽-factor is shared with Ursa Major II,

but who’s coordinates belong to the aforementioned list. The sensitivity studies performed for each

source (Fig. 6.34 and Sec. I) provided 𝑛𝑠 for 1000 trials which we extracted from Eq. (6.8). We

derive ⟨𝜎v⟩ using log10 𝐽 = 19.42 log10(GeV2cm−5). Figure 6.37 shows the results.

Figure 6.37 shows that we have significant but diminishing sensitivity to sources at high

declination. We see in the worse case, the sensitivity at high declination is up to an order of

magnitude worse than at low declination. However, for 𝑚 𝜒 < 1 PeV, the sensitivities are very

similar. The comparable sensitivities imply that a stacking analysis with IceCube is most powerful

in the 500 GeV to 1 PeV region. Above 1 PeV, our limits and sensitivities are dominated by sources

near the horizon. When we additionally consider the 𝐽-factors, we expect Segue 1 to dominate

contributions to sensitivity and limits where 𝑚 𝜒 > 1 PeV.

148

6.9 Conclusions

We utilized advanced computing techniques like parallel programming and spline fitting of

particle physics Monte Carlo to greatly expand and refine IceCube’s sensitivity to DM annihilation

from dSphs. Furthermore, we imported updated astrophysical and particle physics models that

better represent what we believe neutrino signals from DM annihilation should look like. We, for

the first time, build an analysis that is sensitive to PeV DM annihilation.

When we compare to previous IceCube publications of dSphs [100], we see an order of

magnitude improvement to our sensitivity. This analysis has been working group approved within

IceCube and is currently under collaboration review before unblinding. These processes did not

complete in time for this dissertation. Therefore, we do not show data for this thesis and is the clear

next step.

The test statistic distributions in this analysis also demonstrate more characteristic behavior

compared to previous DM analyses [107, 110]. With a 10-year dataset, we finally have enough

statistics to almost trivially combine with other photon observatories, such as HAWC. The first

groundwork for a multi-messenger DM search is provided with concluding remarks in Chapter 7.

149

Figure 6.34 IceCube North Sky Track Sensitivities. Each panel shows sensitivity curves for
various DM annihilation channels. Sensitivities are for the velocity-weighted cross-section
⟨𝜎v⟩ versus 𝑚 𝜒. Doted, colored lines are sensitivities for individual sources. Solid white lines are
for the combined sensitivity of all 15 GS sources used in this study.

150

100101102103104105M [TeV]102510231021101910171015v [cm3 s1]ee+IC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]102510231021101910171015v [cm3 s1]eeIC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]102510231021101910171015v [cm3 s1]+IC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]102510231021101910171015v [cm3 s1]IC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]102510231021101910171015v [cm3 s1]+IC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]102510231021101910171015v [cm3 s1]IC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombinedFigure 6.35 Same as Fig. 6.34 for three additional DM annihilation channels.

151

100101102103104105M [TeV]102510231021101910171015v [cm3 s1]bbIC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]102510231021101910171015v [cm3 s1]ttIC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]102510231021101910171015v [cm3 s1]uuIC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]102510231021101910171015v [cm3 s1]ddIC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]102510231021101910171015v [cm3 s1]WW+IC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]102510231021101910171015v [cm3 s1] ZZIC3 Preliminary90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombinedFigure 6.36 Panel A: Neutrinos from the Northern sky and incident on the IceCube detector will
travel through the Earth. How much of the Earth these neutrinos traverse is a function of zenith
from the vertical axis. Panel B: SM prediction of neutrino transmission probabilities for neutrinos
arriving at 90◦ - 180◦ zenith and with 100 GeV to 100 PeV energies. High-energy neutrinos
traversing the whole Earth are completely absorbed, whereas low-energy neutrinos pass through
unimpeded. Neutrinos coming from above the horizon will arrive unimpeded for all neutrino
energies. Figure taken from [111].

Figure 6.37 ⟨𝜎v⟩ sensitivities for 5 imaginary sources with log10 𝐽 = 19.42 log10(GeV2cm−5).
Each imaginary source shares a declination with a source in Tab. 3.2

152

CHAPTER 7

NU DUCK: CONCLUSIONS AND FUTURE DIRECTIONS

7.1 Future Directions: Multi-Messenger Dark Matter Search

Figure 7.1 The 𝜈𝑒 and 𝛾 spectrum at production from the decay of a 2 EeV DM particle to 𝜈𝑒𝜈𝑒.
Solid lines are from the work of Nick Rodd et al. [25]. Dashed lines are previous models
produced by the particle physics framework PYTHIA [112]. Notice that the flux for both 𝜈𝑒 and 𝛾
are significantly larger than previously predicted, especially at low energies. Similar changes are
seen in DM masses above the electroweak scale.

As was shown previously in Chapter 3 and Chapter 4, a fast and robust analysis was built in

HAWC that can share tools with collaborators in particle astrophysics. A formalism for combining

common DM observations has been established. These works, Chapter 3, and accelerations,

Chapter 4, has laid the groundwork for faster DM searches without sacrificing on the scientific

rigor.

Within IceCube, the first DM annihilation search towards dSphs in over a decade is starting,

Chapter 6. This work was developed with the long-term goal of combining it with the gamma-

ray data for a multi-messenger DM search. There is already promising developments in DM

153

Figure 7.2 (purple line) HAWC 95% confidence limit on ⟨𝜎v⟩ for WIMP DM for 1 TeV to 10 PeV
DM mass. HAWC data is from observations of 3 sources: Coma Berenices, Segue 1, and Sextans.
(Dashed black line) IceCube median 95% confidence limit on ⟨𝜎v⟩ over 300 background trials.
Colored bands around IceCube sensitivity are the 68% (light blue) and 95% (peach) containment
bands. The median IceCube value and HAWC data are most similar in the 𝑚 𝜒 ≈ 1 PeV region.

phenomenology in this regard. Figure 7.1 is the headline figure from HDMSpectra [25] for a DM

decay (𝜒 →𝜈𝑒𝜈𝑒) spectrum in 𝜈𝑒 and 𝛾. What is intriguing from this publication is that although

photons more readily interact with our detector than neutrinos, the expected photon spectrum is

soft enough to be difficult to discern from the background. Whereas, IceCube has exceptional

sensitivity for hard neutrino spectra, see Figs. 6.30 and 6.34. Additionally, the Earth plays a role in

reducing IceCube’s neutrino sensitivity, see Fig. 6.37 and [111]. These known behaviors suggested

a potentially powerful partnership between HAWC and IceCube.

Preliminary work was done to combine HAWC and IceCube data for a multi-messenger DM

search. Through background simulation, Chapter 6 showed that IceCube variables behave mostly

154

103104105106107M (GeV)1024102310221021102010191018v (cm3s1) with HAWC data + IceCube SensitivityIceCube 0(15sources)95% containment68% containmentHAWC Data Combined (3 sources)like normal variables distributed as a 𝜒2 distribution with 1 degree of freedom. For IceCube the

statistical framework for setting confidence limits first made by Fermi-LAT [52], and later Glory

Duck, Section 3.4.2. For this combination analysis, IceCube adopts the 95% confidence limit

standard defined in Eq. (3.9) with a likelihood combination using Eq. (3.17). This differs from the

90% confidence limit considered standard within IceCube and used for Chapter 6. This statistical

definition is standard for HAWC and requires no additional changes than what was presented in

Chapter 4.

Sensitivities are calculated for IceCube on 300 background trials. Figure 7.2 presents the

median, 68 and 95 percentile containment on the confidence limit with IceCube NST; dataset

described in Section 6.2.3. The source and model selection for IceCube is identical to Section 6.3.3.

Confidence limits on HAWC data are calculated using the methods and dataset from Section 4.3.3

and DM density model (GS) methods from Section 3.3.3. HAWC does not have an unblinding

process, like IceCube. Permission to unblind has not been granted, so only sensitivities are included

for now. It is unclear when unblinding will be granted for this combination as this depends heavily

on the publication of the work in Chapters 4 and 6. Yet, they all share much of the same machinery,

so it is not expected to be long after the works are published.

Figure 7.2 features IceCube’s sensitivity superimposed on HAWC’s 95% confidence limit on

DM annihilation: 𝜒 𝜒 → 𝜈𝜇𝜈𝜇 at a 100% BR. We can see that IceCube’s sensitivity is complimented

well by HAWC’s confidence limit in the DM mass region above and around 1 PeV. More complex

models with diverse BRs are possible and the method of analysis would require a substitution as

was described in Section 1.4.2.

A mock combination between HAWC and IceCube has been performed. This mock run was

made for the purpose of building the neutrino + gamma data pipeline for DM searches. Figure 7.3

shows a combined limit between HAWC data and an IceCube simulated background trial treated

as data. From this mock combination, it is evident that there is a powerful combination in the 1

PeV DM mass region. There is an improvement to the combined limit to DM masses as far down

to 100 TeV. Furthermore, the improvement to this limit stay across two decades in DM mass. This

155

Figure 7.3 (orange solid line) HAWC 95% confidence limit on ⟨𝜎v⟩ using data from 3 sources:
Coma Berenices, Segue 1, and Sextans. (blue solid line) IceCube 95% confidence limit on
⟨𝜎v⟩ from one simulated background trial. (dashed black line) Combined 95% confidence limit
on ⟨𝜎v⟩ with HAWC data and IceCube background trial. Combined limit is stronger than either
IceCube and HAWC in the region 𝑚 𝜒 > 200 TeV.

preliminary work is evidence of the strength in multi-messenger DM searches and motivates such

a study between these instruments.

7.2 Conclusions

This dissertation, "Leveraging Multi-Messenger Astrophysics for Dark Matter Searches", ad-

vances our quest to understand dark matter. We used gamma-ray and neutrino observatories

alongside advanced computational techniques. Our goal was to enhance the search for dark matter

within the universe. We have made substantial strides in the search for dark matter using multi-

messenger astrophysics. The collaborative efforts of the Glory Duck team and the methodologies

established in HAWC analyses have set a new precedent for the rapid and robust detection of dark

156

103104105106107M (GeV)1024102310221021102010191018v (cm3s1)95% Mock CL for  with HAWC and IceCubeHAWC Data Combined (3 sources)IceCube Background Trial Combined (15 sources)Multi-Messenger +matter signals. My work within IceCube has revitalized the search for dark matter annihilation from

dwarf spheroidal galaxies, laying the foundation for a comprehensive multi-messenger approach.

The Glory Duck project was a key part of this work. It involved a multi-instrument analysis using

gamma-ray telescopes. These included Fermi-LAT, H.E.S.S., MAGIC, VERITAS, and HAWC. We

focused on 20 dwarf spheroidal galaxies (dSphs). The aim was to detect dark matter annihilation

signals. Although we found no significant deviations from the null hypothesis, we greatly improved

search sensitivity. We set stringent upper limits on the annihilation cross-section for dark matter

candidates. This effort represents a major advance, offering the most comprehensive constraints

for WIMP dark matter search to date. The potential synergy between IceCube and gamma-ray

observatories like HAWC is particularly promising. Preliminary work has demonstrated that

by combining data from these observatories, we can significantly enhance our search sensitivity,

especially in the dark matter mass region above 1 PeV. This is clearly illustrated in Figure 7.2, where

IceCube’s sensitivity complements HAWC’s confidence limit, and Figure 7.3, which showcases the

improved limit that multi-messenger data offers.

Our exploration of multithreading techniques in HAWC analyses showed the benefits of com-

putational methods. By accelerating analysis time, we enhanced the efficiency of dark matter

searches. This approach has set the stage for more ambitious studies. It highlights the importance

of computational innovation in addressing astrophysical challenges.

Furthermore, our work with IceCube’s North Sky Track Data has broken new ground. It aimed

at detecting heavy dark matter annihilation. We used parallel programming and spline fitting

to improve and refine IceCube’s sensitivity. This analysis is a step towards probing dark matter

annihilation up to the PeV scale. It demonstrates a significant sensitivity improvement compared

to previous efforts. The groundwork laid here is a strong foundation for future discoveries.

This dissertation highlights the potential of multi-messenger astrophysics and computational

innovation in dark matter searches. Each analysis has contributed to our understanding and capa-

bilities. Together, they showcase a progressive approach to astrophysical research by integrating

observations from several gamma-ray and neutrino observatories. Additionally, modern computa-

157

tional techniques such as multithreading were developed and deployed to greatly accelerate analyses

in HAWC. By harnessing the collective power of these observatories, we have created a legacy

that will guide future collaborations. Looking back, it’s clear that our journey through the dark

universe is far from complete. The advances made herein beckon the next phase of discovery, where

multi-messenger observations and analyses will illuminate further secrets of the dark universe.

158

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169

APPENDIX A

MULTI-EXPERIMENT SUPPLEMENTARY FIGURES

Figure A.1 Sister figure to Figure 3.3. Sources in the first row from left to right: Bootes I, Canes
Venatici I, II. In second row: Draco, Hercules, Leo I. In the first row: Leo II, Leo IV, Sextans. In
the final row: Ursa Major I, Ursa Major II.

170

1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)01234log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)01234log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)0123456log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)0.00.51.01.52.02.53.03.54.0log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)012345log10(dJd/GeV2cm5sr)1.000.750.500.250.000.250.500.751.00(°)1.000.750.500.250.000.250.500.751.00(°)01234log10(dJd/GeV2cm5sr)APPENDIX B

REMAINING SPECTRAL MODELS

Figure B.1 Sister figure to Figure 4.2 for remaining SM primary annihilation channels studied for
this thesis. These did not require any post generation smoothing and so are directly pulled from
[25] with a binning scheme most helpful for a HAWC analysis.

171

APPENDIX C

MPU_ANALYSIS.PY

import warnings

with warnings . catch_warnings ():

warnings . simplefilter (" ignore ")

# Python base libraries

import os

import sys

import time

# Import general libraries with namespace

import matplotlib

# Necessary for computing on cluster

matplotlib .use("agg")

import numpy as np

import multiprocessing as mp

# Import HAWC software

sys.path. insert (1, os.path.join(os. environ [’HOME ’], ’hawc_software ’, ’threeml -

analysis - scripts ’, ’fitModel ’))

from analysis_modules import *

from threeML import *

from hawc_hal import HAL , HealpixConeROI

from threeML . minimizer . minimization import FitFailed

# Import Dark

Matter HAWC Libraries

import analysis_utils as au

import spectra as spec

import sources as srcs

#* READ ONLY PATHS This block will change eventually

MASS_LIST = ’./ plotting / studies /nd/ masses .txt ’

CHAN_LIST = ’./ plotting / studies /nd/chans.txt ’

#* WRITE PATHS , default location is to scratch

172

OUT_PATH = os.path.join(os. environ [" SCRATCH "], os. environ ["USER"], ’New_duck ’)

print(’Our out path is going to be {}’. format ( OUT_PATH ))

# Define parallel Function . Can also be run serially

def some_mass_fit (sigVs , datalist , shape , dSph , jfactor , mass_chan ,

progress =None , log_file =’’, queue=None , i_job =0):

if progress is None:

progress = [0]

else: # Create log files for each thread

log_file = log_file . replace (’.log ’, ’_ThreadNo_ ’)

log_file = log_file + str(i_job) + ".log"

sys. stdout = open(log_file , "w")

fits = []

try:

for m_c in mass_chan :

print(f’Mass chan tuple: {m_c}’)

mass = int(m_c [0])

ch = m_c [1]

# Build path to output files

outPath = os.path.join(OUT_PATH , ch , dSph)

au.ut. ensure_dir ( outPath )

if progress [i_job] < 0:

# If the master gets a Keyboard interrupt , commit suicide .

break

### Start Model Building for DM mass and SM channel ####

spectrum = spec. DM_models . HDMSpectra ()

spectrum . set_channel (ch)

173

myDwarf = ExtendedSource (dSph , spatial_shape =shape ,

spectral_shape = spectrum )

spectrum .J = jfactor * u.GeV **2 / u.cm **5

spectrum . sigmav = 1e -24 * u.cm **3 / u.s

spectrum . set_dm_mass (mass * u.GeV)

spectrum . sigmav . bounds = (1e -30 ,1e -12)

model = Model( myDwarf )

### End model Building ####

jl = JointLikelihood (model ,datalist , verbose =False)

try:

result , lhdf = jl.fit( compute_covariance =False)

ts = -2.*( jl. minus_log_like_profile (1e -30) - jl.

_current_minimum )

# Also profile the LLH vs sv

ll = jl. get_contours ( spectrum .sigmav , sigVs [0],

sigVs [-1], len(sigVs),

progress =False , log =[’False ’])

sigv_ul = au.ut. calc_95_from_profile (ll[0], ll [2])

# Write results to file

outFileLL = outPath +f"/LL_{dSph}_{ch}_mass{int(mass)}_GD.txt"

np. savetxt (outFileLL , (sigVs , ll [2]) ,

delimiter =’\t’, header =’sigV\tLL\n’)

with open( outPath +f"/ results_ {dSph}_{ch}_mass{int(mass)}_GD.

txt", "w") as results_file :

results_file .write("mDM [GeV ]\ tsigV_95 \tTS\ tsigV_B .F.\n")

results_file .write("%i\t%.5E\t%.5E\t%.5E"%(mass , sigv_ul ,

174

# End write to file

ts , result .value [0]))

except FitFailed : # Don ’t kill all threads if a fit fails

print("Fit failed . Go back and calculate this spectral model

later")

fits. append ((ch , mass , -1, -1))

with open( log_file +’.fail ’, ’w’) as f_file :

f_file .write(f’{ch}, {mass }\n’)

progress [i_job] += 1

matplotlib . pyplot .close () # Prevent leaky memory

fits. append ((ch , mass , result .value [0], ts))

progress [i_job] += 1

matplotlib . pyplot .close ()

except KeyboardInterrupt :

progress [i_job] = -1

fits = np.array(fits)

if queue is None:

return fits

else:

queue.put (( i_job , fits))

def main(args):

masses = np. loadtxt (MASS_LIST , dtype =int)

chans = np. loadtxt (CHAN_LIST , delimiter =’,’, dtype=str)

mass_chan = au.ut. permute_lists (chans , masses )

print(f"DM masses for this study are: { masses }")

print(f"SM Channels for this study are XX -> {chans}")

print( mass_chan )

175

# extract information from input argument

dSph = args.dSph

data_mngr = au.ut. Data_Selector (’P5_NN_2D ’)

dm_profile = srcs. Spatial_DM (args.catalog , dSph , args.sigma , args.decay)

### Extract Source Information ###

if dm_profile . get_dec () < -22.0 or dm_profile . get_dec () > 62.0:

raise ValueError ("HAWC can ’t see this source D: Exitting now ...")

print(f’{dSph} information ’)

print(f’jfac: { dm_profile . get_factor ()}\ tRA: { dm_profile . get_ra ()}\ tDec: {

dm_profile . get_dec ()}\n’)

shape = SpatialTemplate_2D ( fits_file = dm_profile . get_src_fits ())

### Finish Extract Source Information ###

### LOAD HAWC DATA ###

roi = HealpixConeROI ( data_radius =2.0 , model_radius =8.0 ,

bins = choose_bins . analysis_bins (args , dec= dm_profile . get_dec ())

ra= dm_profile . get_ra (), dec= dm_profile . get_dec ())

hawc = HAL(dSph , data_mngr . get_datmap (), data_mngr . get_detres (), roi)

hawc. set_active_measurements ( bin_list =bins)

datalist = DataList (hawc)

### FINISH LOAD HAWC DATA ###

# set up SigV sampling . This sample is somewhat standardized

sigVs = np. logspace (-28,-18, 1001 , endpoint =True) # NOTE This will change

whith HDM

if args. n_threads == 1:

# No need to start || programming just iterate over the masses

kw_arg = dict(sigVs=sigVs , datalist =datalist , shape=shape , dSph=dSph ,

176

jfactor = dm_profile . get_factor (), mass_chan =mass_chan ,

log_file =args.log)

some_mass_fit (** kw_arg )

else:

# I Really want to suppress TQMD output

from tqdm import tqdm

from functools import partialmethod

tqdm. __init__ = partialmethod (tqdm.__init__ , disable =True)

x = np. array_split (mass_chan , args. n_threads )

n_jobs = len(x)

print(" Thread jobs summary by mass and SM channel ")

for xi in x:

print(f’{xi}’)

queue = mp.Queue ()

progress = mp.Array(’i’, np.zeros(n_jobs , dtype=int))

# Define task pool that will be split amongsts threads

kw_args = [dict(sigVs=sigVs , datalist =datalist , shape=shape ,

dSph=dSph , jfactor = dm_profile . get_factor (),

mass_chan =mass_chan , progress =progress ,

queue=queue , i_job=i, log_file =args.log)

for i, mass_chan in enumerate (x)]

# Define each process

procs = [mp. Process ( target = some_mass_fit , kwargs = kw_args [i]) \

for i in range( n_jobs )]

### Start MASTER Thread only code block ###

# Begin running all child threads

for proc in procs: proc.start ()

177

try:

# In this case , the master does nothing except monitor progress of

the threads

# In an ideal world , the master thread also does some computation .

n_complete = np.sum( progress )

while_count = 0

while n_complete < len( mass_chan ):

if np.any(np. asarray ( progress ) < 0):

# This was no threads are stranded when killing the script

raise KeyboardInterrupt ()

if while_count %1000 == 0:

print(f"{np.sum( progress )} of {len( mass_chan )} finished ")

n_complete = np.sum( progress )

time.sleep (.25)

while_count += 1

except KeyboardInterrupt :

# signal to jobs that it’s time to stop

for i in range( n_jobs ):

progress [i] = -2

print(’\ nKeyboardInterrupt : terminating early.’)

### End MASTER Thread only code block ###

fitss = [queue.get () for proc in procs]

print(fitss)

print(f’Thread statuses : { progress [:]} ’)

# putting results in a file

178

print("QUACK! All Done!")

if __name__ == ’__main__ ’:

import argparse

p = argparse . ArgumentParser ( description ="Run a DM annihilation analysis on

a dwarf spheroidal for a specific SM channel for DM masses [1 TeV to 10

PeV]")

# Dwarf spatial modeling arguements

p. add_argument ("-ds", "--dSph", type=str ,

help="dwarf spheroidal galaxy to be studied ", required =

True)

p. add_argument ("-cat", "--catalog ", type=str , choices =[’GS15 ’, ’LS20 ’],

default =’LS20 ’, help=" source catalog used")

p. add_argument ("-sig", "--sigma", type=int , choices =[-1, 0, 1], default =0,

help=" Spatial model uncertainty . 0 corresponds to the

median . +/-1 correspond to the +/1 sigma uncertainty respectively .")

# Arguements for the energy estimators

p. add_argument ("-e", "--estimator ", type=str ,

choices =[’P5_NHIT ’, ’P5_NN_2D ’],

default =" P5_NN_2D ", required =False ,

help="The energy estimator choice . Options are: P5_NHIT ,

P5_NN_2D . GP not supported (yet).")

p. add_argument ("--use -bins", default =None , nargs="*",

help="Bins to

use for the analysis ", dest=" use_bins ")

p. add_argument (’-- select_bins_by_energy ’, default =None , nargs ="*",

help="Does nothing . May fill in later once better

understood ")

p. add_argument (’-- select_bins_by_fhit ’, default =None , nargs="*",

help="Also does nothing see above")

179

p. add_argument ( ’-ex’, "--exclude ", default =None , nargs="*",

help=" Exclude Bins", dest=" exclude ")

# Computing and logging arguements .

p. add_argument (’-nt’, ’--n_threads ’, type=int , default =1,

help=’Maximum number of threads spawned by script . Default

is 4’)

p. add_argument (’-log ’, ’--log ’, type=str , required =True ,

help=’Name for log files. Especially needed for threads ’)

p. add_argument (’--decay ’, action =" store_true ",

help=’Set spectral DM hypothesis to decay ’)

args = p. parse_args ()

print(args.decay)

if args. exclude is None: # default exclude bins 0 and 1

args. exclude = [’B0C0Ea ’, ’B0C0Eb ’, ’B0C0Ec ’, ’B0C0Ed ’, ’B0C0Ee ’]

if args.decay: OUT_PATH += ’_dec ’

else: OUT_PATH += ’_ann ’

OUT_PATH = OUT_PATH + ’_’ + args. catalog

if args.sigma != 0: OUT_PATH += f’_{args.sigma}sig ’

main(args)

180

APPENDIX D

COMPARISON WITH GLORY DUCK

Figure D.1 Comparison of HAWC limits from this analysis to Glory Duck (Fig. 3.5) for Coma
Berenices and 7 DM annihilation channels.

181

1024102310221021102010191018v [cm3 s1]bbHAWC PreliminarySystematic Comparison for New_duckComaBerenices Glory DuckComaBerenices New_duck100101102103104M [TeV]1006×1012×1003×1004×100GD/SysModel RatiosR=1.0R=21024102310221021102010191018v [cm3 s1]ttHAWC PreliminarySystematic Comparison for New_duckComaBerenices Glory DuckComaBerenices New_duck100101102103104M [TeV]1006×1012×1003×100GD/SysModel RatiosR=1.0R=21024102310221021102010191018v [cm3 s1]WW+HAWC PreliminarySystematic Comparison for New_duckComaBerenices Glory DuckComaBerenices New_duck100101102103104M [TeV]1006×101GD/SysModel RatiosR=1.0R=210241023102210211020101910181017v [cm3 s1]ee+HAWC PreliminarySystematic Comparison for New_duckComaBerenices Glory DuckComaBerenices New_duck100101102103104M [TeV]100GD/SysModel RatiosR=1.0R=210241023102210211020101910181017v [cm3 s1]HAWC PreliminarySystematic Comparison for New_duckComaBerenices Glory DuckComaBerenices New_duck100101102103104M [TeV]1006×1012×1003×100GD/SysModel RatiosR=1.0R=210241023102210211020101910181017v [cm3 s1]HAWC PreliminarySystematic Comparison for New_duckComaBerenices Glory DuckComaBerenices New_duck100101102103104M [TeV]1006×1012×1003×100GD/SysModel RatiosR=1.0R=21024102310221021102010191018v [cm3 s1]Z0Z0HAWC PreliminarySystematic Comparison for New_duckComaBerenices Glory DuckComaBerenices New_duck100101102103104M [TeV]1006×1012×1003×1004×100GD/SysModel RatiosR=1.0R=2Figure D.2 Same as Fig. D.1 but for Segue 1.

182

102410231022102110201019v [cm3 s1]bbHAWC PreliminarySystematic Comparison for New_duckSegue1 Glory DuckSegue1 New_duck100101102103104M [TeV]1006×1012×1003×100GD/SysModel RatiosR=1.0R=2102410231022102110201019v [cm3 s1]ttHAWC PreliminarySystematic Comparison for New_duckSegue1 Glory DuckSegue1 New_duck100101102103104M [TeV]1006×1012×100GD/SysModel RatiosR=1.0R=21025102410231022102110201019v [cm3 s1]WW+HAWC PreliminarySystematic Comparison for New_duckSegue1 Glory DuckSegue1 New_duck100101102103104M [TeV]1006×1012×1003×100GD/SysModel RatiosR=1.0R=210251024102310221021102010191018v [cm3 s1]ee+HAWC PreliminarySystematic Comparison for New_duckSegue1 Glory DuckSegue1 New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=21024102310221021102010191018v [cm3 s1]HAWC PreliminarySystematic Comparison for New_duckSegue1 Glory DuckSegue1 New_duck100101102103104M [TeV]100GD/SysModel RatiosR=1.0R=210251024102310221021102010191018v [cm3 s1]HAWC PreliminarySystematic Comparison for New_duckSegue1 Glory DuckSegue1 New_duck100101102103104M [TeV]100GD/SysModel RatiosR=1.0R=2102410231022102110201019v [cm3 s1]Z0Z0HAWC PreliminarySystematic Comparison for New_duckSegue1 Glory DuckSegue1 New_duck100101102103104M [TeV]1006×1012×1003×100GD/SysModel RatiosR=1.0R=2Figure D.3 Same as Fig. D.1 but for Sextans.

183

1023102210211020101910181017v [cm3 s1]bbHAWC PreliminarySystematic Comparison for New_duckSextans Glory DuckSextans New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=21023102210211020101910181017v [cm3 s1]ttHAWC PreliminarySystematic Comparison for New_duckSextans Glory DuckSextans New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=2102310221021102010191018v [cm3 s1]WW+HAWC PreliminarySystematic Comparison for New_duckSextans Glory DuckSextans New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=210231022102110201019101810171016v [cm3 s1]ee+HAWC PreliminarySystematic Comparison for New_duckSextans Glory DuckSextans New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=210231022102110201019101810171016v [cm3 s1]HAWC PreliminarySystematic Comparison for New_duckSextans Glory DuckSextans New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=210241023102210211020101910181017v [cm3 s1]HAWC PreliminarySystematic Comparison for New_duckSextans Glory DuckSextans New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=21023102210211020101910181017v [cm3 s1]Z0Z0HAWC PreliminarySystematic Comparison for New_duckSextans Glory DuckSextans New_duck100101102103104M [TeV]100101GD/SysModel RatiosR=1.0R=2APPENDIX E

DOCKER IMAGE FOR OSCILLATING NEUTRINO SPECTRA

FROM ubuntu :18.04

# Execute commands to install software packages

RUN apt -y update

# Install utility programs

RUN apt -y install vim wget git cmake

ARG DEBIAN_FRONTEND = noninteractive

# Install python

RUN apt -y install python python -dev python -pip libjpeg -dev zlib1g -dev

# We need Python2 for installing Charon .

RUN apt -y install python -numpy python -sympy python - matplotlib \

python -sympy python -h5py python - astropy python - ipython

# Install dependencies of Charon : SQuIDS , NuSQuIDS

RUN apt -y install libgsl -dev libgslcblas0 libgsl23 gsl -bin pkg - config

# Install SQuIDS

RUN mkdir /home/ SQuIDS /home/ SQuIDS_install

WORKDIR /home/ SQuIDS

RUN git clone https :// github .com/ jsalvado / SQuIDS .git

WORKDIR /home/ SQuIDS / SQuIDS

RUN git checkout 7 ad9ba7c6ad06d1f0fa8418f937ebf1a403fef90

# Before executing "make install " an environmental variable has to be set.

ENV PKG_CONFIG_PATH =/ home/ SQuIDS / SQuIDS /lib

RUN ./ configure --prefix =../ SQuIDS_install \

&& make

RUN make install

184

# Set up an enivronmental varialbe that is required to install nuSQuIDS ..

ENV SQuIDS =/ home/ SQuIDS / SQuIDS

ENV LD_LIBRARY_PATH = $SQuIDS /lib: $LD_LIBRARY_PATH

# Install NuSQuIDS

RUN mkdir /home/ nuSQuIDS

WORKDIR /home/ nuSQuIDS

RUN git clone https :// github .com/qrliu/ nuSQuIDS .git

WORKDIR /home/ nuSQuIDS / nuSQuIDS

RUN git checkout 072 d8ef740e2fc7330f1fabaea94f0f4540c46f9

RUN apt -y install libhdf5 -dev hdf5 -tools

RUN apt -y install libboost1 .65 -all -dev

RUN

./ configure --with - squids = $SQuIDS --with -python - bindings --prefix =../

nuSQuIDS_install \

&& make \

&& make install

# Set up an enivronmental variable for nuSQuIDS .

ENV nuSQuIDS =/ home/ nuSQuIDS / nuSQuIDS

ENV LD_LIBRARY_PATH = $nuSQuIDS /lib: $LD_LIBRARY_PATH

# Build the python bindings

WORKDIR /home/ nuSQuIDS / nuSQuIDS / resources / python /src

RUN make

# Set up an environmental variable for the python bindings .

ENV PYTHONPATH = $nuSQuIDS / resources / python / bindings /: $PYTHONPATH

# Install Charon in the /home/ Charon / charon directory .

RUN mkdir /home/ Charon

WORKDIR /home/ Charon

RUN git clone https :// github .com/ icecube / charon .git\

185

&& apt -y install unzip python -scipy

WORKDIR charon

RUN git checkout c531efe4e01dc364a60d1c83f950f04526ccd771

RUN unzip ./ charon /xsec/xsec.zip -d charon /xsec/ \

# Download neutrino spectra tables in the /home/ Charon / charon /data directory

.

&& mkdir ./ charon /data

WORKDIR ./ charon /data

RUN wget --no -check - certificate https :// icecube .wisc.edu /~ qliu/ charon /

SpectraEW .hdf5

\

&& wget --no -check - certificate https :// icecube .wisc.edu /~ qliu/ charon /

Spectra_PYTHIA .hdf5 \

&& wget --no -check - certificate https :// icecube .wisc.edu /~ qliu/ charon /

Spectra_noEW .hdf5

WORKDIR ../../

RUN python setup.py install

WORKDIR /home

186

APPENDIX F

SPLINE FITTING STATUSES

Figure F.1 Current status of spline tables according to contraints defined by Tab. 6.1. Green splines
are splines that passed under the GOOD tolerance. Yellow are splines that are OK. Red are splines
that FAIL. All yellow splines were inspected individually before running the analysis. Splines
were made for the 𝜇 (PID 14; top panel) flavor and 𝜏 (PID 16; bottom panel) neutrino flavors.

187

100101102103104105DM mass (TeV)WWZZHHttbbuuddeemumutautaunuenuenumunumunutaunutaumse Spline Error table for PID 140.000.250.50100101102103104105DM mass (TeV)WWZZHHttbbuuddeemumutautaunuenuenumunumunutaunutaumse Spline Error table for PID 160.000.250.50APPENDIX G

NEUTRINO COMPOSITE SPECTRA

𝜒 𝜒 → 𝑏𝑏

𝜒 𝜒 → 𝑡𝑡

𝜒 𝜒 → 𝑢𝑢

𝜒 𝜒 → 𝑑𝑑

𝜒 𝜒 → 𝑍 𝑍

𝜒 𝜒 → 𝑊 −𝑊 +

Figure G.1 Sister figure to Fig. 6.5 for annihilation channels that did not require kernel smoothing.
These spectra are the composite (𝜈𝜇 + 𝜈𝜏) of neutrino flavors. Every spectral model used for this
analysis is featured as a colored solid line. Bluer lines are for lower DM mass spectral models.
DM masses range from 681 GeV to 100 PeV.

188

0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0122,=0.486100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0122,=0.492100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0122,=0.495100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.038[1e3]0.0122,=0.485100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.039[1e3]0.0122,=0.489100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.039[1e3]0.0132,=0.489100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.040[1e3]0.0142,=0.490100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.039[1e3]0.0122,=0.486100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.039[1e3]0.0122,=0.481100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.039[1e3]0.0122,=0.470100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.038[1e3]0.0122,=0.460100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.036[1e3]0.0112,=0.445100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.035[1e3]0.0122,=0.429100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.034[1e3]0.0112,=0.413100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.032[1e3]0.0102,=0.394100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.030[1e3]0.0102,=0.378100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.029[1e3]0.0092,=0.361100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.028[1e3]0.0092,=0.344100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.026[1e3]0.0092,=0.328100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.025[1e3]0.0082,=0.311100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.023[1e3]0.0082,=0.295100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.022[1e3]0.0072,=0.278100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.020[1e3]0.0072,=0.263100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.019[1e3]0.0062,=0.249100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.018[1e3]0.0062,=0.236100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.018[1e3]0.0052,=0.224100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.017[1e3]0.0062,=0.212100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.015[1e3]0.0052,=0.201100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.015[1e3]0.0052,=0.191100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.014[1e3]0.0042,=0.182100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.014[1e3]0.0052,=0.174100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.014[1e3]0.0042,=0.166100k bg trials103104105106107108E (GeV)1011109107105103101dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  bb0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0122,=0.518100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0122,=0.508100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0132,=0.500100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.039[1e3]0.0132,=0.487100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.039[1e3]0.0132,=0.488100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.039[1e3]0.0122,=0.482100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.038[1e3]0.0122,=0.475100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.038[1e3]0.0122,=0.462100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.036[1e3]0.0112,=0.446100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.034[1e3]0.0112,=0.426100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.032[1e3]0.0102,=0.406100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.031[1e3]0.0102,=0.386100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.030[1e3]0.0102,=0.368100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.030[1e3]0.0102,=0.352100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.028[1e3]0.0092,=0.339100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.027[1e3]0.0092,=0.331100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.026[1e3]0.0082,=0.322100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.026[1e3]0.0082,=0.313100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.025[1e3]0.0082,=0.304100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.024[1e3]0.0082,=0.295100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.023[1e3]0.0072,=0.285100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.022[1e3]0.0072,=0.274100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.021[1e3]0.0072,=0.264100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.020[1e3]0.0062,=0.253100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.019[1e3]0.0062,=0.242100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.018[1e3]0.0062,=0.231100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.018[1e3]0.0062,=0.220100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.016[1e3]0.0052,=0.209100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.015[1e3]0.0052,=0.199100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.015[1e3]0.0052,=0.190100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.014[1e3]0.0042,=0.181100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.014[1e3]0.0042,=0.173100k bg trials103104105106107108E (GeV)1010108106104102100dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  tt0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0122,=0.491100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0132,=0.493100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.038[1e3]0.0122,=0.493100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.039[1e3]0.0122,=0.483100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.039[1e3]0.0122,=0.489100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.039[1e3]0.0122,=0.488100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.039[1e3]0.0122,=0.489100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.039[1e3]0.0132,=0.487100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.039[1e3]0.0122,=0.483100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.039[1e3]0.0122,=0.476100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.039[1e3]0.0132,=0.467100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.037[1e3]0.0122,=0.454100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.036[1e3]0.0112,=0.439100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.033[1e3]0.0102,=0.421100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.032[1e3]0.0102,=0.402100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.030[1e3]0.0102,=0.382100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.030[1e3]0.0102,=0.363100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.027[1e3]0.0092,=0.344100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.026[1e3]0.0082,=0.327100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.024[1e3]0.0082,=0.310100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.023[1e3]0.0072,=0.292100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.021[1e3]0.0072,=0.275100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.020[1e3]0.0062,=0.260100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.019[1e3]0.0062,=0.246100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.018[1e3]0.0062,=0.233100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.018[1e3]0.0062,=0.222100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.017[1e3]0.0052,=0.210100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.015[1e3]0.0052,=0.200100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.015[1e3]0.0052,=0.191100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.014[1e3]0.0042,=0.182100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.014[1e3]0.0052,=0.174100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.014[1e3]0.0042,=0.167100k bg trials103104105106107108E (GeV)1011109107105103101dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  uu0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.039[1e3]0.0132,=0.474100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0132,=0.482100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0122,=0.488100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.039[1e3]0.0122,=0.479100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.039[1e3]0.0132,=0.487100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.039[1e3]0.0122,=0.486100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.040[1e3]0.0132,=0.488100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.040[1e3]0.0132,=0.488100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.038[1e3]0.0122,=0.484100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.039[1e3]0.0122,=0.477100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.039[1e3]0.0122,=0.469100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.038[1e3]0.0132,=0.456100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.036[1e3]0.0112,=0.441100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.033[1e3]0.0112,=0.423100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.033[1e3]0.0112,=0.404100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.030[1e3]0.0102,=0.384100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.030[1e3]0.0102,=0.364100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.028[1e3]0.0092,=0.345100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.026[1e3]0.0082,=0.328100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.024[1e3]0.0082,=0.310100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.023[1e3]0.0072,=0.293100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.021[1e3]0.0072,=0.276100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.020[1e3]0.0062,=0.260100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.019[1e3]0.0062,=0.246100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.018[1e3]0.0062,=0.233100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.018[1e3]0.0062,=0.222100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.017[1e3]0.0052,=0.210100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.015[1e3]0.0052,=0.199100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.015[1e3]0.0052,=0.190100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.014[1e3]0.0042,=0.181100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.014[1e3]0.0052,=0.174100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.014[1e3]0.0042,=0.166100k bg trials103104105106107108E (GeV)1011109107105103101dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  dd0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.038[1e3]0.0122,=0.530100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0122,=0.508100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.038[1e3]0.0122,=0.498100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.038[1e3]0.0122,=0.484100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.038[1e3]0.0122,=0.483100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.037[1e3]0.0122,=0.471100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.037[1e3]0.0112,=0.454100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.034[1e3]0.0112,=0.434100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.033[1e3]0.0102,=0.411100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.031[1e3]0.0102,=0.384100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.029[1e3]0.0092,=0.358100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.026[1e3]0.0082,=0.333100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.025[1e3]0.0082,=0.312100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.024[1e3]0.0082,=0.294100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.022[1e3]0.0072,=0.283100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.021[1e3]0.0072,=0.270100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.021[1e3]0.0062,=0.261100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.021[1e3]0.0062,=0.252100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.020[1e3]0.0062,=0.247100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.019[1e3]0.0062,=0.239100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.019[1e3]0.0062,=0.231100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.018[1e3]0.0062,=0.225100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.018[1e3]0.0062,=0.219100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.017[1e3]0.0052,=0.209100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.016[1e3]0.0052,=0.202100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.015[1e3]0.0052,=0.194100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.015[1e3]0.0052,=0.186100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.014[1e3]0.0052,=0.177100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.014[1e3]0.0052,=0.169100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.014[1e3]0.0042,=0.162100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.013[1e3]0.0042,=0.154100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.012[1e3]0.0042,=0.146100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  ZZ0510152025100101102103104105trials per binM=0.68 TeV[1e2]0.038[1e3]0.0122,=0.531100k bg trials0510152025100101102103104105M=1.00 TeV[1e2]0.039[1e3]0.0122,=0.509100k bg trials0510152025100101102103104105M=1.47 TeV[1e2]0.039[1e3]0.0122,=0.499100k bg trials0510152025100101102103104105M=2.15 TeV[1e2]0.038[1e3]0.0122,=0.485100k bg trials0510152025100101102103104105M=3.16 TeV[1e2]0.038[1e3]0.0122,=0.484100k bg trials0510152025100101102103104105trials per binM=4.64 TeV[1e2]0.038[1e3]0.0122,=0.473100k bg trials0510152025100101102103104105M=6.81 TeV[1e2]0.037[1e3]0.0122,=0.458100k bg trials0510152025100101102103104105M=10.00 TeV[1e2]0.035[1e3]0.0112,=0.438100k bg trials0510152025100101102103104105M=14.68 TeV[1e2]0.034[1e3]0.0112,=0.417100k bg trials0510152025100101102103104105M=21.54 TeV[1e2]0.032[1e3]0.0102,=0.390100k bg trials0510152025100101102103104105trials per binM=31.62 TeV[1e2]0.030[1e3]0.0092,=0.365100k bg trials0510152025100101102103104105M=46.41 TeV[1e2]0.027[1e3]0.0092,=0.340100k bg trials0510152025100101102103104105M=68.13 TeV[1e2]0.025[1e3]0.0082,=0.319100k bg trials0510152025100101102103104105M=100.00 TeV[1e2]0.025[1e3]0.0082,=0.301100k bg trials0510152025100101102103104105M=146.78 TeV[1e2]0.023[1e3]0.0072,=0.289100k bg trials0510152025100101102103104105trials per binM=215.44 TeV[1e2]0.022[1e3]0.0072,=0.276100k bg trials0510152025100101102103104105M=316.23 TeV[1e2]0.021[1e3]0.0072,=0.267100k bg trials0510152025100101102103104105M=464.16 TeV[1e2]0.021[1e3]0.0062,=0.256100k bg trials0510152025100101102103104105M=681.29 TeV[1e2]0.020[1e3]0.0062,=0.250100k bg trials0510152025100101102103104105M=1000.00 TeV[1e2]0.019[1e3]0.0062,=0.242100k bg trials0510152025100101102103104105trials per binM=1467.80 TeV[1e2]0.018[1e3]0.0062,=0.233100k bg trials0510152025100101102103104105M=2154.43 TeV[1e2]0.018[1e3]0.0062,=0.227100k bg trials0510152025100101102103104105M=3162.28 TeV[1e2]0.018[1e3]0.0062,=0.220100k bg trials0510152025100101102103104105M=4641.59 TeV[1e2]0.017[1e3]0.0052,=0.211100k bg trials0510152025100101102103104105M=6812.92 TeV[1e2]0.016[1e3]0.0052,=0.203100k bg trials0510152025100101102103104105trials per binM=10000.00 TeV[1e2]0.015[1e3]0.0052,=0.195100k bg trials0510152025100101102103104105M=14677.99 TeV[1e2]0.015[1e3]0.0052,=0.187100k bg trials0510152025100101102103104105M=21544.35 TeV[1e2]0.014[1e3]0.0042,=0.178100k bg trials0510152025100101102103104105M=31622.78 TeV[1e2]0.014[1e3]0.0042,=0.171100k bg trials0510152025100101102103104105M=46415.89 TeV[1e2]0.014[1e3]0.0042,=0.163100k bg trials0510152025TS100101102103104105trials per binM=68129.21 TeV[1e2]0.013[1e3]0.0042,=0.156100k bg trials0510152025TS100101102103104105M=100000.00 TeV[1e2]0.012[1e3]0.0042,=0.148100k bg trials103104105106107108E (GeV)1010108106104102dN/dE(GeV1)M=681 GeVM=100 PeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  WWAPPENDIX H

SEGUE 1 AND URSA MAJOR II SIGNAL RECOVERY

Figure H.1 Same as Fig. 6.32 but for Segue 1 and 𝜒 𝜒 → 𝑏𝑏.

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0204060801000255075100nsM=1 TeV0204060801000255075100M=2 TeV0204060801000255075100M=5 TeV0204060801000255075100nsM=10 TeV0204060801000255075100M=20 TeV0204060801000255075100M=50 TeV0204060801000255075100nsM=100 TeV0204060801000255075100M=200 TeV0204060801000255075100M=500 TeV0204060801000255075100nsM=1000 TeV0204060801000255075100M=2000 TeV0204060801000255075100M=5000 TeV020406080100ninj0255075100nsM=10000 TeV020406080100ninj0255075100M=20000 TeV103104105106107108E (GeV)1010107104101dN/dE(GeV1)M=1 TeVM=20000 TeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  bbFigure H.2 Same as Fig. 6.32 but for Segue 1 and 𝜒 𝜒 → 𝑡𝑡.

190

0204060801000255075100nsM=1 TeV0204060801000255075100M=2 TeV0204060801000255075100M=5 TeV0204060801000255075100nsM=10 TeV0204060801000255075100M=20 TeV0204060801000255075100M=50 TeV0204060801000255075100nsM=100 TeV0204060801000255075100M=200 TeV0204060801000255075100M=500 TeV0204060801000255075100nsM=1000 TeV0204060801000255075100M=2000 TeV0204060801000255075100M=5000 TeV020406080100ninj0255075100nsM=10000 TeV020406080100ninj0255075100M=20000 TeV103104105106107108E (GeV)109107105103101dN/dE(GeV1)M=1 TeVM=20000 TeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  ttFigure H.3 Same as Fig. 6.32 but for Segue 1 and 𝜒 𝜒 → 𝜈𝜇𝜈𝜇.

191

0204060801000255075100nsM=1 TeV0204060801000255075100M=2 TeV0204060801000255075100M=5 TeV0204060801000255075100nsM=10 TeV0204060801000255075100M=20 TeV0204060801000255075100M=50 TeV0204060801000255075100nsM=100 TeV0204060801000255075100M=200 TeV0204060801000255075100M=500 TeV0204060801000255075100nsM=1000 TeV0204060801000255075100M=2000 TeV0204060801000255075100M=5000 TeV020406080100ninj0255075100nsM=10000 TeV020406080100ninj0255075100M=20000 TeV103104105106107108E (GeV)108106104102dN/dE(GeV1)M=1 TeVM=20000 TeVSegue1(J = 2.27e+19, Dec = 16.06) Chi2 for  numunumuFigure H.4 Same as Fig. 6.32 but for Ursa Major II and 𝜒 𝜒 → 𝑏𝑏.

192

0204060801000255075100nsM=1 TeV0204060801000255075100M=2 TeV0204060801000255075100M=5 TeV0204060801000255075100nsM=10 TeV0204060801000255075100M=20 TeV0204060801000255075100M=50 TeV0204060801000255075100nsM=100 TeV0204060801000255075100M=200 TeV0204060801000255075100M=500 TeV0204060801000255075100nsM=1000 TeV0204060801000255075100M=2000 TeV0204060801000255075100M=5000 TeV020406080100ninj0255075100nsM=10000 TeV020406080100ninj0255075100M=20000 TeV103104105106107108E (GeV)1010107104101dN/dE(GeV1)M=1 TeVM=20000 TeVUrsaMajorII(J = 2.66e+19, Dec = 63.11) Chi2 for  bbFigure H.5 Same as Fig. 6.32 but for Ursa Major II and 𝜒 𝜒 → 𝑡𝑡.

193

0204060801000255075100nsM=1 TeV0204060801000255075100M=2 TeV0204060801000255075100M=5 TeV0204060801000255075100nsM=10 TeV0204060801000255075100M=20 TeV0204060801000255075100M=50 TeV0204060801000255075100nsM=100 TeV0204060801000255075100M=200 TeV0204060801000255075100M=500 TeV0204060801000255075100nsM=1000 TeV0204060801000255075100M=2000 TeV0204060801000255075100M=5000 TeV020406080100ninj0255075100nsM=10000 TeV020406080100ninj0255075100M=20000 TeV103104105106107108E (GeV)109107105103101dN/dE(GeV1)M=1 TeVM=20000 TeVUrsaMajorI(J = 7.46e+17, Dec = 51.94) Chi2 for  ttFigure H.6 Same as Fig. 6.32 but for Ursa Major II and 𝜒 𝜒 → 𝜈𝜇𝜈𝜇.

194

0204060801000255075100nsM=1 TeV0204060801000255075100M=2 TeV0204060801000255075100M=5 TeV0204060801000255075100nsM=10 TeV0204060801000255075100M=20 TeV0204060801000255075100M=50 TeV0204060801000255075100nsM=100 TeV0204060801000255075100M=200 TeV0204060801000255075100M=500 TeV0204060801000255075100nsM=1000 TeV0204060801000255075100M=2000 TeV0204060801000255075100M=5000 TeV020406080100ninj0255075100nsM=10000 TeV020406080100ninj0255075100M=20000 TeV103104105106107108E (GeV)108106104102dN/dE(GeV1)M=1 TeVM=20000 TeVUrsaMajorII(J = 2.66e+19, Dec = 63.11) Chi2 for  numunumuAPPENDIX I

SIGNAL NEUTRINO SENSITIVITIES

Figure I.1 IceCube North Sky Track Sensitivities for 𝑛𝑠/⟨𝑁⟩. 𝑛𝑠 values are the counts fed into
Eq. (6.8) to produceFig. 6.35 and Fig. 6.34.

195

100101102103104105M [TeV]101410121010108106104102100Nsig/NbbIC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]101410121010108106104102100Nsig/NttIC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]101410121010108106104102100Nsig/NuuIC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]101410121010108106104102100Nsig/NddIC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]101410121010108106104102100Nsig/NWW+IC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]101410121010108106104102100Nsig/N ZZIC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombinedFigure I.2 Same as Fig. I.1 for six additional DM annihilation channels.

196

100101102103104105M [TeV]101410121010108106104102100Nsig/Nee+IC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]101410121010108106104102100Nsig/NeeIC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]101410121010108106104102100Nsig/N+IC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]101410121010108106104102100Nsig/NIC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]101410121010108106104102100Nsig/N+IC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined100101102103104105M [TeV]101410121010108106104102100Nsig/NIC3 PreliminaryNsig 90% C.L. Per dSph and CombinedBootesICanesVenaticiICanesVenaticiIIComaBerenicesDracoHerculesLeoILeoIILeoVLeoTSegue1Segue2UrsaMajorIUrsaMajorIIUrsaMinorCombined