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                pdftitle={PhD Dissertation, William A Dawson}, % Insert your title
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\title          {Constraining Dark Matter Through the Study of Merging Galaxy Clusters}
%Exact title of your thesis. Indicate italics where necessary by underlining or using italics. Please capitalize the first letter of each word that would normally be capitalized in a title.

\author         {William Anthony Dawson}
%Your full name as it appears on University records. Do not use initials.

\authordegrees  {B.S. Maritime Systems Engineering (Texas A\& M University, Galveston) 2002\\
  M.S. Physics (University of California, Davis) 2008}
%Indicate your previous degrees conferred.

\officialmajor  {Physics}
%This is your official major as it appears on your University records.

\graduateprogram{Physics}
%This is your official graduate program name. Used for UMI abstract.

\degreeyear     {2013}
% Indicate the year in which your degree will be officially conferred.

\degreemonth    {August}
% Indicate the month in which your degree will be officially conferred. Used for UMI abstract.

\committee{Professor David M. Wittman, Chair}{Professor J. Anthony Tyson}{Professor Maru{\v s}a Brada{\v c}}{}{}
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%\copyrightyear{2020}
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\dedication{\textsl{To my wife Kerri,\\who has sacrificed more for this dissertation than anyone.}}

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\abstract{
\noindent\textbf{Context:} 
The majority ($\sim85$\%) of the matter in the universe is composed of dark matter, a mysterious particle that does not interact via the electromagnetic force yet does interact with all other matter via the gravitational force.
Many direct detection experiments have been devoted to finding interactions of dark matter with baryonic matter via the weak force.
To date only tentative and controversial evidence for such interactions has been found.
While such direct detection experiments have ruled out the possibility that dark matter interacts with baryonic matter via a strong scale force, it is still possible that dark matter interacts with itself via a strong scale force and has a self-scattering cross-section of $\sim0.5$\,cm$^2$\,g$^{-1}$.
In fact such a strong scale scattering force could resolve several outstanding astronomical mysteries: a discrepancy between the cuspy density profiles seen in $\Lambda$CDM simulations and the cored density profiles observed in low surface brightness galaxies, dwarf spheroidal galaxies, and galaxy clusters, as well as the discrepancy between the significant number of massive Milky Way dwarf spheroidal halos predicted by $\Lambda$CDM and the dearth of observed Milky Way dwarf spheroidal halos.
 

% Need: What you want is not what you have

\noindent\textbf{Need:} 
While such observations are in conflict with $\Lambda$CDM and suggest that dark matter may self-scatter, each suffers from a \emph{baryonic degeneracy}, where the observations might be explained by various baryonic processes (e.g., AGN or supernove feedback, stellar winds, etc.)\footnote{At the heart of this is a current lack of knowledge of the influence of baryons on structure formation.} rather than self-interacting dark matter (SIDM).
In fact, the important scales of these observations often coincide with baryonic scales (e.g., the core size in clusters is few factors smaller than the radius of the brightest cluster galaxy).
What is needed is a probe of SIDM where the expected effect cannot be replicated by the same processes responsible for the baryonic degeneracy in the aforementioned probes.
Merging galaxy clusters are such a probe.
During the merging process the effectively collisionless galaxies ($\sim$2\% of the cluster mass) become dissociated from the collisional intracluster gas ($\sim$15\% of the cluster mass).
A significant fraction of the gas self-interacts during the merger and slows down at the point of collision.
If dark matter lags behind the effectively collisionless galaxies then this is clear evidence that dark matter self-interacts.
The expected galaxy-dark matter offset is typically $>$25\,kpc (for cross-sections that would explain the other aforementioned issues with $\Lambda$CDM), this is larger than the scales of that are plagued by the baryonic degeneracies.

%Task: What I did to address the need
\noindent\textbf{Task:} 
To test whether dark matter self-interacts we have carried out a comprehensive survey of the dissociative merging galaxy cluster DLSCL J0916.2+2951 (also known as the Musket Ball Cluster).
This survey includes photometric and spectroscopic observations to quantify the position and velocity of the cluster galaxies,
weak gravitational lensing observations to map and weigh the mass (i.e., dark matter which comprises $\sim$85\% of the mass) of the cluster,
Sunyaev-Zel'dovich effect and X-ray observations to map and quantify the intracluster gas,
and finally radio observations to search for associated radio relics, which had they been observed would have helped constrain the properties of the merger.
Using this information in conjunction with a Monte Carlo analysis model I quantify the dynamic properties of the merger, necessary to properly interpret constraints on the SIDM cross-section.
I compare the locations of the galaxies, dark matter and gas to constrain the SIDM cross-section.
This dissertation presents this work.

% Findings: What I found doing the task
\noindent\textbf{Findings:} 
We find that the Musket Ball is a merger with total mass of  $4.8^{+3.2}_{-1.5}\times 10^{14}$M$_\sun$.
However, the dynamic analysis shows that the Musket Ball is being observed $1.1^{+1.3}_{-0.4}$\,Gyr after first pass through and is much further progressed in its merger process than previously identified dissociative mergers (for example it is $3.4^{+3.8}_{-1.4}$ times further progressed that the Bullet Cluster). 
By observing that the dark matter is significantly offset from the gas we are able to place an upper limit on the dark matter cross-section of $\sigma_{\rm SIDM}m^{-1}_{\rm DM} <$8\,cm$^2$\,g$^{-1}$.
However, we find an that the galaxies appear to be leading the weak lensing (WL) mass distribution by 20.5'' (129\,kpc at $z$=0.53) in southern subcluster, which might be expected to occur if dark matter self-interacts.
Contrary to this finding though the WL mass centroid appears to be leading the galaxy centroid by 7.4'' (47\,kpc at $z$=0.53) in the northern subcluster. 


% Conclusion: What these findings mean to me
\noindent\textbf{Conclusion:}
The southern offset alone suggests that  dark matter self-interacts with $\sim$83\% confidence.
However, when we account for the observation that the galaxy centroid appears to trail the WL centroid in the north the confidence falls to $\sim$55\%.
While the SIDM scenario is slightly preferred over the CDM scenario it is not significantly so.

% Perspectives: What we should do next
\noindent\textbf{Perspectives:}
The galaxy-dark matter offset measurement is dominated by random errors in each cluster.
Thus measuring this offset in other dissociative mergers holds the promise of reducing our uncertainty and enabling us to: 1) state confidently whether dark matter self-interacts via a new dark sector force, or 2) constrain the dark matter cross-section to such a degree that SIDM cannot explain the aforementioned mysteries\footnote{In the case of a null detection of an offset between the galaxies and the DM, SIDM simulations will be necessary to place a quantitative constraint on the SIDM cross-section \citep[see e.g.,][]{Randall:2008hs}.}.
To this end we have established the Merging Cluster Collaboration to observe and simulate an ensemble of dissociative merging clusters.
We are currently in the process of analyzing six dissociative mergers with existing data, and carrying out multi-wavelength observations of a new sample of 15 radio relic identified dissociative mergers.
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\acknowledgments{
I have had the good fortune of being positively influenced by many people during my life, thank you all.
There are several people that deserve special note.
First and foremost I am indebted to my wife Kerri.
She has sacrificed more in the pursuit of this doctorate than any wife should be asked to sacrifice.
I surely would not have succeeded without her support during every facet of this endeavor.
I also thank my two boys, Evry and Lander, who have strengthened my resolve in studying a subject that is not likely to bear tangible fruit during my lifetime, but may bear fruit in their lifetime or their children's lifetime.
I particularly want to thank my mother Marie for instilling in me a healthy sense of overconfidence and curiosity.
Without which I would have never had the courage or desire to pursue a degree in physics.
I thank my father Bill whose exemplary dedication and leadership in his pursuit to serve humanity provided a high mark that I will always strive towards.
I also thank my other father Jim for providing unending support and introducing me to the many wonders of our natural world.
I would like to thank my brother Thomas for sharing a curiosity of how things work and, through his own example, making exceptional career endeavors seem a little less exceptional.
I also owe a great deal of thanks to my grandmother Imogene whose boundless love of the world and people around her gave me a hint to beauty of the universe and has inspired me to share that beauty with others.

I cannot take full credit for the work presented in this dissertation, it is the result of a concerted effort on the part of many researchers.
In particular, I would like to acknowledge and thank my advisor Dr. David Wittman.
He has always encouraged my research-freewill, while at the same time providing invaluable input and correcting guidance.
It was Dave that first encouraged me to pursue my interest of merging galaxy clusters, despite there being more tangible research topics that we could have worked on.
Furthermore for encouraging me to write a Chandra proposal as a second year graduate student, a proposal that was later accepted and provided the impetus for this whole dissertation.
From these modest beginnings to the current state of a multi-national/institutional merging cluster collaboration Dave has been more than an advisor, he has been a partner.

I also owe a great deal of thanks to my other two dissertation committee members, Dr. Tony Tyson and Dr. Maru{\v s}a Brada{\v c}.
They both provided valuable feedback and guidance during the writing of this dissertation, but far beyond that they have been major influences shaping the scientist that I have become.
I can honestly say that I would not be the scientist I am today without Tony.
He taught me single lesson that has influenced me the most: work in the low signal-to-noise regime because that is where the truly surprising science lies, but be ever vigilant of spurious results and pathological science. 
I am honored to be part of his great legacy.
Maru{\v s}a also deserves a great deal of credit for the scientist I am today.
I have come to rely on her unbiased and unabashed feedback in almost every major decision I make.
While I don't always agree with her, I often regard her opinion above all others.

My many collaborators (including Dave, Tony and Maru{\v s}a) deserve much of the credit for this dissertation.
I would particularly like to thank James Jee who performed almost all of the underlying lensing related data reduction, which played a critical role in this dissertation.
I also thank Perry Gee who first discovered the Musket Ball Cluster and laid the spectroscopic ground work that was crucial in providing the first evidence of it being a dissociative merger.
On a related note I thank Dan Marrone for providing the SZE measurements of the Musket Ball Cluster that was also part of the first evidence suggesting that the Musket Ball Cluster was a dissociative merger (in addition to coming up with the ``Musket Ball'' name).
And I thank Jack Hughes for not only reducing the Chandra X-ray data, which proved that the Musket Ball Cluster was a dissociative merger, but for taking the time to teach me how to reduce the data myself.
Crucial to the work of this dissertation was the previous work by all of the Deep Lens Survey collaboration, without which the Musket Ball Cluster may have never been discovered.
Special thanks are due to the many people who worked on the photometry and photometric redshifts, in particular Sam Schmidt.

I would like to thank all of the members of the Merging Cluster Collaboration: Maru{\v s}a Brada{\v c}, Marcus Bruggen, James Bullock, Oliver Elbert, James Jee, Manoj Kaplinghat,  Alison Mansheim, Julian Merten, Karen Ng, Annika Peter, Miguel Rocha, Reinout van Weeren and David Wittman.
Together we have taken raw ideas and turned them into a coherent directive.
Many of the concepts presented in this dissertation are the result of our many discussions.
In this regard a considerable amount of thanks are due to UC-HiPACC which has generously funded our collaboration through travel support.

I would also like to thank the UC Davis cosmology group, which has provided a fertile and supportive environment.
In addition to the aforementioned faculty and researchers, I would like to thank Professor Chris Fassnacht who has always taken the lead to promote a social and healthy group, and Bob Becker for never having security remove me from the premises after the multiple times he has fired me.
I would also like to thank my former officemates, Brian Lemaux, Dave Lagattuta, Greg Zeimann, Nicholas Hall, Marius Millea, Nick Rumbaugh, and Jackie Hodge.
Not only did you provide the most enjoyable and entertaining work environment I have ever been a part of, but I learned a great deal from each of you (well everyone except Marius and Nick).
In particular I have Brian to thank for everything I know about spectroscopy.
He has always been an incredibly patient and thorough instructor.
I would also like to thank Brian, Dave, and Chris Morrison for their invaluable help with formatting this dissertation, and in doing so saved me countless hours.

Finally I would like to thank the citizens of the United States of America.
Without their financial support of scientific research none of this would be possible.
Specifically, my research has been funded directly by the University of California at Davis through multiple block grants and through the support of my advisor.
Support for this work was also provided by NASA through Chandra Award Number GO1-12171X issued by CXO Center, which is operated by the SAO for and on behalf of NASA under contract NAS8-03060, and support for program number GO-12377 was provided by NASA through a grant from STScI, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.
Additional research funding was provided through the NSF under grant AST-1108893 and considerable travel funding has been provided by UC-HiPACC.

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% The UMI abstract uses square brackets!
%\UMIabstract[In this dissertation, we describe observational and theoretical work related to the large-scale clustering of matter in the universe. Such work is crucial in constraining models of the Universe in future surveys and is one of the most powerful probes of the nature of dark energy. In Chapter \ref{magnification}, we present work performed using the Deep Lens Survey (DLS) to measure the growth of structure over cosmic time using weak lensing magnification. This is the first time such a measurement has been performed and represents a significant step forward for this relatively new probe of large-scale structure (LSS) which is known to be complementary to other weak lensing measurements. Later in Chapter \ref{conclusions}, we discuss steps needed for magnification become a competitive, precision probe of cosmology. Chapter \ref{covariance} presents a model for the emulation cosmology dependent error covariances in LSS probes. Estimating these covariances are necessary in order to compare models to the data and require a large amount of computational time to create the simulations required. Tools to reduce the number of simulations required and model the cosmology dependence are needed. We utilize a novel decomposition of LSS error covariances that allows for construction of a emulator that fulfills both of these criteria. In order for future surveys to reach their goals, methods to model measurement error and new probes of LSS complementary to those planned are required.

%The conclusions of this dissertation in Chapter \ref{conclusions} address the future outlook for this work and research that must be done between now and when the next set of survey data is available. Many systematic errors need to be addressed in magnification before it can be considered a precision cosmology tool. For the error covariances, additional methods to reduce the required number of simulations to estimate the matrices are required. In the Appendix, we present a high level description of an open sourced software package that we developed and implemented over the course of these two projects.]

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