ABSTRACT
Title of Dissertation: GAS AND STAR FORMATION
AT THE PEAK OF COSMIC
STAR FORMING ACTIVITY
Laura Lenkic?
Doctor of Philosophy, 2021
Dissertation Directed by: Professor Alberto D. Bolatto
Department of Astronomy
Gas and star formation in galaxies are intimately linked to one another. Molec-
ular hydrogen gas is the material out of which stars form, while the process of forming
stars, in turn, depletes the reservoirs of gas in galaxies and builds up their stellar
mass. Observations of star formation in galaxies over time indicate that they must
form stars for timescales longer than would be expected from their gas content and
star formation rates, indicating that processes that replenish the star forming fuel
must be present. The focus of this thesis is on two components of this qualitative
picture: the molecular hydrogen gas content of galaxies over time, and the link be-
tween gas and star formation in galaxies resembling those observed at the epoch of
most active star formation.
First, I present a systematic search for serendipitous carbon monoxide emit-
ting sources in the second Plateau de Bure High-z Blue-Sequence Survey (PHIBSS2).
These observations presented an opportunity to quantify the mass density of molec-
ular gas in galaxies as a function of time, and to link this to the star formation
history of the Universe. I use a match-filter technique to systematically detect 67
serendipitous sources, after which I characterize their properties, creating a catalog
of their redshifts, line widths, fluxes, estimations of the detection reliability, and
completeness of the detection algorithm. I find that these serendipitous sources
are unrelated to the primary sources that were targeted by PHIBSS2, and use the
catalog to construct luminosity functions spanning a redshift range from ? 0.3? 5.
From these luminosity functions, I place constraints on the molecular hydrogen con-
tent in galaxies over cosmic time. My work presents one of the first attempts to
use existing observations for this measurement and yields results that are consistent
with previous studies, while demonstrating the scientific power of large, targeted
surveys.
Next, I study a sample of rare, nearby galaxies that are most similar to those
we observe at the peak of cosmic star forming activity that occured ? 10 billion
years ago. These galaxies are drawn from the DYnamics of Newly Assembled Mas-
sive Objects (DYNAMO) survey, and their proximity to us allows for very detailed
studies of their massive star forming clumps. I use observations from the Hubble
Space Telescope (HST) to measure colors that are sensitive to stellar population
age and extinction. From these measurements, I find that clumps in DYNAMO
galaxies have colors that are most consistent with very young centers and outskirts
that appear systematically older, by as much as 150 Myr in some cases. I attribute
this age difference to the presence of ongoing star formation in the centers of clumps
that maintains the population of massive, short-lived stars and gives rise to colors
consistent with young ages. Furthermore, I find that within the disks of their host
galaxies, younger clumps are preferentially located far from galaxy centers, while
older clumps are preferentially located closer to the centers. These results are con-
sistent with hydrodynamic simulations of high-redshift clumpy galaxies that predict
clumps form in the outskirts of galaxies via a violent disk instability, and as they age,
migrate to the centers of galaxies where they merge and contribute to the growth
of galactic bulges.
Building on this study, I combine observations of DYNAMO galaxies from
the HST and the Atacama Large Millimeter/sub-millimeter Array (ALMA) to trace
molecular hydrogen gas and star formation. I link these observations to measure-
ments of the molecular gas velocity dispersions to test theories of star formation. I
find that compared to local samples of ?normal? star forming galaxies, DYNAMO
systems have consistently high velocity dispersions, molecular gas surface densities,
and star formation rate surface densities. Indeed, throughout their disks, DYNAMO
galaxies are comparable to the centers of local star forming galaxies. Stellar bar
driven gas flows into the centers of galaxies in these local samples may give rise to
the high observed velocity dispersions, and gas and star formation rate surface den-
sities. For DYNAMO galaxies, the widespread elevated values of these parameters
may be driven by galactic-scale gas inflows, which is predicted by theories. Finally,
current theories of star formation, such as the feedback regulated model, assume
that turbulence dissipates on timescales proportional to the angular velocity of a
galaxy (eddy or crossing time). Yet, I find such models have difficulty reproduc-
ing the DYNAMO measurements, and thus conclude that the turbulent dissipation
timescale in DYNAMO galaxies must scale with galactocentric radius.
GAS AND STAR FORMATION AT THE PEAK
OF COSMIC STAR FORMING ACTIVITY
by
Laura Lenkic?
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2021
Advisory Committee:
Professor Alberto D. Bolatto, Chair/Advisor
Professor Andrew Harris
Professor Sylvain Veilleux
Dr. Deanne B. Fisher, External Examiner
Professor Peter Shawhan, Dean?s Representative
Preface
This thesis focuses on two aspects of star?forming galaxies: the availability
of fuel for star formation across cosmic time and star formation in clumpy, gas?
rich, turbulent galaxies that are nearby analogues of star forming galaxies at the
peak of cosmic star forming activity. Parts of this thesis have been published in
peer-reviewed journals and presented at several conferences.
Chapter 2 has been published in the Astronomy Journal as ?Plateau de Bure
High-z Blue Sequence Survey 2 (PHIBSS2): Search for Secondary Sources, CO Lu-
minosity Functions in the Field, and the Evolution of Molecular Gas Density through
Cosmic Time? and appears in this thesis with minimal changes (Lenkic? et al., 2020).
Chapter 3 has been published in the Monthly Notices of the Royal Astronomical
Society as ?Giant Star Forming Complexes in High-z Main Sequence Galaxy Ana-
logues: The Internal Structure of Clumps in DYNAMO Galaxies? and also appears
in this thesis with minimal changes (Lenkic? et al., 2021). Chapter 4 is currently in
preparation for submission to the Astrophysical Journal.
ii
Dedication
To my parents,
Zdravka Lenkic? and Franko Lenkic?,
who nurtured and encouraged in me
a curiosity in all aspects of life.
iii
Acknowledgments
This thesis would not have been possible without my advisor, Alberto Bolatto.
Thank you so much for believing in me and seeing this thesis through to the end.
It?s been a real team effort and I appreciate all our discussions and everything you
have taught me. I also thank the rest of my committee: Andy Harris for all our
conversations and the great instrumentation class you taught, Sylvain Veilleux for
your insights and help with observing proposals like JWST, Deanne Fisher for all
the early Friday mornings in Australia that you spent meeting with me and Alberto,
sharing with me your incredible knowledge of DYNAMO, and Peter Shawhan for
taking on the role of Dean?s Representative of my committe. Thank you all.
I thank the rest of our research group: Stuart Vogel for always being an
advocate for grad students, Peter Teuben for your endless help with all things radio,
and especially the grad students Becca, Liz, Jialu, Vicente, and Rye for making this
group really feel like being a part of something bigger. You are all amazing people,
scientists, and friends.
Amy, I cherish our friendship; it is one of the best things that happened to me
at UMD. Thank you for your support, for always listening, and for being unapolo-
getically you. You make the world a better place and I admire and respect you.
Derek, thank you for caring about grad students and always being understanding
iv
and compassionate. Thank you for introducing me to birding, and most of all thank
you for your friendship. The memories of all our birding trips are some of the best I
have from my time here. I hope there will be many more! Sara, thank you for your
mentorship, friendship, and sharing your time and experiences with me as we were
both navigating career options and trying to sort out and piece together the next
steps of our lives. Milena, thank you for being a shining light in the department.
Thank you for your friendship, for our swims, book club discussions, attempts to
make burek, and everything in between.
To all the grads I had the pleasure of sharing an office with: Milena, Toma?s,
Pradip, Joe, Jialu, Guangwei, Ramsey, Zeeve, Thomas, Jegug, Sara, ChongChong,
Ginny, Jongwon, Charlotte, thank you for bringing the offices to life with your
personalities. To all grads in the department: I am grateful for, and appreciate all
of you, you make the department a very special place. To everyone on the eclipse
roadtrip of 2017: Zeeve, Thomas, Bernadette, Jialu, Jiali, Liz, Matt, and Pradip:
thank you for one of the most incredible grad school experiences. To Dana and Jeff,
thank you for everything you have done to make College Park feel like home.
To all the administrative and front office staff: Olivia, Susan, Dorinda, Mona,
Barbara, the department would not function without you! Thank you for all your
kindness and patience as I figured out how things worked, messed up my TARs, and
crumbled under the pressure of paperwork in the last few weeks of my thesis. You
are all amazing!
My friends near and far: Julie, Alex, Mladen, Robin, Nathalie; thank you for
your everlasting presence that made me feel like I was never alone or too far from
v
home, even when the world otherwise seemed to be caving in on me.
To my sister, Elizabeth, thank you for always being there for me, for all your
love, for all that you have taught me about life and perseverance. To my brother
Stefan, you?ve listened to all my rants about physics and astronomy for as long as
I can remember and have always supported me in this pursuit. Thank you.
To my parents Zdravka and Franko Lenkic?, words don?t quite seem enough to
express the gratitude I have for you. You uprooted your lives, left behind everyone
and everything you know, learned two new languages, and worked harder than
anyone I have ever known, so that we could have opportunities you didn?t. Mama,
you went to college with three unruly kids running around, became a respiratory
therapist, and over the last 18 months have fought tirelessly to save people?s lives
throughout the pandemic. You are a fierce and inspiring woman who has shown me
that anything is possible. Tata, I know you once dreamed of being an astronomer
too. Thank you for everything you have done to make it possible for me to chase
that dream instead. Thank you both for the values you have taught me and the
infinite support you provide; you are the reason I am here today.
Finally, to Petr, my partner, I know you would rather I write some joke or
something ridiculous, but I want the world to know of the infinite well of love and
support that lives inside your heart. You weren?t just there to see me through these
last five years, you lived every single moment of this time with me, as if you were
going through the PhD yourself. Your unparalleled wit and humour have kept a
smile on my face even at times when I felt like I would just break down. Thank you
for all the big and small ways you have supported me, from fixing my glasses on
vi
my face, to going through homework assignments with me, passing on to me some
of your jedi coding skills, talking through research problems, reading my thesis,
accepting with curiosity and enthusiasm every wild travel/nutrition/exercise ideas
I propose (like driving with me through the desert of Namibia!), and everything in
between. Thank you for everything, I love you beyond words!
vii
Table of Contents
Preface ii
Dedication iii
Acknowledgements iv
Table of Contents viii
List of Tables xi
List of Figures xii
List of Abbreviations xv
Chapter 1: Introduction 1
1.1 The Interstellar Medium and Star Formation . . . . . . . . . . . . . . 6
1.1.1 Dense Molecular Gas and its Tracers . . . . . . . . . . . . . . 7
1.1.2 Star Formation and its Tracers . . . . . . . . . . . . . . . . . 10
1.2 Star Formation and Gas Content History of the Universe . . . . . . . 13
1.3 Radio Interferometry and Synthesis Imaging . . . . . . . . . . . . . . 19
1.3.1 Interferometry Basics . . . . . . . . . . . . . . . . . . . . . . . 20
1.3.2 Deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.4 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Chapter 2: Cosmic Evolution of Molecular Hydrogen Gas Mass Den-
sity 32
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.1 The ?Plateau de Bure High-z Blue-Sequence Survey? (PHIBSS) 36
2.3.2 Ancillary Data . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.1 Line Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.1.1 False Positives . . . . . . . . . . . . . . . . . . . . . 43
2.4.1.2 Completeness . . . . . . . . . . . . . . . . . . . . . . 47
2.5 Results of Line Search . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.5.1 Line Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 51
viii
2.5.1.1 Optical Counterparts . . . . . . . . . . . . . . . . . . 53
2.5.2 Comparing Serendipitous Detections to Central Sources . . . . 60
2.5.3 CO Luminosity Functions . . . . . . . . . . . . . . . . . . . . 65
2.5.3.1 PHIBSS2 CO Luminosity Functions . . . . . . . . . 67
2.5.4 Molecular Gas Mass Density Evolution . . . . . . . . . . . . . 70
2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.6.1 Comparison to Previous Blind CO Surveys . . . . . . . . . . . 73
2.6.1.1 Luminosity Functions . . . . . . . . . . . . . . . . . 73
2.6.1.2 Molecular Gas Mass Density Evolution . . . . . . . . 76
2.6.2 Cosmic Variance . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Chapter 3: The Nature and Fate of Star Forming Clumps in Gas-
Rich, Turbulent Galaxies 82
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.3 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.1 Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.2 HST Observations . . . . . . . . . . . . . . . . . . . . . . . . 88
3.4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.4.1 Kernel Generation for PSF Matching . . . . . . . . . . . . . . 92
3.4.1.1 HST PSFs . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4.1.2 Circularizing the PSFs . . . . . . . . . . . . . . . . . 93
3.4.1.3 Compute the Kernels . . . . . . . . . . . . . . . . . . 94
3.4.1.4 Kernel Testing . . . . . . . . . . . . . . . . . . . . . 94
3.4.2 Clump Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.4.3 Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.4.3.1 Aperture Photometry . . . . . . . . . . . . . . . . . 99
3.4.3.2 Surface Brightness Profiles . . . . . . . . . . . . . . . 103
3.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.5.1 Galactocentric Variations of Global Clump Properties . . . . . 107
3.5.2 Internal colour Gradients of Clumps . . . . . . . . . . . . . . . 113
3.5.3 Galactocentric Variations of Resolved Clump Properties . . . 119
3.5.4 Comparison to Hydrodynamic Models . . . . . . . . . . . . . 125
3.5.5 Toward a General Picture of Star Formation in Clumps . . . . 132
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Chapter 4: Linking it Together ? Gas and Star Formation in Nearby
High?z Analogs 137
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.3 Observations and Data Reduction . . . . . . . . . . . . . . . . . . . . 142
4.3.1 ALMA CO Observations . . . . . . . . . . . . . . . . . . . . . 142
4.3.2 HST Observations . . . . . . . . . . . . . . . . . . . . . . . . 149
4.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
ix
4.4.1 Resolved Measurements . . . . . . . . . . . . . . . . . . . . . 150
4.4.1.1 Molecular Gas Surface Density . . . . . . . . . . . . 150
4.4.1.2 Star Formation Rate Surface Density . . . . . . . . . 151
4.4.1.3 Stellar Mass Surface Density . . . . . . . . . . . . . 152
4.4.1.4 Velocity Dispersion . . . . . . . . . . . . . . . . . . . 152
4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.5.1 CO(4?3)/CO(3?2) Line Ratios . . . . . . . . . . . . . . . . . 155
4.5.2 Resolved KS-Law . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.5.3 Radial Distribution of Velocity Dispersion . . . . . . . . . . . 165
4.5.4 ?mol??mol and ?mol??SFR Relations . . . . . . . . . . . . . . 168
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
4.6.1 Effect of ?SFR on CO(4?3)/CO(3?2) . . . . . . . . . . . . . . 171
4.6.2 Comparison of ?mol??mol and ?mol??SFR to Hydrodynamic
Models and Theory . . . . . . . . . . . . . . . . . . . . . . . . 174
4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Chapter 5: Future Work 183
5.1 The ISM of Clumpy, Turbulent Galaxies . . . . . . . . . . . . . . . . 183
5.2 Large Scale Gas Flows and Clump Scale Gas Kinematics . . . . . . . 184
5.3 Feedback from Clumps . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Appendix A:Appendices for Chapter 2 188
A.1 Description of Individual Candidate Sources . . . . . . . . . . . . . . 188
A.2 Luminosity Function and Molecular Gas Mass Density Constraints:
Tabulated Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Appendix B:Appendices for Chapter 3 209
B.1 Clump Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
B.2 Starburst99 Model Comparison . . . . . . . . . . . . . . . . . . . . 210
Appendix C:Appendices for Chapter 4 212
C.1 Channel Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Appendix D:Facilities and Software 223
D.1 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
D.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Bibliography 225
x
List of Tables
2.1 Comoving Volume Sampled by each CO Transition . . . . . . . . . . 66
2.2 Schechter Function Fit Parameter Constraints from PHIBSS2 . . . . 70
3.1 Properties of HST-DYNAMO Galaxies . . . . . . . . . . . . . . . . . 89
4.1 CO Data Cube Parameters . . . . . . . . . . . . . . . . . . . . . . . . 145
4.2 CO(4?3)/CO(3?2) Line Ratios Compiled from the Literature Com-
pared to DYNAMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
A.1 Properties of Candidate CO Sources . . . . . . . . . . . . . . . . . . 206
A.2 Properties of Potential Optical Counterparts . . . . . . . . . . . . . . 206
A.3 Luminosity functions of the observed CO transitions . . . . . . . . . . 208
A.4 Derived molecular gas mass density evolution constraints . . . . . . . 208
B.1 Properties of HST-DYNAMO Galaxy Clumps . . . . . . . . . . . . . 210
xi
List of Figures
1.1 Color properties of galaxies with different morphological type in the
u? r versus stellar mass parameter space . . . . . . . . . . . . . . . . 3
1.2 Redshift evolution of the main sequence of star formation . . . . . . . 5
1.3 Star formation history of the Universe . . . . . . . . . . . . . . . . . 14
1.4 Illustration of a two element interferometer . . . . . . . . . . . . . . . 22
1.5 Comparison of the uv?plane sampling of ALMA with a short and
long integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.6 Visualization of the Ho?gbom CLEAN algorithm . . . . . . . . . . . . 28
2.1 Channel-by-channel RMS variations for three individual PHIBSS2
data cubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2 Hanning-smoother signal-to-noise ratio map for one PHIBSS2 data
cube, showing the detection of a serendipitous CO source . . . . . . . 42
2.3 Histogram of the positive and negative peaks for one PHIBSS2 data
cube to illustrate the method for determining false positive likelihoods 45
2.4 Fraction of recovered simulated sources for one PHIBSS2 data cube
to illustrate the method for assessing the completeness of the source
detection algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5 The brightest serendipitous CO sources in the COSMOS (top), EGS/AEGIS
(middle), and GOODS-N (bottom) fields. The complete set of figures
is available in Appendix A. . . . . . . . . . . . . . . . . . . . . . . . . 52
2.6 Comparison of the properties of serendipitous CO sources with op-
tical/IR counterparts to ones without, and comparing serendipitous
CO sources to the central sources in the PHIBSS2 data cubes . . . . 55
2.7 Comparison of the molecular hydrogen gas mass of measured from
the PHIBSS2 observations to the masses inferred from the optical/IR
counterpart SED fitting . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.8 Comparison of the serendipitous CO source properties to the targets
specifically targeted by PHIBSS2 . . . . . . . . . . . . . . . . . . . . 62
2.9 Histograms showing the distribution of serendipitous CO sources in
frequency and redshift to check for clustering . . . . . . . . . . . . . . 63
2.10 PHIBSS2 Field CO luminosity functions derived from the serendipi-
tous CO sources detected . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.11 Corner plot of the Schechter model parameters posterior distribution
from fitting the CO (2? 1) luminosity function. . . . . . . . . . . . . 71
xii
2.12 Density of Schechter fits for the CO (2?1) z ? 0.7 luminosity function. 72
2.13 PHIBSS2 derived evolution of the molecular gas mass density from
the serendipitous CO sources detected . . . . . . . . . . . . . . . . . 74
2.14 Comparison of the PHIBSS2 derived CO (3? 2) luminosity function
to previous works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.1 Summary of HST observations for the first three out of six DYNAMO
galaxies in our sample . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.2 Summary of HST observations for the last three out of six DYNAMO
galaxies in our sample . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.3 Results of PSF matching . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.4 Outline of the unsharp masking technique for identifying clumps in
DYNAMO galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.5 Color-color diagram showing the integrated colors of clumps resulting
from aperture photometry . . . . . . . . . . . . . . . . . . . . . . . . 102
3.6 Surface brightness profiles of four clumps in all three HST filters . . . 104
3.7 Clump integrated 336?467 colour with and without disk subtraction
as a function of galactocentric radius . . . . . . . . . . . . . . . . . . 108
3.8 Same as Figure 3.7, but now showing the integrated 225? 336 colour
without (filled yellow diamonds) and with (empty yellow diamonds)
disc subtraction. The gray solid line shows how the 225? 336 colour
evolves across each galaxy when we mask clumps. The 225 ? 336
colours of clumps are generally flatter than the 336 ? 467 and track
the disc colour more closely, suggesting clump extinction does not
differ strongly from the disc extinction. . . . . . . . . . . . . . . . . . 111
3.9 Color tracks of two clumps in the 225?336 versus 336?467 parameter
space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.10 Color tracks of all clumps in all six DYNAMO galaxies . . . . . . . . 116
3.11 Estimated clump ages as a function of galactocentric radius . . . . . . 120
3.12 Inner and outer clump age difference as a function of galactocentric
radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.13 Comparison of the slope of the DYNAMO clump age?radius relation
to simluations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
3.14 Comparison of the galactocentric distribution of DYNAMO clumps
to simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.1 Channel maps of CO(3?2) for the galaxy DYNAMO G04-1 . . . . . . 144
4.2 Summary of all data sets analyzed in this work . . . . . . . . . . . . 148
4.3 Comparison of observed and modeled velocity field and velocity dis-
persion map of DYNAMO G04-1 . . . . . . . . . . . . . . . . . . . . 153
4.4 CO(4?3)/CO(3?2) line ratio maps of DYNAMO galaxies . . . . . . 156
4.5 RADEX prediction of the CO(4?3)/CO(3?2) line ratio . . . . . . . 159
4.6 Kernel density estimator (KDE) for the resolved CO(4?3)/CO(3?2)
line ratio measurements compared to results from the literature . . . 161
4.7 The measured Kennicutt-Schmidt relation in DYNAMO galaxies . . . 165
xiii
4.8 Radial distribution of beam smearing corrected velocity dispersion
measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
4.9 Beam smearing corrected ?mol??mol and ?mol??SFR relations . . . . 169
4.10 CO(4?3)/CO(3?2) line ratio as a function ?SFR . . . . . . . . . . . . 173
4.11 Comparison of the ?mol??mol and ?mol??SFR relation in DYNAMO
to simulations and expectations from theory . . . . . . . . . . . . . . 175
4.12 Testing possible effects on ?mol predicted from theories in DYNAMO 179
A.1 All candidate CO sources detected in the COSMOS field. . . . . . . . 195
A.2 All candidate CO sources detected in the GOODS-N field. . . . . . . 201
A.3 All candidate CO sources detected in the EGS/AEGIS field. . . . . . 204
B.1 Comparison of Starburst99 models with sub-Solar metallicity . . . . 211
C.1 DYNAMO C13-1 CO(3?2) channel maps . . . . . . . . . . . . . . . . 213
C.2 DYNAMO C22-2 CO(3?2) channel maps . . . . . . . . . . . . . . . . 213
C.3 DYNAMO C22-2 CO(4?3) channel maps . . . . . . . . . . . . . . . . 214
C.4 DYNAMO D13-5 CO(3?2) channel maps . . . . . . . . . . . . . . . . 214
C.5 DYNAMO D13-5 CO(4?3) channel maps . . . . . . . . . . . . . . . . 215
C.6 DYNAMO D15-3 CO(4?3) channel maps . . . . . . . . . . . . . . . . 216
C.7 DYNAMO G04-1 CO(4?3) channel maps . . . . . . . . . . . . . . . 217
C.8 DYNAMO G08-5 CO(3?2) channel maps . . . . . . . . . . . . . . . 218
C.9 DYNAMO G14-1 CO(3?2) channel maps . . . . . . . . . . . . . . . 219
C.10 DYNAMO G14-1 CO(4?3) channel maps . . . . . . . . . . . . . . . 220
C.11 DYNAMO G20-2 CO(3?2) channel maps . . . . . . . . . . . . . . . 220
C.12 DYNAMO G20-2 CO(4?3) channel maps . . . . . . . . . . . . . . . 221
C.13 SDSS J013527.10-103938.6 CO(3?2) channel maps . . . . . . . . . . 221
C.14 SDSS J013527.10-103938.6 CO(4?3) channel maps . . . . . . . . . . 222
xiv
List of Abbreviations
Acronyms:
ACS Advanced Camera for Surveys (onboard the HST)
ALMA Atacama Large Millimeter/submillimeter Array
CASA Common Astronomy Software Application
CDF Cumulative Distribution Function
DYNAMO DYnamics of Newly Assembled Massive Objects
FIFI-LS Far Infrared Field-Imaging Line Spectrometer (onboard
SOFIA)
FIR Far-Infrared
FWHM Full Width at Half Maximum
GBT Green Bank Telescope
HAWC+ High-resolution Airborne Wideband Camera Plus (on-
board SOFIA)
HIM Hot Ionized Medium
HST Hubble Space Telescope
IFU Integral Field Unit
IMF Initial Mass Function
IR Infrared
IRAC Infrared ARray Camera (onboard the Spitzer Space Tele-
scope)
ISM Interstellar Medium
JWST James Webb Space Telescope
KDE Kernel Density Estimate
LIRG Luminous Infrared Galaxy
ngVLA Next Generation Very Large Array
xv
NIRSpec Near Infrared Spectrograph
NOEMA NOrthern Extended Millimeter Array
PdBI Plateau de Bure Interferometer
PDF Probability Density Function
PHIBSS Plateau de Bure High?z Blue Sequence Survey
PI Principal Investigator
PSF Point Spread Function
SDSS Sloan Digital Sky Survey
SED Spectral Energy Distribution
SFR Star Formation Rate
SLED Spectral Line Energy Distribution
SMG Submillimeter Galaxy
SOFIA Stratospheric Observatory For Infrared Astronomy
ULIRG Ultra Luminous Infrared Galaxy
UV Ultraviolet
VLA Very Large Array
WCS World Coordinate System
WFC3 Wide Field Camera 3 (onboard the HST)
WNM Warm Neutral Medium
Atoms, Molecules, and Line Transitions:
C Carbon
[CII] Fine-structure line emission of singly ionized carbon at 158
?m
CO Carbon Monoxide
H Hydrogen
HI Neutral atomic hydrogen
HII Ionized hydrogen
H2 Molecular hydrogen
H? Spectral line in the Balmer series of hydrogen correspond-
ing to the n= 3? 2 electronic transition at 6562.8 A?
Pa? Spectral line in the Paschen series of hydrogen correspond-
ing to the n= 4? 3 electronic transition at 1.875 ?m
He Helium
O Oxygen
Symbols:
xvi
M Solar Mass equal to 1.988 ? 1030 kg
M? Stellar Mass
nH Hydrogen volume density
xvii
Chapter 1: Introduction
?The cosmos is within us. We are made of star-stuff.
We are a way for the universe to know itself.?
? Dr. Carl Sagan
Galaxies are the largest individual structures in the Universe that we can
observe. They contain planets, stars, stellar remnants, dust, interstellar gas, dark
matter, have supermassive black holes in their centers, and at least one galaxy that
we know of, the Milky Way, hosts intelligent life: us. We study galaxies, namely
their formation and evolution, to ultimately learn about the formation and evolution
of the Universe itself.
To this end, we observe galaxies across cosmic time and morphological prop-
erties, which give us snapshots at different epochs in the history of the Universe
of the characteristics of galaxies, and the physical processes that shape them, as is
illustrated in Figure 1.1 (from Schawinski et al., 2014). This figure plots the u? r
color on the y-axis and stellar mass on the x-axis. It illustrates in the top left panel
that galaxies occupy two distinct regions in this parameter space, based on their
?color? (see also Salim et al., 2007).
Late-type galaxies, or spirals, occupy the ?blue cloud? (bottom right panel
1
of Figure 1.1) and are characterized by spiral-like morphologies with blue optical
colors, higher rates of star formation, higher cold molecular gas fractions (which
is the fuel for star formation), and motions largely dominated by rotation. As a
result of existing molecular gas reservoirs, these galaxies are able to sustain star
formation, which in turn maintains the population of the short-lived (< 10 million
years), massive O and B stars, whose spectra peak in the UV, giving rise to the blue
colors of spiral galaxies. In contrast, early-type galaxies, or ellipticals1, occupy the
?red sequence? (top right panel of Figure 1.1). These galaxies present elliptical-like
morphologies and are characterized by random motions, red optical colors, low rates
of star formation, and small cold molecular gas fractions. Because these galaxies
do not have large reservoirs of cold molecular gas, their star formation winds down
and shuts off. As the lives of the last massive O and B stars in these galaxies
end, the low-mass stars whose spectra peak at longer (redder) wavelengths remain,
transitioning the colors of these galaxies from blue to red.
As star formation becomes quenched in galaxies, they progress from the blue
cloud to the red sequence through the ?green valley? (indicated by the parallel green
lines in Figure 1.1). This transition must occur rapidly, because if it were a slow
process, galaxies would spend more time in the green valley and we would observe
more of them in that region. Processes that can quench star formation in galaxies
can include a shut down of gas accretion onto disks (a process needed to replenish
gas reservoirs as star formation consumes existing ones), galaxy mergers that strip
1Late-type galaxies are what we commonly refer to today as spiral galaxies, while early-type
galaxies are often referred to as elliptical galaxies. I will preferentially use the spiral/elliptical
terminology, except where for the sake of clarity, the late-/early-type terminology makes more
sense.
2
Figure 1.1: A u ? r versus stellar mass plot from Schawinski et al. (2014), where
higher values of u?r on the y-axis indicate redder colors. This illustrates that early-
type (elliptical) galaxies and late-type (spiral) galaxies generally occupy distinct
regions in this parameter space, with some overlap in between (top left panel).
Elliptical galaxies preferentially occupy the ?red sequence? where star formation
has shut down (top right panel), while spiral galaxies preferentially occupy the
?blue cloud? where star formation is actively ongoing (bottom right panel). The
intermediate region, indicated by the set of two green lines, is dubbed the ?green
valley? and represents a region of quenching or rapid transition between the red
sequence and the blue cloud.
3
galaxies of their gas, and high energy processes such as jets from supermassive black
holes that can drive the gas out of galaxies through outflows. However, as is shown
in Figure 1.1, there are red late-type galaxies and blue early-type galaxies, indicating
that galaxies cannot be neatly separated into these two categories, and the processes
that cause galaxies to move around in this parameter space are complex.
Observations of galaxies not only reveal differences in the properties between
ellipticals and spirals, but they also show that star forming galaxies are very different
in the early Universe when compared to today?s galaxies, like our Milky Way. Figure
1.2 (from Pearson et al., 2018) plots galaxy star formation rates (SFRs) on the y-axis
and stellar mass (M?) on the x-axis. Star forming galaxies, which reside in the blue
cloud, form a fairly tight correlation in this parameter space, that is referred to as the
?main sequence (MS) of star formation? (Brinchmann et al., 2004). Most notably,
observations reveal that the main sequence of star formation evolves with redshift,
as shown by the evolution of the colored lines in Figure 1.2. Galaxies in the early
Universe had more star formation per unit mass than galaxies today, indicating that
as the Universe has aged, star formation activity has decreased. Furthermore, red
sequence galaxies lie below the main sequence of star formation at their respective
redshifts, indicating that they have less star formation per unit stellar mass. On the
other side, galaxies that lie much higher above the main sequence of star formation
at their respective redshifts are considered ?starbursts?, and have much higher star
forming activity than ?normal? main sequence galaxies.
The focus of this thesis is primarily on main sequence galaxies over a large
range of redshifts. Specifically, Chapter 2 will focus on a population of serendipi-
4
Figure 1.2: A star formation rate (SFR) versus stellar mass (M?) plot form Pearson
et al. (2018). Star forming galaxies at similar redshifts form a tight correlation in
this parameter space called the ?main sequence of star formation?. It represents
the level of star formation per unit mass present in galaxies, and shows that in the
early Universe, galaxies were forming stars at a greater rate than they are today.
tously detected galaxies that span redshifts from z ? 0.5 to z ? 5, corresponding to
? 5 ? 12 billion years ago. Chapters 3 and 4 will focus on a population of nearby
(z ? 0.1) galaxies whose properties are much more similar to the very actively star
forming galaxies that populated the Universe when it was just about 2 ? 6 billion
years old (z ? 1? 3). These galaxies lie above the MS of star formation at z ? 0.1
and fall on the MS of star formation at z ? 2, indicating they are starbursts in the
local Universe and are more similar to MS galaxies at z ? 2.
The following sections will introduce the interstellar medium and star forma-
tion and how we trace these with observations; the star formation history of the
Universe and galaxies at the epoch of peak star forming activity; and radio interfer-
ometry. Finally, I will give an overview of each chapter in this thesis.
5
1.1 The Interstellar Medium and Star Formation
The interstellar medium (ISM) of galaxies is composed of dust and hydrogen
(H) gas that exists in multiple phases, distinguished by the temperature and density
at which that gas is found. I will summarize these phases here and the typical
physical conditions that are found in each, and refer readers to Draine (2011) for
more detailed information.
The hottest phase of the ISM is the hot ionized medium (HIM); it is a dif-
fuse plasma, with proton number densities of n ? 10?3 cm?3, heated by shock-waves
from supernova explosions to temperatures of T & 105.5 K. The next hottest phase is
found around massive hot O-type stars whose ultraviolet (UV) photons photoionize
hydrogen and create HII regions. This gas has temperatures of ? 104 K and den-
sities up to nH ? 104 cm?3. The warm neutral medium (WNM) consists of atomic
hydrogen (HI) gas heated by photoelectrons from dust to temperatures of ? 103.7 K
and has densities of n ? 10?1 cm?3H . Similarly, there is a cold neutral medium
(CNM) component also consisting of atomic hydrogen, with cooler temperatures (T
? 102 K) and higher densities (nH ? 30 cm?3). The subsequent phases become cold
and dense enough for molecular hydrogen (H2) to form. Diffuse H2 regions are found
at temperatures of T ? 50 K and densities of n 2 ?3H ? 10 cm , while the densest and
coldest regions of the ISM form gravitationally bound structures of H2 called giant
molecular clouds (GMCs), where star formation occurs. The conditions in GMCs
range from T = 10? 50 K and n 3H ? 10 ? 106 cm?3.
While the ISM consists of multiple phases, it is not static; gas transitions
6
between these phases depending on the physical processes that are acting within
it, including photoionization, radiative cooling, and recombination (see e.g., Heiles
et al., 1999, for a multi-wavelength view of these phases in the Eridanus superbub-
ble). In this thesis, I will focus on the molecular phase of the ISM and how it relates
to the process of star formation.
1.1.1 Dense Molecular Gas and its Tracers
Star formation in galaxies can take place when gas in the ISM cools to suf-
ficiently low temperatures to transition to the molecular hydrogen gas phase: this
is the fuel for star formation (Leroy et al., 2008, Schruba et al., 2011). Studies
in our own Milky Way and nearby galaxies reveal that star formation specifically
takes place in GMCs (McKee and Ostriker, 2007, Kennicutt and Evans, 2012). The
outer edges of these clouds consist of mainly HI; however, H2 begins to form deeper
within a cloud (see for e.g., Figure 1(a) in Bolatto et al., 2013) and is protected from
dissociation by UV radiation through self-shielding and shielding by dust (Tielens,
2005).
We can observe phases of the ISM by detecting emission of photons from atoms
and molecules through their transitions from higher to lower electronic, vibrational,
and rotational energy states. However, molecular hydrogen, despite being the most
abundant molecule in the Universe, has no observable emission lines in the very cold
conditions found in GMCs. Molecular hydrogen is a symmetric molecule composed
of two bound hydrogen atoms. The consequence of this is that H2 has no permanent
7
dipole moment, and thus can emit no photons through dipolar rotational transitions
(Kennicutt and Evans, 2012, Bolatto et al., 2013). The lowest energy rotational
quadrupole transition of H2 has a high upper level energy of E/k ? 510 K; therefore,
it is only excited in conditions where the gas is at temperatures of T & 100 K. The
energy of the vibrational transition of H2 has an even higher upper level energy of
E/k ? 6741 K. This means that H2 is effectively invisible in emission in the very
cold and dense GMC conditions.
After hydrogen and helium (He), the most abundant atoms in the Universe are
carbon (C) and oxygen (O) at the level of ? 10?4 atoms per hydrogen nucleon (see
for e.g., Table 1.4 in Draine, 2011). Within dense molecular clouds, C and O combine
to form the next most abundant molecule: carbon monoxide, 12C16O (hereafter I
will refer to 12C16O, the most common isotopologue of carbon monoxide, as CO).
The ground rotational transition of CO (J = 1?0) at a rest frequency of 115.27 GHz
(2.6 mm) has an excitation energy of E/k ? 5.53 K, and is thus easily excited within
molecular clouds. Higher rotational transitions of CO are spaced at energy levels of
E/k ? 5.53? J (J + 1)/2 K and frequencies increasing by? 115 GHz. Therefore, the
low- and mid-J transitions of CO occur in the submillimeter wavelength regime of the
electromagnetic spectrum and are observable from the ground with instruments such
as the Very Large Array (VLA) and the Atacama Large Millimeter/submillimeter
Array (ALMA). Since CO was first observed (Wilson et al., 1970) and established
to be widespread within the inner Milky Way (Solomon et al., 1972, Wilson et al.,
1974, Burton et al., 1975), it has become the primary tracer of H2 in galaxies (Carilli
and Walter, 2013).
8
To extract the molecular gas mass in a galaxy from observations of the ground
CO transition, it is necessary to scale the integrated luminosity of the emission line
with a ?CO-to-H2? conversion factor, ?CO. The CO-to-H2 conversion factor depends
on environmental factors such as metallicity, temperature, density, and column den-
sity (Leroy et al., 2011, Feldmann et al., 2012, Genzel et al., 2012, Narayanan et al.,
2012); therefore, there is uncertainty when choosing a value to adopt. The CO-to-H2
conversion factor ranges from ?CO = 3.6? 4.3 M pc?2 (K km s?1)?1 in Milky Way
type galaxies, to ?CO = 0.6? 0.8 M pc?2 (K km s?1)?1 for starbursts (Downes and
Solomon, 1998, Papadopoulos et al., 2012).
In addition to environmental factors that may impact the value of ?CO and
introduce uncertainty in deriving molecular gas masses, the uncertainty in the CO
spectral line energy distribution (SLED) in different galaxy populations at different
redshifts also poses a challenge, where the CO SLED quantifies the excitation of
higher-J CO transitions with respect to the ground, CO(J = 1 ? 0), transition. A
difficulty with attempting to quantify the molecular gas content of high-redshift
galaxies is that the CO-to-H2 conversion factor depends upon the luminosity of the
CO(J = 1?0) transition. However, this is only observable up to redshifts of z ? 0.5
with ALMA, at redshifts of z > 2 with the VLA for the brightest sources, and is
observable for example with the Green Bank Telescope and the Effelsberg 100 m
Radio Telescope with the proper receiver bands. Therefore, to observe CO in normal
star forming galaxies across a large range in redshift, one must resort to observing
higher-J transitions of CO and then assume a line ratio between the observed line
and the ground transition.
9
In Chapter 2, I will use observations of CO(2?1) to CO(6?5) to constrain
the evolution of molecular gas content in galaxies over time, while in Chapter 4, I
will use observations of CO(3?2) and CO(4?3) to study the relation between star
formation and gas, and help constrain theories of star formation.
1.1.2 Star Formation and its Tracers
While observations of CO allow us to characterize the molecular gas reservoirs
of galaxies, it is also necessary to quantify the rate of star formation itself. There are
several tracers of star formation that can be used to determine how rapidly galaxies
are forming stars; I summarize a few of these here and refer readers to Kennicutt
(1998b) and Mo et al. (2010) for more details.
The ISM around massive, young stars is ionized by the UV photons they
produce, creating HII regions. The recombination of hydrogen nuclei and electrons
to atomic hydrogen produces a cascade of emission lines as electrons transition from
excited energy states to the ground state, including H?, H?, Pa?, Pa?, Br?, and
Br?. The flux of these emission lines is thus proportional to the ionizing flux from
the young, massive stars, and can be used as a probe of star formation activity;
i.e., because massive stars are short-lived, the amount of emission in these lines
is related to recent star formation. Specifically, because hydrogen is ionized at
an energy of 13.6 eV and only stars with M?& 10 M and lifetimes shorter than
? 20 Myr contribute significantly to the ionizing photon flux, these emission lines
are a nearly instantaneous measure of star formation. The most commonly used
10
line to measure SFRs is H?; there are, however, two caveats associated with this:
(1) dust absorption of H? flux may not necessarily be negligible; this reduces the
observed flux and underestimates the true SFR, and (2) the calibration between
H? flux and SFR depends on the initial mass function (IMF) of stars which is an
empirical description of the distribution of stellar masses in a population of stars.
Typically, there are fewer massive stars and many more lower mass stars that form in
a given population of stars. A related tracer of star formation is the UV luminosity
of a galaxy, optimally over the wavelength range 1250 ? 2500 A?. Because the UV
light from galaxies is dominated by stars with M?& 5 M, the UV luminosity can
be related to the SFR. However, using UV luminosity as a tracer of star formation
suffers from the same caveats as using H? as a tracer.
A significant fraction (35? 3%; Driver et al., 2012) of the total luminosity of
a galaxy is absorbed by dust and re-radiated in the far-infrared (FIR) regime of the
electromagnetic spectrum, because much of the star formation in the Universe takes
place in regions that are deeply embedded in dust. The absorption cross-section of
dust peaks in the UV, which means that young, massive stars are in principle the
dominant heating source of dust, and the FIR emission of a galaxy can then be used
to trace its star formation. There are of course caveats with this method as well.
The FIR emission is not only attributable to the reprocessed UV radiation of young
stars by dust around star forming regions, but also to more extended dust regions
heated by the general stellar radiation field, including radiation from older stars.
Therefore, using the FIR luminosity as a SFR tracer is ideal in starburst galaxies
which can form stars at rates of 100? 1000 M yr?1 .
11
The FIR emission of a galaxy is observed to correlate with fine-structure for-
bidden emission lines of atoms like carbon and as a result, these can also be used as
SFR tracers. For example, the singly ionized carbon fine-structure line at 158 ?m,
[CII], has an excitation energy of ? 91 K and is one of the dominant coolants of the
neutral ISM. It arises from the photodissociation regions (PDRs) of molecular gas
in massive star-forming regions, where the UV radiation of young stars is absorbed
by dust and re-radiated at longer wavelengths, giving rise to the FIR continuum,
as discussed above (though it may also arise from HII regions and neutral atomic
hydrogen gas). These same UV photons eject electrons from dust grains and poly-
cyclic aromatic hydrocarbons, which heat the gas and collisionally excite the [CII]
line, allowing the gas to cool through emission of [CII] photons. Because the excita-
tion of the [CII] is closely linked to the UV radiation field, it can also be used as a
tracer of star formation (see e.g., Herrera-Camus et al., 2015). Similarly, the [OIII]
fine-structure line at 88?m, which has an excitation temperature of T ? 163 K and
an ionization energy of ? 35 eV, originates from the vicinity of a very hard ionizing
source like HII regions hosting massive stars. Since the most massive stars spend
? 3?10 million years on the main sequence, [OIII] line emission can also be related
to recent star formation (see e.g., De Looze et al., 2014).
Finally, additional SFR tracers include emission at radio wavelengths which
correlate linearly with IR emission (Bell, 2003) and X-ray emission of galaxies orig-
inating from high-mass X-ray binaries (Mineo et al., 2012). In Chapter 4, I will use
observations of H? to measure the SFRs of nearby galaxies and study the relation
between gas and star formation.
12
1.2 Star Formation and Gas Content History of the Universe
Galaxies consume their molecular gas reservoirs through star formation, and
in doing so build up their stellar mass. Yet, to fuel ongoing star formation, gas must
be replenished. The gas content, star formation, and stellar mass of galaxies are
properties that we can quantify with observations across cosmic time. Measuring
the combination of these properties across the history of the Universe enables as-
tronomers to build an understanding of how these processes act together to produce
the galaxies that we observe today (see e.g., Walter et al., 2020).
Employing UV and IR observations in galaxies across time has enabled as-
tronomers to trace how the magnitude of star formation has evolved in galaxies; this
is the star formation history of the Universe. It is measured as the total amount
of star formation in galaxies per unit of comoving volume of the Universe, which
corresponds to a SFR volume density (M yr?1 Mpc?3 ). These observations reveal
that the process of star formation in galaxies peaked about 10 billion years ago.
Figure 1.3 shows the SFR density evolution over more than 12 billion years. We
can see that from very early times, star formation in galaxies was increasing until
it reached its peak roughly 10 billion years ago, z ? 1 ? 2, and it has since then
been steadily decreasing up until the present day (see Lilly et al., 1995, Madau et al.,
1996, Hopkins and Beacom, 2006, Madau and Dickinson, 2014, Bouwens et al., 2016,
2020, Loiacono et al., 2021). It is during this period of peak cosmic star forming
activity that roughly half of the stars in the Universe formed. There are several
fundamental physical processes that can shape this evolution: (1) if high-redshift
13
Figure 1.3: The total SFR in galaxies per unit comoving volume of the Universe as a
function of redshift (or lookback time), derived from UV and IR observations (from
Madau and Dickinson, 2014, see their Table 1 for a description of the symbols).
Star formation in galaxies peaked about 10 billion years ago (z ? 1 ? 2), and has
been steadily decreasing to the present day. Studying the neutral and molecular gas
content of galaxies over time can build our understanding of how galaxies consume
and replenish their star forming fuel, and build up their stellar mass (Walter et al.,
2020).
14
galaxies have larger reservoir of molecular gas, then this can fuel more vigorous star
formation, (2) if high-redshift galaxies convert their molecular gas into stars with a
higher efficiency, then this could also translate into a higher stellar mass build up
in the past, and (3) the growth rate of dark matter halos dropped by an order of
magnitude from z = 2 to z = 0 (Griffen et al., 2016), which can impact the ability
of galaxies to replenish their supply of gas.
The HI content in galaxies over time can be constrained by observing Ly?
absorption in the spectra of distant quasars (see e.g., Crighton et al., 2015, Neeleman
et al., 2016). These studies show the mass density of HI in galaxies from z ? 0.3?5
decreases very gradually, unlike the cosmic SFR density evolution. This indicates
that HI is a transitory phase between ionized gas accreted from the intergalactic
medium and recycled gas from galactic outflows, and the H2 that actually fuels star
formation. Beyond the local Universe, however, studies of the H2 content in galaxies
over time have been limited, and have only recently begun to emerge. Therefore, to
fully understand the evolution of the cosmic star formation history, it is imperative
to constrain the mass density of molecular gas in galaxies over cosmic time.
The very first attempts to constrain this density involved the use of galaxies
targeted and observed in carbon monoxide (CO), the most common tracer of H2 (see
?1.1.1). As part of her thesis work, Verter (1987) observed 19 galaxies in CO with
the 7 m diameter offset Cassegrain antenna of Bell Laboratories at Crawford Hill.
Combining these observations with 56 CO detections and 189 upper limits from
the literature, Verter (1987) derived average CO luminosity values and discovered a
trend of increasing number density of CO-emitting galaxies with decreasing galaxy
15
CO luminosity.
Owing to the large number of upper limits, it was not until a few years later
when surveys like the Five College Radio Astronomy Observatory (FCRAO) Ex-
tragalactic Survey (Young et al., 1995) became available, that the CO luminosity
function could be constrained (Verter, 1991, Keres et al., 2003). These studies se-
lected galaxies based on optical magnitudes or infrared (IR) fluxes and constrained
the CO(1? 0) luminosity function in the local universe (see e.g., Figure 4 in Keres
et al., 2003). While these studies mark the first important steps in addressing the
question of how molecular gas content in galaxies over time relates to the star for-
mation history of the universe, they are subject to selection biases. For example,
the correlation between IR luminosity and CO luminosity favours luminous galaxies
if they are selected based on an infrared flux cutoff (see e.g., Figure 2 in Tacconi
and Young, 1987).
More recently, galaxies detected in CO at higher redshifts were initially selected
from rest-frame far-infrared continuum surveys as sub-millimeter galaxies (Blain
et al., 2002, Casey et al., 2014). These studies have shaped our understanding of
the relation between molecular gas content and star formation in known populations
of galaxies. For example, targeted CO studies find that z ? 2 galaxies have much
larger molecular gas reservoirs than local galaxies and that the changes in growth
history are largely driven by the cold molecular gas mass properties of galaxies
(Greve et al., 2005, Daddi et al., 2010a, Genzel et al., 2010, 2015, Tacconi et al.,
2010, 2013, 2018, Freundlich et al., 2019). While these types of studies allow us
to understand the properties of galaxy samples, they are also subject to systematic
16
biases through selection effects (see for example Strandet et al., 2016).
These selection effects are the reason that studies whose goal it is to constrain
the cosmic evolution of molecular gas mass density have shifted to ?blind? CO
surveys where galaxies are selected solely on their CO luminosity. The observing
strategy is to perform spectral scans on specific deep fields, targeting rotational
transitions of CO over wide frequency and redshift ranges, and carrying out blind
searches for CO-emitting galaxies in the data. The detections are then used to
measure the CO luminosity function at different epochs in the history of the universe,
resulting in a measurement of the molecular gas mass density over the range of
redshifts sampled by the observations (Carilli and Walter, 2013). The first efforts
that have implemented this strategy (see Decarli et al., 2014, Walter et al., 2016, for
survey descriptions) provide some of the first constraints on the cosmic molecular
gas mass density evolution, and suggest that the molecular gas mass density of the
universe follows a similar pattern of evolution as the cosmic star formation density,
but are limited by the small comoving volume of space sampled and the small number
of sources detected (Walter et al., 2014, Decarli et al., 2016).
To address this, more recent studies have devoted several hundred hours of
VLA and ALMA time (Pavesi et al., 2018, Gonza?lez-Lo?pez et al., 2019) and have
made significant improvements in terms of survey size; yet the number of sources
detected (Riechers et al., 2019, Decarli et al., 2019) continues to be a large source of
uncertainty, and the time required to observe large fields (100s of hours) is expensive
for current facilities (the next generation VLA2 will be able to address this within
2See also https://public.nrao.edu/news/nsf-awards-funding-ngvla-antenna/
17
the next decade; Walter et al., 2019). To remedy this, in the first chapter of my
thesis, I explore the feasibility of using existing observations of targeted galaxies
to perform a ?blind? search for serendipitous CO sources (see also Klitsch et al.,
2019). Re-using existing data for this purpose provides an alternative way to build
up a large co-moving volume of space for exploration, as long as there is existing
ancillary data that can be used to find counterparts to CO sources and constrain
their redshifts (and hence CO transitions). The second Plateau de Bure High-z Blue
Sequence Survey (PHIBSS2; Freundlich et al., 2019) data set is very well suited to
this purpose.
Finally, galaxies in the era of peak mass assembly are characterized by massive
(107 ? 109 M), kpc-sized, star forming clumps (Genzel et al., 2008, 2011, Fo?rster
Schreiber et al., 2011, Tacconi et al., 2013, Guo et al., 2012, 2015, Huertas-Company
et al., 2020). This mode of star formation is very different from what is observed
in the local Universe. Therefore, to understand star formation in the time when
a significant fraction of stars in the Universe formed, we need to understand star
formation at the peak of cosmic star forming activity. Studies of high-redshift,
lensed, clumpy systems (Livermore et al., 2015) and nearby analogues (Fisher et al.,
2017b) reveal that the physical size of clumps may be smaller than originally inferred
from high-redshift observations, and that this is a result of limitations in angular
resolution which cause multiple smaller clumps to blend and appear as one massive
clump. The size and mass of clumps are important parameters, because these relate
to their ability to withstand stellar feedback and remain intact, and determine their
lifetime. Hydrodynamic simulation studies are actively seeking to characterize the
18
properties of star forming clumps (see e.g., Oklopc?ic? et al., 2017, Buck et al., 2017,
Dekel et al., 2021, Ginzburg et al., 2021); however, observations are ultimately
required to place constraints on the real observed properties of clumps. For this
reason, in Chapters 3 and 4, I turn my attention to a sample of nearby galaxies
drawn from the DYnamics of Newly Assembled Massive Objects (DYNAMO; Green
et al., 2014). These are clumpy, gas-rich systems that are much more similar to
clumpy high-redshift galaxies than they are to local ones. The benefit of using them
as proxies to understanding high-redshift galaxies is that we can obtain much higher
resolution observations that can probe their properties on the scale of individual
clumps.
1.3 Radio Interferometry and Synthesis Imaging
The angular resolution (?) of a telescope determines the smallest sized object
on the sky that the telescope can resolve. This depends on the wavelength of the
observed light (?), and the diameter of the telescope light collecting area (D) through
the relation: ? ? ?/D. This means that in order for a telescope operating at long
wavelengths to have the same angular resolution as a telescope operating at short
wavelengths, a bigger telescope is required. To illustrate, a 100 m diameter telescope
observing at 7 mm will have an angular resolution of ? 17?? (where 1 arcsecond is
equal to 1?/3600 Thompson et al., 2017). In contrast, the Hubble Space Telescope
(HST) observations I present in Chapters 3 and 4 have angular resolution of ? 0.1??.
The largest radio telescopes, the Five-hundred-meter Aperture Spherical Tele-
19
scope (FAST) in China and the now decommissioned Arecibo Telescope (305 m)
in Puerto Rico, are placed within natural depressions in the landscapes, and are
thus unable to observe portions of the sky. The Effelsberg 100 m diameter radio
telescope, and Green Bank Telescope in West Virginia with a 100 m diameter (the
largest steerable radio telescope), are still not enough to reach the sub-arcsecond
resolution of telescopes like the HST. To achieve better angular resolution at long
wavelengths, it is necessary to employ a different approach. Interferometry is one
such approach and will be discussed in the remainder of this section (see Condon
and Ransom, 2016, Thompson et al., 2017, for more detailed discussions).
1.3.1 Interferometry Basics
The simplest radio interferometer consists of two antennas separated by some
baseline distance, B, as illustrated in Figure 1.4. In this illustration, two antennas
(i and j) are separated by a distance B~ ij. A plane parallel wavefront (an electric
field with some amplitude and phase) from a distant point source in the direction
d~ reaches the antenna on the right first, then after a geometric time delay of ?ij =
B~ ij ?d~/c, the wavefront reaches the second antenna. We can write the time dependent
voltage output of each antenna as:
Vi = V ? cos(2??(t + ?ij)) and Vj = V ? cos(2??t) (1.1)
for the left and right antennas respectively, where V is an amplitude and ? is the
observing frequency. If we assume that the interferometer operates over a very
20
narrow range of frequencies, then the voltage output of each antenna has the same
amplitude, and they are only offset in phase by ?ij. The correlator multiplies the
two voltages, Vi and Vj, and after integrating (time averaging) it outputs a response,
Rc:
V 2
Rc = ? cos(2???ij). (1.2)
2
The interferometer, therefore, produces an interference pattern, called fringes, which
depends only on the power received (P = V 2/2), the time delay (therefore the
baseline orientation and source direction), and the observing frequency.
Because the geometric time delay depends on the separation between the two
antennas, the fringe spacing then also depends on this distance; moving the antennas
farther apart moves the fringes closer, and vice versa. However, for an extended
source, the antenna is unable to see the components of the source that fall between
the fringes. This can be addressed by the use of a complex correlator, which consists
of two correlators 90? out of phase, so that one produces a cosine fringe pattern,
and the other a sine fringe pattern. The second correlator in this case produces a
response like equation 1.2, but with a sine function:
V 2
Rs = ? sin(2???ij). (1.3)
2
The response of the complex correlator is then the combination of these two
responses:
21
Figure 1.4: Illustration of a two element interferometer, separated by a baseline
distance D, observing a source in the direction ?. The source is assumed to be
distant enough that the incident wavefront can be assumed to be a plane. Thus,
the incident wave reaches the antenna on the right before it reaches the one on the
left; this introduces a geometric time delay. The signal from each antenna is then
amplified, a instrumental time lag equal to the geometric time lag is introduced in
the signal from the right antenna, then the signals of both antennas are multiplied
and time-averaged by the correlator (adopted from Figure 1 in Mahmoud et al.,
2011).
22
V = Rc ?
~ ~
iRs = Ae
?i2???ij = Ae?i2?(Bij ? d/?) (1.4)
where in the final equality, we replace the geometric time delay with its dependence
on the baseline and source direction vectors, and replace ?/c with 1/? to define
the baseline in units of wavelength. We can define a coordinate system (u,v,w)
to describe the baseline vector in units of wavelength, where u is the component
of B~ ij/? along the east-west direction, v is its component along the north-south
direction, and w is the vertical (up-down) component. Similarly, we can define the
source direction vector, d~, in (l, m) coordinates where l is the east-west direction
cosing and m is the north-south direction cosine on the sky. If we assume that w
is parallel to d~, then we can expand the dot product in equation 1.4 and integrate
over the whole source on the sky to obtain:
? ?
V (u, v) = P (l,m) I(l,m) e?i2?(ul+vm) dl dm (1.5)
where P (l,m) is a function that describes the ?primary beam? of the telescope,
I(l,m) is the source brightness distribution on the sky, and V (u, v) is the response
of the complex correlator, called the ?visibility?. The primary beam for an array of
antennas of equal diameter, D, observing at a wavelength ?, is equal to a Gaussian
function with a full width at half maximum of ? ?/D. The sky is always seen
through the filter of the telescope primary beam; therefore P (l,m) I(l,m) is the
source brightness perceived by the telescope. We can recognize the expression in
equation 1.5 as a Fourier Transform of the sky, which means that to obtain the
23
source intensity, I(l,m), we can perform an inverse Fourier Transform:
? ?
A(l,m) I(l,m) = V (u, v) e?i2?(ul+vm) du dv. (1.6)
However, a single baseline defines only one point in the uv?plane, and thus
measures the source on a spatial scale and direction determined by the antenna
separation ? the telescope cannot ?see? any emission from the source on other scales.
Therefore, to properly observe a source that has emission on multiple scales, like
a galaxy, we need to sample many more points in the uv?plane. This is done
by increasing the number of antenna pairs. For N number of antennas, there will
be N(N ? 1)/2 antenna pairs, and therefore N(N ? 1) baselines, each of which
corresponds to an additional point in the uv?plane. Each pair of antennas will
produce a different fringe spacing and direction, depending on the length of the
baseline distance and orientation relative to the source. This fills in the sampling
of the source in the Fourier domain and allows for better recovery. By observing
for longer periods of time, we can also take advantage of the Earth?s rotation. As
the Earth rotates, the orientation of each baseline with respect to the sky changes,
which further fills in the uv?plane. This is illustrated in Figure 1.5, which shows
the sampling of the uv?plane by the Atacama Large Millimeter/sub-millimeter
Array (ALMA), which has 66 antennas, after observing a source at a declination of
? = ?23? for one minute (left panel) and one hour (right panel).
Because the visibilities measured by an interferometer are related to the source
intensity via a Fourier Transform, an interferometer is essentially a spatial filter,
24
Figure 1.5: An example of the uv? plane sampling for a model ALMA observation
of a source at declination ? = ?23? after one minute of observing (left panel) and
one hour of observing (right panel). The Earth rotates over the course of the longer
observation, and thus each point in the uv?plane ?stretches out? as the orientation
of each baseline changes with respect to the sky. However, the hole at (u, v) = 0 can
never be filled because the spacing between antennas can never be zero. (adopted
from Figure 7.10 in the ALMA Technical Handbook).
where the filtering is set by the separation between antenna pairs. The smallest
angular scale at which an interferometer can detect emission is determined by the
largest antenna separation, while the largest scale emission is determined by the
smallest antenna separation. This means that because the separation between an-
tennas can never be zero, an interferometer cannot measure the total flux of a source,
and the measured source flux will always be less than the true source flux. This
also means that the angular resolution (?) of an interferometer is set by the largest
distance between any two antennas: ? ? ?/B, where ? is the observing wavelength
and B is the length of the longest baseline. Interferometry allows us to ?synthesize?
a telescope whose aperture diameter is the longest baseline, baselines much longer
than would be possible in a single aperture. This is the strength of interferometry,
and what allows astronomers to study objects in the Universe at sub-millimeter and
radio wavelengths in incredible detail.
25
1.3.2 Deconvolution
As with any telescope, the image obtained is a convolution of the true source
brightness distribution (enveloped by the primary beam for an interferometer) and
the point spread function (PSF; the Fourier Transform of the interferometer?s mea-
surements in the uv?plane), or ?dirty beam?, and is often called the ?dirty map?.
We can, therefore, modify equation 1.6 to reflect this:
? ?
P (l,m) I(l,m) ~G(l,m) = g(u, v)V (u, v) e?i2?(ul+vm) du dv. (1.7)
where G(l,m) is the dirty beam, which for an interferometer is determined by the
Fourier Transform of the uv?plane sampling by the antenna array, and g(u, v) is the
weighting function of the sampled uv?plane points (e.g., natural, uniform, Briggs
weighting). As a result of this convolution, the dirty map will have the pattern
of the dirty beam imprinted in it. This can make interpretation of the dirty map
difficult, because the dirty beam causes flux from the source to be distributed in
?sidelobes? and other artefacts that do not represent real structure. It is, therefore,
desirable to remove the dirty beam pattern from the image or to deconvolve it from
the image.
There are several deconvolution procedures; however, the CLEAN method
forms the basis of many deconvolution algorithms that are used in radio interferom-
etry today. The Ho?gbom CLEAN, which I will use in Chapter 4, assumes that the
26
sky brightness distribution can be modeled by a collection of point sources, and it
operates in the image domain (the Fourier Transform of the visibilities). Figure 1.6
illustrates the basic idea for a one-dimensional case3. Panels A and B of Figure 1.6
show the dirty map and dirty beam, respectively, of this mock observation, where
the oscillations beyond the main lobe of the dirty beam are visible in the dirty map
as well.
The algorithm operates iteratively where in each step it: (1) finds the peak
amplitude in the dirty map and stores that as a ?clean component? (panel E), (2)
it then scales the dirty beam by a ?loopgain? factor ?  1, (3) it shifts the scaled
beam to the position of peak amplitude in the dirty map (panel C), (4) the scaled
and shifted dirty beam is then subtracted from the entire dirty map which produces
the residual map (panel H), (5) steps (1)?(4) are then repeated until a specified
threshold is reached; this can be when the root-mean-square (rms) of the residual
map reaches some level (panel D), or until a defined limit on the number of iterations
is reached, (6) finally once the threshold is reached, the procedure convolves the clean
components with the clean beam (panel F) to produce a ?clean signal? (panel G),
and adds the final residuals to this clean signal to produce the final ?clean map?
(panel I). We can see that the final clean map recovers the two signals that we see
in the original dirty map, but the pattern of the dirty beam has been removed.
The clean beam in step (6) is a Gaussian function fit to the main lobe of the
dirty beam. For two-dimensional maps, this will generally be an elliptical Gaussian.
3This is thanks to Andy Harris? instrumentation class where we had to write code to do this
for an assignment!
27
Figure 1.6: A one-dimensional illustration of the Ho?gbom CLEAN algorithm with
a loopgain ? = 0.1, after 50 iterations. In each iteration, the algorithm subtracts
a scaled down version of the dirty beam (panel B) from the dirty map (panel A)
at the location of the peak amplitude (panel C) in the dirty map. This subtracted
map is the residual (panel H) and the peak is saved as a ?clean component? (panel
E). This process continues until a threshold is reached: for example when the root-
mean-square of the residual map reaches a specified threshold (panel D). Once the
threshold is reached, the clean components are convolved with the clean beam (panel
F) to produce the clean signal (panel G). Adding the residuals to the clean signal
produces the final clean map (panel I).
28
The beam size is defined by the major (?maj) and minor (?min) axes of the ellipse
at the FWHM of the Gaussian, and its area (?) is defined by:
?maj ?min
? = . (1.8)
4 ln 2
In reality, programs such as the Common Astronomy Software Application
(casa; McMullin et al., 2007) employ a major/minor cycle approach to deconvolu-
tion where the minor cycles perform multiple iterations of CLEAN in the image
domain, and the major cycles subtract the model image from the visibilities in the
uv?domain to produce a new residual map. Beside the Ho?gbom algorithm, there
are additional versions of CLEAN such as the Clark CLEAN (Clark, 1980) and
the Cornwell-Holdaway Multi-Scale CLEAN (Cornwell, 2008). Besides CLEAN,
there are additional deconvolution methods such as the Maximum Entropy method
(Cornwell and Evans, 1985, Narayan and Nityananda, 1986) and Adaptive Scale
Pixel method (Bhatnagar and Cornwell, 2004).
Regardless of the deconvolution procedure adopted, the final data products
from an interferometer are three-dimensional ?data cubes?, where the x and y di-
rections are the spatial dimensions corresponding to the position on the sky, and the
z direction is the spectral dimension, where every ?channel? is a measurement of the
sky at a particular frequency (or equivalently a particular wavelength or velocity).
As a result, every pixel in a data cube (referred to as a ?voxel?) contains a spectrum
of the source at a particular (x, y) location. These are the data products that I will
use in Chapters 2 and 4.
29
1.4 Thesis Overview
This thesis consists of multi-wavelength studies, spanning from the UV/optical
to the sub-millimeter, that characterize the gas content of galaxies across cosmic
time, and links the gas content of nearby, high-redshift analogue galaxies to their
star formation.
In Chapter 2, I explore and test the feasibility of using existing large survey
data to constrain the molecular gas content in galaxies over cosmic time. PHIBSS2
observed ? 100 galaxies in CO at the peak of cosmic star forming activity. Addi-
tional ?sources? were noted in several resulting data cubes. Therefore, I devised a
systematic approach to detect these serendipitous sources, identify potential coun-
terparts and constrain their redshifts, and characterize their properties, including
the reliability of each detection. With a final catalog of sources, I constructed CO
luminosity functions and derived the evolution of the molecular gas mass density
of galaxies up to redshifts of ? 5. These results probe a comoving volume of space
larger than any previous survey dedicated to this evolution, and found that the
results obtained in this way are consistent with existing measurements.
In Chapter 3, I use HST observations of star forming clumps in DYNAMO
galaxies to constrain their lifetimes. Hydrodynamic simulations of star formation
in clumpy galaxies at z ? 1 ? 3 are very sensitive to the feedback prescription
implementations, resulting in clumps that are disrupted on very short timescales and
have no impact on the evolution of these galaxies, to clumps that remain bound for
timescales & 100 Myr and are able to migrate and coalesce at the centers of galaxies,
30
thus contributing to the growth of bulges. I conclude that clumps in DYNAMO
galaxies have colours most consistent with age spreads predicted by simulations of
long-lived clump scenarios, which challenges the predictions that clumps disrupt on
very short timescales.
In Chapter 4, I combine HST and ALMA observations to measure the SFR
and molecular gas mass surface densities, and velocity dispersions of DYNAMO
galaxies on ? 1?2 kpc scales to test theories of star formation. I find that through-
out their disks, DYNAMO galaxies have velocity dispersions, gas and SFR surface
densities comparable to the centers of nearby galaxies. This suggests that large-
scale turbulent mechanisms, such as gas accretions and inflows, may be responsible
for the higher velocity dispersions and higher gas densities in DYNAMO galaxies.
In addition, I find that current theoretical models relating velocity dispersion to
gas and SFR surface densities are unable to predict the velocity dispersions in our
DYNAMO sample due to the inclusion of the angular velocity as a representation
that turbulence dissipates on eddy timescales. This suggests that an alternative
timescales for turbulent dissipation for galaxies in our sample is required to explain
our observations.
Finally, I summarize a few upcoming and planned research directions that
build upon this thesis and that I will pursue as a post-doctoral researcher at NASA
Ames, in Chapter 5.
31
Chapter 2: Cosmic Evolution of Molecular Hydrogen Gas Mass Den-
sity
2.1 Overview
We report on the results of a search for serendipitous sources in CO emission
in 110 cubes targeting CO (2? 1), CO (3? 2), and CO (6? 5) at z ? 1? 2 from the
second Plateau de Bure High-z Blue-Sequence Survey (PHIBSS2). The PHIBSS2
observations were part of a 4-year legacy program at the IRAM Plateau de Bure
Interferometer aimed at studying early galaxy evolution from the perspective of
molecular gas reservoirs. We present a catalog of 67 candidate secondary sources
from this search, with 45 out of the 110 data cubes showing sources in addition to the
primary target that appear to be field detections, unrelated to the central sources.
This catalog includes the redshifts, line widths, fluxes, as well as an estimation of
their reliability based on their false positive probability. We perform a search in
the 3D-HST/CANDELS catalogs for the secondary CO detections and tentatively
find that ? 64% of these have optical counterparts, which we use to constrain their
redshifts. Finally, we use our catalog of candidate CO detections to derive the
CO (2? 1), CO (3? 2), CO (4? 3), CO (5? 4), and CO (6? 5) luminosity functions
32
over a range of redshifts, as well as the molecular gas mass density evolution. Despite
the different methodology, these results are in very good agreement with previous
observational constraints derived from blind searches in deep fields. They provide
an example of the type of ?deep field? science that can be carried out with targeted
observations.
2.2 Introduction
Detailed measurements of the star formation history of the universe reveal
that the process of galaxy assembly peaked about 10 billion years ago. The star
formation rate (SFR) density in galaxies (i.e., total SFR in galaxies in a comoving
volume of the universe) across cosmic time is observed to gradually increase to
redshifts of z & 2, peak at z ? 1 ? 2, and then decrease from redshifts of z ? 1 to
the present day by almost an order of magnitude (see e.g., Madau and Dickinson,
2014). The fundamental physical processes that shape this evolution, however, are
still uncertain. This evolution may be driven by the availability of larger reservoirs of
cold dense molecular gas (the immediate fuel for star formation) in high-z galaxies,
by higher efficiencies for converting molecular gas into stars, or by a combination of
both. Therefore, it is interesting to constrain the molecular gas content of galaxies
over cosmic time (measured as total gas mass per co-moving volume) in order to
understand the evolution of the cosmic star formation history.
Most studies of the cold molecular gas in galaxies have used CO observations,
the most common molecular gas mass tracer (Bolatto et al., 2013), of galaxies that
33
were pre-selected based on optical or near-infrared surveys. Other galaxies detected
in CO at higher redshifts were initially selected from rest-frame far-infrared con-
tinuum surveys as sub-mm galaxies (Blain et al., 2002, Casey et al., 2014). These
studies have shaped our understanding of the relation between molecular gas content
and star formation in known populations of galaxies. Targeted CO studies find that
z ? 2 galaxies have much larger molecular gas reservoirs than local galaxies (Greve
et al., 2005, Daddi et al., 2010a, Genzel et al., 2010, 2015, Tacconi et al., 2010, 2013,
2018, Freundlich et al., 2019) and that the changes in growth history are largely
driven by the cold molecular gas mass properties of galaxies. While these types of
studies allow us to understand the properties of galaxy samples, they can poten-
tially introduce unknown systematic biases through selection effects. It is therefore
beneficial to complement them with blind searches for CO-emitting galaxies.
Spectral scans on specific deep fields have been used to carry out blind searches
targeting rotational transitions of CO over wide frequency and redshift ranges, mea-
suring the CO luminosity function at different epochs in the history of the universe.
The CO luminosity function so obtained gives a measurement of the molecular gas
mass density over the range of redshifts sampled by the observations (Carilli and
Walter, 2013). Initial efforts that have followed this strategy are the IRAM Plateau
de Bure Interferometer (PdBI) observations in the Hubble Deep Field North, and the
Atacama Large Millimeter Array (ALMA) observations in the Hubble Ultra Deep
Field (the ASPECS-Pilot program). These spectral scans were conducted at 3 mm
and 1 mm wavelengths, covering areas of ? 0.5 and ? 1 arcmin2 in size, respec-
tively (see Decarli et al., 2014, Walter et al., 2016, for survey descriptions). Walter
34
et al. (2014) and Decarli et al. (2016) present luminosity function measurements
for CO (3 ? 2) and higher-J transitions at z ? 2 ? 3, and CO (5 ? 4) and higher-J
transitions at z ? 5? 7. These studies provided some of the first constraints on the
cosmological CO luminosity function, and the cosmic molecular gas mass density
evolution, but they are limited by the small areas covered.
More recently, the COLDz project (> 300 hours of observations on the JVLA)
covered a ? 48 armin2 area in GOODS-N and a ? 8 arcmin2 area in COSMOS in
the 30?38 GHz frequency range, targeting CO (1?0) at z ? 2?2.8 and CO (2?1)
at z ? 4.9 ? 6.7 (Pavesi et al., 2018). This survey provides constraints for the CO
luminosity function at z > 2 (Riechers et al., 2019). The ASPECS Large Program
(LP; 150 hours of observations on ALMA) covers most of the Hubble eXtremely
Deep Field (? 4.6 arcmin2) at 3 mm and 1.2 mm wavelengths (Gonza?lez-Lo?pez
et al., 2019). Decarli et al. (2019) use it to measure the CO luminosity function and
find that the cosmic molecular gas mass density peaks at z ? 1.5 and decreases by
a factor of ? 6.5+1.8?1.4 to the present day.
In this paper, we present CO luminosity function and cosmic molecular gas
mass density evolution measurements we make from repurposed data which takes
advantage of independent deep observations of targeted galaxies. Specifically, we
present the results from a ?blind? CO search in the second Plateau de Bure High-z
Blue-Sequence Survey (PHIBSS2) observations, the follow up to PHIBSS. PHIBSS
and PHIBSS2 have been productive surveys with key results on their main objec-
tive, characterizing normal z ? 1 ? 2 galaxies. Among other results, PHIBSS and
PHIBSS2 have yielded scaling relations for main sequence galaxies at those red-
35
shifts, depletion times and molecular fractions (Genzel et al., 2015, Tacconi et al.,
2018), and characterized molecular reservoirs for z < 1 galaxies (Freundlich et al.,
2019). However, these observations also have the potential to yield impactful ?deep
field? science. Since each PHIBSS2 observation targeted a galaxy selected from the
3D-HST CANDELS fields, characterization of serendipitous detections benefits from
the extensive multi-wavelength coverage available in these legacy fields.
This paper is structured as follows: Section 2.3 summarizes the observa-
tions used, Section 2.4 describes the blind search algorithm, the optical counterpart
search, and our statistical methods for assessing the likelihood that each candidate
is real as well as the completeness of the search algorithm. Section 2.5 presents the
results of the line search, the CO luminosity functions we derive, and the molecu-
lar gas mass density evolution constraints. Sections 2.6 compares to previous works
and Section 2.7 summarizes the work done. The properties of the candidate sources,
their spectra, and optical counterparts are presented in the Appendices.
Throughout the paper, we assume ?CDM cosmology withH0 = 70 km s
?1 Mpc?1,
?m = 0.3, and ?? = 0.7, consistent with the Wilkinson Microwave Anisotropy Probe
measurements (Komatsu et al., 2011).
2.3 Observations
2.3.1 The ?Plateau de Bure High-z Blue-Sequence Survey? (PHIBSS)
The PHIBSS2 survey is an IRAM Plateau de Bure Interferometer (PdbI; Guil-
loteau et al., 1992) 4-year legacy program aimed at studying early galaxy evolution
36
from the perspective of molecular gas reservoirs, while exploiting the capabilities of
the NOrthern Extended Millimeter Array (NOEMA; Schuster, 2014) as they came
online. Observations of 12CO (2?1), 12CO (3?2), and 12CO (6?5) transitions took
place between October 2013 and June 2017. Observation times per target range
from 0.6 to 30.3 hours, with a total of ? 1, 100 hours of 6-antenna equivalent on
source integration time, and were mostly taken in C configuration to ensure that
the galaxies are not spatially resolved (see Freundlich et al., 2019, for more details
on the data reduction process). Given the integration times and configurations, the
synthesized beams range from 1?? to 5??. At the redshifts targeted by PHIBSS, the
typical scales are 6? 8.5 kpc per arcsec.
The survey consists of 110 individual observations of main sequence galaxies,
exploring the CO (2? 1), CO (3? 2), and CO (6? 5) line emission, covering a total
area of ? 130 arcmin2 and sampling a total co-moving volume of ? 200000 Mpc3
(see Table 2.1).
2.3.2 Ancillary Data
We use the 3D-HST/CANDELS survey catalogs (Brammer et al., 2012, Skel-
ton et al., 2014, Momcheva et al., 2016) for the COSMOS, GOODS-N, and EGS/AEGIS
fields to search for optical counterparts. We present cutouts from the HST Advanced
Camera for Surveys (ACS) for filter F814W for each field (where possible) corre-
sponding to the PHIBSS2 observations in Appendix B (see ?2.5.1.1). For targets
lying outside the area covered by the HST ACS optical or WFC3 near-IR mosaics,
37
we show cutouts of Spitzer IRAC 3.6 ?m images.
2.4 Methods
2.4.1 Line Search
The goal of the line search is to systematically select candidate sources from
noisy data, and assess their significance in terms of their corresponding signal-to-
noise ratio (SNR). For our sample of observations, we expect sources to be unresolved
and to mostly have FWHM in the range of ? 50? 500 km s?1, and at most ? 1000
km s?1. Rubin et al. (1985) shows massive galaxies have maximum rotation velocities
that span from ? 100 ? 400 km s?1, while small irregular galaxies have minimum
rotation speeds of ? 50 ? 100 km s?1, and Carilli and Walter (2013) show that
hyper-starburst quasar hosts and sub-millimeter galaxies can have line widths up to
? 1000 km s?1.
Our line search method is a 1D matched filter technique where we select a
Hanning kernel as our template. We Hanning-smooth and decimate each observation
five times, where each iteration of the smoothing increases the width of a channel
by a factor of two while removing one every two channels (that is, decimating the
highly correlated channels). This creates cubes with velocity resolutions spanning
from ? 7 to ? 1000 km s?1, depending on the observation (the original data cubes
have channel widths ranging from 7 to 88 km s?1). The purpose of this matching is
to maximize the signal-to-noise for signals of a given line-width. Hence our choice
of smoothing allows us to attempt to match the velocity resolution of the data
38
cube with that of the potential sources in the data. Each data cube generates
five additional smoothed cubes corresponding to the different velocity resolution
templates.
Figure 2.1: RMS as a function of channel number (both normalized to unity),
showing a typical best case scenario (red line) where the RMS is approximately
flat across all channels, a typical worst case scenario (black line) where the RMS
varies quite significantly across the channels, and a median case (beige line). This
illustrates the need to properly model the RMS variations across the passband in
order to correctly estimate the SNR of every pixel. We do this by modeling the
RMS variations as a function of frequency with a seventh order polynomial for each
data cube.
For each of these cubes (original and smoothed), we compute a significance
(SNR) map by taking the peak value at each pixel along the spectral axis and
39
dividing it by the RMS (taken to be the standard deviation) of the spectral channel.
The RMS as a function of channel number (frequency) is usually fairly flat, but
occasionally it can vary quite substantially across the passband. We illustrate this in
Figure 2.1, where we show three examples of how the noise varies across channels in
three different data cubes. For the purpose of comparing the RMS channel variations
in different data cubes, we normalize the axes. The channel RMS values vary from
one data cube to another, therefore we normalize the y-axis to 1 ? 10?3. The
number of channels in the three data cubes that we compare here also varies, thus
we also normalize the x-axis to unity (the bandwidth is about 3 GHz). We plot
a typical best case scenario in red, a typical worst case scenario in black, and a
median example in beige, while the dashed blue line serves as a reference point for
a straight horizontal line. It is therefore important to properly account for this
when calculating the SNR in order to not over or underestimate the SNR of a given
pixel. To characterize this variation, we fit the distribution of the channel RMS
as a function of channel number for each data cube with a polynomial, in order to
have a smooth representation of the large-scale noise variation to properly calculate
SNR. We then divide each peak pixel by the corresponding channel RMS from our
fit. The order of the polynomial chosen to obtain our smooth representation of the
noise is not particularly important, and a value of seven was found to produce very
reasonable results.
In order to obtain the distribution of the noise, we repeat this process for
the negative peaks, that is dividing the largest negative peak at each pixel by the
channel RMS, thus creating SNR maps of ?negative emission?. Positive emission
40
corresponds to real astrophysical sources as well as noise peaks, while ?negative
emission? corresponds only to noise. The most significant negative peak therefore
provides an estimate of what is the boundary between likely noise and likely signal.
From these SNR maps, we build a list of candidate sources by selecting pixels with
a positive SNR value that is greater than the absolute value of the largest negative
peak SNR. We save a list of all pixels that satisfy this condition, sort it by decreasing
SNR, and filter out all pixels that lie within one beam of the highest SNR pixels to
arrive at a list of independent possible sources. We perform this search and filtering
on all smoothed cubes and then combine the lists into one list, where we filter out
candidate sources that satisfy our detection threshold in multiple cubes for a given
field (original and/or smoothed cubes), but with lower SNR. This leaves us with
a final list of candidate sources for each field in our sample, where the position of
each source corresponds to the position of the most significant pixel for the velocity
smoothing parameter that provides the highest SNR. Figure 2.2 shows an example
SNR map for one of our fields (eg016; see Table A.1) at a velocity resolution of
352 km s?1, with the black contour showing the threshold of the most significant
negative peak in that cube, our chosen boundary between ?likely noise? and ?likely
signal?. In what follows we estimate the probability of this candidate source being
real.
41
Figure 2.2: Hanning-smoothed SNR map for the eg016 data cube, at a velocity
resolution of 352 km s?1. The black contour corresponds to the SNR level of the
largest negative peak in this cube, which is our detection threshold and in this case
corresponds to a SNR of 4.93. A single source appears in this map with SNR above
the detection threshold we impose (see eg016-1 in Table A.1 for physical properties).
The central targeted source in the eg016 data cube has a SNR of 3.1 (see Table 3
in Freundlich et al., 2019), which is below our detection threshold and is therefore
not visible in this SNR map.
42
2.4.1.1 False Positives
The purpose of the false positive analysis is to assign to each candidate source
a probability of it being a real astrophysical source, which we will call reliability
(also called fidelity or purity). To address this question, we use the statistics of
the negative emission, which consists of only noise, to determine the likelihood that
noise could produce a SNR as large as that of each candidate source.
In order to estimate this we would ideally consider the statistics of independent
points in the map. In our significance maps, in principle all pixels within one beam
of a strong emission pixel will be correlated. To remove from our distribution of
peak SNR values pixels that are correlated, we perform a ?cleaning? of the map. We
do that by taking the most significant value in a given map, subtracting a beam-like
Gaussian from that pixel position, and then repeating the process until no values
above 3? the RMS level of the map remain, leaving us with a list of independent
?sources? in terms of SNR. As a comparison, we do the same thing with the SNR
map distribution of positive peaks.
The distributions of independent positive and negative peaks in a given map
overlap very well, and are well approximated by a Gaussian with an exponential
tail toward high significance (Figure 2.3). However, the tail of the distribution
is the region that we are interested in characterizing because this is where the
candidate sources we detect lie. To achieve this goal, we begin by normalizing
the distribution of independent positive and negative peaks so that their integrals
equal unity. We then treat the normalized independent negative distribution as our
43
probability density function, which we fit with an exponentially modified Gaussian
distribution of the form:
( )
? ? (2?+??2?2x) ?+ ??
2 ? x
h(x) = e 2 erfc ? (2.1)
2 2?
where x corresponds to the peak SNR values of the inverted cube, ? and ? are the
mean and standard deviation of the Gaussian, ? is the rate of the exponential, and
erfc is the complementary error function which is equal to 1?erf(x). This function
describes a Gaussian distribution with a positive skew due to an exponential com-
ponent. An example of this fit is shown in Figure 2.3, where the orange histogram
corresponds to the SNR distribution of the negative emission, the blue histogram is
the SNR distribution of the positive emission, and the black line is the exponentially
modified Gaussian; the bottom panel shows the residuals. Figure 2.3 corresponds to
the data cube eg016 (Table A.1), where one candidate source is identified as possi-
ble emission through the line search procedure described above. While the y-axis in
Figure 2.3 is plotted on a log-scale, the fitting procedure is done in linear space. As
such the resulting parameters are not sensitive to the high-SNR ?outliers?. There-
fore the reliability parameters we derive from this method are robust with respect
to the inclusion or exclusion of these data points.
To estimate the probability that the observed significance could be produced by
noise fluctuations, we use the cumulative distribution of the exponentially modified
Gaussian distribution, which has the form:
44
Figure 2.3: The top panel shows the distribution of positive (blue) and negative
(orange) peak SNRs per beam of the eg016 data cube, at a velocity resolution of
352 km s?1 (the gray histogram is the overlap of the blue and orange histograms).
The black line is the exponentially modified Gaussian fit to the negative peaks
distribution. We see one object with positive peak SNR much greater than the
largest negative peak SNR (in absolute values); this corresponds to the candidate
sources. The bottom panel shows the residuals from fitting with an exponentially
modified Gaussian function, which we find represents that data reasonably well.
H(x) = ?(u, 0, ?)? e?u+v2/2+log(?(u,v2,v)) (2.2)
where u = ?(x ? ?) and v = ??, and ?(x, ?, ?) is the cumulative distribution
function of a Gaussian distribution with mean ? and standard deviation ?.
For a given candidate source, the probability that a random fluctuation pro-
duces a source with SNR greater than or equal to that of the candidate source, (i.e.,
45
falls in the range x ? [SNRsrc, ?)), is:
P(x > SNRsrc) = 1?H(SNRsrc). (2.3)
For each candidate source, this gives an estimate of the probability that a given
independent measurement (a beam) in the map could have a peak SNR greater than
or equal to that of the candidate source itself. To assess the significance of these
values, we compare them to the number of independent beams sampled by each SNR
map. We do this by taking the inverse of the false positive probability we calculate
from equation 2.3 as a measure of how many random measurements it would take
to observe the given candidate source SNR value once (i.e., one in every N number
of measurements will have an SNR equal to or greater than what is observed for the
candidate source given only noise; we call this Nexpected). Then the ratio of Nexpected
to the number of independent beams sampled (Nbeams) by each SNR map is the total
number of measurements with a given SNR we would expect to make due to noise
only. As an example, if we measure a probability of 10?3 for a candidate source of
some SNR, but then find that we sample 1000 beams in that map, then we would
expect to find one such ?source? in our map from just noise, so this candidate source
would be considered unreliable. For very strong candidate sources this number is
very small, and for weaker sources it becomes larger and can become on the order
of unity. The reliability parameter (R) we assign to each source is one minus this
ratio:
46
? NexpectedR = 1 (2.4)
Nbeams
Our reliability measurements range from 0.01?1 (i.e., 1?100% reliability), and
we include in our sample candidate sources with R > 5% since this is the threshold
adopted by Riechers et al. (2019). We show these values in Table A.1. Note that we
do not attempt to further filter our list of candidate sources by choosing a higher
reliability cutoff. Note also that this definition of reliability is more conservative
than the ?fidelity? parameter employed by Decarli et al. (2016), for example, as
per our definition there are no candidate sources with lower flux than the absolute
value of the largest negative peak in a map. There is a strong correlation between
integrated flux and reliability, where fainter sources with lower SNR naturally tend
to show lower R (see ?2.5.2, Figure 2.8). The derivation of the luminosity function
(?2.5.3) properly takes into account the statistics by weighting by reliability, and
artificially inserting a high reliability cutoff would cause us to preferentially remove
the contribution from fainter sources. Note also that computation of R for the
central sources, all known to be real, shows a large spread driven by SNR. So it is
clear that real sources can have low reliability when they are faint in relation to the
noise of the observation.
2.4.1.2 Completeness
To assess the completeness of our search algorithm, we perform an analysis
of the chance of detecting sources we artificially inject into each data cube. The
47
purpose of this analysis is to relate the fraction of recovered simulated sources to
the line flux. Since we do not expect resolved sources in the PHIBSS2 data, we do
not account for varying sources sizes.
To simulate sources, we assume a Gaussian line profile along the spectral axis,
and generate sources with five free parameters: the spatial position, the peak flux
density of the line, its velocity width as FWHM, and the velocity of the peak by
drawing random numbers from a uniform distribution. The x and y coordinates are
limited to between 1 and 256, since the cubes are 256 ? 256 pixels in size. We test
the effect of source position on the completeness by simulating sources at the edges
of pixels and at the centers of pixels, and find that this has a negligible impact on
the completeness correction factors. The peak flux density of each artificial source
ranges between the maximum value in the data and 1% of the maximum. Because
completeness is also a function of line width, we simulate sources with FWHM values
ranging from 50 ? 1000 km s?1, to reflect the range of line widths spanned by the
data.
We then assume that each source will be ?beam-like?, so we take the flux
density at each velocity channel that the source appears in to be the peak of a two-
dimensional Gaussian which has the same position angle and size as the synthesized
beam for each data cube. However, since power is lost in the side lobes of the full
synthesized beam, we take this into account by correcting the flux of each simulated
source by the ratio of power in the primary lobe of the beam and its side lobes. We
generate 2500 artificial sources for each data cube in this way, add them to the data
cube 5 sources at a time to avoid crowding, run the search algorithm, and check
48
Figure 2.4: The fractions of recovered sources to artificial sources injected as a
function of integrated flux and FWHM for the eg016 field, from our analysis of 2500
simulated sources. The colored data points correspond to the fraction of recovered
sources for four velocity bins. The colored lines are fits to the four distributions
using a cumulative Gaussian distribution. The vertical dashed lines correspond to
the integrated flux of the candidate source. As we would expect, the recovery of
sources decreases with decreasing integrated flux indicating that fainter sources are
harder to detect than brighter ones. We also see that the recovery of sources at a
given integrated flux decreases with increasing FWHM. This analysis allows us to
correct our CO luminosity functions for the incompleteness of our search algorithm,
particularly at the faint end where this becomes a larger effect (see ?2.5.3).
49
the fraction of sources recovered. Figure 2.4 plots the fraction of recovered artificial
sources as a function of integrated flux (blue circles), for the eg016 data cube.
The recovered fraction is fit with a Gaussian cumulative distribution function (solid
blue line). The vertical dashed black lines correspond to the integrated flux of the
candidate sources for this data cube. We can see that the recovery fraction decreases
with decreasing integrated flux, which is known for each simulated source. We
correct for completeness on a source-by-source basis using the cumulative Gaussian
distribution fit for each data cube. Given the integrated flux of each candidate
source, x, the corresponding completion correction is
[ ( )]
1 x???C(x) = 1 + erf , (2.5)
2 ? 2
where ? and ? are the mean and standard deviation derived from our Gaussian
cumulative distribution function fit for a given cube. Primary beam attenuation, the
sensitivity drop off as a function of distance from the pointing center, will decrease
the chances of detecting weaker sources closer to the edges of each data cube. We
take this effect into account in our comoving volume calculations, which results in
a smaller effective volume sampled by each cube.
50
2.5 Results of Line Search
2.5.1 Line Properties
We extract the spectrum of each candidate source at the position of the peak
SNR pixel, given that the sources in PHIBSS2 are unresolved, in each field at all
velocity resolutions, and apply a primary beam correction. These spectra are fit with
a Gaussian profile using Python?s scipy.optimize.curve fit. Example spectra of
the three brightest candidate sources detected in the COSMOS, EGS/AEGIS, and
GOODS-N fields are shown in Figure 2.5, while the remaining figures are shown in
Appendix A.
The redshift of each candidate source is calculated from the central frequency
of the line, assuming that the emission detected corresponds to a CO transition from
CO (1?0) to CO (6?5). CO emission represents usually the brightest line in galaxy
spectra at wavelengths between 400 and 2600 ?m. Rotational transitions of CO are
spaced by intervals of 115.27 GHz, so with a single transition by itself it is impossible
to determine the redshift of the source. The optical counterpart search discussed
in the next section allows us to, in some cases, determine which CO transitions a
candidate source may correspond to, and in other cases, to constrain the range of
possible CO transitions.
The flux and full-width-half-maximum of each candidate source are calculated
from the best fit standard deviation and amplitude of the Gaussian profile fit. These
results are presented in Table A.1 in Appendix A.
51
Figure 2.5: The brightest serendipitous CO sources in the COSMOS (top),
EGS/AEGIS (middle), and GOODS-N (bottom) fields. The complete set of fig-
ures is available in Appendix A.
52
2.5.1.1 Optical Counterparts
The purpose of identifying counterparts (CPs) for the candidate sources is to
constrain their likely redshift and CO transition, as well as properties like their stellar
masses and SFRs. We search for all optical sources in the 3D-HST/CANDELS
catalogs (Brammer et al., 2012, Skelton et al., 2014, Momcheva et al., 2016) that lie
within one beam FWHM radius of the peak SNR position of each candidate source
we identify in PHIBSS2, while leaving the redshifts unconstrained. The objects in
these catalogs have a distribution of redshifts determined from HST and ground-
based spectral energy distribution (SED) fitting using the EAZY code (Brammer
et al., 2008). To match the redshifts, we then consider all transitions from CO (1?0)
to CO (6?5) and check which, if any, CO transitions are plausible given the posterior
likelihood distributions of the redshift determination from the SED fitting. In several
cases the redshifts of the optical counterparts are poorly constrained by the SED
fitting, allowing a range of possible CO transitions. When grism or spectroscopic
redshifts are available, we compare our redshifts to those because they are much
better constrained than the photometric redshifts. For the purpose of constructing
the CO luminosity functions, we assign a ?redshift probability? to each source based
on the posterior likelihood distribution. We also assign an ?association probability?
for candidate CO sources where multiple optical counterpart candidates lie within
the synthesized beam of the CO data cube (which changes from cube to cube).
This ?association probability? is defined as Pa = 1 ? (?r2/?), where ?r is the
projected angular separation between the CO source and potential counterpart, and
53
? is the synthesized beam area. In this way, optical sources that lie outside of
the synthesized beam area are assigned an association probability of zero, and the
probability of association increases as the projected angular separation decreases.
From this spatial matching, and CO transition/redshift association, we find
that? 64% (43 out of 67) of source candidates in our catalog have at least a tentative
optical counterpart. The lack of an optical counterpart in the 3D-HST/CANDELS
catalog (rest frame optical/UV counterparts) could imply that the candidate source
is spurious, though based on our reliability calculations, we would not expect more
than 25% of sources to be spurious. Thus, this could also be physically caused by
heavy extinction associated with the molecular gas (in which case there may be
infrared counterparts). Whitaker et al. (2017) investigate the relation between dust
obscured star formation and stellar mass as a function of redshift (z = 0 ? 2.5).
They find that for log(M/M) > 10.5, more than 90% of star formation is obscured
by dust at all redshifts, and that at z > 1, there is a tail of heavily obscured
low-mass star-forming galaxies. This highlights the importance of infrared data,
and future work may involve carrying out a systematic infrared counterpart search
beyond existing catalogs (e.g., Spitzer IRAC 3.6 and 4.5 ?m).
The results of our search are presented in the middle panel of the figures in
Appendix A. These are for the most part HST ACS F814W images where the red
crosses mark the positions of the candidate optical counterparts for candidate CO
sources where one could be tentatively identified. For candidate sources where no
ACS optical and/or WFC3 near-IR data was available, we present Spitzer IRAC 3.6
?m images. In the left panel, the redshifts reported correspond to the CO transition
54
Figure 2.6: Comparing the properties of the candidate sources with optical coun-
terparts (dark blue, right-hatched histogram) to those without (cyan, left-hatched
histogram). Left : comparing the integrated flux, Middle: comparing the line width
(FWHM), Right : comparing the reliability. The K-S test results indicate that the
distributions are similar in terms of all three properties.
that most closely matches the ?best? redshift reported in the 3D-HST/CANDELS
catalogs. In the computation of the CO luminosity functions, we however use the
range of possible CO transitions/redshifts allowed by the potential counterparts to
derive CO luminosities, weighted by their respective probabilities (see ?2.5.3 for
details). Finally, these results are also summarized in Table A.1 where we give the
right ascension, declination, and ?best? redshift reported in the 3D-HST/CANDELS
catalogs of each optical counterpart. We also provide the CO based redshifts for the
range of possible CO transitions as determined from the EAZY SED fitting posterior
likelihood distributions. Finally, we provide the angular separation between the
candidate source and potential optical counterpart, with a probability of association
in cases where more than one possible counterpart exists within the synthesized
beam.
In Figure 2.6 we compare the integrated flux, line width, and reliability of
candidate sources with potential optical counterparts (dark blue, right-hatched his-
55
togram), and those without (lighter blue, left-hatched histogram). In all three cases,
both populations of candidate sources span the same parameter space. Both pop-
ulations contain many fainter objects and fewer bright objects, so while some of
those may be spurious detections, the reliability distribution shows that there are
several high-reliability objects with no optical counterpart identified. In terms of
line width, both populations span essentially the same range of line widths probed.
To quantify this we perform the Kolmogorov-Smirnov test and find a K-S
statistic of Dn,m = 0.21, 0.25, and 0.36 for the integrated flux, FWHM, and reliabil-
ity distributions respectively (where n and m are the lengths of the two samples).
The K-S statistic is the maximum distance between the cumulative distributions of
the two compared populations, so a small enough K-S statistic indicates that the hy-
pothesis that two samples are drawn from the same distribution cannot be rejected.
Specifically, the two samples can be said to come from different distributions at a
confidence level ? if ?
n+m
Dn,m > c(?) (2.6)
nm
where
?
c(?) = ?1ln?. (2.7)
2
From the K-S statistics for these three distributions, we find that the hypoth-
esis that both samples are drawn from the same distribution can be rejected at the
74.4%, 86.1%, and 98.1% confidence level for the integrated flux, FWHM, and re-
liability respectively. These confidence levels are usually not considered significant
56
enough to reject the hypothesis. We conclude from this that we lack evidence to say
that the two populations are different and note only that the candidate sources with-
out counterparts tend to be fainter and consequently less reliable that the candidate
sources with counterparts.
For candidate sources where we identify possible counterparts (and hence for
which we have a redshift z), we compare the molecular gas mass from the CO
luminosity to the molecular gas inferred from the potential counterpart SFR, using
the depletion time scale scaling relation of Tacconi et al. (2018):
log(tdep) = At +Bt log (1 + z) + Ct log (?MS) (2.8)
where At = 0.09, Bt = ?0.62, Ct = ?0.44 (for details see Tacconi et al., 2018), and
?MS is the offset from the main sequence of a source. Using the redshift and main
sequence offset of the potential counterpart, we calculate their depletion timescales
and then infer the molecular gas mass based on their SFR (since tdep = Mgas/SFR).
We plot this comparison in Figure 2.7, omitting candidate sources with multi-
ple possible counterparts identified within one synthesized beam and sources where
the product of the CO source reliability (R) times the counterpart probability of
association (Pa) is less than 50%, as we consider these sources and/or counterparts
not highly reliable. The size of the data points is scaled according to the product of
the reliability and the probability of association (higher R?Pa correspond to larger
symbols), and colored according to redshift. The black solid line is the one-to-one
relation and the black stars are primary PHIBSS2 targets plotted as a comparison.
57
These all lie on the one-to-one line, except for one target, which has a large offset
from the main sequence of star formation (log ?MS = +2.41, corresponding to a
target over the main sequence) and therefore a very short depletion timescale. In
contrast, the majority of potential counterparts lie systematically below the one-
to-one relation, which would imply molecular gas reservoirs larger than would be
inferred from the measured star formation.
The SFRs reported in the 3D-HST/CANDELS catalog for these objects are
derived from SED modeling. We have used the catalog by Momcheva et al. (2016),
but with SFR values recomputed according to the Herschel-calibrated ladder of indi-
cators in Wuyts et al. (2011) (see also Tacconi et al., 2018, and references therein).
The SEDs for all objects contain optical to 8?m photometry, and some objects
have photometry at longer wavelengths. At the redshifts of these objects, 8 ?m
corresponds to rest-frame wavelengths of ? ? 1.5 ? 4 ?m. For six data points the
photometry also includes 24 ?m to 160 ?m measurements. These are indicated by
vertical dashed lines, which join the SFR obtained from fitting the ? ? 8?m pho-
tometry to the SFR computed including the longer wavelengths (which corresponds
to the square symbols in Figure 2.7). When the SED modeling includes only the
shorter wavelengths, it results in SFRs one to two orders of magnitude lower than
is estimated when longer wavelength data are included. The agreement between
molecular masses estimated from the optical counterpart star formation activity,
and those directly measured in the PHIBSS2 observations, is very good when the
SFR estimate includes ? ? 24?m information.
Our identification process naturally selects objects that are bright in CO, and
58
Figure 2.7: Comparison of the molecular gas mass measured from the candidate
source CO luminosities to the molecular gas mass inferred from the potential opti-
cal counterpart SFR and the depletion timescale scaling relation of Tacconi et al.
(2018). The size of the colored points is scaled according to the product of relia-
bility and association probability of the detection, and they are colored according
to redshift. The diagonal black solid line is the one-to-one relation. All colored
symbols correspond to SFR measurements from SED modeling of optical to 8 ?m
photometry; the black square symbols show the effect of including longer wavelength
photometry (24 or 160 ?m) on the SFR calculation for the sources where that is
available.
59
indeed they all have very large molecular masses as inferred from their flux. There-
fore they are likely dust-rich, and their star formation activity is highly extincted.
It appears likely that the dust-obscured component of star formation is not prop-
erly accounted for when the longest rest-frame wavelength included in the SED is
? ? 1.5 ? 4 ?m. We believe this is the main cause for the majority of the large
discrepancies between the two estimates of molecular gas mass. It is also possible,
particularly for sources with low reliability or probability of association, that some
of them are not real or that some counterparts are misidentified. The agreement
between the CO luminosity function we derive from these data (?2.5.3) and other
measurements in the literature, however, suggests that this is not the case for the
majority of our objects.
2.5.2 Comparing Serendipitous Detections to Central Sources
The goal of PHIBSS2 is to study galaxy evolution from the perspective of
molecular gas reservoirs. Surveys such as PHIBSS2 that target specific galaxies
selected based on their stellar mass, SFR, and availability of ancillary data have
complex selection functions. The blind search we have performed here, and our
catalog of serendipitous detections provide a sample of objects that are mostly free
of selection biases, other than the selection function imposed by the redshift ranges
surveyed in any given observation and the flux which makes brighter objects easier
to detect. We can therefore compare these two samples to get an idea of their
respective biases.
60
In the left panel of Figure 2.8, we compare the integrated fluxes of all 67 candi-
date sources to those of the central sources targeted by PHIBSS2. In the right panel
of Figure 2.8, we compare the molecular gas masses of the candidate sources with
tentative optical counterpart identifications to that of the central sources. The cen-
tral sources are plotted as the blue hatched histogram and the candidate sources are
separated into histograms corresponding to likelihood levels: the hatched magenta
histogram corresponds to sources with reliabilities between 5 and 50%, the orange
filled histogram corresponds to sources with reliabilities between 50 and 90%, and
the yellow histogram corresponds to sources with reliabilities greater than 90%.
We see in the flux comparison that the sample of central sources and the sample
of secondary candidate detections seem to generally probe objects with similar prop-
erties. To quantify this observation and determine if candidate sources with lower
reliabilities have systematically different integrated flux properties, we perform a
K-S test. We find that Dn,m = 0.13, 0.19, 0.34, which results in rejecting at the
54.0%, 73.3%, and 95.4% confidence level the hypothesis that the candidate source
distributions come from the same distribution of central sources for the 5 ? 50%,
50?90%, and > 90% reliability ranges respectively. These are not strong rejections,
suggesting that regardless of the reliability, the candidate secondary sources have
properties that are very similar to those of the central targeted sources. In terms
of molecular mass, our higher reliability candidate sources seem to correspond to
slightly more massive objects not well represented in the original PHIBSS2 sample,
selected to represent the main sequence at the redshifts of interest. In both panels
we see that the fainter/less massive candidate sources tend to have lower reliabil-
61
ities than the brighter/more massive objects. This is not surprising, since these
candidates will have lower SNRs.
Figure 2.8: Left : Comparison of the integrated flux measurements of the central
galaxies that were specifically targeted by PHIBSS2 (blue hatched histograms) to the
additional serendipitous CO detections. The candidate sources are divided according
to their likelihood parameter. The candidate sources generally seem to follow a
similar distribution of fluxes as the targeted central sources. A K-S test reveals that
at the 48.2%, 94%, and 96.6% confidence level, the candidate source distributions
do not come from the same distribution as the central sources (for the 5 ? 50%,
50 ? 90%, and > 90% reliability ranges). These weak rejections suggest that the
samples are representative of the same parent population of objects. Right : The
same as the left panel, but now comparing the molecular gas masses. The highest
reliability objects tend to have the higher molecular gas masses.
We observe across our sample of candidate detections and tentative optical
counterpart identifications that some candidate sources lie at redshifts similar to
that of the central target source. This raises the question of whether constructing a
CO luminosity function from data targeted at particular objects introduces biases
due to possible clustering of sources around the targeted object. To evaluate whether
this is the case, we compare in Figure 2.9 the difference between the frequency of
62
Figure 2.9: Left : Difference between the central frequency of each candidate source
and the reference frequency of the observation, ??. The dark blue empty histogram
is unweighted by reliability, while the cyan left hatched histogram is weighted by
reliability. The grey shaded histogram is the reliability weighted distribution nor-
malized to the number of data cubes that cover a large enough frequency range to
reach a given ?? value. For randomly distributed objects, we would expect a flat
distribution and this is what we observe. Right : Difference between the redshift
of the central source and candidate source (only for cases where a tentative optical
counterpart is identified), ?z. The dark blue empty histogram is the unweighted
data, the cyan hatched histogram is weighted by reliability, and the grey shaded
histogram is weighted by reliability, the probability of association, and the redshift
probability. There is a tendency here for objects to cluster around ?z? 1, however
this is too large of a redshift separation to form physical associations. We conclude
the candidate sources we detect are not biased by clustering around the central
source.
each candidate source and the frequency of the central source in each data cube (??;
left panel). We also show the difference between the redshift of the central source
and candidate source, for candidates with identified counterparts (?z; right panel).
In both cases we also compare the distribution of ?? and ?z when weighting the
data by reliability, probability of association, and redshift probability.
The left panel of Figure 2.9 shows in both the unweighted and weighted cases
that the candidate sources are approximately uniformly distributed in ?? with a
63
slight decrease for ?? & 1 and a bit of a central bump for completely unweighted
sources. However, the data cubes do not all cover the same frequency range and
therefore the chance of a source to show at a particular ?? has to be weighted
accordingly. To account for this, we normalize the reliability weighted histogram by
the number of data cubes that span the different possible ?? ranges. This is shown
in the gray histogram, where we see that the recovered distribution is very consistent
with a uniform distribution across the spectral range. This shows that our secondary
detections are uniformly distributed in ??, and therefore there is no signature of a
bias introduced by clustering around the targeted central sources. In physical terms,
?? = 1 GHz for a source at z ? 1.5 in a ? ' 3 mm observation represents a physical
velocity difference of over 3,000 km s?1, larger than the central velocity dispersion
of a massive galaxy cluster like Coma (? ? 1200 km s?1V , Kent and Gunn, 1982).
Therefore we would expect a relatively narrow peak in the corrected histogram if
most sources were physically related to the central source, independent of our ability
to identify counterparts.
The right panel of Figure 2.9 shows the distribution in ?z for only those
candidate sources for which we find tentative optical counterparts. The unweighted
case shows a wide peak in the distribution of objects at z?1 from the central sources.
When weighting by reliability, probability of association, and redshift probability
this peak is significantly smoothed but still present. The existence of a broad peak
is to be expected: most of our observations target the 2?1 and 3?2 CO transitions
at z ? 1? 2, and the most likely bright transitions for field objects will be 2? 1 to
4? 3, which would place them in the ?z ? ? 1 range for most observations. Note
64
also that if this were an indication of true physical clustering we would expect the
peak to be much narrower, ?z . ? 0.1.
2.5.3 CO Luminosity Functions
We construct the CO luminosity functions using equation 2.9:
?N1 i Rj
?(logLi) = Pa,j Pz,j . (2.9)
V C
j=1 j
Here Ni is the number of galaxies that fall within the luminosity bin i defined
by log Li ? 0.25 and log Li + 0.25 (log Li ? 0.5 and log Li + 0.5 for cases where we
only have a small number of sources), V is the total volume of the Universe that
is sampled by a given transition across all of our data cubes, Rj is the reliability
of the jth line and Cj is its completeness, Pa,j is the probability that the candidate
source is associated with a particular optical counterpart, and Pz,j is the probability
that a given candidate optical counterpart corresponds to a particular CO transition
(and hence redshift). Each CO line is down-weighted by its likelihood probability
calculated in ?2.4, probability of association, and redshift probability, and then
up-scaled by its completeness fraction. The CO luminosities are calculated from
equation 3 of Solomon et al. (1997):
2
L?
SCO?V D
CO = 3.25? 107 L [K km s?1 pc2] (2.10)?2obs(1 + z)3
where SCO?V is the integrated flux density in units of Jansky kilometers per second,
DL is the luminosity distance of the source in megaparsecs, ?obs is the observed
65
Survey Transition ?rest zmin zmax Volume CV
[GHz] [Mpc3] [%]
PHIBSS2 CO (2? 1) 230.538 0.017 1.562 11250 18.2
CO (3? 2) 345.538 0.492 2.843 26136 15.9
CO (4? 3) 461.041 0.989 4.124 36144 14.9
CO (5? 4) 576.268 1.486 5.405 42380 13.3
CO (6? 5) 691.473 1.983 6.685 46288 15.6
COLDz COSMOS CO (1? 0) 115.271 1.953 2.723 20189 36.9
CO (2? 1) 230.538 4.906 6.445 30398 37.8
COLDz GOODS-N CO (1? 0) 115.271 2.032 2.847 131042 25.5
CO (2? 1) 230.538 5.064 6.695 193286 25.6
ASPECS LP CO (1? 0) 115.271 0.003 0.369 338 59.4
CO (2? 1) 230.538 1.006 1.738 8198 36.9
CO (3? 2) 345.538 2.008 3.107 14931 35.0
CO (4? 3) 461.041 3.011 4.475 18242 35.2
Table 2.1: Comoving Volume Sampled by each CO Transition. The sensitivity drop
off due to the primary beam is accounted for in the volume calculations.
frequency of the line in GHz, and z is its redshift. The volume of the Universe
that is sampled by a given PHIBSS2 data cube is calculated as a three-dimensional
slab of space defined by the field-of-view of the given observation, and frequency
range that is observable by the instrument, for each CO transition we consider in
our counterpart search. These values are summarized in Table 2.1.
We exclude from our CO luminosity functions all central sources since these
were targeted objects and are therefore not the result of our blind search. We
also exclude objects with no optical counterpart identification, because we have no
information on their corresponding redshift or CO transition. We note that because
we choose to not include sources for which we identify no counterpart, that care
should be taken when comparing our results to previous blind survey results in
subsequent sections and figures. The constraints we derive should be considered
66
lower limits since the catalogs we draw counterparts from may be incomplete.
2.5.3.1 PHIBSS2 CO Luminosity Functions
Figure 2.10 plots the PHIBSS2 CO luminosity function for a range of CO
transitions and median redshifts in gray shaded boxes. Our results are plotted as
a moving average, by displacing each luminosity bin by 0.1 dex and recalculating
the CO luminosity function according to equation 2.9. In each panel, we give the
number of candidate sources used to derive the given CO luminosity function and
their median redshift. We are able to constrain CO (2 ? 1) at ?z? ? 0.7 and 1.2,
CO (3? 2) at ?z? ? 1.5 and 2.2, CO (4? 3) at ?z? ? 1.9, 2.2 and 3.3, CO (5? 4) at
?z? ? 3.4 and 4.4, and CO (6?5) at ?z? ? 3.7. We compare each of these to existing
theoretical predictions from Popping et al. (2019)1, Popping et al. (2016), Vallini
et al. (2016), and Lagos et al. (2012) and where possible, to existing observational
constraints. To be able to consistently compare with the work of Walter et al.
(2014) and Decarli et al. (2016, 2019), we calculate our uncertainties on the CO
luminosity function in the same way. Thus the error bars along the y-axis correspond
to Poissonian errors on Ni, the number of sources within a luminosity bin i, at the
1? level according to Tables 1 and 2 of Gehrels (1986), while the ?error bars? along
the x-axis simply reflect the width of the luminosity bin.
We fit our observed CO luminosity functions with a Schechter function (Schechter,
1976) in the logarithmic form used by Riechers et al. (2019) and Decarli et al. (2019):
1We convert the molecular hydrogen mass functions to CO luminosity functions assuming an
?CO = 3.6 M (K km s
?1 pc2)?1 and temperature ratios of rJ1 = 0.76? 0.09, 0.42? 0.07 for J =
2, 3 respectively (Daddi et al., 2015).
67
Figure 2.10: The PHIBSS2 CO luminosity functions observed here (shaded gray
boxes, with sizes corresponding to 1? uncertainties), compared to the PdBI HDF-N
work (blue left-hatched boxes; Walter et al., 2014), the ASPECS pilot work (yellow
left-hatched boxes; Decarli et al., 2016), the ASPECS LP work (magenta right-
hatched boxes; Decarli et al., 2019), the predicted CO luminosity function of Vallini
et al. (2016) based on the Herschel IR luminosity function, and the theoretical
predictions of Lagos et al. (2012) and Popping et al. (2016). Our derived CO lu-
minostiy functions are consistent with constraints from previous work, but are in
tension with the semi-analytic model predictions, particularly at the higher-J CO
transitions where we observe larger number densities at higher CO luminosities than
is predicted by these models.
68
(
L?
)
1 L?
log ?(L?) = log ?? + ? log ?? ? ?? + log(ln(10)) (2.11)L ln 10L
where ?? is the scale number of galaxies per unit volume, L?? is the scale line
luminosity and the parameter that sets the ?knee? of the luminosity function, and
? is the slope of the faint end.
To obtain estimates of the allowed range of Schechter parameters, we fit the
characteristic parameters described above to our CO (2?1) at ?z? = 0.68 luminosity
function due to the small numbers of sources in all other cases. To account for
the uncertainties of each luminosity bin, we draw points from normal distributions
centered in each luminosity bin, with standard deviation corresponding to the size of
the luminosity bin. We fit a Schechter function to that set of points while assuming
unconstrained priors on the characteristic Schechter parameters. We then repeat
the process with a new set of randomly drawn points from each luminosity bin and
do this until enough points have been drawn to determine the posterior likelihood
distributions of each Schechter parameter.
We show the results of this fitting in Figure 2.11, where we also include the
posterior likelihood distribution of each parameter along with the 5th, 50th, and 95th
percentiles. In Figure 2.12, we show the density of Schechter function fits to each
sample of points drawn from the data. This Figure shows that the uncertainties are
dominated by the faint end, below the ?knee? of the luminosity functions. However,
the three parameters L?? ?CO, ?CO, ? are fairly reliably constrained by the data. We
69
Line Redshift log L?? ?CO log ?CO ?
CO (2? 1) 0.33 ? 0.99 9.76+0.41 +0.38?0.31 -3.31?0.58 -0.07+0.55?0.45
Table 2.2: Schechter Function Fit Parameter Constraints from PHIBSS2
summarize the constraints on the Schechter model parameters for each fit in Table
2.2, including the 5th and 95th percentiles.
2.5.4 Molecular Gas Mass Density Evolution
To derive constraints on the evolution of co-moving molecular gas mass, we
need to convert our high-J CO luminosities to CO (1? 0) luminosities. We assume
Rayleigh-Jeans brightness temperature ratios of rJ1 = 0.76 ? 0.09, 0.42 ? 0.07,
0.31? 0.06, and 0.23? 0.04 for J = 2, 3, 4, and 5 respectively (Daddi et al., 2015).
We then convert these CO (1 ? 0) luminosities to molecular gas masses, using an
?CO value of 3.6 M (K km s
?1 pc2)?1 for the sake of consistency with previous
work using
M = ? L?H2 CO (CO (1?0)). (2.12)
The PHIBSS project has consistently used a 20% larger value of ?CO (Tacconi
et al., 2018). Carleton et al. (2017) investigate the dependence of the conversion
factor ?CO on total mass surface density for z > 1.7 in the PHIBSS sample of
galaxies and find that 92 ? 100% of ?CO measurements are similar to the Milky
Way value of 4.36 M (K km s?1 pc2)?1 adopted by PHIBSS. Here we use a value
of 3.6 to compare consistently to other results in the literature who have adopted
this value (Riechers et al., 2019, Decarli et al., 2019). Adopting a different constant
70
Figure 2.11: Corner plot of the Schechter model parameters posterior distribution
from fitting the CO (2?1) luminosity function. The parameters are reasonably well
constrained by the data.
71
Figure 2.12: Density of Schechter fits for the CO (2?1) z ? 0.7 luminosity function.
The black lines correspond to the median points and the boundary where 95% of the
fits lie. For reference, the Popping et al. (2016) prediction is plotted as the dashed
black line. We see from this that the ?knee? of the CO luminosity function is well
constrained by the data, while there is more uncertainty in constraining the slope
of the faint end.
72
value of ?CO will result in a straightforward linear scaling of our MH2 and ?(H2)
measurements.
As in Walter et al. (2014), Decarli et al. (2016), Riechers et al. (2019), and
Decarli et al. (2019), we do not extrapolate to the undetected faint end of the
luminosity functions and only use actual candidate sources. We should note that this
conversion from high-J CO transitions to molecular mass is increasingly uncertain as
J increases: this is unavoidable as the excitation requirements become increasingly
stringent, and so a diminishing fraction of the gas emits brightly in these transitions.
The only way around this constraint is to directly observe the J=1 ? 0 or 2 ? 1
transitions at high redshift, but that requires more powerful facilities than those in
existence (such as the ngVLA, Decarli et al., 2018). Our results are shown as black
boxes in Figure 2.13, where each box corresponds to the combination of candidate
sources observed at any transition in the given redshift range.
2.6 Discussion
2.6.1 Comparison to Previous Blind CO Surveys
2.6.1.1 Luminosity Functions
The CO (2? 1) at ?z? ? 1.2 and the CO (3? 2) at ?z? ? 2.3 were previously
constrained by Walter et al. (2014), Decarli et al. (2016), and Decarli et al. (2019).
The observational constraints from Walter et al. (2014) are the result of a blind
CO survey in part of the Hubble Deep Field North. Decarli et al. (2016) observed a
73
Figure 2.13: The evolution of the molecular gas mass density with redshift, where the
black boxes represent the constraints from the PHIBSS2 data. Orange right hatched
boxes correspond to the constraints derived from the VLA COLDz measurements
of Riechers et al. (2019), purple right hatched boxes correspond to the constraints
of ASPECS LP measurements of Decarli et al. (2019), yellow left hatched boxes
correspond to the work of Decarli et al. (2016), and the blue left hatched boxes
correspond to the constraints from the work of Walter et al. (2014). The dashed
lines correspond to model predictions for the evolution of the molecular gas mass
density, as derived by Obreschkow et al. (2009), Lagos et al. (2011), and Popping
et al. (2014b), Popping et al. (2014a). The constraints derived from serendipitous
detections of CO in the PHIBSS2 fields are consistent with those of previous blind
surveys.
? 1 arcmin region of the Hubble Ultra Deep Field (UDF) with ALMA (the ASPECS
pilot program), while Decarli et al. (2019) derive their constraints from the ASPECS
74
Large Program. The redshift ranges for which we derive constraints from CO (2?1)
and CO (3 ? 2) are very similar to these previous works, so we directly compare
our measurements to them. We see from Figure 2.10 that our results correspond
to approximately the same luminosity bins as Decarli et al. (2016), and are in
agreement with their results. Decarli et al. (2016) report an excess of CO-bright
galaxies in the UDF with respect to theoretical predictions, and our results confirm
this for the galaxies we observe in the 3D-HST/CANDELS fields sampled by our
PHIBSS2 data. This implies that galaxies in this redshift bin are more gas-rich than
is currently predicted by theoretical models.
Riechers et al. (2019) derive the CO (1? 0) luminosity function for a median
redshift of z = 2.4 in the COLDz program. Our CO (3 ? 2) luminosity function
is derived for a median redshift of z ? 2.3. We consider this difference in redshift
to be negligible and therefore compare to the COLDz measurements without any
modifications. To compare these results then, it is only necessary to assume a line
ratio between these two transitions. To convert our CO (3 ? 2) luminosities to
CO (1? 0) we use r31 = 0.42? 0.07 from Daddi et al. (2015).
We show the comparison between our derivation and that of the COLDz results
of Riechers et al. (2019) in Figure 2.14. Overall we find that our measurements are
consistent with those of Riechers et al. (2019) within the uncertainties, although
there is a hint that our results may point to higher number densities than those
measured in COLDz. This could be due to cosmic variance (CV), or it could also be
evidence that higher-J observations or surveys tend to preferentially select higher
gas excitation galaxies. This would then mean that our temperature ratio is too low.
75
Bolatto et al. (2015) find for two CO (3? 2) bright z ? 2.2? 2.3 galaxies r31 ratios
of order unity, while samples of nearby galaxies, luminous infrared galaxies, and
ultra luminous infrared galaxies show mean values of r31 ? 0.66. We convert our
CO (3? 2) luminosities to CO (1? 0) using this higher temperature ratio and show
the result in Figure 2.14 (dashed black boxes). The change in assumed excitation
produces a moderate shift toward lower luminosities, which brings the data into
somewhat better agreement but does not completely eliminate the tension between
both sets of measurement.
2.6.1.2 Molecular Gas Mass Density Evolution
In Figure 2.13, we compare our results to all previous observational constraints:
those from Walter et al. (2014), the ASPECS pilot work of Decarli et al. (2016), the
COLDz measurements of Riechers et al. (2019), and the ASPECS LP measurements
of Decarli et al. (2019). Within the uncertainties, our results are consistent with
all previous observational constraints. Between redshifts of z ? 2 ? 3, our result
is most consistent with the measurement of Walter et al. (2014) and the ASPECS
pilot, and hints at maybe a higher molecular gas mass density than that obtained
by COLDz. From redshifts of z ? 3? 5, our measurements are consistent with the
ASPECS pilot measurements, and hints at a lower molecular gas mass density than
derived in the ASPECS-LP. Given the present state of the art in the uncertainties
it is unclear if these discrepancies are real, but their magnitude is easily explained
by cosmic variance.
76
Figure 2.14: The comparison of our CO (3 ? 2) luminosity function, converted to
CO (1 ? 0) assuming a brightness temperature ratio of r31 = 0.42 (gray boxes) to
the results of Riechers et al. (2019) (orange boxes). Within the uncertainties, our
measurements are consistent with those of Riechers et al. (2019). As an additional
comparison, we convert out CO (3?2) luminosities with a r31 = 0.66 (Bolatto et al.,
2015, black dashed boxes). This shifts our measurements to lower CO luminosities
but our results stay in agreement with Riechers et al. (2019). We plot the predictions
of Lagos et al. (2012), Vallini et al. (2016), Popping et al. (2016) as a reference.
77
2.6.2 Cosmic Variance
To address the question of cosmic variance, we use the results of Driver and
Robotham (2010) to quantify the cosmic variance of the PHIBSS2 data. The authors
repeatedly extract galaxy counts in cells of fixed size at random locations in the Sloan
Digital Sky Survey (SDSS) Data Release 7. They explore the variance of the SDSS
data in square cells from 1 to 2048 square degrees and in rectangular cells with aspect
ratios ranging from 1:1 to 1:128. They find that cosmic variance depends on total
survey volume, the survey aspect ratio, and whether the survey area is contiguous or
composed on independent lines of sight, with cosmic variance decreasing for higher
aspect ratios and non-contiguous survey areas (which essentially help sample a larger
range of environments). Driver and Robotham (2010) provide a general equation
that can be used at any redshift to estimate the cosmic variance of a survey (eq. 4
in Driver and Robotham, 2010):
?
?Cos.Var.(%) = (1.00? 0.03 (A/B)?)
? [219.7? 52.4 log10(AB ? 291.0) ?
+ 3.21[ log10(AB ? 291.0)]2]/ NC/291.0 (2.13)
where A and B are the transverse lengths at the median redshift, C is the radial
depth all expressed in units of h?10.7 Mpc, and N is the number of independent sight-
lines. This empirical expression for estimating the cosmic variance is implemented
as a function in the R library celestial, as cosvarsph. We input into cosvarsph
78
the RA, Dec, and redshift limits that correspond to those values of the PHIBSS2
data cube with the median volume (since not all data cubes have the same size),
and finally take N to be the total number of data cubes. With this estimate, we
derive cosmic variances in the range ? 13%? 18%; these values are summarized in
the last column of Table 2.1.
For comparison, we perform a crude estimate of the cosmic variance in the
COLDz survey. The COLDz survey covers an area of 8.9 arcmin2 at 31 GHz and
7.0 arcmin2 at 39 GHz for COSMOS and an area of 50.9 arcmin2 at 30 GHz and 46.4
arcmin2 at 38 GHz. Using the average area and the redshift limits reported in their
Figure 1 for both the CO (1?0) and CO (2?1) transitions as inputs into cosvararea,
we estimate a cosmic variance of ? 34% and ? 24% for COSMOS and GOODS-N
respectively. Performing the same estimate for the ASPECS-LP using the redshift
limits from Table 1 of Decarli et al. (2019), we find that the cosmic variance is in
the range ? 59% to ? 35% for CO (1 ? 0) to CO (4 ? 3). These estimates are for
a square survey area with aspect ratio 1:1, which is only approximate for either the
COLDz or the ASPECS-LP surveys, and are therefore likely upper limits on their
cosmic variance. However, this still shows that cosmic variance may be less of an
issue in surveys that are composed of multiple independent lines of sight rather than
one contiguous area.
79
2.7 Conclusions
We present a catalog of 67 candidate secondary sources observed in 110 ob-
servations of PHIBSS2, where the primary target is a known optical high-z galaxy,
which includes spectra, redshifts, line widths, integrated fluxes, CO luminosities,
and molecular gas masses. We perform an analysis of the false positive probabilities
for each candidate secondary source, characterizing them with a reliability parame-
ter R, and assess the completeness of the search algorithm. We perform a search for
optical counterparts corresponding to each candidate source, taking into account
the redshift uncertainty for the optical sources in the 3D-HST/CANDELS cata-
logs. We find that ? 64% of these secondary detections have optical counterparts
(in some cases more than one) and include these together with an estimate of the
probability of association in our catalog. Finally, we use the catalog of candidate
sources to build the CO (2? 1), CO (3? 2), CO (4? 3), CO (5? 4), and CO (6? 5)
luminosity functions for a range of median redshifts, spanning z ? 0.6 ? 4.4 and a
volume sampled of ? 13500?57000 Mpc3 depending on the CO transition. We find
broad agreement between our results and those of Walter et al. (2014), Decarli et al.
(2016), Riechers et al. (2019), and Decarli et al. (2019). We also demonstrate that a
blind CO search across many independent fields in observations of targeted objects
can be successfully combined to establish constraints on the luminosity functions
of different CO transitions in different redshift bins. We show that, in the case of
CO, there appears to be little or no bias towards physically associated neighbors
of the primary target down to the luminosities probed. We use an estimate of the
80
cosmic variance to show that an approach which combines multiple independent
fields mitigates the impact of cosmic variance. This is because for a contiguous
survey area, the volume sampled needs to be very large in order to cut across many
different environments; on the order of 107 h?3 30.7 Mpc (for an aspect ratio of 1:1) to
decrease cosmic variance to a 10% level according to the formalism by Driver and
Robotham (2010). This approach also exploits existing data which can significantly
expand blind survey samples. The caveat is that one must deal with non-uniform
sensitivity, which can however be handled through a good SNR characterization of
the data sets.
We have derived the molecular gas mass density evolution from converting our
high-J CO luminosity functions to CO (1? 0), assuming a CO luminosity to molec-
ular gas mass conversion factor of ?CO = 3.6 M (K km s
?1 pc2)?1 for consistency
with previous studies, and find our results to be largely consistent with previous
constraints on the evolution of the cosmic cold gas mass density.
81
Chapter 3: The Nature and Fate of Star Forming Clumps in Gas-
Rich, Turbulent Galaxies
3.1 Overview
To indirectly study the internal structure of giant clumps in main sequence
galaxies at z ? 1 ? 3, we target very turbulent and gas-rich local analogues from
the DYNAMO sample with the Hubble Space Telescope, over a wavelength range of
? 200?480 nm. We present a catalog of 58 clumps identified in six DYNAMO galax-
ies, including the WFC3/UVIS F225W, F336W, and F467M photometry where the
(225?336) and (336?467) colours are sensitive to extinction and stellar population
age respectively. We measure the internal colour gradients of clumps themselves to
study their age and extinction properties. We find a marked colour trend within
individual clumps, where the resolved colour distributions show that clumps gen-
erally have bluer (336 ? 467) colours (denoting very young ages) in their centers
than at their edges, with little variation in the (225 ? 336) colour associated with
extinction. Furthermore, we find that clumps whose colours suggest they are older,
are preferentially located closer toward the centers of their galaxies, and we find no
young clumps at small galactocentric distances. Both results are consistent with
82
simulations of high?redshift star forming systems that show clumps form via violent
disc instability, and through dynamic processes migrate to the centers of their galax-
ies to contribute to bulge growth on timescales of a few 100 Myr, while continually
forming stars in their centers. When we compare the DYNAMO clumps to those in
these simulations, we find the best agreement with the long-lived clumps.
3.2 Introduction
The morphologies of massive star-forming galaxies at z ? 1 ? 3 are irregular
compared to local star-forming galaxies of similar mass. Rest-frame UV and optical
images of these galaxies reveal giant, ? 0.1?1 kpc sized clumps with masses ranging
from 107?109 M (Fo?rster Schreiber et al., 2011, Guo et al., 2012, Huertas-Company
et al., 2020) that are the sites of active star formation, accounting for up to 10?20%
of the total integrated star forming activity of galaxies at this epoch (Wuyts et al.,
2012, 2013). These giant clumps are also observed in resolved molecular gas maps
(Tacconi et al., 2013) and rest-frame optical line emission spectra (Genzel et al.,
2008, 2011), but are less prominent in stellar mass distribution maps (Wuyts et al.,
2012). Galaxies at this epoch are also observed to have high gas-fractions, defined
as fgas = MH2/(MH2 + M?) (fgas ? 0.3 ? 0.8, Daddi et al., 2010a, Tacconi et al.,
2010, 2013, Genzel et al., 2015), high star formation rates (Genzel et al., 2008), and
high velocity dispersions (Fo?rster Schreiber et al., 2006).
There is an ongoing debate as to the nature of these clumps and their eventual
fate. Cosmological simulations (e.g., Dekel et al., 2009, Bournaud et al., 2014, Man-
83
delker et al., 2017) produce clumpy galaxies via cold gas accretion and gravitational
disc instabilities. These clumps survive long enough in some simulations to migrate
to the centers of galaxies through orbit decay by loss of orbital angular momentum,
on timescales of / 500 Myr and thus contribute to galaxy bulge growth (Noguchi,
1999, Immeli et al., 2004, Bournaud et al., 2007, Ceverino et al., 2010). Ceverino
et al. (2012) show in their cosmological simulations that this migration results in
a clump age gradient that is much steeper than the disc age gradients (see also
Mandelker et al., 2017). Observational measurements of clump colours also provide
evidence for this inward migration: redder clumps are found closer to the centers
of galaxies, while bluer clumps are found preferentially at larger galactocentric dis-
tances. These galaxy-wide colour gradients are interpreted as an age gradient, where
the redder clumps are thought to be older (Fo?rster Schreiber et al., 2011, Guo et al.,
2012, Shibuya et al., 2016, Soto et al., 2017, Guo et al., 2018).
This scenario however, requires that clumps survive for timescales of ? 150
Myr. Yet other numerical simulations (such as Feedback in Realistic Environments,
FIRE; Hopkins et al. 2014, and NIHAO; Wang et al. 2015) find that clumps dissolve
on timescales of ? 100 Myr or less and thus do not survive long enough to contribute
significantly to galaxy bulge growth (Buck et al., 2017, Oklopc?ic? et al., 2017), even
though these simulated galaxies show the same clump colour gradients as observed.
Furthermore, other simulations show that increasing clump ages at small distances
can be produced by inside-out formation of the disc, rather than clump migration,
and that clumps disrupt on timescales of ? 50 Myr (Genel et al., 2012).
Buck et al. (2017) propose that the colour gradient found by observers may be
84
the result of contamination from disc light. The density of disc stars is lower in the
outskirts of a galaxy and higher in the center, thus the authors argue that redder
stellar light in the centers of galaxies can artificially produce colour gradients such
as the ones observed. Contrary to this idea, Guo et al. (2018) find that regardless
of the chosen disc subtraction method used (ranging from no disc subtraction to
very strict disc subtraction), the clump colour gradients in their sample of 1270
galaxies at 0.5 ? z < 3.0 are still present and only the amplitude of the gradients
are affected.
Nonetheless, in agreement with observations, the NIHAO galaxies of Buck
et al. (2017) show clumps in light maps but not in stellar mass maps. The authors
use this to argue that the clumps detected in the simulated galaxies are not long-lived
gravitationally bound systems that have any dynamical influence on the evolution of
the disc. Rather they are simply localized (clumpy) regions of star formation. The
authors furthermore postulate that dust attenuation can affect the observed struc-
ture of a galaxy by enhancing intrinsically dim clumps, and suppressing intrinsically
bright ones, suggesting that clumps are simply the result of variations in extinction.
Fortunately, the existence of nearby galaxies with properties similar to those
at high redshift, allows us to study the light and extinction distributions in clumpy
galaxies on a resolved scale. The DYnamics of Newly Assembled Massive Objects
(DYNAMO; Green et al., 2014) sample consists of very rare local (z ? 0.1) galaxies
whose properties are very well matched to those of main-sequence galaxies at z ?
1 ? 3. Green et al. (2014) derive H? rotation curves for DYNAMO galaxies and
find that the mean ionized gas velocity dispersion is ? 50 km s?1, reflecting much
85
larger turbulent motions than in normal local galaxies, and infer gas fractions as
high as fgas ? 0.8, and star formation rates in the 0.1 ? 100 M yr?1 range. The
properties of DYNAMO galaxies place them on the main sequence of star formation
of z ? 1? 2 galaxies (e.g., see Figure 1 in Fisher et al., 2019); as a result, we have
the opportunity to investigate clump properties on resolved scales, where we can
learn more about their true nature and evolutionary fate.
In this work, we investigate the internal radial variation of age and extinction
of individual clumps in six DYNAMO galaxies through colour measurements, as well
as galaxy-wide radial trends in colour and age evolution. The paper is structured
as follows: ?3.3 describes the targets and their HST observations, ?3.4 describes our
clump identification process, point-spread-function matching procedure and other
data analysis, in ?3.5 we present and discuss our photometry results, finally we
summarize and conclude our work in ?3.6.
We assume ?CDM cosmology with H0 = 70 km s
?1 Mpc?1, ?m = 0.3, and
?? = 0.7, and a Kroupa initial mass function (IMF; Kroupa, 2001) throughout this
paper. All magnitudes we report are AB magnitudes. The physical scale corre-
sponding to the typical redshift of our sources (z ? 0.1) is 1.844 kpc per arcsecond
(Wright, 2006).
86
3.3 Observations
3.3.1 Sample
The DYnamics of Newly Assembled Massive Objects (DYNAMO; Green et al.,
2014) sample consists of 67 galaxies selected from the Sloan Digital Sky Survey DR4
(SDSS; Adelman-McCarthy et al., 2006) to cover a range of H? luminosities up to
LH? > 10
42 erg s?1, in the SDSS 3.0?? diameter fiber, and to lie in two redshift
windows to avoid atmospheric absorption of H? (centered at z ? 0.075 and z ?
0.13). DYNAMO galaxies span stellar masses from 109 ? 1011 M and SFRs from
? 0.1? 100 M yr?1.
In this work, we consider a sub-sample of six DYNAMO galaxies selected to
build on a multi-wavelength study of these objects: DYNAMO D13-5, D15-3, G04-
1, G08-5, G14-1, and G20-2, which are classified as rotating discs based on H?
kinematics. Galaxies G04-1, G14-1, and G20-2 are furthermore classified as ?com-
pact? rotating discs (Green et al., 2014). These galaxies are ones for whom the
SDSS r?band exponential scale lengths are less than 3 kpc. Since the resolution
for these objects is poorer, their kinematic classifications are less reliable. All six of
these objects have molecular gas measurements from CO(1 ? 0) observations with
the Plateau de Bure Interferometer (PdBI), and have gas fractions of 20 ? 30%
and depletion timescales of tdep ? 0.5 Gyr (Fisher et al., 2014, White et al., 2017).
Using HST H? observations and Keck/OSIRIS Pa? observations, Bassett et al.
(2017) created spatially resolved (? 0.8 ? 1 kpc) H? extinction maps for galaxies
87
D13-5, G04-1, and G20-2, showing that there is only mild spatial variability in the
amount of extinction within a given galaxy, and finding no evidence for highly atten-
uated star-forming clumps. Finally, the MPA-JHU Value Added Catalog1 provides
gas-phase metallicity measurements for ? 53,000 star forming galaxies, including
the six DYNAMO galaxies we study here, derived from comparing several strong
emission lines ([OII]?3727, H??4861, [OIII]?5007, H?, [NII]?6584, [SII]?6717, and
[SII]?6731) to photoionization models (see Tremonti et al., 2004). These properties
are summarized in Table 3.1.
3.3.2 HST Observations
The six DYNAMO galaxies in our sub-sample were observed with the Hubble
Space Telescope (HST) Wide Field Camera 3 (WFC3) UVIS channel in three filters:
F225W (UV wide), F336W (U), and F467M (Stro?mgren b). Observations were taken
between February and November 2018. The full-width-half-maximum (FWHM) of
the point-spread-function (PSF) of each filter is: ?0.092?? for F225W, ?0.080?? for
F336W and F467M. We note that the observations are not diffraction limited until
longward of 500 nm, thus the broader F225W PSF at shorter wavelengths. We
present these data in Figures 3.1 and 3.2.
1https://wwwmpa.mpa-garching.mpg.de/SDSS/DR4/
88
Table 3.1: Properties of HST-DYNAMO Galaxies
89
Galaxy z M? Mgas fgas SFRH? < AH? > < rclump > 12 + log(O/H)
(M) (10
9 M) (10
9 M) (mag) (pc)
D13-5 0.07535 53.84 20.17 0.36 ? 0.02 21.20 1.80 ? 0.52 400 9.10+9.11?9.09
D15-3 0.06712 54.15 14.74 0.17 ? 0.02 13.70 ? ? ? 394 9.18+9.19?9.17
G04-1 0.12981 64.64 43.68 0.33 ? 0.04 41.61 1.52 ? 0.26 451 9.15+9.16?9.12
G08-5 0.13964 9.65 16.29 0.30 ? 0.05 11.05 ? ? ? 521 9.00+9.02?8.98
G14-1 0.13233 8.30 9.72 0.77 ? 0.08 22.33 ? ? ? 353 9.10+9.11?9.06
G20-2 0.14113 17.27 19.12 0.21 ? 0.05 21.56 0.89 ? 0.14 449 8.98+8.99?8.96
Figure 3.1: HST observations of galaxies D13-5, D15-3, and G04-1: F225W (left),
F336W (middle), F467M (right). The F467M measured effective radius of each
galaxy is shown in the right panels (dashed red circle). The middle panels outline
in white each detected clump, as described in ?3.4. Galaxy G04-1 is classified as a
?compact? rotating disc (Green et al., 2014).
90
Figure 3.2: Same as Figure 3.1, but now showing galaxies G08-5, G14-1, and G20-2.
Galaxies G14-1 and G20-2 are classified as ?compact? rotating discs; therefore, their
classification may be less reliable (Green et al., 2014).
91
3.4 Data Analysis
3.4.1 Kernel Generation for PSF Matching
The goal of this work is to measure the internal colours of clumps in DYNAMO
galaxies, taking full advantage of the HST resolution. To do this, it is necessary to
transform images from different filters to a common point spread function (PSF).
Since the HST filters we use here do not have the same PSFs, the variation of
structure on different spatial scales will result in unphysical colours when directly
comparing images with different PSFs (see e.g., Gordon et al., 2008, Aniano et al.,
2011). To transform images to a common PSF, we need to generate a convolution
kernel, such that when the PSF of one filter (F336W or F467M) is convolved with
this kernel, it will resemble the broader PSF of the second filter (F225W):
?225 = ?336 ~K{336? 225} (3.1)
where ? represents the filter PSFs, and K represents the convolution kernel. The
convolution kernel that will satisfy this equation can be generated by taking the
Fourier Transform (FT) of the same equation:
FT(?225) = FT(?336 ~K{336? 225}) (3.2)
= FT(?336)? FT(K{336? 225}), (3.3)
92
solving for the kernel, and taking an inverse Fourier Transform, we find that:
[ ]
K{336? 225} = FT?1 FT(?225)?
1
. (3.4)
FT(?336)
In reality, computing the convolution kernel numerically requires additional steps to
ensure that it is stable and performs well. We follow the steps to do this as outlined
in detail in Aniano et al. (2011) and summarize them here for completeness.
3.4.1.1 HST PSFs
We obtained the PSFs for the F225W, F336W, F467M filters from the Tiny
Tim2 tool, version 7.5, by downloading and installing the source code available on
GitHub. The three PSFs are 89?89 pixels and have a pixel scale of 0.04?? , matching
the pixel scale of the HST images; therefore, we perform no gridding, padding or
centering of the PSFs.
3.4.1.2 Circularizing the PSFs
The PSFs modeled by Tiny Tim are not rotationally symmetric; therefore,
the first step we take is to circularize them. Following Aniano et al. (2011), we
circularize the PSFs by performing 14 rotations of the PSF, and averaging after
each rotation, such that the final PSF is invariant for any rotation that is a multiple
of 360?/214 = 0.022?. We begin by rotating the original PSF, ?, by the smallest
angle first: ?1 = 0.022
? to produce a new PSF image, ??, and then compute the
2https://www.stsci.edu/hst/instrumentation/focus-and-pointing/focus/tiny-tim-hst-psf-
modeling
93
average of the two: ? = 1 ? (? + ??). We then rotate ? by ?2 = 360?/213 and2
repeat the process until ? = 360?/2114 .
3.4.1.3 Compute the Kernels
We compute the Fourier Transform of each circularized PSF using the Python
numpy two-dimensional Fast Fourier Transform (FFT) function fft.fft2. We com-
pute the K{336 ? 225} and K{467 ? 225} kernels according to equation 3.4, by
evaluating the 1/FT (?336) and 1/FT (?467) terms where they are not equal to zero.
After taking the inverse Fourier Transform of the kernel, we normalize the integral of
the kernels to unity to ensure flux conservation (see also photutils.psf.matching3).
3.4.1.4 Kernel Testing
We test our kernels according to the two metrics defined by Aniano et al.
(2011): measuring how accurately the kernel redistributes flux (D, their equation
20), and studying the negative values in each kernel (W?, their equation 21), and
by comparing the encircled energy of the target PSF (F225W) and the convolved
source PSFs (F336W and F467M). We show the latter in Figure 3.3, where the
black line is the encircled energy of the F225W PSF, the dashed line is the original
source PSF, and red is the convolved source PSF (left: F336W, right: F467M).
We see from this that our PSF-matching reproduces well the target F225W PSF.
The integral of the absolute value of the difference between the target PSF and
the PSF derived from the convolution kernel is the definition of D, and D = 0 for
3https://photutils.readthedocs.io/en/stable/psf matching.html
94
Figure 3.3: A comparison of the encircled energy (energy with an aperture of radius
? divided by the total energy) of the target PSF, F225W, and the source PSFs:
F336W and F467M. The solid black lines are the encircled energy of the F225W PSF,
while the dashed gray lines and and solid red lines are the original and convolved
F336W (left) and F467M (right) PSFs. Our convolution kernels perform well and
are capable of matching the target PSF.
perfect kernel performance. For the K{336 ? 225} and K{467 ? 225} kernels
we derive, D336 = 0.0.00015 and D467 = 0.00016 respectively, which indicate very
good agreement between the PSFs. The W? value is defined as the integral of the
negative values in the kernel, and a kernel with a large value of W? may amplify
image artifacts. Aniano et al. find from experimenting with several kernels that a
value of W? ? 0.3 corresponds to a kernel that is very safe to use. Our kernels have
W?,336 = 0.01 and W?,467 = 0.21, thus we conclude that they are safe to use.
3.4.2 Clump Selection
To systematically select clumps in our sample of galaxies, we use the unsharp
masking technique, after which we run a source detection algorithm to identify
clumps. The unsharp masking technique is a filter that removes low-frequency
95
Figure 3.4: Outline of the unsharp masking technique for identifying clumps in
DYNAMO galaxies: original F336W image of the galaxy G04-1 (left), the F336W
image smoothed by convolving with a Gaussian kernel with a 15 pixel (0.6??) FWHM
(middle), the contrast image that is created by ?blending? the original and smoothed
image (right). The black contours outline regions that are at 5? the standard
deviation of the image, while the crimson coloured crosses mark the central positions
of the clumps that are identified in this galaxy and are selected to be brighter than
5? the standard deviation of the image and to have a minimum diameter of 5 pixels
(0.2??).
components of an image, thereby sharpening said image. Here we describe our
procedure, and refer to Figure 3.4 where we use galaxy G04-1 as an example to
illustrate this. We identify clumps from the F336W images (left panel of Figure
3.4) by first convolving each image with a Gaussian kernel whose full-width-half-
maximum (FWHM) is 15 pixels, which at the pixel scale of the image (0.04??/pixel)
corresponds to 0.6??, or 7.5? the size of the PSF for this filter. The result of this
convolution is a smoothed version of the F336W image, shown in the middle panel
of Figure 3.4. Finally a sharpened (contrast) image is produced by blending the
original image with the smoothed image (right panel of Figure 3.4):
sharpened = original + (original? blurred) ? C (3.5)
where C is a constant that controls how much lighter and darker edge borders
96
become; we use a value of 15 for all galaxies in our sample. We then use these
sharpened images to identify clumps in each of the six galaxies.
To detect clumps, we use the blob detection algorithm based on the Laplacian
of a Gaussian implemented in the Python package scikit-image (see skimage.feature.blob log;
van der Walt et al., 2014). This algorithm works by convolving the image with a
Gaussian kernel of a given size, then applying the Laplacian operator to the con-
volved image, which results in a strong response for clumps (?blobs?) on a given
background. The response of the operator is however sensitive to the relation be-
tween the size of the smoothing kernel, and the size of the clump. For this reason,
the scikit-image implementation of this algorithm, the blob log function, takes
as input the minimum and maximum standard deviation to use for the convolution
kernels, and the number of kernels to test between the minimum and maximum.
We impose the criterion that clumps must have a minimum diameter of 2.5?
the size of the F336W PSF. The F336W PSF has a size of 2 pixels, thus all our
clumps are required to have a minimum diameter of 5 pixels. We therefore input
?
into the blob detector function a minimum standard deviation of 2.5/ 2, and test
smoothing kernels that increase in units of 0.05, up to a maximum of a 9 pixel diam-
eter. The clump finder also takes as input a threshold parameter which controls the
required intensity a clump needs to have to be detected. We set our detection limit
such that clumps are regions that are 5? the standard deviation of the sharpened
image (see black contours in the right panel of Figure 3.4). The clumps that meet
all these requirements are indicated by crimson coloured crosses in the right panel
of Figure 3.4.
97
Fisher et al. (2017b) finds that DYNAMO clumps have a median diameter of
? 450 pc in HST H? images, in two ways: (1) by fitting 2D Gaussian functions to
each clump, then defining the clump size as the geometric mean of the major (a)
?
and minor (b) axes resulting from the 2D Gaussian fit: 2? a? b, and (2) by fitting
a 1D Gaussian to the light profile of each clump, then defining the clump size as
2?? from the 1D Gaussian fits. We adopt the latter technique: for each clump, we
mask neighboring clumps, extract the clump light profile, fit a 1D Gaussian, then
define the clump size as rclump = 2? ?, which encompasses 95% of the clump light.
We report these sizes in Table B.1 in Appendix B.1. From this, we find a median
clump diameter of ? 400 pc, similar to the Fisher et al. (2017b) results.
3.4.3 Photometry
The motivation for the filter choice to observe the six DYNAMO galaxies
in our sample was the fact that they provide colours that are sensitive to stellar
population age and extinction. At the DYNAMO redshifts, the F225W and F336W
filters bracket the UV slope, thus the 225?336 colour is sensitive to changes in dust
extinction. Conversely, the F336W and F467M filters measure the 4000A? break,
thus they bracket stellar emission and the 336?467 colour is sensitive to changes in
the age of the underlying stellar population. With these two colour combinations, we
are able to establish constraints on how much extinction and age each contribute to
the evolution of the clump colours. To this end, we modified Starburst99 (Leitherer
et al., 1999) to use the HST filter transmission curves for determining colours, and
98
to blueshift by 1 + z the transmission curves of the standard HST filters to derive
the colours at the rest wavelengths of interest. We then derive models for a single
burst of star formation at solar metallicity to track how the two colours we measure
here evolve with time, in steps of 0.1 Myr. As we perform our photometry and
derive results from them, we will compare our colours to those of Starburst99 to
infer the age and extinction structures within clumps.
3.4.3.1 Aperture Photometry
We perform aperture photometry for each clump identified by the procedure
described in the previous section. We center a circular aperture on every clump with
radius equal to rclump, and define a circular annulus whose inner radius is 4?rclump,
and whose outer radius is 5?rclump, for disc subtraction. We mask from this annulus
any pixels that are contaminated by other nearby clumps. We then calculate the
clumps flux as:
?nA
F = Fi ? nAB (3.6)
i=1
where F is the total flux in electrons per second, nA is the total number of pixels in
the clump aperture, and B is the median disc light measured in the disc annulus.
We perform the above calculation with and without disc subtraction for comparison.
We estimate the uncertainties on all of our measurements by calculating the
aperture signal?to?noise ratio (S/N) using the CCD equation (see for e.g., Howell,
2006):
99
S
= ? N?t (3.7)
N N t+ n (1 + nA )(N t+N t+N2 +G2?2? A n S DB R f )
where N?t is the total aperture counts (i.e., counts s
?1? exposure time), nA is the
total number of pixels in the clump aperture, nB is the total number of pixels in the
background annulus, NSt is the total counts per pixel from the background, NDt
is the total number of counts due to the dark current, N2R is the total number of
counts per pixel from the read noise, and G2?2f accounts for the error introduced
by the digitization noise within the A/D converter. These terms are obtained in
the following way: (1) N?t and NSt are what we measure, (2) we use a value of
?8e?/hr/pixel for the WFC3 CCD dark current to calculate NDt (late-2017 value
from the WFC3 Data Handbook, version 4.0 ? May 20184), and (3) we obtain the
read noise and gain terms from the images headers. Since we report results in
magnitudes, the final uncertainties are:
1.0857
?magnitudes = . (3.8)
S/N
We perform the above calculations with and without disc-subtraction, and
record the non-disc-subtracted integrated measurements along with their uncertain-
ties in Appendix B.1, Table B.1. We choose to exclude disc subtraction, because as
we will show in ?3.5.1, the disc colour distributions are relatively flat, thus including
disc subtraction will only increase the uncertainties of our measurements.
We plot the non-disc-subtracted integrated colours in Figure 3.5, where each
4https://hst-docs.stsci.edu/wfc3dhb
100
set of coloured points corresponds to one of the six galaxies in our sample. The
solid and dashed coloured grid overlaid in the background represent the change of
the 225?336 and 336?467 colours, as derived by Starburst99 for a single burst of
star formation and solar metallicity, and for varying degrees of extinction. We use
the Cardelli et al. (1989) extinction law to derive a relation between the 225?336 and
336? 467 colours and Av, the extinction at rest-frame V-band. We then begin with
the Starburst99 model with an Av = 0 magnitudes and then redden the model by
increasing Av in steps of 0.2 magnitudes, until we reach Av = 2 magnitudes. Thus,
each individual coloured line represents the evolution of the 225?336 and 336?467
colours at a fixed value of Av, for ages ranging from 5 Myr to 500 Myr.
We can see from this that dust extinction primarily moves the colours hor-
izontally while age primarily moves the colours vertically. Though there is some
diagonal evolution with increasing extinction and age, indicating that both affect
the colours, it is clear that (by experimental design) a change in extinction has a
much larger effect on the 225? 336 colour, while a change in age has a much larger
effect on the 336 ? 467 colour. The integrated colours of the clumps in our DY-
NAMO galaxies all lie within ages of 10? 250 Myr with Av extinction ranging from
0.6 to 2.0 magnitudes. To assess the impact of our choice of metallicity on the ages
we infer, we compare the model we adopt here (single burst of star formation and
solar metallicity), to a model with the same star formation history and 40% solar
metallicity in Figure B.1 in Appendix B.2. This changes the ages we infer from our
current adopted model by a factor of ? 1.4; namely clumps appear older by a factor
of ? 1.4 in the lower metallicity model. Assuming a continuous star formation his-
101
Figure 3.5: Colour-colour diagram of the 336?467 colour (proxy for age) versus the
225?336 colour (proxy for extinction), showing the integrated colours of each clump
in our sample. The grey error bars are the photometric uncertainties, and we show
the median errors bars in the bottom right corner. The coloured lines represent the
evolution of these two colours as modeled by Starburst99, with extinction applied
ranging from AV = 0 to AV = 2: the solid coloured lines are AV = 0, 1, 2, while the
dashed lines increase AV in steps of 0.2 (AV = 0.4, 1, 1.6 are labeled). The points on
each line correspond to specific times after a single burst of star formation: 5, 10, 50,
100, 250, 500 Myr (labeled). These colours suggest clump ages as young as 10 Myr,
and no older than 250 Myr, consistent with the ages derived in high?z simulations
of clumpy star forming galaxies (Bournaud et al., 2014). They also suggest visual
band extinction values in the range AV ? 0.6? 2.0, while for any one given galaxy,
extinction does not vary drastically from clump-to-clump. This is consistent with
the findings of Bassett et al. (2017); in addition, we derive AV clump values that
are in agreement with theirs for our overlapping galaxies (D13-5, G04-1, G20-2).
102
tory rather than a burst of star formation has a much larger impact on the inferred
ages; in this case the inferred ages increase by several factors of 10, with clump ages
? 2 Gyr in some cases, for both the solar metallicity and 40% solar metallicity sce-
narios. We note, however, that these models likely represent a simplified scenario,
and that the true star formation history of these clumps may be a combination of
both bursty and continuous star formation.
3.4.3.2 Surface Brightness Profiles
In addition to measuring integrated fluxes and colours for each clump in our
sample, we also derive surface brightness profiles as a means of investigating clump
properties as a function of distance from the clump center. We use a set of concentric
circular annuli, centered on each clump, where each annulus is two pixels wide
(0.08??, or approximately 150 pc for z ? 0.1), and overlaps with the previous annulus
by one pixel (therefore the central radius of the annulus moves by 0.04??for each
measurement). We do this to smooth the surface brightness profiles because each
clump is only a few pixels across, and we are therefore working with small numbers of
pixels. We sum the signal within the annulus, determine its area, and then calculate
the surface brightness according to:
? [mag arcsec?2] = mHST + 2.5 log10(A) (3.9)
where mHST is the total signal of the annulus, in AB magnitudes, and A is the area
of the annulus in arcsec2.
103
Figure 3.6: Left: The ?f225w (blue circles), ?f336w (yellow circles), and ?f467m (red
circles) surface brightness profiles as a function of distance from the clump center,
for clumps in galaxies D13-5 (clump 4), G08-5 (clump 3), G14-1 (clump 3), and
G20-2 (clump 9). Middle: The 225 ? 336 colour profile (yellow filled circles) and
the conversion of these colours to AV extinction (open yellow circles). Right: The
336 ? 467 colour profile (red filled circles) and the conversion to age (open red
circles). We plot the uncertainties as gray lines, the dashed vertical lines indicate
rclump, and the solid black curve is the F225W PSF. When we map these colours
to age and extinction, we see that there are clumps that show clear increase in age
from the center and outward, such as we show in galaxy D13-5 and G08-5, while
other clumps show a large increase in extinction rather than age, such as we show
in galaxy G14-1 and G20-2.
104
We perform background subtraction in the same manner as we do in our
aperture photometry, but now we apply it to each annulus. Furthermore, we mask
nearby clumps that may contaminate the surface brightness profile of a given clump,
by excluding those pixels from our calculations. Finally, we are also able to derive
colour profiles from the surface brightness profiles.
In Figure 3.6, we show examples of the surface brightness (left panel) and
colour profiles (middle and right panel) for clumps in galaxies D13-5 (clump 4),
G08-5 (clump 3), G14-1 (clump 3), and G20-2 (clump 9). We chose these four
examples to illustrate two typical trends we observe in the clump colour profiles.
We measure the lowest S/N and largest uncertainties in the F225W images, thus the
225?336 colour profiles generally have larger uncertainties than the 336?467 colour
profiles. The filled coloured symbols in the middle and right panels correspond to
the actual colour measurements, while the open symbols show the conversion of
these colours into AV extinction and age.
To map our colours to age and extinction, we first note that:
A225 A336 A467
= 2.667089, = 1.634535, = 1.2229745 (3.10)
AV AV AV
assuming the Cardelli et al. (1989) extinction law. Combining these relations, we
obtain:
A225 ? A336 = C1 ? AV = (225? 336)o ? (225? 336)i (3.11)
105
A336 ? A467 = C2 ? AV = (336? 467)o ? (336? 467)i (3.12)
where the subscript ?o? corresponds to observed colours and the subscript ?i? corre-
sponds to intrinsic colours, and C1 = 1.032554 and C2 = 0.411561. Then, multiply-
ing equation 3.11 by C2 and equation 3.12 by C1, and subtracting the two equations
from each other, we obtain an equation independent of AV :
C2[(225? 336)o ? (225? 336)i]? C1[(336? 467)o ? (336? 467)i] = 0. (3.13)
We use our observed colours from the HST observations and the colours generated
by Starburst99 with 0.1 Myr time steps to solve equation 3.13 and infer an age.
We then use the results to solve for AV from equations 3.11 and 3.12. Those are
the numbers that we present on the right y-axis in both of these panels. We match
to extinction and age in this way because these two parameters are not entirely
independent of one another; i.e., changes in extinction have a small effect on the
336?467 colour, while changes in age also have a small effect on the 225?336 colour
(the model grid lines are not parallel to the x? and y? axes). A significant fraction
of the clumps in our sample show colour (age/extinction) profiles such as the ones
we show for galaxies D13-5 and G08-5 in Figure 3.6, where there is a strong increase
in age, while fewer clumps show profiles such as the ones we show for galaxies G14-1
and G20-2, where there is no strong change in age but a strong change in extinction
106
across the clump. This will be discussed further in ?3.5.2.
3.5 Results and Discussion
3.5.1 Galactocentric Variations of Global Clump Properties
We begin by first inspecting the evolution of clump colours as a function of
their position within their galaxy, and compare clump colours to the disc colours.
In Figure 3.7 and 3.8, we plot for all six galaxies, the integrated 336 ? 467 and
225? 336 colours respectively, of each clump as a function of galactocentric radius,
normalized to the galaxy F467M half-light radius (effective radius: Reff,467). To
assess the impact of disc light on the clump colours we measure, we show the non-
disc subtracted (filled symbols) and disc subtracted clump colours (empty symbols).
We include the photometric uncertainties (section 3.4.3.1) as gray error bars on the
non-disc subtracted colour. The solid black line in each panel shows the disc light
evolution. To measure the disc light, we first mask all pixels that we identify as
clump pixels. We then place a series of annuli at the galaxy center, which we define
as the pixel of peak emission in existing HST F125W images (wide J). We finally
integrate the light in each annulus, out to 4??.
In our clump light to disc light comparison, we notice two things: (1) the 336?
467 clump colours are generally bluer than the disc light, within the uncertainties,
independently of whether we subtract the disc background light from our clump
measurements or not, and (2) the disc light is much flatter as a function of radius,
than the clump colours (these trends were also observed for 0.5 ? z < 3.0 galaxies by
107
Figure 3.7: Clump integrated 336? 467 colour without (red filled circles) and with
disc subtraction (red open circles) as a function of galactocentric radius (the upper
x-axis scale gives the galactocentric radii equivalents in kpc). Photometric uncer-
tainties appear as gray error bars. The gray-shaded regions are the u ? b results
of Guo et al. (2018) at redshifts of 0.5 ? z < 3.0, for comparison. The 336 ? 467
colour, a proxy for age, is redder for clumps closer to the center of their galaxy and
bluer for those on the outskirts, with the exception of galaxy G14-1 for which the
opposite is true. However, the disc colours are relatively flat in comparison (black
solid line). Furthermore, we see that clumps are on average bluer than the disc, and
this is true whether or not we subtract the disc light. This suggests clumps are older
closer to the centers of their galaxies and that this is not an effect of contamination
from disc stars.
108
Guo et al., 2018). With respect to the first point, it is perhaps not surprising that
the clumps exhibit bluer colours than the disc, because we select them as bright
regions in the F336W (U band) images. This does however suggest that clumps
are a structure separate from and embedded within the disc of the galaxy. This
is further supported by our second observation: that the clump colour gradient is
much steeper than the disc light suggests that clumps are structures that exist and
evolve within the discs.
We see in all cases except for G14-1 that the 336? 467 colours of clumps tend
to be redder closer to the galactic centers, and bluer farther in the outskirts. This
trend has been previously observed in the u ? b colours of high?z galaxies (e.g.,
Fo?rster Schreiber et al., 2011, Soto et al., 2017, Guo et al., 2018). We reproduce
here the results presented in Figure 8 of Guo et al. (2018) as the gray shaded area
in each panel of Figure 3.7, to illustrate the trends measured by these authors. The
authors normalize their clump distances to the HST F160W effective radius along
the galaxy major axis. At redshifts of 0.5 ? z < 3.0, they are unable to distinguish
clumps from galaxy bulges at normalized galactocentric radii < 0.5, which is where
we find many of our clumps. This shaded region covers the median u? b values in
the 0.5 < z < 1.0 and 1.0 < z < 2.0 redshift bins, for all three mass ranges the
authors present. Such a colour gradient suggests that since the 336? 467 colour is
age-sensitive, the clumps that are closer to the centers of their galaxies are older
than their bluer counterparts in the outskirts. We will discuss this further in ?3.5.3.
It is important to note that our observations remain true whether we apply
disc subtraction or not. In fact, we can see that when we subtract the disc light, the
109
effects are generally the greatest on the clumps that are farther from the centers of
their respective galaxies: the colours of these clumps become even bluer than the
uncertainties, while the clumps closer to the center do not change so drastically.
This has the effect of steepening the colour gradients we observe when we perform
disc subtraction and is in disagreement with the hypothesis that colour gradients
observed in galaxies are the result of contamination of clump colours by older disc
stars, whose densities are larger closer to the centers of galaxies (Buck et al., 2017,
Oklopc?ic? et al., 2017).
Other authors suggest that negative colour gradients, in which the clumps
deviate from the galaxy gradient, are interpreted as supporting theories in which
clumps migrate to the centers of galaxies and contribute to bulge growth. Dekel et al.
(2009) predict migration timescales on the order of ? 10? the dynamical timescale,
or about 0.5 Gyr, from their theoretical framework, while Ceverino et al. (2010)
perform the first cosmological simulation of high-z clumpy discs and show that
their simulated clumps migrate to the centers of their hosts in ? 8? the dynamical
timescale. From the clump ages suggested by the integrated colours in Figure 3.5 of
? 50 ? 250 Myr, and the colour gradient observed here, we find that this scenario
remains plausible given these observations and our measurements.
In Figure 3.8, we show the behavior of the 225 ? 336 colour and compare
the clumps to the discs (as in Figure 3.7). We see that the disc colour gradient
varies from galaxy-to-galaxy: a flat profile in this colour suggests little variation
in extinction across the disc of the galaxy, while a downward (upward) turn in the
colour would suggest a decrease (increase) in extinction. When inspecting the clump
110
Figure 3.8: Same as Figure 3.7, but now showing the integrated 225 ? 336 colour
without (filled yellow diamonds) and with (empty yellow diamonds) disc subtraction.
The gray solid line shows how the 225? 336 colour evolves across each galaxy when
we mask clumps. The 225 ? 336 colours of clumps are generally flatter than the
336? 467 and track the disc colour more closely, suggesting clump extinction does
not differ strongly from the disc extinction.
111
colours, we do not find a very strong preference for clumps to appear much bluer
than the discs, as we do in the 336?467 colour. Clumps are generally either slightly
bluer than the discs or scatter around the disc colours. It may not be surprising
to measure bluer colours for clumps, because they are F336W-bright regions, and
thus are likely to have less dust. In fact, previous works have observed this trend as
well; for example Wuyts et al. (2013) find that the rest-UV-selected clumps in their
sample of 473 CANDELS galaxies exhibit lower H?/UV ratios than the underlying
disc, which they interpret as an indication that these clumps are viewed through a
smaller column of obscuring material. Conversely, Bassett et al. (2017) find little
spatial variation in extinction across a subset of DYNAMO galaxies, thus it may
also not be surprising to find clumps with 225 ? 336 colours similar to the discs
within which they reside.
However, the gradient of 225? 336 colour with galactocentric radius seems to
in general have a similar sign gradient for the clumps as the disc light, and in some
cases the clumps follows the disc colour gradient closely. This is well illustrated
in G04-1, where the disc colour decreases from the center, flattens, then decreases
again. This same trend is seen in the clumps and is in contrast to what we observe
in the 336 ? 467 colour, where the trends with galactocentric radius of clumps is
not observed in the disc light, indicating that disc contamination is not the source
of the colour gradient.
Our observations of the 225 ? 336 clump colours remain true when we apply
disc subtraction. The effect of disc subtraction on the 225?336 colour is less severe
than on the 336 ? 467 colour and shows that dust extinction is not a contributing
112
factor to the observed colour gradient in the 336? 467 colour. In summary, clumps
are similar to their host galaxy?s disc in extinction, but are very different in age.
3.5.2 Internal colour Gradients of Clumps
The 0.092?? resolution of the F225W HST observations allows us to go beyond
investigating integrated clump colour trends with galactocentric radius, and to in-
spect how these colours vary across the extent of each individual clump (?colour
track?). At the average DYNAMO redshift of z? 0.1, this angular resolution cor-
responds to ? 170 pc; thus, it is not possible to do this analysis in clumps at z? 1.
To derive the internal colour gradient of each clump, we use the surface brightness
profile measurements of Section ?3.4.3.2 to calculate colours in concentric circular
annuli, centered on each clump (essentially combining the two colour profiles in Fig-
ure 3.6 into a two-dimensional representation, which we call a ?colour track?). We
illustrate one example of such a colour track for galaxy DYNAMO D13-5, clump 4,
in Figure 3.9. The axes and the coloured grid are the same as in Figure 3.5; however,
the data points now represent the colour change of one clump from its center (white
point), to its edge (black point). In this particular case, we see that the colour track
suggests a large change in age with fairly constant extinction across the clump. This
is because as we move outward from the center of the clump, the colours track along
the line of a single extinction model (in this case AV ? 1.2), indicating constant
extinction and varying age. In the bottom panel of Figure 3.9, we illustrate another
colour track for clump 9 in DYNAMO G20-2. In this case, the colour track is nearly
113
parallel to a line of constant age (? 50 Myr), and crosses many lines of extinction,
indicating that extinction varies strongly across this clump, while age does not. For
ease of visualization, we fit this colour track with a line that minimizes the distance
between the points and itself. The red line in Figure 3.9 is this fit. We fit the colour
track of all 58 clumps in our sample in this way.
In Figure 3.10 we show the fitted lines of the colour tracks for all clumps. The
axes and coloured grid are exactly the same as in Figures 3.5 and 3.9. We have
added an additional colour bar in the second row to show how AV translates into
A336 when we assume the extinction law of Cardelli et al. (1989). The solid red
shaded lines show the fitted colour track of each clump in our sample. Thus, they
represent the general change of the 225?336 and 336?467 colours across the extent
of each clump. We shade the lines to represent the clump S/N in the F336W images:
darker (lighter) shaded lines have higher (lower) S/N. The single data points found
at one end of each colour track correspond to the central region of each clump, thus
indicating the direction in which the distance from the clump center increases. The
length of each colour track is such that the end point corresponds to the colours
of the outermost annulus of each clump, defined as the ?edge? of the clump as
described in Section 3.4.2 (rclump).
We identify from this collection of colour tracks three scenarios (in increasing
order of occurrence frequency): (1) clumps with colour tracks that suggest little
to no change in age and large changes in extinction across the clump; these are
indicated by shallow positive (increasing extinction) or shallow negative (decreasing
extinction) slopes (i.e., colour tracks that cut across many lines of AV but follow
114
Figure 3.9: The same colour? colour space as we show in Figure 3.5. The data
points now represent the colour track of a two clumps: DYNAMO D13-5 clump 4
(top panel) and DYNAMO G20-2 clump 9 (bottom panel), with colours measured
in concentric circular annuli centered on the clump, showing their internal age and
extinction structure. The shading of the data points corresponds to the distance
from the center of the clump in steps of 0.04??(? 60 pc) as described in ?3.4.3.2:
white represents the colour at the center, black represents the colour farthest from
the center. The red solid lines shows the linear fits to these colour track. The
internal colour gradient of the first clump indicates that it has a constant AV of
? 1.2 and that the age is a few 10 Myr at the center and increases to > 100 Myr
at the clump edge, while the colour track of the second clump indicates it has a
constant age of ? 50 Myr and a large change in extinction (from AV ? 0.8?1.6).
Median error bars on the colour track points are shown in the bottom right corner
of the top panel.
115
Figure 3.10: For each clump in our sample we plot a colour track which represents
how the colour of the clump itself evolves from its center to its edge, in the 225?336
vs 336? 467 parameter space. The coloured lines represent V? band extinction, as
in Figure 3.5. The red lines show the linear fit to the colours of each clump measured
in concentric annuli as a function of distance from the clump center with the dot
indicating the value at the center, and are shaded based on the F336W S/N (these
range from ? 10?150). Thus, lighter shaded lines have lower S/N, while darker ones
have a higher S/N and are more certain. We can see that for high S/N clumps the
colours typically change primarily along the vertical axis, indicating that there is a
gradient present within clumps themselves. Moreover, the majority of these clumps
change in the direction of increasing age farther from their centers. A handful of
the clumps show preferentially an extinction gradient, and for some galaxies (e.g.,
D13-5) the presence of age gradients is more marked than for others (e.g., G20-2).
116
a single age line) ? see galaxy D13-5, D15-3, G04-1, and G20-2 for examples, (2)
clumps whose colour tracks indicate decreasing age with increasing distance from
the clump center; these are indicated by steep negative slopes ? see galaxy G20-2 for
examples, and finally (3) clumps whose colours show large increases in age from the
clump center with ? constant extinction (i.e., these tracks cut across many ages lines
but no, or few, lines of AV ) in some cases, and with large increases (decreases) in
extinction; these are indicated by steep positive (negative) slopes (i.e., these tracks
cut across many lines of AV and many age lines) in other cases. Of the 58 clumps
in our sample, the distribution of clumps per scenario is: (1) 7, (2) 10, and (3) 40.
Thus, ? 70% of the clumps in our sample show colour tracks with increasing ages
away from the centers.
To verify that our PSF matching is not falsely producing these colour gradients,
we create mock clumps to test our PSF matching procedure. We model clumps
with a symmetric 2D Gaussian profile, with sizes matching those of our observed
clumps. We convolve each of these to the PSF profile of each HST filter, to simulate
observations. We measure the internal clump colour gradients of these simulated
clumps, then we perform our PSF-matching and measure the internal clump colours
once more. We find that in cases where we create clumps with zero colour gradients,
we recover no gradient, and in cases where we create clumps with a given gradient, we
are able to recover it as well. Thus, we conclude that our PSF-matching procedure
is not producing artificial gradients.
Clumps in the first category, whose colours suggest constant ages and large
increases in extinction may correspond to ?pseudo-clumps?. This may be an indi-
117
cator that even though we identify these objects as clumps, they may be holes in
extinction that create a clumpy light distribution. This was observed in the NI-
HAO simulation by Buck et al. (2017), where non-clumpy galaxies showed clumpy
U?band light distributions due to clumpy gas distributions and clumpy star forma-
tion events. However, if all clumps that we observe in our DYNAMO sample were
the result of this, then we would expect all of their colour tracks to fall in this first
category, which is not what we find.
Nearly three-quarters (40) of the clumps we select in these six DYNAMO
galaxies lie in the third category: clumps with large increases in age. This trend
is particularly well illustrated in galaxies D13-5, and D15-3. This suggests that
the evolution of these two colours is driven predominantly by age: the clumps are
younger at the centers and older toward the edges, and extinction is not a large
contributor to the clump colour evolution. This observation suggests that these
clumps are an entity separate from the galaxy disc, with an inner structure whereby
star formation is predominantly found in the central regions. These results are
interesting because they indicate that clumps observed in high?z galaxies and local
analogues likely consist of a combination of ?real? physical structures, and ?pseudo-
clumps? that are a result of clumpy light distributions. The ability to distinguish
these would likely be important for simulations of high?z systems, and the colour
tracks of clumps could potentially be used as an additional criterion for selecting
and distinguishing real clumps in galaxies.
Another possibility is that these clumps are perhaps composed of smaller star
forming clusters that follow the cluster pair separation-age difference relation (Efre-
118
mov and Elmegreen, 1998, de la Fuente Marcos and de la Fuente Marcos, 2009,
Grasha et al., 2017). Grasha et al. (2017) show that for eight local galaxies, the age
difference between pairs of star forming clusters increases with their separation to
the power of ? 0.25?0.6. The authors also find that the maximal scales over which
cluster pair separation and age difference are correlated, range from ? 200 pc ?1
kpc. We are unable to resolve any potential smaller clusters within each clump and
measure the cluster pair separation-age difference relation (measuring pixel-to-pixel
differences is not feasible as the photometric uncertainties are too large to yield
meaningful results). It is nonetheless worth noting that these clumps could break
up into even smaller structures at higher resolution, which we cannot ascertain with
currently available data. However, high-resolution simulations of isolated clumpy,
high-z discs do show substructures within giant clumps (see e.g., Ceverino et al.,
2012).
3.5.3 Galactocentric Variations of Resolved Clump Properties
Based on the internal colour gradient observation that the majority of clumps
appear older in their outskirts and younger at their centers, we compare the ?inner?
and ?outer? clump ages as a function of galactocentric radius, shown in Figure 3.11.
Here, we plot the estimated ages of clumps as a function of the clump galactocentric
radius, normalized to the effective F467M radius, Reff,f467m, in three different ways.
We first consider each clump as a whole (left panel), then we split each clump at the
radius corresponding to 0.5? rclump,467, to define an ?inner? (middle panel) and an
119
Figure 3.11: Clump ages estimated for the whole clump region from the integrated
light within rclump (left), the inner 25% regions (middle), and the outer 75% (right),
vs. galactocentric radius, compared to the estimated disc ages (solid coloured lines).
Error bars show the spread in ages when shifting the inner and outer clump bound-
aries by 10%. The strongest correlation is between the outer clump regions and
galactocentric radius, which we quantify with the Spearman Rank-Order correlation
coefficient, ?, where we see clump age increasing with decreasing distance. However,
the disc profiles are flat in comparison (with the exception of galaxy G08-5), sug-
gesting that the clump age?distance relation is not due to an underlying age trend
within the discs themselves. We fit a power law to the outer clump age?distance
relation (black dashed line in the right panel) and report the slope of this fit (?).
The outlying point in galaxy D15-3, which appears much older than other clumps,
is measured as an upper limit in the F225W image.
120
?outer? (right panel) clump region. These regions, thus, cover the inner 25% and
outer 75% of the clump area respectively. In the last panel we also show a fit to the
relationship between outer clump age and normalized galactocentric radius using a
linear relation in log-log space, which corresponds to a power law in linear space.
For the three panels in Figure 3.11, we measure the clump light in (1) a
circular aperture whose radius is rclump, (2) in a circular aperture whose radius is
0.5 ? rclump, and (3) in an annulus whose inner radius is 0.5 ? rclump and whose
outer radius is rclump (we check and ensure that the sum of the inner and outer
regions is equal to the clump light we measure in the circular aperture of size rclump).
Performing this measurement in all three filters, we then calculate both the 225?336
and the 336 ? 467 colours of these regions, and simultaneously match them to the
Starburst99 models, as described in Section 3.4.3.1 and done in Figures 3.7 and
3.8. The clumps are separated according to which DYNAMO galaxy they reside
in, as indicated by the legend. The error bars on the data points indicate how the
spread in estimated ages changes when we shift the boundary between the inner
and outer clump by 10%. The downward directed error bars are generally larger
than the upper error bars because shrinking the inner clump boundary significantly
increases the photometric uncertainties and causes clumps to appear much bluer (as
a result of the intrinsic colour gradient).
To compare the clump ages to the discs, we include the solid coloured lines
which show the disc age distributions derived from the disc colour profiles, and are
the same in all panels. As we show in Figure 3.7, the discs are redder in 336? 467
and thus considerably older than the vast majority of the clumps. We include the
121
non-parametric Spearman rank correlation coefficient, ?, in each panel, showing
that the most significant correlation is between outer clump age and galactocentric
distance. Finally, we also include in the right panel the fitted slope of the outer
clump age?distance relation: ? = ?0.69+0.11?0.28, where the uncertainties correspond
to 1? determined from a bootstrap analysis. We compute the mean age and 1?
standard deviation of each panel to further quantify the spread in the data: (left)
90.5? 69.1 Myr, (middle) 66.2? 70.7 Myr, (right) 96.8? 75.3 Myr.
From the left panel of Figure 3.11, we can see that clumps are generally esti-
mated to be ? a few 100 Myr younger than the galaxy discs, and the ?oldest? clumps
we see are ? 250 Myr old. We also do not see any ?old? clumps in the outskirts
of the galaxies, and we do not see any very ?young? clumps close to the centers.
We note that we generally observe fewer clumps at the smallest galactocentric radii;
however, this may be expected as the infall of clumps closer to the centers of galaxies
would take place faster than for clumps farther out. Thus it would be more likely
to observe clumps at large galactocentric radii, than at smaller ones. Alternatively,
it may also be a geometric effect where we would expect to find fewer clumps in a
galaxy if we decrease its size (radius), and therefore its area.
When we break up each clump into an inner and outer region, we see that in
general the ages of the inner clumps are younger than the outer clumps by a factor of
2 to 4. Furthermore, outer clump regions in clumps closer to the centers of galaxies
tend to be older, while the inner regions of clumps have similar ages regardless of
where in the disc the clump is located. In other words, the inner clump ages do
not show a trend with galactocentric radius, while the outer clump regions present
122
a much clearer trend. We can see this well illustrated when comparing the two
measures of the age of a clump for a given galaxy. For example in D13-5, the inner
clump ages follow a relatively flat distribution with a lot of scatter, while the outer
clump ages increase toward smaller galactocentric radii. If clumps keep forming
stars in their cores as they migrate through the disc, then young stellar populations
will be maintained in these regions and skew the light-weighted ages to younger
values. In contrast, the outer regions of clumps show a stronger preference to be
older when located closer to the centers of galaxies, and younger at the outskirts.
Fo?rster Schreiber et al. (2011) find a steep relation between clump age and distance
in their study of clumps in six z ? 2 galaxies (see their Figure 8, bottom panel),
with a power-law slope of ?2.06 ? 0.63 (slope measured by Genel et al., 2012). In
contrast, Guo et al. (2018) find an increasingly steeper clump age?distance relation
with decreasing redshift (see their Figure 9): at z ? 2?3 this relation is flat, while at
z ? 0.5?1 the slope of the relation becomes ? ?1.5. Similarly, Zanella et al. (2019)
find a relatively flat clump age?distance relation for their sample of 53 star forming
galaxies at z ? 1?3 (see their Figure 8). However they list as possible explanations
for the difference between lower- and higher-redshift results as: (1) signatures of
migration might not yet be visible at z ? 2, (2) the improved spatial resolution at
lower-redshift may improve the detection of clumps at small galactocentric radii,
and (3) measurement uncertainties may ?hide? underlying age gradients.
Finally, in Figure 3.12, we plot the age difference between the inner and outer
clump regions (middle and right panels of Figure 3.11) as a function of normalized
galactocentric distance. Clumps with negative age differences are those with colour
123
Figure 3.12: The age difference between the outer and inner clump region as a
function of normalized galactocentric radius. Negative age differences correspond
to clumps whose colour tracks indicate ?older? inner clump regions compared to
the outer clump regions. In general, the age difference increases with decreasing
galactocentric distance, with the innermost clumps showing age differences as large
as ? 100?150 Myr.
124
tracks that show decreasing ages with increasing distance from the clump center.
For the remaining clumps, we generally observe the smallest age differences for
clumps at the largest galactocentric distances, and the largest age differences for
the more centrally located clumps. For these, we observe age differences as large as
150 Myr. Dekel et al. (2009) predict that if radiative feedback successfully suppresses
star formation in clumps, then the spread in their stellar ages should not exceed
? 50?100 Myr.
3.5.4 Comparison to Hydrodynamic Models
While there is a mixture of results at higher-redshifts, our picture is consistent
with the findings of high?z simulations such as those presented in Ceverino et al.
(2010, 2012), Bournaud et al. (2014), Mandelker et al. (2017). Ceverino et al. (2010)
present results from the first cosmological simulations of three high?z, clumpy galax-
ies that produce disc fragmentation from gas stream driven instabilities. This results
in discs with morphologies that are very similar to observed high?z systems, includ-
ing clumpy star forming rings such as we see in DYNAMO D13-5 (our Figure 3.1;
see their Figure 6). The resulting clumps migrate and coalesce with the bulge on
timescales of ? 250 Myr. This timescale is consistent with the outer clump ages of
the most centrally located clumps in our sample (see Figure 3.11). Ceverino et al.
(2012) build on this by including two additional zoom-in cosmological simulations
at z = 2 ? 3 to study internal support against collapse for 77 clumps. This works
includes three clumps analysed at 2 pc resolution, where they find that they frag-
125
ment into dense subclumps and that resolving these is important for understanding
the internal structure of clumps.
Bournaud et al. (2014) identify a population of massive (? 108 M) clumps
that remain long-lived in the simulations, meaning that they can be tracked in the
simulations for 200 ? 500 Myr, and up to 700 Myr in some cases, which migrate
to the centers of their galaxies. These clumps maintain relatively constant masses
and star formation rates (1 ? 2 M yr?1), despite outflows (1 ? 2 M yr?1 across
a 1 kpc2 section) and the dynamical loss of older stars (0.2 ? 2 M ?1 yr ), thanks
to re-accretion of gas from the surrounding gas-rich discs (2 ? 15 M ?1 yr ). The
observational consequence of this is that the apparent ages of clumps are dominated
by the light of young stars, and therefore saturate at around 200 Myr, thus clumps
can be up to twice as old as the median age of the stars within them. This is
consistent with the lack of clumps much older than ? 200 Myr that we observe,
while the tendency of older clumps to be preferentially located towards the centers
of galaxies supports the clump migration scenario. Furthermore, if the re-accreted
gas falls to the centers of clumps and forms stars there, then this would create clumps
with young centers and older outskirts, consistent with the clump age substructures
we observe in our sample.
Similar results are found by Mandelker et al. (2017), who also find that the
stellar ages of clumps are less than the true lifetime of clumps due to ongoing star
formation. In this work, the authors study the properties of high?z galaxies in
zoom-in hydro-cosmological simulations with and without radiation pressure feed-
back. The authors find that even in the case of radiation pressure feedback, clumps
126
more massive than 108.2 M are able to survive in the disc and migrate to the centers
of galaxies, while less massive clumps are considered short-lived (as long as their
ages are . 20? the clump free-fall timescale; see Mandelker et al., 2017, ? 5.1.2
for details). The authors present a comparison of the ages of short-lived clumps,
long-lived clumps, and ex situ clumps (which are clumps that join the disc after a
merger event), as a function of galactocentric radius (their Figure 15, top left panel).
We reproduce these results in Figure 3.13, where the coloured data points rep-
resent the long-lived clumps (blue circles), short-lived clumps (yellow diamonds),
and ex situ clumps (pink squares), while the solid coloured lines with black outlines
represent the 50th percentile of the respective three clump populations, binned in the
log of the normalized galactocentric distance. We can see from the data points in
Figure 3.13 that the scatter is large for all three populations of clumps. Two factors
make a direct comparison difficult: (1) the galactocentric distances in Mandelker
et al. (2017) are normalized to Rd, the radius that contains 85% of the cold mass
within a cylinder of a certain size (see Mandelker et al., 2017, for a more detailed de-
scription), and (2) the ages of simulated clumps are measured as the mass-weighted
mean stellar age. Neither the cold mass distribution nor the mass-weighted age can
be easily measured in observations: the lack of a good handle on the first introduces
an uncertainty in the scaling of the x-axis, while the light-weighted stellar ages we
observe will be systematically younger than mass-weighted ages. As a result, a di-
rect comparison of the DYNAMO clump age estimates to the simulated clump ages
is not meaningful. However, we can compare the slope of the power law fit to the
DYNAMO outer clump ages as a function of galactocentric distance, to the slopes
127
Figure 3.13: Comparison of the short-lived (yellow diamonds), long-lived (blue cir-
cles), and ex situ (pink squares) clumps of Mandelker et al. (2017). The solid
coloured lines with black outlines correspond to the 50th percentile in bins of log
normalized galactocentric radius, while the coloured lines with no black outline
represent the power law fits to the 50th percentiles. The power law slopes with un-
certainties determined through a bootstrap analysis are included in the figure. For
reference, the black dashed line is the best power law fit to the outer clump ages
which we show in Figure 3.11.
128
of the power law fits of the three clump populations of Mandelker et al. (2017). To
determine the slopes, we fit a power law to the 50th percentile lines; these fits are
represented by the coloured lines (no black outline). Finally, we perform a bootstrap
analysis to determine the uncertainties of these three fits. The three slopes along
with their 1? uncertainties are shown on the figure. They are: ?SLC = ?0.37+0.04?0.17,
? +0.05 +0.17LLC = ?0.46?0.09, and ?ExS = ?0.08?0.19. In comparison, the slope we find for the
DYNAMO outer clump ages is: ? = ?0.63+0.15?0.13.
From this analysis, we are able to conclude that the properties of the DY-
NAMO clumps are distinct from the ex situ clumps, and thus that the clumps we
observe are likely not ex situ clumps. This conclusion is also reported by Huertas-
Company et al. (2020). The authors present a new neural networks based method
for selecting clumps, which they apply to 9,000 star forming galaxies in CANDELS
in the redshift range z ? 1 ? 3. Their method yields ?3,000 clumps in ?1,500
galaxies. They derive clump properties, including stellar mass, from spectral energy
distribution fitting of seven photometric bands, and then construct a clump stellar
mass function. The authors apply the same procedure to 35 galaxies from the VELA
simulations (Ceverino et al., 2014) and find that, under the same conditions, the
cluster stellar mass functions agree well, suggesting an in situ origin for clumps in
CANDELS.
The slope of the age?distance relations for DYNAMO clumps may be as steep
as ?0.76 or as shallow as ?0.48, which puts it within the upper bound of the
long-lived clumps slope (ranges from ?0.41 to ?0.55). However, the slope of the
short-lived clumps ranges from ?0.33 to ?0.54, thus it is not entirely clear if the
129
outer clump regions of DYNAMO clumps are more similar to short-lived or long-
lived clumps in the high?z simulations of Mandelker et al. (2017). This is a result
of the scatter at large galactocentric radii, which drives the large uncertainty toward
steeper slopes for both the short-lived and long-lived clumps. We note that in their
high resolution cosmological simulations of z ? 2 galaxies, Genel et al. (2012) find
a power law slope of -0.57? 0.14 for the relation between clump age and distance,
which is in good agreement with our result. However, the authors explain that their
age gradient is due to the dominance of ?background? stars which are a part of
the galaxy discs and not actually gravitationally associated with the clumps. Then,
since their galaxy discs themselves have a negative age gradient (older disc stars
near the centers of galaxies), the clumps that are at found at smaller galactocentric
radii also appear older, despite no evidence of clump migration. Thus they conclude
that the clump-distance relation is a consequence of inside-out disc formation. In
contrast, the colours we measure for the DYNAMO galaxy discs do not imply such
strong negative age gradients, as was also observed in Ceverino et al. (2012) who
found a slope of ?1.2 for their simulated clump age?distance relation and a slope
of only ?0.3 for the simulated discs; thus we conclude that the age gradients we
observe in the clumps are not driven by the stellar distributions of the discs.
As a final point, we note that the simulated short-lived clumps are not common
at very small radii. Thus, despite the uncertainty introduced by the different radius
normalization between our work and that of Mandelker et al. (2017), we draw a
comparison between the distribution of DYNAMO clumps in galactocentric radius,
to the distribution of the short-lived, long-lived, and ex situ clumps in Figure 3.14.
130
Figure 3.14: Comparison of the distribution of DYNAMO (grey), short-lived (yel-
low), long-lived clumps (blue), and ex situ clumps in terms of normalized galac-
tocentric radius. The DYNAMO clumps are clearly distinct from the short-lived
clumps and cluster at radii < 1, as do the long-lived clumps. The median distance
of DYNAMO clumps (vertical black solid line) is ? 0.5 and is ? 1.1 for the short-
lived clumps. The radius normalization of the simulated clumps corresponds to the
radius that contains 85% of the cold mass, while we normalize to the 50% light-
radius measured in the F467M images. If we choose a larger radius definition as our
normalization, the median distance of DYNAMO clumps becomes ? 0.5 (vertical
dashed black line).
131
We can see that the short-lived clumps cluster at larger galactocentric radii than
do the long-lived and DYNAMO clumps. Thus the DYNAMO clumps and short-
lived clumps appear as two distinct populations in this figure. In fact, 50% of the
simulated short-lived clumps reside within a normalized galactocentric radius of
? 1.1, while 50% of the DYNAMO clumps are found within a distance of ? 0.5;
this implies that a large fraction of our clumps are not short-lived. We use the
50% light-radius in the F467M filter as our normalization for each galaxy; however,
if we instead normalize to the 85% light-radius in the F467M filter the peak of
the distribution shifts to slightly smaller distances. The vertical black solid line
indicates the median galactocentric radius of DYNAMO clumps when normalized
to the 50% light-radius, while the vertical, dashed black line indicates the shifted
peak when we normalize to the 85% light-radius. This shift represents a change of
a factor of 0.15 dex. Thus, we tentatively conclude from these comparisons that the
radial distribution of the DYNAMO clumps is more similar to the long-lived clumps
than the short-lived clumps identified in the high?z simulations of Mandelker et al.
(2017).
3.5.5 Toward a General Picture of Star Formation in Clumps
Putting the results of our HST photometry and colour measurements together,
we have a picture which is consistent with clump ages ranging from 10?250 Myr,
with older appearing clumps preferentially located closer to the centers of their
galaxies. We find that more than half of the clumps in our sample have an internal
132
age gradient, such that stellar population age increases toward the clump edges.
We interpret this as a scenario where continuous star formation in the centers of
clumps replenishes the populations of massive young stars as the clumps age and
move through their galaxy disc. This is consistent with the detailed picture of long-
lived clumps from simulations (Ceverino et al., 2010, 2012, Bournaud et al., 2014,
Mandelker et al., 2017).
White et al. (submitted) find with AO-enabled K-band imaging from Keck/NIRC2
that the stellar masses of clumps in DYNAMO G04-1, included in this sample, are
preferenced toward low masses. The clumps with M 8star > 10 M are located in
the center of the galaxy (after accounting for disc subtraction). This is consistent
with our picture of long-lived stellar clumps that grow as they migrate to the galaxy
center.
The range of ages we find, the trend of increasing age with decreasing galac-
tocentric radius, and the young clump centers are all consistent with high?z sim-
ulations that show the existence of long-lived clumps that are able to migrate to
the centers of their galaxies. The distribution of our clumps in terms of normalized
galactocentric radius is consistent with the long-lived clumps of Mandelker et al.
(2017), which further supports this scenario.
Our data are not consistent with predictions that clumps are only a result of
extinction gradients (Buck et al., 2017), as we observe that more than half of our
clumps have colour tracks that indicate large variations in age with little variation
in extinction. Furthermore, we propose that internal clump colour gradients may
be potentially used as a discriminator between clumps in mass and clumpy light
133
distributions, and suggest that observed clumps in high?z samples may consist of
a combination of these.
These results point to a depiction of clumps, not as monolithic structures, but
as complex objects with substructures that require further study. A comparison of
high resolution clump properties and their substructure with high resolution sim-
ulations would be very interesting in this regard. Several simulations of gas-rich,
clumpy star forming high-redshift galaxies that study the effect of resolution on
observed clump properties find significant substructures within clumps (Ceverino
et al., 2012, Behrendt et al., 2016, 2019, Faure et al., 2021). The giant clumps that
are ubiquitous at z ? 1? 3 appear in these simulations to be collections of smaller
clumps with masses of 107?8 M and sizes on the order of 100 pc. When matched
to the spatial resolution of high-redshift observations, these smaller clumps appear
to coalesce into these giant clumps with very well-matched properties including size,
mass, and high intrinsic velocity dispersions.
3.6 Conclusions
In this work we use HST observations of six DYNAMO galaxies taken in the
F225W, F336W, and F467M filters. We perform aperture photometry and surface
brightness photometry on these data, and use the results to measure the integrated
and clump?resolved 225? 336 and 336? 467 colours of clumps. These colours are
sensitive to extinction and age respectively: while the two colours are not indepen-
dent of each other, changes in extinction result primarily in changes in the 225?336
134
colour, and changes in age are reflected primarily in changes in the 336?467 colour.
Our main findings are:
1. The integrated 336 ? 467 colours of clumps become increasingly redder with
decreasing galactocentric radius. This indicates that clumps closer to the centers
of galaxies are older than ones farther out. Furthermore, the underlying colour dis-
tributions of the galaxy discs are comparatively much flatter than the trends we
observe in the clump colours. This implies that contamination from disc light is not
the source of the trend we find. This is consistent with the findings of Guo et al.
(2018).
2. Comparing the integrated clump colours to outputs from Starburst99 colours,
we find that their colours are consistent with ages between 10 and 250 Myr, and AV
extinction between 0.6 and 2.0. The lack of significantly older clumps is consistent
with the simulations of clumps in high?z galaxies from Bournaud et al. (2014),
who shows that the ages of clumps saturate at ? 250 Myr because the clumps si-
multaneously experience ongoing star formation and the loss of older stars through
dissipation.
3. We analyze the internally resolved colours of clumps and find that for the major-
ity of them the 336?467 colour is progressively redder toward their edges; based on
our stellar population modeling, this is consistent with an age gradient such that age
increases from their centers to their edges. Clump centers tend to be fairly young,
135
and their age does not show a measurable trend with galactocentric distance. The
outer regions of clumps, on the other hand, do show a significant trend with galac-
tocentric distance and a tighter correlation than the clump ages from the integrated
light. This is likely caused by ongoing star formation in clump centers throughout
their lifetime, so we take the age of the stellar population in the outer clumps to be
more indicative of the actual age of the clump.
4. We compare the outer ages of DYNAMO clumps to the Mandelker et al. (2017)
high?z simulations, by analyzing the slopes of the power law fits of the ex situ,
short-lived, and long-lived clumps. We determine from this comparison that the
DYNAMO clumps are distinct from the ex situ clumps. When comparing the dis-
tribution of DYNAMO clumps and simulated clumps in terms of galactocentric
radius, we find a clear distinction between the short-lived clumps and DYNAMO
clumps. The majority of short-lived clumps are found at larger normalized galacto-
centric radii, while the DYNAMO clumps preferentially cluster a smaller distances,
much like the long-lived clumps.
136
Chapter 4: Linking it Together ? Gas and Star Formation in Nearby
High?z Analogs
4.1 Overview
Using ? 1? 2 kpc scale ALMA observations of CO(3?2) and CO(4?3) com-
bined with HST observations of H?, we characterize the molecular gas and star
formation properties of nine local analogs of main sequence galaxies at z ? 1 ? 3,
drawn from the DYNAMO sample. From the ALMA CO observations, we mea-
sure CO(4?3)/CO(3?2) across the disk of each galaxy and find that the median
line ratio of the sample is r43 = 0.54. Comparing to line ratio constraints in the
literature, we conclude that in this regard, DYNAMO galaxies are most similar to
main sequence star forming galaxies at z ? 2, and local Luminous Infrared Galaxies
(LIRGs). In addition, we measure beam smearing corrected velocity dispersions and
relate these to the molecular gas and star formation rate surface densities. Despite
being relatively nearby (z ? 0.1), DYNAMO galaxies exhibit high velocity disper-
sion and surface densities when compared to local star forming samples throughout
their disks. This may be attributed to gas flows which could drive the gas surface
densities to high values leading to higher star formation rate surface densities. Sim-
137
ilarly, if inward radial gas flows were present, the release of gravitational potential
energy could drive the high velocity dispersions. Finally, comparing the DYNAMO
measurements to predictions from star formation theory, we find that if turbulent
dissipation is assumed to depend on the angular velocity, then we are unable to
reproduce the observed DYNAMO velocity dispersions. To reproduce the observa-
tions, the turbulent dissipation would need to depend on a quantity that increases
with galactocentric radius.
4.2 Introduction
Disk galaxies across cosmic time and across a range of stellar mass and gas
content properties are in some ways strikingly similar. One such similarity is the
Kennicutt-Schmidt relation (hereafter KS relation; Kennicutt, 1998a, Kennicutt and
Evans, 2012), which ties the surface density of star formation (?SFR) to the surface
density of molecular hydrogen gas (?mol) through a power law relation with a slope
of N ? 1.4. The KS relation spans several orders of magnitude in both the star
formation rate (SFR) and gas surface density, it holds for both normal star forming
galaxies and starbursting systems (Kennicutt and De Los Reyes, 2021) at low- and
high-redshift (Bouche? et al., 2007, Daddi et al., 2010b, Genzel et al., 2010, Tacconi
et al., 2013), and appears to persist on ? 1 kpc scales (e.g., Kennicutt et al., 2007,
Leroy et al., 2008, 2013, Momose et al., 2013). The KS relation provides a useful
means of scaling the magnitude of star formation in disk galaxies based on the avail-
ability of gas. However, alone it does not provide information about the underlying
138
mechanisms that work to produce the observed relation.
As a result, much theoretical and numerical simulation work has been done to
understand the relation between star formation and the ISM. Theories seek to un-
derstand this relation through an energy and pressure equilibrium. The gas, stellar,
and dark matter potentials that work to collapse the gas are balanced by thermal,
turbulent, radiation, and magnetic pressures. However, turbulence is believed to
be the primary balancing force. An important question in understanding this equi-
librium state is determining what mechanism or mechanisms predominantly drive
turbulence in the ISM. Under the theory of self-regulated star formation, momen-
tum injected by stellar feedback is enough to drive the turbulence needed to balance
the vertical weight of the ISM (Shetty and Ostriker, 2012, Faucher-Gigue?re et al.,
2013). Alternatively, theories of gas dynamics predict that the accretion-powered
release of gravitational potential energy via radial inflows of gas through a galac-
tic disk are the primary drivers of turbulence (Krumholz and Burkhart, 2016) or
that both stellar feedback and gas transport are required to explain observations of
the velocity dispersion?star formation rate surface density relation (Elmegreen and
Burkert, 2010, Klessen and Hennebelle, 2010, Krumholz et al., 2018).
While theoretical studies debate the relative importance of gravitationally-
driven turbulence to stellar feedback, there are hydrodynamic simulation studies
that suggest large-scale turbulent driving such as might result from gas accretion
may be a necessary component of star formation regulation. Bournaud et al. (2010)
study the substructure and turbulence of the interstellar medium (ISM) with reso-
lution reaching up to 0.8 pc, by analyzing the power spectrum of the velocity field
139
components. They find that turbulence on large scales and cloud scales is mainly
regulated by gravitational processes, but that stellar feedback is still required to
maintain the ISM in a steady state. Similarly, Brucy et al. (2020) perform magne-
tohydrodynamic simulations in kpc-sized regions of Milky Way-like and high-redshift
galaxies to study the effects of stellar feedback and large-scale turbulent driving on
the derived KS relation. They find that for Milky Way-like galaxies, stellar feed-
back alone is enough to reproduce the widely accepted slope of the KS relation of
N ? 1.4. However, when considering galaxies with very high gas fractions, as is ob-
served in main sequence star forming z ? 1? 2 galaxies, the addition of large-scale
turbulent driving is required to reproduce the KS relation. With stellar feedback
alone, the simulations of gas-rich galaxies produce a KS relation that is much steeper
than observed. Perhaps in agreement with this finding, Orr et al. (2020) find that
for Milky Way-like galaxies at z ? 0 in the Feedback in Realistic Environments
(FIRE-2; Wetzel et al., 2016, Hopkins et al., 2018) cosmological simulations, stellar
feedback is the primary driver of turbulence, while accretion powering is secondary
to that. Nonetheless, numerical studies predict the presence of radial inflows of gas
on the order of ? 1? 7 M yr?1 (Fensch and Bournaud, 2021, Trapp et al., 2021).
To attempt to observationally differentiate between turbulence powering mech-
anisms, we study the molecular gas velocity dispersions (?mol), molecular gas surface
densities (?mol), and star formation rate surface densities (?SFR) of nine highly tur-
bulent, nearby (z ? 0.1) galaxies from the DYnamics of Newly Assembled Massive
Objects (DYNAMO; Green et al., 2014) sample. Galaxies in the DYNAMO sample
were selected to have H? brighter than 1042 erg s?1 in the SDSS 3?? fiber. Mea-
140
surements of the gas fractions, ionized gas velocity dispersions, and SFRs of these
galaxies indicate they are most consistent with main sequence star forming galaxies
at z ? 2 (Green et al., 2014). Furthermore, the star formation rates and stellar
masses of DYNAMO galaxies place them on the main sequence of star formation
at z ? 2 rather than the local one (Fisher et al., 2019). Their resemblance to high-
redshift spirals and proximity allow us to probe the turbulence powering mechanisms
in gas-rich, turbulent galaxies at scales that are not yet achievable at z ? 2. Thus,
we combine H? observations from the Hubble Space Telescope with CO(3?2) and
CO(4?3) observations from the Atacama Large Millimeter/sub-millimeter Array
to study the ?mol??mol and ?mol??SFR relations resolved on ? 1 ? 2 kpc scales,
and compare these to results from simulations and expectations from star formation
theory.
This paper is structured as follows: ?4.3 describes our observations and data
reduction, ?4.4 describes how we derive our methods for measuring molecular gas
surface density, star formation rate surface density, stellar mass surface density, and
velocity dispersions, ?4.5 and ?4.6 describe and discuss our results, and finally we
conclude in ?4.7.
Throughout this work, we assume ?CDM cosmology with H0 = 69.6 km s
?1,
?m = 0.286, and ?? = 0.714 (consistent with the nine years combined WMAP
results Hinshaw et al., 2013), and a Kroupa initial mass function (Kroupa, 2001).
141
4.3 Observations and Data Reduction
The DYnamics for Newly Assembled Massive Objects (DYNAMO) sample of
galaxies, was first defined by Green et al. (2014), who selected galaxies from the
MPA-JHU Value Added Catalog of the Sloan Digital Sky Survey based on their
redshift and H? emission. The sample consists of 67 galaxies, with half of the
galaxies having LH? > 10
42 erg s?1. DYNAMO galaxies have been well studied, and
their SFRs, stellar masses, molecular gas masses, gas fractions, ionized gas velocity
dispersions, and H? extinctions properties have been constrained (Green et al., 2014,
Fisher et al., 2014, 2017b,a, Bassett et al., 2017, White et al., 2017, Fisher et al.,
2019, Girard et al., 2021, Lenkic? et al., 2021).
4.3.1 ALMA CO Observations
We make use of the CO(3?2) and CO(4?3) observations of nine DYNAMO
galaxies with the Atacama Large Millimeter/Submillimeter Array (ALMA), as-
sociated with project code 2017.1.00239.S. Observations were taken in Band 7
(275? 373 GHz) and Band 8 (385? 500 GHz) between 2018-06-01 and 2018-07-10.
The spectral windows were configured with bandwidths of 2.00 GHz and channel
widths of 15.625 MHz (128 channels). In addition, we also make use of higher res-
olution CO(3?2) ALMA observations of three DYNAMO galaxies (G04-1, G08-5,
and G14-1) associated with the project code 2019.1.00447S. These observations were
taken in Band 7 between 2019-10-09 and 2019-10-10. The spectral windows were
configured with bandwidths of 1.875 GHz and channel widths of 7.8125 MHz (240
142
channels). The data associated with both projects were presented in Girard et al.
(2021).
The visibilities were calibrated and flagged by the observatory with the Com-
mon Astronomy Software Application (casa, McMullin et al., 2007) pipeline ver-
sions listed in the fourth column of Table 4.1. We imaged each observation us-
ing tclean in casa version 6.1.0.188 with parameters deconvolver=?hogbom?,
weighting=?briggs?, robust=0.5, and restfreq set to the redshifted frequency
of the observed CO line. We cleaned the data until the residuals were consistent
with the root-mean-square (rms) noise levels that are listed in the third column of
Table 4.1. To derive these thresholds, we consider data cubes with just a shallow
clean, mask the emission (see below), and calculate the standard deviation of the
masked cubes; i.e., non-line channels. These values are listed in column three in
Table 4.1, and we re-clean the data cubes to that rms level. We convolve the final
cubes to a circular beam, listed in the second column of Table 4.1, with the casa
imsmooth function. At the redshifts of DYNAMO galaxies in our sample, the beam
sizes correspond to physical scales of ? 1? 2 kpc. Finally, we export all data cubes
with the spectral axis in units of velocity, in the local standard of rest frame and
adopting the radio convention. We present channel maps of CO(3?2) for DYNAMO
G04-1 in Figure 4.1 to show an example of the resulting final data sets, with the
circularized beam shown in each panel. The entire set of channel maps of all final
data cubes we produce are in Appendix C.1.
We produce moment zero maps (integrated intensity) by first masking each
cleaned data cube along both the spatial and spectral axes. To produce our masks,
143
Figure 4.1: Channel maps of CO(3?2) for the galaxy DYNAMO G04-1 in units
of mJy beam?1. Each panel is centered at 04h12m19.713s, -05d54m48.62s, and
10.8?10.8?? in size. The velocity range is ?172 to 96 km s?1 in steps of ?8 km s?1,
as indicated in the top right corners. The circularized beam is shown in white in
the bottom left corner of each panel.
144
Galaxy CO Trans. Beam FWHM rms Noise casa Cal.
(arcsec) (mK)
C13-1 3? 2 1.07 11.5 v5.1.1-5
C22-2 3? 2 1.07 16.0 v5.1.1-5
4? 3 0.81 12.5 v5.1.1-5
D13-5 3? 2 1.10 8.2 v5.1.1-5
4? 3 0.79 12.1 v5.1.1-5
D15-3 4? 3 0.96 10.8 v5.1.1-5
G04-1 3? 2 0.42 29.1 v5.6.1-8
4? 3 0.84 21.5 v5.1.1-5
G08-5 3? 2 0.40 32.4 v5.6.1-8
G14-1 3? 2 1.06 3.3 v5.1.1-5
4? 3 0.85 6.3 v5.1.1-5
G20-2 3? 2 1.23 3.7 v5.1.1-5
4? 3 0.86 4.8 v5.1.1-5
SDSS J013527.10-103938.6 3? 2 1.23 5.2 v5.1.1-5
4? 3 0.86 4.5 v5.1.1-5
Table 4.1: CO Data Cube Parameters
145
we first smooth each cleaned data cube to twice the circularized beam full width at
half maximum (FWHM). We then compute the rms of the data cube, and mask all
pixels that are below 3? the cube rms. For each remaining pixel, we then compute
the integrated intensity over the channels that are not masked out. We do this for
both the CO(3?2) and CO(4?3) observations. Figure 4.2 presents these moment
zero maps in the two rightmost panels. Then, we recompute the rms noise per
channel of each cube by determining the rms of all pixels that have values below the
3? rms threshold.
Finally, for the goal of calculating CO(4?3)/CO(3?2) line ratios, we match
the pixel scale and resolution of all 2017 CO(4?3) observations to the pixel scale and
resolution of the 2017 CO(3?2) observations, where data for both transitions are
available. Similarly, we match the pixel scale and resolution of the 2019 CO(3?2)
observations to the 2017 CO(4?3) observations, where available. We match the pixel
scales using the casa function imregrid, while to match the resolution, we use the
casa imsmooth tool to convolve the higher resolution data with a Gaussian kernel
to produce the lower resolution Gaussian beam. Finally, we apply the masking of
the CO(3?2) observations to the CO(4?3) to produce matching integrated intensity
maps. This ensures that the intensities we derive for both lines are integrated over
the same velocity ranges.
146
147
Figure 4.2: Summary of all data sets analyzed in this work for each galaxy in our
sample, as indicated in the top right corners of the leftmost panels. The leftmost
panels show the continuum subtracted HST H? data (Fisher et al., 2017b), the
second panel show the HST F125W data, the third panels show the CO(3?2) in-
tegrated intensity maps, and the rightmost panels show the CO(4?3) integrated
intensity maps. Empty panels indicate that data is absent for the given galaxy.
148
4.3.2 HST Observations
In addition to the ALMA observations of CO in our DYNAMO galaxies, we
make use of HST observations of H? as a tracer of the star formation rate, and HST
WFC3/IR F125W observations (? J band) as a tracer of the stellar mass (we show
these in the two leftmost panels of Figure 4.2). The H? data were processed and
presented in Fisher et al. (2017b), who used HST FR647M continuum maps to pro-
duce continuum subtracted H? maps. We use these continuum subtracted maps in
this work. The H? maps have a pixel scale of ? 0.05?? and a resolution correspond-
ing to physical scales of ? 50? 200 pc (Fisher et al., 2017b), while the F125W data
have a pixel scale of ? 0.12??. Our ability to make resolved measurements in these
DYNAMO galaxies is limited by the resolution of the ALMA data; therefore, we
match the pixel scale and resolution of the H? observations to that of the CO(3?2),
where available, and CO(4?3) otherwise. To achieve this, we convolve each H? ob-
servation with a two-dimensional Gaussian function whose FWHM is equal to the
circularized beam of the corresponding ALMA observation. Then, we re-project and
re-grid the H? observations to match the WCS information and pixel scale of the
CO observations using the Python astropy package reproject1, noting that the
reproject functions assume that input images have surface brightness units. Figure
4.2 summarizes the data that we analyze in this work. Blank panels in Figure 4.2
indicate missing data sets for the given galaxy.
1https://reproject.readthedocs.io/en/stable/index.html
149
4.4 Methods
4.4.1 Resolved Measurements
This work aims to investigate the gas and star forming properties of DYNAMO
galaxies resolved on a 1? 2 kpc scale. Specifically, the properties we are interested
in measuring and studying on these scales are: (1) the molecular gas surface density
(?mol) adopting both constant and variable CO-to-H2 conversion factors (?CO) for
comparison, (2) the SFR surface density (?SFR), and (3) the molecular gas velocity
dispersions (?mol). Here, we describe our method for extracting these measurements
from the data.
For each of our resolution and WCS matched data sets, we define two sets of
?grids? of circular, beam-sized apertures: one that is centered on the galaxy, and
a second that is offset from the center by 0.5? the beam FWHM in both the x
and y directions. This is to ensure that we cover the gaps of the first grid. The
measurements we present and consider in our analysis are only those along lines of
sight where the signal-to-noise ratio of the integrated CO intensity is greater than
five.
4.4.1.1 Molecular Gas Surface Density
We measure the molecular gas surface density from our integrated intensity
maps of CO(3?2) in all cases but DYNAMO D15-3, for which no CO(3?2) data
were available. In that case, we use the CO(4?3) integrated intensity map. Along
150
each sight-line, we extract the integrated intensity at the center and calculate the
molecular gas surface density from:
?mol = ?CO ? r ?2J1 ? ICO [M pc ] (4.1)
where rJ1 is the ratio of Rayleigh-Jeans brightness temperature intensities to convert
CO(J?J?1) emission to CO(1?0), for which we adopt r31 = 0.67 and r41 = 0.36,
and ICO is the CO(J?J?1) integrated intensity in units of K km s?1. In our constant
CO-to-H conversion factor case, we adopt ? = 4.35 M [K km s?1 pc22 CO  ]
?1. We also
adopt a variable ?CO according to the prescription of Bolatto et al. (2013) (equation
31):
( ) ( )?
0.4 ?total
?CO ? 2.9? exp
Z ?
? (4.2)
?100GMC 100 M pc?2
4.4.1.2 Star Formation Rate Surface Density
We measure the SFR surface density from our CO-matched H? observations.
We perform aperture photometry along each sight-line to obtain the H? flux (in
electrons per second). We convert these fluxes to units of erg s?1 cm?2 A??1, apply a
correction for extinction by relating AV to AH? assuming the Cardelli et al. (1989)
extinction law, and assuming the AV measurements from Lenkic? et al. (2021). The
typical H? extinction resulting from this is AH? ? 1 mag. Finally, we calculate H?
luminosities and convert them SFRs using the relation of Hao et al. (2011):
151
SFR [M yr?1 ] = 5.53? 10?42 ? LH? [erg s?1] (4.3)
4.4.1.3 Stellar Mass Surface Density
We measure the stellar mass surface density (??) from our CO-matched HST
F125W observations. We perform aperture photometry as above to extract fluxes
and convert to luminosities. To convert the luminosities to stellar mass, we assume
a constant mass-to-light ratio, ??,f125w = 0.16 based on stellar population modelling
of six DYNAMO galaxies by Ambachew et al. (in prep).
4.4.1.4 Velocity Dispersion
The data in hand allow us to additionally test theories of star formation,
as predicted by theory and simulations. The ALMA CO observations allow us to
measure the molecular gas velocity dispersion on 1? 2 kpc scales, and to compare
these as a function of molecular gas surface density, which we will show in ?4.5.4.
Here, we outline our method for measuring molecular gas velocity dispersions, and
correcting for beam smearing.
To measure the velocity dispersion, we use the CO(3?2) observations when
available, and the CO(4?3) observations otherwise. We begin by creating two over-
lapping grids of beam regions as described in ?4.4.1. Then, for each beam region,
we extract the spectrum of the CO line from the central pixel. We fit the line profile
2 2
with a Gaussian function of the form f(x) = a? e(x??o) /2? , where a is the ampli-
152
Figure 4.3: Observed and modeled velocity field and velocity dispersion map of
DYNAMO G04-1. Left: the observed velocity field (top) and velocity dispersion
(bottom). Middle: the modeled velocity field and velocity dispersion, derived from
creating a model data cube by placing the observed velocity in the closest matching
channel. Right: The velocity field residuals we obtain by subtracting the model
velocity field from the observations (top), and the corrected velocity dispersion map
obtained by subtracting in quadrature the model velocity dispersion from our mea-
sured velocity dispersion. This simulates the effect of beam smearing and corrects
for it.
tude of the line, ?o is its centroid, and ? is its velocity dispersion. We perform our
fitting using the Python SciPy function curve fit. The resulting ? parameters
obtained in this way, are our velocity dispersion measurements.
However, beam smearing has a strong effect on measured velocity dispersion,
particularly close to the centers of galaxies, and along their minor axes. Furthermore,
the effect of beam smearing can be significant even into the disk of the galaxies, if
their rotation curves rise slowly. As a result, we apply a beam smearing correction
to our measured velocity dispersion using the method outlined in Levy et al. (2018),
153
which we summarize here for completeness, which involves creating a model cube
for the galaxy rotation using its rotation curve parameters. To create our model
cubes, we first adopt the arctan model and rotation curve parameters from Girard
et al. (2021) to calculate the rotation velocity (vrot) as a function of distance from
the center (r):
( )
2 r
vrot = ? Vrot ? arctan (4.4)
? rt
where Vrot is the rotation velocity in the flat region of the rotation curve and rt is
the turnover radius of the rotation curve. We then calculate the observed velocity
(vobs) from:
vobs = vrot ? sin(i)? cos(?) (4.5)
where i is the inclination, and cos(?) is defined as:
?(x? xo)? sin(PA)? (y ? yo)? cos(PA)
cos(?) = (4.6)
r ? cos(i)
where xo and yo are the coordinates of the image center and PA is the galaxy
position angle. Finally, r is defined as:
?
(x? x 2o) + (y ? y 2o)
r = . (4.7)
cos(i)2
We create our model cubes by creating an array of zeros with the same size
as the actual observed cube, and then calculate vobs at each pixel. We match the
154
resulting observed velocity to the closest channel, and place a delta function in our
model cube at the corresponding pixel and channel, with an amplitude equal to the
value (in Jy beam?1) of the same pixel in the same channel in the observed data cube.
After performing this for each pixel, we smooth the cube with a Gaussian whose
FWHM matches the beam FWHM of the observation. Then, we create a moment
2 (velocity dispersion) map using the Python spectral-cube linewidth sigma
function: this is our modeled velocity width due to beam smearing. Finally, we apply
the beam smearing correction to the ? values we obtain from our Gaussian fitting,
by subtracting in quadrature from each beam region, the model velocity dispersion
at the center of the same beam region. In Figure 4.3, we show an example of the final
model velocity dispersion map produced in this way for galaxy DYNAMO G04-1.
4.5 Results
4.5.1 CO(4?3)/CO(3?2) Line Ratios
In ?4.3.1, we describe our process for matching our CO(4?3) and CO(3?2)
observations, and deriving integrated intensity maps. We adopt brightness temper-
ature units, thus our integrated intensity maps have units of K km s?1. To visually
determine how the CO(4?3)/CO(3?2) line ratio varies across each galaxy disk, we
simply divide our CO(4?3) integrated intensity map by that of the CO(3?2). This
is what we present in Figure 4.4, where the color scale indicates the ratio variations
across each galaxy disk for which both line transitions were observed, and the black
contours indicate line ratio S/N levels starting at S/N = 3 and increasing in units of
155
Figure 4.4: CO(4?3)/CO(3?2) line ratios (in brightness temperatures) measured
from the pixel scale and resolution matched integrated intensity maps of each transi-
tion, integrated over the same velocity ranges. The positions of star forming clumps
identified by Lenkic? et al. (2021) are included, where available, as crosses. The black
contours indicate S/N levels on the line ratios, beginning at 3 and increasing in units
of 1. The galaxy name is indicated in the top left corner of each panel, along with
the median line ratio across the disk. The black hatched circles in the bottom left
corners indicate the circularized beam sizes. Finally, we show a 1 kpc scale bar in
the bottom right corners. We see that galaxies generally have fairly constant line
ratios within the regions where the uncertainties do not dominate, and that they lie
typically around 0.4?0.7. The regions of very high or very low line ratios have S/N
< 3; therefore, these are regions of high uncertainty and are thus unreliable.
156
one. We derive uncertainties for the integrated intensity maps (?J?J?1) by summing
in quadrature the rms of every channel over which we integrate and multiplying by
the channel width:
???
? ??NJ?J?1 = ?v rmsi (4.8)
i
where ?v is the channel width, rmsi is the rms of the i
th channel (computed as the
standard deviation of all pixels in the channel, excluding those identified as emis-
sion by our masking procedure described above), and N is the number of channels
included in the integration (considering only channels with emission). We compute
this uncertainty at each pixel included in our final integrated intensity maps. To
obtain the final uncertainty on the line ratio, we add in quadrature the uncertainties
of the CO(4?3) and CO(3?2) integrated intensity maps. From Figure 4.4, we see
that the line ratio for galaxies in our sample are fairly constant across the disks,
with typical values ranging from r43 ? 0.4?0.7 with a typical uncertainty of ? 0.09.
Regions with very low or very high line ratios (regions outside the outermost con-
tours of Figure 4.4) correspond to regions of high uncertainty (of order equal to the
measurements), and thus low S/N, and are not reliable.
While we cannot constrain the physical conditions of the gas using a single
line ratio, we run models using the non-LTE radiative transfer code RADEX (van
der Tak et al., 2007) for varying CO column densities to obtain some insight into
the possible physical conditions of the gas. In Figure 4.5, we present the RADEX
model for a CO column density of N(CO) ? 1017 cm?2, where the hatched regions
157
indicate the typical line ratios we measure in DYNAMO galaxies. We choose this as
our fiducial model, assuming that N(H) ? N(HI) + N(H2)? 2 ? 1.9?1021 cm?2AV
(equation 21 in Bolatto et al., 2013). Then, assuming AV ? 4 in a molecular cloud,
a carbon abundance of C/H ? 10?4, and that all carbon is in CO, then the column
density of CO is N(CO) ? 10?4 ? 1.9 ? 1020 cm?2 ? 4 = 7.6 ? 1017 cm?2. Finally,
assuming a typical cloud line width of ? 10 km s?1, we find N(CO) ? 7.6?1016 cm?2
per dv = 1 km s?1. We see that for very hot temperatures (T& 150 K) and higher
densities, the J= 3 level de-populates, the emission becomes optically thin, and
the CO(4?3)/CO(3?2) line ratio becomes greater than one. We can expect that
our line ratios likely correspond to cooler temperatures, T. 60 K and densities
of n 4 ?3H ? 10 cm . At much lower N(CO) (e.g., ? 1013 cm?2), it becomes much
more difficult to produce the line ratios we observe at T. 60 K, and requires
nH & 105 cm?3. Furthermore, in the low N(CO) case, the line ratios surpass unity
at T& 80 K and n & 104 cm?3H .
Next, we perform ? 1 ? 2 kpc sized sightline measurements of the line ratio
across the disk of each galaxy, as described in ?4.4.1, to characterize the typical line
ratio we measure, and the magnitude of the spread. To this end, we construct a
kernel density estimate (KDE), which can be read like a histogram, but incorporates
the uncertainties of the measurements. We construct the KDE by modeling each
beam-averaged line ratio measurement as a one-dimensional Gaussian with centroid
corresponding to the measured line ratio, and with width equal to the line ratio
uncertainty: ? = ?43. The area of each Gaussian is normalized to unity, then
we sum all Gaussians to produce the final KDE. This is what we show in Figure
158
Figure 4.5: Prediction of the CO(4?3)/CO(3?2) line ratio as a function of ki-
netic temperature and H2 number density, from the non-LTE radiative transfer
code RADEX (van der Tak et al., 2007). Hatched regions indicate the typical line
ratios we measure across the disks of DYNAMO galaxies.
159
4.6. From this analysis, we find that the median line ratio and 1? uncertainties for
DYNAMO galaxies are: r = 0.54+0.1643 ?0.15. These values are taken as the 15.9, 50, and
84.1 percentiles of the cumulative distribution function of the KDE.
For comparison, we compile estimates of the CO(4?3) to CO(3?2) line ratio
from the literature and describe them here. Daddi et al. (2015) use IRAM Plateau
de Bure Interferometer observations of CO(2?1), CO(3?2), and CO(5?4), and
Very Large Array observation of CO(1?0) in three main-sequence star forming disk
galaxies at z = 1.5 to study their CO excitations. We use their average r31 and
interpolate their models from their Figure 10 to extract r41, then take the ratio
r41/r31 to obtain r43 = 0.74 ? 0.26, which we include in Figure 4.6 as a black circle.
Henr??quez-Brocal et al. (2021) combine NOrthern Extended Millimeter Array
observations of [CI](1?0), [CI](2?1), and CO(7?6) with ancillary CO(1?0) and
CO(3?2) observations to model the CO spectral line energy distribution (SLED)
of Q1700-MD94, a massive main-sequence galaxy at z ? 2, with a one- and two-
temperature component model using the non-LTE radiative transfer code RADEX
(van der Tak et al., 2007). We interpolate the model curves in their Figure 3 to
extract r43 = 0.92 ? 0.18 and 0.77 ? 0.15 for the one- and two-component models
respectively (taking a 20% uncertainty), and plot these as black and gray squares.
Rosenberg et al. (2015) study the CO SLEDs of 29 (Ultra) Luminous Infrared
Galaxies (U/LIRGs) from CO(1?0) through CO(13?12). They classify their objects
into three classes based on their excitation level. Where available, we compiled
CO(4?3) and CO(3?3) fluxes from their Tables 2 and 3, and divided the resulting
ratios by (J3u/J
3
l ) to convert from units of W m
?2 to K km s?1. Finally, we separated
160
Figure 4.6: Kernel density estimator (KDE) for the resolved CO(4?3)/CO(3?2)
line ratio measurements. The KDE can be read as a histogram with measurement
uncertainties incorporated. We construct the KDE by modeling each measurement
as a Gaussian whose width is the line ratio uncertainty. Summing each individ-
ual Gaussian results in the figure shown here. From the cumulative distribution
function of this KDE, we infer a median line ratio of r43 = 0.54. For comparison,
we include estimates from the literature: r43 = 0.74 ? 0.26 for three z = 1.5 main
sequence star forming galaxies (black circle; Daddi et al., 2015), r43 = 0.92, 0.77
for Q1700-MD94, adopting a one- and two-component temperature model respec-
tively (black squares; Henr??quez-Brocal et al., 2021), r43 = 1.08, 0.70, 1.02 for low-,
mid-, and high-excitation ULIRGs respectively (black diamonds; Rosenberg et al.,
2015), r43 = 0.49 ? 0.18 for LIRGs (black pentagon; Papadopoulos et al., 2012),
and r43 = 1.32, 0.25 for ULIRGs and non-(U)LIRGs respectively (black octagons;
Kamenetzky et al., 2016).
161
the galaxies according to their classification, and plot the median line ratio for each
class as black and gray diamonds. The error bars represent the standard deviation
of line ratios in each class to illustrate their spread.
Papadopoulos et al. (2012) study the CO SLEDs of 70 U/LIRGs; we compile
fluxes from their Tables 4 and 5 and adopt the same approach as above for extracting
the CO(4?3)/CO(3?2) line ratio, and plot this as a black pentagon.
Finally, Kamenetzky et al. (2016) find a linear relation between L ?FIR and LCO
for low- to mid-J CO lines and a slightly sub-linear relation for high-J CO lines. We
adopt the slope and intercepts of the relations for CO(4?3) and CO(3?2) from
their Tables 6 and 7 (for ULIRGs and non-(U)LIRGs respectively), and assume a
far-infrared luminosity of 1012 for the ULIRG case and 1010 for the non-(U)LIRG
case to derive the L ? L?FIR CO relations. Taking the ratio of these we find r43 =
1.32 ? 0.26 and 0.24 ? 0.05 for ULIRGs and non-(U)LIRGs respectively, assuming
20% uncertainty. We plot the resulting non-(U)LIRG line ratio as a black hexagon.
We summarize all line ratios we compile from the literature, the median line ratios
we measure for each DYNAMO galaxy individually, and the median line ratio for
the entire DYNAMO sample studied here in Table 4.2.
This comparison reveals that the CO(4?3)/CO(3?2) line ratio in DYNAMO
galaxies is, within the uncertainties, comparable to those measured in the z = 1.5
sample of three main sequence galaxies of Daddi et al. (2015), the sample of LIRGs
from Papadopoulos et al. (2012), and the z ? 2 main-sequence galaxy G1700-MD94,
when assuming a two component temperature model from Henr??quez-Brocal et al.
(2021). In contrast, the non-U/LIRG line ratio of Kamenetzky et al. (2016) is much
162
Object(s) Line Ratio Reference Notes
z = 1.5 MS Galaxies 0.74 ? 0.26 Daddi et al. (2015) interpolated
G1700-MD94 one component model 0.92? 0.18 Henr??quez-Brocal et al. (2021) interpolated
G1700-MD94 two component model 0.77? 0.15 Henr??quez-Brocal et al. (2021) interpolated
ULIRGs low CO excitation 1.08 Rosenberg et al. (2015)
ULIRGs mid CO excitation 0.70 Rosenberg et al. (2015)
ULIRGs high CO excitation 1.02 Rosenberg et al. (2015)
LIRGs 0.49 ? 0.18 Papadopoulos et al. (2012)
ULIRGs 1.32? 0.26 Kamenetzky et al. (2016) log(LFIR) = 12
non-(U)LIRGs 0.25? 0.0.05 Kamenetzky et al. (2016) log(LFIR) = 10
C22-2 0.62 ? 0.13 This work
D13-5 0.57 ? 0.08 This work
G04-1 0.50 ? 0.08 This work
G14-1 0.71 ? 0.11 This work
G20-2 0.61 ? 0.07 This work
SDSS J013527.10-103938.6 0.44 ? 0.05 This work
+0.16
DYNAMO all 0.54?0.15 This work
Table 4.2: CO(4?3)/CO(3?2) Line Ratios Compiled from the Literature Compared
to DYNAMO
lower and inconsistent with what we observe. DYNAMO galaxies lie on the star
formation main-sequence at z ? 2 (Fisher et al., 2019), and have gas fractions
and velocity dispersions that are more similar to main-sequence galaxies of that
epoch than local ones. Therefore, this result is consistent with lines of evidence
that indicate DYNAMO galaxies are local analogs of high?z main-sequence sys-
tems. Local ULIRG samples have systematically larger line ratios than we observe
in DYNAMO, and this too is consistent with previous observations of DYNAMO
galaxies. Using Herschel PACS+SPIRE observations of nine DYNAMO galaxies,
White et al. (2017) found that despite their large FIR luminosities, log LFIR > 11,
these galaxies have much lower dust temperatures (? 30 K) than ULIRGs. There-
fore, unlike ULIRGs, the star formation in DYNAMO galaxies is more distributed
throughout the disks; thus, colder dust temperatures would be expected and likewise
lower CO(4?3)/CO(3?2) line ratios.
163
4.5.2 Resolved KS-Law
Figure 4.7 shows the resolved measurements of ?SFR versus ?mol, where each
set of colored data points corresponds to measurements within one DYNAMO
galaxy, as indicated by the legend. The left panel assumes a constant ?CO, while the
right panel assumes a variable ?CO as prescribed in equation 4.2. The matching col-
ored data points with black outlines in the left panel correspond to the disk averaged
?SFR and ?mol values, measured within the half-light radius of HST F336W images
reported in Lenkic? et al. (2021). For comparison, we include the measurements of
Leroy et al. (2013) who used CO(2?1) HERACLES maps and H?+24 ?m derived
SFRs to study the relation between ?mol and ?SFR on 1 kpc scales. We include
the results of this work in both panels as black contours which include 50, 68, and
97.5% of the entire data set.
We see that the resolved ?mol and ?SFR measurements in DYNAMO extend
those of Leroy et al. (2013) to higher molecular gas and SFR surface densities. We
fit our measurements, assuming both the constant and variable ?CO, with a power
law of the form
log ?SFR = N ? log ?mol + A (4.9)
by minimizing the distance between each data point and lines with a given set
of parameters N and A. In both cases, we find a sub-linear slope: N = 0.77,
A = ?2.35 for the constant ?CO case (solid blue line in both panels), and N = 0.90,
164
Figure 4.7: The ?SFR??mol relation for DYNAMO galaxies, measured in ? 1 ?
2 kpc sightlines (colored data points). The seven colored data points with black
outlines are the disk-averaged values of ?SFR and ?mol we measure when adopting
the HST F336W half-light radii of Lenkic? et al. (2021). We include the 1 kpc scale
measurements of Leroy et al. (2013) for 30 nearby disk galaxies, using HERACLES
CO(2?1) maps and H?+24 ?m derived SFRs, as black contours which contain 50,
68, and 97.5% of the data.
A = ?2.13 for the variable ?CO case (dashed blue line in the right panel). Leroy
et al. (2013) derive N = 0.80 ? 0.14, A = ?2.35 ? 0.09 when using only H? as
a SFR tracer and assuming AH? = 1 mag (the typical H? extinction we find as
well), and N = 0.95 ? 0.15, A = ?2.40 ? 0.09 when using the combination of H?
and 24 ?m observations to measure star formation (see their Table 4). Thus, our
measurements of the KS relation in DYNAMO galaxies are consistent within the
uncertainties with the Leroy et al. (2013) results.
4.5.3 Radial Distribution of Velocity Dispersion
In Figure 4.8, we present the results of our velocity dispersion measurements,
corrected for beam smearing as a function of radius as discussed in ?4.4.1.4 (black
data points), where each panel corresponds to the galaxy indicated in the legend.
165
The black solid line in each panel is the median velocity dispersion in the disk of all
points beyond a radius of 1.5? the beam FWHM to avoid measurements that are
heavily contaminated by beam smearing near the galaxy centers. For comparison
and as a check of our beam smearing correction, the Girard et al. (2021) molecular
and ionized gas velocity dispersions and uncertainties are included as the black
dashed, black dot dashed, and grey shaded regions respectively. The beam FWHM
and channel width are represented by the error bars in the top left corner of each
panel.
Girard et al. (2021) obtained their velocity dispersion measurements from fit-
ting the ALMA rotation curves using GalPak3D (which accounts for beam smear-
ing Bouche? et al., 2015), assuming a flat dispersion model. Beyond the central beam
region of each galaxy, our beam smearing correction approach produces velocity dis-
persion results that are consistent with the results of Girard et al. (2021).
The DYNAMO galaxies in our sample all appear to have higher velocity disper-
sions in the central beam region than they do in the disk. To assess the significance
of this observation, we include as the solid blue lines the median beam smearing
correction, measured in annuli of increasing radius from our model dispersion maps
(bottom row, middle panel of Figure 4.3). Taking into account the channel width
and comparing to the median beam smearing correction, it is possible to say that
this may be the case for DYNAMO C13-1 and D13-5, and is very likely to be the
case for DYNAMO G04-1, G08-5, and G14-1. These three galaxies are the ones for
which we use the higher resolution ALMA observations. This, combined with the
rotation curve turnover radius of < 1 kpc, suggest that the enhanced velocity dis-
166
Figure 4.8: Radial distribution of beam smearing corrected velocity dispersion mea-
surements in DYNAMO along beam-sized sightlines (black data points). The black
solid line corresponds to the median velocity dispersion in DYNAMO galaxies at
radii larger than 1.5? the beam FWHM. The error bars in the top left corner of each
panel indicate the beam FWHM and the channel size of the CO(3?2) observations
used to measure velocity dispersions. For comparison, the black dashed and dot-
dashed lines mark the molecular gas and ionized gas velocity dispersion respectively
from Girard et al. (2021), while the gray shaded region indicates their uncertainties.
Our beam smearing corrected velocity dispersions are consistent with those found
by Girard et al. (2021). Finally, the blue solid lines are the radial profiles of the me-
dian beam smearing corrections we apply to each velocity dispersion measurement.
From this, we can see that for DYNAMO G04-1, G08-5, and G14-1, the increase in
velocity dispersion towards small radii are likely real and not due to effects of beam
smearing.
167
persions we measure at smaller radii are likely real and not a consequence of beam
smearing.
4.5.4 ?mol??mol and ?mol??SFR Relations
We now explore the relation between beam smearing corrected molecular gas
velocity dispersion, and ?mol and ?SFR. Figure 4.9 presents the ?mol??mol relation
in the left panel, and the ?mol??SFR relation in the right panel, where all mea-
surements are made along ? 1 ? 2 kpc sized lines of sight. DYNAMO data points
are separated by galaxy and color coded according to the legend. Measurements
of ?mol, ?mol, and ?SFR by Sun et al. (2020) from the PHANGS-ALMA CO(2?1)
survey (Leroy et al., 2021), are included as black stars2 whose sizes are scaled by
their inverse galactocentric distance squared. PHANGS-ALMA observed 90 nearby
(d. 20 Mpc) galaxies that are on or near the z = 0 main-sequence in CO(2?1) at
? 100 pc resolution, and Sun et al. (2020) present results for 70 of these targets,
consisting of 102,778 independent lines of sight. The data we show in Figure 4.9
have been matched to the kpc-scale resolution of our observations (J. Sun, private
communication), and only include lines of sight from galaxies with inclinations less
than 49? (corresponding to the largest inclination in our sample).
We make several observations from Figure 4.9. First, we note that the results of
our ?mol??mol and ?mol??SFR relations derived in DYNAMO galaxies are consistent
with the kpc-scale measurements of Sun et al. (2020): increasing values of ?mol
2We caution, however, that the PHANGS-ALMA observations are not corrected for beam
smearing.
168
Figure 4.9: Beam smearing corrected molecular gas velocity dispersions as a func-
tion of molecular gas surface density (left), and star formation rate surface density
(right), for individual ? 1 ? 2 kpc-scale lines of sight in seven DYNAMO galaxies,
as indicated by the legend. The black stars (scaled by the inverse galactocentric
distance squared of each point) correspond to the PHANGS-ALMA derived mea-
surements of Sun et al. (2020) in 70 nearby galaxies, at a resolution of 1 kpc to match
our observations (J. Sun, private communication). Consistent with the PHANGS-
ALMA results, velocity dispersions in DYNAMO galaxies increase with ?mol and
?SFR, with DYNAMO measurements acting as a high ?mol and ?SFR extension of
the PHANGS-ALMA observations. Furthermore, we observe that the molecular
gas and SFR surface densities across the entire DYNAMO disks are more simi-
lar to the central regions of PHANGS-ALMA galaxies. PHANGS-ALMA velocity
dispersions are not corrected for beam smearing; however, we do not expect it to
significantly alter the comparison, except in the central regions where the velocity
dispersions are highest and most heavily affected by beam smearing. Finally, we
also note that the scatter in velocity dispersions within a given DYNAMO galaxy
(on average 12.7 km s?1) is in general less than the overall scatter of our full sample
(? 14.2 km s?1), implying that some property or combination of properties within
each galaxy ?sets? the velocity dispersion of the molecular gas.
169
and ?SFR are correlated with larger velocity dispersions. Combining this with our
velocity dispersion profiles of Figure 4.8, we can see that these high ?mol, ?mol, and
?SFR are preferentially located at smaller galactocentric radii, as we would expect.
We also see that, despite being local galaxies, DYNAMO systems are unlike the
PHANGS-ALMA nearby targets in the sense that DYNAMO measurements act as
an extension of the ?mol??mol and ?mol??SFR relations at high molecular gas and
SFR surface density compared to PHANGS-ALMA.
Secondly, when comparing the distribution of DYNAMO measurements with
respect to those of PHANGS-ALMA and taking into account the galactocentric
distance of each point, we see that even regions within the disks of DYNAMO
galaxies are more comparable to the central regions of PHANGS-ALMA galaxies.
This is even more clearly illustrated in Figure 2 of Sun et al. (2020), where regions
within the central zones of barred galaxies clearly show particularly elevated values
of ?mol and ?mol. Indeed, they find that the central regions of barred galaxies
have ? 20? higher mass-weighted ?mol than disk regions. In PHANGS-ALMA, this
observation is linked to the role of stellar bars driving large inflows of gas into galaxy
centers and boosting ?mol to large values.
However, an alternative mechanism would be required to explain the elevated
?mol values in DYNAMO disks. Theoretical work and numerical simulations of
high?z galaxies show that cold, smooth streams of gas join the disks of these galax-
ies at large radii (? 0.1 ? 0.3? the virial radius, or ? 10? the stellar scale length;
Danovich et al., 2015, Trapp et al., 2021), generating large gas surface densities
in these outer regions (Dekel et al., 2009). Furthermore, the radial inflow of this
170
accreted gas may drive turbulence, and thus velocity dispersion, through loss of grav-
itational potential energy (Elmegreen and Burkert, 2010, Klessen and Hennebelle,
2010, Krumholz et al., 2018). Similarly, magnetohydrodynamic simulations of local
and high?z, gas-rich disks (Brucy et al., 2020) show that stellar feedback alone is
enough to suppress star formation to levels of the KS law in z ? 0 disks, but is
insufficient to do so in high?z systems. For these, large-scale turbulent driving is
required. Furthermore, (Brucy et al., 2020) find that the velocity dispersions in
these objects are highly anisotropic, with dispersions parallel to the disk planes up
to 10? larger than the vertical dispersions. The nature of the large-scale turbulent
driving needed to match high?z disk galaxies to the KS relation is an open question;
however, it provides evidence for the need for additional mechanisms.
Finally, we observe that every galaxy in our sample appears to follow ?its own?
?mol??mol and ?mol??SFR relation. For example, the scatter in velocity dispersion
values for DYNAMO G04-1 (taken to be the standard deviation) is ? 7.8 km s?1,
while the scatter for the whole sample is ? 14.2 km s?1. This implies that galaxy
specific properties ?set? the velocity dispersions.
4.6 Discussion
4.6.1 Effect of ?SFR on CO(4?3)/CO(3?2)
The ? 1 ? 2 kpc-scale ALMA observations allow us to investigate how the
line ratios we measure are affected by the surface density of star formation. We
expect that the CO(4?3) transition will be more highly excited in regions of higher
171
SFR surface densities, because these regions will have larger UV radiation fields,
and thus warmer dust temperatures (Narayanan and Krumholz, 2014). To test this,
we compare out resolved line ratio measurements to the SFR surface density mea-
surements we make in the same beam regions. Figure 4.10 shows the line ratio as
a function of SFR surface density for four galaxies for which all necessary observa-
tions were available, as indicated by the legend. For each galaxy, we plot the set
of beam measurements as previously described. Though the line ratio uncertainties
are large, there is a moderate positive correlation between the line ratios and SFR
surface density measurements, as expected. We perform a Spearman Rank Order
correlation and find a coefficient of ? = 0.614. In addition, we perform a linear
fit of our observed line ratio??SFR relation, which we show with the black solid
line. In contrast, the black dashed line corresponds to the parameterization of CO
line emission intensity as a function of ?SFR, derived by Narayanan and Krumholz
(2014), in their equation 19:
Iij
= A? [log10(?SFR)? ?]B + C (4.10)I1?0
where Iij is the intensity of the CO(i?j) transition, A, B, and C are fit parameters,
and ? = ?1.85. We adopt values for A, B, and C from their Table 3 for CO(3?2)
and CO(4?3) and substitute in our measured values of ?SFR. Finally, we take the
ratio of the two equations and divide by J2/J2u l = 4
2/32 to convert from Jy to K and
produce the line in Figure 4.10.
Overall, our fitted relation suggests a steeper relation between the CO(4?3) to
172
Figure 4.10: CO(4?3)/CO(3?2) line ratio as a function of SFR surface density,
measured in beam-sized regions across the disk of each galaxy, indicated by the
color and symbol coding in the legend. We present this data for galaxies where
observations of both CO transitions and H? exist. Despite the large uncertainties,
there is an indication of an increasing line ratio with increasing SFR surface density
trend. This is parameterized by the Spearman?s rank-order correlation coefficient
of ? = 0.614, suggesting a moderate positive correlation between these two ratios.
We present a linear fit to our measurements, presented here as the black solid line.
For comparison, we include the predicted line ratio using the relation between CO
intensity and ?SFR of Narayanan and Krumholz (2014), presented here as the black
dashed line.
173
CO(3?2) line ratio and ?SFR than is predicted by the parameterization of equation
4.10. At the lowest ?SFR values, equation 4.10 over-estimates our fitted relation by
a factor of ? 1.7, while at the highest ?SFR values, the difference is only a factor of
? 1.2.
4.6.2 Comparison of ?mol??mol and ?mol??SFR to Hydrodynamic
Models and Theory
In this section, we further explore the ?mol??mol and ?mol??SFR relations
by comparing our observational results to results from numerical simulations and
predictions from theory. In Figure 4.11, we show the DYNAMO and PHANGS-
ALMA measurements previously discussed as shaded red and blue regions respec-
tively, that include 68% of the data; i.e., data points within ?1? from the median.
For PHANGS-ALMA, we further scale the shading by the number of data points
within each ?mol bin: the lightest shadings at log ?mol> 2 correspond to fewer than
10 data points (these are upper limits because the PHANGS-ALMA measurements
are not corrected for beam smearing), while the darkest shadings at log ?mol? 1
corresponds to more than 500 data points (this is also similar for the PHANGS-
ALMA ?SFR measurements). Because molecular gas becomes a poor tracer of total
gas at ? . 10 M yr?1mol  , we highlight this region in gray to remind readers of
this caveat. Similarly, we add a gray shaded area in the right panel by convert-
ing ? ?1mol = 10 M yr to a SFR surface density by assuming the KS relation of
Leroy et al. (2013) for H?+24 ?m derived SFRs. We compare the DYNAMO and
174
Figure 4.11: Comparison of the ?mol??mol (left panel) and ?mol??SFR (right panel)
relation observed for DYNAMO galaxies (red shaded region, 68% of data) and the
PHANGS-ALMA results (blue shaded region, 68% of data; Sun et al., 2020), to
the FIRE-2 simulation results (yellow shaded region, 50% of data; Orr et al., 2020).
We shade the PHANGS-ALMA region (which are not corrected for beam smearing)
according to the number of data points that are within each bin; the lightest shaded
regions have fewer than 10 points, while the darkest regions contain several hundred
points. At ?mol< 10 M
?2
 pc (gray shaded region), gas becomes HI dominated and
molecular gas becomes a poor tracer of the total gas. Due to a lack of HI data, the
discrepancy between the observations and FIRE-2 in this region can be attributed to
this effect. At larger ?mol and ?SFR values, the agreement between the observations
and FIRE-2 is reasonably good when considering each relation separately. However,
taken together, DYNAMO galaxies have much larger ?mol values than FIRE-2, yet
comparable ?SFR values, indicating that the depletion times of DYNAMO are not
reproduced by the simulations.
PHANGS-ALMA measurements to the results of Orr et al. (2020) who used the
cosmological zoom-in simulations from the Latte suite of FIRE-2 (Wetzel et al.,
2016, Hopkins et al., 2018) of Milky Way-mass disk galaxies at z ? 0 (yellow shaded
region which includes 50% of the simulation data; i.e., 25th ? 75th percentile), to
study the turbulence driving mechanisms. We note, however, that the FIRE-2 sim-
ulation measures HI+H2; therefore this introduces uncertainties when comparing to
observations, which consist of only H2 measurements.
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In the high ?mol and ?SFR regime, the scaling of the FIRE-2 results with re-
spect to our DYNAMO measurements are seemingly very good, and both the simula-
tions and observations occupy very similar regions of the ?mol??mol and ?mol??SFR
parameter space. However, when we compare both relations simultaneously , we see
that while both FIRE-2 and DYNAMO extend to log?SFR? 0, DYNAMO galaxies
have much higher molecular gas surface densities than the FIRE-2 galaxies. This
indicates that the gas depletion times (tdep =?mol/?SFR) of FIRE-2 galaxies do not
reproduce the depletion times we observe in DYNAMO. At the low ?mol and ?SFR
regime, FIRE-2 galaxies do not show the large velocity dispersion drop off that is
observed in the PHANGS-ALMA galaxies. This can be attributed to the lack of ob-
servational HI data, as we can see that much of the PHANGS-ALMA measurements
reside in the region where atomic hydrogen is believed to become the dominant tracer
of total gas. Because the molecular gas surface densities in DYNAMO galaxies are
so high, they are especially well suited for comparison with numerical simulations.
In addition to FIRE-2, we compare our measurements to theoretical predic-
tions of the ?mol??mol and ?mol??SFR relations, which are indicated by black lines:
(1) the black dotted line shows the expected scaling of ?mol when assuming a constant
star forming efficiency per free-fall time and the FIRE-2 ?mol and ?SFR measure-
ments (see equation 6 in Orr et al., 2020):
? 32G
??2
2 gas
?disk
?z  (4.11)
3? ff ?2SFR
where ? ? vrot/R is the angular velocity; (2) the black solid line corresponds to the
176
expected scaling for marginal gas stability and the FIRE-2 ?mol and ?SFR measure-
ments (see equation 4 in Orr et al., 2020):
?G(??gas + ???)?z = ; (4.12)
2?
where ? is the fraction of the stellar mass surface density (??) that resides within
the disk scale height, (3) the black dashed line shows the ?mol scaling for feedback
regulated star formation assuming the FIRE-2 ?mol and ?SFR measurements (see
equation 5 in Orr et al., 2020, Faucher-Gigue?re et al., 2013):
?z ? ?
2 ?SFR
(P/m?) ; (4.13)
3 ??gas
where P/m? is the momentum injection per unit mass, and (4) the black dashed-
dotted line is the Shetty and Ostriker (2012) feedback regulated scaling of ?mol
(see their equation 20) assuming that fp = 2 (which characterizes the magnitude
of turbulent dissipation and is defined as the ratio between turbulent pressure and
the vertical momentum injected by star formation; fp ? 2 for weak dissipation and
fp ? 1 for strong dissipation), ? = 0 (which accounts for the gravitational potential
due to the bulge relative to the gas self-gravity; see Ostriker and Shetty (2011) for
more details), P/m? = 3000 km s
?1, and ff(n0) = 0.005 (the free-fall efficiency at
the disk midplane density):
( )( )
?1 fp ff(n0) P/m?? = 5.5 km s . (4.14)
(1 + ?)1/2 0.005 3000 km s?1
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While the marginal gas stability and feedback regulated star formation model
of Faucher-Gigue?re et al. (2013) reasonably match the DYNAMO and PHANGS-
ALMA observations, as plotted in Figure 4.11, it is important to note that these
model prediction lines were derived in Orr et al. (2020) from the FIRE-2 measured
values of ?mol and ?SFR. As we note already, the depletion time between FIRE-
2 galaxies and DYNAMO are different; therefore, the model predictions may not
be comparable to the observations. Furthermore, the marginal gas stability model
assumes that the Toomre parameter Q = 1, while studies show that Q < 1 in
DYNAMO galaxies (see White et al., 2017, Girard et al., 2021).
Focusing on the feedback regulated model of equation 4.13, we are able to use
our measured ?mol, ?SFR, and ? values to verify what velocity dispersion scaling is
predicted for DYNAMO. We find from this experiment that the feedback regulated
model in equation 4.13 predicts that the velocity dispersion in DYNAMO should
scale inversely with ?mol and ?SFR, which is contrary to our observations.
To verify that our measurements of ?SFRare not biased, we examine our as-
sumption of constant extinction correction in calculating SFRs. If extinction is
significantly higher in the centers, we would under-predict the ?SFR and find longer
depletion times in these regions. To test this, we plot in the left panel of Figure 4.12
the beam smearing corrected velocity dispersions as a function of the gas depletion
time. We note from this that overall, the velocity dispersions we measure are not
a strong function of depletion time. There are instances of high ?mol values, which
we tend to preferentially measure at the centers of our targeted galaxies, that are
associated with longer depletion times. This indicates that it is possible our extinc-
178
Figure 4.12: Left : Beam smearing corrected molecular gas velocity dispersion as a
function of the gas depletion time (tdep), measured along individual ? 1 ? 2 kpc
sized lines of sight. Despite a few high ?mol values with long depletion times, overall
there is no strong correlation between ?mol and tdep. Right : Comparison of the
inverse angular velocity of DYNAMO D13-5 (red points), compared to the scaling
that would be required in the feedback regulated model of star formation in equation
4.13 to reproduce the observed velocity dispersion measurements.
tion assumptions are affecting the SFRs we measure; however, it does not appear to
be a major effect. Indeed, we find that if we fix the depletion time for each line of
sight measurement (thus fixing the ratio of ?mol to ?SFR and only varying ?), then
the issue persists. This suggests that our ?SFR measurements are not the primary
drivers of the discrepancy between the observed ?mol measurements, and ?mol values
predicted by equation 4.13.
Rather, it is the ??1 scaling that is largely responsible. The dependence of
?mol on ? in the feedback regulated model comes from the assumption that turbulent
momentum decay takes place on a eddy (disk) crossing time. However, this scaling
produces a predicted dependence of ?mol on ?mol and ?SFR that is opposite to what
we observe. Thus, we invert equation 4.13 to solve for the ??? scaling that would be
179
required to reproduce our observed ?mol values, and show the result in the right panel
of Figure 4.12 for the galaxy DYNAMO D13-5. The red data points correspond to
??1 derived from the D13-5 rotation curve of Girard et al. (2021). In contrast,
the blue data points correspond to the ??? value that would produce the velocity
dispersions we observe in this galaxy. We see that ??1 increases with radius, as we
would expect, while the turbulent momentum dissipation timescale would need to
be related to a quantity that decreases with radius. This is perhaps not a surprising
result, since turbulent momentum dissipation might be expected to be related to the
microphysics of the gas, while the angular velocity is a large scale galaxy property.
4.7 Conclusions
In this work, we have combined ? 1 ? 2 kpc scale ALMA observations of
CO(3?2) and CO(4?3), with HST observations of H?, to study the KS relation,
the CO(4?3)/CO(3?2) line ratio and its dependence on SFR surface density, and
the relation between molecular gas velocity dispersion and the surface densities of
star formation and molecular gas. We summarize our findings here:
1. DYNAMO galaxies have typical CO(4?3)/CO(3?2) line ratios of r43 = 0.54+0.16?0.15,
which is most consistent with samples of star forming z ? 1 ? 2 main-sequence
galaxies and LIRGs (Papadopoulos et al., 2012, Daddi et al., 2015, Henr??quez-Brocal
et al., 2021).
180
2. The DYNAMO CO(4?3)/CO(3?2) line ratios are positively correlated with
the ?SFR measurements, with a Spearman Rank Order correlation coefficient of
? = 0.614. Our best fit relation between the CO(4?3)/CO(3?2) line ratio and
?SFR is r43 = 0.2 ? log ?SFR + 0.67. This relation suggests a steeper relation than
predicted by the parameterization of Narayanan and Krumholz (2014); however, the
line ratio uncertainties are large.
3. The resolved KS relation in DYNAMO galaxies has a sub-linear slope of N = 0.77
when assuming a fixed, Milky Way-like ?CO factor. Adopting a variable ?CO (equa-
tion 31 in Bolatto et al., 2013) results in a slope of N = 0.90. These results are
consistent with the kpc-scale measurements of the KS relation from the HERACLES
CO(2?1) and H?+24 ?m measurements of Leroy et al. (2013).
4. The molecular gas velocity dispersions in DYNAMO galaxies are positively cor-
related with molecular gas surface density and SFR surface density, consistent with
observations in other samples of galaxies (e.g., Sun et al., 2020). Furthermore, we
show that the DYNAMO sample extends the range of ?mol and ?SFR conditions
probed compared to local samples of star forming galaxies. When predicting the
molecular gas velocity dispersions in DYNAMO with theoretical models like the
feedback regulated model of star formation, we find that the velocity dispersions
should decrease with increasing gas and SFR surface densities. We find that the
primary driver of this effect is the assumption that the turbulent momentum dis-
sipation is related to the angular velocity of a galaxy. Angular velocity decreases
181
outward as a function of galactocentric radius, while to reproduce the observed DY-
NAMO velocity dispersions, the turbulent momentum dissipation would need to
depend on a quantity that behaves in the opposite way and suggest that it is likely
driven by gas microphysics.
182
Chapter 5: Future Work
While the work I have presented in this thesis addresses important questions
regarding gas and star formation in galaxies across cosmic time, there remain nu-
merous unanswered ones. In this chapter, I outline some of these questions, and
highlight planned and potential future work that will aim to address them.
5.1 The ISM of Clumpy, Turbulent Galaxies
The 158 ?m [CII] fine-structure line is an important coolant of the ISM, and
is thus a probe of the physical conditions of the ISM. We cannot easily study these
conditions in main sequence galaxies at z ? 1 ? 2, the most important epoch of
galaxy assembly. We can, however, observe the fine-structure lines in local analogues
of main sequence high?z galaxies, like DYNAMO. Observations of DYNAMO exist
from facilities such as ALMA, NOEMA, HST, Keck, and Gemini, spanning from
the sub-millimeter to the optical/UV, with a gap in the IR.
I am the PI of a SOFIA Cycle 9 observing proposal that has observed [CII]
emission and FIR luminosity of seven DYNAMO galaxies with the FIFI-LS and
HAWC+ instruments. With these data, I will measure the [CII] line deficits, gas
temperatures (which only exist for nine DYNAMO galaxies), and test the suitability
183
of [CII] as a tracer of star formation, relating these to main sequence galaxies at
z ? 2. As galaxies become more luminous and/or compact, the ratio of [CII] line
emission to the total FIR luminosity decreases. The [CII]/FIR ratio varies by several
orders of magnitude between galaxy types (see Figure 3 in Herrera-Camus et al.,
2018a) and with galaxy properties, such as distance from the main sequence and FIR
surface brightness (see Figure 5 in Herrera-Camus et al., 2018b). This is observed
in local star forming galaxies, galaxies with active galactic nuclei, and high-redshift
main sequence objects. DYNAMO galaxies are interesting because their cool dust
temperatures and high IR luminosities suggest that they may not have a [CII] deficit.
I will test this with my SOFIA observations.
5.2 Large Scale Gas Flows and Clump Scale Gas Kinematics
While the bulk kinematics of galaxies at z ? 1 ? 3 are well studied (see e.g.,
Wisnioski et al., 2015), the detailed kinematics of gas flows fueling the formation
and growth of clumps remain poorly understood. It is widely adopted that the gas is
in a state of marginal instability, which has multiple consequences. Krumholz et al.
(2018) argue that the instability in gas-rich galaxies should naturally lead to large,
non-rotating flows of gas, and that these are responsible for the large gas velocity
dispersions in z > 1 galaxies. Direct observations of these gas flows in samples of
nearby spiral galaxies are rare (Wong et al., 2004, Schmidt et al., 2016), and are
otherwise lacking in samples of high?z star forming galaxies, which may be due to
the high resolution needed. Secondly, instabilities are thought to be the source of
184
large clumps (Dekel et al., 2009), yet how clumps dynamically evolve within their
galaxies remains uncertain even after a decade of research. Basic concepts, such as
the longevity of clumps, remain under debate.
I am the PI of an accepted ALMA Cycle 8 observing proposal that will map the
CO(3?2) kinematics and surface brightness in the nearby galaxy DYNAMO D13-5
(z = 0.0753) at ? 0.2?? resolution corresponding to a physical scale of ?280 pc. The
goals are to: (1) identify inward mass transport via residuals from velocity models
fit to the data, and (2) determine if the clumps are kinematically distinct from the
disk and whether they are bound as indicated by their gas virial parameter.
For the first goal, I will use the upcoming ? 280 pc observations and existing
? 1.4 kpc scale observations of this galaxy (presented in Chapter 4) to generate
a 2-D model of the velocity field, and then search for significant residuals in the
high resolution map. For the second goal, I will use the ALMA observations to
measure the gas velocity dispersions and virial parameters of all 18 clumps in D13-5,
which will provide a measure of clump longevity and boundness that is independent
of the stellar population work I presented in Chapter 4. Because this analysis
requires spatial resolution in both kinematics and gas mass sufficient to isolate the
individual clumps, the new ALMA observations of D13-5 will provide a completely
independent, statistically powerful, assessment of the fundamental nature of clumps
in galaxies.
185
5.3 Feedback from Clumps
Feedback regulated star formation models (e.g., Ostriker et al., 2010) are a
standard component of our picture of galaxy evolution. In these theories, newly
formed stars and supernovae inject momentum into the ISM which balances it
against the inward force of gravity. It is well established at the level of individ-
ual supernovae that these explosions carry momentum into the ISM (e.g., Cioffi
et al., 1988). At the galaxy wide scale, observations of UV absorption lines indicate
that galactic winds are common at z? 1 ? 3 (e.g., Steidel et al., 2010). However,
at intermediate scales, especially in extreme environments like massive star forming
clumps, observations are limited. This is because present day facilities cannot ad-
equately resolve these clumpy star forming structures at z ? 1 ? 3. Therefore, it
is currently unknown if feedback unbinds clumps before they are able to migrate to
the centers of galaxies and contribute to bulge growth, as suggested by theories of
instability driven clump formation and migration (Dekel et al., 2009). Determining
the ultimate fate of clumps, and the role of feedback, is critical to understanding
galaxy evolution in the era of peak star forming activity.
To probe the fate of clumps, I will propose for new observations using the
NIRSpec IFU aboard the James Webb Space Telescope (JWST) to map the Pa?
1.8751 ?m emission line at ? 150 pc resolution in the DYNAMO galaxy D13-5.
Broad-wing emission lines can be used to measure outflows, but in practice this has
only been possible for a handful (? 5) of clumps. The presence of outflowing material
causes a fraction of the Pa? flux to reside in a blue-shifted broad component. JWST
186
is the only facility with the spatial resolution and sensitivity required to detect and
characterize the properties of the outflowing material, and enable us to study the
link between feedback and clump lifetimes. These observations will allow me to:
(1) perform the first measurement of the velocity and flux of ionized gas outflows
from clumps in a nearby galaxy whose properties are very well-matched to main-
sequence, z? 1?3 galaxies, and (2) determine if clumps are truly bound and rotating
structures.
187
Appendix A: Appendices for Chapter 2
This Appendix includes supplementary material for Chapter 2, including data
tables summarizing all candidate CO source properties and their potential counter-
parts, and Figures showing the detection S/N maps, potential counterparts, and CO
line spectra.
A.1 Description of Individual Candidate Sources
Figure 2.5 shows the brightest serendipitous CO sources in the COSMOS,
EGS/AEGIS, and GOODS-N fields. The complete set of Figures is available here.
The left panels show the signal-to-noise maps at the velocity resolution where each
source is detected with the highest SNR. The black contour corresponds to the
detection threshold (largest negative SNR). The black box shows the zoom in region
for the middle panel images, and the beam is shown in the bottom left corner. The
middle panels are HST ACS F814W images where the white contours start at the
3? level and increase in steps of 0.5?, the red contour corresponds to the detection
threshold, red crosses mark the positions of tentative optical counterparts, and the
beam is again shown in the bottom left corner. The size of the red contour appears
small in some cases, this is however not a problem since these contours are really
188
just the peak of the beam over our adopted ?threshold?. The right panel shows the
spectrum of each source extracted at the peak pixel, given unresolved sources. The
blue spectrum corresponds to a velocity resolution of ? 100 km s?1 while the orange
spectrum corresponds to the velocity resolution matching that of the left panel. In
cases where these two are the same, only the blue lines are shown. The FWHM and
redshift of each candidate are added in the top left corners, and the source name
(used in Tables A.1 and A.1) and reliability measurement are included in the top
right corner.
Table A.1 lists each candidate source, divided according to the three fields
(COSMOS, GOODS-N, EGS/AEGIS) with their RA and Dec, central frequency,
flux, FWHM, SNR, and their completeness and reliability measures. Table A.1
lists the potential optical counterparts with their IDs, RA and Dec, redshift, and
angular separation. Redshifts extracted from the 3D-HST/CANDELS catalogs are
photometric redshifts, except where otherwise noted.
189
190
191
192
193
194
Figure A.1: All candidate CO sources detected in the COSMOS field.
195
196
197
198
199
200
Figure A.2: All candidate CO sources detected in the GOODS-N field.
201
202
203
Figure A.3: All candidate CO sources detected in the EGS/AEGIS field.
204
ID RA Dec Frequency Flux FWHM SNR Comp. Rel.
(J2000.0) (J2000.0) (GHz) (Jy km s?1) (km s?1)
co006-1 10h0m31.44 2d12m32.51s 104.582 0.599 ? 0.139 590 ? 104 6.26 0.8209 1.00
co006-5 10h0m30.25 2d12m27.91s 102.524 0.172 ? 0.066 141 ? 41 4.48 0.1973 0.35
co012-1 10h0m44.78 2d33m26.80s 135.900 0.613 ? 0.146 151 ? 27 6.25 0.7720 1.00
co012-3 10h0m44.58 2d33m42.20s 134.577 0.599 ? 0.199 277 ? 69 4.88 0.7510 0.83
co018-1 10h0m58.71 1d45m53.60s 142.039 0.341 ? 0.082 227 ? 41 6.68 0.9219 0.99
co018-2 10h0m58.59 1d46m2.000s 143.244 0.152 ? 0.047 119 ? 27 5.15 0.0968 0.76
co027-2 10h0m44.16 2d07m00.93s 107.631 0.323 ? 0.091 309 ? 66 5.50 0.4237 0.99
xl53-1 10h0m28.36 2d15m49.28s 132.169 0.315 ? 0.091 63 ? 14 5.88 0.0061 0.93
xl53-2 10h0m28.99 2d16m9.28s 133.094 0.304 ? 0.107 63 ? 17 5.38 0.0053 0.46
co007-3 10h0m24.64 2d29m48.88s 153.419 0.315 ? 0.100 167 ? 40 4.92 0.4791 0.91
co007-2 10h0m24.52 2d29m43.48s 153.643 0.216 ? 0.053 59 ? 11 5.23 0.1134 0.76
xu53-5 10h0m40.93 2d23m27.44s 153.676 0.392 ? 0.127 131 ? 32 4.54 0.2351 0.89
xu53-6 10h0m40.11 2d23m39.04s 151.627 0.637 ? 0.226 347 ? 93 4.39 0.2125 0.39
xu53-7 10h0m39.35 2d23m03.24s 151.257 0.782 ? 0.298 282 ? 81 4.37 0.9045 0.35
xh53-2 10h1m10.03 2d30m04.90s 136.249 0.696 ? 0.226 588 ? 144 4.58 0.3127 0.88
co005-1 10h0m27.13 2d17m51.20s 109.715 0.297 ? 0.110 155 ? 43 4.60 0.4130 0.86
co005-2 10h0m28.76 2d17m32.80s 111.352 0.260 ? 0.087 131 ? 33 4.34 0.3219 0.61
co005-3 10h0m28.84 2d17m53.20s 109.868 0.166 ? 0.068 91 ? 28 4.33 0.1388 0.59
co004-1 10h0m39.88 2d20m45.64s 136.209 0.432 ? 0.161 908 ? 255 4.37 0.9414 0.71
xr53-2 10h1m43.05 2d06m55.24s 154.097 0.903 ? 0.228 358 ? 68 4.72 0.0095 0.69
xr53-4 10h1m40.33 2d07m07.24s 152.109 1.395 ? 0.366 766 ? 152 4.33 1.0000 0.09
co002-1 10h0m16.88 2d23m10.77s 109.639 0.177 ? 0.053 93 ? 21 5.20 0.1609 0.63
xg53-1 10h2m15.90 1d37m20.80s 142.676 0.435 ? 0.130 119 ? 27 5.32 0.1321 0.62
xw53-1 10h0m34.62 2d16m38.12s 132.701 1.015 ? 0.339 382 ? 97 4.73 0.6225 0.60
xn53-1 10h0m10.05 2d35m46.24s 135.884 0.678 ? 0.221 130 ? 32 5.03 0.3668 0.31
xj53-1 10h1m47.94 2d23m12.00s 114.346 0.461 ? 0.160 69 ? 18 4.81 0.0150 0.08
gn019-1 12h36m31.31 62d09m58.47s 104.643 1.840 ? 0.247 948 ? 96 7.64 0.9921 1.00
xc55-3 12h36m11.91 62d14m4.80s 130.324 1.289 ? 0.406 638 ? 152 4.56 0.6556 0.99
xc55-2 12h36m12.19 62d14m15.40s 131.516 1.156 ? 0.530 595 ? 232 4.69 0.3219 0.85
xc55-4 12h36m8.04 62d14m9.40s 129.997 0.660 ? 0.267 251 ? 77 3.85 0.4351 0.62
gn010-6 12h36m42.68 62d12m2.73s 137.174 0.587 ? 0.255 642 ? 215 4.04 0.3992 0.96
gn010-3 12h36m39.05 62d12m2.13s 136.516 0.444 ? 0.184 310 ? 107 4.22 0.7280 0.42
gn030-2 12h36m22.27 62d10m19.82s 110.859 0.190 ? 0.056 117 ? 26 5.32 0.1141 0.92
gn030-3 12h36m26.67 62d10m15.62s 110.809 0.148 ? 0.055 90 ? 26 5.16 0.0420 0.36
xg55-2 12h37m1.87 62d14m06.60s 151.712 0.192 ? 0.105 76 ? 38 5.15 0.1196 0.91
xg55-6 12h37m2.73 62d14m26.60s 151.712 0.277 ? 0.111 156 ? 47 4.13 0.1225 0.13
xa55-2 12h36m59.75 62d15m9.80s 132.414 0.286 ? 0.098 28 ? 8 4.95 0.0102 0.62
gn001-3 12h37m26.27 62d20m39.29s 103.518 0.468 ? 0.191 773 ? 238 4.17 0.3312 0.56
xf55-1 12h35m56.17 62d10m46.20s 142.516 0.160 ? 0.173 90 ? 70 4.98 0.0907 0.52
gn011-1 12h37m19.35 62d18m50.56s 137.386 0.543 ? 0.147 136 ? 28 4.85 0.3091 0.51
gn032-1 12h37m16.23 62d15m31.12s 148.202 0.380 ? 0.099 206 ? 41 5.19 0.4593 0.49
gn018-2 12h36m32.26 62d16m03.68s 129.890 0.532 ? 0.225 642 ? 205 4.44 0.2299 0.43
gn018-3 12h36m31.74 62d16m00.48s 128.524 0.595 ? 0.185 637 ? 150 4.35 0.3020 0.27
gn037-2 12h36m25.23 62d10m41.60s 226.683 0.178 ? 0.049 65 ? 14 5.55 0.0113 0.43
gn006-1 12h36m32.72 62d17m48.71s 136.200 0.291 ? 0.091 63 ? 14 5.32 0.0130 0.41
gn007-2 12h36m35.41 62d07m26.53s 145.737 0.431 ? 0.123 154 ? 34 5.29 0.3004 0.41
gn034-2 12h36m20.86 62d19m07.70s 151.152 0.538 ? 0.188 383 ? 101 4.61 0.4066 0.39
gn002-1 12h36m41.56 62d17m01.56s 114.944 0.550 ? 0.158 164 ? 35 4.92 0.4009 0.37
gn021-3 12h36m0.69 62d11m26.18s 142.145 0.303 ? 0.095 58 ? 14 5.40 0.0337 0.37
gn005-1 12h37m18.40 62d12m39.04s 101.340 0.235 ? 0.073 172 ? 42 5.29 0.3657 0.21
gn017-6 12h36m53.43 62d17m04.86s 109.324 0.367 ? 0.132 237 ? 64 4.28 0.2002 0.20
gn017-7 12h36m54.98 62d17m04.26s 106.419 0.320 ? 0.150 191 ? 70 4.27 0.4470 0.18
gn017-1 12h36m53.78 62d17m15.26s 106.817 0.180 ? 0.056 83 ? 19 4.79 0.0950 0.09
gn026-2 12h36m34.68 62d18m02.12s 106.883 0.430 ? 0.168 700 ? 206 4.27 0.3453 0.11
eg016-1 14h18m27.95 52d42m55.28s 140.127 0.635 ? 0.158 791 ? 150 7.90 0.2339 1.00
xb54-2 14h19m36.82 52d51m13.60s 137.437 0.669 ? 0.248 165 ? 47 5.27 0.3905 1.00
xb54-3 14h19m37.57 52d50m53.40s 139.610 0.563 ? 0.207 171 ? 47 4.43 0.2380 0.96
xd54-2 14h19m47.37 52d54m22.80s 132.142 0.365 ? 0.112 108 ? 25 5.19 0.1105 1.00
eg014-1 14h20m31.63 52d59m20.86s 135.400 0.175 ? 0.049 69 ? 15 5.72 0.1315 0.82
xi54-1 14h19m42.46 52d52m05.81s 172.316 0.744 ? 0.182 203 ? 37 5.35 0.2646 0.75
eg012-1 14h19m51.28 52d51m10.86s 150.082 0.241 ? 0.080 48 ? 13 5.67 0.0066 0.69
Continued on next page
205
ID RA Dec Frequency Flux FWHM SNR Comp. Rel.
(J2000.0) (J2000.0) (GHz) (Jy km s?1) (km s?1)
eg012-2 14h19m51.43 52d51m14.66s 148.704 0.622 ? 0.202 353 ? 87 4.69 0.4550 0.69
eg006-3 14h18m44.84 52d43m30.66s 154.766 0.150 ? 0.055 49 ? 14 5.29 0.0419 0.32
eg006-4 14h18m45.72 52d43m37.06s 155.775 0.184 ? 0.099 83 ? 36 5.00 0.0838 0.31
eg006-6 14h18m48.01 52d43m03.46s 154.780 1.262 ? 0.343 829 ? 170 4.46 0.8294 0.25
eg005-1 14h18m58.38 52d42m59.43s 108.805 0.141 ? 0.050 61 ? 18 5.12 0.0537 0.25
eg018-3 14h19m40.06 52d51m38.39s 206.825 0.366 ? 0.122 216 ? 54 4.96 0.8813 0.15
This table lists the properties of all candidate CO sources detected in the PHIBSS2 observations: (1) candidate ID,
(2)-(3) RA and Dec of the source, (4) frequency at the line center, (5) integrated flux of the source, (6) FWHM
of the source CO line, (7) signal-to-noise ratio of the source, (8) completeness measure of the detection, and (9)
reliability of the detection.
Table A.1: Properties of Candidate CO Sources
ID Counterpart RA Dec Redshift CO Redshift ?r Pa
(J2000) (J2000) (??) (??)
co006-1 COS 2997 10h0m31.43 2d12m32.018s 3.52 3.4084 0.5 0.98
co012-1 COS 33686 10h0m44.79 2d33m26.58s 0.6961a 0.6964 0.2 0.99
co012-3 COS 33774 10h0m44.59 2d33m17.67s 0.67 1.5695 1.6 0.70
co018-1 COS 485943 10h0m58.69 1d45m54.00s 0.65 0.6231 0.5 0.98
co027-2 COS 1236431 10h0m44.27 2d7m2.28s 0.95 1.1419 2.1 0.42
co007-3 COS 2345915 10h0m24.48 2d29m50.10s 1.25 1.2539 2.7 0.53
xu53-5 COS 20811 10h0m40.88 2d23m26.84s 1.27 1.2502 1.0 0.89
xu53-6 COS 21168 10h0m40.08 2d23m40.42s 0.67 0.5204 1.5 0.74
xu53-7 COS 20188 10h0m39.28 2d23m2.68s 1.84 2.0481 1.2 0.84
xh53-2 COS 2307212 10h1m9.89 2d30m4.82s 0.67 0.6921 2.2 0.07
co005-1 COS 11546 10h0m26.94 2d17m48.65s 1.15 1.1012 3.8 0.23
co005-1 COS 11595 10h0m26.88 2d17m49.77s 1.34 1.1012 4.0 0.15
co005-1 COS 11549 10h0m26.96 2d17m48.09s 0.94 1.1012 4.0 0.15
co005-2 [Capak2017] 1599172 10h0m28.70 2d17m30.89s 3.11 3.1404 2.1 0.77
co005-3 COS 111603 10h0m29.02 2d17m50.71s 4.26 4.2451 3.7 0.28
co002-1 COS 20413 10h0m16.82 2d23m10.93s 1.85 2.1539 1.0 0.89
xw53-1 COS 09632 10h0m34.57 2d16m38.06s 1.69 1.6058 0.8 0.88
xn53-1 COS 2361883 10h0m9.83 2d35m46.86s 0.73 0.6966 3.4 0.08
gn019-1 GN 05359 12h36m31.29 62d9m58.04s 2.3301b 2.3045 0.5 0.99
xc55-3 GN 18914 12h36m11.79 62d14m7.69s 1.99 1.6534, 2.5377 3.0 0.52
xc55-3 GN 18951 12h36m11.86 62d14m8.36s 2.07 0.7690, 1.6534, 2.5377 3.6 0.30
xc55-2 GN 19484 12h36m12.44 62d14m17.49s 3.83 3.3817, 4.2577 2.7 0.61
gn010-6 GN 11844 12h36m42.78 62d12m3.97s 1.70 1.5209 1.5 0.64
gn010-6 GN 11803 12h36m42.91 62d12m3.46s 2.26 1.5209, 2.3610 1.8 0.48
gn010-6 GN 11666 12h36m42.49 62d12m1.21s 1.65 0.6806, 1.5209, 2.3610 2.0 0.36
xg55-2 GN 18857 12h37m1.50 62d14m7.10s 3.01 2.7984 2.7 0.20
xg55-2 GN 19030 12h37m1.85 62d14m9.47s 0.46 0.5196 2.9 0.08
xa55-2 GN 22587 12h36m59.50 62d15m12.37s 0.67 0.7595 3.1 0.32
gn001-3 GN 36945 12h37m26.17 62d20m39.54s 1.00 1.2270 0.8 0.96
gn018-2 GN 25624 12h36m32.24 62d16m3.10s 3.20 3.4366 0.6 0.91
gn018-2 GN 25623 12h36m32.07 62d16m2.86s 0.42 0.7749 1.5 0.42
gn018-3 GN 25587 12h36m31.77 62d16m1.81s 1.46 0.7937 1.3 0.57
gn006-1 [BIO2015] GNDV 6325117508 12h36m32.51 62d17m50.80 4.65 4.9225 1.7 0.59
gn002-1 GN 28898 12h36m41.28 62d17m3.17s 2.31 2.0084 2.6 0.62
gn002-1 GN 28704 12h36m41.89 62d16m59.95s 1.28 1.0056, 2.0084 2.8 0.56
gn005-1 GN 13860 12h37m18.08 62d12m39.43s 1.27 1.2749 2.3 0.69
gn017-6 GN 28920 12h36m53.66 62d17m4.33s 2.28 2.1630 1.7 0.87
gn017-7 GN 29041 12h36m55.07 62d17m5.93s 2.11 2.2494 1.8 0.85
gn017-7 GN 28807 12h36m55.02 62d17m1.54s 0.70 1.1663, 2.2494 2.7 0.67
gn017-1 GN 1308 12h36m54.11 62d17m12.12s 2.52 2.2373 3.9 0.31
gn026-2 GN 31722 12h36m34.99 62d18m1.07s 1.67 1.1569, 2.2353 2.4 0.31
eg016-1 EGS 33606 14h18m27.92 52d42m55.59s 4.16 3.9337 0.4 0.95
xb54-2 EGS 16871 14h19m36.89 52d51m14.44s 0.86 0.6774 1.0 0.93
xb54-3 [Barro2011] 124112 14h19m37.37 52d50m50.32s 0.68 0.6513 3.6 0.15
xd54-2 EGS 21954 14h19m47.52 52d54m21.54s 1.66 1.6168 1.9 0.69
eg014-1 EGS 10403 14h20m31.70 52d59m22.04s 1.74 1.5539 1.4 0.11
eg012-1 EGS 06254 14h19m51.40 2d51m9.70s 2.04 2.0719 1.6 0.55
eg012-1 EGS 06217 14h19m51.36 52d51m8.85s 1.62 1.3040, 2.0719 2.1 0.22
eg012-1 EGS 06392 14h19m51.46 52d51m12.31s 0.94 0.5361, 1.3040 2.2 0.15
eg006-3 EGS 23517 14h18m44.64 52d43m32.71s 3.39 3.4678 2.7 0.16
eg006-4 EGS 23149 14h18m45.56 52d43m37.29s 1.18 0.4799 1.4 0.78
eg006-6 EGS 18930 14h18m48.11 52d43m3.12s 1.4157b 1.2341, 1.9787 1.8 0.63
eg005-1 EGS 11013 14h18m58.51 52d43m0.15s 1.80 1.1188, 2.1781 1.4 0.92
eg018-3 EGS 16186 14h19m40.07 52d51m39.71s 1.48 0.6719, 1.2291, 1.7863 1.3 0.02
This table lists the properties of all potential optical counterparts to the candidate CO sources: (1) candidate CO source ID, (2)
sesignation of the optical counterpart in the COSMOS, GOODS-N, and EGS/AEGIS catalogs, (3)-(5) RA, DEC, and redshift (?best?)
of the optical counterpart taken from the COSMOS, GOODS-N, and EGS/AEGIS catalogs, (6) list of redshifts corresponding to the
possible CO transitions given the posterior likelihood distributions of the EAZY SED fitting, (7) projected angular separation between
candidate source and the potential optical counterpart, and (8) for cases where multiple potential optical counterparts exist, we assign
a probability of association that is proportional to the inverse square of the projected angular separation. Redshifts in column (5)
with superscript ?a? are spectroscopic redshifts, and ones with superscript ?b? are grism redshifts.
Table A.2: Properties of Potential Optical Counterparts
206
A.2 Luminosity Function and Molecular Gas Mass Density Con-
straints: Tabulated Results
In this appendix, we include the 1? ranges for each luminosity bin, for every
CO luminosity function we measure, as shown in Figure 2.10. Bins are 0.5 dex wide
and given in steps of 0.1 dex, therefore every 5th bin is statistically independent.
We also include the molecular gas mass density constraint for each redshift bin in
tabulated form.
207
log(L?CO) bin log ?, 1? log(L
?
CO) bin log ?, 1? log(L
? ) bin log ?, 1?
(K km s?1 pc?
CO
2) (Mpc?3 dex?1) (K km s?1 pc?2) (Mpc?3 dex?1) (K km s?1 pc?2) (Mpc?3 dex?1)
CO(2-1), z ? 0.34? 0.79 CO(2-1), z ? 1.01? 1.27 CO(3-2), z ? 1.22? 1.66
8.4?8.9 -4.06 , -3.21 9.0?9.5 -3.59 , -2.23 9.0?9.5 -3.00 , -2.34
8.5?9.0 -3.29 , -2.63 9.1?9.6 -3.59 , -2.23 9.1?9.6 -2.99 , -2.44
8.6?9.1 -3.29 , -2.63 9.2?9.7 -3.60 , -2.75 9.2?9.7 -2.99 , -2.44
8.7?9.2 -3.29 , -2.63 9.3?9.8 -3.46 , -2.98 9.3?9.8 -3.00 , -2.52
8.8?9.3 -3.22 , -2.56 9.4?9.9 -3.71 , -3.27 9.4?9.9 -3.74 , -3.19
8.9?9.4 -3.07 , -2.52 9.5?10.0 -3.61 , -3.21 9.5?10.0 -3.79 , -3.24
9.0?9.5 -3.32 , -2.66 9.6?10.1 -3.61 , -3.21 9.6?10.1 -4.05 , -3.50
9.1?9.6 -3.21 , -2.77 9.7?10.2 -3.64 , -3.21 9.7?10.2 -4.05 , -3.50
9.2?9.7 -3.10 , -2.79 9.8?10.3 -3.98 , -3.32 9.8?10.3 -4.19 , -3.54
9.3?9.8 -3.14 , -2.82 9.9?10.4 -4.05 , -2.69 9.9?10.4 -4.37 , -3.71
9.4?9.9 -3.35 , -2.98 ? ? 10.0?10.5 -4.84 , -3.98
9.5?10.0 -3.35 , -2.98 ? ? 10.1?10.6 -4.84 , -3.48
9.6?10.1 -3.57 , -3.14 ? ? 10.2?10.7 -4.84 , -3.48
9.7?10.2 -5.12 , -3.76 ? ? 10.3?10.8 -4.84 , -3.48
9.8?10.3 -5.12 , -3.76 ? ? ? ?
9.9?10.4 -5.12 , -3.76 ? ? ? ?
10.0?10.5 -5.12 , -3.76 ? ? ? ?
CO(3-2), z ? 2.01? 2.31 CO(4-3), z ? 1.03? 1.98 CO(4-3), z ? 2.05? 2.59
9.1?9.6 -3.80,-2.44 8.8?9.3 -8.32,-6.96 9.1?9.6 -2.57,-1.21
9.2?9.7 -3.75,-3.09 8.9?9.4 -8.32,-6.96 9.2?9.7 -2.57,-1.21
9.3?9.8 -3.75,-3.09 9.0?9.5 -8.32,-6.96 9.3?9.8 -2.57,-1.21
9.4?9.9 -3.75,-3.09 9.1?9.6 -8.32,-6.96 9.4?9.9 -2.57,-1.21
9.5?10.0 -3.73,-3.25 9.2?9.7 -5.38,-4.53 9.5?10.0 -2.64,-1.79
9.6?10.1 -4.08,-3.65 9.3?9.8 -5.31,-3.95 9.6?10.1 -4.33,-3.47
9.7?10.2 -4.45,-3.90 9.4?9.9 -5.31,-3.95 9.7?10.2 -4.33,-3.47
9.8?10.3 -4.31,-3.82 9.5?10.0 -5.31,-3.95 9.8?10.3 -4.33,-3.47
9.9?10.4 -4.31,-3.82 9.6?10.1 -5.31,-3.95 9.9?10.4 -4.29,-3.64
10.0?10.5 -4.56,-3.91 9.7?10.2 -5.25,-3.90 10.0?10.5 -4.86,-4.01
10.1?10.6 -4.63,-3.27 9.8?10.3 -5.25,-3.90 10.1?10.6 -4.96,-3.60
10.2?10.7 -4.63,-3.27 9.9?10.4 -5.25,-3.90 10.2?10.7 -4.96,-3.60
10.3?10.8 -4.19,-2.83 10.0?10.5 -5.25,-3.90 10.3?10.8 -4.96,-3.60
10.4?10.9 -4.19,-2.83 10.1?10.6 -5.25,-3.90 ? ?
10.5?11.0 -4.19,-2.83 ? ? ? ?
10.6?11.1 -4.19,-2.83 ? ? ? ?
10.7?11.2 -4.19,-2.83 ? ? ? ?
CO(4-3), z ? 3.14? 3.40 CO(5-4), z ? 3.38? 3.44 CO(5-4), z ? 4.25? 4.51
9.4?9.9 -4.17,-2.81 9.5?10.5 -5.28,-4.43 9.2?10.2 -4.62,-3.77
9.5?10.0 -4.17,-2.81 ? ? ? ?
9.6?10.1 -4.17,-2.81 ? ? ? ?
9.7?10.2 -4.17,-2.81 ? ? ? ?
9.8?10.3 -4.08,-3.22 ? ? ? ?
9.9?10.4 -4.48,-3.12 ? ? ? ?
10.0?10.5 -4.48,-3.12 ? ? ? ?
10.1?10.6 -4.48,-3.12 ? ? ? ?
10.2?10.7 -4.48,-3.12 ? ? ? ?
CO(6-5), z ? 3.47? 3.93
8.8?9.8 -4.85,-4.0
This table lists the (x,y) boundaries of the luminosity function bins in Figure 2.10, for each CO transition and
redshift range we cover.
Table A.3: Luminosity functions of the observed CO transitions
Redshift ?(H2)
0.4799?1.4799 29.31?52.38
1.0056?2.0056 36.55?59.98
2.0084?3.0084 26.27?46.95
3.1404?4.1404 8.22?21.76
4.2451?5.2451 3.83?16.58
This table lists the (x,y) boundaries of the molecular gas mass density bins as a function of redshift in Figure 2.13.
Table A.4: Derived molecular gas mass density evolution constraints
208
Appendix B: Appendices for Chapter 3
B.1 Clump Properties
Galaxy ID RA Dec rclump m225 m336 m467
(J2000) (J2000) (pc) (abmag) (abmag)) (abmag)
D13-5 1 13:30:06.993 +0:31:54.299 389 ? 14 23.78 ? 0.04 22.55 ? 0.01 21.49 ? 0.03
D13-5 2 13:30:06.976 +0:31:54.115 406 ? 9 23.58 ? 0.03 22.48 ? 0.01 21.42 ? 0.03
D13-5 3 13:30:06.961 +0:31:53.949 336 ? 17 24.38 ? 0.05 23.11 ? 0.02 22.07 ? 0.05
D13-5 4 13:30:07.018 +0:31:54.274 256 ? 7 23.85 ? 0.03 22.91 ? 0.02 22.14 ? 0.04
D13-5 5 13:30:06.910 +0:31:53.361 471 ? 29 24.37 ? 0.10 22.82 ? 0.02 21.53 ? 0.04
D13-5 6 13:30:06.930 +0:31:52.802 285 ? 28 25.24 ? 0.14 23.96 ? 0.06 22.76 ? 0.13
D13-5 7 13:30:07.077 +0:31:53.891 410 ? 22 24.04 ? 0.06 22.85 ? 0.02 21.73 ? 0.06
D13-5 8 13:30:07.125 +0:31:54.052 328 ? 10 22.29 ? 0.01 21.61 ? 0.01 21.27 ? 0.02
D13-5 9 13:30:06.985 +0:31:52.257 397 ? 13 23.41 ? 0.03 22.46 ? 0.02 21.64 ? 0.05
D13-5 10 13:30:07.030 +0:31:52.612 402 ? 37 23.79 ? 0.04 22.54 ? 0.02 21.55 ? 0.04
D13-5 11 13:30:07.056 +0:31:52.641 522 ? 93 22.87 ? 0.02 21.71 ? 0.01 20.67 ? 0.02
D13-5 12 13:30:06.999 +0:31:51.873 362 ? 14 23.83 ? 0.04 22.76 ? 0.02 22.03 ? 0.09
D13-5 13 13:30:07.029 +0:31:52.116 422 ? 11 22.42 ? 0.01 21.60 ? 0.01 20.91 ? 0.02
D13-5 14 13:30:07.064 +0:31:52.308 320 ? 11 22.54 ? 0.01 21.75 ? 0.01 21.18 ? 0.02
D13-5 15 13:30:07.052 +0:31:52.161 622 ? 36 21.20 ? 0.01 20.46 ? 0.004 19.90 ? 0.01
D13-5 16 13:30:07.085 +0:31:52.334 459 ? 19 22.69 ? 0.02 21.74 ? 0.01 21.02 ? 0.02
D13-5 17 13:30:07.066 +0:31:52.096 461 ? 33 21.82 ? 0.01 21.17 ? 0.01 20.78 ? 0.02
D13-5 18 13:30:07.088 +0:31:52.140 371 ? 19 23.24 ? 0.02 22.40 ? 0.01 21.78 ? 0.03
D15-3 1 15:34:35.452 -0:28:45.745 243 ? 6 <28.45 24.62 ? 0.04 21.83 ? 0.03
D15-3 2 15:34:35.405 -0:28:46.004 373 ? 16 24.75 ? 0.07 23.50 ? 0.02 22.29 ? 0.05
D15-3 3 15:34:35.420 -0:28:45.217 572 ? 25 24.31 ? 0.12 22.78 ? 0.02 21.35 ? 0.04
D15-3 4 15:34:35.327 -0:28:45.734 277 ? 9 25.63 ? 0.11 24.56 ? 0.06 23.69 ? 0.59
D15-3 5 15:34:35.449 -0:28:43.476 398 ? 22 24.76 ? 0.08 23.37 ? 0.02 22.43 ? 0.08
D15-3 6 15:34:35.436 -0:28:43.562 435 ? 44 24.38 ? 0.07 23.01 ? 0.02 21.97 ? 0.06
D15-3 7 15:34:35.308 -0:28:45.177 359 ? 13 24.11 ? 0.04 22.90 ? 0.02 22.01 ? 0.05
D15-3 8 15:34:35.293 -0:28:45.235 389 ? 32 23.67 ? 0.03 22.60 ? 0.01 21.88 ? 0.04
D15-3 9 15:34:35.382 -0:28:43.822 920 ? 138 23.98 ? 0.20 22.30 ? 0.04 20.74 ? 0.09
D15-3 10 15:34:35.374 -0:28:42.702 496 ? 31 23.94 ? 0.05 22.53 ? 0.02 21.58 ? 0.05
G04-1 1 4:12:19.650 -5:54:48.543 451 ? 14 23.64 ? 0.03 22.73 ? 0.01 21.57 ? 0.03
G04-1 2 4:12:19.719 -5:54:47.291 321 ? 11 23.73 ? 0.03 22.92 ? 0.02 22.20 ? 0.05
G04-1 3 4:12:19.752 -5:54:47.164 308 ? 9 23.66 ? 0.03 22.94 ? 0.02 22.36 ? 0.05
G04-1 4 4:12:19.703 -5:54:48.345 466 ? 10 22.63 ? 0.02 21.62 ? 0.01 20.41 ? 0.01
G04-1 5 4:12:19.707 -5:54:48.789 487 ? 11 22.49 ? 0.01 21.56 ? 0.01 20.46 ? 0.01
G04-1 6 4:12:19.766 -5:54:47.759 572 ? 39 22.95 ? 0.02 22.01 ? 0.01 20.98 ? 0.02
G04-1 7 4:12:19.745 -5:54:48.567 491 ? 15 22.47 ? 0.01 21.47 ? 0.01 20.52 ? 0.02
G04-1 8 4:12:19.774 -5:54:48.052 366 ? 23 23.80 ? 0.03 22.88 ? 0.02 21.90 ? 0.04
G04-1 9 4:12:19.783 -5:54:49.985 402 ? 11 23.77 ? 0.03 23.21 ? 0.02 22.55 ? 0.06
G08-5 1 8:54:18.797 +6:46:21.327 535 ? 25 22.39 ? 0.01 21.81 ? 0.01 21.20 ? 0.02
G08-5 2 8:54:18.798 +6:46:20.935 583 ? 19 22.68 ? 0.02 22.00 ? 0.01 21.26 ? 0.03
G08-5 3 8:54:18.717 +6:46:19.255 335 ? 9 24.27 ? 0.04 23.54 ? 0.02 22.77 ? 0.06
Continued on next page
209
Galaxy ID RA Dec rclump m225 m336 m467
(J2000) (J2000) (pc) (abmag) (abmag)) (abmag)
G08-5 4 8:54:18.792 +6:46:19.894 506 ? 35 24.49 ? 0.08 22.81 ? 0.02 21.70 ? 0.03
G14-1 1 14:54:28.329 +0:44:34.584 353 ? 12 21.08 ? 0.01 20.41 ? 0.004 19.82 ? 0.01
G14-1 2 14:54:28.314 +0:44:33.917 455 ? 10 22.75 ? 0.01 22.10 ? 0.01 21.36 ? 0.02
G14-1 3 14:54:28.393 +0:44:34.258 262 ? 5 23.37 ? 0.02 22.39 ? 0.01 21.58 ? 0.02
G20-2 1 20:44:02.885 -6:46:57.221 452 ? 20 22.72 ? 0.01 22.13 ? 0.01 21.22 ? 0.02
G20-2 2 20:44:02.886 -6:46:57.506 537 ? 29 21.82 ? 0.01 21.15 ? 0.01 20.25 ? 0.01
G20-2 3 20:44:02.900 -6:46:57.535 870 ? 173 21.30 ? 0.01 20.55 ? 0.004 19.51 ? 0.01
G20-2 4 20:44:02.901 -6:46:57.766 612 ? 53 21.37 ? 0.01 20.59 ? 0.004 19.51 ? 0.01
G20-2 5 20:44:02.934 -6:46:57.367 363 ? 48 22.71 ? 0.02 21.95 ? 0.01 20.84 ? 0.02
G20-2 6 20:44:02.911 -6:46:58.218 454 ? 41 22.46 ? 0.01 21.72 ? 0.01 20.71 ? 0.02
G20-2 7 20:44:02.955 -6:46:57.455 491 ? 23 21.87 ? 0.01 21.12 ? 0.01 20.17 ? 0.01
G20-2 8 20:44:02.969 -6:46:57.253 425 ? 20 22.43 ? 0.01 21.76 ? 0.01 21.01 ? 0.02
G20-2 9 20:44:02.928 -6:46:58.409 446 ? 25 22.69 ? 0.02 21.90 ? 0.01 20.99 ? 0.02
G20-2 10 20:44:02.949 -6:46:58.266 352 ? 26 22.99 ? 0.02 22.27 ? 0.01 21.40 ? 0.02
G20-2 11 20:44:02.980 -6:46:57.528 669 ? 47 21.62 ? 0.01 20.82 ? 0.01 20.03 ? 0.01
G20-2 12 20:44:02.964 -6:46:58.029 354 ? 42 23.23 ? 0.02 22.35 ? 0.01 21.38 ? 0.03
G20-2 13 20:44:03.016 -6:46:57.556 331 ? 16 23.87 ? 0.03 23.32 ? 0.02 22.77 ? 0.09
G20-2 14 20:44:02.990 -6:46:58.564 401 ? 18 23.02 ? 0.02 22.64 ? 0.01 22.06 ? 0.04
This table lists all measured properties of the DYNAMO clumps: (1) galaxy ID, (2) clump ID, (3)-(4) RA and Dec
of the clump, (5) size of the clump, and (6)-(8) results of photometry in all three HST filters with uncertainties.
Table B.1: Properties of HST-DYNAMO Galaxy Clumps
B.2 Starburst99 Model Comparison
210
Figure B.1: A comparison of Starburst99 models: gray lines represent a model
with star formation history corresponding to a single burst with solar metallicity,
and the red lines represent a model with the same star formation history, but with
40% solar metallicity. We overlay the clump colors we measure as black circles. The
effect that assuming a lower metallicity has on the inferred ages and extinction of
the DYNAMO clumps is minimal.
211
Appendix C: Appendices for Chapter 4
C.1 Channel Maps
Here we present CO(3?2) and CO(4?3) channel maps for all ALMA data
used in this work. As in Figure 4.1, we show the velocity of each channel in the top
right corner of each panel, and we show the circularized beam as a white circle in
the bottom left corner of the first panel in each subsequent figure.
212
Figure C.1: DYNAMO C13-1 CO(3?2) channel maps. Each panel is centered at
13h26m39.428s, +01d30m01.40s and is 14.4 ? 14.4?? in size.
Figure C.2: DYNAMO C22-2 CO(3?2) channel maps. Each panel is centered at
22h39m49.344s, -08d04m18.11s and is 14.4 ? 14.4?? in size.
213
Figure C.3: DYNAMO C22-2 CO(4?3) channel maps. Each panel is centered at
22h39m49.344s, -08d04m18.11s and is 14.4 ? 14.4?? in size.
Figure C.4: DYNAMO D13-5 CO(3?2) channel maps. Each panel is centered at
13h30m07.014s, +00d31m53.20s and is 14.4 ? 14.4?? in size.
214
Figure C.5: DYNAMO D13-5 CO(4?3) channel maps. Each panel is centered at
13h30m07.014s, +00d31m53.20s and is 14.4 ? 14.4?? in size.
215
Figure C.6: DYNAMO D15-3 CO(4?3) channel maps. Each panel is centered at
15h34m35.399s, -00d28m44.56s and is 14.4 ? 14.4?? in size.
216
Figure C.7: DYNAMO G04-1 CO(4?3) channel maps. Each panel is centered at
04h12m19.713s, -05d54m48.62s and is 10.8 ? 10.8?? in size.
217
Figure C.8: DYNAMO G08-5 CO(3?2) channel maps. Each panel is centered at
08h54m18.740s, +06d46m20.55s and is 7.2??? 7.2?? in size.
218
Figure C.9: DYNAMO G14-1 CO(3?2) channel maps. Each panel is centered at
14h54m28.329s, +00d44m34.37s and is 7.2?? ? 7.2?? in size.
219
Figure C.10: DYNAMO G14-1 CO(4?3) channel maps. Each panel is centered at
14h54m28.329s, +00d44m34.37s and is 7.2?? ? 7.2?? in size.
Figure C.11: DYNAMO G20-2 CO(3?2) channel maps. Each panel is centered at
20h44m02.913s, -06d46m57.93s and is 10.8?? ? 10.8?? in size.
220
Figure C.12: DYNAMO G20-2 CO(4?3) channel maps. Each panel is centered at
20h44m02.913s, -06d46m57.93s and is 10.8?? ? 10.8?? in size.
Figure C.13: SDSS J013527.10-103938.6 CO(3?2) channel maps. Each panel is
centered at 01h35m27.105s, -10d39m38.64s and is 10.8?? ? 10.8?? in size.
221
Figure C.14: SDSS J013527.10-103938.6 CO(4?3) channel maps. Each panel is
centered at 01h35m27.105s, -10d39m38.64s and is 10.8?? ? 10.8?? in size.
222
Appendix D: Facilities and Software
D.1 Facilities
1. ALMA
2. HST/ACS
3. HST/WFC3
4. NOEMA
5. PdBI
6. SDSS
7. Spitzer/IRAC
D.2 Software
1. APLpy (Robitaille and Bressert, 2012)
2. Astropy (Astropy Collaboration et al., 2013, Price-Whelan et al., 2018)
3. CASA (McMullin et al., 2007)
4. corner (Foreman-Mackey, 2016)
5. Cosmological Calculator (Wright, 2006)1
1http://www.astro.ucla.edu/ wright/CosmoCalc.html
223
6. cosvar (Driver and Robotham, 2010)2
7. MatPlotLib (Hunter, 2007)
8. NumPy (Harris et al., 2020)
9. photutils (Bradley et al., 2020)
10. RADEX (van der Tak et al., 2007)
11. scikit-image (Van der Walt et al., 2014)
12. SciPy (Virtanen et al., 2020)
13. seaborn (Waskom, 2021)
14. Starburst99 (Leitherer et al., 1999)
2https://www.rdocumentation.org/packages/celestial/versions/1.4.6/topics/cosvar
224
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