Star Formation at High Redshift: The Confrontation Between Theory &
Observations
by
Rafal Idzi
A dissertation submitted to The Johns Hopkins University in conformity with the requirements for
the degree of Doctor of Philosophy.
Baltimore, Maryland
January, 2007
c Rafal Idzi 2007
!
All rights reserved
Abstract
We investigate properties of Lyman-break galaxies by statistically comparing
photometric observations with predictions derived from semi-analytic models based
on the ΛCDM theory of hierarchical structure formation. We construct samples of U,
B435 , and V775 -dropouts produced by GOODS, and complement the ACS optical B435 ,
V606 , i775 , and z850 data with the VLT ISAAC J, H, and Ks and IRAC 3.6, 4.5, 5.8,
and 8.0 observations. We produce model dropout galaxies derived from semi-analytic
model runs, where parameters controlling star formation and dust content are varied.
We then construct model density functions and convolve them with observational
scatter derived from Monte-Carlo simulations. We find the best-fit models by computing likelihoods using the data and model dropouts and the UV-continuum and
Balmer-break color-magnitude diagnostics. We find that we cannot discern among
models with varying starburst efficiencies due to data limitations. However, we do
favor models with enhanced quiescent star formation. Our best-fit models rule out
any strong dependence of quiescent star formation on circular velocities. We also
favor dusty models. Using the best-fit models we present predictions for the stellar
ii
masses, SFRs, and ages of the z ∼ 3, z ∼ 4, and z ∼ 5 Lyman-break samples. We
find that even though the current optical surveys are effective at selecting UV-bright,
massive galaxies, they fail to select most of the stellar mass, which remains hidden
in UV-faint and moderately massive galaxies. Our best-fit models predict a ∼ 70%
mass build-up between the z ∼ 4 and z ∼ 3 epochs for UV rest-frame L∗ galaxies,
and a smaller, ∼ 50%, build-up between the z ∼ 5 and z ∼ 4 epochs. This implies
an on-going process of quite active stellar-mass assembly between the z ∼ 5 epoch
and the z ∼ 3 epoch. Furthermore, for the z ∼ 3 sample, the stellar masses range
from 108 to 1010 M" , roughly 1.5 orders of magnitude less than the stellar masses of
the present day L∗ spirals and ellipticals – this indicates that the z ∼ 3 Lyman-break
galaxies are not the fully assembled progenitors of the present-day L > L∗ galaxies.
Finally, we find that quite a few of the z ∼ 5 galaxies have stellar masses of > 1010
M" , and that the median age of the z ∼ 5 population is 240 Myrs. This points to an
already active star formation well before the z ∼ 5 epoch.
Advisers: Dr. Henry Ferguson and Professor Timothy Heckman
iii
Acknowledgements
I would like to express my sincerest thanks to my adviser Harry Ferguson.
I had the pleasure to work with Harry for the past four years, and quite honestly
I cannot fathom working with anyone else on my thesis. Thanks a bunch Harry
for your support and especially for your patience. I would also like to thank all
of the other, present and former, GOODS members who have been instrumental in
helping me conduct and finish my work. Special thanks go to Rachel Somerville,
Mark Dickinson, Mauro Giavalisco, Vicky Laidler, and Norman Grogin for providing
help and support when I needed it. I would also like to thank Professor Timothy
Heckman, who acted as my official faculty adviser since my third year here at Johns
Hopkins. I’m grateful for his advice and support over the years, as well all of the
useful Astronomy I’ve learned in his classes as a second and third year student. I
want to thank all of my fellow grad students who have provided so much psychological
support over all of these years, especially Soo who has been my office mate for the
past two years, and thus had to put up with me during some of the most trying times
– thanks Soo! I also greatly appreciate the help I have received over the years from the
iv
JHU Physics and Astronomy administrative office (especially Janet Krupsaw, Pam
Carmen, Carm King, and Connie Fliegel) and from Patty Reeves at Space Telescope.
Finally, I’d like to take this opportunity to thank my wife for supporting me with my
academic aspirations. I know it wasn’t always easy for her and I want her to know
that I appreciate her loving support. I would also like to thank the rest of my family
without whom I wouldn’t accomplish any of this. Special thanks to my son, Lars,
who brought so much joy into my life, that all by himself he brightened every day,
most especially those difficult days.
Thanks to all of you
v
Contents
Abstract
ii
Acknowledgements
iv
List of Tables
viii
List of Figures
x
1 Motivation
1
2 Hierarchical Models of Galaxy Formation
2.1 Historical Overview . . . . . . . . . . . . .
2.2 Semi-Analytic Models – Ingredients . . . .
2.2.1 Merger Trees . . . . . . . . . . . .
2.2.2 Gas Cooling . . . . . . . . . . . . .
2.2.3 Mergers . . . . . . . . . . . . . . .
2.2.4 Merger-Driven Morphology . . . .
2.2.5 Merger-Induced Star Formation . .
2.2.6 Quiescent Star Formation . . . . .
2.2.7 Supernovae Feedback . . . . . . . .
2.2.8 Chemical Evolution . . . . . . . .
2.2.9 Stellar Population Synthesis . . . .
2.2.10 Dust Extinction . . . . . . . . . .
2.3 Fiducial Model . . . . . . . . . . . . . . .
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3 Observational Data
3.1 Introduction to GOODS . . . .
3.2 HST - ACS . . . . . . . . . . .
3.3 ESO VLT - ISAAC . . . . . . .
3.4 Spitzer - IRAC . . . . . . . . .
3.5 Ancillary Data . . . . . . . . .
3.5.1 CTIO 4m - MOSAIC U
3.5.2 ESO MPI 2.2–m - WFI
3.5.3 ESO NTT - SOFI . . .
3.6 Photometric Catalogs . . . . .
3.6.1 SExtractor Catalogs . .
3.6.2 TFIT Catalogs . . . . .
3.7 Galaxy Samples . . . . . . . . .
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33
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49
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4 Model Exploration, Parameter Choices, & Diagnostics
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Model Exploration . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Dust Parameters . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Quiescent & Merger-Induced Star Formation Parameters
4.2.3 Supernovae Feedback . . . . . . . . . . . . . . . . . . . .
4.3 Final Model Parameters & Model Run Attributes . . . . . . . . .
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3.8
3.7.1 Lyman Break Galaxies . . . . . . .
3.7.2 Color Selection Criteria & Samples
Template-Fitting Software Package . . . .
3.8.1 TFIT Overview . . . . . . . . . . .
3.8.2 TFIT Diagnostics . . . . . . . . .
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5 Simulations and Observational Scatter
100
5.1 ACS Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2 ACS–IRAC TFIT Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6 Methodology
6.1 Overview . . . . . . .
6.2 Data . . . . . . . . . .
6.3 Models . . . . . . . . .
6.4 Observational Scatter
6.5 Likelihood Analysis . .
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7 Results & Discussion
7.1 Best-fit Model(s) . . . . . . . . . . . . . . . . .
7.2 Parameter Fits – Implications . . . . . . . . . .
7.2.1 Burst-driven Star Formation Parameters
7.2.2 Quiescent Star Formation Parameters .
7.2.3 Dust Parameter . . . . . . . . . . . . . .
7.3 Properties of High-Redshift Galaxies . . . . . .
7.4 Summary . . . . . . . . . . . . . . . . . . . . .
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Bibliography
166
A Spherical Collapse in a General Cosmology
183
B Table of Model Runs
188
C Tables of Lyman-Break Galaxies
203
vii
List of Tables
2.1
Fiducial Model Parameter Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
3.1
3.2
Instrumental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
38
4.1
4.2
4.3
Grid of Parameter Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Final Parameter Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diagnostic Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
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6.1
Diagnostic Limits & Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.1
7.2
7.3
Best-fit Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Models Within the 68% (in bold) & 99.9% Confidence Intervals. . . . . . . . . . . . 136
Best-fit Models (Refit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
B.1
B.1
B.1
B.1
B.1
B.1
B.1
B.1
B.1
B.1
B.1
B.1
B.1
B.1
List
List
List
List
List
List
List
List
List
List
List
List
List
List
C.1
C.1
C.1
C.1
C.1
C.1
C.1
C.1
U-dropout
U-dropout
U-dropout
U-dropout
U-dropout
U-dropout
U-dropout
U-dropout
of
of
of
of
of
of
of
of
of
of
of
of
of
of
All
All
All
All
All
All
All
All
All
All
All
All
All
All
Models
Models
Models
Models
Models
Models
Models
Models
Models
Models
Models
Models
Models
Models
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Lyman-break
Lyman-break
Lyman-break
Lyman-break
Lyman-break
Lyman-break
Lyman-break
Lyman-break
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Sample
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204
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viii
C.1
C.1
C.1
C.1
C.1
C.1
C.1
C.1
C.1
C.1
C.1
C.2
C.2
C.2
C.2
C.2
C.2
C.2
C.2
C.2
C.3
C.3
U-dropout Lyman-break Sample
U-dropout Lyman-break Sample
U-dropout Lyman-break Sample
U-dropout Lyman-break Sample
U-dropout Lyman-break Sample
U-dropout Lyman-break Sample
U-dropout Lyman-break Sample
U-dropout Lyman-break Sample
U-dropout Lyman-break Sample
U-dropout Lyman-break Sample
U-dropout Lyman-break Sample
B-dropout Lyman-break Sample
B-dropout Lyman-break Sample
B-dropout Lyman-break Sample
B-dropout Lyman-break Sample
B-dropout Lyman-break Sample
B-dropout Lyman-break Sample
B-dropout Lyman-break Sample
B-dropout Lyman-break Sample
B-dropout Lyman-break Sample
V-dropout Lyman-break Sample
V-dropout Lyman-break Sample
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212
213
214
215
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226
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228
229
230
231
232
233
List of Figures
2.1
2.2
2.3
2.4
2.5
Extended Press-Schechter Mass Function . . . . . . .
Cooling Radius . . . . . . . . . . . . . . . . . . . . . .
Efficiency of Merger-Triggered Star Formation . . . . .
Star formation Rate as a Function of Circular Velocity
Sample Star Formation Histories . . . . . . . . . . . .
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9
12
20
23
25
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
Exposure map of the GOODS CDF-S Observations. . . . . . . .
Target Areas of All CDF-S Data Sets . . . . . . . . . . . . . . . .
IRAC Epoch Exposure Layout . . . . . . . . . . . . . . . . . . .
ACS z850 Completeness Limits . . . . . . . . . . . . . . . . . . .
Epoch 1 vs Epoch 2 Normalized Flux Comparison . . . . . . . .
U-dropout Sample Colors . . . . . . . . . . . . . . . . . . . . . .
U-dropout Sample Colors . . . . . . . . . . . . . . . . . . . . . .
B-dropout Sample Colors . . . . . . . . . . . . . . . . . . . . . .
B-dropout Sample Colors . . . . . . . . . . . . . . . . . . . . . .
V-dropout Sample Colors . . . . . . . . . . . . . . . . . . . . . .
V-dropout Sample Colors . . . . . . . . . . . . . . . . . . . . . .
B-dropout Color Selection for Data and Models . . . . . . . . . .
TFIT Flow Chart . . . . . . . . . . . . . . . . . . . . . . . . . . .
TFIT Simulated and Residual Images . . . . . . . . . . . . . . .
TFIT vs SExtractor Errors as a Function of Source Separation .
TFIT Residuals for Pre-Shift vs Post-Shift Runs . . . . . . . . .
TFIT Photometry for Pre-Shift vs Post-Shift Runs - Fluxes . . .
TFIT Photometry for Pre-Shift vs Post-Shift Runs - Magnitudes
TFIT vs Isophotal Flux Test for Isolated Sources . . . . . . . . .
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36
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42
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70
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72
73
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
Power-Law Dust Variation for B-dropouts with a Low τdust, 0
Power-Law Dust Variation for B-dropouts with a High τdust, 0
Power-Law Dust Variation for B-dropouts with a Low βdust .
Power-Law Dust Variation for B-dropouts with a High βdust .
Charlot-Fall Dust Variation for B-dropouts with Low Dust .
Charlot-Fall Dust Variation for B-dropouts with High Dust .
Charlot-Fall Dust Variation for B-dropouts with a Low ndust
Charlot-Fall Dust Variation for B-dropouts with a High ndust
High Star Formation for B-dropouts . . . . . . . . . . . . . .
Low Star Formation for B-dropouts . . . . . . . . . . . . . . .
High vs Low Star Formation Histories - z850 < 28 . . . . . . .
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90
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4.12
4.13
4.14
4.15
4.16
4.17
High vs Low Star Formation Histories - All Galaxies . .
High vs Low Star Formation Histories - Smoothed SFR
Martin-Heckman SNae Feedback for B-dropouts . . . .
Power-Law SNae Feedback for B-dropouts . . . . . . . .
Sample Balmer-break Colors for U-dropouts . . . . . . .
Sample UV-continuum Colors for U-dropouts . . . . . .
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5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
Redshift Distributions for the Simulated B-dropouts . . . . .
Redshift Distributions for the Fiducial Model B-dropouts . .
Input i775 - z850 Colors for the Simulated B-dropouts . . . . .
Output i775 - z850 Colors for the Simulated B-dropouts . . . .
Input V606 - i775 Colors for the Simulated B-dropouts . . . .
Output V606 - i775 Colors for the Simulated B-dropouts . . .
E(B-V) Distribution for the Simulated B-dropouts . . . . . .
SExtractor-TFIT Cumulative Recovery Rates in the CDFS vs
IRAC 3.6 PSF . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulated and Real V606 & IRAC 3.6 Mosaics . . . . . . . . .
Input Magnitude Distributions . . . . . . . . . . . . . . . . .
Intput V606 - IRAC 3.6 Colors for All Galaxies . . . . . . . .
Output V606 - IRAC 3.6 Colors for All Galaxies . . . . . . . .
IRAC 4.5 PSF . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulated and Real z850 & IRAC 4.5 Mosaics . . . . . . . . .
Input z850 - IRAC 4.5 Colors for All Galaxies . . . . . . . . .
Output z850 - IRAC 4.5 Colors for All Galaxies . . . . . . . .
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Source Separation
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6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
Simulation Machinery Flow Chart . . . . . . . . . . . . . . . . . . . . . . . .
Sample U-dropout Model Density Function Probing the UV-continuum . . .
Sample B-dropout Model Density Function Probing the UV-continuum . . .
Sample U-dropout Model Density Function Probing the Balmer-break Colors
Sample B-dropout Model Density Function Probing the Balmer-break Colors
V606 - i775 vs i775 Scatter Density Functions . . . . . . . . . . . . . . . . . . .
i775 - z850 vs z850 Scatter Density Functions . . . . . . . . . . . . . . . . . . .
V606 - IRAC 3.6 vs V606 Scatter Density Functions . . . . . . . . . . . . . . .
z850 - IRAC 4.5 vs z850 Scatter Density Functions . . . . . . . . . . . . . . . .
Pre vs Post Observational Scatter . . . . . . . . . . . . . . . . . . . . . . . . .
Applied Scatter Function - B-dropout UV-continuum . . . . . . . . . . . . . .
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134
Best-fit Model Density Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Random Draws from the Best-fit Model Density Function - U-dropouts, UV Colors .
Random Draws from the Best-fit Model Density Function - U-dropouts, Balmer-break
Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Random Draws from the Best-fit Model Density Function - B-dropouts, UV Colors .
7.5 Random Draws from the Best-fit Model Density Function - B-dropouts, Balmer-break
Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6 Random Draws from the Best-fit Model Density Function - B-dropouts, Balmer-break
Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.7 Stellar Masses for Best-fit U-dropouts . . . . . . . . . . . . . . . . . . . . . . . . . .
7.8 Stellar Masses for Best-fit B-dropouts . . . . . . . . . . . . . . . . . . . . . . . . . .
7.9 Stellar Masses for Best-fit V-dropouts . . . . . . . . . . . . . . . . . . . . . . . . . .
7.10 Stellar Mass Distribution for Best-fit U-dropouts . . . . . . . . . . . . . . . . . . . .
7.11 Stellar Mass Distribution for Best-fit B-dropouts . . . . . . . . . . . . . . . . . . . .
7.12 Stellar Mass Distribution for Best-fit V-dropouts . . . . . . . . . . . . . . . . . . . .
148
149
7.1
7.2
7.3
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7.13
7.14
7.15
7.16
7.17
7.18
Stellar-Mass Weighted Age for Best-fit U-dropouts . . .
Stellar-Mass Weighted Age for Best-fit B-dropouts . . .
Stellar-Mass Weighted Age for Best-fit V-dropouts . . .
Smoothed Star Formation Rates for Best-fit U-dropouts
Smoothed Star Formation Rates for Best-fit B-dropouts
Smoothed Star Formation Rates for Best-fit V-dropouts
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A.1 Halo Mass and Virial Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
xii
In memory of
Jan Idzi
xiii
Chapter 1
Motivation
Ever since Edwin Hubble (1889-1953) confirmed the nature of Kant’s ’island universes’
by detecting Cepheid variable stars in M31 using the 100-inch telescope atop Mount Wilson, the
scientific research into the nature of galaxies has flourished. Over the past several decades scores of
researchers have scrutinized countless galaxies in order to learn more about them. The knowledge
gained over these past few decades stems both from deeper and more comprehensive observations
of galaxies as well as from a slew of theoretical galaxy formation and evolution models based on
analytical, numerical, as we as semi-analytic methods. The progress has been tremendously helped
by the more recent rapid advances in our understanding of the cosmological properties of the universe
and the evolution of the stellar populations that make up the individual galaxies. Without a doubt,
our contemporary understanding of galaxy formation and evolution far surpasses the knowledge
gained in those early days, however, despite our vastly improved knowledge we are still largely
ignorant of how galaxies form and evolve. It has been clear for some time that the results from the
theoretical galaxy formation models, while adept at replicating some of the observational data, have
many problems when it comes to reconciling all model predictions with the observational evidence.
One of the most ill-understood processes in galaxy formation and evolution is the stellar mass
assembly, or in other words, the star formation history. It is still not clear when, at what rate, and
1
by which means galaxies accrue their stellar mass. Given the complicated non-linear nature of the
underlying physics it is difficult to determine which mechanisms play a dominant role in the process
of star formation. This complicated process can either be solved by trying to determine the precise
nature of the physics underlying these phenomenologies, or by employing approximations which
can then be fine-tuned and refined using the observational data. For the latter method, the need
arises for powerful statistical techniques capable of comparing the observed data with an ensemble
of models to determine which models work and which do not.
Over the past several years a good deal of progress has been made towards understanding
the nature of galaxy formation and evolution. However, these advances have been quite limited
in their scope and as a result the problem of galaxy formation and evolution remains unsolved for
the most part. This lack of good understanding has been partially due to the lack of exhaustive
observational data, but also to the lack of sophisticated theoretical models. More importantly
though, the biggest handicap has been the deficiency in robust analysis tools that have the ability
to compare data and models in a quantitative manner. As stated, galaxy evolution is a complex
problem that depends on a multitude of factors, many of which depend on one another and all of
which evolve with time. For any individual galaxy, the star formation and mass assembly history
(Ṁ∗ (t), M (t)) can be quite complicated. There are many factors that regulate galaxy’s star formation
rate, including, radiative cooling via molecular and heavy element line transitions, energy feedback
from supernovae, fresh gas infall rate, and merger induced shocks. In the standard paradigm of
galaxy formation, galaxies grow through the accretion of smaller galaxies and gas infall from the
surrounding medium. One can easily see how these various factors can greatly complicate matters
and as a result make the study of galaxy evolution challenging. The understanding of galaxy
evolution processes is further complicated by the intrinsic limitations of astronomical observations.
The total masses of galaxies can be determined through rotation velocities or velocity dispersions
via high resolution spectroscopy. However, this is observationally expensive and becomes impossible
for distant galaxies. Often this is circumvented by assuming a galaxy’s mass to light ratio and
2
estimating a lower mass limit from galaxy’s total luminosity. A further difficulty is that we are
unable to resolve individual stars for all but the closest galaxies. Because of this limitation we only
observe the integrated light, which is dominated by the youngest stars causing only the most recent
star formation episode to show through, while subduing the older, fainter, stellar populations. To
date, galaxy evolution studies have mostly centered on comparing simple evolutionary models to
one dimensional binned distributions of observable properties such as luminosity, redshift, color,
and morphology. This type of analysis probes a very limited region of parameter space and there
is no way to assign any confidence intervals to the best-fit parameters. Furthermore, if one has
access to multiple data sets, this type of analysis precludes any quantitative comparison among
the data, and only qualitative conclusions can be drawn. Obviously, this severely curtails the use
of observational data. Alternatively, some studies have fit simple parameterized star formation
histories to the photometry of individual galaxies, attempting thereby to derive stellar masses, ages,
dust content, etc., but imposing no requirement of consistency between different slices of redshift.
In order to circumvent the limitations of such previous efforts, we decided to take a different
approach. First, instead of using simple evolutionary models, we chose a semi-analytic hierarchical
model, where model universes are produced using randomly generated merger trees, and various
galaxy properties are generated by a set of physically-based scaling laws that control such processes
as gas cooling, star formation, chemical enrichment, various feedback processes, etc. This provides
us with a far more realistic representation of model galaxies than the representations afforded by
simple evolutionary models. Moreover, the complex feedback processes provide us with a list of
parameters that can be directly adjusted to generate a sets of different models in a manner that is
computationally efficient compared to full N-body hydrodynamic simulations and probably as accurate in its treatment of stellar formation. Our second change, is to use the a the most comprehensive
data set on high-redshift galaxies to date – the Great Observatories Origins Deep Survey (GOODS)
data set. This data set not only affords the depth necessary to explore high-redshift galaxies, but
also provides a large enough area coverage so as to be statistically meaningful. Finally, we choose a
3
more robust methodology to study the models and the data. Briefly, we use the photometric information from the models to construct finely gridded model density functions in color-magnitude space
that are then smoothed with observational scatter taken from Monte-Carlo simulations and then
we compute the likelihoods of the model using the data points from our Lyman-break samples. We
repeat this process for a set of models produced from a set of parameters that control such physics
as star-formation and dust content. The computed likelihoods, taken together with confidence intervals created through post-analysis Monte-Carlo simulations, give us the relative probability of the
models, indicating which models are favored and which are ruled out. This method affords us with
a more robust approach of contrasting models with data as it allows us to assign quantitative measures and allows us to test the models against multiple Lyman-break samples (z ∼ 3 and 4) across
multiple color-magnitude diagnostic combinations. It also takes explicit account of observational
measurement error, biases, and incompleteness in a straightforward way.
In §2 we review the underpinnings of the semi-analytic model used in this project. We also
state some of the parameter choices that we make. In §3 we go over the data used in this project.
We describe how that data were obtained and what are the characteristics of that data. We go into
catalog creation and selection of the galaxy samples. We conclude with a description of the software
package used to create the catalogs. In §4, we continue our discussion from §2, but here we wholly
concentrate on the parameter selection process. That is, we go over how we chose the parameters for
this analysis. We also describe how we chose the diagnostics that were used for the analysis. Finally,
we explicitly state those diagnostics and our parameter choices. In §5 we review the Monte-Carlo
data simulations that were performed to test the stability of our data catalogs and our Lyman-break
samples. We also go over how those simulations were used to create simulated galaxy catalogs that
were directly used in creation of the observational scatter functions that were used to process our
model galaxies. In §6 we describe the methodology of our analysis. We carefully go over all of the
steps of our analysis, listing all of the components used, and how those components were derived.
Finally, in §7, we go over the results of our analysis and review the implications of our results on
4
the physical questions posed in our work.
5
Chapter 2
Hierarchical Models of Galaxy
Formation
2.1
Historical Overview
Recent theoretical advances and Wilkinson Microwave Anisotropy Probe (WMAP) results
have promoted the ΛCDM hierarchical structure formation paradigm to the status of the fiducial
framework for the formation and evolution of galaxies. The various cosmological parameters comprising this framework have been fine-tuned over the past several years with the help of the WMAP
data (Spergel et al 2003). While cosmological parameters have been well established, the physics
that drives galaxy formation and evolution is less certain. Many researchers have used either N-body
simulations or Semi-Analytic models to simulate the processes that are thought to be important.
While N-body simulations provide very detailed modeling of such characteristics as gas dynamics,
they still have great difficulty reproducing the observed properties of galaxies in detail (Steinmetz
(1997)). N-body simulations also suffer a huge dynamic range problem. It is impossible with today’s
technology to cover the requisite range of densities, from those associated with molecular clouds to
6
those associated with intergalactic space. It is also quite apparent that there must be additional
physics that needs to be included in order to obtain realistic galaxies in the ΛCDM framework.
It is likely that many of these processes (e.g. cooling, star formation, supernova feedback, etc.)
form a complicated non-linear feedback loop. It becomes computationally prohibitative to include
realistic physics over the required dynamic range in N-body simulations of significant volume. In
fact, by their design alone, N-body simulations are highly processor intensive, and thus do not lend
themselves to a comprehensive and detailed study of the nonlinear effects driving galaxy evolution.
Nevertheless N-body simulations that include hydrodynamics, shocks, star formation, and feedback
(Nagamine et al. 2004; Springel 2005; Navarro et al. 1996) continue to improve.
Semi-analytic models (SAMs) of galaxy formation are embedded within the framework
of a ΛCDM-like initial power spectrum and the theory of the growth and collapse of fluctuations
through gravitational instability. The models include a simplified physical treatment of gas cooling,
star formation, supernova feedback, dust extinction, and galaxy merging. The approach is MonteCarlo based, which allows us to study individual objects or global quantities. Many realizations can
be run in a moderate amount of time on a workstation. Therefore, this approach is an efficient way
of exploring the large parameter space occupied by the unknowns associated with star formation,
supernova feedback, the stellar initial mass function, metallicity yield, dust extinction, etc. Besides
the computational efficiency, these models provide an important level of understanding that would
be difficult to achieve by running an N-body simulation. Semi-analytic models were first developed
by Kauffmann et al. (1993) and Cole et al. (1994). The model used here (Somerville et al. 1999)
is similar in spirit and adopts many of the fundamentals, however, it differs significantly from
those early models, especially in its current form. All of these models and the underlying physical
assumptions have evolved significantly since the mid-90’s and many of the deficiencies of the early
models have been addressed. In the next few sections we describe the workings of the Somerville
et al. (1999) model, including the treatment of merger trees, gas dynamics, mergers, star formation,
feedback, dust extinction, and more. Due to the intrinsic complexity of semi-analytic models, we
7
cannot cover all the details of the model. Much of the background is covered by Somerville &
Primack (1999) and Somerville, Primack, & Faber (2001). However, for completeness, we cover
the most important aspects of the model in sufficient detail and include description of the model
assumptions and algorithms that have changed since the earlier implementations.
We adopt the following cosmological parameters for our ΛCDM treatment: (ΩΛ = 0.7,
Ωm = 0.3, h = H0 /100 km s−1 Mpc−1 = 0.7). This set of cosmological parameters will be used
throughout this project.
2.2
2.2.1
Semi-Analytic Models – Ingredients
Merger Trees
Semi-analytic models make use of the extended Press-Schechter formalism (Press & Schechter
1974; Bower 1991; Bond et al. 1991; Lacey & Cole 1993) to obtain the probability that a halo of a
given mass m0 at a given redshift z0 has a progenitor of mass m1 at some larger redshift z1 . The
merging histories of the dark matter halos are then assembled via Monte-Carlo realizations (Kauffmann & White 1993; Cole 1991; Somerville & Kolatt 1998). The relative agreement between this
type of formalism vis-a-vis pure N-body simulations is quite good, although it has been well documented that the Press-Schechter theory over-predicts the number of halos by about a factor of two
(Tormen 1998; Somerville et al. 1998; Somerville & Kolatt 1998). In addition, the Press-Schechter
model predicts stronger evolution of the halo mass function as a function of redshift Gross (1997);
Somerville et al. (1998). These problems cannot be easily solved. However, a solution was proposed
by Sheth & Tormen (1999), which proposes a corrective term to the Press-Schechter formalism.
The correction, which is the mass function from the Sheth-Tormen model divided by the standard
Press-Schechter mass function, is shown in Fig. 2.1, and it improves the agreement between PressSchechter derived models and N-body simulations. Despite the above disagreements between the
two varieties of simulations, the overall properties of progenitors within a halo of a given mass are
8
Figure 2.1 The mass function from the improved Press-Schechter model proposed by Sheth & Tormen
(1999) divided by the standard Press-Schechter mass function. This correction factor is a function
of redshift as well as halo mass, and here is shown for z = 0. (This figure was reproduced, with
permission, from Somerville & Primack (1999)).
9
very similar. As long as the error in the Press-Schechter formalism is corrected for, the semi-analytic
implementation serves as a reliable framework for studying hierarchical galaxy formation.
The semi-analytic model used in this work implements the merger-tree method of Somerville
& Kolatt (1998). In it, the merging history of a dark-matter halo is constructed by sampling the
paths of individual particle trajectories using the excursion set formalism (Bond et al. 1991; Lacey
& Cole 1993). This method does not require a grid in mass or redshift, nor does it require the
merger events to be binary. Monte-Carlo techniques are used to randomly pick the redshifts and
masses associated with the halo mergers. The only criterion is that the overall distribution satisfies
the averages predicted by the extended Press-Schechter theory. Each realization then is a particular
merger tree history. This forms the core of the code and it is the most vital stochastic component in
the models. Additional constraints revolve around making the tree finite. This requires a minimum
mass mmin below which merger histories are not traced. Instead the mass that falls below this limit
is accreted as a diffuse component. In our model runs, we set this mass limit to a halo with a circular
velocity of 40 km s−1 at a relevant redshift. This limit seems reasonable since halos smaller than
the limit are unlikely to form due to the photoionization of gas and the consequential inability to
cool (Weinberg et al. 1997; Forcado-Miro 1997). We set an upper limit of 1200 km s−1 for all of our
model runs in order to make processing time manageable.
2.2.2
Gas Cooling
The next important component in the semi-analytic approach is the treatment of gas cool-
ing. When a halo collapses or undergoes a merger with a larger halo, the associated gas is assumed
to be shock-heated to the virial temperature of the halo. This gas then radiates energy and as
consequently cools. The cooling rate typically depends on a variety of factors such as density, metallicity, and temperature of the gas. The treatment of gas cooling in this semi-analytic model follows
a scheme similar to the one used by White & Frenk (1991). A newly formed, dark matter tracing,
halo (residing at top of the tree) contains pristine shock heated hot gas (at virial T ). Radiative
10
cooling then leads to energy loss. The rate of specific energy loss is given by the cooling function
Λ(T ). The expression giving the critical density for gas cooling on a given time scale τcool is
ρcool =
3 µmp kB T
2 χ2e τcool Λ(T )
(2.1)
where µmp is the mean molecular weight of the gas and χe ≡ ne /ntot is the number of electrons per
particle. If we assume that the gas is fully ionized and has a helium fraction by mass of Y = 0.25
then we have
ρcool = 3.52 × 107
kB T
,
τcool Λ23 (T )
(2.2)
where kB T is in degrees Kelvin, τcool is in Gyr, and Λ23 (T ) ≡ Λ(T )/(10−23 ergs s−1 cm3 ). The
2
virial temperature is approximated as kB T = 71.8σvir
, where σvir is the virial velocity dispersion of
the halo. The cooling radius can now be obtained by inverting the above equation and assuming a
gas density profile ρg(r) . The cooling radius is defined as the radius within which the gas has had
time to cool within a given time-scale τcool (see Fig. 2.2). If we assume a singular isothermal sphere
for the gas profile we obtain
rcool =
!
ρ0
ρcool
"1/2
where ρ0 = fhot Vc2 /(4πG), fhot is the hot gas fraction in the cooling front and Vc =
(2.3)
√
2σvir is the
circular velocity of the halo. We adopt the cooling function of Sutherland & Dopita (1993) and
model value of the hot gas metallicity, and use the metallicity-dependent radiative cooling curves
tabulated by Sutherland & Dopita (1993) to compute cooling for different metallicities.
The time interval between halo mergers is divided into small time-steps. For each time-step
∆t, the cooling radius increases by an amount ∆r. In addition, we assume that the mass of gas that
cools in this time-step is given by
11
Figure 2.2 Cooling radius of halos as a function of circular velocity. The straight diagonal line shows
the virial radius, which the cooling radius may not exceed. The curved lines show the cooling radius
predicted by the static halo cooling model (see text), assuming that the hot gas has primordial, 0.3
solar, or solar metallicity. Open circles show the application of the static halo model within the
merger trees, and crosses show the dynamic halo model (see text), assuming a fixed metallicity of
0.3 solar. Earlier conversion of gas from the hot to cold phase and reheating of hot gas by halo
mergers results in a lower cooling efficiency for large halos in the dynamic halo model. (This figure
was reproduced, with permission, from Somerville & Primack (1999)).
12
2
dmcool = 4πrcool
ρg (rcool )∆r
(2.4)
For small halos at high redshifts we assume that the cooling is limited by the accretion rate, since the
amount of gas that can cool at any given time-bin cannot exceed the amount of hot gas contained
within the halo’s virial radius. The mass of accreted hot gas between halo mergers is given by
fbar macc
(2.5)
where fbar ≡ Ωb /Ω0 is the universal baryon fraction. We also assume that the mass accretion rate
is constant over the time interval in between mergers (this is expected from the spherical collapse
model – see Appendix A – where we reproduce the arguments from Somerville & Primack (1999)).
The gas that cools falls onto the disk at a rate given by the sound speed of the gas
cs = (5kB T /3µmp )1/2 ∼ 1.3σv
(2.6)
where σv is the 1-D velocity dispersion of the halo, and cs is roughly the dynamical velocity of the
halo. This behavior of cooling gas infall is supported by the N-body hydrodynamical simulations of
Evrard et al. (1996).
For halos at the top-level (all progenitors less massive than the minimal mass), the fraction
of hot gas fhot is set to the universal baryon fraction fbar , and the cooling time τcool is defined as
the time elapsed since the initial collapse of the halo. In halo mergers, if the mass of the largest
progenitor m1 comprises more than a fraction freheat of the post-merger mass m0 , the cooling radius
and time of the new halo are set to those of the largest progenitor. The gas fraction in the cooling
front is
fhot = mhot /mtot (> rcool )
(2.7)
where mhot is the entire mass of the hot gas from all the progenitors, and mtot (r > rcool ) is the total
13
mass contained in between the cooling and the virial radii (for an isothermal profile). In contrast,
if m1 /m0 < freheat then the hot gas within all the progenitors is heated to the virial temperature
of the new halo, and the cooling radius and time values are reset to zero. The gas fraction in the
cooling front is then
fhot = mhot /m0
(2.8)
In the static halo cooling model we always assume that fhot = fbar and that τcool equals to the age of
the Universe at any given time. Furthermore, no reheating of the gas occurs after any halo merger.
In addition, we modify the literal static cooling model by requiring the cooling rate not to exceed
the available supply of hot gas, or to exceed the sound speed constraint. In Figure. 2.2 we show the
cooling radius in the literal and modified static cooling models. The consequence of this modeling
is that for small halos, the cooling is ultimately limited by the available collapsed gas supply. For
large halos, cooling is suppressed in the dynamic halo model in contrast to the case of a static halo
model. This is due to the lower values of fhot and the ongoing reheating by halo mergers.
2.2.3
Mergers
The treatment of mergers is a complex process and we encourage the reader to refer to
Somerville & Primack (1999) and Somerville, Primack, & Faber (2001) for a detailed description.
Here we present a brief overview. Once halos merge, the galaxies within them remain distinct for
some time. The central galaxy of the largest progenitor halo is set as the central galaxy of the merged
dark matter halo. All the other galaxies become satellites. The satellites of the largest progenitor
remain undisturbed and the central galaxies of other progenitors are placed at a distance fmrg rvir
from the central galaxy, where fmrg is a free parameter and rvir is the virial radius of the new parent
halo. The satellites from the smaller progenitors are scattered randomly in the new halo, preserving
their relative distance to the new central galaxy. All the satellite galaxies then fall in toward the
core galaxy due to dynamical friction. The evolving distance of a satellite galaxy is given by,
14
rfric
drfric
Gmsat
= −0.428f (')
ln Λ
dt
Vc
(2.9)
(Binney & Tremaine 1987; Navarro et al. 1995). where msat is the combined mass of the satellite’s
gas, stars, and dark matter halo, and Vc is the circular velocity of the parent halo. ln Λ is the
Coulomb logarithm, which is approximated as ln Λ ≈ ln(1 + m2h /m2sat ), where mh is the mass of the
parent halo. The value of ' (circularity parameter) is defined as the ratio of the angular momentum
of the satellite to that of a circular orbit with the same energy: ' = J/Jc (E). For each satellite, '
is drawn from a uniform distribution from 0.02 to unity. As the satellite galaxy’s orbit decays, its
dark matter halo is stripped by the parent halo. The tidal radius rt of the satellite halo, which is
taken to be the spatial point where the satellite halo density equals the density of the background
halo, is given by,
ρsat (rt ) = ρhalo (rfric )
(2.10)
The mass of the satellite halo is then taken to be the mass contained within the tidal radius. In
each case, the halos are assumed to be isothermal spheres (ρ ∝ r−2 ).
In addition to the above process we can also have mergers or interactions between satellite
galaxies. The time-scale for this process is given by a mean free path argument,
τcoll ∼
1
n̄σv
(2.11)
where n̄ is the mean density of galaxies, σ is the effective cross section for a single galaxy, and v
is a characteristic velocity. N-body simulations by Makino & Hut (1997) reveal that this simple
argument results in reliable merger rates. The collision time-scale used in our semi-analytic model
is given by an expression adopted from the N-body work,
τcoll = 500 N −2
!
rhalo
Mpc
"3 !
15
rgal
0.12 Mpc
"−2
#
$−4 # σ
$3
σgal
halo
Gyr.
100 km s−1
300 km s−1
(2.12)
where rhalo is the virial radius of the parent halo, rgal is the tidal radius of satellite’s dark matter
halo, σgal and σhalo are the internal 1-D velocity dispersions of the satellite and the parent halo,
respectively. The probability then that a galaxy will merge in a given time step is Pmrg = ∆t/tcoll .
For the post-merger sub-halo we assign a new velocity dispersion by assuming that energy is conserved in the collision and the product satisfies the virial relation. The above expressions describe
all of the merging events in our models.
2.2.4
Merger-Driven Morphology
We adopt a free parameter, fbulge , which determines whether a galaxy merger leads to
formation of a bulge component. If the baryonic mass ratio of the merging smaller galaxy to the
merging bigger galaxy is greater than fbulge , then all the stars from both galaxies are put into the
bulge and the disk is destroyed. If the ratio is smaller then the stars from the smaller galaxy are
deposited into the disk of the bigger galaxy. The cold gas of both galaxies are combined, and if
additional cooling takes place this may lead to the formation of a new disk. The bulge-to-disk
ratio of each galaxy can then be used to assign a morphological classification. In this project we
do not concern ourselves with morphological types. It is sufficient to state that the classification
scheme used in this model leads to morphological properties that are in agreement with a variety of
observations (see Somerville, Primack, & Faber (2001) for details). In all of our simulations we set
the fbulge parameter to a value of one third.
2.2.5
Merger-Induced Star Formation
There is considerable observational and theoretical evidence that mergers and interactions
between galaxies trigger enhanced star formation. In our simulations we adopt a lower limit for
the mass threshold that will induce any sort of starburst (5 to 10%, Cox et al. (2005)). Once that
threshold is met however, we assume that every galaxy-galaxy merger triggers a starburst. The
16
treatment of merger-triggered burst is based on a simple parameterization of the results of N-body
simulations with gas dynamics. Initially, the semi-analytic model used in this work used results of
Mihos & Hernquist (1994; 1996). The authors of that work simulated galaxy-galaxy mergers using
a high resolution N-body/smoothed particle hydrodynamics code (TREESPH) with star formation
modelled according to a Schmidt law (ρSF R ∝ ρngas with n = 1.5). Mihos & Hernquist (1996) found
that 65-85% of the total gas supply (in both galaxies) was converted into stars over a time scale
of 50-150 Myr. These results were for equal-mass mergers, or major mergers. In addition, they
found that the results insensitive to morphology or the orbital geometry. In Mihos & Hernquist
(1994) they studied the case of highly unequal-mass (minor) mergers (at 1:10 ratio). This scenario
produced a non-axisymmetric mode generated by the accretion of the smaller galaxy. This mode
caused majority of the gas to collapse into the core of the larger galaxy, which produced a strong
starburst. The consumption of the gas was at 50% spent over 60 Myr. The major difference between
the two types of mergers is that the latter depends strongly on the morphological properties of the
galaxies. If there is a bulge, the bulge stabilizes the disk against strong radial gas flows, which results
in weaker starbursts (5% of gas consumed). This behavior was observed for substantial bulges with
bulge-to-disk mass ratio of one third or more.
Each merger is then classified as either major or minor depending on whether the ratio of
the smaller to the larger of the galaxies’ baryonic masses is greater than or less than the value of
the bulge-to-total mass ratio (fbulge ∼ 0.25). Major mergers have mass ratios greater than fbulge ,
resulting in the bulge and disc stars of both galaxies plus all new stars formed in the burst being
placed in a bulge component. Minor mergers have mass ratios less than fbulge , and the stars already
present in the smaller of the two galaxies are placed in the disc component of the post-merger
galaxy. N-body simulations by (Walker et al. 1996) show that nearly all (90%) of the satellite mass
is stripped away and distributed in the disc of the larger galaxy. In contrast, all the newly formed
stars end up in the bulge component.
In our current iteration of the semi-analytic model we adopt the latest results of Cox et al.
17
(2005) simulations. These simulations differ from previous simulations in important ways. The
primary differences are as follows:
1. The version of SPH used by Cox et al. integrates entropy, whereas Mihos & Hernquist (1996)
used a version of SPH that integrated energy.
2. Star formation normalization used was different
3. Mihos & Hernquist (1996) represented the ISM as an isothermal gas, set at 104 K, whereas
Cox et al. use adiabatic gas processes and shock heating.
4. Each simulation used a different disk-galaxy model.
We adopt Cox et al. simulations and we refer the reader to their work for elaboration
of why their models are the preferred choice. Based on Cox et al. simulations we adopt a mass
threshold that will induce any sort of burst (5 to 10%). In prior work, typically all mergers induced
star formation. Cox et al. found that 50% of the total gas supply is converted into stars – a
somewhat lower efficiency than the previous simulations indicate. Consequently, galaxy mergers are
less efficient at converting the available gas to stars than was previously thought. We use these
results to guide our treatment of merger-induced starbursts, and we adopt Cox et al. values for our
fiducial semi-analytic model run. Once star formation is triggered, it is modeled with an exponential
function with a time-scale τburst and e-folding time-scale ηburst (see Eq. 2.13).
ṁ∗,burst =
!
Nburst
2 τburst (1 − eηburst )
"
e−x
(2.13)
where x is given by,
%
%
% ti − tpeak %
%
%
x=%
τburst %
where Nburst is the burst normalization value equivalent to the fraction of cold gas that is used in
the burst ('burst × mcold gas ), τburst is the burst time-scale, tpeak is the burst’s temporal peak defined
18
by ti + (τburst × ηburst ), with ti denoting the current time steps, and ηburst defines the number of
e-foldings to the peak of a burst. After each burst the burst parameters are reset if the new burst
fuel trumps the remaining fuel in any ongoing burst. The efficiency of the burst 'burst is defined as
the fraction of the cold gas reservoir of the two merging galaxies that is turned into stars over the
entire duration of the burst. In our treatment, we model the efficiency as a power-law function of
the mass-ratio of the merging galaxy pair (see Eqs. 2.14 and 2.15). In accordance with the N-body
simulation results described above, we differentiate between galaxies with bulges and those without,
in order to take proper account of unequal-mass (minor) mergers. Generally, galaxies with significant
bulges will have a stronger dependence on the power index since the burst efficiency is diminished
in the presence of a bulge.
'burst =
'0burst bulge
!
msmall
mbig
"αburst bulge
where '0burst bulge is the burst efficiency, αburst bulge is the mass ratio power index, and
(2.14)
msmall
mbig
is the
mass ratio of the merged galaxies. The burst time-scale (τburst ) is equivalent to the dynamical time
of the halo which is controlled by a burst length time-scale parameter. If there is no bulge, then a
corresponding burst length time-scale parameter is used together with,
'burst = '0burst
!
msmall
mbig
"αburst
(2.15)
In each case, msmall refers to the smaller value between mbar1 and mbar0 , whereas mbig refers to the
larger value. The mbar1 and mbar0 parameters are defined as the total baryonic mass contained in
the halos (the stellar mass contained in the disk, the bulge, and the baryons locked into the cold gas
phase) of the merged galaxies. In cases where the halos have no baryons present, the ratio of the
masses is taken between the merging halo masses. Fig. 2.3 illustrates the behavior of burst efficiency
as a function of the mass ratio of the two merging galaxies.
19
Burst Efficiency
0.8
eburst
0.6
0.4
0.2
0.2
0.4
0.6
0.8
Mass Ratio
Figure 2.3 This figure illustrates the efficiency of star formation in a burst as given by Eqs. 2.14
and 2.15. The x-axis denotes the baryonic mass ratio of the merging galaxies. The y-axis denotes
the star formation efficiency of the resulting burst. The solid line corresponds to the case of αburst
= 1.0. The dotted, dot-dash, and dash curves correspond to αburst values of 0.5, 1.5, and 10.0,
respectively. In each case the value of '0burst was set to unity. In our nominal simulations, a galaxy
with no bulge would take an αburst value of less than unity, and a galaxy with a bulge would take
an αburst value greater than unity. The net effect would be that when a bulge is present, the burst
efficiency drops off more rapidly at lower mass ratios.
20
2.2.6
Quiescent Star Formation
Apart form starbursts we need to take account of regular (non-merger induced) star forma-
tion, commonly known as quiescent star formation. In Somerville & Primack (1999) and Somerville,
Primack, & Faber (2001), the authors investigated a variety of quiescent star formation laws. Here
we give a brief overview of those scaling laws, and we conclude by noting the forms used in this
work. The simplest assumption for quiescent star formation rate can be expressed in the following
general expression
ṁ∗,quies =
mcold gas
τ∗
(2.16)
where mcold gas is the total mass of cold gas available in the disk and τ∗ is a free parameter that can
be adjusted to match observations and denotes the time-scale at which the cold gas is converted to
stars. This time-scale can be independent of any other physics or it can be a function of circular
velocity, or dynamical time of the disk, or some other physical variables. We start with the most
basic form of star formation in which cold gas is converted to stars with the same efficiency in disks
of all sizes and at all redshifts. The scaling law then takes the following form
ṁ∗,quies =
τ∗ = τ∗0
(2.17)
mcold gas
τ∗0
(2.18)
where τ∗0 is a constant. A more sophisticated form of star formation is a one with variable efficiency.
One choice is to allow the star formation time-scale to scale with the circular velocity of the galactic
disk in the form of a power law (see Fig. 2.4). We then have
τ∗ =
ṁ∗,quies =
τ∗0
!
v0
vc
"α∗
mcold gas
# $α∗
τ∗0
21
v0
vc
(2.19)
(2.20)
where vc is the circular velocity of the galactic disk, v0 is an arbitrary normalization factor (set to
300 km s−1 in Somerville & Primack (1999)), and τ∗0 and α∗ are free parameters. This model has
a strong dependence on the circular velocity of the galaxy, where star formation is less efficient in
halos with small vc . In this type of model, one expects a delay in star formation until lower redshift,
since, in hierarchical models, halos at higher redshift are typically less massive and thus have smaller
circular velocities. Note that there is no explicit dependence on the redshift in this scenario. We can
introduce redshift dependence by setting the star formation time-scale proportional to the dynamical
time of the disk. We then have
τ∗ = τ∗0 tdyn
(2.21)
mcold gas
τ∗0 tdyn
(2.22)
ṁ∗,quies =
where τ∗0 is once again a free parameter, and tdyn is the dynamical time of the galactic disk that
scales with
rdisk
vc .
In Somerville & Primack (1999) the value of rdisk was set to one tenth the virial
radius of the dark matter halo, and vc was set to be the circular velocity of the halo at the virial
radius. In the case of satellite galaxies, the dynamical time was fixed to the value it had the last time
the satellite galaxy was the central one. In this model, the star formation rate is nearly constant
over circular velocity, but has a higher efficiency at earlier times (high redshift). This is because
while the spherical collapse model predicts that the virial radius scales with vc as rvir ∝ vc , the
virial radius of a halo with a given circular velocity increases over time with rvir ∝ (1 + z)−3/2 (for
an Einstein-de Sitter universe). The dynamical time at a given redshift is then nearly independent
of the galaxy’s circular velocity, and at higher redshifts the density of collapsed halos is higher and
so the dynamical times are shorter and thus the available cold gas is converted into stars at a faster
pace. The dynamical time dependent model is more proficient at forming stars earlier then the
previous two models (constant and power-law, Eqs. 2.18 and 2.20).
The latest iteration of our semi-analytic code incorporates two variants for the quiescent
22
Quiescent Star Formation Rate
0.8
ṁ,quies
0.6
0.4
0.2
200
600
1000
Vc
Figure 2.4 Quiescent star formation rate where the star formation time-scale depends on the circular
velocity of the disk. This figure illustrates how varying α∗ affects the behavior of star formation rate
as a function of circular velocity. In this case the value of τ∗0 is set to unity and mcold gas is set to
107 M# (Eq. 2.20). The circular velocity normalization factor is fixed to v0, sf = 200 km s−1 , which
is the value used in our model runs and is set to the value of Cole et al. In the figure, the x-axis
corresponds to vc ranging from 1 to 1200 km s−1 , and the y-axis corresponds to star formation rate
ranging from 107 to 108 M# yr−1 . The solid line corresponds to α∗ = 1.0, or a case of a linear
relationship. The dotted, dot-dash, and dash curves corresponds to α∗ values of 0.5, 2.5, and 5.0,
respectively. Note that all the curves intersect at the fixed V0,sf and mcold gas values. The case of α∗
= 0.0 would correspond to a horizontal line denoting circular velocity independence.
23
star formation rate:
mcold gas
$α∗
#
ṁ∗,quies =
τ∗
v0,sf
vc
(2.23)
that is, the circular velocity is incorporated for the two modes of quiescent star formation. As before,
mcold gas is the total mass of cold gas available in the disk, vc is the circular velocity of the galactic
disk, and v0,sf is a normalization factor (set to 200 km s−1 , using Cole et al. value). The values of
τ∗ and α∗ are allowed to vary. The time-scales for the two modes are
τ∗ = τ∗0
(2.24)
τ∗ = τ∗0 tdyn
(2.25)
the first one is just the familiar constant efficiency time-scale, while the second one is the time-scale
that varies with the dynamical time of the disk. In each case τ∗0 is a free parameter. The quiescent
star formation rate equations then take the from,
ṁ∗,quies =
ṁ∗,quies =
mcold gas
#
$α∗
v
0,sf
τ∗0
vc
mcold gas
#
$α∗
τ∗0 tdyn
v0,sf
vc
(2.26)
(2.27)
While the quiescent star formation is taking place, the merger-induced star formation is still active,
and its contribution is typically far more significant. The total star formation rate for a galaxy
is then set to the total of the burst and quiescent modes. Fig. 2.5 depicts sample star formation
histories that include merge-induced and quiescent components of star formation.
2.2.7
Supernovae Feedback
In our models, the supernovae feedback is modeled using either the disc-halo (first intro-
duced in Somerville & Primack (1999)), power-law, or Martin-Heckman recipe. For our project we
24
Figure 2.5 The total star formation rate for the largest progenitor of the central galaxy within a
halo with a present-day circular velocity of 220 km s−1 . All three models contain constant efficiency
quiescent star formation. The top panel shows the model with no bursts, the middle panel shows
the model with bursts in major mergers only, and the bottom panel shows the models with bursts in
major and minor mergers. (This figure was reproduced, with permission, from Somerville, Primack,
& Faber (2001))
adopt the power-law model as the de facto feedback recipe. Over the several years, the disk-halo
recipe has fallen out of favor, and indeed we find it somewhat inadequate. However, for completeness, we present all the feedback variants. In the disk-halo model, the rate of reheating of cold gas
is given by
ṁrh = 2
'˙SN
2
vesc
(2.28)
2
where '˙SN is the rate at which energy is injected into the cold gas by supernovae, and vesc
is the
mean escape velocity of the disc or halo. The reheating rate and ejected gas mass is calculated
seperately for halo and disk components. The supernovae energy rate is defined as follows,
25
'˙SN = '0SN ESN ηSN ṁ∗
(2.29)
where ESN = 1051 ergs is the total (kinetic and thermal) energy per supernova, ηSN is the number
of supernovae per solar mass of stars (ηSN = 7.4 × 10−3 (Bruzual & Charlot 1993)), and ṁ∗ is the
star formation rate. The escape velocities for the disk and the halo components are given by,
vesc disk = 7.1 × 10
−5
×
&
mcold gas + m∗
rdisk
√
vesc halo = 2 vvir
(2.30)
(2.31)
Beside the disk-halo recipe, we can use one of the two simpler feedback models. The
Martin-Heckman model assumes a simple feedback rate where the feedback rate is proportional to
the star formation rate,
ṁrh = '0SN ṁ∗
(2.32)
a slightly more sophisticated recipe scales the feedback rate with circular velocity in the form of a
power-law,
ṁrh = frh ṁ∗
(2.33)
where,
frh = '0SN
!
vc
v0,fb
"−αrh
(2.34)
where vc is the circular velocity of the disk, v0,fb is a normalization factor chosen so that '0SN is of
order unity (this is fixed to a value of 200 km s−1 in our models), and αrh is a free parameter. In the
Martin-Heckman and power-law models the fraction of gas that is ejected is governed by a preset
ejection criterion – veject . If the halo’s virial velocity is less than the ejection threshold then all of
26
the gas is ejected (this is fixed to a value of 100 km s−1 ). In the disk-halo model, the fraction of the
gas that is ejected is given by
feject = 2
!
vesc disk
vesc halo
"2
(2.35)
The gas and metals that are ejected from the halo are re-incorporated. The material is distributed
outside of the halo with a continuation of the isothermal r−2 profile that we assumed inside the
halo. If the total mass of the halo increases in value by a factor of two then all of the material is
re-incorporated back into the halo. This material falls ingradually as the virial radius of the halo
increases due to the falling background density of the Universe.
2.2.8
Chemical Evolution
Chemical evolution is treated by assuming a constant mean mass of metals produced per
mass of stars, denoted by Y (true yield). The produced metals are first deposited into the surrounding cold gas, at which point they may be ejected from the disk and mixed with the hot halo gas. In
the disk-halo feedback model, these metals may also be ejected from the halo, in the same proportion
as the reheated gas. The metallicity of any newly formed stars is set to equal the metallicity of the
ambient cold gas at the time of formation. It should be noted that since the enriched gas may be
ejected from the halo (using the disk-halo feedback), this treatment of chemical evolution is not
equivalent to the standard closed-box model.
2.2.9
Stellar Population Synthesis
In this project we use the Bruzual & Charlot (2003) stellar population synthesis model to
generate the Spectral Energy Distributions (SED) for the stellar populations produced in our models.
Briefly, the model assumes an Initial Mass Function (IMF) for the stars, which gives the distribution
of the fraction of stars created within a given mass bin. In our case we use the parametrization made
by Chabrier (2003b) of the single star IMF in the Galactic disk:
27
φ(log m) ∝
+
*

mc )2
 exp − (log m−log
, for m ≤ 1M# ,
2σ2

m−1.3 ,
(2.36)
for m > 1M# ,
with mc = 0.08M# and σ = 0.69. We chose the Chabrier (2003b) IMF because first, it is physically
motivated, and second, it provides a better fit to the counts of the low-mass stars and brown dwarfs
(see Chabrier 2001;Chabrier 2002;Chabrier 2003a). Furthermore, we adopt the lower and upper
mass cutoffs of mL = 0.1 M# and mU = 100 M# . Once the IMF is in place the model stars are
evolved in agreement with the theoretical evolutionary tracks for stars of a certain mass. In our
case we use the Padova (1994) evolutionary tracks. The star formation recipe in our model then
creates stars of a given age, which can then be assembled into a composite population. A synthetic
∗
spectrum of this composite population can then be generated. We use the parameter flum
to set
∗
the stellar mass-to-light ratio (flum
is defined as the ratio of the mass in luminous stars to the total
stellar mass, m∗lum /m∗tot ). We set this factor to unity, effectively neglecting contributions from nonluminous objects (like brown dwarfs, planets, asteroids, etc). The SEDs are then convolved with the
response functions intrinsic to ACS, ISAAC, IRAC, and various ground based observatories.
This procedure gives us the photometric information necessary for comparisons with our
observed LBG samples. Even though this field has been well studied, there are still many uncertainties associated with modeling stellar populations. To start with, the IMF is a major source
of uncertainty. The IMF is fairly well determined in our Galaxy (Scalo 1986), but it is unknown
whether this IMF applies universally and whether it depends on such factors as metallicity or other
ambient effects. The results of our simulations are however not that sensitive to the upper and
lower mass cutoffs as well as the slope of the IMF, because we are probing photometric quantities
only. As mentioned, we use the Chabrier (2003b) IMF for our models. We find that this IMF gives
the best representation of the IMF because it is physically motivated and gives better fits to the
low-mass end. Besides the uncertainties surrounding the choice of the IMF there are difficulties with
modeling the complex physics of stellar evolution. The major unreliable components (see Charlot
28
et al. (1996)) are the opacities, heavy-element mixture, helium content, convection, diffusion, mass
loss, and rotational mixing.
2.2.10
Dust Extinction
The effects of dust extinction are quite important due to the fact that the photometric
data for our Lyman–break samples probe the rest-frame UV part of the spectrum. By studying
correlation between the FIR excess (a reliable observational measure of bolometric extinction) and
the far-UV spectral slope in nearby starburst galaxies, Meurer et al. (1999); Steidel et al. (1999)
found an extinction at ∼ 1500 Å of a factor of ∼ 5. Assuming the same correlation for high-redshift
galaxies, the UV spectral slopes of Lyman–break galaxies show an extinction of 4.7 in the bright
(R < 25.5) Lyman–break population studied by Steidel et al. (1999). This extinction tends to
increase for the most UV-luminous galaxies as shown by Meurer et al. (1999). In our treatment
of dust we separate the overall face-on extinction in the V-band (τV ) and the dependence of the
extinction on wavelength (the attenuation curve). The first component is treated via either a star
formation power-law relation or the gas content and metallicity relation. The attenuation curve is
selected from a choice of Calzetti, Galactic, or Charlot-Fall recipes. For the power-law variety, where
the amount of dust for any galaxy scales as function of star formation rate, the face-on optical depth
in the V-band is computed as follows,
βdust
τV, 0 = τdust, 0 (ṁ∗ )
(2.37)
where τdust, 0 and βdust are free parameters typically set to match observations in the local universe.
This power-law expression is fundamentally based on the empirical results of Wang & Heckman
(1996) for nearby starburst galaxies. In the case of the gas-metallicity driven face-on extinction law,
the face-on optical depth in the V-band is given by,
τV, 0
,
1.36 × 10−14 × Zg × mcold gas
=
rgas 2
29
(2.38)
where,
rgas = fgas size × rdisk
with fgas size and rdisk being the gas size and galactic disk radius respectively. The cold gas metallicity
is given by Zg . Once the face-on optical depth is computed, the transmission function of the diffuse
ISM is then calculated via an extinction law. The Galactic and Calzetti extinction curves have
been used extensively in literature so we omit any detailed discussion here, however the Charlot-Fall
recipe (Charlot & Fall 2000) is less well-known so we give a brief overview.
In the Charlot-Fall recipe, plausible physical assumptions are made, from which the Calzetti
attenuation curve is derived. Instead of being a purely data-derived construction, the Charlot-Fall
recipe is based on physical fundamentals. The value of AV in the Charlot-Fall recipe is computed
as follows,
AV =
!
λ
5500
"−ndust
(2.39)
where ndust is the dust extinction slope. The actual transmission function is then calculated as
follows,
TISM =
!
1 − ex
x
"
(2.40)
where,
x=
τλ
cos incl
where cos incl is the inclination angle of the galaxy and τλ is the optical depth at a given wavelength. Birth clouds are assumed to last approximately 10 Myr. The birth cloud transmission
function is,
30
TBC = e−x
(2.41)
where,
x = µ τV, 0
!
λ
5500
"−ndust
where µ is the multiplicative factor for the τV, 0 parameter, which gives the face-on optical depth in
the V-band of a birth cloud. The net transmission is then the sum of the TISM and TBC functions.
2.3
Fiducial Model
Above we reviewed in great detail the semi-analytic model used in this work, but at this
point we need to define a fiducial model that we will use as a reference model for the remainder of
this work. The logic for a reference model is two-fold. It provides us with a fixed set of parameters
that we can then vary individually to explore how models behave as a function of those parameters
(see §4). In addition, the reference model will be used to test our color-selection criteria (see §3.7.2).
The model that we choose is similar to the model used in Idzi et al. (2004), which was based loosely
on models explored by Somerville et al. (1999) and Somerville & Primack (1999). The fiducial model
is similar to those models in that it reproduces a mock-GOODS catalog with the same geometry, sky
area, filter passbands, etc. as the real GOODS and faithfully reproduces some of the observations
in the local universe (e.g. luminosity functions, colors, the Tully-Fisher relation, etc.) as well as
properties of high-redshift galaxies (like dust extinction, colors, etc.). We adopt a power-law dust
recipe (see §2.2.10), with a Calzetti attenuation curve, with τdust, 0 = 1.2 and βdust = 0.3 parameters.
These parameters were adjusted so that we obtain an average extinction correction at 1500 Å of a
factor of ∼ 5 for z ∼ 3 galaxies, typical of the Steidel et al. sample. For quiescent star formation,
we adopt the recipe where the time-scale scales with dynamical time of the disk (see §2.2.6), and
we choose τ∗0 = 12.0 and α∗ = 2.5. These values were chosen to again reproduce local as well
as some of the distant observations (the luminosity functions, the Tully-Fisher relation, etc.). For
31
Table 2.1. Fiducial Model Parameter Choices
Type
Dust
···
Quiescent SF
···
Bursty SF
···
···
···
SNae Feedback
···
Recipe
Power-Law
···
Dynamical Time
···
No Bulge
···
Bulge
···
Power-Law
···
Parameters
Values
τdust, 0
1.2
βdust
0.3
τ∗0
12.0
α∗
2.5
'0burst
0.5
αburst
0.5
'0burst bulge
0.5
αburst bulge
1.5
'0SN
1.0
αrh
2.0
Select parameter choices displayed. To find all values for all
other relevant parameters see §2
merger-induced star formation we adopt Cox et al. (see §2.2.5) values of '0burst = 0.5 and '0burst bulge
= 0.5, αburst = 0.5 and αburst bulge = 1.5 parameters. For supernovae feedback recipe we choose
the power-law recipe (see §2.2.7) with '0SN = 1.0 and αrh = 2.0 (Somerville et al. 1999). All other
recipe and parameters choices were kept the same as stated elsewhere in §2, including, but not
limited to choices of SED, IMF, metallicity, model resolution (halo circular velocities), etc. Table
2.1 summarizes some the parameter choices for our fiducial, mock-GOODS, model. Whenever we
refer to a fiducial model, this will be the model we mean.
32
Chapter 3
Observational Data
3.1
Introduction to GOODS
Observations of fields at high galactic latitude have long been an important tool in our
quest to understand the high-redshift universe. Deep surveys, such as The Hubble Deep Field project
(Williams et al. (1996) and Williams et al. (2000)) showed us the value of deep, multicolor imaging
for studies of galaxy evolution. Such surveys have also provided a roadmap for successful public
dissemination of the data and coordination of the best observations at all wavelengths on common
survey fields (see Ferguson, Dickinson, & Williams (2000) for a review). The Great Observatories
Origins Deep Survey (GOODS) is the progeny of such deep surveys. GOODS couples some of the
deepest observations from space and ground-based facilities over the same field. The Hubble Deep
Field North (HDF-N) and the Chandra Deep Field South (CDF-S) represent the two target fields.
These are the most data-rich deep survey areas on the sky. Apart from HST and Spitzer data,
numerous ground-based observations exist. In addition, deep X–ray observations from the CXO and
XMM–Newton telescopes have been taken at these locations, and deep radio maps are also being
generated.
Deep multi-band observations over an extended and well-sampled wavelength range are
33
required to probe high-redshift universe in a comprehensive and statistically meaningful manner.
The depth is necessary due to the intrinsic faintness of target sources. For example, a z850 > 26
(AB) is needed to detect a z ∼ 7 galaxy (assuming the same rest-frame UV luminosity function of
Lyman-break galaxies at z ∼ 3 and z ∼ 4, (see Giavalisco et al. (2004b)). To actually measure
the luminosity function, one has to go at least one magnitude fainter. The near-IR limits have to
be around z850 ∼ 26 (AB), so that blue-source sensitivity is ensured. For mid-infrared wavelengths
like those of the Spitzer Space Telescope IRAC instrument, the same requirements implies limits
from a fraction to a few µJy. The well-sampled wavelength coverage is necessary in order to derive
either accurate photometric redshifts or ascertain values of physical parameters of galaxies such as
mass, age, metallicity, and dustiness. A well sampled wavelength range is also necessary to obtain
sensitive color selection criteria.
The GOODS project unites very deep observations from space and ground-based facilities
in order to provide the first truly panchromatic deep survey over a relatively large area. The two
GOODS fields, centered around HDF-N and CDF-S, cover a total of 0.1 degrees2 . The GOODS
field centers (J2000.0) are 12h 36m55s ,+62◦ 14m15s , for the HDF-N, and 3h 32m 30s , −27◦ 48m20s , for
the CDF-S. Each field provides an area of approximately 10% × 16% that is common to all the GOODS
imaging observations. These observations include data taken with Chandra, HST, Spitzer, the ESO
VLT, Subaru and NOAO. In addition, GOODS also includes spectroscopic coverage with the Keck,
the VLT and Gemini. The HST Advanced Camera for Surveys (ACS) data consist of B435 , V606 , i775 ,
and z850 images, reaching a sensitivity level of 27.5, 27.9, 27.0 and 26.7 magnitudes (signal-to-noise
∼ 10 contained within 0.%% .5 diameter circular aperture). The Spitzer data consist of IRAC images
at 3.6, 4.5, 5.8 and 8.0 µm reaching 0.11, 0.24, 1.35, 1.66 µJy depth, and of MIPS images at 24 µm
reaching 12 µJy. An overview of the GOODS data used in this work is presented below. All of the
GOODS data, raw and reduced, and some source catalogs are publicly available and can be obtained
from the teams Web site (www.stsci.edu/science/goods/). Fig. 3.1 shows the CDF-S exposure
map for the Chandra, ACS, and IRAC observations, while Fig. 3.2 shows target areas for all CDF-S
34
Table 3.1. Instrumental Data
Facility
CTIO 4-m + MOSAIC
Passbands
Area coveragea
Angular resolutionb
1800
U
1.26
c
CDF-S
d
HST + ACS
BViz
320
0.125
ESO VLT + ISAAC
JHKs
130
0.40-0.65
Spitzer + IRAC
3 .6 4 .5 5 .8 8 .0
320
1.6
a
Total area covered, in arcmin2 .
b
PSF FWHM, in arcseconds
c
Field
HDF-N + CDF-S
CDF-S
HDF-N + CDF-S
The total area with V iz–band coverage is 365 arcmin2 .
d
Modal PSF FWHM of current version of drizzled image mosaics.
data sets (except for Spitzer data). Tables 4.1 and 4.2 list pertinent instrumental data and actual
sensitivities reached. In sections below we briefly describe each data set as well as the catalogs and
samples that were produces as part of this work. In addition, we go over the TFIT software package
used to produce reliable IRAC catalogs. All relevant simulations are discussed separately in §5. All
quoted magnitudes throughout the this work are in the AB magnitude system (Oke 1974). Finally,
although references are made to both the HDF-N and CDF-S data sets, we only make use of the
CDF-S data sets in this work.
35
Figure 3.1 Exposure map of the GOODS CDF-S Observations. In this image, blue represents the
Chandra (CXO) exposure map for the 2 Msec observations described by Alexander et al. (2003).
Green represents the current HST ACS exposure map, and red represents the planned Spitzer IRAC
exposure map. Where all fields overlap, the colors sum to give white in the representation. The
different ACS tiling patterns on even and odd epochs produce the sawtooth pattern around the edge
of the ACS fields.
36
Figure 3.2 Target areas of all data sets for CDF-S (Spitzer data excluded).
3.2
HST - ACS
The HST ACS observations taken by GOODS consist of imaging in the F435W, F606W,
F775W and F850LP passbands. While the B435 images were all acquired at the beginning of the
survey, the V606 , i775 , and z850 images were acquired over five epochs, separated by 40 to 50 days to
optimize the search for high-redshift supernovae. In the odd numbered epochs, each 10% × 16% field
37
Table 3.2. Data Sensitivity
Facility
U
B
V
I
z
J
H
Ks
3.6
4.5
5.8
8.0
4–m MOSAIC
25.9
···
···
···
···
···
···
···
···
···
···
···
HST ACS
···
27.8
27.8
27.1
26.6
···
···
···
···
···
···
···
VLT ISAAC
···
···
···
···
···
25.5
24.9
25.1
···
···
···
···
Spitzer IRAC
···
···
···
···
···
···
···
···
0.11
0.24
1.35
1.66
For each telescope + instrument combination, the first line gives the 10σ point–source sensitivity within an
aperture diameter of 0."" 2 for HST, 1."" 0 for ISAAC, and 2."" 0 for U-band data. Spitzer limits are given in µJy
is tiled by a grid of 3 × 5 individual ACS pointings. Some overlap areas are generated in order to
ensure photometric and astrometric consistency. For the remaining epochs, due to HST pointing
constraints, the field is rotated by 45◦ and as a result a different overlapping tile pattern is generated.
The B435 observations were gathered in the first epoch alone, using the familiar 3 × 5 grid, with six
exposures per position.The typical exposure times are 1050, 1050 and 2100 seconds in the V606 , i775 ,
and z850 bands, respectively. There are two exposures in each of the V606 and i775 bands, and four
exposures in the z850 band. This pattern ensures good rejection of cosmic ray events in the single
epoch z850 bands, which is where the detection of transients is carried out. The telescope field of
view is dithered by a small amount between individual exposures to allow optimal sampling of the
point–spread function and to remove detector gaps and artifacts. For final reductions, the multiple
epochs are combined into a single mosaic, allowing cosmic ray rejection from at least six images per
band. The final, total exposure times are approximately 7200, 5250, 5250, and 10500 seconds in the
B435 , V606 , i775 , and z850 bands, respectively.
Initial reduction of the data was carried out by the ACS calibration pipeline calacs.
The process consists of basic calibration steps of bias subtraction, gain correction, and flat-fielding
(Pavlovsky et al. 2002). The pre-reduced data are then further processed by the GOODS pipeline
using the multidrizzle script (see Koekemoer et al. (2003) for details). The net result is a set of
38
images that have been geometrically rectified and cleaned clean of cosmic rays. These preliminary
reductions – the GOODS public release v0.5 – have been released via the Multimission Archive
at Space Telescope (MAST). The geometric distortion model used in the preliminary reductions
described above had significant flaws that were revealed in the overlap regions. To remedy this, a
new astrometric solution was derived for each tile and each epoch using a list of matched sources
from the GOODS ground based images. For the CDF-S image, the Wide Field Imager (WFI)
R band image was used (see §3.5.2 for WFI data description). The WFI R mosaic was in turn
astrometrically calibrated to the Guide Star Catalog 2 (GSC-2) and put on the ICRS reference
frame. For HDF-N, the reference image was an R-band Subaru image of the field (Capak et al.
2003). The new astrometric solution for the z850 mosaic was derived by performing a least-squares
optimization of the position, orientation, x and y pixel scales, and axis skew of each tile and epoch,
minimizing the inter-epoch variations of the estimated position for ∼ 2000 sources. As a result, the
estimated rms in the source position, internal to the solution, is roughly 0.1 to 0.2 WFC pixels.
The new z850 image astrometric solution was propagated to the remaining ACS bands by
a tile-to-tile matching to the z850 mosaic source positions. The resultant solutions had a residual
rms of about 0.3 pixels, with larger deviations in some localized regions across the field. Once
astrometry was firmed up, all exposures were then drizzled (Fruchter et al. 2002) onto a series of
images with a common pixel grid, so as to create a clean median image, which was subsequently
used to create cosmic ray masks for each exposure. As a last step, the individual exposures were
drizzled using the new masks onto a final monolithic mosaic for each band, measuring 18000 by
24000 pixels with a scale of 0.%% 05/pixel. While the improved astrometry works well, there are a few
faults that need to be noted. The deficiencies become apparent for bright stars, where the cosmic
ray rejection algorithm rejects some good pixels due to slight misregistrations issues. This effect can
bias fluxes faintward for brighter point sources. This effect applies only to the V606 and i775 mosaics.
However, a direct comparison of the v1.1 GOODS mosaics with the original WFPC-2 HDF-N reveals
systematic errors of less than 0.01 magnitude for SExtractor MAGAUTO magnitudes in the range 23 <
39
V606 < 26, with an rms scatter less than 0.2 magnitude. With the new v1.9 reductions (used in this
work) additional improvements have been made. These include: Fixing the slight sky level variation,
masking of satellite trails, perfecting ghost reflection. In addition, supplemental exposure time has
been added, which include 4 exposures through the z850 filter over 15 tiles, and a single exposure
through both i775 and V606 filters over 15 tiles each. The supplemental exposures have effectively
added 7712, 1908, and 330 seconds to the z850 , i775 , and V606 bands, respectively. With the new
reductions we reach
,S-
N z850
∼ 5 at z850 ∼ 28. The reader is urged to refer to the teams Web sites
(www.stsci.edu/science/goods/) for the latest status on GOODS ACS mosaic reductions.
3.3
ESO VLT - ISAAC
As part of the GOODS program, near-infrared imaging observations of CDF-S have been
carried out in the J, H, Ks bands, using the ISAAC instrument mounted at the Antu Unit Telescope
of the VLT at ESO’s Cerro Paranal Observatory, Chile. This work has been conducted as part of
an ESO Large Programme. To cover the GOODS CDF-S field, 32 pointing have been used. The
resultant mosaics cover ∼ 159 and ∼ 160 %2 in the J and Ks bands, respectively. The H-band covers
∼ 127 %2 . The J, H, and Ks data consists of 21,19, and 23 tiles, respectively, with each tile spanning
2.5.% × 2.5.% . All images have a pixel scale of 0.15”, which is exactly a factor of five larger than
the pixels in the GOODS ACS images. The data have an excellent image quality with a median
seeing value of ≈ 0.%% 45 for all bands.The seeing dispersion across tiles is extremely small for the H
band, less than 0.%% 05, somewhat larger for the J band, and largest for the Ks -band, at around 0.%% 15.
The dispersion within each tile is extremely small. The astrometric calibration was derived using
a reference catalog generated from a deep R band WFI image which was astrometrically calibrated
using the Guide Star Catalog GSC–2.3. The astrometry has been compared by the GOODS team
with calibrated data from the HST ACS. An astrometric matching to the ACS list of unresolved
sources shows a rms scatter in astrometry of 0.1” across the entire area.
40
The photometric calibration of the present ISAAC data was done against the J, H, and
Ks mosaics constructed from photometrically calibrated SOFI images of the EIS-DEEP and DPS
infrared surveys conducted over the same region (see §3.5.3 for SOFI data description). The SOFI
images encompass a number of tiles of the ISAAC mosaic, yielding better relative calibration across
the entire surveyed area. Zeropoints for each ISAAC field were determined using SOFI images and
a sample of ∼ 400 unresolved sources. These sources have been identified in the HST ACS images
based on SExtractors stellarity index and flux ratio, yielding a list of potential stars. All ISAAC
images were first PSF-matched to the value of the corresponding SOFI image (∼ 0.9%% ) employing
Gaussian convolution. Aperture magnitudes of these stars were then used to determine zeropoints
for each individual tile in the AB system. Anywhere from 3 to 12 sources have been used per each
tile. This procedure yielded zeropoints with rms values ranging between 0.01 and 0.06 magnitudes
in J-band, up to 0.17 magnitudes in H-band, and between 0.01 and 0.08 magnitudes in Ks -band.
For the tiles where less than three isolated stars were available for accurate photometry all high
signal-to-noise sources that qualitatively appeared pointlike in the ISAAC images were used for
calibrations.
To provide a homogeneous photometric zeropoint across the entire GOODS field, all images
were rescaled to a set zeropoint of 26 (AB). The exposure times were also normalized to unity, so that
AB magnitudes in all released fields, including the mosaics, could be easily obtained via mag(AB)
= -2.5 × Log[flux] + ZP. The following corrections were applied: J(AB) = J(Vega) + 0.90, H(AB)
= H (Vega) + 1.38, and Ks (AB) = Ks (Vega) + 1.86. To take account of any potential systematic
errors in this calibration procedure, independent photometric calibration checks had to be made.
Cross-checking was done against the 2MASS photometry using limited number of stars in the field.
The photometric zeropoints were found to be consistent to within few percent. A comparison of the
present release data with photometric catalogs from Saracco et al. (2001) (J and Ks bands), Cimatti
et al. (2002) (Ks -band), and Moy et al. (2003) (H-band) did not reveal any systematic differences
once error margins were taken into account.
41
2.0
5.8
8.0
3.6
4.5
1.5
1.0
0.5
2.0
1.5
1.0
0.5
0.5
1.0
1.5
2.0
0.5
1.0
1.5
2.0
Figure 3.3 Illustration of the exposure layout for each IRAC epoch and channel combination in
CDF-S. The green and blue points correspond to epoch 2 and epoch 1 sources, respectively, whereas
the red points correspond to dual-epoch sources.
3.4
Spitzer - IRAC
The GOODS Spitzer Legacy program observations cover two fields on the sky, the CDF-S
and the HDF-N. IRAC data consists of four channels, 3.6, 4.5, 5.8 and 8.0 µm taken in two epochs
separated by six months. The telescope orientation is dithered and rotated by 180◦ between the two
epochs. All four channels are used simultaneously, with two channels pointing in one direction, and
the other two in different direction. Fig. 3.3 illustrates the layout of the CDF-S IRAC observations
by epoch. This scheme results in full four-channel coverage of the 10% × 16% GOODS field, with 23
hours worth of exposure per epoch, and double that in the overlap region. The IRAC data is pre42
processed by the Spitzer Science Center (SSC) Basic Calibrated Data (BCD) pipeline. The data is
then post-processed by applying various corrections such as median image subtraction, background
subtraction, cosmic ray and bright sources corrections among others. The next step involves deriving
internally consistent astrometric solution. Images are then combined using procedures akin to the
multidrizzle method used in ACS reductions. Finally, exposure, weight, and flag maps were
generated. The weight maps were re-normalized to inverse variance maps, where the inverse variance
maps represent only the shot noise component of the image noise at the sky background level of the
images, and do not include the Poisson shot noise from the sources themselves, nor any measure
of photometric uncertainty due to image crowding or confusion noise. The flag maps are bit maps
that take into account data defects like residual muxbleed (bright source effect), low exposure time,
or simply no data available. A comprehensive discussion of GOODS Spitzer data acquisition and
reduction can be found in the forthcoming data paper by Dickinson et al.
3.5
3.5.1
Ancillary Data
CTIO 4m - MOSAIC U
Observations of the GOODS CDF-S field through the U -filter were taken with the MO-
SAIC camera mounted on the CTIO 4-m telescope. The data was taken over a period of two runs
(2003, 2004) and it consists of 26 hours of total exposure time. The conditions during both runs
were photometric with mean seeing of FWHM ∼ 1.%% 26. As with the KPNO observations, the data
was reduced with the IRAF mscred package. The package is used to carry out bias subtraction, flat–
fielding, geometric distortion correction, removal of amplifier cross–talk, subtraction of an additive
pupil ghost, image registration, and the subsequent combination. Individual exposures were registered against the GSC 2.0 database, whereas the final mosaic was astrometrically checked against
our reference WFI R mosaic. The WFI R is our standard astrometric reference for ground based
data. The final mosaic combinations were done with the SWarp package (Terapix). SWarp is a
43
program that resamples and co-adds together images using any arbitrary astrometric projection as
defined in the WCS standard. The use of the SWarp package was necessary because part of the
data had astrometric anomalies in the top two corners of images. The anomalies were most likely
due to a U -filter change in the middle of one of the observing runs. As a result, it was necessary
to produce two separate mosaics, one with a full field of view, but shallower due to elimination of
the faulty frames. The second mosaic was produced by masking out the faulty regions, resulting in
a smaller but deeper mosaic. The final exposure times for the two mosaics were 20 and 25 hours,
respectively. Unless otherwise stipulated the second, deeper, mosaic was used for this work since it
completely overlaps the ACS region. This data set was used to select U-dropout galaxies.
3.5.2
ESO MPI 2.2–m - WFI
The WFI instrument, mounted at the top of the ESO-MPI 2.2-m telescope, was used to
image about ∼ 0.4 sq. degrees around the CDF-S, using its U % U BV RI passbands. We refer the
reader to Arnouts et al. (2001) for a complete description of the full data set. Supplemental exposures
in the B, V , R filters were taken as part of the COMBO-17 project (Wolf et al. 2001). All of the
data, including EIS, GOODS, and COMBO, were reduced in a uniform manner using the GaBoDs
WFI reduction pipeline (Schirmer et al. 2003). Photometric calibration was performed using the
color loci of stars. These were then compared to synthetic color-color diagrams generated using the
Gunn & Stryker (1983) spectro-photometric library and our passbands. The resultant zeropoints
were then adjusted as needed, and are now accurate to < 0.1 magnitude. The 10σ point–source
sensitivity within an aperture diameter of 2.%% 0 is ∼ 25.8 (AB) in R-band. The mosaic covers an area
of 1350 arcmin2 with a variable angular resolution of 0.85–1.05 arcsec. This data set was used to
provide a common astrometric reference frame for all data. It should be noted here that the WFI
R mosaic is our de-facto astrometric reference for the GOODS ground based CDF-S data sets.
44
3.5.3
ESO NTT - SOFI
Near-infrared data in the J and Ks bands for the CDF-S were obtained with SOFI on the
NTT as part of the EIS. The observations and reductions are described in Vandame et al. (2001).
The observations consist of 4 × 4 grid of pointings covering 0.1 sq. deg in 5% × 5% tiles. SOFI Hband data were obtained and reduced by Moy et al. (2002), and cover a larger area. Photometric
zero-points were checked by the GOODS team by comparing photometry of stars to measurements
from the Two-Micron All-Sky Survey (2MASS). The 10σ point–source sensitivity within an aperture
diameter of 2.%% 0 is ∼ 22 (AB) in all bands covering an area of 360 (630 for H-band) arcmin2 with
a variable angular resolution of 0.65-1.05 (0.55-0.85 for H-band) arcsec. This data set was used to
calibrate the ISAAC photometry.
3.6
3.6.1
Photometric Catalogs
SExtractor Catalogs
Throughout this work we use several different source catalogs to compile the photometric
information required for the Lyman-break galaxies used in this work. As described in §3.6.2 we use
the TFIT package to extract reliable photometric fluxes. However, while TFIT is extremely useful,
we still rely on other source-extraction packages, namely the SExtractor package developed by Bertin
& Arnouts (1996). TFIT itself requires an SExtractor-like utility for its data preparation purposes,
we make use of SExtractor to procure source lists and segmentation maps. The Lyman-break galaxy
samples used in this work (§3.7.2) were compiled using SExtractor catalogs of the U-band and ACS
images. Lastly, SExtractor-based catalogs of ACS and IRAC data sets were used to calibrate the
TFIT software and the resultant catalogs (see §3.8).
The ACS SExtractor catalogs were constructed with the goal of optimizing the detection of
faint galaxies while at the same time keeping spurious sources to a minimum. This was accomplished
by fine-tuning the detection thresholds and the size and shape of the convolution kernel. Sources
45
Figure 3.4 Sample plot of completeness limits on the ACS z850 Sextractor catalog as a function of
half-light radius and total magnitude for both elliptical and spiral galaxies. This plot is based on
the v1.0 ACS data set – a shallower data set. The data set used in this work is deeper.
were first detected in the z850 mosaic, and then photometry was carried out through matched
apertures in the remaining ACS bands. Photometric uncertainties were then computed internally
using the normalized ACS noise maps and externally through detailed simulations using artificial
sources. Monte-Carlo simulations were carried out to ascertain the completeness of our catalogs.
The description of these simulations can be found in §5.1. Fig. 3.4 shows a sample plot yielded by
the simulations, which shows completeness limits on our ACS z850 SExtractor catalogs as a function
of half-light radius and total magnitude.
Apart from ACS SExtractor catalogs the GOODS team has also produced IRAC and
ISAAC SExtractor catalogs. As was the case with the ACS SExtractor catalogs, these catalogs were
46
created using the best possible SExtractor values to fine-tune the photometry. The primary purpose
of the IRAC catalogs was for TFIT calibration work. The IRAC catalogs were derived individually
for each channel and epoch combination. In the case of ISAAC catalogs, the SExtractor-derived
fluxes were used for some of the work in this project, although no ISAAC data were used for the
actual fitting. The ISAAC is much shallower than the IRAC data and so incorporating this data
into our analysis would severely limit our Lyman-break samples. Nevertheless, the ISAAC data was
useful for other parts of out work (such as exploring ACS-ISAAC colors), so a Ks -band detected
catalog was produced with matched J and H photometry. We then processed the catalogs to correct
the NIR magnitudes so that they could be used alongside our ACS magnitudes. We accomplished
this by correcting each ISAAC isophotal magnitude with a correction factor determined from the
isophotal and total magnitudes. This provided as with a reliable way (at most ∼ 0.1 magnitude
error), of mixing the ACS and ISAAC magnitudes for our ACS-ISAAC color comparisons without
having to produce matched SExtractor ACS-ISAAC catalogs. We wanted to treat the two data
sets (ACS and ISAAC) separately since we needed to retain the full resolution of ACS mosaics for
our TFIT ACS-IRAC catalogs. Producing matched SExtractor ACS-ISAAC catalogs would have
called for seriously degrading the ACS mosaics. The ultimate solution of course is to produce TFIT
ACS-ISAAC catalogs. Whenever ISAAC data is used in this work we explicitly refer the reader to
the caveats just described.
3.6.2
TFIT Catalogs
The IRAC photometric catalogs used in this work were constructed using a template-fitting
package called TFIT. The TFIT software is described in some detail in §3.8.1 along with diagnostics
and calibrations. For full details on how TFIT works we refer the reader to Laidler et al. (2006)
(in preparation). Here we briefly describe the TFIT catalogs used in this work, information on
SExtractor catalogs (like those for ACS) can be found in §3.6.1. The TFIT catalog is ACS-to-IRAC,
where we use SExtractor-derived ACS sources and use TFIT to fit the IRAC fluxes. The ACS z850 -
47
IRAC catalogs were created by template fitting each field, channel, and epoch of IRAC to the ACS
z850 data. Since we have 2 fields, 4 channels, and 2 epochs of IRAC data (see §3.4 for full data
description) this resulted in 16 separate catalogs, although in this work we use CDF-S data only.
For each catalog, channel-field-epoch specific PSFs were used. Most of these PSFs were provided by
SCC (see §3.4). Once we were satisfied with the raw catalogs produced by TFIT we produced final
catalogs by assembling the 2 epochs for each field-channel combination. Each source then had either
data from a single epoch or from both epochs. In the case of dual-epoch data, we used weighted
flux and weighted flux error for those objects that had reliable photometry in each epoch according
to the following prescription,
fe12 =
fe1 × w1 + fe2 × w2
w1 + w2
1
σe12 = √
w1 + w2
where fe is the flux for each epoch, and w1 =
1
2 ,
σe1
w2 =
1
2
σe2
(3.1)
(3.2)
are the weighted flux errors. In addition
to the above information we also propagated flags from the original IRAC flag maps. These flags were
then used to separate spurious sources from good data. Because of the way TFIT works, we could
then easily merge all SExtractor-derived ACS photometry with the TFIT-derived IRAC photometry
to produce master catalogs. These pan-chromatic catalogs (z850 through IRAC 8.0) were then used
to extract photometric information for the Lyman-break samples that were separately constructed
using SExtractor-derived U-band and ACS data.
48
3.7
3.7.1
Galaxy Samples
Lyman Break Galaxies
The Lyman-break color selection technique has been shown to be a highly effective means of
> 2) (Steidel et al 1999; Madau et al. 1996). The Lyman-break
selecting galaxies at high redshift (z ∼
technique, as the name implies, exploits the intrinsic Lyman edge in galaxies and the opacity of
intergalactic neutral hydrogen to separate galaxies located at high and low redshifts. Even though
galaxies exhibit smoothly varying spectra, where the flux is usually a slowly varying function of
wavelength, there a few discontinuities. Most notably, the Lyman-break (912 Å) and the Balmer
break (∼ 4000 Å). It is the first of these two that is used to photometrically select high redshift
galaxies. Photometric color criteria that identify the Lyman-continuum break have been shown,
through spectroscopic work, to be quite successful at picking out a substantial population of high
redshift galaxies (Steidel et al. 1996a,b). Over the past decade, fairly large samples of Lymanbreak galaxies (LBGs) in the redshift range z > 2 have been compiled, and the characteristics of
these objects have been closely examined. Contemporary surveys, such as GOODS, can identify
< z < 5.5 with varying degrees of success depending on the
high redshift galaxies in the range 2.5 ∼
∼
redshift slice (Giavalisco et al. 2003b).
The GOODS samples of Lyman-break samples are identified via color selection criteria as
well as signal to noise considerations derived for each dataset. The selection criteria are largely based
on previous experience with Lyman–break galaxies (e.g. Dickinson 1998; S99; Steidel et al. 2003).
They are visually fine–tuned based on the observed colors of stars and galaxies in the ACS images,
as well as on the ACS synthetic photometry from galaxy spectral templates. This procedure rejects
most interlopers from lower redshifts, while efficiently detecting typical UV–bright, star–forming
galaxies at redshifts of interest. The color selection criteria are further fine-tuned via artificial
galaxy simulations. This is accomplished by modeling the HI cosmic opacity as a function of redshift,
including scattering in resonant lines of the Lyman series and Lyman-continuum absorption, and the
49
use of stellar population synthesis models with a wide variety of ages, metallicities, dust contents,
and redshifts, to derive color selection criteria that provide a robust separation between high redshift
and low redshift galaxies. Of course, due to a multitude of possible star formation paths for any
particular galaxy and the complex nature of chemical evolution of stars, the interstellar medium,
and the dust distribution and content, Monte-Carlo simulations have to be performed to ascertain
the robustness of the selection criteria. The color criteria can also be tested against spectroscopic
samples to confirm the efficiency of photometric selection as in (Steidel et al. 1996b). GOODS
has been gathering spectroscopic data and that information has been used to verify and refine our
samples. Because of the nature of this project we also contrasted our Lyman-break samples against
our nominal semi-analytic model (see §3.7.2).
The advantage of the photometric technique is its ability to rely on photometry and simulation alone to reliably identify distant star forming galaxies. In addition, the photometric technique
goes deeper, yielding larger samples. Spectroscopic work in often an expensive endeaver as it requires
long exposure times and individual measurements for each galaxy. In addition, many of the distant
objects are not easily accessible even with the most powerful telescopes. The advent of multi-slit
spectroscopy and more powerful telescopes will make it easier to obtain useful spectroscopic integrations for many objects at a time, and indeed GOODS has been using the multi-slit approach
to obtain spectroscopy for select objects in the GOODS field. Nevertheless, for medium to large
area surveys, the preferred techniques is the photometric one. The deficiencies of the photometric
technique lie in the uncertainties of redshift estimates as well as reliance on robust photometry.
3.7.2
Color Selection Criteria & Samples
In this section, we shall define the color selection criteria appropriate to the GOODS
bandpasses. The CTIO-U and ACS mosaics allow us to define several Lyman-break samples, namely,
the U-, B-, V-, and i-dropouts. Below we give the color selection criteria used in this work. Unless
otherwise stated, these are also the color selection criteria that have been applied to our model
50
galaxies in the course of our analysis. First, there are the U -band dropouts (z ∼ 3), which use the
following criteria:
(U − B435 ) >= −0.75 + 0.5 × (B435 − z850 ) &
(3.3)
(U − B435 ) >= 0.9 &
(3.4)
(B435 − z850 ) <= 4.0
(3.5)
the B-band (B435 ) dropouts (z ∼ 4) are defined via:
(B435 − V606 ) > 1.1 + (V606 − z850 ) &
(3.6)
(B435 − V606 ) > 1.1 &
(3.7)
(V606 − z850 ) < 1.6
(3.8)
the V-band (V606 ) dropouts (z ∼ 5) are defined via:
(V606 − i775 ) > (1.4667 + 0.8889 × (i775 − z850 )) ||
(3.9)
(V606 − i775 > 2.0)) &
(3.10)
(V606 − i775 ) > 1.2 &
(3.11)
(i775 − z850 ) < 1.3
(3.12)
and the i-band (i775 ) dropouts (z ∼ 6) are defined by:
(i775 − z850 ) > 1.3
In each case we required potential dropout targets to have a
(3.13)
,SN
< 2 in the dropout band
in order to be classified as undetected. In the bands that the object was detected, the
51
,SN
had to be
greater than five. This selection scheme helps to reject interlopers. The samples were than visually
culled to eliminate contaminants, like cosmic rays, stars, satellite trails, diffraction spikes, etc. We
have stated i-band dropout color selection for completeness, but we shall ignore that sample in this
work, since the quality and the number of dropouts is insufficient for our analysis. In addition, we
will not use the V-band dropout sample in our analysis due to the dearth of objects as well as the
lack of robust NIR photometry, but we do use this sample for projection and discussion purposes.
The number counts for the U-, B-, and V-samples, with
magnitude of z850 < 26.5) and
,SN
,SN
> 10 in ACS (corresponding to a total
> 5 in IRAC3.6 and IRAC4.5 bands are: 569, 275, and 53
galaxies, respectively. Including ISAAC J and Ks bands (with a
,SN
> 5 cut) results in much lower
number counts: 345, 91, 18, respectively. This is due to the much shallower depth of the ISAAC
mosaic, but also partly to the fact that we have not applied TFIT to the ISAAC data. Adding
extra IRAC channels, especially channels 3 and 4, diminishes the number counts as well, due to the
shallower nature of those two channels relative to the first two. Therefore for our analysis we stick
with ACS and IRAC (channels 1 and 2) for our samples, excluding IRAC (channels 3 and 4) and
ISAAC data. We do however use the excluded channels for predictions and discussion purposes. In
Fig. 3.6 to Fig. 3.11 we show color-magnitude diagrams for the U, B-, and V-dropouts, both for
UV-continuum and Balmer-Break rest-frame colors.
To test the completeness of our samples we use Monte-Carlo simulations described in §5.1.
According to these simualtions, the B-dropout galaxies’ redshift distribution of the simulated colorselected sample has a mean value of z ∼ 3.91 with a standard deviation of ±0.44. The recovery
percentage, using color criteria, is 87% for the simulated B-dropout galaxies down to z850 < 27 and
in the redshift interval 3.47 < z < 4.35. When we apply the color criteria to the fiducial semianalytic model (see §2.3) run, we select 90% of all model galaxies in the same 3.47 < z < 4.35
redshift range, down to the same limiting magnitude of z850 < 27. This implies that the simulations
and the fiducial semi-analytic model show concordant incompleteness estimates with respect to the
B-dropout selection technique in the above redshift range and down to the given magnitude limit.
52
This is agreement of what we found in our previous work (Idzi et al. 2004).
Similar exercises can be performed with respect to the other dropout samples. We find
similar agreement for the V-dropouts, where the simulation and semi-analytic model completeness
fractions are 82% and 88%, respectively, over a redshift range 4.65 < z < 5.35 (with the mean
redshift derived from the simualtions). For the U-dropouts we cannot ascertain completeness limits
from the simulations since our Monte-Carlo simulations do not incorporate U-band data. However,
we can quote the fiducial semi-analytic completeness based on the mean redshift derived from that
model. We find 92% completeness in the redshift range 2.32 < z < 3.68. As a fun exercise, we
can plot the data-derived Lyman-break samples alongside our fiducial semi-analytic model-derived
Lyman-break samples. Fig. 3.12 shows such a plot for B-dropout samples.
3.8
3.8.1
Template-Fitting Software Package
TFIT Overview
The TFIT (short for Template-Fitting) software package was initially developed by Pa-
povich (2002) and since then it has been re-engineered by the GOODS team to speed-up processing
time and also allow more flexibility. The purpose of this section is to introduce the reader to the
TFIT software package. Here we will only provide a brief introduction, we refer the reader to Laidler et al. (2006) for the latest and the most complete discussion of TFIT. Since this work relies
heavily on TFIT products we devote special attention to the calibration and diagnostic work in
§3.8.2. The TFIT package, which will soon be released to the public through the Spitzer Science
Center, addresses some of the most thorny issues surrounding the creation of photometric catalogs.
These issues stem from a combination of IRAC’s nearly 2.%% resolution and the high density of sources
found in the GOODS HST ACS fields (nearly 200 per arcmin2 ), a large fraction of which are distant
galaxies with significant mid-IR fluxes present at the extreme sensitivities of the GOODS SST IRAC
observations (1 σ = 22 nJy at 3.6 µm). The combination of these factors leads to significant source
53
crowding in the IRAC images. Any reasonably sized photometric aparture of an IRAC source is
frequently contaminated by its neighbors. In addition, catalog matching of IRAC detected sources
is compromised by de-blending issues. The typical existing workarounds, such as the DAOphot
(crowded field, psf fitting) photometry package, are not suitable to our case. This is because the
preponderance of our extragalactic sources are, at a minimum, marginally resolved with IRAC. As
a result, a new approach had to be constructed in order to remedy these difficulties.
The GOODS team has developed a crowded-field, resolved-source photometry package
called TFIT. The basic flow of how TFIT processes data is shown in Fig. 3.13. Briefly, TFIT first
constructs lower resolution (LR) (in this case - IRAC) template images for sources detected at higher
resolution (HR) (in this case ACS) by using the high-resolution position and morphology along with
PSF information about both images. In a final step, the TFIT package scales the templates to
optimally match the lower-resolution image. In short, the TFIT package uses apriori knowledge of
source location and morphology from a high resolution image to construct a low resolution version
of the source. The main assumption to this method is that the intrinsic light profile of the source is
identical, modulo PSF effects, in both the low and high resolution images. To facilitate the fitting
process, the lower resolution input image is divided into overlapping cells, and the objects in the
cells are all fit simultaneously using the technique of singular value decomposition (SVD) to solve
the resulting matrix equation. This simultaneous fitting affords more accurate photometry due to
the extra information coming from many galaxies (Laidler et al. 2006). The matrix equation takes
the form:
LR(image) = β + α1 T1 + α2 T2 + ... + αn Tn
(3.14)
where the Ti are the templates for the n objects that occur in the region. The quantity Ti is actually
divided by Ei , where Ei is the rms error value for the relevant pixels in the LR image. This equation
is solved to determine the best fit flux for each object in the LR image, plus a background term for
54
the cell. The best fit is generated by minimizing a χ2 statistic, using:
2
χ =
.
x,y
/
12
0N
i
L
& xy − β − i=1 αi Txy
σxy
(3.15)
where Lxy and σxy are the fluxes and rms errors of the LR image. The fitted parameters, αi , are
the scaling factors for cell objects, which are used to scale the individual object templates. The
β parameter is a linear constant, which corresponds to the LRI background of the cell. The sum
is performed over the entire cell. The SVD technique used to perform the actual χ2 minimization
see Press et al. 1992) is ideal for this situation since many of the equations to be solved are overdetermined (more data points than parameters). In such cases, the matrix defined in equation
(2) will occasionally be singular or nearly singular. The SVD technique circumvents this problem
by transforming the matrix into a diagonal one containing singular values, and two non-singular,
orthogonal matrices. As a result, the parameters to be fitted (αi , βi ) are linear combinations of
the columns of the dot product of the orthogonal matrices and the data, where each column is
properly weighted by the inverse of the near-singular values. The weight is artificially set to zero
whenever any near-singular value is below some threshold. In addition to the best fit parameters,
TFIT produces uncertainties on the resultant values that are based on the sum of the χ2 per degree
of freedom in the cell and the variance of the parameters in the fit. A full covariance matrix is also
returned for each cell (again, for full details see Laidler et al. (2006)).
In practical terms, in order to run TFIT, we form a library of FITS files, each containing a
single object, and a corresponding catalog of x-y positions and isophotal fluxes. These object images
have been cut out from a high resolution image which has been first cataloged by a tool such as
SExtractor (Bertin & Arnouts, 1996). A SExtractor run also produces a segmentation map that
tells which pixels belong to which object. The local sky background is then subtracted from each
cutout and each cutout is normalized to have a total flux of unity. Each FITS file is also produced
with accurate WCS that precisely locates the image on the sky. Each cutout is then convolved with
55
a convolution kernel in order to transform the HR image to the LR image, producing a template.
Nominally, the convolution kernel, also known as the PSF or the transfer kernel, is constructed using
information from both low resolution and high resolution images. However, the transfer kernel can
be based exclusively on the low resolution image if the high resolution image has sufficiently high
resolution as to be treated perfect. For example, we were able to use the IRAC PSFs exclusively for
the ACS-IRAC TFITing. In contrast, for the ACS-ISAAC TFITing we had to construct transfer
kernels with both ACS and ISAAC PSF information folded in.
Because the LR image is typically at a much coarser pixel resolution than the HR image,
we rebin the convolved images to the LR pixelation. For cell construction, we use the LR image
to determine the size of the cell. The cell has to be large enough to contain all the light produced
by an object close to the cell’s center, but not much larger. We can then use the cells and object
templates in them to run the fitting procedure against the LR image. TFIT produces a catalog of
objects with scaled fluxes and corresponding errors. In addition, a number of diagnostic catalogs
and images are produced, which can be used to ascertain the reliability of the TFIT products. A
model collage can be subtracted from the real LR image to obtain a residual image (see Fig. 3.14),
which can be examined for registration, background, and PSF issues.
There are some subtleties based on the HR and LR bandpass differences (see Laidler et al.
(2006)). Since the LR image often has astrometric properties (such as distortion) not captured
by the WCS matrix, the collage is cross-checked against the LR image in zones. A set of new
transfer kernels can then be created to incorporate any astrometric shifts necessary to produce better
fits. This completes the process, however, many details, especially those regarding preparation, are
omitted in this overview, we refer the reader to Laidler et al. (2006) for all the details regarding
TFIT.
56
3.8.2
TFIT Diagnostics
To ascertain the validity of the TFIT procedure as well as the resulting catalogs, we need to
conduct a number of diagnostic and calibration procedures. Most of the diagnostic work is discussed
in Laidler et al. (2006) so we refer the reader to that work for the full discussion. Here, we briefly
present some of the TFIT diagnostics. One of the main advantages of using TFIT over SExtractor
is its ability to recover reliable photometry in crowded fields. Fig. 5.8 in §5 shows the relative ability
of SExtractor and TFIT to recover closely separated objects, whereas Fig. 3.15 shows the abilities
of SExtractor and TFIT in assigning reliable photometric errors. These two figures demonstrate the
advantage of using TFIT over SExtractor, as TFIT is able to de-blend sources and assign reliable
errors where SExtractor fails.
In §3.8.1 we showed a typical fitted image along with a corresponding residual map (Fig. 3.14).
Much can be gleaned just from the residual map itself, and indeed that is where most of TFIT’s
processing results were identified. Recall that the residual map is simply a fitted image subtracted
from a LR image. If we look at the residual map we can identify a number of features. For instance,
there are halos present in the residual image around many objects. These are a result of using
imperfect PSF. Other features present themselves in the form of: minute positive detections around
bright stars, dipole signatures around objects that are caused by imperfect registration, and annular
residuals caused by transfer kernels which are too narrow. Also, we occasionally detect objects which
are present only in the LR image.
The dipole features caused by mis-registration were fixed by using a post-production registration step, where the fitted and LR images are divided into sections slightly larger than the cell
size and then cross-correlated against each other. New local shifts are then obtained and propagated
into the existing templates. Fig. 3.16 compares the residuals before and after the procedure was
applied for the CDF-S IRAC4.5 epoch 1 image. We can see the improvement in residuals, where we
see better centering on objects. However, the improvement in registration does not have a profound
impact on derived photometry. Fig. 3.17 and Fig. 3.18 show the differences in photometry before
57
and after shifts. We can see that even though there is plenty of scatter, the differences are minimal.
The minute positive features around bright stars are due to poor TFIT fits. The poor fits
are most likely due to saturation or imperfections in the wings of the modeled transfer kernels. We
have devised an imperfect solution to this problem by utilizing a correctly source-weighted RMS
map. This procedure gives a lower weight to pixels belonging to the brighter objects and effectively
reduces the anomalies. Finally, the transfer kernel issues can be eliminated by improving the kernel
itself. This is done via TFIT simulations and additional calibration techniques described below.
The resulting scaled flux is similar to an isophotal flux. We have tested that this so by
comparing a ratio of IRAC TFIT-derived flux over ACS SExtractor-derived isophotal flux to a ratio
of IRAC SExtractor-derived aperture flux over ACS SExtractor-derived aperture flux. In principle, if
the TFIT-derived flux is indeed similar to an isophotal flux, the two ratios should be equal provided
that the apertures used are large enough so that most of the flux from an object is retained and
neighbor contamination is eliminated. To account for these two caveats we choose apertures of 2.82
and 9
%%
in diameter for the ACS and IRAC data, respectively, and we choose isolated objects only.
Fig. 3.19 shows what the behavior of the two ratios is as a function of the total IRAC magnitude.
We can see that the ratio of the two ratios (quantity R in the figure) tends to unity, which confirms
that the flux measured using isophotes correlates fairly well with the flux measured by TFIT. The
actual R values turn out to be 1.01 ± 0.20, 1.02 ± 0.22, 1.07 ± 0.32, and 1.09 ± 0.34 for the CDF-S
IRAC channels one through four, respectively.
58
5.8
8.0
3.6
4.5
250
N
200
150
100
50
250
N
200
150
100
50
-15
-10
-5
0
5
10
15
(tfit_flux_e2-tfit_flux_e1)/(sigma_e12)
-15
-10
-5
0
5
10
15
(tfit_flux_e2-tfit_flux_e1)/(sigma_e12)
Figure 3.5 Difference between epoch 1 and epoch 2 derived fluxes, normalized by the weighted epoch
1 epoch 2 flux error. Each panel shows this distribution for each IRAC channel. We see that
there are not any major deviations between the two epochs for each of the channels. Only best
objects, well-detected, objects were used for these plots. The black curves are gaussian with zero
mean and unity sigma. In the two shorter wavelength channels, TFIT appears to underestimate the
uncertainty, possibly due to imperfections of the PSF and image registration.
59
Figure 3.6 Color vs total magnitude for U-dropout galaxies. The UV-continuum rest-frame colors.
60
Figure 3.7 Color vs total magnitude for U-dropout galaxies. The Balmer-Break rest-frame colors.
61
Figure 3.8 Same as Fig. 3.6, except for B-dropout galaxies.
62
Figure 3.9 Same as Fig. 3.7, except for B-dropout galaxies. The color-magnitude trend seen here is
due mostly to selection effects, where we are reaching limits in our IRAC depth at this redshift.
63
Figure 3.10 Same as Fig. 3.6, except for V-dropout galaxies. The use of ISAAC data that has not
been processed through TFIT affects the number of recovered reliable photometry.
64
Figure 3.11 Same as Fig. 3.7, except for V-dropout galaxies.
65
Figure 3.12 Color selection in the data and fiducial semi-analytic model plane. The small black
dots are all galaxies recovered from ACS catalogs, the green points refer to observed B-dropout
galaxies, the blue points represent all galaxies from the fiducial model, and the yellow points refer
to B-dropouts selected from the fiducial model (§2.3).
66
Figure 3.13 This shows a flow chart of how TFIT works
67
Figure 3.14 The left panel shows the simulated image for the CDF-S IRAC4.5 epoch 1 mosaic
produced by TFIT. This image is then subtracted from the real mosaic to produce the residual
image seen in the right panel. The bull-eye artifacts seen in the residual image are due to the use of
an imperfect PSF.
68
Figure 3.15 TFIT vs SExtractor errors as a function of source separation. Blue corresponds to TFIT
errors, while red corresponds to SExtractor-derived errors.
69
Figure 3.16 The left panel shows the residual image for the CDF-S IRAC 4.5 epoch 1 mosaic produced
by TFIT, whereas the right panel shows the residual for the same image after positional corrections
have been applied.
70
3.6
2000
N
1500
1000
500
-15
-10
-5
0
5
(tfit_flux_p2-tfit_flux_p1)/(sigma_p12)
10
15
Figure 3.17 This shows the normalized flux difference between pass two (post-shift) vs pass one
(pre-shift) for the CDF-S IRAC 4.5 epoch 1 mosaic, for isolated sources. Though there is much
scatter, the mean differences are small. The black curve is a gaussian with zero mean and unity
sigma.
71
0.2
TFIT Mag (Pass2 - Pass1)
0.1
0.0
0.1
3.6
0.2
19
20
21
22
23
Mag_Auto
Figure 3.18 This shows the difference in magnitude between the two passes vs the total magnitude
for the CDF-S IRAC 4.5 epoch 1 mosaic, for isolated sources. The differences between the two
passes are once again minimal.
72
2.5
2.0
R
1.5
1.0
0.5
0.0
-0.5
5.8
8.0
3.6
4.5
2.5
2.0
R
1.5
1.0
0.5
0.0
-0.5
19
20
21
22
23
19
Mag_Auto
20
21
22
23
Mag_Auto
Figure 3.19 For each panel, we present the quantity R (see text) as a function of the IRAC total
magnitude. The different IRAC channels are presented in each panel. The expectation is that the
quantity R would have a value of unity, meaning that the ratio of TFIT to isophotal fluxes would be
equivalent to the ratio of aperture fluxes. We can see that R is about unity and so the flux measured
using isophotes correlates fairly well with the flux measured by TFIT.
73
Chapter 4
Model Exploration, Parameter
Choices, & Diagnostics
4.1
Overview
In order to get a handle on how the semi-analytic models behave as we vary the various
parameters we have to explore how the models behave in both the photometric and physical plane.
Not only will this analysis give us an idea of how strongly the various parameters behave, but also
it will tell us which parameters to vary when doing our analysis, how much to vary them, and which
diagnostics we should be looking at. In the following sections we go over our model exploration and
then state our parameter choices as well the diagnostics that will be used for out fitting analysis.
It is important to note here that this exercise is necessary not only for its educational reasons, but
also for computational reasons. Constructing semi-analytic models is processor-intensive, so it is
imperative to narrow the parameter space before attempting to analytically fit models to data. This
becomes especially apparent when one considers the fact that we have to run multiple iterations
of each model to obtain a sufficient number of points for our fitting analysis (see §6). We run a
74
grid of models based, to start with, on the fiducial model described in §2.3, individually varying
each parameter while holding others constant. Each model is run down to the stellar mass limit of
107 M# , corresponding roughly to a magnitude limit of z850 ∼ 33. Besides computing photometry
and physical properties such as star formation rates, we also independently compute the mean and
variance of star formation rates over smoothed time bins of varying width using the star formation
histories produced by the models such as those in Fig. 2.5. The complete grid of computed models
can be seen in Table 4.1. The final choice of parameters for the fitting analysis can be seen in
Table 4.2. Unlike Table 4.1 however, all of the parameters seen in Table 4.2 were run in all possible
permutations. Whenever we refer to U-, B-, or V-dropouts, we mean that the model galaxies
were processed through the same color selection criteria described in §3.7.2 before being evaluated,
although it must be noted that the color selection criteria were applied on models that have not been
processed through an observational scatter. As a check, we do verify though that the models do
indeed have sensible redshift distributions as compared to simulations carried out in §5 and results
stated in §3.7.2.
4.2
4.2.1
Model Exploration
Dust Parameters
We begin by studying the effect of varying the dust recipes. We study both the power-law
and Charlot-Fall recipes. Fig. 4.1 and Fig. 4.2 show how varying τdust, 0 and keeping βdust constant
affects the rest-frame UV-continuum and Balmer-break colors for B-dropout galaxies. We can see
that varying τdust, 0 between values of 0.1 to 2.0 profoundly affects the rest-frame colors, changing
the colors by several tenths of a magnitude. We see similar behavior for the U-, and V-dropouts. If
we keep τdust, 0 constant but vary βdust instead, we only detect slight variation in the UV-continuum
colors (see Fig. 4.3 and Fig. 4.4). Same type of behavior is observed for U-, and V-dropouts. This
tells us that it makes sense to fix βdust to a constant value while at the same time adopt a coarse
75
Table 4.1. Grid of Parameter Choices
Type
Dust
···
Dust
Recipe
Power-Law
···
Charlot-Fall
Parameters
τdust, 0
0.1, 0.3, 0.5
τV, 0
0.1, 0.5, 1.0, 1.2, 1.5, 2.0
···
µ
···
···
ndust
···
Bursty SF
···
···
···
SNae Feedback
···
Dynamical Time
···
No Bulge
···
Bulge
···
Power-Law
···
0.1, 0.5, 1.0, 1.2, 1.5, 2.0
βdust
···
Quiescent SF
Values
0.05 - 20.0
0.5, 0.6, 0.7, 0.8, 0.9
τ∗0
1.5, 12.0
α∗
2.5
'0burst
0.5
αburst
0.5
'0burst bulge
0.5
αburst bulge
1.5
'0SN
1.0
αrh
2.0
Select parameter choices displayed. To find all values for all other relevant
parameters see §2
grid for the optical depth τdust, 0 parameter. This way we will get a good coverage of model behavior
while focusing our analysis on a narrow range of dust paramters. In the case of Charlot-Fall dust
recipe, we vary τV, 0 , µ, and ndust parameters. Fig. 4.5 and Fig. 4.8 show how varying parameters
that control the optical depth affects the colors of B-dropout galaxies. We see that the Balmer-break
colors are slightly redder for the case where we essentially saturate the optical depth parameters as
opposed to the low-dust case, but the UV-continuum remains largely unchanged. Moreover, it is
apparent that the colors produced by the Charlot-Fall recipe are much too red as compared to the
colors of real Lyman-break galaxies found in §3.7.2. The power-law dust models produce reasonable
colors on the other hand. Varying the slope parameter ndust does not improve things (see Fig. 4.7
and Fig. 4.8) substantially. Similar behavior is observed for both the U-, and the V-dropouts. Either
the Charlot-Fall model does not adequately reproduce the colors of high-redshift galaxies or there
76
is something wrong with our implementation of that model. Because of the significant differences
in the colors and the apparent lack of variation across the Charlot-Fall parameter grid, we exclude
the Charlot-Fall models from our fitting analysis at this time, and instead concentrate our efforts
on the power-law recipe.
4.2.2
Quiescent & Merger-Induced Star Formation Parameters
In Fig. 4.9 and Fig. 4.10 we show the effects of maximizing and minimizing the star forma-
tion rates on the colors of B-dropouts. We produce models where we maximize or minimize both
the quiescent and merger-induced star formation together and independently by choosing proper
parameter values. We can see that there is very little difference between the two color-magnitude
plots when looking at galaxies brighter than z850 < 27. If we go deeper than our magnitude cutoff
and look at quiescent and burst modes separately we begin to note differences. We observe that
models with lower quiescent star formation activity display a higher proportion of red galaxies with
redder Balmer-break colors. Accelerated quiescent star formation models exhibit bluer mean colors.
The photometric differences between the extremes of the quiescent mode are quite apparent even
down to our photometric limits. In contrast though, looking at burst mode recipes, we note subtler
effects. We see that models with higher burstiness display slightly more scatter in the Balmer-break
color distribution down to our magnitude limit. If we drop below our magnitude threshold we see
much more significant differences. Models that have higher burst levels display a larger proportion
of faint and blue objects than low-burst or no burst models. In general, the quiescent star formation
modes display differences more readily down to our magnitude limit, whereas the various bursty
modes mostly exhibit differences below our detection threshold even when we consider the extremes
of burstiness. The only notable differences for the bursty modes down to our magnitude limit occur in the relative Balmer-break color scatter and they are most strongly controlled by the αburst
parameters.
In contrast, when we look at some of the physical attributes of the models like the statistics
77
Figure 4.1 Color-color plots of B-dropout galaxies taken from the fiducial model probing the UVcontinuum and the Balmer-break rest-frame colors. This shows colors from a model with low-dust
(low τdust, 0 ) content.
78
of the star formation histories we see notable differences. Fig. 4.11 shows the normalized variance
of smoothed star formation rates, smoothed over time bins of 10 Myrs, down to z850 ∼ 28, for all
dropouts. We can see that the high star formation model exhibits more positive normalized variance
values. This is due to the higher burst activity of the high star formation model. Interestingly, if
we look at all galaxies we again clearly see the differences in the shapes of the distributions (see
Fig. 4.12). The much broader and uniform distributions exhibited by the high star formation model
are due again to a population of bursting galaxies. Another quantity we can look at is the distribution
of smoothed star formation rates. Fig. 4.13 shows the distribution of star formation rates, smoothed
over 10 Myr time bins. While differences were quite clear when looking at normalized variances,
here the distinctions are more subtle. We have also tried different smoothing bins as well as different
magnitude cuts, however, the apparent lack of distinction remains.
Looking at the photometry and the star formation histories gives us a good idea of how the
models behave when pushed to their limits. If we look at certain star formation history statistics, such
as the normalized variance, we can see clear differences between high and low star formation models.
In contrast, for other statistical quantities, such as the distribution of smoothed star formation
rates, the differences between the two models are not that clear. The situation does not change
when looking at different smoothing bins and magnitude cuts. In the photometric plane and down
to our magnitude limit, the color-magnitude differences between the various bursty star formation
models are seen in the slight width differences in the color distributions. Below our magnitude
threshold we note more significant differences, where we see a higher ratio of bluer galaxies in the
very bursty model. It is difficult to ascertain just how well the different bursty star formation models
will be distinguished when confronted with observational scatter and data. We explored different
color-magnitude combinations to see if we could delineate between the different burst modes with
more effect, but we have not been able to find more useful diagnostics.
Through our exploratory analysis we see that it may be difficult to get a handle on parameters that control the relative burstiness of the models. While the physical diagnostics offer some
79
insight, the photometric differences are small down to our magnitude limit. In light of these facts,
and keeping in mind the behavior of the star formation scaling laws described in §2 we pick parameter values seen in Table 4.2. In the case of quiescent star formation we choose two well-separated
time-scale τ∗0 parameter values of 1.5 and 12.0 so as to provide the widest separation in realistic
model behavior. For the power index α∗ parameter we choose a set of values ranging from 0.0 to 4.5;
where the α∗ = 0.0 case corresponds to the case where the quiescent star formation is independent
of the circular velocity of the disk (see §2.2.6). Fig. 4.16 and Fig. 4.17 show how the Balmer-break
and UV-continuum colors vary for two models with quite different α∗ parameter choices. In the case
of merger-induced star formation we largely choose Cox et al. values (such as the burst threshold,
time-scales, and default efficiencies), although we allow the power indices that control the level of
burst efficiency to vary, using αburst of 0.5, 1.0, 1.5, and αburst bulge of 1.0, 1.5 for the case where a
bulge is present (see §2.2.5). Based on our preliminary work and considering our data limitations
we feel that these parameters will give us the most leverage.
4.2.3
Supernovae Feedback
We decided to see what happens when we vary the supernovae feedback recipes. In Fig. 4.14
and Fig. 4.15 we show two different feedback recipes, the Martin-Heckman and the power-law recipes,
for B-dropouts (recall that we neglect the disk-halo model as it is outdated). We can see that there is
very little difference in the colors between the two models. Recall, that the Martin-Heckman recipe
differs from the power-law recipe only in the sense that the latter depends on the circular velocity.
In fact, running the power-law recipe with αrh set to zero yields exactly the same results as running
the model with the Martin-Heckman implementation. We decided to look at several values of αrh
to see if we can modify the behavior of the model. However, we did not see any notable changes in
photometry, which is not surprising given that the Martin-Heckman and power-law with αrh = 2.0
shows so little difference. We looked at other dropouts and color combinations, but we did not see
any significant differences between the models in the photometric plane. Perhaps our photometric
80
diagnostics are not sensitive enough to distinguish among the supernovae feedback power-law models
that have different αrh values. Because the differences between the models are minute, we decided
to not vary these parameters, but rather keep the power-law fixed to the αrh = 2.0 value.
4.3
Final Model Parameters & Model Run Attributes
We explicitly state all the parameter choices in Table 4.2. Again, these parameters were
computed in all possible permutations (resulting in 144 unique models). Even though we do not
vary the supernovae feedback recipes, we state them as well. All of the remaining values pertinent
to the various recipes are set to the values found in §2. Each model run for the fitting analysis spans
a redshift range of 2 < z < 6, sufficient for our color selection completeness (see §3.7.2), but narrow
enough to minimize processing time. We run each model with two iterations down to the magnitude
limit of z850 < 28. This gives us sufficient number of galaxies for the construction of density functions
(see §6). For each model we compute all of the relevant photometry and we propagate all of the
relevant physical properties. We also compute star formation history statistics, independently from
the model as was the case in §4.2.2. Each model takes approximately 14 hours of processor time.
In addition to these models, we also produce models using the same characteristics and parameter
choices, but using a stellar mass cut of 107 M# , instead of a z850 cut. These models are identical
to the previous ones and they will be used to provide information below the z850 < 28 threshold.
It was necessary to run two separate model runs for each parameter set due to computational
considerations. Finally, based on our experimentation, we decided on using the UV-continuum and
Balmer-break colors and the UV-magnitude as diagnostics for our fitting analysis. The choices of
using UV-continuum and Balmer-break colors stems from our desire to explore the dust content and
the star formation rates of model galaxies. The UV-continuum colors probe the slope of the UV
continuum, which is believed to be primarily an indicator of internal dust content in young stellar
populations (e.g. Meurer, Heckman, & Calzetti 1999). The Balmer-break colors tend to probe the
81
Table 4.2. Final Parameter Choices
Type
Dust
···
Quiescent SF
···
Bursty SF
···
···
···
SNae Feedback
···
Recipe
Power-Law
···
Dynamical Time
···
No Bulge
···
Bulge
···
Power-Law
···
Parameters
τdust, 0
βdust
Values
0.5, 1.0, 1.5
0.3
τ∗0
1.5, 12.0
α∗
0.0, 0.5, 1.5, 2.5, 3.5, 4.5
'0burst
0.5
αburst
0.5, 1.0, 1.5
'0burst bulge
0.5
αburst bulge
1.0, 1.5
'0SN
1.0
αrh
2.0
Select parameter choices displayed. To find all values for all other relevant
parameters see §2
stellar ages and masses. Although these color combinations do not exclusively probe just dust or
stellar ages, due to the effects of dust-age-metallicity degeneracy, historically, they have proved to
approximately work in such a manner (Somerville, Primack, & Faber 2001; Idzi et al. 2004; Papovich,
Dickinson, & Ferguson 2001). The final choices for the U-dropouts (restated in §6) are the V606 - i775
vs i775 and V606 - IRAC 3.6 vs V606 color-magnitude diagnostics. The final choices for the B-dropouts
(restated in §6) are the i775 - z850 vs z850 and z850 - IRAC 4.5 vs z850 color-magnitude diagnostics.
These diagnostics along with the limits used and approximate rest-frame values are stated in Table
4.3. These combinations provided us with the best combination of probing the relevant colors and
magnitudes and retaining close rest-frame correspondence between the two dropout samples.
82
Table 4.3. Diagnostic Choices
Dropouts
U
···
U
···
B
···
B
···
Diagnostic
UV-continuum
···
Balmer-break
···
UV-continuum
···
Balmer-break
···
Selection
V606 - i775
i775
V606 - IRAC 3.6
V606
i775 - z850
z850
z850 - IRAC 4.5
z850
83
Limits
Rest-frame Values (Å)
-0.5 - 1.5
1515 - 1938
20 - 27
1938
-1.5 - 4.5
1515 - 9000
20 - 27
1515
-0.5 - 1.5
1550 - 1700
20 - 27
1700
-1.5 - 4.5
1700 - 9000
20 - 27
1700
Figure 4.2 Same as in Fig. 4.1 but for a model with high-dust (high τdust, 0 ) content. Going above
τdust, 0 of 1.5 does not change colors – indicating saturation.
84
Figure 4.3 Color-color plots of B-dropout galaxies taken from the fiducial model probing the UVcontinuum and the Balmer-break rest-frame colors. This shows colors for a model that uses low
βdust .
85
Figure 4.4 Same as in Fig. 4.3 except for a model that uses high βdust .
86
Figure 4.5 Color-color plots of B-dropout galaxies taken from the fiducial model probing the UVcontinuum and the Balmer-break rest-frame colors. This shows a model with a low dust content.
87
Figure 4.6 Same as in Fig. 4.5 except for a model with a high dust content. The variation in the UVcontinuum colors is very slight. More importantly though it is quickly apparent that the Charlot-Fall
colors are much too red as compared to the real Lyman-break galaxies found in §3.7.2.
88
Figure 4.7 Color-color plots of B-dropout galaxies taken from the fiducial model probing the UVcontinuum and the Balmer-break rest-frame colors. This shows a model with a low ndust .
89
Figure 4.8 Same as in Fig. 4.7 except for a model with a high ndust . The colors are still much too
red as compared to our data, however the low-slope ndust value does produce better UV-continuum
results.
90
Figure 4.9 Color-magnitude plots of B-dropout galaxies taken from the fiducial model probing the
the Balmer-break rest-frame colors. This shows a model with high combined star formation.
91
Figure 4.10 Same as in Fig. 4.9 except for a model with low combined star formation. We can see
very little difference between the low and high star formation color-magnitude plots, except that the
high star formation plot exhibits broader colors when looking at galaxies brighter than z850 < 27.
92
High SFR
z̄3
z̄4
z̄5
Low SFR
-0.5
0.0
0.5
-0.5
Log[7/<sfr>7]
0.0
0.5
Log[7/<sfr>7]
Figure 4.11 Here we can see the difference between the high and low star formation models when
looking at the variance of smoothed star formation rates, smoothed over time bins of 10 Myrs, down
to z850 ∼ 28, for all dropouts. We can see that the high star formation model exhibits more positive
variance values. This is due to the high burst activity of the high star formation model.
93
High SFR
z̄3
z̄4
z̄5
Low SFR
-0.5
0.0
0.5
-0.5
Log[7/<sfr>7]
0.0
0.5
Log[7/<sfr>7]
Figure 4.12 Here we can see the difference between the high and low star formation models when
looking at the variance of smoothed star formation rates, smoothed over time bins of 10 Myrs, for
all galaxies, and for all dropouts. We can see that the high star formation model exhibits broader
distributions. This is due to a population of bursting galaxies.
94
High SFR
z̄3
z̄4
z̄5
Low SFR
-6
-4
-2
0
2
-6
Log[sfr7]
-4
-2
0
2
Log[sfr7]
Figure 4.13 Here we see very little difference between the high and low star formation models.
Nevertheless, we do see that in the case of high SFR model, the bimodal distribution in SFR values,
smoothed over 10 Myr bins, remains, while in the case of low SFR model, the bimodal distribution
dissolves.
95
Figure 4.14 Martin-Heckman feedback model. Essentially, the power-law model with αrh = 0.0.
96
Figure 4.15 We see very little difference between the Martin-Heckman and the power-law feedback
models. Changing the power index αrh makes very little difference. The power-law model shown
uses αrh = 2.0.
97
U-dropout Balmer-break Colors
-1
0
1
2
3
V - 3.6
Figure 4.16 Here we can see the difference in Balmer-break colors for two very different model runs,
where we varied the parameters. The top panel shows a model with α∗ = 0.0, whereas the bottom
panel shows a model with α∗ = 4.5. These models did not have any observational scatter added to
them.
98
U-dropout UV-continuum Colors
0
0.5
1
V-i
Figure 4.17 Same as in Fig. 4.16, but for UV-continuum colors. We can see that the difference in
colors is not as stark as for the Balmer-break colors, however, in this case we have not varied the
dust parameters and so we did not expect much variation in the UV-continuum colors.
99
Chapter 5
Simulations and Observational
Scatter
5.1
ACS Simulations
The Monte-Carlo ACS SExtractor simulations are based on synthetic Lyman-break galaxies
distributed over a wide redshift range (2 < z < 8) with assumed distribution functions of UV
luminosity, SED, morphology, and size, adjusted to match the colors of observed dropouts observed
at the respective redshifts. This technique has been successfully used before by Sawicki & Thompson
(2006), and others. Here we give a brief description of the procedure.
We construct the spectral energy distributions (SEDs) of star forming galaxies using the
(Bruzual & Charlot 1993) spectral synthesis library, with the Salpeter initial mass function and
the solar metallicity with the age of 100 Myr. These SEDs are modeled such that they adequately
represent observed galaxies (Sawicki & Yee 1998; Shapley et al. 2001). Each galaxy is first assigned
a random redshift in the range 2 < z < 6, then dust attanuation is applied using a Calzetti (1997)
extinction curve together with a normal distribution with median E(B-V) = 0.15. Line blanketing
100
ACS Simulation: B-dropouts
N (x1000)
2
1
2.5
3
3.5
4
4.5
Redshift
Figure 5.1 Redshift distributions for B-dropout galaxies taken from ACS simulations.
due to intergalactic neutral hydrogen is then computed using the prescription of (Madau et al. 1996).
Once reddened SEDs are constructed, filters are used to obtain synthetic colors and photometry.
Artificial galaxies are then constructed using IRAF artdata routines. These fake galaxies are then
placed into GOODS mosaics using variable morphology with random orientations and inclinations
and pre-computed magnitude distributions. Profile-wise, the simulated galaxies are split evenly
between disks (exponential surface brightness profiles) and spheroids (r1/4 -law surface brightness
profile). Spheroidal galaxies are assumed to be oblate and optically thin with an intrinsic axial ratio
distribution that is uniform in the range 0.3 < b/a < 0.9. Disk galaxies are modeled as optically
thin oblate spheroids with an intrinsic axial ratio of b/a = 0.05. Each galaxy is assigned a radius
from a log-normal radial distribution. The simulated galaxies are then detected and color selected
101
Semi-Analytic Model: B-dropouts
8
N (x100)
6
4
2
3.5
4
4.5
Redshift
Figure 5.2 Redshift distributions for B-dropout galaxies taken from the fiducial semi-analytic model.
using the same criteria as used in the real sample construction. This allows us to ascertain such
systematics like detection bias, color bias, etc.
Of course with such simulations, one must be aware of possible crowding issues. To this
extent multiple trials were executed to find the best number of fake galaxies. The final simulations
used 200 simulated galaxies at a time, with 200 iterations per image. To obtain enough simulated
data points for the construction of the scatter density functions (see §6) we repeated the procedure
eight times. The detection and photometry was done using SExtractor (akin to what was done for
real data). Master catalogs are then generated that collate all of the input and output magnitudes,
along with whether the simulated objects were recovered or not. With fully-formed catalogs in hand,
redshift distribution functions were constructed for each sample to test the efficiency of color selec-
102
ACS Simulation: Input Colors
4
N (x10000)
3
2
1
0
0.5
1
i_iso - z_iso
Figure 5.3 Input i775 minus z850 colors for the simulated B-dropouts.
tion criteria (see §3.7.2 discussion). The final sample had roughly 320 thousand simulated galaxies.
Fig. 5.1 and Fig. 5.2 shows the distribution of B-dropouts calculated from the simulations using our
color selection criteria, as well as B-dropouts as computed from the fiducial model run. We can see
how well these distributions overlap. Fig. 5.3 and Fig. 5.4 shows the input and output i775 - z850
colors and Fig. 5.5 and Fig. 5.6 shows the input and output V606 - i775 colors. In §6, we show how
these input-output distributions translate to scatter density functions. Finally, in Fig. 5.7 we show
the E(B-V) distribution for the B-dropout galaxies extracted from the simulations.
103
ACS Simulation: Measured Colors
4
N (x10000)
3
2
1
0
0.5
1
i_iso - z_iso
Figure 5.4 Output i775 minus z850 colors for the simulated B-dropouts.
5.2
ACS–IRAC TFIT Simulations
To validate the results from TFIT and to procure scatter density functions we have run
a series of purely synthetic simulations using artificial galaxies for which we know the input fluxes.
Unlike in the ACS simulations, we do not include any of the real data. Ideally, we should, but
computationally this is not feasible. TFIT is a very processor intensive software package, using real
data mosaics would significantly extend processing time. In addition, crowding would be a much
more serious issue. For these reasons and others we choose a purely synthetic approach. For these
tests we use simulated ACS V606 and z850 data for the high-resolution images, and simulated IRAC
3.6 and 4.5 data for the low-resolution image. We randomly generate positions, magnitudes, and
sizes for these galaxies for the high-resolution image. The distributions that we use for the input
104
ACS Simulation: Input Colors
4
N (x10000)
3
2
1
0
0.5
1
V_iso - i_iso
Figure 5.5 Input V606 minus i775 colors for the simulated B-dropouts.
sizes are selected from a log-normal radial distribution and the magnitude distributions are based
on the same distributions as in §5.1. We select an even mix of spiral and elliptical galaxies. The
magnitudes are then transformed based on a gaussian distributions for the V606 - IRAC 3.6 and z850
- 4.5 colors, with µ = 1.7 and σ = 1.5, and µ = 1.1 and σ = 1.5 (respectively), chosen to approximate
the observed properties of the ACS and IRAC images. We used the IRAF task artdata.mkobjects
to generate two high-resolution images containing the simulated objects: one with the simulated
ACS magnitudes and one with the simulated IRAC magnitudes. The latter image is then convolved
(iraf.fconvolve) with an IRAC PSF and re-sampled (iraf.blkavg) to match the IRAC pixel
sampling. The resultant noiseless images are added (iraf.imcalc) to background images generated
using iraf.mknoise to simulate the noise parameters of the two instruments. The noise (RMS)
105
ACS Simulation: Measured Colors
4
N (x10000)
3
2
1
0
0.5
1
V_iso - i_iso
Figure 5.6 Output V606 minus i775 colors for the simulated B-dropouts.
values are derived from the real data mosaic weight maps. Having generated these test images,
we proceed through the usual TFIT pipeline (§3.8): cataloging the high-resolution image, making
cutouts, convolving, culling, fitting, and selecting the best answer for each object. Then, we use the
initial input list to locate the simulated objects (based on cataloged x,y position), and examine the
results.
For simplicity, the initial TFIT simulations were performed using a single pair of objects,
of equal magnitude and varying separation. Those results were analyzed and compared to SExtractor (Fig. 5.8). The nearest-neighbor distances for all objects in the GOODS CDF-S field were
computed and it was found that only a few percent of the objects were sufficiently isolated for optimal measurement by SExtractor in the IRAC field. For approximately 20 percent of the objects,
106
ACS Simulation
N (x1000)
3
2
1
-0.2
0
0.2
0.4
0.6
0.8
E(B-V)
Figure 5.7 E(B-V) distribution for the simulated B-dropouts.
the TFIT measurements would be optimal, while the SExtractor measurements would be degraded.
SExtractor photometry for the remaining 78 percent of the objects would be severely compromised
by deblending failures, while TFIT measurements are only degraded. The case is worse for the
UDF observations, where barely 1 percent of the sources are isolated, and 95 percent are severely
compromised for SExtractor. In all cases, the sense of the error is to overestimate the true flux,
which in our case means over-estimating the true MIR fluxes.
While validating TFIT is important, that task is covered by Laidler et al. (2006) and here
we can only spend so much time discussing the validity. What is more pertinent is to generate largescale simulations of ACS-IRAC catalogs so that we can produce the scatter density functions (see
§6). To assess performance in more realistic conditions, we ran simulations that mimic the number
107
Figure 5.8 Cumulative recovery rates as a function of source separation in the CDFS for simulated
SExtractor and TFIT catalogs. Green refers to results that are as good as for isolated cases for both
SExtractor and TFIT, yellow corresponds to cases where SExtractor produced degraded results and
TFIT gives results as good as for isolated sources, whereas red corresponds to cases where SExtractor
failed to de-blend and TFIT produced degraded results.
density and color characteristics of the V606 - IRAC 3.6 and z850 - IRAC 4.5 data. The simulations
follow the same procedure as described in the previous section, with the addition of a few extra
parameters. We add 220 objects to a 1.7 square arcmin field, with randomly assigned magnitudes
based on the distributions used in §5.1. A color term, drawn from a Gaussian distribution based on
the numbers stated earlier, is added to each object before the simulated IRAC image is created. The
results are then collated and master catalogs are produced with the input and output magnitudes
108
Figure 5.9 IRAC 3.6 PSF used in the simulations.
and whether the simulated galaxies were recovered or not. In all, 200 iterations with 220 objects
per image were generated at each run. Together eight simulations were run, yielding roughly 320
thousand objects for each image pair. Below we post figures that show the effectiveness of the
simulations as well as the input data. Fig. 5.9 and Fig. 5.14 show the input PSF used to convolve
the high-resolution cutouts. Fig. 5.10 and Fig. 5.15 show the resulting fake and real images for the
ACS and IRAC data. Finally, Fig. 5.11 shows the input V606 and z850 magnitude distributions, and
Fig. 5.12, Fig. 5.13, Fig. 5.16, and Fig. 5.17 show the input and output colors for the pair of images
used. The scatter density functions are shown in §6.
109
Figure 5.10 Simulated and actual V606 and IRAC 3.6 mosaics. From top-left, clockwise, we have the
fake IRAC 3.6, real IRAC 3.6, real V606 and fake V606 . We can see that even though the simulations
are purely synthetic, the source density and character are well reproduced in the simulations.
110
V 606
500
300
100
i775
500
300
100
z850
500
300
100
18
20
22
24
Figure 5.11 Input magnitude distributions based on ACS data.
111
26
28
TFIT IRAC Simulation: Input Colors
N (x10000)
2
1
-2
-1
0
1
2
v_input - 3.6_input
Figure 5.12 Input V606 minus IRAC 3.6 colors.
112
3
4
5
TFIT IRAC Simulation: Measured Colors
N (x10000)
2
1
-2
-1
0
1
2
v_iso - 3.6_tfit
Figure 5.13 Output V606 minus IRAC 3.6 colors.
113
3
4
5
Figure 5.14 IRAC 4.5 PSF used in the simulations.
114
Figure 5.15 Simulated and actual V606 and IRAC 4.5 mosaics. From top-left, clockwise, we have the
fake IRAC 4.5, real IRAC 4.5, real z850 and fake z850 . We can see that even though the simulations
are purely synthetic, the source density and character are well reproduced in the simulations.
115
Figure 5.16 Input z850 minus IRAC 4.5 colors.
116
Figure 5.17 Output z850 minus IRAC 4.5 colors.
117
Chapter 6
Methodology
6.1
Overview
In this chapter we describe the full machinery that is needed to accomplish the likelihood
analysis method used in this project. We go over each component of the analysis and refer the
reader to other chapters and section where needed. To get an overview of our analysis method it is
perhaps easiest to start with a view of a flow chart (Fig. 6.1) that shows the various components of
the analysis and how these components interact with one another.
From a computational point of view the goal of the project is to compare semi-analytic
models to real Lyman-break galaxies using photometric information only. We saw in Idzi et al. (2004)
how one can make significant progress in comparing models to data by using strictly qualitative
analysis, or simple quantitative techniques. However, a more robust statistical analysis becomes
a far more powerful tool in delineating which models work, since a more rigorous technique can
provide us with more robust results along with confidence intervals, which in turn provides more
insight into the physics that we are trying to probe.
118
Figure 6.1 Here we see the flow of the likelihood analysis used in this project.
6.2
Data
First, the data used for the analysis is composed of the U-, and B-dropout samples described
in §3.7.2. We refer the reader to that section for the details on the data samples. Briefly though,
the data for the likelihood analysis is composed of 569 and 275 sources taken from the CDF-S Uand B-dropout samples. Each source has SExtractor-derived fluxes and errors for the V606 , i775 ,
z850 data, and TFIT-derived fluxes and errors for the IRAC 3.6 and 4.5 data. The IRAC data is
either composed of single or dual-epoch data depending on coverage and quality of the epoch data.
In addition, these sources already have pre-applied flag and signal-to-noise cuts as defined in §3.7.2.
119
6.3
Models
In §2 we described in great detail the semi-analytic code used in this work, and in §4 we
described and justified the choice of input parameters and diagnostics used. We also elaborated on
how each model set was run. Here we simply restate few items and describe how we formatted the
models to work in the context of the analysis we adopted. To begin with, recall that we ran a grid
of 144 models with the input parameter choices given in Table 4.2. Each model run was conducted
in a survey mode spanning the GOODS area, in the redshift range of 2 < z < 6 to fully capture the
Lyman-break samples used in this work . For each set of model parameters, we ran three iterations
in total, two iterations in a magnitude cut-off mode where only galaxies brighter than z850 ∼ 28 were
output, and one iteration in a stellar-mass limit cut-off mode where galaxies with M∗ > 107 M# were
kept. The magnitude-limited model runs were then used to construct model density functions needed
for the statistical analysis, whereas the mass-limited model run was used as a supplemental catalog
that contained properties of galaxies fainter than z850 ∼ 28, all the way down to galaxies with total
stellar masses of M∗ ∼ 107 M# (roughly z850 ∼ 33). This rather inelegant procedure was necessary
since running multiple iterations of the models in the mass-limited mode would have produced very
large output files that would prove difficult to handle for further analysis. Therefore, we decided
to simply keep the larger mass-limited files separate from the magnitude-limited ones used for the
creation of density kernels. It is important to remember however that the mass and magnitude
cut-offs strictly apply to the output data and so the underlying model runs were statistically the
same, drawn from the same model parameters.
As mentioned, we use the magnitude-limited models to construct density functions. Even
though we limit the models to a z850 < 28 depth, this is sufficient for the analysis since at this
,S∼ 3). In fact, in
z850 magnitude our real Lyman-break samples becomes very incomplete ( N
850
,S∼ 5). The
our analysis we don’t probe models with magnitudes fainter than z850 > 27 ( N
850
dual-iteration for the model run is necessary to obtain sufficient number of artificial Lyman-break
120
Table 6.1. Diagnostic Limits & Resolution
Dropouts
U
···
U
···
B
···
B
···
Diagnostic
UV-continuum
···
Balmer-break
···
UV-continuum
···
Balmer-break
···
Selection
V606 - i775
i775
V606 - IRAC 3.6
V606
i775 - z850
z850
z850 - IRAC 4.5
z850
Limits
Bins
Resolution
-0.5 - 1.5
200
0.01
20 - 27
200
0.035
-1.5 - 4.5
200
0.03
20 - 27
200
0.035
-0.5 - 1.5
200
0.01
20 - 27
200
0.035
-1.5 - 4.5
200
0.03
20 - 27
200
0.035
galaxies for the construction of our density functions. We require a sample of, at a minimum, ∼ 5000
galaxies to construct robust density functions with the limits and bin choices we adopt. Such large
number is necessary since we require a fine resolution in both the magnitude and color space. We
construct density kernels that are 200 × 200 bins on each side, which in the case of the B-dropouts
UV-continuum diagnostic translates to a resolution of 0.035 in magnitude space and 0.01 in color
space, where the limits are: -0.5 < i775 -z850 < 1.5 and 20 < z850 < 27. To sufficiently populate such
fine resolution and to avoid falling victim to low-number statistics, we require the ∼ 5000 sample
limit. We refer the reader to Tables 4.3 and 6.1 for the diagnostic limits and resolution information.
For each model we then construct model functions that are used for further analysis. We
construct these density functions for each dropout-diagnostic combinations, which means we construct four separate templates for each model (UV- and Balmer-break diagnostics for U- and Bdropouts). We produces the dropouts samples by applying the same color Lyman-break selection
criteria stated in §3.7.2, so that the model and data galaxies are selected in a uniform manner. Once
the samples are generated and they have sufficient number of sources we proceed to construct the
actual model density functions. This is accomplished by using a kernel-based probability density
estimator code KPDFadapt (see Silverman (1986) for the mathematical background) to construct a
121
smooth estimate of the density from the discreet data that are output from a semi-analytic model
run (see Fig. 6.2-6.5 for density function examples). Each cloud of model points consists only of
those that fall within the given color-magnitude limits. Once smoothed, the model is normalized
by the integral of the binned 2-D array. Once we generate one set of model density functions we
repeat this same procedure for the remainder of the models. Since this is a time-consuming process
we generate the density kernels once and save them as FITS files.
6.4
Observational Scatter
The next step involves adding an observational scatter to the model density functions.
Recall, that so far we have not added any scatter to the models. We simply took the generated
models, applied color-selection criteria and produced the model density functions. So now we have
to generate observational scatter functions that will take the input model magnitudes and colors
and in effect ’translate’ that information to include the observational scatter that emulates the
behavior of our real data. We generate these scatter functions using catalogs generated by the
Monte-Carlo simulations described in §5. We use the same kernel-based code KPDFadapt as a
foundation to generate the scatter kernels. For each simulated catalog we take the input and output
magnitudes and the recovery information and translate that information into a series of 2-D scatter
density functions. We construct an 8 × 8 matrix of density kernels in the color-magnitude plane
for each diagnostic. For example, for the U-dropout UV-continuum V606 - i775 vs i775 diagnostic,
we construct 64 kernels each of magnitude bin width of 1.75 and color bin width of 0.5, centered
on input magnitude and color information. Fig. 6.6-6.9 show a sample of coarser (3 × 3) kernel
matrices for all of the diagnostics. Note in the kernel figures, how the kernels degrade as we move
to very red and very faint bins. This is a behavior we expect from observed data. With the scatter
density kernels produced, we now convolve (see Eq. 6.1) the (normalized) models density functions
(fm ) by the scatter density functions (fs ) for each diagnostic to produce the scattered model density
122
functions (fsm ). Fig. 6.11 shows sample raw model density functions and scattered model density
functions.
fsm = fm × fs
6.5
(6.1)
Likelihood Analysis
With the scatter properly folded into the model density functions we are now ready to
compute log likelihood values using data points from §6.2 and the observationally-scattered models
found in §6.3 and §6.4. For each Lyman-break and diagnostic combination, we take the data and
construct color-magnitude arrays, masked over pre-specified limits, and put on the same grid as the
models. We compute the log likelihood values for each model by first normalizing each model with
an integral of the model density and the number of data points, then taking the product of the data
and the log of the normalized model, and finally taking the integral of the result. This gives us the
total log likelihood value for the tested model. We can capture this process in the following relation:
log L =
2
D × log fsm
(6.2)
where log L designates the log likelihood, fsm is the (normalized) scattered model density function,
and D designates the data.
As stated, we compute log likelihood values for each model set, using the two dropout
samples and the UV-continuum and Balmer-break diagnostics. We can then derive the best-fit
model for each diagnostic and dropout sample, as well as the best-fit model for combinations of
diagnostics and dropout samples. In order to assign confidence intervals for the best-fit models and
to test the stability of those fits we generate Monte-Carlo realization of the fits. This is accomplished
in three separate ways. First, for each real dropout sample, we boot-strap the photometric errors.
123
The observed galaxy fluxes are assumed to have a gaussian distribution with the mean flux equal to
the observed flux value and σ equal to the flux error. The flux in each filter for each galaxy is replaced
by a value drawn at random from this distribution. The log likelihood value for the model with the
relative maximum log likelihood is re-calculated. This procedure is repeated 500 times to determine
the 68%, 95% and 99.9% confidence intervals on the best-fit log likelihood value. The 68%, 95%,
and 99.9% confidence interval values on the best-fitting model log likelihood value are compared to
original grid of log likelihood values for all tested models. Models with likelihood values less than
the 99.9% confidence interval value can be ruled out, while models with likelihood values greater
than the 68% confidence interval cannot be distinguished from the model with the relative maximum
likelihood. This tells us which model parameters are best-fit and which can be ruled out. In the
second procedure, we do something similar, but instead of drawing from the data, we draw random
points from the best-fit model. We use the best-fit scattered model density function and we draw,
at random, points from that distribution. Effectively re-rebinning the color-magnitude information
at each step. We then reconstruct a new scattered model density function and we re-compute the
log likelihood value. We repeat this process 500 times and once again construct confidence intervals
and compare those results to the results from the first procedure and the original likelihood values.
While the first procedure allows us to study the stability of the results against the photometric
errors in the data, the second procedure allows us to to study the variability of the model density
functions of the best-fit models. In the third, and final procedure, we repeat the second procedure,
but for all models. This gives us new log likelihood values for each model. We repeat this procedure
100 times, and rank the results to test the stability of the analysis across all models. These three
procedures allow us to assign confidence intervals and test the stability of our analysis. In turn this
allows us to state which model parameters work and which can be excluded based on our procedure
and the available data.
124
Figure 6.2 A sample model density function (kernel) for a U-dropout model sample. The vertical
axis corresponds to -0.5 < V606 -i775 < 1.5 and the horizontal axis corresponds to 20 < i775 < 27
125
Figure 6.3 A sample model density function (kernel) for a B-dropout model sample. The vertical
axis corresponds to -0.5 < i775 -z850 < 1.5 and the horizontal axis corresponds to 20 < z850 < 27
126
Figure 6.4 A sample model density function (kernel) for a U-dropout model sample. The vertical
axis corresponds to -1.5 < V606 - IRAC 3.6 < 4.5 and the horizontal axis corresponds to 20 < V606
< 27
127
Figure 6.5 A sample model density function (kernel) for a B-dropout model sample. The vertical
axis corresponds to -1.5 < z850 - IRAC 4.5 < 4.5 and the horizontal axis corresponds to 20 < z850
< 27
128
Figure 6.6 A grid of scatter density functions for the V606 - i775 vs i775 diagnostics. Note the
degradation in kernels as we move to very red and very faint bins.
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Figure 6.7 A grid of scatter density functions for the i775 - z850 vs z850 diagnostics. Note the
degradation in kernels as we move to very red and very faint bins.
130
Figure 6.8 A grid of scatter density functions for the V606 - IRAC 3.6 vs V606 diagnostics. Note the
degradation in kernels as we move to very red and very faint bins.
131
Figure 6.9 A grid of scatter density functions for the z850 - IRAC 4.5 vs z850 diagnostics. Note the
degradation in kernels as we move to very red and very faint bins.
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1.5
1.0
0.5
0.0
-0.5
20
21
22
23
24
25
26
27
21
22
23
24
25
26
27
1.5
1.0
0.5
0.0
-0.5
20
Figure 6.10 U-dropout V606 - i775 vs i775 for model density (top panel) and observationally scattered
model density (bottom panel).
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Figure 6.11 The left panel shows the raw model density function, whereas the right panel shows the
model density function convolved with the matrix of computed scatter functions. We can see the
effect of applying observational scatter to the raw models.
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Chapter 7
Results & Discussion
7.1
Best-fit Model(s)
After the analysis carried out in §6 we collated all of the results for each of the dropout
samples and diagnostics. In Table 7.1 we list the best-fit model for each of the dropout-diagnostic
combinations. We can see that each dropout sample favors only one model. This is interesting as
we have not forced any a priori arguments on the models. The diagnostics used for the two dropout
samples could have favored entirely different models. We see however that only one model is favored
Table 7.1. Best-fit Models
Dropouts
Diagnostic
Model
τ∗0
α∗
αburst
αburst bulge
τdust, 0
U
UV-continuum
93
12.0
0.0
1.5
1.5
1.5
U
Balmer-break
93
12.0
0.0
1.5
1.5
1.5
B
UV-continuum
237
12.0
0.0
1.0
1.0
1.5
B
Balmer-break
237
12.0
0.0
1.0
1.0
1.5
Select parameter choices displayed. To find all values for all other relevant parameters see
§2
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Table 7.2. Models Within the 68% (in bold) & 99.9% Confidence Intervals.
log L
τ∗0
α∗
αburst
αburst bulge
τdust, 0
93
-9963.45
12.0
0.0
1.5
1.5
1.5
75
-9722.25
12.0
0.0
0.5
1.5
1.5
219
-9689.77
12.0
0.0
1.0
1.5
1.5
237
-9685.66
12.0
0.0
1.0
1.0
1.5
147
-9548.18
12.0
0.5
1.0
1.5
1.5
165
-9538.21
12.0
0.5
1.0
1.0
1.5
21
-9535.23
12.0
0.5
1.5
1.5
1.5
3
-9526.60
12.0
0.5
0.5
1.5
1.5
Model
Likelihood values are the total likelihoods taken across all samplediagnostic combinations.
Select parameter choices displayed. To find all values for all other relevant parameters see §2
Table 7.3. Best-fit Models (Refit)
Model
τ∗0
α∗
αburst
αburst bulge
τdust, 0
75
12.0
0.0
0.5
1.5
1.5
93
12.0
0.0
1.5
1.5
1.5
237
12.0
0.0
1.0
1.0
1.5
219
12.0
0.0
1.0
1.5
1.5
Select parameter choices displayed. To find all values for
all other relevant parameters see §2
for each dropout sample, and moreover, only two, very similar models, describe all redshift slices
and color diagnostics. However, this alone does not provide any substantive insight since we lack
information on the relative confidence of the fits. As per discussion in §6.5 we carried out three
separate Monte-Carlo tests. Drawing random data sets and re-fitting those to the best-fit model for
each dropout-diagnostic combination yielded similar results to our second confidence test which was
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based on drawing random samples from the best-fit model and then re-computing the log likelihood
value. In Table 7.2 we list all of the models that fall within the 68% and 99.9% confidence envelopes
for the cumulative dropout-diagnostic results. The second test yielded broader confidence intervals,
so we used the results of the second test for Table 7.2 in order to be conservative. Models outside
of the 99.9% interval can be ruled out, while models within it cannot. Moreover, models within the
68% confidence interval cannot be distinguished amongst one another. With confidence intervals
assigned to our best-fit models we can now discuss which of the semi-analytic models are favored
given our data sets and our methodology. However, before proceeding to the discussion of the
scientific implications of our results, we ran our third Monte-Carlo test to test for the stability of
our results. Table 7.3 lists the best-fit models when we applied our second test, but to all models.
That is for each model we re-computed – multiple times – the log likelihood values by drawing
random samples from the smeared model density functions and then ranking the results. We can see
that the order remains similar to that in Table 7.2, in that all of the re-fit models fall within the 68%
confidence interval. We can therefore state that models 93, 75, 219, and 237 are our best-fit models
using the diagnostic and dropout samples employed in this work. Again, this is without applying
any a priori constraints. In Fig. 7.1 we show a mosaic of color-magnitude density functions for the
overall best-fit model – model 93. In Fig. 7.2-7.5 we show plots of data points that were randomly
drawn from the scattered model density functions of our best-fit model – model 93. We can compare
these figures to the real data figures in §3.7 to see the relative agreement between the model and
the data photometric colors. We also show sample Balmer-break colors for the B-dropouts of one of
the poor-fit models (see Fig. 7.6). Furthermore, the top four models and models 147, 165, 21, and 3
are the only models that are not ruled out by our analysis. A quick glance at Table 7.2 reveals that
the models residing in the 68% confidence interval possess the same values for the parameters that
control the quiescent star formation and the relative dustiness. In contrast, there is a high-degree
of variability in the parameters controlling the relative burstiness of the models. Taking account of
all the models down to the 99.9% confidence interval shows the same behavior, except that the α∗
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parameter takes on a different value. We discuss the implications of these results below.
7.2
7.2.1
Parameter Fits – Implications
Burst-driven Star Formation Parameters
It is quite clear from Table 7.2 that our methodology and the available data have failed
to narrow down the αburst and αburst bulge parameters. In the 99.9% confidence interval, nearly
all permutations are possible. Recall from §2.2.5 that the two burst parameters used for the fitting
control the degree of dependence of burst efficiency on the relative mass ratios of the merging galaxies.
Higher αburst and αburst bulge parameter values indicate a strong dependence on the relative mass
ratio, smaller values indicate the opposite. Stronger dependence leads to more efficient bursts, that
is more available cold gas is turned into stars. However, as stated, it is hard to tell whether stronger
or weaker dependence is preferred, nor can we rule anything out. Looking back at our exploratory
work in §4 this apparent lack of definitive results is most likely a sign that our tests are not sensitive
enough to distinguish between the various αburst and αburst bulge values. Most likely this is due to the
relatively large scatter in the data. From §4 we know that the burst parameters affect the width of
scatter in our color-magnitude diagnostics, however, the relative difference in scatter is quite subtle.
The data sets used in our likelihood analysis simply cannot discern between the low and high αburst
values. In addition, as was shown in §4, the remaining burst parameters that control burst efficiencies
exhibit even subtler effects in our color-magnitude diagrams down to our magnitude limit of z850
< 27. Indeed we require to go much fainter in z850 to observe significant differences in the relative
effects of burstiness in our models. As was stated in §4 the color differences between models with
high degree of burstiness and those that have low burstiness, are only apparent at the faint end,
fainter than z850 ∼ 27. If we probe to z850 ∼ 30 we notice that models with high degree of burstiness
exhibit roughly the same Balmer-break color mean as model with low degree of burstiness, but the
former exhibit many more blue objects. That is we observe a tail of faint and blue objects in very
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bursty models. Looking at the distribution of stellar masses and star formation histories for these
objects reveals that these are largely moderately massive objects that have recently undergone a
merger-induced star formation burst. The magnitude cutoff imposed by our current data results
in us missing many of these faint and blue galaxies. The current implementation of burst-driven
star formation recipe results in only subtle observational effects down to our current photometric
limits. With our current data set, our likelihood analysis fails to discern the relative importance of
burstiness. Substantially deeper data is required to observe the fainter end and perhaps help discern
among the different burst modes.
7.2.2
Quiescent Star Formation Parameters
In the case of parameters controlling quiescent star formation, namely τ∗0 and α∗ , our
models favor a τ∗0 = 12 and an α∗ = 0. The high τ∗0 value corresponds to longer time-scales. From
our exploratory tests in §4, a high τ∗0 value has a much narrower Balmer-break color distribution,
especially at the red end, where a low τ∗0 value has a long red tail. In addition, the mean of
the distribution is significantly bluer in the case of the high τ∗0 value. Our likelihood analysis
excludes models with low τ∗0 . Therefore our likelihood analysis favors models that exhibit accelerated
quiescent star formation; models with enhanced stellar mass production (see §2). These models
produce distribution of galaxies with much narrower Balmer-break color distributions, along with
bluer mean color. The models that fail, or are excluded by our fits, exhibit color distributions that
are much too broad and much too red, on the order of 0.5 mag to red. The α∗ corresponds to the
power index on the circular velocity dependence with respect to the star formation rate (see §2.2.6).
In our work in Idzi et al. (2004) (and the work done by Somerville, Primack, & Faber (2001)) we
used high α∗ values to construct our models. This was in large part due to historical reasons, since
models with high α∗ values matched high-redshift observations quite well, qualitatively speaking.
However, low α∗ could not be ruled out from our earlier work. Through this analysis though we
see that low α∗ values are preferred, and that the high and even moderate values are excluded.
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Indeed, models within the 68% confidence interval all favor α∗ = 0, indicating no direct dependence
on circular velocity. If we include models out to the 99.9% limit, we see models with α∗ = 0.5,
indicating a weak explicit dependence on circular velocity. In §4 we saw how varying α∗ affected the
UV and Balmer-break color distributions (see Fig. 4.16 and Fig. 4.17). The favored models exhibit
Balmer-break color distributions that are relatively broad with a long tail on the blue end. The mean
of the color distribution is also bluer relative to the cases with high α∗ . Even though the UV-color
distribution does not exhibit a strong difference, we still see a bluer color distribution for our best-fit
models. The favored quiescent star formation recipe seems to indicate that the star formation rate
depends exclusively on the product of the time-scale τ∗0 parameter and the dynamical time (see
§2.2.6). The quiescent star formation rate seems to be independent or very weakly dependent on
the circular velocity. The α∗ in our recipe creates a relation between color and luminosity that may
or may not exist in the data, so it seems that the data favors models that do not, or very weakly,
scale the star formation rate with galaxy’s circular velocity.
7.2.3
Dust Parameter
The optical depth parameter, τdust, 0 , is favored to be high. Indeed, back in §4 we extensively
tested the parameters controlling dust and we saw how our preliminary analysis favored more dusty
models. This only re-affirms that high optical-depth models are favored over those with moderate
and low dust. Moreover, the best-fit values of the dust parameter corresponds to the empiricallyderived values found by previous research for the high redshift galaxy population. We now present
the various properties of the best-fit model – Model 93 – galaxies, specifically those pertaining to the
stellar-mass assembly. We include results of V-dropout galaxies, even though we did not explicitly
fit the V-dropout sample.
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7.3
Properties of High-Redshift Galaxies
In Fig. 7.7-7.9 we show the stellar masses of our color-selected model galaxies. The stellar
masses range from 108 to 1010 M# , which is roughly 1.5 orders of magnitude less than the stellar
masses of the present day L∗ spirals and ellipticals – this indicates that the Lyman-break galaxies
are not the fully assembled progenitors of the present-day L > L∗ galaxies (Giavalisco, Steidel, &
Macchetto 1996; Steidel et al. 1996a), and that several generations of merging events, or higher
star generation per event, must take place between V-dropouts and the present epoch. The median
masses of the U-, B-, and V-dropout samples are Log[Mstar ] ∼ 9.75, 9.65, and 9.62, respectively.
The median masses were computed for galaxies brighter than V606 < 27, i775 < 27, and z850 < 27
(∼ 1500 Å), respectively. The median mass for the B-dropouts is about 0.5 dex higher than that
seen in Idzi et al. (2004). The progressive increase in the median stellar mass indicates growth
in stellar content. We also note that even though it is not till the U-dropout population that we
observe galaxies with Log[Mstar ] ∼ 11, the V-dropout population exhibits galaxies on the order of
Log[Mstar ] ∼ 10.5, implying significant stellar populations already present by z ∼ 5 epoch.
To further explore the last point we have looked at the mean stellar masses of all L∗
galaxies measured in rest-frame UV and predicted by our model at z ∼ 3 and z ∼ 4. We find that
at z ∼ 3, with m∗ = 24.358 (UV rest- frame), we get a mean value of Log[Mstar ] = 10.65 (M# ) in a
m∗ ± 0.5 magnitude interval, and at z ∼ 4, with m∗ = 24.998 (UV rest-frame), we get a mean value
of Log[Mstar ] = 10.40 (M# ), again in a m∗ ± 0.5 magnitude interval. This corresponds to a mass
build-up of approximately ∼ 77%. This type of mass build-up between z ∼ 4 and z ∼ 3 is larger
than what was seen by Idzi et al. (2004), where a 40% build-up was seen. However, we note that our
best-fit model predicts much more massive galaxies in those epochs than the results predicted in Idzi
et al. (2004). The mean stellar masses of L∗ galaxies are about a factor of 10 bigger in this case. We
also see a similar stellar mass build up between the z ∼ 4 and z ∼ 3 epochs, albeit somewhat smaller
in scale (∼ 50%). The results remain nearly the same for all of the other models within the 68%
141
confidence interval. In fact, all of the models down to the 99.9% confidence interval exhibit similar
results. It is only when we consider models outside of this statistical envelope where we begin to
see significant differences, however, those models are ruled-out by our analysis. This behavior holds
true for the rest of the properties described here.
Drawing on the stellar mass distribution results we plot in Fig. 7.10-7.12 the mass distributions of all (i.e. not just color-selected) galaxies from our mock catalog, limited to galaxies with
Log[Mstar ] greater than the median values found in Fig. 7.7-7.9 and spanning the corresponding
dropout sample redshift range. We select roughly ∼ 80 − 90% of model galaxies with our color
selection criteria, down to the limiting magnitudes. In terms of stellar mass, we select 91, 87, and
77% of the stellar mass for the U-, B-, and V-dropout samples. Hence, with our color criteria,
we ’observe’ the vast majority of the stellar mass that resides in galaxies more massive than the
respective median Log[Mstar ] values quoted earlier. However, if we include all galaxies down to our
model run stellar mass cut, not just the ones more massive than the median Log[Mstar ], we recover
only 69, 56, and 36% of the stellar mass for the U-, B-, and V-dropouts. Even though our stellar
mass recovery rate is better than what we have seen in our preliminary studies (Idzi et al. 2004),
the current optical survey still only recover the most-massive and most UV-bright galaxies. We miss
large portions of stellar mass which resides in UV-faint galaxies. Moreover, we still miss nearly a
quarter of the stellar mass from the relatively massive UV-faint V-dropout galaxies. In contrast
though, the stellar mass recovery rates are quite high for the relatively massive and UV-bright Uand B-dropout galaxies.
The best-fit model also provides us with the mean ages of our color-selected galaxies. In
Fig. 7.13-7.15 we show the distribution of stellar-mass-weighted ages. The median ages of the U-, B-,
and V-dropout samples are 550, 350, and 240 Myrs, respectively. Again, as with the median stellar
masses, these values were computed for galaxies brighter than V606 < 27, i775 < 27, and z850 < 27,
for the U-, B-, and V-dropout samples. As expected, the median stellar age becomes progressively
older from epoch to epoch. The spread in ages also gets broader. The oldest galaxies in the U-, B-,
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and V-dropout samples are 1.2 Gyr, 730, and 500 Myrs old, respectively. In each sample though,
there is a broad range of both young and old galaxies indicating active star formation. In addition,
the median age of 240 Myrs for the V-droputs indicates that even by the z ∼ 5 epoch substantial
star formation events were taking place. This is further supported by a tail of Log[Mstar ] > 10.0
galaxies seen in the V-dropout distribution. The maximum ages fit within the ages permitted by
our adopted cosmology. The oldest V-dropout galaxies (at ∼ 500 Myrs) are about half the age of
the universe at that epoch.
In addition to stellar masses and mean ages of our color-selected galaxies, we can also look
at the smoothed SFRs of the sample galaxies. In Fig. 7.16-7.18 we show the distribution of star
formation rates. The median SFRs of the U-, B-, and V-dropout samples are 5.62, 7.76, and 10.72
M# per year, respectively. Once again, as with the median stellar masses and the mean ages, these
values were computed for galaxies brighter than V606 < 27, i775 < 27, and z850 < 27, for the U-,
B-, and V-dropout samples. The maximum SFRs for each sample are 120.0, 75.8, and 65.5 M# per
year. We can see that in our best-fit model, the star formation rates are fairly steady across the
various epochs, rising steadily when we move towards the z ∼ 3 epoch. The raw numbers are similar
to those found in previous works (Idzi et al. 2004; Somerville, Primack, & Faber 2001).
With regards to star formation, a useful diagnostic to look at is the mean time since last
merger. We find that the values of the median time since last merger event are 900, 600, and 450
Myrs, for the U-, B-, and V-dropout samples down to the V606 < 27, i775 < 27, and z850 < 27
limits. We see the trend of merging events becoming less common, in an average sense, as we go
from z ∼ 5 to z ∼ 3. However, the distributions for time since last merger events are very broad,
spanning instances where galaxies just underwent a merger to instances where the time since last
merger is comparable to the age of the universe at the given epoch. For example, the distribution
for U-dropouts goes from 0.0002 to 2.5 Gyrs, with a mean of 0.9 Gyr and standard deviation of
0.5 Gyr. This indicates that mergers are quite active throughout all of the redshift slices studied
here. We also find that about 10% of U-dropout galaxies have undergone a major merger within
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the past 500 Myrs, where a major merger occurs when the ratio of the masses of the two merging
galaxies is at least 30%. For B-, and V-dropouts this ratio goes up, as expected, to 20% and 36%,
respectively. Looking at all mergers, the ratios for the U-, B-, and V-dropouts are 18%, 30%, and
54%, respectively.
Finally, we can contrast our results to ISAAC-selected galaxies that had SEDs fitted to
them by Wiklind et al. We can compare the derived ensemble parameters to the results from our
best-fit model – model 93. As a first step we position match the ISAAC-selected galaxies to the
U- and B-dropout samples to select matching sources. We then compute some simple statistics.
We find that 319 sources out of 569 available U-dropouts are matched against the ISAAC-selected
catalog. For B-dropouts we find 77 out of 275 sources. We find that the median log stellar mass is
around 9.57 for the U-dropout matched sample, and around 10.5 for the B-dropout matched sample.
These numbers compare favorably to the best-fit model (model 93) results, however the B-dropout
matched sample’s log stellar mass is 0.4 mag higher than our best-fit model results. Indicating
perhaps that the ISAAC-selected catalog has preferentially more massive Lyman-break dropouts.
Looking at the mean ages we get 226 and 411 Myrs for the U- and B-dropout matched samples,
respectively. Although the B-dropout matched sample’s age compares favorably to the median bestfit model (model 93) age of 350 Myrs, the U-dropout matched sample’s age is considerably lower
than the median best-fit model (model 93) age of 550 Myrs.
7.4
Summary
In this project we adopted a robust approach to investigate several fundamental properties
of Lyman-break galaxies by statistically comparing photometric observations with the predictions
of semi-analytic models based on the Cold Dark Matter theory of hierarchical structure formation.
We used a sample of U and B435 -dropouts from the Great Observatories Origins Deep Survey, and
complemented the ACS optical B435 , V606 , i775 , and z850 data with the VLT ISAAC J, H, and Ks
144
and IRAC 3.6, 4.5, 5.8, and 8.0 observations. We ran a set of 144 semi-analytic models, varying
parameters that control the star formation rates and the relative dustiness of model galaxies. We
then extracted U , B435 , and V606 -dropouts from our semi-analytic mock catalogs using the same
color criteria and magnitude limits that were applied to the observed sample. Using the input model
catalogs, we constructed density functions gridded in color-magnitude space and convolved those
density functions with observational scatter templates derived from Monte-Carlo data simulations.
We then computed likelihoods using the data and the scattered model density functions for UVcontinuum and Balmer-break color-magnitude diagnostics. Finally, we ran Monte-Carlo simulations
to assign confidence intervals and to test the overall stability of our results.
We adopt a forward treatment approach in our analysis. In the traditional approach individual galaxies are fit by spectral energy distribution functions in order to derive physical quantities
such as stellar masses, ages, dust extinctions. There are a number of disadvantages to the traditional
approach. The star formation histories are highly simplistic (i.e. they have singular metallicity, no
bursts, no dependence of extinction on past history, etc.). There is no explicit requirement that
there be any self-consistency in the results from galaxy to galaxy, or epoch to epoch. Moreover, it is
very difficult to take into account systematic biases in the photometry and survey incompleteness. It
is also difficult to draw conclusions of the parent populations of observed galaxies. The traditional
approach speaks to the observed population only. In the forward treatment that we adopt here
we construct noise-free models and subject them to all of the observational imperfections that we
can account for prior to making our statistical comparisons to the data. Rather than attempting
to derive physical quantities galaxy by galaxy, we look at the ensemble of quantities derived from
the models that we find consistent with the data. We also enforce epoch-to-epoch self-consistency
by summing derived likelihoods across redshift slices. Regardless of the merits of a particular star
formation prescription invoked by our models, we at the very least produce a valuable cross-check
on the simplistic models, with an accounting of merging, chemical evolution, and dust that vary in a
sensible way with cold gas mass, metallicity and other variables. In the end, the comparison of our
145
model-derived quantities like mean extinction (and variance), mean age, stellar mass, etc. to the
quantities assigned by simplistic models can give us a much better appreciation for whether these
derived physical quantities are robust.
We find that given our data, models, and our methodology we can rule out certain models
and state which models are preferred. We find that our models favor high dust content and exclude
low dust content models. Furthermore, the optical depth value that yielded the best fit corresponds
to the relative dust abundances observed in the real, high-redshift galaxy populations. We are unable
to discern among models with varying burst efficiencies. The effects of the burst parameters that we
chose to vary, which mainly affect the scatter in the color distribution, are too subtle compared to the
relatively large scatter in the data. The remaining burst parameters that we chose to hold fixed would
not be easily discerned either. In the observational plane, the most significant differences between
the less-bursty and the more-bursty models occur at magnitudes below our detection threshold.
We would need to probe fainter magnitude limits in order to note significant differences among
the various burst modes. The determinant factor, according to our models, lies in the faint, blue,
moderately massive galaxies that have recently undergone an episode of star formation. The more
bursty modes exhibit a larger proportion of these types of galaxies. In addition to varying the
relative burstiness of our models, we explored the effects of quiescent star formation. We looked at
both quiescent and enhanced quiescent models. Our analysis favors models with enhanced quiescent
star formation. The low τ∗0 models are excluded by our fits as they yield Balmer-break and UV
color distributions that do not match our dropout data. The Balmer-break colors of the excluded
τ∗0 models are too red relative to the data, indicating that the data favors models with a higher
ratio of young stellar populations to the old ones. In other words, the enhanced quiescent star
formation mode is preferred. In addition, we find that our best-fit models rule out any strong
explicit dependence of star formation on circular velocity in our quiescent star formation scaling
law. The data shows no explicit correlation between the star formation rate and galaxy’s circular
velocity. It is important to note though that this finding does not state that there is no dependance
146
on circular velocity. Our quiescent star formation recipe still depends on the dynamical time-scale,
which indirectly has a correlation with circular velocity. The overall observational effect of the
cumulative star formation rate is largely governed by the enhanced quiescent star formation mode.
The parameters that control the relative burstiness have very subtle observational effects down to
our magnitude limits. If our models are correct, we need to probe deeper magnitudes to discern the
relative strengths of the various burst modes as they impact the observational plane.
From the properties yielded by our best-fit models we find that we select majority of the
stellar mass (80-90%, across samples) with our color-selection criteria that is contained in massive,
UV-bright galaxies. In contrast, the fractions of seen stellar masses for each sample decline substantially (40-70%) when we consider all galaxies. This indicates that our current optical surveys
are effective at selecting UV-bright, massive galaxies, but fail to select most of the stellar mass
(especially at z ∼ 4, 5 redshifts), which remains hidden in UV-faint, moderately massive to dwarf
galaxies. In addition, we find that our best-fit models predict a ∼ 77% mass build-up between the
z ∼ 4 and z ∼ 3 epochs for the UV rest-frame L∗ galaxies, and a smaller ∼ 50% build-up between
z ∼ 5 and z ∼ 4 epochs. This indicates an on-going process of stellar-mass assembly between the
z ∼ 5 and the z ∼ 3 epochs. Furthermore, we find that for our z ∼ 3 sample, the stellar masses
range from 108 to 1010 M# , which is roughly 1.5 orders of magnitude less than the stellar masses of
the present day L∗ spirals and ellipticals – this indicates that the z ∼ 3 Lyman-break galaxies are
not the fully assembled progenitors of the present-day L > L∗ galaxies. Finally, we find that quite
a few of the z ∼ 5 galaxies have Log[Mstar ] > 10 (M# ), and that the median age of the z ∼ 5 galaxy
population is about 240 Myrs, with quite a few older galaxies – reaching ages as high as 500 Myrs.
This points to an already active star formation well before the z ∼ 5 epoch.
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Figure 7.1 Best-fit model observationally scattered density functions. From top-left, clockwise, Udropout V606 - i775 vs i775 U-dropout V606 - IRAC 3.6 vs V606 B-dropout z850 - IRAC 4.5 vs z850
and B-dropout i775 - z850 vs z850 . The limits are the same as given in Table 6.1.
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Figure 7.2 Random draws from the best-fit model observationally scattered density function. Udropouts with V606 - i775 vs i775 colors.
149
Figure 7.3 Random draws from the best-fit model observationally scattered density function. Udropouts with V606 - IRAC 3.6 vs V606 colors.
150
Figure 7.4 Random draws from the best-fit model observationally scattered density function. Bdropouts with i775 - z850 vs z850 colors.
151
Figure 7.5 Random draws from the best-fit model observationally scattered density function. Bdropouts with z850 - IRAC 4.5 vs z850 colors.
152
Figure 7.6 Random draws from a poor-fit model observationally scattered density function. Bdropouts with z850 - IRAC 4.5 vs z850 colors. Note the different character of the Balmer-break
colors as compared to Fig. 7.5.
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Figure 7.7 Stellar masses of the color-selected U-dropout model galaxies. The filled-diamond symbols
show stellar masses of the individual color-selected model galaxies vs. their corresponding z850
magnitudes. The histogram shows the projected distributions for the same color-selected model
galaxies with an imposed z850 < 27 magnitude limit (shown as a red dash-line). The predicted
masses are about 1.5 orders of magnitude lower than the stellar masses of the present day L∗ spirals
and ellipticals.
154
Figure 7.8 Stellar masses of the color-selected B-dropout model galaxies. The filled-diamond symbols
show stellar masses of the individual color-selected model galaxies vs. their corresponding z850
magnitudes. The histogram shows the projected distributions for the same color-selected model
galaxies with an imposed z850 < 27 magnitude limit (shown as a red line).
155
Figure 7.9 Stellar masses of the color-selected V-dropout model galaxies. The filled-diamond symbols
show stellar masses of the individual color-selected model galaxies vs. their corresponding z850
magnitudes. The histogram shows the projected distributions for the same color-selected model
galaxies with an imposed z850 < 27 magnitude limit (shown as a red line).
156
Figure 7.10 This figure illustrates the stellar mass distribution of all model-derived galaxies spanning
the color-selected redshift range and with Log[Mstar ] > 9.71 (M# ) (the median value from Fig. 7.7).
Galaxies were binned into 0.25 magnitude intervals and weighted by their corresponding stellar
mass. A red dash-line is included to delineate our observational magnitude limit. This figure shows
the amount of model-predicted mass potentially missed by the current optical surveys down to our
magnitude limit.
157
Figure 7.11 This figure illustrates the stellar mass distribution of all model-derived galaxies spanning
the color-selected redshift range and with Log[Mstar ] > 9.65 (M# ) (the median value from Fig. 7.8).
Galaxies were binned into 0.25 magnitude intervals and weighted by their corresponding stellar mass.
A red dash-line is included to delineate our observational magnitude limit.
158
Figure 7.12 This figure illustrates the stellar mass distribution of all model-derived galaxies spanning
the color-selected redshift range and with Log[Mstar ] > 9.62 (M# ) (the median value from Fig. 7.9).
Galaxies were binned into 0.25 magnitude intervals and weighted by their corresponding stellar mass.
A red dash-line is included to delineate our observational magnitude limit.
159
Figure 7.13 Stellar-mass weighted ages of the color-selected U-dropout model galaxies. The filleddiamond symbols show ages of the individual color-selected model galaxies vs. their corresponding
z850 magnitudes. The histogram shows the projected distributions for the same color-selected model
galaxies with an imposed z850 < 27 magnitude limit (shown as a red line).
160
Figure 7.14 Stellar-mass weighted ages of the color-selected B-dropout model galaxies. The filleddiamond symbols show ages of the individual color-selected model galaxies vs. their corresponding
z850 magnitudes. The histogram shows the projected distributions for the same color-selected model
galaxies with an imposed z850 < 27 magnitude limit (shown as a red line).
161
Figure 7.15 Stellar-mass weighted ages of the color-selected V-dropout model galaxies. The filleddiamond symbols show ages of the individual color-selected model galaxies vs. their corresponding
z850 magnitudes. The histogram shows the projected distributions for the same color-selected model
galaxies with an imposed z850 < 27 magnitude limit (shown as a red line).
162
Figure 7.16 Smoothed (over 10 Myr bins) star formation rates of the color-selected U-dropout model
galaxies. The filled-diamond symbols show SFRs of the individual color-selected model galaxies vs.
their corresponding z850 magnitudes. The histogram shows the projected distributions for the same
color-selected model galaxies with an imposed z850 < 27 magnitude limit (shown as a red line).
163
Figure 7.17 Smoothed (over 10 Myr bins) star formation rates of the color-selected B-dropout model
galaxies. The filled-diamond symbols show SFRs of the individual color-selected model galaxies vs.
their corresponding z850 magnitudes. The histogram shows the projected distributions for the same
color-selected model galaxies with an imposed z850 < 27 magnitude limit (shown as a red line).
164
Figure 7.18 Smoothed (over 10 Myr bins) star formation rates of the color-selected V-dropout model
galaxies. The filled-diamond symbols show SFRs of the individual color-selected model galaxies vs.
their corresponding z850 magnitudes. The histogram shows the projected distributions for the same
color-selected model galaxies with an imposed z850 < 27 magnitude limit (shown as a red line).
165
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182
Appendix A
Spherical Collapse in a General
Cosmology
We need to be able to relate the mass, radius, and velocity dispersion of dark matter
halos for any given redshift. This is made possible using the spherical collapse model, one of the
apparently gross oversimplifications that seems to work surprisingly well. We imagine a spherical
patch of the universe with a uniform overdensity δi within a radius ri at a very early time ti (often
called a ”top-hat” perturbation). We assume that the collapsing shells of matter do not cross. If
we consider a particle at radius r, Birkhoff’s theorem Birkhoff (1923) tells us that we can ignore the
mass outside this radius in computing the motion of the particle. The equation of motion for our
particle (in physical, rather than comoving, coordinates) is then,
GM
Λ
d2 r
=− 2 + r
dt2
r
3
(A.1)
where M = (4π/3)ri3 ρb (ti )(1 + δi ) and ρb (ti ) is the background density of the universe at ti . Integrating this equation gives,
183
ṙ = H0
3
Ω0
r3
(1 + δi ) i3 + ΩΛ r2 − K
r
ai
4
(A.2)
where K is a constant of integration. We may fix this by noting that if we have picked ti early
enough that Ω ∼ 1 at that time, linear theory tells us that the initial velocity is,
"5
!
ΩR
Ω0
δi
+ 2 + ΩΛ .
ṙ(ti ) = H0 ri 1 −
3
a3i
ai
(A.3)
Peebles (1984). At the point of maximum expansion, or “turnaround”, ṙ = 0. If we set equation
(A.3) to zero, we obtain a cubic equation for rta , the radius of the perturbation at turnaround,
which must be solved numerically for the general cosmology given here, but for special cases it can
be solved analytically (cf. Padmanabhan (1993)). From a symmetry argument, we note that the
time when the perturbation collapses to a point, tcoll , is always twice tta (the time at maximum
expansion). We can now write an implicit equation for the mass of a perturbation that is collapsing
at tcoll ,
tcoll = 2
rta
2
0
dr
.
ṙ
(A.4)
We know the mass and the radius at turnaround, so we can calculate the density of the perturbation
at turnaround, ρta . Of course the perturbation will not really collapse to a point. Before that
happens, shell crossing will occur, and it will virialize. We can find the radius after virialization in
terms of the turnaround radius using the virial theorem. The total energy at turnaround is Lahav
et al. (1991),
E = UG,ta + UΛ,ta = −
1
3 GM 2
2
− ΛM rta
5 rta
10
(A.5)
where the second term is due to the cosmological constant. Now using the virial theorem for the
final state,
184
1
Tf = − UG,f + UΛ,f .
2
From conservation of energy we then have
1
2 UG,f
(A.6)
+ 2UΛ,f = UG,ta + UΛ,ta . This leads to a cubic
equation for the ratio of the virial radius rvir to the turnaround radius rta . We now know rvir and
can write down the virial density,
∆c (z) ≡
ρvir Ω(z)
.
Ω0 ρ0c (1 + z)3
(A.7)
We now have a relationship between the mass, virial radius, and collapse redshift z. If we assume
a radial profile for the virialized halo, we can use the virial theorem again to relate these quantities
to the velocity dispersion. If we assume that the halo is a singular isothermal sphere, ρ ∝ r−2 ,
truncated at the virial radius, then we have,
GM
Λr2
3 2
σ =
− vir
2
2rvir
18
(A.8)
or, in terms of the circular velocity Vc , assuming Vc2 = 2σ 2 ,
Vc2 =
GM
ΩΛ 2 2
−
H r
rvir
3 0 vir
(A.9)
We can now translate between mass and velocity dispersion at any given redshift. Note that in
universes with a non-zero cosmological constant, halos of a given circular velocity are less massive
because of the Λ contribution to the energy. In practice, we use the fitting formula of Bryan &
Norman (1997) for the virial density,
∆c = 18π 2 + 82x − 39x2
(A.10)
∆c = 18π 2 + 60x − 32x2
(A.11)
for a flat universe and,
185
for an open universe, where x ≡ Ω(z) − 1. This formula is accurate to1 % in the range 0.1 ≤ Ω ≤ 1,
which is more than adequate for our purposes. We now can write down the general expression for
rvir in closed form,
rvir =
3
Ω(z)
M
4π ∆c (z)Ω0 ρc,0
41/3
1
.
1+z
(A.12)
In conjunction with equation A.9, this allows us to calculate the circular velocity and viral radius
for a halo with a given mass at any redshift z. These expressions are valid for open cosmologies with
Λ = 0 and flat cosmologies with non-zero Λ.
186
Figure A.1 The relationship between halo mass and virial velocity from the spherical tophat model,
at z = 0 (bottom set of lines), z = 1, and z = 3 (top), for the cosmologies discussed in the text.
The relation depends (weakly) on cosmology and (strongly) on redshift (This figure was reproduced,
with permission, from Somerville & Primack (1999)).
187
Appendix B
Table of Model Runs
188
Table B.1. List of All Models
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
1
12.0
0.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
2
12.0
0.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
3
12.0
0.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
4
12.0
1.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
5
12.0
1.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
6
12.0
1.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
7
12.0
2.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
8
12.0
2.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
9
12.0
2.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
10
1.5
0.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
11
1.5
0.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
12
1.5
0.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
13
1.5
1.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
14
1.5
1.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
15
1.5
1.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
16
1.5
2.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
17
1.5
2.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
18
1.5
2.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
19
12.0
0.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
20
12.0
0.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
21
12.0
0.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
22
12.0
1.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
23
12.0
1.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
24
12.0
1.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
25
12.0
2.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
26
12.0
2.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
27
12.0
2.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
28
1.5
0.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
29
1.5
0.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
30
1.5
0.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
31
1.5
1.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
189
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
32
1.5
1.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
33
1.5
1.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
34
1.5
2.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
35
1.5
2.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
36
1.5
2.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
37
12.0
0.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
38
12.0
0.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
39
12.0
0.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
40
12.0
1.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
41
12.0
1.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
42
12.0
1.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
43
12.0
2.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
44
12.0
2.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
45
12.0
2.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
46
1.5
0.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
47
1.5
0.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
48
1.5
0.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
49
1.5
1.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
50
1.5
1.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
51
1.5
1.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
52
1.5
2.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
53
1.5
2.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
54
1.5
2.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
55
12.0
0.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
56
12.0
0.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
57
12.0
0.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
58
12.0
1.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
59
12.0
1.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
60
12.0
1.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
61
12.0
2.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
62
12.0
2.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
190
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
63
12.0
2.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
64
1.5
0.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
65
1.5
0.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
66
1.5
0.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
67
1.5
1.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
68
1.5
1.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
69
1.5
1.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
70
1.5
2.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
71
1.5
2.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
72
1.5
2.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
73
12.0
0.0
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
74
12.0
0.0
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
75
12.0
0.0
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
76
12.0
3.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
77
12.0
3.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
78
12.0
3.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
79
12.0
4.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
80
12.0
4.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
81
12.0
4.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
82
1.5
0.0
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
83
1.5
0.0
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
84
1.5
0.0
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
85
1.5
3.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
86
1.5
3.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
87
1.5
3.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
88
1.5
4.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
89
1.5
4.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
90
1.5
4.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
91
12.0
0.0
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
92
12.0
0.0
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
93
12.0
0.0
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
191
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
94
12.0
3.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
95
12.0
3.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
96
12.0
3.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
97
12.0
4.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
98
12.0
4.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
99
12.0
4.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
100
1.5
0.0
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
101
1.5
0.0
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
102
1.5
0.0
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
103
1.5
3.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
104
1.5
3.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
105
1.5
3.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
106
1.5
4.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
107
1.5
4.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
108
1.5
4.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
109
12.0
0.0
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
110
12.0
0.0
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
111
12.0
0.0
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
112
12.0
3.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
113
12.0
3.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
114
12.0
3.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
115
12.0
4.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
116
12.0
4.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
117
12.0
4.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
118
1.5
0.0
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
119
1.5
0.0
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
120
1.5
0.0
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
121
1.5
3.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
122
1.5
3.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
123
1.5
3.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
124
1.5
4.5
1.0
2.0
0.5
0.5
0.5
1.5
0.5
0.3
192
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
125
1.5
4.5
1.0
2.0
0.5
0.5
0.5
1.5
1.0
0.3
126
1.5
4.5
1.0
2.0
0.5
0.5
0.5
1.5
1.5
0.3
127
12.0
0.0
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
128
12.0
0.0
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
129
12.0
0.0
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
130
12.0
3.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
131
12.0
3.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
132
12.0
3.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
133
12.0
4.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
134
12.0
4.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
135
12.0
4.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
136
1.5
0.0
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
137
1.5
0.0
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
138
1.5
0.0
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
139
1.5
3.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
140
1.5
3.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
141
1.5
3.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
142
1.5
4.5
1.0
2.0
0.5
1.5
0.5
1.5
0.5
0.3
143
1.5
4.5
1.0
2.0
0.5
1.5
0.5
1.5
1.0
0.3
144
1.5
4.5
1.0
2.0
0.5
1.5
0.5
1.5
1.5
0.3
145
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
146
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
147
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
148
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
149
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
150
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
151
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
152
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
153
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
154
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
155
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
193
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
156
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
157
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
158
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
159
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
160
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
161
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
162
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
163
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
164
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
165
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
166
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
167
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
168
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
169
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
170
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
171
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
172
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
173
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
174
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
175
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
176
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
177
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
178
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
179
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
180
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
181
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
182
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
183
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
184
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
185
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
186
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
194
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
187
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
188
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
189
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
190
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
191
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
192
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
193
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
194
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
195
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
196
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
197
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
198
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
199
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
200
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
201
12.0
0.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
202
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
203
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
204
12.0
1.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
205
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
206
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
207
12.0
2.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
208
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
209
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
210
1.5
0.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
211
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
212
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
213
1.5
1.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
214
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
215
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
216
1.5
2.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
217
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
195
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
218
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
219
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
220
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
221
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
222
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
223
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
224
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
225
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
226
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
227
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
228
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
229
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
230
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
231
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
232
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
233
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
234
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
235
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
236
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
237
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
238
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
239
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
240
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
241
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
242
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
243
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
244
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
245
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
246
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
247
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
248
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
196
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
249
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
250
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
251
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
252
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
253
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
254
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
255
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
256
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
257
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
258
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
259
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
260
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
261
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
262
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
263
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
264
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
265
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
266
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
267
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
268
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.5
0.5
0.3
269
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.5
1.0
0.3
270
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.5
1.5
0.3
271
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
272
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
273
12.0
0.0
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
274
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
275
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
276
12.0
3.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
277
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
278
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
279
12.0
4.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
197
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
280
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
281
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
282
1.5
0.0
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
283
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
284
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
285
1.5
3.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
286
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.0
0.5
0.3
287
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.0
1.0
0.3
288
1.5
4.5
1.0
2.0
0.5
1.0
0.5
1.0
1.5
0.3
289
12.0
0.5
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
290
12.0
0.5
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
291
12.0
0.5
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
292
12.0
1.5
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
293
12.0
1.5
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
294
12.0
1.5
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
295
12.0
2.5
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
296
12.0
2.5
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
297
12.0
2.5
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
298
1.5
0.5
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
299
1.5
0.5
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
300
1.5
0.5
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
301
1.5
1.5
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
302
1.5
1.5
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
303
1.5
1.5
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
304
1.5
2.5
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
305
1.5
2.5
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
306
1.5
2.5
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
307
12.0
0.5
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
308
12.0
0.5
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
309
12.0
0.5
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
310
12.0
1.5
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
198
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
311
12.0
1.5
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
312
12.0
1.5
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
313
12.0
2.5
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
314
12.0
2.5
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
315
12.0
2.5
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
316
1.5
0.5
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
317
1.5
0.5
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
318
1.5
0.5
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
319
1.5
1.5
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
320
1.5
1.5
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
321
1.5
1.5
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
322
1.5
2.5
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
323
1.5
2.5
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
324
1.5
2.5
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
325
12.0
0.0
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
326
12.0
0.0
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
327
12.0
0.0
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
328
12.0
3.5
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
329
12.0
3.5
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
330
12.0
3.5
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
331
12.0
4.5
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
332
12.0
4.5
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
333
12.0
4.5
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
334
1.5
0.0
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
335
1.5
0.0
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
336
1.5
0.0
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
337
1.5
3.5
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
338
1.5
3.5
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
339
1.5
3.5
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
340
1.5
4.5
1.0
1.0
0.5
0.5
0.5
1.5
0.5
0.3
341
1.5
4.5
1.0
1.0
0.5
0.5
0.5
1.5
1.0
0.3
199
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
342
1.5
4.5
1.0
1.0
0.5
0.5
0.5
1.5
1.5
0.3
343
12.0
0.0
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
344
12.0
0.0
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
345
12.0
0.0
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
346
12.0
3.5
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
347
12.0
3.5
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
348
12.0
3.5
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
349
12.0
4.5
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
350
12.0
4.5
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
351
12.0
4.5
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
352
1.5
0.0
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
353
1.5
0.0
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
354
1.5
0.0
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
355
1.5
3.5
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
356
1.5
3.5
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
357
1.5
3.5
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
358
1.5
4.5
1.0
1.0
0.5
1.5
0.5
1.5
0.5
0.3
359
1.5
4.5
1.0
1.0
0.5
1.5
0.5
1.5
1.0
0.3
360
1.5
4.5
1.0
1.0
0.5
1.5
0.5
1.5
1.5
0.3
361
12.0
0.5
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
362
12.0
0.5
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
363
12.0
0.5
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
364
12.0
1.5
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
365
12.0
1.5
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
366
12.0
1.5
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
367
12.0
2.5
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
368
12.0
2.5
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
369
12.0
2.5
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
370
1.5
0.5
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
371
1.5
0.5
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
372
1.5
0.5
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
200
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
373
1.5
1.5
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
374
1.5
1.5
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
375
1.5
1.5
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
376
1.5
2.5
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
377
1.5
2.5
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
378
1.5
2.5
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
379
12.0
0.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
380
12.0
0.5
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
381
12.0
0.5
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
382
12.0
1.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
383
12.0
1.5
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
384
12.0
1.5
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
385
12.0
2.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
386
12.0
2.5
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
387
12.0
2.5
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
388
1.5
0.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
389
1.5
0.5
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
390
1.5
0.5
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
391
1.5
1.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
392
1.5
1.5
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
393
1.5
1.5
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
394
1.5
2.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
395
1.5
2.5
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
396
1.5
2.5
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
397
12.0
0.0
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
398
12.0
0.0
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
399
12.0
0.0
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
400
12.0
3.5
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
401
12.0
3.5
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
402
12.0
3.5
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
403
12.0
4.5
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
201
Table B.1 (cont’d)
Model
τ∗0
α∗
'0SN
αrh
'0burst
αburst
'0burst bulge
αburst bulge
τdust, 0
βdust
404
12.0
4.5
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
405
12.0
4.5
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
406
1.5
0.0
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
407
1.5
0.0
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
408
1.5
0.0
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
409
1.5
3.5
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
410
1.5
3.5
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
411
1.5
3.5
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
412
1.5
4.5
1.0
1.0
0.5
1.0
0.5
1.5
0.5
0.3
413
1.5
4.5
1.0
1.0
0.5
1.0
0.5
1.5
1.0
0.3
414
1.5
4.5
1.0
1.0
0.5
1.0
0.5
1.5
1.5
0.3
415
12.0
0.0
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
416
12.0
0.0
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
417
12.0
0.0
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
418
12.0
3.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
419
12.0
3.5
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
420
12.0
3.5
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
421
12.0
4.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
422
12.0
4.5
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
423
12.0
4.5
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
424
1.5
0.0
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
425
1.5
0.0
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
426
1.5
0.0
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
427
1.5
3.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
428
1.5
3.5
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
429
1.5
3.5
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
430
1.5
4.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
0.3
431
1.5
4.5
1.0
1.0
0.5
1.0
0.5
1.0
1.0
0.3
432
1.5
4.5
1.0
1.0
0.5
1.0
0.5
1.0
1.5
0.3
202
Appendix C
Tables of Lyman-Break Galaxies
203
Table C.1. U-dropout Lyman-break Sample
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
512
53.0014805
-27.7221255
22.6961
22.3532
22.2688
22.0879
20.2659
20.1823
968
53.0108820
-27.7260919
26.0686
25.5896
25.4363
25.3528
23.2376
23.1146
989
53.0112295
-27.7226726
27.3386
26.7572
26.5359
26.4851
23.7462
23.7243
1007
53.0114940
-27.7243115
26.1487
25.9077
25.7627
25.4897
23.6484
23.6455
1033
53.0119182
-27.7473601
26.9931
27.2173
26.3126
26.1417
25.2342
25.0088
1110
53.0130779
-27.7027692
26.4559
25.7761
25.7833
25.9796
25.0899
25.125
1125
53.0132503
-27.6985973
24.9727
24.8786
24.763
24.7586
23.7021
23.6022
1134
53.0133877
-27.7580074
22.5622
21.616
20.9484
20.6799
19.8234
20.0532
1141
53.0134939
-27.7489608
26.2201
25.283
24.9295
24.85
24.6904
24.782
1150
53.0136625
-27.7037702
24.9867
24.7324
24.5873
24.6105
23.1734
23.1212
1152
53.0137107
-27.7531745
25.2907
24.5246
23.8663
23.6935
23.0862
23.4603
1186
53.0143668
-27.7507923
24.7705
24.1117
23.6917
23.5998
23.5752
23.815
1198
53.0145505
-27.7279131
25.8641
24.9176
24.601
24.5974
23.2546
23.1888
1260
53.0154203
-27.7128851
23.2904
23.0465
22.9907
22.9891
23.844
24.6256
1273
53.0155577
-27.7230478
26.8191
26.2634
26.0296
25.6444
22.9319
22.828
1281
53.0156774
-27.7017035
23.6913
23.0352
22.4697
22.3809
21.9722
22.3712
1300
53.0158761
-27.7666035
26.037
25.7639
25.6764
25.5817
24.6471
24.7092
1332
53.0164951
-27.7336790
24.833
24.2967
23.3707
22.9043
21.1606
21.5253
1578
53.0201112
-27.7815540
24.9692
24.2422
23.577
23.4422
22.8132
23.2719
1617
53.0204803
-27.7117484
23.727
22.6853
21.6957
21.3518
19.8086
20.2616
1783
53.0223738
-27.7500135
26.4214
25.8267
25.641
25.5774
24.3902
24.1376
1851
53.0230720
-27.7525947
25.9217
24.7976
24.1948
23.967
24.2038
24.1266
1864
53.0231916
-27.7634793
26.5259
26.2127
25.8252
25.2922
23.79
23.9365
1907
53.0236441
-27.7088287
24.7481
24.0079
23.1888
22.9489
21.9779
22.4571
1957
53.0242668
-27.7787794
26.7609
26.8602
26.8505
26.5771
23.8988
23.59
2057
53.0257818
-27.7937485
26.1164
25.077
24.7562
24.7085
23.1466
23.5018
2073
53.0259711
-27.7289309
25.6218
25.0794
24.4146
24.2883
23.6286
23.9135
2349
53.0287764
-27.7758726
26.6573
26.4989
26.1108
25.739
22.8093
22.5888
2372
53.0290108
-27.7345758
26.8832
26.4826
25.7205
25.5016
24.5878
24.0665
2537
53.0306642
-27.7325175
24.8172
24.7506
24.5103
24.2537
22.8413
23.1836
2606
53.0312597
-27.7838600
26.1489
25.9777
25.9368
25.4698
24.4043
24.2671
204
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
2661
53.0316537
-27.7710869
25.9513
25.7667
25.4572
25.3568
23.7279
23.526
2670
53.0317854
-27.7053077
26.4644
26.1805
25.9063
25.1607
23.4456
23.6406
2707
53.0321459
-27.7850872
23.0744
22.2065
21.9301
21.705
21.9235
22.14
2721
53.0322830
-27.7722304
26.1307
25.3152
25.201
25.3055
24.4686
24.4961
2792
53.0329282
-27.7667834
22.4367
21.6568
21.4955
21.2655
21.5714
21.7497
2862
53.0335379
-27.7402519
23.7298
21.6288
20.548
20.1588
20.589
21.0245
2879
53.0336810
-27.7050657
24.2847
23.9261
23.7995
23.6996
22.1362
22.0768
3023
53.0349839
-27.7656582
27.0842
26.8014
26.3188
25.9425
23.6813
23.5971
3098
53.0356972
-27.7306395
25.6041
25.306
25.2032
25.2316
23.8268
23.9397
3292
53.0374862
-27.7181720
27.2368
26.3323
26.3217
26.3809
24.5982
25.0932
3297
53.0375433
-27.7824529
24.3758
23.7451
22.9954
22.7158
21.122
21.4354
3363
53.0380892
-27.7658309
25.2525
24.7908
24.5952
24.499
22.6272
22.4807
3414
53.0385707
-27.7132748
26.0732
25.4227
25.4105
25.5957
23.7128
24.1119
3495
53.0394109
-27.7992079
26.0247
25.7077
25.2386
25.5704
23.0307
22.8909
3562
53.0399970
-27.8055615
26.5126
26.4508
26.3003
26.3544
24.8007
24.999
3593
53.0401630
-27.6929450
25.8544
25.1224
24.739
24.6009
22.7802
22.8341
3639
53.0405270
-27.7744656
25.9268
25.8361
25.6276
25.604
23.9129
23.9295
3674
53.0407819
-27.7160198
25.9559
25.166
25.058
24.9936
24.0565
24.5866
3714
53.0411479
-27.8123606
24.9123
24.2925
24.1455
24.1153
24.1569
24.3985
3816
53.0419576
-27.8187116
19.7331
19.204
18.9155
18.9017
20.3017
20.8003
3870
53.0425891
-27.7961663
25.6218
24.9181
24.409
24.314
24.1716
24.709
3908
53.0428591
-27.7436186
24.5697
24.2362
23.6333
23.492
23.2912
23.7247
4068
53.0442326
-27.7742530
26.2413
25.804
25.2282
24.7436
21.2812
21.0845
4110
53.0444750
-27.8138092
24.2519
24.0717
23.5702
23.1576
21.9159
21.9632
4124
53.0445716
-27.7297080
23.8018
23.6765
23.5029
23.0366
22.0718
22.182
4217
53.0453707
-27.7593481
25.0903
24.935
24.8606
24.6653
23.3399
23.3981
4253
53.0456097
-27.7623826
23.1176
23.0316
22.6061
22.3951
21.6965
22.0098
4300
53.0459437
-27.7489047
22.5521
22.128
21.4078
21.1653
20.2831
20.7087
4476
53.0473129
-27.7255895
25.8852
24.907
24.6153
24.4241
24.6807
25.2036
4479
53.0473308
-27.7024629
24.9617
24.2525
23.8558
23.7814
23.7747
24.15
4481
53.0473362
-27.7401594
25.8502
25.5957
25.4336
25.3092
23.5586
23.5779
205
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
4568
53.0479303
-27.8175728
26.4142
26.0525
25.6362
25.1056
22.9692
23.0452
4654
53.0485435
-27.7218622
25.5896
25.4231
25.269
25.0657
23.9129
23.9987
4747
53.0492513
-27.7320127
24.4259
24.3914
24.1367
23.75
22.9208
23.2698
4846
53.0499257
-27.8052925
26.4539
25.6086
25.3449
25.2649
24.4249
25.0281
4901
53.0503405
-27.7034096
24.031
23.2009
22.9026
22.8137
23.0836
23.5632
4911
53.0504296
-27.8210608
25.6507
25.0003
24.8496
24.7506
24.7409
25.5874
4925
53.0505252
-27.8014364
27.004
26.8177
26.8736
26.8472
25.2589
25.4021
4982
53.0509170
-27.7724075
24.7037
23.6879
22.6214
21.9073
19.5814
19.7878
5100
53.0517474
-27.7391040
27.1357
27.0079
26.8763
26.839
25.4228
25.221
5237
53.0526160
-27.7022353
25.7755
24.6801
24.2736
24.1618
23.6644
24.5876
5239
53.0526678
-27.7250285
21.4401
20.1631
19.7069
19.576
20.4513
20.968
5263
53.0528265
-27.8419832
25.2821
25.2452
25.0448
24.6543
23.6675
23.9365
5303
53.0531195
-27.8296973
24.7686
24.4843
23.8944
23.6399
22.3425
23.0299
5348
53.0534055
-27.8360254
27.249
26.8999
26.7628
26.8751
25.5407
25.5783
5383
53.0536962
-27.7590808
26.5347
26.4772
26.3793
26.3379
25.1899
25.1677
5396
53.0538073
-27.7499664
25.7408
25.166
24.5505
23.9322
21.854
21.9562
5515
53.0547155
-27.7597595
23.5065
23.3046
22.9061
22.5626
21.8789
22.2081
5518
53.0547372
-27.7986369
25.3127
24.054
23.2152
22.9512
21.9585
22.3313
5549
53.0549288
-27.8155717
24.0702
23.1853
22.5323
22.3388
21.6356
21.9845
5762
53.0566599
-27.7217222
25.776
25.6101
25.3768
25.0498
23.6158
23.7097
5851
53.0573158
-27.8095195
26.4915
26.336
26.1181
25.7786
24.4486
24.8433
5907
53.0577704
-27.7960226
26.2622
25.9438
25.485
25.1401
24.2676
24.7536
5939
53.0580388
-27.8000818
26.1634
25.5366
25.3974
25.3978
23.9916
24.0359
5987
53.0583483
-27.6878254
26.6364
25.8933
25.6287
25.4807
23.4961
23.4722
6045
53.0587365
-27.7975520
24.5785
24.3302
23.7052
23.3356
22.293
22.7237
6083
53.0589668
-27.8210247
24.3442
24.0152
23.3889
23.0776
22.1816
22.6368
6091
53.0590454
-27.7335640
26.3656
25.868
25.0747
24.897
24.055
24.5162
6175
53.0596280
-27.7118881
25.4927
24.801
23.9829
23.2801
20.842
20.9217
6186
53.0597059
-27.8015439
26.0975
25.9471
25.486
25.149
24.4874
24.9705
6206
53.0598658
-27.7162858
25.8742
24.8493
23.7981
23.1448
21.12
21.4528
6266
53.0602724
-27.8134998
23.4747
22.6938
22.4357
22.2486
22.1514
22.3804
206
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
6273
53.0603191
-27.8237352
26.0191
25.8337
25.2061
25.0326
24.8934
25.7002
6286
53.0603864
-27.7516681
26.4063
26.1281
26.0376
25.9796
24.6253
24.2679
6354
53.0608161
-27.7914375
26.4943
26.0788
25.9963
26.1482
24.6286
24.6389
6432
53.0614832
-27.6962618
26.0581
25.7706
25.6606
25.2984
24.1292
24.093
6454
53.0616173
-27.8462455
24.9178
24.2241
24.1267
24.1543
23.8958
23.7526
6560
53.0622344
-27.7010725
25.6518
25.4732
25.439
25.3554
24.3723
24.4545
6581
53.0623409
-27.7651350
23.8137
23.7399
23.4919
23.1627
22.5259
22.6158
6596
53.0624407
-27.7355465
25.7964
24.9622
24.8044
24.7066
22.8175
22.8415
6599
53.0624543
-27.8839820
23.4385
23.3619
23.2761
22.8117
21.9118
22.0052
6609
53.0625277
-27.8845599
26.4787
26.2757
26.3352
25.7666
24.3956
24.4051
6634
53.0626816
-27.7072908
25.5211
25.3605
25.3301
25.1286
23.3599
23.283
6647
53.0627426
-27.8450141
25.0838
24.9877
24.8314
24.5575
22.6703
22.6172
6648
53.0627436
-27.8216160
25.3174
24.9209
24.2708
24.2092
24.0193
24.4185
6650
53.0627673
-27.7892206
25.4246
25.2201
25.1309
25.0237
23.531
23.6538
6770
53.0636390
-27.8373463
26.6062
25.8704
25.0663
24.8903
24.0477
24.5613
6778
53.0636845
-27.7656247
26.8675
26.623
26.1261
25.507
23.9216
24.0726
6783
53.0637230
-27.7568204
27.0127
26.7394
26.6488
26.6578
25.3205
25.3284
6895
53.0644659
-27.7753761
25.3319
24.0466
23.134
22.8014
20.1932
20.2195
6951
53.0648277
-27.7166206
23.2883
22.3769
22.0577
21.964
22.2081
22.5506
6978
53.0650004
-27.7326926
24.8682
24.6216
24.5878
24.6443
23.97
24.0745
6987
53.0650570
-27.6870680
25.6208
25.2981
25.1054
24.9398
22.9761
22.9642
6997
53.0651192
-27.6898442
25.2752
24.5942
24.4348
24.4503
23.0945
22.9933
7019
53.0652820
-27.6902146
25.6051
25.4062
24.7273
24.5093
23.8125
24.4527
7041
53.0654199
-27.6878477
25.2783
24.6762
23.9084
23.4218
21.0822
21.2664
7046
53.0654690
-27.6963936
23.5496
21.9117
21.1463
20.8866
21.3534
21.839
7066
53.0656542
-27.7678680
24.9832
24.5089
23.995
23.6594
21.0219
20.8379
7089
53.0657639
-27.7361758
27.2831
26.4343
26.3532
26.4734
25.071
24.9251
7100
53.0658292
-27.8901978
24.7638
23.3361
22.2357
21.806
20.0015
20.4054
7127
53.0659586
-27.7309059
24.6408
23.9708
24.4797
24.0015
24.4564
24.7891
7133
53.0660665
-27.6877866
26.0918
24.2948
22.8751
22.3639
22.6853
23.1836
7135
53.0660700
-27.7203376
27.0737
26.4149
26.1986
25.9136
22.963
22.7975
207
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
7165
53.0662755
-27.8118457
26.4365
26.4645
25.9006
25.558
24.6514
25.0544
7250
53.0668846
-27.8377442
25.5202
24.7503
23.9504
23.7559
22.749
23.163
7292
53.0671579
-27.8666991
25.9804
25.3457
24.6544
24.4029
23.5198
23.9109
7369
53.0677289
-27.8418098
27.0514
26.3655
25.5917
25.4325
24.5585
25.0309
7425
53.0681501
-27.8235188
26.5999
26.162
26.0734
25.9118
24.0976
24.1619
7467
53.0684596
-27.7282607
26.4423
25.6925
25.5107
25.3789
22.5978
22.2745
7504
53.0687334
-27.7469545
23.8931
23.3379
22.5831
22.2085
20.1292
20.418
7624
53.0695659
-27.7444353
25.1624
24.5961
23.551
22.9421
21.141
21.5131
7629
53.0696016
-27.6931275
25.1645
25.0255
24.6302
24.436
22.0171
21.8235
7630
53.0696044
-27.7772635
27.4003
26.8032
26.6457
26.4935
24.7614
23.8962
7649
53.0697308
-27.7191384
26.6628
26.4592
26.4638
26.3392
25.6556
25.3402
7786
53.0706082
-27.7553644
25.8458
25.313
24.5969
23.7761
21.1427
21.2536
7867
53.0710660
-27.8227406
22.0545
20.3288
19.4992
19.1641
18.5496
18.744
7916
53.0713817
-27.8774627
24.7681
24.6054
24.0796
23.6819
22.7853
23.2467
7925
53.0714146
-27.7770171
26.6543
26.4189
26.4843
26.1812
24.3677
24.5945
7950
53.0715123
-27.9039369
27.0319
26.5559
26.1161
25.8778
25.4298
25.1201
7973
53.0716248
-27.8148620
24.8147
24.6465
24.4649
24.3014
22.9929
23.0118
8003
53.0718191
-27.9025250
24.3758
23.6211
22.6845
22.1942
20.2888
20.6782
8108
53.0724480
-27.7580853
24.7773
24.5128
24.2507
23.9398
22.5747
22.5333
8166
53.0727705
-27.6980126
25.7282
25.1123
24.9528
24.8132
22.7453
22.6639
8170
53.0727870
-27.7623241
25.7451
25.0847
24.324
24.1192
23.4509
23.9119
8176
53.0728255
-27.6933485
25.1597
24.9724
24.6973
24.4556
22.6733
22.5618
8207
53.0729904
-27.7267992
24.6507
24.4693
24.3475
24.1457
22.8487
22.8608
8226
53.0731563
-27.6931681
25.8904
25.5863
24.9586
24.7819
24.3895
24.9915
8259
53.0733013
-27.7871115
26.5021
25.8237
25.5107
25.4489
23.2579
23.3727
8282
53.0734213
-27.7159527
23.8109
23.0778
22.3702
22.1479
20.8165
21.1902
8335
53.0736528
-27.7441536
25.3942
25.0679
24.2844
23.944
22.9055
23.425
8434
53.0742131
-27.7754049
25.5633
24.9934
24.3423
24.318
24.2742
24.9144
8440
53.0742610
-27.8210939
23.7466
23.7313
23.4803
23.3622
22.7851
23.1496
8562
53.0751366
-27.8422336
25.9229
25.3775
24.8329
24.9344
24.5918
24.9439
8563
53.0751387
-27.9068562
26.1501
25.2387
24.4597
24.3074
23.5106
23.9103
208
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
8581
53.0752682
-27.8885905
25.9747
25.1906
25.0084
24.6662
22.1105
22.0613
8635
53.0756701
-27.8903139
24.4543
23.4205
22.9701
22.7673
22.6373
23.0026
8857
53.0768741
-27.7655254
25.036
22.7573
21.2693
20.763
19.1596
19.6472
8946
53.0775538
-27.7847384
24.3386
24.2328
23.8545
23.4431
21.7748
21.8398
8969
53.0777284
-27.8692820
25.5784
23.599
22.205
21.7263
20.3415
20.8517
9000
53.0779143
-27.8221573
25.9789
24.9312
23.5897
22.8265
19.9634
20.1777
9050
53.0781882
-27.7334556
25.7779
25.4357
24.7032
24.6
24.0824
24.6034
9171
53.0787970
-27.6937487
25.3063
25.0511
25.0644
25.0983
24.0207
23.869
9187
53.0789145
-27.7996397
25.148
24.7128
24.0265
23.7362
22.1437
22.498
9188
53.0789164
-27.7094494
26.5552
26.3781
25.8913
25.5158
23.0013
22.931
9211
53.0791793
-27.6909391
26.2902
26.1797
26.0159
25.8747
23.6197
23.611
9244
53.0793363
-27.8622067
22.8951
21.9331
21.4943
21.2854
21.3732
21.5424
9280
53.0795677
-27.8973651
26.2201
26.1936
26.0726
25.6799
24.5561
24.761
9304
53.0797105
-27.7078072
25.3934
25.2791
25.0517
24.5352
23.3548
23.4352
9361
53.0800296
-27.7473881
24.9047
24.2422
23.2512
22.6393
20.5748
20.8631
9362
53.0800306
-27.7520976
25.0129
24.3818
23.7583
23.6738
23.2539
23.772
9397
53.0802248
-27.8976008
25.3857
25.3567
25.1859
24.8671
23.7551
23.7288
9399
53.0802348
-27.7766689
25.5269
25.5099
25.4907
25.6801
25.4688
25.2701
9489
53.0809145
-27.8308311
25.8565
25.611
25.0721
24.9482
24.483
25.0506
9553
53.0813008
-27.9120161
24.8965
23.988
23.6975
23.6172
23.785
24.2213
9771
53.0825943
-27.7541361
24.785
24.7298
24.5176
23.997
22.8956
23.0763
9837
53.0831774
-27.7471694
24.248
23.6961
22.7924
22.5515
21.5535
22.0034
9929
53.0837175
-27.7484457
26.9787
26.5475
26.273
26.27
23.5346
23.384
9935
53.0837462
-27.6795444
23.499
22.709
22.2717
22.0777
22.0315
22.3614
9950
53.0838628
-27.7600836
24.9418
24.6179
23.8633
23.6823
23.2772
25.3091
10002
53.0841943
-27.9356849
25.4741
25.1476
25.1194
25.1331
24.2985
24.3196
10090
53.0847182
-27.9180034
26.0611
25.8261
25.7061
25.9271
25.382
25.1347
10097
53.0847779
-27.7030838
25.7158
25.1398
25.2032
24.7047
23.7732
24.2519
10169
53.0853058
-27.8398735
26.4192
25.842
25.3957
25.2799
23.355
23.1055
10249
53.0858085
-27.6867495
24.0961
23.8919
23.7966
23.6518
21.8849
21.7519
10265
53.0859043
-27.6746131
25.4115
25.4749
25.0916
24.8646
24.4948
25.0278
209
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
10337
53.0863139
-27.6894700
25.0974
24.934
24.6448
24.2159
22.4803
22.4878
10344
53.0863400
-27.8187300
25.5543
25.159
25.1188
25.1529
24.6387
24.7136
10545
53.0876633
-27.8246730
25.2985
24.6893
23.9395
23.7651
22.7208
23.2742
10586
53.0878596
-27.7376358
25.975
25.9014
25.8866
25.8903
24.9247
25.1728
10631
53.0881515
-27.8238262
24.9356
24.7538
24.6841
24.6811
23.3933
23.3561
10689
53.0885544
-27.8584210
26.0007
25.0647
24.5989
24.448
24.1999
24.6004
10698
53.0886082
-27.8248557
24.2341
23.9719
23.4529
23.3138
22.8794
23.4318
10760
53.0889921
-27.6738992
24.0989
23.8899
23.0214
22.1326
20.067
20.2887
10844
53.0894610
-27.7374277
26.4448
25.7273
25.7856
25.545
23.8992
23.6833
10852
53.0895348
-27.9310159
25.8945
25.6936
25.1838
24.6699
23.5822
24.2276
10875
53.0896232
-27.8999037
25.7663
24.4987
23.7775
23.3337
21.0231
21.1825
10876
53.0896241
-27.6791698
23.9241
23.9322
23.5511
23.2417
22.577
22.9357
10994
53.0903212
-27.9363521
25.0844
24.5093
23.8017
23.636
22.8132
23.2733
11209
53.0915136
-27.7720220
26.3635
26.0239
25.4471
25.2463
24.3431
24.5556
11210
53.0915156
-27.7038938
24.2743
24.0695
23.4785
23.0912
22.127
22.4378
11300
53.0919907
-27.7354664
26.0567
25.9899
25.8489
25.8342
24.1457
24.5489
11381
53.0925505
-27.7408123
26.7391
26.5996
26.5418
26.2531
23.6999
23.7133
11396
53.0926779
-27.7639888
23.8109
23.1837
22.4592
22.2606
21.5317
21.9606
11574
53.0936691
-27.7821512
25.3798
24.5288
23.7151
23.482
22.2363
22.7058
11577
53.0937063
-27.9248215
25.6757
24.8544
24.5525
24.5854
22.9933
22.9942
11592
53.0938090
-27.7033626
25.1976
25.0589
24.7562
24.196
23.1769
23.3834
11696
53.0944359
-27.7458759
24.9762
24.5209
23.8342
23.7068
23.3466
23.7119
11724
53.0945869
-27.8297687
25.5435
25.4448
25.3793
25.0435
24.3835
24.2901
11819
53.0951144
-27.8233102
26.3397
25.6364
25.4017
25.5046
24.6842
24.7623
11848
53.0952947
-27.9039774
26.5904
25.7161
25.3759
25.0581
21.7985
21.722
11976
53.0961461
-27.9167785
26.6051
26.2891
25.9984
25.6555
23.5892
23.6142
12029
53.0964861
-27.9250503
25.1105
24.9945
24.5509
24.395
23.7713
24.0027
12060
53.0965924
-27.8103445
26.7286
26.1986
26.1829
26.0998
25.2843
25.1972
12141
53.0971388
-27.7275896
25.7309
25.6067
25.4131
25.0758
23.864
23.8828
12146
53.0971884
-27.7422576
25.3506
25.1227
24.7315
24.09
22.6852
22.854
12362
53.0986205
-27.9451047
26.7155
26.4996
26.348
25.6618
24.4479
24.753
210
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
12396
53.0988450
-27.8015544
25.4011
25.1561
25.0883
24.9358
23.4095
23.4775
12461
53.0991529
-27.7108190
26.0769
25.9179
25.2289
24.9368
24.0634
24.6842
12680
53.1004056
-27.7597602
25.3772
24.588
24.1738
24.1026
24.3059
24.6874
12763
53.1008577
-27.8153005
26.097
25.8231
25.7502
25.672
23.8979
24.1739
12783
53.1009757
-27.7795956
26.3484
26.081
25.8873
25.798
23.9404
23.8375
12797
53.1010419
-27.8535797
25.6747
25.5232
24.8972
24.7416
24.2551
24.7879
12832
53.1011855
-27.8184357
27.5465
27.0292
27.0061
27.0061
24.0457
23.9473
12869
53.1013658
-27.8603087
26.5337
26.2982
26.3608
26.1207
24.2658
24.2433
13064
53.1025095
-27.6723978
25.3832
24.2089
23.2212
22.5607
20.2397
20.4559
13084
53.1026265
-27.8388907
26.9725
26.6917
26.4633
26.5065
24.9619
24.8946
13136
53.1028786
-27.9397591
26.3975
26.387
26.3426
26.2801
23.9856
23.8469
13162
53.1030428
-27.7808324
27.1421
26.723
26.751
26.852
24.8871
25.0807
13264
53.1036122
-27.7706326
25.5764
25.3759
25.3974
25.3395
24.3272
24.3051
13320
53.1039186
-27.8604201
26.3085
25.9543
25.7361
25.5421
23.2504
23.0901
13343
53.1040638
-27.8227331
26.7146
26.2494
25.5979
25.4186
24.9255
25.2964
13344
53.1040690
-27.6693713
25.4824
25.3864
24.7064
24.4472
24.1298
24.354
13386
53.1043019
-27.7464760
25.7823
25.6005
24.8522
24.448
21.1929
21.0087
13408
53.1044181
-27.7285105
25.1806
24.5791
23.7127
23.5049
22.5798
23.0593
13439
53.1045629
-27.7342140
19.7448
18.5148
17.9775
17.7138
17.9788
18.4359
13504
53.1049310
-27.9397588
24.2175
24.1412
23.7423
23.4265
22.7059
23.1182
13532
53.1050921
-27.6749488
25.0403
24.8728
24.3244
24.1508
23.7566
24.3112
13594
53.1054254
-27.8338755
26.2807
26.2973
26.029
25.6675
24.553
24.748
13659
53.1057752
-27.8697987
24.5412
24.4421
24.2417
23.8614
23.1175
23.2401
13675
53.1059058
-27.7384158
25.6917
24.9229
24.3338
24.1906
24.0491
24.5301
13724
53.1061689
-27.8698943
24.2838
24.2562
24.1922
23.7924
23.2481
23.2713
13802
53.1065932
-27.7580413
25.9757
25.3057
24.6698
24.5717
24.2664
24.5339
13804
53.1065995
-27.6901939
25.245
24.4839
23.8999
23.6801
23.3753
23.632
13838
53.1068236
-27.6938794
26.6148
26.0663
25.8658
25.656
23.3412
23.2979
13840
53.1068364
-27.8173386
26.3936
26.0438
25.2068
24.8624
24.1892
24.5116
13906
53.1071984
-27.8142928
26.2202
26.0678
26.2316
26.1137
25.4026
25.2721
13910
53.1072170
-27.7922500
26.5381
26.0678
25.6819
25.3152
24.7549
25.3431
211
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
13913
53.1072309
-27.6932305
26.5529
26.1944
25.3498
25.1483
24.2416
25.1429
13941
53.1073832
-27.7498124
24.1402
23.6158
23.0214
22.6661
21.4995
21.9553
14068
53.1080652
-27.7020318
25.4299
25.2862
25.1824
25.1353
23.5493
23.7045
14081
53.1081351
-27.6962830
25.8283
25.628
25.4417
25.2358
23.4815
23.4832
14117
53.1082932
-27.6952608
25.4796
24.8412
24.7005
24.783
23.6971
23.8584
14131
53.1083536
-27.8701873
26.0874
25.9211
25.7496
25.7897
24.4686
24.5301
14135
53.1083706
-27.8925768
24.7547
23.9508
23.5104
23.411
23.4406
23.7279
14155
53.1084600
-27.8632548
24.2755
24.1038
23.6668
23.1643
21.9016
22.0414
14221
53.1087712
-27.8807130
25.189
25.0312
24.9703
24.9162
23.6514
23.6778
14236
53.1088508
-27.7254343
26.5639
26.1328
25.7643
25.7072
24.0269
24.2782
14259
53.1089870
-27.8940932
26.7884
26.7187
26.0796
25.9055
24.1623
25.1644
14277
53.1090563
-27.7223834
25.8599
25.691
25.3482
25.1024
24.0487
24.4961
14316
53.1092287
-27.6982887
26.2842
26.15
25.7321
25.2667
24.4395
25.1185
14417
53.1095988
-27.6742146
23.3316
22.986
22.3858
22.0828
20.4352
20.6804
14441
53.1097514
-27.7026751
23.7417
23.5388
22.8957
22.6768
21.9809
22.4616
14447
53.1098183
-27.6757262
24.2115
23.692
22.8717
22.3763
21.2507
21.862
14488
53.1099997
-27.7078331
24.7623
24.4935
24.0401
23.6078
21.0165
20.8587
14537
53.1102693
-27.7059714
26.4276
26.3009
25.8932
25.8849
23.2397
23.5223
14547
53.1103252
-27.6980659
26.3283
26.1227
25.5117
24.8974
22.4294
22.474
14586
53.1105088
-27.8073917
26.6521
25.9669
25.7054
25.6562
24.1629
24.2533
14713
53.1111153
-27.7996539
23.5635
22.7788
22.0414
21.8369
20.5584
20.9304
14798
53.1116278
-27.6915502
25.199
24.5772
24.3598
24.2638
22.6898
22.6532
14821
53.1117077
-27.6990119
23.0683
23.0112
22.907
22.7925
21.7622
21.7171
14848
53.1118186
-27.7470987
26.9471
26.473
26.4679
26.2428
24.7747
24.8022
14907
53.1120508
-27.8687111
25.8707
25.1136
24.6685
24.5541
24.4779
24.6524
14961
53.1123561
-27.8171149
25.2018
24.978
24.8417
24.7636
23.3298
23.366
15036
53.1127751
-27.7538884
26.6909
26.2373
26.0467
25.8798
23.7503
23.7747
15079
53.1130222
-27.7947754
26.0218
25.9504
25.1895
25.0502
24.6421
25.1619
15112
53.1131963
-27.7671218
27.3603
27.0759
27.0265
27.0157
23.7081
24.0924
15143
53.1133193
-27.7550310
25.7733
25.7397
25.7166
25.6562
25.0389
24.7867
15146
53.1133277
-27.8639962
24.2621
24.0604
23.7387
23.4324
23.2849
23.5529
212
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
15203
53.1136137
-27.7774612
24.9658
24.7822
24.5886
24.5442
23.0011
22.9775
15280
53.1139886
-27.8837214
26.3089
24.6052
23.7823
23.5568
24.1651
24.6195
15325
53.1142108
-27.8318568
24.1504
24.1836
24.1693
23.8457
23.4076
23.5278
15385
53.1145204
-27.7381764
25.6774
25.2097
24.4928
24.2318
22.8552
23.5583
15402
53.1145781
-27.6884762
27.1764
26.0714
25.504
25.558
24.4664
24.1739
15477
53.1149464
-27.7675584
23.5592
22.0569
20.9307
20.5208
18.7559
19.1888
15528
53.1152410
-27.7071386
26.1427
26.233
25.7182
25.1206
24.0819
24.4685
15570
53.1154517
-27.7535290
26.2834
26.1335
25.3011
25.0309
23.9778
24.2039
15859
53.1170099
-27.9050395
26.2378
25.5134
24.7805
24.6452
24.2295
24.8986
15908
53.1173632
-27.7801124
25.3756
25.032
24.7678
24.6061
22.5258
22.4798
15968
53.1177740
-27.8304754
22.763
21.6565
21.174
20.9743
21.1967
21.6279
16021
53.1180256
-27.8852454
26.5955
26.3684
25.9461
25.5527
24.5854
25.0916
16119
53.1184867
-27.7843528
24.4085
22.6886
21.3166
20.8514
19.4472
19.9816
16192
53.1188308
-27.8591559
27.3013
26.7515
26.8157
26.6641
25.5206
25.368
16263
53.1191671
-27.7625504
26.5477
26.5971
26.6604
26.5309
25.1249
25.1745
16282
53.1192714
-27.7408974
25.6314
25.4365
24.8983
24.7347
23.6893
24.5965
16335
53.1195725
-27.7867087
26.9798
26.6641
26.2997
26.097
23.6386
23.7706
16363
53.1196495
-27.6806144
23.7149
23.2942
23.0793
23.0929
23.7533
24.4304
16411
53.1198485
-27.7147847
25.6938
25.3597
25.1809
25.1115
23.4746
23.4818
16448
53.1200352
-27.8933158
25.8383
25.3896
24.5269
24.1758
22.7265
23.1018
16550
53.1206452
-27.8241265
26.0139
25.8202
25.6463
25.4752
23.7203
23.7701
16559
53.1206892
-27.7822150
24.2268
22.5077
21.764
21.5207
22.0036
22.458
16570
53.1207345
-27.9111067
26.5799
26.386
25.8752
25.2991
23.9893
24.3724
16585
53.1207762
-27.6684055
25.2668
24.5262
23.6863
23.4768
22.7872
23.2588
16605
53.1208376
-27.8617359
27.2378
26.425
26.2571
26.2785
24.8135
24.9332
16655
53.1211429
-27.6931527
21.9457
21.1211
20.8316
20.6088
20.6392
20.832
16656
53.1211456
-27.6980689
25.8864
25.278
24.7761
24.3743
21.5754
21.4918
16735
53.1215773
-27.7233974
25.865
25.6936
25.5803
25.4105
24.4409
24.4278
16743
53.1216049
-27.7805365
26.158
25.9609
25.8735
25.7039
23.9967
23.9834
16747
53.1216220
-27.7370074
24.9669
24.8377
24.7654
24.5222
23.3407
23.4056
16869
53.1223468
-27.7841688
26.017
25.2689
25.0145
24.9481
24.2134
24.9463
213
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
16951
53.1227418
-27.7353881
23.2898
22.333
21.8896
21.7474
21.5155
21.7878
17025
53.1231250
-27.6865909
25.3959
25.4042
24.9957
24.4864
23.7862
24.2213
17033
53.1231548
-27.7667117
23.5301
22.6463
22.3433
22.1589
22.2549
22.512
17093
53.1234985
-27.8293009
24.6188
24.405
24.0408
23.5199
22.3405
22.6093
17134
53.1237302
-27.7214458
26.3675
26.0937
25.4926
25.1645
22.1755
22.0089
17176
53.1239701
-27.8940950
26.959
27.0109
27.0702
27.1009
23.7149
23.5694
17218
53.1241589
-27.8916932
26.6332
26.252
25.9542
25.8197
24.2185
24.3708
17233
53.1242114
-27.8896716
25.6609
25.2898
24.6435
24.1764
23.383
23.9627
17312
53.1246721
-27.9105856
25.4686
25.1886
25.0625
25.0058
23.43
23.4645
17360
53.1249009
-27.8750833
19.2795
18.551
18.059
17.7789
18.8328
19.3367
17406
53.1251187
-27.7298016
21.8632
21.0267
20.1289
19.8377
18.6901
19.1546
17418
53.1251555
-27.7209043
25.2899
24.2945
23.8041
23.5898
24.0624
24.339
17558
53.1258985
-27.7512762
22.5857
22.0722
21.6851
21.4627
20.4479
20.5502
17584
53.1260175
-27.7060457
26.1554
25.9077
25.7691
25.6025
24.1798
24.2433
17666
53.1264702
-27.9001723
27.0154
26.3733
26.3391
26.1977
24.7381
24.6767
17724
53.1267805
-27.8612246
24.1972
23.4879
22.6054
22.3421
20.9152
21.3272
17769
53.1270533
-27.7095447
24.8582
24.6634
24.2218
24.0803
23.9238
24.6493
17899
53.1277220
-27.8260226
25.8766
25.6786
25.0638
24.8006
23.636
23.9975
17950
53.1280179
-27.7173277
26.6133
25.7778
25.6319
25.566
23.9583
24.0096
17968
53.1280983
-27.8848400
25.3498
24.6758
24.3558
24.32
24.6303
25.1745
17974
53.1281288
-27.7292719
24.1046
24.0802
24.0255
23.7531
23.0561
23.0507
18008
53.1282790
-27.7770572
25.5386
25.4324
24.889
24.248
23.0541
23.3902
18072
53.1285916
-27.7552305
25.8668
25.829
25.8678
26.0738
24.113
24.3227
18133
53.1288235
-27.7804180
25.7967
25.0767
24.254
23.5014
20.695
20.8533
18174
53.1290766
-27.7545388
24.9289
24.7867
24.1482
23.7264
22.6817
23.0182
18427
53.1304553
-27.7758811
25.6789
24.5233
24.2221
24.2202
22.9963
23.0572
18453
53.1305517
-27.8693338
26.2892
26.1684
26.2121
26.25
25.3688
25.0932
18468
53.1306048
-27.8792951
26.4894
26.3313
26.2383
26.1514
25.2083
24.9634
18529
53.1309564
-27.7953371
27.242
26.6524
26.4806
26.5304
25.274
25.6421
18607
53.1313553
-27.8672584
26.4448
26.3091
25.8249
25.3557
24.2352
24.146
18642
53.1315563
-27.8554434
26.0323
25.466
25.1453
24.8313
24.6798
24.9523
214
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
18658
53.1316235
-27.7708730
25.4595
24.1708
23.8047
23.7999
23.214
23.0044
18678
53.1317771
-27.7535793
25.7758
25.5533
24.8831
24.6131
23.8628
24.642
18760
53.1322145
-27.9198433
26.4548
25.9663
25.0818
24.9471
23.9718
24.5623
18774
53.1323045
-27.7366706
25.5211
24.712
24.3423
24.2269
24.3815
24.8895
18791
53.1323594
-27.6676998
26.4287
26.4624
25.9739
25.6154
24.885
24.9944
19004
53.1336239
-27.9420211
26.082
25.0454
24.6293
24.4234
24.3508
24.9278
19038
53.1338005
-27.7819011
26.4276
25.4783
25.2386
25.1986
23.5857
23.5915
19201
53.1347008
-27.7007144
22.1619
20.2626
18.7
18.0575
18.239
18.6509
19265
53.1350820
-27.9427075
26.6983
26.4508
25.7007
25.1856
24.0394
24.3846
19421
53.1358841
-27.8879612
24.5486
24.1408
23.3851
23.0036
21.8059
22.2021
19557
53.1366669
-27.6577648
26.8826
25.629
25.3565
25.2913
24.7354
24.5508
19591
53.1368993
-27.7350227
25.4414
25.2487
24.7457
24.3814
23.3584
23.7531
19636
53.1371634
-27.7541788
24.8376
23.921
22.9175
22.5621
20.9663
21.3659
19779
53.1379599
-27.8064064
26.1661
25.7965
25.1515
25.0305
24.4621
24.8763
19792
53.1380457
-27.8096611
25.724
24.9994
24.2598
24.0911
23.7359
24.3128
19813
53.1381546
-27.7180978
24.9721
24.4773
24.3552
24.352
22.5539
22.8019
19825
53.1382239
-27.8429239
24.7748
22.7466
21.0019
20.3085
20.4545
20.8436
19917
53.1388015
-27.6695396
26.2146
26.0796
25.755
25.3736
24.3736
24.7026
19933
53.1389508
-27.8869142
25.8767
24.4213
23.3592
22.9329
20.8032
21.1868
19976
53.1391213
-27.7303011
21.0292
20.3682
20.0023
19.8954
20.123
20.4973
19999
53.1392651
-27.7379931
26.3294
25.4737
24.6592
24.4495
23.7721
24.2664
20030
53.1393998
-27.7867750
25.9171
25.5849
24.9436
24.2916
21.9772
22.0311
20044
53.1394887
-27.8956462
26.0286
25.9464
25.2134
25.0163
24.3392
25.1396
20158
53.1401304
-27.9345699
25.2645
24.3402
24.0196
23.8154
23.9347
24.2715
20192
53.1403263
-27.7571821
25.5011
25.3574
25.1881
24.9614
23.6943
23.6736
20212
53.1404584
-27.7809222
27.049
26.5792
25.8564
25.6748
24.5338
24.9938
20221
53.1404843
-27.6615117
26.9245
26.3267
26.2353
26.0671
23.9879
24.0708
20230
53.1405570
-27.8771933
26.6918
26.425
25.9669
25.359
23.7142
24.0073
20270
53.1407466
-27.8039884
24.7406
24.6119
24.6332
24.7095
23.94
24.2122
20285
53.1407999
-27.6858889
26.4871
26.5175
26.3892
26.1303
24.6195
25.1058
20331
53.1410276
-27.8721211
25.6421
24.8747
24.5581
24.5442
24.0669
24.1074
215
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
20466
53.1417622
-27.8685037
25.6432
25.5174
24.8396
24.4911
23.5328
23.8639
20483
53.1418485
-27.8413693
24.2017
23.9815
23.5095
22.9544
20.3892
20.2221
20536
53.1421191
-27.7866994
22.1481
21.1838
20.759
20.6029
20.5671
20.7401
20539
53.1421295
-27.8531813
24.9373
24.1711
23.9111
23.7291
23.9129
24.197
20602
53.1424313
-27.7762952
26.6342
26.4603
26.261
25.7933
24.6642
24.6535
20632
53.1425827
-27.8950654
25.8586
24.7328
23.6948
23.2668
21.0976
21.5119
20666
53.1427737
-27.8481157
27.2294
26.9786
26.8338
26.69
25.587
25.207
20682
53.1428501
-27.7069256
23.7291
23.0108
22.0176
21.2091
19.1798
19.416
20817
53.1436506
-27.8879384
26.1568
25.5307
25.4526
25.4487
23.8336
23.7822
20867
53.1439344
-27.7797304
26.26
26.0825
25.9418
25.855
24.918
24.7195
20874
53.1440073
-27.9287703
24.3229
23.7873
22.8776
22.3906
21.0762
21.3946
20885
53.1440631
-27.9231418
26.1456
26.102
26.0613
25.7353
24.4325
24.2983
20886
53.1440660
-27.7346051
25.7912
25.0191
23.9422
23.54
21.7151
22.0915
20916
53.1442039
-27.7067047
23.6745
22.2748
21.4177
20.9817
19.2617
19.3572
20925
53.1442445
-27.7690586
26.2998
25.9218
25.787
25.7663
24.5726
24.7568
20969
53.1444959
-27.7280744
26.0103
25.4912
25.3607
25.3263
23.975
23.9577
20973
53.1445353
-27.6903112
25.3908
25.1721
25.0903
24.9602
23.4311
23.4304
20986
53.1446353
-27.6684999
26.196
26.0877
25.9726
25.6955
24.6642
24.7507
20998
53.1446891
-27.8273257
25.1862
24.8462
24.2573
23.6727
22.2474
22.4312
21008
53.1447655
-27.9284390
25.1291
24.7429
24.3013
23.9975
21.8354
21.832
21029
53.1448638
-27.7434150
25.7119
25.206
24.5812
24.5914
24.2038
24.801
21130
53.1454119
-27.8419961
26.4575
26.0431
25.4471
25.2763
24.902
25.3905
21153
53.1454935
-27.9038384
21.1967
20.2873
19.9166
19.7357
19.7037
19.7755
21254
53.1459842
-27.8257357
25.8141
25.5303
25.3624
25.2094
23.409
23.245
21262
53.1460354
-27.7915877
27.1142
26.4953
26.2602
26.2405
25.5039
25.5839
21289
53.1461707
-27.8919495
25.2938
24.875
24.0698
23.8086
22.5795
23.0219
21292
53.1461773
-27.7710330
24.4382
24.2477
23.826
23.1903
21.7593
21.8977
21336
53.1464535
-27.8872329
25.6592
25.5438
25.1268
24.6219
23.3698
23.6303
21361
53.1465840
-27.8767140
24.0146
23.581
22.835
22.6376
22.0798
22.5066
21387
53.1467045
-27.9045617
23.8925
23.4504
22.9114
22.8608
22.1886
22.5246
21419
53.1468992
-27.8513321
25.6726
24.5283
23.3713
22.924
21.4229
21.896
216
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
21450
53.1470201
-27.7700560
25.2398
24.4861
23.9142
23.7859
23.3532
23.771
21595
53.1477855
-27.7200724
27.1602
26.8917
26.1455
25.9297
24.9558
25.1949
21597
53.1478033
-27.9399749
25.9832
25.5853
25.1357
24.9471
22.66
22.5325
21612
53.1478985
-27.6877008
26.2756
26.1692
26.2431
26.1119
25.003
25.0161
21621
53.1479229
-27.7739666
22.549
22.2536
21.7145
21.2338
19.6904
19.8685
21643
53.1480375
-27.6837162
25.4955
25.4349
25.2208
24.7436
23.7326
23.891
21675
53.1482425
-27.8440983
26.8559
26.5014
26.3235
26.226
24.1419
23.9918
21781
53.1488303
-27.9376066
24.5025
24.0783
23.2961
22.7346
21.2221
21.4941
21794
53.1488901
-27.7775042
27.3911
26.7027
26.1128
25.6391
22.2595
22.1952
21810
53.1489575
-27.7996805
24.7001
22.2844
20.879
20.4009
18.9198
19.4571
21820
53.1490150
-27.7819436
25.6582
25.4597
25.0883
24.8367
22.4772
22.3815
21909
53.1495143
-27.8048124
26.0157
25.4134
25.2667
25.1828
23.2266
23.1156
21919
53.1495648
-27.6756916
25.8203
25.6863
25.4964
25.3325
23.7555
23.7921
22028
53.1502468
-27.7522383
26.1345
24.6116
23.8428
23.6324
24.2243
24.7844
22063
53.1505464
-27.9206154
26.126
25.7193
25.5671
25.4926
22.9251
22.9048
22077
53.1506358
-27.9024465
22.7083
22.223
22.1233
22.0133
22.4644
22.726
22113
53.1508065
-27.9054623
25.4504
23.632
22.6731
22.347
22.7276
23.061
22170
53.1511145
-27.9316070
25.8466
24.798
24.5734
24.4182
22.5725
22.5924
22197
53.1512489
-27.7559362
25.0653
24.7192
24.6392
24.5667
23.3958
23.4603
22220
53.1513548
-27.7052577
26.7216
26.5367
26.0752
25.7046
24.9671
25.362
22305
53.1517125
-27.9256732
26.6819
26.4666
25.7039
25.507
23.6664
23.6706
22338
53.1518202
-27.7757350
26.8931
27.0016
26.7925
26.7002
23.6002
23.0985
22346
53.1518402
-27.7214986
25.3547
25.2573
24.954
24.638
23.0246
23.1123
22376
53.1519525
-27.7412868
26.0567
25.8017
25.7242
25.2107
23.5171
23.5709
22477
53.1524776
-27.8419569
25.0153
24.5644
23.8842
23.7041
23.1109
23.412
22552
53.1529180
-27.8057553
26.4007
26.4038
26.2258
26.1317
24.8651
24.6545
22628
53.1534164
-27.8586368
24.3951
24.3209
23.923
23.4324
22.5554
22.7836
22688
53.1537499
-27.8985816
26.1568
26.192
26.1051
25.8022
24.338
24.5965
22721
53.1539184
-27.8416014
26.8165
26.6013
26.5905
26.6064
24.9424
25.0308
22747
53.1540180
-27.9086904
25.3917
24.9732
24.3026
24.0889
23.4726
24.0788
22765
53.1541135
-27.9350053
25.7274
25.5811
25.3844
25.2104
24.226
24.1214
217
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
22811
53.1543831
-27.8214853
24.337
24.3732
24.2492
23.9758
23.2598
23.5806
22866
53.1547878
-27.7242824
26.6316
26.3694
25.7266
25.5685
24.9763
25.0073
22988
53.1554750
-27.7795274
25.9154
25.9373
25.9879
26.0157
24.226
22.8837
23082
53.1560176
-27.7709408
26.037
25.9845
25.9535
25.8259
24.1002
24.3235
23125
53.1563045
-27.8974074
24.7224
24.602
23.9495
23.6613
22.7736
23.1364
23138
53.1563889
-27.7678324
26.7336
26.7053
26.8996
26.9919
24.2469
24.6767
23292
53.1572595
-27.9234557
26.5692
25.7633
25.556
25.3956
23.4
23.3091
23393
53.1578434
-27.8147559
24.5725
23.9848
23.7245
23.5816
22.5176
22.7051
23542
53.1587342
-27.7574432
25.3823
25.337
24.7664
24.4609
23.6879
24.0986
23552
53.1588013
-27.7050892
25.1687
24.5262
23.7273
23.4197
21.6537
22.0199
23564
53.1588664
-27.7169406
27.3693
26.5784
26.3091
26.4271
24.8405
25.2053
23677
53.1595648
-27.7217102
24.9189
24.8099
24.541
24.0005
22.6373
22.6811
23753
53.1600021
-27.8636693
25.6229
25.4758
24.7683
24.5458
23.302
23.4372
23815
53.1604767
-27.7862937
25.7091
25.5933
24.9448
24.6425
23.9995
24.3813
23970
53.1613194
-27.9152421
25.168
24.4628
24.0034
23.8702
23.7113
23.9199
23998
53.1614942
-27.7676310
25.0135
24.5792
23.9675
23.8487
23.239
23.7265
24024
53.1616106
-27.7469208
25.3531
23.4263
22.025
21.5643
19.5007
19.8852
24050
53.1617434
-27.9313079
26.2439
26.0546
25.792
25.4155
23.6366
23.6018
24133
53.1621880
-27.8054372
24.3802
23.4563
23.059
22.9182
23.0311
23.4701
24155
53.1623473
-27.7844428
26.0363
25.904
25.8899
25.9312
25.1238
25.4914
24167
53.1623895
-27.9063519
26.4183
25.8846
25.7299
25.5292
23.4717
23.3769
24176
53.1624200
-27.8706637
24.6365
24.4999
24.0351
23.4691
21.5739
21.6311
24184
53.1624572
-27.7808475
26.4289
26.4467
26.4509
25.9756
24.5059
24.7293
24199
53.1625195
-27.8165494
26.0361
25.0258
24.7466
24.7974
23.7785
23.8277
24240
53.1627935
-27.6569279
24.7434
23.7936
23.3222
23.1432
23.1183
23.3271
24271
53.1629706
-27.8005117
26.4545
26.3454
26.2656
25.832
24.6195
23.9953
24273
53.1629754
-27.9168787
23.7088
23.7119
23.7627
23.8281
23.387
23.3834
24331
53.1634180
-27.7995476
24.8223
22.5644
21.0988
20.6261
19.1976
19.8214
24332
53.1634219
-27.7766888
25.8381
25.8692
25.9011
25.4527
24.4585
24.8387
24377
53.1636666
-27.6528345
23.3668
21.4519
20.0587
19.5785
19.7511
20.1478
24421
53.1639426
-27.8378714
25.7184
23.6188
22.4933
22.0965
20.9651
21.3848
218
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
24493
53.1644194
-27.8421704
25.1224
22.9378
21.6238
21.1786
19.9106
20.34
24498
53.1644534
-27.7658549
25.6208
25.3233
24.6127
24.2153
23.0643
23.4396
24563
53.1647488
-27.9001864
22.646
22.0347
21.5388
21.4945
21.2181
21.6049
24587
53.1649200
-27.8202369
25.9996
25.829
25.6588
25.3697
23.8181
23.1086
24642
53.1652258
-27.8745277
26.0835
25.6241
24.7601
24.5442
23.7812
24.0265
24647
53.1652522
-27.8511199
26.3302
25.513
25.1241
24.8707
24.7428
25.0669
24747
53.1658838
-27.7815396
24.7647
24.169
23.45
22.9114
21.1813
21.466
24816
53.1663260
-27.7685804
24.2066
23.9666
23.4723
22.8105
21.0216
21.0967
24839
53.1664615
-27.8967688
25.7749
25.6837
25.5907
25.0556
24.0404
24.2333
24919
53.1668882
-27.7986870
24.5365
24.1383
23.7092
23.338
20.8288
20.9516
24933
53.1670009
-27.7846840
25.9286
25.7056
25.4158
25.0887
23.0498
23.0196
25076
53.1679557
-27.9173037
25.7825
25.7311
25.1781
24.6839
23.5076
23.803
25083
53.1680060
-27.8955182
24.9514
24.0836
23.7527
23.6064
23.8612
24.4127
25184
53.1686817
-27.7455783
25.1834
24.2732
23.8682
23.6819
23.6789
24.1005
25225
53.1689598
-27.9258644
25.6507
25.2292
25.269
25.2731
24.5163
24.8921
25236
53.1690556
-27.8037189
26.141
25.6832
25.6428
25.6648
24.4043
24.5652
25360
53.1698429
-27.9181535
23.4618
22.5933
21.5806
21.0512
19.1602
19.4597
25380
53.1699371
-27.7683559
25.8509
25.2224
25.2054
25.3211
24.9641
24.8079
25408
53.1701017
-27.8637822
24.6109
24.5126
24.3308
23.8958
23.2758
23.5499
25465
53.1705219
-27.8066038
24.7576
24.7626
24.5771
24.1092
23.4411
23.6194
25691
53.1720201
-27.6840778
26.2832
25.6884
25.5021
25.3231
22.475
22.3839
25731
53.1722713
-27.7851934
26.8715
26.7914
26.8598
26.8397
25.1963
25.5485
25754
53.1724206
-27.8737467
24.8183
24.0241
23.3348
23.2472
22.9123
23.5008
25795
53.1726273
-27.8214278
24.9549
24.3549
23.6283
23.4075
22.7244
23.2218
25863
53.1729996
-27.8606870
25.1968
24.9858
24.681
24.3971
22.7605
22.7989
25897
53.1732163
-27.8061593
26.5791
26.3713
26.0135
25.8988
23.981
24.0986
26023
53.1740277
-27.7880071
25.2907
24.9828
24.3032
23.7531
22.4568
22.7928
26057
53.1742260
-27.7503394
26.3616
26.1304
25.6362
25.0313
23.7323
24.0335
26075
53.1743685
-27.8816263
24.9458
24.8141
24.2607
23.7752
22.6956
23.0916
26261
53.1756329
-27.8175328
26.5796
25.9723
25.2598
25.1702
24.5982
25.5247
26274
53.1757149
-27.9181423
26.7884
26.222
26.1937
25.9983
23.7904
23.8474
219
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
26320
53.1759928
-27.6919297
25.8595
25.672
25.4282
24.9991
23.3481
23.4789
26322
53.1760006
-27.9145754
24.7105
24.4413
23.7524
23.5888
23.2131
23.698
26324
53.1760124
-27.8362545
24.6725
23.7625
23.1597
23.0196
22.5306
22.8814
26403
53.1766230
-27.6981102
25.603
23.6821
22.3538
21.8631
20.5539
21.0849
26453
53.1770319
-27.7112550
25.6051
25.2791
24.4608
23.7288
20.8084
20.8395
26566
53.1779627
-27.9176939
25.1131
22.6734
21.3522
20.92
19.6904
20.135
26587
53.1781008
-27.7999403
26.3235
26.2847
26.0447
25.7242
24.5507
24.1773
26588
53.1781073
-27.8680779
24.071
23.559
22.9158
22.7733
22.3385
22.7904
26646
53.1784173
-27.8065481
26.5138
26.386
26.3838
26.4743
24.5538
24.5107
26653
53.1784610
-27.7665444
25.6796
25.0528
24.2875
24.17
23.5737
24.1493
26723
53.1789625
-27.6958450
26.4814
25.2549
24.9598
24.9478
24.7345
24.6746
26731
53.1790175
-27.7011329
24.4572
24.1165
23.5994
23.1715
21.5107
21.5862
26775
53.1793252
-27.8920237
25.1997
24.6009
23.7708
23.5919
22.9735
23.4764
26782
53.1793508
-27.8973915
25.3564
24.5828
24.4051
24.4212
23.3032
23.9845
26792
53.1794441
-27.7857469
26.6548
26.1484
26.1678
26.3112
25.3473
25.0502
26842
53.1797610
-27.7656593
26.0966
26.0915
26.0644
25.898
24.9496
25.214
26856
53.1798723
-27.8882188
24.788
24.2575
23.7712
23.8272
23.6453
24.0751
26857
53.1798922
-27.9207284
25.5855
25.0618
24.5989
24.2412
20.4221
20.1644
26868
53.1800140
-27.8653862
26.7433
26.5383
26.2132
25.8125
24.8734
24.4667
26904
53.1802510
-27.7423952
26.5847
26.5021
26.2796
25.7121
24.2283
24.4398
26906
53.1802571
-27.7523896
25.8803
25.1024
24.5836
24.5037
24.0235
24.3524
26941
53.1806052
-27.7048718
26.5584
26.4281
25.854
25.3888
23.892
24.5311
26993
53.1809281
-27.7222162
25.1521
24.9742
24.5973
24.4131
23.785
24.3668
27042
53.1812516
-27.7274391
26.9604
26.6643
26.6091
26.67
24.6737
24.6389
27190
53.1823947
-27.8856560
26.3089
25.7611
25.7247
25.7783
24.5814
24.519
27221
53.1826622
-27.6988455
26.005
25.4564
25.1738
25.0167
23.0219
23.0257
27228
53.1827174
-27.8898145
25.368
25.327
25.1021
24.7546
23.7316
23.9716
27234
53.1827927
-27.7052808
24.5689
24.5414
24.5981
24.6811
24.1782
24.0751
27253
53.1830180
-27.7005601
25.3908
22.9715
21.4974
20.987
19.4139
19.9635
27262
53.1830767
-27.9103023
25.5163
25.3333
25.0766
25.0056
22.8503
22.7596
27285
53.1832374
-27.8810238
26.6669
26.536
26.4036
26.3204
25.1262
25.0669
220
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
27319
53.1835582
-27.8620224
21.1635
19.6388
18.8507
18.4908
17.5656
17.6607
27339
53.1837530
-27.8702571
22.9955
21.6535
21.0753
20.8761
21.5399
22.0575
27357
53.1838960
-27.7482060
25.1542
23.9794
23.1907
22.9216
22.095
22.4289
27388
53.1841604
-27.7797425
25.8705
25.1801
24.5882
24.5157
24.0506
24.5236
27448
53.1845745
-27.7833258
25.9183
25.7119
25.3059
25.0932
24.1876
24.8968
27473
53.1847720
-27.7774443
24.5899
23.8704
23.3524
23.1785
22.8909
23.2777
27474
53.1847725
-27.9184468
25.257
25.153
24.9391
24.341
23.3738
23.5315
27483
53.1848786
-27.9257898
24.711
24.2041
23.4806
23.3178
22.6018
22.6773
27584
53.1857186
-27.7722201
25.7218
23.9869
23.2211
22.9836
23.5899
24.0781
27604
53.1858313
-27.8099672
25.6723
25.1998
24.762
24.698
21.9276
21.6766
27615
53.1858997
-27.8803917
24.3978
23.7599
23.0907
22.9711
22.5068
22.8894
27641
53.1860963
-27.9057857
26.6766
26.5497
26.4064
26.0383
24.4564
24.8475
27642
53.1861020
-27.8078911
26.186
25.884
25.4562
24.8445
23.3037
23.4352
27687
53.1864994
-27.8976000
25.8734
25.8522
25.7735
25.8096
24.8977
24.7136
27745
53.1869709
-27.8690629
25.257
24.7406
24.0106
23.7818
23.3579
23.9533
27803
53.1874076
-27.8122479
24.1861
23.9891
23.7685
23.632
22.0766
22.0311
27852
53.1878153
-27.7726224
23.6835
23.0254
22.6654
22.6203
22.9964
23.365
27949
53.1884712
-27.8796819
25.524
25.2745
25.1605
25.0094
23.4914
23.4291
28041
53.1891436
-27.8351489
26.1892
25.8308
25.548
25.2248
22.8269
22.7274
28092
53.1896102
-27.8383932
24.9228
24.4021
23.6264
23.1328
21.8028
22.1084
28299
53.1914669
-27.7738871
25.0274
24.1607
23.772
23.6158
23.7236
24.2333
28309
53.1915646
-27.7826686
24.2801
23.9708
23.6738
23.0617
21.612
21.7108
28366
53.1920694
-27.8424031
27.4497
27.2196
27.165
27.0684
25.0148
24.9454
28464
53.1928075
-27.9166991
24.9733
24.6799
24.3797
23.97
22.6707
22.6975
28531
53.1933584
-27.9161343
24.4623
24.4873
24.525
24.2929
24.1319
23.9517
28565
53.1936764
-27.8577876
25.7581
25.4899
25.1154
24.5343
23.1264
23.3663
28568
53.1936906
-27.7908932
25.825
24.9646
24.376
24.2393
23.956
24.3684
28591
53.1938675
-27.7932945
24.7585
23.9923
23.2475
23.0609
22.1703
22.6067
28636
53.1942813
-27.8157583
26.2419
26.102
26.0087
25.8226
24.3437
24.3181
28644
53.1943366
-27.8591250
26.2703
25.9845
25.6222
24.9244
23.6869
24.1929
28771
53.1954272
-27.8018188
27.0196
27.0023
26.9034
26.9008
25.1105
25.4944
221
Table C.1 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
28784
53.1955186
-27.7680048
26.1037
25.147
24.8422
24.785
23.1554
23.0376
28808
53.1957370
-27.8071874
25.0147
24.1964
23.7436
23.585
23.4798
23.7692
28841
53.1959426
-27.7312771
26.4245
26.3192
25.7884
25.7429
24.4465
24.9305
28931
53.1966873
-27.8934731
24.6264
24.4416
24.3338
24.2362
22.75
22.7618
28954
53.1968441
-27.8098270
27.6961
27.2717
27.0312
26.9887
24.7737
24.5566
28959
53.1968593
-27.8610285
26.7918
25.9231
25.6297
25.7318
24.6573
24.775
28997
53.1971565
-27.8382556
26.7986
26.68
25.8427
25.5662
24.5553
25.35
29071
53.1978415
-27.9016391
25.1645
24.5707
24.0488
23.9555
23.929
24.4261
29092
53.1980325
-27.8666422
21.7893
21.2713
21.0272
20.9964
22.2262
22.7429
29101
53.1981243
-27.9062649
26.7292
26.1986
25.7771
25.8694
24.0729
24.2811
29275
53.1995637
-27.8632190
24.1937
24.3234
24.2941
24.0955
23.7301
24.0271
222
Table C.2. B-dropout Lyman-break Sample
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
506
53.0012892
-27.7140714
···
24.1618
23.4886
23.4185
23.2714
23.8539
771
53.0076812
-27.7018293
···
25.4839
25.3276
25.3829
23.2731
23.0083
1038
53.0119708
-27.7300404
···
25.9263
25.4945
25.4269
24.8145
24.3406
1164
53.0138774
-27.7376281
···
26.6386
26.09
26.1819
24.9468
24.6338
1168
53.0139426
-27.7418060
···
26.6108
26.0932
26.0383
24.982
24.8154
1214
53.0147716
-27.7517432
···
26.1692
25.5803
25.4684
24.7162
24.4219
1289
53.0157411
-27.7650875
···
25.8522
25.4354
25.3396
24.571
24.641
1340
53.0166033
-27.7448462
···
26.577
25.559
25.4958
22.7419
22.675
1360
53.0168869
-27.7229871
···
27.0578
26.1673
25.9265
24.3815
24.6389
1623
53.0205796
-27.7421451
···
23.9149
23.7182
23.6935
22.5354
22.393
1649
53.0209287
-27.7701811
···
25.2615
24.6195
24.57
23.5705
24.1119
1972
53.0244761
-27.6947526
···
26.5862
25.9695
25.7799
24.1815
24.641
2488
53.0302265
-27.7300466
···
26.7239
26.1863
26.114
25.3252
25.0963
2556
53.0307926
-27.7348899
···
25.7863
25.563
25.6137
25.0486
24.9198
2601
53.0312202
-27.7852309
···
25.7908
25.1208
25.0966
23.4027
23.2435
2717
53.0322537
-27.7310381
···
26.2416
25.7798
25.7507
24.7493
25.0885
3125
53.0359793
-27.7700350
···
26.7882
26.419
26.3145
25.7197
25.3304
3517
53.0395599
-27.8285109
···
26.4973
26.116
26.0568
25.6642
25.4561
3542
53.0398889
-27.7984708
···
26.851
26.5897
26.5397
24.3016
24.2171
3592
53.0401469
-27.8038500
···
26.8242
25.9702
26.0286
24.8304
24.9812
3659
53.0406907
-27.7181709
···
25.8952
25.6297
25.6259
23.0555
23.0533
3709
53.0410891
-27.7561579
···
26.8631
26.077
26.1631
24.5734
24.2613
3746
53.0413958
-27.6957415
···
25.8023
25.2885
25.3279
24.9435
25.1881
3748
53.0414173
-27.8045746
···
25.6488
25.2652
25.3299
24.9853
25.0514
3847
53.0423060
-27.7814212
···
26.1879
25.8992
25.9046
25.071
24.9648
3909
53.0428596
-27.7935259
···
27.363
26.1861
26.1631
24.5277
24.5376
4088
53.0443548
-27.8414304
···
27.0006
25.846
25.8229
24.7605
25.2498
4111
53.0444797
-27.7725276
···
26.3521
26.0174
26.0273
22.7409
22.4502
4210
53.0453172
-27.6984456
···
26.4719
25.8338
25.8001
24.3936
24.1473
4225
53.0454326
-27.7737949
···
26.8671
26.201
26.2099
23.4984
23.7902
4404
53.0468126
-27.7033002
···
26.0345
25.5742
25.5996
24.9073
24.9224
223
Table C.2 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
4449
53.0470991
-27.7170366
···
27.4171
26.5182
26.4598
24.1965
24.2938
4451
53.0471123
-27.8169164
···
27.4232
26.8163
26.7202
24.4896
24.1699
4637
53.0484035
-27.7972102
···
27.2401
26.5801
26.4031
24.7567
25.0655
4642
53.0484391
-27.7724251
···
26.455
26.2912
26.3931
24.7549
24.5236
5161
53.0520491
-27.7616999
···
26.3636
25.7588
25.7249
24.9615
25.1396
5330
53.0532829
-27.8007245
···
27.3984
26.0726
26.0367
24.3743
24.7747
5335
53.0533066
-27.8018702
···
27.407
26.8729
26.5186
26.2067
25.5346
5417
53.0540032
-27.7353427
···
26.7103
26.1331
26.1849
24.5036
24.7147
5427
53.0540957
-27.8114070
···
25.8069
25.1214
25.0856
24.3625
24.4773
5429
53.0541079
-27.8093730
···
26.8991
25.7447
25.6346
24.1915
24.3969
5534
53.0548184
-27.7781618
···
26.4498
25.9766
25.8983
22.8271
22.9482
5568
53.0550669
-27.7784980
···
25.9301
25.6053
25.6441
25.0304
24.7015
5639
53.0556353
-27.8176661
···
26.5768
25.9739
25.9006
23.8865
23.6597
5944
53.0580796
-27.7409968
···
27.4107
26.2469
26.1012
24.0027
23.971
5993
53.0583862
-27.6953527
···
25.7606
25.3582
25.2897
24.2197
24.2826
5996
53.0584111
-27.8750301
···
27.5543
26.9539
26.8821
24.8365
24.6094
6085
53.0589771
-27.8442096
···
26.9416
26.5277
26.4229
25.101
25.2915
6211
53.0599101
-27.8447086
···
27.0976
26.3063
26.3192
25.0477
24.992
6245
53.0600960
-27.7295884
···
26.4943
26.1336
26.1756
25.4159
24.9454
6294
53.0604039
-27.8257471
···
26.8013
25.8068
25.8133
25.1292
25.498
6344
53.0607606
-27.8064526
···
27.1874
26.5536
26.7281
25.328
25.4411
6382
53.0610467
-27.8600422
···
27.5309
26.748
26.6064
25.1844
25.2605
6393
53.0611204
-27.8758259
···
26.3607
25.5959
25.5544
23.2097
23.0721
6404
53.0612026
-27.7744756
···
26.474
25.9493
25.9009
24.8086
24.5594
6830
53.0640577
-27.8051667
···
25.9723
25.4869
25.4214
24.9063
24.8128
6950
53.0648261
-27.7265220
···
26.0714
25.5661
25.4659
24.5051
24.1612
7007
53.0651924
-27.7250957
···
27.0349
26.662
26.5506
25.0006
24.9551
7063
53.0656183
-27.6995433
···
26.8339
26.4624
26.3553
25.7152
25.237
7083
53.0657271
-27.6871892
···
26.9398
26.5184
26.3627
24.6573
24.7553
7266
53.0669563
-27.7405703
···
26.2642
25.6669
25.7227
24.6245
24.7473
7362
53.0676377
-27.8122626
···
27.352
26.0607
26.1154
23.9686
23.8539
224
Table C.2 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
7366
53.0676945
-27.8454207
···
27.3453
26.8889
26.908
25.771
25.5085
7392
53.0678804
-27.8745087
···
27.3604
26.5292
26.3074
24.2323
23.9109
7591
53.0693249
-27.7148192
···
25.3829
24.9482
24.9581
24.5999
24.4989
7701
53.0700709
-27.8415646
···
26.1821
25.5711
25.3922
25.4832
23.2872
7721
53.0702342
-27.8455319
···
26.0488
25.4907
25.2365
22.8541
22.4816
7791
53.0706297
-27.8356332
···
26.5398
26.1986
26.2933
24.1515
23.8434
7890
53.0712010
-27.8675699
···
26.4519
26.137
25.963
24.45
24.5052
7917
53.0713916
-27.7049474
···
25.5165
25.2838
25.2991
25.1529
24.768
7989
53.0717322
-27.7984386
···
25.1893
24.8842
24.9051
24.5663
24.2886
8168
53.0727740
-27.8306020
···
26.423
25.9415
25.9833
24.6421
24.8137
8200
53.0729668
-27.6994880
···
26.3464
25.8773
25.9936
23.7356
23.4621
8269
53.0733626
-27.8874660
···
26.1158
25.7977
25.7089
24.8234
24.8154
8323
53.0735918
-27.8922303
···
24.9291
24.4466
24.3596
23.0132
22.8719
8364
53.0738507
-27.7181465
···
27.2817
26.6651
26.4026
25.1844
24.9305
8373
53.0738963
-27.8852256
···
25.784
25.4309
25.4567
25.0861
24.9292
8536
53.0748911
-27.7534760
···
27.0595
26.1698
25.9917
23.4515
23.167
8575
53.0752105
-27.7552784
···
25.6714
25.0549
24.9606
23.5524
23.3194
8715
53.0760689
-27.8007021
···
25.9097
24.925
24.8058
24.0013
24.5817
8741
53.0761834
-27.8663637
···
25.1151
24.5061
24.3021
23.0144
22.8697
8889
53.0770895
-27.7513444
···
27.5779
26.6631
26.5355
24.3022
24.2227
8893
53.0771143
-27.7347092
···
27.3269
27.2018
27.07
25.5651
25.3461
8974
53.0777424
-27.6967276
···
25.7795
25.2636
25.1893
24.5702
24.5007
9104
53.0784531
-27.8731624
···
26.1628
25.4916
25.3836
22.6977
22.5175
9106
53.0784674
-27.8598579
···
26.1119
25.6384
25.4642
21.6727
21.4093
9131
53.0785983
-27.6967052
···
27.0845
26.3761
26.154
24.2146
24.2276
9237
53.0792861
-27.8772644
···
25.9366
24.6676
24.5393
23.3308
23.5138
9258
53.0794221
-27.7175642
···
27.3515
26.728
26.6326
24.6064
24.5508
9275
53.0795435
-27.6970039
···
26.239
25.4553
25.1869
23.2719
23.2291
9349
53.0799702
-27.8556652
···
26.3128
26.1176
26.226
25.3411
25.2679
9440
53.0805899
-27.7208170
···
27.1695
26.6512
26.233
22.6451
22.4077
9543
53.0812347
-27.8746003
···
26.2775
25.7375
25.7118
24.1099
24.001
225
Table C.2 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
9618
53.0816804
-27.8111118
···
25.8784
25.505
25.4889
25.4307
25.4715
9698
53.0821487
-27.8378219
···
26.7301
26.1319
26.0654
24.8125
24.3668
9762
53.0825519
-27.8835715
···
25.1724
24.6991
24.6052
23.7694
23.6271
9895
53.0835106
-27.8818634
···
26.9061
26.634
26.7232
24.9694
24.8525
9972
53.0840188
-27.8234535
···
25.8796
25.5969
25.517
24.6833
24.4501
10165
53.0852949
-27.6964257
···
27.1829
26.8712
26.9864
24.8204
25.1644
10327
53.0862494
-27.9267091
···
26.8347
25.8158
25.8096
24.7605
24.4312
10469
53.0872303
-27.7295271
···
25.04
24.6641
24.669
24.2973
24.1447
10555
53.0877079
-27.8056858
···
25.8284
25.6518
25.9116
25.0419
24.8076
10619
53.0880708
-27.8820767
···
25.9831
25.4794
25.494
25.1079
24.9958
10649
53.0882919
-27.6751212
···
27.3781
26.6367
26.5381
22.8061
22.6714
10739
53.0888447
-27.9489146
···
24.9087
24.5501
24.614
23.7985
23.8962
10778
53.0891095
-27.7105762
···
26.7531
26.136
26.1493
25.0124
25.0715
11099
53.0909013
-27.6901129
···
25.77
25.269
25.2211
24.4479
24.406
11287
53.0918915
-27.6761308
···
26.2245
25.7916
25.8383
24.8145
24.8702
11647
53.0941388
-27.8550091
···
25.7146
25.2522
25.2188
23.8232
23.8088
11767
53.0948007
-27.7857861
···
27.1596
26.1446
26.1331
24.6395
24.9147
11779
53.0948780
-27.7703875
···
26.093
25.6148
25.6091
24.9948
24.8094
11833
53.0951812
-27.7438469
···
25.2992
25.067
25.0686
23.8404
23.6058
12152
53.0972367
-27.8657967
···
24.184
23.4995
23.4089
21.8889
21.6665
12274
53.0980585
-27.7989094
···
27.0135
26.3623
26.3881
24.9366
25.0595
12533
53.0995912
-27.8021789
···
26.6983
25.7678
25.7732
25.068
25.7336
12774
53.1009203
-27.8275100
···
26.7658
26.3789
26.4474
25.2526
25.2102
12778
53.1009453
-27.6915218
···
26.1765
25.2032
25.0954
23.3701
24.5125
12975
53.1020453
-27.8707117
···
26.0134
25.5078
25.6062
24.2323
24.1793
13177
53.1031448
-27.8083460
···
27.2088
26.6512
26.6847
25.1278
25.2558
13544
53.1051975
-27.7663362
···
27.0666
26.4338
26.6287
25.0401
25.0059
13586
53.1054047
-27.7398731
···
27.5877
27.0038
26.7575
24.8096
24.4389
13770
53.1064311
-27.7334863
···
25.77
25.2807
25.292
24.2664
24.6074
13803
53.1065985
-27.8528046
···
27.0575
26.397
26.2826
24.4686
24.5433
13871
53.1069967
-27.7928889
···
26.183
25.9236
25.9244
24.8436
24.8821
226
Table C.2 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
13949
53.1074174
-27.8693093
···
25.714
25.2621
25.1568
23.3086
23.3012
13986
53.1076011
-27.7139781
···
25.959
25.2838
25.2371
24.0174
24.244
14006
53.1076904
-27.8569629
···
27.2091
26.4504
26.5345
25.6239
25.1847
14113
53.1082772
-27.7986549
···
26.8796
25.9345
25.7827
23.648
23.8145
14285
53.1091005
-27.8698047
···
25.313
24.6597
24.6273
23.7511
23.6838
14374
53.1094515
-27.7440561
···
26.743
26.4042
26.1664
25.2211
25.2939
14391
53.1094949
-27.8793594
···
25.2992
24.9283
24.977
24.2628
24.0472
14406
53.1095619
-27.8692351
···
26.9858
26.1322
25.997
24.7756
24.6671
14555
53.1103747
-27.6899919
···
25.8833
25.3457
25.2511
24.0155
23.8569
14772
53.1115039
-27.8738644
···
24.749
24.2405
24.2349
23.3364
23.2342
14800
53.1116327
-27.8607736
···
26.1429
25.5011
25.3902
24.4779
24.1779
14817
53.1116991
-27.8766974
···
26.9344
26.4367
26.4266
24.8436
25.0263
14880
53.1119471
-27.8711622
···
27.0599
25.9121
25.8326
23.6306
23.3938
15403
53.1145845
-27.8052111
···
26.7421
26.3812
26.4355
24.5201
24.5566
15517
53.1151486
-27.8499118
···
26.0267
25.3334
25.2694
23.7596
23.9677
15696
53.1161257
-27.8889095
···
27.3611
26.4045
26.394
24.8589
25.3905
15713
53.1161770
-27.7822014
···
27.3012
26.6803
26.6209
25.6537
25.4172
15839
53.1168295
-27.8565011
···
26.0892
25.7801
25.8852
25.6386
25.1169
15920
53.1174699
-27.7203930
···
26.8847
26.4986
26.2575
25.071
25.1711
15960
53.1177095
-27.6867688
···
24.9314
24.5375
24.5692
24.3743
24.2276
15997
53.1179148
-27.7343242
···
25.2438
24.7939
24.6035
21.4686
21.2431
16222
53.1189748
-27.8936592
···
27.1183
26.7564
26.7165
25.6428
25.2958
16449
53.1200370
-27.6867180
···
26.7608
26.1424
25.831
23.9897
23.9199
16613
53.1209201
-27.7094327
···
25.4732
25.0876
25.2334
24.693
24.5817
16616
53.1209328
-27.8842767
···
27.2247
26.9369
26.7412
24.996
24.8313
16703
53.1214169
-27.8146166
···
25.1492
24.7324
24.785
24.1683
23.9873
16931
53.1226685
-27.8903671
···
26.9289
26.5321
26.5156
23.8538
23.6702
17250
53.1243736
-27.8516316
···
25.2752
24.695
24.7338
21.8297
22.0423
17468
53.1254117
-27.8493687
···
26.0998
25.7363
25.643
23.5417
24.1119
17508
53.1256247
-27.8493049
···
26.0766
25.5948
25.5832
24.0749
24.6671
18009
53.1282912
-27.8456813
···
26.5491
26.0216
26.0564
24.5484
24.6874
227
Table C.2 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
18188
53.1291404
-27.8010818
···
27.5732
26.9416
26.9008
25.1628
25.2677
18294
53.1297725
-27.8566500
···
26.4655
25.891
25.6507
24.0496
23.9688
18327
53.1299505
-27.9081561
···
27.411
26.6687
26.1887
22.2728
22.2102
18467
53.1306010
-27.7510262
···
27.0161
26.7084
26.8596
25.4742
25.0715
18523
53.1309157
-27.8634076
···
26.6845
26.4888
26.4173
25.1569
25.0278
18602
53.1313182
-27.7929505
···
26.5541
26.1309
26.0806
25.1234
24.8989
18666
53.1317012
-27.7374379
···
26.0781
25.7389
25.7284
25.1542
25.1445
18729
53.1320449
-27.7528047
···
26.3939
25.5773
25.5836
24.4003
24.5585
18948
53.1332585
-27.9029261
···
26.3909
25.335
25.2147
20.9789
20.8404
19015
53.1336817
-27.6934506
···
25.4955
24.9244
24.9056
24.1478
23.9907
19119
53.1342949
-27.7050574
···
26.1756
25.9984
25.9046
23.6723
24.0079
19126
53.1343195
-27.6943113
···
27.4567
26.8706
26.743
24.9009
24.7691
19129
53.1343376
-27.9079528
···
27.2921
26.9301
26.8786
24.9843
25.019
19632
53.1371354
-27.8736829
···
26.3323
25.9964
25.9497
25.4039
25.4389
19640
53.1371812
-27.9158423
···
27.0388
26.3574
26.2789
22.7989
22.6524
19702
53.1376084
-27.8675430
···
25.6498
25.294
25.2608
23.8836
23.5492
19739
53.1377918
-27.7955409
···
26.6066
26.0141
25.9728
23.8324
23.6647
19866
53.1385014
-27.8211264
···
25.975
25.4158
25.4101
23.8802
23.601
20238
53.1406010
-27.8269001
···
26.8475
26.2357
26.0816
24.1361
24.2171
20256
53.1406939
-27.8732570
···
26.7293
25.8045
25.672
22.64
22.4109
20513
53.1420025
-27.7974094
···
26.9149
26.2121
26.3623
25.2346
25.4027
20638
53.1426232
-27.8265447
···
25.3311
25.1689
25.3164
24.1532
23.6997
20721
53.1430508
-27.8761935
···
26.3801
25.846
25.7778
24.0496
23.9879
20730
53.1431208
-27.8155038
···
25.3329
24.4546
24.2851
23.071
23.2299
20840
53.1437820
-27.7321149
···
26.1096
26.0681
26.0823
25.0511
24.94
20954
53.1443858
-27.6875980
···
25.6433
25.0017
24.9124
23.7615
23.6685
21073
53.1451273
-27.8903380
···
25.1442
24.567
24.4958
22.6761
22.4237
21203
53.1456988
-27.6698984
···
26.6209
26.2081
26.2789
24.7949
24.64
21226
53.1458752
-27.6881955
···
26.8412
26.084
26.0495
24.7465
24.5395
21273
53.1460876
-27.8762721
···
25.7739
25.2729
25.3182
23.6723
23.5986
21677
53.1482659
-27.7802574
···
27.2708
26.8128
26.861
25.6382
25.2973
228
Table C.2 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
21727
53.1484969
-27.7772846
···
26.1532
25.547
25.304
24.4543
24.1936
21811
53.1489661
-27.8025095
···
26.9942
26.2217
26.1342
24.6353
24.2701
21960
53.1498240
-27.6972158
···
24.5672
24.2133
24.1554
23.7433
23.5175
22005
53.1500852
-27.8196368
···
27.0714
26.713
26.699
25.5492
25.6075
22101
53.1507393
-27.8208233
···
27.0941
25.9952
25.8694
24.4529
24.986
22169
53.1511113
-27.6955952
···
27.1116
26.6365
26.6086
24.4657
24.508
22205
53.1512654
-27.8733088
···
26.5482
26.0442
26.0276
24.8446
24.9523
22441
53.1522817
-27.9389034
···
26.9653
26.4735
26.4262
23.8328
23.5644
22641
53.1534713
-27.8213967
···
26.7589
26.05
26.0994
25.4959
25.1166
22642
53.1534909
-27.6887222
···
26.725
26.2346
25.9407
23.8288
24.0183
22808
53.1543737
-27.7395083
···
27.1451
26.837
26.7709
25.6177
25.1847
22878
53.1548581
-27.7063473
···
26.4645
25.8633
26.039
24.7502
24.801
23084
53.1560258
-27.7303251
···
27.0142
26.0176
25.8747
23.9962
24.0905
23637
53.1593319
-27.8772007
···
26.9432
26.017
25.9145
23.5976
23.4403
23722
53.1598097
-27.8923887
···
26.4149
25.6423
25.7419
23.4395
23.2359
23851
53.1606907
-27.8191893
···
26.2802
25.8507
25.9006
25.8178
25.4389
23916
53.1610099
-27.8799487
···
26.796
26.1831
26.141
23.8575
23.8049
23943
53.1611265
-27.8863102
···
26.782
26.2865
26.1551
23.7492
23.7794
23958
53.1612496
-27.8763296
···
27.1794
26.4504
26.3518
23.8954
23.6522
23979
53.1613709
-27.7370371
···
26.4189
25.6276
25.4282
23.325
23.4541
24038
53.1616799
-27.9187386
···
27.1112
26.3697
26.131
22.3589
22.2683
24279
53.1630047
-27.7976545
···
27.107
26.4817
25.6657
22.0163
22.0255
24439
53.1640413
-27.7201410
···
27.4128
26.5321
26.5543
25.0635
25.2808
24465
53.1642034
-27.7729285
···
26.7421
26.4571
26.2057
24.3638
24.4093
24500
53.1644566
-27.9068547
···
26.6347
26.2598
26.0675
25.061
24.9251
24650
53.1652745
-27.8140613
···
25.8498
24.9323
24.723
21.0141
20.8606
24804
53.1662376
-27.8198229
···
27.0546
26.6755
26.6948
24.1245
23.9682
24940
53.1670264
-27.8170020
···
27.1701
26.9121
26.9927
25.8717
25.5983
25010
53.1675434
-27.9077053
···
26.9837
26.281
26.2512
24.9095
24.9973
25059
53.1678725
-27.6742245
···
26.8215
26.3348
25.9434
23.3966
22.8729
25118
53.1682704
-27.7419449
···
25.854
25.3399
25.3489
24.4621
25.1728
229
Table C.2 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
25237
53.1690558
-27.9158878
···
26.6922
26.0617
25.1181
20.7388
20.5854
25614
53.1714968
-27.8504161
···
26.4129
25.6158
25.5573
24.3159
24.5749
25809
53.1727140
-27.7932631
···
27.0128
26.9619
26.9397
25.4566
25.7527
26034
53.1741119
-27.7729651
···
27.2279
26.6845
26.8214
25.1824
25.0938
26190
53.1752274
-27.7945985
···
26.3379
25.9405
25.915
23.5956
23.666
26256
53.1755955
-27.7687476
···
26.7268
26.247
26.2381
24.371
24.3445
26308
53.1758950
-27.7615534
···
26.2784
25.4926
25.3027
23.2012
23.0507
26456
53.1770676
-27.7643529
···
24.7445
24.447
24.4533
24.1022
23.8078
26507
53.1774842
-27.7490115
···
26.5192
26.0615
26.1697
25.1014
25.368
26656
53.1784899
-27.7840362
···
24.9588
24.9586
24.9471
23.1841
23.1123
26744
53.1790943
-27.8407428
···
27.1566
27.114
27.1434
25.1014
25.4008
26880
53.1801287
-27.7259055
···
27.2804
26.0459
26.027
24.6514
24.9802
26954
53.1806741
-27.8449086
···
26.786
26.1034
26.1823
25.0647
25.2406
27122
53.1818664
-27.9066391
···
25.4506
24.9697
24.9129
24.2676
24.2819
27248
53.1829444
-27.8804622
···
26.8388
25.775
25.485
23.674
23.7766
27277
53.1831962
-27.9017602
···
26.8074
26.5408
26.7074
25.1079
25.1745
27344
53.1837813
-27.9145986
···
25.3825
25.0261
25.0415
22.9227
22.8674
27370
53.1839721
-27.8436897
···
26.9588
26.592
26.7306
25.1678
25.2496
27462
53.1846713
-27.7386936
···
27.2808
26.5411
26.5927
24.6677
24.4211
27572
53.1856661
-27.7732206
···
26.7838
26.288
26.082
25.3075
25.1251
27622
53.1859646
-27.9219287
···
26.3137
26.0004
25.825
22.931
22.8132
27895
53.1880836
-27.8411358
···
26.2829
26.1453
26.0103
24.5608
24.6535
27931
53.1883446
-27.9058483
···
26.1953
25.6945
25.6696
23.1539
23.0306
28022
53.1890444
-27.8928016
···
26.8435
26.4091
26.4488
25.0925
24.8689
28120
53.1898794
-27.8925963
···
25.4267
24.8527
24.7566
23.9551
23.6497
28130
53.1899717
-27.7702960
···
27.4488
26.9521
26.7728
25.7734
25.5753
28377
53.1921280
-27.7409289
···
27.6027
26.7739
26.4337
23.1445
22.9764
28396
53.1923028
-27.8968011
···
26.5763
26.0642
26.176
24.7643
24.8689
28451
53.1926968
-27.8130525
···
25.7523
24.9697
24.9579
23.8878
23.9867
28556
53.1935948
-27.8152386
···
27.2105
26.3929
26.2982
25.2616
25.2593
28638
53.1942919
-27.8953662
···
26.424
25.9975
26.0578
24.9705
24.8425
230
Table C.2 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
28708
53.1949641
-27.7870439
···
27.3197
26.516
26.6349
24.8096
24.5895
28839
53.1959284
-27.7726881
···
26.9391
26.5923
26.5622
24.3329
24.2916
29022
53.1974288
-27.7905858
···
27.0632
26.1246
25.9703
24.1282
24.2269
29178
53.1987362
-27.7788827
···
26.8155
25.6063
25.5362
24.4057
24.5768
29298
53.1997930
-27.8849342
···
26.3045
25.2537
25.225
24.1629
24.2953
29312
53.1999732
-27.9168683
···
27.5363
26.6936
26.6735
25.5397
25.2846
29399
53.2006942
-27.7727306
···
26.5115
26.1072
26.0888
24.4955
24.497
29411
53.2008080
-27.8972598
···
26.384
25.8586
25.9416
25.1183
24.9676
29436
53.2010159
-27.8602499
···
26.1066
25.1101
24.9731
24.3373
25.0979
29483
53.2015184
-27.9185288
···
26.6249
25.8212
25.7092
24.7345
24.896
29510
53.2017836
-27.9178676
···
26.4783
25.6158
25.4844
24.4736
24.5876
29512
53.2017959
-27.9087751
···
27.0214
26.6243
26.3967
24.7162
24.6155
29605
53.2026046
-27.8156255
···
25.9899
25.5107
25.5166
24.4493
24.6236
30313
53.2093570
-27.8810938
···
26.2019
25.9089
25.898
23.0015
22.431
30744
53.2134329
-27.8680754
···
26.8193
26.2708
26.176
25.6642
25.4113
31228
53.2184145
-27.9175123
···
26.7909
26.447
26.5857
23.5073
23.1146
31272
53.2189137
-27.8042621
···
25.5667
25.1753
25.097
23.9746
23.8126
31478
53.2208654
-27.8649315
···
26.1005
24.8221
24.8027
23.8236
23.9621
31480
53.2208737
-27.8334861
···
25.3277
24.4369
24.3736
23.5283
23.7789
32366
53.2302041
-27.8395714
···
25.4614
24.6422
24.5675
23.5444
23.7655
32634
53.2342683
-27.8992612
···
26.4139
25.795
25.5594
21.9423
21.6441
32900
53.2382032
-27.8625039
···
26.2572
24.739
24.7037
24.2191
24.6297
32979
53.2396377
-27.8638823
···
25.971
25.1522
25.0764
24.2893
24.7081
33367
53.2471541
-27.8859240
···
26.7507
26.1724
26.1235
25.1637
24.962
33532
53.2516339
-27.9048386
···
26.5608
26.1534
26.2218
24.8871
24.7832
33547
53.2519882
-27.9019902
···
26.1936
25.6618
25.7999
24.4977
24.3067
33648
53.2551112
-27.9043989
···
25.7082
25.2932
25.0792
23.7283
23.6889
231
Table C.3. V-dropout Lyman-break Sample
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
753
53.0073861
-27.7336334
···
···
26.341
25.5233
21.2067
21.2445
1669
53.0211687
-27.7823650
···
···
24.0778
23.868
22.4351
22.5517
1707
53.0214958
-27.7872834
···
···
26.4752
26.3949
24.0089
24.1559
1732
53.0217586
-27.7874730
···
···
26.8013
26.4555
23.2374
23.6954
1745
53.0219103
-27.7167829
···
···
25.3391
25.3734
24.4918
24.8264
4532
53.0476899
-27.7940642
···
···
26.1458
25.9395
23.9382
24.0312
4685
53.0488086
-27.6971100
···
···
25.6621
25.4072
24.7409
25.2001
ID
6820
53.0639978
-27.8266912
···
···
26.5785
26.6377
25.765
25.7115
7544
53.0689918
-27.8071872
···
···
26.9652
26.8207
23.059
23.2165
7632
53.0696162
-27.7233673
···
···
20.5824
19.7377
19.4852
19.9056
8585
53.0752957
-27.8127068
···
···
23.9036
23.1773
23.1348
23.6202
8882
53.0770413
-27.7059261
···
···
24.2072
23.1398
22.7305
23.2271
9174
53.0788180
-27.8840956
···
···
25.209
24.6149
22.6989
22.6498
10080
53.0846342
-27.6787341
···
···
25.4273
24.2658
20.4466
20.3317
10329
53.0862593
-27.9171509
···
···
24.1565
23.0951
22.5068
23.0143
10394
53.0866822
-27.8623509
···
···
22.0993
21.1842
20.9623
21.392
10532
53.0875854
-27.8059688
···
···
26.6729
26.7683
25.214
25.368
11180
53.0913824
-27.7591850
···
···
26.4941
26.2619
24.3855
24.7926
11735
53.0946419
-27.8651134
···
···
26.2469
25.9422
24.2736
24.8313
11861
53.0953488
-27.7909903
···
···
25.1154
25.0229
23.674
24.0659
12689
53.1004690
-27.6839079
···
···
24.242
23.3644
23.2883
23.7935
12725
53.1006978
-27.7030501
···
···
22.4477
21.1734
20.4384
20.9233
14042
53.1079230
-27.7281237
···
···
19.8459
18.9729
18.7334
19.1421
14089
53.1081764
-27.8251225
···
···
26.4395
26.0328
22.7071
22.7131
14367
53.1094150
-27.7923849
···
···
27.0351
27.1634
25.7172
25.4883
16226
53.1190121
-27.6821506
···
···
25.7038
25.6801
24.6311
25.0638
16327
53.1195326
-27.6865159
···
···
26.1646
26.1522
24.5148
24.9238
16819
53.1220450
-27.9387382
···
···
25.2529
25.0962
22.5584
22.4439
18249
53.1294908
-27.8549550
···
···
26.4309
26.3028
24.7144
24.8363
18488
53.1307275
-27.8038359
···
···
26.4091
26.0292
24.8264
25.2949
20041
53.1394796
-27.8416660
···
···
26.5863
25.9247
23.8694
23.9555
232
Table C.3 (cont’d)
ID
RA (◦ )
Dec (◦ )
B435
V606
i775
z850
IRAC3.6
IRAC4.5
22860
53.1547388
-27.7273906
···
···
26.8387
26.5717
24.4105
24.6226
23254
53.1570620
-27.9128992
···
···
24.6238
23.5813
23.1918
23.6706
23411
53.1579429
-27.8919595
···
···
26.0112
25.198
21.5744
21.6087
23497
53.1584600
-27.8549141
···
···
23.0262
22.2085
22.0926
22.5376
23763
53.1600829
-27.8980152
···
···
27.0211
26.9678
24.1618
24.4449
25733
53.1722753
-27.8119802
···
···
26.5396
26.533
24.769
25.3782
25783
53.1725614
-27.8137130
···
···
26.1062
26.2068
24.6437
24.5623
26200
53.1753128
-27.8198958
···
···
24.6663
23.406
22.6456
23.1335
26380
53.1764075
-27.7011003
···
···
26.3754
25.474
20.7582
20.7322
26522
53.1775958
-27.9080422
···
···
26.2197
25.9032
23.992
24.641
26924
53.1804396
-27.7196121
···
···
26.392
26.3645
24.7308
24.8651
28054
53.1892715
-27.9107010
···
···
26.0315
25.2313
25.0963
24.6328
29098
53.1980764
-27.7987172
···
···
26.4817
26.4417
25.0706
25.4982
31331
53.2195287
-27.9014149
···
···
26.4979
26.3311
23.5546
23.9004
31377
53.2199494
-27.8571386
···
···
25.3399
24.0927
23.4035
23.9605
31426
53.2203405
-27.9155001
···
···
26.5319
26.0881
24.2581
24.6917
31875
53.2248886
-27.9145574
···
···
26.4397
26.25
24.2827
24.8487
32312
53.2295099
-27.9040246
···
···
25.2675
25.1103
23.1552
23.3669
32535
53.2324141
-27.8626100
···
···
22.3252
21.3289
20.7975
21.2159
32656
53.2345408
-27.8920908
···
···
25.3285
25.2365
24.8175
24.8689
32900
53.2382032
-27.8625039
···
···
24.739
24.7037
24.2191
24.6297
33305
53.2458788
-27.8922815
···
···
25.546
25.2588
23.3504
23.9082
233
Rafal Idzi was born on April 5th, 1977 in Philadelphia, Pennsylvania to Jan and Gabriella
Idzi. He attended high school in Philadelphia, Pennsylvania, though he spent most of his formative years in Poland. He attended Pennsylvania State University and graduated with degrees in
Astrophysics & Astronomy and Physics in May 1999. During his time at Penn State he did Pulsar
research with Dr. Alex Wolszczan. Upon graduation from college he began his graduate studies in
the Department of Physics and Astronomy at Johns Hopkins University. Between 2001 and 2002 he
worked with Dr. B. .G. Anderson conducting Interstellar Medium studies. He then began work in
2003 with the GOODS team under the guidance of Dr. Henry Ferguson, and eventually started his
dissertation work on the formation and evolution of high-redshift galaxies together with Dr. Henry
Ferguson and Dr. Rachel Somerville at the Space Telescope Science Institute and Prof. Timothy
Heckman at Johns Hopkins University. After completion of his doctorate in Astrophysics, Rafal will
leave academia and pursue a different career path.
234