The Fossils of the First Galaxies in the Local Universe

The Fossils of the First Galaxies in the Local Universe
Abstract
Title of Dissertation:
The Fossils of the First Galaxies in the
Local Universe
Mia Sauda Bovill, Doctor of Philosophy, 2011
Dissertation directed by: Professor Massimo Ricotti
Department of Astronomy
We argue that, at least a fraction of the newly discovered population of ultra-faint
dwarfs in the Local Group constitute the fossil relics of a once ubiquitous population of dwarf galaxies formed before reionization with maximum circular velocities,
vmax < 20 km s−1 , where vmax ∼ M 1/3 . To follow the evolution and distribution of
the fossils of the first galaxies on Local Volume, 5 − 10 Mpc, scales, we have developed a new method for generating initial conditions for ΛCDM N-body simulations
which provides the necessary dynamic range. The initial distribution of particles
represents the position, velocity and mass distribution of the dark and luminous halos extracted from pre-reionization simulations. We find that ultra-faint dwarfs have
properties compatible with well preserved fossils of the first galaxies and are able
to reproduce the observed luminosity-metallicity relation. However, because the
brightest pre-reionization dwarfs form preferentially in overdense regions, they have
merged into non-fossil halos with vmax > 20−30 km s−1 . Hence, we find a luminosity
threshold of true-fossils of < 106 L" , casting doubts on the classification of some classical dSphs as fossils. We also argue that the ultra-faints at R < 50 kpc, have had
their stellar properties significantly modified by tides, and that a large population
of fossils remains undetected due to log(ΣV ) < −1.4. Next, we show that fossils of
the first galaxies have galactocentric distributions and cumulative luminosity functions consistent with observations. We predict there are ∼ 300 luminous satellites
orbiting within Rvir of the Milky Way, ∼ 50 − 70% of which are fossils. Despite our
multidimensional agreement at low luminosities, our primordial model produces an
overabundance of bright dwarf satellites (LV > 105 L" ), with this “bright satellite
problem” most evident in the outer parts of the Milky Way. We estimate that,
although relatively bright (LV > 105 L" ), these ghostly primordial populations are
very diffuse, producing primordial populations with surface brightnesses below surveys’ detection limits. Although we cannot yet present unmistakable evidence for
the existence of the fossils of first galaxies in the Local Group, we suggest observational strategies to prove their existence. (i) The detection of “ghost halos” of
primordial stars around isolated dwarfs. (ii) The existence of a yet unknown population of ∼ 150 Milky Way ultra-faints with half-light radii rhl ≈ 100 − 1000 pc and
luminosities LV < 104 L" , detectable by future deep surveys.
The Fossils of the First Galaxies in the
Local Universe
by
Mia Sauda Bovill
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland at College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2011
Advisory Committee:
Professor
Professor
Professor
Professor
Professor
Professor
Massimo Ricotti, chair
Thomas Cohen (Dean’s Representative)
Stacy McGaugh
Eve Ostriker
Derek Richardson
Rosemary Wyse (JHU, External Member)
c Mia Sauda Bovill 2011
$
Preface
The content of this thesis is drawn, sometimes verbatim, from three papers. These
are Bovill and Ricotti (2009), Bovill and Ricotti (2010a), and Bovill and Ricotti
(2010b) with portions of the introduction coming from Mia Bovill’s second year
project.
They are incorporated as follows.
Chapter 1 uses text from the in-
troductions of all three papers. Chapter 2, with a few small modifications, is
Bovill and Ricotti (2009) verbatim. Bovill and Ricotti (2010a) is split between the
method description and tests in Chapter 3 and the discussion of the fossil properties
in the first half of Chapter 4. The distribution of the fossils in Bovill and Ricotti
(2010b) is the second half of Chapter 4 and the bright satellite problem discussion
is Chapter 5. The observational tests presented in the two 2010 papers are compiled
in Chapter 6.
As of July 22, 2011, Bovill and Ricotti (2009) is published and Bovill and Ricotti
(2010a) and Bovill and Ricotti (2010b) are revised and accepted to ApJ. The versions of the latter two papers used in this dissertation are verbatim what will be
published in ApJ.
ii
In loving memory of my grandfathers, Edwin “New Daddy” Bovill and
Jack “Poppa” Sauda, who have been with me every step of the way.
And for my great-grandmother, Mabel “Mimer” Bovill, whom I never
met, but in whose steps I walk.
iii
Acknowledgements
“If the universe puts a mystery in front of us as a gift, then politeness
requires that we at least try and solve it.”
- Delenn, Babylon 5
First and foremost, grazie mille to Massimo Ricotti for his knowledge
and guidance over the last six years. As a second year project turned
into a PhD thesis, he has taught me immense amounts about cosmology,
galaxy evolution and fortran, but also about the kind of astronomer I
want to be, as a researcher and as a member of the community.
Thank you as well to my departmental committee: Derek Richardson, for
his help with many of the computational aspects of the project, and explaining hockey; Stacy McGaugh, for providing an observer’s perspective
and teaching me to question everything, even the dominate paradigms;
and Eve Ostriker, for expecting excellence and pushing me in the classroom and in my thesis. The work in this dissertation is better because
of their input.
iv
After over a decade enrolled at the University of Maryland, the Department of Astronomy has become a second home and members of the community have supported me in many ways. In particular, many thanks to
Doug Hamilton, for teaching me how to teach, Cole Miller for taking on
a young grasshopper, and Grace Deming, who never stopped advising
me. Thanks as well to Chris Reynolds, Richard Mushotzky, Stuart Vogel, Mark Wolfire, Ed Shaya, Eric McKenzie, Tamara Bogdanovic, Peter
Teuben, Leslie Sage and Stef McLaughlin (and Kisses).
No one makes it through graduate school as an island. I am indebted
to my fellow graduate students, past and present; Megan Decesar, John
Vernaleo, Jessica Donaldson, Jonathan Fraine, Katie Phillpot, Ashley
Zauderer, Rodrigo Herrera Camus, Sid Kumar, Anne Lohfink, Lisa Winter, Randall Perinne, Holly Sheets and my fellow “Mo’s”, KwangHo
Park, Emil Polisensky, and Kari Helgason.
To my non-astronomy friends, Jocelyn Knauf, Alix Watson, Beth Vernaleo, Caroline Crow, Solomon and Johanna Granor, Josh Pilachowski,
Kaveh Pahlevan, and especially Erin “Angela” Branigan, you have been
my sanity through the entire process and I cannot imagine going through
graduate school without you.
I owe a huge debt of gratitude, not only to my parents, Jean Sauda
and Carl Bovill, who have kept me fed, laundered and encouraged since
I decided to get a PhD in astronomy 17 years ago, but to my entire
extended family for their unyielding faith. Especially, Jeanne Bovill,
Ted Bovill, Suzanne Knauf, and my second mom, Susan Latchem.
Finally, while many people have contributed to the finishing of this PhD,
v
it began in 1998 when Debora Katz took a 15 year old’s dream and gave
it form. I hope to pay her gift forward for the rest of my career.
vi
Contents
List of Tables
ix
List of Figures
x
1 Introduction
1.1 The First Galaxies . . . . . . . . . . . . . . . . . . .
1.1.1 Description of the Pre-reionization Simulation
1.2 Reionization to the modern epoch . . . . . . . . . . .
1.3 The Local Group . . . . . . . . . . . . . . . . . . . .
1.4 The Local Volume . . . . . . . . . . . . . . . . . . .
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2 Local Group Cosmology
2.1 Data and Completeness Corrections . . . . . . . . . . . . . . . . .
2.1.1 Number of non-fossil satellites in the Milky Way . . . . . .
2.1.2 The strange case of Leo T . . . . . . . . . . . . . . . . . .
2.2 Comparison with Theory . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Statistical properties of simulated “fossils” vs observations
2.2.2 The Missing Galactic Satellite Problem, Revisited . . . . .
2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Method and Tests
3.1 Numerical Method . . . . . . . . . . . . . . . . . .
3.1.1 Approximating Cosmic Variance . . . . . . .
3.1.2 All We Have to do is Run the Halo Finder .
3.1.3 A Note on the Halo Occupation Distribution
3.2 Tests of the Method . . . . . . . . . . . . . . . . .
3.2.1 Mass Resolution . . . . . . . . . . . . . . . .
3.2.2 Softening Length . . . . . . . . . . . . . . .
3.2.3 Subhalo Scale Comparisons . . . . . . . . .
3.2.4 A More Detailed Definition of a Fossil Dwarf
3.2.5 Luminosity Threshold for Fossils . . . . . .
3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . .
vii
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4 The Properties and Distribution of the Fossils
4.1 Fossil Properties . . . . . . . . . . . . . . . . . . . . .
4.1.1 The Inner Ultra-Faints . . . . . . . . . . . . . .
4.2 Baryonic Tully Fisher Relation . . . . . . . . . . . . .
4.3 A Note on Observations . . . . . . . . . . . . . . . . .
4.4 Fossil Distribution . . . . . . . . . . . . . . . . . . . .
4.4.1 Radial Distribution of Fossils Near Milky Ways
4.4.2 Primordial Cumulative Luminosity Functions .
4.5 The Isotropy Assumption . . . . . . . . . . . . . . . .
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
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5 The “Missing” Bright Satellites
5.1 Removing the Bright Satellites . . . . . . . . . . . . . . . . . . . .
5.1.1 Increasing Mass to Light Ratios . . . . . . . . . . . . . . .
5.1.2 Suppression of Pre-Reionization Dwarf Formation in Voids
5.1.3 Lowering the Star Forming Efficiency . . . . . . . . . . . .
5.1.4 The Ghost Halos . . . . . . . . . . . . . . . . . . . . . . .
5.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Observational Tests for the Primordial Model
6.1 The Ultra-Faint Dwarfs . . . . . . . . . . . . . .
6.1.1 Tidal Disruption . . . . . . . . . . . . .
6.1.2 The Undetected Dwarfs . . . . . . . . .
6.1.3 Number of Satellites . . . . . . . . . . .
6.2 Into the Voids . . . . . . . . . . . . . . . . . . .
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7 Summary and Future Work
172
Bibliography
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viii
List of Tables
2.1
2.2
2.3
2.4
2.5
2.6
2.7
Milky Way ultra-faint positions and distances
Milky Way ultra-faint observed properties . .
M31 ultra-faint positions and distances . . . .
M31 ultra-faint positions and distances . . . .
M31 ultra-faint observed properties . . . . . .
M31 ultra-faint observed properties . . . . . .
Number of non-fossils . . . . . . . . . . . . . .
3.1
3.2
3.3
Table of Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Table of Simulated Milky Ways . . . . . . . . . . . . . . . . . . . . . 83
Non-fossil vs. fossil dwarfs . . . . . . . . . . . . . . . . . . . . . . . . 89
4.1
Inner Ultra-faint dwarfs as tidal ultra-faint dwarfs? . . . . . . . . . . 115
ix
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21
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29
List of Figures
1.1
1.2
Pre-reionization Simulations . . . . . . . . . . . . . . . . . . . . . . . 6
The Local Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
ΣV and rhl vs. LV for fossils at z = 8.3 .
σ∗ and M/L vs. LV for fossils at z = 8.3
Galactocentric distance vs. Z . . . . . .
Z vs. LV for fossils at z = 8.3 . . . . . .
Fraction of baryons converted to stars . .
Metallicity vs. star formation efficiency .
Z vs. ΣV for fossils at z = 8.3 . . . . . .
Z vs. LV for fossils at z = 8.3 . . . . . .
GK06 luminosity function . . . . . . . .
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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
Diagram of high resolution particle position shifts . . . . . . . . .
z = 8.3 truncated mass functions . . . . . . . . . . . . . . . . . .
Effective redshift distribution . . . . . . . . . . . . . . . . . . . .
Low Resolution Large Scale Structure . . . . . . . . . . . . . . . .
Run C Large Scale Structure . . . . . . . . . . . . . . . . . . . . .
Run D Large Scale Structure . . . . . . . . . . . . . . . . . . . . .
MW.1 with and without dark matter . . . . . . . . . . . . . . . .
MW.2 with and without dark matter . . . . . . . . . . . . . . . .
MW.3 with and without dark matter . . . . . . . . . . . . . . . .
Mass Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Number of Satellites versus Host Mass . . . . . . . . . . . . . . .
Satellite Velocity Function . . . . . . . . . . . . . . . . . . . . . .
Tidal Stripping of Dwarfs . . . . . . . . . . . . . . . . . . . . . .
Fraction of primordial galaxies in non-fossils at z = 0 . . . . . . .
Number of Galaxy Mergers per. Fossil . . . . . . . . . . . . . . .
GK06 Galactocentric Radial Distribution with vf ilter = 30 km s−1
Number of galaxy mergers as a function of LV . . . . . . . . . . .
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4.1
ΣV and rhl vs. LV for the fossils at z = 0 . . . . . . . . . . . . . . . . 105
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4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
σ∗ and M/L contours for z = 0 fossils using Illingworth (1976) . . .
M/L(rhl ) contours using Walker et al. (2009) for fossils at z = 0 . .
Mass Functions of Detected and Undetected Fossils . . . . . . . . .
Mass Functions of Detected and Undetected Fossils . . . . . . . . .
Z vs. LV contours for fossils at z = 0 . . . . . . . . . . . . . . . . .
vmax vs. LV contours for fossils at z = 0 . . . . . . . . . . . . . . .
rhl vs. σ∗ for fossils at z = 0 . . . . . . . . . . . . . . . . . . . . . .
Baryonic Tully-Fisher relation for fossils at z = 0 . . . . . . . . . .
LV vs. BTF residual for fossils at z = 0 . . . . . . . . . . . . . . . .
Z vs. BTF residual for fossils at z = 0 . . . . . . . . . . . . . . . .
Vc = σ∗ vs. BTF residual for fossils at z = 0 . . . . . . . . . . . . .
rhl vs. BTF residual for fossils at z = 0 . . . . . . . . . . . . . . . .
Galactocentric distance vs. BTF residual for fossils at z = 0 . . . .
Total galactocentric radial distribution . . . . . . . . . . . . . . . .
Fossil galactocentric radial distribution . . . . . . . . . . . . . . . .
Galactocentric radial distribution of the undetected fossils . . . . .
Dwarf fossil fraction . . . . . . . . . . . . . . . . . . . . . . . . . .
Primordial luminosity function for vf ilter = 20 km s−1 . . . . . . . .
Primordial luminosity function for vf ilter = 30 km s−1 . . . . . . . .
Fossil luminosity function . . . . . . . . . . . . . . . . . . . . . . .
Primordial luminosity function with Koposov et al. (2008) ΣV limits
Luminosity and mass functions of the the “unfound” halos . . . . .
Fossil galactocentric radial distribution for a plane of satellites . . .
Fossil luminosity function for a plane of satellites . . . . . . . . . .
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
BSP - M/L = 500M" /L" . . . . . . . . . . . . . . . . .
BSP - M/L = 500M" /L" . . . . . . . . . . . . . . . . .
BSP - void H2 suppression . . . . . . . . . . . . . . . . .
BSP - f∗,crit = 1% . . . . . . . . . . . . . . . . . . . . . .
BSP - f∗,crit = 0.1% . . . . . . . . . . . . . . . . . . . . .
Fossil galactocentric radial distribution for fcrit = 1% and
Num. of Galaxy Mergers for Fossils and Non-fossils . . .
Ghost halo surface brightnesses . . . . . . . . . . . . . .
Primordial luminosity function without the non-fossils . .
Primordial luminosity function with Lnf = 10−3 LV . . .
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. . . . . . . 145
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fcrit = 0.1% 153
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. . . . . . . 157
Chapter 1
Introduction
We currently live in an epoch dominated by large spiral and elliptical galaxies;
however such was not always the case. In the cold dark matter paradigm (CDM), the
galaxies that populate the modern universe were formed from lower mass building
blocks via hierarchical merging. At the time of reionization (z = 6 − 15), the
majority of the universe‘s stellar mass was contained in these dwarf galaxies with
masses no greater than 109 M" . While many of these early dwarfs merged to form
the array of larger galaxies seen today, not all of them became part of spirals and
giant ellipticals. Those that survived unmolested to the modern epoch are very
faint (Gnedin and Kravtsov 2006; Ricotti and Gnedin 2005), and nearly impossible
to see beyond the Local Group. Therefore, in the quest to better understand the
formation of the first galaxies, the best place to look is in our cosmic backyard.
Hierarchical formation scenarios predict that most of the galactic halos formed
before reionization in minihalos which had masses below 108 − 109 M" . During the
epoch of reionization (z ∼ 15 − 6), the intergalactic medium (IGM) transitioned
from neutral H I to ionized H II. We know reionization ended by z ∼ 6 because
of the lack of a Gunn-Peterson trough in quasars with z < 6 (Becker et al. 2001;
Fan et al. 2002, 2006), showing no evidence of a neutral absorbing medium on the
1
line of sight between the quasar and Earth. While we can determine the end point
of reionization from quasar spectra, its extent and the sources that began it are
determined by τ , the optical depth of the universe (Shull and Venkatesan 2008),
derived from the CMB. The WMAP 7 value of τ = 0.088 ± 0.015 (Komatsu et al.
2011).
In addition to turning the IGM transparent to H ionizing radiation, reionization reheated the IGM to ∼ 104 K, cutting off the gas supply to minihalos. Those
minihalos, which formed stars at high redshift and survived to the modern epoch,
constitute a sub-population of dwarf satellites orbiting larger halos. CDM N-body
simulations predict a number of dark matter halos around the Milky Way and M31
that is two orders of magnitude greater than the number of observed luminous satellites (Klypin et al. 1999; Moore et al. 1999), the missing galactic satellite problem.
This may indicate a problem with the CDM paradigm or that feedback processes
are very efficient in suppressing star formation in the mass halos.
New observations (Belokurov et al. 2007, 2006; Geha et al. 2009; Ibata et al.
2007; Irwin et al. 2007; Kalirai et al. 2010; Majewski et al. 2007; Martin et al. 2006;
McConnachie et al. 2009; Walsh et al. 2007; Willman et al. 2005a,b; Zucker et al.
2006a,b) and recent simulations (Ricotti et al. 2002a,b, 2008) require not only a revisitation of the missing galactic satellite problem, but an extensive study of what
the smallest dwarfs can tell us about the epoch of the first galaxies. Cosmological
simulations of the formation of the first galaxies (Ricotti et al. 2002a,b, 2008) (hereafter the pre-reionization simulations) have shown most previously known dwarf
spheroidals (dSphs) to have properties consistent with the surviving fossils of the
first galaxies, and predicted the existence of an undiscovered, lower surface brightness population of dwarfs (Ricotti and Gnedin 2005) (hereafter, RG05). In RG05,
the members of the Local Group were sorted into three categories: non-fossils, pol-
2
luted fossils and true fossils. Non-fossils are galaxies whose total mass today exceeds
109 M" , a scale set by the filtering mass of the IGM Gnedin (2000). These galaxies
have continued to undergo star formation after reionization and today have multiple
stellar populations with at least a fraction of their gas retained. The less massive,
gas free dwarfs are designated as two types of fossils, with polluted fossils being
galaxies that formed more than 30% of their stars after reionization, and true fossils
which formed the majority (> 70%) of their stars before reionization. It is this last
group on which this work concentrates and, for the remainder of this work, “fossil”
refers to the true fossils only.
1.1
The First Galaxies
The formation of the first dwarf galaxies - before reionization - is regulated by
complex feedback effects that act on cosmological scales. Primarily, this involves
the self-regulating interplay of ionizing and non-ionizing UV radiation, and the
resulting formation and destruction of H2 , the only coolant available in the early
universe. As the first stars and galaxies formed, the gas was unenriched with a
primordial composition (75%H25%He). Since no metals were available for cooling,
the presence of H2 was required for star formation. The self-regulation mechanisms
governing the formation and destruction of H2 during these epochs therefore have
dramatic effects on the number and luminosity of the first, small mass galaxies, and
yet, are unimportant for the formation of galaxies more massive than 108 M" . The
mass scale is set by the mass required for Tvir > 104 K, allowing the gas to initially
cool via Lyman-α emission, allowing them to cool gas below their virial temperature.
In addition these more massive halos will retain a sufficient column density of H2
to self shield from FUV dissociating radiation, retaining their coolant for the first
3
generation of stars.
Galaxy formation in the high redshift universe is peculiar due to (i) the lack of
important coolants, such as carbon and oxygen, in a gas of primordial composition
and (ii) the small typical masses of the first dark halos. The gas in halos with
< 108 M
maximum circular velocities (vmax ) smaller than 20 km s−1 (roughly M ∼
"
at zvir ∼ 10, the virialization redshift of a halo with M ∼ 108 M" ) is shock heated
< 10, 000 K during virialization. At this temperature, a gas of
to temperatures ∼
primordial composition is unable to cool and initiate star formation unless it can
> 10−4 ). Although molecular hydrogen is
form a sufficient column density of H2 (xH2 ∼
easily destroyed by far ultraviolet (FUV) radiation (negative feedback), its formation
can be promoted by hydrogen ionizing radiation emitted by massive stars, via the
H− pathway (positive feedback) (Haiman et al. 1996).
H + e− ⇒ H − + H ⇒ H2 + e−
(1.1)
This primarily takes place on the edges of Strömgren spheres and inside relic H II
regions. Since, by definition, the first, massive stars form in pristine regions, their
halos would be able to retain enough H2 due to the inital lack of negative feedback
in those regions. The ionizing radiation from these stars will in turn allow molecular
hydrogen to form in regions where it otherwise would not.
It is difficult to determine the net effect of radiative feedback on the global star
formation history of the universe before reionization. At z > 6, the IGM is optically
thick to ionizing UV radiation, requiring a 3D treatment of radiative transfer to
address the formation of stars in minihalos. Without radiative transfer, we would
be left with only the effects of a dominant FUV background (at energies between
11.34 eV and 13.6 eV), which destroys H2 . Radiative transfer is required to simulate
the H − formation pathway for H 2 in the high redshift universe since the IGM is
opaque to ionizing UV radiation before the epoch of reionization. The FUV radiation
4
emitted by the first few Population III stars would be sufficient to suppress or delay
< 20 km s−1 . A
galaxy formation in halos with maximum circular velocities, vmax ∼
less top heavy Pop II IMF would produce stars with softer SEDs and less ionizing
and dissociating UV radiation. While this would produce fewer and smaller positive
feedback regions, the net effect would a decrease in the suppression of star formation
before reionization due to the drop in dissociating radiation and the resulting higher
survival rates of H2 (Ricotti et al. 2008).
Without the positive feedback, the gas in most halos with masses < 108 − 109
M" (below the Lyman limit) will not create or retain sufficient column densities of
H2 to self shield, cool and form stars. They will remain dark. Therefore, the number
of pre-reionization fossils in the Local Group would be expected to be very small or
zero. In the “tidal scenario,” the Local Group’s dwarf spheroidals (dSphs) are tidally
stripped remnants of more massive dwarf irregulars (dIrrs). However, this model
does not take into account the effect of ionizing radiation and “positive feedback
regions” at high redshift (Ahn et al. 2006; Ricotti et al. 2001; Whalen et al. 2008),
that may have a dominant role in regulating galaxy formation before reionization
(Ricotti et al. 2002a,b).
1.1.1
Description of the Pre-reionization Simulation
For a given cosmological model, simulating the formation of the first stars is a well
defined problem. However, these simple initial conditions become unrealistic once a
few stars form within a volume of several thousand co-moving Mpc3 .
The pre-reionization simulations used in this work differ from many other studies because they self-consistently include “positive feedback” from ionizing radiation
(Ricotti et al. 2002a,b, 2008). The pre-reionization simulations have a spatial resolution of 156 pc h−1 comoving (about 15 pc physical at z = 10) and a mass resolution
5
Figure 1.1: Figure 2 from Ricotti et al. (2008) showing the clustering properties
of first luminous galaxies. We show positions of dark halos with Mdm > 106 M"
in the simulation projected on the x-y plane in a slice with ∆d = 0.2h−1 Mpc at
z = 17.5, 14.6, 12.5, and 10.2 (clockwise from top left panel ). The 106 M" scale is
set by the resolution limit of the Ricotti et al pre-reionization simulations. Below
these masses the parameters found by the halo finder cannot be trusted. Black
circles show halo virial radii, and colored symbols mark halos hosting a luminous
galaxy with LV > 5 × 105 L" ( yellow), 5 × 104 L" < LV < 5 × 105 L" (cyan),
and LV < 5 × 104 L" (red). We assume M∗ /LV = 1/50 (solar), appropriate for
a young stellar population. Most luminous galaxies seem to form in groups or
filaments, with few in isolation in the lower density IGM.
6
of 4.93 × 103 M" h−1 for dark matter and ≈ 657 M" h−1 for the baryons. The stellar masses are always smaller than the baryon mass resolution and can vary from
∼ 0.6 M" h−1 to 600 M" h−1 with a mean of 6 M" h−1 . Note that the stellar
particles do not represent real stars. Instead they are subgrid patches of gas which
formed stars with a local efficiency, $∗ , according to the Schmit law. Note, that this
local star formation efficiency, which is set by hand, is different than the global star
formation efficiency of the galaxy. The global star formation efficiency is not set by
hand, but is dominated by the ability of a halo to form and retain H2 . In addition
to primordial chemistry and 3D radiative transfer, the pre-reionization simulations
include a recipe for star formation, metal production by SNe and metal cooling (see
Ricotti et al. (2002a) for details). The code also includes mechanical feedback by
SN explosions. The effect of SN is somewhat model dependent and uncertain because it is treated using a sub-grid recipe. Hence, the pre-reionization simulation
analyzed in this work includes metal pollution but not mechanical feedback by SNe.
Simulations show that while mechanical feed back from supernova is the dominant
mechanism for expelling gas in halos with M > 108.5 M" (Wise and Cen 2009), it is
only one of several mechanisms for halos in our mass range (M < 108 M" ).
The pre-reionization simulation data used in this work is from the highest resolution run in Ricotti et al. (2002b), evolved further to redshift z = 8.0 after the
introduction of a bright source of ionizing radiation that completes reionization at
z ∼ 9 (see RG05 for details). The need for introducing a bright ionization source is
dictated by the small volume of the simulation (1.53 Mpc3 ); otherwise the volume
would be reionized too late. The H I ionizing source removes all the remaining gas
and shuts down star formation in halos with vmax < 20 km s−1 . As the ionization
front moves through the minihalo, it is trapped and slowed by the neutral gas, producing a D-type front proceeded by shock waves. The heating of the gas by those
7
shockwaves produces a wind which expels the gas into the IGM. removing the halo’s
ability to form stars (Shapiro et al. 2004).
Simulations, including positive feedback, produce galaxies that are extremely
faint and with very low surface brightnesses. Since H2 cooling is inefficient, gas
does not cool quickly and collapse towards the center of the halo. Star formation
occurs throughout the halo at a slow rate and the Ricotti et al simulations do
not have the resolution to determine whether those stars formed in isolated Bok
globules or in clusters, thus producing a low luminosity population extending out
to RS , where
ρ(r) =
ρo
r
RS
!
1+
r
RS
"2
(1.2)
is the NFW profile (Navarro et al. 1996), r is the distance from the center, RS is
the scale radius of the halo, and ρo is the density parameter unique to each halo.
If a minihalo is able to form stars, the number and properties of that population
are determined by, among other things, feedback and enrichment by supernova, the
choice of the initial mass function (IMF) and the star formation efficiency, $∗ . In
§ 5.1.3 we address the effects which changing $∗ has at z = 0 on the primordial
populations in the Milky Way satellites and isolated dwarfs.
1.2
Reionization to the modern epoch
We would like to be able to test simulations of the first galaxies against observations,
but with LV < 106 L" (Ricotti et al. 2002a,b, 2008), these objects may be beyond the
reach of even JWST (Johnson et al. 2009; Ricotti et al. 2008). Therefore, observing
the first galaxies during their epoch of formation is not possible, even with ALMA
(Sheth 2011), but we can detect their remnants in the local universe. The minihalos
8
in which the first galaxies formed have shallow gravitational potentials and are easily
affected by the properties of the surrounding intergalactic medium (IGM). Imagine
a dwarf galaxy before reionization (z > 8) in a halo of a few 107 M" . It has been
able to form enough H2 via the H − pathway to form ∼ 105 M" of stars. When its
local IGM is reionized at z ∼ 9 the temperature of the surrounding gas is heated
to TIGM ∼ 104 K, greater than the virial temperature, Tvir , of our minihalo. The
faster moving gas particles in the hotter IGM are unable to fall into the dwarf’s
shallow potential well, and within a few hundred Myr star formation has ceased.
The threshold for accretion from the IGM and therefore the ability of a halo to
form stars after reionization is set by Tvir of the halo, where gas can only accrete if
TIGM < Tvir . Since
Tvir
Ωm h2
= 10500K
0.147
#
$−1/3 #
Mdm
108 M"
$2/3 %
1 + zvir
10
&
(1.3)
where Ωm and h are the fraction of matter in the universe and the dimensionless
hubble constant in units of (Ho /100 km s−1 /Mpc), Mdm is the mass of the dark
matter halo in solar masses, and zvir is the redshift of virialization. The temperature
threshold is equivalent to a mass threshold for a given redshift of virialization. We
also know that
vmax ∝ M β
(1.4)
where β ( 1/3 and vmax is the maximum circular velocity of a halo with total mass,
M ∼ Mdm , since the baryonic component is insignificant. The β ∼ 1/3 is derived
by equating gravity and centripical acceleration for a particle moving in a circular
orbit in a spherical halo.
ac = ag
(1.5)
σ
M
∝ 2
R
R
(1.6)
9
where σ is the velocity dispersion of particles moving at a radius R inclosing a mass
M. Since R ∝ M 1/3 and at the edge of the halo σ = vmax
2
vmax
∝
M
= M 2/3
M 1/3
vmax ∝ M 1/3
(1.7)
(1.8)
. However, dark matter halos are triaxial rather than spherical so rather than
β = 1/3, β ∼ 1/3.
Throughout this work, we express the threshold for accretion from the IGM in
terms of a filtering velocity, vf ilter , where a halo is only able to accrete additional
gas if vmax > vf ilter . A dwarf is defined as a pre-reionization fossil if its maximum
circular velocity has never been greater than the filtering velocity from reionization
to the modern epoch. For the majority of this work, we use a vf ilter = 20 km s
−1
,
which corresponds to TIGM ∼ 104 K. Like Gnedin and Kravtsov (2006) (hereafter
GK06), we assume the filtering velocity is constant in space and time. While this is
not a valid assumption given the dynamic and highly structured nature of the IGM,
the choice of a constant vf ilter = 20 km s−1 provides the most conservative definition
for the fossil population. GK06 used vf ilter = 30 km s−1 and the temperature of
the warm-hot intergalactic medium (WHIM with TW HIM ∼ 105 K) corresponds to
an even higher vf ilter ∼ 40 km s−1 . These higher filtering velocities will increase
the number and luminosity range of the fossil population. We discuss this in more
detail in § 4.6.
An additional caveat is that isolated fossils may undergo a second stage of gas
< 2. This late stage accretion onto concentrated
accretion and star formation at z ∼
minihalos is permitted by the lower TIGM after He reionization. The hallmark of this
late accretion would be a dwarf galaxy dominated by an old (> 12 Gyr) population
with either an H I reservoir or a small burst of star formation at low redshift (Ricotti
10
2009). This characteristic star formation history is seen in the isolated dwarf UGC
4879 (Jacobs et al. 2011).
However, this late stage accretion would not take place within the WHIM or near
the Local Group, and dwarf galaxies in those regions remain red and dead. This
allows us to connect the smallest dwarf spheroidals (dSphs) in the Local Group and
Local Volume to the high redshift universe, and it has been a great six years for the
Local Group!
The doubling of the Local Group satellite population, and the properties of those
satellites have provided a new laboratory in which we can test our understanding
of star formation on the smallest scales and the substructure “crisis” in CDM.
Unfortunately for the latter, we cannot just match a theoretical mass function to the
one derived from observations since it is only possible to derive the dynamical mass
within the furthest stellar orbit within the dwarfs (Illingworth 1976; Walker et al.
2009). The dark matter halo extends well beyond that. In addition, the observed
dark matter mass assumes an NFW profile in equilibrium, neither of which may be
true for dwarf galaxies near our Milky Way (Ricotti 2003; Walker et al. 2010).
For the local dwarfs, we have luminosity, LV , the line of sight velocity dispersion,
σlos , the half-light radius, rhl , the metallicity, [F e/H], the metallicity spread, σ[F e/H] ,
and various alpha element abundances [α/H].
From the pre-reionzation simulations we have derived values for the luminosity,
LV , line of sight velocity dispersion, σlos , half-light radius, rhl , metallicity, [F e/H],
and metallicity spread, σ[F e/H] for the simulated fossils. Independent alpha abundances are computationally complex and were not included in the pre-reionization
simulations. These data allow us to compare “apples to apples” and test our models against the real universe. As with all simulations, the values used in this work
are dependent on the assumptions and physics in the pre-reionization simulations.
11
In a more general context, our theoretical model assumes a primordial formation
scenario for the smallest Milky Way and M31 satellites.
1.3
The Local Group
Data mining of the Sloan Digital Sky Survey (SDSS) has roughly doubled the census
of Local Group dwarfs. Before 2005, the Local Group looked muck like it had in
Mateo (1998). Two massive spirals, the Milky Way and Andromeda were surrounded
by 18 dwarf satellites (LMC, NGC 55, Sextans A & B, SMC, WLM, Carina, Fornax,
GR8, Leo I, II & A, Sagittarius, Sculptor, Draco, Phoenix, Sextans and Ursa Minor)
and 17 dwarf satellites (IC 10, IC 1613, IC 5152, M32, NGC 185, NGC 205, NGC
3109, NGC 6922, DDO 210, LGC3, Pegasus, And I, II, II, VI & V and Antila)
respectively, with three additional dwarf spheroidals (Tucana, Cetus and KKR 25)
associated with neither galaxy but bound to the Local Group and the smaller,
bulgeless spiral M33 near M31. Of those 38 dwarfs, 12 were identified as fossil
candidates in RG05, Sculptor, Draco, Phoenix, Sextans and Ursa Minor around the
Milky Way and And I, II, II, VI, & V, and Antila around M31 in addition to the
isolated Cetus, KKR 25 and Tucana. All these dwarfs are void of gas and dominated
by old, metal poor stellar populations.
Starting in 2005, data mining of the Sloan Digitial Sky Survey expanded our
picture of the Local Group. This has resulted in the discovery of 15 “new” ultrafaint Milky Way satellites (Belokurov et al. 2010, 2009, 2007, 2006; Geha et al. 2009;
Irwin et al. 2007; Walsh et al. 2007; Willman et al. 2005a,b; Zucker et al. 2006a,b).
At the same time, deep surveys of the halo of M31 have found 17 new Andromeda
satellites (Ibata et al. 2007; Kalirai et al. 2010; Majewski et al. 2007; Martin et al.
2006; McConnachie et al. 2009). All of the new dwarfs, with the exception of Leo
12
T, are dSphs, devoid of gas and dominated by what appear to be old, metal poor
populations. In addition to doubling the census of Local Group dwarfs, the new
satellites have more than tripled the number of potential pre-reionization fossils
within 1 Mpc of the Milky Way. Detailed properties of this new population as of
March 2011 are in Tables 2.1 to 2.6.
We now have an excellent observational sample in the Local Group with which
to test models of the first galaxies and begin to ask and answer questions about our
local satellite population, and ΛCDM itself. Since we will compare our results to
the observed distributions in the Local Volume, a brief inventory and overview of
the current observational and theoretical work on this region is useful.
1.4
The Local Volume
The Local Volume consists of seven large groups of galaxies made primarily of dwarfs
centered around larger, Milky Way-type spirals, and ten groups composed entirely
of dwarfs, all within 5.5 Mpc of the Milky Way and bordering the Local Void. The
majority of these galaxies are concentrated near the super galactic plane (SGP)
(Karachentsev et al. 2003). The distribution is shown looking down from above and
into the SGP plane in Figure 1.2.
The seven major groups are centered around the Milky Way and Andromeda,
M81/M82, Cen A, M83, IC 342 and Maffei respectively. Cen A and M83, and IC 342
and Maffei can be further grouped into dynamical pairs similar to the Local Group.
Excepting Cen A (0.33 Mpc below the SGP), every group is within 0.1 Mpc of the
SGP (Figure 1.2). Typical distances of a group member from the central galaxy
range from 104 to 385 kpc. Each group shows evidence for a population of dwarf
spheroidal galaxies, bereft of neutral hydrogen gas, overwhelmingly located near the
13
5
5
CVnI
M81
M83
CenA
IC342
MW
M31
0
Maffei
0
Sculptor
-5
-5
-5
0
5
-5
x (Mpc)
0
5
x (Mpc)
Figure 1.2: The major groups of the local volume from above (left) and into
(right) the super galactic plane. The size of the circle around each massive host
represents its mass.
massive galaxy at the center of group. In the entire Local Volume, only four isolated
early-type dwarfs are observed, suggesting these galaxies are preferentially located
near the more massive halos (Karachentsev 2005).
The ten minor groups show no evidence for central galaxies. These dwarf groups
contain between two and five galaxies, with a median group population of four
galaxies but have the same typical size (179 kpc) as the groups dominated by a
massive galaxy (Karachentsev et al. 2003).
On the theoretical side we use our knowledge of the Local Volume to ask: Is
the “primordial scenario” consistent with observations when we move beyond the
virial radius of our own galaxy and peer into the voids? Unless the local component
of galaxy feedback is very strong, star formation should proceed similarly in small
mass halos regardless of a halo’s location relative to the Local Group. Therefore, the
voids should be populated with luminous objects (see Figures 3.5 and 3.6). As first
noted in Peebles (2001), they are not. The number of dwarf galaxies with absolute
magnitude MV > −16 (LV < 2 × 108 L" ) observed in the voids is smaller than
14
expected in CDM cosmology (Karachentsev et al. 2006, 2004; Tully et al. 2006).
This discrepancy has been named the “void phenomenon.”
According to Tikhonov and Klypin (2009), the luminosity function can only be
reconciled if halos with vmax < 35 km s−1 are dark. However, such a large mass
threshold for star formation would produce less than 35 luminous satellites between
100-200 kpc of the Milky Way. That is inconsistent with observations unless satellites with LV < 104 L" do not exist beyond 100 kpc (see Figure 4.19).
Alternatively, if the star formation rate is primarily determined by halo mass,
the void phenomenon can be reconciled with CDM by using a halo occupation
distribution for which the M/L ratio increases with decreasing halo mass. However,
this solution has only been tested for halos with M > 1010 M" (Tinker and Conroy
2009), two to three orders of magnitude more massive than our fossils. When we
extend their M/L ∼ M −1 relation to our fossil mass range, we obtain a M/L ratio
5
8
>
<
∼ 10 for the fossil population (M ∼ 10 M" ). This would produce “mega-faint”
dwarfs with M/L ∼ 2 − 3 orders of magnitude greater than those seen for the fossils
in RG05 and observed for the ultra-faint dwarfs.
This dissertation is an investigation of the fate and distribution of the fossils of
the first galaxies near the Milky Way and throughout the Local Volume. Chapter
2 presents the observational motivation provided by the discovery of the ultra-faint
dwarfs and the comparison of their numbers and properties to the simulated first
galaxies at reionization, assumed to take place at z = 8.3. Chapter 3 describes
the new set of N-body simulations we use to trace the fossils of the first galaxies
to the modern epoch. Here, we also present tests of our simulations, proving our
method works, and refining the observational definition of a fossil. Chapters 4 & 5
show the results of the simulations for the fossils and non-fossils respectively. These
simulations ask a series of questions about the Milky Way’s satellite population and
15
the dwarfs inhabiting the nearby void.
First, we want to know if the ultra-faint dwarfs are fossils of the first galaxies
and how many fossils remain undiscovered in the halo of the Milky Way. Then,
what can the Local Group dSphs tell us about star formation in the early universe?
Finally, we investigate the following conundrum: Can we simultaneously account
for the predicted and observed subhalo population around the Milky Way and the
lack of isolated galaxies with MV > −16 in the voids?
16
Chapter 2
Local Group Cosmology
Over the last six years, the census of the Local Group dwarfs has doubled with
the addition of ultra-faint, ultra-low surface brightness satellites around the Milky
Way and M31. These new dSphs provide an excellent opportunity for near field
cosmology in our Local Group, specifically an investigation of the physics of the
formation of the first stars and galaxies. Before we trace the fossil remnants of
these galaxies from reionization to the modern epoch, we compare the new ultrafaint dwarfs to luminous halos in the z = 8.3 output from the pre-reionization
simulations. We extended the work in RG05 to include the new ultra-faint dwarfs
in Bovill and Ricotti (2009) (hereafter, BR09), from which parts of this chapter are
taken verbatim.
This chapter is laid out as follows. In § 2.1, we collect published data on the new
dwarf population and, after correcting for completeness of the surveys, we estimate
the total number of Local Group satellites (which increases from 38 to ∼ 70). Using
the results of published N-body simulations in GK06, we compare the observed
number of luminous satellites to the estimated number of dark satellites that have
or had in the past a maximum circular velocity > vf ilter . Using the results of
published N-body simulations, we conclude that some ultra-faint dwarfs are likely
17
pre-reionization fossils. In § 2.2 we show that the properties of the new Milky
Way and M31 dwarfs are in remarkable agreement with the theoretical data on the
“fossils” from RG05 and with their Galactocentric distribution around the Milky
Way calculated in GK06. In § 2.3 we discuss the implications of the new dwarfs on
the formation of the first galaxies and the missing galactic satellite problem.
2.1
Data and Completeness Corrections
In Tables 2.1 to 2.6, we summarize the observed properties of the new dwarfs as of
March 2011. The new Milky Way satellites were discovered using SDSS Data Release
4, 5, 6 and 7, including SEGUE (Abazajian et al. 2009; Adelman-McCarthy et al.
2008, 2007, 2006; Yanny et al. 2009). When multiple references are available for a
dwarf property, we defer to the measurement with the smallest error bars. Excepting Bootes I and II, Canes Venatici I and Leo T, where central surface brightness
measurements were available, the average surface brightness inside the half light
2
radius, rhl , was used: ΣV = LV /(2πrhl
).
Recent surveys of M31 (Ibata et al. 2007; Kalirai et al. 2010; Martin et al. 2006;
McConnachie et al. 2009) have covered much of the space around the M31 spiral.
The surveys have found 19 new M31 satellites. The Pandas survey, which was
responsible for most of the new M31 dwarfs, is complete around M31 and M33 to
a ∼ 150 kpc projected distance from Andromeda. Any satellite counts within 150
kpc and with Mv < −6 and µV < 29 are complete (Brasseur 2011).
Two new M31 satellites, And XII and And XIV, have velocities near or above
their host’s escape velocity (Chapman et al. 2007; Majewski et al. 2007). Both
galaxies are classified as dwarf spheroidals and show a lack of H I gas, and both
−1
are likely on their first approach towards a massive halo. Their σ∗ of 2.6+5.1
−2.6 km s
18
(Collins et al. 2010) and 5.4 ± 1.3 km s
−1
(Kalirai et al. 2010), respectively, place
them below the 20 km s−1 threshold, and their currently known properties meet the
RG05 criteria for fossils.
In estimating the completeness correction for the number of the Milky Way
dwarfs, one should also account for selection effects from the limiting surface brightness sensitivity of the Sloan of ∼30 mag arcsec−2 (Koposov et al. 2008). The sensitivity limit is shown as a solid line in Figure 2.1. Identification of new satellites
depends on the visibility of the horizontal branch in the color-magnitude diagram,
which, for the typical luminosity of the new faint dwarfs (MV ≈ −4) drops below SDSS detection limits at Galactocentric distances beyond ∼ 200 − 250 kpc
(Koposov et al. 2008). Of the new Milky Way dwarfs, only Leo T is well beyond
this distance threshold and thirteen of the fifteen new Milky Way satellites are
within 200 kpc. We make the most conservative estimate, by assuming that we
have a complete sample of dwarfs within 200 kpc. Additional selection bias for the
new dwarfs comes primarily from the limits of the SDSS coverage on the sky. To
account for this, we apply the zero-th order correction of multiplying the number of
new dwarfs by 5.15. This correction assumes an isotropic distribution of satellites
when observed from the Galactic center. With these simple assumptions we estimate
that the number of Milky Way satellites with galactocentric distance < 200 kpc is
about 85 ± 14, including the 29 previously know satellites. The error estimate is
due to shot noise. When we add in the post 2009 data the completeness drops to
3.56 decreasing the number of Milky Way satellites to 65 ± 10. However, bright
satellites of the Milky Way are distributed very anisotropically (Bozek et al. 2011;
Kroupa et al. 2005; Metz et al. 2007, 2009; Zentner et al. 2005), so the assumption
of isotropy may not be a good one. Our assumption of isotropy is a 0t h order
representation of the distribution of satellites around our Milky Way. While it is
19
consistent with results from our CDM N-body simulations (Chapter 3), observations
suggest that the distribution is not isotropic, but rather in a plane roughly perpendicular to the disk (Kroupa et al. 2005; Metz et al. 2007, 2009; Zentner et al. 2005).
If we assume a planar distribution of satellites relatively symmetric about the disk
then the correction number of Milky Way satellites drops to 37 ± 8.
In addition, the luminous satellites can be radially biased, so the abundance of
the faintest satellites within 50 kpc may not be easily corrected to larger distances
without prior knowledge of this bias. And, of course, satellites of different luminosity and surface brightness will have different completeness limits. These selection
biases have been considered in detail in recent papers by Tollerud et al. (2008) and
Walsh et al. (2009). These studies find that there may be between 300 to 600 luminous satellites within the virial radius of the Milky Way. Their estimate for the
number of luminous satellites within a galactocentric distance of about 200 kpc is
229330
176 , twice as large as our simple (and more conservative) estimate.
20
Name
Type
(l, b)
dM W
(o )
(kpc)
Bootes I
dSph
(358.1, 69.6)
B06b
Bootes II
dSph
(353.7, 68.9)
W 08
Z06a
dSph
(74.3, 79.8)
B07
dSph
(113.6, 82.7)
dSph
(241.96, 83.6)
dSph
(28.7, 36.9)
CVn I
CVn II
Coma Ber.
Hercules
B07
B07
Z06a
B07
B07
B07
Leo IV
B07
dSph
(265.4, 56.5)
Leo V
B08
dSph
(261.86, 58.54)
Leo T
I07
dSph1
(214.9, 43.7)
(79.21, −47.11)
Pisces II
B10
dSph
Segue 1
B07
dSph2
Segue 2
B09
dSph
Ursa Major I
W 05b
B07
B08
I07
B10
66 ± 3
42 ± 8
D06
W 07b
218 ± 10
M 08
160+5
−4
M 08
44 ± 4
B07
133 ± 6
160+15
−14
B07
∼ 180
B08
407 ± 38
dJ08
∼ 180
B10
(151.763, 16.074)
23 ± 2
B07
(149.4, −38.1)
35
dSph
B09
97 ± 4
O08
Ursa Major II
dSph
(152.5, 37.4)
32 ± 4
Z06b
Willman 1
dSph2
(159.57, 56.78)
38 ± 7
W 05a
Table 2.1: Positions and distance of the Milky Way ultra-faint dwarfs. As a
note on the classification of the new objects as dSph, (1) Leo T has a ∼ 105 M"
of H Igas and a young stellar population and (2) Willman 1 and Segue 1 may
be star clusters instead of dSph.
The references are as follows: (B06a) -
Belokurov et al. (2006), (B07) - Belokurov et al. (2007), (B08) - Belokurov et al.
(2008), (B09) - Belokurov et al. (2009), (B10) - Belokurov et al. (2010), (D06) Dall’Ora et al. (2006), (dJ08) - de Jong et al. (2008), (I07) - Ibata et al. (2007),
(M08) - Martin et al. (2008), (O08) - Okamoto et al. (2008), (W08) - Walsh et al.
(2008), (W05a) - Willman et al. (2005a), (W05b) - Willman et al. (2005b), (Z06a)
- Zucker et al. (2006b), (Z06b) - Zucker et al. (2006a)
21
22
28 ± 5
1.0 ± 0.8 M 08
230 ± 40 M 08
7.9 ± 3.7 M 08
3.7 ± 1.8 M 08
11 ± 4
8.7 ± 4.5 M 08
4.5 B08
140 ± 10
8.0 B10
0.34 ± 0.23 M 08
0.86 B09
14 ± 0.4 M 08
4.0 ± 2.0 M 08
1.0 ± 0.9 M 08
Bootes I
Bootes II
CVn I
CVn II
Coma Ber.
Hercules
Leo IV
Leo V
Leo T
Pisces II
Segue 1
Segue 2
Ursa Major I
Ursa Major II
Willman 1
−2
)
M 08
242+22
−20
36 ± 9 W 08
546 ± 36
M 08
74+14
−10
77 ± 10 M 08
229 ± 19
M 08
116+26
−34
42 B08
115 ± 17
60 B10
M 08
29+8
−5
34 B09
M 08
318+50
−39
140 ± 25 M 08
25+5
−6
rhl
(L" pc
6.5 ± 2.0
10.5 ± 7.4 K09
7.6 ± 0.4 SG07
4.6 ± 1.0 SG07
4.6 ± 0.8 SG07
3.7 ± 0.9
3.3 ± 1.7 SG07
2.4+2.4
−1.4
7.6 ± 1.6 SG07
—
+1.4 S10
3.7−1.1
3.4 ± 2.0 B09
11.9 ± 3.5
5.7 ± 1.4
4.0 ± 0.9
σlos
(pc)
−2.1 ± 0.3
−1.79 ± 0.05 K09
−2.08 ± 0.02 K08
−2.19 ± 0.05 K08
−2.53 ± 0.05 K08
−2.58 ± 0.04 K08
−2.58 ± 0.08 K08
−2.0 ± 0.25 W 09
−2.02 ± 0.05 K08
—
−3.3 ± 0.2 G09
−2.0 ± 0.2 B09
−2.29 ± 0.04 K08
−2.44 ± 0.06 K08
−2.2 S08
[F e/H]
(km s−1 )
—
0.14 K09
0.46 K08
0.58 K08
0.45 K08
0.51 K08
0.75 K08
—
0.54 K08
—
—
—
0.54 K08
0.57 K08
—
σ[F e/H]
Table 2.2: Observed properties of the Milky Way ultra-faint dwarfs. Citations are as follows, B08 - (Belokurov et al. 2008),
B09 - (Belokurov et al. 2009), (G09) - Geha et al. (2009), (K08) - Kirby et al. (2008), (K09) - Koch et al. (2009), (S08) Siegel et al. (2008), (S10) - Simon et al. (2010), (W08) - Walsh et al. (2008), (W09) - (Walker et al. 2009)
LV
(103 L" )
Name
23
dSph
dSph
dSph
dSph
dSph
dSph
dSph
dSph
Z07
M 06
M 06
M 06
M 07
I07
I07
I08
And X
And XI
And XII
And XIII
And XIV
And XV
And XVI
And XVII
(120.23, −18.47)
I08
(112.43, −29.4)
(113.95, −23.9)
(111.63, −32)
(112.46, −28.8)
(112.72, −27.4)
(112.57, −28.0)
(125.8, −18)
C10
C10
C10
760+10
−150
830+170
−30
910+30
−160
L09
734 ± 23
B11
525 ± 50
770 ± 70
871 ± 87
B11
C10
621 ± 20
765+5
−150
(kpc)
(o )
(123.2, −19.7)
dM W
(l, b)
H05
B11
B11
L09
L09
73100
49
130
90
162.5
—
—
—
174 ± 29
45
(kpc)
rM 31
—
—
—
—
—
—
—
—
—
(kpc)
rM 33
(2007).
(2009), (M07) - Majewski et al. (2007), (M06) - Martin et al. (2006), (Mc09) - (Z04) - Zucker et al. (2004), (Z07) - Zucker et al.
- Collins et al. (2010), (H05) - Harbeck et al. (2005), (I07) - Ibata et al. (2007), (I08) - Irwin et al. (2008), (L09) - Letarte et al.
Table 2.3: Positions and distance of the Andromeda ultra-faint dwarfs. Citations are as follows: (B11) - Brasseuretal:11, (C10)
dSph
Z04
Type
And IX
Name
24
dSph
dSph
dSph
R11
R11
R11
And XXV
And XXVI
And XXVII
(120.4, −17.4)
(118.1, −14.7)
(119.2, −15.9)
(127.8, −16.3)
(131.0, −23.6)
(132.6, −34.1)
(111.9, −19.2)
R11
R11
R11
R11
R11
M 09
M 09
(112.9, −26.9)
(115.6, −27.6)
757 ± 45
762 ± 42
812 ± 46
600 ± 33
767 ± 44
R11
R11
R11
R11
R11
M 09
M 09
< 1033
[794] ∼
859 ± 51
802 ± 197
933 ± 61
1355 ± 88
(kpc)
(o )
(113.9, −16.9)
dM W
(l, b)
∼ 86 ± 48
∼ 101 ± 42
∼ 97 ± 47
∼ 197 ± 33
∼ 126 ± 44
R11
R11
R11
R11
R11
M 09
M 09
< 315
[224] ∼
152 ± 31
—
—
—
(kpc)
rM 31
—
—
—
—
—
< 227
[42] ∼
—
—
—
—
(kpc)
rM 33
M 09
McConnachie et al. (2009), (R11) - Richardson et al. (2011)
Table 2.4: Positions and distance of the Andromeda ultra-faint dwarfs. Citations are as follows: (M09) - Martin et al. (2009),
dSph
R11
And XXIV
dSph
M 09
And XXII
dSph
dSph
M 09
And XXI
R11
dSph
M c09
And XX
And XXIII
dSph
M c09
dSph
And XVIII
And XIX
Type
Name
25
149
75
49 C10
31 ± 33
41 C10
180 ± 90
711
410 ± 200
238
649
450 ± 260
28 ± 26
780 ± 190 M 09
< 60 M 09
[30 ± 10] ∼
And IX
And X
And XI
And XII
And XIII
And XIV
And XV
And XVI
And XVII
And XVIII
And XIX
And XX
And XXI
And XXII
σlos
(km s−1 )
C10
4.5+3.6
−3.4
3.9 ± 1.2
4.6 C10
C10
2.6+5.1
−2.6
+8.9 C10
9.7−4.5
5.4 ± 1.3
C11
11.5+5.3
−4.4
+3.2 C11
9.4−2.4
—
—
—
—
—
—
rhl
(pc)
C10
552+22
−110
339 ± 6
C10
145+24
−20
+70 C10
289−47
C10
203+27
−44
413 ± 41
220 ± 22
136 ± 14
254 ± 25
363 ± 36
2065 ± 206
146 ± 15
875 ± 127 M 09
< 282 M 09
[217] ∼
−2.2 ± 0.2 C10
−1.93 ± 0.11
−2.0 ± 0.2 C10
−2.1 ± 0.2 C10
−1.9 ± 0.2 C10
−2.26 ± 0.05
−1.58 ± 0.2 L09
−1.3 ± 0.14 C11
−2.0
−1.8 ± 0.1
−1.9 ± 0.1
−1.5 ± 0.1
−1.8 M 09
−2.5 M 09
[F e/H]
—
∼ 0.08
∼ 0.12
0.31 ± 0.03
—
—
—
—
—
—
0.23 ± 0.04 B11 / 0.48
—
—
σ[F e/H]
Table 2.5: Observed properties of the Andromeda ultra-faint dwarfs. Citations are as follows: C11 - Collins et al. (2011), K10
- Kalirai et al. (2010).
LV
(103 L" )
Name
26
1035 ± 50 R11
378 ± 20 R11
732 ± 60 R11
230 ± 20 R11
455 ± 80 R11
1028 R11
94 R11
649 R11
59 R11
124 R11
And XXIII
And XXIV
And XXV
And XXVI
And XXVII
—
—
—
—
—
σlos
(km s−1 )
−1.8 ± 0.2
−1.8 ± 0.2
−1.8 ± 0.2
−1.9 ± 0.2
−1.7 ± 0.2
[F e/H]
R11
R11
R11
R11
R11
—
—
—
—
—
σ[F e/H]
Table 2.6: Observed properties of the newest Andromeda ultra-faint dwarfs. Citations are as follows: R11 - Richardson et al.
(2011).
rhl
(pc)
LV
(103 L" )
Name
2.1.1
Number of non-fossil satellites in the Milky Way
In this section, we use the results of published high resolution N-body simulations (Via Lactea I (Diemand et al. 2007) & II (Diemand et al. 2008), Aquarius
(Springel et al. 2008) and Kravtsov et al. (2004)) to estimate the number of dark
halos in the Milky Way that have, or had, a circular velocity vmax > 20 km/s.
By definition, dwarf galaxies in these more massive dark halos are non-fossils and
polluted fossils. If we find that the number of observed Milky Way satellites exceeds the estimated number of these massive halos in CDM we must conclude that
at least a fraction of the observed Milky Way satellites are pre-reionization fossils,
assuming CDM simulations reflect the real universe. GK06 have estimated that
pre-reionization fossils may constitute about 1/3 of Milky Way dwarfs, based on
detailed comparisons between predicted and observed Galactocentric distributions
of dwarf satellites.
It is clear that if we simply count the number of dark halos within the Milky
> 20 km/s, their number is much smaller than the
Way virial radius with vmax ∼
current number of observed luminous satellites. However, a significant fraction of
dark halos that today have vmax < 20 km/s were once more massive, due to tidal
stripping (Kravtsov et al. 2004). If the stars in these halos survive tidal stripping
for as long as the dark matter, they may indeed account for a fraction or all of the
newly discovered ultra-faint dwarfs. Kravtsov et al. (2004) favor the idea that tidal
stripping of the dark matter halo does not affect the stellar properties of the dwarf
galaxy. Thus, this model is qualitatively similar to our model for pre-reionization
fossils, save a rescaling of the mass of the dark halos hosting the dwarfs.
However, once tidal stripping of dark matter halos reaches the outer most stellar
radii, they lose their stars more rapidly than they lose their dark matter since the
27
cuspy dark matter profile is more resilient to stripping than the flatter King profile
of the stars. (Peñarrubia et al. 2008b). Thus, they may quickly transform from
luminous to dark halos. According to this scenario, tidally stripped dark halos may
not account for the observed ultra-faint population. To summarize, if the number of
> 20 km/s is smaller than the number
dark halos that have or had in the past vmax ∼
of luminous Milky Way satellites, we may conclude that some dwarfs are fossils. Vice
versa, if the number is larger, we cannot make any conclusive statements about the
origin of Milky Way satellites.
High resolution N-body simulations of the Milky Way system give the number
of dark halos in the Milky Way as a function of their circular velocity vmax at z = 0.
The “Via Lactea” simulation by Diemand et al. (2007) finds:
Ndm (> vmax ) = Ndm,20
#
vmax
20km/s
$−α
,
(2.1)
with the number of dark matter halos with vmax = 20 km s−1 , Ndm,20 ≈ 27.7 and
α ≈ 3. However, the Aquarius simulations (Springel et al. 2008) finds a factor 2.5
more satellites at any given vmax , i.e., Ndm,20 ≈ 69 and α ≈ 3.15. Although the
Aquarius simulations have higher resolution than the Via Lactea simulation, the
large disagreement between the two works is due to a systematic difference, possibly
related to the creation of the initial conditions, and it is not due to the improved
resolution. The high σ8 (0.9) used in Aquarius versus Via Lactea (σ8 = 0.74) results
in a higher normalization of the cosmological power spectrum and more power on
small scales (Polisensky and Ricotti 2010). Therefore the Aquarius simulation will
produce more halos with a given vmax than Via Lactea or this work.
To determine the importance of tidal mass loss for satellites around the Milky
Way, we use results from Kravtsov et al. (2004). Figure 5 in Kravtsov et al. (2004)
gives the fraction of halos, f (vmax ), that presently have maximum circular velocity
vmax , but some time in the past had a circular velocity ≤ vf ilter = 20 km/s, where
28
max
Number of Halos with vmax
> vf ilter
Number of Dwarfs
vf ilter (km/s)
20
30
40
this work
65 ± 10
Tollerud
VL I
VL II
Aquarius
73 ± 16 100 ± 10
∼ 300 − 600
20
29
7.3
12
182 ± 40
59
35
Table 2.7: Table showing the number of non-fossils calculated using Equation 2.2
for three different filtering velocities. The columns are (1) filtering velocity in
km s−1 , (2) the corrected number of dwarfs assuming an isotropic distribution of
satellites, (3) the number estimated by Tollerud et al. (2008) within Rvir , and the
number of non-fossils derived from the mass functions of (4) Via Lactea I, (5) Via
Lactea II, and (6) Aquarius.
max
vmax
≡ max(vmax (t)). We approximate the Kravtsov et al. (2004) results for f (vmax )
with the power law f (vmax ) ≈ (vmax /20 km s−1 )β , with β ≈ 3.7. We then calculate
max
the number of dark halos Ndm (vmax
> 20 km s−1 ) analytically:
max
Ndm (vmax
−1
−1
> 20 km s ) = Ndm (vmax (z = 0) > 20 km s ) +
max
Ndm (vmax
> 20 km s ) = Ndm,20
−1
(
'
20 km/s
vmin
dv
dN
f (v)
dv
)
α
1+
(1 − xβ−α
min ) ≈ 2.64Ndm,20 (2.2)
β−α
> < σ >≈ 10 km s−1 roughly equals
where xmin = vmin /20 km/s, and vmin ∼
∗
the mean observed velocity dispersion of the stars, < σ∗ >, of ultra-faint dwarf
satellites. The rationale for integrating to vmin is that observed satellites are dark
matter dominated and cannot be hosted in dark halos that have vmax < σ∗ , unless
σ∗ is not a tracer for the dark matter content of the halo (e.g., due to tidal heating).
max
Using the above equation, we find 73 ± 16 and 182 ± 40 halos with Ndm (vmax
>
20 km s−1 ) within Rvir , for the Via Lactea I and Aquarius simulations respectively.
Both these numbers are smaller than the 300 − 1000 luminous Milky Way satellites
estimated by Tollerud et al. (2008). Taken at face value, these numbers indicate that
if the Via Lactea II simalations are correct, a fraction of Milky Way satellites must
29
be true pre-reionization fossils. However, the number of luminous satellites that
exist within the Milky Way’s virial radius is highly uncertain beyond a distance
from the Galactic center of 50 kpc.
Based on Figures 11 and 12 in Springel et al. (2008) (Aquarius) and Figure 5 in
Tollerud et al. (2008) (Via Lactea II), we estimate that roughly half of the Milky
Way satellites (within the virial radius Rvir ) are < 200 kpc from the Galactic center. Therefore, within 200 kpc we estimate 36 ± 8 and 91 ± 20 dark halos with
max
Ndm (vmax
> 20 km s−1 ) for the Via Lactea and Aquarius simulations respectively.
These numbers can be compared to our estimated number of luminous satellites
with d < 200 kpc (85 ± 14 satellites) and to the estimate from the Via Lactea II
simulations by Tollerud et al. (2008) (229 satellites). Using the Via Lactea I simulation, we still find that some dwarfs are true pre-reionization fossils but the argument
is weak if we use the Aquarius simulation results. In Table 2.7 we summarize the
counts for dark matter and luminous satellites discussed in this section.
Although there is considerable uncertainty in our estimates, it can be safely
concluded that, using the results of the Via Lactea I simulation, at least a fraction
of Milky Way dwarfs are fossils. However, this argument is weakened by results from
the Aquarius simulations, showing a factor 2.5 increase for the number of Milky Way
dark matter satellites in any mass range.
2.1.2
The strange case of Leo T
Almost all the newly discovered dwarfs are dSphs with a dominant old population
of stars and virtually no gas, which makes them viable candidates for being prereionization fossils. However, there is one notable exception that we discuss below.
With the gas and young stars of a typical dIrr and the radius, magnitude, mass
and metallicity of a dSph (Irwin et al. 2007; Simon and Geha 2007), Leo T presents
30
a puzzle. Leo T has a stellar velocity dispersion of σLeoT = 7.5 ± 1.6 km s−1
(Simon and Geha 2007), or an estimated dynamical mass of 107 M" within the
stellar spheroid (although its total halo mass may be much larger). Leo T shows
no sign of recent tidal disruption by either the Milky Way or M31 (de Jong et al.
2008) and is located in the outskirts of the Milky Way at a galactocentric distance
of 400 kpc. Leo T’s photometric properties are identical to those of pre-reionization
fossils. However, if we assume that Leo T is a pre-reionization fossil, it is not
expected to retain significant gas or form stars after reionization.
How did Leo T keep its H I and how did its < 9 Gyr old stellar population
form? Work by Stinson et al. (2007) suggests cyclic heating and re-cooling of gas
in dwarf halos can produce episodic bursts of star formation separated by periods
of inactivity. The lowest simulated dwarf to form stars has σ = 7.4 km s−1 , similar
to Leo T. However, the increasing of the IGM Jeans mass after reionization should
prevent gas from condensing back onto halos with circular velocity vmax < 20 km s−1 .
Another proposal (Ricotti 2009) is that, although the mass of Leo T at formation
was ∼ 107 − 108 M" (i.e., a fossil), as indicated by its stellar velocity dispersion, its
present dark matter mass and the halo concentration has increased after virialization
by roughly a factor of 10/(1 + z). This is expected if Leo T has evolved in isolation
after virialization, as seems to be indicated by its large distance from the Milky
Way. In this scenario, Leo T stopped forming stars after reionization, but it was
< 1 − 2). This
able to start accreting gas again from the IGM very recently (at z ∼
can explain the < 9 Gyr old stellar population and the similarity of Leo T to the
other pre-reionization fossils.
31
2.2
Comparison with Theory
In this section, we compare the properties of the new dwarf galaxies discovered in
the Local Group to the theoretical predictions of the pre-reionization simulations.
We remind the reader of the argument that justifies this comparison.
After reionization, due to IGM reheating, the formation of galaxies smaller than
20 km s−1 is inhibited because the thermal pressure of the IGM becomes larger
than the halo gravitational potentials (e.g., Gnedin 2000). Galaxies formed before
reionization stop forming stars due to the progressive photo-evaporation of their
interstellar medium by the ionizing radiation background (Shapiro et al. 2004) (although most of the ISM was already lost due to UV driven galactic winds and SN
explosions). Hence, if pre-reionization dwarfs do not grow above vmax = 20 km s−1
by mergers, their stellar population evolves passively, as calculated by stellar evolution models such as Starburst99 (Leitherer et al. 1999). We define such galaxies as
pre-reionization “fossils”.
Clearly, we do not expect two perfectly distinct populations of fossils with vmax <
20 km s−1 and non-fossils with vmax > 20 km s−1 , but a gradual transition of
properties from one population to the other. Some fossils may become more massive
than vmax ∼ 20 km s−1 after reionization, accrete gas from the IGM, and form
a younger stellar population. If the dark halo circular velocity remains close to
20 km s−1 the young stellar population is likely to be small with respect to the
old one. We call these galaxies “polluted fossils” because they have the same basic
properties of “fossils” with a sub-dominant young stellar population (see RG05).
Vice versa, some non-fossil galaxies with vmax > 20 km s−1 may lose a substantial
fraction of their mass due to tidal interactions. If they survive the interaction, we
cannot assume that their properties, such as surface brightness and half light radius,
32
stayed the same. Kravtsov et al. (2004) estimate that 10% of Milky Way dark matter
satellites were at least ten times more massive at their formation than they are today
and more were ∼ 2 − 3 times more massive than they are today. Although their
simulation does not include stars, they favor the idea that the stellar properties
of these halos would be unchanged. Conversely, a recent work of Peñarrubia et al.
(2008b) looks at tidal stripping of dark matter and stars, achieving some success
in reproducing the observed properties of ultra-faint dwarfs assuming that they
are tidally stripped dIrrs. Using our simulations, we cannot make predictions of
the internal properties of non-fossil dwarfs, which are too massive to be present in
significant numbers in the small volume of our simulation. However, using the prereionization simulation data (in RG05), GK06 finds that about one third of Milky
Way satellites may be fossils based on comparisons between observed and simulated
galactocentric distribution of the satellites.
2.2.1
Statistical properties of simulated “fossils” vs observations
Here we compare the RG05 predictions from the Ricotti et al. (2002a,b) pre-reionization
simulations for the fossils of primordial galaxies at reionization to the observed properties (see Tables 2.1 to 2.6) of the new ultra-faint Milky Way and M31 dwarfs. The
symbols and lines in Figs. 2.1-2.7 have the following meanings. All known Milky
Way dSphs are shown by circles; Andromeda’s dSphs satellites are shown by triangles; simulated fossils are shown by the small solid squares. The solid and open
symbols refer to previously known and new dSphs, respectively. The transition between fossils and non-fossil galaxies is gradual. In order to illustrate the different
statistical trends of “non-fossil” galaxies we show dwarf irregulars (dIrrs) with asterisks and the dwarf ellipticals (dE) as crosses, and we show the statistical trends
33
dE
dIrr
old M31 dSph
new M31 dSph
old Milky Way dSph
new Milky Way dSph
RG05 prediction
Willman I
Willman I
Figure 2.1: An extension of Figure 7 from RG05 to include new dwarfs in the SDSS
(Belokurov et al. 2007, 2006; Geha et al. 2009; Irwin et al. 2007; Walsh et al.
2007; Willman et al. 2005a,b; Zucker et al. 2006a,b) and recent surveys of Andromeda (Ibata et al. 2007; Majewski et al. 2007; Martin et al. 2006). Surface
brightness and half-light radius are plotted vs. V-band luminosities. Small filled
squares are the RG05 predictions, asterisks are known survivors, crosses are known
polluted fossils, closed circles are the previously known dSph around the Milky
Way, closed triangles are previously known dSph around M31, and open circles
and triangles are new dSph around the Milky Way and M31 respectively. The solid
lines show the SLOAN surface brightness limits and the dashed lines show the
< L < 1011 L )
scaling relationships for more luminous Sc-Im galaxies (108 L" ∼
B ∼
"
derived by Kormendy and Freeman (2004).
34
for more luminous galaxies as thick dashed lines on the right side of each panel.
Figure 2.1 shows how the surface brightness (top panel) and half light radius
(bottom panel) of all known Milky Way and Andromeda satellites as a function of
V-band luminosity compares to the simulated fossils. The surface brightness limit
of the SDSS is shown by the thin solid lines in both panels of the figure. The
new dwarfs agree with the predictions up to this threshold, suggesting the possible
existence of an undetected population of dwarfs with ΣV below the SDSS sensitivity
limit. The new M31 satellites have properties similar to their previously known
Milky Way counterparts (e.g., Ursa Minor and Draco). Given the similar host
masses and environments, it is reasonable to assume a similar formation history for
the halos of M31 and the Milky Way. This suggests the existence of an undiscovered
population of dwarfs orbiting M31 equivalent to the new SDSS dwarfs.
Extreme Mass-to-Light ratios
The large mass outflows due to photo-heating by massive stars and the consequent
suppression of star formation after an initial burst, make reionization fossils among
the most dark matter dominated objects in the universe, with predicted M/L ratios
as high as 104 and LV ∼ 103 − 104 L" (Bovill and Ricotti 2009; Ricotti and Gnedin
2005).
Figure 2.2 shows the velocity dispersion (bottom panel) and mass-to-light ratios, M/LV (top panel), as a function of V-band luminosity of the new and old
dwarfs from observations in comparison to simulated fossils. The symbols are the
same as in the previous figures. While derived mass data is available for all the
previously known dwarfs, we found no published σ values for 9 dIrr, 4 dE and 3
dSph (Antila, Phoenix and SagDIG) (Mateo 1998; Strigari et al. 2008). We observe
a good agreement between the statistical properties of the new dwarf galaxies and
35
Figure 2.2: Mass-to-light ratio and velocity dispersion of a subset of the new
dwarfs (Martin et al. 2007; Simon and Geha 2007) plotted with values for previously known dwarfs and RG05 predictions. The dashed lines show the scaling
< L < 1011 L ) derived
relationships for more luminous Sc-Im galaxies (108 L" ∼
B ∼
"
by Kormendy and Freeman (2004).
36
the RG05 predictions for the fossils, although simulated dwarfs show slightly larger
mass-to-light ratios than observed ones at the low luminosity end, LV < 104 L" .
Theoretical and observed derived masses are calculated the same way, from the
velocity dispersions of stars (i.e., M = 2rhl σ 2 /G) (Illingworth 1976), and do not
necessarily reflect the total mass of the dark halo at virialization. Indeed, the simulation provides some insight on why the derived value of the dynamical mass,
M ∼ (1 ± 5) × 107 M" , remains relative constant as a function of LV . Simulations
show that in pre-reionization dwarfs, the ratio of the radius of the stellar spheroid
to the virial radius of the dark halo decreases with increasing dark halo mass. The
lowest mass dwarfs have stellar spheroids comparable in size to their virial radii
(see Ricotti et al. (2008)). As the halo mass and virial radius increases, the stellar
spheroid becomes increasingly concentrated in the deepest part of the potential well,
thus the ratio of the dynamical mass within the largest stellar orbits to total dark
matter mass is reduced. This is because cooling is less efficient in the lower mass
halos, preventing the gas from cooling rapidly and falling to the center of the halo
before it fragments and forms stars. This effect keeps the value of the dynamical
mass within the stellar spheroid (measured by the velocity dispersion of the stars)
remarkably constant even though the total mass of the halo increases.
If dwarfs are undergoing tidal disruption (e.g., Ursa Major II), the velocity dispersions could be artificially inflated right before destruction (Walker et al. 2009).
However, the agreement with theory is rather good for all the new ultra-faint dwarfs.
The data on the lowest luminosity dwarfs in our simulations are the least reliable,
because they are very close to the resolution limits of the pre-reionization simulation
(we resolve halos of about 105 M" with 100 particles). Let us assume we can trust
the simulation and the observational data, even for the lowest luminosity dwarfs
and the discrepancy between simulation and observation at the low luminosity end
37
is real. The dynamical mass is M ∝ rhl σ 2 . There is good agreement between observations and simulations for σ in faint dwarfs. Thus, it is likely that the the reason
for disagreement in M/LV is due to the value of rhl , being smaller for the observed
dwarfs than the simulated ones. This could be partly due to an observational bias
that selects preferentially dSphs with higher surface brightness and smaller rhl (see
Figure 2.1). Another explanation is a dynamical effect, not included in our simulations that reduces the stellar radius of dwarfs after virialization; for instance, tidal
stripping. A larger sample size of distant dwarfs, including kinematics of And XII
and And XIV, both believed to be on their first approach to M31, would be useful
to better characterize this discrepancy.
The velocity dispersions of the stars for the observed new dwarfs and the simulated pre-reionization fossils are just below 10 km s−1 for luminosities < 106 LV .
The scatter of the predicted velocity dispersions as a function of dwarf luminosity
and the agreement between our simulations and the observed distribution suggests
that observed dwarfs with the same luminosity may be hosted in dark matter halos
with a broad distribution of masses. These results are in agreement with Figure 2.5,
showing that the faintest simulated primordial galaxies of a given luminosity may
form in halos with a total mass at virialization between 106 − 107 M" to a few
times 108 M" . This is because at these small masses the star formation efficiency
is not necessarily proportional to the dark halo mass and there is a large scatter in
f∗ at any given mass. This is due to the nature of feedback effects that are local
and depend on the environment (e.g., positive feedback on the formation of H2 ).
Ricotti et al. (2008) finds that pre-reionization dwarfs that form in relative isolation
have a typically smaller value of f∗ than dwarfs of the same total mass that form in
the vicinity of other luminous dwarfs (see Fig. 4 in Ricotti et al. (2008)).
38
Understanding the luminosity-metallicity relation
The metallicity-luminosity relation of the observed and simulated dwarfs is shown
in Figure 2.4. [Fe/H] is plotted against V-band luminosity in solar units. Symbols
for the previously known dwarfs, the new, ultra-faint dwarfs, and simulated fossils
are the same as in Figure 2.1. In this plot, we also color code simulated fossils
according to their star formation efficiency, f∗ , defined as f∗ = M∗ /Mbar , where M∗
is the mass in stars and Mbar ≈ Mdm /6 is the baryonic mass of the halo assuming
cosmic baryon abundance. Red symbols show simulated dwarfs with f∗ < 0.003,
blue 0.003 ≤ f∗ ≤ 0.03 and green f∗ > 0.03.
The new ultra-faint dwarfs do not follow a tight luminosity-metallicity relationship observed in more luminous galaxies (but see Geha et al. (2009)). This behavior
is in good agreement with the predictions of our simulation. The contentious “dwarf
galaxy” Segue 1 with luminosity of 340L" and metallicity of [Fe/H]∼ −2.8 fills a
gap in the luminosity-metallicity plot that was previously devoid of observed dwarfs,
present instead in the simulation (Geha et al. 2009). However, Segue 1, Segue 2,
Willman 1, and, to a lesser extent, Pisces II and Leo V, have half light radii smaller
than what our simulation predicts. In Figure 4.6 they are the filled green circles
which have [F e/H] abundances too high for their luminosities. In general, when
compared to their previously known counterparts, the new ultra-faint dwarfs have
a slightly lower metallicity but much lower luminosities.
There are several physical mechanisms that may produce the observed scatter
in metallicities of dwarfs at a given constant luminosity. Here, we identify the two
mechanism that are dominant in our simulation for primordial dwarf galaxies: 1) the
large spread of star formation efficiencies producing a dwarf of a given luminosity is
the dominant mechanism (to zero-th order approximation, in a closed box model,
we have Z ∝ f∗ ) and 2) the existence of dwarfs experiencing either a single or
39
multiple episodes of star formation contribute to the metallicity spread as well.
Metal pollution from nearby galaxies at formation might also play a role. For more
massive dwarfs that form after reionization, there may be different processes that
dominate metal enrichment. See Tassis et al. (2008) for a discussion.
Let’s start with the first mechanism. Contrary to what is usually the case for
more massive galaxies, the Ricotti et al pre-reionization simulations find that in
< 5 × 107 M the star formation efficiency f does
primordial dwarfs with masses ∼
"
∗
not monotonically increase with halo mass (i.e., f∗ has a large spread for a given
halo mass or for a given mass in stars, M∗ , see Figure 4 and Figure 7 in Ricotti et al.
(2008)). The wide range in values results from the sensitivity of f∗ on a halo’s environment and is due to local feedback effects that are of fundamental importance in
determining star formation in the shallow potential wells typical of pre-reionization
dwarfs. Figure 2.5 (Figure 7 in Ricotti et al. (2008)) shows that below a few 107 M" ,
halos with the same dark mass can be dark or luminous (depending on the environment). Thus, feedback from non-ionizing and ionizing UV radiation, mechanical
feedback and chemical enrichment can produce two halos with the same dark mass
and very different star formation efficiencies. This appears to be the main effect
responsible for the observed spread in metallicity for a given luminosity, in the new
dwarfs. In Figure 2.6, we plot the metallicity as a function of the mean star formation efficiency for the halo, f∗ . As expected, simulated dwarfs with higher values of
the star metallicity are the ones with the larger value of f∗ .
However, this effect alone cannot account for all the observed scatter of the
metallicity as illustrated by the color coding of simulated dwarfs in Figure 2.4. It
appears that the metallicity is not simply proportional to f∗ (otherwise the boundaries between symbols of different colors would be horizontal). Instead, for a given
value of f∗ , the metallicity is larger for fainter dwarfs. It is not too surprising that
40
Z is not simply proportional to f∗ . Even when using a very simple chemical evolution model, neglecting gas inflows and assuming instantaneous metal recycling, the
mean metallicity of the stars is proportional to M∗ /Mgas rather than f∗ = M∗ /Mbar ,
where Mgas is the initial value of the gas mass available for star formation. Thus,
Z ∝ f∗ (Mbar /Mgas ). If feedback effects reduce the value of Mgas /Mbar below unity
in the smallest and lowest luminosity primordial dwarfs, the metallicity of the stars
will be larger for a fixed value of f∗ , as observed in Figure 2.6 and Figure 2.4. The
reduction of Mgas /Mbar below unity can be produced by three effects: the increase
of the Jeans mass of the IGM over the virial mass of the halo due to reheating
(see Figure 6 in RGS08), heating of the gas via ionizing radiation from stars within
the halo, and by multiple episodes of star formation with a first burst that lowers
Mgas substantially, but does not produce sufficiently large values of f∗ and Z when
compared to subsequent bursts.
Figure 2.7 shows [Fe/H] versus the surface brightness in the V-band, ΣV . The
symbols are the same as in Fig. 2.1 and the solid line shows the SDSS sensitivity
limit. No trend is observed between metallicity and ΣV for the simulated dwarfs.
Observed dwarfs show less scatter for ΣV -metallicity relation than for the luminositymetallicity relation in Figure 2.4. There is one dwarf with metallicity below [Fe/H]=
−2.5: Segue 1 that has [Fe/H]= −2.8. Since the spectral synthesis method used in
Kirby et al. (2008) and Geha et al. (2009) may not be subject to the overestimation
of metallicities seen with measurements using the CA triplet, the lack of dwarfs with
[Fe/H]< −3.0 could be a sign of a change in the IMF at very low [Fe/H].
Finally, in Figure 2.3 we have examined whether there is a dependence of the
metallicities on the distance of the galaxy from the Milky Way or Andromeda. For
the new Milky Way dwarfs there is a slight trend of higher metallicities at smaller
galactocentric distances; however, the upward trend is dominated by Ursa Major II
41
Figure 2.3: The galactocentric distance vs. metallicity for the ultra-faint dwarfs
as of March 2011. The black symbols have the same meaning as in Figure 2.1.
and Coma Ber., both of of which show evidence for tidal disruption. For the M31
dwarfs, no trend was observed.
Figures 2.8 show the scatter of the metallicity of the stars, σ[F e/H] , plotted against
V-band luminosity and [Fe/H] respectively. Once more, the various point types and
colors are the same used in Figure 2.4. The observational data for the new dwarfs
matches the predictions, though Figure 2.8 shows a lack of low LV objects with
42
σ[F e/H] < 0.4. However, given the small number of data points available, it is not
possible to rule out selection effects of small number statistics as an explanation.
Dwarfs with low values of σ[F e/H] tend to have higher luminosities and are equally
likely to be a dE or dSphs. However, dwarfs with the highest σ[F e/H] are faint
dSphs with LV < 106 L" , and occupy the lowest mass dark matter halos. It is not
clear at this point how reliable the simulation data for σ[F e/H] is for dwarfs with
luminosities LV < 103 − 104 L" . However, all the dwarfs we analyze have at least 10
stellar particles and 100 dark matter particles. The masses of stellar particles vary,
depending on the star formation efficiency and the duration of the star burst.
As with the metallicities, we looked at how the metallicity spread depends on
the distance from the host. For both previously known and ultra-faint dSphs there
is no dependence on distance within the virial radius of the Milky Way. There is a
lack of dwarfs with high σ[F e/H] beyond 400 kpc; however, given the small number
of data points and the luminosity and surface brightness limits of current surveys,
the trend is not statistically significant.
2.2.2
The Missing Galactic Satellite Problem, Revisited
In order to simulate a representative sample of the universe, the size of cosmological
simulations must be significantly larger than the largest scale that becomes nonlinear at the redshift of interest. At z = 0, this scale is at least 50 to 100 Mpc.
Current computational resources are not able to evolve a cosmological simulation
of this size, including all relevant gas and radiation physics, to z = 0. However, as
argued in § 2.2, the properties of those fossil galaxies that survive tidal destruction
change only through passive aging of their stars formed before reionization (but see
Ricotti (2009)), allowing their properties at z = 0 to be simply related to their
properties at reionization. GK06 uses this approximation in conjunction with high-
43
Figure 2.4: Metallicity vs. luminosity for the new and old dwarfs plotted with
the RG05 predictions.
resolution N-body simulations of the Local Group, to evolve a population of dwarf
galaxies around a Milky Way mass halo from z = 70 to z = 0. For details of the
simulations, see § 2 in GK06.
GK06 defines a fossil as a simulated halo which survives to z = 0 and remains
below the critical circular velocity of 20 km s−1 with no appreciable tidal stripping. They calculate the probability, PS (vmax , r), of a luminous halo with a given
44
Figure 2.5: Figure 7 from Ricotti et al. (2008) showing the fraction of baryons
converted into stars as function of halo mass of the galaxy at z = 10. Circles, from
smaller to the larger, refer to galaxies with gas fractions fg = Mgas /Mb < 0.1%
(blue), 0.1% < fg < 1% (cyan), 1% < fg < 10% (red) and fg > 10% (green),
respectively.
45
Figure 2.6: Metallicity versus star formation efficiency f∗ = M∗ /Mb for the simulated fossils from Ricotti et al. (2008). The large squares show galaxies with
LV ≥ 103 L" , and the small squares galaxies with LV < 103 L" .
maximum circular velocity vmax to survive from z = 8 (the final redshift of the
RG05 simulation) to z = 0. For a given vmax , the number of dwarfs at z = 0 is
N(vmax , z = 8)PS (vmax , r). The surviving halos are assigned a luminosity based on
the LV versus vmax relationship from RG05. At z = 0, GK06 has a population of
dwarf galaxies with a resolution limit of vmax = 13 km s−1 . Unfortunately, this limit
corresponds to a lower luminosity limit of LV ∼ 105 L" , which includes Leo T and
46
Figure 2.7: Metallicity vs. surface brightness for the new and old dwarfs. The
surface brightness limit of the SDSS is shown by a solid vertical line. Note the
predicted dwarfs with Z<-2.5 and surface brightnesses above Sloan detection limits.
47
Figure 2.8: Metallicity spread vs. V-band luminosity for the new and old dwarfs.
Simulation data for the metallicity spread may be unreliable for dwarfs with
luminosities LV < 103 − 104 L" , due to the small number of stellar particles in
the galaxies.
48
Figure 2.9: Luminosity function of pre-reionization fossil dwarfs predicted in
GK06 (red) plotted with the luminosity function for the new and old Local Group
dSphs. The black lines are the observations corrected for completeness as discussed in Section 2. Corrections to the theory account for an under-abundance of
small halos near the hosts due to numerical effects (GK06).
49
Canes Venatici I, but excludes all the other new ultra-faint Milky Way satellites. We
do not show the prediction of the GK06 model below this lower luminosity limit. A
new N-body method with a resolution limit of LV ∼ 103 L" that follows the merger
histories for the halos will be presented in Chapter 3 of this work.
In Figure 2.9, we show the cumulative luminosity function from GK06 for the
Milky Way and M31 satellites with the addition of the new ultra-faint dSphs. The
lower panel shows satellites with distance from their host d < 100 kpc, the middle
panel d < 300 kpc and the upper panel d < 1 Mpc. The gray lines show the GK06
predictions, and the shaded region encompasses the error bars. Since, the resolution
limits of GK06 causes halos with vmax < 17 km s−1 to be preferentially destroyed by
tidal effects, the predicted luminosity function is corrected. Both the uncorrected
(lower) and corrected (upper) luminosity functions are plotted in the lower panel.
On all three panels, the black histogram and the points with error bars represent
the observed luminosity function of fossil dwarfs around the Milky Way and M31.
Their numbers have been corrected for completeness as discussed in § 2. For the
purposes of this plot, we are considering all the new dwarfs to be fossil candidates.
For d < 100 kpc (bottom panel), there is an overabundance of observed satellites with respect to the simulated luminosity function from 105 to 106 L" . This
discrepancy is likely due to excessive destruction rate of satellites caused by the
insufficient resolution of the GK06 N-body simulations. At distances d < 300 kpc
(middle panel), there is excellent agreement between theory and observation. Canes
Venatici I and the new Andromeda satellites are included in the latter panel. The
upper panel shows the luminosity function for all dwarfs within 1 Mpc of the host,
including Leo T. Note, that GK06 assumes an isolated Milky Way type galaxy (with
total mass comparable to the Local Group mass), while observations with d < 1 Mpc
of the Milky Way include the satellite system around M31. For d < 1 Mpc, there
50
is an under-abundance of observed satellites between 105 to 106 L" with respect to
the simulation predictions. However, this is consistent with the theory since beyond
250 kpc dwarfs with LV ∼ 105 L" drop below SDSS detection limits (Koposov et al.
2008). Hence, the under-abundance of observed dwarfs at large distances may be
due to the completeness limit of the survey.
2.3
Discussion
There are two main ideas for the origin of dSphs in the Local Group. Most importantly, these two ideas have very different implications for models of galaxy
formation, and the minimum mass a dark halo needs to host a luminous galaxy.
The “tidal scenario” holds the dwarfs we see today were once far more massive,
having been stripped of most of their dark matter during interactions with larger
galaxies (e.g., Kravtsov et al. 2004). In this model, we would expect the halos with
original dark matter masses below 108 M" to be mostly dark at formation and at
the modern epoch. The “primordial scenario,” has dwarf galaxies starting with close
to their current stellar mass of about 103 − 106 M" and, with several dark halos
with mass at formation below the threshold of about 2 × 108 M" hosting a luminous
galaxy. Star formation in halos this small is possible only before reionization and is
widespread if “positive” feedback plays a significant role in regulating star formation
in the first galaxies (Ricotti et al. 2001, 2002a,b).
In this chapter, we argue that the recent discovery of the ultra-faint dwarfs in
the Milky Way and M31 supports the “primordial scenario”. The existence of the
ultra-faint dwarfs was predicted by simulations of the formation of the first galaxies
(see RG05) and, as shown in the present work, the observed properties of this new
population are consistent with them being the “fossils” of the first galaxies.
51
While tidal stripping can reproduce properties of an individual galaxy, it is unable to completely reproduce all the trends in the ultra-faint population. This is
primarily seen in the kinematics of the ultra-faint dwarfs. Tidal stripping predicts a
steeper drop in σ with LV than is observed for the ultra-faint dwarfs (Peñarrubia et al.
2008b; Wadepuhl and Springel 2010), while our simulations show primordial dwarfs
which match the observed trends in σ extremely well. It has not been shown yet that
star formation in dwarf galaxies more massive than 108 − 109 M" can reproduce the
observed properties of ultra-faint dwarfs without requiring tidal stripping of stars.
The tidal model predicts that gas rich dIrr lose their gas and transform into
dSphs due to tidal or ram pressure interaction with a host halo. And XII, which
shows a proper motion close to current published escape velocity of M31, may be
on its first approach to the Local Group (Chapman et al. 2007; Martin et al. 2006).
A similar situation exists for And XIV. With a dynamical mass of M ∼ 3 × 107 M" ,
And XIV has vdwarf > vesc,M 31, suggesting it is also just entering the Local Group
(Chapman et al. 2007). In the tidal model (Mayer et al. 2007, 2006), And XII and
And XIV would be expected to still harbor significant reservoirs of gas, however,
observations show And XIV has MHI < 3 × 103 M" (Chapman et al. 2007) and
And XII has no detected H I (Martin et al. 2006). If neither of these dwarfs have
undergone significant tidal interactions with their hosts, as their velocities suggest,
how did they lose their gas? Though its velocity is unknown, the recently discovered
And XVIII (McConnachie et al. 2008), shows the same characteristics. At a distance
of 600 kpc from M31 and 1.35 Mpc from the Milky Way, it is unlikely that And
XVIII has undergone significant interaction with either Local Group spirals. And
XVIII is classified as a dSph with no detected H I and is similar to the Cetus and
Tucana dwarfs (McConnachie et al. 2008), both of which are good candidate fossil
galaxies (Ricotti and Gnedin 2005).
52
On the opposite end of the spectrum is the strange case of Leo T, the properties of
which are discussed in Section 2.1.1. While, Leo T has an H I mass fraction typical of
dIrr, its other properties are indistinguishable from the other newly discovered ultrafaint dwarfs (Simon and Geha 2007), all of which are dSph and potential fossils.
Leo T’s large distance from its host, H I reservoir and low probability of recent
tidal interactions (de Jong et al. 2008) make it a good candidate for a precursor
to a dSph in the tidal scenario. Particularly given that Leo T’s dynamical mass
within the stellar spheroid is small: 8.2 × 106 M" (Simon and Geha 2007), its gas
is unlikely to survive a single tidal encounter intact. Therefore, Leo T may have
formed at or near its current mass, and the striking similarity of Leo T to its ultrafaint counterparts suggests that they too could have formed as primordial dwarfs at
their current masses.
By our definition, pre-reionization fossils are dwarfs that form before reionization
in dark halos with vmax < vf ilter ∼ 20 km s−1 , while non-fossils dwarfs form in halos
with vmax > vf ilter before and after reionization. The value vf ilter ∼ 20 km s−1
that we use to define a fossil is primarily motivated by fundamental differences in
cooling and feedback processes that regulate star formation in these halos in the
early universe. This value of the circular velocity is also very close to estimates
based on the suppression of star formation in dwarfs after reionization (Gnedin
2000; Okamoto et al. 2008). However, as argued in (Ricotti 2009), fossil dwarfs can
have a late phase of gas accretion and star formation well after reionization, at
redshift z < 1 − 2. Thus, a complete suppression of star formation after reionization
is not necessarily what defines a “fossil galaxy”.
The number of Milky Way dark satellites that have or have had vmax > vf ilter
can be estimated using the results of published N-body simulations (see § 2.1.1).
We find that using the Via Lactea I N-body simulation there are approximately
53
Ndark ≈ 73±16 halos with vmax > 20 km s−1 within the virial radius (Diemand et al.
2007). The Aquarius simulations (Springel et al. 2008), however, show a factor of
2.5 increase in the number of halos with vmax > 20 km s−1 , i.e., Ndark ∼ 182 ± 40
dark halos. Within a distance of 200 kpc we estimate Ndark ≈ 36 ± 8 for the Via
Lactea and Ndark ≈ 91 ± 20 for the Aquarius simulation.
If the number of observed dwarf satellites within the Milky Way (after applying
completeness corrections) is larger than Ndark we must conclude that some satellites
are fossils. Twelve new ultra-faint dwarfs have been discovered around the Milky
Way by analyzing SDSS data in a region that covers about 1/5 of the sky. Applying
a simple correction for the sky coverage we estimate that there should be about
at least 85 ± 14 Milky Way satellites. However, the data becomes incomplete for
ultra-faint dwarf that are further than about 200 kpc from the Galactic center.
Comparing this number of luminous satellites to Ndark within 200 kpc we cannot
conclusively conclude that some ultra-faint dwarfs are fossils because Ndark for the
Aquarius simulation is comparable to the estimated number of luminous satellites.
Once both sensitivity and survey area corrections are applied, Tollerud et al.
(2008) estimates the existence of 300 to 600 luminous satellites within the virial
radius (Rvir ∼ 400 kpc) of the Milky Way and 229330
176 within 200 kpc. Comparing
Ndark to the Tollerud et al. (2008) estimates of the number of luminous Milky Way
satellites implies that a significant fraction of them are fossils (regardless if we use
the Via Lactea I, II or the Aquarius simulations estimates for Ndark ). In Table 2.7
we have summarized the aforementioned results.
Another argument for the existence of fossils is provided by detailed comparison
of the galactocentric distribution of fossils in the Milky Way (GK06). Based on these
comparisons GK06 finds that about 1/3 of Milky Way dwarfs may be fossils. In this
paper, we show the GK06 theoretical results in comparison to updated observational
54
data, including the new ultra-faint dwarfs found using SDSS data, and applying
completeness correction due to the limited area surveyed by the SDSS (about 1/5
of the sky). Assuming that the Local Group has a mass of 3 × 1012 M" , as in
the GK06 simulation, we find that there are no “missing galactic satellites” with
LV ≥ 105 L" within the virial radius of the Milky Way. When the new dwarfs
are included, the observed and predicted numbers of satellites agree near the Milky
Way, however, for distances greater than 200 kpc, it is clear that there is still a
’missing’ population of dwarfs. However, given that for d > 200 kpc, dwarfs with
LV ∼ 105 L" drop below SDSS detection limits (Koposov et al. 2008), the underabundance of observed dwarfs at large distances is not surprising and likely due to
the SDSS sensitivity limit.
A final comment regarding the cosmological model. The RG05 and GK06 simulations use cosmological parameters from WMAP 1. N-body simulations show
that the number N(M) of Milky Way dark matter satellites as a function of their
mass is not overly sensitive to the cosmology, although there are some differences on
the number of the most massive satellites (Madau et al. 2008). However, N(vmax )
should be sensitive to the cosmology (Zentner and Bullock 2003), and changes of σ8
and ns may affect the occupation number and galactocentric distribution of luminous halos. The collapse time of small mass halos in high density regions probably
dominates the 20% variations in σ8 between WMAP 1 and WMAP 3, limiting effects
due to the cosmology near large halos. A decrease in luminous dwarf numbers, due
to the lower σ8 , could be evident in the distribution of the lowest mass luminous
halos in the voids.
In conclusion, the number of Milky Way and M31 satellites provides an indirect
test of galaxy formation and the importance of positive feedback in the early universe. Although the agreement of the SDSS and new M31 dwarfs’ properties with
55
predictions from the RG05 and GK06 simulations does not prove the primordial
origin of the new ultra-faint dwarfs; it supports this possibility with quantitative
data and more successfully than any other proposed model has been able to do thus
far. At the moment, we do not have an ultimate observational test that can prove
a dwarf galaxy to be a fossil. Even a test based on measuring the SFH of the dwarf
galaxies may not be discriminatory because, as has been recently suggested, fossil
galaxies may have a late phase of gas accretion and star formation at z < 1 − 2,
during the last 9 − 10 Gyrs (Ricotti 2009). The distinction between fossils and
non-fossils galaxies thus is quite tenuous and linked to our poor understanding of
star formation and feedback in dwarf galaxies. Arguments based on counting the
number of dwarfs in the Local Universe probably provide the most solid argument
to prove or disprove the existence of fossil galaxies. In the future, a possible test
may be provided by deep surveys looking for ultra-faint or dark galaxies in the local
voids. Some fossil dwarfs should be present in the voids if they formed in large
numbers before reionization.
To extend our argument that the new ultra-faint dwarfs represent the high luminosity and surface brightness tip of a fossil distribution, we need to trace these
first galaxies from reionization to the modern epoch. The simulations described in
the next chapters were designed to do exactly that.
56
Chapter 3
Method and Tests
In this chapter, we present a novel method for generating initial conditions for a
set of cosmological N-body simulations. These runs allow us to directly trace the
distribution and evolution of the fossils of the first galaxies from reionization to the
modern epoch.
GK06 uses the filtering velocity approximation, in conjunction with high-resolution
N-body simulations of the Local Group, to evolve a population of dwarf galaxies
around a Milky Way mass halo from z = 70 to z = 0. For details of the simulations, see § 2 in GK06. GK06 defines a fossil as a simulated halo which survives to
z = 0 and remains below vf ilter = 30 km s−1 with no appreciable tidal stripping.
They calculate the probability, PS (vmax , r), of a luminous halo with a given maximum circular velocity vmax to survive from z = 8 (the final redshift of the RG05
simulation) to z = 0. For a given vmax , the number of surviving dwarfs at z = 0
is N(vmax , z = 8)PS (vmax , r), where PS is the survival probability for a satellite a
distance, r, from the host halo. The surviving halos are assigned a luminosity based
on the LV versus vmax relationship from RG05. At z = 0, GK06 has a population of
dwarf galaxies with a resolution limit of vmax = 13 km s−1 . Unfortunately, this limit
corresponds to a lower luminosity limit of LV ∼ 105 L" , which includes Leo T and
57
Canes Venatici I, but excludes all the other new ultra-faint Milky Way satellites.
Here, we describe and test a new method of generating N-body initial conditions which allows us to follow the evolution, merger rates and tidal destruction of
pre-reionization halos to present day and to overcome some of the limitations of
the GK06 method. The initial distribution of particles in the N-body simulations
represents the position, velocity and mass distribution of the dark and luminous halos extracted from pre-reionization simulations. Our simulations have a sufficiently
large volume and dynamical range to explore the distribution of fossil galaxies outside the Local Group, in nearby filaments and voids using limited computational
resources.
Our method improves on the GK06 work by removing the constraints that preclude a comparison of the GK06 simulations with the observed distributions of the
ultra faints: (1) Due to the resolution of their N-body simulations, GK06 cannot
resolve dwarfs with circular velocity, vmax , < 13 km s−1 which roughly corresponds
to a simulated dwarf with LV < 105 L" . With two exceptions, no ultra faint dwarfs
have LV > 105 L" (CVn I (Zucker et al. 2006b) and Leo T (de Jong et al. 2008)).
(2) The statistical matching of the baryonic properties of the pre-reionization halos
to equivalent z = 0 halos in their N-body simulation does not allow GK06 to account for mergers of pre-reionization halos after reionization. For z = 0 halos which
contain only one primordial galaxy the lack of mergers is not significant since not
accounting for them will not change the baryonic properties of the halo. However,
for the z = 0 halo which contain > 1 primordial galaxies the mergers of luminous
components will change the baryonic properties of the fossils at z = 0. While the
majority of mergers would not involve two luminous pre-reionization halos, the effect cannot be ruled out a priory. (3) The GK06 statistical matching also does not
account for the clustering bias of the most luminous pre-reionization halos. The
58
formation efficiency of H2 is dependent on stochastic effects, so the most luminous
pre-reionization halos form in the highest density regions of the Ricotti et al. (2002b)
simulations and are more likely to have undergone a merger with another massive,
luminous pre-reionization halo. (4) Extracting the baryonic properties of their fossils at z = 0 from the final output of the pre-reionization simulation does not allow
GK06 to account for cosmic variance. By z = 0, the faster evolution of structure in
over-dense regions (ie. Local Group) and the slower structural evolution of underdense regions (ie. Local Void) have produced significant variance in the numbers
and types of objects seen in both.
This chapter is laid out as follows. § 3.1 describes the simulations and § 3.2
show the variety of test we performed to ensure that our method produced results
equivalent to those of other published N-body simulations. Finally, in § 3.2.4 we
present a more detailed definition of a fossil and refine the observational criterion
for the “fossil” Local Group satellites.
3.1
Numerical Method
To achieve the resolution necessary to study the ultra-faint dwarfs in a z = 0
volume equivalent to the Local Volume, we developed a method for generating initial
conditions for N-body simulations which provides the required mass resolution, while
using only limited computational resources. Our simulations allow us to trace the
merger rate and tidal stripping of the first galaxies from reionization to the modern
epoch. Traditional initial conditions for CDM simulations begin with an evenly
distributed grid of uniform mass particles before the positions and velocities are
perturbed according to a given power spectrum. Our method follows the same
concept, except the initial distribution of the particles is not a uniform grid, but
59
represents the distribution of halos in the final outputs of a 1Mpc3 high resolution
cosmological hydrodynamical simulation run to z = 8.3 (Ricotti et al. 2002b) (we
refer to these as the pre-reionization simulations and the halos found in their 1 Mpc3
outputs as pre-reionization halos). Thus, each particle represents a dark or luminous
halo with a different mass and given stellar properties.
All of the initial conditions described in this section were run from their initial redshift, zinit , to z = 0 using Gadget 2 (Springel 2005) on the University
of Maryland HIPCC Deepthought and analyzed with the Amiga halo finder AHF
(Knollmann and Knebe 2009). A more complete discussion of the various halo finders used in this thesis is provided in § 3.1.2.
Figure 3.1 shows how we construct our high resolution region. We produce a lattice of the pre-reionization simulation z = 8.3 output. This gives us a grid similar to
that used in traditional CDM, except power on scales below 1 Mpc is already present
through the positions of the pre-reionzation halos. To add the larger scale power, we
perturb the particle positions and velocities of the pre-reionization halos according
to a power spectrum with no power for modes l < 1 Mpc. This method, similar
to the one described in Tormen and Bertschinger (1996), is described in detail below.
The hybrid initial conditions are set using the following steps. (1) We locate
an analog to the Local Volume within a low resolution 503 Mpc3 volume run from
z = 40 to z = 0. (2) A high resolution region is built out of the final outputs
from the pre-reionization simulations at zinit = 8.3. (3) Finally, we insert our high
resolution, ‘Local Volume’ into the larger low resolution simulation at zinit = 8.3
and run it to z = 0 using Gadget 2 (Springel 2005). We now explain these steps in
more detail.
We need to generate and run a volume large enough to contain at least one sub-
60
Figure 3.1: Diagram of how we add the large scale density perturbations to our
high resolution region. In this diagram we show the upper, front, left-hand corner
of our high resolution region. The size of each box enclosed by the dotted lines
−1/3
is 1 Mpc×NM pc on a side where N is the number of course particles per Mpc3 .
In each box, the black cross shows the position of an unperturbed, low resolution
particle and the red blob shows that particle after the large scale positions and
velocity perturbations have been applied. A pre-reionization halo at the same
location as the black cross will have its position perturbed as shown. If the prereionization halo is between the black crosses, the perturbation on its position
will be a linear interpolation between those of nearby black crosses, representing
the perturbed positions of the low resolution particles.
61
volume analogous to the Local Volume. Our low resolution simulation is a 503 Mpc3
volume with 2503 particles run from z = 40 to z = 0. The power spectrum at z = 40
is generated by the cosmological initial conditions generator P-GenIC. At z = 0, we
use the friend-of-friend halo finder HOP (Eisenstein and Hut 1998) to locate potential Milky Ways. In our ‘Local Volume,’ we look for a filament between two
Virgo-like clusters with 2 − 3 halos with M ∼ 1012 M" within a 73 − 103 Mpc3 volume. Ideally, one of our Milky Ways has an equal mass companion within 1 Mpc,
however, we were not able to find such a pair in our volume. Since the Milky Way
and M31 are on first approach, within the virial radius where we can make the most
accurate comparisons, the effect of the companion is minimal.
From the location of our Milky Ways, we define our ‘Local Volume’ as a region
∼ 5 − 10 Mpc across, centered on one of our Milky Ways. Once we have a ‘Local
Volume’ at z = 0, we estimate its equivalent volume at zinit = 8.3. We do this via
tagging the low resolution particles in our present day Local Volume, and, using
their positions at z = 8.3, determine the equivalent rectangular prism containing
the majority of the tagged particles. At this point, we have defined a high resolution
region with dimensions m × n × p.
We turn the 1 Mpc3 z = 8.3 output from the pre-reionization simulations to
an equivalent cube of N-body particles as follows. First, any pre-reionization halo
in the output becomes an N-body particle with that halo’s position, velocity, mass
and, critically, unique ID. We then choose a mass resolution, mtrun , for our high
resolution simulations and truncate the mass function of the pre-reionization halo
at that resolution. To account for the additional mass needed to bring each 1 Mpc3 to
the average density of the universe, we add a population of lower mass dark particles.
Hereafter we will refer to this population as tracer particles. These tracer particles
< m
have a mass, mtrace ∼
trun . The positions and velocities of the tracer particles are
62
determined from the position and velocities of the pre-reionization halos with masses
below the truncation mass. This dark tracer population preserves our mass budget
while allowing us to follow the dynamical evolution and locations of the lowest mass
minihalos which were unable to from stars even with positive feedback.
At the end of this process we have a 1 Mpc3 cube of N-body particles with
mmin ∼ mtrace , where positions, velocities and masses are determined by the z = 8.3
output of the pre-reionization simulations. The mass function produced by this
method is shown in the upper left panel of Figure 3.2. The spike in the lowest mass
bin shows the mass of the tracer particles. Critically, each particle has a unique ID
allowing us to trace each pre-reionization halo to z = 0 and retrieve its baryonic
properties in the modern epoch.
We have generated a 1 Mpc3 cube for which each particle is a tracer for a prereionization halo. From the location of our Local Volume, we have a rectangular
prism at z = 8.3 where our high resolution region will go. We duplicate the 1 Mpc3
box to form the m × n × p prism used for the high resolution region. We now have a
m×n×p prism with power on l < Mpc scales. We add power on l > Mpc scale using
the position shift, δx, of the low resolution particles via linear interpolation between
them. Once we have δx, we use the linear relation, δv = A(z)δx to calculate the
velocity perturbation, δv, for our high resolution particles where A(z) is the ratio of
the δv/δx at a given redshift. We now have a high resolution region with m × n × p
embedded inside a 503 Mpc3 simulation at z = 8.3. In the low resolution region, all
power comes from the power spectrum, and in the high resolution region the power
comes from the power spectrum on l > Mpc scales and from the z = 0 mass function
of the pre-reionization simulations on l < Mpc scales. This mass function matches
the Press-Schetcher at high redshifts.
The high resolution region ∼ 10 Mpc on a side, with a mass resolution of
63
∼ 3.2 × 105 M" , is embedded in a low resolution volume 50 Mpcs on a side containing 2503 particles at z = 8.3.
When compared to traditional zoom simulations, our high resolution region
has several key differences. Primarily, each of our particles represents a resolved
halo from the pre-reionization simulations. Each of these pre-reionization halos has
a set of dark matter and stellar properties derived at z = 8.3. This technique
allows us to push our simulations to higher mass resolutions over a ‘Local Volume’ sized region without a prohibitive increase in the number of particles. However, this technique precludes us from determining detailed density profiles of prereionization halos at z = 0. Since we assume the primordial galaxies have been
relatively unaffected by tidal forces and significant mergers, their baryonic properties at reionization can be simply mapped to their stellar properties at z = 0
by accounting for the evolution of their stellar properties. The stellar properties
of the pre-reionization halos are preserved through the unique IDs of each particle
in our simulation. If, in the modern epoch, a given pre-reionization halo is in a
halo whose maximum circular velocity has never exceeded the filtering velocity, it
has not accreted gas from the IGM after reionization. If a halo has gone above
the filtering mass it may have accreted gas and likely formed stars. Since we do
not simulate baryonic evolution after reionization, we have only limited information on the primordial populations of these more massive halos and none on the
< 12.5 Gyr) stars and gas. This filtering velocity, v
younger ( ∼
f ilter is the point below
which star formation is suppressed by the reheating of the IGM via reionization
feedback (Babul and Rees 1992; Benson et al. 2006; Efstathiou 1992; Gnedin 2000;
Hoeft et al. 2006; Navarro and Steinmetz 1997; Quinn et al. 1996; Shapiro et al.
1994, 2004; Susa and Umemura 2004; Thoul and Weinberg 1996). The subsequent
64
lack of star formation in these low mass halos allows us to approximate its present
day observable properties from those at reionization. If a halo is able to exceed the
filtering mass and accrete gas after reionization, it is not considered a fossil and we
have only very limited information on its z = 0 baryonic properties. We consider
the initial conditions built using the method described above as our first order simulations, specifically, runs A, B and C (Table 3.1). The initial conditions for run D,
which are significantly different than those described for runs A-C, are described in
the next section. For the remainder of this work we focus on Run C since Runs A
and B do not have the resolution necessary to study the dwarf populations inside
the Milky Way’s virial radius.
3.1.1
Approximating Cosmic Variance
For our first order simulations (see Table 3.1), we assume that every part of our
‘Local Volume’ evolves at the rate associated with the mean density of the universe,
before and after reionization. However, there are deviations from this mean due to
linear perturbations on large (> 1 Mpc) scales . The evolution of a given region
depends on its mean density with regions of higher density evolving faster than
their lower density counterparts (Cole 1997; Crain et al. 2009; Reed et al. 2007). As
a result, halos will collapse, and form stars, at later times in the voids compared to
the filaments. To account for this effect, we relate the over-density or under-density
of each region of our high resolution region to the speed of its evolution. We express
the evolution of a region as a function of its densities as zef f = zinit + ∆z, where
zef f is the effective redshift, zinit is the redshift of the simulations, and the effective
redshift of a region whose local density is the average density of the universe, ρo (zo ),
and:
∆z = (1 + zinit )[(1 + δ)−0.6 − 1)]
65
(3.1)
Figure 3.2: Truncated mass function of the pre-reionization outputs from z = 8.3
(top left), z = 10.2 (top right), z = 12.1 (bottom left), and z = 14 (bottom right).
The spike in the lowest mass bin at all four redshifts is due to the dark tracer
particles.
66
Figure 3.3: Fraction of 1 Mpc3 cubes with a given effective redshift, zef f . The
red curve shows the distribution for all the Mpc3 cubes in our entire 503 Mpc3 ,
low resolution volume. The black histogram show the fraction of 1 Mpc3 volumes within the high resolution region which use a given pre-reionization output.
Specifically, z = (8.3, 10.2, 12, 1, 14). Sub-regions with zef f ∼ 17 use the zef f = 14
pre-reionization output. The dashed vertical line shows the zinit = 10.2 for our
second order initial conditions.
is the correction to zinit due to δ, the local over-density or under-density of a given
region.
To approximate this variance effect, we produce a set second order initial conditions as in Cole (1997) (run D). The sole difference between runs D and C lies
in the construction of the high resolution volume. Instead of using a single prereionization simulation output at z = 8.3 (runs A-C), we use outputs at multiple
redshifts (z = 8.3 − 14) to approximate the differential evolution of the universe
67
up to zinit = 10.2. Before constructing our high resolution region, we calculate the
effective redshift of each 1 Mpc3 sub-volume. Each sub-volume is then assigned a
pre-reionization output based on its effective redshift, with the lowest density voids
at zef f = 14 and highest density regions at zef f = 8.3. The details of this second
order method are described below.
To account for the different rates of structure formation, we take the following
additional steps when generating our high resolution region. (1) First, for each
1 Mpc3 cube within our low resolution volume, we calculate local density at z = zinit .
(2) From the density, we use Equation 3.1 to find the shift in effective redshift
due the over-density or under-density of each subvolume, and then calculate zef f
(Figure 3.3). (3) Since we have a discrete set of pre-reionization outputs at z =
(8.3, 10.2, 12.1, 14), we divide the 1 Mpc3 cubes within our high resolution region
into four bins based on their densities and effective redshifts. The fraction of cubic
Mpcs within our high resolution region in each effective redshift bin is shown as the
black histogram overlaid on the zef f distribution in Figure 3.3. Note, that both the
histogram and the smoother curve follow the same general shape. (4) Finally, based
on which bin each Mpc3 falls into, we assign it a pre-reionization output.
To account for the faster evolution in our high density regions, for Run D we use
a zinit = 10.2 instead of the zinit = 8.3 used in Runs A-C. This allows us to assign
a zef f = 8.3 to place near Milky Ways in our high density region. Nothing else
substantially changes, except for using the z = 10.2 output from the low resolution
simulation to generate the l > 1 Mpc structure in the high resolution region.
All the pre-reionization outputs are truncated to the same mass resolution using
the same method described in the previous section. As near as possible, we use tracer
particles of the same mass in each pre-reionization output. The truncated mass
68
functions of the three additional pre-reionization outputs used in our second order
initial conditions are the additional panels (bottom and top right) in Figure 3.2.
After the high resolution has been built and the large scale modes added at
zinit = 10.2, we embed it inside the low resolution volume region and run to the
present with Gadget 2. Run D has two key differences when compared to Runs AC. First, the 503 Mpc3 snapshot used to generate the l > 1 Mpc modes is z = 10.2
instead of z = 8.3. Second, the z = 8.3 pre-reionization output is not used for the
entire high resolution volume, but only in the over-dense regions, with outputs from
z = (10.2, 12.1, 14) used for the average and under-dense regions.
In addition to accounting for cosmic variance, comparisons of runs A-C and run
D allow us to probe two different reionization scenarios. Since we cannot account
baryonic evolution after “reionization” when the pre-reionization outputs are transformed into our N-body simulation, we assume no baryonic evolution occurred after
reionization in our fossils. During UV reionization we assume our entire volume was
reheated to ∼ 104 K (Ricotti and Ostriker 2004). We also assume that the entire
volume was reionized by zinit and that the photo-evaportation of gas in minihalos
completely cuts off star formation in the smallest galaxies. For runs A-C this approximates reheating at zinit ∼ 8.3 by UV photons generated by stars in the first
galaxies (Sokasian et al. 2004; Wise and Cen 2009). Since the voids evolve at a
slower rate than the filaments, using the same pre-reionization output for our entire
simulation is effectively allowing the low density regions to evolve for a longer time
before their IGM is reheated to 104 K. This is consistent with reionization and reheating beginning in the filaments before spreading into the voids. In this scenario,
low mass halos in the voids would have had more time to accrete gas and form stars
than their counterparts in the filaments before reionization and reheating cut off
69
their gas supply. We therefore expect the “filaments out” reionization scenario in
run C produces brighter voids than the “simultaneous” reionization approximated
in run D. This is seen in Figures 3.5 and 3.6
Since each 1 Mpc3 subvolume in Run D used a pre-reionization output consistent
with its effective redshift, the entire high resolution region has been given the same
amount of time to evolve. When we transition from the pre-reionization output to
our N-body simulations, Run D does not allow low mass halos in the low density
regions to continue to evolve as the denser filaments are reheated. Instead, Run
D approximates a universe in which all of space is reionized and reheated at approximately the same time by X-rays from the accretion of the ISM onto Pop III
stellar remnants. Uniform reheating of the filaments and voids is a characteristic
of reionization and reheating from X-rays produced by remnants of the first stars
accreting from the ISM at high redshift (Ricotti and Ostriker 2004; Ricotti et al.
2005; Ripamonti et al. 2008; Shull and Venkatesan 2008; Venkatesan et al. 2001).
X-rays could also be produced by primordial black hole binaries (Mirabel et al. 2011;
Saigo et al. 2004). When compared to the “filaments out” reheating by UV radiation, the simultaneous X-ray reheating scenario produces noticeably darker voids.
3.1.2
All We Have to do is Run the Halo Finder
We use the halo finders to find bound structures within our cosmological simulations
at various redshifts. In this thesis we use two codes using different methods, HOP
(Eisenstein and Hut 1998), a friend of friend algorithm, and the Amiga halo finder
AHF (Knollmann and Knebe 2009), a grid based density method. In this section,
we discuss these two methods and codes in more detail.
A friend of friend algorithm (FoF) finds halos by linking all particles closer than
70
Name
IC Method
Volume
(Mpc3 )
HR Volume
(Mpc3 )
Mass Res.
(106 M" )
$
(kpc)
zinit
A
B
C
D
1st order
1st order
1st order
2nd order
503
503
503
503
∼ 93
∼ 93
∼ 93
∼ 93
3.16
1.0
0.316
0.316
1
1
1
1
8.3
8.3
8.3
10.2
Table 3.1: Table of simulation runs. From left to right the columns are (1) the
simulation identifier, (2) the type of initial conditions used, (3) the co-moving
volume of the larger, low resolution volume, (4) the approximate cubic co-moving
volume of the high resolution region in Mpc3 , (5) the minimum mass of the dark
particles in 106 M" , (6) the softening length of the high resolution particles in
kpc, and (7) the redshift at which the zoom simulation is started.
a given linking length, l (Davis et al. 1985). While it is fast and computationally
cheep, pure FoF codes does not find halos based on any physical property and can
artificially link halos via filamentary bridges between them. In addition, they do not
consider the binding energy of each particle when deriving halo properties. HOP
uses a modified FoF algorithm where the density of each particle is calculated base
on a smoothed kernel and used to link the particles based on local density as well
as location to remove artifacts from the FoF algorithm. However, while HOP is fast
and efficient (∼ 30 minutes for 4003 particles on a single i7 processor with 8 GB of
RAM), it is unable to find halos with N < 100 particles. Unfortunately many of
our fossils have N < 100, but HOP works wonderfully to find the locations of the
Milky Way mass halos (N ∼few100) at z = 0 and guide the placement of our high
resolution region.
To find the small fossil halos and substructure near the Milky Way we use a gird
based density method. Initially we used PMHalos (Klypin), but found it insufficient
for our needs for two reasons; (1) using a serial code on a simulation of 83 million
particles is not feasible and (2) the spectrum of masses used in our high resolution
region and the derivation of baryonic particles at z = 0 require a particle to particle
71
particle matching PMHalos could not supply. We therefore switched to the Amiga
halo finder, AHF (Knollmann and Knebe 2009) which is a parallel grid based code.
It uses a set of grids supplied by the uses which is then refined via criterion also
supplied by the user. Only the refinement criteria used on the already refined grids,
RefRef effects the results. A lower value of RefRef uses more memory but produces
a more complete distribution of halos with N < 50 particles. Once the halos are
found, AHF uses the binding energy of each particle and the escape velocity of
the halo to “unbind” particles whose energies are too high to belong to the halo.
While AHF runs quickly (∼ 30 minutes) and finds the fossil halos and substructure
required for our work, it requires significantly more memory than HOP (∼ 16 GB
of RAM) requiring it be run on the Maryland HPCC Deepthought.
In summary, we use HOP, a modified friend of friend (Eisenstein and Hut 1998),
to locate the Milky Way mass halos in our large (50-100 Mpc) low resolution boxes
and the parallel grid based AHF (Knollmann and Knebe 2009) to locate the fossils
within the high resolution of our re-run simulations.
3.1.3
A Note on the Halo Occupation Distribution
The luminosities of the z = 0 halos are determined by the luminosity/luminosities
of their component pre-reionization halos. These pre-reionization luminosities are
taken directly from the Ricotti et al. (2002a,b) pre-reionization simulations and are
determined by the feedback prescriptions and star formation efficiencies used in that
work. Predictions made based on the resulting luminosity function and galactocentric radial distribution are a result of the primordial formation model we assume for
the smallest dSphs. Note, that the match of luminosity and dark matter mass in
this simulation is not statistical, but rather a direct result the distribution of the
remnants of the first galaxies in the modern epoch.
72
3.2
Tests of the Method
In this section, we present consistency checks of our method to confirm that it reproduces known results from previous CDM simulations. We also discuss numerical
effects introduced by our use of a spectrum of masses in our high resolution region.
First, we confirm that the large scale structure and clustering of matter is consistent with traditional CDM simulations run with constant mass per particle. Then,
we see that the halo mass function is consistent with the mass function of halos
derived from the Press-Schechter formalism (Press and Schechter 1974). Finally,
we confirm that the number of subhalos and their galactocentric distribution agree
with the published results of the Via Lactea II (Diemand et al. 2008), Aquarius
(Springel et al. 2008) and Polisensky and Ricotti (2010) simulations and that mass
loss due to tidal stripping of the z = 0 halos is also in agreement with Kravtsov et al.
(2004).
Figures 3.4 - 3.6 show a region of our Local Volume 5 Mpc across at z = 0.
In order are the low resolution simulation, Run C and Run D seen from the same
viewing angle. For Runs C and D, the luminous pre-reionization halos are shown as
large red dots plotted over the white distribution of dark tracer particles. We find
both Run C and D reproduce the large scale structure seen in the low resolution
simulation. In CDM, the thickness of the filaments in our Local Volume is set by the
mass scale we are considering. It is set during pancake collapse and can be thought
of as the size of an over-density of ρ ∼ ρta ∼ 5, where ρta is the over-density at
which a halo decouples from the Hubble flow in the top hat collapse model.
The existing differences result in the slight difference between the initial condition
generated for run C and run D. There is only one Milky Way mass galaxy in run
C because the second over-density which would have produced a Milky Way was
73
Figure 3.4: Large scale structure of the same region of our simulations for the low
resolution simulations. The bar across the top shows the scale in Mpc.
“polluted” with the low resolution particles and thrown out. Of the two Milky Ways
in run D one is undergoing an approximately 1:10 merger which its counterpart in
run C has completed by z = 0. This difference is due to the starting redshift of run
C versus run D. Run C was started at zinit = 8.3 using the z = 8.3 pre-reionization
outputs. In contrast, while the region around the Milky Ways in run D uses the
zef f = 8.3 pre-reionization outputs, it is started at z =init = 10.2, giving the Milky
Ways in that simulation more time to evolve, allowing it to complete the 1:10 merger
before z = 0. The output 300Myr before z = 0 shows the Milky Way in Run C
undergoing an approximately 1:10 merger.
74
Figure 3.5: Large scale structure of the same region of our simulations for Run C.
White shows the halos with no luminous component while the larger, red points
show the luminous pre-reionization halos. The color of the latter does not depend
on luminosity. The bar across the top shows the scale in Mpc.
3.2.1
Mass Resolution
Our simulations produce maps of the present day distribution and properties of
pre-reionization fossils in a 53 Mpc3 volume around a Milky Way type halo and in
local filaments and voids. One of our goals is to map the distribution and properties
of fossil galaxies outside the large hosts. This is done to quantify the number
and properties of luminous dwarfs in the voids if stars formed in minihalos before
reionization. These dwarfs would have evolved in relative isolation, and, if found
by observations, would represent unambiguous and unperturbed fossils of the first
galaxies. However, at this time, the only observational sample to which we can
75
Figure 3.6: Large scale structure of the same region of our simulations for Run D.
White shows the halos with no luminous component while the larger, red points
show the luminous pre-reionization halos. The color of the latter does not depend
on luminosity. The bar across the top shows the scale in Mpc.
compare our simulations is the classical dSphs and ultra-faint dwarfs near the Milky
Way and M31. The faintest known dwarfs (LV < 103 L" ) are found at less than
50 kpc from the Galactic center. Observations are likely incomplete at R > 50 kpc
with some dependence on luminosity (Koposov et al. 2008; Simon and Geha 2007;
Walsh et al. 2009). To compare our simulations to observations of the faintest known
dwarfs, we must resolve halos within 100 kpc of the Milky Way center.
Run A, with a minimum particle mass of a 3.5 × 106 M" , was not able to resolve
subhalos within 200 kpc of the Milky Way mass halos. In Run C, we increase our
mass resolution to 3.5 × 105 M" by increasing the number of pre-reionization halos
76
in the initial conditions. By decreasing our minimum pre-reionization halo mass to
3.5 × 105 M" we are able to resolve subhalos at R > 50 kpc (see Figure 3.7). At
z = 0, a luminous pre-reionization halo, evolving in isolation, is surrounded by a
cloud of lower mass pre-reionization halos and tracer particles. The number of dark
particles increases with the total mass of the luminous pre-reionization halo and the
mass resolution of the simulation. The detectability of the lowest mass halos by
the halo finder AHF is dependent on the ability of the luminous pre-reionization
halos to accrete and retain their clouds of tracer particles. The larger number of
low mass pre-reionization halos and tracer particles in runs C and D will allow more
pre-reionization halos to accrete large enough clouds to be detected as a present day
halo.
Resolving subhalos near a large galaxy is complicated by the background density
field of the host halo and the stripping of the clouds of tracer particles during tidal
interactions. To resolve a subhalo in the inner 100 kpc of Milky Way mass halo,
the pre-reionization halo must retain enough of its cloud to be considered a bound
system. In addition, it must have a high enough central density to be seen against
the background of the host halo. The effect of the larger mass of the pre-reionization
halo on the central concentration of the subhalo will be discussed in § 3.2.2. For
AHF, the lower limit to robustly detect halos at z = 0 is a cloud of ∼ 50 tracer
particles (Knollmann and Knebe 2009).
Our simulations cannot provide information on the z = 0 stellar properties of
a halo for a pre-reionization halo which has undergone significant tidal disruption.
Beyond the stripping of the accumulated dark cloud described above, our simulations do not allow for the breaking apart of the pre-reionization halos. We only
consider a pre-reionization halo unaffected by tides if its cloud of dark particles
remains intact and detectable. This negates comparisons within 50 kpc of a host
77
Figure 3.7: We show images MW.1 (1.82×1012 M" ) from Run C. In Figure 3.5 it is
large galaxy located in the center of the image. The left panel shows both the dark
(white) and luminous (red) pre-reionization halos. The right panel shows only the
luminous pre-reionization halos in greyscale with the brightest pre-reionization
halos in white. In the right panel our Milky Way has been rotated ∼ 180o relative
to the view in the left hand panel. The bar across the top shows the scale in Mpc.
Figure 3.8: We show images of MW.2 (0.87 × 1012 M" ) from Run D. In Figure 3.6 it is large galaxy located in the center of the image. The left panel shows
both the dark (white) and luminous (red) pre-reionization halos. The right panel
shows only the luminous pre-reionization halos in greyscale with the brightest prereionization halos in white. In the right panel our Milky Way has been rotated
∼ 180o relative to the view in the left hand panel. The bar across the top shows
the scale in Mpc.
78
Figure 3.9: We show images of MW.3 (1.32 × 1012 M" ) from Run D. In Figure 3.6
it is large galaxy located in the bottom-center of the image. The left panel shows
both the dark (white) and luminous (red) pre-reionization halos. The right panel
shows only the luminous pre-reionization halos in greyscale with the brightest prereionization halos in white. In the right panel our Milky Way has been rotated
∼ 180o relative to the view in the left hand panel. The bar across the top shows
the scale in Mpc.
halo where a significant number of the observed ultra-faint dwarfs have been modified by tides and our luminous pre-reionization halos are stripped of their clouds of
tracer particles. In the galactocentric radial distributions and luminosity functions
presented in Chapters 4 and 5, we only include the simulated and observed sample
at R > 50 kpc.
3.2.2
Softening Length
In this section, we discuss one of the most prevalent numerical effects of using
a spectrum of particle masses in our high resolution region instead of a uniform
particle masses. The effects of this spectrum of masses primarily manifests in the
lower mass halos and are sensitive to our choice of the softening length, $. We also
show the mass functions from Runs C and D for our chosen softening length.
Typically, the softening length is set at 2% of the average distance between
particles in co-moving coordinates. For a representative volume of the universe with
particles of uniform mass, $ = 0.02N −1/3 Mpc, where N is the number of particles
79
per Mpc3 . For the high resolution region, we have a particle mass range between
3.5×105 M" −2.5×108 M" , requiring particle softening lengths from 0.5 kpc to 2 kpc.
The public version of Gadget 2 does not have the capability of assigning softening
lengths to each particle. Therefore, we must choose a single softening length for all
the particles in the high resolution region. To determine the optimal value of $, we
have run the same initial conditions with softening lengths in our high resolution
region of $ = 0.1 kpc, 1 kpc and 5 kpc. We find that the best results for $ = 1 kpc
(corresponding to a uniform particle mass of ∼ 107 M" ).
The right panel of Figure 3.10 shows the mass functions of Runs C and D compared to the Press-Schechter mass function run with $ = 1 kpc . For C and D we
see a deficit in the number of 109 − 1011 M" halos when compared to the PressSchechter and an over abundance of M < 107 M" halos. The deficit for larger halos
may result from the location of our high resolution region. The Press-Schechter is
the mass function of a typical volume of the universe. Our high resolution region
is under-dense, containing three filaments bordering a void. The overabundance
for M < 107 M" halos has a slope similar to the initial halo mass function from the
pre-reionization simulations. At those masses, the z = 0 halos are dominated by one
pre-reionization halo. This suggests that the steeper slope of the mass function at
low masses is a numerical effect reflecting the behavior of the z = 8.3 mass function
from the pre-reionization simulations.
When $ is set lower than 1 kpc (red curve in Figure 3.10), low mass halos
with one or more luminous pre-reionization halos are preferentially destroyed by
numerical effects. Statistically, luminous pre-reionization halos are more massive
than their dark counterparts, hence they migrate to the centers of their modern
halos via dynamical friction. Any two body interaction between a luminous prereionization halo and lower mass dark tracer particle will result in artificial heating.
80
Over the entire simulation, such interactions artificially heat the cloud of tracer
particles until is disperses. We find that for $ = 0.1 kpc only the most massive
pre-reionization halos with the deepest potentials are able to retain their clouds.
Isolated pre-reionization halos are surrounded by an extremely tenuous cloud of low
mass dark particles, which is not detected by AHF as a bound halo.
Using $ > 1 kpc also artificially decreases the number of the low mass halos
(blue curve on Figure 3.10). Unlike the deep potentials of the massive halos, the
potentials of halos with masses M < 108M" are relatively shallow. If $ is too large,
the low mass potentials will be flattened to the point where the pre-reionization
halos are unable to accrete the tracer particles required for AHF detection. In halos
> 109 M , this effect is minimal. However we are primarily interested in
with M ∼
"
halos with M < 109 M" .
3.2.3
Subhalo Scale Comparisons
In this section, we study the distribution of subhalos around our Milky Ways. We
use runs C and D to explore the simulated distribution of z = 0 subhalos around
our Milky Way mass hosts. Comparisons are made with other CDM simulations
and with observations.
In each simulation, we search for Milky Way type halos, using observational and
theoretical constraints. This gives us a range of halo masses for candidate Milky
Ways of ∼ 0.6 × 1012 M" − 4 × 1012 (Kallivayalil et al. 2009; Klypin et al. 2002;
Watkins et al. 2010; Zaritsky et al. 1989), and upper mass estimates for the Local
Group of ∼ 5.3 × 1012 (Li and White 2008; van der Marel and Guhathakurta 2008).
These criteria give us three Milky Ways, one in the Run C and two in the Run D,
respectively (Table 3.2). All three hosts have masses on the low end of the observed
Milky Way mass range.
81
Figure 3.10: Left : Mass functions for Run C evolved with three different softening
lengths, 100 pc (red), 1 kpc (black) and 5 kpc (blue). Note that while there is a
negligible difference at large masses, ! = 1 kpc gives us the least residual when
compared to the expected mass function. The dotted line is the Press-Schechter
for a ∼ 7 Mpc3 volume, equivalent to the mass of the bound halos. Right :
Mass function of all halos found by AHF in our high resolution region for run C
(gray line) and run D (black line). The dotted line is the Press-Schechter for a
∼ 7 Mpc3 volume at z = 0, equivalent to the mass of the bound halos. In both
mass functions we only include z = 0 halos which contain only high resolution
particles.
The Milky Way halo in Run C, MW.1, is in one of the highest density regions of
our volume, with a companion galaxy of mass 1011 M" at a distance of 2 Mpc. The
Milky Ways in Run D have masses of 0.87 × 1012 M" for MW.2 and 1.32 × 1012 M"
for MW.3. Though they are both in filaments, the nearby environments of MW.2
and MW.3 differ (see Figure 3.6). MW.2 sits at the intersection of three filaments,
and there are ∼ 1011 M" halos within 1.5 Mpc. In contrast, MW.3 is only 1-2 Mpc
away from a complex of galaxies with masses ∼ 1011 M" that appears to be in the
process of merging to form another Milky Way mass system. For our comparisons
with traditional simulations, and with observations, we use all three Milky Way
mass halos. This allows us to explore differences between the first and second order
as well as variations introduced by environmental effects.
82
Name
Run
MW.1
MW.2
MW.3
C
D
D
Mass
Rvir
12
(10 M" ) (kpc)
1.82
0.87
1.32
248.1
222.6
194.7
vmax
(km s−1 )
203.4
196.6
177
Table 3.2: Table of the three Milky Ways in runs C and D. The columns are (1)
the Milky Way identifier, (2) the mass of the host in 1012 M" , (3) the virial radius
in kpc, and (4) the maximum circular velocity in km s−1 .
Before looking at the distribution of satellites around individual Milky Ways, we
check the distribution of the number of dark matter subhalos as a function of host
mass. In Figure 3.11, we show a linear relation between host mass and the number
of satellites for both Runs C and D. There is good agreement with the Via Lactea
and Aquarius runs when we adjust their results for our lower mass resolution. Our
> 5.5 km s−1 ). To
simulations can robustly resolve halos with M > 107 M" (vmax ∼
scale the number of subhalos within Rvir in the Via Lactea and Aquarius simulations,
we use vmax ∼ 5 km s−1 for Via Lactea and vmax ∼ 7 km s−1 for Aquarius (from
Figure 27 in Springel et al. (2008)).
We use knowledge of the stellar properties of the pre-reionization halos to investigate the expected number of luminous satellites for a given host mass. We consider a
subhalo luminous if it contains at least one pre-reionization halo with M∗ > 102M" ,
or has a z = 0 mass M > 109 M" . To study the distribution of the number of luminous satellites, Nsat (LV > 102 L" ) vs. Mhost we do not need to know the luminosity
of the satellite at z = 0, only whether it is luminous. We find all of the luminous
subhalos in Figure 3.11 formed stars before reionization since we have no z = 0 halos
above the threshold for post-reionization gas accretion (109 M" : vmax = 20 km s−1 )
which do not contain a primordial stellar population. For Runs C and D, we find
the number of luminous satellites increases linearly with host mass. For hosts with
M < 1011 M" , we see a larger scatter in the total number of satellites. Additionally,
83
Figure 3.11: Number of satellites as a function of the mass of the host halo. The
total number of satellites within Rvir for each halo are represented by circles, and
the number of luminous satellites within Rvir for each halo by triangles. The
results from runs C and D are shown as the opened and filled symbols respectively. The predictions from Via Lactea II (Diemand et al. 2008) and Aquarius
(Springel et al. 2008), scaled to our mass resolution, are shown as the opened
stars. Aquarius is the star with a greater number of satellites within Rvir . The
ranges of the Tollerud et al. (2008) and Walsh et al. (2009) predictions at 200 kpc
are the green and purple barred lines, respectively.
84
in that host mass range, we see greater scatter in the mapping of the total number
of satellites to the number of luminous satellites. Since Runs C and D contain only
three Milky Way mass systems, the lack of scatter may also be due to small number
statistics. The decrease in scatter may be a function of how dominant the halo is
in its environment. In the filaments, a 1012 M" halo dominates the region around
it, negating any environmental effects inside the virial radius. A lower mass host,
however, is not able to dominate its environment. Therefore, the number of satellites for low mass hosts will be more sensitive to the environment in which they are
embedded.
The current observational sample of the faintest dwarfs with LV < 103 L" is
complete only to within 50 kpc with the completeness limit dependent on the detectability of an overdensity of RGB stars against the red dwarfs and red giants of
the halo (Koposov et al. 2008; Simon and Geha 2007; Walsh et al. 2009). A more
luminous dwarf will have more stars on the red giant branch and therefore be detectable at greater distances than its dimmer counterpart.
Tollerud et al. (2008) used the detection limits of the SDSS and the Via Lactea
II simulations to estimate the total number of satellites around the Milky Way given
the currently known population and assuming the subhalo distribution in Via Lactea
II accurately reflects the true satellite distribution of the Milky Way. They used
halos from Via Lactea II (Diemand et al. 2007), assuming a simple relationship
between halo mass and luminosity for the subhalos. The range of Tollerud et al.
(2008) is shown on Figure 3.11 as the shorter, thick black line. Unlike their work,
our simulations do not assume a relationship of luminosity to halo mass. Instead,
we draw the stellar properties of the z = 0 halos directly from the cosmologically
consistent pre-reionization simulations. This accounts for the large scatter in stellar
mass as a function of halo mass for the smallest galaxies (Ricotti et al. 2002b). Our
85
results are consistent with the upper end of the Tollerud et al. (2008) range for the
number of luminous satellites within ∼ 200 kpc. Based on these comparisons, the
total number of subhalos and number of luminous satellites around MW.1, MW.2,
and MW.3 are in agreement with results of other published works.
We next compare the distribution of maximum circular velocity for all subhalos
around a Milky Way for our simulations with other CDM simulations. We find that
the satellite mass functions for halos from Runs C and D are consistent with one
another, and results from Aquarius, Via Lactea and Polisensky and Ricotti (2010)
(Figure 3.12). Based on this, we argue that our simulations can reproduce the
number and distribution of subhalos around the Milky Ways, as well as traditional
N-body simulations. In the next section, we discuss the observational and theoretical
criteria for a halo to be defined as a fossil of the first galaxies.
3.2.4
A More Detailed Definition of a Fossil Dwarf
For observed dwarfs, a fossil is defined as a dSph which underwent > 70% of its
star formation before reionization, and today is a diffuse spherical system devoid of
gas (Ricotti and Gnedin 2005). These dim dwarfs populate dark matter halos whose
circular velocities have never been above the filtering velocity, preventing them from
accreting gas from the IGM after reionization.
In our simulations, we define a fossil halo for which max(vmax (z)) < vf ilter . Any
halo with vmax (z = 0) < vf ilter is referred to as a candidate fossil. However, in
regimes where tidal stripping is considerable, there is a significant chance that a
halo with a vmax < vf ilter at z = 0 had a maximum circular velocity above the
threshold for accretion from the IGM at an earlier time (Kravtsov et al. 2004).
Given these criteria, we classify our z = 0 halos into three populations as follows.
(1) A non-fossil is a z = 0 halo for which vmax (z = 0) > vf ilter . (2) Halos which are
86
Figure 3.12: Number of satellites within Rvir with greater than a given vmax for
our two second-order (black lines) and one first-order (gray line) Milky Ways.
The two versions of our method produce equivalent distributions and match the
CDM simulations from Polisensky and Ricotti (2010).
87
Fossils
Non-fossils
RG05 only
RG05 & BR11a
BR11a only
LMC
Sculptor
Draco
Bootes I & II
NGC 55
Phoenix
CVn I & II
Sextans A & B
Sextans
Hercules
SMC
Ursa Minor
Leo IV & T1
WLM
Pisces II
Milky Way
Carina
Fornax
GR8
Leo I, II & A
Sagittarius
M31
IC 10
And I & II
And V
And XI XII
IC 1613
And III
And XIII & IV
IC 5152
And VI
And XV & XVI
M32
Antila
And XVII & XVIII
NGC 185
KKR 25
And XIX & XX
NGC 205
And XXI & XXII
NGC 3109
And XXIII & XXIV
NGC 6822
And XXV & XXVI
DDO 210
And XXVII
LGC3
Pegasus
88
Fossils
Non-fossils
RG05 only
RG05 & BR11a BR11a only
Cetus2
Isolated
—
—
Tucana
—
Table 3.3: Classification of the known dwarfs into non-fossils and fossils. We also
split the fossils into three groups. The classical fossil candidates from RG05 with
LV > 106 L" and LV < 106 L" , and the ultra-faint dwarfs discovered since 2005.
When we compare our simulated fossils to the observed sample we only use the
latter two categories.
candidate fossils but for which max(vmax (z)) was above the IGM accretion threshold
in the past are classified as polluted fossils. The non-fossils and a fraction of the polluted fossils accreted gas from the IGM and formed a significant population of stars
after reionization. Therefore, our simulations cannot provide robust information on
the non-fossil and polluted fossil stellar properties in the modern epoch. (3) For the
true fossils, we are able to generate detailed information on their stellar properties.
A true fossil is defined as any z = 0 halo for which vmax never exceeded the IGM
filtering mass, suppressing gas accretion and star formation after reionization.
To separate the polluted fossils from the true fossils of the first galaxies, we
follow the vmax evolution for each candidate fossil back from z = 0 to zinit . We find
that f (vmax ), the fraction of candidate fossils which have max(vmax ) > vf ilter , as
a function of their vmax (z = 0), is consistent with results found by Kravtsov et al.
(2004) (see Figure 3.13). In addition, we find that f (vmax ) does not have a strong
dependence on the environment of the fossils. When we compare the results for all
the fossils (solid line) with those within 1 Mpc (dotted line) and 400 kpc (dashed
line) of MW.2 and MW.3 we do not see a significant difference. These results are
89
Figure 3.13: Fraction of candidate fossils with max(vmax (z)) > vf ilt where vf ilt =
20 km s−1 for Run D (lines) and Kravtsov et al. (2004) (asterisks). The solid,
dashed and dotted lines show the fraction of true fossils for three different subpopulations. The solid line shows the relation for all the candidate fossils in Run
D, while the dashed and dotted lines show the fraction of true fossils for candidate
fossils within 1 Mpc and 400 kpc of MW.3 respectively.
independent of the choice of the filtering velocity. For the remainder of this work,
we use the term fossil in reference to only these true fossils.
In addition to maintaining vmax < vf ilter for its entire evolution, a fossil must
also survive to z = 0 without being tidally stripped. Objects which have undergone
90
significant tidal stripping are unlikely to retain their pre-reionization stellar properties (Peñarrubia et al. 2008b). Once ∼ 90% of the dark matter is stripped, the stars
are stripped preferentially, trending the dwarfs towards lower σ∗ and higher M/L.
However, our initial conditions do not allow us to simulate tidal effects beyond the
stripping of a z = 0 halo’s tracer particles and our knowledge the baryonic properties of the fossils at z = 0 depends on the stellar population of the primordial dwarfs
evolving only via stellar evolution, not via tides or additional gas accretion.
The use of N-body particles to represent pre-reionization halos forces the masses
of those halos to be conserved. No matter how strong the tidal forces are, the stellar
and dark matter properties will not change, inconsistent with the current understanding of the effect of tidal stripping on a satellite’s stellar population. While the
dark matter halo can be stripped away, leaving the stellar properties relatively intact (Choi et al. 2009; Peñarrubia et al. 2008a), once the mass loss reaches the outer
stellar radii, the stripping of the stellar populations will occur at a faster rate than
the denser dark matter cusp (Peñarrubia et al. 2008b). We have no way of tracking
the mass loss of an isolated pre-reionization halo to determine which components
have been disrupted. We address this limitation by using the destruction of a z = 0
halo’s dark particle cloud to flag halos which have undergone tidal stripping. Any
present day halo whose cloud of tracer particles has been destroyed or stripped down
< 50 particles, will not be robustly detected as substructure and its mass will
to N ∼
be added to that of the host galaxy. If N < 20, the z = 0 halo will not be detected
at all (Knollmann and Knebe 2009). Any pre-reionization halo which is not found
at z = 0 is assumed to be tidally disrupted and is not considered a fossil.
Given these criteria, we can say a few things about our fossil population. For the
vf ilter = 20 km s−1 used in the majority of this work 82% of the primordial galaxies
are in non-fossils with the fraction approaching 70% as vf ilter nears 80 km s−1 . For
91
the vf ilter = 30 km s−1 used in GK06 ∼ 30% of primordial galaxies are not in
non-fossils at z = 0. Our fossils are dimmer and less massive than the polluted
fossils and non-fossils. As a population, they are less likely to have undergone
mergers involving two or more luminous pre-reionization halos (Figure 3.15). We
define a merge between two or more luminous pre-reionization halos as a galaxy
merger. Using an vf ilter = 20 km s−1 , 25% of the fossils have two or more luminous
pre-reionization halos compared to 40% of candidate fossils. The majority of true
fossils (75%) contain only one luminous pre-reionization halo, however the remainder
do not represent a negligible fraction. We find the same result when using the
vf ilter = 30 km s−1 adopted by GK06. As with the 20 km s−1 case, 75% of true
fossils have only one luminous pre-reionization halo. Therefore, while the majority
of fossils have not undergone galaxy mergers, it is not an effect that can be ignored.
3.2.5
Luminosity Threshold for Fossils
Before making detailed comparisons between our simulations and observations, we
compare our work and the N-body simulations in GK06. Unlike our method, which
allows us to directly trace the pre-reionization halos to the present day, GK06 statistically matches pre-reionizaion halos to their counterparts at z = 0 based on their
vmax at z = 8.3. To make a direct comparison with GK06 we must use our MW.1
from Run C, since GK06 only used the z = 8.3 outputs from the pre-reionization
simulations.
Figure 3.16 shows the galactocentric radial distribution for GK06 (blue band) and
for MW.1 (black lines). Both curves only include the true fossils. For LV > 105 L"
(lower panel) we find that our simulations are consistent with GK06, if on the low
end of their range. However, the brightest true fossils in GK06 with LV > 106 L"
have no counterparts around MW.1. We ascribe this discrepancy to the difference
92
Figure 3.14: The fraction of primordial galaxies in non-fossils as a function of a
given filtering velocity. Note, that above 30 km s−1 the fraction drops below 75%,
approaching 70%, so at least 25 − 30% of the primordial galaxies survive outside
massive halos to z = 0.
93
Figure 3.15: Fraction of luminous true fossils which have undergone < 6 galaxy
mergers after reionization for vf ilt = 20 km s−1 (black) and vf ilt = 30 km s−1
(red). We define a galaxy merger as any merger in which two or more of the
components contain a luminous population. For > 4 − 5 galaxy mergers, the
fraction of z = 0 true fossils becomes negligible.
94
Figure 3.16: The radial distribution of the true fossils around MW.1 in Run C
(black lines) and the results from GK06 (blue band) for halos with LV > 105 L"
and LV > 106 L" . We have used a vf ilter = 30 km s−1 threshold to determine
whether a z = 0 halo is a true fossil.
95
in how this work follows the pre-reionization halos to the modern epoch.
While both methods allow for the growth and stripping of a halo via accretion
and tidal forces, our simulations also account for clustering of the pre-reionziation
halos. The most luminous pre-reionization halos correspond to the most massive
halos at z = 8.3. These 107 − 108 M" galaxies are preferentially located in higher
density regions within the 1 Mpc3 pre-reionization simulation. This increases the
probability that the pre-reionization halos with LV > 105 L" will have undergone
a galaxy merger relative to those with LV < 105 L" . In Figure 3.17, we show the
histogram of the number of luminous pre-reionization halos for true fossils with
LV < 105 L" (left panel) and LV > 105 L" (right panel). Only ∼ 0 − 5% of the
highest luminosity fossils have never undergone a galaxy merger compared to ∼ 90%
of fossils with LV < 105 L" . This is independent of our choice of filtering velocity.
Why does this explain the discrepancy between our results and GK06 in Figure 3.16? The definition of a true fossil is a dwarf whose maximum circular velocity
has never gone above the threshold for accretion for the IGM. In Figures 3.16 and 3.17,
we set vf ilter = 30 km s−1 . Since the brightest pre-reionization halos are also the
most massive, one or two galaxy mergers at high redshift would be enough to push
vmax above the filtering velocity and classify the halo as a non-fossil. In Run C,
there are only 11 true fossils with LV > 106 L" , none of which are within 1 Mpc of
MW.1.
This gives us a maximum luminosity threshold, 106 L" , above which an observed
dwarf is unlikely to be a primordial fossil. Of the true fossil candidates identified in
RG05, this puts seven into question; And I (4.49 × 106 L" ), And II (9.38 × 106 L" ),
And III (1.13 × 106 L" ), And VI (2.73 × 106 L" ), Antila (2.4 × 106 L" ) and KKR
25 (1.2 × 106 L" ) around M31, and Sculptor (2.15 × 106 L" ) around the Milky Way.
The remaining seven, And V, Cetus, Draco, Phoenix, Sextans, Tucana and Ursa
96
Figure 3.17: (Left) Histogram of the fraction of true fossils at z = 0 with a given
number of galaxy mergers after reionization for vf ilter = 20 km s−1 (black line)
and vf ilter = 30 km s−1 (red line). As in Figure 3.15, the number of galaxy
mergers is a proxy for the number of luminous pre-reionization halos in a z = 0
halo. In this panel we show only the true fossils with LV (z = 0) < 105 L" . (Right)
The fraction of true fossils with a given number of luminous pre-reionization halos
for only those with LV (z = 0) > 105 L" for vf ilter = 20 km s−1 (black line) and
vf ilter = 30 km s−1 (red line). Note the shifted peak and different shape of the
histogram in this panel.
Minor all have LV < 106 L" and remain reasonable candidates for the fossils of
the first galaxies. The classical Milky Way fossils, Draco, Sextans, Ursa Minor, as
well as the ultra-faint Canes Venatici I, all have metallicity distributions suggesting star formation durations < 1 Gyr and populations > 10 Gyr old (Kirby et al.
2011a). These dwarfs, in addition to Sculptor, have star formation histories that are
dominated by outflows, in contrast to their brighter counterparts (“polluted fossils”
Fornax and Leo I & II) (Kirby et al. 2011b). However, unlike the other outflow
dominated dwarfs which have relatively short star formation bursts, Sculptor has
undergone star formation over several Gyrs (Babusiaux et al. 2005; Shetrone et al.
2003; Tolstoy et al. 2003) and a fraction of Draco’s stars may be of intermediate age
(Cioni and Habing 2005).
97
3.3
Discussion
We have presented a new method for generating initial conditions for cosmological
N-body simulations which allows us to create simulated maps of the present-day
distribution of fossils in a “Local Volume.” In order to produce these maps, we
assume pre-reionization fossils do not accrete gas and form stars after reionization.
They are hosted in dark halos that maintain circular velocities below a critical
threshold, vf ilter ∼ 20 − 30 km/s. The precise value of vf ilter depends on details of
the reheating in the local IGM by stars and AGN. Therefore, we explore different
values for vf ilter , but find little variation. For our purposes, we do not need to
include gas dynamics. The lack of post-reionization baryonic evolution in the fossils
allows us to simply simulate the evolution of the dark matter and stars using N-body
techniques.
We have combined the results from previous cosmological simulations of the
formation of the first galaxies (Ricotti and Gnedin 2005; Ricotti et al. 2002b, 2008)
with N-body simulations in which each particle in the initial conditions represents
a pre-reionization minihalo. Our N-body simulations zoom in on a Local Volume
containing one to two Milky Ways. We follow the merger history and tidal stripping
of pre-reionization fossils as they merge to form more massive galactic satellites of
the Milky Way. We also trace the evolution of more massive non-fossil satellites,
but we do not account for star formation taking place after reionization.
Our goal is to determine if a widespread population of primordial dwarfs is
consistent with the observed population of Milky Way and Andromeda satellites,
and, at the same time, if our simulations match observations of dwarfs in the Local
Void. It is not well established whether halos with vmax < 20 km/s, too small to
initiate collapse via Lyman-alpha cooling, remain dark or form luminous dwarfs.
98
Our simulations are a first attempt to constrain the theory of self-regulated galaxy
formation before reionization using “near field” observations. Observational tests
based on our results can constrain models of star formation in minihalos before
reionization.
We present maps of the Local Volume showing the distribution of stars formed
before reionization in the present day universe. We find that primordial fossils are
present in the voids regardless of the details of reionization, however, reionization
by X-rays produces darker voids.
We find that most classical dSph satellites are unlikely true-fossils of the first
galaxies, even though they have properties expected of fossils: diffuse, old stellar
populations with no gas (Bovill and Ricotti 2009; Ricotti and Gnedin 2005). The
reason that true-fossils in the Milky Way have luminosities < 106 L" , is that the
most luminous pre-reionization fossils, with vmax ∼ 20 km/s form in over-dense
regions and are strongly clustered. Thus, they are likely to merge into more massive
non-fossil dwarfs. The surviving fossils found today are a sub-population with lower
typical luminosities, and formed in less clustered regions in which feedback effects
suppress rather than stimulate star formation.
The results from this chapter are as follows:
• Voids contain many low luminosity fossil galaxies. However they have surface brightnesses and luminosities making them undetectable by SDSS. One
possible way to detect these void dwarfs is if they experience a late phase of
gas condensation from the IGM as proposed in (Ricotti 2009). Future and
present 21cm surveys such as ALFALFA and GALFA may be used to find
these objects (Begum et al. 2010; Giovanelli et al. 2005).
• We find a linear scaling relation between the number of luminous satellites
and the mass of host halos. The scaling has scatter similar to the relationship
99
between the total number of sub-halos with M > 107 M" (vmax > 5 km s−1 )
and the host mass, although the normalization is 3 − 4 times lower.
• Due to the dependence of the properties of primordial dwarfs on their formation environment (Ricotti et al. 2008), we find very few true fossils with
LV > 106 L" , and none within 1 Mpc of our Milky Ways. This places the
identification of some of the more luminous classical dSphs fossils in doubt.
100
Chapter 4
The Properties and Distribution
of the Fossils
In this chapter, we present the stellar properties and distribution of our simulated
true fossils and compare them with observed stellar properties and distribution
of Milky Way satellites. These comparisons include V-band luminosity, LV , halflight radius, rhl , metallicity, [F e/H], and mass inside the half-light radius M1/2
(Walker et al. 2009). In Chapter 2, we showed strong statistical agreements between
the stellar properties of the pre-reionization halos, and the observed distribution of
known classical dSph and ultra-faint dwarfs. Here we improve our previous results
by relaxing some of the assumptions made in Chapter 2.
As in GK06, Chapter 2 assumed that none of the luminous pre-reionization
halos had undergone a galaxy merger. Thus, the present day distribution of stellar
properties for the fossils would be identical to that of the pre-reionization halos.
In addition, our previous work assumed the voids were reheated to T ∼ 104 K
well after the clusters and filaments, as expected for UV reionization by stars. As
seen in Figures 3.5 & 3.6, a universe reionized by stars, Run C, produces a larger
101
number of luminous objects in the voids when compared to a universe reionized
and reheated by X-rays emitted by accretion from the ISM onto BHs in the early
universe (Ricotti and Ostriker 2004; Ricotti et al. 2005) (Run D). As in Chapter 2,
for all observed stellar properties, we use the measurements with the lowest error
bars.
4.1
Fossil Properties
From hierarchical formation models, we know that all halos have undergone merger
and/or accretion events since their epochs of formation.
For 60% of our pre-
reionization halos, these mergers are with dark halos, producing a daughter halo
with the same stellar properties as the parents. We are assuming that the stellar
velocity dispersion radial profile of the stars within the fossil halos is undisturbed
by these “minor” mergers.
However, for all runs and all halos, fossil and non-fossil, ∼ 40% of the z = 0
halos contain more than one luminous pre-reionization halo. These galaxy mergers
will change the stellar properties of the systems.
True fossil halos in the modern epoch derive their stellar properties solely from
their pre-reionization populations. For the 75% of luminous true fossils which contain only one luminous pre-reionization halo, the z = 0 stellar properties are taken
directly from those of the pre-reionization halo. We account for the reddening of
the stellar population by using a M∗rei /L ∼ 5. Note that we use such a large stellar
mass to light ratio to account for stellar mass lost since reionization. The stellar
mass to light ratio of our simulated galaxies at z = 0 is,
M today
M∗rei
M∗rei
= ∗
 today 
L
L
M∗
(4.1)
where M∗rei and is the mass of the stellar population at reionization, and M∗today is
102
the mass of the stellar population at z = 0. The ratio between them, M∗rei /M∗today
is between 2 and 20 depending on the IMF of primordial stellar population. RG05
used a range of M∗rei /L ratios and found no dependence of the fossil properties on
the choice of mass to light ratio.
For the one-quarter of true fossils which have undergone a galaxy merger, the
stellar properties are calculated as follows. Throughout this section, the superscript
f will denote the stellar and dark matter properties of the z = 0 halo, and the
superscript i the properties of the component, luminous pre-reionization halos.
The final V-band luminosity, LfV of a fossil halo at z = 0, is the sum of the V-band
luminosities, LiV , of the component pre-reionization halos. We assume stellar mass
is conserved during all mergers of luminous pre-reionization fossils, an assumption
that will be addressed in future, higher resolution simulations.
f
We determine the half light radii, rhl
, for z = 0 fossils using the 3D rhl from the
pre-reionization simulations, with the following assumptions. (1) The dynamical
evolution of the stars is decoupled from that of the dark matter. (2) The kinetic
energy of the stars is conserved. Dark matter provides the gravitational potential
in which the stars move and the orbits of the stars are not dragged along with
the dark matter while it mergers and interacts dynamically. (3) The collision of
the luminous pre-reionization halos is elastic with respect to the stars. We assume
this for convenience since we were unable to derive a clean analytical expression
which included an injection of kinetic energy into the stellar population from the
merger or that allowed for the loss of kinetic energy. Since we do not account for
this additional source of energy, the final velocity dispersions of the merged fossils,
and therefore their half-light radii represent lower limits to what we would expect
if a full merger simulation had been run for each interaction. (4) Enough time has
passed since the collision for the halo to return to an equilibrium state. Given the
103
kinetic energy conservation of the stars:
(σ∗f )2 = (LfV )−1
,
LiV × (σ∗i )2 ,
(4.2)
where σ∗i and σ∗f are the 3D stellar velocity dispersions of the parent and daughter
halos. For a halo in equilibrium, rhl ∼ σ∗2 , therefore:
f
rhl
= (LfV )−1
,
i
LiV × rhl
.
(4.3)
f
We use rhl
to calculate an average surface brightness, <ΣV >, for our fossils in units
of L" / pc 2 . The ΣV and rhl distributions as a function of luminosity are shown in
Figure 4.1.
In Figure 4.1, the black symbols are the observed Milky Way and M31 satellites
overlaid on colored contours showing the equivalent distributions for the simulated
true fossils. The cyan and red contours show the stellar properties of the fossils above
and below the SDSS detection limits, respectively. We see that, as in Chapter 2,
our simulations are able to reproduce the observed ΣV and rhl distributions for the
ultra-faint and classical dSphs, with a few exceptions. We are unable to account for
the ultra-faints with rhl < 60 pc (Segue 1 and 2, Leo V, Pisces II and Willman 1),
all but two of which (Leo V and Pisces II) are within ∼ 50 kpc of the Milky Way.
In Chapter 2, we called attention to a population of ultra-faints, as yet undetected, with surface brightnesses below SDSS limits. The existence of these dwarfs
was independently proposed in Bullock et al. (2010), who named them ‘stealth
galaxies.’ The detection of these ultra-faint dwarfs is a test for the fossil scenario.
In this section, we summarize the properties expected of these extremely ultra-faint
fossils.
In Figures 4.1 - 4.8, the simulated true fossils are shown as two sets of contours.
Up until now, we have been comparing the ultra-faints and a subset of the classical
dSphs to the simulated true fossils with ΣV > 10−1.4L" pc−2 . These true fossils,
104
Willman I
dE
dIrr
old M31 dSph
new M31 dSph
old Milky Way dSph
new Milky Way dSph
RG05 prediction
Willman I
Figure 4.1: Left : Figure 2.1. Surface brightness and half-light radii are plotted
against V-band luminosity. The small black squares show the properties of the
pre-reionization halos at z = 8.3. The other black symbols show the dwarf populations for the Milky Way and M31. The asterisks are non-fossils (dIrr), crosses
are polluted fossils (dE and some dSph), the filled circles and triangles are the
fossils (dSph) known before 2005 for the Milky Way and M31 respectively and the
opened circles and triangles are the ultra-faint populations those galaxies found
since 2005. Right : Surface brightness and half-light radii are plotted against Vband luminosity. The cyan contours show the distribution for the fossils from Run
D and the overlaid black symbols show the observed dwarfs. In this panel we color
the observed dwarfs whose half-light radii are inconsistent with our simulations
green. The magenta contours show the undetectable fossils with ΣV below the 0th
order detection limit of the SDSS, ∼ −1.4, (Koposov et al. 2008). In both panels,
the solid black lines show the surface brightness limit of the Sloan (Koposov et al.
2008) and the dashed black lines show the trends from Kormendy and Freeman
(2004) for luminous Sc-Im galaxies (108 L" < LB < 1011 L" ).
shown by the cyan contours, would be detectable by the SDSS (Koposov et al. 2008).
The red contours show the true fossils which would remain undetected by SDSS. In
Chapter 6, we present the existence and properties of the true fossils with surface
brightnesses below the SDSS detection limits as a test for primordial star formation
in minihalos. For the remainder of this section, we direct the reader to the red
contours on Figures 4.1- 4.8.
The mass to light ratios and σ∗ of the observed and simulated populations are
105
Figure 4.2: The stellar mass to light ratios calculated from Illingworth (1976)
and stellar velocity dispersons versus the V-band luminosities for Run D (blue
contours) and observations (red symbols). Symbols are the same as in Figure 4.1.
Once again, the dashed lines show the Kormendy and Freeman (2004) trends for
Sc-Im galaxies with 108 L" < LB < 1011 L" .
106
Figure 4.3: The M/1/2LV versus 1/2LV using the Walker et al. (2009) mass
estimator.
shown as the top and bottom of in Figure 4.2. As in Figure 4.1, the five dwarfs
which do not match the rhl of the simulated fossils are marked with filled green
circles. Excepting this subpopulation, the ultra-faints show the same distribution
as the simulated true fossils for both M/L and stellar velocity dispersions. In the
left panel of Figure 4.2, the masses of our simulated halos are calculated from the
stellar properties using Illingworth (1976). The right panel shows the mass to light
107
ratios inside the half-light radii, M/L1/2 versus half the V-band luminosity using the
Walker et al. (2009) mass estimator. The latter mass estimator is more accurate for
dispersion supported systems, but we note that the agreement between the mass to
light ratios of our fossils and ultra-faint dwarfs is independent of the mass estimator
we use to calculate M(σ∗ , rhl ). As expected, the undetected dwarfs (red contours in
Figure 4.2 & 4.3) would have M/L > 103 M" /L" , higher than even the most dark
matter dominated ultra-faint dwarfs. However, the range of their stellar velocity
dispersion is 2 − 10 km s−1 , equivalent to the ultra-faint dwarfs and detectable
fossils, and shows no evolution with decreasing luminosity.
As seen in the left panel of Figure 4.4 & 4.5, the mass function of the detected
fossils peaks at 108 M" while the undetected fossil peak at 5 × 107 M" . Note,
however, that this mass function is for the total dark matter mass, not the dynamical
mass calculated from the velocity dispersion and half-light radius. Our simulations
provide us with the information needed to plot a mass function of the dynamical
mass, referred to in the right panel of Figure 4.4 & 4.5 as the derived mass. For
the observed mass function both the detected and undetected fossils peak at 2 ×
107 M" . This peak corresponds to the ‘common mass scale’ for dwarf spheriodals
(Strigari et al. 2008), however, no such sudden peak is seen in the dark matter mass
function. The difference is due to the stochastic star formation in the first galaxies
(Ricotti et al. 2008), two dwarfs may have stellar population of the same stellar
velocity dispersion and extent, producing the dynamical mass, but those populations
can be embedded within halos whose masses vary by an order of magnitude. As
discussed in § 2.1.1, while the more massive halo’s population is concentrated at the
center of its potential, the lower mass halo’s stars fill a larger fraction of its dark
matter halo.
More specifically, the lower limit in dwarf size of rhl ∼ 100 pc can be understood
108
by the following. In low mass dark halos cooling is very inefficient. Since the
temperature of the ISM in these galaxies remains near the virial temperature after
reionization, their gas is more extended during fragmentation and star formation,
with the ratio of the temperature of the ISM to the virial temperature setting the
outer most stellar radius. Inefficient cooling produces a higher ratio, and the closer
TISM /Tvir is to one, the more extended the dwarf’s stellar population will be. In
hydrostatic equilibrium, the gas density profile of a NFW halo can be described by
the beta-model (Makino et al. 1998) with a core radius rc ∼ 0.22Rvir /c, where c is
the halo concentration and c ∼ 4. Before stars form, the gas density inside the core
radius is > 100 cm−3 and drops as ∝ r −3 outside of the core radius. To use some
numbers, the typical virial radii of the least luminous fossils in these simulations at
z = 0 is 10-15 kpc, and given c ∼ 4, rc ∼ 0.07Rvir , a core radius of ∼ 70 − 120 pc.
Thus, star formation can extend to a decent fraction of the virial radius in small
halos, roughly to rhl ∼ rc ∼ 100 pc (the pre-reionization simulations use ρ∗ ∝ ρ1.5
gas ).
The net effect of this is that rhl remains nearly constant as a function of the mass, in
the first small mass halos. Galaxy-galaxy interactions and merges can increase rhl
above the minimum values set by the structure of the ISM in primordial galaxies.
For more massive halos, rc becomes a smaller fraction of Rv ir because gas cooling
is more efficient, and the ISM in larger galaxies cools rapidly to values below the
virial temperature.
For the metallicity distribution, we also use a luminosity weighted average:
[F e/H]f = log(
,
i
10[F e/H] × LiV ) − log(LfV ).
(4.4)
The distribution of metallicity versus LV is shown for our z = 0 fossils and the
known ultra-faint and classical dwarfs. As in Chapter 2, the fossil metallicities
from Run D are consistent with the observed distribution for the ultra-faint and
classical dSph. We also find our results for LV > 104 L" to be in agreement with
109
Figure 4.4: Left : The mass function of the detected (solid) and undetected
(dashed) fossils with LV > 102 L" within 1 Mpc of MW.3 from Run D. Right :
Same as the left panels except the x-axis is the dynamical mass inside the half light
radius (Walker et al. 2009) calculated from the velocity dispersion and half-light
radius of our fossils.
Figure 4.5: Left : The mass function of the detected (solid) and undetected
(dashed) fossils with LV > 102 L" within 1 Mpc of MW.2 from Run D. Right :
Same as the left panels except the x-axis is the dynamical mass inside the half light
radius (Walker et al. 2009) calculated from the velocity dispersion and half-light
radius of our fossils.
110
Figure 4.6: The [Fe/H] distribution for the true fossils plotted against the V-band
luminosities for Run D (blue contours) and observations (red symbols). Symbols
are the same as in Figure 4.1. Our results agree with Salvadori and Ferrara (2009)
for LV > 104 .
Salvadori and Ferrara (2009) while for the dimmest fossils our work finds comparatively lower metallicities. The undetected dwarfs (red contours in Figure 4.6) have
[F e/H] < −2.5 and as low as −3.5 with slightly larger scatter than their detectable
counterparts.
The maximum circular velocity versus LV contours for our simulated true fossils
111
are shown in Figure 4.7 to illustrate the following. While vmax does decrease by
approximately a factor of two over four decades of luminosity, the scatter in vmax
at a given LV is large. Though a halo with vmax < 6 km s−1 is likely to have a
LV < 104 L" , there is, at most, a minimal trend of decreasing vmax with decreasing
luminosity for the primordial fossils. This highlights a theme across all our stellar
property comparisons. Because of the strong dependence of their stellar properties
on stochastic feedback effects, there is no baryonic property that shows a strong
trend with maximum circular velocity and the size of the dark matter halo.
We now briefly discuss the M31 satellite population. Figure 4.8 shows the σ∗
plotted against rhl on a similar scale to the top left panel of Figure 18 in Collins et al.
(2010). The circles show the Milky Way dSphs, while the triangles show the dSphs
associated with M31. We find that four of the six M31 dSphs plotted are within,
albeit at the edges of, the contours of detectable true fossils. Like their Milky Way
counterparts, the new M31 dSphs show reasonable agreement with our simulated
primordial fossils excepting of rhl , which are higher than expected by our simulations
for two of the M31 dwarfs. However, this does not represent a major problem for
our model since ∼ 65% of simulated true fossils with LV > 104 L" have undergone
one or more major mergers that may have puffed up their stellar populations. Our
estimates do not account for extra heating of the stellar populations by the kinetic
energy of the collision. A higher σ∗ would result in a more extended stellar population in the same mass halo. We will discuss the comparison between the M31 dSphs
and our simulated fossil dwarfs in an upcoming paper.
112
Figure 4.7: The maximum circular velocity, vmax of our simulated true fossils
plotted against the V-band luminosities. The cyan and red contours are the same
as in Figure 4.1. Here we show no observed dwarfs due to the lack of data.
4.1.1
The Inner Ultra-Faints
In this section, we discuss a possible origin scenario for the inner ultra-faint dwarfs,
ie. the ultra-faints whose half light radii and mass to light ratios are lower than
our true fossils. These dwarfs are, Segue 1 and 2, Leo V, Pisces II and Willman 1,
and excepting Leo V and Pisces II (both at ∼ 180 kpc) all are within 50 kpc of the
113
Figure 4.8: The stellar velocity dispersion, σ∗ against the half-light radius, rhl .
The black symbols are the observed dwarfs and blue and red contours from Run
D have the same meanings as in Figure 4.1.
Milky Way.
However, their mass to light ratios follow a shifted power law with a similar slope
to the true fossils and more luminous dwarfs. The stellar velocity dispersions are in
the range expected for primordial fossils, but the inner ultra-faints show an LV − σ∗
combination which would be expected for true fossils below the detection limits of
SDSS (red contours on Figure 4.2). These properties are either directly affected by
114
Inconsistent
Consistent
R < 50 kpc
R > 50 kpc
Segue 1
Segue 2
Willman 1
Pisces II ∗
Leo V ∗
Coma Ber.
Bootes I & II
CVn I & II
Hercules
Leo IV & Leo T
Ursa Major I
Table 4.1: Table of Milky Way ultra-faint dwarfs classified by their distance from
our galaxy (columns) and whether or not they are consistent with our predictions
for the fossils of the first galaxies (row). Note the correlation between distance
and consistency. (*) Pisces II and Leo V are both on the lower end of radii
expected for fossils, as such they are marked as “inconsistent,” but are not as far
from predictions as the “inconsistent” ultra-faints within 50 kpc.
tidal stripping (rhl and σ∗ ) or are derived from affected properties (ΣV and M/L).
However, the metallicity of the stars is not affected by tidal stripping.
Figure 4.6 shows the metallicities of the inner ultra-faint dwarfs do not fall
on the luminosity-metallicity relation. However, their scatter is consistent with
expectations for true fossils. To place the Segues, Leo V, Pisces II and Willman 1
on the luminosity-metallicity relation traced by the majority of the ultra-faints and
our fossils, their luminosities would need to be increased by one to two orders of
magnitude. We suggest these dwarfs may be a subset of bright primordial fossils
which have been stripped of 90% − 99% of their stars.
4.2
Baryonic Tully Fisher Relation
In § 4.1 we demonstrated good agreement between the properties expected of primordial galaxies and those observed for a subset of the new ultra-faint dwarfs. We
now extend that comparison to the baryonic Tully-Fisher (BTF) relation. The
baryonic Tully-Fisher relation is a relatively tight correlation between the rotation
115
Figure 4.9: (Left) : The baryonic Tully-Fisher relation for the observed dwarfs
(same symbols as FIgure 4.1) and our simulated fossils (blue points). In this
panel we show all the simulated fossils regardless of their detectability by the
SDSS. (Right : The BTF, except we show only the simulated fossils with Σ >
10−1.4 L" pc−2 (Koposov et al. 2008).
velocity or velocity dispersion of a galaxy and its total baryonic mass which ex√
tends from disk galaxies to dwarfs with Vc = 3σ∗ = 20 km s−1 (McGaugh et al.
2000; Stark et al. 2009; Trachternach et al. 2009; Verheijen 2001). However, when
the Local Group dSphs are plotted on the BTF they do not continue the correlation
to lower Vc , instead deviating by up to two orders of magnitude in baryonic mass
(McGaugh and Wolf 2010). We now investigate whether the stochastic star formation in the primordial model can reproduce the scatter in the baryonic Tully-Fisher
relation seen for the smallest galaxies McGaugh and Wolf (2010).
Figure 4.9 shows the baryonic Tully-Fisher relation for the observations (black
and green symbols) and our simulated fossils (blue squares). The left and right
panels show all of the fossils and only those with ΣV < 10−1.4 L" p−2 (Koposov et al.
2008), respectively. Note, that since we can only work with the primordial galaxies
produced in the pre-reionization simulations we have a discrete sampling of the fossil
properties. This is particularly true for the 75% of fossils which are not the result
116
of one or more galaxy mergers between pre-reionization dwarfs.
We find that we are able to reproduce the scatter of the baryonic Tully-Fisher
at Vc < 20 km s−1 well. However, when we only include the detectable fossils, the
inner ultra-faints (green circles) are completely inconsistent with our predictions,
more so when we include any other set of properties we have plotted thus far.
McGaugh and Wolf (2010) explored whether the large scatter in the baryonic
Tully-Fisher at low masses was correlated with any other properties. To do this, they
used the baryonic Tully-Fisher residual, Mb /MbBT F , where MbBT F is the expected
baryonic content of a halo if it fell directly on the relation. We next see if any
of their trends can be reproduced by our fossil population. We look at the BTF
√
residual versus LV (Figure 4.10), [F e/H] (Figure 4.11), Vc = 3σ∗ (Figure 4.12),
rhl (Figure 4.13), and galactocentric distance (Figure 4.14). In Figures 4.9 to 4.14,
the left and right panels show all and only the detectable simulated fossils (blue
squares), respectively.
In general, we are able to reproduce the observed trends quite well with a few
exceptions. We are unable to reproduce the Mb /MbBT F > 10 seen for a few of the
M31 ultra-faint dwarfs (opened triangles). The pre-reionization simulations do not
produce objects which form stars at efficiencies above a few percent (Ricotti et al.
2008), making it unlikely that our model would produce objects which sit that high
above the BTF relation.
A more critical discrepancy is the population of inner ultra-faint dwarfs (green
circles). Throughout, they are either at the edge of (right panels of Figures 4.10 to
4.12) or clearly distinct from (right panels of Figures 4.13 and 4.14) the detectable
fossils. This clearly distinguishes them from their larger, generally more distant
counterparts. Note in Figure 4.14 that the Mb /MbBT F of our simulated fossils shows
little evolution with galactocentric distance and the observed population follows this
117
Figure 4.10: (Left) : The luminosity versus the residual of the BTF relation for
the observed dwarfs (black symbols) and the simulated fossils (blue points). As
in Figure 4.9, in this panel we show all of the simulated fossils. (Right) : Same
as the left panel except with only fossils with Σ > 10−1.4 L" pc−2 (Koposov et al.
2008).
> 60 kpc. The distinct properties of the inner ultra-faint dwarfs and
trend for R ∼
the steep evolution of the BTF residuals with galactocentric distance supports the
scenario postulated in § 4.1.1, that they are a population which either currently, or
in the past has been strongly affected by tides.
4.3
A Note on Observations
As in Chapter 2, we approach the observations as follows. The majority of the information on the classical dwarfs comes from the Mateo (1998) review. For the ultrafaint dwarfs we generally defer to measurements with the smallest error bars with
some weight given to more recent work (Wolf et al. (2010) and references therein).
We direct the reader to § 2.1 for a more complete discussion of these criteria.
When calculating the observed distributions of dwarfs around the Milky Way, we
account for two effects, the sky coverage of the SDSS, and its detection efficiencies
118
Figure 4.11: (Left) : The [F e/H] versus the residual of the BTF relation for the
observed dwarfs (black symbols) and the simulated fossils (blue points). As in
Figure 4.9, in this panel we show all of the simulated fossils. (Right) : Same as
the left panel except with only fossils with Σ > 10−1.4 L" pc−2 (Koposov et al.
2008).
Figure 4.12: (Left) : The Vc versus the residual of the BTF relation for the
observed dwarfs (black symbols) and the simulated fossils (blue points). As in
Figure 4.9, in this panel we show all of the simulated fossils. (Right) : Same as
the left panel except with only fossils with Σ > 10−1.4 L" pc−2 (Koposov et al.
2008).
119
Figure 4.13: (Left) : The half-light radius, rhl , versus the residual of the BTF
relation for the observed dwarfs (black symbols) and the simulated fossils (blue
points). As in Figure 4.9, in this panel we show all of the simulated fossils.
(Right) : Same as the left panel except with only fossils with Σ > 10−1.4 L" pc−2
(Koposov et al. 2008).
Figure 4.14: (Left) : The galactocentric versus the residual of the BTF relation
for the observed dwarfs (black symbols) and the simulated fossils (blue points). In
this panel we show all of the simulated fossils within 1 Mpc of MW.2 and MW.3.
(Right) : Same as the left panel except with only fossils with Σ > 10−1.4 L" pc−2
(Koposov et al. 2008).
120
(Koposov et al. 2008; Walsh et al. 2009). For the classical dwarfs, we assume the
entire sky has been covered and only apply sky coverage corrections to the ultrafaint population. To correct for the SDSS sky coverage, we assume that the satellite
distribution around the Milky Way is isotropic, and multiply the number of ultrafaints by 3.54 to account for the nearly three-quarters of the sky not surveyed by
SDSS, now past Data Release 7 (Abazajian et al. 2009).
Next, we apply a correction for the detection efficiency of the SDSS using the
results from Walsh et al. (2009). If an ultra-faint is bright enough to be detected
with 99% efficiency, we assume the sample is complete for that luminosity and distance. However, if the ultra-faint is too dim for 99% detection, but bright enough
to be detected half the time, we assume that, statistically, there is another satellite with similar luminosity and distance missed by SDSS. This second correction
produces only a minor increase in the number of satellites; approximately one additional satellite over a total of ∼ 60 from sky coverage correction alone. We also
use a correction factor of 2.0 to approximate a plane of satellites (Kroupa et al.
2005; Metz et al. 2007, 2009; Zentner et al. 2005) and explore the dependence of
our conclusions on the assumption of an isotropic distribution of satellites.
As discussed in § 4.1.1, we also divide the ultra-faint dwarfs into two groups.
The first is a group of seven, including CVnI and II, Coma Ber., Hercules, Leo IV,
Leo T, and Ursa Major I and II, which have half light radii and surface brightnesses
which are consistent with the stellar properties of fossils of the first galaxies. In
contrast, the second group composed of five members, including Willman 1, Segue
1 and 2, Leo V, and Pisces II, have half light radii which are too small, and surface
brightnesses which are too high, to be consistent with the simulated primordial
population. Excepting Leo V and Pisces II, all the satellites in the later group are
within 50 kpc of the Milky Way. We note that in addition to their larger distances,
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Leo V and Pisces II sit significantly closer to our predictions for primordial fossils
than the Segues and Willman 1. We will refer to this second population collectively
as the “inner ultra-faints,” to emphasize their placement around our galaxy.
Though we are agnostic about its status, Segue 1 may be an exception. Recent
work (Martinez et al. 2010; Simon et al. 2010) suggests that its stellar population
has remained well within its tidal radius (thus tides are not important) and its stars
are unaffected by interactions with the Milky Way. However, other work suggests
that Segue 1 is a highly disrupted star cluster or dwarf (Niederste-Ostholt et al.
2009; Norris et al. 2010b). We note that, if Segue 1 is an undisrupted dwarf, the
high concentration which has protected Segue 1’s stars also identifies it as a rare
object formed in a high sigma peak at high redshift. The 1 Mpc3 volume of our
pre-reionization simulations does not represent a large enough volume to contain a
Segue 1. If Segue 1 is an undisrupted dwarf, than yes, if there are more than one
or two additional Segue 1 like objects in the Milky Way halo it is a problem for
our model that produces larger half-light radii than Segue 1’s. However, if Segue
1 is disrupting then (i) we would not expect to see objects of that type beyond
∼ 100 kpc from the Milky Way, and (ii) the presence of additional Segue 1 objects
would not pose a problem.
The ultra-faint dwarfs in the first group, and the classical dSph mentioned in
Ricotti and Gnedin (2005) are the best candidates for an observed population of
primordial fossils, with stellar spheroids not significantly modified by tides. However,
as noted in Chapter 3, classical dwarfs with LV > 106 L" are too bright to be hosted
in halos with vmax < vf ilter for vf ilter = 20 km s−1 or 30 km s−1 . While they may have
formed most of their stars before reionization, we exclude them from our comparison
to be as conservative as possible.
Throughout this work, we compare the observed Milky Way satellites to our
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luminous z = 0 halos with ΣV > 10−1.4 L" pc−2 . We are also able to use our
simulations to study the distribution of a hereto undetected population of ultra< 104 L . The possible existence and
faints with ΣV < 10−1.4 L" pc−2 and LV ∼
"
undetectability of this population was first noticed in Chapter 2, from the analysis
of RG05 simulations (see also Ricotti 2010 for a review). However, using independent
arguments, Bullock et al. (2010) have also proposed the existence of this population
they refer to as “stealth galaxies.”
4.4
Fossil Distribution
In this section, we compare the distributions of non-fossils and true-fossils to the
galactocentric radial distribution of the observed Milky Way satellites. We first compare the galactocentric radial distributions of our simulations to observations. We
then make detailed comparisons between the observed cumulative luminosity function of the Milky Way satellites and the simulated cumulative luminosity functions
of our non-fossil and true fossil populations. Note, that our simulated cumulative
luminosity functions only include stellar populations formed before reionization.
Therefore, we refer to our simulated cumulative luminosity functions as primordial
cumulative luminosity functions. Any star formation that may take place in halos
with vmax > vf ilter after reionization is not accounted for in our simulated luminosity functions. Thus, only the cumulative luminosity function of true fossils can be
directly compared to observations, while the luminosities of the non-fossils are lower
limits.
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Figure 4.15: Left Galactocentric radial distribution of all simulated satellites for
MW.2 and MW.3 from Run D (black curves) compared to the radial distribution
of all observed Milky Way satellites (red triangles). We have included all simulated
subhalos and known satellites regardless of their classification or whether they are
detectable. Right Same as the left panel but we have convolved our populations
with Walsh et al. (2009) detection limits and only included simulated subhalos
which can be detected in the SDSS data.
4.4.1
Radial Distribution of Fossils Near Milky Ways
Figure 4.15 shows the galactocentric radial distribution of all the simulated and
observed Milky Way satellites. In the left panel of Figure 4.15, we compare observations to simulations without correcting for the sensitivity limits of the SDSS
(Koposov et al. 2008; Walsh et al. 2009) or whether a satellite is a fossil. In the
right panel, we show all the satellites again, now applying the Walsh et al. (2009)
limits to the simulated halos around MW.2 and MW.3. Figure 4.16 shows the
galactocentric radial distribution for only the observed and simulated fossils. As
in Figure 4.15, the right and left panels show the simulated true fossils with and
without the Walsh et al. (2009) corrections. The observational and theoretical fossil
definitions are discussed in § 3.2.4. Our simulations do not account for tidal stripping of stars, and do not reproduce the properties of the inner ultra-faint dwarfs,
124
and we do not include them in Figure 4.16.
The left panels of Figures 4.15 and 4.16 show that at LV ∼ 105 L" the fossils become a significant fraction of the satellite population, with fossil dominance increasing as satellite luminosity decreases. This is further illustrated in Figure 4.18, which
shows the fraction of subhalos which are fossils, Nf os /Nall , as a function of distance
from the host for the same luminosity bins as Figure 4.16, excepting LV > 106L" .
We find that for 105 L" < LV < 106 L" bin, the fraction of fossils is 0.05-0.1, with
the fraction decreasing as host halo mass increases. For the lower luminosity bins,
Nf os /Nall converges to 40 − 50% and 70 − 80% for 104 − 105 L" and 103 − 104 L"
bins, respectively. If we include the inner ultra-faints in our galactocentric radial
distributions, we find a significant overabundance of observed dwarfs within 50 kpc
of the Milky Way. The stellar properties of the inner ultra-faint dwarfs do not agree
with the simulated stellar properties of the fossils. As discussed in § 4.1.1, and § 4.3,
we argue the majority of these objects may represent a population of tidally stripped
remnants of once more luminous dwarfs. A possible exception, Segue 1, is discussed
in § 4.3. Our simulations are also unable to reliably resolve z = 0 halos within
50 kpc of the Milky Way. We therefore have excluded anything with R < 50 kpc
from our comparisons.
Without the ultra-faints with R < 50 kpc, the right panels of Figures 4.15 and
4.16 show good agreement between the simulated satellite distributions of the true
fossils around MW.2 and MW.3 and the observed Milky Way galactocentric radial
distribution. When we convolve our simulated satellite populations with the limits
from Walsh et al. (2009), we find that the agreement between the distribution of
dwarfs around MW.2 and MW.3 and that observed around the Milky Way agree at
all radii and luminosity bins for LV < 106 L" (see right panel of Figure 4.16). We
thus argue that, in addition to matching the stellar properties of the ultra-faints,
125
Figure 4.16: (Left) : Same as Fig. 4.15 but the observed satellite distributions
only include bona fide fossils: the classical dSph which were designated fossils
in Ricotti and Gnedin (2005) and the ultra-faints whose stellar properties match
those of the simulated fossil population. Note that this excludes most of the ultrafaints within 50 kpc. In our simulated distributions we use vf ilter = 20 km s−1
to define a fossil. We have included all simulated fossils, including those which
would sit below the SDSS detection limits. (Right) : Same as the left panel but
simulated radial distributions only include the true fossils which would fall within
the Walsh et al. (2009) detection limits.
our simulated fossils also agree with their galactocentric radial distribution.
Figure 4.17 shows the galactocentric radial distribution of the undetected fossils in
our simulations, after excluding detectable fossils according to the detection criterion
from Walsh et al. (2009). We have not included the bins with LV > 105 L" because
there are no undetected fossils in this luminosity range within 1 Mpc of the Milky
Way. In addition, all fossils with LV > 104 L" are detected within 200 kpc. For
the lowest luminosity fossils (LV < 104 L" ) we find ∼ 400 − 500 undetected dwarfs
within 1 Mpc and 150 within 200 kpc. We have included a panel for the very low
luminosity bin (102 − 103 L" ) to look at the distribution of the dimmest fossils which
are invisible beyond a few tens of kpc. While the shape of the distribution in the
lowest luminosity bins is similar, there are approximately two times fewer undetected
fossils in the 102 − 103 L" bin. Given that fewer of the fossils in this bin would be
126
Figure 4.17: The galactocentric radial distribution of the fossils excluding the
detectable dwarfs as determined by Walsh et al. (2009). Note that the bins have
shifted down one order of magnitude in luminosity since there are no undetected
fossils with LV > 105 L" and we have included the distribution for the lowest
luminosity fossils with LV < 103 L" .
detected compared to its higher luminosity counterpart, we are seeing the decline
of star formation in the minihalos with the lowest mass. There are simply fewer
102 − 103 L" pre-reionization fossils around the Milky Way than their 103 − 104 L"
counterparts.
On the other end of the luminosity function, the right panel of Figure 4.15 shows
127
Figure 4.18: The galactocentric radial distribution of the fraction of luminous
subhalos which are true fossils around MW.2 and MW.3 from Run D. They are
divided in the luminosity bins from Figures 4.15 and 4.16 for which there is a
fossil population (LV < 106 L" ).
that while our simulated fossils are able to reproduce the ultra-faint distribution, we
see too many bright (LV > 105 L" ) satellites at R > Rvir , even after the Walsh et al.
(2009) corrections are applied. This is the first evidence of an apparent discrepancy
between simulations and observations we refer to as the “bright satellite problem.”
In the next sections, we will analyze this discrepancy, try to understand its origin,
128
and whether it can be removed while maintaining the agreement of the simulations
with observations at smaller radii and lower luminosities.
4.4.2
Primordial Cumulative Luminosity Functions
We next explore the fossil distribution and “bright satellite problem” from another
angle via comparisons between simulated cumulative primordial luminosity functions
and the observed cumulative luminosity function at different galactocentric distances
from the Milky Way center. Results are equivalent for all three simulated Milky
Ways and for both versions of our initial conditions. Therefore, for the remainder
of this section and the next we will be discussing the results for MW.3 in Run D.
Each cumulative luminosity function in this paper is split into four radial bins to
probe different regimes. We choose not to include the sample at R < 50 kpc, where
the observational sample is the most complete, because tidal effects are prevalent
and our simulations do not have sufficient resolution to determine whether or not
pre-reionization halos stripped of their enveloping cloud of tracer particles have been
tidally disrupted. The first bin we consider shows 50 kpc < R < 100 kpc. The next
bin out, the outer portion of the Milky Way halo from 100 kpc to 200 kpc, has
observations which are fairly complete for LV > 104 L" , including the brightest
ultra-faints. From 200 kpc to 500 kpc all but two of the ultra-faints (CVnI and
Leo T) would be below the detection limits of the surveys and would not be visible.
Roughly, this region corresponds to the virial radius (R200 ∼ 200 kpc) to R50 for a
Milky Way mass halo. Specific to our Local Group, this is the regime where M31
begins to play a significant role in the satellite counts, increasing the care required
to separate the Milky Way and Local Group dwarfs from those bound to M31. The
final radial bin, from 500 kpc to 1 Mpc, probes the transition region from the edge of
the Milky Way halo to the surrounding filament and void. Subhalos at these radii
129
Figure 4.19: Cumulative primordial luminosity function of MW.3 from Run D
with the observed luminosity function of Milky Way satellites. We have used
a vf ilter = 20 km s−1 to determine whether a simulated halo is a non-fossil or
true fossil. We show the luminosity functions for four distance bins, 50 kpc< R <
100 kpc (upper left), 100 kpc< R < 200 kpc (upper right), 200 kpc< R < 500 kpc
(lower left), and 500 kpc< R < 1 Mpc (lower right). In all distance bins the
relevant populations are noted as follows. The solid black curves show the total
cumulative luminosity function from our simulations, the red solid lines shows the
same for only the star forming halos (non-fossils, including polluted fossils). We
show the true fossil population with the blue dashed curve. The total observed
population is shown as magenta triangles with the ultra-faint dwarf distribution
corrected for sky coverage of the SDSS. The detection limits given in Walsh et al.
(2009) are shown as vertical black, dashed lines. Long dashed for the luminosity
limit for the outer radii and shorter dashes for the inner radii in a given bin.
130
Figure 4.20: Cumulative primordial luminosity function of MW.3 from Run D
and the observed luminosity function of the Milky Way satellites. The curves
have the same meanings as Figure 4.19 but with a vf ilter = 30 km s−1 .
are just beginning to fall into the host system, and all the ultra-faints are below
detection limits.
We divide the simulated satellites into fossils and non-fossils: Figures 4.19 and 4.20
show the primordial cumulative luminosity functions in the four radial bins for fossil
thresholds vf ilter = 20 km/s and vf ilter = 30 km/s, respectively. The observed cumulative luminosity function is shown as magenta lines and includes all the classical
131
Figure 4.21: Cumulative primordial luminosity function for MW.3 in Run D and
observations with only the fossils plotted. The simulated fossils are shown as the
blue dashed line and the observed fossils as the magenta triangles. The fossil
criteria for the observed satellites is the same as in Figure 4.16. We have only
shown subhalos around MW.3 which would be detectable by SDSS.
132
Figure 4.22: Cumulative primordial luminosity function for MW.3 in Run D and
the total observed population. Only simulated dwarfs which have ΣV above the
Koposov et al. (2008) limit are shown.
dwarfs and the ultra-faints, excepting the population at R < 50 kpc. The simulated non-fossils are shown as the red solid curve, and for all bins they dominate
for LV > 104 − 105 L" . These halos may have been able to accrete gas and form
stars after reionization, and their primordial cumulative luminosities represent a
lower limit for their present day luminosity. If we were to allow for additional star
formation after reionization, the total number of luminous non-fossils would remain
133
Figure 4.23: The luminosity (top) and mass (bottom) functions for prereionization halos within Rvir of MW.3 which are not part of a bound subhalo
at z = 0. We only include those unbound luminous pre-reionization halos between 20 kpc and 50 kpc, where all but two of the known tidal ultra-faints are
located. The horizontal dotted lines show the approximate number of stripped
pre-reionization halos required to reproduce the inner ultra-faint dwarf population, ∼ 30.
134
constant, but the curve would shift to higher luminosities (to the right). The primordial cumulative luminosity function of the true fossils (blue dashed curve) has
no such caveat. Their luminosities are known since they have not undergone postreionization baryonic evolution aside from the aging of their stellar populations.
The primordial cumulative luminosity function of the entire simulated population is
the solid black curve. Note, that for LV < 105 L" , the total primordial cumulative
luminosity function is increasingly dominated by fossils.
Before looking at the primordial cumulative luminosity functions in detail, we
insure we are comparing equivalent populations. By definition, all observed Milky
Way satellites are above current detection limits, however, as seen in Figure 4.1, a
subset of our simulated fossils have surface brightnesses below the detection limit
of the SDSS. We use both the Walsh et al. (2009) and Koposov et al. (2008) limits
to test the distribution of detectable true fossils against observations. Figure 4.21
shows the true fossil luminosity function convolved with the Walsh et al. (2009)
limits (blue dashed line) and the observed fossil sample (magenta line) used in
Figure 4.16. As in the galactocentric radial distributions, we find good agreement
between the primordial luminosity function of the true fossils and the observed fossils
for 50 − 100 kpc and 100 − 200 kpc. We do not make comparisons at R > 200 kpc
because of the inability of current surveys to detect fossils at these larger distances.
In Figure 4.22, we next use the surface brightness limits from Koposov et al. (2008)
to remove any simulated fossil satellite not detectable by current surveys. Using
the straight surface brightness cuts in Koposov et al we all but eliminates the fossil
population for vf ilter = 20 km s−1 . This is a much stronger effect on the detectability
of our true fossils than that seen for the Walsh et al. luminosity and distance cuts.
In all distance bins, there is an overabundance of the bright satellites at luminosities typical of the classical dwarfs (LV > 105 L" ). These should be easily detectable
135
by the SDSS according to Walsh et al. (2009) (assuming the undetected dwarfs have
the same distribution of half light radii as the ultra-faints). In Figure 4.19, the detectable dwarfs are to the right of the dashed line. During our discussion of the
missing bright satellites, we use cumulative luminosity functions which have not
been corrected for the SDSS limits. We now look at each distance bin individually.
Inner Ultra-Faint Dwarfs ( R < 50 kpc )
In § 4.1, we argue that, while the inner ultra-faints have likely lost significant
fractions of their stellar populations to tidal striping, they were not necessarily dIrr
at the start of their encounters with the Milky Way. Instead, they may have been
more massive primordial fossils. We base this conjecture on Figure 4.6 which shows
that the inner ultra-faints have metallicities, [Fe/H], that are similar to fossils that
are slightly more luminous. But are there enough massive fossils to account for the
inner ultra-faints? Figure 4.23 shows the mass function (bottom) and luminosity
function (top) of the pre-reionization halos which are not part of a bound halo at
z = 0 and are between 20 kpc and 50 kpc from MW.3. The dotted horizontal lines
show the approximate number of stripped fossils required to reproduce the inner
ultra-faints. We see that to produce the ∼ 30 inner ultra-faints around the Milky
Way, we would only need to consider the largest primordial fossils with masses at
reionization M > 108 M" and initial luminosities LV > 106 L" .
50 kpc < R < 100 kpc
A strong piece of evidence for the primordial model would be the total number
of observed satellites in one or more radial bins being greater than the number of
non-fossils. When we look at R < 100 kpc without the R < 50 kpc cut, we see such
an overabundance of observed dwarfs. However, when we do not include the dwarfs
within 50 kpc of the galactic center the case is no longer clear cut. If the satellite
count from 50 − 100 kpc increases to greater than 25, there is a case for fossils even
136
using the most conservative vf ilter = 20 km s−1 . For vf ilter = 30 km s−1 the number
of non-fossils available from 50 − 100 kpc drops to ∼ 18.
For luminosities at which the observational sample is complete, to the right
of the dashed lines, we see too many bright (LV > 104 L" ) objects, even in this
inner most radial bin. In addition, as our simulations do not account for postreionization star formation, it is likely that the overabundance of bright objects is
worse than shown in Figure 4.19. Unless all of the non-fossils have accreted no gas
and formed no additional stars after reionization, the simulated curve must lie below
the observations. This allows these star forming halos to increase in luminosity,
shifting the luminosity function of the non-fossils to the right.
100 kpc < R < 200 kpc
In this bin, we probe the outer reaches of the Milky Way’s virial halo and there
are a few notable characteristics of the luminosity functions. First, with the addition
of the observed dwarfs in this bin, the total number of known satellites around the
Milky Way increases to ∼ 65, ∼ 45 not including the inner ultra-faint dwarfs. The
sample at these larger radii is only complete for LV > 104 L" . For 100−200 kpc, with
a vf ilter = 20 km s−1 and the less conservative vf ilter = 30 km s−1 there are ∼ 60 and
∼ 40 simulated non-fossils, respectively. Second, the presence of undetected dwarfs
is corroborated by the shape of the observed luminosity function around 104 L" .
Not only is it rising steeply to the detection limit at R = 100 kpc, but its shape is
similar to the simulated primordial luminosity function for the true fossils.
In the outer virial halo, we once again overproduce the number of bright satellites.
At these radii the discrepancy between theory and observation is more severe than
for 50 kpc< R < 100 kpc since for these radii there is only one observed satellite
with LV > 3 × 104 L" .
R > 200 kpc
137
Figure 4.24: (Left) : Same as Fig. 4.15 but the observed satellite distributions
only include bona fide fossils and assume the Milky Way satellites are distributed
in a plane instead of isotropically. The fossils include classical dSph which were
designated fossils in Ricotti and Gnedin (2005) and the ultra-faints whose stellar
properties match those of the simulated fossil population. Note that this excludes
most of the ultra-faints within 50 kpc. In our simulated distributions we use
vf ilter = 20 km s−1 to define a fossil. We have included all simulated fossils,
including those which would sit below the SDSS detection limits. (Right) : Same
as the left panel but simulated radial distributions only include the true fossils
which would fall within the Walsh et al. (2009) detection limits.
For R > 200 kpc, we can only make observational comparisons for LV > 105 L" .
Beyond the virial radius the discrepancy between the observed number of satellites
and our simulations is up to ∼ 1.5 orders of magnitude, compared with factors of
∼ 2 and ∼ 10 for the 50 kpc < R < 100 kpc and 100 kpc< R < 200 kpc bins,
respectively.
4.5
The Isotropy Assumption
In this section, we test our assumption of an isotropic distribution of subhalos and
satellites. Rather than using an isotropic correction factor of 3.56 for the number of
ultra-faint dwarfs, we use a correction factor of 2 to approximate a plane of satellites
138
Figure 4.25: Cumulative primordial luminosity function for MW.3 in Run D and
observations with only the fossils plotted and the distribution of fossils assumed to
be in a plane perpendicular to the disk instead of isotropic. The simulated fossils
are shown as the blue dashed line and the observed fossils as the magenta triangles.
The fossil criteria for the observed satellites is the same as in Figure 4.16. We
have only shown subhalos around MW.3 which would be detectable by SDSS.
139
roughly perpendicular to the disk. Figures 4.24 and 4.25 show the galactocentric radial distribution and cumulative primordial luminosity function for the fossils using
the 2.0× planar correction factor. We find that the difference between isotropic and
planar correction factors for the satellites does not affect our finding of a reasonably
good match between the simulated and observed galactocentric radial distribution
and cumulative luminosity function of the fossils.
4.6
Discussion
One of the key predictions of the primordial model is a total number of satellites
for the Milky Way between 200 − 300, only a maximum of 100 of which are nonfossils (here we assumed vf ilter = 20 km s−1 ). The number of Milky Way satellites
which are not fossils provides an important test for star formation in minihalos at
high redshift. If, after PanSTARRS and LSST are online, the number of ultra-faint
Milky Way satellites remains < 100, we have a strong constraint on star formation in
pre-reionization dwarfs. Either no pre-reionization fossils survived near the Milky
Way, or almost none of the halos with masses at formation M < 108 M" formed
stars. However, if the satellite count rises to > 100, some of the dimmest Milky
Way dwarfs must be fossils of reionization. Using details of the stellar populations
and their distributions, observations of these fossils can constrain models of star
formation at high redshift.
A caveat to this picture is that the number of non-fossils is highly sensitive to
the choice of the filtering velocity. When we raise the filtering velocity to 30 km s−1 ,
the number of non-fossils drops by a third to 60 ± 8 from the 90 ± 10 for vf ilter =
20 km s−1 . The choice of 20 km s−1 assumes a constant IGM density with TIGM =
104 K throughout a minihalo’s evolution. In reality, the situation is not so simple.
140
The gas near 1012 M" halos, and in the filaments between, may be heated to ∼ 105 −
106 K by AGN feedback. The higher temperatures of this local intergalactic medium
> 40 km s−1 . In addition to the higher filtering velocity,
may correspond to vf ilter ∼
the higher density near a Milky Way mass halo reduces the effective potential depth
of the subhalos, increasing the mass threshold for post-reionization gas accretion
still further. Simulations to determine the temperature and density of the IGM
near a Milky Way from reionization to the modern epoch are needed to determine
the vf ilter (x, z), and whether these factors can explain the existence of Milky Way
and M31 dwarfs with the observed properties of fossils, but luminosities above the
106 L" threshold.
The observed distributions, to which we compare our simulations, depend on
how we correct for the incomplete sky coverage of the SDSS. In this work, we have
assumed an isotropic satellite distribution at R > 50 kpc. Under this assumption,
the SDSS completeness correction for the ultra-faints is 3.54. We briefly check if the
agreement between the observed and simulated distributions is dependent on the
isotropic assumption. Recent work (Bozek et al. 2011; Metz et al. 2007, 2009) has
suggested that rather than being isotropic, the Milky Way satellites are oriented
in a plane approximately perpendicular to the disk. We approximate this nonhomogeneous satellite distribution by correcting for the SDSS sky coverage by a
factor of 2.0 instead of 3.54. The number of classical fossils remains the same. The
different correction does not change the consistency of our simulated galactocentric
distribution with observations, though the lower correction factor suggests a higher
Milky Way mass. It also does not change the bright satellite problem, in fact,
the lower observational correction factor makes the overabundance of simulated
LV > 104 L" dwarfs worse by about a factor of two.
Our simulated true fossils produce an excellent agreement in properties and
141
distribution with the observed lowest luminosity Milky Way satellites. In § 4.1,
we showed that a subset of the ultra-faints, all with LV < 105 L" , have half-light
radii, surface brightnesses, mass-to-light ratios, velocity dispersions, metallicities
and metallicity dispersions consistent with the expected stellar properties of the
true fossils. We have now compared the galactocentric radial distributions and
primordial cumulative luminosity functions of simulated fossils to observations of
Milky Way satellites. When we compare the observed and simulated distributions,
we find them to be in agreement with each other for LV < 105 L" . In addition,
a large population of primordial fossils have surface brightness below the detection
limits of current surveys (e.g., SDSS). The following list summarizes the main results
of this chapter.
• Overall ∼ 25% (for vf ilter = 20 km s−1 ) to ∼ 30% (for vf ilter = 30 km s−1 )
of the primordial fossils at the present day have undergone a merger with
another luminous fossil. This fraction increases with the modern luminosity
of the dwarf. Hence, the typical half light radii of this population can be larger
than the original distribution at reionization. These fossils are even harder to
detect due to their lower surface brightness. This effect also increases the
spread of the relationship between half light radii vs. luminosity and surface
brightness vs. luminosity of fossils at z = 0.
• Leo V, Pisces II. Segue 2 and Willman 1 have half-light radii which are too
small, and metallicities too large, for their luminosities. Due to their proximity to the Milky Way, we speculate that their stars and dark halos have
been affected by tides. Hence, these ultra-faints may represent a population
> 90% of their stars via tidal
of massive primordial dwarfs which have lost ∼
interactions.
142
• We reiterate the existence of a yet undetected population of fossils with luminosities LV < 104 L" and surface brightness < 10−1.4 L" /pc2 . We present
plots showing, in detail, the expected properties of this population. We also
notice that some of the new ultra-faint satellites in Andromeda have half light
radii in agreement with the properties of the undetected fossil population, but
luminosities ∼ 105 L" .
• We are able to reproduce the distribution of the ultra-faints with our simulated
primordial fossils. We find no missing satellites at the lower end of the mass
and luminosity functions, but our model predicts ∼ 150 additional Milky Way
satellites that can be found in upcoming deeper surveys (PanSTARRS, LSST).
• At all radii, we see an overabundance of bright (LV > 104 L" ) satellites
which, even with only their primordial luminosities, would be easily detected
by current surveys. Given the agreement between the stellar properties and
distributions of the ultra-faints and those of our fossil dwarfs, we cannot account for the excess bright satellites by imposing a blanket suppression of star
formation below a given mass.
143
Chapter 5
The “Missing” Bright Satellites
Our simulations of the fossils of the first galaxies are consistent with the observed
Milky Way satellite galactocentric radial distributions (§ 4.4.1), primordial cumulative luminosity functions (Figure 4.21), and internal stellar properties (§ 4.1). More
intriguing is, that at first glance, the model appears to fail in the outer parts of
the Milky Way by over-producing the number of bright non-fossil satellites. In this
chapter, we explore possible solutions to the bright satellite problem and whether
the proposed solutions maintain the agreement between the observed ultra-faint
dwarf population and our simulated true fossils. First, we will explore whether
the pre-reionization simulations overestimate the star formation efficiency in prereionization dwarfs, and, then, whether we have too many luminous galaxies forming
before reionization (§ 5.1.3). It would be of great interest if we could use current
observations to constrain galaxy formation models before reionization. We conclude
the analysis with a proposal in which the bright satellites do exist in the outer parts
of the Milky Way halo but may still be elusive to detection due to their extremely
low surface brightnesses (§ 5.1.4).
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Figure 5.1: Cumulative luminosity functions of MW.3 from Run D (colored
curves) with the total observed population (magenta triangles). All the symbols and lines mean the same as in Figure 4.19. Here we increase the stellar
mass-to-light ratio by a factor of 10 to 50 M" /L" .
145
Figure 5.2: Cumulative luminosity functions of MW.3 from Run D (colored
curves) with the total observed population (magenta triangles). All the symbols and lines mean the same as in Figure 4.19. Here we increase the stellar
mass-to-light ratio by a factor of 100 to 500 M" /L" .
146
5.1
5.1.1
Removing the Bright Satellites
Increasing Mass to Light Ratios
First, we explore whether our pre-reionization simulations overestimate the luminosity of galaxies independent of dark matter halo masses. This could be due to
using an incorrect IMF in the pre-reionization simulations. We use a mass-to-light
ratio for the aged stellar population,
M∗rei
=
L
#
M∗today
L
$#
M∗rei
M∗today
$
(5.1)
where M∗rei and is the mass of the stellar population at reionization, and M∗today
is the mass of the stellar population at z = 0. The ratio of M∗rei /M∗today depends
on the primordial IMF. The ratio of M∗rei /M∗today depends on the primordial IMF,
and M∗today /L ∼ 1 − 2 as for the oldest globular clusters in the Milky Way. A
more top heavy IMF for the primordial stars will result in greater stellar mass loss
after reionization and fewer low mass stars which can survive to the modern epoch.
Conversely, the ratio drops as the primordial IMF produces fewer high mass stars.
To approximate this effect, in Figure 5.1 we plot the cumulative luminosity
functions as in Figure 4.19, but increase the stellar mass to light ratio by a factor
of 10 in our pre-reionization dwarfs to 50M" /L" . The figure shows that increasing
the mass to light ratio to 50M" /L" does not decrease the number of luminous
satellites enough to match observations. In the 50 kpc < R < 100 kpc bin, we can
match observations. However, since the primordial luminosities of the non-fossils are
only lower limits, the agreement disappears if the population formed any stars after
reionization. If they did, we are still over-producing luminous satellites. We need
to use a mass to light of 500M" /L" to not over-produce the number of non-fossil
satellites in any radial bin. However, this high mass to light ratio makes the fossils
147
virtually dark, with LV < 102 L" .
A blanket suppression of star formation in all halos does not solve the bright
satellite problem unless we suppress all star formation in most halos before reionizatioin. We next explore suppression mechanisms which are dependent on the
environment or properties of the halos.
5.1.2
Suppression of Pre-Reionization Dwarf Formation in
Voids
The formation of H2 in the early universe is catalyzed by ionizing UV radiation
emitted by nearby star forming regions (Ricotti et al. 2002b). In the voids, two
factors work against H2 formation. The delay of structure formation in the voids
relative to higher density regions will prevent the minihalos from collapsing until
lower redshifts when the H2 dissociating background is stronger. In addition, the
importance of positive feedback is reduced due to the larger mean distances between
minihalos in the voids and sources of ionizing radiation (Ricotti et al. 2002a,b, 2008).
The combination of these factors may result in a reduced abundance of H2 relative
to the regions around a Milky Way. This may produce a star formation efficiency
before reionization that depends on the environment. We approximate the most
extreme case of H2 suppression in the voids by suppressing all star formation in
< 0.4. The extreme suppression of the star formation in the
halos in regions with δ ∼
voids we use treats all halos but those in the overdense regions (zef f = 8.3) as dark.
Since the bright satellite problem is most prominent in the outer regions of the
Milky Way halo, the lack of star formation in low density regions may decrease the
number of bright halos beyond the virial radius while leaving the satellite luminosity
functions unchanged at smaller radii and lower luminosities. However, Figure 5.3
shows that, even in the most extreme case, suppressing H2 formation in the voids
148
Figure 5.3: Cumulative luminosity functions of MW.3 from Run D (colored
curves) with the total observed luminosity function (magenta triangles). All the
symbols and lines mean the same as in Figure 4.19. Here we have completely
suppressed star formation in any halo outside the highest density regions. This is
the most extreme case of lower H2 formation, and therefore lower star formation
in the voids.
149
does not decrease the number of bright satellites enough in any radial bin to bring
our simulations into agreement with observations. In this scenario, there is no
appreciable reduction of the number of bright satellites for R < 200 kpc. There
is a decrease in the luminosity function at larger radii, but it is neither strong nor
focused enough on the high luminosity subhalos to solve the overabundance of bright
satellites in the outer parts of the Milky Way. Enough of the region within 1 Mpc
of our Milky Way is at the highest density in our simulation (zef f = 8.3) that the
complete suppression of star formation in even moderately less dense regions does
not sufficiently change the luminosity functions or radial distributions.
With the inability of H2 suppression in the voids and overall suppression of star
formation to account for the missing bright satellites, we shift our focus to properties
of the halos which vary with halo mass.
5.1.3
Lowering the Star Forming Efficiency
In the pre-reionization simulations, the sub-grid recipe for star formation depends
on a free parameter, $∗ , controlling the efficiency of conversion of gas into stars per
unit dynamical time. One of the main results of the pre-reionization simulations
is that the global star formation rate and f∗ (M) = M∗ /Mbar (the fraction of total
mass converted into stars, where Mbar = Mdm /7.5) is nearly independent of $∗ in
small mass dwarfs due to the self-regulation mechanisms of star formation. However,
> 5 − 10 × 107 M , f (M) is typically proportional to $
in halos with masses M ∼
"
∗
∗
since the higher mass minihalos are less sensitive to self-regulated feedback. We used
$∗ = 5% in our fiducial runs, but that may be too large (e.g., Trenti et al. 2010). The
pre-reionization simulations may have overestimated the luminosity of primordial
> 5 × 107 M , for which the f vs M relationship is tighter. We
dwarfs with M ∼
"
∗
explore the effect of reducing $∗ by introducing a maximum stellar fraction, f∗,crit .
150
Figure 5.4: (Left). Cumulative luminosity function of MW.3 from Run D (colored
curves) and the total observed population (magenta triangles). All symbols and
lines mean the same as in Figure 4.19. We have applied an fcrit = 1%.
Roughly, f∗,crit corresponds to the mass threshold where feedback effects no longer
dominate and where the value of $∗ becomes important. If we reduce f∗,crit , we
will decrease the luminosities of our most luminous halos. Roughly, for halo masses
M ∼ 3 ×107 M" (virial mass at formation) our simulations have f∗ (M) ∼ 1%. This
is in agreement with observed values for dwarfs with vc ∼ 10 km s−1 (McGaugh et al.
2010).
151
Figure 5.5: Same as Figure 5.4 but for fcrit = 0.1%.
Figure 5.4 shows the luminosity functions of our simulations with all halos with
f∗,crit = 1% and Figure 5.5 shows the same for f∗,crit = 0.1%. The figures show
that lowering the star formation efficiency preferentially for the higher mass halos
is effective in decreasing the number of non-fossil subhalos with LV > 105 L" .
Adopting f∗,crit = 1% decreases the number of luminous halos enough to bring the
luminosity functions in agreement with observations, while preserving the agreement
for the fossil population. However, in the radial bins 50 kpc < R < 500 kpc, there
152
Figure 5.6: Left : Radial distribution for our simulated MW.2 and MW.3 with
a fcrit = 1% (black solid curves) and for the fossil Milky Way satellites (red
triangles). Note, that while we are still able to reproduce the radial distribution
of the lowest luminosity bin, we are no longer able to match the fossil population
for LV > 105 L" . Right : Radial distribution for fcrit = 0.1%. Note that for the
more extreme suppression, we have lost the fossils population with LV > 104 L"
still are too many subhalos with LV > 105 L" , though the discrepancy has dropped
significantly. Coupling a lower $∗ with a higher mass to light ratio or H2 suppression
in the voids does not correct the remaining bright satellite overabundance. However,
when we use an f∗,crit = 0.1%, the cumulative primordial luminosity function of our
simulated dwarfs becomes consistent with observations at all radii, but requires a
deduction of f∗ in halos with mass M ∼ 7 × 106 M" whose f∗ is self-regulated and
thus independent of $∗ (Ricotti et al. 2002b).
Any solution for the overabundance of bright satellites must preserve not only
the existence of the true fossil population, but also its distribution and properties.
We next look at the other dimensions of the agreement between the true fossil
populations with an fcrit = 1% and 0.1% and the ultra-faints and classical dSph.
Figure 5.6 shows the radial distribution of the true fossils around MW.2 and MW.3
from Run D, the observed Milky Way population for an fcrit = 1%. While for
153
103 L" < LV < 104 L" and 104 L" < LV < 105 L" the fossil population with
fcrit = 1% reproduces the observed radial distribution; we no longer have any true
fossils with LV > 105 L" . If the star formation efficiency of our pre-reionization
halos is lowered enough to bring the number of luminous satellites in line with
observations, the fossil luminosity threshold discussed in Chapter 3 is dropped to
LV < 105 L" . For fcrit = 0.1% the threshold drops further to 104 L" .
The loss of the multi-dimensional agreement between our true fossils and the
ultra-faints shows that lowering $∗ enough to account for the missing luminous satellites is not a viable solution for the bright satellite problem if the ultra-faint dwarfs
are fossils of the first galaxies. In this interpretation, we need a different mechanism which will either preferentially suppress star formation in the most luminous
pre-reionization halos to a greater degree, or cause their lower redshift counterparts
to lose the majority of their primordial stellar population after reionization. We
continue to seek a baryonic solution to the bright satellite problem before treating
it as an issue for CDM cosmology.
5.1.4
The Ghost Halos
As discussed in Chapter 3, our N-body method does not allow us to determine the
dynamics of the stars in halos that undergo mergers, or the degree to which those
stars are tidally stripped. However, we have used analytic relationships to estimate
the importance of dynamical heating of the stars when z = 0 fossils (about 20%)
are produced by mergers of more than one pre-reionization dwarf (§ 4.1) We refer to
such interactions as galaxy mergers. Here, we focus on those dynamical processes in
non-fossils which result in the dispersion of the primordial stellar populations of the
brightest satellites, the net effect of which is to either make the non-fossil populations
invisible to current surveys by reducing their surface brightnesses below the SDSS
154
Figure 5.7: (Left). Histogram of the fraction of luminous true fossils with a
given number of luminous pre-reionization halos, Nlum . Nlum is a proxy for the
number of significant mergers the system has undergone. (Right). Histogram
of the fraction of non-fossils with a given Nlum . Note, that unlike the Nlum
histograms for the true fossils and polluted fossils the peak is not at Nlum = 0,
but shifted to Nlum ∼ 5. Note also, that the vertical scale is 0.1 instead of 1.0.
Figure 5.8: Histogram of the fraction of non-fossils with a given V-band surface
brightness, ΣV , for the primordial population. We assume that the primordial
stars have been puffed up by interactions until they fill the full extent of the dark
−2 , where R
matter halo, giving us ΣV = LV × Rmax
max is the radius at which
v(r) = vmax . The dashed vertical line is the surface brightness limit of the SDSS
from Koposov et al. (2008). Only ∼ 1% of the non-fossils are to the right of the
dashed line, with expanded primordial populations detectable by the SDSS.
155
Figure 5.9: Cumulative luminosity functions of MW.3 from Run D (colored
curves) with the total observed population (magenta triangles). All the symbols and lines mean the same as in Figure 4.19. In this figure we assume that
all the non-fossils are below the detection limits or have lost their entire stellar populations due to a combination of heating due to major mergers and tidal
interactions.
156
Figure 5.10: Cumulative luminosity functions of MW.3 from Run D (colored
curves) with the total observed population (magenta triangles). All the symbols
and lines mean the same as in Figure 4.19. Unlike Figure 5.9, here we allow the
non-fossils to retain 0.1% of their stellar populations.
157
detection limits or preferentially strip them during interactions with more massive
> 500 kpc where
halos. The former mechanism would be relevant to non-fossils at R ∼
tidal forces are negligible.
The number of pre-reionization halos in a z = 0 dwarf increases with mass. In
this section, we explore the role of mergers to rend invisible, or strip, the primordial
populations of stars in the the more massive dwarfs (non-fossils). Unlike in the
previous sections, here we differentiate between the non-fossils and polluted fossils
in our simulations. We remind the reader, that though both populations have vmax
which were large enough for them to accrete gas from the IGM in the past, only the
non-fossils are at or above that threshold at z = 0.
Throughout the next section we relax the assumption made in § 4.1 that kinetic
energy is conserved during galaxy mergers and no energy is transferred from the
movement of the component galaxies before merger to the stellar population of the
daughter dwarf. When a system undergoes a galaxy merger, kinetic energy from the
collision is imparted to the stars. Immediately after the collision, the new system
will be in its most diffuse state. We define a galaxy merger as the interaction of two
or more primordial galaxies. Although there is significant scatter in the luminosities
of minihalos of the same mass, in general, those which host primordial galaxies are
more massive than their dark counterparts. An interaction between two luminous
minihalos is therefore more significant. We use Nlum , the number of primordial
galaxies within at z = 0 halo, as a proxy for the number of galaxy mergers. If there
are multiple galaxy mergers in a short amount of time, these stars will be susceptible
to loss. In addition, recent work on increasing the extent of the stellar population in
the bright ellipticals from z = 2 to z = 0 suggests that many minor interactions over
several Gyrs can increase the size of the galaxy by a factor of 2-5 without significantly
increasing mass (Naab et al. 2009). Roughly, the larger the number of significant
158
interactions, the greater the spatial extent of the pre-reionization population and the
more likely the halo will have lost a significant fraction of its primordial population
to dynamical heating.
For isolated halos, with large Nlum , the radius of the primordial population increases, possibly until it fills the spatial extent of the dark matter halo. Such an
extended system would have extremely low surface brightness and would be susceptible to tidal stripping. We next look at which of our three subhalo populations has
a significant number of members with Nlum > 3. The fractions of the true fossil,
and non-fossil populations with a given Nlum are shown in the left and right panels
of Figure 5.7. Neither fossil population has a significant fraction of subhalos with
Nlum > 3 with the fractions at ∼ 1% and ∼ 10% respectively. We therefore assume
that, while a few of our true and polluted fossils may have had their primordial
populations diffused by mergers, the vast majority remain dynamically cold.
The non-fossils show the opposite trend. The right panel of Figure 5.7 shows that
< 10% of the non-fossils have Nlum < 3 and the distribution peaks at Nlum ∼ 5. A
population of non-fossils would be much more likely to have a primordial population
dispersed by multiple major interactions than their fossil counterparts.
The non-fossil populations (see Figure 4.19) could have either lost their stellar
populations, or had their primordial populations increase in size to the point where
they are undetectable by the SDSS. Near the Milky Way, we assume they lost
their entire primordial stellar population to tidal interactions. After falling into the
Milky Way halo, the non-fossils were unable to form a significant younger stellar
population.
At larger radii, the non-fossils are less likely to have their primordial populations
stripped. However, as the stars expand to fill the spatial extent of the dark matter
halo, the non-fossils end up with a primordial population with ΣV ∼ LV × Rp−2 ,
159
where LV is the luminosity of the primordial population and Rp is the radius of
the primordial population. Figure 5.8 shows the fraction of the non-fossils with
a primordial population with surface brightness, ΣV , for Rp = Rmax and Rp =
0.25 × Rmax , where Rmax is the radius of the maximum circular velocity. We find
that for Rp = Rmax about 1% of non-fossils would have an extended primordial halo
above the SDSS detection limits (to the right of the dashed line), and, when Rp is
decreased to 0.25 × Rmax , the detectable fraction only rises to 20%. If these nonfossils formed few or no stars after reionization the majority would be undetectable
by SDSS. The non-fossils which did form stars after reionization would be dIrr
today or perhaps one of the few isolated dSphs or dSphs/Irrs: e.g., Cetus, Tucana,
Antlia. In our scenario, they would be surrounded by “ghost halos” of primordial
< − 2. But does this solve the “bright satellite
stars ∼ 12 Gyr old with [F e/H] ∼
problem”?
We quantitatively approximate this for our simulations by using a circular velocity cut. We look at the primordial luminosity functions as if all the ghost halos
are either stripped or below SDSS detection limits. Practically, we set the luminosities to zero for all the non-fossils. We look to see if this cut solves the bright
satellite problem while preserving the fossils better than lowering the star formation
efficiency. We find it to be a good solution to the bright satellite problem.
Since setting the non-fossils luminosities to zero is able to decrease the number
of luminous satellites, we look at the luminosity function it produces in more detail.
All the curves in Figure 5.9 are the same as in Figure 4.19, excepting the red curve
for the non-fossils that now represents only the polluted fossils.
We now look at each distance bin to see what turning off the non-fossil population
has done to our various arguments. For 50 kpc < R < 100 kpc, the necessity of a
primordial dwarf population is even stronger when we only consider the fossil and
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polluted fossil populations. There are only ∼ 7 polluted fossils within 100 kpc, less
than one-fifth of what is required to account for the ∼ 50 observed satellites. For
LV > 104 L" , the luminosity function now sits below observations. This gives the
remaining star forming halos room to form additional stars without overproducing
subhalos with LV > 104 L" . The total number of subhalos within 100 kpc decreasing
to 35 is consistent with observations. First, our MW.3 is on the low end of the mass
range for the Milky Way for both observational estimates and simulations. Second,
as seen in Figure 4.23, there are more than enough stripped down fossils which
formed in halos with M > 107 M" and LV > 105 L" to fill in the deficit. Since these
objects would lack a cloud of tracer particles, they are marked as unbound by the
halo finder AHF and included in the host halo and therefore not included in any of
our dwarf luminosity functions.
The complete invisibility of the non-fossils is not quite as successful for 100 kpc<
R < 200 kpc as we are still slightly overproducing the number of LV > 105 L"
satellites compared to observations. However, we are better able to reproduce the
sudden steepening in the observed luminosity function in Figure 5.9 than with any
of our other suppression mechanisms (Figures 5.2, 5.3, and especially 5.4). This
feature may be unique to the Milky Way so we are not unduly concerned with
matching it. In addition, if the non-fossils are dark, our argument for the existence
of primordial fossils becomes straightforward. There are only ∼ 30 polluted fossils
in this distance bin, only 75% of the ∼ 40 observed galaxies, with any dwarf with
LV < 104 L" difficult, if not impossible, to detect with current surveys.
Beyond the MW.3 virial radius (R ∼ 200 kpc), turning the non-fossils dark easily
places the primordial luminosity function into agreement with observations. This
allows for the formation of post-reionization populations of stars in the polluted
fossils and non-fossils. We remind the reader that the z = 0 halos at these radii
161
would likely be on first approach to the Milky Way system and more likely to accrete
and retain gas at later times. The diffuse primordial population in these distant nonfossils is an observational test of star formation in pre-reionization dwarfs and the
existence of pre-reionization fossils.
5.2
Discussion
Through this work, we have used results of the simulations described in Chapter 3
to study the origin of the observed Milky Way and M31 satellites and understand
whether they are compatible with models of star formation before reionization. In
the primordial model, a subset of the Milky Way satellites formed with their current
properties with minimal modifications by tidal stripping. However, the primordial
model produces too many bright (LV > 105 L" ) satellites at all distances from the
Milky Way. Our attempts to reduce the bright satellite problem while preserving
the fossils are summarized below.
• Lower H2 formation rates and subsequent lower minihalo star formation rates
in the voids are not able to bring the number of bright satellites into agreement
with observations.
• Effectively lowering the star formation efficiency can fix the bright satellite
problem if we assume only pre-reionization halos with M < 7 × 106 M" had
SFR dominated by local, stochastic feedback. However, not only is this contrary to current understanding of star formation in minihalos, but the fossil
population this “solution” produces cannot reproduce the distribution of the
ultra-faint population.
• We bring the number of bright satellites into agreement with observations,
162
while leaving the fossil population untouched, by assuming the primordial stellar populations of our non-fossils (with maximum circular velocities, vmax (z =
0) > vf ilter ) become extremely diffuse via kinetic energy from galaxy mergers.
The existence of “ghost halos” of primordial stars is a new powerful observational prediction of our model that can be straight forwardly tested using
HST observations of isolated dwarfs around the Local Group.
We have suggested two solutions which correct for the overabundance of bright
satellites while preserving at least a fraction of the primordial fossil population.
Each presents a different picture when we consider it in the context of the voids.
The first, and less effective, solution calls for a low star formation efficiency. In this
picture, the 1010 M" halos visible in current surveys will have their star formation
dampened, however as we move to ∼ 107 M" we enter the regime where stochastic
feedback effects dominate over the choice of $∗ . Thus, the voids would appear
relatively empty, but only because we cannot yet detect the less than 105 L" fossil
populations which formed in the 107 M" halos before reionization.
The dispersal of the non-fossils’ primordial populations into ghost halos is a
more effective solution to the “bright satellite problem” within 1 Mpc of the Milky
Way, but leaves a conundrum in the voids. Regardless of whether the primordial
population would be detectable, how do we keep the post-reionization star formation
in these non-fossils low enough to prevent this later star formation from producing
more MV > −16 galaxies than are currently observed?
Any post-reionization star formation in the non-fossils results in a young population which would be (i) brighter, (ii) more concentrated, since enriched gas will cool
faster and sink deeper into the gravitational potential, and (iii) possibly accompanied by an H I reservoir. Any of these properties would make the post-reionization
population easier to see, and the non-fossil harder to hide. To suppress the post-
163
reionization baryonic evolution in the non-fossils, we examine our naive assumption
that they all undergo significant baryonic evolution after reionization.
The easiest way to suppress star formation in the lower mass non-fossils is to
raise the filtering velocity. As has already been discussed in Chapter 4, any non-fossil
embedded in the WHIM (T ∼ 105 K) would have a vf ilter ∼ 40 km s−1 . However,
the WHIM is predicted to exist at z < 1 (Smith et al. 2010), leaving ∼ 6 Gyr after
reionization when the non-fossils could have accreted gas and formed stars. A final
possibility is that reionization was extremely efficient at quenching star formation
in 20 − 40 km s−1 halos and the non-fossils were never able to build up enough gas
from the post-reionization IGM to form additional stars.
In summary, while the bright satellite problem can be “solved” for the primordial
population alone, we still need to account for the post-reionization evolution of the
non-fossils. In order to maintain the agreement with observations, only ∼ 10% of the
non-fossils can form significant stellar populations after reionization. Determining
how and if the other ∼ 90% can be suppressed will tell us how much of a problem
the bright satellite problem is.
164
Chapter 6
Observational Tests for the
Primordial Model
In this chapter, we present a set of observational tests which can provide support for
a primordial formation scenario for the faintest Milky Way satellites and constrain
models of high redshift star formation. We will begin with what the currently known
ultra-faints can tells us, before presenting a set of predictions for the properties of
the ∼ 100 undetected fossils the primordial model predicts are orbiting the Milky
Way. We then explain what the current number of known satellites and the number
which will be detected, or not, by upcoming surveys can tell us about star formation
in minihalos at high redshift. Finally, we discuss two predictions for more distant,
isolated non-fossils and fossils; the ghost halos and late stage gas accretion.
165
6.1
The Ultra-Faint Dwarfs
6.1.1
Tidal Disruption
Better determination of whether the ultra-faints are being tidally disrupted can help
determine whether a subset of the faintest Milky Way satellites are pristine fossils.
The ultra-faint dwarfs whose rhl do not match our simulated true fossils, shown as
filled green circles in Figures 4.1 - 4.8, display the signs of being tidally disrupted by
the Milky Way, including proximity to the Milky Way (R < 50 kpc). While Willman
1, Segue 1 & 2, Leo V, and Pisces II show signs of tidal disruption, this does not
prove the primordial scenario. However, it would place their origin as disrupted
objects in line with our proposal in § 4.1.1 and 4.2. If additional observations show
these tidal ultra-faints are not tidally disrupted, then our primordial formation
model can not explain their current properties. The exception to this picture is
Segue 1. The tidal status of Segue 1 has been recently debated (Martinez et al.
2010; Niederste-Ostholt et al. 2009; Norris et al. 2010b; Simon et al. 2010) and it
remains unclear whether it is a disrupting system or a highly concentrated halo
which formed at high redshift in a rare, high σ peak.
6.1.2
The Undetected Dwarfs
We next outline the stellar properties we can expect of the undetected dwarfs around
the Milky Way if they are part of a population of fossils of the first galaxies. The
red contours of Figures 4.1 - 4.8 show the properties of the predicted population.
1. Half-light radii
The undetected dwarfs should have the same distribution of half-light radii as
the currently known, ultra-faint population, from ∼ 100 pc to ∼ 1000 pc.
166
2. Mass to Light Ratio
The mass to light ratio of undetected dwarfs should generally be greater than
103 M" /L" and as high as approximately 105 M" /L" and follow a roughly
linear relation for dwarfs with LV < 105 L" .
3. Stellar velocity dispersion
There should be no decrease in the stellar velocity dispersion, σ∗ , with V-band
luminosity. This directly contradicts the decreasing σ∗ with LV seen for tidally
stripped dwarfs in Figure 4 of Wadepuhl and Springel (2010).
4. Metallicity
The undetected dwarfs should have typical [F e/H] < −2.5, a significant number with [F e/H] < −3.0. This would make these undetected dwarfs excellent
candidates for the search for ultra-metal poor stars (Frebel and Bromm 2010;
Frebel et al. 2010; Norris et al. 2010a,b,c).
6.1.3
Number of Satellites
The number of Milky Way satellites alone provides a test for star formation in
minihalos. For a given filtering velocity, there is a number of satellites, Nnf , which
max
max
have a vmax
above the filtering velocity. Roughly, vmax
occurs as the halo falls into
the Milky Way, before its accumulated mass has enough time to be tidally stripped.
For vf ilter = 20 km s−1 , Nnf is 90 ± 10 and for vf ilter = 30 km s−1 , Nnf is 60 ± 8,
the latter is equivalent to the number of currently known Milky Way satellites after
applying the sky coverage correction. If the number of satellites, Nsat , is greater
than Nnf , some minihalos had to have formed stars before reionization. Conversely,
if Nsat < Nnf , either no minihalos formed stars or none survived near the Milky
Way.
167
6.2
Into the Voids
Although the existence of pre-reionization fossils seems likely, observations do not
unequivocally demonstrate their existence due to the large uncertainties in estimating the number of yet undiscovered ultra-faint dwarfs (Tollerud et al. 2008). In this
section, we summarize three observational tests for the existence of fossils of the
first galaxies that we propose based on our results. The first test of our model is
especially interesting as it can be performed using HST observations and does not
require waiting for future all sky surveys deeper than SDSS, like PanSTARRS or
LSST, to be online.
1. “Ghost halos” around dwarfs on the outskirts of the Local Group
The primordial stellar populations in minihalos that formed before reionization should produce diffuse “ghost halos” of primordial stars around isolated
dwarfs. We have shown that the total luminosity of the “ghost halos” is comparable to the one of classical dwarfs, but the surface brightness of the stars
is well below the SDSS detection limits. Contrary to the difficulties of finding
ultra-faints, we know where these diffuse stars are and we can plan deep observations to detect them. The diffuse primordial stellar populations around
non-fossils should not be tidally stripped in dwarfs with galactocentric distance > 1 Mpc from the Milky Way. We do not know within which distance
tidal stripping would become important, but due to their large half light radii,
they certainly are the stellar population that would be stripped first. “Ghost
halos” can be best detected by resolving their individual main sequence stars
around isolated dIrrs or dSphs before using spectra to determine their metallicities and dynamics. Unlike younger stars dispersed from the central galaxy,
the primordial ghost halo would have a [F e/H] < −2.5, and we are currently
168
running simulations to determine their dynamics.
Recent HST observations of M31 have resolved the main sequence using ACS
(Brown et al. 2008, 2009, 2006). A low-luminosity dwarf at ∼ 800 kpc on
the other side of the Milky Way from M31 would be an excellent candidate
for the ghost halo search, and detection of its main-sequence primordial stars
would be within the reach of HST. At 800 kpc, the field of view of WFC3
(162”) is ∼ 630 pc, at 1 Mpc, ∼ 785 pc, and at 2 Mpc, ∼ 1.6 kpc. The ghost
halos are > 1 kpc, often up to a few tens of kpc in radius therefore, WFC3
would not be able to image the entire dwarf with its ghost halo. However,
aimed at the outskirts of a likely ghost halo host, it could look for signs of a
primordial halo in the color magnitude diagram and radial surface brightness
distribution. We would be able to resolve the individual stars in the ghost
halos at ∼ 1 Mpc. The ghost halos have surface densities of stars of 0.001
and 1 star pc−2 depending on the extent of the ghost halos and the slope of
the IMF at low masses. Assuming a stellar density of 1 star pc−2 , the angular
distance between each star is ∼ 0.26$$ , larger than the WFC3 resolution of
0.04$$ per pixel. Since the stellar population can be resolved, determining the
details of a ghost halo population is a matter of taking deep enough exposure
to detect the main sequence stars and differentiate those faint stars from the
extremely distant, equally faint background galaxies. Red giant branch stars,
while brighter and easier to detect, have a density three orders of magnitude
lower than the main sequence.
Deep observations work well for detecting the ghost halos when we already
know where they are. These primordial populations surround dwarf galaxies
that have undergone significant star formation since reionization and may
have detectable gas and active star formation today. However, as discussed in
169
§ 5.1.4, in order to reproduce the observed satellite distribution, only a fraction
of the ghost halos can have formed a significant younger stellar population.
We remind the reader that our definition of a fossil versus a non-fossil in
the simulations assumes a constant vf ilter = 20 km s−1 . Assuming a larger
filtering velocity would produce a smaller number of non-fossils (see Table 2.7).
Therefore, some of the halos we define as non-fossils, and containing ghost
halos, may have been unable to accrete gas and form stars after reionization
due to additional heating of the IGM. This population of “dead” ghost halos
would have only an extremely diffuse, primordial population. Without H I or
more concentrated, younger stars, the best chance for detecting these ghost
halos would be large scale surveys. Figure 5.8 shows that the majority of the
ghost halos are beyond the reach of the SDSS, but what about upcoming,
deeper surveys such as PanSTARRS?
Diffuse stellar systems like the ultra-faint dwarfs and the ghost halos are found
in surveys by looking for overdensities of stars relative to the background. In
many cases, by detecting stars at the tip of the red giant branch (RGB). In
low luminosity systems the detection of the RGB depends on two factors, the
distance to the halo and the population of the RGB. Low luminosity systems,
like the ultra-faint dwarfs, can have as few as a thousand stars, and therefore
a sparsely populated, and difficult to detect, RGB. For example, with SDSS
(magnitude limit r = 22.5) Hercules (1.1 × 104 L" ) could only be detected to
300 kpc, while the more luminous CVn I (2.3 × 105 L" ) would be seen at a
Mpc from the Milky Way (Koposov et al. 2008). PanSTARRS (magnitude
limit r=24) will reach 1.5 magnitudes deeper that SDSS, detecting the same
RGB twice as far. However, the primordial populations in the ghost halos are
extremely diffuse, and it is unclear that the overdensity of their RGB stars
170
would be high enough to be detected against foreground M dwarfs and distant
galaxies. In short, while PanSTARRS is expected to detect new ultra-faint
dwarfs, it may not the best tool for finding ghost halos.
If some of the discovered ultra-faint dwarfs are fossils, then “ghost halos”
should exist. Vice versa, the detection of “ghost halos,” regardless of the
method, can be used to constrain the star formation rates before reionization
and would imply the existence of fossils, although these fossils may not have
yet been discovered due to their low surface brightnesses.
2. Dark and ultra-faint gas rich dwarfs in the voids
According to the model proposed in Ricotti (2009), a subset of minihalos in
the voids may have been able to condense gas from the IGM after Helium II
reionization (at z ∼ 3). However, they would not form stars unless their
gas reached a critical density that is dependent on the metallicity of the gas.
These minihalos may or may not have formed stars before reionization, and
any stellar populations they did have would be below the detection limits of
both current and future surveys. The H I in these objects could be detected by
blind 21 cm surveys. Recently, ALFALFA and GALFA surveys have reported
the discovery of several small and compact clouds of neutral hydrogen, some
of which may represent a population of pre-reionization minihalos. Some of
these clouds could be “dark galaxies” and represent the smallest detectable
halos around the Milky Way and others may be ultra-faint dwarfs in the voids.
The location of unassociated H I detections could then guide optical surveys to
these primordial fossils in a focused deep search for their ancient populations.
171
Chapter 7
Summary and Future Work
Below we summarize the results of this dissertation before briefly sketching out our
future plans. The bullet points are compiled from the Discussion and Conclusions
sections of Bovill and Ricotti (2009, 2010a,b).
Conclusions
• Voids contain many low luminosity fossil galaxies. However they have surface brightnesses and luminosities making them undetectable by SDSS. One
possible way to detect these void dwarfs is if they experience a late phase of
gas condensation from the IGM as proposed in (Ricotti 2009). Future and
present 21cm surveys such as ALFALFA and GALFA may be used to find
these objects (Begum et al. 2010; Giovanelli et al. 2005).
• We find a linear scaling relation between the number of luminous satellites
and the mass of host halos. The scaling has scatter similar to the relationship
between the total number of sub-halos with M > 107 M" (vmax > 5 km s−1 )
and the host mass, although the normalization is 3 − 4 times lower.
• Due to the dependence of the properties of primordial dwarfs on their for172
mation environment (Ricotti et al. 2008), we find very few true fossils with
LV > 106 L" , and none within 1 Mpc of our Milky Ways. This places the
identification of some of the more luminous classical dSphs fossils in doubt.
• Overall ∼ 25% (for vf ilter = 20 km s−1 ) to ∼ 30% (for vf ilter = 30 km s−1 )
of the primordial fossils at the present day have undergone a merger with
another luminous fossil. This fraction increases with the modern luminosity
of the dwarf. Hence, the typical half light radii of this population can be larger
than the original distribution at reionization. These fossils are even harder to
detect due to their lower surface brightness. This effect also increases the
spread of the relationship between half light radii vs. luminosity and surface
brightness vs. luminosity of fossils at z = 0.
• Leo V, Coma Berenics, Segue 2 and Willman 1 have half light radii which
are too small, and metallicities too large, for their luminosities. Due to their
proximity to the Milky Way, we speculate that their stars and dark halos have
been affected by tides. Hence, these ultra-faints may represent a population
> 90% of their stars via tidal
of massive primordial dwarfs which have lost ∼
interactions.
• We reiterate the existence of a yet undetected population of fossils with luminosities LV < 104 L" and surface brightness < 10−1.4 L" /pc2 . We present
plots showing, in detail, the expected properties of this population. We also
notice that some of the new ultra-faint satellites in Andromeda have half light
radii in agreement with the properties of the undetected fossil population, but
luminosities ∼ 105 L" .
• We are able to reproduce the distribution of the ultra-faints with our simulated
primordial fossils. We find no missing satellites at the lower end of the mass
173
and luminosity functions, but our model predicts ∼ 150 additional Milky Way
satellites that can be found in upcoming deeper surveys (PanSTARRS, LSST).
• At all radii, we see an overabundance of bright (LV > 104 L" ) satellites
which, even with only their primordial luminosities, would be easily detected
by current surveys. Given the agreement between the stellar properties and
distributions of the ultra-faints and those of our fossil dwarfs, we cannot account for the excess bright satellites by imposing a blanket suppression of star
formation below a given mass.
• Lower H2 formation rates and subsequent lower minihalo star formation rates
in the voids are not able to bring the number of bright satellites into agreement
with observations.
• Effectively lowering the star formation efficiency can fix the bright satellite
problem if we assume only pre-reionization halos with M < 7 × 106 M" had
SFR dominated by local, stochastic feedback. However, not only is this contrary to current understanding of star formation in minihalos, but the fossil
population this “solution” produces cannot reproduce the distribution of the
ultra-faint population.
• We bring the number of bright satellites into agreement with observations,
while leaving the fossil population untouched, by assuming the primordial stellar populations of our non-fossils (with maximum circular velocities, vmax (z =
0) > vf ilter ) become extremely diffuse via kinetic energy from galaxy mergers.
The existence of “ghost halos” of primordial stars is a new powerful observational prediction of our model that can be easily tested using HST observations
of isolated dwarfs around the Local Group.
174
Simulating the Ghost Halos
We are currently running a set of higher resolution simulations to determine the
radial distribution and dynamics of the primordial population in the ghost halos.
To do this, we need to resolve the stellar populations during the galaxy mergers to
determine how much the primordial stars have been puffed up by the galaxy and
dark mergers. In addition, we want to derive an estimate of the primordial stellar
mass lost during mergers to refine our calculations of the properties of fossils and
non-fossils which have undergone galaxy mergers.
Generating the initial conditions for the new simulations uses the same method
described in Chapter 3, with one significant difference. After we have identified an
isolated 109 −1010 M" halo at z = 0, we build a high resolution region which contains
the component pre-reionization halos of our z = 0 non-fossil. Unlike the simulations
presented in this thesis, the high resolution region of the new simulations will trace
the stellar and dark matter particles of the pre-reionization simulation instead of the
halos. This will allow us to resolve the dynamical evolution of the chosen non-fossil
from reionization to the present. We note that, once again, we are not including the
post-reionization baryonic evolution of our halo and assuming that all star formation
was quenched by reionization.
Our current initial conditions have a mass resolution of mdm = 4935.3 M" for
the dark matter particles and mst ∼ 102 − 104 M" for the stellar particles in a
1 × 1 × 2 Mpc3 region embedded within our 503 Mpc3 box. As this thesis is printed
we are attempting to discern if and how we can increase the new simulation’s speed
so it will use a reasonable amount of computational resources.
175
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