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THES'S

{UM

This is to certify that the

dissertation entitled

EARLY CHEMICAL EVOLUTION OF THE GALAXY

presented by

LAMYA AHMAD SALEH

has been accepted towards fulfillment
of the requirements for

 

 

 

Ph. D- degree in Physics
flung” fl/W
Major profesrsor
T. Beers

Date 05/09/01

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6/01 cJCIRClDatoDuepes-pJS

Early Chemical Evolution of The Galaxy

By

Lamya A. Saleh

A DISSERTATION
Submitted to Michigan State University

In Partial Fulfillment of the requirements
for the degree

DOCTOR OF PHILOSOPHY

Field of Physics and Astronomy

2001

ABSTRACT
Early Chemical Evolution of The Galaxy

By

LAMYA A. SALEH

We perform a numerical simulation to describe the evolution of pre-Galactic
clouds in a manner similar to that suggested by the cold dark matter scenario of
hierarchical galaxy formation, and adopting a SN-induced star-formation mechanism.
The model includes chemical enrichment of the clouds by SN of type II and type Ia, and
their associated energy input. It utilizes metallicity-dependent yields for all elements at
all times, and takes into consideration the lifetimes of stars.

The model calculates the metallicity distribution functions for stars in the clouds,
their age-metallicity relation, and relative elemental abundances for several alpha- and
Fe-group elements. The stability of these clouds against destruction is discussed, and
results are compared for different initial mass functions.

We find that the dispersion of the metallicity distribution function observed in the
outer halo is reproduced by evolving many clouds with different initial conditions. The
scatter in metallicity as a function of age for these stars is very large, implying that no

age-metallicity relation exists in the early stages of galaxy formation.

Clouds with initial masses similar to presently observed globular clusters were
found to be destroyed within the first 0.1 Gyr from the onset of star formation,
suggesting that these systems could not have been responsible for the formation of the
first stars, and were probably not self-enriched. More massive clouds are only stable
when one assumes an initial mass function that is not biased towards massive stars,
indicating that even if the first stars were formed according to a top-heavy mass function,
subsequent star formation was likely to have proceeded with a present-day mass function,
for happened in an episodic manner.

The predicted relative abundances of alpha- and F e-group elements compared to
iron show good agreement with the observed values down to a metallicity [Fe/H]
= — 4. The observed scatter is reproduced fairly well for most elements but the model
shows larger deviations for some elements. The contributions to the abundances from SN
with different progenitor masses and metallicity are discussed. The results suggest that
the low-mass end of SN of type-II was probably absent at the very lowest metallicities,

and that the high-mass limit for the first stars that contributed to nucleosynthesis may be

less than 40Mo,

ACKNOWLEDGEMENTS

I would like to express my deep gratitude to Dr. Timothy Beers for his guidance
in this work. I have seen in him complete devotion to his scientific goals and am
grateful to have been able to learn from him. Thanks for the long discussions, and your
continuous feedback, and for your comments on the thesis. I would also like to thank the
committee members, prof. Horace Smith, prof. Jack Baldwin, prof. Scott Pratt, and prof.
Brad Sherrill for reviewing this work. Special thanks are due to prof. Grant Mathews for
his guidance, along the way and for the many useful comments and suggestions. I would
also like to thank prof. Jim Truran, my mentor during the year I spent at U of C as an
exchange student, for his help and support and for the fruitful discussions. Everyone I
met at U of C was very supportive and helpful. I would like to mention specially prof.
Donald York, Sandy Heinz, and Chris Mallouris.

Special thanks go to my dear husband, for his continuos support and
encouragement and for being around when I most needed it, and to my beloved parents,

sisters, and brothers for their encouragement and continuous prayers.

iv

TABLE OF CONTENTS

ABSTRACT: EARLY CHEMICAL EVOLUTION OF THE GALAXY ...................................... ii
ACKNOWLEDGEMENTS ................................................................................................ iv
TABLE OF CONTENTS .................................................................................................... v
LIST OF FIGURES ........................................................................................................ viii
LIST OF TABLES ........................................................................................................... xi
CHAPTER 1 : INTRODUCTION ........................................................................................ 1
I. [Overview ................................................................................................................ 1
1.2 This Thesis ............................................................................................................ 6
CHAPTER 2 :APPROACHES TO GALACTIC CHENICAL EVOLUTION ................................. 8

2.1 Observational Approach: Extremly metal-poor stars...... .8

2.2 The Theoretical Approach: Galactic chemical Evolution Models. . . . .. .11

2.3 Towards a Chemical Evolution Model of the Halo ............................................. 15
2.4 Chemical Evolution and the r-processes. . . . .. .................................................... .20
2.5 Overview of the Model ......................................................................................... 22
CHAPTER 3 : THE CHEMICAL EVOLUTION MODEL ..................................................... 25
3.1 Introduction ......................................................................................................... 25
3.2 Methods for modeling Chemical Evolution ........................................................ 26
3.2.1 The Star Formation Rate (SFR) ....................................................... 27
3.2.2 The Initial Mass Function ................................................................ 29
3.2.3 The metallicity dependent Yields .................................................... 31

V

3.3 Formulation of the problem ................................................................................ 3 7

3.3.1 Introduction ...................................................................................... 37
3.3.2 The first Stars ................................................................................... 38
3.3.3 Star Formation Method .................................................................... 40
3.3.4 The Calculation ................................................................................ 41
CHAPTER 4 I PROPERTIES OF THE CLOUDS ................................................................ 48
4.1 Introduction ......................................................................................................... 48
4.2 Initial Conditions .............. i .................................................................................. 48
4.2.1 The gas ............................................................................................. 48
4.2.2 The nature of the IMF ...................................................................... 50
4.3 Results and Discussion ....................................................................................... 54
4.3.1 Stability of the clouds ...................................................................... 54
4.3.2 Star formation .................................................................................. 56
CHAPTER 5 : STELLAR ABUNDANCES AND METALICITIES ......................................... 61
5.1 Introduction ......................................................................................................... 61
5.2 Metalicity and Ages of Stars ............................................................................... 62
5.3 The Metalicity Distribution Function (MDF) ..................................................... 67
5.4 Relative Elemental Abundances .......................................................................... 76
5.4.1 The observed trends in halo stars ..................................................... 76
5.4.2 Overview of model predictions ........................................................ 77
5.4.3 [Alpha / Fe] ...................................................................................... 78

vi

5.4.4 [Fe-peak / Fe] ................................................................................... 82

5.4.5 Contributions from different SN ......................................... 84
CHAPTER 6 FINAL REMARKS ..................................................................................... 95
6.1 Conclusions ......................................................................................................... 95
6.2 The Future ........................................................................................................... 97
REFERENCES ............................................................................................................. 102

vii

LIST OF FIGURES

Figure 3.1 The metallicity-dependent yields of Fe, Mg, and Mn. Each is shown
for four different progenitor masses, 40 Mo (triangles), 30 M9

(circles), 20 Mo (squares), and 15 Mo ( plus Sign ). .....................................

Figure 4.1 The mass functions, ¢, = m'l'”, ¢ 2 =(1—e’m/2)m"'35,

¢ 3 = (1 + m/md'l'”, ¢, = m'l°35 e""/'" . ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

Figure 4.2 Star formation rate in the model for the different mass functions. ,,,,,,,,,,,,,,,,

Figure 4.3 The percentage of mass in low-mass stars (solid line), and in high-mass

stars(dashed line). ______________________________________________________________________________________________

Figure 5.1 Metallicities produced in shells of different progenitors vs. time. The

progenitors shown have masses 13,20,30 and 40 Mo _____________________________________

Figure 5.2 Metallicity vs. time for stars produced by the model. ....................................

Figure 5.3 Metallicity Distribution functions of stars produced in our models,
1.35

assuming a Salpeter mass function: (pl: ”1' ...............................................

Figure 5.4 Metallicity Distribution Functions among stars produced by our

models, assuming a mass function: (p2 = m”'” (1 - em") . mj = 40. ............

Figure 5.5 Metallicity Distribution Functions among stars produced by our
[.35

models, assuming a mass function: cp3 =(1 + m/ m1)’ ................................

Figure 5.6 Metallicity Distribution Functions among stars produced by
-I.35 -m /m

our models, assuming a mass function: (p4 = m e I ..........................

Figure 5.7 The sum of the MDFs for the four clouds shown in figures 5.3 to 5.6 ,,,,,,,,,

Figure 5.8 The abundances of the alpha elements Mg, Ca, Si, and Ti. Data is from
Ryan et al (1996) (triangles) and Norris et a1 (2001) (circles). The

small (dots) represent the model stars. .............................................................

Figure 5.9 The abundances of the alpha elements when Fe yields are reduced by a
factor of 2. Data is from Ryan et a1 (1996) (triangles) and Norris et al

(2001) (circles). The small (dots) represent the model stars. _________________________

viii

36

53

59

6O

64

66

7O

71

72

73

75

79

81

Figure 5.10 The abundances of the Fe-group elements, Mn, Ni, Cr, and Co . Data

is from Ryan et a1 (1996) (triangles) and Nom's et a1 (2001)

(circles). The small (dots) represent the model stars. ______________________________

Figure 5.11a The contribution from different progenitor masses to the value of
[Ca/F e]. The mass ranges are given in solar masses. The top left
figure shows the whole range. Data is from Ryan et a1 (1996)
(triangles) and Norris et al (2001) (circles). The small (dots)

represent the model stars. ___________________________________________________________________________

Figure 5.11b The contribution from different progenitor masses to the value of
[Mg/Fe]. The mass ranges are given in solar masses. The top left
figure Shows the whole range. Data is from Ryan et a1 (1996)
(triangles) and Norris et a1 (2001) (circles). The small (dots)

represent the model stars. ___________________________________________________________________________

Figure 5.11c The contribution from different progenitor masses to the value of
[Si/F e]. The mass ranges are given in solar masses. The top left
figure shows the whole range. Data is from Ryan et al (1996)
(triangles) and Norris et al (2001) (circles). The small (dots)

represent the model stars. ...........................................................................

Figure 5.11d The contribution from different progenitor masses to the value of
[Ti/Fe]. The mass ranges are given in solar masses. The top left
figure shows the whole range‘. Data is from Ryan et a1 (1996)
' (triangles) and Norris et al (2001) (circles). The small (dots)

represent the model stars. ...........................................................................

Figure 5.12a The contribution from different progenitor masses to the value of
[Cr/F e]. The mass ranges are given in solar masses. The top left
figure shows the whole range. Data is from Ryan et al (1996)
(triangles) and Norris et a1 (2001) (circles). The small (dots)

represent the model stars ____________________________________________________________________________

Figure 5.12b The contribution from different progenitor masses to the value of
[Co/F e]. The mass ranges are given in solar masses. The top left
figure shows the whole range. Data is from Ryan et a1 (1996)
(triangles) and Norris et al (2001) (circles). The small (dots)

represent the model stars. ...........................................................................

Figure 5.120 The contribution from different progenitor masses to the value of
[Mn/F e]. The mass ranges are given in solar masses. The top left

1X

83

87

88

89

90

91

92

figure shows the whole range. Data is from Ryan et a1 (1996)
(triangles) and Norris et a1 (2001) (circles). The small (dots)
represent the model stars. __________________________________________________________________________________ 93

Figure 5.12d The contribution from different progenitor masses to the value of
[Ni/Fe]. The mass ranges are given in solar masses. The top left
figure shows the whole range. Data is from Ryan et al (1996)
(triangles) and Norris et al (2001) (circles). The small (dots)

represent the model stars. .................................................................................. 94

LIST OF TABLES

Table 4.1 Survival Times of The Clouds

xi

Chapter 1

Introduction

1.1 Overview

Understanding the origin of the Milky Way has been the fascination of
astronomers for many decades, and much work has been devoted to this field of science,
both observational or theoretical. On the observational front, the search for stars that
provide clues to the nature of galaxy formation has been going on for the past fifty
years. Today, better observational techniques make it possible to obtain reasonably
accurate determinations of the basic information required to understand the formation of
our Galaxy, for instance, stellar kinematics, metallicities, and the relative abundances
of chemical elements in individual stars. Such information not only sheds light on the
formation processes of these stars, but also on the environments in which they formed.
With even larger and more powerful ground-based telescopes, and with the enormous
technological achievement of launching the first large telescope into Space, the Hubble
Space Telescope, the search for understanding the process of galaxy formation has

extended not only deeper into the Milky Way, but now includes other galaxies at
1

redshifts as high as 2 = 5. By studying galaxies at high redshifts one is actually

looking back in time, hence one witnesses the formation of galaxies billions of years
ago, providing insight on what processes might have been in play in the case of our
own galaxy.

The wealth of information provided by ground- and space-based observations
is growing rapidly, and is raising new questions, in addition to providing at least partial
answers to old issues. Theoreticians have addressed the subject of galaxy evolution
for decades, and have had many successes. Recent years have witnessed great advances
in our understanding of the origin of structure in the universe and the apparent
connection with the formation of galaxies. Today, chemical and chemo-dynamical
evolution models are being performed with improving success, due to the leap in
computational power (leading to much larger numbers of test particles that might be
included in the simiulations), increased reliability of nucleosynthesis calculations, and
the addition of new chemical abundance data for many more stars than was not
available even in the recent past.

The first attempts to model the evolution of the Milky Way (Hartwick 1976;
Tinsley & Larson 1979; Matteucci & Francios 1989; Page] 1989a) were strongly
inspired by the work of Eggen, Lynden-Bell, and Sandage (1962), who found a
correlation between kinematics and chemical properties of a sample of nearby stars.
This led them to suggest that the Galaxy formed by a dissipative, monolithic collapse of

a spherical proto-Galactic cloud, with a free-fall timescale of ~ 108 yrs. In 1978, Searle

2

& Zinn (hereafter, SZ) compared the metallicities and inferred ages of a small
sample of outer-halo globular clusters in the Galaxy, but found no evidence of the
predicted correlations. AS an alternative, they proposed that the halo formed by
accretion of metal-poor fragments (similar in size to presently observed nearby dwarf
galaxies) over a much longer timescale, up to several times 109 yrs.

Since then it has been a matter of debate as to which of these two scenarios, if
either, is more likely to account for the formation of the Milky Way, and other large ,
spirals like it. Aspects of the 82 scenario are supported by a great deal of observational
evidence. The most direct is the observed tidal disturbance of the Sagittarius dwarf
galaxy caused by the Milky Way (Ibata, Gilmore, & Irwin 1994; Ibata et al. 2000).
Furthermore, field stars in the outer and the inner halo seem to exhibit differences in
their kinematic properties (Majewski 1992; Carney et al. 1996; Sommer-Larsen et al.
1997) and possibly also in their ages, with the outer-halo stars appearing several Gyrs
younger than those of the inner halo (Lance 1988; Preston et. al. 1991; Preston et. al.
1994; Lee, & Carney 1999). In addition to supporting the S2 scenario, this duality in
the kinematics and the ages of the halo field stars has been taken to suggest that the
inner part of the halo may have undergone a coherent contraction in the manner
suggested by ELS (Carney et al. 1996; Sommer-Larsen et al. 1997; Chiba & Beers

2000)

Further support of the SZ scenario is provided by the observed apparent
clustering of field horizontal-branch (FHB) stars, and the possible detection of
kinematic substructure in the halo (Doinidis & Beers 1989; Majewski, Munn, & Hawley
1994, 1996; Helmi et al. 1999) that has been explained as the result of the later merging
of Smaller systems (perhaps similar to dwarf galaxies) with the Milky Way. Chiba &
Beers (2000) studied the kinematic and chemical properties of a large sample (N ~
1200) of non-kinematically selected metal-poor stars with full space motions available,
and re-identified the ‘clumps’ in angular-momentum space of stars previously identified
by Helmi et al. (1999). They also reported an observed elongated feature in angular-
momentum space extending from the clump to regions with higher azimuthal rotation,
which they referred to as a ‘trail’.

The results of the Chiba & Beers study could not all be explained with either of
the ELS or the $2 scenario alone. For example, they reported no observed correlation
between the overall metallicity of their sample stars (quantified as [Fe/H], a logarithmic
measure of the difference between the abundance of heavy metals in the star as
compared with the sun) and their orbital eccentricity, and no change in the average
rotational velocity of stars with abundances [Fe/H] < —1.7. This result is inconsistent
with a monolithic collapse from the halo to the disk of a homogeneous spheroid. In
such a scenario, stars born from the infalling gas would be expected to Show a
continuous increase in their average orbital rotational velocities (hence a continuous

decrease in e) with increasing [Fe/H] as the spheroid spins up in order to conserve

4

angular momentum. The SZ scenario, on the other hand, fails to explain the
observed vertical gradient of rotational velocity found in the inner halo by the Chiba &
Beers analysis.

Another interesting observation is that some halo stars have been found to
exhibit rather low alpha-element (e.g., Ca and Mg) abundances relative to iron (King
1997; Carney et al. 1997; Preston & Sneden 2000) as compared to the majority of low-
metallicity stars, which exhibit an over-abundance in alpha elements with respect to
iron. This suggests that these stars may have experienced a nucleosynthesis history that
differs from the bulk of the halo stars, perhaps occurring in smaller systems such as
proto-galactic fragments or dwarf galaxies (Gilmore & Wyse 1998).

Taken as a whole, the extent data suggests a halo formation scenario in which
the outer halo is assembled by the merging of sub-galactic clumps, while a dissipative
collapse forms the inner halo on a shorter timescale (Norris 1994; Freeman 1996;
Carney et al. 1996; Sommer-Larson et al. 1997; Chiba & Beers 2000). This picture is
also qualitatively consistent with the present favored theory of galaxy formation, the
hierarchical clustering scenario. According to this scenario, the Galaxy is initially
assembled by formation of cold dark matter dominated mini-halos (Peacock 1999) that
subsequently accrete primordial gas from their surroundings. Density perturbations in
the early universe are believed to be the origin of these sub-galactic clumps, which
eventually merge to form larger structures, and finally build up the Galaxy. Smaller

clumps are more susceptible to destruction by tidal interactions and merging during the

5

collapse of the Galaxy, in addition to the energy feedback from SN events as
soon as they begin to form stars. Therefore, the stars formed in these small clouds are
believed to reside in the outer halo of the Galaxy, and have no net rotational velocity,
Since the clouds they come from must have a distribution of velocities with no specific
bias . This is in full agreement with the results of Chiba & Beers. More massive clouds,
on the other hand, are less likely to be destroyed by interactions, and therefore
experience multiple merging events while moving towards the central region of the
proto-Galaxy. Because these clouds grow in mass and gain a large amount of orbital
angular momentum, they experience a very violent and dissipative destruction, forming
the observed flattened inner halo with prograde rotation

It should be noted that the details of the parameters required by cold dark matter
models to reproduce the observed kinematic and chemical properties of the Galactic
halo, in addition to the origins of the different populations residing in the Galaxy today,
are questions that require firrther testing before they might be answered with

confidence.

1.2 This Thesis

It is most likely that the history of the Milky Way may combine aspects of both
the ELS and the 82 scenarios, occurring on different timescales, and that halo stars did
not all form at the same time and did not all come from the same Source. The older stars
occupying the inner halo today were likely to have formed previously in the first clouds

that merged to form the early halo, whereas the younger stars observed in the outer halo
6

were accreted later from smaller nearby systems that may have gone through

slower enrichment scenarios. There is a growing consensus that the halo of our Galaxy
formed in a hierarchical manner, although a fully developed picture of how it occurred
has not yet been developed.

In this thesis we are specifically interested in these early stages of the Galaxy’s
evolution, which astronomers have only recently been able to tackle due to the many
poorly understood factors believed to be involved, and the scarcity of data that was
available from the Galaxy's older component, the halo population.

We have performed a numerical simulation based on a chemical evolution
model for individual sub-Galactic clouds, the aim of which is to test the bottom-up
galaxy formation scenario and impose constraints on the early phases of galaxy
evolution. We believe this study will be one of the first steps in understanding this

period of galaxy evolution, and will be a stepping stone for future attempts.

Chapter 2

Approaches to Galactic Chemical Evolution

2.1 Observational Approach: Extremely Metal-Poor Stars

Since the surface elemental abundances of (non-evolved) stars are expected not to
differ from those of the gas from which they formed, stars showing similar chemical and
kinematic properties are believed to share the same history, and even may have had the
same origin. Stellar populations in the Galaxy are commonly divided into the halo,
bulge, and the thick and thin-disk populations.

It is among the field population in the halo of our Galaxy that the oldest and most
metal-deficient stars are found. These stars contain in their elemental and isotopic
abundances the fossil record of nucleosynthesis processes that took place in the first
epochs of galaxy formation, and also reflect the inhomogeneity of the interstellar medium
(ISM) during halo formation (McWilliam 1997). For this reason, astronomers today
consider the search for metal-poor stars a main focus of their research efforts to
understand the beginning of structure in the universe, with the halo of our Galaxy as the

best available laboratory.

The first stars to form out of primordial gas that emerged from the big bang are
especially significant since, if still detectable, they would contain within their chemical
composition answers to many questions regarding bi g-bang nucleosynthesis and the early
universe. Number counts of at least the low—mass stars in this population might be used
as probes of the primordial Initial Mass Function (IMF), an essential parameter in

hierarchical models. These stars, often referred to as Pop-HI stars, are believed to have

metallicities ranging anywhere between the primordial abundances, Z ~ 10'10 lo

(Applegate et a1. 1988), and the lowest observed abundances in Pop-II stars

(Z ~ 104 lo ). Unfortunately, in spite of the long history of search for Pop-HI stars, only

a few stars of metallicity near [Fe/H] = -4 have been found, and no star has been found
with a significantly lower abundance (Beers 1999). Perhaps this result Should not be
surprising, since the only ultra metal-poor stars that could have survived until today are
the low-mass stars with main-sequence lifetimes exceeding the Hubble time (~ 10 Gyrs)
If the IMF of Pop-III stars favored the formation of massive stars, as predicted by Larson
(1998), then there are probably none left behind today because of their proportionately
shorter lifetimes. Even if some low-mass ultra metal-poor stars are still to be found, it
may be possible that that the surface abundances of these stars could have changed during
their long lifetimes. Two scenarios have been suggested: extrinsic pollution -- the
accretion of heavy elements onto their atmospheres while passing through the more

metal- rich ISM of the Galactic disk (Yoshii 1981; Iben 1983), and intrinsic pollution --

as suggested by new stellar-evolution models for extremely metal-poor stars of Fujimoto
et. al. (1999) and others, since a low-mass metal-deficient star can be converted into a
carbon- and nitrogen-enhanced star due to passing through a period of intense internal
mixing during late stages of evolution on the giant branch (at the time of the so-called
helium shell flash). This idea gains some support by the fact that up to 25% of the stars in
the HK survey (see the description below) with [Fe/H] < —3 exhibit strong carbon and
nitrogen features in their spectra (Rossi, Beers, & Sneden 1999). Perhaps it is the case
that all Pop-III stars with [F e/H] < —4 do indeed undergo this conversion, and hence are
not detected in normal surveys. Clearly, the origin of the metal-deficient carbon stars is
of great interest, and requires a detailed understanding in the future.

In most of the surveys for metal-deficient stars carried out to date, the majority of
the stars identified are located within a distance less than 10 kpc from the sun. It is not
yet clear, however, whether lower metallicity stars will be found by conducting surveys
of the more distant regions in the Galaxy. The scenario of galaxy formation favored by
Chiba & Beers (2000), for example, suggests that the largest fraction of the oldest (and
most metal-deficient) stars might be presently found in the inner-halo population (up to
20 kpc from the center of the Galaxy) rather than in the outer halo (see Beers & Chiba
2001 for a discussion).

There are a number of current projects aimed at the discovery of extremely
metal-poor stars based on wide-field objective-prism surveys. The HK survey of Beers
and collaborators (Beers et al 1985; Beers et al 1992; Beers 1999), for example, has

10

a”

identified some 1000 stars with [Fe/.H] < —2 that comprise the bulk of the low-metallicity
targets for high-resolution Spectroscopic studies with 8m-10m class telescopes, such as
the VLT, SUBARU, and KECK.

One recent project holds particular promise. The Hamburg/ESQ objective-prism
survey (HES) covers the full southern sky at Galactic latitude |b| > 30 degrees (Christlieb
et al 2000). The great advantage of this survey is its use of automated scans, rather than
the visual scanning used in the HK survey. The HES is capable of detecting stars down
to apparent magnitudes B ~ 17.0, and at distances up to 25 kpc from the Sun. The next
generation of astrometric satellites (e.g., FAME, SIM, GAIA), in addition to ongoing
ground-based astrometric programs (e. g., SPM, NPM, USNO) and full-sky (or nearly so)
photometry programs ( e.g., 2MASS, and SDSS) should dramatically improve the
amount and detail of information that will be obtained from Galactic stars in the near
future. These promising efforts are expected to increase the number of known extremely
metal-poor stars considerably, and could perhaps lead to the discovery of Pop-1H stars in

the near future.

2.2 The Theoretical Approach: Galactic Chemical-Evolution Models

Modeling the evolution of our Galaxy may be seen as a first step towards
understanding the formation and evolution of galaxies in general. The direction in which
these modeling efforts are focused is governed by the availability of data, and by the

status of theoretical approaches to the various physical processes involved.

11

A complete model of the formation and evolution of a galaxy must include both
chemical and dynamical aspects. Chemical processes include the production of heavy
elements and their redistribution into the ISM, which includes star formation, stellar
evolution and nucleosynthesis, and supernova events. Dynamical effects include merging
of subsystems to form larger structures, heating and cooling processes, and gas dynamics.

Since the Milky Way is the best-studied individual galaxy, a fair amount of
observational data for its constituent stars and clusters has been available for decades,
leading to many efforts aimed at understanding its evolution. The first attempts (ELS,
SZ) were mostly dynamical in nature due to the poor understanding of the physical
processes governing chemical evolution, and the lack of detailed elemental abundance
measurements for most halo stars. The Solar System abundances were established and
tabulated by Andres & Grevesse in 1989. As a result, many chemical-evolution models
were developed in attempts to reproduce the abundance patterns observed in the Galactic
disk (Wyse & Silk 1989; Pagel 1989; Matteucci & Francois 1992; Edvardson 1993;
Wang &.Silk 1994; Pardi 1995; Times et al. 1995).

Most of these disk models divided the disk into radial zones, and as an
unavoidable approximation, treated each zone as a “closed box,” allowing no gas
exchange to take place except for the gas accreted into each zone either from the halo or
the extragalactic medium. In order to simulate the observed change in density with
Galactocentric distance, the accretion rate of gas was varied in these models along the

disk plane. This necessarily led to a variable Star Formation Rate (SFR) in the models

12

that used density-dependent SFRs. Although reasonable agreement was reached between
the theoretical results of these studies and the extant observations, these studies generally
were forced to focus on a very limited set of observables. This indicates the need for
more inclusive models that consider additional physical processes, including the
dynamics of the gas. Still, our understanding of these processes is relatively limited, and
in manymodels they were (and are) ignored. The importance of dynamical processes in
chemical evolution can be realized from the correlation between a galaxy’s morphology
and its chemical composition, and from the systematic changes of chemical composition
with position in our own Galaxy. In order to account for all of these observed trends it is
necessary to treat the whole Galaxy-with self-consistent models that follow its evolution,
including Galactic dynamics and chemistry, in addition to the heating and cooling of the
ISM (Burkert & Hensler 1987a;1987b ; Hensler et al 1992; Theis, Burkert & Hensler
1992; Sommer-Larsen et a1. 1997; Samland 1998). In addition, the importance of
energetic processes in the evolution of galaxies has been demonstrated through several
studies (Blumenthal et a1 1984; Silk 1985; Burkert & Hensler 1989; Burkert, Truran, &
Hensler 1992). Their inclusion is necessary in order to create a multi-component ISM in
which several gas phases can co-exist. Although these chemo-dynamical models treated
the Galaxy as one whole system, and were successful in reproducing many observables.
such as stellar kinematics, stellar and gas density distributions, SN rates, and the observed

abundance gradients in the ISM, their treatment of the early stages of the Galaxy’s

evolution was brief and incomplete.

l3

The lack of basic data, and the need for higher accuracies of the extant
measurements, in addition to the complicated dynamical, nuclear, and atomic processes
involved (many of which are still poorly understood), has made it impossible to formulate
a complete evolution model of the Galaxy from a set of simple assumptions. Thus, most
chemical-evolution models have been strongly focused on one or another aspect of the
Galaxy’s history. This can be seen as a necessary step, since the Galactic disk, halo and
bulge do show unique abundance patterns (McWilliam 1997), suggestive of different
enrichment histories. At present, complete evolution models for the Galaxy are
achieved by evolving each of these populations in isolation. However, the manner in
which the different populations found in the present Galaxy are related to one another is
still unclear, making it difficult to combine the partial descriptions into a coherent whole.

For example, the question of whether the halo and disk populations evolved
separately, or were strongly interacting with one another on similar timescales, has not
yet been answered. In some models, it was assumed that the major part of the gas in the
disk originally came from the subsystems that formed the halo and were disrupted by the
energetics of massive stars (Sommer-Larsen et al. 1997; Pardi et a1. 1995; Travaglio et al
1999a). Others excluded this scenario, and claimed that the disk accreted the majority of
its gas from the extragalactic medium and evolved separately from the halo (Chiappini et
a1. 1997; Goswami & Prantzos 2000). In the majority of disk models, infall of gas was
assumed without any specification of its origin (Timmes et al. 1995; Prantzos & Aubert

1995; Prantzos & Silk 1998).

14

2.3 Towards a Chemical Evolution Model of the Halo

There seems to be an urgent need for better understanding of the earliest stages of
the Galaxy’s evolution. The stars that formed at these earlier times, and the subsequent
dynamical interactions that shaped the Galaxy, probably played a role in the nature of all
of the various populations observed today.

Understanding the early epochs of the Galaxy’s evolution is also crucial to the
development of other branches of astronomy. Examples include high-redshift galaxies
and damped Lyman—or systems, where astronomers hope to explain details of the heavy-
element abundance distributions associated with these objects (Pettini et. al. 1997) . In
addition to the important role the first stars are believed to play in the early evolution of
galaxies, they are believed to contribute to the formation of early generations of black
holes ( Ostriker & Gnedin 1996; Haiman et a1. 1996; Tegmark et al. 1997).

Nucleosynthesis calculations in stars is a rapidly evolving area of research, and
one that is expected to benefit greatly from detailed studies of extremely metal-poor stars.
By comparing the observed elemental abundances of extremely metal-poor stars with the
predictions of chemical-evolution models, one can impose constraints on the theoretical
nucleosynthesis calculations in massive stars. One can also predict the abundance
patterns expected in metal poor stars from theoretical SN models, starting with specific
assumptions about the formation processes of these stars. By comparing the predictions

with the observed abundances, one can gain some insight about the validity of the

15

assumptions made, and add to the understanding of the formation processes and the
efficiency of mixing of the ejected elements into the surrounding ISM.

Most pictures for the formation of the first structures suppose that they are the
result of gravitational amplification of primordial fluctuations. The halos of galaxies
would then form by the merging of smaller sub-structures. The mass of these sub-

structures has been estimated by hierarchical clustering models to be of the order of

present—day dwarf galaxies, or large globular clusters ( ~106 to 108 Mo) . These models

predict that the first systems to collapse under their own gravity (and presumably that
went on to form stars), are of this mass range (Blumenthal et. al. 1984, Peebles 1985;
Peebles 1993; Haiman, Thoul, & Loeb 1996; Tegrnark et al. 1997; Nishi & Susa 1999;
Miralda-Escude 2000).

Monolithic collapse scenarios also predict fragmentation via gravitational and/or
thermal instabilities into subsystems of the same mass range (Fall & Rees 1985). The
stellar halo population would then originate, in this view, from disrupted subsystems.
Later, the remaining gas would settle and form the disk (Katz 1992; Steinmetz & Muller
1994,1995). This scenario was also suggested by Sommer-Larsen et a1. (1997), as the
result of their analysis of the kinematics and dynamics of blue horizontal-branch stars in
the Galactic halo. These authors found that there appears to exist a rapid decrease in the
radial component of the halo’s stellar velocity ellipsoid, associated with an increase in
tangential velocity dispersion with Galactocentric distance. This, together with the

observed abundance gradient in the inner halo that is absent in the outer halo, led them to

16

suggest that the outer halo formed by accretion and merging processes, while the inner
halo arose from a more dissipative and coherent collapse on a shorter timescale. In this
picture, the more compact subsystems of the halo would survive to form the globular
clusters observed today, whereas the more diffuse and probably lower-metallicity
subsystems would break up due to the energetics of massive stars, tidal destruction, and
dynamical friction. The majority of the gas from these systems, left in a dilute state after
their destruction, would gradually settle in the disk. This galaxy formation scenario has
also been supported by observations of the Sagittarius dwarf galaxy, which is presently
being disrupted by the Milky Way, as well as a group of small galaxies at high redshift,
possibly in the process of merging into a larger galaxy (Pascarelle et al. 1996).

Our ability to ask specific, detailed questions about the process of halo formation
and evolution is being greatly expanded by the large amount of spectroscopic information
now becoming available from high-resolution studies of metal-poor stars. As the result
of efforts by Beers and his collaborators (Beers, Preston, & Shectrnan 1985, 1992; see
Beers 1999 for a summary), the number of known metal-poor stars has increased
dramatically in the last few years. The abundance trends of individual elements observed
in these stars appear to be in agreement with the simple existing models of Galactic
evolution.

Earlier, Gilroy et. al. (1988) showed that a real star-to-star abundance scatter of
heavy elements exists amongst metal-poor stars, indicating that the proto-halo was not

well mixed when these stars formed. This was also confirmed by Ryan, Norris, & Beers.

17

(1996), who performed an abundance analysis for 19 very metal-poor stars with [Fe/H] <
—2.5, and found a dispersion in their measured abundances greater than the observational
uncertainties. This study also confirmed Similar results by McWilliam et al. (19953),
who found that the abundance ratios of several iron-group elements (such as Co and Ni)
relative to iron showed a shift in slope at [Fe/H] ~ —2.5, indicating that different
processes must have dominated before this “chemical time” than later in the evolution of
the Galaxy. McWilliam et al. suggested that metallicity-dependent yields of type-H SN
may have been responsible for the observed shift in slope for a number of elements
observed below [F e/H] = —2.5.

Ryan et. al. (1996) also proposed an explanation for the observed abundance
patterns at extremely low metallicity. They noticed that, in spite of the existence of a
large scatter in neutron-capture element abundances relative to iron, the iron-group
elements themselves show rather well-defined trends. Adopting the supernova remnant
evolution model of Cioffi, McKee & Bertschinger (1988), they offered the explanation
that the mass of the ISM that mixes with the SN ejecta, though being only weakly
dependent on the cloud conditions (e. g., density and metallicity), depends linearly on the
SN explosion energy. Since iron-group elements are thought to form near the
collapsing proto-remnant of most Type-II SN explosions, it seems reasonable that two
SN producing the same amount of these elements should impart the same kinetic energy
to their envelopes, allowing the ejecta to mix with the same amount of mass in the ISM,
thereby producing similar enrichment. This picture would allow the proto-halo to include

18

a combination of many clouds, evolving separately at different times and places, and still
produce the well-defined chemical patterns observed for iron-group elements.

In the same paper, Ryan et al. calculated the mass of ISM that would be polluted
by 3 SN with energy of the order ~ 1051 ergs, and found it to be of the order ~ 105 solar
masses. They deduced that enrichment by a typical SN event in the proto-halo could
produce a metallicity [Fe/H] ~ -2.7 when its ejecta are expelled into a bubble of
primordial gas. This value coincides with the observed lower limit to the metallicity of
Galactic globular clusters, and with the metallicity for field halo stars below which larger
scatter in abundance ratios is seen, in addition to the observed shift in iron-group element
abundance patterns. This is also consistent with the idea that field halo stars formed in
less tightly-bound syStems than those in which the globular clusters (GCs) formed. More
massive clouds would survive one or more SN events, whose cumulative enrichment
would set the lower limit on the metallicity of the clusters they form.

The idea that halo field stars formed originally in globular clusters that were later
disrupted has been considered by several groups. Brown et a1. (1995), for example,
developed a dynamical evolution model for GCs, including self-enrichment, and showed
that SN explosions of the first-generation stars trigger the formation of an expanding
shell, which would be decelerated by the surrounding hot ISM, and can then form second
generation stars. They also studied the conditions under which a GC can survive.
Recently, Jehin et al. (1998), based on their analysis of abundances of 21 metal-poor

stars, suggested a scenario for the formation of metal-poor stars based on two phases of

19

chemical enrichment. The first is during the explosions of massive stars as SN of type-II
events, the second is where enrichment is provided by stellar winds from intermediate-
mass stars. In this view, all halo and thick-disk stars are assumed to be formed in GCs,
from which they escaped either during an early disruption of the cluster, or later, through
an evaporation process. There is also evidence in the halo of later accretion of stars from
nearby systems such as dwarf galaxies.

This thesis is intended to test this early galaxy evolution scenario, by evolving
individual clouds with different initial conditions, and following their chemical evolution.
These clouds are intended to represent the first systems that formed stars, whether they
were proto-Galactic and contributed directly to the formation of the halo, or extra-
Galactic systems from which the Galaxy later accreted material. One major strength of
our, calculation is the use of metallicity-dependent yields, which is specifically crucial
during these early times when the first enrichment events took place. Several studies
used only metallicity-independent yields and followed the evolution of specific elements

.(Pagel & Trautvaisiene 1995; Chiappini et al. 1997; Chiappini & Matteucci 1999).

2.4 Chemical Evolution and the r-process

There have been a number of recent studies that follow the chemical evolution
of neutron-capture elements in the halo. Almost all of these models were able to
reproduce the inhomogeneties observed for elemental abundances through a stochastic

evolution scenario, but were generally limited to the study of a single neutron-capture

20

element (Raiteri et a1. 1999; Tsujimoto et al. 1999; McWilliam & Searle 1999; Travaglio
et a1 2000). Since the production processes of neutron-capture elements are still rather
uncertain, we believe that the best approach to the problem of halo evolution would be to
follow the evolution of elements with better understood origins, such as the alpha and F e-
group elements. The results of such models can then be used to set constraints on the
evolution process, and shed more light on the neutron-capture production sites.

The only group that followed the evolution of several alpha and Fe—group
elements at extremely low metallicities is Argast et al. (1999). However, this study,
which made use of metallicity-independent SN yields, was unable to reproduce the
observed trends at very low metallicity for some elements, and also lacked any
mechanism to include accretion events that are believed to contribute greatly to the halo
population.

A complete chemical evolution model that follows the production of multiple
elements during the halo phase, within a framework that includes SN events and mixing
processes, is absolutely necessary at this stage. If the observed trends for these elements
in metal-poor stars can be reproduced fully under a given set of assumptions about the
formation processes of second- and third-generation stars, then one could attempt to set
limits on the formation Sites of neutron-capture elements.

Truran (1981) suggested that r-process elements are produced by type-II SN
events on timescales comparable to the halo formation timescale, while s-process

elements require longer timescales. This is consistent with the observation of some very

21

low-metallicity stars that show large overabundances (relative to solar) of r-process
elements (e.g., the well-known metal-poor star CS 22892-052, Sneden et al. 1996, 2000;
also the recently discovered giant CS 31082-001, in which uranium was detected for the
first time, Cayrel et al. 2001). Some theoretical calculations were also able to reproduce
the solar system r-process abundances through the action of the “neutrino wind” expected
to occur in the first few seconds following SN explosions (Takahashi et al. 1994;
Woosley et al. 1994). Although it has been suggested that other astrophysical sites for the
source of the r-process elements might exist (Cowan et al. 1999; Freiburghaus et al.
1999), it is still believed that there must be a single dominant source for at least the heavy
r-process elements. This can be deduced from the observations of halo stars which Show
r-process abundance patterns in full agreement with the scaled solar system r-process
abundance pattern (Cowan et a1. 1998 ).

Since the neutron-capture elements show the greatest dispersion at low
metallicities, they are the best representatives of the inhomogeneities that existed in the
halo at early times. Therefore, understanding the production mechanisms of these
elements and their inclusion into stars is crucial for understanding this era of our

Galaxy’s history.

2.5 Overview of the Model
Since models that adopted a canonical one-zone approach to the chemical

evolution of the Galaxy, where mixing of SN ejecta into the ISM is assumed to be

22

complete and homogeneous, failed to reproduce the scatter observed in metal-poor stars
(Primas et a1. 1994; McWilliam 1995), we attempt a more realistic approach to the
problem that treats the dynamics of the gas and the enrichment process in more detail.

Complete mixing of the ejecta of type-II SN with the ISM would imply the
existence of an age metallicity relationship, where the metal abundances of stars would
reflect those of the ISM at the time the star formed, and therefore would increase with
time. Such a relationship was shown to be broken by extremely metal-poor stars with
[Fe/H] < -2.5 (McWilliam et al. 1995; Ryan et al. 1996). In fact, the abundance patterns
of these stars resemble those calculated for first-generation SN events, which led to the
idea that very low-metallicity stars must have formed from individual, or at most, a few,
SN explosions (Audouze & Silk 1995).

Tsujimoto et. al (1999) proposed a model of Galactic evolution based on SN-
induced star formation, where the elemental abundances of the next-generation stars are
the result of mixing of the ejecta of a SN with the gas swept up by the explosion forming
a shell in which star formation is induced. This scenario takes into consideration the
stochastic nature of early star formation when yields are used that depend on the initial
mass and metallicity of the progenitor. It also allows for the testing of the idea that the
elemental abundances in extremely metal-poor stars are the products of one or several SN
events. We adopt this theory of star formation in our model. The first-generation stars

are assumed to form in the cores of primordial clouds by some unspecified process.

23

Our chemical-evolution model includes enrichment of the ISM with several alpha
and Fe-group elements, taking into consideration the lifetimes of different mass stars. It
also includes dynamical processes through the mixing of the ejecta with their
surroundings and through the effects of the energetics caused by SN events. Merging and
tidal interactions among the different clouds are not considered in this model. Since such
interactions are sure to take place, we must consider the ensemble average of our
predictions for individual clouds.

The third chapter presents a detailed description of the model and the technical
methods used in our code. A detailed comparison between the current results and
observational data is given in chapters four and five. Finally, concluding remarks, as

well as future directions, are presented in chapter six.

24

Chapter 3
The Chemical Evolution Model

3.1 Introduction

There is a general consensus that early evolution of our Galaxy took place in a
manner consistent with the hierarchical clustering scenario. Many details of this
evolution can only be explored by constraining galaxy-evolution models with the
observed properties of stellar populations. The elemental abundances observed in stars of
our Galaxy reflect a complex chemical evolution process. This is particularly clear in the
halo population, where a large scatter is observed in the abundances of some of the heavy
elements (mostly the neutron-capture species), indicating a chaotic early history. Even in
the solar neighborhood, where stars exhibit a much lower star-to-star scatter in their
elemental abundances, there is evidence that suggests a fairly non-uniform enrichment
history (Rocha-Pinto et al. 2000).

On a larger scale, galaxies in general show non-uniformities in their chemical
evolution, where more massive galaxies reflect richer enrichment histories, and

individual galaxies Show higher metal abundances towards their centers. This all

25

suggests that the early evolution of galaxies may have been dominated by the subsequent
evolution of gravitationaly amplified primordial fluctuations.

The main purpose of the present study is to test the bottom-up theory for galaxy
formation, where primordial fluctuations resulted in the gravitational collapse of
subsystems forming sub-galactic halos. Such subsystems would then merge and accrete
diffirse matter to form mini-halos. We follow the chemical evolution of individual clouds,
assuming all stars formed initially in proto-Galactic clouds, adopting the SN-induced star
formation model of Tsujimoto et a1. (1999). We follow the evolution of several alpha
elements and Fe-group elements and compare to the observed abundances of individual

stars in the halo and thick disk of our galaxy.

3.2 Methods of Modeling Chemical Evolution

A Galactic chemical-evolution model is concerned with the time evolution of the
chemical content in the Galaxy, including stellar metallicities, abundance gradients in the
ISM, and variations in the relative abundances of heavy elements. Since there are many
physical processes involved in the production and distribution of heavy elements,
chemical evolution models can be very complex unless certain approximations and
assumptions are made regarding processes such as star formation, nucleosynthesis, gas
flow, as well as the production sites and mechanisms for the re-distribution of heavy
elements. The set of assumptions made give a model its identity, and defines the set of

equations to be solved that represent the system. By solving these equations numerically

26

or analytically one can trace the abundance gradients in the ISM as a function of time and
position and follow the predicted elemental abundance distribution in stars.

The classical chemical-evolution equations for a one-zone model, which considers
the entire ISM of the Galaxy as a medium of uniform composition at any given time,
were first derived by Tinsley (1980), and have been the basis for chemical-evolution
models since then. In this approach, the total mass of the system is divided into gas mass
and star mass, and these constituents are followed as a function of time, allowing for
infall and outflow of gas into and out of the system.

Before we present the details of our chemical evolution equations we introduce a

few important definitions.

3.2.1 The Star Formation Rate (SFR)

The SFR is defined as the rate at which mass is converted into stars, and is given
in units of MIL Gyr". The present-day SFR has been estimated empirically for the solar
neighborhood ( Miller & Scalo 1979) from the total surface density of the Galactic disk
and from star counts in a number of local regions. For estimates of the SFR in more
remote regions, counts of the most massive and brightest stars were used and a total SFR
was obtained by assuming an IMF for the region (often taken as the local initial mass
function), in addition to several other methods that were used to estimate its value (see
Searle et. al. 1973; Larson & Tinsley 1974). These studies suggest that the star formation

rate is different from galaxy to galaxy, and from place to place in a given galaxy, which

27

has made it impossible to assign to it a universal function that can be used in Galactic
evolution models. Although the function suggested by Schmidt (1959) assumes that the
star formation rate is proportional to a power 'n' of the gas density, attempts to assign a
value for 'n' that applies everywhere have failed. This suggests that the SFR depends on
other properties of the environment in addition to the gas density. In fact, it has been
pointed out by Lynden-Bell (1977) that this function may depend on so many other
parameters of the gas that it would become too complicated to use in evolution models.
Therefore, the best approach for models would be to use simple expressions for the SFR
with a limited number of parameters to be tested.

Other pararneterizations and modes of star formation have been suggested, such

as the exponentially time-dependent SF R :

‘I’(t) = ‘11, e" 4’

Still others include self-propagating star formation, self-regulated star formation, density
thresholds, and bursts of star formation triggered by interactions or mergers.

In our model we adopt the SFR suggested by Tsujimoto et. al (1999), in which
star formation is triggered by a SN event, thus its value depends on the frequency of

type-II SN explosions in the early Galaxy, a parameter which must be estimated.

28

3.2.2 The Initial Mass Function (IMF)

The initial mass function (IMF) describes the distribution of stellar masses that
result when a generation of stars is born. The important role this function plays in
chemical evolution comes from the fact that stellar mass affects greatly the other
properties of stars, such as main-sequence lifetimes, mass loss, nucleosynthesis, and the
type of death a given star will eventually experience. Thus, knowledge of the nature of
the IMF is crucial for determining the properties of stellar populations and their evolution
with time.

The IMF has been studied in the solar neighborhood intensively, both empirically
and theoretically, since its introduction by Salpeter (1955). Based on observational data
of the counts of stars per unit volume, he first obtained the luminosity function for the
local region. A mass-luminosity relationship was then used to convert this to a mass

function for the solar neighborhood. The Salpeter mass function takes the form:

m—1.35

Q? a

sal

It is still not clear whether the IMF is a universal function, or if it varies with space and
time. There have been many studies of the IMF in different environments, and other
functional forms have been suggested (Kroupa et a1 1993; Adams & Fatuzzo 1996;
Padoan et al. 1997, Larson 1998). It is generally thought that the IMF at early times was

different from what is observed today. In particular, a number of recent studies
29

(Elmegreen 2000; Nakamura & Umemura 1999; Kroupa 2001) have presented evidence
that the early IMF was quite likely to have been biased towards massive stars. As noted
above, this might help to explain the present lack of “metal-free” stars observed today.
Such a top-heavy IMF would also be able to explain the deficiency of metal-poor stars in
the solar neighborhood when compared to simple chemical-evolution models (the so-

called “G dwarf problem”).
Analytically, the IMF has been treated with different definitions and notations in

the literature. Therefore, we will introduce here the definition we adopted for our
calculation. If ‘I’(t) is the star formation rate (SFR), and go(m) is the IMF, then the rate at

which mass goes into forming stars in the mass range [ m, m + dm ] is:

‘I’(t) - (0(m) - dt - dm

So the number of stars formed in that mass range will be:

‘I’(t)-((p(m)/m)-dt-dm

In order for cp(m) to represent correctly the relative birth rates of stars, it must be

normalized to unity over the whole allowed range of stellar masses,

30

m

u
j¢(m)dm= 1
”’1

where mu is the upper mass limit for stars, and m, is the lower mass limit. This function
allows the calculation of many quantities that vary with stellar mass. One example is the
yields of different elements. If Y,- , is the total yield of element i from all stars, it can be

calculated by the integral

Y. = jy.(m)-(¢(m) / m)‘I’(t —t..).dm

where y,(m) is the yield of element i from a star with mass m, and m, is the mass cut-off at
time t, representing the lowest mass stars that will contribute to the enrichment process at

that time. The time t,,, is the lifetime of the star with mass m.

3.2.3 The Metallicity-Dependent Yields

For intermediate stellar masses, we adopt the standard nucleosynthesis yields of

Renzini and Voli (1981). This study covers stars of masses in the range 1 Mo< mass < 8

Mo. They calculate the yields for two different metallicities, Z = 0.004, and Z = 0.02. In
31

the current model, we interpolated between these two values and used Z = .004 yields for
lower metallicities. The need to make use of predicted yields from rather high-
metallicity intermediate-mass stars has been relieved only very recently (Abia et al.
2001), unfortunately too late to be incorporated into our present calculation.
Intermediate-mass stars mainly eject H, He, C, and N into the ISM at the end of their
lives, affecting greatly the value of the metal/H ratio. These stars end their lives as
carbon-oxygen rich white dwarfs. If they are members of a binary system these dwarfs
may accrete mass from the remaining member to the point where their mass exceeds the
Chandrasekhar limit. At this point, the star becomes unstable causing a thermonuclear
explosion and expelling its thermonuclear products into the ISM. These events are
referred to as Type-Ia SN. For these events we use the yields calculated by Thielemann
et al. (1986). The time between the formation of a white dwarf and its evolution into a
SN is referred to as the ‘delay time’. This time is taken in our model to be 1 Gyr, which
provides a good fit to the observed age-metallicity curve. Therefore, these events will
only have a significant effect on clouds that evolve and self-enrich for more than 1 Gyr.
This can be the case for clouds that are at least as massive as dwarf galaxies. Less

massive structures are expected to be destroyed due to energy input from SN of Type-II

events during the first Gyr of the onset of star formation. Stars less massive than 1 Mo

serve in this model only as reservoirs of gas mass, Since they do not evolve significantly

during the considered time.

32

For massive stars we adopt the metallicity-dependent stellar yields of Woosley &

Weaver 1995 (Hereafter, WW95) who were the first to include stars with progenitor
masses ranging from 11 to 40 Mo, and metallicities from zero to solar, and to calculate
yields for elements from H to Zn. This permits more solid limits to be set on Galactic
chemical evolution models, and enables comparisons between the results of Simulations
and the empirical data from hi gh-resolution spectral measurements in stars.

While the yields presented by WW95 cover stars up to 40 Mo, other studies, such
as Thielemann, Nomoto & Hashimoto (1996) obtain yields for stars up to 70 Mo.

Although the fate of stars more massive than 40 M0 is still uncertain, a study by Heger,

Woosley, & Waters (2000) suggests that metal-free stars with masses between 35-100

.Mo are expected to collapse into black holes, while stars with masses between 10-35 Mo

can explode as type-II SN, and contribute to the enrichment process. In addition,
including such massive stars will have very little effect on the results of a chemical-

evolution calculation when adopting a Salpeter IMF, since very few stars will form that

are more massive than 40 Mo. Therefore, we believe that the stellar mass range covered

by the calculation of WW95 is a reasonable range for a realistic model. This is also

consistent with the findings of Samland (1998), that the mass range of stars to form
Type-II SN is 11 to 30-40 MO.

In contrast to the stellar yields calculated by Thielemann et al. (1996), in which

they use a constant solar progenitor metallicity, the Woosley & Weaver yields have the
33

advantage of covering the whole metallicity range from zero to solar for the progenitor

stars. Although their predicted yields of heavy elements are not affected greatly by small

changes in the initial metallicity of the progenitor for Z/ 20 > 0, there are large
differences between the predicted yields for stars with metallicity Z/ 20 > 0 and those for

stars with Z/ Zo= 0. This will have a great effect on the metallicity distribution of

extremely metal-poor stars, and on the Stars of the next generation that will form in their
shells. Therefore such a detailed study has made models of the earliest stages of galaxy
evolution possible for the first time.

WW95 also considered the energy of the explosion an important parameter in
determining the yields of 3 SN event, in addition to the initial mass and metallicity.
Depending on the energy of the explosion, part of the synthesized elements will be

ejected, whereas elements in the deeper layers will fall down onto the core after the

explosion. For stars more massive than 25 Mo , they distinguish different models A, B,

and C, corresponding to three increasingly different values for the initial kinetic energy of
the “piston” (a theoretical construct used to simulate a real explosion). The larger this
energy, the more heavy elements escape from the explosion. We adopt model B, an
intermediate value for the energy.

Figure 3.1 shows the yields of stars from this calculation for three different

elements, Fe, Mg, and Mn, as a function of the metallicity of the progenitor. The yields

are shown for progenitor masses of 40, 30, 20 and 15 Me. It is clear fi'om the figure that

_34

as metallicity goes down, a wider range of yields is produced. This will allow, in part,
for the production of increased star-to-star scatter observed in elemental distributions of
metal-poor stars.

The only models that used the metallicity-dependent yields of WW95 are Timmes et
al. (1995), Samland (1998), and Goswami & Prantzos (2000). Times et al. (1995) is a
chemical-evolution model of the Galaxy in which they followed the evolution of all
elements from H to Zn and compared their results to the observed stellar abundances in
the solar neighborhood. They discuss the strengths and weaknesses of the WW95 yields,
suggesting that the main weakness is that the Fe yields are too high, and may need to be
revised. But this study failed to treat the halo evolution with much detail, and did not
follow the trends of elemental ratios to metallicities less than [F e/H] = —3, where stellar
abundance data now exist. Goswami & Prantzos (2000) treated the disk and halo
separately, and followed the evolution of elements from C to Zn using the WW95 yields.
This study also failed to follow the earliest stages of the Galaxy’s evolution, and did not
attempt to reproduce the scatter observed in stellar abundances at very low metallicities,

as the classical model they employ assumes complete mixing of SN ejecta with the ISM.

35

Yields ( Mo)

 

 

 

 

 

 

 

 

 

 

10 . W, - . ...fi. . . -..... . -
e (é m
A
a) '5 A
u. 10 A
10.10 4 l 4 r I I I.“ l . . . r. .r I . I . ..
-4 -3 -2 -l
10 10 10 10 10°
0
10 "it - "é. . . -WH‘ . . n
E E] .
a) h d
z ’ 5
.10: 1 IL 41.1 L l 1. AL:
10 -4 3 ~2 -1 D
010 10 10 10 10
10 T Y I "fi 7 '7 I V 'V
J»
D o as
c -6
2 10 i- A -
b A 4
t A
4045 1 r
10 -4 -3 -2 -l 0
10 11'] 1n 1n 1C]

Metallicity of Progenitor (20)

Fig. 3.1 The metallicity-dependent yields of Fe, Mg, and

Mn. Each is shown for four different progenitor masses, 40

Mo (triangles), 30 Mo (circles), 20 Mo (squares), and 15

Mo ( plus Sign ).
36

Samland (1998) is a chemo-dynamical model that attempts to model the collapse of the
Galaxy from which both the halo and disk form. This study also treats the early evolution
with little detail, and makes several approximations regarding the metallicity-dependent
yields of WW95, and the stellar lifetimes.

The model I have explored utilizes the stellar yields calculated by WW95 in a
more detailed discussion of early halo evolution. We use finely spaced mass and
metallicity grids in our simulation, and linearly interpolate the yields in both dimensions.
The yields of every SN event are mass- and metallicity- dependent, and the metallicities

are calculated for all stars at the time of their formation and stored for use at later times.

3.3 Formulation of the Problem
3.3.1 Introduction
It has been predicted that the first gravitationally bound systems capable of

forming stars appeared during the first 108 years of the history of the universe, and had

masses between about 105 and 108 Mo (Peebles 1993; Haiman at al. 1996; Tegmark et al.

1997; Nishi & Susa 1999; Ciardi et al. 2000; Hernandez & F errara 2000; Miralda-Escude
2000). It is also believed that these subsystems might be proto—globular cluster clouds
(Fall & Rees 1985; Cayrel 1986; Brown et al. 1995; Jehin et al. 1998) with masses in the

same range, and that these clouds formed stars only under

37

certain conditions. Most of these clouds would have been disrupted by energetic
processes, and their stars now form the observed halo population.

Therefore, we perform our model by evolving individual clouds of the mass range

105—108 Mo, and following the chemical evolution of each cloud based on a one-zone

closed box model up to a metallicity of [Fe/H] = —2.5. We assume that all halo field stars
were formed originally in these proto-Galactic clouds. By varying the total masses and
the star formation histories of these clouds, one can attempt to reproduce the trends and
scatter in elemental abundances observed in metal-poor stars of the halo and thick-.disk

populations.

3.3.2 The First Stars

Although some predictions have been made about the formation processes of the
first stars born in these clouds, their nature is not known due to the lack of direct
observational data from Pop-III stars. Simulations show that once these clouds cool,
mostly via molecular hydrogen, they become self-gravitating and form central cores
(Abel et a1 1999; Norman et al., 2000) which are believed to form stars at their centers,
the type of which is still uncertain (Silk 1983; Carr et al. 1984). Nakamura & Umemura

(1999) studied the gravitational contraction and fragmentation of filamentary primordial

38

gas clouds and found that the masses of the first stars could range between 1-2 Mo and ~

1000 MQ.

It seems likely that the IMF of early star formation favored much more massive
stars than the standard present-day IMF (Larson 1998; Hernandez & Ferrara 2000). This
is due to the fact that the Jeans mass was much larger at early times than it is today
because of the initially much higher temperature of the primordial material. Although the
predicted size and mass of the first star-forming systems is not very different from those

of today's molecular clouds, their temperatures were an order of magnitude larger,

leading to a calculated Jeans mass of around 103 Mo compared to a present-day Jeans

mass of 1 Mo. Another reason one might expect the first stars to have formed from a

high- mass biased IMF is the presence of r-process elements in metal-poor stars, which is
indicative of the Galaxy being enriched by early generations of massive stars, as
suggested by Truran (1981). As for the lower mass limit, Uehara et al. (1996) suggested
that stars smaller than a solar mass cannot form under primordial conditions because the
onset of high opacity to the H2 cooling radiation sets a minimum fragment mass that is
approximately the Chandrasekhar mass, somewhat above 1 solar mass.

The low metallicity of these clouds is expected to lower their efficiency of star
formation. It has been shown that if metallicity is lower than about 0.01 solar, the host

cloud depletes its main coolant, H2, by the explosion of one 05 type star (Tashiro &

39

Nishi 1999). This implies that when the metallicity is lower than this value, stars can only

be formed by SN-induced star-formation processes. (N ishi, Susa, & Omukai 2000).

3.3.3 The Star Formation Method

We assume that each cloud starts with primordial material, and forms one massive
star at its center by some unspecified process. This Pop-HI star later explodes as a SN
event, triggering the formation of Pop-II stars in its high-density shell. Subsequent star
formation progresses in the shells of later SN events. Such a SN—induced star formation
scenario was suggested by Tsujimoto et al. (1999), and was shown to fit the observed
relative abundances at early times better than models where SN ejecta mix completely
with all the gas in the ISM (Nakamura et al. 1999). Thus, the trends of elemental relative
abundances observed in metal-poor stars is consistent with this theory of star formation.
A dispersion in heavy elements, varying from less than lO-fold for alpha and iron-group
elements, to about 300-fold for n-capture elements, implies that these lowest-metallicity
stars were the result of mixing of the ejecta from single, or at most a few SN, with a
limited amount of gas in the parent cloud (Audouse & Silk 1995; Ryan et al. 1996;
McWilliam 1997; 1998). This will result in a difference between the abundances
observed in stars and those of the ISM at the time they were formed, as opposed to what
has been assumed in previous Galactic chemical-evolution models, where the stellar and

gas abundances were assumed to be identical.

40

In the Tsujimoto et al.(1999) scenario, the material from which the generation of
stars that forms following a given SN explosion is the result of complete mixing of the
SN ejecta with the gas swept up from the ISM by the explosion. This star formation
scenario will produce low metallicity stars with elemental abundances resembling those
of high mass SN ejecta.

Our model utilized metallicity-dependent yields, and follows the evolution of the
gas ratio in the cloud and the evolution of individual elements as a function of time. It
also follows the chemical evolution of stars and compares them to the observed

distribution fimction for halo stars.

3.3.4 The Calculation

We perform a numerical computation of the chemical-evolution equations in each
cloud, expressing the evolution of gas mass, Mg, and the evolution of the mass of

individual elements, M,, as differences in finite steps of time. At each time step, the

equations are integrated over a grid of stellar masses, ranging from 0.09 to 40 M0. The

length of the time step, At, is chosen such that it is longer than the time required for 3 SN
shell to form and disperse, and also short enough to be sensitive to the short lifetimes of
massive stars. The expansion time of a SN event is of the order of 0.01 Myr (Binney &
Tremaine 1987), while the lifetime of the most massive stars included in our model is ~

6 Myrs. Since the sensitivity to the lifetimes is very crucial at the earliest times, the time

41

step was taken to be 1 Myr up to the point when the least-massive SN have contributed,
at 20 Myrs. Thereafter, At was given a larger value of 25 Myrs.

We also take into consideration the lifetimes of these stars, relaxing the
instantaneous recycling approximation. This is of fundamental importance when dealing
with timescales as short as the halo formation time, and when treating elements, such as
Fe, that are mostly produced by long-lived stars. We adopt the mass-dependent lifetimes

used by Timmes et al. 1995, where the lifetimes of Schaller et al. (1992) were used for

stars less massive than 11 Mo . For massive stars, the lifetimes given by the stellar

evolution calculations of Weaver & Woosley (1994) were adopted.

For a given cloud, the time of formation of the first shell is taken as t = 0, and the

star formation rate in the cloud at that time is

910:0):5 -Msh(mi,0)/At (3.1)

where e is the mass fraction of the shell that is used up in forming stars and will be
considered a constant free parameter. M5h(m,t) is the mass of the shell formed in a SN

explosion at time t with the progenitor mass being m, and is given by :

Msh(m,t)=Ej(m,Z)+MSW (3.2)

42

where MSW is the mass of the interstellar gas swept up by the expansion. This quantity is

considered constant with a value of 5"‘104 MO (Ryan et al. 1996; Shigeyama & Tsujimoto

1998; Tsujimoto et al. 1999), since the explosion energy of a core-collapse supernova
depends only weakly on the progenitor mass (WW95; Thielemann et al. 1996). [SJ-(m, Z)
is the mass of all the ejected material from the SN with a progenitor mass m and
metallicity Z. For the first SN event the metallicity Z is zero for a Pop-HI star, and m is
m I. For later generations, the metallicity of a star is calculated from the metallicity of the

shell that formed it Z,;,(m,t). This will be calculated as a function of time, and is given by:

zsh (m,t)=1—(xHSh (m,t)+xHeSh (m,t)) (3.3)

Here xH,;. and xHeMl are the fractions of H and He in the Shell, respectively, and are given

by:

sth (m,t)=(yH(m,t)+ngaS (t)- Msw)/Msh (m,t) (3.4)
xHesh (m,t) = (yHe(m,t) + xHegas (t) ~ Msw) / Msh (m,t) (3.5)

ngas and xHega, are the fractions of H and He in the interstellar gas at the time of

formation of the shell t. This fraction is given for any element xigas by:

43

xigas (t)=Ml.(t)/Mg (z) (3.6)

where yH and yHe are the amount of ejected H and He from the explosion, given in solar
masses. We will refer to these quantities as the 'yields', which are metallicity dependent
and therefore are functions of time. For the first explosion, y,(m,,t,) is the yield of
elements i from the star with mass m, and metallicity zero. For subsequent star
formation, the SFR at a given time ‘I’(t) is summed over all shells that form at time t, and
depends on the SFR at the time the progenitor star formed ‘P(t- rm), where rm is the

lifetime of the progenitor.

m

u
‘I’(t>0) = jdm £MSh(m,t)((o(m)/m)‘P(t—rm) (3.7)
max(mt,10)

where (p(m) is the initial mass function. The upper and lower mass limits for stars are m,

and m, respectively, The lower mass limit for stars that produce SN events of type-II

will be taken as 10 Mg. m, is the mass of a star with lifetime equal to t, measured from

the time of formation of the first shell.

44

Since the ejected mass from a SN changes with metallicity of the progenitor, the
quantity E,(m,Z,;,) in equation 3.2, must now be replaced by an averaged value over all

stars of mass m and different values of Z,;, ,exploding at a given time t :

m
u
M..(m,t)= jdm' (<o(m'>/m')Ej(m,zsh(m',z-rm)) (3.8)
max(m ,10)
(t — 2m)

Z,;, is expressed here as a function of the mass of the progenitor m’ to the shell from
which star m' formed. The expression t -r,,, refers to the time of formation of star m and

the death of star m'. The same applies for the yields of individual elements y,-

m

ll
yi(m.t)= Jdm‘ (¢(m')/m') iej(m.zsh(m',t—rm» (3.9)
910)

max(m(t _ m)

where ie,(m, Z,;.(m',t- 13,,» is the mass, in solar masses, of the element i ejected from the

star with mass m and metallicity Z,;,(m',t- rm). The change in gas mass with time is then

given by:

45

m
u

dMg/dt = ~‘IJ(t) + j dm(¢(m)/m)Mej(m,t)‘I’(t — rm) (3.10)

max(mt , ml)

The first term in this equation is the SFR, equal to the amount of gas going into forming
stars at time t and is substituted for from equation (3.7). The second term represents the
enrichment process by all stars, the life of which will end at t, including the whole
possible range from m( to mu.

The change in the mass of element i in the gas, is given by:

m
u
dMi/dt = — Idm.(09(m)/m)£ Msh(m,t) xish(m,t) ‘I’(t — rm)
max(m t ,1 0)
(3.11)
mu
+ Jdm ((p(m) / m) yi(m,t)‘I’(t — rm)
max(m t ,ml)

The first term in this equation gives the rate at which element i is put into stars at time t,
where the second term represents the rate at which it is being added to the ISM by stars.
By substituting equations 3.7-3.9 into equations 3.10 and 3.11, this set of integro-

differential equations is solved numerically. An auto-regressive computation of the star
formation rate and the metallicity of each shell that forms was employed, and previous

values were substituted in equations (3.7) - (3.11) at each time step. At every time step,

46

the metallicities of all shells formed are calculated and stored for use at later times. Each
shell is recorded and the age-metallicity relation is constructed. The evolution of the

metal contents in both the gas and stars are followed as a function of time.

47

Chapter 4
Properties of the Clouds

4.1 Introduction

In this model, we start with clouds of primordial gas and allow one massive star to
form at its core. Later star formation is induced by SN explosions, so the gas from which
stars form is a mixture of the ejecta of a SN with an amount of gas from the ISM. For

comparison, the IMF is varied from a simple Salpeter function to a top-heavy IMF.

4.2 Initial Conditions
4.2.1 The Gas

The masses of globular clusters observed in the Galaxy range between 104 and

106 Mo, while the minimum mass of dwarf galaxies in the Local Group are ~ 2 * 107 Mo

( Mateo 2000). Therefore, we chose initial masses for our clouds in the range (105-108)

Me. In this mass range, the clouds are extremely sensitive to stellar feedback, whether in
terms of chemical enrichment or energetics. We start with gas in a single phase and

48

uniform density, and choose the volume of each cloud such that we maintain a reasonable

initial density in the clouds of ~ 0.25 particles / cm3, corresponding to about 0.01 Mg

/pc3. This is necessary in order to calculate the initial potential energy of the cloud, and
its lifetime prior to destruction by SN energy input.

The clouds are composed initially of 77% (by mass) Hydrogen, 23% Helium, and
a metal fraction Z equal to zero. The first massive star forms at the core and initiates
subsequent events of SN-induced star formation. This method of star formation produces
local inhomogeneities in the clouds as soon as the first SN event takes place. Each SN
event will produce a group of stars reflecting the pattern of that particular core-collapse
SN, since the stellar yields of a SN are different for different progenitor masses.

It has been shown that mixing timescales in the halo were sufficiently long that
chemical inhomogeneities in the gas would not be erased on the timescale over which
stars would form (Audouze & Silk 1995). Therefore, we do not allow mixing between
shells. Still, we assume instantaneous mixing of the shell material left behind after the
explosion with the gas in the ISM.

Our clouds are self-enriched over a timescale of ~ 1 Gyr. The timescale for the
formation of the early halo is estimated to be of the order of a few Gyrs (Bekki & Chiba
2000), in disagreement with the 108 yrs suggested by ELS, although most of the
processes that contributed to the formation of the earliest generations of stars will take

place in the first 0.5 Gyr after the initiation of the first enrichment events.

49

4.2.1 The Nature of the IMF

The enrichment of the halo depends on the type and number of SN events that
took place, in addition to the type of mixing processes following the explosion.
Therefore, the central role that the IMF plays at these early times cannot be ignored. For
a SN-induced star formation model, the SFR depends on the rate of death of massive stars
at a given time. In other words, the SFR today depends on the SFR at previous times.
Therefore, the IMF of the first stars (perhaps more properly referred to as the First Mass
Function, FMF) will affect greatly the subsequent evolution of these clouds. Although
the shape of the IMF that dominated in primordial conditions is still not certain, there is
substantial observational evidence pointing to a top-heavy IMF. This includes the paucity
of metal—poor stars in the solar neighborhood (the G-dwarf problem), in addition to
observations pointing to the rapid early enrichment of the ISM by heavy elements
produced in the explosions of high-mass stars, followed by slower enrichment at later
times. The high abundances of heavy elements found in the hot gas trapped in the
potential wells of rich clusters of galaxies is also larger than what would be predicted by
a standard present-day IMF. Finally, the elemental abundances observed in halo stars
suggest that they were made out of gas enriched only by type-H SN (N issen et al. 1994).

The power law IMF suggested by Salpeter (1955) represents the stellar
distribution in the solar neighborhood very well down to 1 Mnt‘ At lower masses the form
of the function is not clear due to the difficulty of obtaining a mass-luminosity relation

for such faint stars. However, it is believed that it declines rapidly and flattens below 0.1

50

Mo in order to explain the paucity of observed brown dwarfs compared to the predictions
(Basri & Marcy 1997). Empirical studies of the IMF have been conducted recently in
different environments including clusters and associations in the Galaxy and the
Magellanic Clouds (von Hippel et a1 1996; Hunter et a1 1997; Hillenbrand 1997; Massey
& Hunter 1998). Although all of these studies support a Salpeter IMF with a slope in the
neighborhood of ~ —1.35 for stars more massive than a solar mass, some different slopes
were suggested (Scalo 1998; Massey & Hunter 1998).

A top-heavy IMF for the first stars was also suggested by ( Larson 1998; Bromm
et al. 2001). Two functional forms were proposed by Larson (1998), which approach the

power law with a Salpeter slope at high masses and fall off at the low-mass end.

—1.35
4%(logm) a (1+m/ml) (4.1)

and

— /
—1.35,e( ”'1 m) (4.2)

d%(log(m)) a m

The first has a peak at mp = m,/ 1.35, and falls off exponentially with increasing negative

power at lower masses, while the second falls off asymptotically to a slope zero at the

low end. The characteristic mass scale, m, , has a value of 0.35 M0 for the present-day

solar neighborhood. This mass function was used by Hernandez & Ferrara (2000), who
51

suggest that the IMF for Pop-III stars was strongly weighted towards high masses at
redshifts 6 < z < 9. They infer a value for m, of 13.2 at redshift 2 ~ 9, and metallicity
Fe/H] ~ —3.5, based on number counts of metal-poor stars from the HK survey of Beers
and colleagues.

Both functions were tested in this model and compared to the Simple power law.

The mass scale was chosen to be a linear time dependent quantity of the form

m,=l3.2—0.9t. The range of the IMF is taken from 0.09 — 40 Mo, and results for the

different functions are compared.

Figure 4.1 shows the different mass functions. The first is the simple Salpeter
function with index —1.35. The second is a more moderate high-mass biased Salpeter-like
function that shows a slower decline towards high masses than the simple function, but
still steeper than the top-heavy functions of Larson. The two functions by Larson behave
differently at low masses. While the first produces a fair amount of low-mass stars and
declines slowly at the massive end, the second function produces very few low-mass stars
and peaks at an intermediate value before it declines exponentially. The percentages of

low- and high-mass stars produced by these functions will be shown in the next section.

52

¢(m)=m-l.35 ¢(m)=(1_e—In/2)m—135

10° 100

 

 

42—... mj=40
“ —_%—._____—‘—

1
——__

——-.___4

log (¢) 10") . 10-2. we
10"

0 40
¢(m)=(1+m/ml)—l.35
1 .

 

 

 

 

 

 

 

 

¢ \.

R. _
Kik- .\ 1:01 Gyrs

 

 

 

 

 

fatOGyrs

0 20 40
Mass

 

 

 

Fig. 4.1 The mass functions, (p, =m'l'35 , (p2 =(1-e’m/2)

-I.35 4.35 -I, _ /

53

4.3 Results and Discussion
4.3.1 Stability of the clouds

We follow a simplified treatment when considering the stability of these clouds
against destruction. Ignoring any tidal effects, heating and cooling, and any
inhomogeneities in the gas, we calculate the number of SN events required for the gas to

disperse,

n = (GMZ/R) / ESN

where G is the gravitational constant, M is the total mass of the cloud, R its radius, and

ESN is the energy input per SN event. This energy is taken to be 105' erg. Under the

adopted initial conditions, clouds less massive than 3"‘106 Mo do not survive the first SN

explosion. For more massive clouds, the survival time depends on the SFR chosen and
on the form of the IMF. IMF s that are biased towards massive stars produce more SN
events in a shorter time allowing star formation to stop and/or the cloud to disperse at an
earlier time. The initial density has a great effect on the stability of a cloud, and we must
keep in mind that star-forming regions become cooler and denser as time passes. As they
form stars, the clouds are heated by the thermal input from massive stars. Therefore, such
a simple treatment can only give a rough estimate of the fate of these clouds.
Table 4.1 Shows the survival times of our model clouds against destruction as a

function of initial mass, for three different mass functions.

54

Table 4.1 Survival Times of the Clouds

 

 

 

 

Mcloud (M) 3 x106 5 x106 1x107 1 x108
¢(m)=m—1'35 -- > 10 Gyrs >10Gyrs > 10 Gyrs
¢(m)=(l _e—m/2) . m—1.35 -- 9 Myr 80 Myr 200 Myr
—m /4 -- 8 Myr 12 Myr 90 Myr

“Mm-1.35 ,e 1

 

 

 

 

 

 

 

It is clear from the table that, aSsuming it survives the first explosion, the fate of a
cloud varies greatly depending on the type of the IMF chosen. The Salpeter function,

producing very few massive stars, allows enrichment to continue in all clouds more

massive than 5"‘106 M0 for times longer than 10 Gyrs. At the same time, clouds as

massive as 108 Mo do not survive more than ~ 0.1 Gyr with a top-heavy IMF. This leads

to the suggestion that even if the first stars were formed according to a top-heavy IMF,
the subsequent star formation must have become more similar to a present day IMF. This
also explains the slower enrichment observed in galaxies after the episode of rapid

enrichment caused by the first stars.

The vulnerability of clouds less massive than 3*10° Mo to destruction after the

first SN event does not favor the idea that they were responsible for the formation of the

55

first generations of Pop-II stars. This also suggests that if the clouds of material in which
the globular clusters first formed were of similar mass to the present mass of globular
clusters, they could not have been self-enriched. A more likely picture, according to our
model, is that the globular clusters must have formed initially in more stable systems
such as dwarf galaxies. The homogeneous chemical composition of stars within most
globular clusters suggests that they formed out of gas that was already pre-enriched and
well mixed in structures that were more stable against destruction. The globular cluster
population of the halo might then be explained as the result of accretion events during
tidal interactions with other galaxies. This was suggested previously by Larson 1999 and
Armandroff 1993.

In clouds that do survive SN explosions, star formation stOps after a time T, when
there is not enough gas to form the shells. Hence, the SN-induced star formation method
used here is capable of regulating star formation in these clouds. If these clouds are
allowed to accrete gas from any other source, another sequence of star formation is
possible. This is consistent with the observations that suggest that the Sgr dwarf galaxy

has had an episodic star formation history (Mi ghell et al. 1999).

4.3.2 Star Formation

Figure 4.2 shows the SFR in our models as a function of time. It is shown for all

four mass functions. All clouds were taken with the same initial mass of 107 M0. The

first explosion takes place at time zero, and is represented in the figure as the first peak.

56

This is followed by a short fluctuation corresponding to the delay caused by the lifetime
of the most massive star of about 6 Myrs. The subsequent evolution depends on the type
of mass function. A Salpeter function with index —l.35 allows slower enrichment, as a
result of producing less massive stars. The SFR declines in this case until it reaches
considerably low values within the first tenths of a Gyr. With more massive stars
produced, as in the case of the other functions, the SFR grows rapidly in a self-
propagating manner. This is an upper limit since, although star formation is believed to
self-propagate, it can be regulated on local levels by the heating radiation of newly
formed stars, and the explosions of massive stars (Koeppen, Theis, & Hensler 1995). The
rapid increase in star formation can be seen clearly from the two lines corresponding to
the top heavy functions which terminate at the time of destruction of the clouds.

The percentage of mass locked up in low-mass stars is also varied greatly when

different mass functions are used. Figure 4.4 shows the percentage of mass locked up in

stars less massive than 2 Mo compared to the percentage of mass in stars more massive

than 30 M0 for the different mass functions. The Salpeter firnction puts ~ 3 orders of

magnitude more mass into low-mass stars than into massive stars, and maintains this ratio
as star formation proceeds with a declining rate. The second function, represented in the
top right figure, shows a smaller ratio of low-mass to high-mass stars, while the total
number of stars continues to rise as star formation continues. When star formation is

truncated, the percentage of mass in low-mass stars ceases to rise while the percentage in

57

high-mass stars declines suddenly since they continue to contribute to SN events. A
similar behavior is shown in the third figure, except that this function produces a ratio in
mass of low-mass to high-mass stars of ~ 1. The final function represented in the fourth
figure puts an exceptionally low ratio of mass into low-mass stars allowing for the rapid
enrichment by type-II SN to take place and for star formation to truncate at earlier times
compared to the other clouds. Again, the important role the first mass function plays in

the evolution of the pre-Galactic clouds cannot be neglected.

58

SFR ( Mo/Gvrs)

 

 

 

 

107 . . .
: —m /m _
: ' /¢(m)=e ’ -m 1'35
o
10 . K, / 1
: ’ / m —
g rfn/ ¢(m)=(1+m—) 13? H -
. ‘i _,.---»-
5 , f . _, - F ' F _ _
10 E' \ l‘ u ‘ _,_, - —" ¢(m):(1_e—m/2)m 1.35
104’ '\-':\’-.~ _
marl ‘n‘“n. ‘
2 : “INN-
1° : ¢<m>=m“'35 '
10‘ l l I;
0.05 0.1 0.15 0.2

Time (Gyrs)

Fig. 4.2 Star formation rate in the model for different mass

functions

59

NtNtot

NtNtot

“Mm-1.35

 

10'

 

 

 

 

10'

10"n

0.1 0.2

¢I(m)='(1+m/m,v)"'35

0.3

 

:7

 

[ \
./\

 

H

 

 

0.2
Gyrs

0.3

 

10.) .v' \]

 

 

 

0.3
—1.35

0 0.1 0.2
—m /m

¢<m>=eT 1

‘ é

 

./\

‘—. —- —— — _— —.(

 

 

 

10"“

 

0.2 0.3
Gyrs

Fig. 4.3 The percentage of mass in low-mass stars (solid

line), and in high-mass stars(dashed line).

60

Chapter 5

Stellar Abundances and Metallicities

5.1 Introduction

The elemental abundances of halo stars potentially provide detailed information
about the envirOnments in which they formed, and the nature of the enrichment processes
that took place during the evolution of the halo. Study of the elemental abundance
patterns in the atmospheres of these stars, and their variations with the overall metal
abundance, is thus crucial for a better understanding of the types of systems that
contributed to this population and their evolution.

The elemental abundances observed in extremely metal-poor stars are believed to
have resulted from the enrichment of primordial gas with the ejecta of a small number of
(possibly including individual) Type-II SN events (Audouze & Silk 1995). Hence, before

the destruction of pre-galactic clouds, stars within them were born on a timescale smaller

61

than the time needed for type-Ia SN to start contributing F e-rich material. This time is
estimated to be of the order of 1 Gyr (Smecker & Wyse 1991; Yungelson & Livio 1998).
These self-enriching fragments of gas are eventually destroyed either by stellar feedback
or external effects such as tidal forces, and star formation is truncated. The extremely
metal-poor stars left behind contain information about the nucleosynthesis of elements in
zero-metallicity stars, their initial mass function, and the environment in the first clouds.
Thus, the identification and study of these stars is especially important if we wish to

explore the earliest times of the Galaxy’s evolution.

5.2 Metallicities and Ages of Stars

The metallicities of stars are calculated in this model from the metallicities of the
shells formed by SN events. These are the result of mixing of the ejecta expelled during
the explosion with a constant amount of gas from the ISM of the cloud. The first star that
explodes is a metal-free Pop-III star, the ejecta of which mix with primordial gas. The
metal composition of second-generation stars depends on the mass and the metallicity of
the first star.

Fig. 5.1 shows the metallicities produced in shells of different progenitors as a

function of time. They are shown for four different progenitor masses: 13, 20, 30 and 40

Mo. The metallicities produced at early times range from [Fe/H] ~ —2.5 to values well

below [F e/H] ~ —4 for the most massive progenitors of ~ 40 Mo. This implies that Pop-II

62

stars with [Fe/H] < —4 might be possible to form, though that would be in contradiction to

present observational limits (Beers 1999). If the first stars were less massive than about
40 Mo this could be avoided, since progenitors with masses ~ 30 Mo produce shells with
a limiting metallicity of [Fe/H] ~ —2.5. Then, shells with metallicities as low as [Fe/H] ~
—4 will not Show up until the less massive (M< 20 M9) SN start to contribute. This is in

agreement with the predictions by (Heger, Woosley, & Waters 2000) for SN of type-H to

be in the mass range from 10-35 Mo, while more massive stars, up to 100 Mo will

probably end up as black holes, and may not contribute significant amounts of material to
the ISM. Another explanation might be that the pre-Galactic clouds from which the first

stars formed were already pre-enriched. Since the amount of Fe ejected by progenitors

with masses ~ 40 Mo increases with metallicity, this rules out shells with extremely low

metal content.

63

Metallicity of shells (dex)

Metallicities ofthe shells for differnt Progenitors

 

I

 

I I I I I I I I I I

 

“I”:
0. M.-. ,3.
a .....o:f,—v I}!
noon...concoct-ooaoooaoaaguard_,.v-P //
-u — --— a - o—-— —----— - / d
I‘ x
I /
/ -l
| /
1
1 / -

/_..._ __._ _______. J

 

 

 

 

 

 

/ — Progenitor mass=40 Mo
' f — =30Mo
- - =20 Mo
* l - =13 Mo
0 0.2 0.4 0.5 0.8 1 1.2 1.4 1.6 1.8 2
Time (Gyr)
Fig. 5.1 Metallicities produced in shells of different

progenitors vs. time. The progenitors shown have masses

13,20,30 and 40 Mo

64

The figure also Shows that type-II SN produce shells with metallicities that do not
exceed [Fe/H] ~ —2.5. This is the value of metallicity at which McWilliam et al (1995b)
observed a shift in the slope for relative abundances vs. metallicity. This suggests that
this value of metallicity seperates two different stages of chemical evolution. The era of
inhomogeneous composition dominated by type-II SN, followed by a stage of rapid iron
enrichment by type-Ia SN. This is also consistent with the suggestion by Audouze & Silk
that only a few SN events are requiredito raise the level of the heavy elements from zero
to that which is observed in the most metal-poor stars in the halo.

Fig. 5.2 shows metallicity vs. age for stars in a cloud of initially primordial gas,
and assuming a Salpeter mass function. This cloud was allowed to evolve up to 10 Gyrs,
and the ejecta of type-Ia SN were allowed to contribute with a delay time of 1 Gyr. Each
point on the figure represents a shell that formed stars. The mean value of [Fe/H] -
increases with time, as expected, and shows a dispersion in metallicities among stars of
the same age that increases with increasing age. This is not predicted by a simple one-
zone model that assumes complete mixing. This large scatter, decreasing with time, can
be explained by the star formation mechanism in which stars are formed only during SN
events and therefore, are the result of the mixing of SN ejecta with a limited amount of
gas. This will produce stars of different elemental ratios even if they form at the same
time, Since the SN ejecta are dependent on both the initial mass and metallicity of the

progenitor.

65

metallicity of shells (dex)

 

Age-metallicty relation

 

 

I I T I I I I I I

 

 

1 2 3 4 5 6 7 8 9
Time (Gyrs)

Fig 5.2 Metallicity vs. time for stars produced by the

model.

66

10

The most-massive SN would contribute first and reflect their yields in the first
Pop—II stars to appear, then at later times the products of the less-massive SN are
expected to appear with different elemental ratios (WW95). This does not necessarily
mean that the first and most massive SN will produce the lowest metallicity Pop-II stars,

since it is the lowest mass SN of type-II that produce shells as low in metallicity as

[Fe/H] ~ —4, while 20 to 30 Mo progenitors produce higher metallicity shells. When

enough time has passed for the ISM to mix on a large scale, the element ratios are
expected to reflect an average of the ejecta of SN events of all masses, including those of
type-Ia.

The steep rise at early times reflects the dominance of SN events, and the high
efficiency of the enrichment of the metal-poor ISM. The gradual increase at later times is
due to the slower enrichment process involving a well-mixed ISM. It is clear from the
scatter in the figure that a simple age-metallicity relation does not result from our model,

at least at early times.

5.3 The Metallicity Distribution Function (MDF)
Carney et al. (1996) compared the kinematics and chemical properties of metal-
poor stars with distance from the Galactic plane for samples of stars more distant than
4 kpc, against those confined within 2 kpc from the plane. They found that stars that are

closer to the plane exhibit a slightly more metal-rich mean abundance, <[Fe/H]> = —1.7,

while those farther from the plane have <[Fe/H]> = —2.0. This was explained by the
67

existence of two discrete components in the halo. The flattened, inner component was
probably formed in a manner resembling the ELS model, while the more spherical, outer
halo had a large contribution from nearby smaller systems Similar to the Sagitarius dwarf
galaxy or other proto-dwarf galaxies. This is in agreement with the 82 picture of halo
formation and with the hierarchical CDM model (Kauffman, White, & Guiderdoni 1993).
The halo MDF is therefore generally believed to be the result of combining the
distribution functions of individual proto-dwarf galaxies accreted by the Galaxy.

The observed MDF of metal-poor stars in the Galaxy shows a relatively broad
peak with a maximum at [F e/H] ~ —1.6, and a smooth tail extending to values of [Fe/H]
< —3, in contrast to the metallicity distribution of disk stars, which shows a more
localized peak with a sharp cutoff (Ryan; & Norris 1991a; 1991b). This suggests that the
environment in which the disk formed was probably more uniform than that which
formed the halo stars. The review by Norris (1999) suggests there is a hint of a “bump” in
the halo MDF at lower metallicities. A feature not expected from the simple model, this
bump might be suggestive of non-uniform enrichment at early times. In any case, in our
models, the MDF is expected to vary from cloud to cloud depending on the initial
conditions and the duration of chemical enrichment. We calculate the MDFs of stars for
four different clouds and follow their evolution with time. A different IMF was chosen
for each cloud and the time evolution of the MDF was followed up to the time of the
cloud’s destruction. In the case of the Salpeter mass function, the evolution was followed
up to 5 Gyrs and was found to saturate at 1 Gyr. Figures 5.3 to 5.6 Show the results for

68

the four clouds, where the type of mass function chosen for each cloud is shown on the
figure (all MDFS were normalized to unity).

The figures Show that the chemical enrichment in the first cloud, with a simple
power-law mass function, is much slower than in the other three clouds with mass
functions biased toward massive stars. Therefore the timescales chosen for this figure are
different since the enrichment is slower. At the beginning, all of the clouds Show a

dispersion, with the majority of stars at metallicities below [Fe/H] = —5. This describes
the first stars that form from the shells of the most massive progenitors with M>35 Mo.
This could be Concluded also from figure 5.1, which shows that these stars are the only to
form such low metallicity shells. As time goes on, less-massive stars will contribute

shells in the metallicity range —3 < [Fe/H] < —2.5. These will produce a rapid increase in

the numbers of stars in this metallicity range that will greatly outnumber the first stars

formed from higher-mass explosions. As soon as stars of mass 20 M0 start to

contribute,shells with metallicities down to [Fe/H] ~ -4.5 form and a dispersion is seen

once again.

69

 

1 _1=.009 Gyr

0.5

 

 

0
-5 -4.5 -4 -3.5 -3 -2.5 -2

 

 

A

rt=1 Gyr

0.5 >

 

 

-‘L

0 a A
-5 -4.5 -4 -3.5 -3 -2.5 -2
[Fell-l]

 

 

0.5 ~

 

1 -t=.15 Gyr

 

l

/\\

 

 

U . - A
-5 -4.5 -4 -3.5 -3 -2.5 -2

 

0.5 1

 

1 I
I I

’t=2Gyrs

r
I
l

V
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I

-----l

 

---------d

  

 

 

0
-5

-4.5 4

-35
[Will

-3

-2.5

Fig.5.3 Metallicity Distribution functions of stars produced

in our models, assuming a Salpeter mass function: (p ,= m'

70

[.35

-2

‘

 

 

b

t=.009 Gyr

 

 

 

 

      

 

 

0.5-
.5 «1.5 .4 -35 .3 4.5
. i . . T
I
' t= .02 Gyrs l
. . . I
I I I I
I I I I
I I I I
0.5- i I t 1
I I I
I I I
I I I
I I I
I I
o A '/'\ . i l
.5 4.5 4 3 5 .3 .23

 

d

4:015 Gyr

0.5 >

 

 

 

 

‘

rt= .12 Gyr

 

o A A— A A

 

 

.5 4.5 .4 .35 -3 .2}:
[FelH]

Fig. 5.4 Metallicity Distribution Functions among stars

produced by our models, assuming a mass function:

(p; = m'l'35(1 — em“) , m,- = 40.

71

 

 

 

 

 

 

 

 

1 i=9 MW 1 «=15 Myr
2
0.5 . 0.5
o i AAA 4 o ._ . . 4
-5 4.5 4 4.5 .3 -2.5 -2 4.5 -5 4.5 4 4.5 -3 -2.5 -2 4.5

0.5 >

 

 

-
-
-4
-<
.-

H
II
:_.
M
Q
‘S
U)

0.5 -

 

 

 

 

   

h---—-----
b-------—

 

 

- 'A o
.5 4.5 4 .35 .3 .25 .2 4.5 .5 4.5 4 4.5

O
N h----------------d

I
(0

4.5

E

[FelH]

Fig. 5.5 Metallicity Distribution Functions among stars

produced by our models, assuming a mass function:

((13 =(1 + m/mu'I’”.

72

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

1 0:9 MY' 1 »t=15 Myr
2
0.5 - 0.5.
o L AMA—J A 0 AA A A A
.5 4.5 4 -3.5 -3 -2.5 -2 -1.5 -5 4.5 -4 -3.5 -3 -2.5 -2 1.5
Y 7 i 1 i i i
I I
1-t=20Mrr . t=.15Gyrs : :
I I I I I
I I I I I
I I I I I
Z I I I I I
M. . 0.5. : : : : :
I I I I I
I I I I I
I I I I I
I I I I I
I I I I I
I I I I I
a 4 4L A L o L L L r
-5 4.5 4 -3.5 -3 4.5 -2 -I.5 -5 4.5 .4 3.5 -3 -2.5 2 -1.5
[FetH] : [FelH]

Fig. 5.6 Metallicity Distribution Functions among stars

produced by our models, assuming a mass function:

_ -l.35 - mI/m

(04 —m e

73

This dispersion eventually fades out as the inhomogenieties start to disappear and
the stars become more metal rich. The final stage shows a peak at a different value of
metallicity for each cloud. This indicates the different enrichment produced by the
different mass functions.

The first cloud, with a simple mass function, achieves a peak at [Fe/H] ~ —2.7, a
value consistent with the calculations of Ryan et al ( 1996) and Nakasato & Shigeyama,
(2000) for the expected metallicity of Pop-II stars formed in the Shell of a typical SN
expelled into primordial gas. The other clouds produce higher metallicity peaks,
corresponding to the larger number of massive stars they produce. These peaks have the
values [Fe/H] = —2.6, -2.5, and -2.2, respectively. The last corresponds to the fourth mass
function shown in figure 3.1, which produces the largest number of massive stars.

In figure 5 .7 we show the sum of the final stages of all four clouds. This produces
a broader distribution extending from about [Fe/H] = —3.2 to about [Fe/H] = —2.2 and
peaked at a value of [F e/I-I] = —2.6. The MDF observed in the halo shows a still broader
distribution, probably due to the high number of different systems that contributed to it,
and a higher value for the maximum indicating the contributions from systems that may

have produced stars from pre-enriched gas.

74

 

IIIIII

 

 

 

 

 

 

 

 

-5

-0.2

[F e/H]

Fig. 5.7. The sum of the MDFS for the four clouds shown in

figures 5.3 to 5.6

75

5.4 Relative Elemental Abundances
5.4.1 The observed trends in halo stars

Very metal-poor halo stars show a great diversity in their element abundances and
a considerable scatter in the observed abundances of heavy elements relative to Fe, up to
a range of 100 (Ryan & Norris 1991; Gratton & Sneden 1994; McWilliam et al. 1995b;
Ryan et al. 1996; McWilliam 1998; Sneden et al. 1998; Norris, Ryan & Beers 2001). At
higher metallicities the scatter gradually decreases until this ratio terminates at a value
that corresponds to an average over the IMF of the element to iron ratios of the stellar
yields. McWilliam et. al. ( 1995b) detected a shift in the slope of the abundances of the
elements Al, Mn, Co, Cr, Sr, and Ba relative to Fe below [Fe/H] ~ —2.5. They suggested
that this unusual chemical composition must have originated from the fact that
supernovae yields must have changed with time, or in other words, are metallicity
dependent. These results were confirmed later by Ryan et. al. (1996) , who also showed
that scatter in the abundance ratios increases with decreasing [F e/H] . These observations
support the idea that the most metal-poor stars exhibit the ejecta of very small numbers of
supernovae. The metallicity-dependent yields used in our present model, together with
the unique method of SN-induced star formation, are capable of explaining these trends.
The observed relative abundances in the halo are fully reproduced with this model for

several elements. These results are shown and discussed in the following sections.

76

5.4.2 Overview of model predictions

For determination of elemental abundances, our code was run for 5 Gyr, using a

massive cloud ( 107 Mo), and forming stars according to a Salpeter mass function. After

1 Gyr, SN of type-Ia were allowed to contribute their ejecta. The elemental abundances
are calculated and recorded for every Shell that forms during the simulation.

The model produces a small number of stars at very low metallicities, [Fe/H] < —3,
showing a considerable spread in [X/F e] ratios, ranging from 0.5 dex in the case of Ni to
more than 2 dex in the cases of Mg. This scatter of the abundances for model stars is
given by the spread in metallicities of the SN models. Therefore, the large scatter in the
abundance ratios observed in low-metallicity stars is reproduced by this model.

Local inhomogeneities start to disappear at —3.0 < [Fe/H] < —2.5, corresponding to
about ~ 0.1 Gyr from. the onset of star formation. At this stage most of the massive SN
have contributed, and their ejecta have already mixed with the gas in the ISM. This
metallicity range marks the end of the early phase and the beginning of the transition to
the well-mixed phase. At this stage, the gas becomes more metal-rich, hence newly
formed stars will no longer exhibit abundance patterns of single SN, but rather an average
over the IMF of the SN that contributed to the enrichment of the local ISM. These values
resemble the predictions of a simple one-zone model. The Spread in the relative
abundances decreases gradually, reflecting the ongoing mixing process as more SN

pollute the ISM, and the values of [X/F e] starting to get closer to the solar value of zero.

77

5.4.3 [Alpha/Fe]

Figure 5.8 shows values of [alpha/Fe] vs. [Fe/H] calculated by the model, and
compared to two sets of data (see figure caption). The observed values show an over-
abundance relative to solar, and a scatter that is significant at all values of [Fe/H], larger
at the lowest abundances. This is true for Mg, Ca, and Si. Ti, on the other hand, shows a
scatter that is almost constant over the metallicity range. This dispersion can set strong
limits on the nature of the first SN, and the nature of the enrichment process when
compared to the predictions of chemical evolution models. The so-called plateau for
[alpha/Fe] ratios at low metallicities is proving not to be really constant, as the most
recent data are showing more dispersion at lower metallicities (Ryan et al 1996;
McWilliam 1997; Norris et a1 2001). The over-abundance in alpha elements relative to
iron compared to the sun can be understood as the result of the dominance of SN of type-
II at the time, since they are believed to be the major production Sites for alpha elements:
This also indicates that the corresponding stars formed within the first Gyr of the onset of
significant star formation. After 1 Gyr, type-Ia SN events are expected to shift the trends
with large amounts of Fe. Therefore, the ratios decline gradually towards solar
metallicities.

The observational trends for alpha elements relative to iron are fairly well
produced by the model at very low metallicities, [Fe/H] < —3, except for Ti, which shows
lower values than the data and rather little dispersion. Although Ti shows abundance

behavior similar to other alpha elements, it is believed to be produced in the same way as

78

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 5.8 The abundances of the alpha elements Mg, Ca, Si,

and Ti. Data is from Ryan et al (1996) (triangles) and Norris
et al (2001) (circles). The small (dots) represent the model

stars.

79

iron-peak elements and therefore is sensitive to the SN explosion mechanism, which is
still not fully understood. Therefore, the yields of this element are probably not as certain
as the yields of the other alpha elements. Mg shows a good agreement with the data
below [F e/H] = —3, but declines with a larger slope than expected and becomes more than
0.5 dex below the observed values beyond that point. At higher metallicities, [Fe/H] >
—3, the suggestion by Timmes et al (1995) of reducing the amount of Fe produced by
massive stars seems to be required, especially in the cases of elements Mg and Ti.
Fig. 5.9 shows the results of the model when Fe is reduced by a factor of 2. The
agreement between the data and the calculation in this case is almost perfect.

The metallicity-dependent yields of Si and Ca reproduce the values of [X/Fe] and
the Scatter at low metallicities very well, and seem to suggest that the Fe yields suggested

by WW95 are correct.

80

 

 

 

 

.~ _ -' , . '9';
‘ . .2 . 0; fi-f’mi‘ \

.._‘..,._"\’.;, _
‘3’". thig-

 

 

 

 

 

 

 

 

 

 

 

Fig. 5.9. The abundances of the alpha elements when Fe
yields are reduced by a factor of 2. Data is from Ryan et al
(1996) (triangles) and Norris et al (2001) (circles). The

small (dots) represent the model stars.

81

5.4.4 [Fe-peak/ Fe] :

The behavior observed for Fe-peak elements is that the ratio iron-peak/F e is close
to solar down to metallicity [Fe/H] ~ -—2.5, except for Mn, which is underabundant in all
halo stars. Below this value the behavior changes (McWilliam et al. 1995; Ryan et al.
1996; McWilliam 1997; Norris et al. 2001). Cr/Fe and Mn/Fe decrease to sub-solar
values, Co/F e increases to super-solar values, and Ni maintains an average slightly above
solar. The scatter increases towards lower metallicities as in the case of alpha elements.

Figure 5.10 shows the calculated values of relative abundances for Cr, Co, Mn
and Ni. The observed ratios of Mn and of Ni are reproduced well by the metallicity-
dependent yields of WW95 in this model. Cr, on the other hand, does not seem to
produce satisfactory results. The stars produced at very low metallicity show a small
over-abundance relative to solar, contrary to the observed under-abundance. The excess
in Co/Fe was produced fairly well with the metallicity-dependent yields below [Fe/H] =
— 2.5. This behavior of Co at the lowest metallicities has not been produced by any
previous models, and no known stellar yields were able to predict it even by
modifications in explosion parameters of SN-II models (Nakamura et al. 1999).

Our calculations should help set limits on nucleosynthesis predictions of massive
stars, especially progenitors of low metallicity. The dependence of the yields of these
elements on the position of the mass cut for material ejected from SN is one of the
primary reasons for potentially large errors in their calculation. Mn and Cr are produced

mainly during explosive Si burning, and therefore have a complicated dependence on the

82

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 5.10. The abundances of the Fe-group elements, Mn, Ni,

Cr, and Co . Data is from Ryan et a1 (1996) (triangles) and
Norris et al (2001) (circles). The small (dots) represent the

model stars.

83

progenitor mass. Efforts to understand the abundance trends of iron-peak elements, which
are formed close to the mass cut, have focused on the possible alpha-rich freeze-out
(McWilliam et al. 1995), the location of the mass cut, and the dependence of yields on
the star mass, metallicity, and neutron excess (Nakamura et al. 1999).

Our model predicts a scatter in the ratios for Fe-group elements that is larger at
very low metallicities than the observed values. The true situation will have to await

future observations, which will better fill out the phase space at low metallicity.

5.4.5 Contributions from different SN
The ejecta of the most massive stars are expected to dominate the earliest phases
of the chemical evolution of each cloud. These stars produce values of [Fe/H] in their

shells of < —2.5. According to WW95, at zero metallicity, the most massive stars (35

Mo < M < 40 Mo) produce metallicities lower than observed while the lowest observed

metallicities of [Fe/H] ~ -4 are produced by progenitors of masses less than 20 Mo.

These different behaviors of SN with progenitor mass is responsible for the dispersion in
metal abundances at low metallicities. Studying the dispersion in the relative abundances
of elements in the halo will allow for constraints to be set on chemical evolution models.
It can help us understand the nature of the first SN, and the inhomogeneous enrichment

processes that took place, in addition to the nature of the IMF and star formation rates at

the corresponding times.

84

Figures 5.11a to 5.11d show the contributions to the elemental abundances by different
progenitor masses up to metallicities [F e/H] = — 2.5. The mass ranges are shown on the
figures. The same is shown for Fe-group elements in figures 5.12a to 5.12d. The main
observation that can be seen in all eight figures is that the stars responsible for producing

the extremely low metallicities unobserved in the Galaxy are either more massive than 35
M0 or less massive than 20. This can be explained simply by suggesting that Pop-III
stars with such low metallicities do exist and will be found in the near future by the many

groups devoted to finding stars with low metal abundance. If such stars have not been

available in the halo from the beginning, then one can suggest that stars more massive

than 35 Mo do not contribute their ejecta, and instead, end their lives as black holes.

Another way to explain this is that the first stars that formed in pre-Galactic clouds
formed out of pre-enriched gas, and that there are no Pop-III stars in our Galaxy. For

higher metallicities [Fe/H] > -4, contributions from progenitors more massive than 25
Mo seem to fit very well into the observations up to 40 M0 in the case of alpha-
elements, and fairly well for Fe-group elements, except for Co. The calculated values
from the high-mass progenitors do not fit the observed values for Co even at higher
metallicities, while the rest of the mass range down to 10 Mo reproduces the observations
very well. This result for the low-mass end is in contrast to what is found for the other

elements Mg, Ti, Cr, and Mn. In these cases, the low-mass progenitors produce values of

the relative abundances out of the range of the data. This may be suggestive of the fact

85

that the first stars were massive and that the SN that contributed before [F e/H] ~ —2.5
were all massive SN. The alpha-element enhancement observed for stars with [Fe/H]
<—2.5 is indicative of a high-mass IMF in the first Gyr of the Galaxy’s formation. After
this time, as type-1a SN contribute their Fe ejecta, at [Fe/H]~ —2.5, the alpha-element

ratios go down to solar values.

86

[CatFe]

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

40 2M>35
g r_ J. ;":;*33;/hg ‘ ' '
_2 . I g . _2 I I . .
-5 4.5 4 -3.5 -3 -2.5 -5 4.5 4 -3.5 -3 -2.5
2 . . - 2 . . .
35gM>30 30§M>25
,3 a. . A... -
0.--..-441W 0.--“-.315542145
_2 . I . . _2 . . . .
-5 4.5 4 -3.5 -3 -2.5 -5 4.5 4 -3.5 -3 -2.5
2 . r . - 2 . . . .
25 2M>20 20 2M>10
0 _ _“__ _ ELQW g @84— —. magi-W
_2 I . . . _2 . I L I
-5 4.5 4 -3.5 -3 -2.5 -5 4.5 4 -3.5 -3 -2.5
[FelH] [FelH]

Fig. 5.11a. The contribution from different progenitor
masses to the value of [Ca/F e]. The mass ranges are given in
solar masses. The top left figure shows the whole range.
Data is from Ryan et al (1996) (triangles) and Norris et a1

(2001) (circles). The small (dots) represent the model stars.

87

[MglFe]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

40 2M>35
_2 . . . a
~5 ~45 ~4 ~3.5 3 ~25
2
no ‘
n. O
302M>25
-2 ~ _2 . . . .
-5 ~45 -4 ~35 -5 ~4.5 ~4 ~35 ~3 ~25
2 2
no
0 'T-——_-"—.‘"'f 0 Has-7'. ———————
25 2M>20
_2 A . . . _
6 ~45 -4 ~35 -3 ~25 -5
[Fe/H1

 

Fig. 5.1 lb. The contribution from different progenitor
masses to the value of [Mg/F e]. The mass ranges are given
in solar masses. The top left figure shows the whole range.
Data is from Ryan et a1 (1996) (triangles) and Norris et al

(2001) (circles). The small (dots) represent the model stars.

88

 

[SilFe]

 

 

 

 

 

 

 

 

 

 

252M>20

 

~45 ~4 ~35
[FeIH]

 

 

 

 

 

40 2M>35

_2 I L . A
5 ~45 -4 ~35 -3 ~25
2

n 0 A a A 30
0 L _____ j-Efiii-kgo

30 2M>25

-2 J 5

 

 

-5 ~45 ~4 ~35 -3 ~25

 

20 2M>10

 

 

A

2 A A A .
~5 ~45 ~4 ~35 ~3 ~25
[FeIH]

Fig. 5.11c. The contribution from different progenitor

masses to the value of [Si/Fe]. The mass ranges are given in

solar masses. The top left figure shows the whole range.

Data is from Ryan et al (1996) (triangles) and Norris et al

(2001) (circles). The small (dots) represent the model stars.

 

[TilFe]

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

2 2 . .
4O 2 M > 35
lat-'0 .' , . ““3“
0 L:~WFp—..—.—-.‘§£—W U L‘- — — —.—..-:. fiw‘
_2 . . _2 . .
5 ~45 -4 5 ~45 ~4
2 v .
30 2 M >25 0
0 —————— “2.35.2.3? . . ..
_2 . . . g
~5 ~45 -4 «35 ~3 ~25
2 . . °
20 2M>10
U baa-.rr.:.—-Tn:.‘89%-% ~.
~2

 

 

 

 

 

-5 ~45 ~4 ~35 ~3 ~25
[FelH]

 

Fig. 5.11d. The contribution from different progenitor
masses to the value of [Ti/Fe]. The mass ranges are given in
solar masses. The top left figure shows the whole range.
Data is from Ryan et a1 (1996) (triangles) and Norris et a1

(2001) (circles). The small (dots) represent the model stars.

90

 

 

1 402M>35

a. .V.\O’. ‘ as. _- ——.

U'::—-:————rc.— fififl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1* 35 2M>3O . 1 30>M>25
. . -- w... o 4
0 '—————.—.n5 -.-3—§‘§=m 0 * —————— ans—0 yqf
8.
“omdflgh “g‘ “OOMA‘AQCIR fie,
-1 . ° . _1 .
~45 ~4 ~35 -3 ~25 ~45 -4 ~35 ~3 ~2 .
1 L" I l ' g.- 1 1 : I
0 25 >M>20 «w, 0 20 2M>10 .
——————— A T— tfiofifier WE”? f——————Afi5 —0 w-
“_OMH$ A: “.OMAAEfR‘ A ‘
-1 _ '3 _1 _ u
~45 ~4 ~35 ~3 ~25 ~45 ~4 ~35 ~3 ~25
[Fe/H] [Fe/H]

Fig. 5.12.a. The contribution from different progenitor
masses to the value of [Cr/Fe]. The mass ranges are given
in solar masses. The top left figure shows the whole range.
Data is from Ryan et al (1996) (triangles) and Nonis et al

(2001) (circles). The small (dots) represent the model stars.

91

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 . , 1 ..

auoomo‘fi; ‘0’: anoomo‘fi; A
g._____::$:+_g%‘ 0.______f_t“‘3‘_'_£:3_°‘
_1 35 >M>30 .. ‘j -1_ 3o 2M>25
-45 -4 -35 3 -2.5 -4 5 -4 -35 -3
1 - av. . ‘ 1 r V I" .

Ana 0 in 1:50;"..6‘Ié I ““0 o a? «fuck? ‘30 on
o.-_____—»__~:..... 0~———-—————£§—.~1
_1_ 25 2M>20 AM": _1_ 20 2M>10 " . j
-45 -4 -35 -3 -25 -45 -4 -35 -3 -25

[Fele [Fe/H]

Fig. 5.12b. The contribution from different progenitor
masses to the value of [Co/Fe]. The mass ranges are given
in solar masses. The top left figure shows the whole range.
Data is from Ryan et al (1996) (triangles) and Norris et al

(2001) (circles). The small (dots) represent the model stars.

92

 

 

1- 402M>35

'. -zii‘i-..-:':'~u'£ .KQAAiel g
‘ 0 On 10;?! 0"‘23: {I

-1 . P C“

~45 ~4 ~3. 5 ~13 ~25

A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 - 3O 2M>25

0 ————— L ——————— 1 U ————— L——w————w

ADA“. ‘AOA 641 ‘00‘ *A03 L
_1 _ ADO-D" mofiwwzfifi -1 . 0 0A 210;?!“ A A
~45 -4 ~35 -3 ~25 ~45 -4 ~35 ~3 ~25
1 _, ‘ 1 ‘ 20 2M>10
U 35:34:22.5“: 7° —' “a": E U ————— L 1:557: a}?
-1, £00.; “:03 foggfi‘ -1. £00; 90% ‘AO‘
~45 ~4 ~3.5 ~3 -2.5 ~45 ~4 ~35 ~3 ~25

[FelHl [Fe/H]

Fig. 5.12c. The contribution fi'om different progenitor
masses to the value of [Mn/Fe]. The mass ranges are
given in solar masses. The top left figure shows the whole
range. Data is from Ryan et al (1996) (triangles) and
Norris et a1 (2001) (circles). The small (dots) represent the

model stars.

93

 

 

 

 

 

 

n 0 fltOnfl'
-1 - . '-—*
~45 ~4 ~35 ~3 ~25

 

1* 35 >M>3O A

 

 

 

 

 

 

0..--..”21‘2‘1293". ..

-1.

-4.5 4 -3.L5 5 ~25
1~ . A
o_l——7J‘.a€qi§

-1. 25>M>20 4

 

 

 

~45 ~4 ~3. 5
[FelH]

 

___—_BAO

4O >M>3S a

hjfiw

”‘ ".'.--..lm-——

 

 

 

~45 ~4 ~35 ~3 ~25

 

 

 

 

 

1* 302M>25 r“
0.____;.n.9q9-2 .0. A :9“
-1t

-45 -4 -35 -3 -25
03———-f‘

 

20 2M>10

 

 

 

~45 ~4 ~35 ~3 ~25

[Fe/H]

Fig. 5.12d. The contribution from different progenitor

masses to the value of [Ni/Fe]. The mass ranges are given

in solar masses. The top left figure shows the whole range.

Data is from Ryan et al (1996) (triangles) and Norris et a1

(2001) (circles). The small (dots) represent the model stars.

94

Chapter 6

Final Remarks

6.1 Conclusions

This thesis presents the results of a chemical-evolution simulation in which we
have evolved pre-Galactic clouds similar to those suggested to exist in the early Galaxy
by the cold dark matter scenario of hierarchical galaxy formation. The clouds were
studied for several sets of initial conditions and total mass. All clouds contained initially
primordial gas and were assumed to form a single metal—free Pop-III star at their cores.
Subsequent star formation was taken to occur under the assumption of a SN-induced star
formation mechanism in which stars form only in SN shells.

We studied the stability of these clouds against destruction from the energy input
of SN explosions, taking into account the main-sequence lifetimes of individual stars. We
ignored all tidal interactions with other systems and heating and cooling effects in the
gas. The total mass and initial mass functions were varied and results were compared.

Four different IMFS were employed: a Salpeter mass function with an index of —l.35, a

95

 

Salpeter function moderately biased towards high masses, and two IMFS that were
strongly biased toward the formation of hi gh-mass stars.

We find that clouds in the mass range of globular clusters are very vulnerable to
destruction and could not have formed the first stars. We conclude that these clusters
were probably not self-enriched, but rather must have formed from an ISM which was
likely to have been unifomly mixed in higher-mass systems, such as dwarf galaxies.
Systems with masses and sizes of presently observed dwarf galaxies were found to
survive destruction for more than 10 Gyrs, using the present-day mass function. This
indicates that if systems like these did form the first stars, then a top-heavy IMF could not
have operated (except during the formation of the first stars) and that later star formation
must have been slower or episodic.

These results are consistent with expectations from the cold dark matter
hierarchical clustering model of galaxy formation. In this scenario, the smaller clouds
will contribute their material to the halo at the time of their destruction, while the gas
may also contribute to stars that form in the later collapse of the disk. More stable
systems will then continue to form stars and contribute to the halo population during tidal
interactions. Globular clusters may have formed from pre-enriched gas with a population
of older, less-massive stars.

The metallicities and relative elemental abundances in stars were calculated, using
metallicity-dependent yields for type-II SN, and SN of type-Ia were allowed to contribute

with a delay time of 1 Gyr. The MDF was calculated for stars in the different clouds and

96

 

compared for all four assumed IMF s. The evolution was followed for each cloud up to
the time of its destruction, in the cases of high-mass biased IMFS. For the Salpeter IMF,
the evolution was followed up to 5 Gyrs. All distributions showed a dispersion in the
metallicities of the stars formed in the first stages, followed by the formation of a well-
defined peak at a metallicity that varied for the different mass functions. This final
metallicity ranged between [Fe/H] = —2.7 in the case of the simple function to [Fe/H] =
—2.2 in the case of the top-heavy mass functions. Assuming that the stars formed in these
clouds will become members in the field halo population due to later interactions, we
sum the final stages of all four clouds. The result is a broad distribution peaked at [F e/H]

= —2.6. When compared to the observed MDF of halo field stars, which shows a broader

distribution peaked at [Fe/H] = —l.6, we conclude that the halo must have had'

contributions from many systems, some of which were not initially primordial in

composition.
We were able to reproduce the observed trends in relative elemental abundances

observed in very metal-poor stars fairly well with the SN-induced star formation

mechanism, together with the metallicity-dependent yields.

6.2 The Future

With no doubt, this is an era of astronomy. So much that has been hidden from us
is now becoming understood, and the future holds within it many promises for

understanding the beginning of structure in the universe, leading to the formation of

97

rar'"!"' "1.. -

 

galaxies in general, and the formation and evolution of the Milky Way in particular. So
much remains to be done.

The cold dark matter scenario holds much promise, but needs to be tested further.
The first clouds of primordial material predicted by this theory to have been the result of
density fluctuations in the early universe need to be studied in more detail, including the
effects of gas dynamics, heating and cooling of the gas, and interactions with the other
systems. The initial conditions in these clouds and the mechanism by which the first stars
are formed still need to be investigated in more detail.

Our results show that the role of the IMF at these early times cannot be ignored. A
better understanding of the types of mass functions that dominated at different times as a
result of the changing conditions is crucial for the understanding of the chemical and
dynamical evolution of the Galaxy.

There is still a great deal to learn about the nature of Pop-HI stars. How massive
were they? Did they have a different IMF than later generations? What kind of
nucleosynthetic yields did they produce? And finally, do low-mass stars that may have
occasionally formed at that time still exist? Whether true Pop-III stars are found or not,
the following generation of Pop-II stars hold within them a fossil record that reveals a
great deal about their progenitor stars and the environments in which they formed.
Therefore, the identification and analysis of large numbers of extremely metal-poor stars
is a key to many questions, and gives great hope for the future. The very near future

holds so much promise, with the anticipated completion of many ongoing and proposed

98

 

observational programs. The next generation of astrometric satellites, NASA’s SIM
(Space Interferometric Mission), and ESA’s GAIA (Global Astrometric Interferometer
for Astrophysics), will provide direct geometric distances and space motion information
for halo stars with accuracies a thousand times greater than those obtained by the
HIPPARCOS satellite. In the meantime, much can be learned from ongoing ground-
based proper motion programs such as SPM, NPM, and USNO. In addition, we can soon
expect results from full sky (or nearly so) photometry programs such as 2MASS and
SDSS, as well as radial velocity and abundance information from 'wide-field
spectrosc0pic surveys being conducted with 2DF and 6DF. All of this is expected to
create a huge leap forward in our understanding of the halo population in the Galaxy, and
open the door for a new generation of testable models to emerge.

The amount of information that can be deduced from halo stars is enormous.
From their chemical composition, one can learn about the enrichment processes (Ryan et
a1 1996; Tsujomoto et al. 1999; Nakasato & Shigeyama 2000), the nature of the first IMF
(Larson 1998), and set constraints for nucleosynthesis calculations. Such calculations in
massive stars are being performed intensively at present (Heger et al. 2000a; Heger et al.
2000b; Nakamura et al. 2000; Rauscher et al. 2000; Rosswog et al 2000) due to great
improvements in the reliability of the input data, including opacity tables (Iglesias &
Rogers 1996), nuclear reaction rates (Rauscher & Thielemann 2000), and physical
processes such as winds and the associated mass loss (Langanke & Martinez-Pinedo

2000). Still, nucleosynthesis calculations need to be tested further, specially for the

99

 

yields of iron-group elements which require better understanding of the SN explosion
mechanism including the position of the mass cut, and the explosion energy.

The oldest stars in the Galaxy can also set limits on the age of the Galaxy (and
hence the universe), with better estimates of their ages. The use of the ratios of
radioactive elements in these stars, compared with those predicted from r-process models,
is a very useful tool that has been used with great success lately (Cayrel et a1 2001; Hill et
al 2001; Toenjes et al. 2001; Sneden et a1 2001).

Since it is believed that halo stars have kinematic properties similar to those of the
systems in which they were formed, studies of the kinematics of halo stars can help us
understand how the halo was assembled. Clumping of at least a small number of halo
stars in angular momentum phase space has already been observed, indicating that such
stars were accreted by the Galaxy from a previous system. Helmi et al (1999) suggested
that about 10% of metal-poor stars in the halo may have come from a single coherent
structure that was disrupted during or soon after the Galaxy’s formation. Chiba & Beers
(2000) confirm these findings and identify an additional elongated feature in angular
momentum space. They summarize the global kinematics of the halo stars and report that
they do not show a net retrograde rotation at large heights above the Galactic plane, as
claimed previously, but rather exhibit a near zero systematic rotation, with a continuous
decrease in rotational velocity with increasing height above the plane. They also observe
no correlation between [Fe/H] and eccentricity e and no change of the average rotational

velocity with abundance for stars with [Fe/H] < —l.7. These results are basically in

100

 

agreement with the 82 scenario, in which the halo is assembled from different fragments
accreted from merging nearby systems

There is also great interest today in nearby dwarf galaxies, which are believed to
have contributed to the halo population by merging and tidal destruction. The halo stars
identified as members in clumps in angular-momentum space, and therefore believed to
have been accreted from such nearby systems, are being pursued by observers hoping that
they may be able to give some insight as to how dwarf galaxies evolved, and influenced
the evolution of the Milky Way. The low alpha-element abundances observed in some
halo stars are suggestive of slow star-formation rates in such systems, allowing little
enrichment by SNII before SNIa events take place and contribute their iron-rich material.
Therefore, the substructure observed in the halo is a very important finding that needs to
be pursued further, and promises to help astronomers tell a story .of the formation of the

Galaxy and its relation with other nearby systems.

101

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