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3 LIBRARY
260? Michigan State
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This is to certify that the
dissertation entitled

The SEGUE Stellar Parameter Pipeline and The Alpha
Elements of Stars in The Milky Way

presented by
Young Sun Lee

has been accepted towards fulﬁllment
of the requirements for the

Ph.D. degree in Astronomy and Astrophysics

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THE SEGUE STELLAR PARAMETER PIPELINE AND THE ALPHA
ELEMENTS OF STARS IN THE MILKY WAY

By

Young Sun Lee

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

2008

ABSTRACT

THE SEGUE STELLAR PARAMETER PIPELINE AND THE ALPHA
ELEMENTS OF STARS IN THE MILKY WAY

By

Young Sun Lee

I describe the development and implementation of the SEGUE (Sloan Extension for
Galactic Exploration and Understanding) Stellar Parameter Pipeline (SSPP). The
SSPP derives, using multiple techniques, radial velocities and stellar atmospheric pa-
rameters (effective temperature, Teﬂ', surface gravity, log 9, and metallicity, [Fe/H])
for AF GK type stars, based on medium-resolution spectroscopy and ugrz'z photome-
try obtained during the original Sloan Digital Sky Survey (SDSS-I) and its Galactic
extension (SDSS-II/SEGUE). The SSPP also provides spectral classiﬁcation for a
wider range of stars, including stars with temperatures outside of the window where
stellar parameters can not be estimated with the current approaches. Adding the
average internal scatter from the multiple methods and the external uncertainty from
the comparisons with the high-resolution analysis, quadratically, the typical uncer-
tainties in the stellar parameters delivered by the SSPP are 0(Teff) = 157 K, 0(log g)
= 0.29 dex, and a([Fe/H]) = 0.24 dex, over the range 4500 K S Teff S 7500 K.

Tests of the accuracy and precision of the SSPP, by comparing the stellar param-
eters for selected members of three globular clusters (M 13, M 15, and M 2) and two
open clusters (N GO 2420 and M 67) to the literature values, are also presented. Spec-
troscopic and photometric data obtained during the SDSS-I and SDSS-II/SEGUE are
used to determine atmospheric parameter and radial velocity estimates for stars in
these clusters. Based on the scatter in the metallicities derived for the members of

each cluster, I quantify the typical uncertainty of the SSPP values, a([Fe/H]) = 0.13

dex for stars in the range of —0.3 S g — r S 1.3 and 2.0 S logg S 5.0, at least
over the metallicity interval spanned by the clusters studied (-—2.3 3 [Fe/ H] S O),
and with signal-to—noise ratios greater than ~ 10/1. The surface gravities and ef-
fective temperatures derived by the SSPP are also compared with those estimated
from the comparison of the color-magnitude diagrams with stellar evolution models;
satisfactory agreement (0(Teff) < 200 K and 0(logg) s 0.4 dex) is found.

From the above considerations it is concluded that the SSPP is able to determine
radial velocities and atmospheric parameters for stars (in the range 4500 K S Teﬂ S
7500 K) with sufﬁcient accuracy and precision to enable detailed explorations of the
chemical compositions and kinematics of the disk and halo populations of the Galaxy.

A method for determining the abundance ratio of the a-elements (O, Mg, Si,
Ga, Ti) with respect to Fe (collectively parameterized as “[a/Fe]”) is also explored.
Results of a comparison with the ELODIE spectral library and from a noise injection
experiment suggest that an accuracy in [a / Fe] of about 0.1 dex for spectra with
S/N 2 20/1 is achievable. This technique is used to estimate [a / Fe] for a total of
39,167 spectrophotometric and telluric calibration stars from the most recent public
release (DR-6; Adelman—McCarthy et a1. 2008), in order to study the a-abundance
patterns in stars of the Galactic halo. Local space velocities (U, V, W) and orbital
parameters (such as Zmax, Rape, Rperi, V¢, and eccentricity) were calculated for this
sample, and a total of 7590 potential halo stars were selected by applying cuts of
V45 3 80 km s‘l, Zmax 2 1 kpc, and [Fe/H] S —1.0. Furthermore, the sample was
divided into two groups : a “dissipative component (or inner halo)” with stars having
40 S V¢ S 80 km 8—1 and Rape < 16 kpc and an “accreted component (or outer
halo)” with stars having V¢ < 40 km 3‘1 or Rapo Z 16 kpc, or both. Results for the
comparison of these two samples are presented as a ﬁrst step toward understanding

the assembly history of the halos of the Galaxy.

Copyright by
YOUNG SUN LEE
2008

Dedicated to my lovely wife, Ducksoon Noh

ACKNOWLEDGMENTS

It is a pleasure to thank the many people who helped make this thesis possible.
Among them, especially, I would like to express my deep and sincere gratitude to my
advisor, Dr. Timothy C. Beers, whose enthusiasm, inspiration, and encouragement
greatly helped me get through the difﬁcult times during my graduate study. Because
of his support and encouragement, I was able to get involved with the Sloan Digital
Sky Survey/ Sloan Extension for Galactic Understanding and Exploration, and to
learn how to collaborate with other great scientists who participated in the project
to develop tools for reducing and handling the data. More importantly, I became a
person capable of doing research. This is a priceless experience for my future career
and research. I would also like to thank him for his patience and understandings in
all the different situations I faced along the way. I appreciate his proofreading of
my thesis as well. He was a truly great teacher for me and his inﬂuence, help, and
support will remain in my mind forever. It must have been “meant-to-be” that I met

him in Korea back in 2001.

I should also acknowledge Thirupathi Sivarani who taught me how to generate
models of stellar atmosphere and synthetic spectra and provided for the initial start
of developing the SEGUE Stellar Parameter Pipeline. Without her, I wouldn’t have
even started to think of constructing the pipeline. I also wish to express my warm
and sincere thanks to Brian Yanny and Constance Rockosi who helped reﬁne the
SSPP with their valuable comments and suggestions. I would also like to thank my
dissertation committee - Dr. Horace Smith, Dr. Stephen Zepf, Dr. Edward Brown,

and Dr. Bernard Pope - for its useful comments on my thesis.

I am also indebted to my fellow graduate students for providing home-like at-

mosphere and for having a good time together. I am especially grateful to Brian

vi

Marsteller, who is now in California, for our valuable research discussions, for teach-
ing me how to observe using the 0.9 m telescope at Kitt Peak National Observatory
and to reduce data, and for sharing a room with me at many meetings. I will surely
miss the times we spent hanging out together at various conferences.

I should also thank Nathan DeLee for kindly providing solutions to the Linux
problems that I encountered from time to time, and Christopher Waters for letting
me use the LATEX class ﬁle, which made it much easier for me to write this thesis
without hassling with the very tricky formatting guide line.

Finally, I owe my special thanks to my lovely wife, Ducksoon Noh, who trusted
in me and depended on me. She came to this foreign soil with her very limited
English, and we got married in a small chapel. During my last graduate study, her
devoted support, dedication, and sacriﬁce made it possible for me to ﬁnish my thesis
successfully. I would have loved to give her a big wonderful wedding with her parents
present; however, we will remember and cherish our small but very beautiful wedding

at the cozy and comfortable chapel with our friends forever.

 

‘ T

 

TABLE OF CONTENTS

List of Tables ........................................................ xi
List of Figures ....................................................... xiii
1 Introduction ...................................................... 1
1.1 The Milky Way Galaxy ...................... 1
1.1.1 Thin Disk ............................ 1
1.1.2 Thick Disk ........................... 3
1.1.3 Stellar Halo ........................... 4
1.1.4 Bulge .............................. 4
1.1.5 Dark Matter Halo ....................... 5
1.1.6 Formation of the Milky Way ................. 5
1.2 Chapter Outline .......................... 7
2 Sloan Extension for Galactic Understanding and Exploration ..... 9
3 The SEGUE Stellar Parameter Pipeline (SSPP) .................. 12
3.1 Philosophy ............................. 12
3.2 Determination of Radial Velocities ................ 15
3.2.1 The Adopted Radial Velocity Used by the SSPP ...... 15
3.2.2 Checks on Radial Velocities - Zero Points and Scatter . . . 18
3.3 Calculation of Line Indices .................... 20
3.3.1 Continuum Fit Techniques ................... 21
3.3.2 Measurement of Line Indices ................. 23
3.4 Methodology ............................ 24
3.4.1 Spectral Fitting With the R24 and 1:113 Grids ........ 24

3.4.2 Parameters Obtained from the Wilhelm et al. (1999) Proce-
dures : WBG ........................... 28
3.4.3 The Neural Network Approaches : ANNRR and ANNSR . . . . 30

3.4.4 The X2 Minimization Technique Using the NGS1 and NGS2
Grids .............................. 34

3.4.5 Metallicity and Gravity Estimates from 3850—4250 A : CaI 1K1
and Call ............................ 46

3.4.6 The Ca II K and Auto-Correlation Function Methods : CaIIK2,

CaIIK3, and ACF ........................ 47
3.4.7 Calibration of a Ca II Triplet Estimator of Metallicity : CaIIT 50

3.4.8 Calibration of a Gravity Estimator Based on the Ca I (4227
A) and Mg I b and MgH Features : CaI2 and MgH ...... 51
3.5 Empirical and Theoretical Predictions of Teff and g — 1‘ Color . 52
3.5.1 Predictions of T eff ....................... 52
3.5.2 Predictions of g — r Color ................... 54

viii

3.6

The Impact of Signal-to—Noise on Derived Atmospheric Parameters 56

3.7 Flags Raised During Execution of the SSPP ........... 61
3.8 The SSPP Decision Tree for Final Parameter Estimation . . . . 66
3.8.1 Decisions on Effective Temperature Estimates ........ 67
3.8.2 Decisions on Surface Gravity Estimates ........... 67
3.8.3 Decisions on Metallicity Estimates .............. 68
3.9 Validation of the Final SSPP Parameter Estimates ....... 69
3.9.1 Validation from High-Resolution Spectroscopy ........ 70
3.10 Assignment of Spectral Classiﬁcations for Early and Late-Type
Stars ................................ 77
3.11 Distance Estimates ......................... 79
3.12 Empirical Uncertainties of Stellar Parameters of the SSPP . . . 80
3.13 Summary .............................. 81
Validation with Galactic Open and Globular clusters ............. 84
4.1 Photometric and Spectroscopic Data ............... 84
4.1.1 Photometric Data ....................... 87
4.1.2 Spectroscopic Data ....................... 89
4.2 Radial Velocities .......................... 94
4.3 Membership Selection from Spectroscopic
Samples ............................... 94
4.3.1 Likely Member Star Selection for Globular Clusters ..... 94
4.3.2 Likely Member Star Selection for Open Clusters ....... 105
4.4 Determination of Overall Metallicities and Radial Velocities of
the Clusters ............................. 106
4.4.1 Selection of True Members ................... 107
4.4.2 Determination of Overall Estimates of Mean Cluster Metal-
licity and Radial Velocity ................... 110
4.5 A Comparison of Derived Metallicities and Radial Velocities for
True Cluster Members with Previous Studies .......... 113
4.5.1 M 13 (NGC 6205) ....................... 113
4.5.2 M 15 (NGC 7078) ....................... 115
4.5.3 M 2 (NGC 7089) ........................ 116
4.5.4 NGC 2420 ............................ 116
4.5.5 M 67 (NGC 2682) ....................... 117
4.6 A Comparison of Derived Metallicities and Surface Gravities for
True Cluster Members with Color-Magnitude Diagrams . . . . 120
4.7 Summary .............................. 127
The [a/ Fe] Abundance Patterns of Stars in the Galactic Halo ..... 128
5.1 Introduction ............................ 128
5.2 Previous Studies .......................... 130
5.3 Determination of [a / Fe] ...................... 135
5.3.1 Methodology .......................... 135
5.3.2 Validation ............................ 137
5.4 Sample Selection .......................... 139
5.5 Computation of Kinematic and Orbital Parameters ....... 142

ix

 

5.6 Distributions of [a / Fe] ....................... 147
5.6.1 Distributions of Vd> and [Fe/ H] with [a/ Fe] cuts ....... 148

5.6.2 Distributions of [a/ Fe] with [Fe/ H] cuts ........... 150

5.6.3 Distributions of [a/ Fe] with Rapo cuts ............ 154

5.6.4 Distributions of [a / Fe] with Vd> cuts ............. 156

5.7 Discussions and Implications ................... 159
5.8 Summary and Conclusions .................... 168

6 Conclusions and Future Work .................................... 173
A Line List for Line index Calculations .............................. 181
B Output Format of the SSPP ...................................... 185
C Properties of Selected Cluster Members .......................... 193
References ....................................................... 243

 

3.1

3.2

3.3

3.4

3.5
3.6
3.7
3.8

3.9

4.1

4.2

4.3

5.1

5.2

A.1

B.1

C.1
C2

C3

LIST OF TABLES

Parameter Sensitivities to Radial Velocity Errors ............. 13
Summary of High-Resolution Observations ................. 16
Valid Ranges of g -— r and S /N for Individual Methods .......... 25
Comparison of NGSl and NGS2 Grids with Spectral Libraries and High-
Resolution ................................. 44
Parameter Sensitivities to Signal-to—Noise ................. 57
Brief Descriptions of SSPP Flags ...................... 61
Comparison of Teff of Individual Methods with High-Resolution Analyses 70
Comparison of log 9 of Individual Methods with High-Resolution Analyses 73
Comparison of [Fe/H] of Individual Methods with High-Resolution Analyses 76
Properties of the Clusters .......................... 91
Derived Radial Velocities and Metallicities of the Clusters ........ 111
Mean and 1 a Values of Residuals in Teff and log 9 ............ 119
Variation of [a / Fe] with S/N ........................ 139
Results of KS tests .............................. 151
Line Band and Sideband Widths and Output Format ........... 181
Key to Each Column and Format of SSPP Parameter File ........ 185
SSPP-Derieved Properties for Selected Member Stars of M 13 ...... 194
SSPP-Derived Properties for Selected Member Stars of M 15 ....... 214
SSPP-Derived Properties for Selected Member Stars of M 2 ....... 221

xi

 

C.4 SSPP—Derived Properties for Selected Member Stars of N GC 2420 . . . . 227

C5 SSPP-Derived Properties for Selected Member Stars of M 67 ....... 238

1.1

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10

3.11

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

4.9

LIST OF FIGURES

Side view of the Milky Way .........................

Comparison plots of the radial velocity ...................
Example of a ﬁtted global continuum ....................
Atmospheric parameter estimation with ANNRR ...............
Atmospheric parameter estimation with ANNSR ...............
Two examples of the results of the application of the N631 grid ......
Comparison of parameters of NGS1 grid with ELODIE library ......
Comparison of parameters of NGS1 grid with MILES library .......
Comparison of parameters of NGS1 grid with high resolution analysis
Comparison of Teff of individual methods with high-resolution analysis
Comparison of log 9 of individual methods with high-resolution analysis .

Comparison of [Fe/ H] of individual methods with high-resolution analysis

Stars with available photometry in the ﬁeld of M 13 ............
Stars with available photometry in the ﬁeld of M 15 ............
Stars with available photometry in the ﬁeld of M 2 ............
Stars with available photometry in the ﬁeld of NGC 2420 .........
Stars with available photometry in the ﬁeld of M 67 ............
CMDs of the M 13 stars inside tidal radius and ﬁeld region ........
CMDs of the M 15 stars inside tidal radius and ﬁeld region ........
CMDs of the M 2 stars inside tidal radius and ﬁeld region ........

CMDs of the NGC 2420 ﬁeld region .....................

xiii

17

21

31

33

38

40

42

45

72

74

78

85

86

88

90

92

95

96

97

98

4.10 CMDs of the M 67 ﬁeld region ........................
4.11 M 13 CMD based on the likely member stars ................
4.12 M 15 CMD based on the likely member stars ................
4.13 M 2 CMD based on the likely member stars ................
4.14 NGC 2420 CMD based on the likely member stars .............
4.15 M 67 CMD based on the likely member stars ................
4.16 Distributions of [Fe/ H] and radial velocity for stars in M 13 region . . . .
4.17 Distributions of [Fe/ H] and radial velocity for stars in M 15 region . . . .
4.18 Distributions of [Fe/ H] and radial velocity for stars in of M 2 region . . .
4.19 Distributions of [Fe/ H] and radial velocity for stars in NGC 2420 region .
4.20 Distributions of [Fe/ H] and radial velocity for stars in M 67 region . . . .
4.21 Distributions of [Fe/H] as a function of (g — r)0 and average S/N . . . .
4.22 Distributions of [Fe/ H] as a function of estimated log 9 ..........
4.23 Distributions of Teg and log 9 for M 13 ...................
4.24 Distributions of Teﬂ' and log 9 for M 15 ...................
4.25 Distributions of Teff and log 9 for M 2 ...................
4.26 Distributions of Teﬁ and log 9 for NGC 2420 ................

4.27 Distributions of Teff and log 9 for M 67 ...................

5.1 Comparison of [a / Fe] from our estimates with the literature .......
5.2 Schematic diagram of U, V, and W velocities ...............
5.3 Schematic diagram of cylindrical reference frame ..............
5.4 Spatial distribution and a plot of [a / Fe] versus [Fe/ H] ..........
5.5 Run of [a/Fe] over U, V, W, and V¢ ....................

5.6 Distributions of [a / Fe] with Zmax, Rperi, Rape, and e ...........

xiv

100
101
102
103
104
106
107
108
110
112
114
118
121
122
123
124
125

126

138

143
144
146

147

5.7 Distributions of V4, and [Fe/ H] with [a / Fe] cuts .............. 149

5.8 Distributions of [Oz/Fe] and Rperi with [Fe/H] cuts ............. 152
5.9 Distributions of [a / Fe] with RapO ...................... 155
5.10 Distributions of [a / Fe], [Fe/ H], and eccentricity with V), ......... 157
5.11 Distributions of [a / Fe] with V¢ ....................... 158
5.12 Distributions of Va, and [Fe/ H] ........................ 160
5.13 Distributions of mean [a / Fe] ......................... 164
5.14 Distributions of [a/ Fe] and Rperi with [Fe/ H] ............... 167
5.15 Distributions of [a / Fe] and Zmax with [Fe/H] ............... 169

Images in this dissertation are presented in color.

 

XV

 

CHAPTER 1:
INTRODUCTION

 

1.1 THE MILKY WAY GALAXY

The Milky Way Galaxy is a spiral galaxy which resides in a relatively low over-
density region of the Universe (the Local Group). Its total mass is estimated to be
~ 1012MQ. Based on stellar ages, spatial distributions, kinematics, and chemical
compositions (e.g., metallicity parameterized by [Fe/HP), stars in the Galaxy can be
divided into several distinct populations, and structural components. The primary
stellar components of the Galaxy are the disk systems, a stellar halo (or halos), and
a central bulge. In addition to these, one can also infer the presence of a dark matter
halo, whose properties are not well known at present. In this chapter, we brieﬂy
review each of these components. Figure 1.1 shows an edgeon schematic view of the

major components of the Galaxy.

1.1.1 THIN DISK

The thin disk is not only the most luminous component of the Milky Way galaxy but
it is the main site of active star formation in the Galaxy. It contains gas, dust, and
open clusters, as well as both old and young stars, which are collectively known as
Population 1. Our Sun resides 8.5 kpc from the center of the Galaxy, and about 30

“[Fe/H] = log10(Npe/NH) — log10(Npe/NH)®. N is the total number density of Fe or H
atoms in a given volume in the star and the Sun (indicated by the G subscript). “Metals”

are understood to pertain to all elements heavier than He. The terms “metallicity” and
[Fe/ H] are used interchangeably throughout this thesis.

 

 
 

Dark Matter Halo

  
   
 
 
 

Stellar Halo

Bulge

  

Thin Disk Sun

 

 

Figure 1.1 Schematic side view of the Milky Way.

pc from the Galactic plane. The radius of the luminous thin disk is about 25 kpc,
including the gaseous disk. Most of the thin disk stars move around the Galactic
center at a speed near 220 km s‘1 (at the Sun’s location) on circular orbits. Studies
indicate that main sequence stars with spectral types G, K, or M, inhabit an old thin
disk with a vertical scale height of about 300 pc (and a vertical velocity dispersion of
0(W) ~ 20 km s‘l), while young thin disk stars (spectral types 0, B, and A) exhibit

a scale height of 50 pc, and have a lower vertical velocity dispersion. The young thin

2

disk stars have metallicities ranging over [Fe/ H] = —0.5 to +0.3. The old thin disk
includes stars with metallicities over a similar range, but also somewhat lower. A
recent study by Abadi et al. (2003) raised a possibility that some fraction of the old

thin disk stars might have been accreted from a few satellite galaxies.

1.1.2 THICK DISK

The thick disk, identiﬁed by star counts more than 20 years ago (Gilmore & Reid
1983), is a kinematically and chemically distinct component of the Galaxy. The
metallicity range of the thick disk stars is —2.0 to —0.5, with a peak at [Fe/H]
~ —0.6. It has a vertical scale height of ~ 1 kpc and a radial scale length of ~ 3 kpc.
The stellar mass of the thick disk is 10—20% of the thin disk stellar mass, and it
is as about as old as the globular cluster 47 Tue. The rotational velocity of the
thick disk population is somewhat poorly known; some authors report a value ~ 170
km s’1 (Norris 1986; Morrison, Flynn & Freeman 1990; Chiba & Beers 2000), while
others (e.g., Wyse & Gilmore 1986; Gilmore, Wyse & Norris 2002) have derived ~ 100
km 5.1. The vertical velocity dispersion of the thick disk stars is 0(W) ~ 40 km 3*.
There is also evidence (Chiba & Beers 2000) that the thick disk has a metal deﬁcient
tail, reaching as low as [Fe/ H] = —2.0. This tail of the thick disk, whose origin still
remains controversial, is referred to as the “metal-weak thick disk”. The thick disk
stars with [Fe/ H] < —0.6 possess [01/ Fe] = +0.4 (Bensby et al. 2000, and references
therein), which indicates likely enrichments from core collapse supernovae. A decline
of the a-abundance with respect to the Fe is also noticed for the metal rich stars of
this component, implying Fe contributions from Type Ia supernovae. The thick disk
might have formed from the pre-existing thin disk heated by interactions with dwarf
galaxies or from the debris of disrupted dwarf galaxies involved in past encounters

with the Galaxy.

1.1.3 STELLAR HALO

The stellar halo includes the globular clusters (GCs) and ﬁeld stars, with ages that
are among the oldest objects in the universe (between 12 and 14 Gyr). The GCs are
spherical conglomerations of stars, up to about 50 pc across, that contain 104 to 106
member stars. About 1% of the halo stars are contained in globular clusters. The
stellar halo is roughly spherical or a slightly oblate spheroidal shape, extending to as
large as 100 kpc. The main constituents of the stellar halo are old, low-metallicity
stars with a mean [Fe/ H] = —1.6. Its total mass is about 109MQ. Members of the
halo population exhibit a negligible net rotation around the Galaxy, and high velocity
dispersions (e.g., 0(W) ~ 90 km s‘l). The stellar density distribution in the halo
can be described by a r-3'5 form with a scale height of about 3 kpc. The typical
[0: / Fe] of the halo stars is [a / Fe] 0.3 to 0.4 dex, which suggests chemical enrichments
from SNe II, probably at very early times.

Very recently, the stellar halo has been argued to comprise two distinct popula-
tions, a slowly rotating (0 to 50 km 3*) inner halo population with a metallicity peak
at [Fe/ H] = —1.6, and a counter rotating (—40 to —70 km s‘l) outer halo population
with a metallicity peak at [Fe/ H] = —2.2. While the inner halo appears to dominate
up to distance of 10-15 kpc, the outer halo dominates beyond 15—20 kpc (Carollo et
al. 2007). The majority of the inner halo may have formed from dissipative collapsing
gas clouds or proto—Galactic clumps, while the outer halo is suggested to have been

accreted from the disruption of numerous dwarf satellites.

1.1.4 BULGE

The bulge of the Galaxy appears as box shape from our perspective, with a diameter of
2 kpc and a height of 400 pc. Due to the difﬁculty in decoupling the bulge population
from stars of the inner disk, this region is not presently well studied. Its outer regions

rotate at about 100 km s“1 and its total mass is around IOIOMQ. The bulge is mainly

composed of Old stars Of the same age as the stellar halo, although the bulk of their
metallicities are roughly solar. It appears that star formation in the bulge is still
ongoing. The bulge populations exhibit a very broad metallicity distribution, with a
peak of [Fe/ H] ~ —0.3, which can be well described by a Simple closed box model
(Sadler, Terndrup & Rich 1996, and references therein). High-resolution elemental
analysis of several bulge stars indicates enhancement of [a / Fe] from SNe II (Rich &
McWillian 2005, and references therein), implying very rapid star formation. The
dominant old, metal-rich population of the bulge suggests an formation of the bulge
by early, very intense star formation, likely from the gas ejected by halo star forming
regions (Ferreras, Wyse, 85 Silk 2003). There is solid evidence for the existence of a

bar connected to the bulge.

1.1.5 DARK MATTER HALO

The dark matter halo is only detectable by its gravitational inﬂuence. Its existence
was ﬁrst inferred from studies of the Galactic rotation curve, which shows no sign
of a decline out to a radius of 20 kpc, indicating a substantial amount of (unseen)
matter must exist at least out to that radius, and probably much farther. Because
this non-luminous matter has never been directly observed at any wavelength, it is
known as dark matter, with no clear understanding of its nature. From an inventory
of the mass of the other constituents of the Galaxy, the total mass of the dark matter
in the Milky Way is ~ 10 times greater than the total mass of stars, and about 100

times greater than that of the gas and dust.

1.1.6 FORMATION OF THE MILKY WAY

Over the past ﬁfty years, two major formation scenarios of the Milky Way galaxy
have been suggested. The ﬁrst was a rapid monolithic collapse model, proposed by

Eggen, Lynden-Bell, & Sandage (1962). These authors made use of an observed

correlation between the metallicity of halo stars with their kinematics (in particular,
their rotational velocity, or total angular momentum) to claim that a rapid collapsing
protogalactic gas could have formed the stellar halo and continued (as it spun up) to
form the disk. In this model, the collapse time is shorter than the Galactic revolution
period (~ 2 x 108 yrs), but sufﬁciently long for massive stars to form in the metal
deﬁcient infalling gas so that the gas is able to be enriched with heavy elements.
The series of star formation and collapse would lead to newly formed stars that
exhibit different orbital eccentricities (changing from high eccentricity orbits for the
low metallicity stars to low eccentricity orbits for the higher metallicity stars). and
have higher metallicity as the collapse occurs. In this scenario, one would expect
to ﬁnd a metallicity gradient as a function of eccentricity in the resulting sample of
stars.

The rapid collapse model was criticized by Searle & Zinn (1978). They gath-
ered relatively accurate metallicity and horizontal-branch morphologies for about 50
globular clusters (GCs), based on the data available at that time, and searched for
correlations in their properties with Galactocentric distance, RG0. They divided the
GCs into inner and outer halo groups by separating them at a distance of ECG ~ 8
kpc. They found that not only did there exist no metallicity gradient with distance
from the Galactic center for the outer halo GCs, but also that horizontal-branch mor-
phologies between the inner and outer GCs is very different (which they attributed to
age differences). These ﬁndings led them to conclude that the outer halo GCs formed
through accretion of what they called “proto—Galactic fragments” over an extended
period of time, up to several Gyrs.

Later, Zinn (1993) expanded the model further, and based on horizontal-branch
morphology, distance, spatial distribution, rotational velocity, and velocity dispersion,
he divided the GCs into two groups: “old” and “young”, which were associated with

a “dissipative” inner halo and an “accreted” outer halo.

The widely accepted ACDM (cold dark matter) structure formation paradigm
(e.g., Navarro et al. 1997) favors the ideas envisioned by Searle & Zinn (1978). In
this paradigm, all galaxies form from local over-densities in the primordial matter dis-
tribution, and grow hierarchically via mergers and the accretion of numerous smaller
fragments over time. The manifest candidates for the building blocks are the dwarf
spheroidal (dSph) and irregular (dlrr) galaxies we see today (actually, these might
just be the survivors of the process). One of the predictions of the hierarchical struc-
ture formation approach is that one might expect to observe many more satellite
galaxies surrounding existing large galaxies like the Milky Way than are in fact ob-
served today. This is known as the “missing satellite problem”. Although a number
of faint dwarf galaxies have been recently discovered by the Sloan Digital Sky Survey
(SDSS), the total number of the satellite galaxies around the Milky Way is still about

four times smaller than modern predictions (Simon & Geha 2007).

1.2 CHAPTER OUTLINE

Chapter 2 describes the Sloan Extension for Galactic Understanding and Exploration
(SEGUE), which is one of the three surveys conducted during the ﬁrst extension of
SDSS, known as SDSS—II. The radial velocity and the methodology which are adopted
in the SEGUE Stellar Parameter Pipeline (SSPP) are presented in Chapter 3. The
stellar parameters derived by individual methods in the SSPP are compared with the
results of high-resolution spectroscopic analysis in this chapter. In Chapter 4, the
membership selection for two open clusters (M 67 and N GC 2420) and three globular
clusters (M 15, M 13, and M 2) are presented, and the stellar parameters estimated
from the SSPP are validated with the selected likely members of the clusters. Chap-
ter 5 addresses a method for estimating [a / Fe] for SDSS/SEGUE stars, and validates
the a—abundance determination by making comparisons with the ELODIE spectral

library. The sample selection and the computation of the orbital parameters are

also described. The [a/ Fe] patterns Of Galactic halo stars, after dividing the stars
into various sub-samples by several cuts (such as the rotational velocity, V¢, around
the Galactic center, the metallicity, the maximum distance, Zmax, from the Galactic
plane, and the apo—Galactic distance, Rape) are discussed. Finally, conclusions are
provided in Chapter 6. Note that throughout the thesis, the term [a / Fe] is inter-
changeable with the a-abundance (e.g., high (low)-a is regarded as high (low) value
of [a/Fe]).

 

CHAPTER 2:

SLOAN EXTENSION FOR GALAOTIO
UNDERSTANDING AND
EXPLORATION

 

The Sloan Extension for Galactic Understanding and Exploration (SEGUE) is one Of
three surveys that are being executed as part of the current extension of the Sloan
Digital Sky Survey (SDSS-II), which comprises the sub-surveys LEGACY, SUPER-
NOVA SURVEY, and SEGUE. LEGACY is a continuation of SDSS-I, in order to
complete (in the northern Galactic cap) the imaging and spectroscopy which were
not Obtained due to weather and mechanical problems. SDSS—I (York et al. 2000)
was designed to obtain ﬁve-color photometry over a quarter of the entire sky, and
medium-resolution spectroscopy of 106 galaxies, 100,000 quasars, and several tens Of
thousands of stars, over the course of ﬁve years. SUPERNOVA SURVEY (Frieman
et al. 2008) searches for supernovae in the redshift range 0.05 < 2 <0.35 by repeated
scans of 300 deg2 over an equatorial region.

The SEGUE program is designed, in part, to Obtain ugrz'z imaging of some 3500
square degrees of sky outside of the original SDSS-I footprint (Fukugita et al. 1996;
Gunn et al. 1998, 2006; York et al. 2000; Stoughton et al. 2002; Abazajian et al.
2003, 2004, 2005; Pier et al. 2003; Adelman—McCarthy et al. 2006, 2007, 2008). The
regions of sky targeted are primarily at lower Galactic latitudes (lbl < 35°), in order
to better sample the disk/ halo interface of the Milky Way. As of Data Release 6 (DR-
6, Adelman-McCarthy et al. 2008), about 85% of the planned additional imaging has

already been completed. SEGUE is also obtaining R 2 2000 spectroscopy, over the
wavelength range 3800—9200 A, for some 250,000 stars in 200 selected areas over the
Sky available from Apache Point, New Mexico. The spectroscopic candidates are se-
lected on the basis of ugrz’z photometry to populate 14 target categories (see Table
2 in Adelman—McCarthy et al. 2008 for the target selection algorithms employed),
chosen to explore the nature of the Galactic stellar populations at distances from 0.5
kpc to over 100 kpc from the Sun. Spectroscopic observations have been obtained for
roughly 75% of the planned targets thus far, a total of about 190,000 spectra. The
SEGUE data clearly require automated analysis tools in order to eﬂiciently extract
the maximum amount of useful astrophysical information for the targeted stars, in
particular their stellar atmospheric parameters, over wide ranges of effective temper-
ature (T83), surface gravity (log 9), and metallicity ([Fe/H]).

The photometric data of SDSS-I and SEGUE are collected on moonless and cloud-
less nights of good seeing in ﬁve broad bands (u, g,r,z', z) with central wavelengths
3551, 4686, 6166, 7480, and 8932A (Fukugita et al. 1996), respectively, using an
imaging array of 30 (6 x 5) 2048 x 2048 Tektronix CCDs (Gunn et al. 1998). The
pixel size is 24 pm, corresponding to 0.396” on the sky. A series of software pro-
cedures, collectively known as the SDSS PHOTO pipeline (Lupton et al. 2001),
processes and reduces the scanned images shortly after data are obtained. As part
of these procedures, the instrumental ﬂuxes and astrometric positions (Pier et al.
2003), as well as a determination of whether an object is likely to be stellar (i.e., a
point source), or not (an extended source) are obtained. Afterwards, the photometric
data are further calibrated by matching to brighter known standards observed with
a smaller calibration telescope on Apache Point (Hogg et al. 2001; Smith et al. 2002;
Tucker et al. 2006). The processed photometric data have been shown to exhibit 2%
relative and absolute errors in g, r, and 2', and 3%—5% errors in u and z for all stellar

objects brighter than g = 20 (Stoughton et al. 2002; Abazajian et a1. 2004, 2005;

10

Ivezié et al. 2004).

After gathering detailed information on objects from the photometric data, sub—
sets of them are targeted during SEGUE for spectroscopy. A pair of plug-plates
(referred to as the “bright” and “faint” plates) are obtained over the 3° ﬁeld of the
ARC 2.5m. A total of 640 optical ﬁbers are employed to obtain R = 2000 spectra
for approximately 600 program objects for each plug-plate (the remaining ﬁbers are
used for spectrophotometric and reddening calibration objects, and observations of
the night sky). The exposure time depends on the observation conditions. For a
bright plate, exposures are set to achieve a total (S/N)2 > 15 / 1 from the two blue-
side CCDS on the SDSS spectrographs; the exposure for a faint plate is set such that
a total (S/N)2 > 50/1 for all four (red and blue CCDS) on the SDSS spectrographs is
achieved. In order to identify and remove cosmic ray hits, each plug—plate must have
at least three exposures; the integration time for any single exposure is not longer
than 30 minutes. For the purposes of targeting objects on these plug-plates, the
boundary between the bright and faint plates is set at 7' ~ 18.0. The data thus ob-
tained are processed through the SDSS spectroscopic pipeline software (SPECTRO2D
and SPECTROlD), which produces wavelength and ﬂux-calibrated spectra, and also
obtains estimates of radial velocities and line indices (Stoughton et al. 2002).

In the following, the colors (u — g, g — r, r — i, z’ — z, and B — V) and magnitudes
(u, g, r, i, z, B, and V) without subscript “0” are understood to be de-reddened
and corrected for absorption (using the dust maps of Schlegel et al. 1998), unless

stated speciﬁcally otherwise.

11

 

CHAPTER 3:
THE SEGUE STELLAR PARAMETER
PIPELINE (SSPP)

 

3.1 PHILOSOPHY

Numerous methods have been developed in the past in order to extract atmospheric-
parameter estimates from medium—resolution stellar spectra in a fast, efﬁcient, and
automated fashion. These approaches include techniques for ﬁnding the minimum
distance (parameterized in various ways) between observed spectra and grids of syn-
thetic spectra (e.g., Allende Prieto et al. 2006), non-linear regression models (e.g., Re
Fiorentin et al. 2007, and references therein), correlations between broadband colors
and the strength of prominent metallic lines, such as the Ca 11 K line (Beers et al.
1999), auto-correlation analysis of a stellar spectrum (Beers et a1. 1999, and refer-
ences therein), obtaining ﬁts of Spectral lines (or summed line indices) as a function
of broadband colors (Wilhelm et a1. 1999), or the behavior of the Ca 11 triplet lines
as a function of broadband color (Cenarro et al. 2001a, 2001b). However, each of
these approaches exhibits optimal behavior over restricted temperature and metallic-
ity ranges; outside of these regions they are often un-calibrated, suffer from saturation
of the metallic lines used in their estimates at high metallicity or low temperatures,
or lose efﬁcacy due to the weakening of metallic species at low metallicity or high
temperatures. The methods that make use of speciﬁc spectral features are suscep—

tible to other problems, e.g., the presence Of emission in the core of the Ca II K

12

line for chromospherically active stars, or poor telluric line subtraction in the region
of the Ca 11 triplet. Because SDSS stellar spectra cover most of the entire optical
wavelength range, one can apply several approaches, using different wavelength re-
gions, in order to glean optimal information on stellar parameters. The combination
of multiple techniques results in estimates of stellar parameters that are more robust
over a much wider range of Teff, log 9, and [Fe / H] than those that might be produced
by individual methods. The SSPP implements this “multi-method” philosophy.

Table 3.1: Parameter Sensitivities to Radial Velocity Errorsb

 

 

RV 50 (km 8*) 100 (km 3*) 150 (km 3*) 200 (km S“)

NameMethod<A> 0‘ <A> a <A> a <A> a

 

 

Teff
Ad Adop —0.6 18.8 -22.0 29.5 ——48.3 44.4 -—83.8 55.0
T1 1:113 21.0 31.3 46.6 64.8 85.41047 113.7149.0
T2 1:24 1.4 8.8 —2.4 16.5 —4.7 30.6 —19.7 53.5
T3 WBG 0.0 12.4 —l.5 6.1 ~52.5 70.1 ~81.0106.0
T4 ANNSR —17.8 72.1 -131.6 100.2 —281.4 153.1 —458.3 232.9
T5 ANNRR -8.2 15.6 —45.2 39.4 —99.8 67.2 —164.0 95.4
T6 NGS1 7.4 16.9 19.2 35.3 38.7 61.8 55.3 99.1
T7 HA24 —4.6 10.9 —18.9 19.1 —41.1 29.0 -72.0 41.1
T8 HD24 3.8 5.8 2.8 8.1 —0.9 10.1 —5.6 14.8
T9 TK
T10 TG
T11 TI

logg

Ad Adop 0.037 0.052 0.071 0.091 0.077 0.135 0.008 0.207
G1 1:113 0.034 0.099 0.066 0.148 0.127 0.224 0.122 0.379
G2 k24 --0.019 0.050 —0.035 0.093 —0.025 0.162 —0.027 0.251

 

13

Table 3.1: Parameter Sensitivities to Radial Velocity Errors (continued)

 

 

RV 50 (km S“) 100 (km 3*) 150 (km S“) 200 (km 3'1)

NameMethod<A> a <A> 0 <A> a <A> a

 

G3 WBG —0.011 0.039 —0.044 0.198 —0.076 0.413 —0.081 0.620
G4 ANNSR 0.077 0.119 0.151 0.126 —0.236 0.463 —0.317 0.624
G5 ANNRR 0.092 0.068 0.116 0.139 0.046 0.229 —0.103 0.356
G6 NGSl —0.034 0.054 —0.079 0.145 —0.156 0.293 —0.223 0.464
G7 NGS2 0.012 0.117 —0.001 0.259 —0.009 0.471 —0.131 0.632
G8 CaI1 0.057 0.118 0.143 0.173 0.241 0.249 0.331 0.331
G9 CaI2 —0.042 0.036 —0.116 0.091 —0.233 0.185 —0.385 0.294
G10 MgH —0.001 0.011 —0.015 0.030 —0.037 0.057 —0.060 0.095

 

[Fe/H]
Ad Adop —0.019 0.019 -0.096 0.047 —0.203 0.074 —0.353 0.116
M1 1:113 —0.012 0.034 —0.085 0.057 —0.209 0.090 —0.384 0.118
M2 1:24 0.002 0.024 —0.057 0.046 -0.192 0.092 -0.404 0.145
M3 1436 -—0.046 0.057 —0.122 0.147 -0.256 0.411 —0.734 0.559
M4 ANNSR —0.082 0.090 —0.171 0.161 —0.251 0.488 -0.526 0.524
MS ANNRR —0.027 0.027 -0.163 0.095 —0.364 0.196 —0.574 0.319
M6 NGSl —0.008 0.021 —0.056 0.038 —0.l57 0.061 —0.292 0.083
M7 NGS2 —0.044 0.033 —0.113 0.074 —0.261 0.136 —0.414 0.219
M8 CaKIIl 0.010 0.054 0.029 0.082 0.023 0.144 —0.007 0.238
MQ CaKII2 0.000 0.000 0.014 0.034 0.000 0.095 0.003 0.051
M10 CaKII3 0.001 0.020 0.001 0.032 0.002 0.029 0.006 0.040
M11 ACF 0.005 0.013 0.012 0.021 0.021 0.025 0.030 0.026
M12 CaIIT —0.000 0.000 0.013 0.071 0.022 0.088 0.062 0.120

 

 

bSee Chapter 3.4 and 3.5 for descriptions of each method. < A > is the average of
the differences between parameters obtained with, and without, the velocity shift; a is the
standard deviation of the differences. The T9, T10, and T11 estimates do not change with
velocity errors because they are computed from the g — 1' color.

14

3.2 DETERMINATION OF RADIAL VELOCITIES

3.2.1 THE ADOPTED RADIAL VELOCITY USED BY THE SSPP

The sprest ﬁts ﬁle, which is generated from the SDSS spectroscopic reduction
pipeline (Stoughton et al. 2002), provides two estimated radial velocities. One is an
absorption (or emission)-line redshift computed from a cross-correlation procedure
using templates that were obtained from SDSS commissioning spectra (Stoughton
et al. 2002) — the spectro 1d redshifts. Another estimate comes from performing a
“best-match” procedure that compares the observed spectra with externally measured
templates (in this case, the ELODIE library of high-resolution spectra, as described
by Prugniel & Soubiran 2001), degraded to match the resolving power of SDSS spectra
(Aldeman-McCarthy et a1. 2008).

Previous experience with the analysis of SDSS stellar spectra suggested that the
radial velocity estimated from the ELODIE template matches is often the best avail-
able estimate, in the sense that it is the most repeatable, based on spectra of “quality
assurance” stars with multiple determinations. In addition, the spectrold redshifts
exhibit larger systematic offsets, as high as 12 km s"1 (Aldeman McCarthy et al.
2008). Hence, as a ﬁrst choice, we adopt the radial velocity from the ELODIE tem-
plate matches and set the radial velocity indicator ﬂag to ‘ELRV’. However, there
are some cases where the velocities from the ELODIE template matches are not re-
ported, because an adequate match to the (somewhat incomplete) ELODIE library
could not be made with conﬁdence. In such cases, we check the spectro 1d redshifts;

if a velocity is reported by this routine, we adopt it, and the radial velocity ﬂag is set
to ‘BSRV’.

15

Table 3.2: Summary of High-Resolution Observations for SDSS and SEGUE Stars

 

 

Telescope Instrument Resolving Wavelength Number

power coverage (A) of stars

 

Keck - I HIRES 45000 3800—10000 11

Keck - 11 E81 6000 3800— 10000 25
HET HRS 15000 4400 —8000 110
Subaru HDS 45000 3000—8000 9

 

If neither of the above two velocities are reported (which happens only rarely, and
mainly for quite low S/N (< 5/ 1) spectra, then we obtain an independent estimate
of the radial velocity based on our own IDL routines. The calculation of this radial
velocity estimate is carried out by determining wavelength shifts for several strong
absorption line features (Ca 11 K, Ca 11 H, H6, Ca 1, H7, H6, Na 1, Ha, and the Ca 11
triplet). After ignoring any likely spurious values (calculated velocity above +500 km
3’1 or below —500 km s—l) from the individual lines, we obtain a 3 a-clipped average
of the remaining radial velocities. If this computed average falls between —500 km
5‘1 and +500 km s—l, we take the calculated radial velocity as the adopted radial
velocity, and set the radial velocity ﬂag to ‘CALRV’. We have noticed that certain
types of stars, in particular cool stars with large carbon enhancements, present a
challenge for the radial velocity estimates adopted by the SSPP. We have developed
new carbon-enhanced templates, based on synthetic spectra, which appear to return
improved estimates. These will be implemented in the next version of the SDSS
spectroscopic reduction pipeline, which we anticipate applying for the ﬁnal SDSS-II
data release, DR—7.

It should be noted that many of the techniques used for atmospheric parameter

estimation in the SSPP work well even when the velocity determination for a given star

16

 

 

   
    

 

 

 

 

 

 

 

 

 

7O YW I ﬁ1#:1125 400 12 W W 7

60' mean=-6.13' A . E

50- std=4.7l E 200 , 50;

40- d‘, g

z e 0 « > o ' °
30- 8 1 °.‘ . 9173555.?» “"'" l
>m 200 1 °‘ 1

20' a: ‘ $60: ‘

10- >‘” i

0.. .. .;.. ”mince“ .- °‘ . A “a ‘
-40 -20 0 20 40 —400 -200 0 200 400 0.0 0.2 0.4 0.6 0.8 1.0

Figure 3.1 Comparison plots of the radial velocity adopted by the SSPP with that
measured by high-resolution analyses (HR). An offset of —6.13 km 3'1, with a = 4.71
km s‘l, is noted from the Gaussian ﬁt to the residuals. This offset appears constant
with g — r, as shown in the right-hand panel.

has errors of up to 100 km s‘1 or more. Table 3.1, which summarizes an experiment on
how the derived atmospheric parameters change as a result of systematically shifting
the radial velocity estimate by 50, 100, 150, and 200 km S_1 relative to the original
value, conﬁrms this. We made use of 125 SDSS-I/SEGUE high-resolution calibration
stars (obtained with the Hobby-Eberly Telescopy; HET, see Allende Prieto et al. 2008;
hereafter Paper 111), all of which have well-determined stellar parameters, thanks to
their high quality (S/N > 50/ 1). See Chapter 3.4 and 3.5 for the naming convention
and the description of each parameter estimation method. As can be seen in the
table, most of the methods suffer zero-point shifts in log 9 and [Fe/ H] less than 0.1
dex, with a scatter of below 0.2 dex, even for radial velocity shifts as high as 100
km s‘l. This level of scatter is on the order of the typical uncertainty (~ 0.2 to 0.3
dex) for these parameters obtained from our analysis of medium-resolution spectra
in SDSS. The reason for the lack of signiﬁcant scatter is that many of our methods
compare with synthetic spectra over wide spectral ranges, rather than by a line-by-line
comparison to weak individual lines, to determine the stellar parameters. Even for
those techniques that employ line-index approaches, the SSPP employs relatively wide

bandwidths, which mitigates against large variations due to radial velocity errors.

17

 

 

Thus, small shifts in a spectrum due to a poor radial velocity determination will not
strongly inﬂuence our estimates of the stellar parameters.

If none of the above methods yields an acceptable estimate of radial velocity, or if
the reported velocity is apparently spurious (greater than 1000 km 3‘1 or less than
—1000 km s‘l), we simply ignore the spectrum of the star in our subsequent analysis,

and set the radial velocity ﬂag to ‘N ORV’.

3.2.2 CHECKS ON RADIAL VELOCITIES — ZERO POINTS AND SCAT-

TER

In order to check on the accuracy of the radial velocities adopted by the SSPP, we
compare with over 150 high-resolution spectra of SDSS-I/SEGUE stars that have been
obtained in order to calibrate and validate the stellar atmospheric parameters. Table
3.2 summarizes the available high-resolution data. We plan to continue enlarging this
sample of validation/ calibration stars in the near future.

The high-resolution spectra have been reduced and analyzed independently by two
(GA. and TS.) of the authors in Paper 111. A detailed description of the analyses can
be found in Paper 111. During the course of deriving the stellar parameter estimates
from the high-resolution spectra, the radial velocities of stars are ﬁrst measured. Note
that C.A. only considered the HET spectra, while T.S. considered all available spectra.
Thus, only the HET stars have radial velocities obtained by both analysts; for these
stars we take an average of their independent determinations, which typically differ
by no more than 1—2 km 3*. A more detailed discussion is presented in Paper 111.

Here we focus on the systematic errors of the adopted radial velocities. After
rejecting problematic (e.g., S /N < 20 / 1) high-resolution spectra, or stars that appear
to be spectroscopic binaries at high spectral resolution), 125 stars remain to compare
with the adopted radial velocity results from the SSPP. Figure 3.1 shows the results

of these comparisons. A consistent Offset of —6.13 km s"1 (with a standard deviation

18

of 4.71 km s‘l) is computed from a Gaussian ﬁt to the residuals; this offset appears
constant over the color range 0.1 S g — 7‘ S 0.9. An additional comparison with
the radial-velocity distribution of selected member stars in the Galactic globular and
open clusters reveals similar offsets (—8.68 km s‘1 for M 15, —7.03 km s‘1 for M
13, —7.47 km s"1 for M 67, and -8.26 km 3’1 for NGC 2420; see Lee et al. 2008
for the membership selection criteria; hereafter Paper 11). The origin of this velocity
offset is as yet unclear; it may stem from the use of different algorithms in the ﬁts
to arc and sky lines (Adelman-McCarthy et al. 2008). It should be noted that
an offset of +7.3 km s‘1 is added to all DR—6 (Adelman—McCarthy et al. 2008)
stellar radial velocities. This offset was computed by averaging the offsets of —6.8
km s‘1 (M 15) and —8.6 km s"1 (M 13), and a —6.6 km 3‘1 offset for individual
ﬁeld stars, all Obtained from preliminary results of an analysis of the clusters and the
high-resolution spectroscopic analysis of SDSS-I/SEGUE stars that were carried out
prior to DR-6 (Adelman-McCarthy et al. 2008). In Paper 111, this offset is taken
into account in the comparison of the radial velocity determinations. From the new
high-resolution Spectroscopic analysis of SDSS-I/SEGUE stars (Paper 111) and the
analysis of member stars of the clusters (Paper 11), an average offset is —7.51 km s’l.
Therefore, in future data releases (e.g., DR—7), this very minor difference will likely
be reﬂected in all adopted stellar radial velocities. However, in order to account for
its presence and to be consistent with the DR—6 database, we apply an empirical +7.3
km 3‘1 shift to each adopted radial velocity obtained by the SSPP. After application
of this velocity shift, the zero—point uncertainties in the corrected radial velocities
determined by the SSPP (and the SDSS spectroscopic reduction pipeline it depends
on) should be close to zero, with a random scatter on the order of 5 km s—1 or less.
Note that the scatter in the determination of radial velocities, based on the average
displacements of the “quality assurance” stars with multiple measurements varies

from 5.0 km S_1 to 9.0 km s-l, depending on spectral type, and exhibits a scatter of

19

2 km s-1 between Observations Obtained with the “faint” and “bright” spectroscopic

plug-plates (Adelman-McCarthy et al. 2008).

3.3 CALCULATION OF LINE INDICES

The initial step in calculation of line indices for SDSS spectra is to transform the
wavelength scale of the original SDSS spectrum over to an air-based (rather than
vacuum-based) wavelength scale, and to linearly rebin the spectrum to 1 A bins in
the blue (3800—6000 A), and 1.5 A bins in the red (6000—9000 A). This slightly larger
bin size is due to the degradation of the resolution in the red regions of the spectra.
Then, based on the adopted radial velocity described above, the wavelength scale is
Shifted to a zero velocity rest frame.

The SSPP measures line indices of 82 atomic and molecular lines. Line-index cal-
culations are performed in two modes; one uses a global continuum ﬁt over the entire
wavelength range (3850—9000 A), while the other obtains local continuum estimates
around the line bands of interest. The choice between which mode is used depends on
the line depth and width of the feature under consideration. Local continua are em-
ployed for the determinations of stellar atmospheric parameters based on techniques
that depend on individual line indices. Other techniques, such as the neural network,
spectral matching, and auto-correlation methods, require wider wavelength ranges
to be considered; for these the global continuum (or their own internal continuum
routine) is used. We make use of the errors in the ﬂuxes reported by the SDSS spec-
troscopic reduction pipeline to measure the uncertainty in the line indices. Details of
the procedures used to obtain the continuum ﬁts and line index measures (and their

errors) are discussed below.

20

 

Flux

 

spSpec-52932—1492-535. Tm: 5515, logg=2.21, [Fe/H]=-2.52
20 l l l 1 ML V l

llllllllJlllllllll

8
lllllllllllllllllll

 

 

llll

 
  

  

ungui—
119:) —

0.6

Normalized ﬂux

0.4

0.2

O
m
lllllllllllllllllllllllT

 

0.0 l l I I I I I l l I I l I I
4000 5000 6000 7000 8000 9000
Wavelength (Angstrom)

Figure 3.2 An example of a ﬁtted global continuum for a metal-poor star. The derived
parameters from the SSPP for this star are shown in the upper panel. The red line in
the upper panel is the ﬁtted continuum over the 3850—9000 A wavelength range; the
black line is the observed spectrum. The bottom panel shows the normalized ﬂux,
with strong metal and Balmer features labeled.

3.3.1 CONTINUUM FIT TECHNIQUES
A. GLOBAL CONTINUUM FIT

Determination of the appropriate continuum for a given spectrum is a delicate task,
even more so when it must be automated, and obtained for stars having wide ranges
of effective temperatures, as is the case for the present application.

In order to obtain a global continuum ﬁt, the SSPP ﬁrst divides the wavelength

21

range into two pieces: blue (3850—5800 A) and red (5800—9000 A). After removing
the strong Balmer lines present in most spectra, the blue side is iteratively ﬁt to
a ninth-order polynomial, rejecting points that are more than 3 a above the ﬁtted
function. The same procedure is applied to the red side, but using a fourth-order
polynomial. Then, the two ﬁtted pseudo-continua are spliced together, and the joined
continuum is again ﬁtted to a ninth-order polynomial. This is the ﬁnal global pseudo-
continuum used to calculate line indices.

The reason for dividing a spectrum into two regions is to avoid the continuum
being placed at too high a level around the Ca 11 Triplet, due to the poor sky-line
subtraction in this region in some cases. Fitting the entire range of a spectrum
requires a high-order polynomial. As a result, the continuum on the red side of a
spectrum will be artiﬁcially boosted due to the presence of poorly subtracted sky
lines or noise spikes, if any. Use of a lower order polynomial ﬁt to the red side avoids
this potential problem.

The upper panel of Figure 3.2 shows an example of a ﬁtted global continuum for
a metal-poor giant, obtained by application of the procedure described above. The
atmospheric parameters determined by the SSPP are also listed on the plot. The
bottom panel is the normalized spectrum, obtained by division of the spectrum by
the global continuum ﬁt. Strong lines that play important roles in estimating the
atmospheric parameters are labeled. It can be seen that a reasonable continuum
estimate is obtained even in the region of the Ca 11 triplet, where residuals from poor

sky subtraction can sometimes be problematic.

B. LOCAL CONTINUUM FIT

To compute a local continuum over the line band of interest, we ﬁrst calculate a 5 0-
clipped average of the observed ﬂuxes over the (blue and red) sidebands corresponding

to each feature, as listed in Table A.1. Using these two points, a linear interpolation is

22

carried out over the region between the end point of the blue Sideband and the starting
point of the red Sideband. This linearly interpolated ﬂux is then connected piecewise
with the ﬂuxes of the red and blue sidebands, and a robust line ﬁt is performed over
the entire region of the blue Sideband + line band + red Sideband to derive the ﬁnal

local continuum estimate.

3.3.2 MEASUREMENT OF LINE INDICES

Line indices (or equivalent widths) are calculated by integrating a continuum-normalized
ﬂux over the speciﬁed wavelength regions of each line band. Two different measure-
ments of line indices, obtained from the two different continuum methods described
above, are reported, even though the line-index based methods for stellar parame-
ter estimates only make use of the local cOntinuum-based indices. In order to avoid
spurious values for the derived indices, if a given index measurement is greater than
100 A, or is negative, we set the reported value to —9.999. No parameter estimates
based on that particular line index are used.

Table A.1 lists the complete set of line indices made use of by the SSPP. Note
that, unlike the case for most of the features in this table, the line indices listed in
rows 74 (T101), 75 (TiO2), 76 (TiOB), 77 (TiO4), 78 (TiO5), 79 (CaHl), 80 (CaH2),
81 (CaH3), 82 (CaOH), and 83 (Ha), are calculated following the prescription given
by the “Hammer” program (Covey et al. 2007). The line index for Ca I at 4227 A,
and the Mg Ib and MgH features around 5170 A, are computed following Morrison et
al. (2003), so that they might be used to estimate log 9, as described in Chapter 3.4.

We follow the Cayrel (1988) procedure to compute an error for each line index
measurement. The uncertainty (EWermr) in the index or measured equivalent width

is:

1.6 x (resolution x pixel size)”2

EWerror = SNR a

 

23

 

where SN R is the signal-to—noise ratio in the local region of the spectrum, the
resolution is taken to be ~ 2.5 A, and the pixel size is set to 1A for the blue re-
gion (3800—6000 A), and 1.5 A for the red region (6000—9000 A), respectively. The
noise spectrum provided by the SDSS spectroscopic reduction procedure is used to

compute the local SN R.

3.4 METHODOLOGY

The SSPP employs a number of methods for estimation of effective temperature,
surface gravity, and metallicity, based on SDSS spectroscopy and photometry. In this
section the methods used by the SSPP are summarized. Since many of the methods
implemented in the SSPP are already described by previously published papers, we
will address those techniques brieﬂy, and refer the reader to individual papers for
detailed descriptions. The methods that are introduced here for the ﬁrst time are
explained in more detail. Note that some approaches derive all three atmospheric
parameters simultaneously, while others are speciﬁc to an individual parameter. A
given method is usually Optimal over speCiﬁc ranges of color, g—r, and S / N . Table 3.3
lists the ranges we have adopted in these observables for the SSPP. Details regarding

the choice of the S/N cuts are presented in Chapter 3.6.

3.4.1 SPECTRAL FITTING WITH THE 1:24 AND 1:113 GRIDS

These two methods are based on the identiﬁcation of parameters for a model atmo-
sphere that best matches the observed ﬂuxes in a selected wavelength interval, as
described in detail by Allende Prieto et al. (2006). Classical LTE line-blanketed
model atmospheres are used to compute a discrete grid of ﬂuxes; interpolation al-

lows sub-grid resolution. The search is performed using the Nelder-Mead algorithm

(Nelder & Mead 1965).

24

 

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26

The 1:24 grid described by Allende Prieto et a1. (2006) is used by the SSPP. It in-
cludes a predicted broadband color index g—r, as well as normalized spectral ﬂuxes in
the region 4400—5500 A, at a resolving power of R = 1000. Kurucz (1993) model at-
mospheres and simpliﬁed continuum opacities are used to calculate synthetic spectra.
The synthetic broadband photometry was derived from the spectral energy distribu-
tions provided by Kurucz (1993), using the passbands for point sources determined
by Strauss & Gunn (2001), and an assumed (average) airmass of 1.3.

In addition to the k24- grid, a second grid, referred to as 1:113, is implemented
in the SSPP. This second grid covers the same spectral window as the 1:24, but no
photometry is considered. The use of only the normalized spectra de-couples the
results based on this grid from reddening and photometric errors, although valuable
information, mainly on the effective temperature, is sacriﬁced.

There are several other differences between the k24- and 1:113 grids. The new
grid (1:113) includes molecular line opacities, with the most relevant molecules in the
range of interest being the CH G-band near 4300 A, as well as the MgH band. In
addition, the k113 grid takes advantage of a novel concept that allows for a signiﬁcant
increase in the speed of the calculation of model ﬂuxes. The relevant opacities are not
calculated for all depths in all models, but instead are obtained on a temperature and
density grid, and later interpolated to the exact points in any given model atmosphere
(Koesterke et al. 2008). The opacity grid includes 4 points per decade in density and
steps of 125 K in temperature. With these choices, linear interpolation leads to errors
in the normalized ﬂuxes smaller than 1%.

Allende Prieto et al. (2006) made use of several libraries of observed spectra and
atmospheric parameters to study systematic and random errors obtained from the 1:24
analysis. Even at inﬁnite signal-to—noise ratios, random errors appear signiﬁcantly
larger than systematic errors, and amount to 3% in T eff, 0.3 dex in log 9, and 0.2

dex in [Fe/ H] This is most likely the result of using over-simpliﬁed model ﬂuxes

27

with a solar-scaled abundance pattern (including an enhancement of the (1 elements
at low iron abundance), which is too limited to account for the chemical spread in
real stars. The new ki13 grid offers a signiﬁcant improvement in random errors,
which at high signal-to—noise amount to 2% in T63, 0.2 dex in log g, and 0.1 dex
in [Fe/ H], but a less robust behavior (due to the lack of color information) at low
signal-to-noise ratios. Small systematic offsets in 1:113 detected from the analysis of
the spectra in the ELODIE library (Prugniel & Soubiran 2001) are corrected using
linear transformations.

As discussed in Allende Prieto et al. (2006), the 1:24 approach performs best in
the color range of roughly 0.0 S g — r S 0.8; this range is also applied to the 1:113
grid. When it is run, the SSPP restricts the adopted parameters from these methods
to fall in this color range. The SSPP refers to the T83, log 9, and [Fe/ H] estimated
with the 1:113 grid as T1, G1, and M1, respectively, while the parameters estimated

from the 1:24 grid are referred to as T2, G2, and M2, respectively.

3.4.2 PARAMETERS OBTAINED FROM THE WILHELM ET AL. (1999)

PROCEDURES : WBG

This method, which is referred to as WBG in this thesis, is based on the routines
described by Wilhelm, Beers, & Gray (1999), to which we refer the interested reader.
Extensions of this method, as used in the SSPP, are described below.

The procedures implemented in the SSPP are optimized for two separate temper-
ature ranges one for the warmer stars (9 — r S 0.25), and one for the cooler stars,
with redder colors than this limit. The stellar parameter determinations make use
of comparisons to theoretical ugr colors and line parameters from synthetic spec-
tra, both generated from ATLASQ model atmospheres (Kurucz 1993). The synthetic
spectra used in these procedures were generated using the spectral synthesis routine

SPECTRUM (Gray & Corbally 1994).

28

For the hotter stars, the Balmer lines of the observed normalized spectra are ﬁt
with a Voigt proﬁle to determine the Balmer—line equivalent widths and the D02 (the
line width at 20% below the local pseudo-continuum level) widths for H6, H7, and
Hﬂ. The combination of Balmer-line equivalent widths, D02, and u — g and g — 1"
colors are used to establish initial Teff and log 9 estimates, computed from functional
trends in the theoretical model parameters. For stars cooler than Teﬁ‘ ~ 8000 K, the
surface gravity is mainly determined by the u - 9 color. For hotter stars the surface
gravity is primarily determined by the D02 parameter. A metallicity estimate is
determined through the use of a combination of the equivalent width of the Ca 11 K
line and a comparison to synthetic spectral regions that contain other (much weaker)
- metallic lines. Once an initial abundance is established, the procedure is iterated to
convergence in all three stellar parameters.

For the cooler stars, only the g — 7‘ color is used to establish an initial estimate
of Tag. For these stars, log 9 is determined from the u — g color for stars as cool
as Teff = 5750 K. For stars cooler than this limit, the strength of MgH is compared
to synthetic spectra of similar Teff and [Fe/ H] through the use of a band-strength
indicator. The metal abundance is determined by the combination of the Ca II K
line strength and a minimum X2 comparison to metallic-line regions in the spectra.
The procedure is then iterated to convergence.

For stars with S/N 2 10/ 1, the derived errors for the NBC approach are on the
order of 0(Teﬁ) = 225 K, 0(log g) = 0.25 dex, and a([Fe/H]) = 0.3 dex. The color
range of g — 7‘ over which this approach is used for the SSPP is —0.3 S g — r S 0.8.
The effective temperature, surface gravity, and [Fe / H] estimated from this technique

are referred to as T3, G3, and M3, respectively.

29

3.4.3 THE NEURAL NETWORK APPROACHES : ANNRR AND ANNSR

The SSPP implements ﬂexible methods of regression that provide a global non-linear
mapping between a set of inputs (the stellar Spectrum x,) and a set of outputs (the
stellar atmospheric parameters, 8 = {Teff, log 9, [Fe/H]}). These methods have been
described in detail by Re Fiorentin et al. (2007), to which the interested reader is
referred for more details.

For the present application, it should be noted that we have chosen not to in-
clude input photometry, although this certainly could be added if desired. Moreover,
thanks to improved stellar models and data calibrations the models have been further
developed in order to investigate the impact of noise and to extend the application of
neural networks for low signal-to—noise spectra (P. Re Fiorentin et al., in preparation).

The procedures implemented in the SSPP use an initial Principal Component
Analysis compression of the data, and are based on two different approaches - train-
ing the model on real (RR, e.g., SDSS spectra) or synthetic (SR) spectra to obtain
atmospheric parameter estimates for the observed spectra. The method for training
the model on the SDSS/SEGUE spectra is called ANNRR, while that for the synthetic

Spectra is referred to as ANNSR.

A. THE ANNRR APPROACH

We build the models based on a set of 61,069 selected stars from the current SEGUE
plug-plates, in directions of low reddening, for which have had atmospheric parameters
estimated by a preliminary version of the SSPP.

The RR regression model (ANNRR) adopts a sample that is randomly split into
two equal-sized sets, one for training and one for evaluation. Although not optimal,
as one would ideally like to use a completely independent basis set for the training,
this approach automates and — more importantly — generalizes the basis parameter-

izer. Indeed, the basis parameterizer may even comprise multiple algorithms, perhaps

30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 T 12 I 12:
A 4 A 10* A 10:
g 3 g 8E g 8: ‘
as 2 es 65 es 6*
z z 4f z 4:”
l 2. 2r 1
0 . 0’ 1-1 0: 1 ‘
-0.04 -0.02 0.00 0.02 0.04 -1.0 -O.5 0.0 0.5 1.0 -l.O -0.5 0.0 0.5 1.0
Delta log T eff Delta log g Delta [Fe/H]
4. ’ v v v v I v ’ v v v
0 5 ' 0-
39 . a .
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,L3.8 - a, :’ ‘ .
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3.6 3.7 3.8 3.9 4.0 1 2 3 4 5 -3 -2 -l 0
log T eff_SSPP log g_SSPP [Fe/H]_SSPP

Figure 3.3 Atmospheric parameter estimation with ANNRR. We compare log Teff’ log
9, and [Fe/ H] estimates from ANNRR with those from the SSPP. There are 30,000 stars
compared for the ANNRR approach. Perfect correlation is shown with the solid red
lines. The histograms of the discrepancies between the ANNRR approaches and the
SSPP are shown in the ﬁrst and third sets of panels, with a Gaussian ﬁt shown as a
red curve.

operating over different parameter ranges or used in a voting system to estimate at—
mospheric parameters. This is true in the present case, where the basis parameterizer
comes from a preliminary version of the SSPP.

Figure 3.3 compares the stellar parameters obtained from the ANNRR approach with
those from an earlier version of the SSPP adopted parameters, based on an evaluation
set of some 30,000 SEGUE spectra. Overall we see good consistency, especially for
stars with T63 < 8000 K (log Teﬂ' = 3.90). Above this effective temperature our
models Slightly underestimate log Teff relative to the SSPP adopted values. Most
regression models such as ours are designed to interpolate, rather than extrapolate.

Extrapolation of the model to estimate atmospheric parameters that are not spanned

by the training set is relatively unconstrained. Furthermore, the accuracy of the

31

RR model is limited by the accuracy of the target atmospheric parameters used
in training, as well as their consistency across the parameter Space. In this case,
the SSPP estimates are combinations from several estimation models, each of which
operates only over a limited parameter range. Thus, the transition we see above
8000 K may indicate a temperature region where one of the SSPP sub-models iS
dominating the SSPP estimates; such cases are not well generalized by our model.
From this comparison, we ﬁnd that the accuracies of our predictions (mean absolute
errors) for each parameter are 0(Teﬂ‘) = 60 K, 0(log g) = 0.11 dex, and a([Fe/H]) =
0.07 dex, which are very low. This is partly due to the fact that the ANNRR method
makes use of exactly the same type of data used in the training and application
phases, thus eliminating the issue of discrepancies in the ﬂux calibration or cosmic

variance of the two samples.

B. THE ANNSR APPROACH

Recently, an adequate noise model for SDSS spectra has been developed (see Chapter
3.6 for details). The SR regression model (ANNSR) adopts a sample of thase noise-
added synthetic spectra as the training set. This approach thus directly models the
mapping between synthetic spectra and the atmospheric parameters, independent
of any intermediate estimates. The ANNSR method is optimized to be able to deal
separately with low S/N real spectra (S/N < 35/1, 22,196 stars) and high S/N real
spectra (S/N > 35/ 1, 38,873 stars).

Figure 3.4 compares the atmospheric parameter estimates from the ANNSR with
those from the SSPP for the 61,069 stars in the evaluation set. While the overall
consistency between the two models is reasonably good, we notice discrepancies at
the extreme parameter values, in particular for Teﬂ‘ and log g.

Despite the fact that determinations of gravity and metallicity for low 8' / N spectra

are underestimated, as measured by their mean accuracies with respect to the SSPP

32

 

 

 

 

 

 

 

 

 

 

6 15
A 5 A ‘ A
§ 4- § 1 § 10
z i z z 5' l
0 > . 0
-2 -1 0 1 2 -1.0 -0.5 0.0 0.5 1.0

Delta log g Delta [Fe/H]

“*7-

 

,_

    

    

log g_ANNSR
[Fe/H]_ANNSR

 

3.6 3.7 3.8 3.9 4.0 1 2 3 4 5 -3 —2 —1 0
log T eff_SSPP log g_SSPP [Fe/H]_SSPP

Figure 3.4 Atmospheric parameter estimation with ANNSR. We compare log T eff, log
g, and [Fe/ H] estimates from ANNSR with those from the SSPP. There are 61,069 stars
compared for the ANNSR approach. Perfect correlation is shown with the solid red
lines. The histograms of the discrepancies between the ANNSR approaches and the
SSPP are shown in the ﬁrst and third sets of panels, with a Gaussian ﬁt shown as a
red curve.

predictions, we can obtain estimates of Teﬂ‘ with residuals of ~ 125/ 129 K, log 9
with residuals of 0.21 /0.28 dex, and [Fe/ H] with residuals of 0.14/ 0.23 dex for the
high/ low S /N regimes, respectively. The reliability of the neural network approaches
included in the SSPP is currently limited to S/N 2 10/1.

The advantage of the ANNSR approach is that it is trained directly on synthetic
spectra, dispensing with the need for a basis parameterizer. A very important aspect
of this method is processing the synthetic and real data to appear as similar as
possible; noise acts as a regularizer in the training phase. Inaccurate synthetic spectra
(e.g., poor models or a poor ﬂux calibration) degrade performance and / or give rise to

systematic errors. However, there are inevitably problems with spectral mismatches,

in the sense that the synthetic spectra do not reproduce all of the complexities of the

33

spectra of real stars. The absence of some molecular species in the linelists for the
synthetic spectra may also be contributing to this problem, especially for cooler stars
where they are expected to become more important.

Prior experience with the behavior of the neural network approach on the SDSS-
I/SEGUE data indicated that the ANNRR performs well over a color range —0.3 S
g — r S 1.2, so we restrict its application for the SSPP to this interval. The color
range is restricted to —0.3 S g — r S 0.8 for the ANNSR estimates. The Teff, log
9, and [Fe/ H] obtained from the ANNSR approach are referred to as T4, G4, and
M4, respectively; for the ANNRR approach, they are referred to as T5, G5, and M5,

respectively.

3.4.4 THE X2 MINIMIZATION TECHNIQUE USING THE NGSI AND

NGSQ GRIDS

A. GRIDS OF SYNTHETIC SPECTRA

We have made use of Kurucz’s NEWODF models (Castelli & Kurucz 2003), which
employ solar relative abundances from Grevesse & Sauval (1998), to generate two
sets of grids of synthetic spectra. The model atmospheres assume plane-parallel line—
blanketed model structures in one—dimensional local thermodynamical equilibrium
(LTE), and an enhancement of a-element abundances by +0.4 dex for stars with
[Fe/H] S —1.0 and +0.3, +0.2, and +0.1 for [Fe/H] = —0.75, —0.5, and —0.25,
respectively. These new models include H20 opacities, an improved set of TiO lines,
and no convective overshoot (Castelli, Gratton, & Kurucz 1997).

For production of the synthetic spectra we employed the turbospectrum synthesis
code (Alvarez & Plez 1998), with solar abundances from Asplund, Grevesse & Sauval
(2005), which use the treatment of line broadening described by Barklem & O’Mara
(1998). The sources of atomic lines used by turbospectrum mainly come from the

VALD database (Kupka et al. 1999). Linelists for the molecular species CH, CN, OH,

34

TiO, and CaH are provided by B. Plez (see Plez & Cohen 2005, and Plez, private com-
munication), while the lines of NH, MgH, and the C2 molecules are adopted from the
Kurucz line lists (see http://kurucz.harvard.edu/LINELISTS/LINESMOL/). The
grid of the synthetic spectra has resolution of 0.01A or 0.005 A, and spans from
3500 K S Teﬂ S 10,000 K in steps of 250 K, 0.0 S logg S 5.0 in steps of 0.25
dex, and —4.0 S [Fe/H] S +0.5 in steps of 0.25 dex. The wavelength coverage is
from 3000 A to 10,000 A. The micro-turbulence was assumed to be 2 km s’l. These
synthetic spectra are referred to as the NGS1 grid. After their generation, these syn-
thetic Spectra were degraded to R = 1000, using a Gaussian convolution algorithm,
then sampled into 1.67 A per pixel for application of the NGSl grid spectral matching
technique described below. There are two reasons for the degradation of the spectra
to the lower resolution than that of the SDSS spectra. First, degrading the observed
spectrum allows us to obtain higher S/ N than the original; more reliable estimates of
the parameters can thus be determined. Secondly, this grid is also used for applica-
tion of the SSPP to non-SDSS spectra with lower resolution (1000 S R S 2000; e.g.,
Beers et al. 2007).

A second grid of model atmospheres was constructed from the Kurucz ATLAS9
models (Castelli & Kurucz 2003), which do not employ a-element enhancements for
models with [Fe/ H] S —0.5. The turbospectrum synthesis code was again used to
generate the synthetic spectra. The synthetic spectra have a resolution of 0.1A, and
cover 4000 K S Teff S 8000 K in steps of 250 K, 0.0 S logg S 5.0 in steps of
0.25 dex, and —3.0 S [Fe/H] S +0.5 in steps of 0.25 dex. Ranges in [a/Fe] were
introduced for spectral synthesis, over —0.2 S [a/ Fe] S +0.8, in steps of 0.2 dex for
each value of Teff, log 9, and [Fe/ H] The Spectral range of this grid is 4500—5500
A. The micro-turbulence was assumed to be 2 km s-l. These synthetic Spectra are
referred to as the NG82 grid. This grid is smoothed to the resolution of the SDSS

spectrographs (R = 2000); in contrast to the N081 grid, this grid is not degraded to a

35

lower resolution. We retain the full resolution of this grid to enable the development
of (future) methods for the determination of [a / Fe] for stars in the range 4000 K
S Teff _<_ 8000 K (See Chapter 5.3). Since this is an independent grid, it is also
possible to obtain another set of predicted stellar atmospheric parameters for the

stars within this temperature range.

B. PRE-PROCESSINC OBSERVED SPECTRA FOR THE X2 MINIMIZATION TECHNIQUE

The observed SDSS spectra are processed as described in Chapter 3.3 above. The
blue region of the spectrum contains most of the information required to constrain
the stellar parameters, but for cooler stars, the observed Signal-to-noise ratio peaks
in the red region. As a compromise, and in order to speed up the analysis, we only
consider the spectral range 4500—5500 A. For the NGSQ grid, we sample the spectrum
into 1 A bins; 1.67 A bins are used for the NGSI grid, after degrading to R = 1000.
The spectrum under consideration is normalized after obtaining a pseudo-continuum

over the 4500—5500A range. The continuum ﬁt is carried out in a similar fashion
to that described in §3, but iteratively rejecting the points which lie 10 below and 4
a above the ﬁtted function, obtained from a ninth-order polynomial. The synthetic
spectra used to match with the observed spectra are also normalized in the same

fashion over the same wavelength range.

C. THE PARAMETER SEARCH TECHNIQUE

Following the above steps, we next carry out a search for the best-ﬁt model parame-
ters, i.e., those that minimize the difference between the observed flux vector, 0, and
the synthetic ﬂux vector, S, as functions of Teff, log 9, and [Fe/ H], using a reduced

X2 criterion. That is,

m+1
x2/DOF = Z (0.- - 552/03. (3.2)

i=1

36

where a; is the error in flux in the ith pixel and DOF is the number of degrees of
freedom.

To reduce the number of model spectra that must be considered in the calculation
of the the reduced X2 values, we ﬁrst obtain an approximate effective temperature
based on a simple approach. This procedure, which we refer to as the Half Power
Point (HPP) method (Wisotzki et al. 2000), obtains an estimate of the wavelength
at which the total integrated ﬂux over a spectrum is equal to half of the flux obtained
over the entire wavelength region (in this case we use 3900—8000 A). Since the ﬂux
distribution for a given stellar spectrum varies strongly with effective temperature,
once we have determined the HPP wavelength, we are able to obtain a reasonably
accurate estimate of effective temperature (or a broadband color such as g — r) by
comparing with the HPP wavelengths obtained from a grid of synthetic spectra. The
relation between effective temperature and HPP wavelength is established by ﬁtting

a polynomial:

Te“ = (25.63 — 114.51 . HPP + 177.17 . HPP2 — 93.55 - HPP3) x 10, 000 K, (3.3)

where HPP = /\/10,000.

We initially select synthetic spectra over a broad range around this predicted ef-
fective temperature, within :L-1500 K. For example, if the HPP predicted temperature
of a star is 5000 K, we consider models between 3500 K and 6500 K. As long as the
observed spectrum doesn’t have a grossly incorrect spectrophotometric calibration,
the estimated temperature will be well within this range. We then obtain the reduced
x2 values between the observed and the selected synthetic spectra over a 4500-5500 A

wavelength window.

37

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WMMWI,5-I/‘WA~WT
>< 1 I
:1 _
E
'c 0.8 l _
O
.E -
5 l -
o _
2 0.6 l _
D spSpec-53446-2053-346, Teff = 6687, log g = 4.09, [Fe/H] = -O.52 d
(I) 0-4 — l l I l I I . I l __‘
a 0.02 '— .1 J . A A . /\ A - _f
32 0.00 \l V” DAV/\Vzv mnwwﬂuva/V mvva/w WWW/JV 'V" WW V\V _
a”; —0.02 - —
a: _
4600 4800 5000 5200 5400
Wavelength (Angstrom)
1.0 W W W
1 11 g _
>< _ _
= _ _
t: _ .2
E 0.8 1 _
ﬂ _ _
E _ _
0
Z 0.6 — —
: spSpec-53534-2184-120, chf= 5023. log g = 2.10, [Fe/H] = -2.42 _
v: 04 — . 1 I l i n . 1 . . . 1 . . . 1 f
E 0.02 ,W . A , . . -- .. —:
:2 0.00 {w 'W LAY /\A BY vw «M'AM ’\1\]\/\'r'\vl \m/v" "\I\M.AA../\v/'\A.nvl"V vwvmv mw'v‘
8 -o.0 , V V V' i.
x I
4600 4800 5000 5200 5400
Wavelength (Angstrom)

Figure 3.5 Two examples of the results of the application of the NGSl grid, for a
warmer, metal-rich star (top panel), and for a cooler, metal-poor star (bottom panel).
The black dots are the observed data points; the red lines are synthetic spectra gen-
erated with the atmospheric parameters adopted by the technique. The residuals
between the observed and synthetic spectrum are also plotted at the bottom of each
panel, with superposed red lines representing the one—sigma deviations of the residu—
als.

38

After trying out several function minimization techniques (e.g., Nelder & Mead
1965), we found that a simple biweight average of several dozen of the lowest reduced
x2 values is sufﬁciently fast for computation in the IDL code used in the SSPP, and
predicts the stellar parameters with the desired accuracy (S 0.30 dex in [Fe/H]),
thanks to the dense grid of the synthetic Spectra employed. It also returns a robust
estimate of the parameters for lower S/N (< 20/ 1) spectra.

Note, however, that whereas the values of reduced X2 respond sensitively to small
changes in Teff and [Fe / H], allowing for their optimal determinations, variations in the
log 9 values do not strongly impact the reduced X2, due to a lack of gravity-sensitive
lines in the Spectral window we examine. This leads to potentially large errors in
the estimated log 9. This effect also appears in the function minimization techniques
(e.g., Allende Prieto et al. 2006). We obtain a biweight average of the lowest 20
points of the reduced X2 values for the N081 grid, and 50 points for the NGS2 grid; the
larger number of points included for the NGS2 grid is to accommodate the addition of
an a-abundance parameter.

Figure 3.5 shows two examples of synthetic spectra (red lines) with parameters set
to those estimated by the procedure described above, over-plotted on the observed
spectral data (black dots). The upper panel is for a warm, metal-rich main-sequence
turn-off star; a cool metal-poor giant is shown in the bottom panel. The residuals
between the observed and the synthetic spectrum are plotted at the bottom of each

panel; superposed red lines Show the standard deviation of the residuals to these ﬁts.

D. COMPARISONS WITH SPECTRAL LIBRARIES AND ANALYSIS OF HIGH-RESOLUTION

SDSS-I/SEGUE STARS

In order to validate that the NGSl and NGS2 grid approaches perform well in deter-
mining stellar parameter estimates, we compare the results from these techniques

with literature values from two spectral libraries: ELODIE (Prugniel & Soubiran

39

 

 

 

200 140154650 " ' " V ' #:620'

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

, 120 ' litigan =291' 1 1 1 250* mtgangl-g).22 *
150’ 00 S ‘ « S ’ '
z ' z 80 £2
100’ ‘ 60F .
L
50% 40f
3 20[L
0 . . l O: -4. . 7
400 -200 o 200 400 -2 -1 0 1 2 -1.0 -o.5 0.0 0.5 1.0
T eff_Fit - T eff_1=.LODIE log g_Fit - log g_ELODIE [Fe/H]_Fit - [Fe/HLEDODIE
9000 ' ' . 7 5» ' ' ' é It" ' . . .
8000 - 3 4? or" 3:5 — .. 03 '
E ' a . . 0: '.ﬁ . ‘ u" E
7 r -
% 000 w 3 ~. . g 1, r),
[- 1 2 . . ° a; ’9."
6000 . - 4 29 . ° , 2:» {in
..- , F o * : ..'
50006000700080009000 l 2 3 4 5 -3 -2 -1 o 1
T eff_ELODIE log g_ELODIE [Fe/H]_ELODIE

Figure 3.6 Comparison of parameters obtained from the NGSl grid (Fit) with those
from the ELODIE spectral library (ELODIE). The temperatures agree very well,
while the surface gravity is over-estimated by +0.11 dex. The metallicity is under-
estimated by -0.22 dex, but with a very small scatter, based on Gaussian ﬁts to the
residuals.

2001; Moultaka et al. 2004) and MILES (Sanchez-Blazquez et al. 2006), as well as
with parameter estimates from an analysis of the SDSS-I/SEGUE stars with available

high-resolution spectroscopy.

D.1 VALIDATION FROM THE ELODIE AND MILES SPECTRAL LIBRARIES

The spectra in the ELODIE library were obtained with the ELODIE spectrograph at
the Observatoire de Haute-Provence 1.93 m telescope, and cover the Spectral region
4000—6800 A. We employ 1969 spectra of 1390 stars with a resolving power R =
10,000, which are publicly available as part of the ELODIE 3 release (Moultaka et
al. 2004). The Spectra are ﬁrst smoothed with a Gaussian kernel to match the SDSS

resolution for the NGSZ grid and R = 1000 for the NGSl grid, then are processed in the

40

same fashion as described in Chapter 3.4.4. Most of the spectra have quite high S / N
ratios, and are accompanied with estimated stellar parameters from the literature.
Each spectrum (and parameter estimate) has a quality flag ranging from 0 to 4, with
4 being best. In our comparison exerciSe, we only select stars with 4000 K S Teff S
10,000 K with a quality ﬂag 2 1 for the Spectra and all of the parameters.

Our examination indicates that the NGSl grid approach works best in the range
5000 K S Teﬂ‘ S 9000 K, and marginally well outside this range. Comparison plots
between the literature values and the estimated parameters in this temperature range
for 620 stars among the ELODIE Spectral library are shown in Figure 3.6. A Gaussian
ﬁt to the residuals of each parameter reveals that the N081 estimate of Teff is very
close to the ELODIE zero point (offset by only 12 K), with a scatter of only 74 K;
the surface gravity is larger by 0.11 dex (a = 0.24 dex); the metallicity is lower by
0.22 dex (a = 0.11 dex), on average. For cooler stars, with 4000 K S Teﬂ' S 5000 K,
we ﬁnd that < A(Teff) > and < A([Fe/H]) > are 243 K (a = 91 K) and 0.03 dex
(a = 0.17 dex), respectively, which are relatively small offsets and scatter, while the
< A(log g) > is 0.45 dex, with a = 0.31 dex.

Because the Spectra from the ELODIE library are of very high quality, one might
wonder how the parameter estimates would compare for the lower S /N data in-
cluded among the SDSS-I/SEGUE stars. In order to test this, we inject Gaussian
noise into the ELODIE spectra to force them to S/N = 50/ 1, 25/ 1, 12.5/ 1, and
6.25/1 per pixel at 5000A, respectively, degrade them to R = 1000, and apply
the same procedures as above for estimation of the stellar atmospheric parameters.
These test spectra, and more detailed information on noise models can be found in
ftp: / / hebe.as.utexas.edu/ pub/ callende/ sdssim/ . Table 3.4 lists the results of this ex-
ercise. Inspection of this table shows that, for S/N 2 12.5/ 1, the shifts and scatter
in the determinations of the parameters remain acceptably small.

The MILES library includes 985 spectra obtained with the 2.5m INT and the

41

 

 

 

 

    

 

 

 

 

 

 

 

 

 

80 #:40'3 ' " T 70 #'=T463 ' 150,
_mean=64 60-mean=0.l '
60. std: 120 50 _std=0.31 I
’ O 100%
Z 40* Z Z .
: 30- -
20'. 20‘ 50':
i 10. .
O L 1 A1 214A 0 . 1 0b 1 - . 1
-400-200 0 200 400 -2 -1 0 l 2 -l.0 -0.5 0.0 0.5 1.0

T eff_Fit - T eff_MILES log g_Fit - log g_MILES [Fe/HLFit - [Fe/I-I]_MILES

 

 

 

   
   

 

 

 

 

 

 

 

9000 g 5; l‘
.l l .2 s j ‘ .
8000 < 4'; .3”, {y «j .. 0
f: f: '\'. ‘ .. 1 L: .,
LL LL. ‘3 . l
$7000 at 3 .~ "g -1 ~
0 co ' - .
l" 3 a .- #5
6000 2g -2 3':
i . , '
5000 6000 7000 8000 9000 l 2 3 4 5 -3 -2 -l 0 l
Teff_MILES log g_MILES [Fe/H]_MILES

Figure 3.7 Comparison of parameters obtained from the N681 grid (Fit) with those
from the MILES spectral library (MILES). The temperature and surface gravity are
over-estimated, by +64 K and +0.10 dex, respectively, while the metallicity is under-
estimated by —0.24 dex, with a very small scatter, based on Gaussian ﬁts to the
residuals.

IDS spectrograph at La Palma. The wavelength coverage is 3530—7430 A, and the
resolution is ~ 2.3 A (Sanchez-Blazquez et al. 2006). We processed these spectra in
the same manner as ELODIE to derive the stellar parameters from the N681 and NGS2
grids, but with no degradation of the Spectra for the NGS2 grid, since the resolution
is similar to that of the SDSS spectra. After dropping the spectra with missing
parameters, and outside the temperature range 5000 K S Teff S 9000 K, 403 spectra
remain. Figure 3.7 Shows the comparison plots between the selected literature values
and the parameters estimated from the NGS1 procedure. It appears that the scatter of
the temperature (a = 120 K) and the gravity (0 = 0.31 dex) estimates are higher than
those from the ELODIE spectral library comparison, while the metallicity estimate

is in good agreement (a = 0.17 dex), except for a small negative offset (—0.24 dex).

42

For the cooler stars, with 4000 K S Teﬂ‘ S 5000 K, we obtain < A(Teﬁ—) > = 235 K
with a = 130 K, < A([Fe/H]) > = —0.10 dex with a = 0.17 dex, and < A(log g) >
= 0.45 dex with a = 0.34 dex.

Very Similar behaviors were found for the comparison with the NGS2 grid technique
as for the NGSl grid technique, as listed in Table 3.4, which summarizes the offsets and
scatter between the literature values and the estimated parameters for both synthetic

grid approaches.

D.2 VALIDATION FROM SDSS-I/SEGUE STARS WITH AVAILABLE HIGH-RESOLUTION

SPECTRA

As part of a long-term program to validate and improve estimates of stellar atmo-
spheric parameters determined by the SSPP, over the past two years we have obtained
higher resolution spectra for over 150 SDSS-I and SEGUE stars. The targets cover a
wide range of temperature and metallicity, but somewhat less so in surface gravity.
Existing “holes” in the parameter space will be given high priority for future high-
resolution campaigns. The data have been independently reduced and analyzed by
two authors (CA. and TS.) in Paper III; we refer to the analysis by CA. as HA1,
and to that by TS. as HA2, For a detailed description of these analyses, the interested
reader is referred to Paper III in this series. For simplicity of our present comparison,
we adopt the values of stellar atmospheric parameters obtained by HA1, which con-
sists of a homogeneous sample (observed with the same telescope and spectrograph)
of stars used to derive the empirical error estimates for the atmospheric parameters
determined by the SSPP.

Figure 3.8 shows a comparison between the parameters estimated from the NGS1
grid approach and those determined from the HA1 high-resolution analysis, over
5000 K S Teff S 8000 K. As summarized in Table 3.4, the temperature and sur-

face gravity estimates obtained from the NGSI result in offsets of +85 K (a = 164 K)

43

and +0.13 dex (a = 0.30 dex), respectively, which are somewhat larger than for the
two spectral libraries, However, the average metallicity offset (—0.24 dex) and scatter
(0.16 dex) are very close to those obtained by comparison with the two libraries. A

similar behavior can also be noticed for the NGS2 grid in Table 3.4.

Table 3.4: Comparison of Parameters from NGSl and NGS2 Grids with ELODIE and MILES

Libraries and High-Resolution Valuesd

 

 

Teff logg [Fe/H]
Grid Library S/N N <A> a <A> a <A> 0
(K) (K) (dex) (dex) (dex) (dex)

 

NGS1
ELODIE Full 620 +12 74 +0.11 0.24 —0.22 0.11
ELODIE 50/1 617 +10 87 +0.09 0.25 —0.23 0.12
ELODIE 25/1 617 +13 103 +0.09 0.28 —0.21 0.14
ELODIE 12.5/1 601 +15 175 +0.13 0.37 —0.09 0.19
ELODIE 6.25/1 541 +36 269 +0.25 0.50 +0.23 0.29
MILES Full 403 +64 120 +0.10 0.31 —0.24 0.13

 

HR F1111 81 +85 164 +0.13 0.30 -0.24 0.16
NGS2

ELODIE F1111615 +0.15 0.26 —0.22 0.13

MILES Full 385 +0.16 0.29 -0.24 0.15

HR Full 81 +0.17 0.29 —0.25 0.13

 

Considering the results from these three different comparisons for the N081 and

NGS2 grids, a small systematic offset in our derived metallicity and gravity from these

 

dHR comes from the results of HA1 which is used, in Paper III, to determine empirical
errors of the SSPP parameters.

44

 

 

 

 

 

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

14 _* I '1'
12 1:12:11 25 fhea§11= -O.24
td 1 F- std=0.l6
10 203
8 .
z 6 215g
10?
4 .
2 5f
0 0*1-._L.....
-2 -l 0 l 2 -l.5-l.0-0.5 0.0 0.5 1.0 1.5
log g_Fit - log g_HR [Fe/H]_Fit - [Fe/H]_HR
80001' 1 I ' j 5 ‘ ' '. . ‘ l: . - . .
= 1 . ° .-: s
7000:- - . : 4» ,.."I{..-5 .. 0:-
$6000; . 4: mi 3 g -1? ‘3
a” E .. 3:” a t
5000;- ‘i 2 -2;
4000 5000 6000 7000 8000 l 2 3 4 5 -3 -2 -l 0 1
T effJ-IR log g_HR [Fe/HLHR

Figure 3.8 Comparison of parameters obtained from the N681 grid (Fit) with one
of the analyses of high-resolution spectroscopy of SDSS-I/SEGUE stars (HR). The
parameters for the high-resolution data are the HA1 results, which are used in Paper
III to derive empirical errors of the SSPP parameters. The temperature exhibits a
slightly higher offset than those from the comparisons with the ELODIE and MILES
spectral libraries, but very similar offsets for the gravity and metallicity offsets.
two methods may exist. The Slightly different offsets of the parameters between the
two grids may come from the different resolutions employed. Therefore, we choose
to adjust the offsets in log 9 by +0.11 dex and in [Fe/ H] by —0.23 dex for the NGSI
method, and +0.16 dex and —0.24 dex for the NGS2 method, respectively, in order to
place those two grids on the same abundance scale, on average, as the two external
libraries and the high-resolution analysis results. The offsets represent averages of
those from the ELODIE, MILES, and HA1 comparisons.

The noise experiment summarized in Table 3.4, and another test (in Table 3.5,

see Chapter 3.6 for details) indicate that a lower limit on S/N for obtaining useful

parameter estimates from these two methods is, conservatively, S/N 2 15 / 1 for the

45

NGSl approach, and S/N _>_ 20/1 for the NGS2 approach. The color ranges we adopt
for these techniques are —0.3 S g — r S 1.3 for the N081 approach, and 0.0 S g — r S
1.3 for the NGS2 approach. The T eff, log g, and [Fe/H] estimated from the NGSl
approach are designated as T6, G6, and M6, respectively, whereas the log 9 and
[Fe / H] estimated from the NGS2 technique are referred to as G7 and M7, respectively.
No independent estimate of Teﬂ‘ is obtained from the NGS2 grid, as it is essentially

degenerate with that determined from the N081 grid.

3.4.5 METALLICITY AND GRAVITY ESTIMATES FROM 3850—4250

A : CaIIK1 AND Call

This method utilizes the NGSl grid to estimate the metallicity and surface gravity, in a
similar fashion as described in Chapter 3.4.4, but making use of a different wavelength
window: 3850—4250 A. Even though it covers a relatively short wavelength region, it
is desirable for the determination of stellar parameters because it includes the Balmer
lines as temperature indicators, the metallicity sensitive Ca II K and H lines, and the
gravity sensitive Ca I (4226 A) line. Comparisons with the results of the HA1 high-
resolution analysis indicates an average zero-point offset in [Fe/ H] of —0.06 dex, with
a scatter of 0.25 dex, and an average zero-point offset in log g of +0.05 dex, and a
scatter of 0.30 dex. The color range adopted for this approach is —0.3 S g - r S 0.8.
The surface gravity and metallicity estimates obtained by this technique are referred

to as G8 (Call) and M8 (CaIIKl), respectively.

46

3.4.6 THE Ca 11 K AND AUTO-CORRELATION FUNCTION METH-

ODS : CaIIK2, CaIIK3, AND ACF
A. METALLICITY FROM CaIIK2 AND CaIIK3

These methods are based on the procedures outlined by Beers et al. (1999), where
the interested reader should look for more details. A brief summary follows.

The Ca II K method, which is designated as CaIIK2, makes use of a “band—
switched” estimate of the pseudo-equivalent of the Ca II K line at 3933 A, in combi-
nation with an estimate of a broadband color, to obtain a prediction of the [Fe/ H]
for a given star. The approach has been used for two decades during the course of
the HK (Beers, Preston, & Shectman 1985, 1992) and the Hamburg/ESQ objective
prism surveys (Reimers & Wisotzki 1997; Christlieb 2003) for the determination of
metallicities of stars with available medium—resolution (2—3 A resolution, similar to
the resolution of the SDSS spectra) follow—up spectroscopy. The original calibration
is based on high-resolution abundance determinations (and B —- V colors) for a sample
of ~ 500 stars.

This method has been shown to perform well over a wide range of metallicities, in
particular for stars with [Fe/ H] < —1.0; external errors from the calibration indicate
that it has an intrinsic error no greater than 0.15—0.20 dex in the color range 0.3 S
B — V S 1.2. Above [Fe/ H] = —1.0, and in particular for cooler stars (below Teﬂv =
5000 K), the Ca II K line gradually begins to saturate. As a result, for cool, metal-
rich stars, the method will generally return an estimate of [Fe/ H] that is on the order
of 0.5 dex too low. This is ameliorated somewhat by empirical corrections that are
built into the program used to calculated this estimate, but it remains a source of
concern. It is important to recognize that for stars with very low metallicities, and
for warmer stars in particular, the Ca II K line is one of the few (in some cases only)

metallic lines available in medium-resolution spectra. Hence, this estimator plays an

47

especially important role in such situations.

This method makes use of a broadband B — V color, which we have to obtain
by application of a transformation of the observed (or predicted, as discussed in
Chapter 3.5.2) g — 7‘ colors. In order to accomplish this task, we made use of several
hundred stars with existing B — V colors obtained during the course of the HK and
Hamburg / ESO surveys that happened to fall in the SDSS footprint, and had available
g—r colors (note that only the fainter, non-saturated stars could be used). These stars
covered a variety of metallicities, but in particular a large number of stars with [Fe / H]
< —1.0 were included. An approximate transformation, suitable for low-metallicity
stars, was obtained by Zhao 8r, Newberg (2006); the transform B — V = 0.187 +
0.916(g — r) was employed.

Comparison of the metallicities obtained from the CaIIK2 method with those
derived from the HA1 high-resolution analysis, and for member stars of open and
globular clusters with known [Fe/ H], indicates that the [Fe/ H] for stars with g — r >
0.8 are consistently underestimated (due to saturation of the Ca II K line).

As an alternative Ca II K-line approach, we have calibrated a new index, K24,
which covers a broader region around the Ca 11 K line than the widest band considered
for Cal IK2, and make use of the synthetic grids of predicted g — 7' colors discussed
above. Note that no “band switching” is used in this approach. A simpliﬁed neural
network was designed to implement the prediction of [Fe/ H] based on K24 and the
synthetic g -— 7' color. As summarized in Table 3.9, this new calibration, which we
refer to as CaI 1K3, appears to exhibit similar (small) zero-point offsets and scatter as
CaI 1K2 approach.

Due to concerns about the saturation of the Ca II K line for cooler stars, we
consider only metallicities determined for stars using these two methods in the color
range 0.1 S g — r S 0.8. The parameters from these two approaches are referred to

as M9 (CaIIK2) and M10 CaI 1K3), respectively.

48

B. ACF

The auto-correlation function technique (ACF) was developed as an alternative method
for metallicity estimation which should perform well at higher metallicities, where
the Ca II K line-index techniques described above are limited by saturation. As
described in Beers et al. (1999), and references therein, the method relies on an auto-
correlation of a given stellar spectrum, which generates a correlation peak whose
strength is proportional to the frequency and strength of weak metallic lines in a
given spectrum. The more such lines exist, the stronger the Signal.

The calibration from Beers et al. (2000) relied on a broadband B — V color.
Encouraged by our success with the re—calibration of the Ca II K approach to a
(synthetic) native system 9 — 7‘ color, we have designed a simple neural network that
considers the auto-correlation function and the g - 1‘ colors as inputs in order to
predict [Fe/H].

The auto-correlation Signal is expected to depend strongly on the signal-to-noise of
a given spectrum, growing with decreasing S/N. In the low S/ N limit (S 10/ 1), this
function is responding to noise peaks rather than to the presence of metallic features.
Our experiments with the sensitivity of abundance estimatae on S / N (Chapter 3.6)
reflects this expectation. As can be seen from Table 3.5, the ACF approach exhibits
a reasonably small zero—point offset (+0.12 dex) and scatter (0.17 dex) at S /N levels
as low as 15/ 1. We thus adopt this lower limit on S/N for determinations based on
this method. The range of color adopted for application of this method is taken to
be 0.1 S g — r S 0.9. Blueward of this range, the auto—correlation signal becomes
too weak to be useful. Note that this range extends slightly redder than the Ca 11
K line-index methods. The [Fe/ H] estimate from the ACF approach is referred to as
M11. ’

49

3.4.7 CALIBRATION OF A Ca II TRIPLET ESTIMATOR OF METAL-

LICITY : CaIIT

The SDSS spectra extend to sufﬁciently red wavelengths to include the prominent
Ca II triplet feature, which covers the spectral region 8400—8700 A. These lines are
known to be sensitive to both luminosity (surface gravity) as well as metallicity, so
care must be exercised in their use as a metallicity indicator.

We have employed a line index that measures the integrated strength of these
lines, corrected for the presence of the Paschen Series H lines, which also occur
in this wavelength interval. The line index deﬁnition, and the calculation of the
summed index, is as described by Cenarro et al. (2001a,b). In order to calibrate
this index for use with SDSS spectra, we have taken the library of some 700 spec-
tra (and their listed atmospheric parameters) given by Cenarro et al. (see http:
//www.ucm.es/info/Astrof/ellipt/CATRIPLET.html), rebinned the spectra to the
SDSS spectral resolution, and calculated the corrected Ca 11 triplet index (which
they refer to as CAT’. This index, along with their listed de-reddened value of the
B - V color, are used as inputs to an artiﬁcial neural network procedure in order to
predict the estimated [Fe/ H] This procedure was able to reproduce the metallicity
of the Cenarro et al. stars to within :l:0.3 dex over the temperature range 4000 K
to 8000 K, with some residual sensitivity to surface gravity. Clearly, the application
of this approach would require a transform from B — V to g — 7“, which we prefer to
avoid.

Hence, we proceeded to test an approach that calibrated (with a simple neural
network) the Cennaro et al. CAT’ index along with synthetic g - 1" colors, both
obtained from the synthetic spectra described above. This approach appears to work
reasonably well, as demonstrated by inspection of the results shown in Table 3.9.
The offsets and scatter obtained, relative to the high-resolution analyses, are quite

competitive with other methods we have tested. However, it should be noted that the

50

predicted sensitivity of this method to S / N is, according to the summary in Table 3.5,
apparently somewhat high; although the zero-point offsets remain small, the scatter
appears large compared to other methods (0.3 to 0.5 dex, even at S/N 2 20/1). The
results in Table 3.5 are obtained from the application of noise models for SDSS spectra
(see Chapter 3.6), and we suspect that these may be imperfect in the red regions, or
at least over-aggressive, in the sense of injecting more noise than is typical for SDSS
observations. We plan to investigate this behavior further in the near future.

The color range over which this estimate is employed by the SSPP is 0.1 S g — r S
0.7. It may prove to be the case that we can set the red limit to larger values, once
we understand the origin of the (apparently) large scatter obtained from the noise-
injection test. For now, we set a conservative limit of S/N Z 20 / 1 for application of

this method. The [Fe/ H] estimated from this method is referred to as M12 (CaIIT).

3.4.8 CALIBRATION OF A GRAVITY ESTIMATOR BASED ON THE
Ca I (4227 A) AND Mg I b AND MgH FEATURES : CaI2 AND
MgH

Among the prominent metallic species in stellar spectra, the two that are most sen-
sitive to surface gravity are the Ca I line at 4227A and the Mg I b and MgH features
around 5170 A. Both of these lines exhibit sensitivity to metallicity as well. We have
adopted the line index measurements and quoted atmospheric estimates of [Fe / H] for
the dwarfs and giants in the calibration sample of Morrison et al. (2003), which were
measured at a similar spectral resolution to the SDSS (2.5—3.5 A). Surface gravity
estimates for the stars involved in this calibration were obtained from the compila-
tion of Cayrel de Strobel (2001), while B -— V colors were obtained from the SIMBAD
database.

These indices, along with their de—reddened B — V colors and [Fe/ H], are used

as inputs to an artiﬁcial neural network procedure in order to predict the estimated

51

surface gravity log 9. This procedure indicates that the prediction errors of the surface
gravity, based on the Ca I and MgH indices are on the order of 0.35 dex and 0.30 dex,
respectively. Small zero-point offsets, and similar levels of scatter, are indicated from
the comparison with the high-resolution analyses in Table 3.9. Hence, we decided to
proceed with these estimates (which require a color transform), rather than attempt
a re—calibration to the synthetic spectra and colors.

As indicated by Morrison et al. (2003), these two methods are valid in the color
range corresponding to 0.4 S g — r S 0.9. The gravity estimated from Ca I is referred

to G9 (CaI2), while that obtained from the MgH feature is referred to as G10 (MgH).

3.5 EMPIRICAL AND THEORETICAL PREDICTIONs OF

T8,, AND g — r COLOR

3.5.1 PREDICTIONs OF Tea:

Effective temperatures predicted by the observed 9 — 7‘ color, or through the strength
of the Balmer lines, are sufﬁciently accurate to be considered as auxiliary estimators
to those methods described in Chapter 3.4. We obtain two theoretical and three

empirical temperature estimates during execution of the SSPP.

A. THEORETICAL T33 ESTIMATES : TK AND TG

Two theoretical temperature estimates are based on the NGS1 grid of synthetic Spectra
generated using the Kurucz models described in Chapter 3.4, and by consideration
of predicted colors from the Girardi et al. (2004) isochrones. For the temperatures
based on Kurucz models (T K), we calculate an estimated 9 — 7" color, adopting the
SDSS ﬁlter and instrumental response functions (Strauss & Gunn 2001), then ﬁt a

fourth-order polynomial:

52

T9,; = 779222—6586.18(g—r)—4637.23(g—r)2—1994.29(g—r)3—386.24(g—r)4 (3.4)

In deriving the above relationship, we take into account stellar models with atmo-
spheric parameters in the range —2.0 S [Fe/ H] S —0.5 and 3.0 S logg S 5.0, where
most SDSS-I/SEGUE stars are found. Stars at the extrema of these ranges will have
less than ideal estimates of temperature, due to the sensitivity of g — r color to either
metallicity, surface gravity, or both. The effective temperature (T K) estimated from
this relation is referred to as T9.

For the temperature estimates based on the Girardi et al. isochrones (Ta), we
assume that the stars are all older than 10 Gyrs, are moderately metal-poor (i.e.,
have metallicites in the range —1.5 S [Fe/ H] S —0.5), and are subgiants or main-
sequence stars, which is true for the great majority of the SDSS-I/SEGUE stars. The

temperature relationship, based on a third-order polynomial, is:

Teﬂ» = 7590.26 — 6191.78(g — r) — 4270.92(g — 7")2 — 1225.12(g — r)3 (3.5)

This temperature estimate is referred to as T10.

B. EMPIRICAL Teff ESTIMATES : HA24, HD24, AND T;

Two of the three empirical temperature estimates we employ are derived from the
Balmer-line strengths, similar to the color estimates discussed above, but calibrated
to the effective temperature estimates obtained from the methods discussed in §4.
The temperatures estimated from the H A24 and H D24 indices, via the simple linear

relationships below, are referred to as T7 (HA24) and T8 (HD24), respectively.

53

T9,,» = 4133 + 371 - HA24 (3.6)
T83 = 5449 + 206 . HD24 (3.7)

We restrict the regions over which the above relationships are applied to 1.0A S
HA24 s 120A and 10A 3 HD24 g 15.0 A, respectively. If the HA24 index lies the
validity range, we adopt Teff estimate from H A24, and ignore the H D24 temperature
estimate. If H A24 is out of range, we make use of the H D24 estimate of temperature.

The ﬁnal empirical temperature estimate (TI) comes from the relationship be-
tween the effective temperature derived from a previous version of the SSPP and
the observed 9 — 7' color (Ivezié et al. 2008). The temperature estimated from the

relationship below is referred to as T11:

log Tee, = 3.8820 — 0.3160(g — r) + 0.0488(g — 7‘)2 + 0.0283(g — 7‘)3. (3.8)

It should be noted that T K, T0, and T I are taken into account by the SSPP, provided
that the color flag (see below) is not raised, and the expected temperature is beyond
the region where the primary estimates derived from the techniques described in §4

apply. That is, they are used when the expected temperature is outside the range

4500 K g T6,—f g 7500 K.

3.5.2 PREDICTIONS OF g — r COLOR

For a variety of reasons (e.g., nascent saturation, difficulties with de-blending of
sources, high reddening, etc.), the SDSS PHOTO pipeline (Lupton et al. 2001)
occasionally reports incorrect, or less-than-optimal, estimates of the broadband colors
for a given target. Because several of the methods we employ in the SSPP require a

good measurement of (at least) the g —r color, it is useful to check if the reported g—r

54

color is commensurate with that predicted from the ﬂux-calibrated spectrum of the
source, or with the strength of spectral lines that correlate with effective temperature.
This predicted color is used to raise a cautionary flag for stars with possibly incorrect
reported colors, within some tolerance. We have developed three different methods

to predict g - 7" color in the SSPP, as described below.

A. PREDICTION OF 9 — 7‘ COLOR FROM THE HALF POWER POINT METHOD

The ﬁrst technique, the Half Power Point (HPP) method (Wisotzki et al. 2000),
has been described in Chapter 3.4 above, in connection with reﬁning grid searches
of parameter space. Here we obtain an empirical calibration of the g — 7‘ color by
ﬁtting a functional relationship between the HPP wavelength of spectra for stars with
well-measured SDSS colors, and located in regions of high Galactic latitude, where

reddening is minimal. The best-ﬁt relationship is:

g — r = —3.354 + 4.318 - HPP + 3.247- HPP2, (3.9)

where HPP = A/10,000. The expected error in prediction is about 0.08 magnitudes,
over a broad range of color.

The predicted color obtained in this fashion is (obviously) also a way to iden-
tify stellar spectra with poor spectrophotometric flux calibrations. If the observed
color reported by the SDSS PHOTO routine is believed to be correct, and there re-
mains a difference with the color obtained from the above relationship, one might
be justiﬁably concerned about the quality of the spectrophotometric correction that
has been applied. Unresolved binaries, especially those involving a red and a blue
member, can also be identiﬁed by looking for discrepancies between the observed and

predicted g — 7‘ colors.

55

B. PREDICTION OF 9 — r COLOR FROM THE H6 AND Ha LINES

The strengths of the Balmer lines are also tightly correlated with g — r color, over
wide ranges of effective temperature. We have made use of the line indices for H6

and Ha, as determined by the SSPP, to obtain the following relationships:

g — 7" = 0.469 — 0.058 . HD24 (3.10)

and

g - r = 0.818 — 0.092 . HA24, (3,11)

where H D24 and H A24 are the H6 and Ha line indices calculated over a 24A band
centered on these lines. Note that since the Ho line is stronger, at a given color, than
the H6 line, it can be used to determine predictions of colors for cooler stars. The
Ha line is also located in a region of the spectrum where one expects generally fewer

problems with contamination of the index from nearby metallic features.

3.6 THE IMPACT OF SIGNAL-To-NOISE ON DERIVED

ATMOSPHERIC PARAMETERS

Only the very brightest stars in the SDSS-I/SEGUE sample were accessible for follow-
up high-resolution spectroscopic observations as part of the SEGUE calibration effort
(see Paper III). Thus, the high-resolution data by themselves provide no information
on the accuracy of the parameter estimates from the SSPP for SEGUE spectra with
lower signal-to-noise ratios (< about 30/1). To evaluate the accuracy and precision
of the SSPP estimates of atmospheric parameters over a wide S /N range, we have
developed a noise model for SEGUE data, applied it to the SDSS-I/SEGUE high-

resolution calibration sample to create test spectra at many (more than 50) S /N

56

values, and compare with the outputs of the SSPP, as run on these noise-added
spectra, with the SSPP parameters determined from the original SEGUE spectra,

and from the analysis of the high-resolution data.

Table 3.5: Parameter Sensitivities to Signal-to—Noisee

 

 

S/N 5 10 15 20 25

NameMethod<A> a <A> 0 <A> a <A> a <A> a

 

 

Teﬂ'
Ad Adop —32 175 0 103 7 74 1 57 1 49
T1 1:113 —0 316 -20 174 —8 119 —6 94 —5 72
T2 1:24 —59 95 —39 74 —31 65 —24 54 —20 50
T3 086 4 12 4 9 4 8 4 8 4 8
T4 ANNSR 225 676 142 343 69 199 30 143 24 115
T5 ANNRR -111 255 —13 154 19 106 24 78 27 62
T6 NGSl —11 315 —15 166 —4 117 —3 92 —3 75
T7 HA24 199 510 58 238 40 167 25 123 18 101
T8 HD24 57 256 —29 155 —45 124 —52 97 —56 90
T9 TK
T10 TG
T11 T1

logg
Ad Adop —0.18 0.48 —0.11 0.28 -—0.07 0.20 —0.06 0.16 -0.04 0.14

G1 1:113 —0.11 0.93 —0.07 0.50 —0.04 0.32 —-0.04 0.27 —0.02 0.22
G2 k24 —0.20 0.62 —0.10 0.33 —0.07 0.26 +0.05 0.20 —0.04 0.17
G3 WBG 0.01 0.05 0.01 0.09 0.02 0.06 0.01 0.06 0.01 0.06
G4 ANNSR —0.53 1.04 —0.32 0.66 —0.15 0.42 —0.10 0.31 —0.07 0.23
G5 ANNRR —0.08 0.23 —0.03 0.19 —0.00 0.15 0.00 0.12 0.01 0.11
G6 NGSl —0.07 0.94 —0.02 0.45 —0.02 0.31 -—0.03 0.25 —0.02 0.20
G7 NGS2 —0.10 0.75 —0.05 0.40 —0.05 0.28 —0.05 0.22 —0.03 0.19

 

57

Table 3.5: Parameter Sensitivities to Signal-to—Noise (continued)

 

 

S/N

5

10

15

20

25

NameMethod<A> a <A> a <A> a <A> a <A> a

 

 

G8 CaI1 —0.03 0.68 —0.01 0.42 —0.02 0.32 —0.03 0.23 —0.03 0.20
G9 CaI2 —0.47 1.64 —0.05 0.75 —0.04 0.54 —0.03 0.42 —0.03 0.34
G10 MgH —0.01 0.40 -0.03 0.22 —0.03 0.15 —0.02 0.12 —0.01 0.10
[Fe/H]
Ad Adop 0.14 0.47 0.05 0.21 0.05 0.14 0.02 0.10 0.00 0.08
M1 1:113 0.51 0.56 0.17 0.25 0.11 0.18 0.07 0.14 0.04 0.11
M2 k24 —0.01 0.37 —0.03 0.20 —0.01 0.14 -—0.02 0.11 —0.01 0.09
M3 WBG —0.27 0.40 —0.01 0.14 —0.01 0.07 0.01 0.05 0.01 0.05
M4 ANNSR. ‘ 0.20 0.86 —0.03 0.43 -0.02 0.31 —0.08 0.23 —0.12 0.16
M5 ANNRR —0.02 0.37 —0.01 0.17 0.00 0.11 —0.00 0.08 —0.00 0.07
M6 NGSl 0.51 0.51 0.16 0.24 0.10 0.17 0.05 0.12 0.03 0.10
M7 NGS2 0.53 0.58 0.24 0.26 0.22 0.19 0.14 0.14 0.09 0.11
M8 CaKIIl 0.21 0.51 0.06 0.32 0.04 0.22 0.02 0.15 0.01 0.13
M9 CaKII2 —0.14 0.47 -—0.03 0.19 0.01 0.11 0.02 0.07 0.02 0.06
M10 CaKII3 —0.05 0.75 0.00 0.29 0.00 0.19 0.01 0.13 0.00 0.11
M11 ACF 0.92 0.14 0.41 0.35 0.12 0.17 0.06 0.12 0.03 0.09
M12 CaIIT 0.10 0.88 —0.04 0.82 —0.03 0.57 ——0.03 0.48 -0.01 0.41

 

The noise characteristics of SDSS-I/SEGUE data are modeled down to a lower
limit of signal-to-noise per pixel of 5 / 1. These estimates are based on the extracted,
ﬂux-calibrated, spectra and variance arrays from the SDSS/SEGUE spectroscopic re-

duction pipelines directly, not on the raw spectroscopic frames. Each SDSS-I/SEGUE

 

8< A > is the average of the differences between the noise-added spectra and the original
spectra; a is the standard deviation of the differences. The temperature estimates T9, T10,

and T11 do not change with S/N, because they are computed from the g — 7' color.

58

plug-plate has spectroscopic targets that span the entire magnitude range of the bright
or faint plug-plates. The boundary between the faint and bright plug—plates is set to
7' ~ 18.0. Since all targets on a given plug-plate receive the same total exposure time,
the relative contribution from the sky and object components of the noise changes
over the magnitude range of the survey, with object noise dominant at high S /N
and sky noise dominant at low S / N . The sky and stellar spectra have different spec-
tral energy distributions, so in order to make a high S / N SEGUE spectrum and its
variance array resemble lower S / N data, simply adding Poisson noise is not sufﬁcient.

The noise model is constructed by measuring the ratio of sky-to-object ﬂux for
a large subset of all the SEGUE spectra, 85,000 in the case of the tests described
here, and parameterizing the mean value of that ratio and the width of the scatter
about the mean vs. S/N. This accounts for the increasing contribution from sky
noise at lower S/N, and the range of ﬁnal S/N for targets at any magnitude because
of variable conditions, etc. Then, to make a spectrum of any desired ﬁnal S /N , the
model uses that relation to scale the input spectrum and variance. The model then
enforces equality between that ratio of sky-to-object flux and the ratio of the variances
of the sky and object ﬂux, Since both the ﬂux and variances should be proportional
to the total counts. This deals with differences in how the reduction pipeline flux
calibrations are applied to the sky and objects ﬁbers and their variances. The model
then randomly draws a sky residual spectrum from the set of all sky ﬁbers on all the
SEGUE plug-plates and adds that zero-mean spectrum, now at the correct relative
magnitude for the output S/N, to the noise-added data spectrum. We construct
many (more than 50) realizations of each spectrum at each S /N value, each one with
a different sky residual, and with the value used for the initial scaling of the input
spectrum and its variance drawn as a Gaussian random deviate, described by the

mean and scatter of the ratio of sky-to-object ﬂux in the survey data.

59

The end result is a noise—added Spectrum for which the signal-to—noise vs. wave-
length is (as much as possible) indistinguishable from real data at similar a signal-to-
noise ratio.‘Our test spectra have S/N values ranging from 2.5/1 to 55/1. We have
tested the noise-added spectra by checking the accuracy of the radial velocities for
the test spectra vs. S/N, and ﬁnd good agreement with the accuracy as determined
by comparing duplicate SEGUE observations that span the same range in S/N (C.
Rockosi et al., in preparation). We have also measured the signal-to-noise ratio at
important spectroscopic features as blue as Ca 11 K vs. the average signal-to—noise
ratio for the test spectra, and found good agreement with the same measurement for
real Spectra at similar 9 — 7' colors.

From a sample of 108 calibration stars with ~450 different realizations in each
S /N bin, we selected a sub-sample of spectra with 40 different realizations per bin,
and examined how the stellar parameters determined by the methods used by the
SSPP depend on S/N (over the range 5/1 S S/N S 25/1). Table 3.5 summarizes the
results. The S / N ratio is calculated by averaging over the spectral region 4000—8000
A. Since we have numerous realizations of each spectrum at the same approximate
S/N, we calculated the average S/N, as well as the mean offset and scatter of the
parameters (compared to the non noise-injected spectra) by, e.g., selecting spectra
with S /N between 3/1 and 7/1 for S/N ~ 5/1. The same procedure is applied to the
other S/N regimes.

The S / N cuts we have chosen for the individual methods used by the SSPP (listed
in Table 3.3) are based on this experiment. The results for the temperature estimates
T9, T10, and T11 are zeroed out in Table 3.5, because they are computed from the

g — 1" color alone.

60

3.7 FLAGS RAISED DURING EXECUTION OF THE SSPP

It is important that the SSPP be able to identify situations where the quoted atmo-
spheric parameters may be in doubt, or simply to make the user aware of possible
anomalies that might apply to a given star. We have designed a number of flags that

serve this purpose.

Table 3.6: Brief Descriptions of SSPP Flagsf

 

 

 

 

Position Flag Description Category Parameter

First
n Appears normal ...... Yes
D Likely white dwarf Critical No
d Likely st or sdB Critical No
H Hot star with Teff > 10,000 K Critical No
h Helium line detected, possibly very hot star Critical No
1 Likely late type solar abundance star Cautionary Yes
E Emission lines in spectrum Critical N o
S Sky spectrum Critical N o
V N o radial velocity information Critical N o
N Very noisy spectrum Cautionary Yes

Second
n Appears normal ...... Yes

C The photometric g — 1* color may be incorrect Cautionary Yes

 

 

Third
Appears normal ...... Yes
B Unexpected Ha strength predicted from H6 Cautionary Yes
Fourth
n Appears normal ...... Yes
G Strong G-band feature Cautionary Yes

 

61

Table 3.6: Brief Descriptions of SSPP Flags (continued)

 

 

 

 

Position Flag Description Category Parameter
g Mild G-band feature Cautionary Yes
Fifth
n Appears normal ...... Yes

P Parameters reported for 5.0 S S /N < 10.0 Cautionary Yes

 

No parameters Critical No
RV
NORV N o radial velocity information ...... No
ELRV Radial velocity from ELODIE template ...... Yes
BSRV Radial velocity from spectra 1d ...... Yes
RVCAL Radial velocity calculated from SSPP ...... Yes

 

There are two primary categories of ﬂags — critical ﬂags and cautionary ﬂags.
When a critical ﬂag is raised, the SSPP is set to either ignore the determinations of
atmospheric parameters for a given star, or it is forced (in the case of the color ﬂag
described below) to take steps that differ from normal processing in an attempt to
rescue this information. Obviously, even when information is salvaged, the presence
of a critical ﬂag means the user must be aware that special steps have been taken,
and the repOrted estimated parameters must be viewed with this knowledge in mind.
The second category of ﬂags are the cautionary ﬂags, which are provided for user
consideration, but are not necessarily cause for undue concern. Indeed, sometimes
these ﬂags are raised when all is in fact OK, but the ﬂag has been raised due to a
peculiarity in the spectrum that is relatively harmless, and which will not unduly

inﬂuence determination of atmospheric parameters. The user Should nevertheless be

 

fNo parameters are reported when ‘Critical’ ﬂags are raised.

62

aware of the existence of these ﬂags.

The ﬂags are combined into a single set of ﬁve letters, the meanings of which are
summarized in Table 3.6, and described below in more detail. Five placeholders are
used in order to accommodate cases where more than one sort of ﬂag is raised.

The nominal condition for the ﬁve letter ﬂag combination is ‘nnnnn’, which indi-
cates that the SSPP is satisﬁed that a given stellar spectrum (and its reported 9 — 7“
colors and S /N ) has passed all of the tests that have been performed, and the stellar
parameters should be considered well determined.

The ﬁrst letter in this combination iS set to one of 10 different values: ‘n’, ‘D’, ‘d’,

‘H’, ‘h’, ‘l’, ‘E’, ‘S’, ‘V’, and ‘N’. Their explanations follow:
0 ‘n’: The letter ‘n’ indicates nominal.

e ‘D’: This ﬂag is raised if a comparison of the breadth of the H6 line at 20% below
its continuum, D02, and the line depth below the continuum, RC, relative to
their expected relationship for “normal stars”, provided below, does not apply.

The expected relationship is given by:

RC = —0.009503 + 0.027740 . 00,2 — 0.000590 - 03.2 + 0.000006 - 193.2 (3.12)

If 00.2 is greater than 35.0 A, and the predicted R; from the above relationship
is less than the measured value, then the star is most likely a white dwarf. This

is a critical ﬂag.

0 ‘d’: This ﬂag is raised if D02 is less than 35.0 A, and the predicted RC from
above is less than the measured value. In this case, the star is most likely a SdO

or sdB star. This is a critical ﬂag.

63

e ‘H’: This ﬂag is raised when the estimated T eff from the SSPP is greater than

10000 K, and is meant to indicate a hot star. This is a critical ﬂag.

0 ‘h’: This ﬂag is raised if the estimated Teﬂ‘ from the SSPP is greater than
8000 K, and either of the line indices of He I (at 4026.2 A) or He I (at 4471.7 A)
is greater than 1.0 A. This indicates that the star is likely to be a hot star. This

is a critical ﬂag.

0 ‘1’: This ﬂag is raised if the SSPP judges the star to have a high likelihood
of being a late-type star (generally late K, M, or later spectral type), beyond
the ability of the present pipeline to determine acceptable atmospheric param—
eter estimates. The condition used for raising the ‘1’ ﬂag is that the Na line
(5892.9 A) index, as measured over a 24A band centered on this feature, is
larger than 10 A, and the g — 7‘ color is greater than 0.8. This is a cautionary

ﬂag.

0 ‘E’: This ﬂag is raised if signiﬁcant emission lines are detected in a spectrum.

This is a critical ﬂag.

0 ‘S’: This ﬂag is raised if the spectrum (according to the header information) is

a night-sky spectrum. This is a critical ﬂag.

0 ‘V’: This ﬂag is raised when an adequate radial velocity could not be found for

a given spectrum. This is a critical ﬂag.

0 ‘N’: This ﬂag is raised if the spectrum is considered noisy at the extremes of
the wavelength range (e.g., around Ca 11 K and the Ca II triplet). This is a

cautionary ﬂag.

The ﬂags that are used to ﬁll out the remaining four positions of the ﬁve letter
ﬂag combination are ‘C’, ‘B’, ‘G’, ‘g’, ‘P’, and ‘N’, as described below. If none of

these ﬂags is raised, then the ‘n’ ﬂag is raised in their place:

64

e ‘C’: This ﬂag is raised if the SSPP is concerned that the reported 9 — 7‘ color is
incorrect. As mentioned above, we calculate three estimates of predicted g — 7"
colors, based on H A24, H D24, or the Half Power Point method. For each of
these three predicted colors, we ﬁnd the one which is closest to the reported
9 -r color based on the photometry. If the difference between the reported color
and the closest predicted color is larger than 0.2 magnitudes, the color ﬂag (‘C’)
is raised. The SSPP is set up to proceed with its calculations of atmospheric
parameters using the predicted g — 7' color. This ﬂag is always found in the

second position of the combination ﬂag parameters. This is a cautionary flag.

0 ‘B’: This ﬂag is raised if the SSPP is concerned that there exists a strong
mismatch between the strength of the predicted Ha line index H A24, based
on the measured H6 line index, H D24. For the great majority of “normal”
stars, the predicted value of the Ho line index is found to be H A24 = 2.737 +
0.775-H D24. For stars with signiﬁcant H A24 and H D24 measurements (which
we take to mean that the values of these indices exceed zero by more than 2 a,
where a is the error in the measured line index), if the difference between the
predicted H A24 line index and the measured H A24 index is larger than 2.5 A,
then the ‘B’ ﬂag is raised. This ﬂag is always found in the third position of the

combination ﬂag parameters. This is a cautionary ﬂag.

0 ‘G or g’: This ﬂag is raised if the SSPP suggests that the star may exhibit a
strong (‘G’) or mild (‘g’) CH G~band (around 4300A), relative to expectation
for “normal” stars. This ﬂag is always found in the fourth position of the

combination ﬂag parameters. This is a cautionary ﬂag.

0 ‘P or N’: This ﬂag is raised in order to indicate if a spectrum either does (‘n’),
which is innocuous, or does not (‘P’), which may be of concern, pass through

the S/N cuts listed in Table 3.3, but still has an average S/N 2 5/ 1. If no

65

parameters are reported, or the average S / N < 5 / 1, the ‘N’ ﬂag is raised. The

ﬂag ‘P’ is cautionary, while ‘N’ is a critical ﬂag.

3.8 THE SSPP DECISION TREE FOR FINAL PARAME-

TER ESTIMATION

The SSPP uses multiple methods in order to obtain estimates of the atmospheric
parameters for each star over a very wide range in parameter space. Each technique
has limitations as to its ability to estimate each parameter, arising from, e.g., the
coverage of the grids of synthetic spectra, the methods used for spectral matching,
and their sensitivity to the S / N of the spectrum, the range in parameter space over
which the particular calibration used for a given method extends, etc.. Hence, it is
necessary to specify a prescription for the inclusion or exclusion of a given technique
for the estimation of a given atmospheric parameter. At present, this is accomplished
by the assignment of a null (0, meaning the parameter estimate is dropped), or
unity (1, meaning the parameter estimate is accepted) value to an indicator variable
associated with each parameter estimated by a given technique, according to the
g -- r and S/N criteria listed in Table 3.3, and the ﬂags that are raised. In the
future, we plan to devise an improved weighting scheme for the combinations of the
parameter estimates, once the grid of high-resolution spectroscopic determinations of
atmospheric parameters is more completely ﬁlled out.

The S/N of a given spectrum plays a crucial role in the ﬁnal decision as to the
estimate of a set of atmospheric parameters, and the techniques used (which differ
in their sensitivity to S/N). Table 3.3 lists the ranges of S/N where each particular
method is considered valid. All derived parameters that fall outside of the color and
S/N ranges listed in this table, for a given technique, are set to Teﬂ‘ = —9999, log g

= —9.999, and [Fe/ H] = —9.999, and have an indicator variable attached to a given

66

parameter set to zero by the SSPP. However, if the S /N of a Spectrum is greater than
5/1, the parameters are saved (with the cautionary ﬂag ‘P’ raised).

Recall that in cases where the color ﬂag ‘C’ is raised, the predicted g — 7' color
determined by the procedures described above is used as an input (rather than the

reported color) for the techniques that require this information.

3.8.1 DECISIONS ON EFFECTIVE TEMPERATURE ESTIMATES

There are six primary temperature estimates determined by the SSPP, and an auxil-
iary set of ﬁve empirically and theoretically determined estimates. Note that a few of
the primary techniques extend to temperatures below 4500 K and above 7500 K,
although the accuracy obtained by these are lower than in the interval 4500 K
< Tag < 7500 K. Thus, for stars with temperatures outside of this interval, we
also include the auxiliary temperature estimates (in fact, just those that lie within
3 a of the mean of the full auxiliary set) in assembling the ﬁnal average estimate of
Teff. Averages are taken using the robust biweight procedure (See Beers, Flynn, &
Gebhardt 1990, and references therein).

In cases where the color ﬂag ‘C’ is raised, we ignore all temperatures that rely on
the reported g—r color, and only consider those based on spectroscopy alone (e. g., the
Spectral matching techniques and Balmer-line based temperature). A robust average
of the accepted temperature estimates (those with indicator variables equal to 1) is
taken for the ﬁnal adopted temperature. An internal robust estimate of the scatter

around this value is also obtained.

3.8.2 DECISIONS ON SURFACE GRAVITY ESTIMATES

There are ten methods used to estimate surface gravity by the SSPP. Application of
the limits on g — r and S/ N eliminates a number of these estimates, and the biweight

average of the accepted log 9 estimates (those with indicator variables equal to 1) is

67

taken for the ﬁnal adopted surface gravity. An internal robust estimate of the scatter

around this value is also calculated.

3.8.3 DECISIONS ON METALLICITY ESTIMATES

Twelve different methods are employed to determine [Fe/ H] in the present SSPP. AS
before, indicator variables of 1 or 0 are assigned to the result from each method,
according to whether or not it satisﬁes the range of validity listed in Table 3.3.
Rather than simply averaging the (accepted) metallicity estimates for each star,
we have introduced a routine to identify and remove likely outliers. This involves the
calculation of correlation coefficients between the observed and the synthetic Spectrum
generated with the adopted temperature and gravity, and the individual estimates of
the metallicity. Brieﬂy, we start with the individual estimates of [Fe/ H] (with indica-
tor variables of 1), the adopted Teffa and log 9, and use these parameters to generate
a synthetic spectrum by interpolating the pre-existing grid of the synthetic spectra
(speciﬁcally the N681 grid). Then, we compute correlation coefﬁcients between the
observed and the generated synthetic Spectrum in two different wavelength regions:
3850—4250 A and 4500—5500 A, where the Ca II K and H lines, as well as numerous
metallic lines are present. We have avoided the region surrounding the CH G-band
feature, as this molecular band can vary widely for stars with enhancements of carbon.
Thus, for each estimator of [Fe/ H] there are two values of the correlation coeﬂicient
determined. We then select the region with correlation coefﬁcient closest to unity.
This applies for all estimates of [Fe/ H] from the individual methods. At the end of
this process, we have N values of the correlation coefficient (maximum of N = 12)
for the N estimates of [Fe/ H] with indicator variables of 1. After this, we take a
robust average of the N values, and reject the values that are less than 1 a from the
average. By application of this procedure, metallicity estimates that produce poor

matches with the synthetic spectra are ignored, and are assigned indicator variables

68

of 0. The ﬁnal adopted value of [Fe / H] is the biweight average of the remaining values
of [Fe/ H] (those with indicator variables of 1). This procedure is followed for all stars
with adopted temperatures Teff 2 5000 K. For stars with adopted temperatures below
this value, we do not consider the region 3850—4250 A for calculation of a correlation
coefﬁcient, because the Ca II K line is subject to saturation (and sometimes) the
presence of line-core emission (due to an active chromosphere).

This procedure has been adopted after consideration of numerous alternative ap-
proaches for the ﬁnal metallicity averaging. It appears to work (almost) as well as
individual inspection by a trained spectroscopist, which would not be practical for

the large numbers of spectra obtained by the SDSS.

3.9 VALIDATION OF THE FINAL SSPP PARAMETER Es-

TIMATES

We do not yet have at our disposal a completely satisfactory set of external Spectral
libraries, with suitable wavelength coverage and available atmospheric parameter es-
timates, that extends over the full range of parameter space explored by techniques
employed by the SSPP. Hence, we are limited to comparison with the sets of pa-
rameters obtained from analysis of the high-resolution spectra for SDSS-I/SEGUE
stars obtained to date, and with information available from the literature for stars in
Galactic open and globular clusters that have been observed during the course of the
SDSS. Since Paper III focuses on the global uncertainties in the derived parameters
from the SSPP, in this thesis we concentrate on the comparison of individual methods

with the results from the high-resolution analyses.

69

Table 3.7: Comparison of T95 Estimates from Individual Methods with Those from Two

High-Resolution Analysesg

 

 

Name Ad T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11

Method Adop 1:113 k24 WBG ANNSR ANNRR NGSl HA24 HD24 TK Tc; '1‘]

 

HA1 N 81 79 81 79 81 81 81 81 60 81 81 81
< A > +194 +142 +312 +230 +300 +179 +85 +139 +163 +125 +45 +146
0 182 231 249 196 197 182 164 142 147 295 252 268

 

HA2 N 125 120 120 116 122 125 125 123 96 125 125 125
< A > —32 —90 +46 —4 +36 —29 —140 -99 —74 —108 —178 —81
a 147 184 186 201 218 144 183 202 253 167 205 186

 

MEAN N 125 120 120 116 122 125 125 123 95 125 125 125
< A > +64 —2 +136 +94 +132 +56 —37 +8 +43 —39 —83 —2
a 126 171 219 195 218 135 174 162 187 208 209 193

 

3.9.1 VALIDATION FROM HIGH-RESOLUTION SPECTROSCOPY

Table 3.2 summarizes the high-resolution data for SDSS-I/SEGUE stars obtained to
date. Although the stars in this table cover most of the range explored by the SSPP
techniques, there remain gaps in this coverage that we hope to ﬁll in the near future.

As noted above, these data have been reduced and analyzed independently by
two (CA. and TS.) of the authors in Paper III, making use of different method-
ologies. Details are discussed in Paper III. Tables 3.7, 3.8, and 3.9 summarize the
systematic offsets and scatters obtained for estimates of Teﬁ‘, log 9, and [Fe/ H] from

each of the techniques used by the SSPP, relative to high-resolution analyses carried

 

g‘Ad’ is the adopted estimate of Tag. HA1 indicates the analysis performed by C.A.;
HA2 for T.S. MEAN is the average of the two analyses. ‘N’ is the number of stars compared.
< A > is the mean zero-point offset from a Gaussian ﬁt to the residuals of T eff between the
SSPP and the high-resolution analysis; a is the standard deviation of the ﬁt.

70

out individually and collectively. The differences in the numbers of stars considered
independently arises because T.S. (results shown as HA2 in the tables) analyzed all
available spectra, while C.A. (results shown as HA1 in the tables) performed analysis
only for those stars observed with the Hobby-Eberly Telescope (HET). In the HA2
analysis, two different approaches were employed. The ﬁrst is a routine that opti-
mizes the minimum distances between the Observed and synthetic spectra over a grid.
This method was employed for the HET and Keck-ESI spectra. The second is the
traditional high-resolution analysis approach, using Fe I and Fe II lines to constrain
Teﬂ‘, log 9, [Fe / H], and the microturbulence parameter. This approach was applied to
the Keck-HIRES and Subaru-HDS data. More detailed explanations on the methods
can be found in Paper 111. The Keck-ESI, Keck-HIRES, and Subaru-HDS spectra
with available parameters are deﬁned as OTHERS in Paper III. In Paper III only
the HET data analyzed by CA. are used to derive the empirical random errors of
the adopted parameters from the SSPP. However, in the present study, we consider
all available parameter estimates from all methods considered in the SSPP. The rows
labeled MEAN in Tables 3.7, 3.8, and 3.9 are the averaged results from HA1 and HA2
(for stars in common), supplemented with stars from HA2 where HA1 results were not
obtained.

Figures 3.9, 3.10, and 3.11 provide comparisons of the estimates of atmospheric
parameters for individual techniques used by the SSPP with those obtained from the
high-resolution analysis (HA1), for Teff, log 9, and [Fe/ H], respectively.

Comparison of the estimated temperatures from the SSPP indicates, overall, very
satisfactory results, although Table 3.7 reﬂects an interesting trend for Teff; estimates
are mostly higher for the HA1 residuals, and mostly lower for HA2. However, as can
also be noted from this table, the ﬁnal adopted value of effective temperature from
the SSPP exhibits a very small offset (+64 K) compared to the MEAN, and a one-sigma

scatter of 126 K, both of which are encouragingly small. It is clear from inspection

71

 

 

 

 

 

 

 

 

 

 

 

 

 

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4000500060007000800050006000700080005000600070008000
T eff—HR (K) T eff_I-IR (K) T eff-HR (K)

Figure 3.9 Comparison of effective temperatures estimated from individual methods
with those from the HA1 high-resolution analysis of SDSS-I/SEGUE stars. ‘HR’ indi-
cates the (HA1) high-resolution analysis results. Residuals are the differences between
the individual estimates and the high—resolution results. The red solid line is the
zero-point; the blue dashed line is a least squares fit to the residuals.
of Figure 3.9 that additional high-resolution observations are required of stars with
both higher and lower temperatures than the present sample. The distribution of the
ﬁnal adopted temperatures indicates no signiﬁcant trends in the temperature range
4500 K S Teﬁ' S 7500 K, compared with the values from HA1, but there may exist a
systematic offset of about 200 K.

Table 3.8 and Figure 3.10 for the surface gravity estimates reveal that the estimate
G3 exhibits the highest offset, and largest scatter, relative to the high-resolution
analyses, for reasons that are not presently clear. The residuals of the adopted values

for surface gravity estimates from the SSPP are reasonably well distributed around

72

zero for the high-gravity regime. High-resolution spectra for additional stars with
lower surface gravities are required in order to conﬁrm whether the slopes in the
regression ﬁts to the residuals for individual methods are real, or simply inﬂuenced
by a few low gravity stars. The mean Offsets and one-sigma scatters in the ﬁnal
adopted estimate of log 9 from the comparison with HA1 are +0.02 dex and 0.21 dex,
respectively, and 0.00 and 0.23 dex for the MEAN comparisons. These are surprisingly

good results for this difficult-tO-estimate parameter.

Table 3.8: Comparison of log 9 Estimates from Individual Methods with Those from Two

High-Resolution Analyses

 

 

Name Ad G1 G2 G3 G4 G5 G6 G7 G8 G9 G10
Method Adop kil3 k24 WBG ANNSR ANNRR NGSI NGS2 CaI1 CaI2 MgH

 

HA1 N 81 79 81 79 80 81 81 80 77 32 35
< A > +0.02 +0.03 +0.06 —0.16 +0.01 +0.06 +0.06 +0.05 +0.05 +0.06 +0.04
0 0.21 0.34 0.33 0.69 0.25 0.22 0.30 0.29 0.30 0.30 0.26

 

HA2 N 125 120 120 116 118 123 122 120 117 47 51
< A > —0.02 —0.05 +0.00 —0.19 +0.01 +0.01 —0.01 —0.04 +0.00 —0.03 +0.00
0 0.33 0.44 0.43 0.82 0.45 0.37 0.41 0.39 0.37 0.40 0.24

 

MEAN N 125 120 120 116 118 123 122 120 117 47 51
< A > +0.00 —0.01 +0.03 -0.19 +0.03 +0.02 +0.03 +0.01 +0.02 —0.00 +0.03
0 0.23 0.36 0.40 0.80 0.33 0.28 0.31 0.33 0.33 0.39 0.24

 

It can be seen from Table 3.9 and Figure 3.11 that, except for M12, which exhibits
a somewhat larger zero—point offset in HA2 and MEAN, but a small deviation from this
zero point, all of the individual methods display satisfyingly small offsets with low

scatter.

73

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 3.10 Same as Figure 3.9 but for the surface gravities, log 9.

It is clear from inspection of Figure 3.11 that we could beneﬁt from high-resolution
analyses for more stars with intermediate metallicities, as well as for stars at the lowest
metallicities. The mean offset (+0.02 dex) and one-sigma scatter (0.15 dex) of the
residuals between the SSPP predictions of [Fe/ H] and the high-resolution analysis
(HA1) are quite encouraging, at least over the parameter space explored to date;
_ the mean zero-point offset of +0.03 dex and scatter of 0.23 dex from MEAN is quite
acceptable as well.

In summary, based on the sets of parameter comparisons with high-resolution
analyses, in the effective temperature range of 4500 K S Teﬂ‘ S 7500 K, if we take the
results from MEAN as “ground truth”, the SSPP is capable of producing estimates of the

atmospheric parameters for SDSS-I/SEGUE stars to precisions of 0(Teﬂ‘), 0(log g),

74

and a([Fe/H]) of 141 K, 0.23 dex, and 0.23 dex, respectively, after adding systematic
offsets quadratically. These uncertainties will be slightly reduced if we take into
account the error contribution from the high-resolution analysis, as is done in Paper
III. However, it should be kept in mind that the stars for which these comparisons
are carried out are among the very brightest (high S / N > 50 / 1) observed with SDSS,
and the overall precision of parameter determination will slightly decline with S/N,

as shown in Table 3.5.

75

 

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76

3.10 ASSIGNMENT OF SPECTRAL CLASSIFICATIONS FOR

EARLY AND LATE-TYPE STARS

It is Often useful to group stars into rough MK spectral classiﬁcations. It should
be kept in mind, however, that for this, and any other exercise of assigning MK
spectral types, that the MK system does not apply to stars other than Population I.
That is, typing of metal-poor Population II stars is, by deﬁnition, not a strictly valid
procedure. Nevertheless, the SSPP attempts to carry out this exercise using two
approaches. The ﬁrst is based on the Spectral type listed in the ELODIE database
for the best template match obtained for the determination of radial velocity (as
described above), and applies to stars with spectral classes 0 to M.

For the coolest stars, measurement of accurate values of Tear, log 9, and [Fe/ H]
from spectra dominated by broad molecular features becomes extremely difﬁcult (e. g.,
Woolf & Wallerstein 2006). As a result, the SSPP does not estimate atmospheric
parameters for stars with T eﬂ‘ < 4000 K, but instead estimates the MK spectral type
of each star using the “Hammer” spectral-typing software developed and described
by Covey et al. (2007) h. The Hammer code measures 23 spectral indices, including
atomic lines (H, Ca 1, Ca II, Fe I, Mg 1, Na 1) and molecular bandheads (CN, G
band, TiO, VO, CaH, FeH), as well as a select set of broadband color ratios. The
best-ﬁt spectral type of each target is assigned by comparison to the grid of indices
measured from more than 1000 spectral-type standards derived from spectral libraries
of comparable resolution and coverage (Allen & Strom 1995; Prugniel 86 Soubiran
2001; Hawley et al. 2002; Bagnulo et al. 2003; Le Borgne et al. 2003; Valdes et al.
2004; Sanchez-Blazquez et al. 2006).

Tests of the accuracy of the Hammer code with degraded (S / N N 5/ 1) STELIB
(Le Borgne et al. 2003), MILES (Sénchez-Blazquez et al. 2006), and SDSS (Hawley

 

hThe Hammer has been made available for community use: the IDL code can be down-
loaded from http://www.cfa.harvard.edu/ kcovey/

77

 

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Residuals (dex) Residuals (dex) Residuals (dex) Residuals (dex) Residuals (dex)

 

 

 

Figure 3.11 Same as Figure 3.9 but for the metallicities, [Fe / H]

et al. 2002) dwarf template spectra reveal that the Hammer code assigns spectral
types accurate to within :l:2 subtypes for K and M stars. The Hammer code also
returns results for warmer stars, but as the set of indices used is optimized for cool
stars, typical uncertainties are i4 subtypes for A—G stars at S/N ~ 5/ 1; in this
temperature regime, the SSPP atmospheric parameters are a more reliable indicator
of Teﬂ‘.

Given the science goals of, in particular, the SEGUE program, we emphasize two

limitations to the accuracy of spectral types derived by the Hammer code:

78

o The Hammer code uses spectral indices derived from dwarf standards; spectral
types assigned to giant stars will likely have larger, and systematic, uncertain-

ties.

o The Hammer code was developed in the context of SDSS-I’s high Galactic lat-
itude Spectroscopic program; the use of broadband color ratios in the indices
will likely make the spectral types estimated by the Hammer code particularly
sensitive to reddening. Spectral types derived in areas Of high extinction (i.e.,
low-latitude SEGUE plug-plates) should be considered highly uncertain until

veriﬁed with reddening-insensitive spectral indices.

3.11 DISTANCE ESTIMATES

A number of techniques are presently being explored by members of the SEGUE
team in order to derive the best available estimates of distances for stars in the
SDSS/SEGUE database. Many rely on the existence of either theoretical or empirical
transformations Of the substantial amount of photometric data that exists for Galactic
clusters Obtained with photometric systems other than ugrz’z. An et al. (2008)
have recently reported accurate globular and open cluster ﬁducials for a set of 20
clusters observed by SDSS, making use of crowded-ﬁeld photometric measurements.
We expect to revise the distance estimates obtained by the SSPP, based on this work,
in the near future.

For now, the SSPP assigns preliminary distance estimates for stars of different
luminosity classiﬁcations based on the empirical ﬁts of Beers et a1. (2000) to the
observed color-magnitude diagrams of Galactic clusters of different metallicities and
with reasonably well-known distances (in the Johnson V, B — V system). For con-
venience, we use the same transformations as mentioned above, based on the work

of Zhao & Newberg (2006); V = g — 0.561(9 — r) — 0.004, and B — V = 0.187 +

79

0.916(g — r).

Beers et al. (2000) argue that their distances should be accurate to on the order of
10—20%; a typical value of 15% can be adopted for our distance estimates, although
this needs to be conﬁrmed with future work.

The SSPP does not make a stellar luminosity classiﬁcation, but rather, it provides
the atmospheric parameters from which the user can make an appropriate choice. Dis-
tance estimates are Obtained for the following rough luminosity classes: Dwarf, Main-
Sequence 'I‘urnoff, Giant, Asymptotic Giant Branch, and Field Horizontal-Branch.
Note that distance estimates are obtained for all (feasible) cases where a star may fall
into one or more of these classiﬁcations, but only one of the listed distances is likely
to apply to a given star. The choice is left up to the user.

An alternative method for distance estimates in the SSPP is described by Al-
lende Prieto et al. (2006), to which the interested reader is referred for a detailed

description.

3.12 EMPIRICAL UNCERTAINTIES OF STELLAR PARAM-

ETERS OF THE SSPP

By directly comparing the stellar parameters Obtained by the SSPP with the results
of the high resolution analyses, The typical empirical errors of the stellar parameters
delivered by the SSPP have been determined. Paper III describes in details the
reduction of the data, comparison with spectral libraries, and other procedures of how
to derive those quantities so that we refer to the paper for the detailed information.
Therefore, this section will be a summary of Paper III.

We made use Of the same sample (125 stars) which were used to compare the pa-
rameters from the individual methods with those of the two high resolution analyses.

We divided the sample into two groups: HET (81 stars) and OTHERS (44 stars).

80

HET group consists of stars observed by Hobby-Eberly Telescope and OTHERS for
others telescopes such as SUBARU, KECK—I and II. Table 3.2 summarizes the ob—
servation. The stars in HET sample were analyzed by the ﬁrst author (C.A.) in the
paper and the second author (T.S.) for the OTHERS sample.

By comparing S4N (Allende Prieto et al. 2004) catalog as literature values with
the results of the analysis of the HET sample, we estimated for the high resolution
analysis the uncertainties of 90 K, 0.13 dex, and 0.05 dex Teﬂ, log 9, and [Fe/H],
respectively. The comparison of the analysis of the HET sample with the SSPP
returns the uncertainties of 158 K, 0.25 dex, and 0.12 dex Teff, log 9, and [Fe/H],
respectively. Therefore, considering the errors from the comparison with the S4N
catalog as bench-marking uncertainties, by quadratically subtracting the uncertainties
from the SN catalog comparison from the SSPP results, we empirically determine
the uncertainties in the stellar parameters estimated by the SSPP. The end results of

the uncertainties are a (Teﬂ‘) = 130 K, a (log 9) = 0.21 dex, a ([Fe/H]) = 0.11 dex.

3.13 SUMMARY

We have described the development and execution of the SEGUE Stellar Parameter
Pipeline (SSPP), which makes use of multiple approaches in order to estimate the fun—
damental stellar atmospheric parameters (effective temperature, Teﬂ‘, surface gravity,
log 9, and metallicity, parameterized by [Fe/H]) for stars with Spectra and photome-
try obtained during the course of the original Sloan Digital Sky Survey (SDSS-I) and
its current extension (SDSS-II/SEGUE).

The use of multiple approaches allows for an empirical determination of the inter-
nal errors for each derived parameter, based on the range of the reported values from
each method. Among 128,000 spectra from 200 SEGUE plug-plates, typical internal
errors for stars which have derived stellar parameters available, from the SSPP, in the

range 4500 K S Teff g 7500 K, are 0(Teff) = 70 K (s.e.m), 0(log g) = 0.18 (s.e.m),

81

and a([Fe/H]) = 0.07 (s.e.m). Paper III points out that the internal scatter estimates
obtained from averaging the multiple estimates of the parameters produced by the
SSPP underestimate the external errors, owing to the fact that several methods in
the SSPP use similar parameter indicators and atmospheric models.

The results of a comparison with an average of two different high-resolution spec-
troscopic analyses Of over 100 SDSS-I/SEGUE stars suggests that the SSPP is able to
determine Teﬁ‘, log 9, and [Fe / H] to precisions of 141 K, 0.23 dex, and 0.23 dex, respec-
tively, after combining small systematic Offsets quadratically for stars with 4500 K
S Teﬂ' S 7500 K. These errors differ slightly from those obtained by Paper III (0(Teﬁ‘)
= 130 K, 0(log g) = 0.21 dex, and 0([Fe/H]) = 0.11 dex), even though they share
a common set Of high—resolution calibration observations. This arises because Paper
III derived the external uncertainties of the SSPP only taking into account the stars
observed with the HET (on the grounds of internal consistency). The sample referred
to as OTHERS in Paper III exhibits somewhat larger scatter in its parameters, when
compared with those determined by the SSPP. Observation of several hundred addi-
tional stars from SDSS-I/SEGUE with HET is now underway. Thus, in the future,
we will be able to use a homogeneous sample gathered by HET in our tests. Also,
additional high-resolution data for stars outside of our adopted temperature range
will enable tests for both cooler (Teff < 4500 K) and warmer (Teff > 7500 K) stars.

Considering the average internal scatter from the multiple approaches and the
external uncertainty from the comparisons with the high-resolution analysis together,
the typical uncertainty in the stellar parameters delivered by the SSPP are 0(Teg) =
157 K, 0(log g) = 0.29 dex, and a([Fe/H]) = 0.24 dex, over the temperature range
4500 K S Teff S 7500 K.

However, it should be kept in mind that the errors stated above apply for the very
highest S/N spectra obtained from SDSS (S/N > 50/1), as only quite bright stars

were targeted for high-resolution observations. The uncertainty Of the parameter

82

estimates will be larger, with declining S/N, as shown in Table 3.5. In addition,
outside of the quoted temperature range (4500 K S Teff S 7500 K), we presently do
not have sufficient high-resolution spectra to fully test the parameters obtained by
the SSPP.

The results of a comparison to literature values of the overall [Fe/ H] of selected
member stars in a sample of Galactic open and globular clusters suggests that the
metallicities estimated by the SSPP are within :1: 0.1 dex of these values, for a wide
range of colors (-0.3 S g— r _<_ 1.3), down to a spectroscopic Signal-to—noise of S/ N =
10/ 1. The following chapter discusses this analysis in great detail, and indicates that
the valid range of the effective temperature for determining the stellar parameters
by the SSPP is wider than that presently testable with the high-resolution analysis.
Once we obtain high—resolution spectroscopy of hotter (Teﬂ‘ > 7500 K) and cooler
(Teﬁ‘ < 4500 K) stars, we will be able to better conﬁrm the color range where the
SSPP is capable of estimating accurate parameters.

Approximate spectral types are assigned for stars, based on two methods, with
differing limitations. A set of distance determinations for each star is also obtained,
although future work will be required in order to identify the Optimal method.

We conclude that the SSPP determines, with sufﬁcient accuracy and precision,
radial velocities and atmospheric parameter estimates, for stars in the effective tem-
perature range from 4500 K to 7500 K, to enable detailed explorations of the chemical

compositions and kinematics Of the disk and halo populations of the Galaxy.

83

 

CHAPTER 4:
VALIDATION WITH GALACTIC OPEN
AND GLOBULAR CLUSTERS

 

4.1 PHOTOMETRIC AND SPECTROSCOPIC DATA

Galactic globular and Open clusters are nearly ideal testbeds for validation of the
stellar atmospheric parameters estimated by the SSPP. In most clusters, it is ex-
pected that their member stars were born simultaneously out of well-mixed, uniform-
abundance gas at the same location in the Galaxy. Therefore, with the exception
of effects due to post main-sequence evolution, primordial variations in carbon and
nitrogen, or contamination from binary companions that have transferred material,
the member stars should exhibit very similar elemental abundance patterns. Three of
the clusters in our study, M 13, M 15, and M 2, have well known CN variations that
extend to the main-sequence turnoffs (Smith & Briley 2006 for M 13; Cohen, Briley, &
Stetson 2005 for M 15; Smith & Mateo 1990 for M 2). However, these abundance vari-
ations can be ignored when deriving metallicities from regions of the spectra that do
not include CH, CN, or NH features, as is the case with most of our techniques (those
that may be affected by the presence Of such features are automatically de-selected
in the determination of the adopted [Fe/H]).

True cluster members should exhibit small radial velocity differences with respect
to their parent clusters. Furthermore, it is possible to examine theoretical predic-

tions of temperatures and surface gravities for member stars that lie along the cluster

84

 

”'1 v , -
'.’-]"I. a '. .

37.0

36.5

DEC (Degree)

'-
o
n
a
o

,.
__
V:

o ‘l

..

.' I?

234

1
J.
. d

36.0

 

 

 

 

Figure 4. 1 Stars with available photometry in the ﬁeld of M 13. The red dots represent
photometry from the SDSS PHOTO pipeline, while the black dots are from the
crowded—ﬁeld photometry analysis. Blue open circles indicate stars with available
SDSS spectroscopy. The green circle is the tidal radius. The area inside this radius is
regarded as the cluster region; the annulus between the two black circles is considered
the ﬁeld region.

main sequence (MS), red giant branch (RGB), or horizontal branch (HB) in color-
magnitude diagrams (CMDS). As part of tests of the SEGUE star-selection algorithm
(Adelman—McCarthy et al. 2008) and the SSPP, and during normal SEGUE opera-

tion, we have obtained ugrz‘z photometry and medium-resolution (R ~ 2000) spec-

85

 

13.0 —

y—s
I"
LII

DEC (Degree)

p—
I"
O

11.5

 

 

Figure 4.2 Same as Figure 4.1 but for M 15. Unlike M 13, the ﬁeld region for M 15
is not annuli centered on the clusters, due to the proximity of these clusters to the
edges of the scans. The region inside the black circle is taken for the ﬁeld region.
This is taken as the region where likely member stars are considered. See Chapter
4.3 for likely member selection.

troscopy for large numbers of stars along lines of sight toward the globular clusters

M 13, M 15, and M 2 and the open clusters NGC 2420 and M 67. Below we discuss

these photometric and spectroscopic data in more detail.

86

4.1.1 PHOTOMETRIC DATA

The ﬁrst-pass photometric data for each of the clusters used in the present study were
secured by querying the DR—3 (Abazanjian et al. 2005), DR—5 (Adehnan—McCarthy
et al. 2007), and DR—6 (Adelman-McCarthy et al. 2008) releases from the SDSS
Catalog Archive Server (CAS).

Figure 4.1 illustrates one Of the primary challenges in working with data for clus-
ters Obtained with SDSS — the automated PHOTO pipeline (Lupton et al. 2001) was
not designed to adequately deal with crowded ﬁelds such as the central regions Of
globular clusters. As a result, essentially all of the stars in this region (which are by
deﬁnition the most likely ones to be cluster members) do not have reported apparent
magnitudes in the SDSS CAS. To circumvent this limitation as much as possible,
we have instead performed crowded ﬁeld photometry for the center of the clusters,
using the DAOPHOT/ALLFRAME suite Of programs (Stetson 1987, Stetson 1994).
A full description of the methods used and the photometric measurements Obtained
is provided by An et a1. (2008). Briefly, DAOPHOT was run on each image, and the
ﬁve images of each ﬁeld (one for each ﬁlter) were then simultaneously run through
ALLFRAME. HSTDAOGROW, which is a modiﬁed version of DAOGROW (Stetson
1990), was used to derive aperture corrections to the point-spread—function photom-
etry for the SDSS aperture radius of 7.4”. Finally, the DAOPHOT photometry was
tied to the native 2.5-meter photometric system, using data in ﬁelds farther away
from the clusters. This procedure also permits a check on the techniques used by
the SDSS PHOTO pipeline in regions outside the cluster where the areal density Of
sources on the sky is sufﬁciently low.

After completing the above procedures, we ﬁnally combine the results from the
PHOTO pipeline with those from the crowded-ﬁeld photometry to Obtain an almost
complete catalog of ugrz‘z photometry for stars in the region of each of our program

clusters. All photometric data are corrected for extinction and reddening by appli-

87

DEC (Degree)

,, I! 3.

f 3:
-. n 7: ,. ‘J- . .
.'- ‘~."~.’:‘r..' ,‘. “3'; '1...

 

 

l l l l l l l l

I
322.5 323.0 323.5 324.0
RA (Degree)

H1 1 I | I l l l l l 1

 

 

Figure 4.3 Same as Figure 4.1 but for M 2. Unlike M 13, the ﬁeld region for M 2 is
not annuli centered on the clusters, due to the proximity of these clusters to the edges
of the scans. The region inside the black circle is taken for the ﬁeld region. This is
taken as the region where likely member stars are considered. See Chapter 4.3 for
likely member selection.

cation of the Schlegel, Finkbeiner, 85 Davis (1998) maps. The average reddening
(E(B — V)) for stars in the direction of these clusters is 0.017, 0.110, 0.045, 0.041,
0.032 for M 13, M 15, M 2, NGC 2420, and M 67, respectively. An et al. (2008)

also adopt very similar values of the reddening. Comparing with the literature values

88

listed in Table 4.1, most of the average reddenings of the clusters agree within about

0.02 mags of our adopted values.

4.1.2 SPECTROSCOPIC DATA

The spectroscopic data discussed in this section were Obtained during the course Of
SEGUE tests and normal SEGUE Observations.

An initial set of candidate member stars of the globular and open clusters studied
in this thesis were selected on the basis of photometric and astrometric data (proper
motions) from the literature. The central cores Of the clusters were not targeted
because the PHOTO pipeline does not resolve the very crowded ﬁelds into single star
detections, and also due to limitations on the separations of the ﬁbers during the
spectroscopic follow-up stage. The primary method for selecting member candidates
was performed by plotting a photometric CMD for a given cluster, and choosing stars
from regions of this diagram that correspond to location on the MS turnoff or RGB
of the cluster. An additional list Of bright stars for M 15 and M 2 with previously
available proper motions consistent with membership in the clusters was provided
by Cudworth (1976 and private communication) and Cudworth 8; Rauscher (1987).
Other stars in the ﬁelds of these clusters were used to ﬁll spectroscopic ﬁbers using
the default SEGUE target selection algorithm (Adelman-McCarthy et al. 2008).
While many of these additional targets turned out to be stars from the general ﬁeld
populations, a signiﬁcant fraction turned out serendipitously to be members of the
clusters.

For M 13, three specially designed plug-plates were Obtained. Two of the three
plug-plates followed the standard SEGUE target selection procedure (Adelman-McCarthy
et a1. 2008) of sampling stars with a variety of spectral types based on the SDSS imag-
ing and PHOTO processing. An additional set Of likely M 13 members, including

several stars that were saturated in the SDSS image (7‘ < 14.5) and with coordi-

89

 

DEC (Degree)

 

 

114.4 114. 114.8 115.0
RA(Degree)

 

. v

 

 

Figure 4.4 Same as Figure 4.1 but for NGC 2420. The green circle is 18, in radius;
this is taken as the region where likely member stars are considered. See Chapter 4.3

for likely member selection.

nates from Cudworth & Monet (1979) and Cudworth (private communication), were
added to the target list for the third plug-plate with high priority (bumping ordi—
nary SEGUE targets), in order to Obtain spectra Of several likely giant—branch and

horizontal-branch members.

In the case of NGC 2420, the stars chosen for spectroscopy were primarily tar-

90

geted from the SDSS photometry Obtained by the PHOTO pipeline, using the normal
SEGUE target selection algorithm. Additional stars with apparent magnitudes in the
range 14.5 < 9 < 20.5 that fell within 0.5 degrees from the center of NGC 2420 were
also targeted for spectroscopy. However, due to crowding, if two objects were within
55” of one another, then only one received a ﬁber. Thus, not every star in the central
region Of N GO 2420 was targeted. There were about 480 objects selected in this way,

including a number Of non-cluster members that are located in the NGC 2420 ﬁeld.

Table 4.1: Properties of the Clustersi

 

 

 

M 13 M 15 M 2 NGC 2420 M 67
(NGC 6205) (NGC 7078) (NGC 7089) (NGC 2682)
RA (J2000) 16:41:41.5 21:29:58.3 21:33:29.3 07:38:23 08:51:18

DEC (J2000) +36:27:37 +12210:01 —00:49:23 +21:34:24 +11:48:00

(1,5) (59.0, +40.9) (65.0, —27.3) (58.4, —35.8) (198.1, +19.6) (215.7, +319)
[Fe/H] -—1.54 -—2.26 —1.62 —0.44 +0.02

m — M 14.48 15.37 15.49 12.54 9.97
v,(km s-l) —245.6 -107.0 —5.3 75.5 32.9
E(B — V) 0.02 0.10 0.06 0.03 0.06

r, 2518’ 21.50’ 21.45’ 5’ 25’

 

For M 67 , the initial targets came from the SDSS imaging data processed by the

PHOTO pipeline. However, for this cluster, many candidate members with positions,

 

iThe parameter rt is the tidal radius in arc minutes for M 13, M 15, and M 2 and the
apparent diameter in arc minutes for NGC 2420 and M 67 from Dias et al. (2002). The
listed distance modulus, m—M, is corrected for extinction. The parameters for the globular
clusters, M 13, M 15, and M 2 are from Harris (1996); those for the open clusters N GO 2420
and M 67 are from WEBDA (http://www.univie.ac.at/webda/). The radial velocity (V,)
listed for NGC 2420 and M 67 is the average of the literature values (see Chapter 4.5). The
[Fe/ H] of NGC 2420 and M 67 is based on the high-resolution spectroscopy described by
Gratton (2000).

91

 

 

DEC (Degree)

 

 

 

Figure 4.5 Same as Figure 4.1 but for M 67. The green circle is 30’ in radius; this
is taken as the region where likely member stars are considered. See Chapter 4.3 for
likely member selection.

magnitudes, and colors from the WEBDA (http://www.univie.ac.at/webda/) cata-
logs were added to the target lists. The bright targets (with r < 14) saturate the
SDSS imaging camera, so these were added from the literature (Sanders 1989; Fan
et al. 1996). Such bright stars present diﬁiculties for regular SDSS spectroscopic

observations (such as scattering light onto adjacent ﬁbers), so there were exposed for

92

shorter than normal integration times. About 200 very bright stars between about
12 < 9 < 14 were targeted.

Note that in each cluster ﬁeld some stars with no pre-existing ugriz photometry
from the PHOTO pipeline were also targeted from the catalogs in the literature. For
those stars, we Obtained ugrz’z photometry from the DAOPHOT procedure.

In total, we obtained SDSS spectroscopy for 1920, 1280, 1280, 1280, and 640
targets, including Sky spectra and calibration object spectra, in the ﬁelds of M 13,
M 15, M 2, NGC 2420, and M 67 respectively. Therefore, the total number of
selected member stars will vary from cluster to cluster. The particular clusters that
were chosen was essentially set by their presence (or not) in the SDSS-I/SEGUE
footprint, since the usual observing process requires that photometry be available
prior to spectroscopic targeting. Some otherwise problematic clusters were included
as a result. For example, M 2 presents a special challenge for separation of its likely
members from the general ﬁeld population, as its radial velocity is close to zero, where
it overlaps strongly with several Galactic stellar populations. In addition, this cluster
is the most distant among the sample under investigation; as a result, the spectra
Obtained are generally of lower S/N than the rest of our sample. However, M 2 is
located in the equatorial stripe (—1.27° < 6 < 127°), which was scanned multiple
times during SDSS-I and SDSS-II; hence we have very accurate photometry to employ.
For the remaining sample of clusters with available photometry, we attempted to
cover as wide a metallicity range as possible for spectroscopic study. The reduced
spectra were processed through the SSPP in order to estimate Teﬂ', log 9, and [Fe/ H],
among other quantities. Table 4.1 summarizes the global properties of the clusters
under consideration in this study, taken from the compilation Of Harris (1996) for
the globular clusters and from the literature, and WEDBA or Gratton (2000) for the

Open clusters.

93

4.2 RADIAL VELOCITIES

There are two estimated radial velocities provided from the SDSS Spectroscopic
pipeline. One is an absorption-line redshift Obtained by cross-correlating the spectra
with templates that were acquired from SDSS commissioning spectra (Stoughton et
a1. 2002). Another comes from matching the spectra with ELODIE template spec-
tra (Prugniel 87: Soubiran 2001). In most cases the velocity based on the ELODIE
template matches appears to be the best available estimate, as Spectra of “quality
assurance” stars with multiple measurements Show the most repeatable values for this
estimator. We adopt this velocity in most of our analysis. A more detailed descrip-
tion of the determination of the best available radial velocity, and of the zero-point

offsets in the radial velocities, can be found in Chapter 3.

4.3 MEMBERSHIP SELECTION FROM SPECTROSCOPIC

SAMPLES

Owing to an insufﬁcient number of stars with available spectroscopy for each cluster,
it is not possible to obtain a well-deﬁned Color Magnitude Diagram (CMD) based
solely on spectroscopically observed stars. Thus, we make use of photometric data in
the ﬁeld of each cluster, and describe below how we obtain a relatively clean CMD

for individual clusters, and select likely member stars from the spectroscopic data.

4.3.1 LIKELY MEMBER STAR SELECTION POR GLOBULAR CLUS-
TERS

One of the primary issues that one needs to address when creating a CMD for a star

cluster, or for selecting likely member stars, is the removal of contamination from

ﬁeld stars. In order to approximately isolate the likely cluster members from the

ﬁeld stars along the line of sight, we have made use of the CMD mask algorithm

94

 

12111111111111111111(1111llTIIYIIIIIITlllVIIIIIVY

20-

 

 

 

 

22.....1....1i...1'.-..1.... 7.111 .
-l.0 -0.5 0.0 0.5 1.0 1.5 —0.5 0.0 0.5 1.0 1.5
(g-r)0 (g-r)0

 

Figure 4.6 Color-Magnitude Diagrams of the M 13 stars inside the tidal radius (left
panel), and inside the ﬁeld region (right panel), shown as black dots. The selected
sub-grids from the CMD mask algorithm are shown as red squares in the left panel
and green squares in the right panel. These selected sub-grids are used in the analysis.
described by Grillmair et al. (1995). We illustrate the basic idea by application of
this algorithm to the M 13 ﬁeld shown in Figure 4.1. We ﬁrst select all stars inside
the estimated tidal radius (25.2,; Harris 1996), shown as the innermost green circle
in Figure 4.1. This is regarded as the cluster region. The red dots represent stars
with available photometry from the SDSS PHOTO pipeline (Lupton et al. 2001);
the black dots are stars with photometry obtained from DAOPHOT. The blue open
circles indicate stars with available spectroscopy. We then choose an annulus outside
the cluster region, indicated on the ﬁgure as the region between the two black circles,

as the ﬁeld or background region.

95

 

16~

18*

 

 

 

 

22 I 1 I I 1 l 1 1 1 1 l l 1 1 1 l 1 1 I l l 1 1'1 - 1 1 1 1 l 1 1 1 1 l 1 1 1 l 1 1 1 1 l 1 1 1 1
-l.0 -0.5 0.0 0.5 1.0 1.5 -0.5 0.0 0.5 1.0 1.5
(g - 00 (g - r)0

 

Figure 4.7 Same as Figure 4.6 but for M 15.

We next obtain CMDs of each region, spanning —1.0 S (g — 7')0 S 1.5 and
12 S go S 22, and then subdivide these diagrams such that the size of each sub—grid
is 0.2 mag Wide in go and 0.05 mag wide in (g — r)0 color. The total number of
sub-grids for the CMDs in each region is thus 2500 (50x50). Figure 4.6 shows the
resulting CMDs of the cluster (left panel) and ﬁeld (right panel) regions, over-plotted
with squares representing the selected sub—grids, obtained as described below.

We ﬁrst calculate the signal-to—noise (3/71) in each preliminary sub-grid by applica-
tion of equation 4.1 over the entire CMD region shown in Figure 4.6. Here we assume
that the ﬁeld stars outside the tidal radius are uniformly distributed throughout the

annulus area.

96

 

12 ITﬁITIIIllIITIIITTTTIIII IIIIIIIIIITIIVTIIIIIIIII
.

167

18—

 

 

 

 

22 lllllllmjlllllllllLallj‘ lllllllllllllLlllllLLill

-1.0 -0.5 0.0 0.5 1.0 1.5 -0.5 0.0 0.5 1.0 1.5
(8‘00 (8-r)0

 

Figure 4.8 Same as Figure 4.6 but for M 2.

"C(zij) _ gnf(z,j) .
(ﬂu-(231') + 92nf(i,j)

In the above, nc and nf refer to the number of stars in each sub-grid with color

 

 

s/n(z',j) = (4-1)

index 73 and magnitude index j, counted within the cluster region and ﬁeld region,
respectively. The parameter 9 represents the ratio Of the cluster area to the ﬁeld area.

The following procedures are applied in order to ﬁnd the optimal range of colors
and magnitudes that correspond to the likely members of each cluster. First, we sort
the elements Of s/n(z’, j) in descending order, so that we obtain a one-dimensional
array of s/n(z’, j ) with index I; the array element with the highest s/n(z’, j ) corresponds

to l = 1. The next step is to obtain star counts in gradually larger regions of the

97

 

141f1 ITfTIIIOIIIITNIIIIIIII

l

16

 

 

 

22IIIIL.111.111.111.111HmH
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
(g-r)0

 

Figure 4.9 Color-Magnitude Diagrams of the NGC 2420 ﬁeld. The red line is the
ﬁducial obtained by application of a robust fourth-order polynomial ﬁt. The stars
inside the blue lines, determined by offsets from the adopted ﬁducial of :1: 0.06 mags
in (g — r)0, are regarded as likely member stars from the photometric sample.

CMDS. The accumulated area is represented as ak = kal, where a, = 0.01 mag2,

which is the same for all sub-grids, and is the area Of a single sub-grid in the CMD

98

array, and the k is the number of sub-grids to combine. Finally, the cumulative

signal-to—noise ratio, S /N (ak), as a function Of ak, is calculated from:

Nc(ak) — 9Nf(ak)
\/N.<ak) + gZNNak)

 

 

S/ N (Gk) = (42)

where

Nc(ak)= 2:710“), Nf( ak) =an(l) (4.3)

The parameter 736(1) denotes the number of stars within the cluster region having
ordered color-magnitude index l; n f(l) represents the same quantity for the ﬁeld
region. Based on the maximum value of S /N (ak), a threshold value of s/n is picked
in order to select high-contrast surface-density areas (i.e, high s/n) between the cluster
and ﬁeld regions. These are considered to be the sub-grids that contain likely cluster
members. After removing Single-star events in areas of the CMDS where the ﬁeld-star
density is low, all stars in sub-grids with s/n(z', j) greater than the threshold value
of s/n are selected. These stars are considered as the photometrically likely member
stars for a given cluster.

The red squares Shown in the left panel of Figure 4.6 are the sub-grids with s/n
greater than the threshold value; the corresponding sub-grids in the ﬁeld region are
shown as green squares in the right panel of this ﬁgure. Figure 4.11 depicts the
CMD of the selected likely members of M 13 from the photometry data, shown as
black dots. The same procedures are performed to differentiate the likely member
stars of M 15 and M 2, based on photometry alone. Figures 4.2 and 4.3 Show ﬁelds
in the the vicinity of M 15 and M 2, respectively. Due to the lack of photometry

data (the available scans do not allow for full regions, centered on the cluster, to be

99

 

14

15

IITIITWI‘IIITITIWII

162—

b— .
'e e.

18

IJIOITLTjIIIIIIIIIIIIII‘IOI
o

0 8

19

   

e‘
3"
. 5'

0 o
0“.

Illllllllll1111111111111llllllllllllLLLlIIJIJLLlllllllllllL

I'IJ’IIIIIOIFJIg—FI
.3

 

 

 

...z’..':‘..-.,... . : . . . .t' . . ‘. . ., . 2.:
20 303.1. 0f :vl .1°-.1..°:1: .°l'"1.:s. 1 lHI -l I l l'.1 1. l .1 1 “Eff? . 1 7
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

(g - r)0

Figure 4.10 Color-Magnitude Diagrams of the M 67 ﬁeld. The red line is the ﬁducial
obtained by application of a robust fourth-order polynomial ﬁt. The stars inside the
blue lines, determined by Offsets from the adopted ﬁducial of :1: 0.10 mags in (g — r)0,
are regarded as likely member stars from the photometric sample.

examined), the ﬁeld regions (black circles in the ﬁgure) are offset from the clusters.

Furthermore, the cluster region for M 15 is a bit smaller than the tidal radius for this

100

 

14R 9 L

16 _ . Q

 

 

 

22 1 I I I I 1 I I I I 1 I I I I
-O.5 0.0 0.5 1.0
(8 - r)0

 

Figure 4.11 The M 13 Color-Magnitude Diagram based on the likely member stars
(black dots) selected from the photometric sample. The likely members identiﬁed
from the spectroscopic sample are indicated with red Open circles.

cluster. Choosing a smaller region for M 15 doesn’t affect our analysis, since the full

tidal radius of M 15 is considered as we select likely members from the spectroscopic

sample. Figures 4.7 and 4.8 Show the CMDS of the cluster and ﬁeld regions for M 15

101

 

14*—

l .:,:t,::;_,~:._,

16—

18:-

 

221IIII1III

 

 

 

(g - 1)0

Figure 4.12 Same as Figure 4.11 but for M 15.

and M 2, respectively, with the sub—grids determined.

1.0

We now proceed to select the stars that are likely members of the globular clusters

from the available spectroscopic sample. This step begins by selection of the stars

within the cluster tidal radii that pass the photometric criterion for membership,

102

 

14— —

15001.0 . .f‘.
_ . o: ,
16 _ ' _.
O
on r -
18 — ~
20 *- E

 

 

 

22 l l I I l l l 1 l 1 l l l l l

 

Figure 4.13 Same as Figure 4.11 but for M 2.

based on their location on the cluster CMDS according to the algorithm described
above.
Figure 4.11 displays the cleaned CMD of M 13, overplotted with the likely mem-

bers from the spectroscopic sample (shown as red circles). The same procedures are

103

 

 

I I I I I I I ‘ I I I Iﬁ 1 I I I I I I
14 . I D
: %v-. I :1
: 3f", 3
E 39% f
_ ., I.
16 _— {Ia-.1:
: xii-3.:
: .31133- 3
17 : Praia .. ' i
: ;Q33§: :
_ . 10.. _
50° : Aggie; :
: - 1.03%.}, :
18 T “lag-:39. _:
: -'.(§;4‘E§?0 .- :
: gigs” :
‘ .‘5‘:*m= 4 j
195— ' 3%; —:
: - : é€9l% :
_ Q ' ' _.
3 53:8; . 3
; g _
20: °°§os° j
: «a? j
213III1IIIIII IIIIIIIIIIII

 

 

II
0.0 0.2 0.4 0.6 0.8 1.0 1.2
(g-r)0

Figure 4.14 Same as Figure 4.11 but for NGC 2420.

carried out to identify likely member stars of M 15 and M 2 from their spectroscopic
data. Figures 4.12 and 4.13 are the cleaned CMDS Of M 15 and M 2, respectively,
with the likely members indicated by the red Open circles. At this stage of the anal—
ysis there are 458 likely members for M 13, 164 for M 15, and 105 for M 2 identiﬁed.

104

Additional cuts, based on the derived metallicity estimates and RVs, in order to select

“true member stars”, are described in Chapter 4.4.

4.3.2 LIKELY MEMBER STAR SELECTION FOR OPEN CLUSTERS

Since the ﬁelds of nearby open clusters are not as crowded as those of globular clusters,
the signal-tO-noise ratio between the cluster region and the background region is not
sufﬁciently high to select likely cluster members by means of the CMD mask algorithm
(see Figure 4.4 and 4.5). As an alternative, we ﬁrst Obtain a ﬁducial line for an open
cluster (including its main sequence and sub-giant branch, if it exists) by use of an
robust polynomial ﬁtting procedure. As an example, Figure 4.9 displays the CMD
of the NGC 2420 ﬁeld inside a radius Of 0.3 degrees from the center of the cluster.
According to the Open cluster catalog of Dias et al. (2002), the apparent diameter
of this cluster is only 5, on the sky, but we prefer to adopt a 18’ radius, in order to
include as many member stars as possible. The red line is the ﬁducial line derived
from the robust polynomial ﬁt. The blue lines are the upper and lower limits (ﬁducial
i006 dex in (g — 7')0), determined by eye. Stars from the spectroscopic sample that
fall within the 18’ radius and inside the blue limit lines in Figure 4.9 are identiﬁed.
A similar procedure is applied to M 67, except that a 30' (apparent diameter of
25,; Dias et al. 2002) radius and ﬁducial :I: 0.10 mag in (g — r)0 is used. Figure 4.14
and 4.15 depict the selected likely member stars as red circles (from the spectroscopic
data) and black dots (from the photometry data). Based on this selection method,
there are 238 and 65 (66) for NGC 2420 and M 67, respectively. The ﬁrst listed
number for M 67 indicates the stars with available estimates Of [Fe/ H] from the
SSPP, while the quantity in parentheses represents the number of stars with available
radial velocities (RVs). Additional cuts, based on the derived metallicity estimates

and RVs, in order tO select “true member stars”, are described below.

105

 

13III‘IIIITIIIﬁIIIIIII

14

15

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Figure 4.15 Same as Figure 4.11 but for M 67.

t-d
O\

4.4 DETERMINATION OF OVERALL METALLICITIES AND

RADIAL VELOCITIES OF THE CLUSTERS

In order to investigate the accuracy of our derived metallicities and RVs, we now con-

sider the global distribution of these parameters Obtained from the current version

106

 

 

 

 

 

 

 

 

 

250wrrrrrrrrrrrrrrTrHITrr rrrrrr I rrrrrrrrr I rrrrrrrrrrrrr rrvrlrl rrrrrrr I rrrrrrr rrlrrrrrrrrr] rrrrrrrrr
t . .
. ---- Full plate: 1714 : —--- Full plate: 1779
_ - - Likely members : 458 g - - ~Likely members : 458
_ — Members : 293 1* —Members : 293
200 r «e L
150 ~ 1i + 4
I. ”ii 4» J
z I i ‘
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O I .LHJI'LI'i-I'. 11 Ian—111.111.::ILIIIII-l—I‘IIl-mhrlfu
-4 1 -300 -200 -100 0 100
Radial velocity (km/s)

Figure 4.16 Distributions of [Fe/ H] and radial velocity for stars in the direction of
M 13. Gaussian ﬁts (blue solid curves) to the distribution of the selected true mem-
bers, shown in the green histograms, are over-plotted.

of the SSPP for the likely cluster members. In this section, we describe a method to
isolate “true member stars” from the selected likely member stars from the spectro-

scopic samples described above. We then use these subsamples to determine our best

estimates Of the overall metallicities and RVs of the clusters considered in this study.

4.4.1 SELECTION OF TRUE MEMBERS

We establish the criteria for carrying out metallicity and RV cuts as follows.

The left panel Of Figure 4.16 illustrates the [Fe/ H] distribution for three different
subsamples of stars in the region of the globular cluster M 13. The ﬁrst, shown as the
black dot-dashed line, represents the distribution of derived metallicities for the 1714

stars with available estimates of [Fe/ H] along the line of sight to this cluster. Note

107

 

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- - Likely members : 164
— Members : 98

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Figure 4.17 Same as Figure 4.16 but for M 15.

that this distribution includes numerous stars that cannot be considered members of
the cluster, as they cover a much wider range Of [Fe/ H] than might be expected if
they were drawn exclusively from the cluster member population. The dot-dashed
line in the right panel Of Figure 4.16 shows the RV distribution of these same stars.
The red dashed line in the left panel of Figure 4.16 is the distribution of [Fe/ H] for
the 458 likely members selected from the spectroscopic sample as described in §3. We
obtain a Gaussian ﬁt to the highest peak of the distribution of these stars (red dashed
line in Figure 4.16), and obtain an estimate of the mean (<[Fe/H]>) and standard
deviation (0) for this distribution. Similar ﬁts are Obtained for the distribution of
RVs for the likely members Shown in the right panel of Figure 4.16. On the basis Of
these ﬁts, we now trim likely outliers by application of a 2-0 clipping procedure, for

example:

108

< [Fe/H] > ’20[Fe/H] S [Fe/H]* S< [Fe/H] > +2‘7[Fe/H] (4.4)

< RV > —20’RV S RV* S< RV > +2URV (4.5)

In the above, [Fe/H],r and RV* correspond to the values of these parameters for
each star under consideration. The stars surviving both of these clips are considered
true cluster members for the purpose of this study. Note that at no point have we
considered the external “known” values of [Fe/ H] and RV for the clusters as a whole.

The same procedure is performed for stars in M 15, M 2, N GC 2420, and M 67.
Based on the application of these membership cuts, we now have a total of 293 stars
identiﬁed as true members of M 13, 98 stars as true members of M 15, 76 stars as
true members of M 2, 163 stars as true members of NGC 2420, and 52 stars as true
members of M 67. The distribution of [Fe/ H] and RV for the surviving members (true
cluster members) Of M 13 are shown as green histograms in the left and right panels
of Figure 4.16, respectively. Similar plots for M 15, M 2, NGC 2420, and M 67 are
shown in Figures 4.17, 4.18, 4.19, and 4.20, respectively. M 2 is the most distant
object among the clusters considered in this study, and the Signal-to-noise ratio of
the spectra Obtained for its members are generally lower than for stars in the other
clusters of our sample. This results in a smaller number Of stars with reliable [Fe/ H]
estimated than for the other globular clusters. Tables C.1—C.5 list the observed and
derived quantities for all of the individual stars considered as true member stars in

the analysis of each cluster. The columns are as deﬁned in the table notes for Table

C1

109

 

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120 mu Full plate: 1054 A —.-..Full plate: 1164
— - Likely members : 105 - — . Likely members: 105

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-4 -3 -2 -l 0 l -200 -100 100
[Fe/H] Radial velocity (km/s)

Figure 4.18 Same as Figure 4.16 but for M 2.

4.4.2 DETERMINATION OF OVERALL ESTIMATES OF MEAN CLUS-

TER METALLICITY AND RADIAL VELOCITY

We now obtain ﬁnal estimates of the cluster metallicities and radial velocities, based
on Gaussian ﬁts to the surviving true member stars for each cluster, as shown by
the blue curves in Figures 4.16—4.20. The parameters in the top half in Table 4.2
summarize these determinations. The mean and 1 a spread of the metallicities of the
true member stars are listed in columns (2) and (3), respectively; columns (4) and
(5) are for the radial velocities. Column (6) lists the total number Of selected true
member stars associated with each cluster, based on our analysis. External estimates
of the metallicities and radial velocities for the globular clusters, adopted from the
Harris ( 1996) compilation, are listed in columns (7) and (8). The radial velocities for

the Open clusters are averages of literature values. See Chapter 4.5 for the details.

110

Column (9) lists metallicity estimates for these clusters obtained from high-resolution
spectroscopy of a limited number of brighter stars by Kraft & Ivans (2003) for M 15
and M 13, Ivans (private communication) for M 2, and Gratton (2000) for NGC 2420
and M 67.

Table 4.2: Derived Radial Velocities and Metallicities of the Clustersj

 

 

 

 

Cut Cluster <[Fe/H]> a ([Fe/H]) <RV> 0 (RV) Ntot [Fe/H]H RVH [Fe/H]HR
dex km 3‘1 km 8‘1 km s‘1
(1) (2) (3) (4) (5) (6) (7) (8) (9)
[Fe/H]
& RV
M 13 -1.59 0.13 —244.8 8.8 293 —1.54 -245.6 —1.63
M 15 -2.19 0.17 —108.2 11.7 98 —2.26 —107.0 —2.42
M 2 —1.52 0.18 —2.1 9.8 76 —1.62 -5.3 -1.56
NGC 2420 —0.38 0.10 +75.l 5.9 163 +75.5 —0.44
M 67 —0.08 0.07 +349 4.1 52 +32.9 +0.02
RV
M 13 —l.59 0.13 -244.8 8.9 319 —1.54 —245.6 —1.63
M 15 —2.19 0.18 —108.4 12.2 110 —2.26 —107.0 —2.42
M 2 —-1.51 0.18 —1.8 10.3 82 -1.62 — 5.3 —1.56
NGC 2420 -O.38 0.11 +75.1 6.0 171 + 75.5 -0.44
M 67 —0.08 0.07 +348 5.8 56 + 32.9 +0.02

 

 

J'[Fe/H]H and RVH for the globular clusters M 13, M 15, and M 2 are from Harris (1996).
Values of [Fe/H]HR, which are based on high-resolution spectroscopy, are from Kraft &
Ivans (2003; M 13 and M 15), from Ivans (private communication; M 2), and from Gratton
(2000; N GC 2420 and M 67). RVH for the open clusters is computed by taking averages of
the literature values. See Chapter 4.5 for details. The column labeled Ntot lists the total
number of true members assigned to each cluster. The parameters in the upper portion of
the table are derived with both [Fe/ H] and RV cuts imposed; only the RV cuts are imposed
for the lower portion.

111

 

 

 

        

 

 

 

 

250TIITTTIIIIIIIYITl-YIII rrrrrrr l IIIIIIII aTI—mTIIIIIIIIT—Y—T—ITI rrrrrrr [rtlrrrrlv
_ .1 _1
_ -.... Full plate: 1113 .1 -...-Full plate: 1171 I! ,
_ — - - Likely members : 238 _, - - - Likely members 1 233 l ! 4
_ — Members: 163 0 —Members: 163 i i .
200 — ~~ I I a
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-3 -2 -1 0 1 -100 O 200

[Fe/H] Radial velocity (km/s)

Figure 4.19 Same as Figure 4.16 but for NGC 2420.

We have checked to see if there is any change of the mean and scatter of our
derived metallicity and the radial velocity for the clusters if we only impose radial
velocity cuts (and not metallicity cuts) to the membership selection. As seen in the
lower half of Table 4.2, little change in these quantities occurs. The total number of
the true members identiﬁed is not much different either. Thus, cluster membership
could have been made by consideration of the radial velocity, tidal radius, and CMD
alone.

In order to check for trends in our metallicity determinations as a function of color
or quality of the the spectra, the distribution of [Fe/ H] for the true member stars of
each cluster, as a function of (g - 'r)0 (left panel) and <S/N>, the average signal—to—
noise ratio per pixel for spectra of member stars over the 4000—8000 A region (right
panel), is shown in Figure 4.21. The red line is the literature value listed in Table

4.2; the green dashed line applies to our our derived mean estimates. Although, as

112

expected, the scatter becomes larger with declining <S/N>, it is clear that there
exist no signiﬁcant trends on [Fe/ H] with color or <S/N>; the SSPP determinations
appear quite robust.

The distribution of the SSPP-derived estimates of metallicity as a function of
estimated log 9, shown in Figure 4.22, also conﬁrms that the [Fe/ H] estimated by
the SSPP is reliable over a wide range of luminosity classes; no signiﬁcant trends are

found with respect to the estimated surface gravity estimates.

4.5 A COMPARISON OF DERIVED METALLICITIES AND
RADIAL VELOCITIES FOR TRUE CLUSTER MEM-

BERS WITH PREVIOUS STUDIES

In this section we present a more detailed comparison of our derived metallicity and

radial velocity of each cluster with various values reported in the literature.

4.5.1 M 13 (NGC 6205)

The three Spectroscopic plug-plate observations of this cluster provide the largest
number (293) of true members selected among the clusters in this study. Our estimate
of the mean abundance, <[Fe / H] > = —1.59, is very close to the Harris (1996) estimate
([Fe/H] = —1.54). However, the recent study of Kraft & Ivans (2003) reported a
revised cluster abundance for this cluster, derived from high-resolution spectroscopy
of 28 giants. Their value indicates a metallicity for M 13 (based on Fe 11 lines) that
is a bit lower than that given by Harris, [Fe/ H] = -1.60, but only 0.01 dex different
than the value we obtained from the SSPP. An alternative [Fe/ H] (from Fe I lines)
reported by these authors indicates a slightly lower value, [Fe/ H] = —1.63. Sneden
et al. (2004) obtained [Fe/ H] = —1.62 (from Fe I lines) and [Fe/ H] = —1.55 (from Fe
II lines), based on a sample of stars observed with the KECK/HIRES spectrograph

113

 

 

 

 

 

 

 

 

r TTTTTTTTT I IIIIIIIII I TTTTTTTTTTTTTTTT . IIIIIIIII I IIIIIIII l IIIIIIIIIIIIIIIII
140 3*- —--.- Full plate : 596 -~-- Full plate : 608 !”i -
L. ' I -I
_ - - - Likely members : 65 - - - Likely members : 66 i i
~ — Members : 52 ——-Members : 52 i : ~
120 T + E g -
. I. I ! .
i . E i i
100 ~ ~~ i i w
I .. : g I
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40 I” LL ' _ I L
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.J ! i
.--' .. ,. :.l
20 5" ~~ 'i ._ ..
I”. _ I .. ! .. .
! : :_.., 2 4,, !-- ! ‘
'- . I”'—-: ...:J- "" 5 AL- P!" J L :J.i""l r”. ‘
O 9-I_I l L_J !-1 1'1 ILL J_I 1 l4 l_L'!- ' I J LL n1 1'l_l l l_l J l'Lb-rq-jz-I'I-I I I-I-tl'x l .‘1 1 I l l l L 1”] l 1.1"
-3 -2 -l l -100 0 100 200
[Fe/H] Radial velocity (km/s)

Figure 4.20 Same as Figure 4.16 but for M 67.

(R ~ 45, 000). Cohen & Meléndez (2005) reported higher values for the metallicity
of this cluster, [Fe/ H] = —1.50, based on a high-resolution (R = 35,000) analysis of a
sample of 25 stars, extending from the giant branch to near the main-sequence turnoff.
Pritzl et al. (2005) determined [Fe/ H] = —1.57 from a compilation of high-resolution
data in the literature. Very recently, Kirby et al. (2008) obtained medium-resolution
(R ~ 6000) spectroscopy for 69 giants in this cluster, over the wavelength range 6300—
9100 A. They report an average of [Fe/ H] = —1.66 , which is slightly lower than our
estimate. Considering the range of [Fe/ H] Obtained from previous studies, it is clear
that the SSPP determination of overall [Fe / H] for M 13 is in excellent agreement. Our
derived spread in the metallicities of the M 13 true member stars (0.13 dex) is also
satisfyingly low, especially considering the wide range of temperatures and gravities
for true members that are considered here.

Our estimate of the mean radial velocity, <RV> = —244.8 km s‘ 1, with a standard

114

deviation of 8.8 km s—l, is in good agreement with that given by Harris (-245.6 km
s‘l). It is important to note that, as mentioned in Paper I, we have already added
+7.3 km s"1 to all DR-6 (Adelman-McCarthy et a1. 2008) stellar radial velocities, in

order to correct a recognized systematic offset.

4.5.2 M 15 (NGC 7078)

There are a total of 98 stars selected by our procedures as true members of this cluster.
Our derived overall abundance of M 15, <[Fe/H]> = —2.19, is close to the value listed
by Harris ([Fe/H] = —2.26). Sneden et al. (1997) reported [Fe/H] = -2.40, based
on high-resolution spectra for 18 bright giants, in good agreement with the value of
[Fe/ H] = —2.37 Obtained by Sneden et al. (2000), from observations of giants at the
tip of the RGB. Kraft & Ivans (2003) obtained [Fe/H] = —2.42 (from Fe 11 lines) and
[Fe / H] = —2.50 (from Fe I lines) for this cluster, based on high-resolution spectroscopy
of nine giants. A value of [Fe/ H] = —2.38 was reported by Pritzl et al. (2005) from
a compilation of high quality data in the literature. Otsuki et al. (2006) reported
[Fe/ H] = —2.29 from an analysis of high-resolution Spectra obtained for six giants
in this cluster. Most recently, Kirby et al. (2008) calculated [Fe/ H] = —2.42 from
medium-resolution Spectra of 44 giants. Since most of the high—resolution analyses
indicate [Fe/ H] ~ —2.40 for M 15, this might indicate that the SSPP overestimates
[Fe / H] by about 0.2 dex at low metallicities. A forthcoming study of the cluster M 92
(based on SDSS-II data that has only been recently obtained) will seek to conﬁrm
this tendency. The spread in the metallicities of true member stars in M 15 reported
by the SSPP is quite low (0.17 dex).

Our estimate of the mean radial velocity, <RV> = —108.2 km 5’1, with a standard

deviation of 11.7 km s—l, agrees very well with that of Harris (—107.0 km 8‘1).

115

4.5.3 M 2 (NGC 7089)

Only a limited number of true member stars (76) are selected by our procedures for
this distant cluster, as the Spectra obtained by SDSS for this cluster are generally of
lower quality than for other clusters in our study. The faintness of M 2 is also a reason
it has not received a great deal of attention by studies at high spectral resolution.
Our derived average metallicity, <[Fe/H]> = —1.52, is slightly higher than the Harris
(1996) value ([Fe/ H] = —1.62), but in very good agreement with the value obtained
by Ivans (private communication), [Fe/H] = —1.56. The estimated spread in our
derived metallicities, 0.18 dex, is quite small, but larger than the spreads obtained
for M 13 and M 15, as expected due to the inclusion of stars in our analysis with low
S /N (~ 10/1).

Our estimate of the mean radial velocity, <RV> = —2.1 km 8.1, with a standard
deviation of 9.8 km s‘l, is a bit higher (by about 3.2 km s-l) than that provided by
Harris (—5.3 km s—l). Although still small, this is the largest offset in radial velocity
among the clusters we consider in this study. However, it should be recalled that the
mean metallicity of M 2 is quite close to that expected for members of the ﬁeld halo
population ([Fe/ H] ~ —1.6), and its (near zero) radial velocity is buried in the peak
of foreground disk stars, which increases the likelihood that non-cluster stars could

have crept into our true member sample.

4.5.4 NGC 2420

There are 163 true member stars selected for this open cluster. The mean metallic-
ity of the selected true member stars reported by the SSPP is <[Fe/H]> = —0.38,
which is only slightly higher than the value determined by Gratton (2000) from high-
resolution spectroscopy of a single member star ([Fe/H] = —O.44). Friel & lanes
(1993) reported [Fe/ H] = —0.42 for nine member stars, based on medium- and low-

resolution spectroscopic data. F‘riel et a1. (2002) determined [Fe/ H] = —0.38 :l: 0.07,

116

based on medium-resolution spectra of 20 member stars. The most recent study, by
Anthony-Twarog et al. (2006), indicated [Fe/H] = —0.37 :t 0.05 dex, derived from
intermediate-band vbyCaHﬁ photometry. These values agree excellently with our
own metallicity estimate for this cluster. The derived Spread in the metallicities of
the true member stars is also very low (0.10 dex).

Concerning the radial velocity for this cluster, Ffiel et al. (1989) derived 80.0 :I:
6 km s"1 from 6 stars. Scott et al. (1995) reported 67.0 km s—1 from 19 member
stars. Friel (1993) reported 84.0 km 3*. Rastorguev et al. (1999) reported a value
of 71.1 km s—l. The literature value of radial velocity for N GO 2420, listed in Table
4.2, is an average of these four values (+755 km 3'1). This average is in excellent
agreement with our derived estimate of +751 km S_1, with a standard deviation of

5.9 km 8.1.

4.5.5 M 67 (NGC 2682)

Only one plug-plate (640 spectra) has been obtained for this open cluster. This, and
the expected large amount of contamination from disk stars, resulted in a relatively
small number (52) of true members being identiﬁed by our procedures. The SSPP-
derived mean metallicity is <[Fe/H]>= —0.08, with a small spread (0.07 dex). This
is lower by 0.1 dex than that of Gratton (2000), [F e/ H] = +0.02, derived from a high-
resolution study of a single member star. Shetrone & Sandquist (2000) determined
[Fe/ H] = —0.05 for 10 blue stragglers and turnoff stars, based on high-resolution
(R ~ 30, 000) spectroscopy. A value of [Fe/ H] = +0.02 :1: 0.03 dex was determined
by Yong et al. (2005) from a high-resolution (R ~ 28, 000) spectroscopic analysis
of three member stars. Randich et al. (2006) analyzed 10 member stars of this
cluster, based on high-resolution (R ~ 45,000) spectroscopy, and derived [Fe/ H]
= +0.03 :1: 0.01 dex. Ffiel & Boesgaard (1992) computed [Fe/H] = +0.02 1 0.12

dex for three F dwarfs observed at medium spectral resolution. From a medium-

117

 

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_ . - e 1 4 : I - .L 1- I a. - 1;" --- v- .1; : - -- - .
: .M2 N=76, Red: [Fe/H]lit=-1.62 3; Green:<[Fe/l-l]>=-l.52, sIgma=o.18 ;
-102 :- . .0 :0— 0 ~ j
: . S o . o o q, a, j

I—I .- ‘0 0 0 __ .-
E -1.4L'. ... . a j
o 6&- -------- -.--;<.-.-.--—-----—::----—+,--,----.-.‘-.---. ----- -3
u. -1. :-. —— -;°'. =- , ' —
ind ’ a. e .' 0 .. . . o .I
h on. . .. «I— .0 o . . . .4
.1.8 h .. o o .,_ I o o :

h 1»
I- <1-
- O L A >—

 

 

0 0 :L NGC 2420 N = 163, Red: [Fe/11]“t — -0.44 1; Green : <[Fe/H]> = -0.38, Sigma = 0.10 L

O 1,- d

I- 4~ 1

H -002 L- . . . O . . .. 0. j?— . o L

I- o 0' o .... ° . e . .0 f . ' 0

$3 _0 4 I: ------- !:~:ﬁ"°'."‘:.r.-.g-.°:: 13:5.‘5: - - :i: - - - - éezht-gté, -' —"- — 1~—'_ ._ _ 33:15.}. :
a . I- 3: ° 8". o . 0 :‘o ' 8 . ’ if ' . '0‘.I;’:o \ v A

-0.6 T 1:- ' ' —

r-
P ~0-
-
o
D I-
I
Y

 

 

0'4 :— M 67 N = 52, Red : [Fe/H]m = 0.02 “:— Green : <[Fe/H]> = 5.08, Sigma = 0.07
0.2 _- —:— _
I.
"‘ 0.0 i - —— .
§ :- --------- Ativ’iza-va-uf-—-—--~ZZ- --------------- efﬂuﬁt—
E __ .. . o '5 _‘0: ' .. o co

,.
I
I.
.— 1.-
5- '0-
I
h 1»
h '4P

JllLiLlLLlllllA

 

 

 

 

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 10 20 30 40 50 60 70
(3'00 <S/N>

Figure 4.21 Distributions of [Fe/ H] as a function of (g — r)0 (left panels) and average
ratio of signal to noise (right panels) for selected true member stars of M 13, M 15,
M 2, NGC 2420, and M 67. The overall mean [Fe/ H] determined in this study for
each cluster is Shown with the green dashed line; the red solid line represents the
adopted literature value in each panel. N o obvious trends exist as a function of either
color or signal-to—noise.

118

resolution spectroscopic study of of 25 members, Friel et a1. (2002) estimated [Fe/ H]
= —O.15 i: 0.05 dex. Other catalogs of open clusters (e.g., Twarog et al. 1997; Chen et
al. 2003) report a solar metallicity for this cluster. All of these literature values agree
(within our observed scatter of 0.1 dex) with our metallicity estimate, which suggests
that the metallicity estimated by the current version of the SSPP is reliable for stars
with abundances near the solar value. Note that this is a marked improvement with
respect to previous versions of the SSPP, which tended to underestimate [Fe/ H] for

solar-metallicity stars by up to 0.5 dex.

Table 4.3: Mean and l a Values of Residuals in Tea and logg Between SSPP and Model

Fitsk

 

 

Tea logg
Cluster N <A> a <A> 0

(K) (K) (deX) (deX)

 

M 13 293 +165 194 —0.29 0.40
M 15 98 —13 134 —0.25 0.31
M 2 76 +31 114 —0.22 0.35
NGC 2420 163 +71 193 —0.14 0.46
M 67 52 -—31 58 +0.15 0.07

 

For the radial velocity of M 67, Girard et al. (1989) reported 33.6 i 0.72 km s‘l,
based on a reanalysis of the compilation of a large set of member stars with radial
velocity measurements (Mathieu et al. 1986). Scott et al. (1995) determined 32 km
s‘1 from 26 member stars. Values of 32 :1: 11 km s-1 from 4 stars, 33 km 8'1, and 33.6
km s—1 were estimated by Friel et al. (1989), Friel & Janes (1993), and Rastorguev

 

kThese values are 5 a-clipped averages and standard deviations. N is the total number
of the selected member stars.

119

et al. (1999), respectively. Yong et al. (2005) obtained a very similar value, of 33.3
km s‘l, from three member stars. Taking an average of all these measurements, we
obtain 32.9 km 3*, as listed in Table 4.2. This value agrees with our derived mean
radial velocity of +349 km 3‘1 within the standard deviation of our measurements,
4.0 km s’l.

As discussed above, taking into account only the scatter in the metallicities and
radial velocities calculated from the members of each cluster, we are able to derive
estimates of the typical external uncertainties for the SSPP estimates of these quanti-
ties, a([Fe/H]) ~ 0.13 dex, and 0(RV) ~ 8.0 km s‘l. The scatter in the radial velocity
is also noted to increase with decreasing [Fe/ H] This is the expected behavior, since
the metallic lines of a metal-poor star are weaker than those of a metal-rich star of
the same effective temperature, making it more difﬁcult to identify strong features
to anchor the determinationof radial velocity. A similar behavior can be found for

[Fe/ H], that is, larger errors with declining metallicity, from inspection of Table 4.2.

4.6 A COMPARISON OF DERIVED METALLICITIES AND
SURFACE GRAVITIES FOR TRUE CLUSTER MEM-

BERS WITH COLOR-MAGNITUDE DIAGRAMS

In the previous section, we considered the accuracy with which the SSPP obtains
estimates of metallicity and radial velocity. We now consider the accuracy with which
the SSPP obtains estimates of effective temperatures, T83, and surface gravities, log
9. One excellent “global” test of these estimates is to examine the locations of the
true member stars on the observed CMD (based on the totality of likely photometric
member data) for each cluster. One can also compare with corresponding theoretical

CMDS.

Figures 4.23—4.27 Show plots of the SSPP-estimated temperatures and gravities

120

 

-l.2
-l.4
-1.6_ , , . .. . . . -
-l.8E— °' I: if “.112

IIIIIIII

 

[Fe/H]
I
I
I
I
I
l
I
I
I
1
Q
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:1"
' 1
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..‘r u
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‘ .
I.
't
J.
J
P
‘f
I
j!
r
I
.l
I
I
I
I
I
I
I

-2.0
-1.8 :— M 15
.2.0 E—
-2.2 *
-2.4
-2.6

-l.2
-l.4
-l.6

-l.8

-2.0
0,0 :— NGC 2420

-O.2 . - 31.2,: .-
-04 ------------------------------ ° H-'j"-°3'.‘,:".°' fjégkg 7 :1» -. -
-0.6 ' ' ‘

-0.8
0.4

0.2
0.0
-0.2
-O.4

 

 

[Fe/H]

11111111l.L.li_LLl.I_l_l_IJ.111iJJlJI IIIIIIIIII JlIIllil

[Fe/H]

TTTIIII
I

111111

[Fe/H]

 

Z
31‘

 

[Fe/H]

5..
_____________________________________ ' Lu», _ .. _
I 0.05 8

TITIIIIIIIIIIIIIIIIIIIIIIIIl

 

 

 

3 4
log g

_d
N .

U: 11lL11l11'1111l111 I111I1111111111111111111111111

Figure 4.22 Distributions of [Fe/ H] as a function of estimated log 9 for the selected
true member stars of M 13, M 15, M 2, NGC 2420, and M 67. The overall mean
[Fe / H] determined in this study for each cluster is shown with the green dashed line;
the red solid line represents the adopted literature value in each panel. No obvious
trends exist as a function of surface gravity.

for true member stars superposed on the photometrically cleaned CMDS for each of
our clusters. Note that in order to obtain the theoretical temperature scales (shown

along the top of the left-hand panels in each ﬁgure), we make use of a linear relation

between (9 — r)0 color and Teff by performing aleast square ﬁt in this plane to the

121

Eff8ective twerature £060

13:9 :""'*’7‘**—"'_f " 1':7—r1'|"'1"1"111" ' f—ﬁV’rT'I'TV 1""1.
14 T +23
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18 "5.:1- ' "9,5,
: Q'I. >23.
19 T m275001< 4 l0gg24.5
7000K<Teff<7500K 4.0510gg<4.5

   

20 65001<<Tl <7000Kf- 't- ‘ ‘ 3.551(1gg<~1.()
: amx< 1‘ . <6SUOK‘7 : 3.11:1ngg<3.5

eff -
5500K<IC - <NXX)K ~ 253mg '<}.()

 

 

 

 

 

21_ 51111K<T:H,<551111K 211111.; g<35
Teff<5000K ‘ Iogg<2.0
22=m11111 1. 11 1 -1-11_1_11_1_1_L
-0..6-O4 -0.2 0.0 0.2 0.4 0.6 0.8 -0.4-0.2 0.0 0.2 0.4 0.6 0.8
(g-r)0 (g- r)0

Figure 4.23 Distributions of effective temperature (left panel) and surface gravity
(right panel) of the selected true member stars superposed on the CMD for M 13.
Each color represents a temperature range of width 500 K, and a surface gravity range
of 0.5 dex, respectively. The temperature scales on the top of the left—hand panel come
from a linear relation between (9 — r)0 color and Teﬂ obtained by performing a least
square ﬁt to the theoretical models of Girardi et al. (2004). A similar procedure is
applied for transforming the go magnitude to a theoretical log 9 scale Shown on the
ordinate in the right—hand panel.

theoretical models of Girardi et al. (2004). We choose the isochrones from this study
that have the closest [Fe/ H] to the derived metallicity of each cluster, and adopt an
age of 13.5 Gyr for the globular clusters, 2.2 Gyr for NGC 2420, and 4.3 Gyr for
M 67 (adopting the ages from WEBDA for the open clusters). A similar procedure is
applied for transforming the go magnitude to a theoretical log 9 scale (shown along
the far right axis in the right—hand panels of each ﬁgure). Distance moduli from the

Harris (1996) compilation for the globular clusters and WEBDA for the open clusters

122

Effective tern rature K)
9000 8000 7 6000 5 4000

 

   
   
  

 

 

 

13 1111111111.111111 11111 11111.1111111 11‘ 11 113: [111,1111111l111_1w1—y—1—v—131
14? f:
:1. ’ ‘ I
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J'- J'-
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00° .1‘ .1‘ ‘3 w
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19—T m27500K 1 —l11)gg24.5 :
7000K<T ff<75" _, 4.0SIOgg<4.5 Q4
20 g 6500K<T 8118:1(7000 2- 22 3.5Slogg<4.() I
6(I()1)K<Ttﬂ.<6500'5, ‘ 3 3,03Ingg<3.5
55()()K<TCH.'<6000K _. ,7 ‘ 25<lmg<30
21:5(KXJK: T <5500K ' — 21th g< <25
Tceff<5000K logg<2.0 5
2 W1114 .1_1_1_ml_mi_1J_i_i_i_‘: 1.1m 1m.1_l_au_l_1_;1_;m_1 *L1_i_i_.
—O.6 -0.4 0-2. 0.0 0.2 0.4 0.6 0.8 -O.4 -02 0.0 0.2 0.4 0.6 0.8
(8'00 (g-r)0

Figure 4.24 Same as Figure 4.23 but for M 15.

(also listed in Table 4.1) are used in order to compute apparent magnitudes.

In these ﬁgures, we plot the SSPP-estimated parameters for true member stars in
different colors, corresponding to different ranges of temperature and surface gravity
(as shown in the legend for each plot). Each color represents a range of 500 K in
Teff and 0.5 dex in log 9, respectively. The effective temperature estimated by the
SSPP appears in excellent agreement for most of the true member stars, with only a
few exceptions. Such stars could either be outright errors in the SSPP predictions, or
could just be foreground / background stars that survived the various membership cuts
we have applied. Inspection of the ﬁgures also reveals the presence of a few stars close
to the main-sequence T0 in M 13, M 15, and M 2 that appear to have slightly higher

or lower SSPP-estimated log g than expected from the theoretical scale. The surface

123

Effectivete oocperature 60009600

 

9000 8000 783336
13 TTTITTTTTTTTIITTTTT TTTTrro frrﬂr Tl TTTTTT TTTTTT _L T T T I l T T ITTT T T T T T T T T T I T T T T T T Til
i :1
14 I .
E i
15 _’ ,, 3. -i
I.- 5...: y.“ 2
16% 'HH- .°° 3. g? ‘H-l.
17'E 3—
: ,- 50
on 18 i . 32
‘1‘ "
E
+

 

 

 

 

19 Teﬂ27500K . log g24.5
7000K<Teff<7500 ..' .. 4.05]ogg<4.5 4
20E 6500K<T H<7000 K3)“ 3.5510gg<4.0 .
6000K<Tsz<6500 K"... .7; . 3.()Slogg<3.5 i
55()()K<T <151"-.>00K‘~-= 2.5s1ogg<3.0 I
21 <1‘1_>111}\'--'| fle‘SéHHK ., L!'11_i.1-_':~:l.5 :
Teff<5000K $10gg<2.0 ‘
x .
22.........111..1...1-.1#¥...1...1...1.-.mu...1n35
-O...6-O4-O2 0.0 0.2 0.4 0.6 0.8 -0..4-02 0.0 0.2 0.4 0.6 0.8
(g r)O (g r)0

Figure 4.25 Same as Figure 4.23 but for M 2.

gravities of stars along the RGB appear to be very well estimated. Such behavior is
perhaps to be expected, since the stars close to the TO region are at the low end of
the S /N range that we accept for SSPP parameter determinations (~ 10 / 1), and thus
are subject to greater errors in the determination of their atmospheric parameters.
The RGB stars are among the brightest stars in the globular clusters, and hence are
likely to have the best-determined estimates.

Careful inspection of Figure 4.26 for NGC 2420 indicates that gravity estimates for
most of the main-sequence stars are well estimated from the SSPP, with the exception
of the faintest stars. These stars have only low S/N (~ 10/1) spectra available,
resulting in higher uncertainties in determinations of their surface gravities. It should

also be recalled that surface gravity is a difﬁcult parameter to estimate, especially

124

Effective temperature (K)
7000 6000 5000 4000

 

    

 

 

 

 

 

l4 Iﬂ—FITTYﬁ—rlTrl—VTIWIWITTTTTIIIIIIIIY TT—IjYIT‘l'TTIITTYI1TT’I—VTTTTTTITTT
1* . 4
' _i 3.8
16 - a i
l — 4.0
4 4.2 on
O -- 4— 4 00
on 18 o
I—I
~ 4.4
l Teﬂe 7500 K . ' " log g 2 4.5 :3. .
20 - 7000 K s Teff< 7500 K i- 4.0 3 log g < 4.5
6500 K 5 TC“. < 7000 K m 3.5 5 log g < 4.0 m 4
* 6000 K s Teff< 6500 K 4, 3.0 s log g < 3.5 a 4,6
. 5500 K 5 Tc“. < 6000 K J 2.5 3 log g < 3.0
Fruit.) K :«i’!‘ <. Swim K ’ -: ii 1. -_ ._ ~_ -.
, Teff < 5000 K i. log g < 2.0 ‘
22Lillllllllllllllllllllllll1111111111111111111]lllllllLllllllLL4.8
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
- l‘ - 1‘
(g )0 (g )0

Figure 4.26 Same as Figure 4.23 but for NGC 2420.

from spectra of the resolving power obtained by the SDSS. Overall, we are pleased
to see as good a behavior in the estimates of this parameter as that demonstrated in
Figures 4.23—4.27. I

In addition, using the derived relations between (9 — r)0 and Teff, and go and
log 9 from the isochrones, we predicted T eff and log 9 from the observed (9 — r)0 and
go, respectively. Table 4.3 lists the averages and standard deviations of the residuals
of the effective temperatures and surface gravities between the SSPP estimates and
the calculated values. Even though we have employed a simple relationship between

(9 — r)0 with Tea, we see good agreement between the SSPP estimates and the

125

Effective temperature (Kg
6000 5000 4000

 

 

 

  

 

ll. ‘ﬁ—FTW ‘TTWI IjllinT l Ill-l ETTT—TTTIIIIIEIYVIIVI4
i i
._ 4
15 l 3
C T
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on 17 r 5‘5"". T ' ,
'- “1""
.33 f . _ ‘
ﬁr» : - ‘
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18 7000 K s Teff< 7500 K - “3’1:- 1 4.0 5 log g < 4.5 ' 3,5.»-
> . . . ‘ ... ...
6500 K s Tct‘t‘ < 7000 K #6,!" ; 3.5 3 log g < 4.0 3‘15: _
- (mo K g Ten.< 6500 K “-in f in < log g < 3.5 ”ii!
.'-’-‘."-'i' . .'- ..i' .
SSOUKST n 0000K .-~~’. ‘ 2.5: _- 3. .--~’
19 >7 clt< 33!: T logg< ‘0 any;
: 500:an runasmk i’g-rl.‘ ; 24):- |ngg<25 gﬁ$ﬁ —
: reﬁ<5000K ~34:- . E logg<2.0 «3o;- .
- "I "1
33V" 1 ‘ 3‘...
201||l| |lillllllllllllerll- ‘lliliii lAL‘JJLm

 

4.0

4.2

5.2

5.4

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.4 0.6 0.8 1.0 1.2 1.4 1.6
(g-r)0

Figure 4.27 Same as Figure 4.23 but for M 67.

(g - r)0

theoretical values in Teff. Although, as expected, there is a rather large offset and

scatter in the gravity, indicating a more complex function is needed (or the isochrones

themselves are in doubt), the scatters are still within the bin sizes (0.5 dex) for this

parameter used in Figures 4.23—4.27. The relatively larger zero-point offsets in Teﬂ?

for M 13 and NGC 2420 is caused by the linear relation having to cover a large range

of (g — r)0 : —0.4 to 0.8 for M 13 and 0.1 to 1.2 for NGC 2420.

126

4.7 SUMMARY

Based on photometric and spectroscopic data reported in SDSS-I and SDSS-II/SEGUE,
we have examined estimates of stellar atmospheric parameters and heliocentric radial
velocities obtained by the SEGUE Stellar Parameter Pipeline (SSPP) for selected
true members of three Galactic globular clusters, M 13, M 15, and M 2, and two open
clusters, NGC 2420 and M 67, and compared them with those obtained by external
estimates for each cluster as a whole.

From the derived scatters in the metallicities and radial velocities obtained for the
selected true members of each cluster, we quantify the typical external uncertainties
of the SSPP-determined values, a([Fe/H]) = 0.13 dex, and 0(RV) ~ 8.0 km s'l,
respectively. These uncertainties apply for stars in the range of —0.3 S g—r g 1.3 and
2.0 3 log 9 S 5.0, at least over the metallicity interval spanned by the clusters studied
(—2.3 3 [Fe/ H] S 0.0). Therefore, the metallicities and radial velocities obtained
by the SSPP appear sufficiently accurate to be used for studies of the kinematics
and chemistry of the metal-poor and near-solar metallicity stellar populations in the
Galaxy. We have also conﬁrmed that Teff and log 9 are sufﬁciently well determined by
the SSPP to distinguish between different luminosity classes, through a comparison

with theoretical predictions.

127

 

CHAPTER 5:
THE [oz/Fe] ABUNDANCE PATTERNS OF
STARS IN THE GALACTIC HALO

 

5.1 INTRODUCTION

The currently favored hierarchical structure formation model (e.g., White 81. Bees
1978) suggests that galaxies like the Milky Way grow by means of mergers and accre-
tion of numerous smaller fragments (often referred to as “mini-haloes”), dark matter
dominated systems that collapsed around defects imprinted on the universe as it
emerged from the Big Bang. It is believed that primordial gas falls into these systems
as it cools, and star formation commences. Although it is not established with cer-
tainty, the preponderance of evidence suggests that the ﬁrst stellar systems formed
in this manner should bear a resemblance to low luminosity dwarf spheroidal (dSph)
galaxies.

It follows from the above that the early dwarf-like galaxies would each have their
own star formation and chemical enrichment history before they are assimilated into
their host galaxy. Thus, there may exist differences in the observed elemental abun—
dances of stars that originated in dwarf galaxies of different masses, and had different
star—formation rates and histories. In addition, as pointed out by Gilmore & Wyse
(1998), because the orbits of the accreted stars from a given dwarf galaxy (stripped
due to the tidal effects from the parent galaxy) are not altered much over time, cap-

tured stars from the dwarf galaxy will preserve distinct kinematics which can persist

128

for a long period of time. Therefore, a detailed elemental abundance analysis of stars
in a galaxy (especially its halo), along with their kinematics, can provide clues to the
accretion history of a giant galaxy like the Milky Way.

The chemical elements 0, Mg, Si, Ca, and Ti are often referred to as the “a”
elements, since they share a common formation mechanism, the capture of an a-
particle (nucleus of a He atom), are produced by massive stars (> 8 Mg) during
their explosions as a core collapse supernovae (Timmes, Woosley, 85 Weaver 1995).
This so-called Type II Supernova (SN e II) explosion occurs only a few million years
after the formation of a massive star, due to the short main-sequence lifetimes of
such stars. Iron (Fe) is also produced in these events, but much more Fe is generated
during a Type Ia supernova (SN e Ia), over a much longer timescale, on the order of
0.1 to a few Gyr (Matteucci & Recchi 2001). Type Ia supernovae are thermonuclear
explosions that take place in a binary system when material in the envelope of a
binary companion star is transferred onto the surface of a white dwarf (mostly made
of Carbon and Oxygen), to the point that its mass approaches the Chandrasekhar
limit (1.4 Mg). Nucleosynthesis occurs during these explosions and a large fraction of
the iron-peak elements (Ni, Co, etc.) are produced (Nomoto, Thielemann, 86 Wheeler
1984).

Thus, the ratio of the abundance of the a-elements to that of iron, which is
expressed as “[a/Fe]” (the mean of [O/Fe], [Mg/ Fe], [Si/ Fe], [Ca/ Fe], and [Ti/ Fe] in
most cases), has often been used as an indicator of not only the star formation and
chemical enrichment history of the Galaxy and its known satellite galaxies, but also to
search for distinctive chemical signatures of accreted stars from dwarf galaxies. While
a typical halo star exhibits [a / Fe] ~ 0.3 to 0.4 dex, indicating enhancement from SNe
II, many stars in dSphs exhibit relatively lower [a/ Fe] compared to Galactic halo
stars with the same metallicity (Shetrone et al. 2001, 2003; Fulbright 2002; Tolstoy

et al. 2003; Geisler et a1. 2005). It is thought that the low a-abundances in these

129

systems is due to the slower star formation rates (therefore, more contribution of Fe
from SNe la) in the dSphs than occurred for the bulk of the halo of the Milky Way
(Unavane et al. 1996). However, it should be kept in mind that observations are only
now being obtained for the lowest luminosity dSphs (many of which were discovered
from SDSS imaging), and it may indeed be the case that the [a / Fe] in these galaxies
is more similar to those of the Galactic halo.

Stars on extreme retrograde orbits, or stars that exhibit distinct orbital parameters
(e.g., large apo-Galactic distance or large distance from the Galactic plane), which
differ from the majority of halo stars, have been proposed to originate in previously
stripped dwarf galaxies. For example, a few halo stars that do not exhibit typical halo
a—enhancements have been found (Carney et al. 1997; King 1997) and interestingly,
these stars have large apo-Galactic distance (Rape) or are on counter—rotating orbits.
One possible explanation for these a-poor stars with peculiar orbits is that these
stars might have come from smaller galaxies with low star formation rates, which
were self-enriched with Fe from the contribution of SN e la before they torn apart.
For this reason, some studies (e.g., Stephens & Boesgaard 2002) speciﬁcally targeted
stars with distinct orbital parameters to compare their elemental abundances with
those of typical halo stars, in order to investigate this possible accretion signature
among the stars in the Galactic halo. In the following section, we summarize some
of major efforts to search for such accretion signatures, focusing on the a—abundance

analysis.

5.2 PREVIOUS STUDIES

Nissen & Schuster (1997) performed an elemental abundance analysis of 13 halo and
16 disk stars, with atmospheric parameters in the range 5400 S T93 S 6500 K, 4.0
5 log 9 S 4.6, and —1.3 S [Fe/ H] S —O.5. Some of them were of similar metallicity,

even though they belonged to different stellar populations. After they derived their

130

orbital parameters, such as the maximum distance (Rapo) from the Galactic center
and the maximum distance (Zmax) from the Galactic plane, they divided their sample
into two groups by cutting on the Galactic rotational velocity (V¢) — halo stars with
Vd) S 50 km s‘1 and disk stars with V¢ 2 150 km s'l. They found that 8 of their halo
stars had signiﬁcantly lower [a / Fe] ratios than those of the disk stars with the same
metallicity, and that these stars have the largest values of Zmax and Rapo among their
sample. They concluded that the low a-stars may have come from external systems
such as the dwarf satellites of the Milky Way, and further argued that the oz-poor stars
may belong to an accreted outer halo population while the a-rich stars may belong
to an inner halo, which formed from the dissipative collapse of a proto—galactic gas
cloud (i.e., similar to the model of Eggen, Lynden-Bell, & Sandage 1962).

However, just one year later, Gilmore & Wyse (1998) argued that these stars
could not possibly have been accreted from systems that are similar to the presently
observed dSphs, because most of the stars in the sample of Nissen & Schuster (1997)
have low Rperi (< 1 kpc). They reasoned that low mass dSphs would be tidally
disrupted before they obtained such small Rperi orbits. They claimed that the stars in
the Nissen & Schuster (1997) sample might have formed in sufficiently dense “transient
star-forming regions”, which could survive from close encounters with the Galactic
center and self-enrich to relatively high metallicities.

Fullbright (2002) studied the elemental abundances and kinematic properties of
73 stars in the metallicity range —2.0 < [Fe/H] < —1.0. He noted, after dividing
his sample into three velocity bins, that the a-abundances in this metallicity range
decline with increasing Galactic rest-frame velocities. He also compared the abun-
dance pattern of the ﬁeld halo stars with the dSph giant stars studied by Shetrone
et al. (2001), and noticed different abundance patterns between them. From the
disagreement in the chemical abundance patterns between the two, he suggested that

the a—poor stars may not have been accreted from the dSph galaxies like those in the

131

sample Of Shetrone et al. (2001).

Stephens & Boesgaard (2002) measured elemental abundances for metal-poor
halo dwarfs selected based on their kinematics (those with Rapo larger than 16 kpc,
Zmax greater than 5 kpc, and V velocity less than —400 km s-l). The stars chosen by
these criteria represent the outer halo, and the extreme retrograde stars, respectively.
Their analysis indicated that the a—abundance increases as the metallicity decreases
(on average), stars with [Fe / H] < —2.0 have higher values of [a / Fe] than more metal-
rich halo stars (~ 0.3 dex), and that metal-rich halo stars ([Fe/ H] 2 —1.0) exhibit
lower [a / Fe] values than typical halo stars. They further divided their sample into two
subsets on apo-Galactic distance — a presumed inner halo with Rapo < 16 kpc, and
an outer halo with Rape > 16 kpc. They concluded that the inner-halo stars possess
higher [a / Fe] than the outer halo stars of the same metallicity. Following the reason-
ing of Gilmore & Wyse (1998), and since most of their halo stars have apo-Galactic
distances large enough to reach to the orbits of debris from dwarf satellites (and have
peri—Galactic distances of ~ 7 kpc), they inferred from a kinematical point of view
that their sample might have come from disrupted dwarf galaxies. They conjectured
that their halo stars could perhaps have formed around 1 Gyr after the initial burst
of star formation in a distant halo region. Based on this argument, they concluded
that late accretion of objects similar to the present-day dwarf satellites was rare in
the history of the formation of the Milky Way.

An analysis of the a-and Fe abundances for about 150 ﬁeld metal-poor subdwarfs
and subgiants in the solar neighborhood was performed by Gratton et al. (2003).
After computing the orbital parameters for their sample, they grouped them into three
subsets, which they referred to as a “dissipative collapse component”, an “accretion
component”, and a “thin disk” component. Their ﬁrst group had Galactic rotational
velocities greater than 40 km s“1 and apo-Galactic distances less than 15 kpc. This

population included both halo and thick-disk stars, which possibly formed from a

132

dissipative collapsing proto—Galactic system. Their second group consisted of stars
with orbits consistent with minimal or retrograde rotation about the Galaxy. These
stars, they argued, could have presumably been accreted from other systems. Their
third component, the thin-disk stars, had (Zmax2+4c22)1/2 < 0.35, where e is the
orbital eccentricity.

Their analysis indicated that, although both the dissipative and the accretion com-
ponent share the same metallicity range, the dissipative component exhibits higher
a-abundances, with a smaller scatter than that of the accretion component, which
agrees with the result of N issen & Schuster (1997). This higher a-abundance implies
that the dissipative component experienced a higher star formation than that of the
accretion component, and the smaller scatter indicates that the stars in the dissipa-
tive component formed out of a well-mixed interstellar medium (ISM). A much larger
scatter in a-abundances at a given [Fe/ H] was noticed for the stars of the accretion
component. They pointed out that the accretion component stars probably formed
in a slow star formation environment with a different chemical history, leading to the
lower average values of [a / Fe] at the same metallicity. They also found that in their
sample the a-abundances correlated better with the peri-Galactic distances than with
apo-Galactic distances.

Venn et al. (2004) compiled an extensive set of Galactic stars with chemical
abundances measured from the literature, and compared them with those measured
for the dSphs around the Milky Way. First, these authors separated their Galactic
sample into thin, thick disk, and halo components, using a Bayesian classiﬁcation
criterion based on Gaussian velocity ellipsoids. In addition, extremely retrograde
stars with V < —420 km s‘1 were selected. Their analysis indicated that the Galactic
halo stars had abundance ratios in the range 0.0 < [a/ Fe] < 0.4, with a plateau at
0.4 dex at low metallicity, while the counter-rotating stars exhibited [oz / Fe] = 0.2,

on average. The [a / Fe] distribution of the low mass dwarf galaxies generally doesn’t

133

follow that Of the halo stars, although the extreme counter-rotating stars exhibits
values that are somewhat close to those of the dwarf spheroidals. Based on this, they
pointed out that there might exist the possibility of early merging of both low mass
dwarf galaxies and higher mass galaxies.

In their recent review paper, Geisler et al. (2007) gathered all existing Galac-
tic stars with detailed elemental abundances measured to date, and compared the
[a/Fe] distribution, as a function of [Fe/H], of the Galactic stars with that of 13
dSphs around the Milky Way galaxy. Their comparison revealed that while 12 of the
dSphs exhibited very similar abundance patterns to one another, these were rather
different from stars in the halo of the Galaxy. The [a / Fe] of the dSphs is slightly lower
than that of the Galaxy at [Fe/ H] < —2.0, but substantially lower at [Fe/ H] = —1.0.
However, the Sagittarius (Sgr) galaxy, a massive dSph, proved a bit of an exception.
The Sgr galaxy has some stars with a—abundances similar to the halo at intermediate
metallicity ([Fe/ H] ~ —1.0). Fr0m this comparison, they concluded that it is unlikely
that a signiﬁcant fraction of the more metal-rich halo stars came from disrupted low-
mass dSphs. However, they also suggested that at least some of the metal-poor halo
stars may have come from typical dSphs. A portion of the intermediate metallicity
and metal-rich halo stars may have come from massive dwarf galaxies like Sgr.

Summarizing the previous studies, although the abundance patterns (focusing on
[a/Fe]) of the stars in the Galactic halo are not similar to those of the stars in most of
the present-day dSph galaxies, the Galactic halo stars with low metallicity ([Fe/ H] <
—2.0) do appear to overlap, at least somewhat, with those of the dwarf galaxy stars,
especially those with lower metallicity. Therefore, some of the metal-poor ([Fe/ H] <
—2.0) halo stars could have come from the low mass dwarf galaxies very early in the
history of the Galaxy, or even at later times, depending on the accretion timescale.
There is also the possibility that some fraction of the halo stars (in particular the

metal-rich ones) might have been accreted from massive dwarf galaxies like Sgr in

134

very early times, before SNe Ia kicked in to contribute Fe to the ISM in the massive
dwarf galaxies. This picture may well agree with numerical simulations (Robertson
et al. 2005; Font et al. 2006a, 2006b) which claim that the bulk of the Galactic halo
formed through the accretions of a few massive dwarf galaxies (5 x IOIOMQ) as much
as 10 Gyr ago.

In our present study, which focuses on the a-abundance for very large samples of
stars in the Galactic halo, several of the issues raise by previous work can be con-
fronted. It should be kept in mind that, although the accuracy of the a-abundance
estimates for our halo sample is deﬁnitely somewhat lower than that of the stars in
other studies (due to the much lower resolution of the SDSS spectra from which they
are measured), we have a significantly larger sample size than any previous stud-
ies, so the uncertainty of individual a-abundance measurements can be statistically

compensated for on average.

5.3 DETERMINATION OF [cu/Fe]

5.3. 1 METHODOLOGY

As described in Chapter 2, we have obtained large numbers of stellar spectra through
the SDSS-I and SEGUE surveys. Hence, we need tools for determining a parameter
such as [a/ Fe] in a fast and automated fashion, as done with the SSPP. One of
the best ways to achieve this goal is to make use of a pre-existing grid of synthetic
Spectra. With the pre—existing grid there is no need to generate a synthetic spectrum
iteratively while attempting to estimate a parameter that ﬁts an observed spectrum.

Thus, in order to estimate [a / Fe], we have generated a grid of synthetic spectra,
using Kurucz NEWODF models (Castelli & Kurucz 2003) and the TURBOSPEC-
TRUM synthesis code (Alvarez & Plez 1998). More detailed descriptions of the Ku-

rucz NEWODF models and the source of the linelists used to synthesize the spectra

135

can be found in Chapter 3.4.4. The grid spans 4000 K S T83 S 8000 K in steps
of 250 K, 1.0 S log 9 S 5.0 in steps of 0.2 dex, —3.0 S [Fe/H] S 0.2 in steps of 0.2
dex, and -0.1 S [01/ Fe] S 0.6 dex, in steps of 0.1 dex. In generating the synthetic
spectra, we increased, by the same amount, the abundances for all a-elements (O,
Mg, Si, Ca, Ti). The resolution of the generated synthetic spectra is 0.1 A, and a

micro-turbulence of 2 km 3‘1

was assumed. Each spectrum covers the wavelength
range 4500—5500 A. The reason for choosing this wavelength range is that it contains a
large set of metallic lines, but avoids the CH G band (4300 A), which is often a strong
feature in metal-poor stars. Most importantly, this region of the wavelength possesses
strong Mg I, Mg Ib, and MgH lines, which are sensitive features for estimation of the
a-abundance.

After their creation, the synthetic spectra were degraded to the SDSS resolution
(R = 2000) and processed in the same manner as described in Chapter 3.4.4 for the
NGS2 grid to obtain the normalized spectra. Our target spectra were also normalized
in the same fashion.

The parameter search technique is the same as for the NGS2 grid, which is described
in Chapter 3.4.4. However, for the application of the a-abundance determination, we
employ the stellar parameters derived by the SSPP as initial starting guesses. This
choice is made because we are dealing with a lot of synthetic spectra (~ 50,000), and
calculating the reduced X2 values for the entire synthetic spectra for each observed
spectrum would require a large amount of computing time.

We select the synthetic spectra that are within :i: 1000 K of the SSPP Tea, :l:1.5
dex of the SSPP log 9, and :l: 1.5 dex of the SSPP [Fe/ H], and compute the reduced
X2 values for the selected synthetic spectra against an observed spectrum. After
this calculation, using the IDL multi-dimensional optimization routine AMOEBA, we
search for the best matching synthetic spectrum. Because this routine is susceptible

to becoming stuck in a local minimum for lower S / N spectra, we determine another

136

set of the parameters by taking an average of 20 points near the minimum reduced X2

values. The ﬁnal estimate of [a / Fe] is the average of the two sets of determinations.

5.3.2 VALIDATION

Once a tool to determine a physical quantity is developed, one has to calibrate and
validate it with external measurements. For the purpose of this comparison, we again
introduce the ELODIE spectral library (Moultaka et al. 2004) as an external source.
First, we performed a literature search for previously measured oz-element abundances
for the stars in the library, using the VizieR1 database, and found 414 stars with the
required information. As mentioned above, due to the nature of the wavelength range
selected for determining [a / Fe], Mg will have the most weight in the a-abundance es-
timate. Therefore, we also gave more weight to previously measured Mg abundances,
rather than taking the average of all available a-element measurements for a given
star.

The chosen spectra from the library were processed exactly in the same way as the
synthetic spectra, after degrading them to R = 2000, and the [a / Fe] abundance for
the selected individual stars was estimated. Figure 5.1 shows the results of the com-
parison. The subscript “Lit” indicates the value from the literature and “Fit” from
our determination. The red crosses in the bottom left ﬁgure denote our determina-
tions. A Gaussian fit to the residuals between our values and those from the literature
indicate that there is little systematic offset, and further indicates a very small scat—
ter (standard deviation of 0.04 dex). No trends in the estimated a-abundance as a
function of [Fe/ H] are noted for stars with [Fe/ H] < -0.5 in the ﬁgure.

Since the spectra in the ELODIE library have very high S/N (> 100/1), while
the SDSS spectra cover a wide range of S/N, we also have to check how the S /N

of a spectrum impacts our determination of the a-abundance. We have used the

 

1http: / /webviz.u-strasbg.fr/viz-bin/VizieR

137

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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-0.4 -0.2 0.0 0.2 0.4 -0.10.0 0.1 0.2 0.3 0.4 0.5 0.6
[tr/Fe]Fi t -[0t/Fe]Lit [(x/Fe]Lit
0.6:;rvvvrryvvI ........ I ........ 1'44; 0.4.ff1 Tyr..,y.VTj ........ I'V‘VVVYVVW
05% : :
0.4: : j 0.2: 0 o 1
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ii: 0.3 % ,' ,' ; u: '. " l
T H 00 e . v 40 '0‘. e
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0.1 €02; . ° . . .0 _
0.0, _. . :
"(LlE '().4h ..................... 1 11111111 A
-3.0 -2.5 -2.0-1.5 -1.0-0.5 0.0 0.5 -3.0 -2.5 -2.0-1.5-1..0-05 0.0 0.5
[Fe/HJLit [Fe/mLit

Figure 5.1 Comparison of [a / Fe] from our estimates (Fit) with those from the litera-
ture (Lit). The red crosses in the bottom left panel are our determinations.

already existing noise-added high resolution calibration stars presented in detail in
Chapter 3.6. In this experiment, and likewise for the SSPP noise test, we attempt
to quantify the mean standard deviation of the a-abundance obtained from the noise
added spectra by comparing with the a-abundance estimated from the spectra before
noise injection. Table 5.1 reflects the Gaussian means and standard deviations from
the noise experiment. As can be seen in the table, although no signiﬁcant offset and a
small standard deviation (< 0.1 dex) are found down to S/N ~ 15/ 1, in our analysis

of the a-determinations we only consider stars with S/N Z 20. At S/N = 20/1, it

138

is expected that the typical maximum uncertainty in [a / Fe] will be < 0.1 dex, after
quadratically adding the offsets and standard deviations at S / N = 20/1 and for the
original ELODIE S /N .

Table 5.1: Variation of [a/ Fe] with S/N

 

 

S/N Mean Sigma

 

5.0 0.029 0.202
10.0 —0.014 0.128
14.9 -0.022 0.092
19.9 —0.016 0.075
24.9 —0.013 0.065
29.9 —0.010 0.057
35.0 —0.008 0.052
40.0 -0.006 0.047
45.1 -0.005 0.044
50.2 -0.005 0.041

 

5.4 SAMPLE SELECTION

Our program stars are the spectrophotometric and reddening standards from Data
Release 6 (DR-6; Adelman—McCarthy et al. 2008). In a typical SDSS spectroscopic
observation, together with other original targets, spectra of 16 calibration stars per
plug-plate are obtained (the calibration stars are further divided into two subsets, the
spectrophometric and telluric calibration stars).

The spectrophotometric calibration stars are used during the course of SDSS

pipeline reductions to remove the effects on the ﬂux distribution of the SDSS spectra

139

arising from the wavelength response of the telescope, the spectrographs, and the
Earth’s atmosphere. Normally, there are three conditions imposed to select stars
for the spectrophotometric calibration: (1) the spectra of the stars should not be
rich in absorption lines produced by metallic species, (2) the stars are bright enough
to achieve high S/N(> 20/ 1) in their spectra, and (3) their spectra can be well-
synthesized to match stars of known ﬂux distributions. Stars with [Fe/ H] ~ —2.0,
near the main-sequence turnoff of the halo, satisfy these requirements. The ranges
of color and apparent magnitude used for selecting such stars are 0.6 < u — g < 1.2,
0 < 9 - r < 0.6, and 15.5 < 9 < 17.0, respectively. In order to ﬁnd possible spec-
trophotometric calibration stars even in a low density region, such as the Galactic
pole, rather wide color ranges are chosen. Stars as blue as possible are selected
because they are the mostly likely candidates for [Fe / H] ~ —2.0.

The telluric calibration stars are used during the SDSS pipeline for subtracting
features due to night sky emission and absorption lines from the observed spectra. The
same color ranges are used to select these stars, however, their apparent magnitudes
are fainter (17.0 < 9 < 18.5) than the spectrophotometric calibration stars, resulting
in lower S/N than the former. The typical range of S/N for these stars is 20/1 to
30/1.

From the selection criteria (especially for the spectrophotometric calibration stars),
a bias is introduced by the effort to identify metal-poor stars. However, it is almost
impossible to distinguish more metal deﬁcient stars among stars with [Fe/ H] < -2.0,
because the sensitivity of the broad color bands to the metallicity is not sufficiently
high to discriminate the lowest metallicity stars ([Fe/ H] < —2.5). Therefore, it is
believed that the metallicity distribution of the calibration stars mimics the true
shape of the low metallicity tail of the metallicity distribution function (MDF) for
stars outside the disk populations. This does not apply to stars with [Fe/ H] > —2.0.

Since proper motion is not used to select the calibration stars, no kinematic bias is

140

 

Galactic Center U

+ ‘ >

 

 

 

Figure 5.2 Schematic diagram of the U, V, and W Galactic velocity components.

introduced.

A total of 39,167 calibration stars are selected and processed by the SSPP in or-
der to derive the stellar atmosphere parameters. During the execution of the SSPP,
distances to each star are estimated by assigning each star to luminosity classes of
“dwarf ’, “subgiant”, or “giant”, using the derived gravity of each star and by com-
paring its observed apparent magnitude with its calculated absolute magnitude from
calibrated Open and globular cluster sequences (see Beers et al. 2000). The accuracy
of the distance estimated in this way is expected to be between 10 % and 20 ‘70. The
radial velocity of a star is also determined from the SSPP. Once the stellar parameters
of the program stars are derived by the SSPP, the a-abundances of our objects are
estimated. As mentioned above, we choose to only retain a-estimates for the stars

with S /N > 20 / 1 for further analysis.

141

5.5 COMPUTATION OF KINEMATIC AND ORBITAL PA-

RAMETERS

We impose three additional cuts on our sample to derive the most accurate estimates
of their kinematics and orbital parameters. First, stars which are in the range 5000 K
< Teff < 6800 K are selected, a range that corresponds to the region where the SSPP
is best able to derive the atmospheric parameters. Secondly, stars with distances d
< 4 kpc from the Sun are chosen, in order to conﬁne the kinematical and orbital
analyses to a local volume. This distance out also reduce the uncertainties in the
transverse velocity which are computed from the proper motion and the distance.
The typical error in the derived transverse velocities at d = 1 kpc is 22 km s‘l, under
the assumption that the errors in the proper motion is 3.5 mas/ yr and the distance
error is 15%. Similarly, transverse velocity errors of 37 and 46 km s’1 are calculated
at d = 2 kpc and d = 4 kpc, respectively. The ﬁnal cut is 6 < R < 12 kpc, where R
is the Galactocentric distance projected onto the Galactic plane. The total number
of stars surviving these cuts is 18,769.

The proper motions for our sample stars are gathered from the re-calibrated
USN O-B catalog, with typical errors of 3 to 4 mas/yr (Munn et al. 2004). Along
with the distance estimates and radial velocities, the proper motions enable us to
calculate the three dimensional space motions, which are represented by the U, V, W
velocities. The zero point of these velocities is the Local Standard of Rest (LSR),
which is deﬁned as a frame in which the average space motions of the stars in the
Solar neighborhood are zero. The direction toward the Galactic anti-center is positive
for the U velocity component, positive toward the Galactic rotation direction for the
V velocity component, and positive toward the Galactic north pole for the W veloc-
ity component. Figure 5.2 shows a schematic diagram of this kinematic coordinate

system. The values of (U9, VQ, We) = (—9, 12, 7) km s—1 (Mihalas & Binney 1981)

142

 

 

GC

 

4’ Sun

 

 

Figure 5.3 Schematic diagram of the Galacto—centric cylindrical reference frame. GC
stands for the Galactic Center.

for the Sun’s peculiar motions with respect to the LSR is corrected for during the
computation of the full space motions of the stars.

By adopting an analytic Stackel-type gravitational potential (which assumes the
Galaxy possesses a ﬂattened, oblate disk and a nearly spherical massive halo) and
by integrating orbital paths of the stars, we calculate V¢, the rotational component
of a star’s motion about the Galactic center in a cylindrical coordinate system, as
illustrated in Figure 5.3 (assuming the rotational velocity of the LSR is 220 km
s“1 (Kerr & Lynden-Bell 1986), Rperi, the closest distance of a stellar orbit from the
Galactic center, Rape, the farthest distance of a stellar orbit from the Galactic center,
Zmax, the maximum distance of a stellar orbit above or below the Galactic plane,
and the orbital eccentricity (e).

A total sample of 17,450 stars with S/N 2 20 spectra and suitably estimated

143

 

 

Galactic latitude (b)

 

 

 

 

 

0.6
0.5

0.4
0.3
0.2
0.1

0.0
-0.1 L .

[OI/Fe]

 

 

ll :IJHI LIIHIII lllllwlll‘n IllHJlllr leu II llllvlJ-IIM,

 

 

Figure 5.4 Spatial distribution of the sample (17450 stars) in a Galactic coordinate
system (top) and a plot (bottom) of [a /Fe] as a function of [Fe/ H]

parameters was assembled. The top panel of Figure 5.4 displays the spatial distribu-
tion of this ﬁnal sample in Galactic longitude (l) and latitude (b). The lower panel
shows the [a/ Fe] distribution with respect to [Fe/ H] At lower metallicities, one can
notice the existence of a plateau with [a / Fe] ~ 0.4 dex, which is a typical value for
halo stars below [Fe/H] = —1.0. Above [Fe/H] = —1.0, the a-abundance decreases

with metallicity and reaches the solar value at [Fe/ H] = 0, as found in other studies

144

(Fuhrmann 1998, 2004; Prochaska et al. 2000; Feltzing, Bensby, & Lundstrom 2003;
Bensby et al. 2005). The plateau with the high-a value indicates that the halo stars
have been chemically enriched from Type II supernovae, apparently including the
metal-poor ([Fe/ H] < -O.5) thick disk stars. The lower half of the downturn feature
also consists of metal-rich thick disk stars with lower a-abundance, as indicated by
Feltzing, Bensby, & Lundstrom (2004). These lower a-abundances are presumably
caused by a greater Fe contribution from Type Ia supernovae. This implies that
whatever is the astrophysical origin of the thick disk, its progenitor had to have a
period of star formation long enough for SNe Ia to explode and pollute the ISM with
Fe. Studies (e.g., Matteucci & Greggio 1986; Smecker—Hane & Wyse 1992) indicate
that the duration of the star formation can be from several hundred million years
to 2 Gyrs. There are not many thin disk stars in our sample, but we still see them
([Fe/H] > —0.3) with [a/Fe] < 0.1 in the ﬁgure.

The [a / Fe] patterns with respect to the U, V, W, and V43 velocities are depicted in
Figure 5.5. Note the mixed population of thin and thick disk stars with low-a (< 0.2
dex) around V¢ ~ 200 km 8‘1, and a population with higher a-values with slightly
lower V¢ (around 180 km 8*). Below V¢ < 100 km 8*, which is going into the
halo-dominated regime, we see stars with high-a, but also a signiﬁcant number of
stars with low-a. It is interesting to see that there are not many low -a stars between
80 km S_1 and 170 km s‘1 in V4, velocity. While Chiba &: Beers (2000) reported
V45, ~ 170 km s‘l, Gilmore, Wyse, &, Norris (2002) derived V¢ ~ 100 km s”1 for
the thick-disk population. If the value of 100 km s"1 by Gilmore, Wyse, & Norris
(2002) represents the thick-disk population, the region showing the smaller number of
stars with low-a is the thick disk regime. Furthermore, if the thick disk formed from
debris of mergers with satellite systems, as envisioned e.g., by Abadi et al. (2003),
the satellites should have been massive enough so that they would not be disrupted

until they arrived in the disk plane. It is believed that massive dwarf galaxies (not

145

 

 

[OI/Fe]
[OI/F61

 

 

 

 

 

 

 

[olFe]
[OI/Fe]

 

 

 

 

 

 

400 -400 -300 -200 -100 O 100 200 300
V,» (km/s)

 

Figure 5.5 Run of [a/Fe] over U, V, W, and V4,.

the present dwarf galaxies, which are of lower mass) experienced an early era of rapid
star formation, which produced high values of a by SNe II from dying high mass
stars. Relatively few low-a stars might be produced as a result. This may account,
at least in part, for the region devoid of stars near 100 km s‘1 in the ﬁgure.

Plots of [a/ Fe] with various orbital parameters, such as Zmax, Rapo, Rpm, and
eccentricity are shown in Figure 5.6. Not much trend of [a/ Fe] with respect to the
orbital parameters is noticed, but after excluding the thin- and metal—rich thick disk
stars, we see that as Rpeﬁ decreases, the spread of [a/ Fe] becomes larger; a similar

behavior applies as the eccentricity increases.

146

 

 

 

 

 

 

 

 

 

'0.1 .I . A I I ’0.1E ‘ A

 

0 20 40 6O 80 0.0 0.2 0.4 0.6 0.8 1.0
R a po (kpc) Eccentricity (c)

Figure 5.6 Distributions of [a / Fe] with respect to Zmax, Rperi, Rape, and eccentricity
(6)

5.6 DISTRIBUTIONS OF [a/Fe]

In order to investigate the a—abundance patterns for stars in the Galactic halo, we
ﬁrst have to set the selection criteria for halo stars. We impose three criteria on the
parameters V¢, Zmax, and [Fe/ H] First, we select stars with V¢ S 80 km s“1, which
is more than 2 o (2 x 39 km s‘l) away from the typical thick-disk velocity ellipsoid
centered on V4) = 180 km 3‘1 (Soubiran et al. 2003). In addition, by cutting the
sample with [Fe/ H] S —1.0, we are able to eliminate most of metal-poor disk stars.
Finally, we choose stars with Zma‘x 2 1 kpc, so that potential thin and thick disk

stars that slip through the above cuts can be excluded. Applying these conditions

147

to the total sample of 17,450 stars allows us to assemble 7580 stars with a very high
probability of halo membership. Following the scheme of Gratton et a1. (2003),
throughout this study we will refer to stars with V,» Z 40 km s'1 and Rape < 16 kpc
as a “dissipative” component, which is the dominant population in the inner halo,
and with V¢ < 40 km 3’1 or Rapo 2 16 kpc (or both) as an “accreted” component,
which presumably makes up most of the outer halo stars, including accreted stars
from disrupted dwarf galaxies. We also refer to these components as the inner halo,
and outer halo, respectively, even though it is understood that some overlap of these
components surely exists. The dividing line of 40 km s—1 and 16 kpc will also provide
an adequate number of stars for both groups. Mostly, the observed properties of the
distribution of [a / Fe] of the accreted and dissipative components made with various
cuts on several parameters such as V¢, Rapo, [Fe/ H], etc., will be discussed in this
section. Detailed discussions and implications of the patterns found in this section

are deferred to the following section.

5.6.1 DISTRIBUTIONS OF V¢ AND [Fe/H] WITH [oz/Fe] CUTS

Figure 5.7 shows histograms of V¢ (left) and [Fe/ H] (right) with various bins of
[a / Fe] for the accreted (or outer halo; red line) and dissipative (or inner halo; black
line) components divided at Rapo = 16 kpc. The black vertical line is the division
between prograde and retrograde motion around the Galactic center. The cuts on
[a / Fe] for each histogram are shown in the top of each right-hand panel. Ntot is the
total number of stars in each [a / Fe] bin. It is clear from inspection of the left-hand
panels that while the dissipative component (Rape < 16 kpc) are more concentrated
on zero or slightly positive rotation velocity, the accreted components are somewhat
shifted to counter-rotational velocities, with a long tail of negative velocities for all 0:-
cuts, conﬁrming Carollo et al. (2007)’s claim that the outer halo population exhibits a

net retrograde rotation between —40 and ~70 km s’l, while the inner halo population

148

 

 

 

 

 

 

 

 

 

 

 

0'25 E Nto’t = 808‘ ' SE -0.10 <'[0L/Fe] {0.15 .
0.20 — NI0t = 379 :E 16 > Rapo (kpc) -j
I < 2
§ 0.15 — 5f 16 ‘ R3130 (kpc) —I
z 0.10; -
0.05 53
0'25 E Nto't = 1056 ' i 0.15 < Eon/Fe] s 0.25 '
0.20:— Ntot = 454 £3 16 > Ra (kpc) :
_ ' 1 16 S R (kpc) ‘
3 0.15 r “: apo ‘
Em;— —5
0.05 I» 5
0'25; Nm‘t = 1503 ' IE 0.25?[er] s 0.35 3
0.20:— N ,0, = 574 I— 16 > Rapo (kpc) i
I I < ‘
§o.15— :— 16‘Rapo(kpc) 3
z 0.10; 3
0.05
0'25 E Nto‘t = 2136 ' ;; 0.35 < tat/Fe] s 0.60 :
0.20:— N,0t = 670 {— 16 > Ra (kpc) -i
.. : " Iést°(kpc) 3
3 0.15 — —— apo E
4 -3 -2 -1 0 -30 -25 —2.0 -15 .10
V¢(x 100 km/s) [Fe/H]

Figure 5.7 Distributions of V¢ (left) and [Fe/ H] (right) with different bins of [a / Fe] for
the accreted (red line) and dissipative (black line) components, divided at Rapo = 16
kpc.

consists of stars on net prograde orbits between 0 and 50 km 3‘1. It is also interesting
to note that there is a greater fraction of extremely retrograde (ng < —250 km 5*)

stars included for the outer halo stars than for the inner halo stars, giving more

149

weight to the net retrograde property of the outer halo. The distribution Of [Fe/ H]
provides another intriguing feature — more stars are seen below [Fe / H] = -1.8 for
the outer halo in the range —O.1 < [Oz/Fe] < 0.15 and 0.35 < [oz/Fe] < 0.6. Carollo
et al. (2007) demonstrated that the peak Of the metallicity distribution function
(MDF) of the outer halo population occurs at [Fe / H] = -2.2, which is close to what is
seen here. This may imply that the low-metallicity stars in the outer halo may split
into distinct populations with varying levels of a-enhancement, preferentially low and
high a-abundance, hinting they would form in environments which had gone through
different chemical enrichment history. There may be a similar weak feature among
the inner halo stars as well, although it is not as apparent as that for the outer halo

stars.

5.6.2 DISTRIBUTIONS OF [a/Fe] WITH [Fe/H] CUTS

In order to further examine the features found in Figure 5.7, after breaking up the
sample into the dissipative component with V4, 2 40 km s-1 and Rapo < 16 kpc, and
the accreted component with V¢ < 40 km s-1 and Rapo Z 16 kpc, we constructed
histograms of [a / Fe] and Rperi for various metallicity regimes, as shown in Figure 5.8.
The metallicity cuts used to make the histograms is listed in the top legend of each
right-hand panel. The distribution in black applies to the dissipative component,
while the accreted component is shown in red. The prominent pattern that can be
noticed in the left hand panels of the ﬁgure is that as the cut on [Fe / H] decreases, the
fractional number Of stars with intermediate a-abundance (~ 0.25 dex) is reduced,
whereas that of the low (below 0.2 dex) and high(above 0.3 dex)—a stars is increasing,
implying a bifurcation Of the population in a given metallicity range. It appears that
this pattern occurs for the inner halo stars, too, although the outer halo stars have a
more conspicuous feature at the low metallicity end. It is clear from the peaks of the

a-abundance distribution in the ﬁrst two top left-hand panels that the outer halo stars

150

have, on average, lower [a / Fe] with a larger scatter than the inner halo stars for the
range [Fe / H] > —1.8, conﬁrming the claims of previous studies (e. g., Nissen & Schuster
1997; Gratton et al. 2003) that the stars with exotic kinematics (e.g., retrograde
motion) have lower mean values of a-abundance at a given metallicity. Below [Fe / H]
= —1.8, the difference in mean [a / Fe] values between the two components disappears,
owing to the much larger scatter in the [a / Fe] distribution.

In the histograms Of the right-hand panels shown in Figure 5.8, it can be seen
that most Of the inner halo stars with [Fe/ H] > —2.2 are clustered at Rperi less than
3 kpc, with a small spread. Below this metallicity, the fraction of high Rperi stars
increases; the scatter in Rperi becomes larger as well. A more salient feature in the
distribution Of Rperi can be seen for the outer halo stars in the histograms, which
exhibit a much ﬂatter distribution as [Fe/ H] decreases. Since it is thought that if
stars possess a common set of kinematics they are likely to share a common origin,
the presence of multiple (and different) features in the kinematics within one group
in the narrow range of the metallicity may indicate a mixture Of diverse populations.

A more detailed discussion on this point is presented below.

Table 5.2: Results of Kolmogorov-Smirnoff (K-S) tests

 

 

 

[Fe/ H] Inner Outer Inner + Outer Inner vs Outer
—1.4 ~ —1.0 1.000000 1.000000 1.000000 0.000012
—l.8 ~ —1.4 0.228898 0.015397 0.030933 0.000144
—2.2 ~ -1.8 0.026533 0.000000 0.000000 0.309947
—2.5 ~ —2.2 0.000366 0.000000 0.000000 0.543394
—3.0 ~ -2.5 0.060502 0.000246 0.000271 0.562488

 

One Of the best ways Of testing whether a distribution Of one sample differs from

151

 

 
   
  
  
   
  
  
      
  

 

 

83(5) .Ntot = 1202 16 > Ra 0 (kpc) [Fe/H] s -10
.. 0,25 _Nl0t = 1844 16 3 R330 (kpc) -- 40 s v¢ (km/s)
.9 0,20 — — FL 40 > V4) (km/s)

E 0.15 - ~

0.10 - ﬂ __

0.05 ‘ - J

833 .Ntot = 807 16 > Rap0 (kpc) [Fe/H] s —1.4
- 025 .Ntot = 1369 16 3 R21 0 (kpc) 40 s V¢ (km/s)
8 0.20 — p 40 > V q) (km/s)

E 0.157 -~—L
0.10» --
0.05- --

 

 

8:33 —N,,,,=345 16>Ra (kpc) ire/Hi $-13
.. 0.25 -N,O, = 628 16 3 Rap: (kpc) 40 s V¢ (km/s)
9 0.20 p 40 > v¢ (km/s)

E 0.15 - ,,
0.10 -l
0.05 - --

7 16>Ra (kpc)
025 tot 91 16 S Rapo (kpc)

 

 

 
  
    

[[Fe/H] s -22
40 s V q) (km/s)
40 > V (D (km/s)

 

 

 

 

 

 

0.15
z 0.10 ;

0.05 -
0.35 * 1 - "" 1 °
0,30 . Ntot = 19 16 > Rape (kpc) ., [Fe/H] s -25

.. 0,25 Ntot = 47 16 s Rapo (kpc) ,, 40 s V¢ (km/s)

.9 0.20 - - 40 > V¢ (km/s)
0.15 -
0.10 - — _
8.83 . MHI

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 2 4 6 8 10 12
101/Fe] kpc,, (kpc)

Figure 5.8 Distributions of [a/Fe] (left) and Rpeﬁ (right) with different bins of
[Fe/H] for the inner (black) and outer (red) halo. Note that the inner and outer
halo should satisfy both Rapo and V,» cuts.

that of another is to use a Kolmogorov-Smirnoff (K-S) test. Therefore, in order to
examine if there exist diﬁerent populations in our data, we performed a K-S test,

with a null hypothesis that the distribution of [01/ Fe] shown in the lower panels for

152

the individual cuts on metallicity could be drawn from the distribution Of the same
parent population as that shown in the upper panels. In this test, we Obtained for
-1.8 < [Fe/H] _<_ —1.4, one-sided probabilities Of 0.228898, 0.015397, and 0.030933
for the inner, outer, and the inner and outer combined cases, respectively. For —
2.2 < [Fe/ H] S —1.8, one-sided probabilities Of 0.026533 for the inner, and less than
0.000001 for both the outer and inner and outer combined data set were calculated.
For —2.5 < [Fe/H] _<_ —2.2, one-sided probabilities Of 0.000366 and below 0.000001
for both the outer and the inner and outer combined stars. For —3.0 < [Fe/ H] S
—2.5, one-sided probabilities Of 0.060502, 0.000246, and 0.000271 were derived for the
inner, the outer, and the inner and outer together, respectively. The second, third,
and fourth column in Table 5.2 summarize the test results. As listed in the table,
the null hypothesis is strongly rejected for most cases, in particular below [Fe/ H] =
—1.8, conﬁrming the existence of multiple populations in our data. Thus, it can be
inferred that the stars in individual metallicity bins were born from an ISM that had
been polluted by different processes.

We also carried out a K-S test between the inner and outer halo populations
under the hypothesis that the distribution of [01/ Fe] shown in black (inner halo)
for each metallicity bin could be reproduced from the distribution of the same parent
population as that shown in the red (outer halo). The ﬁfth column in Table 5.2 shows
the results Of this test. It is very interesting to see that the null hypothesis is only
rejected for the metallicity range —1.8 <[ Fe/ H] S —1.0, but not for lower metallicities.
Hence, the inner and outer halo stars with [Fe/ H] > —1.8 formed in environments that
experienced different enrichment histories. A plausible interpretation for the cases
with [Fe/ H] < —1.8, which are not highly rejected, is that no matter whether those
stars were accreted from smaller subsystems or formed in dissipatively collapsing
protO-galactic clouds, it may be the case that the chemical enrichment history in the

regions where they were born may be the same at very low metallicity.

153

5.6.3 DISTRIBUTIONS OF [a/Fe] WITH Rapo CUTS

Inspection Of the right-hand panels Of Figure 5.9, which display the distributions of
[a / Fe] separated by various cuts on Rape, clearly reveals that there are a greater
fraction Of low -a stars for the accreted component than found for the dissipative
component as the apO—Galactic distance increases. The apO-Galactic distance range
for each plot is listed in the top Of each left-hand panel. This agrees with the results
from Stephens & Boesgaard (2002), who claimed that the average value Of [a / Fe] for
the stars with Rape > 16 kpc at the same metallicity is slightly lower than that Of the
lower orbit stars with Rapo < 16 kpc. The inner halo stars seem to exhibit similar
properties, but is not completely clear. The relative number of the high-oz stars with
Rapo > 16 kpc, however, is reduced signiﬁcantly, and the low-a stars are relatively
increased. This ﬁgure (the third right-hand panel) also indicates that there are some
fraction of low [a / Fe] stars even among the prograde stars having Rapo as large
as twice the Sun’s orbit. These kinematically peculiar prograde stars may form in
localized star-forming regions at large Galactic distances, which had prolonged star
formation until the onset Of SNe Ia. Considering their large apo—Galactic distances,
an external origin cannot be ruled out.

The left-hand panels of Figure 5.9 show [a / Fe] as a function of [Fe/ H] The mean
value Of [a / Fe] at a given metallicity was calculated by averaging the a-abundance
in a bin of 0.5 dex in metallicity. The mean a-abundances, with error bars indicating
the standard error Of mean (s.e.m) for both the inner (blue diamond) and the outer
(green triangle) are over-plotted in the ﬁgure. An odd feature in Figure 5.9 is that,
as exhibited in the left-hand panels Of the ﬁgure, below [Fe/ H] = -—-2.0 the mean value
of the a-abundance for the accreted component at a given metallicity is substantially
lower than that Of the dissipative component, although the uncertainty could be
higher due to the small number of stars in that regime. The discrepancy becomes

higher as the apO-Galactic distance becomes larger. It appears that is also the case for

154

 

 

=N,,=1'435 40<V (km/s)--<>i
N,°,= 6—145 402v (km/S)—-A~

j

[OI/Fe]

 

 

 

 

 

N,O,=134 3 40<V (km/s)--<>j

N},O,=5911402v (km/six

:g i
i

1

N,',=2334 0V< (km/s)- -<>

N,g,=1844 40 0V2 (km/s)--A€

[tr/Fe]

 

 

 

   
 

‘ + ' . ‘ 0.30 *1“ ‘ ‘ ‘ ‘ ‘

0.6» 245R (k c) — N =69 40<V (km/s) <>

‘ o “-39: 53. _: , _ - ‘ ~ :N‘°‘= 860 402v (km/s)--A-

_ 0.45: -- :5 :— ,

g l '" i 1

I—a 0.2T ‘ i I
0.0}

 

 

 

 

 

 

 

-3.0 -2.5 -2.0 -1.5 -1.0 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
[Fe/H] [a/Fe]

Figure 5.9 Distributions of [Oz/Fe] (right) and plots of [a/Fe] versus [Fe/H] (right)
with various cuts on Rape. The blue diamonds denote mean values of [01/ Fe] of the
inner halo stars at a given metallicity and the outer halo stars for the green triangles.
the range [Fe/ H] > —1.5, but we don’t clearly see the same behavior in the range —2.0
< [Fe/ H] < —1.5. The larger discrepancy in mean a-abundance may be attributed to

a more clear separation between the inner and outer halo stars at high RapO at low

155

metallicity, but smaller differences due to overlapping populations at low Rape.
Another interesting fact is that there may be trends in a-abundance with metal-
licity, provided that the low-a stars are removed, as found in Figure 20 and 21 in the

paper by Stephens & Boesgaard (2002). This will be discussed in more detail below.

5.6.4 DISTRIBUTIONS OF [er/Fe] WITH Vd, CUTS

Now we make use Of V4, as a cut to examine how [a / Fe] (left panels), [Fe/ H] (middle
panels), and eccentricity (right panels) are distributed over this variable, Figure 5.10
displays the results. The range Of V¢ used to cut the sample is listed in the top of
each middle panel. Just as before, the sample is divided into the inner and outer
halo stars by cutting on the Ram distance at 16 kpc. The ﬁrst thing noticed in this
ﬁgure is that as the V¢ cut declines, the fraction Of the number Of low metallicity
stars increases for the outer halo stars, as found by Carollo et al. (2007). The same
effect, but somewhat smaller, is exhibited by the inner halo stars, presumably due
to overlapping populations. The distribution of [a / Fe] for the outer halo stars is
shifted to lower a down to V4, ~ —200 km s‘l, compared to that of the inner halo
stars. Below Vg = —200 km s’l, the distribution is again shifted to high-a for the
accreted component, but still, some low -a stars exist. It is very interesting tO note
the somewhat larger fraction Of the low-a stars among the accreted sample with even
moderate rotation velocity, as shown in red in the top left panel. This is already seen
in the third right—hand panel Of Figure 5.9.

From the distribution Of the eccentricity, it can be inferred that without separating
the sample into two groups, the inner halo component with stars having V¢ > —50
km s-1 is oblate, since it has lots of stars with high eccentricities, while the outer
halo component with stars having V4, < —50 km s‘1 has a slightly spherical shape,
with lower eccentricity, as also identiﬁed by Carollo et al. (2007).

The left-hand panels Of Figure 5.11, which show [a / Fe] versus [Fe/ H] for various

156

 

   
 

  

 

  

 

 

 

 

 

 

 

N ' =1202 ' ‘ ‘ 802 'v (km/s) 16 >' R ' (kpc)
0.25 ~— -»
thg: = 233 4’ 16 s R apo(kpc)
0.20% «- -— apo
9 0.15
z 0.10,
0.05:
025 gNm, f 3534 ‘ __40 2 V4) (km/SW .12 :’ 15a 7 (kpc)
020,) tot _ ‘_ _, — apo (kpc)
9 0.15 t
z 0.10
0.05
N =‘16‘20 ‘ _-50 2V (kin/s) ‘ _16>‘ R ' (kpc)
0.25 . -
ENE": = 768 4’ 16 s R apo(kpc)
0.20% 0 ~» -~ 3P0
9 0 15 l «-
z 0.10,- _FFFDD-liLL, ._
0.05) -—
’N =87 _,-2002v (km/s): 016>HR ' (kpc)
0.25 tot _ (1) apo
020 EN“), _ 295 __ 016 s Rapo (kpc)
E§ 0.15 ‘L
z 0.10 ~—
0.05 i
0.00

 

[cl/Fe] [Fe/H] Eccentricity

Figure 5.10 Distributions Of [a / Fe] (left), [Fe/ H] (middle), and eccentricity (right) for
the stars selected by various cuts on V¢.

cuts on V,», exhibit somewhat different results from those found from Figure 5.9.
Note that each histogram is cumulative in K», as indicated in the top of each panel.
The mean values of[a/ Fe] were calculated with the same way as in Figure 5.9. and

the symbols represent the same groups (blue diamond - inner halo, green triangle -

157

 

 

      
   
  

 

 

 

 

 

 

 

 

 

 

 

 

. 0.30
0.6» 80<_V km/ EN =5503 16> R
.- ... '(" 2a.: o.25;-N‘°‘=2077 16<Raiopo(kkpc))-A~:
_ 0.4:: "2 80.20,— 1
g :’ i f" ,5 z 0.15 {
h—A 0.2 :- :‘ “"- Z 0.10_ i
00;.- ,.' 0.05~ :
0.6— - =4301 16> (kpc)<>
;. . Nt°t= 1844 16<Ra$P0°(kpc)- A
H 0.4? ’
o .
E. 0.2~
0.04
0.6:
0.41-
'8'
E 0.2—
0.03 , _ p
0.30.
0.6* —200<V km/ — N 8-7 16>R
: 95,. f) . _: 0.25.— Nfgt=295 16SRa :po(l<pc)-O 13%
”a- .-'- :1” ‘ . .
_ 0.4— i it"? 1 80.20:— :
g f “‘6’ 3 1"1g“0.15§ —:
... 02: -:._':-' ;. I z 0.10E 5
0.0; ' 351’ . . - 0.05 '
_ . . 0.00r
—3.0 -25 -20 -1.5 —1.0 0.1 0.0 0.1 0.2 0.3 0.4 0.5
[Fe/H] [fl/Fe]

Figure 5.11 Fractional histograms of [Oz/Fe] (right) and plots of [a/Fe] versus
[Fe/ H] (right) for the stars selected by various cuts on V¢.

outer halo). In this ﬁgure, down to [Fe/H] = —2.25, the accreted stars display lower
a values on average for all rotation velocity cuts, as seen by other studies (Nissen
& Schuster 1997; Gratton et al 2003; Stephens & Boesgaard 2002). Below [Fe/H] =

—2.25, although not many stars are involved, the dissipative component exhibits lower

158

(or at the same level) a-enhancement on average, which is directly Opposite to what
was found in Figure 5.9. Furthermore, the discrepancy in the mean a values becomes
larger with lower V4,. This may be because Of the sample selection. We may regard
the stars with V4, < -200 km 3‘1 as outer halo stars, no matter what the Rapo they
have. This behavior may also suggest that Vd) is a better parameter to distinguish the
low metallicity outer halo stars from the inner halo stars. Yet, since we separated the
sample into two groups for Vd> 200 km s—l, we may see this kind of behavior. There
may be a weak trend Of [a / Fe] with respect to [Fe/ H] for both the inner and outer
halo, at least down to [Fe/ H] = —2.0. However, below this metallicity, it is hard to
tell due to the downturn of [a / Fe]. Larger numbers of low metallicity stars are clearly
required. The histograms of [a / Fe] in the right-hand panels of the ﬁgure reveals the
same results seen in Figure 5.9; the overall mean value of [a / Fe] is lower for the stars

with higher Rapo than those with lower Rapo over all ranges Of Vg.

5.7 DISCUSSIONS AND IMPLICATIONS

What do the patterns and behaviors identiﬁed in the previous section imply? We
ﬁrst consider the inner halo stars. Since a typical halo star has [a / Fe] = 0.3 to 0.4,
even taking into account the uncertainty in estimating [a / Fe] from our technique,
the fact that most Of the inner halo stars with [Fe/H] > —1.8 are concentrated at
high-a in Figure 5.8 indicates that the more metal-rich inner halo is well described
by a canonical Galactic chemical model (Tinsley 1979). In this simple model, second
generation stars were born in a low metallicity gas cloud with a standard initial mass
function (IMF), and are expected to have a-enhancements on the order of 0.4 dex, the
standard SN 11 ratio. Another possible interpretation is that, as Font et al. (2006a)
demonstrated in their simulations of hierarchical formations of stellar halos within
the context of a standard ACMD universe, the inner halo could have been built up

from dwarf galaxies with high levels of a—elements, with a signiﬁcant contribution

159

 

0.25 . mNt;£;.2.22., .........,....T..ﬁ ......... : .-d.l.of<j [we] .SIO:O.5 . . . . . . I,
N = 89 :: 16 > R (kpc) 1

0.20. ‘0‘ 5 16 s Rapo (kpc) 7
= ,_ apo

l

 

 

 

 

 

 

 

 

 

-3.0 -2.5 -2.0 -1.5 -1.0
[Fe/H]

 

Figure 5.12 Distributions of V45 (left) and [Fe/ H] (right) for stars with [a/ Fe] < 0.05

from a few high mass systems very early in the process, before contributions from
Type Ia SNe could lower the ratio of [a/ Fe].

In contrast, the dissipative component with [Fe/ H] < —1.8 is not well explained
by only SNe II enrichment, due to the apparent bifurcation Of the a distribution
into both high and low -a stars. One might naively think that the low-a stars with
[Fe / H] < —1.8 might have formed in another environment, such as the low mass dwarf
galaxies, and were accreted later on. The hierarchical galaxy formation (e.g., Font et
al. 2006a, 2006b) also suggests that the accretion of the low-a, low metallicity stars
is possible at later epochs of halo formation. The histograms of the right-hand panels
of Figure 5.8 might support this conjecture. Even though in the histograms most Of
the inner halo stars with [Fe/ H] > —2.2 are clustered at Rperi less than 3 kpc, with
a small spread, there are some stars with high values Of Rperi and [Fe/ H] < —2.2,
which might have been accreted. However, taking into account the prograde motion
of these stars, and the likely inside-out formation Of the halo, late accretion Of the
inner region of the halo is not expected to have occurred.

One possible origin for the low-a inner halo stars is that, as Gilmore & Wyse

160

(1998) suggested for the metal-rich, low-a halo sample Of Nissen & Schuster (1997),
those stars might have formed in fragmented star-forming regions of the protO-galactic
cloud which had a persistent star formation period Of more than a few Gyr, so that
they were self-enriched by SNe Ia. In this case, the regions where those stars were
born should be a low mass (or low density) environment; otherwise, the stars would
have higher metallicity due to rapid star formation. At present, this explanation
seems at least plausible.

Others (e. g., McWilliam 1998; Ryan et al. 1996) have reasoned that low metallicity
stars formed in an early Galaxy which was chemically contaminated by stochastic
star formation. Hence, stars with [Fe/ H] < —1.8 might have formed from gas clouds
polluted by a single, or only a few SNe (Audouze & Silk 1995; Tsuijimoto et al.
1999), which might account for the larger scatter we see in our data at the very low
metallicity end. This is, however, in conﬂict with the ﬁndings of Arnone et al. (2005),
who detected a very small cosmic scatter in Mg abundance for stars in the metallicity
range —3.0 < [Fe/ H] < —2.2, pointing toward a well mixed, homogeneous ISM. It
seems that our data are likely tO be more consistent with inhomogeneous chemical
evolution models (e.g., Ishimaru 86 Wanajo 1999; Argast et al. 2000), at least in the
range [Fe/H] < —1.8.

As Carollo et al. (2007) asserted that the outer halo formed through assembly of
smaller subsystems, assuming that all outer halo stars were accreted from external
systems, the low-a outer halo stars might have formed in low mass dwarf galaxies
and accreted early in the history Of the Galaxy, similar to the conclusions Of other
studies (Gratton et al. 2003; Venn et al. 2004; Geisler et al. 2007). Geisler et al.
(2007) reported that there is marginal overlap between the stars in dSphs and the
halo stars at the very low metallicity end, but more metal-poor stars with [Fe/ H] <
—2.4 in dSphs are need to be Observed at high spectral resolution in order to conﬁrm

this. This picture agrees with the recent simulations of the stellar halo formation

161

models by Font et al. (2006a, 2006b) and Johnston et al. (2008) who claimed that
the stars accreted from the surviving satellites possess low-oz abundance.

Font et al. (2006b) suggested that one may be able to track down the debris (e.g.,
cold tidal streams) Of dwarf galaxies disrupted by recent interaction with their parent
galaxy by selecting stars with [a / Fe] < 0.05. If we apply this cut to our halo sample
and look at the distribution of V4, as plotted in Figure 5.12, it can be noticed that a
larger portion of the stars exhibit retrograde motion for both the inner and outer halo.
The MDF is also shifted to lower metallicity compared to the ﬁrst right-hand panel Of
Figure 5.7. This MDF shift to lower metallicity and low a-abundance implicate that
the progenitors of the low-a stars selected were not that massive, and the accretion
happened recently. This is due to the fact that if the progenitors Of the low-a stars
were massive and the epoch of the accretion was early, the overall metallicity should
have been shifted to higher metallicity with high a-abundance. On the other hand,
if the mass of the progenitors was low and the epoch of the accretion was early, then
although we might expect stars Of low metallicity, the overall a-abundance would
be high. This interpretation is well described in the recent paper by Johnston et
a1. (2008), especially their Table 1. These authors found from their models of eleven
stellar halos, simulated within the context of a standard ACMD, that the distribution
Of [a / Fe] Of stellar halo stars is a good indicator Of the epoch of halo accretion, thanks
to the few Gyr time interval between the onset of SNe II and SNe Ia, while the [Fe / H]
distribution of the stars is sensitive to the mass Of accreted dwarf galaxies. Based on
this scheme, we may be able to roughly estimate the epoch Of the accretion and the
dominant mass scales involved.

Where did the high-a outer halo stars with [Fe/ H] < —1.8 seen in the ﬁgure come
from? One could argue that the progenitors of the high-a outer halo stars should
have been massive enough to produce the typical halo level Of the a-enhancement

(~ 0.3 dex or more) from SNe II. This would exclude the current low mass dwarf

162

galaxies around the Milky Way as progenitors Of the accreted stars, because most Of
the stars Observed in the dSphs do not exhibit such high-a enhancements (Shetrone et
al. 2001, 2003; Fulbright 2002; Tolstoy et al. 2003; Geisler et al. 2005). SO, it remains
possible that they might have been accreted very early from massive dwarf galaxies
such as Sgr, as pointed out by Geisler et al. (2007), who found good agreement in
[a / Fe] between the Sgr stars and the halo stars in the metallicity range —1.6 < [Fe/ H]
< —1.0. This may account at least for the high-a stars for [Fe/ H] > —1.8 in the ﬁgure.
For the low metallicity end, more metal-poor stars in Sgr are needed to conﬁrm that.
Font et al. (2006a, 2006b) also suggested that the high-a, low metallicity outer halo
stars formed in a few massive systems and were accreted very early before signiﬁcant
Fe contribution from SNe Ia could take place.

Another credible explanation, although contrary to the above argument, could be
that the high-a outer halo stars with [Fe/ H] < —1.8 formed in very low mass dwarf
galaxies in which the ISM was not so well mixed after the ﬁrst burst of star formation.
It is known that only a few SNe II are sufﬁcient to enrich the ISM Of small parcels of
gas to that Of the typical halo a-abundance level. The recent study by Recchi et al.
(2008) revealed that a differential galactic wind may cause the global metallicity of
a galaxy to be reduced by preferentially pushing away the metallic elements. Such a
wind might therefore generate the high-a and low metallicity environment required to
explain these stars. This might suggest that the presently Observed ultra faint dwarf
galaxies (e.g., Belokorov et al. 2006; Zucker et al. 2006; Belokurov et al. 2007),
recently found from the SDSS photometry, might be good candidates. In these very
low mass dwarf galaxies, the galactic winds would be very effective to push out the
ISM, due to their weak internal gravity. The recent discovery (Kirby et al. 2008) Of
stars with [Fe/ H] < —3.0 in these low luminosity dwarfs provides an additional clue.
These authors argued that the low luminosity dwarf galaxies might be the building

blocks of the Galactic halo, since the MDFs Of these galaxies have very similar low

163

 

 

[OI/Fe]

 

 

 

 

 

Figure 5.13 Distributions of mean [a / Fe] at a given metallicity for two separate sam-
ples. The blue diamonds with error bars are mean values of [a / Fe] in a bin of 0.5 dex
in metallicity, Obtained from the sample after removing the stars with [01/ Fe] < 0.25
for [Fe/ H] < —1.8. The green triangles with error bars are mean values Of [a / Fe] in a
bin Of 0.5 dex in metallicity from the stars with [a/ Fe] < 0.15. The cut of [Fe/ H] =
—1.8 is chosen because the bifurcation starts showing in Figure 5.8 at this metallicity.
The red lines are linear ﬁts to the average values of the a-abundance for each group.
metallicity tails as the MDF Of the halo, as also suggested by Carollo et al. (2007).
Once the a-abundance of the stars in the low luminous dwarf galaxies is measured, this
connection would become clearer. This picture is also in line with the inhomogeneous
chemical evolution model. It could be the case that the stars with [Fe/ H] < —2.2 for
both the accreted and the dissipative components formed from an ISM which had
experienced stochastic star formation, while above this limit stars more likely formed
in well mixed and homogeneous star forming regions.

It is very intriguing to compare Figure 5.9 and 5.11 with Figure 9 in Font et
al. (2006a) and Figure 9 in Font et al. (2006b), who simulated various types Of

stellar halos formed solely by accretions from dwarf satellite galaxies in a ACMD

164

cosmology. In their models, while the stellar halos generally exhibit a gradient of
a-abundance against [Fe/ H] (increasing a with decreasing metallicity), the surviving
satellites exhibit around the solar a-abundance, which closely follow the abundance
patterns of the present-day dSphs and the Milky Way halo. In order to illustrate
this with our data, Figure 5.13 shows [a / Fe] versus [Fe/ H], after separating the entire
sample Of halo stars into two sub-samples. One group consists of stars with [a / Fe] >
0.25 for [Fe/H] = —1.8, which is the point where the bifurcation begins to show in
Figure 5.8. The blue diamonds with error bars in Figure 5.13 are the mean values
Of [a / Fe] in a bin Of 0.5 dex in metallicity for this group. The red line is the linear
ﬁt to the average values Of the a—abundance. The other group is composed of stars
with [a/ Fe] < 0.15, and the green triangles in the ﬁgure are the mean values Of a-
abundance for this group. This ﬁgure exhibits a very similar behavior to the stellar
halos formed by Font et al. (2006a, 2006b), including the low-a stars as well, under
the assumption that all low-a stars were accreted from low mass dwarf galaxies. This
similarity suggests that at least some of the low-a stars in our sample may have come
such a process. These papers claimed that the low-a stars were accreted from dwarf
galaxies about 5 to 6 Gyr ago, rather late in the Galaxy formation process, after SNe
Ia went off to pollute the ISM with Fe.

Interestingly, Stephens & Boesgaard (2002) also identiﬁed a gradient of the a4
abundance with respect to [Fe/ H] in their sample with abnormal kinematics (e.g.,
Figure 20 and 21 in their paper). They reported a slope of —0.15, assuming a linear
relation. From our data, we derive a slope of —0.093 from a linear ﬁt to the average
values Of [a / Fe]. The slight difference between the two values may be caused by the
cut-Off in [Fe/ H] = —1.0 in our data.

From the above statements and looking at the a-abundance distribution for [Fe / H]
< -1.8 in Figure 5.8, we can conclude that there is no signiﬁcant fraction of stars that

may have been accreted from the small systems similar to the low mass dSphs we

165

Observe today around the Milky Way, since we there is a much larger fraction of the
stars (from both the inner and outer halo populations) clustered at high a-abundance,
which is not the case for the low mass dSphs. This agrees with other previous studies
(Shetrone et al. 2001, 2003; Fulbright 2002; Venn et al. 2004; Geisler et al. 2007).
However, there remains the possibility for early accretion from massive satellites,
which are responsible for the low metallicity, low-a stars. The ultra low luminous
dwarf galaxies are also possible sources for the low metallicity, low-a halo stars.

In Figure 5.14 we plot [a / Fe] as a function Of Rperi (right), in hopes Of exploring the
origin Of the bifurcation at the very low metallicity end. Note that the distributions
are cumulative on [Fe/ H] as denoted in the top Of each panel, unlike the panels Of
Figure 5.8. The behavior of the bifurcation in the a-abundance is more apparent
in this ﬁgure. Gilmore 86 Wyse (1998) argued that the low mass dwarf galaxies like
the ones we see today around the Galaxy cannot be the source of the low-a halo
stars with low Rperi values, because they are not massive enough to hold the stars
with their internal gravity, and member stars would be tidally dissolved into the halo
before they Obtain orbits with such small Rperidistances. Generally, it is known that
a small system interacting with a larger system will lose most Of its mass if its internal
average density is less than about three times the mean density of the larger system
(e.g., Johnston, Hernquist, & BOlte 1996). This was the argument they put forward
to dispute the claims of Nissen & Shuster (1997) that the metal-rich ( —1.4 < [Fe/ H]
< —0.8) and low-a halo sample they studied could have been a population accreted
from the low mass galaxies like the dwarf Sphs.

By extending their argument to lower metallicity and looking at the [a / Fe] distri-
bution of the very low metallicity sample, as a function of Rperi, we may check if this
logic also holds for our low-a, low metallicity stars. As can be seen in the ﬁgure, the
majority of the presumably accreted stars with [Fe/ H] g —2.2 have Rperi > 2 kpc,

which is about twice the distance than for the sample of Nissen & Schuster (1997).

166

 

 

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pen

Figure 5.14 Distributions of [a / Fe] (left) and Rpeﬁ (right) with various cuts on [Fe / H]
As in Figure 5.8 the dissipative (black) and the accreted (red) components are shown.
Therefore, some of the counter-rotating stars with low-a might come from low mass
dwarf satellites, as Stephens & Boesgaard (2002) claimed for their halo stars with
abnormal kinematics. It is probable that while the high-a stars with Rperi < 2 kpc

originated from high mass dwarf galaxies, the high-a stars with Rpeﬁ > 2 kpc might

167

have formed in very low mass dwarf galaxies where ISM mixing was not efficient.
These issues will only become clearer once the a—abundance is measured for the stars
in the low luminosity dwarf galaxies, and for the low metallicity stars in the Sgr
galaxy.

With the exception of a few stars having Rperi > 3 kpc, most Of the low metallicity
inner halo stars have 1.0 < Rperi < 3.0 kpc. This is partly due to the rotation velocity
cut (40 km s’1 < V4, < 80 km 5‘1), but they still represent the typical value Of the
inner halo. Most Of them are found with [a/ Fe] > 0.25, so that they may have
formed in a homogeneous ISM enriched by SNe II. Considering all of the evidence, it
may be the most reasonable interpretation that the low a-inner halo stars formed in
fragmented, localized star-forming regions Of protO-Galactic clouds that experienced
periods Of persistent star formation.

Figure 5.15 is a very similar plot as Figure 5.14, but for Zmax. The fact that most
Of low-oz and low metallicity stars with prograde orbits are located within Zmax < 5
provides more evidence for the fragmented proto—Galactic cloud origin, rather than
the accretion origin. Some stars with Zmax < 2 kpc might be members Of the metal
weak thick disk, which are located at the very low metallicity tail of the metallicity

distribution function.

5.8 SUMMARY AND CONCLUSIONS

We have developed a method for estimating the a-abundance, parameterized as
[a / Fe], and have compared our results with the ELODIE spectral library, after search-
ing the literature for a-abundance measurements available for the stars in the library.
A Gaussian ﬁt to the residuals between the estimated and the literature values shows
a very small scatter (l a = 0.04 dex) with negligible Offset (-0.01 dex). Furthermore,
we tested the abundance variation as a function of signal to noise (S /N ); results of

that test indicated that the standard deviation Of our determinations is less than 0.1

168

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0 20 40 60 30
[we] Zmax (kPC)

Figure 5.15 Distributions of [a/Fe] (left) and Zmax (right) with different bins of

[Fe/ H]

dex with a very small offset (—0.022 dex) for stars with spectra having S /N as low as

15. We chose to adopt a more conservative cut of S/N 2 20 for the present analysis.
A total Of 39,167 spectrophotometric and telluric calibration stars from the SDSS

DR—6 (Adelman—McCarthy et al. 2008) was assembled in order to study the a-

169

abundance pattern in stars Of the Galactic halo. Using the stellar parameters, he-
liocentric radial velocity, proper motions, and distance estimates, we derived local
space velocities (U, V, W) and orbital parameters such as Zmax, Rape, Rperi, V4,,
and eccentricity. After calculation Of these parameters, we selected samples Of likely
halo stars by imposing cuts Of V4, 5 80 km s—l, Zmax _>_ 1 kpc, and [Fe/H] S —1.0.
A total sample of 7590 stars survived these additional cuts. The sample was divided
into two groups, a dissipative component (or inner halo) with stars having 40 3 V4, 3
80 km s‘1 and Rapo < 16 kpc, and an accreted component (or outer halo) with stars
having V¢ < 40 km s‘1 or Rape 2 16 kpc, or both. We examined a-abundance distri-
butions of these components with various cuts on the metallicity and the kinematic

parameters. Our major ﬁndings can be summarized as follows:

0 The distribution of V4, for the accreted component is shifted toward the counter-
rotating direction for all [a / Fe] bins (Figure 5.7). There are larger fractions of
stars with low metallicity ([Fe/H] < —1.8) for —0.1 < [oz/Fe] < 0.15 and 0.35
< [a / Fe] < 0.6 among the outer halo stars. This behavior may imply that
the low metallicity outer halo stars may comprise multiple populations with
different levels of a-enhancement; preferentially low and high-oz. These two
properties agree with the ﬁndings by Carollo et al. (2007), both kinematically

and chemically.

o The distribution Of [a / Fe] in each [Fe/ H] cut reveals that as the metallicity Of
outer halo stars decreases, the fraction of stars with intermediate a-abundance
(~ 0.25) decreases, while that Of the low (below 0.2)- and high (above 0.3)-
a stars increases, as shown in Figure 5.8. This implies bifurcation of the popu-
lation in a given metallicity range. This may also apply to the inner halo stars.

The outer halo stars have lower [a / Fe], on average, than the inner halo stars

for the range [Fe/ H] > —2.2.

170

o The low-a inner halo stars with peculiar kinematics (high Rperi or high Rape)
may possibly have formed in low mass gas clouds fragmented from proto-
Galactic halo clouds, while the high-a inner halo stars are well described by
canonical halo formation models. Or it can be understood, within the context
of hierarchical galaxy formation models, that a few very massive systems could
build up the halo with a high level of the a-abundance like in our inner halo
stars. The existence of both low and high-a stars at the very low metallicity
end in the inner halo suggests a stochastic star formation process in the halo,
which is consistent with the inhomogeneous chemical evolution model. This is
also the case for the outer halo population, as shown by application of a K—S

test (Table 5.2).

o It is not clear where the high-a stars with very low metallicity ([Fe/ H] < —2.5)
in the outer halo came from. However, one possible solution is that these stars
may have their origin due to the accretion Of objects similar to the very low mass
dwarf galaxies which have been discovered recently from SDSS. Those galaxies

would have been expected to have very inhomogeneous ISM, enriched by only

a few SNe II.

o It is plausible, by comparing with models Of stellar halo formation from Font et
al. (2006a, 2006b), that some fraction Of the low —a stars with low metallicity
([Fe/ H] < —2.0) might have once been members of low mass dwarf galaxies like
the ones we see at present. However, it is not likely that metal-rich ([Fe/ H] >
—1.8) outer halo stars could have been accreted from low mass dwarf galaxies,
because their a-abundance, on average, are much higher than that of the typical
stars in dSphs. They might have been accreted from massive systems at during
early epochs of halo formation. It seems unlikely that a large fraction Of halo
stars have been accreted from low mass dwarf galaxies like those around the

Milky Way at present.

171

0 Assuming all low-a stars ([a / Fe] < 0.15) were captured from other small sys-
tems, and excluding them in the averaging the a—abundance in each bin Of
metallicity, there may exist a relation between [a / Fe] and [Fe/ H] (Figure 5.13)
as found by Stephens & Boesgaard (2002). A slope Of -0.093 is derived by a

linear ﬁt to the mean values of [a / Fe].

o The mean value Of [02/ Fe] for stars on prograde orbits is slightly higher than
that of the counter-rotating stars at a given Rape distance, providing evidence
for the extra-galactic origin for the counter-rotating stars. The discrepancy

becomes larger as the metallicity decreases and Ram increases.

0 For metallicities above [Fe/ H] = —2.25, the accreted stars display lower a values,
on average, for all rotation velocity cuts (Figure 5.11). Below [Fe/ H] = —2.25,
although not many stars are involved, the dissipative component exhibits lower
(or at the same level) a-enhancement, on average. The discrepancy in the mean
a values becomes larger with lower V¢, providing more supporting evidence for

the accretion of these stars from very low mass dwarf galaxies.

From these ﬁndings, we can conclude that there is no signiﬁcant fraction of halo
stars that may have been accreted, especially at very late time, from small systems
like the low mass dSphs we Observe today around the Milky Way. There exists
the possibility for early accretion from massive satellites, which are responsible for
intermediate metallicity, low-a halo stars. The ultra low luminous dwarf galaxies
discovered recently may be possible sources for the very low metallicity, very high-

07 halo stars.

172

 

CHAPTER 6:
CONCLUSIONS AND FUTURE WORK

 

We have presented the development and execution Of the SEGUE Stellar Parameter
Pipeline (SSPP), which makes use of multiple approaches in order to estimate the fun-
damental stellar atmospheric parameters (effective temperature, Teﬂ', surface gravity,
log 9, and metallicity, parameterized by [Fe/H]) for stars with spectra and photome-
try Obtained during the course Of the original Sloan Digital Sky Survey (SDSS-I) and
its ﬁrst extension (SDSS-II/SEGUE).

The use of multiple methods provides an empirical determination of the internal
errors for each derived parameter, based on the range of the reported values from
each method. Among 128,000 spectra from 200 SEGUE plug-plates, all Of which
have derived stellar parameters available from the SSPP, typical internal errors, in
the range 4500 K S Teff g 7500 K, are 0(Teff) = 70 K (s.e.m), 0(log g) = 0.18 (s.e.m),
and a([Fe/H]) = 0.07 (s.e.m). However, Allende Prieto et al. (2008; Paper III) point
out that the internal scatter estimates obtained from averaging the multiple estimates
of the parameters produced by the SSPP underestimate the external errors, because
several methods in the SSPP make use Of similar wavelength regions and atmospheric
models.

A comparison with the averaged results of two different high-resolution analyses
of over 100 SDSS-I/SEGUE stars indicates that the SSPP is able to determine Teff,
log 9, and [Fe/H] to precisions of 141 K, 0.23 dex, and 0.23 dex, respectively, after

combining small systematic Offsets quadratically for stars with 4500 K S Teﬂ‘ g

173

7500 K. These errors are slightly different from those obtained by Paper III (0(Teff)
= 130 K, a(logg) = 0.21 dex, and a([Fe/H]) = 0.11 dex), although they share a
common set of high-resolution calibration observations. The reason for this is that
Paper III derived the external uncertainties of the SSPP only considering the stars
observed with the HET (on the grounds of internal consistency). The sample referred
to as OTHERS in Paper III exhibits somewhat larger scatter in its parameters, when
compared with those determined by the SSPP. ‘

Taking into account the average internal scatter from the multiple approaches
and the external uncertainty from the comparisons with the high-resolution analysis
together, the typical uncertainty in the stellar parameters determined by the SSPP are
0(Teff) = 157 K, 0(log g) = 0.29 dex, and a([Fe/H]) = 0.24 dex, over the temperature
range 4500 K S Teff S 7500 K.

Observation of several hundred additional stars from SDSS-I/SEGUE with HET,
which is now underway, will provide a more homogeneous sample for our tests. In
addition, additional high-resolution data for stars outside of our adopted temperature
range will help test the uncertainties in the stellar parameters for both cooler (Teff <
4500 K) and warmer (T65 > 7500 K) stars. These data, and a much more extensive
set of high-resolution observations of stars over the full parameter range, are planned
to be taken over the next several years. Once obtained, we plan to use the new
observations to make use of a method for applying zero-point corrections and inverse
variance weighting for obtaining an optimal estimate of stellar parameters over the
entire parameter space.

Using photometric and spectroscopic data reported in SDSS-I and SDSS-II/SEGUE,
we have examined estimates of stellar atmospheric parameters and heliocentric radial
velocities obtained by the SEGUE Stellar Parameter Pipeline (SSPP) for selected
true members of three Galactic globular clusters, M 13, M 15, and M 2, and two open

clusters, NGC 2420 and M 67, and compared them with those obtained by external

174

estimates for each cluster as a whole.

From the estimated scatters in the metallicities and radial velocities calculated for
the selected true members of each cluster, we quantify the typical external uncertain-
ties of the SSPP-determined values, a([Fe/H]) = 0.13, down to a spectroscopic signal-
to-noise limit of S/ N = 10 / 1, and 0(RV) ~ 8.0 km s-l, respectively. These uncertain-
ties apply for stars in the range of —O.3 S g — r _<_ 1.3 and 2.0 S logg S 5.0, at least
over the metallicity interval spanned by the clusters studied (—2.3 S [Fe/ H] S 0.0).
We have also conﬁrmed that Teff and log 9 are sufﬁciently well determined by the
SSPP to distinguish between different luminosity classes, through a comparison with
theoretical predictions.

From the above considerations of the uncertainties achieved from the comparisons
with the high resolution analyses and the selected true member stars of the globular
and open clusters, we conclude that the SSPP determines, with sufﬁcient accuracy
and precision, radial velocities and atmospheric parameter estimates, for stars in the
effective temperature range from 4500 K to 7500 K, to enable detailed explorations
of the chemical compositions and kinematics of the disk and halo populations of the
Galaxy.

The SSPP also Obtains approximate spectral types for stars, based on two meth-
ods, with differing limitations. A set of distance determinations for each star is
obtained as well, although future work will be required in order to identify the opti-
mal method. An et a1. (2008) have developed a set of cluster ﬁducials in the “natural
system” of SDSS, ugriz, based on crowded ﬁeld photometric analysis of SDSS Obser-
vations. Once available, we plan to implement distance estimates from these ﬁducials
into the SSPP.

We have developed a method for estimating the a-abundances, parameterized as
[a / Fe], and compared with the ELODIE spectral library, after searching the literature

for the a-abundance measurements available for the stars in the library. A Gaussian

175

ﬁt to the residuals between the estimated and the literature values shows a very small
scatter (1 a = 0.04 dex) with negligible offset (—0.01 dex). Furthermore, we tested
the abundance variation as a function of signal to noise (S/N); results of that test
indicated that the standard deviation is less than 0.1 dex with a very small offset
(—0.022 dex) for stars with spectra down to S/N = 15. We chose to adopt a more
conservative cut of S /N Z 20 for the present analysis.

A total of 39,167 spectrophotometric and telluric calibration stars from the SDSS
DR—6 (Adelman—McCarthy et al. 2008) was assembled in order to study the a-
abundance pattern in stars of the Galactic halo. Using the stellar parameters, he-
liocentric radial velocity, proper motions, and distance estimates, we derived local
space velocities (U, V, W) and orbital parameters such as Zmax, Rapo, Rperi, V¢,
and eccentricity. After calculation of these parameters, we selected samples of likely
halo stars by imposing cuts of V¢ S 80 km 3*, Zmax Z 1 kpc, and [Fe/H] S —1.0. A
total sample 7590 stars survived these additional cuts. The sample was divided into
two groups, a dissipative component (or inner halo) with stars having 40 S V¢ S 80
km S_1 and Ram < 16 kpc, and an accreted component (or outer halo) with stars
having V¢ < 40 km s-1 or Rape 2 16 kpc, or both. We examined a-abundance distri-
butions of these components with various cuts on the metallicity and the kinematic

parameters.

Based on this analysis, our primary conclusions are the following:

o The distribution of V¢ for the accreted component is shifted toward the counter-
rotating direction for all [a / Fe] bins (Figure 5.7). There are larger fractions of
stars with low metallicity ([Fe/H] < —1.8) for —O.1 < [oz/Fe] < 0.15 and 0.35
< [a/Fe] < 0.6 among the outer halo stars. This behavior may imply that
the low metallicity outer halo stars may comprise multiple populations with
different levels of a-enhancement; preferentially low- and high-a. These two

properties agree with the ﬁndings by Carollo et al. (2007), both kinematically

176

and chemically.

o The distribution of [a / Fe] in each [Fe/ H] cut reveals that as the metallicity Of
outer halo stars decreases, the fraction of stars with intermediate a-abundance
(~ 0.25) decreases, while that of the low (below 0.2)- and high (above 0.3)-
Oz stars increases, as shown in Figure 5.8. This implies bifurcation of the popu—
lation in a given metallicity range. This may also apply to the inner halo stars.
The outer halo stars have lower [a/ Fe], on average, than the inner halo stars

stars for the range [Fe/ H] > —2.2.

o The low-a inner halo stars with peculiar kinematics (high Rperi or high Rape)
may possibly have formed in low mass gas clouds fragmented from proto-
Galactic halo clouds, while the high-a inner halo stars are well described by
canonical halo formation models. Or it can be understood, within the context
of hierarchical galaxy formation models, that a few very massive systems could
build up the halo with a high level of the a—abundance like in our inner halo
stars. The existence of both low and high-a stars at the very low metallicity
end in the inner halo suggests a stochastic star formation process in the halo,
which is consistent with the inhomogeneous chemical evolution model. This is
also the case for the outer halo population, as shown by application of a K-S

test (Table 5.2).

o It is not clear where the high-a stars with very low metallicity ([Fe/ H] < —2.5)
in the outer halo came from. However, one possible solution is that these stars
may have their origin due to the accretion of objects similar to the very low mass
dwarf galaxies which have been discovered recently from SDSS. Those galaxies

would have been expected to have very inhomogeneous ISM, enriched by only

a few SNe II.

o It is plausible, by comparing with models of stellar halo formation from Font et

177

al. (2006a, 2006b), that some fraction Of the low -a stars with low metallicity
([Fe/ H] < —2.0) might have once been members of low mass dwarf galaxies like
the ones we see at present. However, it is not likely that metal-rich ([Fe/ H] >
-1.8) outer halo stars could have been accreted from low mass dwarf galaxies,
because their a-abundance, on average, are much higher than that of the typical
stars in dSphs. They might have been accreted from massive systems at during
early epochs of halo formation. It seems unlikely that a large fraction of halo
stars have been accreted from low mass dwarf galaxies like those around the

Milky at present.

0 Assuming all low-a stars ([a / Fe] < 0.15) were captured from other small sys-
tems, and excluding them in the averaging the a-abundance in each bin of
metallicity, there may exist a relation between [a / Fe] and [Fe/ H] (Figure 5.13)
as found by Stephens & Boesgaard (2002). A slope of -0.093 is derived by a

linear ﬁt to the mean values of [a / Fe].

0 The mean value of [a / Fe] for stars on prograde orbits is slightly higher than
that of the counter-rotating stars at a given Rapo distance, providing evidence
for the extra-galactic origin for the counter-rotating stars. The discrepancy

becomes larger as the metallicity decreases and Rape increases.

0 For metallicities above [Fe / H] = -2.25, the accreted stars display lower 0: values,
on average, for all rotation velocity cuts (Figure 5.11). Below [Fe/ H] = -—2.25,
although not many stars are involved, the dissipative component exhibits lower
(or at the same level) a-enhancement, on average. The discrepancy in the mean
a values becomes larger with lower V4,, providing more supporting evidence for

the accretion of these stars from very low mass dwarf galaxies.

From these ﬁndings, we can conclude that there is no signiﬁcant fraction of halo

stars that may have been accreted, especially at very late time, from small systems

178

like the low mass dSphs we Observe today around the Milky Way. There exists
the possibility for early accretion from massive satellites, which are responsible for
intermediate metallicity, low-a halo stars. The ultra low luminous dwarf galaxies
discovered recently may be possible sources for the very low metallicity, very high-
a halo stars.

The next extension of SDSS, known as SDSS—III, includes a program to continue
the SEGUE effort, known as SEGUE—2. This will result, over the course of the
next year, with about another 200,000 stars with medium-resolution spectra. The
techniques we have developed will naturally be applied to these stars. In addition, we
can also expect large numbers of additional calibration stars to be observed during
the course of other surveys that are part of SDSS-III. The much larger samples will
enable more detailed studies of the 0 patterns in the different stellar populations
of the Milky Way. Equally necessary is the development of new numerical Galactic.
chemical evolution models, with which these large data sets can be compared in the

future.

179

APPENDICES

180

 

APPENDIX A:
LINE LIST FOR LINE INDEX

CALCULATIONS

 

Table A.1: Line Band and Sideband Widths and Output Format

 

 

 

Column Format Description Central Width Red Width Blue Width
(A) (A) (A) (A) (A) (A)

1 A22 spSpec name
2 F83 H8 (3) 3889.0 3.0 3912.0 8.0 3866.0 8.0
3 F83 H8 (12) 3889.1 12.0 4010.0 20.0 3862.0 20.0
4 F83 H8 (24) 3889.1 24.0 4010.0 20.0 3862.0 20.0
5 F83 H8 (48) 3889.1 48.0 4010.0 20.0 3862.0 20.0
6 F83 Ca II K12 (12) 3933.7 12.0 4010.0 20.0 3913.0 20.0
7 F83 Ca II K18 (18) 3933.7 18.0 4010.0 20.0 3913.0 20.0
8 F83 Ca II K6 (6) 3933.7 6.0 4010.0 20.0 3913.0 20.0
9 F83 Ca II K30 (30) 3933.6 30.0 4010.0 5.0 3910.0 5.0
10 F83 Ca II H & K (75) 3962.0 75.0 4010.0 5.0 3910.0 5.0
11 F83 He (50) 3970.0 50.0 4010.0 5.0 3910.0 5.0
12 F83 Ca 11 K16 (16) 3933.7 16.0 4018.0 20.0 3913.0 10.0
13 F83 Sr II (8) 4077.0 8.0 4090.0 6.0 4070.0 4.0
14 F83 He I (12) 4026.2 12.0 4154.0 20.0 4010.0 20.0
15 F83 H6 (12) 4101.8 12.0 4154.0 20.0 4010.0 20.0
16 F83 H6 (24) 4101.8 24.0 4154.0 20.0 4010.0 20.0

 

181

Table A.1: Line Band and Sideband Widths and Output Format (continued)

 

 

 

Column Format Description Central Width Red Width Blue Width
(4) (A) (A) (A) (A) (A)
17 F83 H6 (48) 4101.8 48.0 4154.0 20.0 4010.0 20.0
18 F83 H6 (64) 4102.0 64.0 4154.0 20.0 4010.0 20.0
19 F83 Cal (4) 4226.0 4.0 4232.0 4.0 4211.0 6.0
20 F83 Ca I (12) 4226.7 12.0 4257.0 20.0 4154.0 20.0
21 F83 Ca I (24) 4226.7 24.0 4257.0 20.0 4154.0 20.0
22 F83 Cal (6) 4226.7 6.0 4257.0 20.0 4154.0 20.0
23 F8.3 G-band (15) 4305.0 15.0 4367.0 10.0 4257.0 20.0
24 F83 H7 (12) 4340.5 12.0 4425.0 20.0 4257.0 20.0
25 F83 H7 (24) 4340.5 24.0 4425.0 20.0 4257.0 20.0
26 F8.3 H7 (48) 4340.5 48.0 4425.0 20.0 4257.0 20.0
27 F83 H7 (54) 4340.5 54.0 4425.0 20.0 4257.0 20.0
28 F83 He I (12) 4471.7 12.0 4500.0 20.0 4425.0 20.0
29 F8.3 G-blue (26) 4305.0 26.0 4507.0 14.0 4090.0 12.0
30 F83 G-whole (28) 4321.0 28.0 4507.0 14.0 4096.0 12.0
31 F83 B3. II (6) 4554.0 6.0 4560.0 4.0 4538.0 4.0
32 F83 120130 (36) 4737.0 36.0 4770.0 20.0 4423.0 10.0
33 F8.3 12C (256) 4618.0 256.0 4780.0 5.0 4460.0 10.0
34 F8.3 Metal-1 (442) 4584.0 442.0 4805.8 5.0 4363.0 5.0
35 F83 H3 (12) 4862.3 12.0 4905.0 20.0 4790.0 20.0
36 F83 H3 (24) 4862.3 24.0 4905.0 20.0 4790.0 20.0
37 F8.3 H3 (48) 4862.3 48.0 4905.0 20.0 4790.0 20.0
38 F83 H3 (60) 4862.3 60.0 4905.0 20.0 4790.0 20.0
39 F83 C2 (204) 5052.0 204.0 5230.0 20.0 4935.0 10.0
40 F8.3 C2+Mg I (238) 5069.0 238.0 5230.0 20.0 4935.0 10.0
41 F83 MgH+Mg I+C2 (270) 5085.0 270.0 5230.0 20.0 4935.0 10.0

 

182

Table A.1: Line Band and Sideband Widths and Output Format (continued)

 

 

 

Column Format Description Central Width Red Width Blue Width
(A) (A) (A) (A) (A) (A)
42 F83 MgH+Mg I (44) 5198.0 44.0 5230.0 20.0 4935.0 10.0
43 F83 MgH (20) 5210.0 20.0 5230.0 20.0 4935.0 10.0
44 F83 Cr I (12) 5206.0 12.0 5239.0 8.0 5197.5 5.0
45 F83 Mg I + Fe II(20) 5175.0 20.0 5240.0 10.0 4915.0 10.0
46 F83 Mg I (2) 5183.0 2.0 5240.0 10.0 4915.0 10.0
47 F83 Mg I (12) 5170.5 12.0 5285.0 20.0 5110.0 20.0
48 F83 Mg I (24) 5176.5 24.0 5285.0 20.0 5110.0 20.0
49 F83 Mg I (12) 5183.5 12.0 5285.0 20.0 5110.0 20.0
50 F83 NaI (20) 5890.0 20.0 5918.0 6.0 5865.0 10.0
51 F83 Na I (12) 5892.9 12.0 5970.0 20.0 5852.0 20.0
52 F83 N31 (24) 5892.9 24.0 5970.0 20.0 5852.0 20.0
53 F83 Ha (12) 6562.8 12.0 6725.0 50.0 6425.0 50.0
54 F83 Ha (24) 6562.8 24.0 6725.0 50.0 6425.0 50.0
55 F83 Ha (48) 6562.8 48.0 6725.0 50.0 6425.0 50.0
56 F83 Ha (70) 6562.8 70.0 6725.0 50.0 6425.0 50.0
57 F83 CaH (505) 6788.0 505.0 7434.0 10.0 6532.0 5.0
58 F83 TiO (333) 7209.0 333.0 7434.0 10.0 6532.0 5.0
59 F83 CN (26) 6890.0 26.0 7795.0 10.0 6870.0 10.0
60 F83 O I tri (30) 7775.0 30.0 7805.0 10.0 7728.0 10.0
61 F83 K I (34) 7687.0 34.0 8080.0 10.0 7510.0 10.0
62 F83 K I (95) 7688.0 95.0 8132.0 5.0 7492.0 5.0
63 F83 Na I (15) 8187.5 15.0 8190.0 55.0 8150.0 10.0
64 F83 Na I-red (33) 8190.2 33.0 8248.6 5.0 8140.0 5.0
65 F83 Ca II tri (26) 8498.0 26.0 8520.0 10.0 8467.5 25.0
66 F83 Paschen (13) 8467.5 13.0 8570.0 14.0 8457.0 10.0

 

183

Table A.1: Line Band and Sideband Widths and Output Format (continued)

 

 

 

Column Format Description Central Width Red Width Blue Width
(A) (A) (A) (A) (A) (A)
67 F83 Ca II tri (29) 8498.5 29.0 8570.0 14.0 8479.0 10.0
68 F83 Ca II tri (40) 8542.0 40.0 8570.0 14.0 8479.0 10.0
69 F83 Ca II tri (16) 8542.0 16.0 8600.0 60.0 8520.0 20.0
70 F83 Paschen (42) 8598.0 42.0 8630.5 23.0 8570.0 14.0
71 F83 Ca 11 tri (16) 8662.1 16.0 8694.0 12.0 8600.0 60.0
72 F83 Ca II tri (40) 8662.0 40.0 8712.5 25.0 8630.5 23.0
73 F83 Paschen (42) 8751.0 42.0 8784.0 16.0 8712.5 25.0
74 F73 TiOl (5) 6720.5 5.0 6720.5 5.0 6705.5 5.0
75 F73 TiO2 (5) 7059.5 5.0 7059.5 5.0 7044.5 5.0
76 F73 TiO3 (5) 7094.5 5.0 7094.5 5.0 7081.5 5.0
77 F73 TiO4 (5) 7132.5 5.0 7132.5 5.0 7117.5 5.0
78 F73 TiO5 (9) 7130.5 9.0 7130.5 9.0 7044.0 4.0
79 F73 CaHl (10) 6385.0 10.0 6415.0 10.0 6350.0 10.0
80 F73 CaH2 (32) 6830.0 32.0 6830.0 32.0 7044.0 4.0
81 F73 CaH3 (30) 6975.0 30.0 6975.0 30.0 7044.0 4.0
82 F73 CaOH (10) 6235.0 10.0 6235.0 10.0 6349.5 9.0
83 F73 Ha (6) 6563.0 6.0 6563.0 6.0 6550.0 10.0

 

184

 

APPENDIX B:
OUTPUT FORMAT OF THE SSPP

 

Table B.1: Key to Each Column and Format of SSPP Parameter File

 

 

Column Format Description

 

1 A10 Running number
2 A16 SPEC NAME - MJD-Plate—Fiber
3 A3 Initial target type - BHB (Blue Horizontal Branch),
CVR (Star Caty Var), WD (White Dwarf),
KD (Brown Dwarf), FTO (Serendipity Blue),
MD (Serendipity Red), AGB (Serendipity Distant),
SER (Serendipity First), HOT (Hot Std), ROS (ROSAT_D),
KG (Star Carbon), GD (Star Red Dwarf),
LOW (Star Sub Dwarf), RED (Reddening Standard),
PHO (Spectrophotometric Standard), QA (Quality Assurance),
GAL (Galaxy), QSO (QSO), SKY (SKY), SER (Serendipity Manual)
4 A3 Spectral Type based on HAMMER program. N A-Not Applicable
5 A3 Spectral Type based on ELODIE templates
6 A5 Flag raised for a variety of reasons. Combination of four letters.
- First letter : indicates several things
11 = all appears well
D = likely white dwarf selected by 003 and RC
(1 = st or sdB selected by Dog and Rc

 

185

 

Table B.1: Key to Each Column and Format of SSPP Parameter File (continued)

 

 

Column Format

Description

 

10
11

F83
I3
F83
F83
13

H = too hot for abundance determinations

h = Helium line detected

1 = late—type star with solar abundance

E = emission lines noted (usually more than one)
S = Sky spectrum, ignore

V = Radial velocity missing

N = spectrum quite noisy

- Second letter : color flag

n = g — 7' color is OK, compared with predicted color
C = g - 1' color could be wrong

- Third letter : Balmer ﬂag, disagreement between Ha and H6
= n if normal

= B if not

- Fourth letter : G-band ﬂag

= n if normal

= G if likely G-band strong relative to expectation
= g if mildly G-band strong relative to expectation
- Fifth letter : parameter ﬂag

= n if normal

= P if 5.0 S S/N < 10.0

= N if no parameters estimated

Adopted [Fe/ H]

Number of estimators used

Error in the adopted [Fe/ H]

[Fe/ H] estimate from NGS2

Indicator variable

 

186

Table B.1: Key to Each Column and Format of SSPP Parameter File (continued)

 

 

Column Format

Description

 

12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37

F83
F83
I3
F83
F83
13
F83
F83
I3
F83
F83
I3
F83
F83
I3
F83
F83
I3
F83
F83
I3
F83
F83
I3
F83
F83

Error in [Fe/ H] estimate from NGS2
[Fe/H] estimate from NGSl

Indicator variable

Error in [Fe/ H] estimate from NGSl
[Fe/ H] estimate from ANNSR method
Indicator variable

Error in [Fe/ H] estimate from ANNSR
[Fe/ H] estimate from ANNRR

Indicator variable

Error in [Fe/ H] estimate from ANNRR
[Fe/ H] estimate from CaIIKl
Indicator variable

Error in [Fe/ H] estiimate from CaI IK1
[Fe/ H] estimate from CaIIK2
Indicator variable

Error in [Fe/ H] estimate from CaIIK2
[Fe/ H] from estimate CaIIK3
Indicator variable

Error in [Fe/ H] estimate from CaIIK3
[Fe/ H] estimate from ACF

Indicator variable

Error in [Fe/ H] estimate from ACF
[Fe/H] estimate from CaIIT
Indicator variable

Error in [Fe/ H] estimate from CaIIT

[Fe/ H] estimate from WBG

 

187

Table B.1: Key to Each Column and Format of SSPP Parameter File (continued)

 

 

Column Format

Description

 

38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63

I3
F83
F83
I3
F83
F83
13
F83
16
I3
16
16
13
I6
16
I3
16
I6
13
16
16
13
I6
16
I3
16

Indicator variable

Error in [Fe/ H] estimate from WBG
[Fe/H] estimate from k24
Indicator variable

Error in [Fe/ H] estimate from k24
[Fe/ H] estimate from k113
Indicator variable

Error in [Fe/H] estimate from ki13
Adopted Tea

Number of temperature estimators used
Error in the adopted temperature
T eff estimate from HA24

Indicator variable

Error in Teff estimate from HA24
Teg estimate from HD24

Indicator variable

Error in Tea estimate from HD24
Teff estimate from TK

Indicator variable

Error in Ten estimate from T K
Teﬁ' estimate from T0

Indicator variable

Error in Teff estimate from To
Teff estimate from T1

Indicator variable

Error in Ten: estimate from T; K

 

188

Table B.1: Key to Each Column and Format of SSPP Parameter File (continued)

 

 

Column Format

Description

 

64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89

I6
13
16
I6
13
16
I6
13
16
I6
13
I6
16
13
I6
16
13
16
F83
13
F83
F83
I3
F83
F83
13

T83 estimate from NGS1

Indicator variable

Error in T83 estimate from NGSl
Tag estimate from ANNSR
Indicator variable

Error in Teff estimate from ANNSR
Teff estimate from ANNRR
Indicator variable

Error in T83 estimate from ANNRR
Tear estimate from NBC

Indicator variable

Error in Teff estimate from NBC
Teg estimate from 1:24

Indicator variable

Error in Teff estimate from k24
Tea estimate from ki 13

Indicator variable

Error in Teff estimate from k113
Adopted log 9

Number of log 9 estimators used
Error in the adopted log 9

log 9 estimate from NGS2
Indicator variable

Error in log 9 estimate from NGS2
log 9 estimate from NGS1

Indicator variable

 

189

Table 8.1: Key to Each Column and Format of SSPP Parameter File (continued)

 

 

Column Format

Description

 

90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115

F83
F83
I3
F83
F83
I3
F83
F83
I3
F83
F83
13
F83
F83
I3
F83
F83
I3
F83
F83
13
F83
F83
I3
F83
F83

Error in log 9 estimate from NGS1
log 9 estimate from ANNSR
Indicator variable

Error in log 9 estimate from ANNSR
log 9 estimate from ANNRR
Indicator variable

Error in log 9 estimate from ANNRR
log 9 estimate from CaIl
Indicator variable

Error in log 9 estimate from CaI1
log 9 estimate from CaI2
Indicator variable

Error in log 9 estimate from CaI2
log 9 estimate from MgH

Indicator variable

Error in log 9 estimate from MgH
log 9 estimate from NBC

Indicator variable

Error in log 9 estimate from NBC
log 9 estimate from 1:24

Indicator variable

Error in log g estimate from k24
log 9 estimate from 1:113
Indicator variable

Error in log 9 estimate from 1:113

[01/ Fe] estimate from NGS2

 

190

Table B.1: Key to Each Column and Format of SSPP Parameter File (continued)

 

 

Column Format

Description

 

116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141

13

F83
F93
F93
F93
F93
F93
F93
F93
A10
F81
F81
F81
F81
F81
F81
F81
F81
F81
F81
F81
F83
F83
F83
F83
F83

Indicator variable

Error in [a/ Fe] estimate from NGS2

Dwarf distance in kpc from Beers et al. (2000)
Turnoff distance in kpc from Beers et al. (2000)

Giant distance in kpc from Beers et al. (2000)

AGB distance in kpc from Beers et al. (2000)

FHB distance in kpc from Beers et al. (2000)
Distance in kpc from Allende Prieto et al. (2006)
Distance (z) from the Galactic plane

Radial velocity ﬂag

Adopted heliocentric radial velocity

Error in the adopted heliocentric radial velocity
Calculated radial velocity, based on IDL code

Error in the calculated radial velocity

Radial velocity estimate (RVBS) from SDSS templates
Error in SDSS template radial velocity determination
Radial velocity estimate (RBEL) from ELODIE template
Error in ELODIE template radial velocity

Radial velocity; set to —9999.9

Error in Radial velocity; set to -9999.9
Galactocentric radial velocity based on adopted velocity
9 magnitude

V magnitude from V = g — 0.561(g — 7') -— 0.004

g — 7' color

Adopted g — 7' color prediction

9 — 7‘ color prediction from 0.818 — 0.092-H A24

 

191

Table B.1: Key to Each Column and Format of SSPP Parameter File (continued)

 

 

Column Format

Description

 

142
143
144
145
146
147
148
149
150
151
152
153
154
155
156

157
158
159
160
161
162

F83
F83
F83
F83
F83
F83
F83
F83
F83
F83
F83
F83
F83
F71
I3

F12.7
F12.7
F12.7
F12.7
F64
F74

g — 7 color prediction from 0.469 — 0.058-H D24
9 —- 1' color prediction from half power point (HHP)
B - V color from B — V = 0.916(g - r) + 0.187
B — V color predicted color from Balmer lines

71 — 9 color

7" — 2' color

7' — 2 color

Error in 11 mag in PSF

Error in g mag in PSF

Error in 7' mag in PSF

Error in 2' mag in PSF

Error in z mag in PSF

E‘(B - V) from Schlegel et al. (1998)

Average S/N per pixel over 4000 — 8000 A
Quality check on spectrum. 1 for S /N > 30, 2 for 20 < S /N S 30,
3 for 15 < S/N S 20, 4 for 10 < S/N S 15,
5for5<S/NS 10,6forS/NS5

RA in decimal degrees

DEC in decimal degrees

Galactic longitude (l) in decimal degrees
Galactic latitude (b) in decimal degrees
Correlation coefficient over 3850—4250 A region

Correlation coefficient over 4500—5500 A region

 

192

 

APPENDIX C:
PROPERTIES OF SELECTED CLUSTER
MEMBERS

 

193

 

 

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