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_—__,...—_ ___.__._.—_— . . ._ —___—. _—

ANALYSIS OF RR LYRAE STARS OF THE NORTHERN SKY VARIABILITY
SURVEY

By
KAREN KINEMUCHI

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

2004

ABSTRACT
ANALYSIS OF RR LYRAE STARS OF THE NORTHERN SKY VARIABILITY
SURVEY

By
KAREN KINEMUCHI

RR Lyrae variable stars are important astronomical objects for the investigation
of the structure and evolution of the Milky Way Galaxy. These pulsating stars are
known to be found in old populations in our Galaxy and have the useful feature that
we can readily derive distances from them. With a large survey of the Galaxy, the
RR Lyrae stars can be used to map Galactic structures.

The Northern Sky Variability Survey (NSVS), whose data was obtained through
the Robotic Optical Transient Search Experiment (ROTSE-I) telescope, provides an
opportunity to study RR Lyraes found near the Sun. The RR Lyrae stars can be
detected up to 7-9 ki10parsecs from the Sun and can probe the inner halo and thick
disk component of the Galaxy. This survey is an excellent complement to other
Galactic surveys of the bulge and halo components.

We have found that almost 90% of the RR Lyraes in the NSVS survey are not
included in the General Catalog of Variable Stars (Kholopov 1985). Our sample of
RR Lyraes consists of approximately 1430 ab-type RR Lyrae and 375 c-type RR
Lyrae candidates. We have determined the periods and amplitudes, and have derived
phased light curves for these stars. Metallicity ([Fe/H]) of these stars was derived from
the photometric data using empirical methods developed by Jurcsik & Kovacs (1996)
and Sandage (2004). To derive distances, we made use of an Mv-[Fe/H] relation
from Cacciari & Clementini (2003). We have also found that our sample of c-type

RR Lyraes close to the plane is contaminated by other types of short period variable

stars.

RR Lyrae stars of both Oosterhofi I and II groups are present in the field pop-
ulation of RR Lyraes, but we find that the Oosterhoff I is dominant. A metal-rich
group of stars was found in our ab-type RR Lyrae sample. These metal-rich stars
were identified as belonging to the thick disk population. This metal-rich group was
used to find the scale height of the thick disk. The result is approximately 0.4 kpc,
which is lower than many estimates of the thick disk scale height. Our low value may
indicate that a thin disk component may be present in our metal-rich sample. We
have also found evidence for a mix of halo and disk populations for the metal-poorer
([Fe/H] < —1) RR Lyraes sample.

There is a need for additional kinematic information for these stars. The kine-
matics can help clearly associate the stars with their parent Galactic component
population. The sample of the ab-type RR Lyraes used for analysis was restricted to
a magnitude brighter than the actual limit of NSVS. The consequence of using this
magnitude limit is the removal from this study of stars found 5 kpc or further from
the plane of the Galaxy. The fainter RR Lyrae candidates need to be included in

future work for a more complete analysis of the inner halo regions.

DEDICATION

This Ph.D dissertation is dedicated to Dr. Horace A. Smith, my advisor. He is the
best role model for any graduate student. Not only is he a wonderful teacher and
researcher, but a very caring and kind individual. He is the best possible mentor any
student could ever wish to have. Horace has shown me that not all people in this
field are rotten bastards, and that nice people do exist. I only hope that I grow up
to be just like him.

iv

ACKNOWLEDGEMENTS

This publication makes use of data products from the Two Micron All Sky Survey,
which is a joint project of the University of Massachusetts and the Infrared Process-
ing and Analysis Center/ California Institute of Technology, funded by the National
Aeronautics and Space Administration and the National Science Foundation.

This research has made use of the SIMBAD database, operated at CDS, Stras-
bourg, France.

This research has made use of N ASA’s Astrophysics Data System.

A big thank—you to Timothy McKay and the University of Michigan for providing
a version of the NSVS database. Without their kindness, there would be no thesis.
Thanks also go to Eli Rykoff and Don Smith at University of Michigan for all their
help in the navigation of the dataset and in running their IDL routines. Thanks to
Carl Akerlof, the principal investigator for the ROTSE projects, for spear heading
this ambitious project.

I thank the ROTSE collaborators at the Los Alamos National Laboratory for
allowing me to work on the ROTSE-I / N SVS dataset. Thanks to Katherine McGowan
for graciously letting me stay with her during one of my visits. Thanks to Przemyslaw
Wozniak and his energy to keep this project going.

I would like to thank Kern Cook and Anthony Miceli allowing me to use the
Supersmoother period searching algorithm, as well as their helpful advice for running
this code and interpreting the results.

Thanks go to Peter Stetson for his advice on the variability index used in this
work. Without his clarity, the variable star catalog would still be a work in progress!

Thanks also go to Alex Schwarzenberg-Czerny for providing a version of his Anal—
ysis of Variance period searching program and prompt diagnosis to problems I en-

countered with this method.

Thanks to Joern Wilms and Sara Benlloch for providing the Lomb-Scargle period
searching code for IDL.

Thanks to Brian Sharpee for supplying versions of his spline fitting routine to
derive amplitudes and mean magnitudes.

Thanks to Timothy Beers for supplying the magnitude standard calibration rela-
tion and useful science discussions about the results.

Thanks to Christopher Waters for helping me produce figures 2.2 and 4.11, and
for the useful discussions of statistical analysis.

And now the special thank you’s....

Thanks to the thesis committee members: Dr. Horace A. Smith, Dr. Jack Bald-
win, Dr. Timothy Beers, Dr. Wayne Repko, and Dr. S.D. Mahanti. Thanks for
reading my funny “little” thesis. You missed my pirate joke! Thanks to Dr. Horace
Smith for reading, re-reading, re-re—reading, and nxre-reading the many drafts of the
thesis and all the helpful comments.

Thanks to the Astronomy Group in the Physics & Astronomy Department at
Michigan State University. Without their support and the pizza/relativistic-croquet-
bbq/ bad science fiction movie parties and their general sense of fun, I would not have
had such a good graduate school experience. Thanks for putting up with my practical
jokes and sense of humor.

Thanks to Amparo Alvarado, Shawna Prater, Debbie Simmons and all the secre-
taries in the department. I know who is really in charge of things around here!

Thanks to astronomy graduate students for being such a fun group of people.
The sense of community we have is special and hopefully it will continue long after
I am gone. And 1) write your thesis early, 2) save some money for the graduation
process (there are a lot of hidden costs!), and 3) see you sometime at some conference

somewhere.

vi

Thanks to my office mates, Mike Davis, Aaron “Cluze” LaCluyze, Brian Marsteller,
and Christopher Waters. Thanks for putting up with my Hello Kitty obsession, my
swearing, and all my crap precariously balanced on my desk, ready to fall at a mo-
ment’s notice.

Thanks to the peOple who made F reecell. The 12642 games helped keep my sanity
while I was waiting for code to finish running.

Thanks to the professors who did NOT believe in me, who thought I was not
graduate school material, who thought I would never make it in astronomy because I
did not know how to program and the general bastards who tried to make me quit this
field. Without your negativity, I would not have pulled myself up by my bootstraps
and motivated myself to achieve getting a Ph.D. I suppose this thesis is proof to
myself that I can do it.

Thanks to John Martin and Christopher Waters for their support throughout the
whole Ph.D experience. A special thanks to Chris for making me understand being
happy is the most important thing.

Okaasan to Otousan ni, arigatou gozaimasu. Yatto dekita nee!

vii

Table of Contents

1 Introduction 1
1.1 The Project ................................ 2
1.2 Goals of the Dissertation ......................... 2

2 Background on HR Lyrae Stars 5
2.1 RR Lyrae Variable Stars ......................... 5

2.1.1 Subtypes of RR Lyraes ...................... 6
2.1.2 Pulsation Mechanism ....................... 10
2.1.3 RR Lyraes as Distance Indicator ................ 12
2.2 Galactic Structure ............................ 15
2.2.1 The bulge ............................. 16
2.2.2 The disk .............................. 16
2.2.3 The halo .............................. 18
2.3 Galactic Formation Models ........................ 19
2.3.1 Eggen, Lynden-Bell, and Sandage (ELS) Model ........ 19
2.3.2 Searle and Zinn (SZ) Model ................... 21
2.3.3 Hierarchical Galaxy Formation ................. 22
2.4 The Oosterhoff Dichotomy ........................ 25

3 Instrumentation and Data Reduction 31

3.1 Robotic Optical Transient Search Experiment (ROTSE) ....... 31
3.1.1 Instrumentation .......................... 32
3.1.2 Observational Program ...................... 36

3.2 Data Reduction .............................. 37
3.2.1 First Pass Data Reduction .................... 37
3.2.2 Second Pass Data Reduction ................... 39

3.3 Data Analysis of ROTSE-I Observations ................ 41
3.3.1 Heliocentric Julian Dates ..................... 41
3.3.2 Variability Index ......................... 42
3.3.3 Identification of Candidate Variable Stars ........... 47

viii

4 Determination of RR Lyrae Properties

4.1 Period Searching Algorithm .......................
4.1.1 Phase Dispersion Minimization .................
4.1.2 Lomb-Scargle Periodgram ....................
4.1.3 Cubic Spline ............................
4.1.4 Analysis of Variance (AoV) ...................
4.1.5 Supersmoother ..........................
Amplitude Work .............................
4.2.1 Amplitudes from Spline Fitting .................
4.2.2 Amplitudes from Template Fitting ...............
Magnitude Calibration ..........................
4.3.1 Absolute Magnitude of RR Lyraes and Distances .......
Photometric Metallicities .........................
4.4.1 The Jurcsik & Kovacs [Fe/H]—¢31-P relation ..........
4.4.2 Sandage’s [Fe/H]-log P-AV relation ...............

4.2

4.3

4.4

5 Results from the Analysis of the NSVS RR Lyraes

5.1 Criteria for RR Lyrae Selection .....................
5.1.1 Description of the Selection Criteria ...............
5.1.2 Cutoffs for a Clean Sample of RR Lyraes ............
5.1.3 Absolute Magnitudes and Distances for the RRab Stars . . . .
5.1.4 Cross-correlation with the General Catalog of Variable Stars .
Period of the RRab Stars .........................
RRab Amplitudes .............................
5.3.1 Period-amplitude diagram ....................
5.3.2 Interesting outliers ........................
Metallicities ................................
5.4.1 [Fe/ H] from Jurcsik & Kovacs’ Method .............
5.4.2 [Fe/H] from Sandage’s Method .................
5.4.3 The Best Estimate of [Fe/ H] ...................
5.4.4 The Oosterhoff and Metal-Rich Groups .............
C-Type RR Lyraes ............................
5.5.1 Period-Amplitude Diagram ....................
5.5.2 RRc Identification Problem ...................

5.2
5.3

5.4

5.5

6 Discussion of the Results

6.1 Oosterhoff Dichotomy and Galaxy Formation Implications ......
6.1.1 Contour Plots of the Period-Amplitude Diagram ........
6.1.2 Distribution of the Groups ....................
6.1.3 ALog P and the Oosterhoff Dichotomy .............
6.1.4 Implications for Galactic Evolution ...............
6.2 The Thick Disk ..............................

ix

52
52
54
55
56
57
61
64
65
65
73
74
78
78
85

88
89
89
93
98
98
99
101
102
103
104
104
106
107
107
109
114
114

123
123
123
124
134
137
137

6.2.1 The Scale Height of the Thick Disk ...............
6.2.2 The Metallicity Gradient .....................

7 Future Work and Suggested Projects

7.1 Survey Completeness ...........................
7.2 Need for Kinematic Information .....................
7.3 Spectroscopy ...............................

7.3.1 Radial velocity measurements ..................

7.3.2 AS Metallicity ..........................
7.4 Obstacles Encountered with the RRc Stars ...............
7.5 Other Types of RR Lyraes ........................

A Best Estimate [Fe/ H]
B N SVS RRab Parameters

C NSVS RRc Parameters

138
141

144
144
146
147
147
148
149
150

152

171

200

2.1
2.2

4.1

5.1
5.2
5.3
5.4

6.1
6.2

7.1
A.1
B.1
C.1

List of Tables

RR Lyrae properties (Smith 1995) .................... 8
PrOperties of the Oosterhoff I and Oosterhoff II groups (Smith 1995) . 26
Factors of 7r to add for the 45,-,- Fourier parameters ........... 81
RRab candidate criteria for selection from the N SVS survey. ..... 90
RRc candidate criteria for selection from the N SVS survey. ...... 93
RRab classification criteria (Akerlof et al. 2000b) ........... 117
RRc classification criteria (Akerlof et al. 2000b) ............ 117
Number of stars of each group per Z bin ................. 129
Number distribution of the Oosterhoff I metallicity groups ...... 130
Blazhko Effect and Double-Mode RR Lyrae Candidates. ....... 151
Photometric Metallicity ......................... 153
NSVS RRab Properties .......................... 172
NSVS RRc Properties .......................... 201

xi

2.1
2.2

3.1
3.2
3.3
3.4
3.5

3.6

4.1
4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10

List of Figures

Example Hertzsprung—Russell diagram (Smith 1995). ......... 7
Diagram of the Milky Way Galaxy ................... 17
ROTSE-I Fields with constellations ................... 33

ROTSE-I Telescope. The four telephoto lenses and the CCDs are shown. 34
ROTSE-I telescope enclosure at Los Alamos National Laboratory, Fen-

ton Observatory .............................. 35
95th-Percentile L index trend with magnitude in the Galactic planar
region. ................................... 49
95th-Percentile L index trend with magnitude in the mid Galactic lat-
itude regions. ............................... 50
95th-Percentile L index trend with magnitude in the Galactic polar
region. ............. - ...................... 51
Aliasing problem with AoV ....................... 60
Supersmoother phased light curves. Upper plot: correct period. Lower
plot: alias period .............................. 63
RRab phased light curves from the ROTSE-I survey. The ROTSE
magnitude is the Y-axis quantity. The periods are in units of days. . 66
RRc phased light curves. The ROTSE magnitude is the Y-axis quan-
tity. The periods are in units of days ................... 67
Spline fitting method. Filled triangles are values from the spline fit.
Circles are the actual N SVS data ..................... 68
Example of output from the Template fitting method for SW And.
These are the 4 best template fits (smallest RMS values) ........ 70
Example of output from the Template fitting method for SW And.
This plot shows the best fitted light curve to the N SVS data ...... 70
Amplitude calibration for RRab and RRc stars. Slope and Y-Intercept
of the fitted line are also shown ...................... 72
Tycho calibrated ROTSE magnitude versus the Landolt standard mag—
nitude. Note the color term dependence. ................ 75
V magnitude calibration with Landolt standard stars. Note the same
symbols are used for each color range as in Figure 4.6. ........ 75

xii

4.11

4.12

4.13
4.14

4.15

5.1

5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10

5.11

5.12

5.13

Diagram of the the geometry to determine the distances. The solar
distance (R6 was assumed to be 8.5 kpc). The X in the diagram is the
center of the Galaxy or where there is buried treasure. ........
Distribution of the 660 RRab stars projected into the plane of the
Galaxy. The solid circle is the Sun, at location (0,0) kpc. The Galactic
center is at 8.5 kpc from the Sun. The open diamond at (8.5,0) kpc
identifies its location ............................
Calibration of the $31 values to the published values (Sandage 2004).
Calibration for the metallicities derived from Jurcsik & Kovacs (1996)
method on to metallicity system adopted by Sandage and used by
Layden (1994). ..............................
Comparison of [Fe/ H] from the Sandage relation using amplitude and
log period with Layden (1994) [Fe/ H] values ...............

This plot was used to determine the appropriate ratio range to select
the RRab candidates. Note the clump of stars between 0.4 and 0.8
days. The line is the function for the ratio parameter ..........
Ratio distribution with period. The boxed regions are where the RRc
candidates were selected ..........................
1430 RRab candidates selected from the N SVS survey. The coordinate
system is in Galactic l and b. ......................
1471 RRc candidates selected from the NSVS survey. The coordinate
system is in Galactic l and b. ......................
1430 RRab candidates selected from the NSVS survey. The coordinate
system is in the equatorial system (right ascension and declination). .
1471 RRc candidates selected from the NSVS survey. The coordinate
system is in the equatorial system (right ascension and declination). .

77

79

83

84

87

91

92

94

95

96

96

RRab sample of 660 stars in Aitoff projection (in equatorial coordinates). 97
RRc sample of 375 stars in Aitoff projection (in equatorial coordinates). 97

Period distribution histogram for RRab candidates from the NSVS
survey. ...................................
Period distribution histogram for 608 RRab’s, divided by IZ| distance
zones. ...................................
Period-Amplitude diagram for 608 RRab’s. The Oosterhoff trend lines
are from Clement & Rowe (2000). The solid line is Oosterhoff I and
the dashed line is the Oosterhoff II trend line. .............
Distribution of the metallicities as a function of distance from the
Galactic Plane. Note the clump of stars at high metallicity and low
|Z| distance. This may be the thick disk component. These stars have

[Fe/ H] values determined only from the Jurcsik & Kovacs (1996) method.105

Distribution of metallicity from Sandage’s method as a function of |Z|
distance ...................................

xiii

106

5.14 Comparison of the [Fe/ H] from the Jurcsik & Kovacs method with the
[Fe/ H] value from Sandage’s method. ..................
5.15 Regions in the period-amplitude diagram occupied by three groups of
RRab stars. The dotted line separates the Oosterhoff I and II groups.
The boxed area identifies the metal-rich RRab group in this sample.
Note that most of these metal-rich stars have a comparatively shorter
period than the Oosterhoff I group. ...................
5.16 Period distribution histogram for 375 RRc candidates from the NSVS
survey. ...................................
5.17 Period distribution histogram for 375 RRc candidate stars in |Z| dis-
tance zones. ................................

108

110

112

113

5.18 Period-Amplitude diagram with the inclusion of the RRc candidate stars. 115

5.19 Fourier parameter ¢41 vs. Period. In contrast to the similar diagrams
in Poretti (2001), no clear separation is seen between 6 Scuti and RRc
stars .....................................

5.20 Fourier parameter R21 vs. Period. As with the 4541 plot, no clear

118

separation is seen between the two types of short period variable stars. 119

5.21 Szymanski et a1. (2001) method of weeding out the eclipsers from the
sample of RRc stars. The trend lines here are the location of Szymanski
et a1. (2001)’s relation (Equation 5.7). The right hand trend line was
created by adding 27r to the left hand trend line .............

6.1 Lower resolution contour map of the RRab period-amplitude diagram.
Number of contour levels is 5. Note that there is a higher density of
stars near the Oosterhoff I locus. The trend lines are the same ones
from Figure 5.11. .............................

6.2 Higher resolution contour map of the RRab period-amplitude diagram.
Number of contour levels is 10. Note that there is now some clumps
associated with Oosterhoff II. The trend lines are the same ones from
Figure 5.11. ................................

6.3 [Fe/ H] distribution for the three groups with respect to |Z| distance. .

6.4 Oosterhoff II RRab candidates. .....................

6.5 Oosterhoff I RRab candidates .......................

6.6 Oosterhoff I group of RRab stars. This group is divided into two
groups by [Fe/ H] = -1.25. The solid circles are those stars with [Fe/ H]
< —1.25 and the open squares are the stars with [Fe/ H] > —1.25. Note

121

125

126
127
128
131

the metal richer clump close to the plane of the [Fe/ H] > —1.25 group. 132

6.7 Thick disk candidates. Notice the trend that the more metal rich stars
are constrained to the plane. This may be indicative of a thin disk
component. ................................

xiv

6.8 This shows the metal-rich thick disk group for different My values.
The asterisks are for those distances determined from the Mv-[Fe/ H]
relation. The open squares are for those distances where Mv was fixed

to the value of 0.6 and the crosses are for My = 0.7 ........... 135
6.9 The ALog P plot. The Oosterhoff groups do not appear to separate in

this plot as in Suntzeff et al. (1991)’s figure 8a .............. 136
6.10 Scale height plot derived from using 10 stars per Z bin. Stars here all

have [Fe/H]> —1 ............................. 139
6.11 Scale height plot derived from using 6 stars per bin. All the stars in

the bins have [Fe/H]> —1 ........................ 140
6.12 The average [Fe/ H] distribution with galactocentric distances. . . . . 142

XV

Chapter 1

Introduction

Variable stars provide valuable information, not only of the objects themselves, but
of their parent systems, such as globular clusters. Stellar characteristics of variable
stars give clues to physical processes within the stars. These stars have intricate
stellar astrophysical properties that can describe the surroundings in which they are
found (i.e. the structure of a galaxy). Analysis of the chemical composition of these
variable stars also gives information about their histories.

All variable stars are interesting objects for study, and some have particularly
important uses in different fields of astronomy. This dissertation will focus on one
kind of variable star, RR Lyrae stars. Key to their importance is the ability to
determine their distances from their apparent brightness (or magnitude). We will use
the RR Lyraes from an all sky survey and investigate the stellar properties of these
variable stars. From the properties, we investigate the history, or evolution, of the

Milky Way Galaxy.

1.1 The Project

The Robotic Optical Transient Search Experiment (ROTSE-I) was originally de-
signed to look for the optical counterparts to gamma ray bursters (Akerlof et a1. 1999,
2000a). The telescope for this experiment sweeps the entire sky from Los Alamos,
New Mexico, and tries to capture the optical flashes of the gamma ray bursters.
While searching for these flashes, the telescope collects vast amounts of data by tak-
ing images of the sky continuously. This particular operation is referred to as “patrol”
mode. The ROTSE team of scientists divided the observable sky from Los Alamos
into 209 areas, which corresponds to —30° in declination (6) to +90°. This telescope
was online 365 days a year, except during inclement weather.

Preliminary results on a variable star survey have been published in Akerlof et al.
(2000b). These results were obtained from only five fields out of the 209, which
corresponds to about 5% of the total sky surveyed by ROTSE-I. Their analysis of
the five fields yielded 299 probable RR Lyraes, of which 89% were not listed in the
General Catalog of Variable Stars (Kholopov 1985). Of these RR Lyrae candidates,
some may have been misidentified (for example, some c-type RR Lyraes could be 6
Scuti variable stars or other types of variable stars (Jin et a1. 2003)). Nonetheless,
any program with the potential to have such large numbers of newly discovered RR
Lyraes can have the potential to reveal important information regarding the structure

and history of our Galaxy.

1.2 Goals of the Dissertation

A large catalog of variable stars can be produced from the Northern Sky Variability
Survey (NSVS), which is created from the observations of ROTSE-I. These variable
stars, in turn, can be used as probes of the Galaxy. The variable star properties can
tell us much about the structure, evolution, and kinematics of the Galaxy. For this
project, RR Lyraes will be used as the diagnostic tool in the investigation of a 5
kiloparsec (kpc) region of the Milky Way Galaxy, centered near our Sun. The actual
limit defined by the RR Lyraes in the survey may extend to 7 or 9 kpcs.

There are two main scientific objectives to this project. The first goal is to produce
a catalog of the RR Lyraes found within the regions ROTSE-I observed. This part
of the project is a collaborative effort with the ROTSE team at both the University
of Michigan and Los Alamos National Laboratory. The second objective for this
dissertation is to use the RR Lyraes from the catalog to probe the disk and inner
halo components of the Galaxy.

One important advantage of the dataset obtained by the ROTSE-I telescope is its
well sampled light curves. This is due to the observations being made from night to
night for a span of a year (1999 to 2000). Most of the variable star candidates in the
northern fields of the ROTSE-I survey have plenty of observations, and thus good
quality light curves. Stars found in the southern fields or near the Galactic plane
have fewer observations. The stars in the southern skies are more sparsely observed
because the southern fields were not up in the sky as long as the northern fields. Stars
in the Galactic plane tend to be underobserved because they have near neighbors or
crowding issues so that photometry could not be cleanly determined.

Once light curve information has been produced for all the candidate variable
stars, several steps must be taken in order to analyze the information the RR Lyraes
can tell us. Due to the size of the dataset, automated methods (written in IDL and

C) were preferred and used. The first major task is to identify all the variable stars

within the survey limits. The second task is to pick out the RR Lyraes from all the
variable stars. Once the RR Lyraes are identified, the properties of these stars such
as periods, brightnesses, and metallicities, must be determined.

The ROTSE-I dataset complements well other surveys. The OGLE and MACHO
surveys cover the Galactic bulge, whereas QUEST and SDSS study the more distant
halo of our Galaxy. The ROTSE-I survey fits in between these surveys of the bulge
and the halo. Because of its coverage of the Galaxy, the ROTSE-I dataset can allow
one can look at the stars in the transition region from bulge to halo, as well as the
thick disk. The properties of those stars should help to clearly associate the stars
with particular galactic populations.

With such a wealth of information locked in the survey, many questions can be an-
swered, as well as generated, about the Galaxy, specifically about its field population,
and about the stars themselves. Do we find support for one particular galaxy forma-
tion scenario over another? Do we find different populations of RR Lyraes within the
region of the NSVS survey? The RR Lyraes should provide tantalizing clues about
the nature of the thick disk and inner halo component of the Galaxy.

The dissertation is organized in the following manner. Chapter 2 will provide an
overview of the RR Lyraes, astronomical terms, and a brief description of the galaxy
formation scenario we will be investigating. The instrumentation and data acquisition
of the ROTSE-I telescope will be described in Chapter 3. Chapter 4 will discuss the
work done to calibrate and to determine the parameters of the RR Lyraes. Chapter
5 will focus on the some of the basic results from the RR Lyraes of the NSVS survey.
Chapter 6 contains an in depth discussion of the results and their implications for
Galactic structure. Suggestions of future projects stemming from this dissertation as

well as problems encountered in the analysis are presented in Chapter 7.

Chapter 2

Background on RR Lyrae Stars

2.1 RR Lyrae Variable Stars

RR Lyrae variable stars are very important objects to study in astronomy. They
are excellent distance indicators since these stars are both luminous and ubiquitous
in the Galaxy. These stars have a periodic change in brightness which makes RR
Lyraes easy to find. RR Lyraes are pulsating stars, which means as there are changes
in brightness, size and temperature of the star.

A Hertzsprung—Russell (HR) diagram, which plots brightness (or magnitude) ver-
sus temperature (or color), shows where RR Lyrae stars are in relation to other types
of stars, both variable and non-variable. Figure 2.1 shows a simple color-magnitude
diagram (CMD), which is a version of an HR diagram. The diagram depicts the evo-
lutionary sequences found in a globular cluster or other old population of stars. RR
Lyraes are low mass (~ 0.7MQ) Population II objects, which means they represent
an older population of stars (Smith 1995).

In evolutionary terms, these stars have stopped fusing hydrogen in their cores and

are burning helium for the main energy generation. Some amount of energy is also
being produced in a shell of hydrogen burning surrounding the helium burning core.
Generally, if a low mass star is burning helium in the core, this places the star in
the horizontal branch on the CMD. Furthermore, RR Lyraes are only found in one
specific part of the horizontal branch. This location is the “instability strip”, a zone
that crosses the horizontal branch and that contains pulsating stars.

RR Lyrae stars are found in all components of the Galaxy: the bulge, disk, and
halo. They are also found in globular cluster systems as well as extragalactic objects
of the Local Group such as the Magellanic Clouds, dwarf spheroidal galaxies, and
M31. RR Lyrae stars trace the old parent population in which they are found. In
this dissertation, we will be investigating RR Lyraes of the field population (not
associated with a globular cluster) of the thick disk and inner halo in the vicinity of

the Sun.

2.1.1 Subtypes of RR Lyraes

The period of the pulsation cycle can be determined from the time evolution of the
light variation, i.e. the “light curve”. From the light curves, we can also obtain the
amplitude of the change in brightness. These two properties (period and amplitude),
along with temperature and other characteristics are used to classify the RR Lyraes
into subtypes. RR Lyraes can be divided into three main groups: RRab, RRc, and
RRd.

The “ab” and “c” divisions of RR Lyraes are called Bailey types (Bailey 1902).
“RRab” RR Lyraes are the most abundant form of these stars. There are small

differences between Bailey type “a” and “b”, but these stars are usually lumped

 

l l i i

Asymptotic Giant

 
  

 

  
   

Branch
_2 .— i
an Lyrae Stars ‘ . Rod Giant
O - r—n—q 6 Branch

 

Horizontal {—— Sungant'c
Branch
+4 _
Main
+6 - Sequence
+8 1 l 1 , 1 1
0.0 0.4 0.8 ,1 ..2 1 .6

(B-Vio

”Figure 2.1 Example Hertzsprung-Russell diagram (Smith 1995).

 

Table 2.1. RR Lyrae properties (Smith 1995)

 

 

Property |RRa RRb RRc

 

Period (days)
Temperature (Kelvin)

 

0.5 0.6 0.3
6300 6100 7400

 

together as “ab”. A Bailey type “a” RR Lyrae has a period around 0.5 days and an
asymmetric light curve shape. The amplitude of the light curve is approximately 1
magnitude in the V passband. The “b” type RR Lyrae periods are slightly longer,
averaging 0.6 days. The light curves are also asymmetric, except the amplitude is
shallower, ranging between 0.5 and 0.8 magnitudes (Petit 1987, Smith 1995). It has
been observed that shorter period RRab stars have larger amplitudes whereas the
longer period ones have smaller amplitudes.

Both the RRa and RRb stars are pulsating in the fundamental radial mode. The
fundamental pulsational mode has a single node in the center of the star. The best
analogy would be an oscillating string attached at one end while the other end is free.
This mode is often referred to as the “breathing” mode. However, the pulsation is
actually negligible at the star’s core and is significant only in the star’s outer envelope.

Bailey type 0 RR Lyraes have a shorter average period near 0.30 days. The RRc
light curves are more sinusoidal in shape than the RRab light curves, but usually
display some asymmetry. The amplitude of the light curve averages to about 0.5
magnitudes in V. The pulsational mode for RRc stars is the first overtone radial
mode. This mode is characterized as having a node in the center of the star and
another somewhere in the stellar atmosphere. Table 2.1 summarizes the important
properties of RR Lyraes.

The third major type of RR Lyrae is the double mode RR Lyrae or “RRd”. These

are not as numerous as the RRab or the RRc types. The RRd stars pulsate in both
the fundamental and first overtone modes. Hence, their light curves appear to have
more scatter than normal when they are plotted with any single period. One can
deconvolve the light curves to find the corresponding light curves of the fundamental
and first overtone modes. RRd first overtone periods range from 0.390 to 0.429 days
(Smith 1995), and they are often lumped together with the RRc stars.

Another category of RR Lyraes has been recently proposed, the second overtone
RR Lyraes, or “RRe” type (Clement & Rowe 2000, Clement et a1. 2001). These RR
Lyraes are even more rare than the RRd stars, and astronomers have disputed whether
they exist or not. They are characterized by short periods, smaller amplitudes than
the RRc stars, and sinusoidal light curve shapes. Because of their low amplitudes
and light curve shapes, it is often difficult to distinguish RRe stars from other types
of short period, low amplitude variable stars.

The MACHO consortium (Alcock et a1. 2000) has advocated a new naming con-
vention for the RR Lyraes. Rather than using the Bailey type nomenclature of RRab
and RRc, the new system refers to them as “RRO” and “RRl”, respectively. Double
mode RR Lyraes are designated as RR01, and the second overtone RRe stars as RR2
(Clement et al. 2001). We will not be using this new naming convention for RR
Lyraes.

In the history of observing RR Lyrae variables, a long term secondary modulation
of the light curve has been detected for some of these stars. This phenomenon is called
the Blazhko Effect, after S. Blazhko, who first discovered it in RW Dra (Blaiko 1907).
The Blazhko effect can easily be seen in the shape of the light curve. The period of the
star remains the same, but the amplitude of maximum changes. Often it is revealed
because it produces noisy looking light curves when the curves are plotted according

to just the primary period. The period of this secondary modulation can be anywhere

from 11 to 533 days (LaCluyzé et al. 2004). This effect is predominantly seen in RRab
type RR Lyraes, but also has been observed in RRc types. The Blazhko effect appears
to affect roughly 20-30% of the known RR Lyraes in our Galaxy (Kovacs 2001) and
stars exhibiting the Blazhko effect are found in the field population, in Galactic
globular clusters, and in other nearby galaxies. Unfortunately, the mechanism for
the Blazhko effect is unknown. It has been speculated that the cause of the Blazhko
effect could be related to either magnetic fields or resonance with non-radial pulsation
(Cousens 1983, Moskalik 1986, Kolenberg 2004).

In the CMD, the RRab and RRc stars appear in different regions within the
intersection of the instability strip and the horizontal branch. This is determined by
the temperature of the RR Lyraes. The RRab stars have an effective temperature
of approximately 6100 K whereas the RRc stars are hotter at 7400 K (Smith 1995).
Thus, the RRab stars are located in the red end of the instability strip and the RRc
type stars in the blue end. It has been speculated that RRd stars are those RR Lyraes
evolving from one side of the instability strip to the other. This could explain the
existence of the double mode pulsation observed in RRd stars. However, RRd type
stars are not observed ubiquitously. Some systems contain these stars, while in others

they are absent.

2.1.2 Pulsation Mechanism

The pulsation of a variable star, such as an RR Lyrae, can be described by Ritter’s

relation:

Q = 1% (2.1)

This relation relates the pulsational period (P) with the density p of the star. Q is

10

the pulsational constant. If the constant Q is known (for example, from theory) and
the pulsational period is also known, parameters such as radius, temperature, and
mass of the star can be determined.

Many pulsating variable stars can be best described as driven by the n mechanism.
For this mechanism to work, the star must have a partial ionization zone of an abun-
dant element at the right depth in the stellar envelope. This partial ionization zone
is often referred to as the “Eddington Valve” after Arthur Stanley Eddington, who
first noted the need of such a “valve” to maintain stellar pulsation. This zone can be
comprised of either neutral hydrogen (HI) and singly ionized hydrogen (HII) or singly
and doubly ionized helium (He II). An ionization zone that contains the HI to HII
transition will have a characteristic temperature of 10000 to 15000 K. An He II ion-
ization zone is found deeper in the atmosphere and has a characteristic temperature
of 40000 K (Carroll & Ostlie 1996).

The K. mechanism can be described starting with a star being perturbed away
from hydrostatic equilibrium. Usually, such perturbations will damp out in a star in
a relatively short time scale. In order to keep this perturbation, or pulsation, going
some kind of driving mechanism is necessary. Eddington’s valve is just such a driving
mechanism. For the “valve” to work effectively, it must block off the outflow of energy
when the star is at maximum compression. This then leads to a pressure maximum
after the star reaches maximum compression. This provides the star the necessary
“kick” to start it expanding again. At this point, the valve must open and release
the energy. The star then expands and cools.

The opacity (K3) in the partial ionization zone contributes to the Eddington valve
driving mechanism. Opacity is a quantity that describes the cross section for pho-

tons (of a particular wavelength) to be absorbed by a given mass of stellar material.

11

Usually, in stellar envelopes, the opacity can be described by Kramer’s Opacity law:
is = pT-3-5 (2.2)

where T is the temperature and p is the density. Kramer’s opacity law can explain
the usual case where the star is most transparent when it is compressed and at
its hottest. However, this is not what we want for the valve. Rather, the partial
ionization zone should follow an opacity law that scales as pT”, where s is smaller
than 3.5 or even negative (King & Cox 1968). Thus, back in the pulsation scenario,
as the star contracts and compresses, the Opacity increases in the ionization zone, and
the radiation is essentially blocked. When the stellar envelope expands and cools, the
partial ionization becomes less efficient at blocking the radiation. At this expanded
state, the hydrostatic equilibrium is not balanced. The star will contract again to
achieve this state. Thus, this sets up the cycle for pulsation.

Another way for the partially ionized zone to act as an Eddington Valve is through
the 7-mechanism (King & Cox 1968). Essentially, the partial ionization zone will
absorb heat during the compression phase of the pulsation cycle. This phenomenon
can happen because the heat energy going into the zone does not raise the temperature
of the material. Rather, this energy goes into ionizing the gas in the zone. Thus, the
ionization zone can absorb more heat/energy during the compression. Then, at this
point in the pulsation cycle, the pressure in this zone will again approach a maximum
after the minimum volume is achieved from compression. This provides a “kick” to

the outer layers and drives the pulsation.

2.1.3 RR Lyraes as Distance Indicator

12

One of the most important characteristics of RR Lyraes is that we can readily
derive their distances. These stars are distance indicators called “standard candles”.

The distance to the objects are calculated from the distance modulus:

m — M = 5 x Loglod - 5 (2.3)

Magnitudes are a logarithmic scale of brightness, where the fainter the object,
the larger the magnitude value. Bright objects can even have negative values. In
Equation 2.3, to determine the distance (in units of parsecs), one must have the
difference in the apparent magnitude, m, and the absolute magnitude, M (or My
if in the Johnson V filter system). The apparent magnitude is simply the observed
brightness. The absolute magnitude is the brightness an object would have if it
were placed 10 parsecs away from the observer. RR Lyraes are an excellent distance
indicator because there is a narrow range of absolute magnitudes for these objects
and because they are comparatively bright stars, visible to very large distances.

Unfortunately, the absolute magnitudes of RR Lyraes are dependent on at least
one quantity, metallicity. Metallicity, or [Fe/ H], of a star or celestial object refers
to the relative amount of heavy elements (elements other than hydrogen or helium)
compared to the amount found in the Sun. The value of [Fe/ H] is actually a loga-
rithmic ratio of the iron to hydrogen abundance of the star to the iron to hydrogen

abundance in the Sun.

NFe
NH

 

 

[Fe/H] = log(N“) — log(

NH )0 (2.4)

For example, if a star has an [Fe/H] of —2, the Sun has 100 times more iron than
this star. [Fe/ H] is often used as a proxy for the overall heavy element abundances

of a star. If the metallicity of a collection of stars in a star cluster or dwarf galaxy is

13

known, that metallicity is often assigned to that parent object as its own metallicity.
For the case of this study, the metallicity of the individual RR Lyraes are determined
from an empirical relation, which is discussed in detail in Chapter 4.

Several different methods are used to derive the absolute magnitude as a function
of metallicity and it is, unfortunately, still an issue of some contention. Different
methods of obtaining My have various uncertainties and different systematic errors.
Thus, the published values of My have a range from as bright as 0.45 magnitudes
to as faint as 0.77 magnitudes for a metal-poor RR Lyrae population (Layden et a1.
1996, Popowski 2001).

The average absolute magnitude of RR Lyrae stars is usually parameterized as

(My) = a + b[Fe/H] (2.5)

which may be oversimplified. Thus, there are two parameters that need to be deter-
mined: the zero point and the slope of the relation. There is a general agreement
that the more metal rich stars have fainter My values. Some My-[Fe/H] relations are
discussed in Bono et a1. (2003), Chaboyer (1999), and Cacciari & Clementini (2003).

Some of the methods of finding My include: trigonometric parallax, statistical
parallax, the Baade-Wesselink method, and the usage of the double-mode RR Lyrae
properties (Benedict et al. 2002). The trigonometric parallax is the simple geometric
measurement of the distance to a star, using the orbit of the Earth around the Sun as a
baseline. Statistical parallax is a more difficult measurement since it needs kinematic
information on these stars, namely proper motions and radial velocities. The Baade-
Wesselink method uses the varying color, light and radial velocity information to
obtain distances and absolute magnitude (Carretta et a1. 2000). Other versions of

the Baade-Wesselink method include the surface brightness method and the use of

14

infrared flux (Cacciari et a1. 1992). Double-mode RR Lyraes, although rare, can
also be used to determine My from the ratio of their fundamental to first overtone
mode periods. This ratio is related to the mass and using a mass-luminosity relation,
absolute magnitudes can be derived (Carretta et a1. 2000).

For this dissertation, I will use the My-[Fe/ H] relation of Cacciari & Clementini
(2003), which is consistent with most recent results. The Cacciari-Clementini relation

is given below:

My = (0.17 :i: 0.04)[Fe/H] + (0.80 :l: 0.10) for [Fe/H] < —1.5 (2.6)

My 2 (0.27 :i: 0.06)[Fe/H] + (1.012f: 0.12) for [Fe/H] > —1.5 (2.7)

2.2 Galactic Structure

The luminous part of the Milky Way Galaxy can be broken up into three main
components: the central bulge, the disk, and the halo. Each component has its own
distinguishing characteristics, as defined by its stars and the stellar systems. Numer-
ous surveys have been conducted to investigate the components and their properties
(such as metallicity or rotational velocity). Some notable Milky Way Galaxy vari-
able star surveys are the OGLE and MACHO surveys of the Galactic bulge, and the
SDSS and QUEST surveys of the outer halo. These surveys produced catalogs of RR
Lyraes found in each component of the Galaxy. This dissertation will focus in the
region of the inner halo and thick disk centered around the Sun, which is a region

intermediate to those covered in other surveys. More details about the ROTSE-I

15

survey and its database are presented in Chapter 3. Here, we will briefly discuss each
Galactic component, and the reader is directed to Figure 2.2 for a rough diagram of

the Galaxy.

2.2.1 The bulge

The central bulge is often a difficult Galactic component to observe in the optical
wavelengths due to dust obscuration. Often, studies of the bulge, where it is close
to the Galactic center, must be done in the radio or infrared wavelengths, in which
dust is more transparent. Stars of the bulge have a spheroidal distribution, like the
halo component, though studies have shown that a bar may exist in this region as
well. Astronomers have found that the bulge stars are also quite metal rich, averaging
around [F e/ H] = —1. The range in metallicity for the bulge has been observed to be
between [Fe/ H] = —1.25 and 0.5 (Binney & Merrifield 1998).

2.2.2 The disk

The disk can be considered to be comprised of two components: the thin disk and
the thick disk. The stars in both the thin and thick disk have a flattened distribution,
with the former more flattened than the latter. Disk stars also generally have circular
rotation around the Galactic center.T he thin disk, with its scale height of roughly
300 parsecs, contains a mix of young and old stars. The thin disk is generally more
metal rich (with —0.5 < [F e/ H] < 0.3) than the thick disk (Carroll & Ostlie 1996).
It is generally believed that the thin disk may have had a different origin than the

thick disk, but they have interacted with each other as they evolved.

16

 

Thin Disk

      
    

Sun 61%
<1 O

 

Thick Disk

\Globular
Cluster

    

Figure 2.2 Diagram of the Milky Way Galaxy

17

The thick disk contains older and more metal poor stars. The thick disk has a scale
height of approximately 1 kiloparsec. The thick disk stars have an average [Fe/ H] of
—0.6, but can range down to —2 (Chiba & Beers 2000 Beers, private communication).
Several different scenarios have been developed to describe the formation of the thick

disk. A brief outline of these possible scenarios are listed in King et al. (1990).

2.2.3 The halo

The halo component of the Galaxy is mostly composed of old stars in a roughly
spherical distribution that is symmetric about the Galactic center. Studies have
shown that the inner regions of the halo have a more flattened distribution than the
outer regions (Hartwick 1987, Carney et al. 1996, Sommer-Larsen et a1. 1997, Chiba &
Beers 2000). Globular clusters and field stars found within the halo indicate a density
fall off that can be described by a -3 or -3.5 power law with increasing distance from
the Galactic center. The orbits of the halo stars have been observed to be highly
eccentric. Overall, the halo stars appear to have a rotation about the Galactic center
that is much smaller than the disk stars (but see the discussion in section 2.3.3).
Studies of the halo objects have also shown the lack of a metallicity gradient beyond
about 10 kpc from the Galactic center (Rich 1998, Suntzeff et al. 1991). The mean
metallicity of the halo has been estimated to be around [Fe/ H] = -1.6, with a spread
of 0 ~ 1 dex1 (Carney et a1. 1996). Compared to the disk, the halo must have had a

very different origin and evolutionary processes.

 

ldex is an increment in base 10 logarithm.

18

2.3 Galactic Formation Models

One of the big questions in astronomy is how our Galaxy formed. Using the
observations collected in catalogs and surveys, and results of theoretical simulations,
two major models were produced in the early 19608 and late 19708. Eggen, Lynden-
Bell, & Sandage (1962) (hereafter referred to as “ELS”) described the Milky Way
Galaxy forming from a monotonic collapse of a large protogalactic cloud. Searle &
Zinn (1978) (hereafter referred to as “SZ”) advocated a chaotic merger/accretion
scenario of small sub-galactic “fragments”. Many observational results were used to
develop these models for formation of the Galactic features.

However, the current picture of the Galaxy has made things complicated. Some
astronomers have suggested the existence of a “dual halo” component of our Galaxy
and have required a galaxy formation model that best explains this. Neither ELS
nor SZ alone can explain this feature in the halo. One possibility that has been
supported by many astronomers is a hybrid scenario of the two main models. This
new composite model, coupled with the hierarchical assembly of cold dark matter
(CDM) (Peacock 1999, Longair 1998), has emerged to describe the features found in
the Galaxy’s dual halo.

In this section, the two main “classical” galaxy formation models are discussed
briefly. In the last subsection, a description of the hierarchical assembly scenario and

observational evidence supporting the existence of a dual halo are presented.

2.3.1 Eggen, Lynden—Bell, and Sandage (ELS) Model

The ELS, or the “top—down”, model envisions a proto-Galaxy as a large gas cloud

with some angular momentum undergoing a systematic collapse. This monotonic

19

collapse was estimated to occur in a time span of ~ 108 years, which is a rather rapid
collapse comparable to the free-fall collapse time of the proto-Galactic cloud. Stars
formed early during the collapse episode became the observed metal-poor stellar halo
population we see today. These early stars are now observed to have highly eccentric
orbits. The more massive early stars have evolved to the supernova stage during the
collapse episode and helped enrich the interstellar medium. In the radial direction,
the collapse of the gas was stopped by rotation, but it continued in the z direction
(using the sense of cylindrical coordinates). This latter collapse is believed to have
formed the rotating disk. Thus, in the now denser disk, star formation is encouraged
and increased.

The kinematically hot gas in this proto-Galaxy helped to dissipate the collapse
energy and condensed into the central region (now the Galactic bulge). The gas,
and any stars formed from this gas, began to orbit in a circular motion. Meanwhile,
stars in the halo still follow the eccentric orbits from the collapse episode. The old
population of stars observed in the bulge that are metal rich are stars formed from
the enriched gas, due to supernovae deaths of halo stars formed even earlier in the
collapse.

There are certain aspects of the ELS model that are no longer viable. One aspect
is the observed motion of the halo stars and globular clusters. Many of the halo
objects are moving with retrograde motion or have net 0 rotational velocity. Under
the ELS description, all the halo stars and globular clusters should be moving in the
same direction. Even if there were some chaos in the collapsing cloud of this model,
the halo systems would be expected to still have a small net rotation in the same
sense as the disk. Under this model, no substantial halo subsystem would have a
net retrograde motion. The halo stars, under this model, also are expected to have

a correlation between metallicity and the eccentricity of their orbits. As the cloud

20

dissipates and the orbits of these newly formed halo stars are less plunging, the cloud
enrichment is also greater. The existence of this correlation has been disputed.

The globular clusters themselves also provide contradictions to the ELS model.
Variations in chemical composition and cluster age have been observed in both the
bulge and halo components. The bulge globular clusters are generally metal-rich and
old (although there are exceptions), whereas the halo population, in general, has a
wide variety of metallicities and a range of ages. The large range in age (several

billion years) indicates that no rapid formation occurred.

2.3.2 Searle and Zinn (SZ) Model

In the SZ model, protogalactic cloud “fragments” gravitationally coalesce to form
the Galaxy. These cloud fragments have masses on the order of 106 to lOSMG and are
assumed to be spherically distributed about the proto-Galaxy. This model assumes
a rapid collapse for the central (and more mass concentrated) region of the proto-
Galaxy. Globular clusters in this region should have roughly the same cluster age.

The outer halo, however, formed more slowly (longer than 109 years). From
collisions and tidal disruptions of the cloud fragments, the outer halo globular clusters
formed. These parent cloud fragments were still in the process of being chaotically
accreted onto the Galaxy when these globular clusters were forming.

SZ proposed that the outer cloud fragments evolve independently of each other and
of the proto-Galaxy. Supernovae self-enrich these fragments. Thus, these fragments
would have their own unique chemical composition, globular cluster systems, and
stars. These evolutionary processes in the fragments are slower than the similar

processes that formed the bulge.

21

Kinematically, these cloud fragments become tidally disrupted and accrete onto
the halo, or even the disk. The stars and clusters from the fragments are expected to
retain the eccentric orbits of the parent fragments. The retrograde motions observed
in some of the outer halo stars are best described by this scenario. The chaotic
accretion/ merger events also predict a range in age and chemical composition (but
no metallicity gradient) for the stars and globular clusters of the outer halo, which
has been observed. However, the SZ model does not adequately explain the observed
metallicity gradient in the inner halo component. The ELS model with a dissipative

collapse episode predicts this feature.

2.3.3 Hierarchical Galaxy Formation

As larger surveys become available for study of the kinematics and chemical abun-
dances of the stellar population of the Milky Way Galaxy, questions arise over the
results. One wonders which galaxy formation scenario can explain the trends in the
observed properties of various tracer objects in each Galactic component (RR Lyraes,
horizontal branch (HB) stars, etc.). Many investigators have called for a hybrid of the
ELS and SZ models, since neither can completely explain all of the observed trends
(Hartwick 1987, Carney et a1. 1996, Sommer-Larsen et a1. 1997). These observed
trends, and the discrepancies will be discussed at the end of this section.

Recently, astronomers have tried to apply the hierarchical assembly of CDM model
to explain the formation of the Milky Way (Bekki & Chiba 2001). Since this work
focuses on the thick disk and inner halo of our Galaxy, the model developed by Bekki
& Chiba (2001) is particularly apropos.

The hierarchical assembly of CDM (Peacock 1999, Longair 1998) requires that

22

the lowest mass objects form first. These objects, or “clumps” will cluster and coa-
lesce. These processes are influenced by the underlying perturbations in the cosmic
microwave background (CMB). It is expected that the large scale structures in the
universe are built up by these clumps coalescing together. This model has conceptual
similarities with the SZ model and can be applied in larger scales than the Milky Way
Galaxy.

Bekki & Chiba (2001) apply this hierarchical assembly model in their numerical
simulations for the formation of the Galaxy. They describe the Galaxy formation in
the following manner. The proto—Galaxy starts off as in the ELS model, gravitation-
ally collapsing. While this is occurring, subgalactic fragments that have relatively
low mass form in large numbers. The clumps are predicted by the small-scale per-
turbations requisite in the CDM hierarchical assembly model. The clumps merge
into our Galaxy with or without dissipation, and thus gradually build our Galaxy.
In particular, the halo is constructed by these clumps without any dissipation. Dif-
ferent mechanisms are involved in the formation of the inner halo, but essentially, a
dissipative merger of clumps and collapse is required. Additionally, stars will form in
the clumps, and die, thus enriching the environment with metals. The clumps will
merge and become progressively more massive. The largest central conglomeration
will become the bulge. The subgalactic clumps and gas from the halo will continue
to accrete into the bulge and help form the disk of the Galaxy. However, this model
has not been fully tested to recreate all the observed structure, kinematics, chemical
abundance properties, and explicit formation of the stellar Galactic halo.

The Bekki & Chiba (2001) model helps explain a possible dual halo nature in
our Galaxy. Several studies have advocated the existence of a dual halo component
(Hartwick 1987, Norris 1994, Carney et al. 1996, Sommer-Larsen et al. 1997, Chiba &.

Beers 2000). An important feature of this dual halo is the stellar distribution. It has

23

been observed that the inner halo (Ryc < 15 kpc) is flattened whereas the outer halo
has a spherical distribution. This has been observed through surveys of RR Lyraes
(Hartwick 1987), blue HB stars (Kinman et al. 1994), and metal-weak stars (Chiba
& Beers 2000).

The inner halo, in addition to its flattened distribution, has interesting features
that are clues to its formation history. A metallicity gradient has been observed
for galactocentric distances less than 10 kpc (Zinn 1993, Sommer-Larsen et al. 1997,
Suntzeff et al. 1991). Kinematically, Sommer-Larsen et al. (1997) report that the
inner halo stars are moving in a more radial direction with respect to the Galactic
center rather than tangentially. One pr0posed characteristic, a net prograde motion
of the inner halo stars, has garnered some dispute. Norris (1994) found the inner halo
stars to have disk-like properties and to be kinematically “hot” (i.e. having large
velocity dispersions) with a prograde motion. Carney et al. (1996) argue that the
inner halo stars observed in their survey were “cooler” kinematically than Norris’s
results and are rotating about the Galactic center more slowly than the metal-rich
thick disk stellar population. Carney et al. also supported a prograde motion (average
rotational velocity (vmt) = +2721: 7 km/s) for the inner halo stars. However, Chiba &
Beers (2000) did not find this prograde motion in their kinematically unbiased sample
of metal-weak stars.

Regardless of the kinematic disagreements, all the investigators agree that the
inner halo stars come from a dissipative collapse episode. The gas in this region
dissipates into the bulge and the inner halo distribution flattens. The local (solar
neighborhood) halo stars studied by Sommer-Larsen et al. (1997) appeared to have
similar angular momentum distributions as the bulge stars. This scenario also predicts
the existence of a metallicity gradient for the inner halo, which has been observed.

The outer halo stellar distribution has been observed to be spherical. Metal-

24

weak (Chiba & Beers 2000) and blue HB (Sommer-Larsen et al. 1997) stars both
trace out the spherical distribution. The best scenario that describes the formation
of the outer halo may be an accretion/merger model similar to that of Searle &
Zinn (1978). Several observed characteristics support this idea. The absence of a
metallicity gradient has been reported by Norris (1994) and Sommer-Larsen et al.
(1997). This absence is to be expected since each subgalactic fragment (or satellite
galaxy) would evolve separately and have its own metallicity distribution before being
accreted into the Galactic halo. The outer halo stars have a net retrograde motion
((vmt) = —45 :l: 22 km/s (Carney et al. 1996)), and Sommer-Larsen et al. (1997)
report this population to have a tangential motion rather than a radial motion with
respect to the Galactic center. Carney et al. (1996) also fit isochrones to the outer
halo star pOpulation and found them to be generally younger than the inner halo
stars. This also supports the idea that the merged systems should be younger than

those formed from the dissipative collapse.

2.4 The Oosterhoff Dichotomy

Oosterhoff (1939, 1944) first discovered this unique phenomenon in the Galactic
globular clusters (GGC) that contained RR Lyrae populations. His original work
consisted of a study of five clusters, but today, many GGC’s with RR Lyraes have
been investigated. Oosterhoff noted that the observed properties of the RR Lyraes
separated into two distinct groups. The Oosterhoff dichotomy is defined by the mean
period of RRab and RRc stars ((Pab) and (Pab)) and the number ratio of RRc stars
to RRab (or all RR Lyraes) in the cluster. Later, other astronomers investigating the

Oosterhoff dichotomy found correlations with metallicity (Arp 1955) and kinematics

25

Table 2.2. Properties of the Oosterhoff I and Oosterhoff II groups (Smith 1995)

 

 

Property Oosterhoff I Oosterhoff II

 

(Pub) 0.55 0.64
(PC) 0.32 0.37
—"r— 0.17 044
”R31.

 

(Lee & Carney 1999).

Oosterhoff type I is distinguished by an average period of (Pub) z 0.55 days, but
can have a range of 0.52 < (Pub) < 0.58 days (Catelan 2004). The number of first
overtone pulsators (nc) to the total number of RR Lyrae stars (N RRL) is N—ng a: 0.17.
Oosterhoff I GGC’s tend to have more RRab’s than RRc’s or RRd’s. Oosterhoff II
type clusters have an average RRab period of 0.65 days, but can span from 0.62 to 0.66
days (Catelan 2004). The number fraction for Oosterhoff II clusters is N—Zfi z 0.44,
which shows more RRc stars are expected than in Oosterhoff I clusters. Studies with
metallicity shows that [F e/ H] ’5 —1.7 separates the two Oosterhoff groups. Oosterhoff
I RR Lyraes tend to have [Fe/H] > —1.65 while Oosterhoff II have [Fe/ H] < —1.6
(Catelan 2004). The zone where RR Lyraes do not pOpulate in period space is often
referred to as the “Oosterhoff gap”. The current description of the Oosterhoff groups
is summarized in Table 2.2.

The existence of the Oosterhoff dichotomy raises the question of its origin and
how it is tied to the formation of the Galaxy. The Oosterhoff dichotomy has been
searched for not only in GGC’s, but in the field population of RR Lyraes (Suntzeff
et al. 1991, Vivas et al. 2004), in the Large Magellanic Cloud (Alcock et a1. 2004),
and in dwarf spheroidal galaxies of the Milky Way.

Kinematically, the Oosterhoff I and Oosterhoff II clusters have been found to

26

have different rotational motion about the Galactic center. Lee & Carney (1999)
found that the Oosterhoff I clusters have a slight retrograde rotational motion of
(UM) = ~68 :l; 56 km/s, and for Oosterhoff II clusters, they found a prograde motion
of (0,0,) = 94 :E 47 km/s. Layden et al. (1996) confirmed these kinematics for field
RR Lyraes.

These results remind us of the studies of outer halo stars by Carney et a1. (1996).
Carney et al. (1996) found the outer halo stars tended to have a net retrograde
rotational motion and associated this motion with the scenario of the accretion of
small, subgalactic fragments into the Galactic halo as the Milky Way was forming.
This implies that an Oosterhoff I population is more dominant in the outer halo. As
for the Oosterhoff II, the prograde motions indicate an origin similar to the inner
halo (Carney et al. 1996). Lee & Carney (1999) also found most of the Oosterhoff
II clusters in their sample to populate closer to the disk. Thus, Oosterhoff II trends
may be dominant in the inner halo.

What causes the Oosterhoff dichotomy to exist is not exactly known or clearly
understood. One plausible solution was proposed by van Albada & Baker (1973).
They propose that the existence of the two Oosterhoff groups depends on the evolu-
tion and morphology of horizontal branch stars within the globular clusters. They
postulate that in the region where the RR Lyraes are found on the horizontal branch,
a transitional zone for pulsational modes must exist. In their model, an RR Lyrae
star evolves across this transitional region (or hysteresis zone) starting with one pul-
sational mode and evolves through the hysteresis zone before switching into the other
mode. For example, if the RR Lyrae star starts from the red end of the instability
strip, it will be pulsating in the fundamental mode. If it evolves toward the blue end,
and thus becomes hotter, the star will keep pulsating in the fundamental mode until

it has completely crossed the hysteresis zone. As the star moves out of the hysteresis

27

zone and enters the first overtone zone, the pulsational mode will switch. The oppo-
site scenario works for an RR Lyrae star starting on the blue side of the instability
strip and evolving toward the red (cooler) end. The pulsational mode initially starts
out as the first overtone mode. The star will continue to pulsate in the first overtone
mode as it crosses the hysteresis zone, and then change over to the fundamental mode
once it moves out of this zone.

Furthermore, in the van Albada & Baker model, the RR Lyraes evolving from the
red to the blue end will be distributed evenly across the horizontal branch. As the
RR Lyraes evolve from the blue end to the red end, evolutionary processes proceed
faster as the star evolves toward the asymptotic giant branch. Thus, most of the
RR Lyraes should be strongly populating the blue side of the instability strip. This
model was able to describe the number ratios observed in the Oosterhoff groups.

Briefly mentioned in van Albada & Baker (1973) is Sandage’s conclusion that
Oosterhoff II RR Lyraes must be more luminous. In Sandage et al. (1981), this result
is revisited, and it was shown that, at a given effective temperature, the Oosterhoff II
RR Lyraes must be more luminous than the Oosterhoff I stars. According to stellar
pulsation theories, the fundamental period is related to the star’s luminosity, mass,
and effective temperature (i.e. equation 2.1, Ritter’s relation). If we assume the stars
of Oosterhoff I and II have the same masses, the Oosterhoff II stars with the longer
periods have lower densities and larger radii than their Oosterhoff I counterparts of
equal effective temperature. Then using the luminosity equation that relates effective
temperature and radius, Sandage et al. were able to conclude that the Oosterhoff II
stars are more luminous. This conclusion still holds if the masses of Oosterhoff I and II
are not equal, but differ by the amounts suggested by stellar evolution theory. Thus,
the Oosterhoff dichotomy not only shows up in the average quantities of globular

clusters, but also on a star-by-star basis.

28

Lee, Demarque, & Zinn (1990) investigated this phenomenon of the Oosterhoff II
stars being more luminous. With evolutionary simulations of the horizontal branch
stars, they concluded that the Oosterhoff II stars are more evolved than the Oosterhoff
I stars. To explain why the Oosterhoff II stars were more luminous than Oosterhoff
I stars, they found that the Oosterhoff II stars must have evolved off of the zero age
horizontal branch (ZAHB). The Oosterhoff II stars are evolving from initial positions
on the blue horizontal branch toward the red with luminosities higher than their
ZAHB values. The Oosterhoff I stars are closer to the ZAHB and are less evolved.
However, there is some debate whether the Oosterhoff II systems can produce enough
blue horizontal branch progenitors to become the observed number of RR Lyraes (see
discussion in Catelan (2004)).

It should be mentioned here that a third Oosterhoff group has been introduced
by Pritzl et al. (2000). This is based on two metal rich ([Fe/ H] ~ -0.5) GGC’s, NGC
6388 and NGC 6441. These clusters are some of the most metal rich globular clusters
to contain RR Lyraes. A peculiar feature of the RR Lyraes in these clusters is their
very long periods - longer than that expected even from Oosterhoff II RR Lyraes.
Particular details of this Oosterhoff class are presented in Pritzl et al. (2000).

An intermediate Oosterhoff class is needed when analyzing the RR Lyraes found
in dwarf spheroidal galaxies of the Milky Way and M31. This intermediate Oosterhoff
class is usually characterized by a average RRab period falling in between those that
define Oosterhoff I and Oosterhoff II, in the Oosterhoff gap. However, Catelan (2004)
emphasizes that this class should be determined by the properties of the individual
RR Lyraes, and not just from average quantities such as (Pa ). The danger is that
this class can be misinterpreted if the system has a mix of Oosterhoff I and 11 RR
Lyraes rather than a true Oosterhoff intermediate population.

One issue we would like to address is whether the Oosterhoff properties can be dis-

29

tinguished among the field RR Lyraes. Whether we will see the Oosterhoff dichotomy
or not is not entirely clear for this kind of RR Lyrae sample. In figure 8a of Suntzeff
et al. (1991), an Oosterhoff gap appears in a plot of [Fe/ H] versus log P for their
sample of field RR Lyraes. However, Vivas et al. (2004)’s period-amplitude diagram
for RRab stars from the QUEST survey does not show a clean separation between
Oosterhoff I and II groups. We will return to this issue when we have selected our

sample of solar neighborhood RRab stars based on the ROTSE-I observations.

30

Chapter 3

Instrumentation and Data

Reduction

3.1 Robotic Optical Transient Search Experiment
(ROTSE)

The Robotic Optical Transient Search Experiment (ROTSE-I) project’s telescope
collected the data used in this dissertation. This telescope is located at Los Alamos,
New Mexico, and collected data from March 1998 until 2001. The telescope is main—
tained by the astrophysicists of Los Alamos National Laboratories and of the Uni-
versity of Michigan. This telescope was originally designed to capture the optical
transients of gamma ray busters. Their only notable detected optical transient of a
gamma ray burster was GRB 990123 (Akerlof et al. 1999).

Due to the daily data collection capabilities of this telescope, ROTSE-I provides

a large photometric dataset. ROTSE-I covers all the sky down to declination (6) of

31

—30°. Since this telescope has been in operation year round, all right ascension ((2)

positions have been observed.

3. 1 . 1 Instrumentation

The ROTSE-I telescope is actually composed of 4 small telescopes arranged in a
2 x 2 array. These telescopes are mounted on a rapidly slewing platform. The entire
telescope is housed inside a military surplus electronics enclosure with a clamshell
cover, which is opened automatically on nights of good observing quality. ROTSE-
I is located on Fenton Hill Observatory, which is part of the Los Alamos National
Laboratory in Los Alamos, New Mexico. The telescope and the data acquisition are
entirely automated.

Each telescope is equipped with a charge-coupled device (CCD) camera with a
Thompson TH7899M chip (Kehoe et al. 2001). The chip contains 2048 x 2048 pixels,
and each pixel is 14 microns on a side. The camera is thermoelectrically cooled,
so removing any dark (thermally-generated) noise is important. The main optical
element of each telescope is a Canon FD 200 mm f/ 1.8 telephoto lens. Figures 3.2
and 3.3 show the ROTSE-I telescope when it was operational.

The plate scale is 14.4”/pixel for the CCD chips and the setup of this robotic
telescope. This corresponds to 164° x 16.4° coverage of the sky or field-of-view. Each
individual telescope had a field-of—view of 82° x 8.2° (Akerlof et al. 2000b). Unlike
most regular optical observing programs, this telescope system does not have a filter
system installed. All observations were made without a standard filter set, with the
unfiltered system perhaps being closest to the broad-band Johnson R filter. Calibra-

tion of the data to a standard filter system will be discussed in section 3.2.1. With

32

5282 29”.

 

 

 

 

 

 

 

 

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33

Figure 3.1 ROTSE-I Fields with constellations

 

Figure 3.2 ROTSE-I Telescope. The four telephoto lenses and the CCDs are shown.

just the telephoto lenses, the point spread function for stellar objects is approximately
a full width at half-max (FWHM) of 20” (Akerlof et al. 2000b).

For the ROTSE-I project, five Linux PC computers were dedicated to run the
telescope. One main computer controlled the opening of the enclosure, monitoring the
weather, camera status and mount positioning, and received notices from the Gamma
Ray Burst Coordinates Network (Kehoe et al. 2001). The other four computers were
each dedicated to a camera. Some preliminary data processing was done at the site
and is discussed in the data reduction section of this dissertation. All the data is
currently being stored at the Los Alamos Computing Division Mass Store System.
This mass storage system has a petabyte capacity, which is more than adequate for
the amount of data generated for this project. The dataset used for this dissertation

is approximately 4 terabytes, which includes the processing and calibration files.

34

.. ;= -.i w 5"”,
‘ i w '
dwiui .

0': m ...,,

I!” " [(HI iii!!! H. ’
11“)?“le “it” ””‘fimmfliutoI—L..of-','.‘_','",'".' '1! m.
it JULA“

U
E {Ill-5!:

 

Figure 3.3 ROTSE-I telescope enclosure at Los Alamos National Laboratory, Fenton
Observatory

35

3.1.2 Observational Program

As mentioned previously, the ROTSE-I telescope was originally designed to ob-
serve the optical transients of gamma ray bursts (GRBs). GRBs are outside of the
scope of this dissertation and will not be discussed in detail. Due to the short life-
times of the optical counterparts to GRBs, a requisite of the telescope was an ability
to slew quickly to the position of the detected GRB. GRBs were monitored from two
satellites orbiting around the Earth. When a GRB was detected, this information was
distributed throughout the GRB astronomy community by the the GRB Coordinates
Network (GCN). ROTSE-I received the notices from the GCN and positioned itself
to the GRB location, if it was visible from its Los Alamos site. This is the higher
priority mode of the ROTSE-I telescope, as well as the next generation of this project,
ROTSE-III.

The lower priority mode of ROTSE-I, which is basically the main observing pro-
gram for most nights, was sky patrol mode. During sky patrol mode two images are
taken of each part of the sky that is visible. The sky was divided up into 206 square
fields (see Figure 3.1). On most nights, ROTSE-I was able to obtain two sets of field
images, resulting in four images per field. Exposure times for the dataset obtained
between April 1999 to March 2000 were 5, 20, and 80 seconds. Most of the calibration
images have the shorter exposure times. The object images are taken at 80 second
exposure times with a little over a minute between pairs. Sky patrol occurred on most
nights except during precipitating weather or if mechanical maintenance was being
performed.

From the sky patrol observations, the resulting dataset can be used in a survey of

variable stars. This dataset is ideal for some kinds of variable stars since it spans a

36

year and there are multiple observations per night. For long period variables, often
only part of the light curve can be observed. RR Lyrae variable stars can be picked
out from this dataset from their distinct characteristics and light curve shapes. Other
auxiliary stellar astronomy projects are being developed for a wide variety of objects

ranging from supernovae to flare stars (Akerlof et al. 2000b).

3.2 Data Reduction

Observations obtained from ROTSE-I go through two iterations of reductions
before the data can be used. The first data reduction step is done on-line and au-
tomatically at the telescope. In this first step a bias, dark, and flat field correction
are performed. Additionally astrometry and calibration are also done. Details of the
first reduction step are outlined in the following subsection. These “reduced” data
are moved to the mass storage system. At a later date, a more thorough relative
photometric correction is done, as described in subsection 3.2.2. The resultant data
from the two reduction phases can then be used for variable star work. This section
will outline and describe each of the reduction steps taken from the exposure at the

telescope to the production of light curves.

3.2.1 First Pass Data Reduction

The raw data are processed through the basic data reduction steps each night.
This online processing makes it possible to quickly find GRBs. For each night that
observing was possible, multiple dark images are obtained. These are images taken

at the same exposure time as the object images, but with the shutter, or in this

37

case the clamshell, closed. This will provide the mean level of thermal noise that is
contaminating each object frame. Several of these darks are taken and averaged to
create a reference dark frame to be used in reducing the data.

The next important calibration frame that must be created is the flat. These
frames help correct for any sensitivity variations on the camera chip. The preferred
method in creating a useful flat for ROTSE—I data is to use object frames that have
the dark level subtracted out and have been median-averaged (Kehoe et al. 2001).
These flat frames were most useful in correcting vignetting, as seen in the corners
of each well exposed image. Vignetting is the obstruction of the light due to the
instrument itself.

Once these processing steps are completed on the images, the data are run through
an external software package called Source Extractor, or “Sextractor” (Bertin &
Arnouts 1996). This program finds and classifies stellar or galactic sources from
images. The resultant product from running Sextractor on the dataset is a list of
objects, or “cobj files” for all the fields. After these steps are completed on the raw
data, the calibrated data are moved to the mass storage system at Los Alamos.

ROTSE-I was operational and started observing in 1998, but it was determined
that data obtained between April 1, 1999, and March 31, 2000, are the optimal
dataset. Early in the life of ROTSE-I, many of hte images were not optimized for
study. Later, after 2000, the telescope was beginning to degrade and the quality of
the images became poorer. For this time interval’s worth of data, the raw images were
extracted from mass storage and was re-reduced carefully in 2001. The entire dataset
was divided into thirds and distributed to three workers, including myself. The same
basic reduction steps are completed - dark subtraction and flat-fielding correction.
Sextractor is still used as the main software package to distinguish the stellar and

galactic sources, as well as providing the calibrated object lists (cobj files). During

38

this reduction phase, it was noted that Sextractor had problems with fields near the
Galactic plane, since there are many more stars in these regions. Another problem
encountered in this phase, and flagged, is the misidentification of the cameras. This
misidentification is known as “flipped” fields where camera A was identified as camera
C and camera B as camera D. This error occurred mostly in fields near the Galactic
North Pole.

Astrometry was also performed on the dataset. Astrometry is the science of ac-
curately identifying the positions of astronomical objects. For the ROTSE-I dataset,
the Tycho catalog of stars is used as the main calibration reference. The Tycho cat-
alog is a product from the European Space Agency’s Hipparcos Space Astrometry
Satellite (Hoeg et al. 1997). The Tycho catalog was produced in conjunction with the
Hipparcos catalog. It has been estimated that within one ROTSE-I field, one would
expect roughly 1500 Tycho catalog stars.

The magnitude range of the Tycho catalog stars matched that of the ROTSE—I
telescope, which is between an instrumental magnitude, mu 2 9.0 and my 2 15.0
(Akerlof et al. 2000b). Another advantage in using the Tycho catalog is the addi-
tional photometric information of the stars. The Tycho stars have measurements
in the Tycho magnitude system for BT and VT magnitudes and color, (BT — VT).
Cross referencing can be done to obtain standard Johnson magnitudes from the main

Hipparcos/ Tycho catalogs (van Leeuwen et al. 1997).

3.2.2 Second Pass Data Reduction

The second data reduction phase for the dataset is the relative photometry cor-

rection. For this step, a relative photometry correction factor is derived for each field.

39

The relative photometry correction factor scales each image of each field to the field
template. This accounts for any clouds or unwanted external light-polluting sources
that may affect the photometric measurements.

The relative photometry correction factors are derived by taking the residuals of
the photometric measurements of a star to the same star found in the template field.
Template fields were chosen with the criteria of good seeing and transparency. Each
image of the field is compared to this template by dividing both images into macro-
pixel boxes of a predetermined size. All the stars in the macro-pixel boxes are cross
identified with the template stars. Their residuals, i.e. the difference between the
instrumental magnitude of the image and the template image, are recorded. Those
instrumental magnitude residuals are averaged to a value, which becomes the relative
photometry correction factor for that macro-pixel box. This effectively scales the
boxes to the same photometric level as the corresponding macro-pixel box of the
template image.

In this portion of the data reduction, problems with the image are also identified.
These are set as flags and stored in the headers of the each frame’s file. Common
problems identified are nearest neighbor stars that may contaminate photometric
measurements of the target stars, blended stars (two stars overlapping in the image),
saturation, and stars found near the edge of the frame. Typically, if these flags are set,
their measurements can be thrown out for further analysis. Other problems flagged
are related to errors occurring during relative photometry correction. Regardless, all
measurements are kept, but corrupt or problem images can be excluded by checking

these flags prior to analysis.

40

3.3 Data Analysis of ROTSE-I Observations

Once the relative photometry correction has been finished, and problem flags have
been set, light curve information is available. For this portion of the data reduction,
Interactive Data Language (IDL) software is used. All the data is stored in a FITS
(Flexible Image Transport System) file format. This programming language is ideal
for reading, writing, and manipulating FITS-format files. Throughout the reduction
steps, all the data is stored in FITS format.

The program actually performs several analysis steps before light curves can be
generated. First, the observation date and time must be converted from the modified
Julian date to heliocentric Julian date. Next, the variability index is calculated for
each star. And finally, for the variable star candidate, the period is determined. The
variability index calculations will be discussed in the following subsections. Period

searching algorithms are described in Chapter 4.

3.3.1 Heliocentric Julian Dates

For variable star work, the Julian dates must be corrected to heliocentric Julian
dates. Originally, all observedd epochs were identified by a “modified” Julian date.
This is the Julian date with a constant of 24000005 days subtracted. Essentially,
we want all the epochs to reflect observations done as if at the Sun’s position (hence
heliocentric) rather than on the orbiting Earth. A correction is added to the Julian
date to reflect this. The shift in time and location is calculated by using the star’s
positional coordinates (right ascension and declination) and other solar orbital ele-

ments (such as mean solar anomaly). These new dates are stored in the FITS header

41

files of each frame.

3.3.2 Variability Index

Estimating from the nine fields analyzed in Akerlof et al. (2000b), we extrapolated
the approximate number of variable stars to be found in the total ROTSE-I dataset.
The full survey has over 19 million objects for the fields observed by the ROTSE-I
telescope. On the order of 30000 periodic variable stars are expected to be contained
in these fields. For the RR Lyraes, we expected on the order of 3000 RR Lyraes from
the entire ROTSE-I survey.

The variability index is a diagnostic tool for finding variable stars from photomet-
ric data. Those stars with large variability indices have a high likelihood of being a
real variable star. This index also should not discriminate too much between pulsat-
ing and non-pulsating (eclipsing) variable stars. The algorithm used to calculate the
variability index was incorporated into the light curve extraction program.

The variability index algorithm used for the analysis of the ROTSE-I dataset is
a modified version of the Welch & Stetson method (Welch & Stetson 1993, Stetson
1996). All the variability indices described in Stetson (1996) are computed, but the
Stetson L index is primarily used in this analysis. The L index is a composite of
two other Stetson indices, J and K, which are described in detail in the following
subsections. This particular method of finding variables was chosen because the
variability index is optimized for pairs of observations. This method also allows us
to weight spuriously bright or faint measurements and to avoid misidentifying non-

variable stars.

42

J Index

The calculation of the index requires the computation of the weighted mean mag-
nitude from each star’s observations. The observational measurement (magnitudes)
and their uncertainties are also necessary for the calculation. The first variability
index calculated is the Stetson J index (Stetson 1996).

_ 22:. mama) W

J — 3.1
22:1 wk ( )

 

This is used for pairs of observations. For each observation, wk is the weighting
factor. The factor changes for the case of either a pair or single observation. In
the case where both observations of a pair are good and included in the variability
index calculation, the weighting factor for that pair is assigned a value of 1.0. If only
one of the observations in the pair is of good quality and is used in the calculation,
wk is assigned a weight of 0.5. The expression Pk is a product of residuals of two
observations, i and j (Stetson 1996). The function “sgn” is a sign function that returns
either 1, 0 , or -1. If the numerical value or expression going into the sgn function is

positive, the result is one. If the input is negative, the output value is -1.

6 .

Pk=6 1k

., (3.2)

The residual or the “relative error” of each observation, 6,“ is defined (for a

particular band pass, in this case the visual band, v) as:

 

 

6.: ““”( n (3.3)

where n is the total number of observations that go into the calculation of the weighted

43

mean magnitude, 5.

Most of these indices were designed for paired observations in two filter band-
passes. The indices can be adapted for observations taken in one filter. This is the
case for the ROTSE-I survey and all the variability indices are modified for paired
observations in one filter. For the J index, the Pk expression is different for the cases
where a single or pair observation is good. If a pair of observations are used, then
the Pk expression (Equation 3.2) is correct. For single observations, Pk is defined as

(Stetson 1996),

Pk = 6;: — 1 (3.4)

This expression comes from statistical arguments for a random dataset with single

observations instead of pairs. This is fully explained in Stetson (1996).

K Index

The K index, or kurtosz’s index, can be used in place of the J index or used in
conjunction with the J index to form the L index (see next subsection). This index
is ideal for datasets where the number of observations is small and the number of
bad data points can affect the outcome of any analysis (Stetson 1996). Again, the

“relative error”, 6, is used in the K index. It is constructed as follows:

% 251:1 I51!
75 2.4:. 5,2

where N is the number of observations without regard to pairing of observations. For

K = (3.5)

our analysis of the ROTSE-I dataset, the K index calculation is an intermediate step

in the final determination of the main variability index.

44

L Index

As mentioned in the K index description, the combination of the J and K index

gives a more robust variability index, L. The L index is:

L = (0%) (if) <36)

The value 0.798 in the denominator comes from the statistics of the K index. If we

 

consider the K index in the limit where the range of the variable star’s variation is
larger than the 0’s of each observation, then for a Gaussian-like magnitude distribu-
tion, K —> fl = 0.798 (Stetson 1996). Thus, if the magnitude distribution is truly
Gaussian, the L index reverts back to the definition of the J index with an additional
weighting factor multiplied.

The weighting factor to the L index is included for the cases where the star does
not appear in one of the images. This can be an important problem in survey work.
Many spurious variable candidates can be found if the star happens not to be present
on one or several frames. This “disappearance” of the star can be attributed to
technical issues, such as the star being on the edge of the frame (it might be left off of
the frame if the telescope moves and returns to the original field, but slightly offset)
or it can be near a cosmetic blemish on the CCD chip. As the telescope moves from
object to object or field to field, and cycles through again, there is no guarantee that
the camera will be pointing in the same exact location of the sky. Thus, stars can
“fall off” the edge of the frame or “fall into or out” of CCD blemishes.

However, in the case of the ROTSE-I survey, there is a reasonable amount of
overlap between fields, so “edge dropoffs” are not a problem and potential candidates

are not lost forever. Multiple observations of the same star can occur, if there are tiny

45

difl'erences in the astrometry assignment. This particular problem was documented
in Wils (2001).

In this analysis of the ROTSE-I survey, a flag system is instituted for various
problems associated with the astrometry (Sextractor) and the photometry. For the
calculation of the variability index, all these flags are checked for each star in all the
frames. Thus, if the star is found near the edge of the frame or near a blemish on the
CCD, it is flagged. Those flagged observations can be excluded from the variability
index calculations. Therefore, the need for the weighting factor on the L index is
unnecessary. All the “good” observations of the stars are used for the calculation,
so the weighting factor will be unity. The set of optimal flags for the best data are
described and listed in Woz’niak et al. (2004).

Thus, the final variability index used in this work is a modified L index:

L = — (3.7)

In a previous, preliminary work on variable stars in the ROTSE-I survey (Akerlof
et al. 2000b), Equation 3.7 was used to find the variable candidates. For the ROTSE-
1 fields in this study, this index also provided the greatest number of real variable star
candidates. However, in early tests, this index also chose stars that would have one
or two bright outlier observations. These could be possible flare stars, as described
in Akerlof et al. (2000b), but may also be stars with undetected problems in the
photometry. Periods were sought for these stars, but none were cleanly found. By
our best guess, these stars are not the variable candidates we would like to include
for a general variable star catalog and will be subsequently ignored.

To help weed out these spurious candidates, a special weighting factor was im-

plemented (Stetson 1996, 1987). This weighting factor reduces the influence of any

46

outliers of a set of measurements. The weighting factor is:

”(134))” .3.)

where a = b = 2 (Stetson 1996). Again, 6 is the relative error definition, Equation

w:

 

3.3. This weighting factor is used in the calculation of the mean magnitude, which
is then used in determining the variability indices. Those magnitude measurements
with large uncertainties or that are unusually bright or faint, are given a smaller
weight in the calculation of the mean. With the new weighted mean magnitude, the
variability indices are less sensitive to the flare-type stars and pick out more small
amplitude, short period variable stars. Equation 3.8 is iterated a minimum of five

times in order for the mean magnitude to stabilize in value.

3.3.3 Identification of Candidate Variable Stars

To pick out the variable star candidates, a cutoff value had to be chosen for the
range of L indices calculated. Those candidates with large L indices are generally
considered to be highly probable in being a variable star. In Akerlof et al. (2000b),
this cutoff value was determined from a Gaussian fit for the L indices per magnitude
bin. The magnitude range of the ROTSE-I dataset was binned. For each magnitude
bin, a Gaussian was fitted for the variability index values of the stars in that bin
(McKay, private communication). A mean and standard deviation were calculated.
The standard deviation was used to determine the L index cutoff value, which was
4.750.

However, this coefficient of 4.75 was chosen ad-hoc. Akerlof et al. (2000b) had

chosen the best observed fields from ROTSE-I and only used paired observations

47

for analysis. Thus, this affects the quality of the light curves and the calculation of
the variability index. For the analysis in this work, a more rigorous and conservative
approach was used to determine the L index cutoff. Two test fields were used to check
the validity of this method as well as the quality of the variable star candidates’ light
curves.

The variability index should have some dependence on magnitude and position
in the sky (as opposed to position on the CCD chip) due to its dependence on the
magnitude uncertainty. The positional dependence comes from the number of obser-
vations taken as well as from crowding in the Galactic plane. More observations of
the ROTSE fields were done in the polar regions compared to the southern regions.
The dependence on magnitude comes from the formal and systematic errors of each
observation. Tests showed that the formal errors were overestimated for the brighter
magnitudes (about 10th magnitude and brighter) and underestimated for the fainter
(about 15th and fainter). This in turn, affects the resultant value of the L index. To
account for both effects of the position and magnitude on the variability index, the
cutoff values are determined for each field. Within each field, the cutoff value is cal-
culated per magnitude. Breaking up the sky into the small fields helps to determine
any local changes to the index rather than having a large global value, which may or
may not be the Optimal cutoff value.

All the stars in a test field, per camera, were binned by magnitude. The bin
size was one magnitude, but the calculations overlapped the bins by 0.5 magnitudes.
In each magnitude bin, the median and 95th-percentile of the variability index were
calculated. The range of magnitudes is from 9th magnitude (bright end) to 16th
magnitude (faint end), so 13 values were calculated. The 95th-percentile value of the
L indices were then fitted by an IDL polynomial fitting routine (POLY_FIT.PRO).

This provided the cutofl value for the L variability index with respect to magnitude.

48

Goloctic Plonor Region

 

 

 

 

8 l I r I I I
)— u-i
5—+ _,
g e _
’5 — + _
84H ++
ii) ++++++
5 _ + a
if) +
on — a
_ + _
2— + —-
+
_ + _
.. + _
+
+ +
.. +++++ _
O . 1 . 1 . r . l . n 1 1 1+I+T+r
8 10 12 i4 16
magnitude

Figure 3.4 95th-Percentile L index trend with magnitude in the Galactic planar region.

Figure 3.4-3.6 show the trend of the cutoff value with respective low, mid and high
latitude Galactic regions. One thing to note is that stars brighter than 10th magnitude
were considered to be saturated. For stars found to be brighter than 10th magnitude,
the cutoff value at 10th magnitude was used to determine whether the star was a

variable candidate or not.

49

 

Mid Goloctic Lotitude Region
I r . .

 

 

 

4?— T 7 I I 17 I I I I l' f _
Z + :
3; L
— ++ —<
f + 5
_ .1
a . .. .
S : + Z
8 ._ -.
m2— +-i- —
0. ~ _
g I + 3
to ~ _
on — + q
,_ + —
i + Z
1— + -
Z + i
_ ++ _
_ ++ "
_. ++ “
‘ ++++++ ‘
_ ++ :1
: +
O l L l l L L l I A I; l I J 1 l
8 1O 12 14 16
magnitude

Figure 3.5 95th-Percentile L index trend with magnitude in the mid Galactic latitude
regions.

50

 

Galactic Polar Region

 

 

 

3 I I I I I I ‘l' T r I I I I
i—+ -«
_ + ..
_ + a
.— + —1
2— —1
a) ' + ‘
0C) ” + d
g 7 + + 4
Q) ~ + + d
a. _ _
:5 .1
in L + —
a» _ _
1- ++ _
_ + _
_ + _
i-D + —
_ ++ + ..
r— + c-J
- ++++++++ a
I— + —4

Oh I l l I l l 1 I l 1 l l l l l
8 10 12 14 16

magnitude

Figure 3.6 95th-Percentile L index trend with magnitude in the Galactic polar region.

51

Chapter 4

Determination of RR Lyrae

Properties

This chapter will focus on the determination and calibration of various prOper-
ties of the RR Lyraes. For many of the quantities, several different algorithms or
methods were tested for facility in use for the ROTSE-I dataset. Explanations are
given concerning which method(s) were preferred for the analysis. No one method is
really always better than another, rather the choice of method is dependent on the
characteristics of the dataset. Starting from this chapter, the dataset will be referred
as the Northern Sky Variability Survey (NSVS) (Wozniak et al. 2004) rather than
the ROTSE-I dataset.

4.1 Period Searching Algorithm

In variable star research, one of the desired goals is to find the period of the light

52

variation. There are many different algorithms available currently to find the peri-
odic variations. For the NSVS dataset, five methods were tested, but one algorithm
appeared to be most suited for this particular survey. This section will describe each
of the methods briefly along with advantages and disadvantages of the algorithm.
Regardless, no one algorithm is perfectly ideal, and the best one can do is to adapt
it for one’s dataset.

Phased light curves are an easy way to see immediately if the period solution is
correct. Phasing the observations assigns each observation the corresponding point
in the pulsational cycle of the variable star. To do this, one needs all the heliocentric
corrected Julian dates and the period for a particular variable star. All the Julian
dates are divided by the period. Those values are then subtracted by their respective

integer portion. The formulae which describe these steps are:

d = Heliocentric Julian Dates/ Period (days) (4.1)
phase = d — (integer portion of d)) (4.2)

One of the major criteria used to choose the optimal period searching routine was
its ability to distinguish period aliases from the correct period of the RR Lyraes.
The alias problem can be significant in some methods, whereas in others, it is clear
that some period solutions do not give the best phased light curves. Often, these
aliases will be a subharmonic to the correct frequency (or period). In some cases,
when phased light curves are produced with the period alias, the light curve will
appear as good as that phased from the correct period. For those cases in the NSVS
sample of RR Lyraes, both period aliases were kept, as the correct period could not

be determined.

53

4.1.1 Phase Dispersion Minimization

An old reliable algorithm readily available through IRAF 1, although a stand-alone
version does exist, is the Phase Dispersion Minimization (PDM) method (Stellingwerf
1978). This method is actually a minimization of the scatter of the data in phase
space. The phase space mentioned here refers to the ordering of the observed points
according to where they should be in the varying light cycle. A range of periods
is tested, usually set within the task by the individual. Thus if the actual period
is found, its phased light curve should have the least amount of scatter in a PDM
periodgram. The measurement of this scatter in the phased light curve is called
the O-statistic. A better description of this statistic and the method is provided in
Stellingwerf (1978).

PDM has been used often in variable star research. However, for this dataset,
PDM is not efficient and requires a great deal of user interaction. The N SVS dataset
has millions of objects, of which it is estimated that there will be thousands of variable
stars. The ideal period searching algorithm needs to be non-interactive and fairly
automated for these thousands of stars. Since PDM requires one to check minima of
the O-statistic for the correct period, period searching can become time consuming.
This is especially true if there are many period aliases. A period alias can easily be
confused with the actual period because the alias may produce an acceptable phased
light curve. For the reasons of efficiency and difficulty in distinguishing the minima
(i.e. the correct period versus all the aliases), PDM is not an ideal period searching

algorithm for this dataset.

 

1IRAF is distributed by the National Optical Astronomy Observatories, which are operated by
the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with
the National Science Foundation.

54

4.1.2 Lamb-Scargle Periodgram

Another often used period searching algorithm is the Lamb-Scargle Periodgram.
According to Reimann (1994), periodgrams and many least-squares methods are em-
ployed to find frequencies (or periods, i.e. V = 277/ P) assuming the light curve of
a variable star can be described by a simple harmonic model. The Lamb-Scargle
periodgram is actually a least-squares method (Lamb 1976, Scargle 1982). The peri-
odgram is calculated at equally-spaced frequency intervals via a fast Fourier transform
(Press & Rybicki 1989). This method requires a computation of the Fourier power
series over frequency intervals. The major periodicities refer to frequencies where the
Fourier power is maximized (Akerlof et al. 1994).

The version of the Lamb-Scargle periodgram that was tested for the N SVS survey
was written in IDL (Wilms, private communication). After choosing test candidate
variable stars, several period searching runs were done using this method. Two input
parameters can be changed with each run of the program. The parameters are pmax
and pmz’n which define the maximum and minimum period search range. I found that
if these input parameters changed (for example, pmax from 80000 seconds to 100000
seconds), different solutions would be returned for the same candidate variable. Thus,
depending on the adequacy of the chosen search range, potentially incorrect values
for period will be derived. To complete a wide range search of periods for different
types of variable stars in the NSVS survey, this method could provide many spurious
results unless finely tuned. To use this method, the search period range must be set
for each type of variable star, and the search must be run several times through the
list of variable candidates to ensure complete coverage. This method, in light of the

results of the test runs, is not very efficient.

55

Other disadvantages include poor detection of multimodal stars or eclipsing bi-
naries (Reimann 1994). The Lamb-Scargle periodgram also does not use weights on
good versus poor Observations. All observations are treated equally. The dataset at
this point should have most of the problem observations omitted for any calculation.
However, there are those outliers with small observational errors that are included in
the light curve information. Thus, the Lamb-Scargle periodgram algorithm, as well as
the other period searching methods described in this chapter, can become confused by
these sharp dips or peaks. Another disadvantage with this method is that it assumes
the data have a uniform distribution of the variance (Akerlof et al. 1994). One loses
statistical confidence for those light curves that have non-sinusoidal shapes, such as
is the case for RRab type stars. Thus, this method was not chosen as a viable period

searching algorithm.

4.1.3 Cubic Spline

The cubic spline method was used for the variable star candidates in the original
analysis of the ROTSE-I test fields published in Akerlof et al. (2000b). The basic idea
behind the cubic spline method is to fit a function, preferably a cubic polynomial,
between “knots”. These knots are placed in equally-spaced intervals in a phased
light curve. A least—squares fit of the sum of the cubic spline functions is calculated.
The best frequency (or period) for the phased light curve is found when the X2 is
minimized.

One of the advantageous things about this method is how easily this algorithm
can be implemented automatically. However, as reported in Akerlof et al. (1994),

this method has problems in determining periods for RR Lyraes. Also, the cubic

56

spline method expects the data to be equally spaced in phase space, when in reality,
this is not true. Tests were done with candidate variable stars where the period had
been determined by at least one other method. It was found that the cubic spline
could pick out the correct frequency. However, this was dependent on what inputs
were used when the cubic spline was run. Revising the number of knots and the
maximum frequency changed all the results. In some cases, the correct frequency was
not even listed. Again, this can be a problem with running this algorithm on the
N SVS dataset. The periods of all the candidate variable stars are unknown ab initio
nor are the data expected to be evenly spaced.

When the test fields were analyzed, as described in Akerlof et al. (2000b), an IDL
graphical interface was used to check each frequency choice as determined from this
algorithm. This method needs a person to check if the program is correctly finding
the frequency/period. Since now this algorithm must be applied to over 200 fields
and not just the 9 test fields, this may not be the most ideal period searching routine.
However, there still will be some user interface necessary to see if any algorithm is
choosing the correct period or an alias. The human element cannot be totally removed

from the variable star analysis.

4.1.4 Analysis of Variance (AOV)

A successful period—searching algorithm called the Analysis of Variance (Schwarzenberg-
Czerny 1989) was extensively used in variable star analysis of the OGLE survey
(Schwarzenberg-Czerny 1998, Mizerski & Bejger 2002). This particular period algo-
rithm is designed to be used for large survey projects. In the literature, AOV has

been cited to be highly successful in finding periods for candidate variable stars.

57

The AOV method is based on the F -distribution. The F -distribution uses two
independent x2 random variables, U and V, with a and b degrees of freedom, respec-
tively. A X2 random variable, U, has a chi-squared distribution lwith one degree of
freedom, which is described by U = Z2. Z is a standard Gaussian random variable
(Rice 1995). The F-distribution is constructed as follows:

w = (4.3)

srl<|n It:

Schwarzenberg-Czerny (1989) constructed the AOV statistic based on the formula

of the F-distribution:

 

 

(4.4)

 

The U variable is assigned the summed function in the numerator of Equation
4.3 and V is the summed function in the denominator. The degrees of freedom are
a = :11- and b = 3%; in this statistic.

The number Of observations, 11, is divided into r bins. In each bin there are n,-
observations, where i,- is the average of those observations. The average of all the
observations is it, and 10,-]- is the 3"” individual observation in the 2"“ bin. One thing to
note here is that the uncertainty in each observation (merr) is not used as a weight
in the statistic. Good and bad observations are both used.

The AOV statistic is used to check the validity of a solution for a given periodgram.
As in the Fourier methods (such as the Lamb-Scargle algorithm), a maximum power
is assigned to the correct frequency. This statistic checks this solution validity of

being the correct frequency of the periodgram. The AOV statistic can also be used

58

to check alias solutions. A nice feature of this method is its use for non-sinusoidal
light curves. The Fourier series methods are the best method for light curves with
sinusoidal shapes.

The AOV code has two separate subroutines which calculate the AOV statistic.
The slower calculation of the AOV statistic, “saov”, uses bins with a fixed number of
observations. The advantage with saov is its insensitivity to the sampling of the obser-
vations. The faster calculation of the statistic, “faov”, uses bins of fixed phase width.
Although the subroutine runs faster than saov, if the phase bins are underpopulated,
spurious results are more likely to occur in the periodgram (Schwarzenberg-Czerny,
private communication). Another subroutine was developed which took the best at-
tributes of saov and faov, which produced consistent results (Schwarzenberg-Czerny,
private communication).

The advantage of this period-searching algorithm is that it is easily automated
and fast. Again, this method is designed for large survey projects, which is ideal for
the NSVS database. However, this method is not entirely free of user interaction. In
some tests, the alias frequencies can be confused easily with the correct frequency.
An example of this problem can be seen in Figure 4.1. This may be a problem if the
candidates have poor time coverage, as is the case for some of the southern fields of
NSVS. One would need to check the results of AOV by inspection of the phased light
curves.

Another one of the advantages with AOV is that one can easily control the fre-
quency interval steps for the period search. The bin sizes can also be readily changed.
However, the output files (which contain the periodgrams) can be large compared with
the outputs from other methods. Regardless, AOV can easily be adapted to the cur-
rent software to find periods of variable candidates. For a more complete description

of this method see Schwarzenberg-Czerny (1989).

59

 

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Figure 4.1 Aliasing problem with AOV

60

1.5

0.5

frequency (c/d)

4.1.5 Supersmoother

Another new period searching algorithm proved to be both efficient and non-
interactive in determining periods for candidate variables in the NSVS survey. “Su-
persmoother” (Miceli, private communication, Reimann (1994)) is different in its
approach to finding periods compared to the other methods, but is slightly similar
to the cubic spline method. Supersmoother was originally used in the variable star
analysis in the MACHO dataset (Alcock et al. 1995).

The general idea behind Supersmoother (and all smoothing routines) is to fit the
observations as the function of phase for a particular frequency (Reimann 1994). Algo-
rithms that are considered smoothers use this principle. Some example smoothers are
algorithms that use a running mean or running linear regression on the data. Super-
smoother uses a “variable-span” method. There are three running linear smoothers
with three different relative span lengths (short, medium, and long). These three
different spanned smooths are run on the data in phase space. To check which span
interval is appropriate to the phased observation, a “local cross-validation” is done.
This is where the fitted value is compared to the observed value at each span inter-
val and checked if the residual is minimized. The calculation of the cross validation
is done by using the following formula, called the sum of absolute residuals (SAR)
(Reimann 1994):

" 1|?!
SARA?) =Z| — -- 31.1 v (4.5)

11: s
For this statistic, v is the frequency, 3,- is the sample variance, yj is the magnitude from
the dataset, and 3),,” is the fitted calculated magnitude. This statistic is summed over

all n observations. To find the best period, the global minimum of the SAR statistic

61

is determined.

Reimann (1994) conducted exhaustive tests comparing how supersmoother fared
against other period searching algorithms. Reimann compared the PDM, Lomb-
Scargle algorithm, cubic spline and Fourier methods against the supersmoother method.
All the advantages and disadvantages are discussed in depth in his thesis. One of his
conclusions was that the supersmoother method was found to work well for all kinds
of light curves (i.e. all kinds of variable stars). This algorithm is self-adjusting and
does not need the light curve shape to be inputted for the calculation. This fea-
ture makes this method particularly attractive for use in large variable star survey
projects.

However, one of the problems discussed in Reimann (1994) is that the fitted curve
can be discontinuous to the phased points. If the frequency is changed, the phase will
also change, and this will affect the fit. Reimann (1994) did cite that in this case, the
SAR may become discontinuous, but the changes will be small.

In the tests conducted on the N SVS dataset, supersmoother was able to find the
periods quickly. The correct frequency/period was usually found within the first
15 guesses or less. This program also was easy to implement and to include in
programs used to find the variable star candidates. The program contains algorithms
using a trigonometric polynomial or a cubic spline routines to fit phased points for
period searching. Often the trigonometric polynomial is used for fitting longer period
variables (period > 50"), and the cubic spline is good for the shorter period variables.

Again, as with the other period searching algorithms, one cannot totally eliminate
the human factor in this analysis. One must see if the period choice is correct or if
it is an alias or subharmonic. For pulsating variables, the “cycles” number from the
Supersmoother output provided a clue to the best period for the data. The cycles

refer to the number of times the Supersmoother curve crosses the mean value divided

62

SUN 10203057 Pefiod (159374293

 

12.5
13.0

L35

14C

145

15f) . 1

00 05 LC
Phase (days)

ROTSE Magnitude

IIII'IIIIIIIIIIIITIIIIII
4
,
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140

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00 05 L0 15
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ROTSE Magnhude

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llllIlIlIlllllIllllIllli

 

 

IIIIIIIIIIIIIJIIIIIIIIII

 

5’
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Figure 4.2 Supersmoother phased light curves. Upper plot: correct period. Lower
plot: alias period.

63

by two (K. Cook, private communication). Thus one should look for a cycles value
of 1 for the best period guess of a pulsating variable star. Any more than that, the
choice is most likely an alias. However, one runs into ambiguity problems with W
Ursa Majoris (W Uma) stars or other eclipsers (particularly if the two minima are of
similar minimum depth). Then the cycles value should be equal to 2.

For the period determination of the NSVS RR Lyraes, Supersmoother was the
main period searching algorithm used. The phased light curve for each star was
inspected by eye to ensure the correct period was recorded for the RR Lyrae candidate.
An example of phased light curves for a period and an alias from Supersmoother is
shown in Figure 4.2. All the Supersmoother period solutions were also compared with
a solution from the cubic spline method (Akerlof et al. 1994). This was particularly
useful when multiple Supersmoother solutions gave reasonable looking phased light
curves. In cases where Supersmoother and the cubic spline method produced two
different period solutions, PDM was used to determine which is the correct period and
which is the alias period. At most, for certain stars, periods were derived from three
different methods to arrive at the correct solution. In cases where PDM could not
distinguish between the alternatives, both periods were kept for analysis, even though
one of them is surely the alias period. Often these alternative periods corresponded

to the frequencies near 2 cycles/ day or 3 cycles/ day.

4.2 Amplitude Work

With periods for all the RR Lyrae candidates, phased light curves are produced.
Figure 4.3 and 4.4 show some typical phased light curves of NSVS RRab and RRc

stars, respectively. Note that the fainter stars have larger photometric errors than

64

the brighter stars, regardless of how well observed the stars are. The number of

observations were as few as 15 and as many as over 300.

With phased light curves, one can start analyzing light curve shapes. The first step
is to determine the amplitude of the light curves. To find amplitudes, two different
methods were employed. One was a spline fitting routine which also calculated the
mean magnitude. The second method performed a template fit to the observed light

curve. Each method and its results are described in the following subsections.

4.2.1 Amplitudes from Spline Fitting

The spline fitting method is based on a Numerical Recipes algorithm (Press et al.
1992). The program (written in perl) uses the subroutines spline and splint (Sharpee,
private communication). The results from this program include the minimum and
maximum magnitude of a spline fit to a set of observations for a star, the amplitude
(which is just the difference of the previous quantities), and the mean magnitude
(magnitude and intensity weighted). Figure 4.5 shows an example of the spline fit to

one of the program stars.

4.2.2 Amplitudes from Template Fitting

This template fitting method was developed by and described in Layden (1998)
and in Layden & Sarajedini (2000). The computer code can be obtained from Andy

Layden’s website,

physics.bgsu.edu/‘layden/ASTRO/DATA/EXPORT/progs.htm

65

 

 

 

 

 

 

 

 

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O ‘— «—

Figure 4.3 RRab phased light curves from the ROTSE-I survey. The ROTSE magni-
tude is the Y-axis quantity. The periods are in units of days.

66

 

 

 

 

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Figure 4.4 RRc phased light curves. The ROTSE magnitude is the Y—axis quantity.

The periods are in units of days.

67

 

 

 

 

I I I ' I I I I
1 ea. 1
8
63
10.5 - a ‘ d
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8
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11.5 1 1 1 1 1 1 l
O 02 0.4 06 08 1
Phase

Figure 4.5 Spline fitting method. Filled triangles are values from the spline fit. Circles
are the actual NSVS data.

68

This template fitting routine is based on well sampled light curves and should perform
well for many of the RRab candidates in this sample. However, what was found was
that some stars that lacked observations in the rising branch part of the light curve
had problems with the template fit. The correct template would not be chosen and a
spurious result would occur. Tests were made with a subsample of “standard” RRab
stars that have been well observed (Sandage 2004).

The average residual from the spline fit, 0.087 :1: 0.013, was tighter than from the
template fit. The average residual for the template fit is 0.113 :1: 0.024. Both values
are based on 55 RRab stars that had well sampled light curves and for which the
average uncertainty in the observations is about 0.02 magnitudes. Figure 4.6 and 4.7
show the results from the template fitting routine.

Comparisons were also made with published amplitudes (Bookmeyer et al. 1977)
for the set of 55 RRab stars. The amplitudes derived from the N SVS data needed to
be scaled into a “standard” system. All the N SVS observations were obtained from a
filterless ROTSE-I telescope, so the best approximation is a Johnson R for the data.
As one goes redder in the Johnson filter set, the shape of the light curve flattens.
This effect can be explained by a Planck blackbody radiation distribution. The bluer
filters of the Johnson system (UBV) are near the peak of the blackbody radiation
curve, whereas the redder filters are near the tail of the curve. The flux at the visible
portion of this radiation distribution has a T4 dependence whereas in the infrared
end, it is more of a TI'6 dependence (Jameson 1986). As the temperature changes
during the RR Lyraes’ pulsational cycle, there will be a greater change in flux at the
bluer end than in the redder end. Hence, the amplitudes derived from observations
in a bluer filter will be relatively larger than those from a redder filter. Therefore,
the ROTSE amplitudes are expected to be slightly smaller than what we would find

if the stars were observed through a Johnson V filter.

69

standdat

 

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0.5 1 0 0.5 1

96

¢

Figure 4.6 Example of output from the Template fitting method for SW And. These
are the 4 best template fits (smallest RMS values).

mag

stand.dat

 

 

I I T I I I I r r I' r I

 

I j

 

 

1
0 0.5 1
Phase

Figure 4.7 Example of output from the Template fitting method for SW And. This
plot shows the best fitted light curve to the N SVS data.

70

To calibrate our ROTSE amplitudes to amplitudes in the standard Johnson V filter
system, the standard V amplitude values were taken from Bookmeyer et al. (1977) and
Simon & Teays (1982). Some discrepancies were found between the amplitude values
of Bookmeyer and those published in Simon & Teays. Bookmeyer’s observations were
done in the Johnson system, and in their publication, light curve data are provided
as an additional check. For the Simon & Teays published amplitudes, the values were
obtained from Lub (1977), whose observations were done in the VBLUW Walveran
system. Lub does provide a conversion of the observations from the Walveran to
the Johnson system (Lub 1977). However, for those discrepant amplitude values, a
third source was checked (the General Catalog of Variable Stars (Kholopov 1985)).
Ultimately, it was decided to use the Bookmeyer amplitudes for our calibration to
avoid any discrepancies.

In addition to the RRab sample from Sandage (2004), a sample of well observed
RRc stars was also used for the calibration of N SVS amplitudes. These RRc stars
were selected mainly from Bookmeyer et al. (1977), but a few RRc stars amplitude
values were taken from other more recent publications (Pena et al. 1990, Fernley et al.
1990, Skillen et al. 1993, Heiser 1996).

Using a set of 55 well observed field RRab stars and 12 field RRc stars, the scaling

relation for the amplitudes is:

AV 2 1-185ANSVS + 0.065 (4.6)

Figure 4.8 shows the calibration for the amplitudes of the 55 RRab stars. With
this scaling relationship, we can now produce period-amplitude diagrams. This result

will be discussed in chapter 5.

71

 

o RRAB
RRC

   

m = 1.185 +/— 0.046 ..
s b = 0.065 +/— 0034

Q Bookmeyer/Literature Amplitude

 

 

1 1 l i l 1 1

0.2 0.4 0.6 0.8 1 1.2

 

Unsealed NSVS Amplitude

Figure 4.8 Amplitude calibration for RRab and RRc stars. Slope and Y-Intercept of
the fitted line are also shown.

72

4.3 Magnitude Calibration

Since all the observations are on the V magnitude system of the Tycho catalog,
more work needs to be done to put the NSVS observations onto the standard Johnson
V system. The main reason to do this is for easy comparison to quantities in the
literature, which is usually cited in Johnson V. To calibrate the data, we can use the
Landolt standard stars (Landolt 1992).

The first selection criterion for Landolt standard stars was location. Most of the
standard stars are located near the celestial equator, but we excluded those far in the
southern celestial hemisphere. The second selection criterion is based on the color
(B — V) of the Landolt standard star. For the RR Lyraes, a representative B — V
color is 0.4. Thus, Landolt standard stars with a B — V between 0.0 and 1.0 should
be used. In this analysis, the entire range of B — V was used (—0.3 < B — V < 2.0),
but emphasis was made to cover the B - V range from 0.0 to 1.0.

A search was conducted for the Landolt standard stars in the NSVS catalog. A
number of the standard stars were not found in this catalog due to a crowded field
or a bright, near neighbor that made identification difficult. A search radius cone of
0.1’ to 0.8’ was used. In the end, a total of 147 Landolt standard stars were used for
magnitude calibration.

For the calibration, a linear regression fit was performed. The fit took into account
the B —— V and V magnitude provided in Landolt (1992). The regression fit produced

the following relation (T. Beers, private communication):

VNSVS : 0.092(0072) + 0'981(0'006)V:91andard — 0..549(0015)(B _ V)standard (47)

73

The quantities in parentheses are the uncertainties in the coefficients. This equa-
tion was rearranged so that the input is the NSVS magnitude and the output is the
standardized magnitude. A color term exists for the calibration, as can be seen in
Figure 4.9. This color term was taken into account in the transformation and the
results can be seen in Figure 4.10. For the RR Lyrae standard magnitudes, we chose

a (B — V) color of 0.35.

4.3.1 Absolute Magnitude of RR Lyraes and Distances

To derive photometric distances, the absolute magnitude of the object of interest
must be well known. However, obtaining this value can be a difficult endeavor. RR
Lyraes are an ideal distance indicator for old stellar populations since they are found
in all components of the Galaxy and in extragalactic sources, such as the Magellanic
Clouds and M31. The absolute magnitudes of the RR Lyraes are however, still not as
well defined as one would want. Different methods used to obtain RR Lyrae absolute
magnitudes, though now yielding similar results, still show some discrepancies.

For this project, many of the results depend on some distance measurement of
the NSVS RR Lyraes. The absolute magnitude was obtained through a Mv-[Fe/H]
relation first (see section 2.1.3), and then the distances were calculated. To derive

the distance, the distance modulus was employed:

m—M=5log10d—5+A (4.8)

The parameters are defined as: apparent magnitude (m), absolute magnitude (M),

distance in parsecs (d), and some extinction (A). The extinction parameter must be

74

 

 

 

 

I V V V T ‘17' V V V I V V V f I V V V Y I V V V V T V T Y
+ B—V < 0.0
+

,. 0.5 < B—V 1.0 o n:
U — ”3:1 .
g . B V>1.0 +++BJ£§ “ A
9 (‘0’: ‘ “
‘6 + ,3 ‘
‘c’ 3&1”
3 t
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5 080 A ‘
K10 ,— ++O “ d

o ‘A ‘

‘Afi
11111.11111.1....11..11.r.111...
9 10 11 12 13 14 15

Landolt Standard V Magnitude

Figure 4.9 Tycho calibrated ROTSE magnitude versus the Landolt standard magni-
tude. Note the color term dependence.

 

 

 

 

I V V I fi I V V V V I V V V Y I V V Y Y T Y I V Y I Y 7’ V
B—V < 01)
O 0.0 < B-V < 0.5
‘4 * m. ‘

., 0.5 < B—V 1.0 ..
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3 A B—V > 1.0 gfi
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03
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0 4

1 1 A 1 m 1 A 1 1 L 1 4L 1 A 1 1 A 1 L A 1 1 A 1 A #1 A 1 1

9 10 11 12 13 14 15

Landolt Standard V Magnitude

Figure 4.10 V magnitude calibration with Landolt standard stars. Note the same
symbols are used for each color range as in Figure 4.6.

75

used to account for any diminishing of the brightness due to any interstellar dust
found between the observer and the star. To determine the extinction, the Schlegel
dust maps were used to find A for each RR Lyrae candidate.

The Schlegel dust maps are an ideal resource to derive the extinction since the
maps have direct measurements of reddening from dust in the Galaxy. The Schlegel
dust maps were produced from COBE/DIRBE and IRAS/ISSA maps of the Galaxy
with all of the zodiacal light and cosmic infrared background removed (Schlegel et al.
1998). A fuller description of the process of creating these maps and converting the
information into absorption information is provided in their paper and is beyond the
scope of this dissertation.

To access this information, the entire Schlegel dust maps were downloaded as
well as programming tools to access it. To retrieve the reddening information in
the form of E(B — V), the galactic coordinates (l,b) are needed. Using the relation
Av = 3.2E (B — V) for Johnson V, the absorption correction is obtained.

Once the absorption correction is known, the distance to the RR Lyraes in the
sample can be determined. In addition to finding the distance of the RR Lyraes from
the Sun, a Z distance was calculated. This is the distance above or below the Galactic
Plane (Z = 0) in parsecs. The Z distance is a simple geometric relation between the

galactic latitude (b) and the distance from the distance modulus ((1):

Z = dsin b (4.9)

For the distance from the Galactic center (R), simple geometric relations are
used. Figure 4.11 is a diagram showing all the distances and angles used for these
calculations. Since we now know the distance (d) in parsecs from the sun for an

object, the galactic coordinates (which are really angles) are related to find R. Galactic

76

 

 

 

Figure 4.11 Diagram of the the geometry to determine the distances. The solar
distance (R@ was assumed to be 8.5 kpc). The X in the diagram is the center of the
Galaxy or where there is buried treasure.

longitude is l and the galactic latitude is b. The projection of the distance to the RR

Lyrae candidate from the Sun onto the Galactic plane is:

a = dcos b (4.10)

Then, on the plane of the Galaxy, we can determine the projected distance, p, of

the RR Lyrae candidate to the Galactic center by using the law of cosines:

 

p = \/(dcos b)2 + R39 — 2dR® cosbcosl (4.11)

where R9 is 8.5 kpc (the distance of the Sun from the center of the Galaxy).

We assume the additional 2 distance of the Sun from the Galactic plane to be
negligible compared to R9 or to z. This 2 distance is about 8 pc from the Galactic
plane. Therefore, the distance of the star from the Galactic center is found from the

Pythagorean theorem:

77

12,. = Z2 + ,02 (4.12)

Furthermore, the relative a: and y projections on the Galactic plane can be calcu-
lated, and graphically show the distribution of the RR Lyrae candidates about the

Galactic center. Figure 4.12 shows this distribution.

:1: = RCos(l) (4.13)

y = RSz'nU) (4.14)

4.4 Photometric Metallicities

Traditionally, metallicities of RR Lyraes are derived from spectroscopic observa-
tions. In the case of large surveys where there are many thousands of stars, obtaining
spectra for each of these stars may take more than the lifetime of a graduate student!
Instead, metallicities can be derived from empirical relations based on photomet-
ric observations. Two empirical relations were used, and they are described in the

following subsections.

4.4.1 The Jurcsik & Kovacs [Fe/H]-¢31-P relation

Jurcsik & Kovacs (1996) introduced a method using the period and the Fourier

decomposition parameters of the light curve to determine the metallicity. This method

78

 

 

 

 

4 T I 7 fl I
A
U _
Q .4
x
v 2— —
Q)
C
_O ’- —1
CL
0 F _
113
U
.9 _ ..1
O
O 0— O O '—
Q)
.C ._ ..
...:
.E
8
z - a
8
L.
0- - _
>.

—4 1 1 1 1 1 1 1 1 1 1 1 1 1
—5 0 5 10

X projection in the Galactic Plane (kpc)

Figure 4.12 Distribution of the 660 RRab stars projected into the plane of the Galaxy.
The solid circle is the Sun, at location (0,0) kpc. The Galactic center is at 8.5 kpc
from the Sun. The open diamond at (8.5,0) kpc identifies its location.

79

is based on a set of well observed field RRab stars. They were careful not to include
field stars that are experiencing the Blazhko Effect, as this affects the shape of the
light curve, and hence the Fourier parameters. They performed a 15th order Fourier
decomposition using sine functions on their sample of RRab stars. To accurately
determine the Fourier parameters, it is necessary to have well sampled light curves,
since the parameters are derived from the shape of the phased light curve. Lower
quality light curves often have gaps in various parts of the light curve which can
cause spurious values of the Fourier parameters.

The Fourier parameters can be calculated from fitting a sine or cosine Fourier

series to the observed light curve:

m = A0 + Z A,- cos(iw(t — to) + (152') where i = 1,2, ... (4.15)
or
m = A0 + Z A, sin(z’w(t — to) + (0,) where i = 1, 2, (4.16)

In both equations, m is the observed magnitude or brightness of the variable star,
and the A,- and d),- are the coefficients of the fit. For this dataset, the FORTRAN

program MINFIT was used to calculate up to an 8th order fit (Simon 1979).

Raj = _ (4-17)
¢ij = i¢j—j¢i (4-18)

An important thing to note here is that for the (15,-,- terms, different factors of
7r need to be added or subtracted depending on whether one uses a sine or cosine
Fourier series. Table 4.1 shows the correct factors that must be added/subtracted.

The output files from MINFIT provide all the coefficients of the Fourier series up to

80

Table 4.1. Factors of II to add for the (15,-1- Fourier parameters

 

 

Conversion direction Factor Fourier Parameter

 

COSINE to SINE —7r/2 4521
+7r €531

—37l'/2 $41

SINE to COSINE +7r/2 $21
—7T (P31

+37T/2 (I541

 

8th order (2' = 8) and the corresponding Fourier parameters. MINFIT uses a cosine
Fourier series. To use the J urcsik & Kovacs (1996) metallicity relation, the ¢ij terms
must be converted to a sine Fourier series. The Fourier parameter of interest for the
RRab metallicity relation is (1531, so a factor of +7r was added.

The 4531 parameter is a shape parameter that best identifies the RR Lyrae vari-
able stars. Other Fourier parameters have been used for analysis, but were not as
distinctive as the (1)31 parameter. Specifically, the 4531 parameter appears to be corre-
lated with period and metallicity. Jurcsik & Kovacs (1996) found that this relation
is actually a linear one.

Jurcsik & Kovacs derived a linear relationship with [Fe/ H], period (P), and the
Fourier phase parameter (1531. This relation and the uncertainty in the [Fe / H] value are
reproduced here. The uncertainty equation comes from J urcsik & Kovacs (1996), their
equation 4 and 5. This uncertainty relation is rather complex due to the circumstances
that the regression variables (period and (2531) were not completely independent from

each other.

81

[Fe/H] = -5.038 — 5.3941D + 1.345(1)31 (4.19)

“ire/HI =
1.8090,";31 + 2(—0.01753)¢31 + 2(—0.00289)P¢31

+0.08910 + 0.0252919? + 0.003741%, (4.20)

For comparison, a set of well observed field RR Lyraes (Bailey type ab) were
processed to check this relation. These 55 RRab stars were among those used by
Sandage (2004) for his work on the period shift and the Oosterhoff phenomenon.
Sandage had compiled values for both (1531 and [Fe/ H] from the literature. We cross
referenced those stars from NSVS and obtained all the stars’ photometric data.

We found that the NSVS 031 values had to be scaled into a “standard” system,
specifically the one Sandage had used. The reason for this scaling is similar to the one
described in section 4.2 for the amplitudes. The Fourier parameter was derived from
the light curves obtained with the filterless ROTSE-I telescope. To derive Fourier
parameters as would be obtained with Johnson V observations, the NSVS (1531 values

((1)31 in equation 4.21) must be scaled. The scaling relation is :

(1531 = 0.855(0.046)q>§,1 + 0.063(0.105) (4.21)

Once the (1531 value is scaled, the J urcsik & Kovacs (1996) metallicity formula can

be used. Figure 4.13 shows our 0331 values compared with published values (Sandage

82

 

215

N

Sandage ¢_31

 

 

 

1 1 1 1 l 1 1 l l 1 L

1.6 1.8 2 2.2 2.4 2.6 2.8
NSVS ¢_31

 

Figure 4.13 Calibration of the (1531 values to the published values (Sandage 2004).

83

 

.0
01

Jurcsik & Kovacs [Fe/H]
I

 

 

 

y—

l 1 1 1 1 1 1 1 l 1 1 1 1 1 1 1 1 J J 1 1
—2 —1.5 -1 —0.5 0
Layden (1994) [Fe/H]

 

Figure 4.14 Calibration for the metallicities derived from Jurcsik & Kovacs (1996)
method on to metallicity system adopted by Sandage and used by Layden (1994).

2004). However, Sandage noted that the metallicity from the Jurcsik & Kovacs rela-
tion should be scaled when it is used with other metallicity systems that have been
published in the literature. Specifically, Sandage’s and our [Fe/ H] scale is the [Fe/ H]
scale used by Layden (1994), which in turn is based on the Zinn & West scale (Zinn
& West 1984). The plot of the calibration of the Jurcsik & Kovacs [Fe/ H] with pub-
lished values is presented in Figure 4.14. The J urcsik & Kovacs metallicity was scaled

onto the Zinn & West system by using Sandage (2004)’s relation:

[Fe/H] = 1.05[Fe/H]Ju,c,.k&xmc, — 0.20 (4.22)

In order to check if a given RR Lyrae star’s light curve is adequate for the metal-

84

licity calculation, J urcsik & Kovacs developed a compatibility test. They construct a

“deviation parameter”, Dp, to check the Fourier parameters. It is defined as:

: lFobs _ Fcalcl
0F

 

DF (4.23)

where Fob, are the Fourier parameters, a set of Rij and 45,], from the observations.
The theoretical values of Fcalc and 0;: were updated by Kovacs & Kanbur (1998) (see
their table 2). Specifically, Fcalc are the corresponding theoretical values of the set
of Fourier parameters. The 0;: are the uncertainties for Fem determined from their
calculations. In Jurcsik & Kovacs (1996), they state that the compatibility test is
satisfied when Dm (the maximum of the set of BF parameters) is less than 3.0. For
the sample of RRab stars, a majority of the stars did not pass the compatibility test.
However, for stars that did pass this test, their light curves were very well sampled
and did not contain any large gaps in the phased light curve. Therefore, we did not
use the Dm parameter to obtain a clean sample of RRab stars, since most of the stars

are known to have adequate, but not high quality, light curves.

4.4.2 Sandage’s [Fe/H]-log P—AV relation

In addition to the Jurcsik & Kovacs method of deriving photometric metallicities,
Sandage himself developed a way to obtain this quantity using different observational
parameters. Sandage (2004) investigated the Jurcsik & Kovacs relation and its cor-
relation to the period shift of the Oosterhoff groups. Sandage defines a period shift,
ALog P, with respect to RR Lyraes found in M3, which is an Oosterhoff I globular
cluster. The period shift can be calculated by comparing an RRab star to its coun-

terpart of equal amplitude in M3. Sandage found that the (1531 parameter is indeed

85

correlated with the period shift, ALog P, in the same manner as the amplitude or
color (see Sandage et al. (1981) for the complete period shift explanation). He argues
that (031 is correlated with metallicity, just as the period shift and the luminosity of
RRab stars are. Therefore, using his results from Sandage et al. (1981), the derived
metallicity is no longer dependent on (1)31, but rather another parameter correlated
with the period shift. In this case, the parameter was amplitude.

Sandage’s log P-amplitude relation is reproduced here:

[Fe/H] = —1.453(i0.027)Av — 7.990(10091) logP - 2.145(:I:0.025) (4.24)

To determine the uncertainty of the [Fe/ H] value from this relation, we assume the
largest source of error comes from the amplitude measurement. Since the true uncer-
tainty of the amplitude is unknown and we have only calculated the external error,
we adapt an uncertainty of [F e/ H] to be m 0.32 dex. This was determined empirically
by comparing the spectroscopic [Fe/H] from Layden (1994) to the [Fe/H] derived
from Equation 4.24, subtracting in quadrature the uncertainty Layden attributed to
his [Fe/ H] values. Figure 4.15 shows how well the [Fe/ H] from the log P-amplitude

relation compared with Layden’s values.

86

 

Sandage's log P—Amplitude [Fe/H]

 

 

 

l 1 1 1 1 l 1 1 1 1 1 1 1 1 1 l 1 1 1 1 1
—2 —1.5 —1 —0.5 0
Layden (1994) [Fe/H]

 

Figure 4.15 Comparison of [Fe/ H] from the Sandage relation using amplitude and lag
period with Layden (1994) [Fe/H] values.

87

Chapter 5

Results from the Analysis of the
NSVS RR Lyraes

Most of the results presented in this chapter are for the RRab candidates from the
N SVS survey. The sample used for this dissertation was obtained from a copy of the
full database at the University of Michigan. Two samples were extracted: one for the
RRab stars and another for the RRc candidates. Many problems were encountered
with the analysis of the RRc stars (see section 5.6). As for the RRab stars, the
number of candidates shrank with certain cutoffs used to get a clean sample of stars.
We will also discuss in the sections below some of the basic analysis tools constructed
from the observed parameters. A more in depth discussion of the implications of

these RRab results is deferred to Chapter 6.

88

5.1 Criteria for RR Lyrae Selection

5.1.1 Description of the Selection Criteria

For the sample obtained through the University of Michigan, two sets of criteria
were used to extract a subsample of RRab and RRc candidates. It was assumed
there would be some contamination of other types of variable stars in our RR Lyrae
candidate sample. These criteria sets were designed to mine almost all of the RR
Lyraes.

The criteria for the RRab candidates are listed in table 5.1. The period and
amplitude range were set from the known general observational properties of RRab
stars. The “ratio” is defined as a function of the brightest and faintest measurement
with the median magnitude of the star. This parameter identifies whether a star
spends most of the time brighter or fainter than its median magnitude. The ratio was
originally deve10ped to find contact binaries in the NSVS survey (T. McKay, private

communication).

max magnitude — median magnitude

 

ratio = (5-1)

max magnitude — min magnitude

The ratio criterion depends on the period of the RRab stars. Since the period
and amplitude are correlated to each other, the ratio is also correlated to the period.
In Figure 5.1, the ratio is plotted against the period range of 0.0 to 1.2 days for all
the stars in the database. A clump of stars appears in the period range between 0.4
and 0.8 days. This clump is believed to contain the majority of the RRab candidates.
The stars below this clump are other types of variable stars. A shallow sloped line

was fit to include these RRab candidates. This limit is used as one of our filters to

89

Table 5.1. RRab candidate criteria for selection from the N SVS survey.

 

 

Parameter Range of Values

 

Period 0.30 to 0.95 days
Amplitude 0.20 to 1.5 magnitudes

Ratio > -—0.625Peri0d + 0.719

J — H -0.1 to 0.5

H — K -0.1 to 0.25

 

obtain the RRab sample.

Furthermore, the NSVS survey was cross correlated with the 2MASS catalog by
the ROTSE team at the University of Michigan (T. McKay, private communication).
This now gives us infrared color (J - H and H — K) information on all the NSVS
stars. To check if the color criteria range was adequate, a sample of known RRab
from the General Catalog of Variable Stars (Kholopov 1985) was found in the 2MASS
catalog. The average J — H color was 0.219 and 0.063 for H — K. Thus, the color
criteria was broad enough to ensure the RRab stars could be chosen.

For the RRc sample, the criteria set changed slightly. Table 5.2 lists the RRc
criteria. Two regions were needed for the ratio criterion. This ensured that the
previously selected RRab stars and short period, non-RR Lyrae variable stars (e.g.
eclipsing binaries and 6 Scuti stars) would not be included in this sample. Figure 5.2
shows the regions in ratio-period space where the RRc stars were expected to exist.

Again, the period and amplitude criteria were based on the known general ob-
servational parameters of RRc stars. The 2MASS color ranges were kept the same.
As with the RRab stars, the average 2MASS colors of RRc stars were obtained and
found to be within the given range. The average J — H color was calculated to be

0.164 and the average H — K color was 0.04. Thus, the color range was broad enough

90

 

 

 

 

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0.0 0.2 0.4 0.6 . 0.8 1.0 1.2
Period (days)

Figure 5.1 This plot was used to determine the appropriate ratio range to select the
RRab candidates. Note the clump of stars between 0.4 and 0.8 days. The line is the
function for the ratio parameter.

91

 

 

 

 

 

0.3 0.5
Period (days)

 

0.4

Figure 5.2 Ratio distribution with period. The boxed regions are where the RRc
candidates were selected.

92

Table 5.2. RRc candidate criteria for selection from the N SVS survey.

 

 

 

Parameter Range in Triangular region Range in Rectangular region
Period 0.225 to 0.3 days 0.3 to 0.55 days
Amplitude 0.2 to 0.7 magnitudes 0.2 to 0.7
Ratio 0.2 to 0.8 > 0.2 and < (—0.625Perz'od + 0.719)
J — H -0.1 to 0.5 —0.1 to 0.5
H — K —0.1 to 0.25 -0.1 to 0.25

 

to select RRc stars.

5.1.2 Cutoffs for a Clean Sample of RR Lyraes

In total, we obtained 2196 RRab and 2558 RRc candidates using these sets of
criteria. One of the first cutoffs for extracting the RR Lyraes stars from the sample
was to remove all the duplicate entries of the stars. This particular problem was
noted by Wils (2001). These “duplicate” stars have multiple entries in the NSVS
database due to the way the star entries were created. Each star has its own unique
position. However, the NSVS positions for an individual star occasionally can vary as
much as 10 arcseconds. When this happens, another separate entry is made for the
star. The duplicates were removed by comparing the equatorial coordinates (right
ascension and declination), the period of the star, and the number of observations.
A duplicate was found if the difference in equatorial coordinates was less than 10
arcseconds. Due to the small differences in photometric zero point, the observations
for multiple identifications of the same star were not combined. Instead, we chose
the entry with the most observations for the analysis. Using these requirements, 228

duplicate RRab and 205 RRc candidates were removed from our sample.

93

 

 

 

 

 

Figure 5.3 1430 RRab candidates selected from the NSVS survey. The coordinate
system is in Galactic l and b.

In addition to these duplicate entries, stars whose light curves were clearly not of
an RR Lyrae type were removed. These stars were often found to be eclipsing binary
stars. Ten RRab stars were found in the RRc sample and 17 RRc stars were in the
RRab sample. These stars were placed in the respective samples. With these results
and the identification of the duplicate stars, the RRab sample was reduced to 1430
candidates. The RRc sample shrank to 1446 candidates. Figure 5.3 and 5.4 are the
Aitoff plots of the RRab and RRc samples at this point.

Furthermore, a second cutoff was applied after the duplicates and the obvious
non-RR Lyraes were removed. We noticed the fainter RR Lyrae candidates had noisy
phased light curves. With such light curves, it becomes difficult to determine accurate
parameters such as amplitude or the Fourier parameter $31. Therefore, we instituted

a cutoff in magnitude in order to obtain a clean sample of RR Lyrae stars. Stars

94

 

 

 

 

 

Figure 5.4 1471 RRc candidates selected from the NSVS survey. The coordinate
system is in Galactic l and b.

fainter than 14th magnitude (in ROTSE’S Tycho magnitude system) were omitted.
The star’s intensity weighted mean magnitude1 was used for this cutoff.

Also in consideration of determining the observational parameters, stars with fewer
than 40 observations were omitted from the analysis. Often the light curves of these
stars exhibited large gaps, and in some cases, missing maximum or minimum of the
light curve cycle. The combination of these two cutoffs reduced the size of our samples
further. The RRab sample now has 660 stars where the RRc sample contains 375
stars. Figure 5.7 and 5.8 show the Aitoff projection of the RR Lyraes for these reduced

samples.

 

1Intensity weighted mean magnitude is calculated by simply taking the magnitude measurements
and converting them to fluxes via the luminosity equation. The fluxes are then averaged and this
value is converted back into a magnitude.

95

 

 

Figure 5.5 1430 RRab candidates selected from the NSVS survey. The coordinate
system is in the equatorial system (right ascension and declination).

 

 

 

Figure 5.6 1471 RRc candidates selected from the NSVS survey. The coordinate
system is in the equatorial system (right ascension and declination).

96

 

 

 

5.1.3 Absolute Magnitudes and Distances for the RRab Stars

For some of our results, we wished to compare stars found in different regions of
the thick disk/ inner halo covered by NSVS. To determine distance, we did not use an
average absolute magnitude, but rather the Mv-[Fe/ H] relation (Equations 2.6 and
2.7). The metallicities were all obtained through the photometric methods described
in section 4.4. The metallicity results will be discussed in section 5.4. The average
My for our sample of 660 RRab stars is 0.58 i 0.15.

Each star’s distance was determined from their individual absolute magnitudes
derived from the MV-[Fe/H] relation. These distances were calculated by the usual
way with the distance modulus (Equation 4.8) and applying extinction corrections as

described in section 4.3.1. All distances are in units of ki10parsecs.

5.1.4 Cross-correlation with the General Catalog of Variable

Stars

As a check, we searched for the 1430 NSVS RRab candidates in the General
Catalog of Variable Stars (GCVS) (Kholopov 1985). We had to consider that many
of the stars in the GCVS have poor positions, with errors of up to one arcminute.
Nonetheless, to match the NSVS RRab stars in the GCVS, we had to use the positions.
The search grid limit was varied from 1 and 2 arcminutes and down to 3 arcseconds.
For 2 arcminutes, there were 312 matches whereas for 1 arcminute, 291 stars were
matched. In the smallest search grid size of 3 arcseconds, 133 N SVS RRab stars were
found in the GCVS. Out of approximately 1400 RRab stars used in the analysis,

between 80 and 90% of the stars found in the NSVS survey are not found in the

98

GCVS catalog. The RRc stars were not matched with the GCVS since a final clean

sample of RRc stars can not be produced at this time (see discussion in section 5.6).

5.2 Period of the RRab Stars

The periods of the RRab candidates were derived from the supersmoother method
or from the cubic spline routines (see Section 4.1). The original database contained
the periods determined through the cubic spline methods described in Akerlof et al.
(2000b). Supersmoother was run on all of the candidates, deriving periods indepen-
dently from the cubic spline routines. In most cases, the periods from supersmoother
agreed with the cubic spline result to about 0.001 days. For 111 stars, the periods
from the two different methods had a difference of more than 0.01 days. These period
discrepant stars had a third pass in determining their periods using the IRAF task
PDM. If the PDM period solution agreed with one of the two period choices, that
period was chosen.

However, there are cases where the PDM solution did not resolve the period
alias. Often the aliases were at a third or half day periods. For this situation,
both supersmoother and the cubic spline solutions were kept, but not used for any
analysis involving periods. This applies to six RRab candidates. Of the 111 stars
checked with PDM, PDM suggested a third period solution for four stars. With three
different period solutions from the three methods, the phased light curve shape was
examined to determine which period was correct. In this situation, the PDM solution
was chosen. Uncertainties in the periods are roughly at the level of 10'4 days. This
was determined from an examination of the period aliases close to the true period, as

seen by the solutions from supersmoother and from PDM.

99

 

150 I I Vi fir f I ‘ 7 I I

<Pob> = 0.56.3 days A

O
O
l
1

UT
0
I
I
1

Number of RRob Candidates

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O 4 l m 7 7 l l L

O 0.2 0.4 0.6 0.8 l 1.2
Period (doys)

 

Figure 5.9 Period distribution histogram for RRab candidates from the N SVS survey.

To graphically show the range of periods of the NSVS RRab sample, a histogram
was produced. Figure 5.9 shows the periods for the RRab stars, and Figure 5.10
shows how the periods are distributed by zones of |Z| distance.

The average period in each zone is close to the value of an RR Lyrae population
from an Oosterhoff I globular cluster. There does seem to be a tail into the longer
periods, which would indicate a population of RR Lyraes similar to those found
in an Oosterhoff II population. We see from the histogram that the Oosterhoff I
signature is dominant for the RRab stars in the solar neighborhood, but there is still
a contribution from Oosterhoff II. We will demonstrate later that the short period

RRab stars in the low |Z| zone also indicates the presence of a thick disk population.

100

 

100

I Y—Y 1—V—T Y—'—_I—' v v v I 1 Y v v I v v v V—

O<z<2kpc _

80
r

P_ob = 0.557 d i

40
r
L

RR Lyroes
20
I
g
L

 

100
Y 1
1
.4
l
1
J

2<z<5kpc§

Number of
80
I

60

P_ob = 0.580 d L

40
r
1

20
I
1

 

 

P Wm ‘
..........| ,, .1...._.1.g...

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

 

Period (days)

Figure 5.10 Period distribution histogram for 608 RRab’s, divided by |Z| distance
zones.

5.3 RRab Amplitudes

The amplitudes of the RRab stars were the next observational parameter calcu-
lated for this project. The amplitude can be used with other parameters to investigate
trends in the population. Section 4.2 described the important step of calibrating the
amplitudes onto the Johnson V filter system. This calibration was performed for the
sample of 660 RRab stars. After this calibration, the light curves were checked for
quality and completeness. In some cases, the light curves were not complete, i.e.
the maximum or minimum of the light cycle was not observed. Fifty-two stars with
questionable amplitudes were omitted from the study and our sample is now at 608
stars.

It should be mentioned here that the intrinsic uncertainty of the amplitude is un-

101

known since it was determined from either the spline fit or a template fit. The fitting
routines did not return a useful formal error to the amplitudes. However, inspection
of the phased light curves indicates that the amplitudes have an uncertainty of ~ 0.1
magnitudes. This is assuming the star was well observed with many data points. The
calibration uncertainty was calculated from the scaling relation onto the Johnson V
filter system (see Equation 4.6). This uncertainty from the calibration of the NSVS

amplitudes onto the V amplitude system is on average about 0.02 magnitudes.

5.3.1 Period-amplitude diagram

One of the diagnostic tools to investigate the Oosterhoff dichotomy is the period-
amplitude diagram. Clement & Rowe (2000) confirmed earlier results that in a period-
amplitude diagram, RRab stars from the Oosterhoff I and 11 groups lie in two different
regions. A trend line for both groups was determined by Clement & Rowe based on
the RR Lyraes found in M3 (an Oosterhoff I cluster) and w Cen (an Oosterhoff II
cluster). These trend lines can shift with metallicity in these diagrams, but the general
locations of the Oosterhoff I and Oosterhoff II locii do not change.

In order to use the Oosterhoff trend lines developed by Clement & Rowe, the log
base 10 of the periods was calculated and plotted with the scaled amplitudes. Figure
5.11 shows the N SVS RRab stars with the Oosterhoff trends overplotted. One should
note that the RRab stars do not all fall on one or the other trend line. It appears that
a majority of stars fall near the Oosterhoff I trend line, which is in agreement with
the result from the period histograms. However, there are stars populating the region
where Oosterhoff II stars reside in the period-amplitude diagram. This presents a

stronger case for the existence of an Oosterhoff II population in the region covered

102

 

 

 

 

 

2 I I 4 r I Tm I I
Oosterhoff | (M3) Oosterhoff H (w Cen)
1.5 — ~
0)
U
D A
E I
‘5
< 1 _ 1
0.5 - ~
4
+
....1. .1....1m...1....1....
—O.6 -O.5 -O.4 —O.3 -O.2 -O.1 0
Log Peflod

Figure 5.11 Period-Amplitude diagram for 608 RRab’s. The Oosterhoff trend lines
are from Clement & Rowe (2000). The solid line is Oosterhoff I and the dashed line
is the Oosterhoff II trend line.

by the NSVS survey.

5.3.2 Interesting outliers

Not only does the period amplitude diagram show the Oosterhoff I and 11 pop-
ulation, interesting stars show up in the plots as outliers. In a few instances, there
were legitimate reasons to omit these outlier stars. Usually the reason was that the
light curve was too poor for accurate amplitude measurements. However, one long
period outlier was found to be a possible anomalous type II Cepheid variable star.

Other shorter period variables were found to be possible thick disk RR Lyraes or

103

long period RRc stars not yet excluded from the RRab sample. The RRc stars were
omitted from the RRab sample, but placed in the RRc sample (see discussion of RRc
stars in section 5.6). In the period-amplitude diagram presented here, the thick disk

candidates were left in the plot. In section 6.2, we will revisit these thick disk stars.

5.4 Metallicities

'IIaditionally, metallicities of RR Lyraes are derived from spectrOSCOpic observa-
tions. In the case of large surveys where there are many thousands of stars, obtaining
spectra for each of these stars may take more than the lifetime of a graduate student!
Instead, metallicities can be derived from empirical relations based on photometric
observations. Two empirical relations were used to obtain photometric metallicities,

which are described in the following subsections.

5.4.1 [Fe/ H] from Jurcsik & Kovacs’ Method

The Jurcsik & Kovacs method (see section 4.4.1) was used to derive photometric
metallicities in the cases where the uncertainty in on was less than 0.2. We found that
if the uncertainty is large, unrealistic or very uncertain metallicities were determined.
This particular cutoff in (1531 uncertainty reduced the number in the RRab sample
from 608 to 433 stars. Figure 5.12 shows the metallicity derived from this method as

a function of |Z I distance.

104

 

 

 

 

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Photometric [Fe/H] from Jurcsik & Kovocs‘s relotion

Figure 5.12 Distribution of the metallicities as a function of distance from the Galactic
Plane. Note the clump of stars at high metallicity and low |Z| distance. This may
be the thick disk component. These stars have [Fe/ H] values determined only from
the Jurcsik & Kovacs (1996) method.

105

 

 

 

 

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Photometric [Fe/H] from Sondoge’s relotion

Figure 5.13 Distribution of metallicity from Sandage’s method as a function of |Z|
distance.

5.4.2 [Fe/H] from Sandage’s Method

A second metallicity calculation was made by the method of Sandage (2004) (sec-
tion 4.4.2). This method was applied to the RRab stars with good amplitude mea-
surements. While the Jurcsik & Kovacs method reduced our sample to 433 stars,
the Sandage method provides metallicities for the 608 stars. Figure 5.13 shows the
metallicity distribution of the 608 stars with |Z I distance. Again, we see a clump of
stars at [Fe/ H] > —1 and close to the plane. However, compared to Figure 5.12, this

clump appears to be more scattered.

106

5.4.3 The Best Estimate of [Fe/ H]

The [Fe/ H] values from the two methods were compared to each other, since both
methods seem to provide reasonable values of [Fe/ H] for the calibrating RRab set.
In some cases there were large discrepancies between two values of [Fe/ H] for the
same star. This difference could on rare occasion be as large as 3 dex. The light
curves for these discrepant stars were checked, and it was found that the light curves
often contained large gaps, which affect the on value, or gaps that coincided with
the maximum or minimum, which affects the amplitude value. Due to this result,
50 stars were omitted from the analysis, reducing our sample of RRab stars to 608.
Figure 5.14 shows how well matched the two values of [Fe/ H] are with respect to each
other. The X2 of the fit is 6.01.

In the cases where there was adequate agreement between the two [Fe / H] values, a
weighted average of the metallicity was calculated. This value is our “best estimate”
for [Fe/ H] of that star. In the cases where the Jurcsik & Kovacs method [Fe/ H] was
not calculated, the Sandage method [Fe/ H] is our best estimate. A table of our best
estimate [Fe/ H] values for 608 NSVS RRab stars is given in Appendix A. Column 1
is the NSVS identification number, column 2 is the [Fe/ H] from Sandage’s relation,
column 3 and 4 are the [Fe/ H] and uncertainty from the Jurcsik & Kovacs method,

and column 5 is the best estimate for the metallicity.

5.4.4 The Oosterhoff and Metal-Rich Groups

Three groups of RRab stars were identified from their location in the period-

amplitude diagram. These groups are 1) the Oosterhoff I RRab stars, 2) the Ooster-

107

 

I
_L

Sondoge Log P—-Amp [Fe/H]

l
N

 

 

 

1 1 L 1 1 4 I l l l l 1 A 1 g l I l L 1 l l 1 1

 

-2 —1.5 —l —O.5 O
Jurcsik—Kovacs [Fe/H]

Figure 5.14 Comparison of the [Fe/H] from the Jurcsik & Kovacs method with the
[Fe/ H] value from Sandage’s method.

108

hoff II RRab stars, and 3) a metal-rich group that we will discuss later in the context
of a thick disk population. A more thorough discussion is presented in sections 6.1
and 6.2.

The period-amplitude diagram is reproduced here with the divisions for the three
groups indicated (see Figure 5.15). The dotted line between Oosterhoff I and II is
an arbitrary boundary between the two groups. The stars found to the right of this
boundary are considered to be Oosterhoff II stars while those on the left of this
boundary are associated with the Oosterhoff I class.

The region contained by the “metal-rich” box was carefully scrutinized for any
RRc stars. Having found that stars within the box appear to be RRab types, we
checked their photometric metallicity values. The stars in the box almost always
have an [Fe/ H] > —-1. The right end boundary of the “metal-rich” box is defined by
[Fe/H] = --1 based on the Sandage [Fe/H]-Log P-Amplitude relation. These stars
are identified in the plot as an open circle with a solid square inside it. There are a
few open circles in the “metal-rich” box. These stars have a Jurcsik & Kovacs [Fe/H]
value but a Sandage [Fe/ H] > —1. Note that some of the stars identified as metal-rich
([Fe/ H] > —1) appear in the region occupied by Oosterhoff I stars. Those stars were
for some purposes reclassified into our metal-rich group.

Layden (1995) suggests a metal-rich RRab p0pulation exists in the disk. As we
will discuss in the next chapter, our metal-rich stars also appear to be associated with

the disk p0pulation.

5.5 C-Type RR Lyraes

As discussed in section 5.1, the final sample of RRc candidates contained 375

109

 

 

    
  

 

 

 
  

 

 

2 I I I I I
. Oosterhoff 1 (M3) 3 Oosterhoff II (a) Cen)
1.5 P x
.(
1
Q)
‘o r ‘
3
'5. i
E l r- -1
<
C15 - I
. . = suns whh .
1 l 1 L I L 41 L 4L 1 1 1 l 1 I. 1 L J 1 1 l 1 l L l l l 1 l
—06 —05 —O4 —03 -O2 -OJ 0

Log Peflod

Figure 5.15 Regions in the period-amplitude diagram occupied by three groups of
RRab stars. The dotted line separates the Oosterhoff I and II groups. The boxed
area identifies the metal-rich RRab group in this sample. Note that most of these
metal-rich stars have a comparatively shorter period than the Oosterhoff I group.

110

stars. Figure 5.16 shows the period distribution of these stars. The average period
((Pc)) for this sample is ~ 0.309 days. We note that in this histogram, there appears
to be a large number of short period stars between 0.2 and 0.3 days. Most likely the
inflation of the numbers of stars in these bins are high amplitude 6 Scuti stars. These
6 Scuti stars are difficult to weed out by looking at the light curves (as opposed to the
obvious eclipsers). Long period, high amplitude (5 Scuti stars overlap with the shorter
period RRc stars. A second histogram, divided by |Z| distance, shows that these
short period, non-RR Lyrae stars are concentrated close to the plane. A discussion
on the attempts to obtain a clean sample of RRc stars is presented in section 5.5.2.
Figure 5.17 shows the period distributions in |Z| regions from 0 to 2 kpc and 2 to 5
kpc.

It should be mentioned here that the distances calculated for the RRc sample are
not based on the MV-[Fe/H] relation from Equations 2.6 and 2.7. Rather, a fixed
value of My = +0.6 was chosen (Smith 1995), which may not be the best value for
these stars. This was due to the fact that metallicities could not be derived for the
RRc stars.

In the bottom histogram of Figure 5.17, we see less of a contamination of these
short period, non-RR Lyraes. This indicates that the contaminating star may belong
to a disk population. The mean period for the RRc stars found in 2 < |Z| < 5 kpc
is very close to what is expected for an Oosterhoff I system. The average period is
typically (PC) z 0.32 days for an Oosterhoff I group. Therefore, we find that the RRc
sample agrees in this respect with the RRab sample. However, there might still be

some contamination from the 6 Scuti population even in this |Z I distance region.

111

 

100 . a . 1 , . . .

<Pc> = 0.309 doys

 

 

 

 

 

 

 

 

 

 

 

 

80 - —
U)
.9
O
'U
‘6 __
g 60 — 1
c)
U
(z
a I— ~--.
8 40 — I —
Q) .—
_o ._
E 1 —
D
:2
20 - a
O 1 E i I I l—I l 1 1 1
O 0.2 0.4 0.6 0.8

Pedod (days)

Figure 5.16 Period distribution histogram for 375 RRc candidates from the NSVS
survey.

112

 

 

 

 

 

 

 

 

 

 

 

 

g T Y Y 171’ T I I Y I I V I Y 1* I Y 1 I V V 1 I I Y I I I I Y I Y I I Yfi T I
. 0 < z < 2 kpc .
o _ <P> = 0.308 d -
... 1
m 9 ‘ F f
L
C »—J
4.4
(f) 8 _ I
U 4
DC
0: O . 7 7 . . 1 . 1 . 1 1 . . . . 1 . . . . 1 . . . .
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
O
H— fi' I I I I I I I I I
O 1
L i 2 5 k ‘
Cl) ’ .
D 9) T < Z < pc 1
E <P> = 0.316 d «
3 :
Z 8 — q
o ’_ _
o 1 1 1—1 I 1 1 1 L l 43 L 1 1 l 1 4 1 1 I 1 1 L 1 L A A A J
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Period (doys)

Figure 5.17 Period distribution histogram for 375 RRc candidate stars in |Z| distance
zones.

113

5.5.1 Period-Amplitude Diagram

Figure 5.18 is the period-amplitude diagram with the inclusion of the RRc stars.
Unlike the RRab stars, clear linear trend lines for the Oosterhoff groups do not exist
for the RRc stars. In Clement & Rowe (2000), parabolic trend lines were used for the
RRc p0pulation. For this dataset, their trends were not used. It is difficult to discern
any preferred trend in the region spanned by the RRc’s in Figure 5.18. Again, it is
noted that the very short period stars (log Pc < —0.65 days) could be high amplitude
6 Scuti stars. For complete assurance, all the stars with log periods less than -0.60
should all be carefully analyzed to see if they are all RRc stars or a mix of short
period variables and the very short period RRc stars.

Based on our RRab period-amplitude diagram and period histograms, we would
expect the RRc stars to exhibit strong Oosterhoff I characteristics. However, there
should be a p0pulation of Oosterhoff II RRc stars as well. Furthermore, in Oosterhoff
11 systems, RRc stars are more common than in Oosterhoff I systems. We would then
expect a stronger Oosterhoff II component among the RRc stars than for the RRab.
As we noted for the RRc candidates in the |Z I range between 2 and 5 kpc, the average
period is very close to the value of (PC) of Oosterhoff I RR Lyraes. However, until we
eliminate the contamination in the RRc sample of the short period, non-RRc variable

stars, we cannot draw any strong conclusions.

5.5.2 RRc Identification Problem

In an attempt to pick out the short period, non-RRc stars from our sample, three

methods were used. The first method was the original variable star classification

114

 

A NSVS RRab
i- O NSVS RRC

 

 

____ Oosuwhofl |(M3)
1,5 _.._- Oosuyhoff|l(w Cen)

 

 

 

 

Q)

‘0 .

.3

ii 1 ~ 0 fi

E ’- 4

< >-

0.5 e ° %
b 'l
I o
O ‘ 1 1 1 1 1 ,
_08 —06 ‘04 —02 0

Log Pefiod

Figure 5.18 Period-Amplitude diagram with the inclusion of the RRc candidate stars.

115

scheme used on the ROTSE-I variables in Akerlof et al. (2000b). The second method
is that of Poretti (2001), who showed that the OGLE variable stars separated into
groups when the Fourier decomposition parameters were plotted against period. The
third method was developed by Szymanski et al. (2001), who also used the Fourier
decomposition parameters. Each method is described in depth in their respective
papers, but is briefly summarized here.

Akerlof et al. (2000b)’s variable star classification scheme utilizes the Fourier de-

composition of the light curves. The light curves were decomposed via:

Am(t) = Zp,cos(2—F7r—t) (5.2)

where Am(t) is the phased light curve information in the Tycho magnitude system,
and I‘ is the derived period. The p,- coefficients, which are related to the a,- coefficients

of the usual formula for Fourier decomposition) were combined to form the ratios:

P2
r = — 5.3
1 P1 ( )
P3
7‘ = — 5.4
2 P1 ( )
P2
r = — 5.5
3 P3 ( )

These ratios actually correspond to the Fourier decomposition parameters R21,
R31, and R23. With these ratios and a period range, the variable stars were classified
into 8 categories: RRab, RRc, 6 Scuti, Cepheid, contact and eclipsing binaries, Miras,
and long period variables. For the RRab stars, the combination of parameters is listed
in Table 5.3

These criteria were tested on the current sample of RRab candidates and almost

116

Table 5.3. RRab classification criteria (Akerlof et al. 2000b)

 

 

Parameter Values

 

Period 0.3 < F < 2.0
r1 ratio 0.08 < r1 < 1.0
7‘2 ratio 0.01 < r2 < 1.0
r3 ratio 73 < 0.6

 

Table 5.4. RRc classification criteria (Akerlof et al. 2000b)

 

 

Parameter Values

 

Period 0.2 < I‘ < 1.0
r1 ratio r1 < 0.16
r2 ratio r2 < 0.24

 

95% were returned as “RRab” under this method. For the RRC candidates, we expect
a similar result in obtaining a clean sample of RRc stars.

The set of parameters for RRC stars is listed in Table 5.4. However, for RRC periods
greater than 0.4 days, the criteria of r1 < 0.08 and r2 < 0.24, and amplitude greater
than 0.35 magnitudes were required. To distinguish eclipsers from the RRC stars, the
additional criterion of the sign of the largest deviation was taken into consideration.
This “sign of the largest deviation” is determined from the mean magnitude of the
variable star and depends upon whether most of the observed points are brighter or
fainter than this mean. For eclipsers, this value is usually negative, whereas for RRC
stars it is positive.

As applied here, the upper period was changed to a period of 0.6 days rather than
1.0 day. With the application of this variable star classification scheme, the final

number of RRC candidates was 375 stars. We believe the bulk of the stars dr0pped

117

 

I I I T I T I I I I fT I I I I I I I I I

¢_41
c3

 

 

_J._ J l L J— I I I 1 I 1 I I I I I I 1 I I l L

0.2 0.3 0.4 0.5 0.6
Period (doys)

 

 

Figure 5.19 Fourier parameter 0541 vs. Period. In contrast to the similar diagrams in
Poretti (2001), no clear separation is seen between 6 Scuti and RRc stars.

from the original sample were either short period, non-RR Lyraes or eclipsers.

As a check, we used the analysis scheme of Poretti (2001), which compared Fourier
decomposition parameters to period (see his Figure 4, 5, 6, and 7). For our RRc
candidates, plots of 041 versus period and R21 versus period were produced because
the 6 Scuti stars are expected to cleanly separate away from the RRC stars in these
diagrams.

Despite our expectations, in Figures 5.19 and 5.20, a separation between the RRC
candidates and our supposed contaminant population could not be seen clearly. One
thing to note here is that the Fourier parameters R21 and 041 were not scaled to
a standard system as the (1531 parameter was for the RRab stars (see discussion in

section 4.4). We could not produce an adequate calibration relation for the Fourier

118

 

0.5 P

 

 

|1111111111111|111114111

0.2 0.3 0.4 0.5 0.6
Period (days)

 

 

Figure 5.20 Fourier parameter R21 vs. Period. As with the (1541 plot, no clear separa-
tion is seen between the two types of short period variable stars.

119

parameters of the RRc stars to a standard V system equivalent. There were only a
few well observed RRC stars in the literature for which we also had good observations
from the NSVS survey. Most likely this is not the major reason why a separation
was not observed since a general separation should occur regardless of the particular
calibration on the Fourier parameters. Why the separation of 6 Scuti and RRC stars
was not observed is unknown at this time.

The third method was obtained from Szymanski et al. (2001), whose sample of
stars came from the MACHO survey. In their method, again a Fourier decomposition

was performed on the light curves. Their formula is reproduced here:

A(t) = a0 + z a,- cos(iwt + f,) A (5.6)

A(t) is in magnitude units and is essentially the light curve information. The f,-
terms are the phase terms, often shown as 43,- in the usual convention of the Fourier
decomposition. The main impetus behind the deve10pment of this method was to
weed out the pulsating variables and to get a clean sample of eclipsing stars. In our
case, we desire to exclude the binary stars but keep the pulsators. Szymanski et al.
found that a strong correlation between f2 (or 052) and f4 (or 04) phase term exists

for eclipsing stars, but is weak for pulsators. This trend for the eclipsing binaries is:

f2 — 2f4 = 0 (5-7)

Figure 5.21 shows the application of this method on the RRC sample. One could
be convinced that the trends seen in Szymanski et al.’s figure 1 are present in our
Figure 5.21. It may also be plausible that a majority of the eclipsing binaries have
already been removed. Regardless, the strong trend Szymanski et al. had observed

in their figure is not present in Figure 5.21. In any case, we have decided this method

120

 

 

 

 

 

Figure 5.21 Szymanski et al. (2001) method of weeding out the eclipsers from the
sample of RRc stars. The trend lines here are the location of Szymanski et al. (2001)’s
relation (Equation 5.7). The right hand trend line was created by adding 27r to the
left hand trend line.

was not useful in weeding out the eclipsers with very shallow and equal minima.
Szymanski et al.’s method does not easily facilitate the separation of those types of
eclipsers and the RR 0 stars with very sinusoidal looking light curves.

Another RRc separation method developed by Rucinski (1997, 1993) was not
tested, but may be a promising technique. Akerlof et al. (2000b) proposed to use
Rucinski’s method for the full ROTSE-I/NSVS variable star catalog. The Rucinski
method fits a cosine series function to the light curve data, which is in flux units. The
coefficients of this fit are to be used to separate out, in particular, the binary stars
from the pulsating stars. Until we can test this method on the NSVS sample of RR

Lyraes, we can neither advocate nor oppose this use of Rucinski’s method.

121

From the results of these three methods, extracting the RRC stars from the N SVS
survey is no easy endeavor. There is an apparent contamination by some type of
short period, non-RR Lyrae star near 0.2 days. These stars are most likely to be high
amplitude 6 Scuti stars that have sinusoidal looking light curves. These stars overlap
in period space with the shortest period RRc stars. We find that the techniques used
by Poretti (2001) and Szymanski et al. (2001) did not produce a clear separation of the
RRC stars from the other variable stars. The ROTSE-I variable classification scheme
(Akerlof et al. 2000b) caused the removal of a large portion of the RRc candidate
sample. However, even this scheme did not remove all the shortest period non-RRC
stars. At this point, either the Rucinski method or another technique is needed to

obtain a clean sample of RRc stars from the NSVS survey.

122

Chapter 6

Discussion of the Results

In this chapter, aspects of our sample of N SVS RRab stars relevant to galactic

structure are discussed. The implications of galaxy formation scenarios are addressed.

6.1 Oosterhoff Dichotomy and Galaxy Formation

Implications

As discussed in section 5.4.4, three groups have emerged from the sample of RRab
stars. Here, we take a closer look at the Oosterhoff I, Oosterhoff II, and the metal-rich

group. The thick disk will also be discussed separately in section 6.2.

6.1.1 Contour Plots of the Period-Amplitude Diagram
An interesting test of the Oosterhoff groups is to overlay contours determined

123

by the density of stars for each locii. To produce this map, a grid with box sizes
determined by the log period and amplitude was constructed. We assume a box size
of the grid is 0.25 in log period space and 0.1 magnitudes in amplitude space. Next,
the number of stars in each grid box was counted up. To determine the density, this
number is divided by the area of the grid box. Once the density, or “concentration
number” is determined, the IDL task CONTOUR can be used to produce the contour
map of the period-amplitude diagram.

Figure 6.1 shows our contour plots at two different resolutions. This contour plot
is the low resolution contour map of the period-amplitude diagram. Note the high
concentration of stars near the Oosterhoff I locus. In Figure 6.2, the higher resolution
contour map shows some clumps that may be associated with Oosterhoff II. However,
it is also clear that there is some population of RRab stars between the Oosterhoff I

and II lines.

6.1.2 Distribution of the Groups

To take a closer look at the Oosterhoff groups and the metal-rich group from
section 5.4.4, we plot the [Fe/ H] distribution with respect to |Z| distance from the
plane. In Figure 6.3, each group is identified by a different symbol. We see in this
figure the metal-rich stars with [Fe/ H] > —1 all appear close to the plane. For the
6 stars that are above this group have their metallicities derived from teh Sandage
relation (Equation 4.24). The metallicities may be more uncertain for these stars.
The metal-poor stars may exhibit a more extended distribution and may be mostly a
halo population. We will argue later that even some of these metal-poor RRab stars

are likely to belong to a disk population. We present individual plots of each group

124

 

2.0IIIIIIIIfTIIIII

1.5"

1.0"

Ann)

(15*

 

 

 

0.0 ...1.1n1.111...

—0.6 -0.4 —0.2 —0.0 0.2
Log Pedod

 

Figure 6.1 Lower resolution contour map of the RRab period-amplitude diagram.
Number of contour levels is 5. Note that there is a higher density of stars near the
Oosterhoff I locus. The trend lines are the same ones from Figure 5.11.

125

 

 

 

 

 

ZOIIIlfirwlllfiTrII
1.5"

O— r

E 1.0~

<
0.5’
0.0411l111l111l111
—0.6 —0.4 —-0.2 —0.0 0.2

Log Peflod

Figure 6.2 Higher resolution contour map of the RRab period-amplitude diagram.
Number of contour levels is 10. Note that there is now some clumps associated with
Oosterhoff II. The trend lines are the same ones from Figure 5.11.

126

 

 

 

FT I I I I I I I I I I I I I I T I I I I I
. Oosterhoff II
o Oosterhoffl
Thick Disk
4 ...
A
A
U
a
)1
V
(D
U
C
o
...J
.‘I.’
Q 2 _ ‘ s
E
‘ t
‘#
$
t
t t "
t
0 Pl ...

 

 

 

 

Figure 6.3 [Fe/ H] distribution for the three groups with respect to |Z I distance.

in Figures 6.4—6.7.

The Oosterhoff II group’s metallicity distribution with |Z| is shown in Figure
6.4. The Oosterhoff II very metal-weak stars ([Fe/H] < -2.5) have an uncertain
metallicity since the calibrating stars used from the literature do not go weaker than
[Fe/ H] ~ -2.5. The stars of this group are found up to 4 kpc from the plane.

In Figure 6.5, the distribution of [Fe/H] of the Oosterhoff I stars with respect
to |Z| is shown. These stars are found from close to the plane up to |Z| ~ 4 kpc.
From the number ratios of Table 6.1, we chose to divide the Oosterhoff I group into 2
subgroups to investigate the large population of these stars. We institute a division
of the stars at [Fe/ H] = —1.25. In Figure 6.6, we see the stars distributed from close

to the plane to over 4 kpc. However, when we looked at the number distribution of

127

 

IZI Distonce (kpc)
D
.
5
t

M
I
gt
:9;
D
'
.
l

 

 

 

[Fe/H]
Figure 6.4 Oosterhoff II RRab candidates.

the Oosterhoff I stars, a large fraction of the stars close to the plane were from the
metal-rich Oosterhoff I group. Table 6.2 has the number distribution of stars for each
Oosterhoff I subgroup. With the subdivision at [Fe/ H] := —1.25 in the Oosterhoff I
group, we find a clump of stars do exist close to the plane. This could imply that this
clump may belong to a disk population that is more metal-weak than the stars in our
[Fe/H] > -1.25 sample. However, the spread of stars up to |Z| ~ 4 kpc indicates
that the halo population is present in this group. One caveat to keep in mind is
that the uncertainty of the [Fe/ H] measurements may scatter stars into or out of the
Oosterhoff I group (similarly, this is also true for the Oosterhoff II and metal-rich
group). Because of this scatter, the groups are not as distinct as would be the case if
perfect measurements of metallicity were available.

To get a rough answer to whether a metal-weak disk population really exists in this

Oosterhoff I group, we look to the number ratios of the Oosterhofl groups at different

128

Table 6.1 Number of stars of each group per Z bin.

 

 

 

 

|Z| Zone Metal-Rich 00 I 00 II Metal-Rich 00 I 00 II
(kpC) (lbl > 12°) (lbl > 12°) (Ibl > 12°)
0.0-0.25 13 13 1 1 1 0
0.25-0.5 19 19 9 7 10 3
0.5-0.75 12 28 8 6 19 5
0.75-1.0 11 37 8 7 22 5
1.0-1.25 5 44 14 3 32 9
125-15 9 41 9 6 29 2
1.5-1.75 l 25 12 0 19 9
1.75-2.0 6 29 22 1 19 16
2.0-2.25 1 25 17 1 21 15
225-25 0 20 17 O 15 10
25—275) 1 16 8 0 10 5
275-30 0 21 9 0 18 7
3.0-3.25 l 16 11 0 10 7
325—35 0 10 7 0 7 5
3.5-3.75 0 12 6 0 11 5
3.75-4.0 0 4 6 0 2 4
40-425 0 1 3 0 1 3
4.25-4.5 0 1 0 0 0 0
4.5-4.75 0 0 0 0 0 0
4.75-5.0 0 0 0 0 0 0
50-525 0 0 0 0 0 0
525-55 0 0 0 0 0 O

 

129

Table 6.2 Number distribution of the Oosterhoff I metallicity groups

 

|Z| Zone Oosterhoff I Oosterhoff I
(kpc) (metal-poor) (metal-rich)

 

 

0.0-0.25 12 1
0.25-0.5 11 8
0.5—0.75 24 4
0.75-1.0 24 13
1.0-1.25 32 12
125-15 31 10
1.5-1.75 20 5
1.75-2.0 27 2
2.0-2.25 24 1
225-25 18 2
25-275 13 3
275-30 18 3
3.0-3.25 14 2
325-35 9 1
3.5-3.75 11 1
375-4.0 4 0
4.0-4.25 1 0
425-45 1 O
4.5-4.75 O O
4.75-5.0 0 0
50-525 0 0
525-55 0 0

 

130

 

 

 

 

A
0
a o :3
3.3 o
0
<1)
0 <9
c
.9 °%
1, o o
E ° a»
o o
o o 0.", .
5‘0"‘..“'
° °até°
0a
l .,--:
000 213
o
0%
000
O "1 1 1 1 1 "
—4 -3 —2 O 1

 

Figure 6.5 Oosterhoff I RRab candidates.

|Z| distance zones. It is assumed that the halo population is best represented by
the Oosterhoff II group, but that some thick disk stars may be found in both the
more metal-rich and more metal-poor Oosterhoff I groups. We expect the region
2.5 < IZ I < 3.5 should be dominated by the halo population. The number ratio,
N(Oo II)/N(Oo I) in this region is z 0.56 :1: 0.12 for all [Fe/H] values. Therefore,
this shows that the Oosterhoff I stars outnumber the Oosterhoff II by nearly a 2 to 1
ratio. Let us assume this is the Oosterhoff II/Oosterhoff I ratio in the halo near the
Sun.

Now we look at the number ratios for the region 0 < |Z| < 2 kpc, but avoid the
Galactic plane by instituting a cutoff in galactic latitude, |b| > 12°. Here, we find the
N(Oo II) / N (00 1) ratio to be z 0.32 :1: 0.05. This result could reflect a change with Z
of the halo RR Lyrae population. More likely, however, is that this result shows the

existence of a thick disk population in the Oosterhoff I group at low IZI. More than

131

 

IZI Distance (kpc)

 

 

 

[Fe/H]

Figure 6.6 Oosterhoff I group of RRab stars. This group is divided into two groups
by [Fe/ H] = -1.25. The solid circles are those stars with [Fe/ H] < —-1.25 and the Open
squares are the stars with [Fe/ H] > —1.25. Note the metal richer clump close to the

plane of the [Fe/ H] > —1.25 group.

a third of all Oosterhoff I RRab stars in the 0 < IZI < 2 kpc zone would belong to
the thick disk in this interpretation.

Now we can perform the same kind of analysis for the two Oosterhoff I subgroups,
again comparing with the Oosterhoff II group. These subgroups, as mentioned above,
are separated into a metal-rich ([Fe/ H] > —1.25) and a metal-poor ([Fe/ H] < —1.25)
group. The number ratio of Oosterhoff II to Oosterhoff I-metal-poor at 2.5 < IZI <
3.5 kpc is 0.59. Near the plane, the ratio is 0.41 :1: 0.07 (again, only using stars
that meet the Ibl > 12° criterion). Comparatively, the Oosterhoff II/Oosterhoff I-

metal-rich ratio is 6.0 :t 3.2 in the high Z range whereas at the low Z range, it is

1.6 :l: 0.4.

132

Thus, we find from our number ratios that a thick disk component is strong in a
metal-rich Oosterhoff I sample. We estimate that approximately 60% of our metal—
rich Oosterhoff I group in the low |Z| zone belongs to the thick disk. There is some
evidence for a metal-weak thick disk component in our Oosterhoff I group with [F e/ H]
< —1.25. For this metal-weak case, the evidence is weaker as it is not quite a 2 sigma
result. Again, we must be aware of the fact that the observational uncertainties can
scatter some of the metal-rich thick disk stars into the metal-weak sample and vice
versa. To avoid this caveat, kinematic information is necessary. The motions of these
stars can also provide clear evidence of a disk component in our Oosterhoff I group.

We should note here that the metal-weak thick disk star population in the Oost-
erhoff I group falls along the period-amplitude relation for halo RR Lyraes, as well
as the Oosterhoff I cluster RR Lyraes, of the same metallicity. The metal-rich thick
disk stars appear to extend this period—amplitude relation to a shorter period domain.
This indicates that there is a continuum of the RR Lyrae properties with metallic-
ity when transitioning from a metal-poor Oosterhoff I RR Lyrae to their metal-rich
counterparts. However, there are exceptions to this suggestion (e.g. the metal rich
clusters of NGC 6388 and NGC 6441 studied by Pritzl et al. (2000)). The existence
of these two cluster may suggest that they have a different history than the thick disk
stars.

Figure 6.7 shows the metal-rich distribution of stars with respect to IZI. Note
that these stars are found close to the plane of the Galaxy. The combination of the
location of the stars in the Galaxy and their high metallicity establishes that they
are a part of the thick disk component. Note the interesting feature of the thick disk
stars declining toward the plane at [Fe/ H] between —1 and 0. This may indicate a
component of a thin disk in our thick disk sample.

To check if this trend in the “metal-rich”, now “thick disk” group, is real and not

133

 

 

 

 

Fl I I I T I
4 '- -1
A
U
C.
x
v
Q)
U
C
C
‘0—1
(2 I
o 2 _ .. _
_N_ . ‘
‘
¢*"" t ‘
t
1t“ .
h tin-1:“ 1
. ‘ “z. t
t
2:55
”1".: t
‘3 ‘11:. .
O *1 1 1 1 h ‘ 1 1
—4 —3 —2 -1 o 1

[Fe/H]

Figure 6.7 Thick disk candidates. Notice the trend that the more metal rich stars are
constrained to the plane. This may be indicative of a thin disk component.

an artifact of our adopted Mv-[Fe/ H] relation, the IZI distances were derived again
from using fixed absolute magnitudes. Figure 6.8 shows the same group, but with
slightly different IZI distance values. We see that the trend is still present in each

calculation, therefore, this declining slope feature is not an artifact.

6.1.3 ALog P and the Oosterhoff Dichotomy

In addition to the period-amplitude diagrams, we used the ALog P parameter
to obtain a clearer picture of the Oosterhoff dichotomy in our sample of RRab’s.
In Suntzeff et al. (1991), the field RR Lyraes appeared to separate into distinct
Oosterhoff groups when the ALog P and metallicity were plotted against each other.

The ALog P, or period shift, is the same parameter that Sandage et al. (1981) had

134

 

 

 

 

3 I I I r I
0
+ o 1
t + 1
A 2 + *
8 0 ..
e: i a
8 i 0 on D +
(C3 0 i :4» o + a:
.7) 11' D “ 1* at
”c5 3“? 2
RT 1 _ 0" 9:3 _.
— 23$ 5 :g 53" . 9
9 S 9 i 2‘? ‘E S 1
Q 9 3929
9 Q 9 9 f I31
19% 9 9 9 '
W 9 e W 9
o — “a“ - -
l l l l l l l l l 4 1 l J 1 l l
—1 —O.5 O 0.5
[Fe/H]

Figure 6.8 This shows the metal-rich thick disk group for different My values. The
asterisks are for those distances determined from the MV-[Fe/ H] relation. The open
squares are for those distances where Mv was fixed to the value of 0.6 and the crosses

are for My = 0.7.

135

 

 

 

 

 

 

 

0.2 Y 1 I 1 I T 1 fl 1 j r I I I I 1
r- . 1
o 1 i
.1 f . . a
r- -1
O — _
CL
‘2
O‘
2
<1 0
—o.1 — —
F -1
l' -1
1 1
-0 2 :_ ° 1
~ 0 .Oosterhoff l
1 oOosterhoff ll
1 O 1
_O.3 1 1 1 1 l L 1 1 1 1 1 1 1 1 1 1 1 J
—4 —3 —2 -1 o

[Fe/H1

Figure 6.9 The ALog P plot. The Oosterhoff groups do not appear to separate in
this plot as in Suntzeff et al. (1991)’s figure 8a.

defined in their work with Oosterhoff clusters. Figure 6.9 is our plot of ALog P versus
[Fe/H]. To help the eye, stars associated with Oosterhoff I are the solid circles and
the Oosterhoff II are the open circles. Compared to Suntzeff et al. (1991)’s figure 8a,
we do not see a gap at ALog P = —0.03. Rather, the stars appear to be continuous
from one group to the other.

Knowledge of the kinematics of the RR Lyrae stars would help us relate them
to particular Galactic components. For the kinematic information, we would need
proper motions and radial velocities. There have been many proper motion surveys
where the N SVS stars have already been observed and thus some kinematic informa-
tion is already available. Therefore obtaining proper motions will be an exercise of

cross-correlating our database with the published proper motion catalogs. The radial

136

velocities are a different story. These motions are not readily available for the N SVS
stars since this kinematic information is obtained only through spectroscopy. More

on this topic will be discussed in Chapter 7.

6.1.4 Implications for Galactic Evolution

We have shown the dominance of an Oosterhoff I RRab population in the solar
neighborhood. At the start of our investigation, we had hoped to test the relative
proportions of Oosterhoff I to Oosterhoff II stars as a function of Z distance, as
suggested by the work of Lee & Carney (1999). However, the strong contribution of
the thick disk stars in our Oosterhoff I sample makes it difficult to test this at the
moment. Once the kinematic information is available, we will be able to distinguish
more cleanly the halo and disk populations in our Oosterhoff samples and then return
to this issue. Our results indicate that the thick disk is an important contribution to
the local pOpulation of RRab stars, even at [Fe/ H] values lower than —1.

However, to make a stronger case, the kinematics of these stars need to be ob-
tained. Through the correlation of the Oosterhoff groups and the kinematics (Lee
& Carney 1999), we can specifically identify which stars belong in the halo and disk
populations. For now, we rely on the Oosterhoff correlation to the kinematics to make

our suggestions of the Galaxy formation scenarios.

6.2 The Thick Disk

In our sample of 608 RRab stars, 70 were found to have an [Fe/ H] > —1. As

seen in Figure 6.7, these stars also lie close to the plane. We therefore refer to

137

this subsample as our thick disk sample. We also have convincing evidence that a
thick disk component extends down to [Fe/H] 2’ —1.25. We believe that an even
more metal-weak component of the thick disk may exist, but to clearly identify this
component the kinematic information is needed. For the remainder of this section,

we will discuss only the metal-rich ( [Fe/ H] > —1) thick disk group.

6.2.1 The Scale Height of the Thick Disk

The scale height of the thick disk is essentially the height above the plane where

1. To derive this structural feature of

the number density of the stars falls off by e‘
the Galaxy, we binned our data into an average of either 6 or 10 stars per IZI bin.
The choice of 6 and 10 stars per bin was decided by how many data points were
available to determine the scale height and how uncertain those points were. We also
implement a limit to the volume in which we calculate the densities in the thick disk.
The limits of lb] > 12° and radially 2 kpc from the Sun were used. Therefore, the
shape of the volume used to determine the densities was frustrums of a cone. After
reaching the height corresponding to 2.0 kpc search radius, the volume was a disk.

Once the binning was complete, an exponential function was fitted to the data using

an IDL task called CURVEFIT. We assume the exponential function was of the form:

F(z) 2' A682 (6.1)

where A and B are parameters from the fit.
For our sample of metal-rich thick disk stars, the scale height parameters from

CURVEFIT were A = 18.1 i 6.3 and B = —2.3 :l: 0.7 with a x2 value of 0.71 for

the fit in the case where we averaged the sample to 10 stars per bin. This yielded

138

 

 

 

 

 

 

 

8 ’— 0 T
Q
6 _ -1
A
’7
U
Q.
i
z”: <9
V
3 1»
Q)
Q
0
on
2 1— '~ _.
1 1 1 1 1 1 1 1 1 1 1M1 +1
0.5 1 1.5

IZI Distance (kpc)

Figure 6.10 Scale height plot derived from using 10 stars per Z bin. Stars here all
have [Fe/H]> —1

a scale height of 0.44 i 0.13 kpc. For the case of 6 stars per bin, the parameters
were A = 23.0 :t 5.0 and B = —2.9 :t 0.5 with a X2 value of 1.2. The corresponding
scale height was determined to be 0.34 :1: 0.06 kpc. Figure 6.10 and 6.11 show the
exponential fits to the scale height data.

These scale heights are much smaller than the canonical scale height of ~ 1 kpc
(Binney & Merrifield 1998). An important reason for the difference may be that our
[Fe/ H] > —1 RRab sample includes a thin disk component as well as a thick disk
component. This is best shown in Figure 6.7 of the thick disk sample in [Fe/H]-|Z|
space. The sharp decline of stars toward IZ I may suggest of this thin disk contamina-
tion. Layden (1995) had suggested the possibility of an old, thin disk population of
RRab stars. Compared to the scale height derived by Layden (1995), which was a: 0.7

139

 

 

 

 

 

 

 

' I fl I 1
0
1O 7 <1 "
.1
.4
r?
o 0. 1
c1
x .
Q 1. 1
v .
3‘
... >— 4- .4
m 5 o.
C '.
8 ' 1
0
.4
1
0 ...... +
1 1 1 1 1 1 1 1 1 1 1 """" g -------- , 1
0.5 1 1.5 2

IZI Distonce (kpc)

Figure 6.11 Scale height plot derived from using 6 stars pier bin. All the stars in the
bins have [Fe/H]> —1

140

kpc, our values are slightly smaller. Layden (1995) commented that for increasing
metallicity, the scale heights become smaller. This suggestion seems applicable to
our result, although our sample of thick disk stars may contain more metal-rich stars

than in Layden’s work.

6.2.2 The Metallicity Gradient

Suntzeff et al. (1991) reported a metallicity gradient among the RRab stars as
a function of galactocentric distance (R) close to the center of the Galaxy. In their
figure 4a, which is a plot of mean [Fe/H] and R distance, the metallicity of their
sample decreased in going from R = 4 kpc to R = 10 kpc. To produce this plot, their
sample was averaged into bins containing 20 stars each. Our version of ([F e / H ]) as a
function of galactocentric distance is presented in Figure 6.12. The stars used for this
plot are those stars in the Oosterhoff I and II groups (i.e. [Fe/ H] < —-1). Our sample
is limited to R ~ 6 kpc from the Galactic center to about 12 kpc. In the region that
overlaps with Suntzeff et al.’s metallicity gradient, we do not see this trend in our
plot. In fact, we observe a zero gradient for metallicity in this range of galactocentric
distance!

A couple of things can be concluded from our plot. It is plausible that since we do
not go down to R = 4 kpc as Suntzeff et al. does, we may not be seeing part of a trend.
Another possibility is that our metallicities are on different systems. Suntzeff et al.
(1991) derived their [Fe/ H] values from the AS method (Preston 1959), which uses the
spectra of RR Lyraes (specifically the calcium K and Balmer lines). However, both
our [Fe/H] and their metallicity values should be on the same system, i.e. the Zinn-

West system (Zinn & West 1984). If there are any systematic differences, they should

141

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-2.5 ~
0 (I

—2 h—
/\ 0
F—l
I I
\ 0 0 0 ‘L o 000 0 1)
Q) o 1. 0 0 0 0 0

0 0

“U; o l 0 0 0 000 0
V l’ D

-1 _
_ 1 1 1 L L 1

0.5

4 6 8 1O 12

R (kpc)

Figure 6.12 The average [Fe/ H] distribution with galactocentric distances.

142

be small and should not erase any metallicity trend. Also, it is possible that despite
our exclusion of stars with [Fe/ H] > —1, our sample may have more thick disk stars,
which can erase our inner halo trends. The sample Suntzeff et al. used contained
fainter stars than our sample from the NSVS survey and may be less affected by this
problem.

Until we can positively separate out the thick disk stars from the inner halo, we
will not be able to make a conclusive statement for or against the observed gradient
in Suntzeff et al. (1991). Again, the best solution for this is to obtain kinematic

information from spectroscopic observations for our sample of thick disk stars.

143

Chapter 7

Future Work and Suggested

Projects

As one finds interesting results, new questions are always generated. Throughout
the work done in this project, various results from MACHO and SDSS (Alcock et al.
2004, Vivas et al. 2004) have appeared, which have guided and/or influenced some
of the work here. By no means is this project absolutely complete. There are topics
that have not been addressed and many problems that either hindered the project
or needed to be resolved by obtaining new data. These points are discussed in this
chapter, and it is the hope of this scientist that more people will use the NSVS survey,

whether to study the RR Lyraes or gamma ray bursters or to discover asteroids!

7. 1 Survey Completeness

The NSVS survey is expected to provide the first kinematically unbiased and

144

complete RR Lyrae catalog for stars brighter than V = 15” magnitude. However,
for the results in this dissertation, only a specific portion of the full catalog was used.
Appendix B lists some of the parameters calculated for 608 RRab stars. As mentioned
in previous chapters, a magnitude limit was enforced which resulted in the exclusion
of stars found at IZ I > 5 kpc. The full RR Lyrae catalog should reach to a Z distance
of 7 to 9 kpc, depending on the quality of the observation of the faint RR Lyrae
candidates.

With the addition of stars found from 5 kpc to the survey limit, we will have
a better handle on what the halo region is like within the NSVS survey. However,
we must first understand any biases inherent in the use of these fainter stars. We
know, for example, we will lose some number of long period RRab stars and any RRC
stars. The amplitudes of these stars are low, and the noise in the observations may
prevent them from being discovered. These biases will affect any discoveries at these
faint magnitudes and possibly influence a correlation with the galactic coordinates l
and b. Nonetheless, with a larger sample, we will be able to see if there is a greater
dominance of Oosterhoff I at |Z| = 5 - 9 kpc or if there is still the same mix of
Oosterhoff populations as exists closer to the plane. We will also have more stars for
the analysis of the metallicity distribution in the solar neighborhood. With a complete
catalog of RR Lyraes, one would also be in a better position to look for clumps of these
stars. The clumps could be associated with a tidal stream or subgalactic fragment
that is accreting into the Galaxy. In order to interpret any observed clumping in the

RR Lyrae distribution, we will need to have a full understanding of all the biases that

exist in the sample.

145

7 .2 Need for Kinematic Information

One important and still lacking piece of information needed for the analysis of
the RRab stars is a full knowledge of their kinematics. With a combination of their
motions, locations, and metallicities, the RR Lyraes can provide deeper clues to the
evolution and structure of the Galaxy. This requires knowing the proper motions
and radial velocities of these stars. Useful proper motions are available for many of
the NSVS RR Lyraes. Unfortunately, there are comparatively few sources for the
radial velocities. However, if we do have this kinematic information, we will be able
to determine the rotational motion of these stars about the Galactic center. Do we
see the prograde motions indicative of a dissipative collapse scenario in our thick disk
sample? Are the motions of the metal-weak thick disk group of RRab stars similar
to those motions of the metal-rich thick disk stars? Do we see more of a retrograde
motion for those stars far from the Galactic plane and center (.2 > 5 kpc and R > 10
kpc)? Do those stars show evidence of being part of an accreted system, such as the
Sagittarius dwarf ’s tidal stream (Martinez-Delgado et a1. 2004)?

With kinematics to the individual stars, we will have a better handle as to which
population (halo or thick disk) these stars belong. As shown with the work done by
Lee & Carney (1999), we can also use Oosterhoff groups to study the kinematics of
these field stars. With the kinematic information and subsequent classification of the
stars to their appropriate Galactic component population, a better assessment of the
Galactic structure and evolutionary scenario can be made.

In particular, with kinematic information, the thick disk sample can be reevalu-
ated. Are the clump of stars in the Oosterhoff I group with —1.25 < [Fe/H] < -1

actually a disk component? How many of the Oosterhoff I stars with —1.25 <[Fe/H]<

146

—-1.6 actually belong to a metal-weak thick disk population? Do all the stars with

[Fe/ H] > —1 exhibit thick disk kinematics?

7 .3 Spectroscopy

Observational astronomy can be split into two camps: photometry and spec-
troscopy. While the database contains photometric data, spectroscopic data are
needed to obtain other useful quantities. Two of these quantities are the radial
velocities and the AS metallicity.

Obtaining spectra for all the RR Lyraes of a complete catalog will take a large
number of observing hours as well as man hours analyzing the data. Large telescopes
can cut the exposure times for the fainter stars. Multi-fiber spectrographs are un-
fortunately not a very efficient way to obtain large numbers of field RR Lyraes in a
single run. The RR Lyraes of this survey are too spread out for more than one star
to be in a single spectroscopic field of view. The optimal situation at the present
time is to use a telescope large enough to have short exposure times for the faint RR
Lyrae stars and to use a single slit spectrograph. Perhaps an off-shoot project from
this dissertation may be to obtain spectra for a select sample, such as the thick disk

candidates, and exclusively study those stars.

7 .3.1 Radial velocity measurements

The radial velocities are measured from a Doppler shift of the absorption (or
emission) lines found in the spectra of an object with respect to an object at the rest

frame. These tiny shifts in the line (in terms of wavelengths) correspond to how fast

147

the objects are moving toward or away from us. In conjunction with proper motions,
which are motions perpendicular to the line of sight, radial velocities can be used to
determine statistical parallax distances of the RR Lyraes.

In particular, there are very few statistical parallax solutions for RRc type stars.
The NSVS survey should provide a wealth of RRc stars that are good candidates
for determining this. However, the kinematics of the field population must be well
understood for the calculation of the statistical parallax. Thus, there will be a need
for spectroscopic projects to obtain radial velocities to many for the RRc stars found

in the NSVS survey.

7 .3.2 AS Metallicity

Preston (1959) proposed an innovative way to measure the metallicity of an RR
Lyrae called the “AS” method. This method, which is a rather reliable way to obtain
the [Fe/H] values, uses the spectral type of the star based on the calcium K line
()1 = 3933A) and the Balmer lines to find the metallicity. The calcium K and Balmer
lines are ordinarily strong in the spectra of RR Lyraes. For this calculation, the RR

Lyraes should be observed at minimum light. The A8 relation is defined as:

as = 10[Sp(H) — Sp(K)] (7.1)

where “Sp” stands for the spectral type as determined from the Balmer lines (Sp(H))
and the spectral type from the K line (Sp(K)). The value of AS is correlated to the
metallicity of the star, with small values being more metal rich and larger values of
AS being metal poor. The work presented in Layden ( 1994) is an elaboration of this

technique.

148

Obtaining the AS method [Fe/ H] value will be useful as a check on the [Fe/ H]
value we have calculated from the photometric methods. There are many possible
ways for the photometric metallicity to be spurious, i.e. the quality of the Fourier
parameters or amplitude measurements. As seen in our use of the Jurcsik & Kovacs
(1996) method alone, over 200 stars had to be omitted because the [Fe/H] value
was either spuriously high or low, or because of an uncertain ¢31 measurement. In
addition, stars with the Blazhko Effect could not be analyzed with the Jurcsik &
Kovacs method. The AS method should not discriminate against these stars, or the

double mode RR Lyraes (which also exhibit noisy looking light curves).

7 .4 Obstacles Encountered with the RRC Stars

A major problem encountered in this project is the lack of well observed field
RRc reference stars in the literature. Kemper (1982) and Bookmeyer et al. (1977)
were among the few references that contained good observational parameters for field
RRc stars. In addition to the paucity of RRc star research in the literature, some of
the reference RRc stars that were observed by the ROTSE-I telescope turned out to
have poor ROTSE-I light curves. As a consequence of this, good measurements of
amplitude and Fourier decomposition parameters could not be performed. Appendix
C is a table of parameters derived for 375 RRc stars.

Even if we had a good sample of RRc stars from N SVS and were able to calibrate
parameters, such as amplitude, onto the Johnson V filter system, the relations used
for determining [Fe/ H] were only developed for RRab stars. For example, the (1531
parameters are different for the asymmetric light curves of RRab stars and the sinu-

soidal light curves of the c-types. Thus, the J urcsik & Kovacs method for determining

149

[Fe/ H] is applicable only to the RRab stars. Until a similar ¢31-period-[Fe/ H] relation
(if there is one) is developed for the RRC stars, we are left to determine the metal-
licity of these stars only through spectroscopy or through multi-color photometric

metallicity parameters.

7 .5 Other Types of RR Lyraes

As mentioned in section 2.1.1, there are two types of multi-periodic RR Lyraes.
These are the double mode RR Lyraes (RRd) and the RR Lyraes with the Blazhko
effect. The NSVS survey allows us an opportunity to find these types of stars in the
solar neighborhood. Studies of these stars can be excellent side projects from this
research.

The RRd and Blazhko RRab stars have very similar looking, messy light curves.
The RRd light curves would need to be deconvolved in order to derive the fundamental
and first overtone mode periods. Astrophysically, the ratio of these periods can be
used to derive stellar masses of the RRd stars (Petersen 1973, Bono et al. 1996).
Finding Blazhko effect stars would be useful astrophysically, to study possible non-
radial oscillation mechanisms in these stars. A complete survey of Blazhko RR Lyraes
in the NSVS sample will be useful to characterize the pulsational properties of the
RR Lyraes in the solar neighborhood. In Table 7.1, a list of Blazhko effect and RRd

candidates is provided.

150

Table 7.1 Blazhko Effect and Double-Mode RR Lyrae Candidates.

 

 

 

NSVS id RA (2000) DEC (2000) Period (days)
12962968 136.2020 5.5024 0.496977
14715713 22.2010 —11.4534 0.516926
5207932 240.1340 46.9240 0.469995
5222075 236.6080 44.3125 0.494065
8877855 336.3470 34.8855 0.503446
10806470 256.4160 21.5167 0.613090
15726118 144.3830 -18.2703 0.520967
16240332 230.4710 -12.1128 0.441802
1088956 258.3330 69.1317 0.403212
13439616 233.3780 2.7768 0.575426
16100815 214.1080 -17.0918 0.566316
5152352 223.4170 40.5286 0.353033
10905292 266.4960 10.5037 0.537722
12252066 69.5150 -1.9958 0.579259
12919471 131.9460 -3.6501 0.420834
13961527 283.7150 -0.5452 0.685244
14411401 318.6800 4.4937 0.444705
11559601 316.5430 10.3862 0.557333
12900308 127.6250 -2.7110 0.508529
13144198 175.8840 2.6986 0.595013
13343643 217.0410 6.5455 0.483731
2094282 61.6630 55.4999 0.368768
5377085 273.2430 42.0625 0.442158
9294409 39.7350 8.7423 0.604376

 

151

Appendix A

Best Estimate [Fe/ H]

This table contains the [Fe/ H] values determined from Sandage (2004) and from
Jurcsik & Kovacs (1996). The first column is the identification number in the NSVS
catalog. Columns 2 and 3 are the [Fe/ H] and its uncertainty values from Sandage’s
relation. Columns 4 and 5 are the [Fe/H] and its uncertainty from the Jurcsik &
Kovacs method. The entry 9.99 for either of these columns indicates the [Fe/ H] value
was not calculated using this method. Columns 6 and 7 are the best estimate [Fe/ H]

and its corresponding uncertainty.

152

 

 

 

153

Table A1 Photometric Metallicity
NSVS ID [F6/H]Ap GAP [F6/H]JK O'JK [Fe/H] 0[Fe/H]
47456 -1.47 0.30 —1.84 0.19 -1.73 0.16
95598 -2.17 0.30 -2.32 0.19 -2.28 0.16
219254 -1.16 0.30 9.99 9.99 -1.16 0.30
253438 -1.71 0.30 9.99 9.99 -1.71 0.30
258743 -0.49 0.30 -0.06 0.29 -0.27 0.21
272579 -1.20 0.30 -1.38 0.23 -1.31 0.18
653553 -1.37 0.30 -1.22 0.29 -1.29 0.21
660817 -1.95 0.30 -1.57 0.21 -1.69 0.17
683309 -2.56 0.30 9.99 9.99 -2.56 0.30
768199 -1.86 0.30 -2.44 0.24 -2.22 0.19
777166 -1.83 0.30 -1.64 0.27 -1.73 0.20
877851 -2.18 0.30 -1.79 0.21 -1.92 0.17
887046 -1.63 0.30 -1.27 0.21 -1.39 0.17
933594 -1.47 0.30 -1.57 0.27 -1.53 0.20
972122 -1.20 0.30 -0.71 0.32 {-0.97] 0.22
975558 -2.24 0.30 -1.89 0.23 -2.02 0.18
979936 -1.47 0.30 -1.95 0.29 -1.72 0.21
1048200 -1.51 0.30 -1.33 0.24 -1.40 0.19
1062497 -1.39 0.30 -1.85 0.21 -1.69 0.17
1117769 -1.74 0.30 -1.30 0.29 -1.51 0.21
1127821 -1.49 0.30 9.99 9.99 -1.49 0.30
1132042 -1.57 0.30 -1.50 0.26 -1.53 0.20
1156866 -2.16 0.30 -2.53 0.23 -2.39 0.18
1227428 -0.58 0.30 9.99 9.99 -0.58 0.30
1251329 -2.23 0.30 -1.58 0.21 -1.80 0.17
1328589 -1.87 0.30 -1.90 0.21 -1.89 0.17
1363670 -0.91 0.30 -0.88 0.23 -0.89 0.18
1376650 -0.95 0.30 -0.32 0.25 -0.58 0.19
1412375 -1.59 0.30 -1.46 0.23 -1.51 0.18
1437682 -2.19 0.30 -2.64 0.25 -2.46 0.19
1633417 -1.46 0.30 9.99 9.99 -1.46 0.30
1693393 -1.33 0.30 9.99 9.99 -1.33 0.30
1731449 -0.49 0.30 -0.67 0.21 -0.61 0.17
1751270 -0.49 0.30 9.99 9.99 -0.49 0.30
1945919 -1.82 0.30 -1.68 0.22 -1.73 0.18

Table A.1 (cont’d)

 

 

 

154

NSVS ID [Fe/[1],”: O'Ap [Fe/H]JK O'JK [FE/H] U[Fe/H]
2029729 -1.19 0.30 -0.23 0.27 -0.65 0.20
2132727 -1.78 0.30 9.99 9.99 -1.78 0.30
2198205 -2.29 0.30 -2.11 0.23 -2.17 0.18
2284758 -2.06 0.30 -1.54 0.26 -1.76 0.20
2431223 -1.60 0.30 -1.82 0.22 -1.74 0.18
2462143 -1.37 0.30 -1.57 0.23 -1.50 0.18
2508765 -1.52 0.30 -1.89 0.27 -1.72 0.20
2543920 -1.90 0.30 -2.17 0.24 -2.06 0.19
2549610 -2.47 0.30 -2.32 0.23 -2.38 0.18
2587991 -1.26 0.30 9.99 9.99 -1.26 0.30
2589437 -2.01 0.30 -1.78 0.21 -1.85 0.17
2595352 -1.34 0.30 -1.43 0.23 -1.40 0.18
2601261 -2.42 0.30 9.99 9.99 -2.42 0.30
2610846 -1.71 0.30 -1.64 0.29 -1.67 0.21
2676458 -1.98 0.30 -2.16 0.27 -2.08 0.20
2681536 -1.07 0.30 -1.27 0.22 -1.20 0.18
2696951 -1.81 0.30 -1.74 0.21 -1.76 0.17
2731333 -1.78 0.30 -1.37 0.27 -1.55 0.20
2737869 -1.88 0.30 -2.12 0.24 -2.02 0.19
2745643 -1.61 0.30 -1.52 0.22 -1.55 0.18
2773160 -1.79 0.30 9.99 9.99 -1.79 0.30
2792534 -1.76 0.30 9.99 9.99 -1.76 0.30
2810184 -1.53 0.30 -1.55 0.28 -1.54 0.20
2830505 -1.05 0.30 -1.42 0.28 -1.25 0.20
2909040 -1.77 0.30 9.99 9.99 -1.77 0.30
2927295 -1.11 0.30 9.99 9.99 -1.11 0.30
2927471 -1.31 0.30 -1.63 0.24 -1.50 0.19
2930718 -1.30 0.30 -1.21 0.24 -1.25 0.19
3022099 -0.75 0.30 -1.06 0.22 -0.95 0.18
3030972 -2.08 0.30 -1.79 0.20 -1.88 0.17
3078092 -1.14 0.30 -1.45 0.19 -1.36 0.16
3087037 -1.25 0.30 —0.96 0.25 -1.08 0.19
3117503 -2.19 0.30 -1.95 0.19 -2.02 0.16
3306144 -1.03 0.30 -0.51 0.24 -0.71 0.19
3611791 -0.67 0.30 -0.29 0.24 -0.44 0.19

Table A.1 (cont’d)

 

 

155

NSVS ID [FE/HlAp UAP [Fe/H]JK O'JK [FE/H] U[Fe/H]
3619355 -1.22 0.30 -1.35 0.22 -1.31 0.18
3633663 -2.05 0.30 -2.54 0.22 -2.37 0.18
3713191 -1.64 0.30 -1.90 0.21 -1.82 0.17
3817372 -2.53 0.30 -2.03 0.21 -2.20 0.17
3939459 -1.96 0.30 -0.76 0.31 -1.38 0.22
3962805 -0.85 0.30 -0.53 0.29 -0.68 0.21
3963833 -1.13 0.30 -0.73 0.22 -0.87 0.18
3964415 -2.45 0.30 -3.15 0.23 -2.89 0.18
3994860 -2.26 0.30 -2.76 0.26 -2.54 0.20
4160839 -1.80 0.30 -2.00 0.25 -1.92 0.19
4180591 0.12 0.30 9.99 9.99 0.12 0.30
4241455 -1.40 0.30 -1.37 0.22 -1.38 0.18
4275987 -0.32 0.30 -0.12 0.24 -0.20 0.19
4493602 -1.48 0.30 9.99 9.99 -1.48 0.30
4661441 -1.35 0.30 -1.65 0.25 -1.53 0.19
4694845 -0.83 0.30 -0.67 0.20 -0.72 0.16
4700160 -1.28 0.30 -1.38 0.28 -1.34 0.20
4720404 -1.16 0.30 0.58 0.28 -0.23 0.21
4760770 —0.91 0.30 -2.97 0.17 {-2.47] 0.15
4762874 -1.67 0.30 -2.04 0.27 -1.88 0.20
4820869 -1.44 0.30 9.99 9.99 -1.44 0.30
4828496 -1.38 0.30 -1.51 0.21 -1.47 0.17
4837927 -1.47 0.30 9.99 9.99 -1.47 0.30
4838954 -1.62 0.30 -1.23 0.25 -1.39 0.19
4876765 -1.59 0.30 -1.48 0.26 -1.53 0.20
4930109 -2.48 0.30 -1.90 0.24 -2.13 0.19
4959080 -1.36 0.30 9.99 9.99 -1.36 0.30
4979454 -1.37 0.30 9.99 9.99 -1.37 0.30
4990594 -1.34 0.30 3-1.72 0.23 -1.58 0.18
4993764 -2.02 0.30 -1.79 0.21 -1.87 0.17
4996441 -2.43 0.30 -2.08 0.24 -2.22 0.19
4998847 -1.60 0.30 -1.47 0.21 -1.51 0.17
5007979 -1.05 0.30 -0.74 0.26 -0.88 0.20
5013760 —1.50 0.30 -1.58 0.21 -1.56 0.17
5028197 -2.39 0.30 -1.95 0.21 -2.10 0.17

Table A.1 (cont’d)

 

 

156

NSVS ID [Fe/H]Ap O'Ap [F6/H]JK O'JK [FE/H] 0[Fe/H]
5034190 -2.19 0.30 -1.78 0.28 -1.97 0.20
5039296 -1.30 0.30 9.99 9.99 -1.30 0.30
5039914 -2.18 0.30 9.99 9.99 -2.18 0.30
5047909 -1.51 0.30 -1.43 0.24 -1.46 0.19
5058465 -1.81 0.30 -1.81 0.27 -1.81 0.20
5089958 -1.20 0.30 -1.61 0.29 -1.41 0.21
5090118 -1.29 0.30 -1.70 0.22 -1.55 0.18
5113606 -2.22 0.30 -1.91 0.22 -2.02 0.18
5120617 -1.55 0.30 -1.49 0.23 -1.51 0.18
5133135 -2.19 0.30 -1.65 0.21 -1.83 0.17
5144530 -1.41 0.30 -1.19 0.28 -1.29 0.20
5149126 -1.50 0.30 -1.54 0.19 -1.53 0.16
5152352 0.26 0.30 9.99 9.99 [0.26] 0.30
5181224 -0.18 0.30 -1.63 0.21 {-1.15} 0.17
5206471 -1.25 0.30 9.99 9.99 -1.25 0.30
5207932 -1.39 0.30 9.99 9.99 -1.39 0.30
5216041 -1.47 0.30 9.99 9.99 —1.47 0.30
5222075 -0.61 0.30 9.99 9.99 -0.61 0.30
5222117 -1.60 0.30 9.99 9.99 -1.60 0.30
5232275 -1.85 0.30 9.99 9.99 -1.85 0.30
5248399 -2.24 0.30 -1.92 0.21 -2.03 0.17
5249019 -2.43 0.30 -2.05 0.22 -2.18 0.18
5249836 -2.41 0.30 -1.67 0.25 -1.98 0.19
5250334 -2.10 0.30 -2.04 0.29 -2.07 0.21
5259122 -1.60 0.30 9.99 9.99 -1.60 0.30
5270815 -1.42 0.30 -1.19 0.23 -l.28 0.18
5288795 -1.92 0.30 -2.29 0.27 -2.12 0.20
5300614 -1.89 0.30 9.99 9.99 -1.89 0.30
5301154 -1.46 0.30 9.99 9.99 -1.46 0.30
5316660 -1.07 0.30 9.99 9.99 -1.07 0.30
5401722 -1.44 0.30 9.99 9.99 -1.44 0.30
5406476 -2.14 0.30 -1.92 0.28 -2.02 0.21
5415960 -1.49 0.30 9.99 9.99 -1.49 0.30
5484202 -1.64 0.30 9.99 9.99 -1.64 0.30
5494745 -1.47 0.30 -1.45 0.23 -1.46 0.18

Table A.1 (cont’d)

 

 

157

NSVS ID [Fe/HjAp O'Ap [F8/H]JK O’JK [FE/H] 0[Fe/H]
5525580 -1.85 0.30 -1.83 0.27 -1.84 0.20
5526812 -1.41 0.30 -1.87 0.21 -1.72 0.17
5568043 -2.57 0.30 -2.00 0.25 -2.23 0.19
5568339 -1.36 0.30 -1.10 0.25 -1.20 0.19
5587647 —1.36 0.30 9.99 9.99 -1.36 0.30
5654619 -0.65 0.30 9.99 9.99 -0.65 0.30
5666134 -1.62 0.30 9.99 9.99 -1.62 0.30
6094124 -2.21 0.30 -1.87 0.20 -1.97 0.17
6231458 -1.69 0.30 -1.62 0.23 -1.65 0.18
6248007 -2.00 0.30 -1.63 0.23 -1.76 0.18
6264114 -1.57 0.30 9.99 9.99 -1.57 0.30
6302329 -0.57 0.30 -0.30 0.23 -0.40 0.18
6392775 -1.50 0.30 -1.64 0.21 -1.59 0.17
6429831 -1.75 0.30 -1.16 0.26 -1.42 0.20
6480339 -0.71 0.30 -1.17 0.22 [-1.01] 0.18
6705217 -0.78 0.30 -0.53 0.25 -0.63 0.19
6808365 -0.91 0.30 9.99 9.99 -0.91 0.30
6860143 -0.73 0.30 -0.51 0.22 -0.59 0.18
6885646 -1.19 0.30 9.99 9.99 -1.19 0.30
6899769 -1.73 0.30 -1.47 0.26 -1.58 0.20
7058441 -0.63 0.30 9.99 9.99 -0.63 0.30
7231539 -0.62 0.30 -0.55 0.20 -0.58 0.17
7235546 -1.89 0.30 -1.48 0.21 -1.61 0.17
7267812 -0.95 0.30 -0.43 0.29 -0.68 0.21
7394810 -1.98 0.30 -1.88 0.20 -1.91 0.17
7404883 -1.34 0.30 -1.75 0.28 -1.56 0.20
7411607 -1.66 0.30 -1.56 0.23 -1.60 0.18
7412670 -1.47 0.30 -1.22 0.23 -1.31 0.18
7454552 -1.51 0.30 9.99 9.99 -1.51 0.30
7458704 -1.70 0.30 -1.98 0.23 -1.87 0.18
7472262 -1.62 0.30 -2.06 0.21 -1.91 0.17
7484923 -1.54 0.30 -1.34 0.23 -1.41 0.18
7496219 -1.37 0.30 -1.37 0.19 -1.37 0.16
7496252 -1.50 0.30 -1.20 0.25 -1.32 0.19
7512212 -1.78 0.30 -1.31 0.23 -1.48 0.18

Table A.1 (cont’d)

 

 

158

NSVS ID [F6/H]Ap O'Ap [F8/H]JK O'JK [FE/H] 0[Fe/H]
7517103 -1.64 0.30 —1.53 0.24 -1.57 0.19
7539425 -1.76 0.30 9.99 9.99 -1.76 0.30
7540718 -1.66 0.30 -1.42 0.20 -1.49 0.17
7554734 -2.37 0.30 9.99 9.99 -2.37 0.30
7564332 -1.79 0.30 -1.34 0.24 -1.51 0.19
7585321 -1.52 0.30 -1.72 0.20 -1.66 0.17
7614129 -1.29 0.30 -1.24 0.23 -1.26 0.18
7635590 -1.95 0.30 -1.77 0.19 -1.83 0.16
7643254 -2.09 0.30 -4.01 0.18 -3.49 0.16
7649368 -1.47 0.30 -1.39 0.25 -1.43 0.19
7654631 -2.07 0.30 -1.76 0.20 -1.86 0.16
7656719 -1.18 0.30 9.99 9.99 -1.18 0.30
7666038 -2.44 0.30 -2.18 0.25 -2.29 0.19
7685674 -1.92 0.30 9.99 9.99 -1.92 0.30
7703549 -1.65 0.30 -1.79 0.20 -1.75 0.17
7706106 -1.73 0.30 -1.97 0.21 -1.89 0.17
7709213 -1.87 0.30 -1.69 0.20 -1.74 0.17
7711863 -1.23 0.30 0.03 0.27 -0.53 0.20
7726595 -1.71 0.30 -1.64 0.23 -1.67 0.18
7741095 -2.07 0.30 -2.27 0.24 -2.19 0.19
7742142 -1.42 0.30 -1.45 0.22 -1.44 0.18
7752384 -1.47 0.30 -1.63 0.19 -1.59 0.16
7753756 -1.38 0.30 9.99 9.99 -1.38 0.30
7755406 -0.47 0.30 -0.53 0.20 -0.51 0.17
7756950 -1.68 0.30 -1.53 0.25 -1.59 0.19
7777447 -2.07 0.30 -1.79 0.27 —1.92 0.20
7783855 -2.17 0.30 -2.49 0.22 -2.38 0.18
7785359 -1.30 0.30 -1.27 0.22 -1.28 0.18
7799920 -1.90 0.30 -1.98 0.19 -1.96 0.16
7818285 -1.36 0.30 -1.47 0.19 -1.44 0.16
7823144 -2.17 0.30 -1.82 0.22 -1.94 0.18
7824713 -1.80 0.30 -1.44 0.23 -1.57 0.18
7826584 -1.89 0.30 -2.01 0.24 -1.96 0.19
7861269 -1.07 0.30 -1.06 0.29 -1.06 0.21
7866619 -2.15 0.30 -2.01 0.21 -2.06 0.17

Table A.1 (cont’d)

 

 

159

NSVS ID [F6/H]Ap GAP [Fe/H]JK UJK [FE/H] 0[Fe/H]
7871803 -3.41 0.30 -2.68 0.26 -2.99 0.20
7872648 -1.94 0.30 -2.07 0.22 -2.03 0.18
7912479 -2.43 0.30 9.99 9.99 -2.43 0.30
7919183 —1.54 0.30 -1.97 0.21 -1.83 0.17
7927997 -2.01 0.30 -1.77 0.21 -1.85 0.17
7954067 -1.27 0.30 -1.35 0.18 -1.32 0.16
7962127 -1.19 0.30 9.99 9.99 -1.19 0.30
7970685 -1.17 0.30 -1.27 0.26 -1.23 0.20
7990146 -1.52 0.30 -1.79 0.23 -1.69 0.18
7998286 -0.83 0.30 9.99 9.99 -0.83 0.30
8023769 -0.83 0.30 -0.63 0.20 -0.69 0.17
8050089 -1.52 0.30 -1.16 0.30 -1.34 0.21
8108614 -1.66 0.30 -1.47 0.21 -1.53 0.17
8125354 -1.44 0.30 -0.98 0.32 -1.22 0.22
8160195 -0.73 0.30 9.99 9.99 -0.73 0.30
8179854 -1.79 0.30 -1.40 0.27 -1.57 0.20
8192311 -2.23 0.30 9.99 9.99 -2.23 0.30
8234127 -1.69 0.30 -2.05 0.19 -1.94 0.16
8293251 -2.09 0.30 9.99 9.99 -2.09 0.30
8360536 -2.13 0.30 9.99 9.99 -2.13 0.30
8572436 -0.84 0.30 -1.08 0.24 -0.99 0.19
8651514 -1.36 0.30 -1.40 0.22 -1.38 0.18
8702062 -0.73 0.30 -0.49 0.21 -0.57 0.17
8706200 -2.08 0.30 -1.52 0.27 -1.77 0.20
8724691 -1.72 0.30 -2.00 0.28 -1.87 0.20
8770585 -0.98 0.30 -0.74 0.24 -0.83 0.19
8776606 -0.81 0.30 -0.49 0.27 -0.64 0.20
8782730 -2.14 0.30 9.99 9.99 -2.14 0.30
8783505 -1.70 0.30 -1.90 0.23 -1.83 0.18
8817268 -0.56 0.30 -0.09 0.26 -0.30 0.20
8877855 -1.18 0.30 9.99 9.99 -1.18 0.30
8903282 -1.25 0.30 -2.13 0.20 -1.86 0.17
8909217 -0.73 0.30 -0.80 0.27 -0.77 0.20
8951389 -1.33 0.30 -0.94 0.23 -1.09 0.18
8956174 -1.67 0.30 -1.70 0.21 -1.69 0.17

Table A.1 (cont’d)

 

 

 

NSVS ID [F6/H]Ap O’Ap [F6/H]JK O’JK [Fe/H] 0[Fe/H]
9047405 -1.10 0.30 -1.13 0.29 —1.12 0.21
9050491 -2.09 0.30 -1.72 0.24 -1.87 0.19
9063964 -2.90 0.30 -1.43 0.30 -2.16 0.21
9075932 -1.60' 0.30 -1.47 0.20 -1.51 0.17
9088465 -2.27 0.30 -1.90 0.22 -2.02 0.18
9091170 -1.76 0.30 9.99 9.99 -1.76 0.30
9130768 -1.89 0.30 -1.32 0.29 -1.60 0.21
9154382 -2.23 0.30 -1.69 0.26 -1.92 0.20
9230082 -1.91 0.30 9.99 9.99 -1.91 0.30
9240847 -0.74 0.30 9.99 9.99 —0.74 0.30
9254455 -1.51 0.30 -1.39 0.28 -1.45 0.21
9310411 -1.94 0.30 -2.14 0.20 -2.08 0.17
9338383 -1.31 0.30 -1.44 0.19 -1.40 0.16
9671363 -1.46 0.30 9.99 9.99 -1.46 0.30
9995853 -1.59 0.30 -1.70 0.19 -1.67 0.16
10083412 -1.40 0.30 9.99 9.99 -1.40 0.30
10141482 -1.39 0.30 -1.46 0.24 —1.43 0.19
10147460 -1.30 0.30 9.99 9.99 -1.30 0.30
10175326 -1.24 0.30 -1.60 0.21 -1.48 0.17
10203057 -2.02 0.30 -1.73 0.23 -1.84 0.18
10228104 -1.61 0.30 -1.08 0.27 -1.31 0.20
10235938 -2.39 0.30 -2.06 0.22 -2.18 0.18
10241977 -1.63 0.30 -1.27 0.26 -1.43 0.20
10329394 -1.54 0.30 9.99 9.99 -1.54 0.30
10332182 —1.24 0.30 -2.09 0.23 -1.78 0.18
10337183 -1.48 0.30 -0.90 0.28 -1.16 0.20
10338359 -2.12 0.30 -1.89 0.22 -1.97 0.18
10347356 -1.49 0.30 9.99 9.99 -1.49 0.30
10350273 -1.91 0.30 -1.97 0.27 -1.94 0.20
10352408 -1.17 0.30 -0.67 0.24 -0.86 0.19
10358221 -1.92 0.30 -1.94 0.24 -1.93 0.19
10360493 -1.48 0.30 -1.31 0.19 ' -1.36 0.16
10360815 -2.15 0.30 -1.71 0.20 -1.85 0.17
10360975 -1.98 0.30 -1.60 0.27 -1.77 0.20
10363810 -2.35 0.30 -2.00 0.29 -2.17 0.21

160

l

 

Table A.1 (cont’d)

 

 

NSVS ID [FE/HlAp GAP [F8/H]JK UJK [Fe/H] U[Fe/H]
10371698 -1.51 0.30 -1.12 0.30 -1.31 0.21
10395081 -1.64 0.30 -1.20 0.28 -1.41 0.20
10395582 -2.17 0.30 9.99 9.99 -2.17 0.30
10403252 -1.14 0.30 -1.62 0.28 -1.39 0.20
10418706 -1.57 0.30 9.99 9.99 -1.57 0.30
10431935 -0.95 0.30 9.99 9.99 {-0.95} 0.30
10437330 -1.88 0.30 -1.32 0.23 -1.53 0.18
10446172 -1.20 0.30 -1.33 0.20 -1.29 0.17
10451724 -1.55 0.30 -1.27 0.22 -1.37 0.18
10453784 -2.01 0.30 -2.12 0.21 -2.09 0.17
10464169 -1.80 0.30 -1.64 0.24 -1.71 0.19
10488920 -1.85 0.30 -1.84 0.25 -1.84 0.19
10491545 -1.37 0.30 -2.35 0.23 -1.99 0.18
10492034 -1.24 0.30 9.99 9.99 -1.24 0.30
10514624 -2.15 0.30 -1.76 0.22 -1.90 0.18
10530833 -2.07 0.30 9.99 9.99 -2.07 0.30
10531095 -1.84 0.30 -1.73 0.27 -1.78 0.20
10534194 -1.60 0.30 -0.84 0.31 -1.23 0.22
10547760 -1.67 0.30 9.99 9.99 -1.67 0.30
10549959 -2.02 0.30 9.99 9.99 -2.02 0.30
10567739 -2.20 0.30 9.99 9.99 -2.20 0.30
10591456 -1.24 0.30 -1.31 0.19 -1.29 0.16
10614618 -1.55 0.30 9.99 9.99 -1.55 0.30
10614900 -1.32 0.30 9.99 9.99 -1.32 0.30
10628156 -2.28 0.30 -1.83 0.26 -2.02 0.20
10642059 -1.86 0.30 -1.44 0.26 -1.62 0.20
10642884 -1.38 0.30 -0.52 0.23 -0.84 0.18
10647103 -1.56 0.30 -1.04 0.27 -1.28 0.20
10652318 -2.35 0.30 -2.13 0.23 -2.21 0.18
10685785 -1.57 0.30 -1.36 0.22 -1.43 0.18
10706905 -1.26 0.30 -1.46 0.18 -1.40 0.16
10751419 -2.14 0.30 9.99 9.99 -2.14 0.30
10758202 -1.40 0.30 9.99 9.99 -1.40 0.30
10767117 -0.41 0.30 -0.35 0.29 -0.38 0.21
10769204 -1.47 0.30 9.99 9.99 -1.47 0.30

161

Table A.1 (cont’d)

 

 

NSVS ID [FE/HjAp O’Ap [Fe/H]JK O'JK [Fe/H] 0[Fe/H]
10773700 -1.04 0.30 9.99 9.99 -1.04 0.30
10781555 -1.57 0.30 -1.80 0.20 -1.73 0.17
10782844 -1.99 0.30 -1.61 0.25 -1.76 0.19
10806470 -2.26 0.30 9.99 9.99 -2.26 0.30
10824625 -1.83 0.30 9.99 9.99 -1.83 0.30
10824661 -1.45 0.30 -1.12 0.21 -1.23 0.17
10869885 -0.54 0.30 9.99 9.99 -0.54 0.30
10885456 -0.45 0.30 9.99 9.99 -0.45 0.30
10887396 -1.58 0.30 9.99 9.99 -1.58 0.30
10891107 -1.08 0.30 9.99 9.99 -1.08 0.30
10905292 -1.79 0.30 9.99 9.99 -1.79 0.30
10955591 —0.11 0.30 -0.85 0.23 -0.58 0.18
10994614 -1.57 0.30 -1.81 0.23 -1.72 0.18
11015121 -1.50 0.30 9.99 9.99 -1.50 0.30
11061928 -1.65 0.30 9.99 9.99 -1.65 0.30
11327182 -1.07 0.30 9.99 9.99 -1.07 0.30
11379204 -0.98 0.30 -1.19 0.21 {-1.12] 0.17
11420828 -1.29 0.30 9.99 9.99 -1.29 0.30
11491796 -0.67 0.30 -0.38 0.25 -0.50 0.19
11527986 -1.23 0.30 -1.28 0.29 -1.25 0.21
11533492 -0.70 0.30 -0.49 0.24 -0.57 0.19
11622871 -1.13 0.30 9.99 9.99 -1.13 0.30
11643237 -1.46 0.30 9.99 9.99 -1.46 0.30
11647104 -2.78 0.30 9.99 9.99 -2.78 0.30
11656645 -0.98 0.30 -1.34 0.23 {-1.21] 0.18
11668678 -1.60 0.30 9.99 9.99 -1.60 0.30
11670319 -2.44 0.30 -2.12 0.22 -2.23 0.18
11672831 -0.41 0.30 -0.21 0.21 -0.27 0.17
11677349 -1.29 0.30 9.99 9.99 -1.29 0.30
11747453 -2.07 0.30 9.99 9.99 -2.07 0.30
11753751 —1.16 0.30 -1.18 0.22 -1.18 0.18
11757688 -1.44 0.30 -1.71 0.18 -1.64 0.16
11762920 -1.59 0.30 9.99 9.99 -1.59 0.30
11770209 -1.92 0.30 9.99 9.99 -1.92 0.30
11772445 -2.05 0.30 -1.36 0.21 -1.58 0.17

162

Table A.1 (cont’d)

 

 

163

NSVS ID [Fe/H]Ap O’Ap [Fe/H]JK UJK [Fe/H] ogre/H]
11798849 -1.56 0.30 9.99 9.99 -1.56 0.30
11803133 -1.59 0.30 -1.31 0.23 -1.42 0.18
11828256 -1.91 0.30 9.99 9.99 -1.91 0.30
11840237 -2.43 0.30 9.99 9.99 -2.43 0.30
11864349 -1.93 0.30 -1.17 0.29 -1.54 0.21
11869181 -1.73 0.30 -1.63 0.26 —1.67 0.19
11870671 -2.21 0.30 -1.67 0.21 -1.84 0.17
11872085 -1.97 0.30 -1.62 0.23 -1.75 0.18
11902531 -1.56 0.30 -2.14 0.24 -1.91 0.19
11910764 -1.27 0.30 -1.59 0.27 -1.45 0.20
11929610 -1.69 0.30 9.99 9.99 -1.69 0.30
11951363 -1.14 0.30 9.99 9.99 -1.14 0.30
11967991 -1.38 0.30 -1.49 0.29 -1.43 0.21
11990963 -2.30 0.30 -2.33 0.23 -2.32 0.18
11996470 -1.38 0.30 -1.58 0.23 -1.51 0.18
12007998 -1.41 0.30 -1.46 0.21 -1.44 0.17
12009122 -1.65 0.30 9.99 9.99 -1.65 0.30
12010601 -1.61 0.30 -1.40 0.25 -1.49 0.19
12073505 -2.95 0.30 —2.67 0.29 -2.80 0.21
12096932 -1.31 0.30 -2.31 0.22 -1.96 0.18
12140779 -0.42 0.30 -0.44 0.22 -0.43 0.18
12248877 -1.13 0.30 -0.98 0.28 -1.05 0.20
12250977 -1.21 0.30 9.99 9.99 -1.21 0.30
12252066 -2.45 0.30 9.99 9.99 -2.45 0.30
12370362 —1.50 0.30 9.99 9.99 -1.50 0.30
12678415 -1.40 0.30 -0.80 0.26 -1.06 0.20
12680188 —1.62 0.30 -0.36 0.27 —0.92 0.20
12680351 -2.12 0.30 -2.00 0.23 -2.05 0.18
12728156 -1.25 0.30 -0.32 0.26 -0.72 0.20
12778072 -1.37 0.30 -1.35 0.22 -1.35 0.18
12843002 -1.63 0.30 -2.14 0.19 -2.00 0.16
12871389 -2.25 0.30 9.99 9.99 -2.25 0.30
12872211 -1.47 0.30 9.99 9.99 -1.47 0.30
12880089 -1.26 0.30 -1.14 0.26 -1.19 0.20
12892356 -1.51 0.30 -0.96 0.32 -1.25 0.22

Table A.1 (cont’d)

 

 

 

 

NSVS ID [F8/H]Ap GAP [F6/H]JK O’JK [FE/H] 0[Fe/H]
12900308 -1.31 0.30 -2.80 0.26 -2.16 0.20
12916018 -1.06 0.30 9.99 9.99 -1.06 0.30
12919471 -0.00 0.30 9.99 9.99 -0.00 0.30
12929278 -2.48 0.30 -2.04 0.23 -2.20 0.18
12962968 -0.77 0.30 9.99 9.99 -0.77 0.30
12985723 -1.29 0.30 -1.18 0.27 -1.23 0.20
12990484 -1.69 0.30 -1.73 0.22 -1.72 0.18
13001998 -1.99 0.30 9.99 9.99 -1.99 0.30
13002450 -1.09 0.30 -1.42 0.23 -1.30 0.18
13017408 -2.40 0.30 -1.82 0.24 -2.04 0.19
13039828 -2.76 0.30 9.99 9.99 -2.76 0.30
13094756 -1.55 0.30 -0.98 0.24 -1.21 0.19
13095983 -1.59 0.30 -1.36 0.30 -1.47 0.21
13108142 -2.50 0.30 -2.26 0.20 -2.34 0.17
13124901 -1.85 0.30 9.99 9.99 -1.85 0.30
13151540 -2.02 0.30 -2.34 0.22 -2.22 0.18
13155113 -2.07 0.30 -1.87 0.20 -1.93 0.17
13196916 -1.75 0.30 -1.73 0.22 -1.73 0.18
13197108 -1.54 0.30 9.99 9.99 -1.54 0.30
13197686 -1.58 0.30 -1.75 0.22 -1.69 0.18
13207963 -2.62 0.30 -2.88 0.26 -2.77 0.20
13221776 -1.20 0.30 9.99 9.99 -1.20 0.30
13231809 -1.56 0.30 -1.87 0.18 -1.79 0.16
13236188 -1.81 0.30 9.99 9.99 -1.81 0.30
13264395 -1.95 0.30 -1.71 0.20 -1.78 0.16
13265072 -1.63 0.30 9.99 9.99 -1.63 0.30
13282686 -0.66 0.30 -1.84 0.18 {-1.52} 0.16
13287612 -2.36 0.30 9.99 9.99 -2.36 0.30
13288116 -1.76 0.30 -1.69 0.21 -1.71 0.17
13291329 -1.84 0.30 -2.30 0.26 -2.10 0.20
13294241 -2.48 0.30 9.99 9.99 -2.48 0.30
13302749 -1.46 0.30 9.99 9.99 -1.46 0.30
13311476 -1.94 0.30 9.99 9.99 -1.94 0.30
13322484 —0.92 0.30 -0.80 0.21 -0.83 0.17
13343221 -2.12 0.30 -1.66 0.28 -1.87 0.20

164

 

w-n-e- .

 

 

Table A.1 (cont’d)

 

 

NSVS ID [FE/H11”: GAP [F8/H]JK O'JK [Fe/H] 0[Fe/H]
13350457 -2.10 0.30 9.99 9.99 -2.10 0.30
13362899 -1.59 0.30 -1.93 0.22 -1.81 0.18
13373556 -1.53 0.30 9.99 9.99 -1.53 0.30
13373760 -2.04 0.30 9.99 9.99 -2.04 0.30
13377175 -2.30 0.30 -1.91 0.28 -2.09 0.20
13415461 -1.72 0.30 -1.31 0.22 -1.45 0.18
13419553 -1.61 0.30 -1.63 0.22 -1.63 0.18
13425077 -1.52 0.30 -1.86 0.22 -1.74 0.18
13425719 -1.38 0.30 -1.55 0.29 -1.47 0.21
13436085 -1.80 0.30 -1.91 0.22 -1.87 0.18
13437790 -2.01 0.30 -1.74 0.23 -1.84 0.18
13438360 -2.62 0.30 9.99 9.99 -2.62 0.30
13439616 -1.02 0.30 9.99 9.99 -1.02 0.30
13440706 -1.69 0.30 -1.48 0.29 -1.58 0.21
13444030 -1.45 0.30 -1.40 0.28 -1.42 0.20
13453020 -2.18 0.30 -1.85 0.25 -1.99 0.19
13456880 -2.56 0.30 -2.09 0.23 -2.26 0.18
13466900 -0.59 0.30 9.99 9.99 -0.59 0.30
13467814 -1.09 0.30 9.99 9.99 -1.09 0.30
13479853 -2.44 0.30 -1.84 0.27 -2.11 0.20
13489599 -1.76 0.30 9.99 9.99 -1.76 0.30
13504920 -1.12 0.30 9.99 9.99 -1.12 0.30
13533108 -2.11 0.30 9.99 9.99 -2.11 0.30
13551179 -1.94 0.30 9.99 9.99 -1.94 0.30
13567201 -2.10 0.30 9.99 9.99 -2.10 0.30
13570612 —1.53 0.30 9.99 9.99 —1.53 0.30
13572504 ~2.42 0.30 9.99 9.99 -2.42 0.30
13574815 -2.46 0.30 -1.95 0.31 -2.21 0.22
13578753 -1.43 0.30 9.99 9.99 -1.43 0.30
13644720 -1.92 0.30 -1.49 0.25 -1.67 0.19
13667152 -0.59 0.30 —0.86 0.28 -0.73 0.21
13682137 -1.30 0.30 9.99 9.99 -1.30 0.30
13687028 -2.20 0.30 9.99 9.99 -2.20 0.30
13688630 -1.88 0.30 -1.11 0.33 -1.53 0.22
13721372 -1.54 0.30 -1.65 0.26 -1.61 0.20

165

Table A.1 (cont’d)

 

 

NSVS ID [Fe/H)“: GAP [F6/H]JK O'JK [FE/H] 0[Fe/H]
13758491 -1.32 0.30 -1.16 0.24 ~1.22 0.19
13961527 -1.44 0.30 9.99 9.99 -1.44 0.30
14205594 -0.68 0.30 9.99 9.99 -0.68 0.30
14215652 -1.85 0.30 -2.14 0.25 -2.02 0.19
14266156 —0.62 0.30 9.99 9.99 -0.62 0.30
14279000 -1.32 0.30 9.99 9.99 -1.32 0.30
14284107 -2.03 0.30 -1.71 0.20 -1.81 0.17
14312323 -1.34 0.30 9.99 9.99 -1.34 0.30
14332976 -2.31 0.30 9.99 9.99 -2.31 0.30
14357980 -2.37 0.30 9.99 9.99 -2.37 0.30
14361529 -1.41 0.30 -1.06 0.30 -1.23 0.21
14371460 -1.53 0.30 -0.86 0.22 -1.09 0.18
14378728 -0.94 0.30 9.99 9.99 -0.94 0.30
14411401 -0.50 0.30 9.99 9.99 -0.50 0.30
14412075 -1.25 0.30 -1.66 0.18 -1.55 0.16
14433599 -1.29 0.30 9.99 9.99 -1.29 0.30
14439563 -1.63 0.30 -1.82 0.19 -1.77 0.16
14440338 -1.81 0.30 9.99 9.99 -1.81 0.30
14447741 -1.99 0.30 -2.24 0.25 -2.14 0.19
14487932 -1.38 0.30 1.09 0.33 {-0.26] 0.22
14495865 -1.39 0.30 9.99 9.99 -1.39 0.30
14505896 -1.32 0.30 -1.40 0.23 -1.37 0.18
14512123 -1.60 0.30 -1.37 0.28 -1.48 0.20
14528813 -1.32 0.30 9.99 9.99 -1.32 0.30
14554493 -2.15 0.30 -1.15 0.27 -1.61 0.20
14560814 -1.87 0.30 9.99 9.99 -1.87 0.30
14561489 -3.77 0.30 -3.93 0.27 -3.86 0.20
14564729 -012 0.30 9.99 9.99 {-0.12} 0.30
14581148 -1.23 0.30 9.99 9.99 -1.23 0.30
14617414 -1.31 0.30 -0.99 0.20 -1.09 0.17
14629388 -2.08 0.30 -1.66 0.26 -1.84 0.20
14641661 -1.34 0.30 -1.43 0.27 -1.39 0.20
14654206 -2.44 0.30 -2.64 0.24 -2.56 0.19
14669479 -1.26 0.30 9.99 9.99 -1.26 0.30
14682479 -1.09 0.30 9.99 9.99 -1.09 0.30

166

:1,- run-TI.

 

 

 

 

Table A.1 (cont’d)

 

 

167

NSVS ID [FE/HjAp UAP _ [F6/H]JK O'JK [FE/H] 0(Fe/H]
14685163 -1.89 0.30 9.99 9.99 -1.89 0.30
14698705 -1.96 0.30 9.99 9.99 -1.96 0.30
14715713 -1.18 0.30 9.99 9.99 -1.18 0.30
14762123 -1.42 0.30 -1.18 0.31 -1.30 0.21
14768130 -1.32 0.30 -1.22 0.20 -1.25 0.17
14782274 -2.21 0.30 9.99 9.99 -2.21 0.30
14791206 -2.21 0.30 9.99 9.99 —2.21 0.30
14818780 -2.29 0.30 -2.30 0.24 -2.30 0.19
14908249 -1.67 0.30 -0.93 0.25 -1.23 0.19
14910117 -1.47 0.30 9.99 9.99 -1.47 0.30
14915325 -1.21 0.30 9.99 9.99 -1.21 0.30
14925915 -2.46 0.30 9.99 9.99 -2.46 0.30
14941696 -1.44 0.30 -1.50 0.21 -1.48 0.17
14943427 -1.95 0.30 -1.87 0.19 -1.89 0.16
14979434 -1.31 0.30 9.99 9.99 -1.31 0.30
14990007 -1.29 0.30 -1.06 0.29 -1.17 0.21
15004446 -1.43 0.30 9.99 9.99 —1.43 0.30
15016349 -1.75 0.30 9.99 9.99 -1.75 0.30
15021359 -1.14 0.30 -0.84 0.30 -0.99 0.21
15206916 -1.02 0.30 9.99 9.99 -1.02 0.30
15218044 -0.76 0.30 9.99 9.99 -0.76 0.30
15657369 -1.52 0.30 -1.81 0.18 -1.73 0.16
15671445 -1.52 0.30 —1.66 0.24 -1.60 0.19
15679506 -1.31 0.30 9.99 9.99 -1.31 0.30
15681945 -1.97 0.30 9.99 9.99 -1.97 0.30
15692808 -2.33 0.30 9.99 9.99 -2.33 0.30
15726118 -1.41 0.30 9.99 9.99 -1.41 0.30
15781327 -1.32 0.30 -1.14 0.22 -1.20 0.18
15806847 -1.08 0.30 -1.14 0.22 -1.12 0.18
15820266 -2.06 0.30 9.99 9.99 -2.06 0.30
15827760 -1.98 0.30 -1.62 0.25 -1.76 0.19
15854954 -0.62 0.30 -0.93 0.20 -0.84 0.16
15889152 -1.96 0.30 -2.35 0.22 -2.21 0.18
15893670 -1.98 0.30 -1.96 0.24 -1.97 0.19
15896141 -2.07 0.30 9.99 9.99 -2.07 0.30

 

 

Table A.1 (cont’d)

 

 

NSVS ID [F6/H]Ap O'Ap [FE/HIJK UJK [FE/H] 0[Fe/H]
15897529 -1.75 0.30 9.99 9.99 -1.75 0.30
15901810 -1.90 0.30 9.99 9.99 -1.90 0.30
15972928 -1.98 0.30 -1.83 0.26 -1.89 0.20
15975024 -0.98 0.30 -1.19 0.26 {-1.10] 0.19
15977770 -1.50 0.30 -1.93 0.24 -1.77 0.19
15979689 -1.42 0.30 -1.24 0.29 -1.33 0.21
15985119 -1.70 0.30 9.99 9.99 -1.70 0.30
16053601 -1.28 0.30 9.99 9.99 -1.28 0.30
16100815 -0.96 0.30 9.99 9.99 -0.96 0.30
16109407 -2.53 0.30 9.99 9.99 —2.53 0.30
16117767 -1.63 0.30 9.99 9.99 -1.63 0.30
16127147 -1.17 0.30 9.99 9.99 -1.17 0.30
16155643 -1.71 0.30 —1.54 0.29 -1.62 0.21
16157754 -1.84 0.30 9.99 9.99 -1.84 0.30
16164702 -1.56 0.30 -1.34 0.26 —1.43 0.20
16184196 -1.44 0.30 9.99 9.99 -1.44 0.30
16185842 -1.09 0.30 -1.08 0.30 -1.09 0.21
16197858 -1.47 0.30 9.99 9.99 -1.47 0.30
16224995 -1.48 0.30 9.99 9.99 -1.48 0.30
16238329 -1.43 0.30 9.99 9.99 -1.43 0.30
16239733 -2.23 0.30 9.99 9.99 -2.23 0.30
16240332 -0.77 0.30 9.99 9.99 -0.77 0.30
16241026 -2.04 0.30 9.99 9.99 -2.04 0.30
16244466 -1.65 0.30 9.99 9.99 -1.65 0.30
16258860 -0.72 0.30 9.99 9.99 {-0.72] 0.30
16267747 -2.42 0.30 9.99 9.99 -2.42 0.30
16283172 -1.46 0.30 -0.94 0.28 -1.18 0.20
16292601 -1.51 0.30 9.99 9.99 -1.51 0.30
16304023 —1.41 0.30 -1.31 0.21 -1.34 0.17
16360132 -1.11 0.30 9.99 9.99 -1.11 0.30
16362273 -1.44 0.30 -0.94 0.26 -1.15 0.20
16372425 0.01 0.30 1.94 0.33 [0.88] 0.22
16372447 -1.04 0.30 -1.05 0.20 -1.05 0.17
17011064 -0.65 0.30 9.99 9.99 -0.65 0.30
17022191 -2.30 0.30 9.99 9.99 -2.30 0.30

168

 

 

' T‘. W,

 

Table A.1 (cont’d)

 

 

 

NSVS ID [F6/H]Ap GAP [F8/H]JK O'JK [FE/H] 0[Fe/H]
17109617 -1.38 0.30 -3.21 0.27 -2.40 0.20
17122030 -1.75 0.30 -1.84 0.30 -1.79 0.21
17130621 -1.63 0.30 9.99 9.99 -1.63 0.30
17147354 -1.64 0.30 9.99 9.99 -1.64 0.30
17176196 -0.24 0.30 9.99 9.99 -0.24 0.30
17212765 -2.02 0.30 -2.36 0.23 -2.23 0.18
17246508 -2.39 0.30 9.99 9.99 -2.39 0.30
17280732 -1.61 0.30 9.99 9.99 -1.61 0.30
17291542 -2.53 0.30 -2.86 0.29 -2.70 0.21
17293210 -2.21 0.30 9.99 9.99 -2.21 0.30
17295262 -2.13 0.30 9.99 9.99 -2.13 0.30
17331060 -1.66 0.30 -1.80 0.23 -1.75 0.18
17344990 -1.50 0.30 -2.02 0.24 -1.81 0.19
17348071 -2.19 0.30 -1.89 0.22 -2.00 0.18
17358579 -2.43 0.30 -1.94 0.22 -2.11 0.18
17368466 -1.96 0.30 -1.53 0.24 -1.70 0.19
17407836 -1.75 0.30 -1.24 0.25 -1.45 0.19
17438804 -1.82 0.30 -0.36 0.33 -1.15 0.22
17474384 -1.66 0.30 9.99 9.99 -1.66 0.30
17478335 -1.54 0.30 9.99 9.99 -1.54 0.30
17510931 -1.48 0.30 -2.50 0.24 -2.10 0.19
17530683 -1.80 0.30 -2.25 0.26 -2.06 0.20
17570707 0.05 0.30 9.99 9.99 0.05 0.30
17572475 -2.08 0.30 -1.84 0.21 -1.92 0.17
17578791 -1.36 0.30 -0.79 0.31 -1.09 0.22
17591359 -1.78 0.30 9.99 9.99 -1.78 0.30
17612485 -1.78 0.30 -2.10 0.25 -1.97 0.19
17620888 -1.27 0.30 9.99 9.99 -1.27 0.30
17633766 -1.35 0.30 -1.45 0.30 -1.40 0.21
17678949 -0.03 0.30 9.99 9.99 {—0.03] 0.30
17702479 -1.34 0.30 -1.14 0.25 -1.23 0.19
17765419 -1.10 0.30 -1.01 0.23 -1.04 0.18
17826311 -1.59 0.30 9.99 9.99 -1.59 0.30
17866005 -2.96 0.30 9.99 9.99 -2.96 0.30
18443369 -1.37 0.30 9.99 9.99 -1.37 0.30

169

Table A.1 (cont’d)

 

 

 

NSVS ID [FEB/[1],”: GAP [FE/Hle O’JK [Fe/H] U[Fe/H]
18473830 -1.34 0.30 9.99 9.99 -1.34 0.30
18479042 -1.82 0.30 9.99 9.99 -1.82 0.30
18551452 -0.67 0.30 9.99 9.99 -0.67 0.30
18552406 0.10 0.30 9.99 9.99 0.10 0.30
18558434 -2.03 0.30 -2.98 0.19 -2.71 0.16
18577666 -2.40 0.30 -0.73 0.31 -1.59 0.22
18621887 -1.33 0.30 9.99 9.99 -1.33 0.30
18688076 -0.97 0.30 9.99 9.99 {-0.97} 0.30
18691062 -1.29 0.30 -1.56 0.28 -1.44 0.21
18714268 -1.16 0.30 -1.11 0.26 -1.13 0.20
19097293 -0.90 0.30 9.99 9.99 -0.90 0.30
19972017 -1.34 0.30 9.99 9.99 -1.34 0.30
19991510 -1.58 0.30 -1.41 0.24 -1.48 0.19

 

170

1";- 9‘5" .ivolux. '

’

 

Appendix B

NSVS RRab Parameters

 

The parameters obtained for the analysis of the RRab stars are listed here. This
table contains information for 608 RRab stars from the N SVS database. Column 1 is
the identification number of the star in from NSVS. Column 2 and 3 are the galactic
coordinates in degrees. Column 4 is the period. Column 5 is the amplitude scaled
onto the Johnson V filter system. Column 6 and 7 are the apparent V magnitude and
its uncertainty. Column 8 and 9 are the best estimate [Fe/ H] value and its uncertainty.
Column 10 and 11 are the distance to the star and the Z distance from the Galactic
plane in units of kiloparsec. Column 12 and 13 are the absolute magnitude and its

uncertainty.

 

171

 

 

 

 

25 2.3 2.2 22 as 2.2- 2.8 2.2 So 823 822.2 222.22 2822
.25 as 2.2 22.. and 22- :s 2.2 as 22.3 22222 222.82 2222
28 Es 2.“ :2. as $2- :8 3.2 2.2 2.3.: 2:22 823.22 2:2:
28 as 2: was 28 8.2- :5 8.2 28 8%? 22.3.3. 22.832 32.22
25 28 :2 so.” 28 32- 2.: 8.2 22 2528 @2822” 23.2.22 82::
2.8 as 8.2 22 as 2.2- 28 2.: 2.9 2528 @8228 223.22 283
28 23 2.2 R.” 28 2.2 2.8 2.2 2.2 @288 2:22. 328.22 223
2.3 28 2E 2.” 28 :21 :8 8.2 88 2.3.1.8 222.2. 223.22 «22¢
2.o Ed was was 88 2.2- :s :2 m2 823 832.2 2:18.82 322
28 Es $8 :3 Ss 22- 2.2. 2.2 as 28215 222.2. 2.2832 2.22
28 :3 25 28 28 22- 25 2s :2 3888 228.2. 233.22 32%
28 as 2.1m m3. O28 2.2- :s 2.2 22 :28 882.2 $22.22 8::
Ed 28 22 2; 2.8 2.2 :8 $2 Ed 383 282.2“ 322.3 222:
2d 28 22 £2. and 8.2 2.0 2.2 23 888.8 $82.2 32.282 822
2s :3 82 ”Z 25 3.2. :s 8.2 2.2 2.33. 822.2 2532 228
2.0 23 8.2 m: as 2.2- :8 5.2 2: $23 582: 238.22 2.22
28 88 Rd 2.2 2.2. :2- :s 2.2 23 :22. 238.2 282.2 222
25 as and 2.2 as as- :8 2.2 m; 2.23 222.2 88822 2.22
2.o as as 22 one :2- :8 32 2:. 223 538.: $28.22 22.2“
28 Ed mod 2; and 2.2- o; 2.2 23 $288 33.2.: 282.2 322
Ed :8 2.2 22 2d 2.2 :8 3.2 2: 2228 282.2 22.232 2me
2.3 as 23 2.2 2.: 2.2- 2.: 8.2 82 22.1.8 22.3.2 228.22 3%
39¢ 85 was 3 3
45 >2 N m is 2:11.: Es >5 >< m 2 s 9 252
82892 2.22 262 .3 @321

172

 

28 88 8.8 :8 2.8 8.8- :8 2.2 :2 8288 8:88 888.2 2888
28 88 8.8 88 2.8 88- :8 2.2 88 88.8 E888 888.82 8888
28 88 8.2 88 88 2.2- :8 8.2 :8 8888 288.8 888.82 888
28 88 8.8 8.2 28 8.2.. 28 8.2 88 888.8 828.8 88882 888
28 88 8.2 8.8 28 8.2- :8 8.2 8.8 888 888.8 888.2 8288
28 8.8 88 8.8 88 2.2- :8 2.2 :2 8888 888.2 882.22 8888
28 88 88 88 28 2.8- :8 8.2 8.2 888 888.2 888.82 8888
28 88 28 8.2 88 8.2- :8 8.2 8.8 8888 8888 888.82 8828
2.8 88 88 8.8 88 88- 28 2.: 88 828 228$ 888.82 8288
28 88 88- :8 28 2.2- :8 8.2 8.8 888 888.8- 8882 2882
28 88 88- 8.2 88 88.. :8 8.2 88 :88 8888- 88282 8282
2.8 88 88- 88 28 88- 28 2.2 88 828 888.8- 288.2 8222
28 88 88 28 8.8 8.2- :8 8.2 88 8888 8888 828.82 8882
28 88 8.8 28 88 8.2- :8 8.2 8.8 8888 8888 888.82 22.82
28 88 8.8 8.2 28 8.8- :8 2.2 8.8 888.8 2882 8282.22 82.82
2.0 88 88 8.2 28 8.2- :8 8.2 8.2 88.8 288.2 8888: 8.4.2:
28 88 28 88 28 88- :8 8.2 2.2 888 888.: 8828.22 8882
28 :8 88 8.2 28 8.8- :8 8.2 8.2 8888 828.: 888.2 8882
28 88 88 88 28 8.2- :8 2.2 8.2 8888 888.8 888.82 8882
28 88 8.2 8.8 28 8.2- :8 8.2 8.2 888 882.8 228.22 822
28 8.8 2.8 88 8.8 88- :8 8.2 88 E88 8888 £88.82 8882
28 88 8.2 8.8 28 88- :8 8.2 88 288 882.8 888.22 8822
39: sec 883 E 3
:8 8 N a is 251.: Es >5 3.. m N s 8 m>mz

 

 

8.83 am @521

173

 

 

 

28 8.8 2.8 88 2.8 8.2 8.8 88 2.2 888.8 888.2 888.8 8828
2.8 8.8 8.8 8.8 2.8 8.2- :8 8.2 2.2 8888 888.8 888.8 2888
8.8 8.8 8.8 8.8 2.8 8.8-. 2.8 2.2 8.8 888.8 888.8 888.8 8828
2.8 8.8 8.8 8.2 2.8 8.2 2.8 8.2 2.8 288.8 888.8 888.8 2888
2.8 88 8.2 8.8 2.8 8.2 :8 8.2 8.8 888.8 882.8 888.8 2888
2.8 2.8 8.2 88 8.8 :2- :8 8.2 8.8 888.8 828.8 888.8 8288
2.8 8.8 8.8 8.8 8.8 2.2 :8 8.2 8.8 888.8 888.8 882.8 8888
2.8 8.8 8.8 82 88 8.2 2.8 8.: 2.2 888.8 888.8 888.8 8888
2.8 88 88 88 8.8 8.2 :8 8.2 8.2 828.8 888.8 882.8 8228
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8.253 am @88-

199

Appendix C

N SVS RRC Parameters

The parameters obtained for the RRC stars are presented here. This table contains
information for 375 RRC stars from the NSVS database. Column 1 is the ID of the
star in the NSVS database. Column 2 and 3 are the galactic coordinates in degrees.
Column 3 is the period of the RRC star. Column 4 is the amplitude scaled onto the
Johnson V filter system. Column 5 is the intensity weighted mean magnitude in the

ROTSE-I magnitude system.

200

Table C.1.

NSVS RRC Properties

 

 

NSVS id

1

O

b

O

P
days

Av

 

100670
100771
274511
275145
358966
431054
445756
530227
576841
644472
766402
1045426
1046926
1048405
1089620
1132768
1136059
1184638
1206915
1221668
1228707
1230621
1274340
1293676
1357112
1411823
1420035
1487938
1961900
1996966
2005448
2099913
2273941
2354674

129.270416
129.917755
126.721222
126.022820
126.314789
131.741852
133.383270
138.539963
135.617981
141.356979
142.179657
117.731552
113.273239
112.257011
102.383820
114.020813
108.439919
102.028183
101.185959
104.933861
102.879326
104.143295
112.659676
110.970345
106.880234
118.355530
118.840981
115.718384
144.270157
139.009735
139.510651
151.333603
155.765778
152.651657

29.883783
31.728859
19.011028
15.614045
11.221107
14.718515
19.140774
16.372107
20.534494
19.842054
30.800709
33.386520
34.792645
34.701321
32.977276
25.860584
27.273951
29.995337
24.201981
21.801950
19.745369
19.597635
19.836754
25.083467
12.709002
21.920290
19.869600
2.980748
-1.629497
3.613680
5.893476
1.205521
15.256597
26.209362

201

0.27721
0.29152
0.23642
0.22690
0.23345
0.33096
0.31800
0.38671
0.29355
0.33203
0.26704
0.23623
0.24004
0.30951
0.23980
0.32676
0.25858
0.22852
0.26089
0.27972
0.32675
0.35713
0.24674
0.31116
0.31425
0.30347
0.42677
0.43508
0.34256
0.34733
0.27258
0.38150
0.30468
0.41883

0.83
0.40
0.51
0.44
0.68
0.43
0.53
0.40
0.43
0.76
0.51
0.51
0.60
0.40
0.41
0.54
0.41
0.48
0.53
0.64
0.63
0.37
0.61
0.14
0.51
0.54
0.60
0.46
0.56
0.66
0.29
0.43
0.38
0.69

13.67
12.59
12.71
12.55
13.61
12.44
13.44
10.68
11.80
13.99
11.89
13.48
13.28
13.48
10.90
12.31
12.12
11.91
11.94
12.31
13.57
11.77
13.70
13.73
12.92
12.10
13.33
12.45
12.20
12.77
11.63
13.27
12.87
13.62

Table C.1 (cont’d)

 

 

NSVS id

1

O

b

O

P
days

Av

 

2355916
2388495
2389900
2413271
2468181
2506354
2545934
2672695
2733101
2812349
2823966
2829408
2880024
2941753
2957161
3014041
3037032
3041762
3117162
3143986
3197352
3224111
3275156
3310907
3625232
3652211
3732137
3778236
3795183
3802178
3867878
3871660
3936667
3962006

152.101929
155.538605
151.971161
159.193298
151.919724
160.916275
148.834305
119.577309
104.792572
88.509232
83.755150
83.623642
95.594063
84.019463
93.016953
94.175804
88.018242
87.580826
97.232666
98.425873
98.581642
90.872154
95.585999
99.226440
109.985779
116.345078
118.991379
119.446762
123.323280
125.153069
128.791397
129.671204
135.261688
134.249710

26.718040
29.288443
29.595310
27.554525
36.162468
38.739815
43.009747
59.516796
57.222061
47.751503
44.021393
42.031776
36.101936
26.787584
31.605032
23.955090
25.212988
23.990103
22.090036
17.204224
13.100430
11.626518
4.372744
10.250599
-22.342701
-18.681414
-13.529486
-22.456173
-20.559044
-22.948662
-14.353570
-16.243986
-9.242709
-17.003263

202

0.26703
0.42274
0.39395
0.34031
0.25239
0.34527
0.29850
0.23332
0.27428
0.40645
0.30629
0.28345
0.34178
0.23929
0.27618
0.34808
0.29869
0.29551
0.35856
0.38812
0.40417
0.39673
0.42894
0.22612
0.28277
0.26020
0.39196
0.22561
0.28617
0.25348
0.30542
0.37919
0.49010
0.23681

0.36
0.55
0.33
0.35
0.45
0.54
0.46
0.38
0.29
0.52
0.44
0.46
0.61
0.53
0.46
0.33
0.33
0.35
0.60
0.61
0.32
0.33
0.61
0.62
0.49
0.74
0.69
0.93
0.38
0.54
0.59
0.38
0.46
0.35

12.78
12.25
11.51
12.40
12.90
11.62
11.21
11.93
11.83
13.36
11.81
13.13
13.76
13.44
13.32
11.60
9.31

11.82
13.09
13.03
12.04
11.61
10.15
12.77
13.46
13.65
12.46
13.82
13.25
13.06
12.83
12.72
12.90
12.14

Table C.l (cont’d)

 

 

N SVS id

1

O

b

O

P
days

 

3964811
3965004
4173293
4180588
4248644
4291961
4330579
4497479
4511557
4515424
4696344
4721053
4830676
4832302
4854765
4878614
4894894
4909939
4934543
4959078
4966884
4969618
5071531
5082447
5225506
5253581
5258665
5271037
5334748
5339632
5394110
5396898
5403828
5414485

137.846313
135.512466
155.768494
153.414734
151.404312
158.074448
160.262268
162.263184
170.483322
172.028641
179.106812
174.765060
178.798431
180.630783
169.949371
162.192307
180.365723
175.016754
157.345261
173.677475
173.532013
164.758789
100.690086
100.099426
68.098763

71.334785

64.146767

73.944229

66.803291

69.376541

78.225723

76.539467

74.857765

75.463776

-23.845339
-18.338594
-13.889706
-8.826829
0.311229
-1.146471
-4.489732
14.304114
4.301557
4.303196
20.683613
28.021643
42.409698
42.926617
43.032730
47.161285
49.428013
56.116264
55.663219
61.183609
65.779640
65.519691
69.154335
73.423172
49.855972
39.730148
38.476971
42.837440
34.532963
33.561829
30.559233
29.710617
27.902426
25.678295

203

0.28778
0.30612
0.31275
0.29741
0.24987
0.26831
0.33799
0.25770
0.42967
0.41016
0.34197
0.33961
0.31036
0.22951
0.24062
0.35565
0.35877
0.36000
0.34942
0.28845
0.31801
0.23804
0.30541
0.27669
0.31710
0.33974
0.38488
0.23834
0.23564
0.46012
0.23409
0.29483
0.28024
0.29777

0.74
0.33
0.81
0.64
0.38
0.52
0.58
0.60
0.87
0.52
0.67
0.48
0.46
0.36
0.50
0.39
0.52
0.56
0.55
0.54
0.47
0.39
0.41
0.37
0.41
0.38
0.63
0.41
0.49
0.47
0.38
0.41
0.65
0.72

13.68
12.61
13.49
12.42
12.48
12.98
11.38
13.56
13.29
13.44
13.76
11.66
11.70
11.57
13.70
11.10
13.50
13.66
11.53
12.72
11.85
11.68
12.28
12.09
11.48
10.52
13.13
12.92
11.22
12.45
12.33
12.68
12.95
13.19

Table C.1 (cont’d)

 

 

NSVS id

1

O

b

O

P
days

Av

 

5422752
5423881
5445163
5497311
5526732
5597754
5602108
5645451
5649335
5856839
6117001
6129647
6176482
6202363
6218057
6254694
6259045
6304258
6326608
6335770
6364806
6371473
6391062
6396811
6410297
6429575
6441014
6455098
6504379
6551824
6566467
6624543
6687550
6734929

79.899796
76.987450
75.716408
71.201775
69.485527
78.800728
78.362946
81.266396
81.512070
93.123497
99.946220
99.705017
102.614426
108.889923
110.822098
110.471527
99.873497
116.072739
114.285416
116.56407 9
122.093323
124.015739
121.758667
124.115730
129.592896
125.946930
129.835052
134.183701
140.855545
144.825974
147.907349
155.811295
159.131775
166.790756

24.342773
23.841221
22.944822
19.366034
13.190183
13.355254
12.452659
10.122531
9.580833
1.179625
-12.188179
-16.594318
-10.657374
-7.890906
-9.777617
-28.154781
-34.215569
-34.739391
-28.895668
-30.082813
-26.826324
-27.041729
-36.284412
-36.961384
-38.159473
-26.660509
-30.907660
-31.575314
-36.956890
-27.980558
-25.504044
-27.048969
-14.885459
—23.197241

204

0.26912
0.27085
0.35511
0.31983
0.23691
0.22898
0.52312
0.33032
0.31438
0.35597
0.49062
0.40695
0.38046
0.31233
0.32823
0.22567
0.36721
0.28256
0.23733
0.27172
0.38759
0.24528
0.33825
0.24532
0.39034
0.26835
0.21714
0.35388
0.24022
0.24118
0.33164
0.32828
0.45362
0.41144

0.65
0.51
0.39
0.64
0.40
0.40
0.38
0.47
0.45
0.45
0.52
0.85
0.53
0.45
0.66
0.40
0.41
0.94
0.45
0.50
0.37
0.65
0.75
0.34
0.51
0.54
0.67
0.29
0.48
0.55
0.36
0.57
0.60
0.62

13.43
12.58
12.42
13.46
12.01
12.56
12.56
10.94
12.17
12.34
12.52
13.94
12.92
12.73
13.45
12.95
12.96
13.96
13.21
10.34
12.29
13.45
13.80
12.81
10.47
12.17
13.52
12.01
12.54
11.87
11.25
11.83
12.09
13.51

Table 0.1 (cont’d)

 

 

N SVS id

1

O

b

O

P
days

Av

 

6737414
6855021
6911093
7175575
7195883
7235165
7237529
7272542
7280723
7343080
7365267
7416581
7444716
7459875
7483757
7577789
7619767
7651368
7662319
7676759
7723298
7724334
7736895
7848125
7866630
7903602
7961459
7962118
8011261
8044823
8047300
8102280
8104613
8160526

164.945816
171.807343
176.230270
181.169540
181.027100
187.793808
185.228622
195.537552
195.045837
190.306610
190.005569
198.126633
186.544769
188.210327
206.451904
185.807037
231.008728
113.287689
321.271332
46.874016
47.463070
29.338892
38.129833
55.024960
46.140427
47.516312
61.754261
56.824986
49.696148
57.971466
63.018482
65.115730
62.104633
52.887600

-20.646034
—4.192020
-4.493929
13.058206
17.070852
20.237804
21.542217
16.891264
18.877190
27.514090
31.873558
39.134239
43.331841
46.720387
47.214970
69.155823
83.606888
79.992416
89.103676
81.376518
75.230606
74.380234
68.043030
49.004917
49.089909
36.756310
32.944923
31.810413
25.817089
29.571711
29.966068
22.736937
21.282692
15.705971

205

0.23025
0.30841
0.26441
0.43945
0.31482
0.32414
0.23678
0.33220
0.27460
0.23900
0.26073
0.33744
0.24700
0.39017
0.30905
0.33970
0.32243
0.30815
0.25603
0.42500
0.32907
0.32004
0.30599
0.24567
0.31534
0.46531
0.37308
0.31587
0.23411
0.22624
0.27267
0.28645
0.30331
0.23608

0.40
0.47
0.52
0.61
0.48
0.44
0.50
0.76
0.54
0.31
0.51
0.47
0.38
0.49
0.48
0.48
0.68
0.40
0.36
0.51
0.48
0.64
0.71
0.57
0.63
0.55
0.72
0.65
0.37
0.68
0.44
0.33
0.41
0.32

11.70
13.39
12.98
13.68
11.76
12.41
12.64
13.86
13.25
12.43
12.89
12.21
11.90
12.66
12.97
13.10
13.46
10.52
10.62
12.11
11.64
13.87
13.64
12.79
13.98
13.76
12.55
12.79
12.60
13.50
10.76
11.38
11.16
13.01

Table C.1 (cont’d)

 

 

 

N SVS id 1 b P Av m
o 0 days

8187518 56.348953 12.489247 0.24464 0.43 12.04
8251846 68.551468 15.005470 0.52466 0.58 10.13
8508217 76.626305 -0.503263 0.29910 0.78 12.30
8554140 70.110695 -4.600965 0.22522 0.56 11.34
8559749 67.484940 -7.712886 0.23991 0.34 12.78
8588794 68.650909 -12.337778 0.33606 0.75 12.03
8681429 81.184387 -10.291162 0.25338 0.63 12.39
8693990 82.303886 ~7.547287 0.23188 0.47 9.52

8711606 83.581680 -10.211844 0.38417 0.42 12.11
8794962 79.273788 -23.261797 0.30081 0.53 12.24
8795419 82.887459 49.725647 0.26018 0.38 11.96
8806325 80.680511 -24.817566 0.38523 0.78 13.68
8808550 83.446083 -22.655369 0.24173 0.33 12.47
8845503 89.551147 -13.224326 0.23335 0.37 12.48
8868525 89.580856 -19.085112 0.23913 0.37 12.85
8868558 91.229416 -17.183275 0.32862 0.46 12.38
8902831 92.360771 -20.799198 0.32073 0.38 12.54
9005333 98.876770 -22.635584 0.38116 0.40 13.29
9006322 98.724716 -23.336769 0.30046 0.31 12.51
9052484 103.672058 -40.635361 0.26842 0.41 11.26
9069445 98.918617 -46.519657 0.25486 0.53 12.99
9104210 110.805115 -39.686264 0.25162 0.36 12.32
9108069 111.490372 -44.075348 0.27661 0.47 12.75
9116801 116.302307 -43.345966 0.32459 0.55 12.73
9160913 130.119568 -52.222069 0.35195 0.46 12.38
9184496 130.943527 -41.443817 0.28669 0.64 12.47
9186812 131.950943 -40.626926 0.28778 0.46 11.21
9255199 147.454330 -38.590065 0.37469 0.63 13.67
9294293 158.191818 -41.100468 0.27939 0.33 12.24
9311873 170.865982 -40.319599 0.23197 0.44 12.16
9313163 169.543869 -38.194382 0.28932 0.48 10.87
9469890 182.316589 -14.069934 0.25993 0.40 11.69
9480935 185.738815 -22.312019 0.33121 0.72 12.84
9481703 186.415894 -22.448172 0.23253 0.72 13.90

206

Table C.1 (cont’d)

 

N SVS id

1

O

b

O

P
days

 

9484367

9485503

9486446

9927549

9984319

10080683
10085444
10086452
10123418
10147580
10160266
10169623
10180261
10207146
10223742
10235317
10323641
10332963
10346621
10471644
10502199
10548943
10556949
10568869
10585624
10606707
10618445
10626169
10631442
10706395
10713473
10733284
10774934
10806788

189.368423
187.265701
186.592361
199.626419
202.956223
200.374664
204.301056
200.299057
204.092941
211.705490
215.518097
216.495697
222.951645
215.972046
210.146011
221.664581
244.010910
230.258057
241.079361
1.023201
3.303787
10.844966
17.241270
12.773267
24.019337
27.938969
35.712620
19.616404
24.238859
38.368664
36.855305
23.900723
32.809776
39.635838

-23.337019
-21.639187
—20.894581
10.973780
18.949072
24.779287
24.539936
26.250927
33.455822
30.349247
33.173321
36.472832
38.080631
42.685646
49.702747
43.344654
66.136841
65.629097
69.984459
72.226959
63.435036
61.338264
59.329361
52.310093
58.033188
52.209923
49.147488
50.262951
49.640526
40.218548
37.456886
35.380604
27.483202
31.522345

207

0.26079
0.44008
0.27852
0.39139
0.27153
0.35201
0.23049
0.34409
0.22930
0.26092
0.40620
0.31783
0.31676
0.29703
0.42224
0.28889
0.34565
0.42128
0.36283
0.23804
0.38629
0.27900
0.28188
0.34080
0.34007
0.31308
0.27906
0.33523
0.31701
0.32937
0.31458
0.26698
0.30979
0.22912

0.55
0.73
0.76
0.50
0.46
0.53
0.40
0.56
0.58
0.39
0.39
0.53
0.43
0.65
0.34
0.41
0.54
0.59
0.53
0.37
0.79
0.75
0.58
0.57
0.58
0.51
0.81
0.69
0.66
0.63
0.34
0.40
0.37
0.39

13.05
13.64
13.93
12.71
12.07
12.79
12.24
12.46
13.09
12.10
11.70
13.61
11.07
12.86
12.47
11.03
12.32
13.85
11.91
12.21
13.75
13.72
12.27
11.43
12.96
12.98
13.77
13.40
13.93
13.76
11.68
12.28
11.42
11.48

Table C.1 (cont’d)

 

 

N SVS id 1 b P Av m
o 0 days

10812050 42.118481 30.949932 0.36286 0.33 11.80
10826152 39.984615 27.047895 0.32386 0.57 12.82
10851353 39.993771 23.606880 0.26879 0.63 12.54
10897604 32.822731 19.708948 0.32010 0.40 12.38
10907674 35.256382 18.842327 0.24507 0.65 12.32
10915546 35.179249 17.288055 0.22819 0.42 10.20
10939618 41.372036 15.699781 0.36838 0.63 13.55
11039298 47.618771 12.887670 0.35159 0.61 12.75
11062878 48.221699 9.143929 0.28932 0.54 12.42
11087999 41.420021 10.672621 0.30142 0.64 12.83
11216261 50.880520 1.606691 0.24683 0.42 12.13
11369857 50.122723 -15.536270 0.31770 0.57 12.72
11453654 63.576683 -9.674345 0.25418 0.33 11.81
11464227 60.655930 -13.752760 0.23879 0.41 12.47
11577968 60.127472 -27.774405 0.22683 0.50 12.80
11621286 71.004814 -19.387995 0.34005 0.59 11.45
11623858 69.877548 -20.859077 0.24818 0.44 12.57
11649451 69.982460 -24.233786 0.42980 0.39 12.26
11698983 69.592484 -28.107746 0.28855 0.57 11.52
11725468 71.255241 -36.350800 0.28969 0.54 13.37
11757787 80.467873 -28.427000 0.25250 0.43 12.57
11857987 89.668961 -37.759232 0.26223 0.48 12.05
11879431 96.460945 -42.858765 0.32950 0.55 13.47
11906467 87.822990 -60.046894 0.27687 0.58 12.59
11963569 112.625015 ~66.796928 0.34457 0.73 13.40
11990107 126.982407 -56.003624 0.32774 0.68 13.12
12017790 151.363556 -56.503864 0.30161 0.53 13.43
12034782 162.110748 -63.234550 0.30149 0.50 12.37
12046016 167.950302 -57.758030 0.32172 0.52 11.00
12149036 184.826996 -37.055897 0.22594 0.46 12.59
12167526 192.179779 -41.029232 0.24545 0.63 12.50
12209023 193.308502 -31.752964 0.24372 0.42 12.99
12267781 201.252701 -26.459351 0.37567 0.68 13.23
12353908 200.849594 -13.951427 0.23999 0.71 13.84

208

Table C.1 (cont’d)

 

 

N SVS id

1

O

b

O

P
days

 

12369230
12380585
12453519
12694915
12731514
12967357
13000052
13009628
13036186
13079296
13087665
13093893
13095859
13240381
13266377
13291516
13320653
13340275
13341685
13366719
13370177
13375187
13400513
13472973
13503007
13557030
13570725
13573565
13600796
13602900
13704508
13713798
13922338
14180830

203.603531
204.410599
204.926636
214.695679
215.389542
226.682434
236.707275
236.866974
248.927719
245.522186
249.339996
256.448029
253.526199
313.264801
321.576935
325.051422
343.322998
347.153503
354.635742
345.269775
345.115875
348.334015
358.205261
3.287261
8.770260
19.093407
22.115299
25.865915
15.968682
13.747386
31.174009
29.543032
39.917992
38.607605

-11.522971
-18.186193
—9.210847
10.350087
15.571384
32.349972
39.560318
33.922630
38.748844
53.159607
45.366241
43.921864
47.513908
60.297836
61.795872
59.433193
52.414982
56.308456
59.910160
52.419621
49.889870
49.467781
43.064568
38.329628
30.468061
31.544914
29.422520
30.438231
27.352701
25.516621
22.233915
19.585894
2.994995
-17.254089

209

0.27460
0.42615
0.37149
0.32186
0.39644
0.23614
0.23277
0.28220
0.31369
0.25511
0.31662
0.30583
0.36333
0.40686
0.33975
0.23684
0.28964
0.40640
0.32534
0.33437
0.38076
0.22937
0.31690
0.49645
0.29747
0.35044
0.51541
0.29314
0.22706
0.26189
0.22680
0.27038
0.26918
0.22860

0.70
0.35
0.53
0.57
0.62
0.61
0.42
0.45
0.46
0.48
0.57
0.34
0.79
0.67
0.63
0.37
0.65
0.36
0.67
0.80
0.60
0.44
0.57
0.29
0.43
0.34
0.33
0.30
0.62
0.54
0.43
0.35
0.33
0.53

13.51
10.67
13.55
11.73
10.59
11.42
10.37
12.75
11.31
13.48
12.63
11.89
13.78
13.96
12.97
12.45
13.60
12.20
13.67
13.76
13.41
11.74
11.77
11.44
12.29
11.64
12.09
11.07
13.66
12.21
11.53
11.61
10.80
10.66

Table C.1 (cont’d)

 

 

NSVS id

1

O

b

O

P
days

Av

 

14300598
14307859
14438283
14453645
14539755
14541901
14559767
14621398
14654114
14705456
14729341
14764485
14781930
14795340
14842973
14978941
14991786
15011994
15016085
15023875
15025254
15050581
15119318
15543698
15544076
15595338
15686648
15692686
15708493
15729930
15863238
15902803
15955497
15974125

49.212009

47.768051

55.001221

62.972698

67.066093

70.442497

64.403938

81.396339

78.278465

134. 187531
171.963501
185.941376
192.958328
206.172897
204.712814
211.267700
212.463516
215.439072
217.333450
218.002884
214.496796
221.178497
221.964279
233.198990
238.007584
241 .334732
243.451218
241.929123
247.827560
250.731186
264.853271
276.642914
290.422241
300.917938

-23.369699
-25.661430
-35.276958
-35.648949
-46.989979
-45.861233
48.313282
-65.644630
-73.444740
-74.781601
-68.946083
-65.612328
-58. 177902
~61.483536
-45. 165657
-26.932749
-23.585995
-20.786266
-20.273819
-18.242340
-16.237423
-21.091024
-15.036404
17.234991
14.104473
14.063331
28.464273
29.795527
31.840040
26.646395
43.760876
42.060917
51.627125
52.180897

210

0.26789
0.25678
0.21556
0.43574
0.23866
0.29919
0.25476
0.24071
0.52726
0.29327
0.31030
0.32369
0.22854
0.22941
0.23231
0.29721
0.38348
0.32698
0.35242
0.35186
0.39405
0.37677
0.32008
0.42320
0.29579
0.23258
0.27135
0.40306
0.29397
0.22588
0.37696
0.23185
0.23257
0.33994

0.35
0.56
1.00
0.39
0.57
0.42
0.62
0.44
0.41
0.38
0.65
0.57
0.39
0.48
0.61
0.53
0.35
0.41
0.42
0.48
0.70
0.55
0.43
0.51
0.30
0.42
0.42
0.72
0.39
0.67
0.58
0.41
0.40
0.39

11.94
12.08
13.71
11.42
12.32
9.84

12.62
10.71
11.14
10.50
13.88
11.99
12.28
12.71
13.48
11.39
12.18
12.39
12.38
11.42
13.14
13.41
12.06
13.33
10.88
10.95
11.23
12.66
13.19
13.57
12.57
12.82
13.01
11.36

Table 0.1 (cont’d)

 

 

N SVS id

1

O

b

O

P
days

Av

 

16018678
16166066
16194218
16227319
16283847
16309498
16376359
16394081
16989220
17002449
17048204
17116519
17135302
17151684
17212680
17265263
17269781
17285380
17287608
17382133
17386234
17573448
17577125
17638053
17675110
18318050
18433211
18440572
18458089
18501806
18563622
18720155
19101566
19937092

313.694458
331 .316681
340.596008
348.924164
348.319061
351.261719
7.460183
7.018230
32.024185
19.758013
22.126772
33.204647
35.831547
37.791306
35.381809
40.846790
42.396095
29.807364
31.605921
47.676540
54.971199
223.055145
218.708984
226.400406
229.249939
257.396454
262.634399
263.592957
264.556000
275.353973
277.448639
299.633087
349.918701
28.336639

41.739189
35.591228
32.168770
40.462734
30.736151
24.674549
26.933979
22.772858
-17.849466
-16.422264
-24.500483
-25.590487
-26.902031
-29.898062
~39.516193
-43.426998
-44.464317
-44.991295
-45.433327
-64.497932
-65.197739
-62.259953
-59.753479
-45.503700
-40.073483
16.238852
22.002930
23.588711
27.165705
17.750219
31.715849
31.741343
23.798420
-56.363834

211

0.23924
0.32669
0.29107
0.30647
0.41656
0.34379
0.32324
0.23674
0.46488
0.26265
0.45608
0.23823
0.39448
0.33711
0.27344
0.20746
0.22590
0.33843
0.36182
0.31421
0.23505
0.39312
0.26334
0.24039
0.26532
0.24192
0.26221
0.35549
0.27 267
0.22919
0.27605
0.35076
0.25418
0.22799

0.60
0.56
0.72
0.93
0.40
0.39
0.70
0.58
0.39
0.49
0.52
0.61
0.60
0.62
0.53
0.54
0.31
0.69
0.65
0.49
0.38
0.54
0.40
0.39
0.39
0.45
0.73
0.46
0.48
0.58
0.61
0.47
0.55
0.63

10.56
12.83
13.61
13.93
11.77
11.83
13.60
12.95
11.60
13.05
12.02
12.74
12.95
12.86
11.56
13.10
11.51
12.78
13.63
12.68
10.21
13.11
10.36
11.88
12.50
12.78
13.38
12.75
12.68
13.11
12.57
12.03
11.76
13.00

Table C.1 (cont’d)

 

 

N SVS id l

O

b P Av m
0 days

 

19989934 30.672920

-68.631020 0.30562 0.47 12.36

 

212

 

 

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