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Transcript
K INEMATICS AND POPULATION
MEMBERSHIP OF BHB AND EHB
STARS
Dissertation
zur
Erlangung des Doktorgrades (Dr. rer. nat.)
der
Mathematisch-Naturwissenschaftlichen Fakultät
der
Rheinischen Friedrich-Wilhelms-Universität Bonn
vorgelegt von
M ARTIN A LTMANN
aus
Pretoria/Südafrika
Bonn 2002
Für meine Mutter Maria Altmann,
die mir mit ihrer Unterstützung diese Arbeit erst ermöglicht hat.
Angefertigt mit Genehmigung
der Mathematisch-Naturwissenschaftlichen Fakultät
der Rheinischen Friedrich-Wilhelms-Universität Bonn
1. Referent:
2. Referent:
Prof. Dr. K. S. de Boer
Prof. Dr. W. Seggewiß
Tag der Promotion: 28. November 2002
C ONTENTS
1
An Introduction to the structure of the Galaxy and the role of HB stars in Galactic research
1
1.1
The study of Galactic structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1
Motivation: Why do we study the structure and evolution of galaxies? . . . .
1
1.1.2
Characteristics of the components of the Milky Way . . . . . . . . . . . . .
4
1.1.3
Studies of Galactic structure . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.1.3.1
Star counts and scale heights . . . . . . . . . . . . . . . . . . . .
6
1.1.3.2
Kinematical studies . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.2
1.3
Horizontal Branch Stars, and their role as tracer tools in studies of Galactic structure
7
1.2.1
Physical aspects of HB stars, typology, evolutionary status . . . . . . . . . .
7
1.2.2
Are HB stars good tracers for studies of Galactic structure? . . . . . . . . . .
10
Short overview of the structure of this study and previous results . . . . . . . . . . .
12
1.3.1
Previous Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
1.3.2
Overview of the structure of this work . . . . . . . . . . . . . . . . . . . . .
12
2 Data and data reduction
15
2.1
The sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.2
Obtaining the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.2.1
Spectroscopic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
2.2.2
Astrometric and photometric data . . . . . . . . . . . . . . . . . . . . . . .
16
Data reduction and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.3.1
Spectroscopy: Deriving radial velocities, log g and Teff . . . . . . . . . . . .
17
2.3.2
Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.3.3
Astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.3.3.1
2nd epoch material: . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.3.3.2
Reference catalogues: . . . . . . . . . . . . . . . . . . . . . . . .
25
2.3.3.3
Reduction: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.3.3.4
Calibration: . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
The final sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
2.3
2.4
iii
CONTENTS
3
Kinematical trends among the field horizontal branch stars
37
3.1
Introduction: HB-stars, their population membership and the galactic structure . . . .
37
3.2
The data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
3.2.1
Composition of the sample . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
3.2.2
Physical properties of the stars, extinction . . . . . . . . . . . . . . . . . . .
41
3.2.3
Absolute magnitudes and distances . . . . . . . . . . . . . . . . . . . . . .
41
3.2.4
Proper motions and positions . . . . . . . . . . . . . . . . . . . . . . . . . .
43
3.2.5
Radial velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
Kinematics and orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.3.1
Calculating orbits and velocities . . . . . . . . . . . . . . . . . . . . . . . .
45
3.3.2
Morphology of the orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
3.3.3
Velocity components and dispersions . . . . . . . . . . . . . . . . . . . . .
47
3.3.4
Kinematics of sdB/O stars . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
3.3.5
Trend of kinematics along the HB? . . . . . . . . . . . . . . . . . . . . . .
49
RR Lyrae stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
3.4.1
A sample of RR Lyrae stars from the literature . . . . . . . . . . . . . . . .
49
3.4.2
RR-Lyrae kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
3.5
Selection effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
3.6
Discussion: trends and population membership . . . . . . . . . . . . . . . . . . . .
52
3.6.1
Overall trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
3.6.2
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3.6.3
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.3
3.4
4
Kinematics and population membership of sdB stars
55
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
4.1.1
The sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
4.1.1.1
Selection effects due to sample composition? . . . . . . . . . . . .
56
Kinematics and orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
4.2.1
Calculating velocities and orbits . . . . . . . . . . . . . . . . . . . . . . . .
57
4.2.1.1
Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
Analysis of the velocities and velocity dispersions . . . . . . . . . . . . . .
65
4.2.2.1
Analysis of the velocities and dispersions of “pure” samples . . . .
65
The orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
4.2.3.1
Orbit morphology . . . . . . . . . . . . . . . . . . . . . . . . . .
72
4.2.3.2
Analysis of the the kinematics over the whole orbits . . . . . . . .
73
4.2.4
Notes on individual stars . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
4.2.5
Selection effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
4.2
4.2.2
4.2.3
iv
CONTENTS
4.3
4.4
4.5
5
7
80
4.3.1
z-probability plot and scale height . . . . . . . . . . . . . . . . . . . . . . .
80
4.3.2
Effects of Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
4.3.3
Scale height and galactocentric distance . . . . . . . . . . . . . . . . . . . .
81
4.3.4
Robustness of the scale heights, separating the different populations . . . . .
83
4.3.5
Midplane number ratio of the two components found . . . . . . . . . . . . .
84
4.3.6
Constraining the Thin Disk component . . . . . . . . . . . . . . . . . . . .
84
4.3.7
Discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
Discussion: kinematics and the population membership of sdB stars . . . . . . . . .
87
4.4.1
The Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
4.4.2
The Halo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
4.4.3
Aspects of the stellar evolution history of sdB stars . . . . . . . . . . . . . .
88
Summary & Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
The Kinematics of HBB stars
91
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
5.2
Sample composition and data reduction . . . . . . . . . . . . . . . . . . . . . . . .
92
5.2.1
Selection effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
Kinematics and Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
5.3.1
Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
5.3.2
Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
5.4
The vertical probability distribution and the scaleheight . . . . . . . . . . . . . . . .
95
5.5
Discussion & conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
5.3
6
Determining a scale height for the stars using their orbits . . . . . . . . . . . . . . .
Discussion of the results
101
6.1
The kinematic trend revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2
The populations of the Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2.1
The Thin and Thick Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2.2
The Halo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.2.3
Bulge and Bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.2.3.1
BHB stars in the Galactic Bulge – or do they belong to the Halo? . 112
6.2.3.2
Disturbance of the Thick Disk by the presence of a Galactic bar? . 112
6.2.4
Moving groups and stellar streams . . . . . . . . . . . . . . . . . . . . . . . 114
6.2.5
Relationships of the components, evolution of our Galaxy . . . . . . . . . . 116
Outlook
119
7.1
Further steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.2
The future: DIVA and GAIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
v
CONTENTS
7.3
Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
A Correcting large gradients with combined dawn/night sky flat field exposures
125
B Data of the stars of the equatorial field
127
C Variables and Definitions used in this study
131
C.1 Photometric quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
C.2 Stellar physical quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
C.3 Spatial and kinematic quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
C.3.1
Observed quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
C.3.2
Spatial quantities and velocities . . . . . . . . . . . . . . . . . . . . . . . . 132
C.3.3
Morphological parameters of the orbits . . . . . . . . . . . . . . . . . . . . 134
C.3.4
Scaleheights and Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
D List of abbreviations
137
Bibliography
141
Zusammenfassung (Summary in German)
149
Curriculum vitae
154
Lebenslauf (Curriculum vitae in German)
155
Acknowledgements
156
vi
L IST OF F IGURES
1.1
The Hercules galaxy cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2
NGC 2997 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3
M 51 (NGC 5194)/NGC 5195 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.4
M 83 (NGC 5236) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.5
NGC 4565 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.6
M 15 (NGC 7078) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.7
Sample spectra of an HBA and sdB star . . . . . . . . . . . . . . . . . . . . . . . .
8
2.1
Typical example of a line fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.2
Two colour diagram of the HE-stars . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.3
Separating stars and galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.4
Vector point plot diagram of the measured proper motions of faint background galaxies 29
3.1
CMD of the stars of our sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.2
Orbits of the HBA/HBB stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
3.3
Kinematic trend of stars along the field horizontal branch . . . . . . . . . . . . . . .
48
3.4
Histogram showing the distribution of orbital velocities . . . . . . . . . . . . . . . .
50
4.1
Current distribution of the stars of our sample and 100 Myr ago . . . . . . . . . . . .
57
4.2
Histogram of the orbital velocities . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
4.3
Toomre diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
4.4
Bottlinger and Θ − W diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
4.5
The orbits of our stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
4.6
Histograms of ecc and nze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
4.7
Plots of Θ against ecc and log nze . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
4.8
Diagram of Θ against the total kinetic energy . . . . . . . . . . . . . . . . . . . . .
75
4.9
Histogram of the z distance-statistics of all the stars . . . . . . . . . . . . . . . . . .
82
5.1
Histogram of the orbital velocities . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
5.2
Toomre diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
5.3
Bottlinger and Θ − W diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
vii
LIST OF FIGURES
5.4
The orbits of all 20 stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
5.5
Histograms showing the distribution of ecc and nze . . . . . . . . . . . . . . . . . .
98
5.6
Histogram of the z distance-statistics of the 19 HBB stars . . . . . . . . . . . . . . .
98
6.1
The kinematic trend of stars along the HB revisited . . . . . . . . . . . . . . . . . . 102
6.2
Histogram of Θ of all stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3
Bottlinger and Θ − W diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.4
Toomre diagram of all stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.5
Diagram of Θ against total kinetic energy of all stars . . . . . . . . . . . . . . . . . 104
6.6
Parameters of the stars of Peterson et al. (2001) . . . . . . . . . . . . . . . . . . . . 111
6.7
3D plots of the orbits of HE 0516-2311 & HE 0521-3914 . . . . . . . . . . . . . . . 115
7.1
The DIVA satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2
The GAIA satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.3
sdB orbits superimposed on NGC 4565 . . . . . . . . . . . . . . . . . . . . . . . . 123
C.1 Spatial and velocity coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
viii
L IST OF TABLES
2.1
Photometric data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.2
Comparison of magnitudes obtained on the 2.10.2000 with magnitudes from the HEcatalogue (which corresponds to the B magnitude) and other sources in literature
(passband of literature value is in parentheses). Close neighbours affect the bjdss
magnitudes: such stars have been marked in column “remarks”. . . . . . . . . . . .
23
2.3
Proper motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.4
The spatial and kinematic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
3.1
Physical properties of our sample . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.2
Spatial and kinematical data of our sample . . . . . . . . . . . . . . . . . . . . . . .
40
3.3
Orbital and kinematical characteristics . . . . . . . . . . . . . . . . . . . . . . . . .
43
3.4
Mean velocities and orbital parameters . . . . . . . . . . . . . . . . . . . . . . . . .
46
4.1
Positions, velocities and morphological data of all stars . . . . . . . . . . . . . . . .
59
4.2
Mean velocities, morphological quantities and their dispersions . . . . . . . . . . . .
63
4.3
Compilation of our results for the scale heights and mid plane densities . . . . . . .
85
5.1
Spatial and kinetic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
5.2
Mean velocities and morphological quantities and their dispersions . . . . . . . . . .
94
6.1
Compendium of published scale heights and initial densities . . . . . . . . . . . . . 108
B.1 Data of stars in the equatorial field . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
ix
LIST OF TABLES
x
C HAPTER 1
A N I NTRODUCTION TO THE STRUCTURE
OF THE G ALAXY AND THE ROLE OF HB
STARS IN G ALACTIC RESEARCH
1.1
1.1.1
T HE STUDY OF G ALACTIC STRUCTURE
M OTIVATION : W HY DO WE STUDY THE STRUCTURE AND EVOLUTION OF GALAX IES ?
Galaxies are among the premier building blocks of the structure of matter distribution in the universe.
Moreover they are the sites of the formation of stars such as our Sun. Therefore knowledge about their
morphology and evolutionary history is of utmost importance for the understanding of the structure
formation process in the universe and hence the process which in the end leads to the birth of stars
like the Sun and eventually to the development of life on Earth.
To gain access to information about galaxies one has an enormous amount of objects at hand, galaxies
of all sizes and distances ranging from our “backyard”, namely the Milky Way itself and the Local
Group to galaxies at a redshift of z ' 11 and higher. Each approach can deliver different information
and has its advantages and disadvantages. In the following, I briefly describe what can be learned by
research conducted on galaxies at various distances.
• Galaxies at cosmological distances may show us how they are actually forming and how early
stages of galaxies looked like long (several Gigayear) ago. However these objects are very far
away, and thus appear very small and faint, so that observational constrictions blur the picture
severely. Thusfar only minor evolutionary changes have been found by looking into the distant
past (see e.g. the review by Abraham & van den Bergh 2001).
• Galaxies at large “non-cosmological” distances (∼100 Mpc to ∼1000 Mpc) give us information
about the large scale distribution of these objects as we have a vast number in a large volume at
our disposal. They are clearly brighter than those at larger distances, can therefore be accessed
with more moderate efforts and are reachable with wide field surveys such as the Sloan Digital
Sky Survey (SDSS, Kent 1994; Bahcall 1995). For this reason such objects are ideally suited for
studies of clustering of galaxies (a typical example of a galaxy cluster is shown on Figure 1.1),
1
z = 1 corresponds approximately to the magnitude and resolution limit of such studies.
1
Figure 1.1: The Hercules galaxy cluster: A
laboratory for galaxy studies (1 m Cassegrain
+ Focal Reducer + HoLiCam, Observatory
Hoher List (O.H.L)).
Figure 1.4: M 83 (NGC 5236): A barred
galaxy; Our Milky way is also known to have
a small bar (ESO-La Silla, 1.54 m + DFOSC).
Figure 1.2: NGC 2997: A typical spiral
galaxy seen face on (ESO-LS).
Figure 1.5: NGC 4565: An edge-on spiral
galaxy, showing its disk (O.H.L.).
Figure 1.3: M 51 (NGC 5194)/NGC 5195:
An example of a “grand design” spiral with
some interaction with its companion (O.H.L).
Figure 1.6: Globular clusters like M 15
(NGC 7078) are amongst the most important
objects for studies of Galactic structure and
horizontal branch stars (O.H.L.).
1.1. The study of Galactic structure
evolution of galaxies within galaxy clusters (which is shown to be somewhat different than that
of single galaxies) and the overall arrangement of galaxies and galaxy clusters in the universe.
However, for such far away stellar systems, detailed studies of the morphologies of individual
objects are very difficult, if not impossible, with current technology.
• Nearby galaxies provide us with detailed morphological information, such as the examples
shown in Figures 1.2, 1.3, 1.4 and 1.5; we can study their shapes, sizes, types etc. using many
observational strategies and techniques. We can study interactions and companions (see Figure
1.3) and many other aspects and characteristics such as spiral arms (see Figures 1.2 and 1.3)
and bars (Figure 1.4) using these nearby galaxies. In fact most of our knowledge about galaxies
came from these objects located just outside our Local Group. Of course the further away these
objects are the fewer details are accessible.
• The same applies more or less to the members of our Local Group (LG) of Galaxies. As they are
even nearer to the Milky Way than other galaxies, more and more information becomes reachable, more detailed studies of stellar populations are feasible. On the other hand the number
and hence the types of galaxies in the Local Group are very limited, so some very interesting
types of galaxies are not found in the Local Group.
• The Magellanic clouds (MCs) and some other nearby dwarf galaxies can be studied in even
greater detail than the other galaxies of the Local Group; This means that very detailed studies of
stellar populations are possible. In the near future we will even have access to their transversal
velocities which we do not have for other galaxies (and cannot hope to obtain at least in the
foreseeable future). One problematic aspect when contemplating using the MCs as test objects
is that they are only two objects, so we do not gain much knowledge about the wealth of other
galaxy types.
• The galaxy which can be studied in greatest detail is our Milky Way (MW). Here even properties of relatively faint stars can be analysed. We have access to many substructures such as the
different populations, and aggregates like open and globular clusters (see Figure 1.6) and OB
associations, which provide us with a wealth of information since they consist of stars of common origin. Looking at nearby stars, we can study their kinetic behaviour in very great detail,
which means we can to a certain extent see how the galaxy actually moves internally, how it
rotates, and how different parts relate to each other. In addition, the history of metal enrichment
can be studied closely, leading to a better understanding of how galaxies evolve. Actually the
MW is the only galaxy that we can study in three dimensions.
The older populations of stars in the Milky Way may give us insight into how the Galaxy formed
and evolved. Evidence of past events such as collisions and merging events of smaller stellar
aggregates (like dwarf galaxies) with the MW can be found by studying kinematics of stars or
gas (One example for this is the discovery of the Sagittarius Dwarf Irregular Galaxy (see e.g.
Ibata et al. 1994). Therefore such enterprises add essential evidence e.g. to results coming from
studies of galaxies at high z. Thus, old stars serve as “tracer fossils” for Galactic evolution in
general.
Of course one of the problems present in studies of the MW is that it is one individual galaxy.
Our Galaxy may be a typical example of spiral galaxies as a whole, but certainly has many
unique properties. Therefore only looking at the MW to understand galaxies or even spiral
galaxies will lead to false conclusions, just like trying to make a judgement of all people by just
looking at one individual. Furthermore because we are inside the MW, the overall structure is
3
1. I NTRODUCTION TO HB STARS AND THE STRUCTURE OF THE G ALAXY
hidden, gaining information about this is tedious and difficult and may easily lead to misinterpretations. However, overall, studies of the structure of the Milky Way provide many valuable
aspects of structure and evolution of galaxies on the whole; these studies are therefore very
important and should be carried out as intensively as possible.
Far away galaxies, nearby galaxies, the Local group – “groups” of objects suited to different kinds
of research which are, from the observers point of view, not sharply defined; the transitions between
them are fluent. For instance, much of what is said about galaxies of the Local Group (LG) also
applies to the nearest galaxies just beyond the borders of the LG. Furthermore every new generation
of telescopes extends the range in distance in which a certain observing strategy is possible, but then
again other more sophisticated methods become available for the nearer objects.
Many new aspects found by looking at one of the groups of objects can help solve problems arising
from another, e.g. the idea that Disk galaxies are in fact spirals was first seen in the photographs of
bright nearby galaxies and then it was proposed that the MW might also be a spiral which then lead
to efforts to find these spiral arms. Another example is the Thick Disk which was first found as an
overabundance of certain stars in star counts in the MW, and later as an extra slope in the decrease
of light moving vertical from the plane of some local edge-on galaxies similar to NGC 4565 shown
in Figure 1.5 (see e.g. de Grijs & Peletier 1997). These examples show that while it is certainly not
possible to contribute to every aspect of galaxy research, interdisciplinary interaction in this field is
essential.
The study presented here focuses on aspects concerning the Milky Way and its populations, mainly
the Disk(s) and the Halo. Like many attempts before, we study the distribution of stars perpendicular
to the Galactic plane. This is an almost classical method and will be briefly described in Section
1.1.3. But before starting off we will first describe the components of the Milky Way (Section 1.1.2).
Section 1.2 gives an introduction to the stars we use for study, the stars of the blue (BHB) and extreme
(or extended, EHB) horizontal branch. Section 1.3 gives a brief overview of this work and previous
results from preceding studies.
1.1.2
C HARACTERISTICS OF THE COMPONENTS OF THE M ILKY WAY
Classically, the stellar component of the Galaxy can be divided into four populations, namely the Thin
Disk, the Thick Disk (which is also known as the Intermediate Population II (IPII)) the Halo, and
finally the Bulge and the Bar, forming the inner part of our Galaxy.
The Thin Disk is the population which is associated with star formation and thus with the gas disk.
The density of this component at the Galactic plane is very high, with over 90% of the local stars
(including the Sun) being part of the Thin Disk. It has a small scale height of about 100-300 pc
depending on the type of stars used to derive the scale height, with the lower values being for mass
rich and thus short-lived stars. The lower the (initial) mass of the stars examined and therefore the
higher their age spread the higher the scale height is (see Elvius (1965) for a detailed account on Thin
Disk scale heights). The velocity dispersions range between ∼ 15 km s−1 and 30 km s−1 .
As our stars are evolved low mass stars, the interesting part of the Thin Disk is the older part, also
dubbed Old (Thin) Disk. The HB stars studied here are late evolutionary stages of stars with masses
of less than ∼ 2 M , which means that some of them are only about 1 Gyr old and would for this
reason belong to the younger Thin Disk population. However these objects can be neglected when
compared to the far more numerous less massive stars so that the vast majority of the stars of our
sample belonging to the Thin Disk can be considered to be part of the oldest group.
4
1.1. The study of Galactic structure
Therefore in our context, the Thin Disk has a scale height of ∼300 pc and velocity dispersion of
30 km s−1 . The mean orbital velocity is in the order of 210 km s−1 .
The second component with a disk-like structure is the Thick Disk, introduced by Gilmore & Reid
(1983). The need for another disk component has arisen because star count results were better reproduced by having a second exponential distribution with a scale height of about one kiloparsec. Furthermore, studies of the light distribution perpendicular to the planes of other edge-on spiral galaxies
show an increase in scale height further away from their planes (see e.g. de Grijs & Peletier 1997).
This component is also called Intermediate Population II (IPII, Majewski 1993).
In our context, the Thick Disk has a scale height of ∼1 kpc, a mean velocity of ∼175 km s−1 and a
dispersion of ∼50 km s−1 .
The kinematic behaviour of the Thick Disk is hotter than that of the Thin Disk, meaning that the
velocity dispersions are higher (∼ 50 km s−1 ) and the orbits of thick disk stars are more eccentric
and reach larger distances from the Galactic plane, resulting in the larger scale height. Furthermore
this population features an asymmetric drift of 40-50 km s−1 , meaning that the stars lag that amount
behind the orbital velocity of the Local Standard of Rest (LSR). The maximal density is about 2-5%
of that of the Thin Disk. Metallicities are intermediate, with a low metallicity tail.
The third part of the Galaxy is the Halo. In contrast to the previous two populations, which have
a disk-like mass distribution, this component is a spheroid or an ellipsoid. Therefore any measured
scale height is a lot larger that that of the parts described previously (Note however, that while the
disks can be described with an exponential z-distribution, this does not really apply for the Halo as
in this case we are looking from an off centre position into a sphere). The stellar density declines
radially, probably with a power law such as with R1/4 . Although the z-distribution of the halo stars is
not exponential, one may fit an exponential to roughly characterise the z-distribution.
In our context, the Halo is a population with slow rotation (Θ ∼20 km s−1 ) but high velocity dispersions of more than ∼ 100 km s−1 and a very flat z-distribution (large scale height).
The Halo rotates only slowly, if at all, and there is a retrograde subgroup belonging to this population.
The rotational velocity of the Halo is small, its velocity dispersions are very large, in the order of 100
km s−1 and more. The stellar orbits are mostly very elliptic and can reach high distances above the
Galactic plane. The density of the Halo is small, less than 10% of that of the Thick Disk. As in the
case of the Thick Disk the stellar population is old, as it lacks bright, hot, short-lived main-sequence
stars. Generally the Halo stars have low metallicities.
Finally there is the Bulge. The bulge is when seen from the outside, its most prominent part. In
contrast to this the Galactic Bulge is not easy to access due to the huge amount of obscuring material
in the direction towards the Galactic centre. Nevertheless there are a few regions, the most well
known of these being Baade’s Window, where the obscuration by interstellar dust is small. From
these we have gained most knowledge we have about the Milky Way’s Bulge. The stars seem to have
a large distribution in metallicity, with a relatively high mean value of [Fe/H]=−0.25. Studies of the
kinematics show that the ensemble of Bulge stars shows a significant net rotation (see e.g. Minniti
et al. 1992; Minniti 1996; Tiede & Terndrup 1999). Peterson et al. (2001) claim to have found a
number of hot HB stars in the Bulge.
In recent times it became more and more clear that our Galaxy contains a small Bar. This Bar may
have some influence on the kinematics of stars near the solar circle, i.e. those which we can observe
and are dealt with in this work. These express themselves in non zero values for mean Φ or W
velocities, meaning net movements of stars of the solar vicinity into a certain direction as described
in Fux (2001).
5
1. I NTRODUCTION TO HB STARS AND THE STRUCTURE OF THE G ALAXY
Apart from the two points mentioned above this population plays almost no role in our study and is
therefore not discussed further.
For a detailed description of the Galaxy’s components and populations, see e.g. Freeman (1987),
Majewski (1993) or Binney & Merrifield (1998).
1.1.3
S TUDIES OF G ALACTIC STRUCTURE
As described in the previous section a vital aspect for the understanding of structure and evolution of
our Galaxy and thus of galaxies in general is the study of older stars (assuming that our galaxy is a
typical spiral galaxy with no or only small peculiarities). In this section some of the strategies and
methods to accomplish such investigations are briefly described.
1.1.3.1
S TAR COUNTS AND SCALE HEIGHTS
Star counts and other attempts to derive the vertical structure of the Galactic Disk have been conducted
for a long time. For a review of results obtained in the 1930s to 1950s mainly for the Thin Disk, see
Elvius (1965). In more recent times these studies were continued mostly with more elaborate methods
reaching to fainter and fainter magnitudes but being still in principle done the classical way such as
the study by Bahcall & Soneira (1984).
Today there are basically two approaches to study the distribution of stars in the Milky Way. One
is to conduct a star count over all stars in fields at different Galactic latitudes such as carried out by
Reid & Majewski (1993). Fitting models accounting for luminosity class, metallicity, completeness,
distributions and number densities of populations etc. to the raw results then leads to scale heights and
densities of stars belonging to different Galactic populations. With this method one obtains results
relying on a very large number of stars, which also means the statistical errors are small. On the
downside, these studies heavily rely on models, introducing uncertainties caused by possibly poorly
known input parameters, whose magnitudes can not be estimated in many cases. Moreover, because
most of the stars at high Galactic latitudes are stars of the lower main-sequence which are intrinsically
faint, such star counts are often limited in range.
Therefore many studies use a second way, namely to use a certain well defined star type as a tracer
rather than all available stars. In most cases these tracers are evolved stars, which, while being relatively rare, are bright so that studies using them extend deeper into the galaxy. Widely used objects
are giants and horizontal branch (HB) stars (especially RR-Lyraes, because they are as variables very
easily identified). Nowadays, deep surveys enable studies using very low mass main-sequence stars
as tracers as well (Phleps et al. 2000). A list of results of scale height determinations is presented in
Table 6.1.
1.1.3.2
K INEMATICAL STUDIES
Studies of the spatial distribution of a sample of stars give important insights into the general structure
of the Galaxy, e.g. revealing various populations of stars. Adding kinematic data gives us access to
the motions of the stars forming these groups. Stars belonging to different populations show widely
differing kinematic behaviour. Some components of the Milky Way are rapidly rotating with little
dispersion in the velocities of the members while others show only little net rotation but high dispersions. These differences between the populations give us evidence of how these parts of the Galaxy
are formed. Such studies have been conducted for quite a variety of different object types, such as high
6
1.2. Horizontal Branch Stars, and their role as tracer tools in studies of Galactic structure
proper motion stars (Carney et al. 1996), local dwarfs (Schuster & Allen 1997) or globular clusters
(Dinescu et al. 1997, 1999a,b). The kinematics of sdB stars have been studied by Colin et al. (1994),
Thejll et al. (1997) and de Boer et al. (1997a).
If a certain discrete group of stars is selected for a study of their kinematics one should be very aware
of possible selection effects. For instance, many stars were found because they are peculiar in one
way or another, such as being metal-poor or high proper motion stars. If certain types of stars, such
as our field blue horizontal branch stars (see. Chapter 3), have this peculiarity as the sole finding
criterium this may introduce quite severe selection effects. Others, such as RR Lyraes, (identified by
their variability) and sdB stars, (which are found by their colour and identified by their quite unique
physical parameters), do not suffer from selection effects to such an extent. As the selection effects of
the samples dealt with in this work are of quite different nature, they are discussed under the relevant
chapters (Chapters 3, 4 and 5).
Some studies only rely on partial knowledge about the kinematics, i.e. using only radial velocities,
as done by Kinman et al. (1994, 1996) or only proper motions. However in these cases one only
has part of the story, and must therefore be very careful with interpretations, or use methods, such as
field selection (e.g. in a field located at one of the Galactic poles the orbital velocity (Θ) is almost
completely the transversal velocity (i.e. the proper motions) and the velocity perpendicular to the
plane is represented by the radial velocity) or statistical approaches.
In addition, studying the kinematics of stars gives us information about a larger section of the Galaxy
than that in which the objects are currently located. The reason for this is that stars which are now
near the Sun were often far away from the Sun in the past and will venture away from the Sun in the
future (see Sect. 4.1.1.1). By including their trajectories one can study the distribution of a group
of stars to much larger distances than the distance limit of the sample; this has e.g. been done by
de Boer et al. (1997a) for a sample of sdB stars. However there can be selection effects due to the
sample composition, if there is an upper brightness (i.e. lower distance) limit or if nearby stars are
underrepresented. In this case, stars with tight orbits reaching not as far as the minimum distance of
the sample are missed. This type of selection effect and its possible effects on our sample is described
in detail in Section 4.1.1.1.
1.2
H ORIZONTAL B RANCH S TARS , AND THEIR ROLE AS TRACER TOOLS
IN STUDIES OF G ALACTIC STRUCTURE
Horizontal Branch stars are particularly suitable for studying the Galactic structure because they have
spectra that can be analysed with relatively simple methods (see Figure 1.7). Furthermore, as their
spectra are quite unique for stars at high Galactic latitude (unfortunately this does not apply to HBB
stars which have spectra and surface gravities very similar to late B-main-sequence stars), there are
no other objects they can be easily confused with. But before starting off, we outline their physics,
and evolution and discuss the points which make HB stars good tracers and which points are rather
adverse.
1.2.1
P HYSICAL ASPECTS OF HB STARS , TYPOLOGY,
EVOLUTIONARY STATUS
Horizontal Branch stars have Helium burning cores and they represent the evolutionary stage after the
(first) red giant (RGB) phase. Their appearance depends on the mass of the Hydrogen envelope they
retain after the mass loss during the RGB evolution. In contrast to the mass of the envelope which
7
1. I NTRODUCTION TO HB STARS AND THE STRUCTURE OF THE G ALAXY
Figure 1.7: Two spectra of typical examples of HB stars. HS 0702+6043 is a (variable) sdB star,
HS 2300+0451 an HBA. The typical lines in the spectra of these stars can clearly be seen and are
indicated along with their wavelengths. The spectra were taken at the 2.2 m telescope at Calar Alto
observatory using the CAFOS spectrograph in Nov. 2000
has a large range in mass along the HB, the mass of the He core is relatively constant over all types,
having a mass of about 0.5 M . They can be divided into several groups:
• the Red HB Stars (RHB) which are all HB stars cooler than the instability strip.
• the RR-Lyrae stars (RR, RR-Lyr), named after the prototype, which are variable stars of
intermediate temperature and colour, located in the HRD in the instability strip.
• the Blue HB Stars (BHB) which are bluewards of the RR-Lyraes. Temperatures range from
about 7500 K to 20,000 K. This group is subdivided into HBA (Teff <
∼ 10, 000 K) and HBB
>
stars (Teff ∼ 10, 000 K), the limit corresponding to the limit between A and B spectral class.
8
1.2. Horizontal Branch Stars, and their role as tracer tools in studies of Galactic structure
The main-sequence crosses this region in the HRD in the HBB region.
• the Extended or Extreme HB stars (EHB) which are the hotter extension of the HB. Because
these stars lie below the MS in the HRD, they are referred to as hot subdwarfs2 . This group is
subdivided into sdB (20, 000 ≥Teff <∼ 32, 000 K), sdOB (∼ 32, 000 <Teff < 40, 000 K) and
sdO stars (40, 000 <Teff < 70, 000 K) depending on their temperature, and strength of HeI and
HeII lines in their spectrum (for rules of spectral typing see de Boer et al. 1997c). The sdO stars
are probably not (all) genuine HB-stars but present a later (post-EHB) stage of stellar evolution
(Groth et al. 1985) such as AGB-Manque stars (evolved HBB & sdB/OB stars) or post AGB
stars during cooling down to become white dwarfs.
Red HB stars (RHB) have a H envelope mass of up to 0.5 M , RR Lyrae stars about 0.1 - 0.2 M ,
BHB stars yet less. Stars of the extreme horizontal branch (EHB) only have a very thin H envelope of
less than 0.02 M .
Because the least massive stars which since the first appearance of stars could possibly have evolved
to HB stars have a mass in the order of 0.9 M , the bluer HB-stars in particular must have undergone
significant mass loss during their RGB phase, losing up to 40% of their initial mass and almost all of
their non-processed material. The issue of what leads to this large mass loss in some stars but not in
others is still under debate, as is the question whether this mass loss only caused by stellar winds of
varying strength or also due to mass exchange between components of a binary system (see e.g. Iben
& Tutukov 1987; D’Cruz et al. 1996; Brown et al. 2001) – in principle: which star turns into which
kind of HB star?
Unfortunately this problem is not easy to solve. Studies of horizontal branches are mostly conducted
in globular clusters (GCs, such as M 15, see Figure 1.6), which are (apart from external (dwarf)
galaxies, which are fainter and less easy to observe) the only places where a complete older stellar
population can be studied, because their stars are of the same origin. These studies show that there is
no simple relationship between any of the usual parameters used to describe stars of different origin,
such as metallicity, age, rotational velocity etc., and the morphology of the HB. Metallicity clearly
has an influence on the shape of the HB (i.e. how HB stars are distributed along the HB), with the
more metal-rich globulars having rather red HBs and metal-poor GCs having blue HBs. However this
is not always the case. Moreover, objects with very similar metallicity can have completely different
HB morphologies, such as the pair NGC 288 ([Fe/H]=−1.40 (Zinn & West 1984), blue HB) and
NGC 362 ([Fe/H]=−1.27 (Zinn & West 1984), red HB) as pointed out by Bolte (1989). Therefore
another parameter in addition to metallicity must be in play. This is referred to in literature as the 2nd
parameter problem.
Age has been suspected to be another parameter causing the so very different appearance of horizontal
branches of GCs. The analysis of Bolte (1989) indeed leads to the result that the ages of NGC 288 and
NGC 362 differ by several Gyr, a result which has been qualitatively confirmed by more recent work
such as Bellazzini et al. (2001) but is not without difficulties as pointed out by Catelan et al. (2001).
However, other authors such as Vandenberg & Durrell (1990) question this and come to the conclusion
that age is probably not the 2nd parameter influencing the formation of HB stars. Therefore the debate
which parameter(s) influence the shape of HBs of globular clusters is still going on.
HB stars in the field can of course not be analysed this way, because they are single objects and it
is generally not wise to consider them as being coeval as those in a cluster. Presumably they are
2
not to be confused with Pop. II (metal-poor) main-sequence stars which are also called “(red) subdwarfs” because
the metal-poor MS lies below the MS of solar metallicity in the HRD. In contrast to the hot sd-stars these are rather cool,
because they are less massive than the Sun.
9
1. I NTRODUCTION TO HB STARS AND THE STRUCTURE OF THE G ALAXY
however also subject to the 2nd parameter problem, which would cause them to be distributed over all
populations, metallicities, and ages in a similar manner as the HBs in clusters. And the same problem,
of what causes the mass loss and what determines the amount of mass lost, persists for the field HB
stars (also called FHB stars) as well. Here the question is: how do stars lose so much mass that they
become EHB stars?
There are several hypotheses on the market. Quite old is the theory that EHB stars are the result of
mass transfer in close binary systems (Iben & Tutukov 1987). Indeed many sdB stars have been found
in recent times to have variable radial velocities, in some cases having periods of only a few hours,
which indicates close binarity (see e.g. Maxted et al. 2001). Most of these variable radial velocity
stars do not show any signs of binarity in their spectra such as excess flux in the red, which means
that the secondary component must be very faint, such as a white dwarf or a M-type main-sequence
star. On the other hand, most of the binaries, which reveal themselves in their spectra, do not show
the short periodic variations in radial velocity. Still others show neither. This means that binarity can
be a cause of sdB formation, but might not be the only one.
Other studies prefer single star evolution. D’Cruz et al. (1996) have developed a scenario in which
some stars have stronger stellar winds in their RGB phase than others (which means greater mass loss)
and thus leave the giant branch prematurely, a phenomenon they call “peel off” theory. A study by
Brown et al. (2001) of EHB stars in the globular cluster NGC 2808, lead the authors to the conclusion
that some of the sdB stars in that cluster are in fact reborn stars, being prior to their sdB stage on the
white dwarf cooling track and then experiencing a late Helium flash. This means that there could be
several channels leading to the formation of sdB stars.
The HBA stars known in the field are more or less all metal-poor, metallicities ranging between
−2.2 dex and about −1 dex (Adelman & Hill 1987; Adelman & Philip 1990, 1992, 1994, 1996; Kinman et al. 2000), while RR-Lyraes span a wider range of metallicities (Martin & Morrison 1998;
Layden 1994; Layden et al. 1996) although most of them are metal-poor as well. All HB stars hotter
than about 10 500 K have metal abundances heavily altered by effects of diffusion and levitation in
their stable and non-convective atmospheres, as has been found in some field BHB stars (Bonifacio
et al. 1995) and in globular cluster stars (Moehler et al. 1999; Behr et al. 1999). Therefore the present
element abundances do not give any information about the initial metal content so that determining
their population membership and hence their history is only possible by looking at their spatial distribution and kinematics.
1.2.2
A RE HB
STARS GOOD TRACERS FOR STUDIES OF
G ALACTIC
STRUCTURE ?
In principle every type of star, excluding a few extraordinary or unique objects, is a suitable tracer
of one or the other populations of the Milky Way, and none is ideal. The choice depends on what
kind of analysis is intended, what population is primarily aimed at (old or young stars), should only
the spatial distribution be considered or also kinematic aspects, metallicities etc., and how far out
should the sample go. These are important points when choosing a type of stellar object for such an
undertaking.
HB stars bluewards of the instability strip have several virtues which make them excellent tracers of
older populations. They are found in old and very old stellar groups. The absolute magnitude of the
cooler BHB stars can be easily determined to a fair accuracy using the constant absolute magnitude
of the HB (beware: metallicity effects!), and determining their physical parameters (Teff , log g, see
Section 2.3.1) is straightforward, so that distances of HBB and sdB/OB stars, where the HB is no
longer horizontal in the CMD, can be derived easily. Moreover the prominent Balmer lines in their
10
1.2. Horizontal Branch Stars, and their role as tracer tools in studies of Galactic structure
spectra (see Figure 1.7) should also lead to accurate radial velocities. As these stars are all relatively
bright, at least brighter than most old main-sequence stars, they have a relatively large range. Furthermore, their colour is so unique that they can very easily be found and classified (the only other
numerous type of hot star normally found at intermediate to high Galactic latitude fields, are white
dwarfs, which are easily discerned from other stars by their very broad absorption lines). While not
being a common type of star, HB stars are still numerous enough to be used for detailed studies. The
absolute magnitudes of HBB and sdB/OB stars are not prone to metallicity effects (unlike HBA and
RR-Lyrae stars), due to their stable atmospheres (see above).
On the other hand there are some less favourable points to be considered: while most of the BHB/EHB
stars are easy to find and identify, there are severe problems in the HBB regime when dealing with
stars which are either local or at low Galactic latitudes, because they can very easily be confused
with B main-sequence stars. To a lesser extent this also applies to the hotter HBA stars which could
be mistaken for slightly evolved A main-sequence stars. Fortunately, these stars only exist in young
to intermediate populations; therefore HBA and HBB stars become more and more important when
moving to higher Galactic latitudes and to fainter and fainter magnitudes, thus moving more and more
away from the solar neighbourhood and Galactic plane. However, in the solar neighbourhood most
HBB stars have probably not been found, and many of the HBA (especially those having rather solar
like orbits, thus not appearing in surveys for high proper motion stars) will presumably also be missed.
sdB stars do not present us with this problem. Here the trouble comes mainly from binarity. Every
sample of stars probably contains a significant number of binaries. These seem to be brighter than
their colour would indicate 3 , radial velocities become variable etc. Many of the sdB stars are not only
binaries but close binaries, which means that they have short period variations in their radial velocity,
and in some cases (depending on the inclination angle) also large amplitudes. This potentially poses a
severe problem for all studies of sdB kinematics. When studying stars which have a large velocity with
respect to the Sun, expressed by either a large proper motion or a large radial velocity, it is therefore
important to examine whether these motions are caused by the proper motion and/or radial velocity or
the radial velocity alone. Fortunately more and more systemic4 velocities for these sdB binary systems
are becoming available while high spatial resolution data help to settle binarity questions (Heber et al.
2002). Apart from this, the only other potential disadvantage of sdBs as tracers is that they may be
formed via several channels (as described above), which could mean that there could be differences
in mass and thus in luminosity. But this is at the moment purely hypothetical.
The HB stars hotter than about 10,000 K do not give us any useful information about metallicities,
as their atmospheric metal content has been severely altered by diffusion and levitation processes as
mentioned in the previous section.
Other points to be aware of are the ways and criteria the objects one wishes to study are found and
identified in the surveys you select them from. Because this aspect is discussed in the relevant chapters
(Chapter 3, 4 and 5) we refer to these at this stage.
In short, while BHB/EHB stars are very suitable for studies of Galactic structure, one should be aware
of some pitfalls.
RR-Lyrae stars are also very suitable as tracer objects, and have been used for a long time. Their
variability makes them very easy to find, they are bright, and their spatial parameters can be derived
with relatively simple methods; for this reason almost all types of studies (spatial distribution and
kinematics) can be conducted using RR-Lyraes. They are, however, significantly less numerous than
BHBs and RHBs.
3
4
That is why there are many stars to the right of the MS by up to 0.7 mag in the HRD.
radial velocity of the binary system.
11
1. I NTRODUCTION TO HB STARS AND THE STRUCTURE OF THE G ALAXY
Field RHB stars are very difficult to classify as such unambiguously as they look very similar to
other red subgiant stars. For this reason RHB stars have hardly ever been used as subjects in studies
concerning Galactic structure.
1.3
S HORT OVERVIEW OF THE STRUCTURE OF THIS STUDY AND PREVI OUS RESULTS
This current study is a continuation of the work done by de Boer et al. (1997a), increasing the number
of stars by a factor of almost three, adding some more local stars and stars from the Hamburg-ESO
survey (HE) performed by the Hamburger Sternwarte. These are on average a little further away than
those of the PG-survey (Green et al. 1986) used in the earlier work, but on the whole at significantly
larger z-heights as most of them are located at higher Galactic latitudes than the PG-stars used in de
Boer et al. (1997a). Therefore with this enlarged sample, one can expect the probability to include
halo objects in the sample to be larger, because their relative density is higher than near the sun where
disk stars dominate.
1.3.1
P REVIOUS R ESULTS
Scale heights of sdB stars have been studied for more than a decade. Early studies, such as Heber
(1986), Downes (1986) and Bixler et al. (1991) derived scale heights of ∼ 200 pc, which is similar
to values expected for the Thin Disk. This also applies to the works of Moehler et al. (1990) and
Theissen et al. (1993). Green et al. (1986) obtained, using a much larger sample (∼ 750 stars), a
scale height of 325 pc, which corresponds to values for the old Thin Disk. The study by Villeneuve
et al. (1995) arrived at a far higher value of 450 - 900 pc, which is more typical of the Thick Disk
or a mixture of both Thin and Thick Disk. Because they also used a rather large sample of 223 stars
to a magnitude of Bpg =16.2 mag and the earlier studies used a much smaller quantity of stars with
a brighter faint limit, it seems that to find the true vertical distribution of these stars one must have a
fairly large and deep sample. A study by Mitchell (1998) of a very small sample going to very faint
magnitudes claims to have found a Halo component in the sdB star distribution.
The kinematics of sdB stars have also been the subject of study. Colin et al. (1994) have calculated
orbits of a few sdB stars, one of them being a Halo candidate5 . The rest showed Thick Disk-like orbits
and velocities. Thejll et al. (1997) analysed the kinematics of a sample of sdB and sdO stars and found
values for the asymmetric drift and average velocities consistent with those found by other studies of
the Thick Disk. The same applies to the study by de Boer et al. (1997a). Here the derivation of a scale
height from the orbits was attempted for the first time; the result was 1 kpc. In the course of time it
became quite clear, that most of the sdB stars are members of the Thick Disk6 .
Because of the difficulties in properly identifying them, HBB stars have been studied far less than the
sdBs. Schmidt (1996) calculated orbits for six HBB stars; these results were in part used in a relevant
study by Altmann & de Boer (2000) and in part represented in Chapters 3 and 5.
1.3.2
OVERVIEW
OF THE STRUCTURE OF THIS WORK
The studies presented here have two main goals:
5
6
12
Which was later found to be a disk star when a new value for the proper motion was derived
See, however the discussion on selection effects underrepresenting Thin Disk stars.
1.3. Short overview of the structure of this study and previous results
• One aim is to analyse the population membership of HB stars bluewards of the instability gap
and find similarities and differences. As for most of these stars, one of the important parameters
for characterising stars - the metallicities - are not accessible. A study of population membership can give clues about whether they are metal-rich or metal-poor or have a wide range in
metallicity, by comparing e.g. their distribution of kinematics with those of other stars. Additionally we will try to find evidence for or against different formation channels for stars along
the HB, like the proposed binary evolution scenario for sdB stars (see e.g. Iben & Tutukov
1987) or the “peel off” model by D’Cruz et al. (1996).
• Once having assigned the stars to certain populations, one can also derive constraints on the
parameters defining these populations themselves. As described in previous sections, blue HB
stars can serve as valuable tracers for the older populations. Therefore a main point of discussion throughout this study is the shape of the Galactic Disk, its components Thick and Thin
Disk, their scale heights and rotational velocities and those of the Halo.
Further results are e.g. the distance derived for the horizontal part of the HB7 (see Section 3.2.3),
which may be of cosmological interest.
This study is organised in the following manner: after the preceding introduction, the data acquisition
and reduction of the samples of stars dealt with in Chapters 4 and 5 is described in Chapter 2. Chapters
3, 4 and 5 present the actual analyses done: Chapter 3 is a study of Horizontal Branch stars with
Hipparcos data, showing that a trend in kinematics exists, with HBA stars showing a halotic behaviour
and most sdB stars being disk stars; Chapter 4 is a study of sdB kinematics with a greatly enlarged
sample, showing for the first time positive evidence for sdB stars in the Galactic Halo, and Chapter
5 is an extended study of the kinematics of HBB stars, which are the field BHB stars of which we
know least. The results of these studies are then discussed in detail in Chapter 6, an outlook is given
in Chapter 7. This outlook is especially important with the DIVA and GAIA satellite missions at
the horizon. These will give an enormous impetus to this type of work and studies of the structure
of the Milky Way in General. The Appendices give some supplementary information on reduction
techniques and definitions.
7
The HB consists of stars having nearly the same luminosities. There is just a little decline in luminosity with temperature
caused by the decline and finally the cessation of H-shell fusion. However the absolute magnitude (e.g. MV ) starts to get
fainter at a certain colour/temperature (e.g. near B − V =0.1 mag for V ) following a rather steep slope. Therefore the blue
and extended HBs look nearly vertical in a Colour-Magnitude-Diagram (CMD). The reason for this is that in the optical
regime hot stars show the Rayleigh-Jeans region of their spectra, the slope of which is no longer dependent on temperature.
Given a similar luminosity the stars become fainter with increasing temperature. The part of the HB which is not affected
by this observational effect, i.e. the RHB, RR-Lyr and late HBA stars are called members of the horizontal part of the HB.
13
1. I NTRODUCTION TO HB STARS AND THE STRUCTURE OF THE G ALAXY
14
C HAPTER 2
D ATA AND DATA REDUCTION
C OLLABORATORS : H. E DELMANN
2.1
T HE SAMPLE
The samples of 114 sdB stars, 19 HBB and 14 HBA stars composed of objects originate from several
sources: 79 sdB candidates, located in the southern polar cap (SPC) of our galaxy have been taken
from the Hamburg-ESO-survey (HE). Of these 59 turned out to be sdB type stars, 13 are HBB stars.
For these new data have been obtained. We further included the 41 sdB stars published in de Boer
et al. (1997a) and 4 HBB stars taken from Schmidt (1996), which were mainly taken from the Palomar
Green catalogue (Green et al. 1986). 17 sdB stars, 2 HBB and all of the HBA- and RR Lyrae stars
dealt with in Chapter 3 have been taken from the Hipparcos catalogue (In one case from the Tycho
catalogue and Geffert (1998)). Sole criteria for the selection of objects and the composition of the
samples i are unambiguous spectral classification and availability or obtainability of data.
A few objects, also located in the SPC on a strip just north of the celestial equator, come from the
Hamburg-Schmidt-survey (HS, Hagen et al. 1995). However, from the original ∼60 sdB-candidates
from this field only ∼15 were sdBs indeed, others being either AGNs, white dwarfs or cool stars.
Because of this and the faintness of most of the stars remaining in the sample the stars taken from this
field are not further considered for the main study. Nevertheless, some of the data is made available in
Appendix B; therefore data reduction for the stars of this field is also briefly described in this chapter.
More details about the composition of each sample and possible selection effects are discussed in the
relevant chapters (see Sections 3.2.1, 2.1,4.1.1.1 and 5.2). The distance determination of the objects
of Chapter 3, which mostly relies on the Hipparcos catalogue and other literature sources, is described
there. This chapter exclusively deals with the data reduction of the stars of which new data have been
obtained, i.e. those analysed in Chapters 4 and 5.
2.2
O BTAINING THE DATA
The data have been acquired over the past few years, mainly from the ESO La Silla and DSAZ Calar
Alto observatories, a smaller part of the spectroscopic data has been obtained at the NOT-Telescope of
the Nordic observatory on the Roque de los Muchachos, La Palma. For the 41 stars of de Boer et al.
(1997a) we took all of the data, except for a few cases, from that work. A few proper motions have
15
2. DATA AND DATA REDUCTION
been taken from the Hipparcos catalogue (ESA 1997), some of the other data from various sources in
literature (see Sect. 2.3).
2.2.1
S PECTROSCOPIC DATA
The spectra of the southern HE-stars have been taken at La Silla, Chile, with the ESO 1.54m Danish
telescope using the Danish Faint Object Spectrograph and Camera (DFOSC) covering a spectral range
from 3500 . . . 5500 Å and with the ESO 1.52m telescope using the Boller and Chivens spectrograph
covering a spectral range from 3500 . . . 7000 Å, The spectral resolution is about 5.0 and 5.5 Å, respectively. In order to conduct the wavelength calibration, especially because radial velocities were to
be derived, a emission lamp spectrum was taken after the object spectrum, while the telescope was in
the same position as during the object exposure. For the flux calibration spectra of the Oke-standard
star Feige 110 (Oke 1990) were obtained. Exposure times were between 120 s and 3600 s, depending
on the brightness of the object The data acquisition of the spectral data for the HE-stars was accomplished by Heinz Edelmann and Michael Lemke. The data for the HS-stars were obtained at the 2.2m
with the Calar Alto Faint Object Spectrograph (CAFOS) and the 3.5m with the TWIN spectrograph,
as well with the 2.6m NOT-Telescope with ALFOSC which is identical to the DFOSC. The resolution
of the Calar Alto instruments were ∼ 5.5 Å (CAFOS) and 2.5 Å (TWIN).
2.2.2
A STROMETRIC AND
PHOTOMETRIC DATA
For each object photometry in B and V is required. For the astrometry images in bands in the redder
part of the spectrum are needed to minimise effects from differential refraction (see e.g. Brosche et al.
1989). Therefore images were taken in B,V ,R passbands. In order to calibrate the proper motions to
the extragalactic reference frame, deep and relatively wide field exposures of the fields surrounding
the stars are also needed.
Data acquisition of CCD images for photometry and as second epoch material for the determination
of proper motions has been combined wherever possible.
The data was obtained with the 1.23 m-telescope at Calar Alto in October 1998 and September 1999
and at the 1.54 m Danish telescope and the DFOSC focal reducer at La Silla in January 1999, October
1999 and September 2000. The exposure times for the images were generally 900 s each in V ,R and
a somewhat shorter exposure in B (exposure time depending on approximate magnitude of the star)
for the images taken at Calar Alto and between 600 s and 900 s (V and R only) for those obtained at
La Silla. As the electronic gain of the CCD camera used for the La Silla images is such, that the target
star is overexposed in most cases, an additional short exposure was made with an exposure time of 5
to 120 s depending on the approximate magnitude of the star. To complete the photometry a short B
exposure was taken as well. On all nights Landolt standard stars (Landolt 1992) were taken at least
twice per night, mostly three times per night.
9 of the 11 nights at La Silla were photometric, for the rest the short exposures were repeated during
the next night. Unfortunately the second half of the last allocated night was not photometric, so here
magnitudes from literature had to be included (see Sect. 2.3.2).
16
2.3. Data reduction and analysis
Figure 2.1: Typical example of a line fit done with the line fitting program of Napiwotzki
(priv.comm.). Here all three parameters, namely Teff , log g and log(n(He)/n(H)) are fitted using the
lines shown in the figure. For further details, see text.
2.3
2.3.1
DATA REDUCTION AND ANALYSIS
S PECTROSCOPY: D ERIVING RADIAL VELOCITIES , log g
AND
Teff
The spectra were extracted from the two-dimensional frames and reduced to linear wavelength and
intensity scales using the ESO-MIDAS package. They were corrected for bias and the pixel-to-pixel
sensitivity variations of the CCD (flat-fielding). The sky background was removed by extracting a
(cosmic-ray events cleaned) stripe on each side of the stars spectrum and subtracting the average of
these two stripes from each row of the stellar signal on the CCD. These corrected rows were combined to a one dimensional stellar spectrum. Thereafter a wavelength calibration was performed with
calibration spectra recorded immediately after each stellar spectrum. Then all wavelength calibrated
spectra were corrected for atmospheric extinction using the extinction coefficients of La Silla, Chile
(Tug 1977).
The Calar Alto and NOT spectra were in principle reduced the same way as the ESO-spectra, with the
difference that the IRAF reduction package was used.
The spectra were then fitted to fully line blanketed LTE model atmospheres (Heber et al. 2000) as
well as hydrogen and helium blanketed NLTE model atmospheres (Napiwotzki 1997). The model
17
2. DATA AND DATA REDUCTION
spectra were convolved to match the spectrograph’s resolution and shifted by the approximate radial
velocity. The fitting was accomplished using the fitting routine of Lemke (1997), which is based on
the procedure of Bergeron et al. (1992) and Saffer et al. (1994). Fitting parameters are Teff , log g
and nHe, the helium abundance. In an iterative process using the Balmer- and HeI/HeII lines (if
applicable), final values for these quantities were derived (see Edelmann 1998). A typical output of
the fitting program is represented in Figure 2.1. The values for Teff , log g and nHe will be published
in Edelmann et al. (2002).
Spectroscopic distances were determined using the method of flux conservation. For this we first
obtained the angular stellar diameter by comparing model atmospheric fluxes with the dereddened
apparent V -magnitude. From the determined log g, the radii of the stars are calculated. We assume
the mass of the sdB stars to be 0.50 M , and that of the HBB stars 0.52 M , accounting for their
somewhat larger H-envelope mass. The error of the distances was determined by error propagation to
be in the order of 10%.
The radial velocities were obtained by determining the centre of gravity for all Balmer and Helium
lines and some metal lines. These wavelengths were then compared to the unshifted values for the
corresponding lines. From these the radial velocity of each line was derived; finally their mean was
calculated. Unfortunately the radial velocities obtained for the spectral lines show usually considerable scatter, often as a trend with wavelength. The exact reason for this is not known, the most
probable effect lies in the wavelength calibration, which most often relies on only very few emission
lines1 (Many lines were non resolved doublets, overexposed or underexposed lines, which cannot be
used for wavelength calibration). In some cases, when the seeing was better than the slit width, this
could lead to a slight offset of the barycentre of the stellar image in respect to the centre of the slit.
This may cause a slight shift in the spectrum (in respect to the wavelength calibration) and therefore a
trend in the resulting radial velocities. Therefore the resulting radial velocities have an error of about
30 km s−1 . With better lamps with more suitable lines, the radial velocities could in principle be much
better, with errors of about 2-10 km s−1 . Finally the radial velocities were transformed to heliocentric
values.
Some of the stars show clear signs of companions in their spectra. These spectroscopically obvious
secondary components contribute significantly to the continuum flux. The routine we employed to
fit spectral models to the spectra critically depends on the local continuum. Therefore in the case of
a binary star the continuum of the secondary star must be taken care of. As this is a rather tedious
procedure and only a few stars are affected we did not include these in our final sample. This does
not apply for those stars taken from literature which were measured using other fitting techniques, or
in the case of SB 744, where the secondary continuum was subtracted (Unglaub & Bues 1990). The
photometry (where the effect of the secondary can be seen in the B − V colours, see also Fig. 2.2)
and proper motions of these stars (named sdB+x) are included in the according data tables, i.e. Table
2.1 and 2.3.
sdB stars may be the result of close binary evolution. This means that even many of those that do
not show any sign of binarity in their spectrum have indeed a close companion. This star, being
either a White Dwarf or a low mass main sequence star, is too faint to show up in the spectrum,
neither as additional absorption lines or a redder continuum. Therefore such unseen companions do
not play a role for the method of the determination of physical parameters. They however do play
an important role for the radial velocity determination. Especially if the secondary star is a White
Dwarf of similar or even higher mass as the sdB primary, the measured radial velocity may have a
1
At CAFOS the situation has even worsened since the replacement of the He-lamp. The new device delivers hardly any
He-line, when exposed with an exposure time for which the important lines of the other lamps are not overexposed!
18
2.3. Data reduction and analysis
Figure 2.2: Two colour diagram of the HE-stars of our sample. Filled hexagons are sdB/OB stars,
open pentagons HBB stars and crosses sdB+x binaries
large amplitude – in some cases over 200 km s−1 . Indeed, recent studies have found many stars with
variable radial velocities (see e.g. Maxted et al. 2001; Morales-Rueda et al. 2002 etc.). As far as
possible we have used systemic radial velocities2 published in those studies and some by Marsh (priv.
comm.). Unfortunately we only have access to a few values – for most of our stars we only have
a single value. Luckily are the amplitudes of the majority of the variable radial velocities far less
dramatic, in the order of 50 km s−1 or less. The percentage of affected stars is by no means certain
– the most recent (unpublished) results show that only about 30% of the sdB stars do indeed show
a variation in their radial velocity, in contrast to two thirds as published in Maxted et al. (2001) or
Morales-Rueda et al. (2002). At present we cannot quantify the influence of variable radial velocities
on our results; we will have to bear this problem in mind, and try to determine the systemic radial
velocities of object with suspicious (i.e. very large) values in the future. This however requires
several nights of observing time and can probably not be accomplished for all or even most objects.
2.3.2
P HOTOMETRY
The basic CCD data reduction was done using the IRAF reduction software package. As the bias
frames of the DFOSC data were very uniform and constant with time and the overall gradient was
2
i.e. the velocity of the system.
19
2. DATA AND DATA REDUCTION
less than 3 ADU, we subtracted the mean, which gives the most noise-free way of subtracting a bias.
For the data of September/October 2000 (new CCD chip) the bias level changed a little from night to
night, so here the mean bias of each night had to be subtracted. The Calar Alto data had more structure
on the bias frames so we subtracted a mean bias image.
Flat field correction of the ESO data was somewhat more cumbersome. There were noticeably different large scale structures on the twilight flats made in the evening and during the morning twilight.
In extreme cases this residual gradient could be as much as 10% over the chip area, in general it was
∼4%. A residual gradient remained on the flat field corrected images as well.
To correct the images properly, we used a somewhat more sophisticated method (see App. A): All
of the long exposed object frames were combined in such a way that all stellar images vanish (except
some residuals of the target stars, because these were always near the same spot on the images and
were therefore not removed completely and had to be patched). These images have the correct gradient
but not a good S/N ratio. After normalising, both types of flats (the twilight flats and those derived
from the science frames) were blurred with a Gaussian. The twilight flat was then divided by the
blurred twilight flat leading to an image which shows only the small scale structure. This was then
in turn multiplied (transplanted) to the science frame flat. This method could not be used for the
B passband, because the object frames had only short exposure times. The result was then in turn
applied to the science frames. The Calar Alto frames did not have a problem with residual gradients.
However we used a similar technique to include short exposure flats which suffer from shutter timing
effects.
The correction of the various bad columns and pixels was done with IRAF’s task fixpix. An occasionally appearing bad line could not be corrected but was uncritical for our purposes.
The photometric reduction has been done using the photometry packages of IRAF. As only the magnitude of the target star was of interest we measured the stars magnitude using the aperture photometry
task phot. The aperture diameter used was 1400 , which is the size also used by Landolt (1992) for his
standard star photometry used for our calibration. The calibration was done with the equations
Vinst = Vcal + ζV + κV · XV + χV (B − V )cal
(2.1)
Binst = ((B − V )cal + Vcal ) + ζB + κB · XB
+ χB (B − V )c
(2.2)
Rinst = (Vcal − (V − R)cal ) + ζR + κR · XR
+ χR (V − R)cal
(2.3)
where Minst (M, N = B, V, R) means the instrumental magnitude in the appropriate passband,
Mcal ,(M − N )cal the calibrated magnitude/colour index, ζM the magnitude shift, κM the extinction coefficient and χM the colour term. The values of the calibration parameters were determined by
fitting the instrumental magnitude of the standard stars to the literature values using a least squares fit.
The solution was then applied to the programme stars. The photometric data is shown in Table 2.1.
A few of the stars spectroscopically identified as binaries having a cool companion clearly showed
up in a (B − V ) − (V − R) diagram, because their colour indices are much redder than those of
apparently single sdB stars. The star HE 0021−2326, which is spectroscopically classified as single,
has a slightly (but significantly) redder B − V index than that of single sdB stars, possibly indicating
that it has a companion too faint to have its spectral features (like the g-band or the Ca II H+K lines)
show up in its spectrum. This may mean that photometry is somewhat more sensitive for sdB binarity.
Comparison of the B-magnitudes of the HE-stars to the photographic bjdss-magnitudes listed on the
HE-finding plates shows generally agreement much better than inferred by the magnitude error of 0.1
20
2.3. Data reduction and analysis
Table 2.1: Photometric data of the part of the sample taken from the HE-catalogue. The 59
sdB/sdOB/sdBv stars are part of the sample dealt with in Chapter 4, the 14 HBBs are dealt with
in Chapter 5. The EB−V data is adapted from Schlegel et al. (1998) (for details, see text).
No. Name
V
B-V
V-R Airmass EB−V
Type
remarks
[mag] [mag] [mag]
1 HE 0000−2355 13.293 −0.246 −0.130
1.04 0.009
sdB
2 HE 0001−2443 13.876 −0.256 −0.136
1.20 0.009 He-sdB
3 HE 0004−2737 13.967 −0.277 −0.155
1.01 0.010
sdOB
4 HE 0021−2326 15.942 −0.064 +0.010
1.01 0.008
sdB
5 HE 0023−2317 14.57 −0.11
–
– 0.007
HBB
6 HE 0031−2724 14.229 −0.292 −0.115
1.01 0.005
sdOB
7 HE 0049−3059 14.413 −0.236 −0.126
1.00 0.007
sdB
8 HE 0049−2928 15.781 −0.221 −0.116
1.08 0.004
sdB
9 HE 0123−2808 16.089 −0.242 −0.067
1.13 0.006
sdB
10 HE 0127−4325 14.597 −0.226 −0.126
1.10 0.008
sdB
11 HE 0128−4311 14.455 −0.153 −0.081
1.03 0.013
HBB
12 HE 0136−2758 16.173 −0.233 −0.143
1.22 0.011
sdB
13 HE 0151−3919 14.311 −0.218 −0.101
1.04 0.004 sdB/HBB
14 HE 0218−3437 13.391 −0.253 −0.122
1.01 0.008
sdB
15 HE 0218−4447 12.887 −0.285 −0.144
1.10 0.006
sdO
16 HE 0221−3250 14.700 −0.243 −0.102
1.04 0.006
sdB
17 HE 0225−4007 12.042 −0.104 −0.045
1.03 0.012
HBB
18 HE 0226−3639 13.582 +0.069 +0.126
1.01 0.024 sdB+x
19 HE 0227−4012 14.854 +0.046 +0.286
1.10
???
20 HE 0230−4323 13.779 −0.223 −0.112
1.13 0.013
sdB
21 HE 0231−3441 14.828 −0.258 −0.131
1.07 0.012
sdB
22 HE 0238−1912 12.598 +0.154 −0.068
1.08 0.024
HBB
23 HE 0255−1814 13.896 −0.134 −0.068
1.03 0.014
HBB
24 HE 0258−2158 14.645 −0.217 −0.107
1.06 0.011
sdB
25 HE 0307−4554 15.063 −0.213 −0.100
1.11 0.013
sdB
26 HE 0315−4244 16.918 −0.221 −0.086
1.03 0.006
sdB
27 HE 0319−5105 13.253 −0.176 −0.074
1.25 0.004
sdB
28 HE 0324−2529 14.624 −0.241 −0.132
1.10 0.007
sdB
29 HE 0337−2508 13.843 +0.171 +0.166
1.02 0.003 sdB+x
30 HE 0340−3820 14.771 −0.280 −0.154
1.03 0.000
sdB
31 HE 0341−2449 14.889 −0.285 −0.156
1.07 0.001
sdOB
32 HE 0343−4748 14.193 −0.172 −0.066
1.06 0.000
sdB
33 HE 0351−3536 14.107 −0.228 −0.113
1.09 0.000
sdB
34 HE 0405−3859 14.392 −0.256 −0.123
1.10 0.000
sdB
35 HE 0405−1719 14.003 −0.276 −0.139
1.04 0.015
sdOB
36 HE 0407−1956 13.610
–
–
– 0.020
sdB
Beers et al.
1992
37 HE 0410−4901 14.508 −0.210 −0.059
1.09 0.007
sdB
38 HE 0419−2538 13.666 −0.227 −0.125
1.01 0.034
sdB
39 HE 0420−1806 14.607
–
–
– 0.030
HBB
40 HE 0429−2448 15.301 −0.240 −0.116
1.28 0.038
sdOB
41 HE 0430−2457 14.155 −0.046 +0.085
1.10 0.039 sdB+x
21
2. DATA AND DATA REDUCTION
No. Name
42
43
44
45
46
47
48
49
50
51
52
52a
53
HE 0430−5341
HE 0442−1746
HE 0444−4945
HE 0447−3654
HE 0452−3654
HE 0500−3518
HE 0504−2041
HE 0505−3833
HE 0505−2228
HE 0510−4023
HE 0513−4632
HE 0513−4632
HE 0516−2311
V
[mag]
13.628
15.150
15.113
14.552
13.836
15.044
14.959
14.185
15.547
14.837
15.341
15.338
15.600
54 HE 0519−3512 13.157
55 HE 0521−3914 15.550
56
57
58
59
60
61
62
63
63a
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
22
HE 0523−1831
HE 0532−4503
HE 0538−5637
HE 0539−4246
HE 2134−4119
HE 2135−3749
HE 2137−4221
HE 2154−4143
HE 2154−4143
HE 2155−1724
HE 2156−3927
HE 2156−1732
HE 2201−2113
HE 2203−3740
HE 2204−2136
HE 2205−1952
HE 2213−4158
HE 2222−3738
HE 2226−4005
HE 2230−4000
HE 2337−2944
HE 2340−2806
HE 2343−2944
HE 2349−3135
HE 2355−3221
HE 2359−2844
14.307
16.056
15.027
14.804
14.720
13.926
14.468
15.183
15.164
15.042
14.448
15.064
15.903
13.487
13.232
14.591
16.153
14.889
14.535
14.806
14.452
15.013
15.059
15.908
15.181
16.620
Table 2.1: Photometric data (cont.)
B-V
V-R Airmass EB−V Type remarks
[mag] [mag]
−0.151 −0.063
1.12 0.000 HBB
−0.271 −0.150
1.07 0.033 sdOB
−0.265 −0.115
1.12 0.001 sdB
−0.249 −0.125
1.22 0.001 sdB
−0.269 −0.126
1.21 0.000 sdB
−0.227 −0.113
1.36 0.003 sdB
−0.246 −0.106
1.37 0.022 sdB
−0.245 −0.116
1.21 0.014 sdB
−0.261 −0.089
1.09 0.024 sdB
−0.217 −0.084
1.30 0.038 sdB
+0.069 +0.134
1.46 0.013 sdB+x
+0.074 +0.137
1.42 0.013
−0.28:
–
– 0.027 sdB phot. B-mag.
+0.28 mag
−0.106 −0.048
1.50 0.033 HBB
–
–
– 0.016 sdBv Koen et al.
1999
−0.275 −0.130
1.35 0.048 sdB
−0.225 −0.109
1.42 0.027 sdB
+0.117 +0.193
1.44 0.049 sdO+x
−0.195 −0.108
1.10 0.036 sdB
−0.156 −0.085
1.05 0.014 HBB
−0.227 −0.135
1.03 0.024 sdB
−0.149 −0.046
1.03 0.009 HBB
−0.243 −0.107
1.07 0.009 sdB
−0.262 −0.136
1.05 0.009
−0.243 −0.110
1.16 0.036 sdB
−0.187 −0.055
1.02 0.031 sdB
−0.218 −0.082
1.08 0.009 sdB
−0.230 −0.111
1.06 0.028 sdB
−0.151 −0.083
1.02 0.012 HBB
−0.045 −0.032
1.07 0.032 HBB
−0.283 −0.135
1.01 0.019 sdB
−0.338 −0.115
1.18 0.002 sdB
−0.230 −0.132
1.07 0.006 sdB
+0.113 +0.131
1.02 0.006 sdB+x
+0.042 +0.109
1.08 0.007 sdB+x
−0.247 −0.147
1.04 0.009 sdB
−0.161 −0.053
1.00 0.007 sdB
−0.213 −0.133
1.04 0.003 sdB
−0.282 −0.107
1.07 0.009 sdB
−0.219 −0.135
1.10 0.002 sdB
−0.28:
–
– 0.009 sdOB Lamontagne
et al. 2000
+0.28 mag
2.3. Data reduction and analysis
tabsolsep1.8mm
Table 2.2: Comparison of magnitudes obtained on the 2.10.2000 with magnitudes from the HEcatalogue (which corresponds to the B magnitude) and other sources in literature (passband of literature value is in parentheses). Close neighbours affect the bjdss magnitudes: such stars have been
marked in column “remarks”.
Name
V
B
bjdss
mlit
Source
remark
[mag] [mag] [mag]
[mag]
HE 0001-2443 13.88 13.62 13.66 13.77(B) Lamontagne et al. (2000)
HE 0023-2317 14.57 14.46 14.44
–
–
HE 0238-1912 12.60 12.75 12.57
–
–
HE 0407-1956 13.67 13.41 12.81 13.61(V) (Beers et al. 1992)
close companion
HE 0516-2311 16.82 16.59 15.32
–
–
HE 0521-3914 16.66 15.94 14.92 15.55(V) Koen et al. (1999)
close companions
HE 0539-4246 14.80 14.61 14.52
–
–
HE 2201-2113 15.90 15.68 15.68
–
–
HE 2204-2136 13.23 13.19 13.30
–
–
HE 2359-2844 17.31 16.01
–
16.34(B) Lamontagne et al. (2000)
mag given for the bjdss-magnitudes, except when the star has close companions.
Part of the night of 2.10.2000 to 3.10.2000 was not photometric. As this was the last allocated night,
the photometric observations could not be repeated. While the first part could still be calibrated
properly, there were scattered clouds coming up after midnight. This means, that while there were
clear periods during this later part of the night, at other times the sky was nearly overcast. Therefore
no measurement obtained during this time can be trusted without some independent confirmation.
We thus compared our magnitudes with values taken from literature or from the photographic bjdss
magnitude of the HE-catalogue. This comparison, shown in Table 2.2 shows that during most of the
time our magnitudes agree rather well with the comparison magnitudes.
Of the stars observed on that night, HE 2201−2113, HE 2204−2136 and HE 0001−2443 were observed in the beginning of the night which was photometric, while for HE 0407−1956 (Beers et al.
1992), HE 0521−3914 (Koen et al. 1999) and HE 2359−2844 (Lamontagne et al. 2000) we could take
the values from literature. HE 0521−3914 is a EC 14026 multi modal variable star, which probably
is the case several other of the stars, especially to those having a Teff between 29 000 K and 35 000 K.
The amplitudes of EC 14026 stars is normally less than a few 1/100th mag so that this variability is
neglectable when compared to the other errors. In the cases where we had no measurement from literature, but the bjdss matches well we adopted our value. Finally, HE 0516−2311, has no published
magnitude and our magnitudes are not reliable. Therefore we adopted the bjdss magnitude (the star
has no close neighbours, which would falsify the bjdss value, see Table 2.2) as the B magnitude and
derived the V magnitude by adding 0.28 mag, which is a typical B − V value for a single sdB star
with little interstellar extinction. While we are convinced that the magnitudes adopted for these stars
are sufficiently accurate, it is clear that these have a somewhat greater uncertainty than those made in
other nights.
The majority of our stars is located at intermediate to very high galactic latitudes. Nevertheless the
photometry must be extinction corrected, to minimise systematic distance effects. As almost all stars
of our sample are located at |z| > 200 pc, thus likely above the galactic dust layer, one can assume
that all interstellar extinction is in front of the star. Therefore we decided to use reddening maps, such
as those from Schlegel et al. (1998) or Burstein & Heiles (1982). The latter have no data for about
23
2. DATA AND DATA REDUCTION
30% of our stars, namely those located near the SGP. Apart from that, a large part of the reddening
values turned out to be slightly negative, which could mean that their zero point of EB−V is a bit
to low or due to problems with interpolation. The average values taken from Schlegel et al. (1998)
are somewhat larger. Subtracting 0.02 mag from their values, which the authors suggest to make the
data comparable with that from Burstein & Heiles (1982) seems to overdo it. As a good compromise
we decided to take the Schlegel et al. (1998) reddening values, reduced by 0.01 mag. The very few
resulting negative values were taken as EB−V = 0. The absorption was then calculated with
AV = EB−V · 3.315
(2.4)
and applied to the V -magnitudes. For the majority of the stars EB−V was below 0.02 mag, a few
had an EB−V of between 0.04 and 0.05. This means that a residual EB−V will cause an error in the
distances which is small compared to the influences of the other errors. For the brighter and hence
nearer Hipparcos stars taken from Altmann & de Boer (2000), we took the extinction values published
there.
2.3.3
A STROMETRY
The biggest problem encountered when determining proper motions of stars is the availability of
suitable 1st epoch material. Before ∼ 1950 the photographic plates taken are mostly from areas of
special interest, such as fields containing a star cluster, a nebulosity, a bright galaxy or a dense region
of the Milky Way. Therefore one has to rely on whole sky surveys, such as the Palomar Observatory
Sky Survey (POSS), and its southern extension, the UK-Schmidt Survey. The latter was completed
in the 1970’s and early 1980’s while the POSS was accomplished between 1948 and 1958. In recent
times several scanned version of these plates became available, like the Digital Sky Survey (DSS)
or the APM catalogue (Automated Plate Measuring maschine, Irwin & McMahon 1992, Irwin et al.
1994). The APM comes as a positions catalogue and is first retransformed to plate coordinates by
a backwards gnomonic projection (Geffert, priv. comm.). This catalogue was found to be accurate
enough to provide the first epoch data, and 12 of the proper motions published in de Boer et al. (1997a)
have been determined using the APM (see also Altmann 1997). Unfortunately for δ < −15◦ , the
positions of the APM mainly rely on recent plates, rendering them unsuitable as first epoch material.
Therefore we took positions derived from DSS plates. These scans have a image scale of 1.700 /pix
and are made from the blue plates of the UK Schmidt-survey. This could mean a problem, because
blue light is affected more than red light by differential refraction (Brosche et al. 1989). However the
plates were taken at very low airmass, most of them near the meridian. The declinations of our objects
are between −17◦ and −55◦ , so they are not more than 25◦ off zenith when passing the meridian.
Of the position determining methods generally used to get the plate coordinates, DAOPHOT is presumably not the best way to determine positions of stars on a digitised photographic plate, because
it uses a PSF, and the PSFs of each photographic stellar image differs in contrast to those of a CCD
image. The PSFs of the galaxies needed for calibration purposes are unique anyway. For this reason
we decided to use SExtractor (Bertin & Arnouts 1996).
Comparing positions derived using DAOPHOT and SExtractor shows a good agreement for well exposed stars, with σ(∆x, ∆y) ' 0.02 pix, or 0.03500 (The image scale of the DSS1 is 1.700 /pix). In
order to compare DSS and APM positions, we derived proper motions for 9 stars from the equatorial
strip using both first epoch material. The standard deviations of the differences between the pairs of
proper motions was ∼ 2.5 mas/yr. This shows that with the usage of SExtractor the DSS1 can be used
for the determination of proper motions unlike Irafs task IMEXAM which does not seem to be well
suited (Altmann 1997). Taking the results of this comparison into account we conclude that the error
24
2.3. Data reduction and analysis
of the proper motions of the southern stars, which have a much smaller epoch difference is about 4 - 5
mas/yr. Adding the error of the galaxy calibration (using error propagation), which is in the order of
1 - 2 mas/yr, the proper motions derived from DSS first epoch material are good to about 5 - 6 mas/yr.
However one of the 9 proper motion pairs showed a larger deviation of about 10 mas/yr. So a few of
the proper motions have a larger error than the general error. But on the whole the DSS is suited for
this kind of work, so we decided to use this method for the southern stars. For the northern stars we
chose to use the APM for reasons of convenience.
The star HE 0407−1956 is partially merged with its neighbour, and SExtractor considered the two as
one object. Therefore we determined the centre of gravity for HE 0407−1956 by hand. The error of
this determination is however similar to those of the other stars.
2.3.3.1
2nd
EPOCH MATERIAL :
As second epoch material, the same CCD-exposures were used as for the photometry (See Sect. 2.2.2).
The ESO data has a image scale of 0.3900 /pix, the Calar Alto data 0.5300 /pix. For the determination of
plate coordinates, SExtractor was used for the CCD-images as well. DAOPHOT requires a lot of user
interaction during creation of the PSF (takes about 2 hours per star for the whole DAOPHOT process).
SExtractor reduces a complete data set within 5 minutes(!). The reason for using SExtractor, rather
than DAOPHOT is apart from time and convenience, the problem of galaxy PSFs. The agreement
between the positions derived with the two methods of reasonably bright not saturated stars is very
good.
2.3.3.2
R EFERENCE CATALOGUES :
The third item required for the derivation of proper motions is a reference catalogue which includes
position proper motions. However, for small field-astrometry, e.g. with CCD data, there are not
enough stars with measured proper motions in a typical field. Even the Tycho catalogue has only
about 1 - 5 entries in a DFOSC field of 13.70 ×13.70 . Still worse, almost all of these are saturated even
on the shortest exposures.
This means we had to rely on catalogues without proper motions taking into account the tradeoff that
the resulting proper motions are relative ones, which have to be calibrated to an absolute reference
frame. We accomplish this by using the background galaxies in the field which have by definition a
zero proper motion. As in these high galactic latitude fields the majority of the objects are already
galaxies, we expect the correction to be small.
For the stars north of the celestial equator we used the APM as the reference catalogue, no further
objects from the CCD data need to be added, because the APM catalogue already includes all objects
with first epoch data. Only objects in both data sets take part in the reduction anyway. In the south we
created a reference catalogue based on our CCD-data using the USNO2.0 catalogue (Monet 1998) as
start catalogue.
2.3.3.3
R EDUCTION :
The astrometric reduction was done using the BAP-software of Michael Geffert (see e.g. Geffert
et al. 1997; for a detailed description of the various programs and their usage, see Sanner (2001), his
Appendix C). In a two step iteration we first determined celestial positions for each plate/CCD-frame,
which were then averaged to give a catalogue with positions and proper motions. This catalogue was
25
2. DATA AND DATA REDUCTION
Table 2.3: The proper motions of all 79 stars. µα cos δ and µδ are the relative proper motions, µα cos δ 0 and µδ0 the absolute proper motions calibrated
to the extragalactic reference frame and ∆µα cos δ, ∆µδ their errors (based on the second epoch only, because only one set of first epoch data was
available, see text; the first epoch error is estimated to be about 4-6 mas/yr).
No.
Name
µα cos δ
µδ
µα cos δ 0
µδ0
∆µα cos δ
∆µδ
µα cos δ s
µδs
∆µα cos δ s
∆µδs
#gal
[mas/yr]
[mas/yr]
[mas/yr]
[mas/yr]
[mas/yr]
+5.9
−12.4
+9.2
−14.4
0.4
0.7
−3.3
+2.0
1.4
1.6
33
+3.8
−26.6
+7.0
−29.0
1.6
1.7
−3.2
+2.3
1.4
1.4
33
+18.4
−6.1
+20.1
−7.6
0.6
0.4
−1.7
+1.6
0.9
1.0
70
+8.2
+2.0
+6.5
−1.3
0.8
0.2
+1.7
+3.3
1.5
1.4
35
+2.0
−19.6
+2.8
−21.0
0.2
1.8
−0.8
+1.4
0.9
1.3
41
−3.9
+9.1
−2.7
+8.6
0.2
0.0
−1.2
+0.5
1.3
1.2
41
+15.6
−13.0
+15.4
−17.5
0.5
0.7
+0.1
+4.5
1.9
2.1
31
+16.0
−0.8
+16.9
−2.1
0.0
2.9
−1.0
+1.3
1.8
1.3
29
+4.0
−1.3
+6.0
−3.0
1.2
0.6
−2.0
+1.7
1.8
1.5
28
+4.8
+8.5
+8.3
+7.9
0.2
1.6
−3.6
+0.6
1.7
1.6
29
+14.0
−1.0
+17.0
−3.2
0.8
0.7
−3.0
+2.3
1.9
2.3
14
+14.0
−20.9
+15.6
−22.9
0.9
1.0
−1.7
+2.0
1.1
0.8
47
−5.6
−42.6
−7.4
−43.0
0.9
1.9
+1.8
+0.4
1.7
1.6
23
−1.6
−3.3
+2.0
−2.8
0.5
0.2
−3.6
−0.5
1.4
1.3
30
+47.1
+3.0
+47.9
+1.7
0.9
0.6
−0.8
+1.4
0.8
0.8
60
+21.6
−32.2
+23.4
−34.0
2.3
0.7
−1.8
+1.8
1.7
1.8
23
+16.2
−19.7
+18.7
−20.9
1.2
1.0
−2.5
+1.2
1.2
1.0
58
−1.1
+10.6
+0.5
+10.0
0.4
0.2
−1.6
+0.6
1.4
1.4
38
−14.3
−8.3
−11.7
−9.2
0.6
0.3
−2.6
+1.0
0.8
0.8
81
+5.7
+18.7
+5.0
+20.3
1.0
0.6
+0.7
−1.6
1.5
1.3
50
−9.9
−14.7
−9.1
−17.2
2.1
1.6
−0.8
+2.5
2.6
2.5
15
+9.3
−14.6
+13.8
−11.9
0.3
0.8
−4.6
−2.7
2.4
2.7
14
−0.3
+0.8
−0.8
+2.2
0.7
0.2
+0.6
−1.4
3.1
3.0
20
+20.2
−5.3
+25.7
−6.6
0.4
0.4
−5.5
+1.3
1.4
1.5
31
+18.5
−4.8
+21.7
−8.1
0.9
1.2
−3.2
+3.3
1.6
1.3
27
+1.00
−3.0
+4.1
−4.5
1.0
0.8
−3.1
+1.5
1.5
1.9
21
1
HE 0000−2355
2
HE 0001−2443
3
HE 0004−2737
4
HE 0021−2326
5
HE 0023−2317
6
HE 0031−2724
7
HE 0049−2928
8
HE 0049−3059
9
HE 0123−2808
10
HE 0127−4325
11
HE 0128−4311
12
HE 0136−2758
13
HE 0151−3919
14
HE 0218−3437
15
HE 0218−4447
16
HE 0221−3250
17
HE 0225−4007
18
HE 0226−3639
19
HE 0230−4323
20
HE 0231−3441
21
HE 0238−1912
22
HE 0255−1814
23
HE 0258−2158
24
HE 0307−4554
24a
HE 0307−4554
25
HE 0315−4244
continued next page
26
Name
26
HE 0319−5105
27
HE 0324−3749
28
HE 0337−2506
29
HE 0340−3820
30
HE 0341−2449
31
HE 0343−4748
32
HE 0351−3536
33
HE 0405−1719
34
HE 0405−3839
35
HE 0407−1956
36
HE 0410−4901
37
HE 0419−2538
38
HE 0420−1806
39
HE 0429−2448
40
HE 0430−2457
41
HE 0430−5341
42
HE 0442−1746
43
HE 0444−4945
44
HE 0447−3654
45
HE 0452−3654
46
HE 0500−3518
47
HE 0504−2041
48
HE 0505−2228
49
HE 0505−3833
50
HE 0510−4023
51
HE 0513−4632
52
HE 0516−2311
continued next page
No.
µα cos δ
µδ
[mas/yr]
+7.4
−0.4
−3.1
−8.5
+0.4
−5.0
+2.7
+8.3
+19.0
−5.6
+4.1
−3.0
+0.6
−8.7
−0.5
+15.4
+1.9
+3.9
+13.5
+39.3
+4.8
+11.0
+4.6
−5.6
+0.7
−1.1
−6.3
−9.8
+8.3
−15.5
+16.5
−23.8
−7.4
+12.9
+8.9
+20.6
+14.2
−18.3
+7.8
+9.4
+8.4
+15.8
+8.0
+3.0
+16.9
−0.9
+2.2
+5.0
+2.8
−6.0
+2.0
−4.5
−17.0
+14.1
Table 2.3: The proper motions of all 79 stars (cont.).
µα cos δ 0
µ0δ
∆µα cos δ
∆µδ
µα cos δ s
µsδ
[mas/yr]
[mas/yr]
[mas/yr]
+7.1
+0.7
1.3
0.7
+0.3
−1.2
−0.8
−10.8
0.9
0.8
−2.3
+2.3
+2.3
−6.3
0.7
1.1
−1.8
+1.3
+4.2
+7.8
0.4
0.2
−1.6
+0.5
+20.0
−5.0
0.5
2.0
−1.0
−0.6
+5.8
−2.7
0.2
0.9
−1.7
−0.3
−0.6
−8.2
1.6
0.6
+1.2
−0.5
−2.6
+15.8
0.5
0.3
+2.2
−0.4
+5.2
+2.8
1.5
1.0
−3.2
+1.2
+13.9
+41.7
0.9
1.0
−0.4
−2.4
+5.4
+10.7
0.5
0.4
−0.6
+0.3
+4.1
−8.2
0.3
0.6
+0.5
+2.6
+0.5
0.0
1.0
1.4
+0.2
−1.1
−5.6
−9.0
1.2
0.6
−0.6
−0.8
+11.0
−15.8
2.4
1.5
−2.7
+0.3
+19.3
−23.3
0.8
0.6
−2.8
−0.5
−5.3
+11.5
0.8
0.5
−2.1
+1.4
+9.4
+23.9
0.5
0.5
−0.5
−3.4
+16.5
−20.1
1.1
0.5
−2.4
+1.8
+7.4
+9.8
1.1
0.7
+0.3
−0.3
+8.3
+15.8
1.6
0.2
+0.1
−0.1
+7.1
+2.3
1.5
1.0
+0.9
+0.7
+16.6
+1.1
1.1
0.6
+0.2
−2.0
+3.1
+6.5
0.9
0.5
−0.8
−1.5
+3.3
−6.2
1.4
0.4
−0.6
+0.2
+3.9
−3.7
1.1
0.2
−1.9
−0.9
−17.9
+17.8
0.9
3.1
+0.9
−3.6
∆µα cos δ s
∆µsδ
[mas/yr]
1.1
1.1
1.3
1.7
1.8
1.8
1.0
1.0
1.3
1.6
1.0
0.9
1.4
1.3
1.8
1.8
1.4
1.4
2.1
1.9
0.9
1.0
1.6
1.5
1.4
1.7
1.9
1.8
1.7
1.3
1.0
1.1
2.0
1.5
2.2
1.9
1.2
1.3
0.9
0.9
1.8
1.5
1.4
1.8
1.6
1.7
0.9
0.8
0.8
0.7
1.0
1.0
2.0
2.0
50
26
31
56
33
66
54
45
35
23
92
38
31
32
46
78
29
37
50
79
44
38
43
102
115
44
29
#gal
2.3. Data reduction and analysis
27
2. DATA AND DATA REDUCTION
53
54
55
56
57
58
59
60
61
62
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
No.
HE 0519−3512
HE 0521−3914
HE 0523−1831
HE 0532−4503
HE 0538−5637
HE 0539−4246
HE 2134−4119
HE 2135−3749
HE 2137−4221
HE 2154−4143
HE 2154−4143
HE 2155−1724
HE 2156−1732
HE 2156−3927
HE 2201−2136
HE 2203−3740
HE 2204−2136
HE 2205−1952
HE 2213−4158
HE 2222−3738
HE 2226−4005
HE 2230−4000
HE 2337−2944
HE 2340−2806
HE 2343−2944
HE 2349−3135
HE 2355−3221
HE 2359−2844
Name
µα cos δ
µδ
[mas/yr]
+1.1
−9.8
−16.4
+11.0
+3.1
−10.1
+7.1
−4.5
+4.5
−14.1
−6.0
+3.9
−6.9
+2.6
+6.8
+8.3
+1.7
−3.4
+5.2
+7.1
+4.6
+6.2
+11.6
+0.4
+7.1
−7.2
+5.6
+24.6
+8.4
−2.5
−5.2
+3.7
−11.0
−14.1
+7.8
−3.8
+7.2
+10.9
+28.7
−2.0
+1.0
−3.5
+1.9
−10.1
+15.1
+11.8
−1.2
+12.7
+5.2
−15.2
−4.1
−4.9
−0.6
−13.9
+6.1
−11.9
Table 2.3: The proper motions of all 79 stars (cont.).
µα cos δ 0
µδ0
∆µα cos δ
∆µδ
µα cos δ s
µδs
[mas/yr]
[mas/yr]
[mas/yr]
+1.2
−8.9
2.1
0.6
−0.0
−0.9
−15.0
+11.2
0.4
0.6
−1.4
−0.2
+4.8
−10.1
1.0
0.5
−1.7
+0.0
+8.2
−2.7
1.2
0.5
−1.1
−1.8
+3.9
−13.6
0.6
0.2
+0.6
−0.6
−0.2
+3.7
0.5
0.6
−5.8
+0.2
−7.0
−0.3
0.4
0.6
+0.1
+2.9
+5.3
+6.0
0.2
0.0
+1.4
+2.3
+0.2
−5.9
0.0
0.6
+1.5
+2.4
+5.6
+5.5
0.4
0.6
−0.4
+1.6
+5.0
+5.8
0.6
0.5
−0.4
+0.3
+11.6
−2.2
0.0
0.2
−0.0
+2.6
+8.7
−10.2
0.7
0.5
−1.6
+3.0
+4.4
+22.0
1.1
0.4
+1.2
+2.5
+9.2
−3.9
0.4
0.6
−0.8
+1.4
−4.9
+1.9
0.6
0.4
−0.3
+1.8
−5.5
−19.8
0.7
0.9
−5.5
+5.7
+7.5
−8.8
0.2
0.2
+0.2
+5.1
+5.6
+10.3
1.0
0.4
+1.6
+0.6
+32.0
−6.0
1.2
0.4
−3.3
+4.0
+2.6
−6.9
0.4
0.3
−1.6
+3.4
+3.8
−12.1
0.4
0.2
−1.8
+2.0
+14.3
+8.4
0.8
0.4
+0.8
+3.3
+1.7
+11.3
1.0
0.9
−2.9
+1.4
+5.5
−15.2
0.8
0.4
−0.3
+0.0
−6.6
−1.9
1.5
0.6
+2.5
−2.9
−0.1
−15.5
0.4
0.6
−0.5
+1.5
+7.8
−12.0
0.8
0.6
−1.7
+0.1
∆µα cos δ s
∆µδs
[mas/yr]
1.1
1.0
1.4
1.0
1.2
1.3
1.0
1.2
0.9
0.9
1.4
1.7
0.9
1.0
1.3
1.1
0.8
0.9
1.6
2.1
1.8
2.1
2.0
2.7
1.5
1.8
2.5
2.5
1.0
1.2
1.7
1.6
2.0
1.6
1.2
1.4
2.0
2.6
1.2
1.7
1.0
1.2
1.3
1.5
2.3
2.1
1.3
2.0
1.5
1.8
1.9
1.7
0.9
0.9
1.4
1.3
#gal
68
34
56
65
81
31
50
40
79
30
31
19
31
15
50
33
20
39
21
30
46
34
21
37
37
20
73
29
28
2.3. Data reduction and analysis
Figure 2.3: Separating stars and galaxies.
Shown is a plot magnitude against fwhm,
showing the stars (vertical distribution of
points along f whm=2.7 pix), probable galaxies to the right of this and spurious objects to
the left of the stars. Also shown are two linear equations which are used to throw out low
S/N objects.
Figure 2.4: Vector point plot diagram of the
measured proper motions of faint background
galaxies. These (galaxies have µ = 0 mas/yr)
are used to calibrate the proper motion of the
star into an absolute reference frame
then in turn used as new reference catalogue for the second iteration. For the plate reduction we used
a plate model with 3rd order terms.
The resulting errors (based alone on the second epoch, since there is only one first epoch position) are
in the order of 1 mas/yr with only a few stars having an error larger than 2 mas/yr.
2.3.3.4
C ALIBRATION :
As stated before, the resulting proper motions are relative only. Therefore we transfer them to an
absolute reference frame using the background galaxies. For this one determines the apparent galaxy
proper motion centroid and subtracts this from the stellar proper motions. The galaxies are identified
and separated from stars by criteria of FWHM of their images, SExtractor’s stellarity index and additional user defined selections to account for the larger error of FWHM for faint objects. This method
is well established and often used in galaxy searches (see Figure 2.3). For each star we found between
15 and 120 galaxies, mostly between 40 and 70. The limiting factor is the 1st epoch material; the long
CCD exposures, which were used for galaxy searching, usually yielded several hundred galaxies.
Unfortunately the galaxies are very faint or show too much structure to be centered properly. Therefore
the derived proper motions of these objects scatter considerably. The faintness of the objects leads
to undersampling in the digitised photographic plates. The brighter galaxies have a slightly different
shape or light distribution in different parts of the spectrum, e.g. star forming regions in spirals. To
get rid of the most extremely deviating cases we expunged those objects deviating by more than 2σ
completely. In general the standard deviation was about 10 to 15 mas/yr and a resulting error of 0.5 to
2.5 mas/yr in almost all cases. These large standard deviations are not unusual, given the difficulties
described earlier on; Ojha et al. (1994) arrived at values of 8 mas/yr for their standard deviation of the
29
2. DATA AND DATA REDUCTION
Table 2.4: The spatial and kinematic data of all stars dealt with in Chapters 4 and 5. This table contains positions, distances, proper motions and radial
velocities of all objects and the sources where they have been taken from
Name
α(2000.0)δ
d
µα cos δ
µδ
vrad
Sourcea
Type
Chapter
[h m s ]
[◦ 0 00 ]
[kpc]
[mas/yr]
[km s−1 ]
Astr.
Sp.
00 03 22.059
−23 38 57.99
0.76
+9.2
−14.4
−64
TW
HE
sdB
4
00 06 46.264
−27 20 53.40
0.71
+20.1
−7.6
+27
TW
HE
sdB
4
00 07 33.770
+13 35 57.65
1.41
+3.0
−25.0
−37
B97
B97
sdB
4
00 23 59.331
−23 09 53.92
2.72
+6.5
−1.3
−67
TW
HE
sdB
4
00 26 14.545
−23 00 36.11
4.17
+2.8
−21.0
+70
TW
HE
HBB
5
00 33 53.889
−27 08 24.08
0.93
−2.7
+8.6
−12
TW
HE
sdB
4
00 42 58.309
−38 07 37.30
0.26
+43.8
−7.0
−62
HIP
HE
sdB
4
00 47 29.219
+09 58 55.69
0.17
+4.1
+24.0
+3
HIP
HE
sdB
4
00 42 06.110
+05 09 23.37
1.05
+7.5
−12.0
+87
B97
B97
sdB
4
00 51 57.737
−29 12 07.54
2.20
+15.4
−17.5
−15
TW
HE
sdB
4
00 51 37.702
−30 42 56.19
1.22
+16.9
−2.1
+52
TW
HE
sdB
4
01 01 17.569
−33 42 45.42
0.54
−11.0
−12.9
−56
HIP
HE
sdB
4
01 04 21.670
+04 13 37.26
0.45
+12.2
−40.0
+8
B97
M99
sdB
4
01 08 26.774
−32 43 11.63
0.44
−7.7
+1.7
−24
HIP
HE
sdB
4
01 25 33.347
−27 53 04.74
2.61
+6.0
−3.0
+35
TW
HE
sdB
4
01 29 11.441
−43 10 27.85
1.71
+8.3
+7.9
+16
TW
HE
sdB
4
01 30 28.935
−42 55 53.99
2.54
+17.0
−3.2
+12
TW
HE
HBB
5
01 36 26.259
+11 39 30.95
0.77
+20.7
−34.4
+6
TW
M02
sdB
4
01 38 26.93
+03 39 38.0
0.81
+11.1
−17.9
0
B97
B97
sdB
4
01 39 14.456
−27 43 21.81
2.20
+15.6
−22.9
−159
TW
HE
sdB
4
01 43 48.548
−24 05 10.22
0.26
+88.4
−46.2
+30
HIP
HE
sdB
4
01 45 39.57
+15 04 41.5
1.17
−17.4
−0.4
−131
B97
B97
sdB
4
01 48 44.038
−26 36 12.83
0.46
+90.6
−47.0
+27
HIP
K
sdB
4
01 53 11.196
−39 04 17.97
2.11
−7.4
−43.0
−176
TW
HE
sdB
4
02 15 11.078
+15 00 04.55
1.75
−3.8
−9.2
+50
B97
B97
sdB
4
02 15 41.602
+14 29 17.97
1.85
+11.2
−1.4
+77
B97
B97
sdB
4
HE 0000−2355
HE 0004−2737
PG 0004+133
HE 0021−2326
HE 0023−2317
HE 0031−2724
SB 290
HD 4539
PG 0039+049
HE 0049−2928
HE 0049+3059
SB 410
Feige 11
SB 459
HE 0123−2808
HE 0127−4325
HE 0128−4311
PG 0133+114
PHL 1079
HE 0136−2758
SB 707
PG 0142+148
SB 744
HE 0151−3919
PG 0212+148
PG 0212+143
continued next page
30
HE 0218−3437
HE 0218−4447
HE 0221−3250
HE 0225−4007
HE 0230−4323
HE 0231−3441
HE 0238−1912
PG 0242+132
HE 0255−1814
HE 0258−2158
HE 0307−4554
HE 0315−4244
HE 0319−5105
HE 0324−3749
HE 0340−3820
HE 0341−2449
PG 0342+026
HE 0343−4748
HE 0351−3536
HE 0405−1719
HE 0405−3839
HE 0407−1956
HE 0410−4901
HE 0419−2538
HE 0420−1806
HE 0429−2448
HE 0430−5341
continued next page
Name
Table 2.4: The spatial and kinematic data (cont.)
α(2000.0)δ
d
µα cos δ
µδ
vrad
h
m
s
◦
0
00
[
]
[
]
[kpc]
[mas/yr]
[km s−1 ]
02 20 59.750
−34 23 35.19
0.81
+2.0
−2.8
+38
02 20 24.432
−44 33 28.47
0.64
+47.9
+1.7
−15
02 23 58.146
−32 36 32.61
1.60
+23.4
−34.0
−73
02 27 29.160
−39 53 37.89
1.29
+18.7
−20.9
+140
02 32 54.678
−43 10 27.79
1.03
−11.7
−9.2
−102
02 34 00.251
−34 27 54.90
1.02
+5.0
+20.3
−62
02 41 03.940
−19 00 11.48
0.97
−9.1
−17.2
−174
02 45 38.855
+13 26 02.41
1.39
+17.2
−9.7
+11
02 57 57.306
−18 02 07.54
2.82
+13.8
−11.9
+58
03 00 17.805
−21 46 31.16
1.78
−0.8
+2.2
+72
03 09 25.927
−45 43 33.08
1.02
+23.7
−7.4
−31
03 17 47.119
−42 33 41.24
5.21
+4.1
−4.5
+121
03 21 21.781
−50 55 15.79
2.90
+7.1
+7.0
+267
03 26 14.984
−25 18 37.95
1.14
−0.8
−10.8
+74
03 42 47.061
−38 11 26.43
1.43
+4.2
+7.8
−66
03 43 36.351
−24 39 46.76
1.13
+20.0
−5.0
+10
03 45 34.578
+02 47 52.81
0.36
+8.6
−28.9
+13
03 45 09.523
−47 38 53.96
2.12
+5.8
−2.7
+44
03 53 51.176
−35 27 35.26
0.86
−0.6
−8.2
+64
04 07 27.543
−17 11 15.50
0.91
−2.6
+15.8
+70
04 07 02.847
−38 51 46.09
1.47
+5.2
+2.8
−44
04 10 11.142
−19 48 53.59
0.96
+13.9
+41.7
−6
04 11 30.168
−48 53 47.96
1.71
+5.4
+10.7
−27
04 22 04.170
−25 31 00.46
1.29
+4.1
−8.2
−29
04 22 25.182
−17 59 19.38
5.13
+4.8
0.0
−64
04 31 28.288
−24 41 56.76
1.18
−5.6
−9.0
+15
04 31 11.068
−53 35 27.10
3.29
+19.3
−23.3
+63
Sourcea
Astr.
Sp.
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
B97
B97
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TYC
—
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
sdB
sdB
sdB
HBB
sdB
sdB
HBB
sdB
HBB
sdB
sdB
sdB
HBB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
HBB
sdB
HBB
Type
4
4
4
5
4
4
5
4
5
4
4
4
5
4
4
4
4
4
4
4
4
4
4
4
5
4
5
Chapter
2.3. Data reduction and analysis
31
2. DATA AND DATA REDUCTION
Name
HE 0442−1746
HE 0444−4945
HE 0447−3654
HE 0452−3654
HE 0500−3518
HE 0504−2041
HE 0505−2228
HE 0505−3833
HE 0510−4023
HE 0516−2311
HE 0519−3512
HE 0521−3914
HE 0523−1831
HE 0532−4503
HE 0539−4246
PG 0856+121
PG 0907+123
PG 0918+029
PG 0919+273
PG 1101+249
PG 1114+073
PG 1232−136
PG 1233+427
Feige 66
PG 1256+278
PG 1343−101
HD 127493
continued next page
Table 2.4: The spatial and kinematic data (cont.)
α(2000.0)δ
d
µα cos δ
µδ
vrad
[h m s ]
[◦ 0 00 ]
[kpc]
[mas/yr]
[km s−1 ]
04 44 34.883
−17 40 42.73
1.26
−5.3
+11.5
+18
04 46 14.091
−49 40 10.85
1.53
+9.4
+23.9
+75
04 49 15.625
−36 49 28.73
1.12
+16.5
−20.1
+128
04 53 52.657
−36 49 15.20
0.86
+7.4
+9.8
−62
05 02 31.672
−35 14 19.41
1.29
+8.3
+15.8
+19
05 06 39.673
−20 37 38.40
1.44
+7.1
+2.3
−11
05 07 47.457
−22 24 27.63
1.19
+16.6
+1.1
−12
05 06 58.854
−38 29 15.46
0.93
+3.1
+6.5
+69
05 12 18.203
−40 19 34.46
1.51
+3.3
−6.2
+49
05 18 06.975
−23 08 45.18
2.27
−17.9
+17.8
−12
05 20 48.576
−35 09 30.57
0.94
+1.2
−8.9
+228
05 23 25.477
−39 11 54.33
1.82
−15.0
+11.2
−87
05 25 31.316
−18 29 08.61
1.78
+4.8
−10.1
−6
05 33 40.499
−45 01 35.33
2.56
+8.2
−2.7
−166
05 41 06.688
−42 45 31.94
1.28
−0.2
+3.7
+71
08 59 02.723
+11 56 24.73
0.99
−19.4
−19.8
+85
09 10 07.6
+12 08 26.1
1.52
+6.4
−2.6
+85
09 21 28.230
+02 46 02.25
1.04
−28.5
−20.0
+104
09 22 39.830
+27 02 26.15
0.35
+22.9
−19.8
−65
11 04 31.731
+24 39 44.75
0.39
−30.3
+16.0
−48
11 16 49.670
+06 59 30.83
0.45
−12.3
−14.4
+9
12 35 18.915
−13 55 09.31
0.57
−46.4
−1.7
+55
12 35 51.641
+42 22 42.64
0.32
+3.6
−18.1
+61
12 37 23.517
+25 03 59.87
0.18
+2.7
−26.7
+1
12 59 21.266
+27 34 05.22
0.78
−24.6
+3.5
+64
13 46 08.069
−10 26 48.27
0.72
−28.0
−3.7
+49
14 32 21.492
−22 39 25.64
0.12
−32.8
−17.2
+13
Sourcea
Astr.
Sp.
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
B97
B97
B97
M02
B97
TM
B97
B97
B97
B97
B97
TM
B97
B97
B97
B97
HIP
E67
B97
B97
B97
B97
HIP
W53
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
HBB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
Type
4
4
4
4
4
4
4
4
4
4
5
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
Chapter
32
PG 1432+004
PG 1433+239
PG 1452+198
PG 1519+640
PG 1619+522
HD 149382
PG 1647+252
PG 1708+602
PG 1710+490
PG 1716+426
PG 1722+286
PG 1725+252
PG 1738+505
UV 1758+36
HD 171858
HE 2134−4119
HE 2135−3749
HD 205805
HE 2137−4221
HE 2154−4143
HE 2155−1724
HE 2156−1732
HE 2156−3927
HE 2201−2136
HE 2203−3740
HE 2204−2136
PG 2204+035
continued next page
Name
Table 2.4: The spatial and kinematic data (cont.)
α(2000.0)δ
d
µα cos δ
µδ
vrad
h
m
s
◦
0
00
[
]
[
]
[kpc]
[mas/yr]
[km s−1 ]
14 35 19.833
+00 13 47.96
0.76
−9.4
−25.8
+1
14 35 20.359
+23 45 27.52
0.47
−3.5
−18.5
−56
14 54 39.810
+19 37 00.88
0.81
−7.2
−21.0
+51
15 20 31.320
+63 52 07.95
0.65
+28.1
+41.2
+2
16 20 38.740
+52 06 08.78
0.77
−3.6
+9.0
−52
16 34 23.334
−04 00 52.02
0.08
−6.0
−3.9
+3
16 49 08.974
+25 10 05.74
0.71
−3.8
+12.3
+26
17 09 15.900
+60 10 10.79
1.79
−14.9
+12.1
−8
17 12 18.740
+48 58 35.88
0.72
+10.8
−7.0
−54
17 18 03.538
+42 34 18.40
1.20
+7.1
−21.8
−4
17 24 11.970
+28 35 26.93
0.87
−4.0
+10.0
−34
17 27 57.390
+25 08 35.69
0.66
−17.7
+9.0
−60
17 39 28.440
+50 29 25.11
0.97
−7.6
+9.0
+22
18 00 18.865
+36 28 56.34
0.20
−28.2
+7.3
0
18 37 56.675
−23 11 35.20
0.16
−15.0
−24.7
+74
21 37 59.914
−41 06 13.16
3.43
−7.0
−0.3
+64
21 38 40.590
−37 36 22.73
0.72
+5.3
+6.0
−156
21 39 10.614
−46 05 51.53
0.20
+76.4
−9.9
−57
21 40 09.544
−42 08 18.66
2.85
+0.2
−5.9
+33
21 58 01.977
−41 28 49.72
1.49
+5.3
+5.7
−15
21 58 15.920
−17 09 45.31
1.27
+11.6
−2.2
−27
21 59 30.144
−17 18 21.63
1.39
+8.7
−10.2
−77
21 59 35.504
−39 13 14.84
1.40
+4.4
+22.0
−200
22 04 06.714
−20 59 09.27
1.88
+9.2
−3.9
−23
22 06 27.426
−37 26 11.52
2.56
−4.9
+1.9
+63
22 07 12.285
−21 21 20.56
2.49
−5.5
−19.8
−13
22 07 16.490
+03 42 19.82
1.18
+7.5
−6.0
+81
Sourcea
Astr.
Sp.
B97
TM
B97
B97
B97
B97
TYC
TM
B97
M02
HIP
W53
B97
B97
B97
B97
B97
TM
G98
M02
B97
TM
B97
M02
B97
B97
HIP
HE
HIP
M02
TW
HE
TW
HE
HIP
B97
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
TW
HE
B97
B97
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
HBB
sdB
sdB
HBB
sdB
sdB
sdB
sdB
sdB
HBB
HBB
sdB
Type
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
5
4
4
5
4
4
4
4
4
5
5
4
Chapter
2.3. Data reduction and analysis
33
2. DATA AND DATA REDUCTION
Name
HE 2205−1952
HE 2213−4158
PG 2218+020
HE 2222−3738
PG 2226+094
PG 2259+134
Feige 108
Feige 109
PG 2337+070
HE 2337−2944
HE 2340−2806
SB 815
HE 2343−2944
HE 2349−3135
PG 2349+002
SB 884
HE 2355−3221
PG 2358+107
HE 2359−2844
Table 2.4: The spatial and kinematic data (cont.)
α(2000.0)δ
d
µ cos δ
µ
vrad
α
δ
[h m s ]
[◦ 0 00 ]
[kpc]
[mas/yr]
[km s−1 ]
22 08 41.304
−19 37 39.44
1.01
+7.5
−8.8
−52
22 16 17.704
−41 43 22.20
3.95
+5.6
+10.3
−4
22 21 24.83
+02 16 18.6
1.15
+1.1
−11.8
+21
22 24 56.433
−37 23 30.22
1.39
+32.0
−6.0
−134
22 28 58.41
+09 37 21.8
1.13
+14.3
+0.4
−48
23 01 45.82
+13 38 37.5
1.38
+0.6
−9.6
+16
23 16 12.41
−01 50 34.50
0.40
−7.8
−16.5
+40
23 17 26.890
+07 52 04.93
1.13
−1.2
+8.1
−37
23 40 04.83
+07 17 11.00
0.77
−19.1
−37.4
−27
23 40 15.331
−29 27 59.82
0.87
+14.3
+8.4
−26
23 42 41.388
−27 50 01.62
1.46
+1.7
+11.3
−20
23 44 22.008
−34 27 00.40
0.25
−22.3
−7.2
+24
23 46 17.749
−29 27 49.88
1.29
+5.5
−15.2
−0
23 51 43.637
−31 18 52.87
2.08
−6.6
−1.9
+180
23 51 53.26
+00 28 18.00
0.82
−10.1
−15.7
−84
23 52 36.092
−30 10 09.12
0.37
+30.4
−13.2
−3
23 58 22.471
−32 04 39.07
1.69
−0.1
−15.5
+61
00 01 06.730
+11 00 36.32
0.83
−3.0
−14.0
−19
00 01 38.463
−28 27 42.83
1.53
+7.8
−12.0
−129
Sourcea
Astr.
Sp.
TW
HE
TW
HE
B97
B97
TW
HE
B97
TM
B97
B97
B97
B97
B97
TM
B97
B97
TW
HE
TW
HE
HIP
HE
TW
HE
TW
HE
B97
B97
HIP
HE
TW
HE
B97
B97
TW
HE
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
sdB
Type
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
Chapter
a
: References of sources of data. The column called “Astr.” means astrometric data, “Sp.” refers to spectroscopic and photometric data sources (i.e. radial velocities
and the used for the calculations of the distances): The abbreviations mean: TW: This work, HE: Edelmann, B97: de Boer et al. 1997a, HIP: Hipparcos catalogue
(ESA 1997), TYC: the Tycho2 catalogue (Høg et al. 2000), M99: Moran et al. 1999, M02: Morales-Rueda et al. 2002, TM, Marsh (priv comm.)
34
2.4. The final sample
galaxy proper motions, which is consistent with our value, taking into consideration that their epoch
difference is more than twice of ours. A typical example is represented in Figure 2.4. The errors are
almost as large as the values in all but a few cases, so that the proper motion was not really improved
by the correction. We nevertheless applied the galaxy calibration to put the proper motion in the
extragalactic reference frame, to eliminate systematic effects, such as the general motion of stars in
that particular field.
2.4
T HE FINAL SAMPLE
Table 2.4 shows the input values (coordinates, proper motions and radial velocities) for the further
calculations and analyses as described in Chapters 4 and 5. All stars not further considered (whose
measurement results are shown in the other data tables for reasons of completeness) are omitted in
this table. Apart from the HE-stars, of which the data reduction was described in this chapter, we
also show the objects taken from literature (Hipparcos, de Boer et al. 1997a etc.), with the according
source listed in Table 2.4. Also listed are the sources of the radial velocities and distances.
The final sample includes 114 sdB stars and 19 HBB stars with magnitudes 8.9 to 17 mag. Most of
the stars have V magnitudes between 13 and 16, placing them at distances of between 0.7 and 2.5
kpc. The HBBs are on average at larger distances, the PG and HE stars being at distances larger than
2 kpc. Accordingly, their tangential velocities have much greater errors.
35
2. DATA AND DATA REDUCTION
36
C HAPTER 3
K INEMATICAL TRENDS AMONG THE
FIELD HORIZONTAL BRANCH STARS
C OLLABORATORS : K LAAS S. DE B OER
A BSTRACT: Horizontal branch (HB) stars in the field of the Milky Way can be used as tracers for the study of early stages
of the evolution of our galaxy. Since the age of individual HB stars is not known a priori, we have studied the kinematics of
a sample of field HB stars measured with Hipparcos to look for signs of age and population nature. Our sample comprises
14 HBA, 2 HBB and 5 sdB/O stars. We found that the kinematics of the HBA stars is very different from that of the sdB/O
stars (including those from an earlier study). The HBA stars have low orbital velocities, some are even on retrograde orbits.
Their orbits have large eccentricities and in many cases reach large distances above the galactic plane. In contrast, the
sdB/O stars show disk-like orbital characteristics. The few HBB stars (with Teff > 10, 000 K) in our sample seem to have
kinematics similar to that of the sdB/O stars. In order to see if there is a trend among the HB stars in their kinematics,
we investigated also RR Lyrae stars measured with Hipparcos. Here we found a mixed kinematical behaviour, which was
already known from previous studies. Some RR Lyrae stars have disk-like orbits (most of these being metal-rich) but the
majority has halo-like orbits, very similar to those of our HBA stars. Since the atmospheres of most types of HB stars do not
reflect original metallicities any more the kinematics is the only aspect left to study the origin and population membership
of these stars. Thus, the clear trend found in kinematics of stars along the HB, which is also a sequence in stellar mass,
shows that the different kinds of field HB stars arose from stars having different origins in age and, e.g., metallicity or mass
loss rate.
3.1
I NTRODUCTION : HB- STARS , THEIR POPULATION MEMBERSHIP AND
THE GALACTIC STRUCTURE
Field HB stars with accurately known distances such as those with Hipparcos data (ESA 1997) are
excellently suited for an analysis of the distribution of older populations (see Chapter 1). Unfortunately the number of such stars in the Hipparcos catalogue is very small. Including their kinematics
and orbits into the analysis enables us to obtain results that give us a clearer view of the kinematic
characteristics and population membership of these stars. Furthermore it may enable us to study the
kinetic properties of these populations themselves, using the stars as tracers (see Chapter 1).
In this chapter we have attempted to perform a similar analysis for HBA and HBB stars (for short:
HBA/B stars). Our sample consists of the local HB stars which were observed by the Hipparcos
satellite. These are the HB-like stars with the most accurate spatial and kinematic data available to
date.
However, only for a few HBA/B stars are the parallaxes accurate enough to calculate reliable distances
37
3. K INEMATICAL TRENDS AMONG THE FIELD HORIZONTAL BRANCH STARS
(de Boer et al. 1997d). For the other stars the distance still must be derived from photometry. Here one
needs to know the absolute magnitude of field horizontal branch stars. Especially since the publication
of the Hipparcos catalogue a lot of effort has gone into fixing this value. However, this has not yet led
to total agreement. For a review of various approaches to solving this problem we refer to de Boer
(1999) and Popowski & Gould (1999).
An important parameter in these studies is the metallicity of the stars, as it is generally thought to be
correlated with age. For dwarf stars metallicities can be estimated using photometric indices or spectroscopy (see the summary by Majewski 1993). For HB stars this is, unfortunately, not a trustworthy
method. The atmospheres of many HB stars have most probably been altered chemically with respect
to the original composition. Gravitational settling of heavy elements in the sdB/O star and possibly
HBB star atmospheres leads to a present lower content of elements like He, while levitation of heavy
elements leads to atmospheres with enhanced abundances of certain elements like Fe or Au as found in
several field horizontal branch stars, e.g. Feige 86 (Bonifacio et al. 1995). Levitation must also be the
explanation for the high metal abundances in blue HB stars in M 13 (Behr et al. 1999) and NGC 6752
(Moehler et al. 1999) finally uncovered to explain deviant flux distributions near the Balmer jump of
globular cluster blue HB stars (Grundahl et al. 1999). Therefore, original metallicities (as well as the
original masses) are no longer accessible quantities. Determining the kinematic properties can help
deciding which of the HB stars are intrinsically more metal-poor and which are more metal-rich, and
hence of somewhat younger origin.
The main subjects of our study are the HBA/B stars which are located in the colour magnitude diagram
on the horizontal branch between the RR-Lyrae stars and the hot subdwarfs. Unfortunately the main
sequence crosses the HB at the HBB region, so that HBB stars can be confused with normal B stars.
Therefore we have only few HBB stars in our sample. We mainly focus on HB stars with temperatures
lower than 10000 K which lie above the main sequence.
Sect. 3.2 deals with the data necessary for our study. In Sect. 3.2.3 we determine the absolute
magnitudes and distances of the HBA/B and sdB/O stars with the method of auto-calibration using
the shape of the HB defined by the stars with the best Hipparcos parallaxes. In Sect. 3.3 we discuss
the kinematical behaviour of the HBA/B and sdB/O stars and make comparisons with the results of
de Boer et al. (1997b). To further explore a possible trend in kinematics of stars along the HB we
investigate (Sect. 3.4) the orbits of a sample of RR-Lyrae stars.
3.2
3.2.1
T HE DATA
C OMPOSITION OF THE SAMPLE
Our sample consists of the Hipparcos (ESA 1997) measured HB stars. In order to identify them we
searched through lists of bright HB-candidates in publications concerning horizontal branch stars,
such as Corbally & Gray (1996), Huenemoerder et al. (1984), and de Boer et al. (1997d) for the
HBA/B stars and Kilkenny et al. (1987) for sdB/O stars. However, for a few stars in these lists
indications exist that they are probably not horizontal branch stars. Among these are HD 64488 (Gray
et al. 1996), HD 4772 (Abt & Morrell 1995; Philip et al. 1990), HD 24000 (Rydgren 1971), HD 52057
(Waelkens et al. 1998; Stetson 1991) and HD 85504 (Martinet 1970). This sample, although being of
limited size, represents the HB stars with by far the best kinematical data currently available.
Two further stars are HB-like but were excluded from the study nevertheless. BD +32 2188 has a
rather low value for log g so that it lies considerably above the ZAHB in the log g − Teff diagram.
Being metal deficient (Corbally & Gray 1996) it can be considered a horizontal branch star evolving
38
3.2. The data
Table 3.1: Physical properties of the sample of horizontal branch stars.
Name
HIP
V a B − V a EB−V b δMV b Typec Teff log g
Sourced
[mag] [mag] [mag] [mag]
[K]
HD 2857
2515 9.967
0.219 0.050 −0.001 HBA 7700 3.1 GCP, HBC
HD 14829
11124 10.228
0.023 0.020 −0.580 HBA 8700 3.3 GCP
HD 60778
36989 9.131
0.135 0.020 −0.040 HBA 8600 3.3 GCP, S91, HBC
HD 74721
43018 8.717
0.042 0.000 −0.330 HBA 8600 3.3 GCP, S91, HBC
HD 78913
44734 9.291
0.094 0.030 −0.215 HBA 8700 2.5 IUE-fit, S91
HD 86986
49198 8.000
0.119 0.035 −0.130 HBA 7900 3.1 B97b, S91
BD +36 2242 59252 9.904 −0.065 0.010 −1.188 HBB 11400 4.4 HBC
HD 106304
59644 9.077
0.027 0.040 −0.696 HBA 9500 3.0 IUE-fit, S91
BD +42 2309 60854 10.820
0.043 0.000 −0.324 HBA 8400 3.3 GCP
HD 109995
61696 7.603
0.047 0.001 −0.307 HBA 8300 3.15 B97b, S91
BD +25 2602 64196 10.148
0.057 0.065 −0.659 HBA
S91
HD 117880
66141 9.059
0.082 0.015 −0.201 HBA 9200 3.4 GCP, S91, HBC
Feige 86
66541 10.006 −0.140 0.050 −2.193 HBB 15300 4.1 HBC
HD 130095
72278 8.155
0.032 0.064 −0.840 HBA 8800 3.15 B97b, S91
HD 139961
76961 8.857
0.098 0.107 −0.666 HBA 8750 3.3 B97b, S91
HD 161817
87001 7.002
0.166 0.020 −0.001 HBA 7500 2.95 B97b, S91
CD −38 222
3381 10.400 −0.224 0.013 −2.639 sdB 28200 5.5 B97b, B97a
Feige 66
61602 10.602 −0.286 0.040 −3.556 sdB 28000 4.9 KHD, S94
HD 127493
71096 10.040 −0.251 0.095 −3.756 sdO 40000 5.8 KHD
HD 149382
81145 8.872 −0.280 0.050 −3.598 sdOB 40000 5.8 KHD, S94
HD 205805 106917 10.158 −0.241 0.025 −2.929 sdB 25000 5.0 B97b, B97a
a) V , B − V from the Hipparcos Catalogue
b) E
B−V , δM , see Sect. 3.2.2 and 3.2.3
c) Type: HBA stars: T
eff < 10500 K; HBB stars: 20000 K > Teff ≥ 10500 K; sdB/O stars: from
literature (see under source)
d) The values for log g and T
eff have been taken from the first work cited. HBC: Huenemoerder et al.
(1984), GCP: Gray et al. (1996), B97a: de Boer et al. (1997b), B97b: de Boer et al. (1997d), KHD:
Kilkenny et al. (1987) and references therein, S91: Stetson (1991), S94: Saffer et al. (1994),
IUE-fit: see Sect. 3.2.2
away from the ZAHB. Because the evolutionary state is not fully HB the star cannot be part of our
sample. HD 49798 is a subluminous O-star. However, its log g is relatively low and its trigonometrical
parallax implies a star with absolute brightness of about −2 mag, far too bright for a normal sdO star.
It is probably on its way from the horizontal branch to become a white dwarf or it is a former pAGB
star. Because of these aspects we excluded this star.
A large fraction of the known horizontal branch stars has no published radial velocity and could
therefore not be used for our study. A few stars had radial velocities but no Hipparcos data.
There is no constraint on the position, so that the sample stars are located in all parts of the sky.
However, as many studies were made in fields near the galactic poles we have relatively more stars at
very high galactic latitudes. Although our sample of stars is certainly not statistically complete in any
way, we do not expect noticeable selection effects due to position in the sky (see Sect. 3.5).
39
3. K INEMATICAL TRENDS AMONG THE FIELD HORIZONTAL BRANCH STARS
Table 3.2: Spatial and kinematical data for the starsa of our sample
Name
RA (Eq. 2000.0) DEC
µα cosδ
µδ
∆µα cosδ
∆µδ
π
∆π
d
vrad
ref.b
◦ 0 00
hr, min, sec
mas/yr
mas/yr
mas/yr
mas/yr
mas
mas
pc
km s−1
vrad
HD 2857
00 31 53.80
−05 15 42.3
−6.85
−66.05
1.58
0.85
1.79
1.67
687
−149
CG
HD 14829
02 23 09.23
−10 40 38.9
+31.31
−46.85
1.89
1.58
4.40
1.96
619
−176
P69
HD 60778
07 36 11.79
−00 08 14.9
−20.92
−84.04
1.21
0.73
2.35
1.23
479
+39
eE
HD 74721
08 45 59.29
+13 15 49.6
−41.83
−112.42
1.31
0.93
0.34
1.46
356
+9
eE
HD 78913
09 06 54.78
−68 29 22.1
+36.48
+22.87
0.95
0.80
2.69
0.88
469
+313
cE
HD 86986
10 02 29.48
+14 33 27.0
+144.06
−208.27
1.05
0.53
3.78
0.95
267
+9
bE
BD +36 2242
12 09 15.84
+35 42 42.9
−5.57
−1.83
1.20
0.88
1.83
1.25
409
−4
dE
HD 106304
12 13 53.63
−40 52 23.7
−90.36
−117.00
0.99
0.71
2.83
1.12
336
+95
cE
BD +42 2309
12 28 22.18
+41 38 52.7
−21.30
−33.61
1.19
1.39
0.47
1.76
942
−152
dE
HD 109995
12 38 47.69
+39 18 32.9
−114.81
−144.19
0.83
0.68
4.92
0.89
215
−132
BB
BD +25 2602
13 09 25.64
+24 19 25.3
−84.51
−18.73
1.83
1.44
1.40
1.54
540
−74
eE
HD 117880
13 33 29.86
−18 30 53.1
−85.65
−140.33
1.18
0.75
4.80
1.10
433
−45
cE
Feige 86
13 38 24.77
+29 21 57.0
−15.34
−109.79
1.49
0.92
4.61
1.65
255
−22
cE
HD 130095
14 46 51.35
−27 14 53.3
−213.89
−79.77
1.29
0.75
5.91
1.08
199
+58
BB
HD 139961
15 42 52.97
−44 56 40.0
−187.04
−92.41
1.28
1.19
4.50
1.19
280
+145
dE
HD 161817
17 46 40.65
+25 44 57.3
−37.05
−43.23
0.50
0.57
5.81
0.65
183
−363
bW
CD −38 222
00 42 58.28
−38 07 37.2
+43.85
−7.00
1.88
1.23
3.07
1.73
262
−52
GS
Feige 66
12 37 23.52
+25 04 00.1
−2.72
−26.71
1.80
1.36
5.11
1.74
182
+1
cE
HD 127493
14 32 21.51
−22 39 25.5
−32.80
−17.22
1.45
1.37
5.21
1.49
118
+13
bW
HD 149382
16 34 23.34
−04 00 52.0
−5.95
−3.92
1.83
1.73
13.07
1.29
79
+3
cW
HD 205805
21 39 10.55
−46 05 51.4
+76.39
−9.93
1.20
0.90
3.77
1.70
201
−57
B97a
a) Positions, proper motions and parallaxes (with errors) listed in this table are from the Hipparcos Catalogue, the distances, as derived in Sect. 3.2.3
b) References for radial velocities: E: The Revision of the General Catalogue of Radial Velocities (Evans 1967), W: The General Catalogue of Radial
Velocities (Wilson 1953); here the small case letters indicate the quality of the radial velocity:
a: ∆vrad < 0.9 km s−1 , b:∆vrad < 2.0 km s−1 , c: ∆vrad < 5.0 km s−1 , d: ∆vrad < 10.0 km s−1 , e: ∆vrad > 10.0 km s−1 .
B97a: de Boer et al. (1997b), BB: Barbier-Brossat (1989), CG: Corbally & Gray (1996), GS: Graham & Slettebak (1973), P69: Philip (1969)
40
3.2. The data
3.2.2
P HYSICAL PROPERTIES OF THE STARS , EXTINCTION
While many of the stars are classical template HB stars, like HD 2857, HD 109995, HD 130095 or
HD 161817, others are not as well studied.
For most of our stars values for log g and Teff are available in the literature from a variety of methods.
Sources are given in Table 3.1. For HD 78913 and HD 106304 log g and Teff were derived from
a fit of Kurucz models to spectrophotometric IUE data and photometry. For BD +25 2602 no data
are available to determine log g and Teff . We keep it as part of our sample, as it was identified as a
horizontal branch star by Stetson (1991).
Wherever possible we took the values for EB−V from de Boer et al. (1997d), supplemented by values
listed in Gratton (1998). For the other stars we derived the EB−V , with (B − V )- and (U − B)values taken from the SIMBAD archive and a two-colour-diagram. Note that with this method there
may well be metallicity dependent effects having an influence on the reddening derived. For the star
CD −38 222 no (U − B) data are available; the reddening is very small as follows from the IRAS
maps of Schlegel et al. (1998). We adopted the value from that study.
3.2.3
A BSOLUTE MAGNITUDES AND DISTANCES
We obtained the distances of the HB stars using the absolute magnitude of the relevant portion of
the HB rather than directly using the Hipparcos parallaxes. The reason for this is that most of the
parallaxes are smaller than 3 mas which means that their error of on average 1 mas is too large to
calculate accurate distances. The absolute magnitudes MV , which are a function of the temperature
and thus of (B − V )0 , have been derived through self calibration as follows.
We started with the determination of the shape of the field horizontal branch. For this we calculated
the absolute magnitudes of those HB and sdB/O stars which have reasonably good parallaxes. For
the determination of the mean absolute magnitude of the HB sample we excluded HD 74721 and
BD +42 2309 because their absolute magnitudes, calculated from their parallaxes, are too bright
by more than 3.5 magnitudes. Also excluded at this point are HD 14829 and HD 117880, whose
parallaxes lead to absolute magnitudes far too faint. With this medianization (leaving out the extremes
to both sides) we ensure that our result is not affected by stars with extreme values. Furthermore the
stars having parallaxes with ∆π/π > 1 were excluded for the determination of the shape of the HB.
We then fitted by eye a curve to our sample in the colour magnitude diagram. In order to smooth this
curve, it was approximated by a polynomial. Note that we aim to fit the observed parameters of the
field horizontal branch and that we do not rely on a shape taken from globular clusters or theoretical
models (see Fig. 1).
From this we determined the value δMV giving the difference of MV for each (B − V )0 with respect
to MV at (B − V )0 =0.2 mag. Although the available metallicity measurements show a large spread
for individual stars (see table II of Philip 1987), the averages for each lie around [Fe/H] ∼ −1.5 dex.
Since the effect of metallicity on MV is small for RR Lyr stars (about 0.1 mag per 0.5 dex, see de
Boer 1999) we will neglect the metallicity effects for the HBA stars.
Distances and absolute magnitudes of a sample of stars obtained through trigonometric parallaxes
have to be corrected for the Lutz-Kelker bias (Lutz & Kelker 1973). This statistical effect, depending
on the relative error of the parallaxes, leads to an over-estimation of the parallax on average, leading
to too faint absolute magnitudes and too short distances of the sample.
The correction we applied is based on the averaging of parallaxes. For that we have to correct the
parallaxes of individual stars, acknowledging that such a correction is only valid in a statistical sense.
41
3. K INEMATICAL TRENDS AMONG THE FIELD HORIZONTAL BRANCH STARS
Figure 3.1: Colour magnitude diagram showing the stars of our sample and the curve which was used
as the shape of the FHB.
Hexagons: HBA/B stars (open symbols mean stars not used for the fit), crosses mean sdB/O stars, the
square depicts RR Lyrae.
The expected parallax π ∗ given by
π ∗ = 100.2[MV −V −δMV ]−1+0.62EB−V
(3.1)
with MV being the absolute magnitude, V the apparent magnitude, EB−V the reddening. δMV is a
term which accounts for the temperature and/or B − V dependence of the absolute magnitude of BHB
stars in the same way as done by Gratton (1998). Now MV is varied and
χ2 (MV ) =
X
(πi∗ (MV ) − πi )2 /(∆πi )2
(3.2)
i
is calculated (formula as revised by Popowski & Gould 1999). At the correct MV the average of χ2
should be minimised.
42
3.2. The data
Table 3.3: Orbital and kinematical characteristics
Ra
Rp zmax ecc nze U
V
W
Θ
Iz
Type
−1
−1
[kpc] [kpc] [kpc]
[km s ]
[kpc km s ]
HD 2857
11.81 0.44 6.47 0.93 1.04 +156 +25
+67 +29 +251
HBA
HD 14829
11.29 2.69 8.11 0.62 1.01 +108 +71 +156 +71 +622
HBA
HD 60778
9.35 2.41 4.56 0.59 0.56 +53 +82 −115 +80 +714
HBA
HD 74721
8.65 1.95 4.42 0.63 0.59 +22 +70 −109 +69 +606
HBA
HD 78913
9.52 1.79 0.38 0.68 0.05 +107 −77
+24 −83 −695
HBA
HD 86986
16.96 0.33 13.26 0.96 1.63 +248 +24
+50 +20 +217
HBA
BD +36 2242 9.96 8.58 0.42 0.04 0.05 +3 +227
+3 +227 +1945
HBB
HD 106304
8.42 1.65 7.27 0.67 1.62 −22 +38 −150 +39 +327
HBA
BD +42 2309 9.96 0.91 5.26 0.83 0.89 +29 +34 −110 +35 +300
HBA
HD 109995
9.41 0.48 5.52 0.90 1.00 +4
+30
−96 +30 +258
HBA
BD +25 2602 10.80 1.51 1.71 0.75 0.18 −146 +72
−53 +72 +607
HBA
HD 117880
8.91 4.17 9.29 0.36 4.89 −55 −28 −199 −26 −217
HBA
Feige 86
9.18 2.95 0.27 0.51 0.03 +76 +117
−7 +118 +995
HBB
HD 130095
8.94 0.49 5.13 0.90 0.93 −58 +30
+65 +31 +258
HBA
HD 139961
8.26 1.57 1.68 0.68 0.22 +3
−69
+81 −69 −568
HBA
HD 161817
12.51 1.30 7.36 0.81 0.74 −169 −54 −129 −56 −473
HBA
CD -38 222
9.31 7.29 1.23 0.12 0.13 −38 +206 +59 +207 +1749
sdB
Feige 66
9.10 7.76 0.22 0.08 0.02 +24 +217
+8 +217 +1841
sdB
HD 127493
8.53 7.71 0.20 0.05 0.02 +10 +212 +15 +212 +1780
sdO
HD 149382
9.64 8.33 0.13 0.07 0.01 +13 +233 +10 +233 +1966
sdB
HD 205805
11.48 6.72 0.19 0.26 0.02 −82 +225
−3 +225 +1880
sdB
Note: Due to a change in the convention (see Geffert 1998), the values of Iz have changed their sign
(positive Θ have now positive Iz ) in contrast to previous work (e.g. de Boer et al. 1997b)
Name
MV is now found using all stars, regardless of their ∆π/π, except the four excluded above. We
arrived at an absolute magnitude of MV = 0.63 ± 0.08 mag for the horizontal part ((B − V )0 ∼ 0.2
mag) of the horizontal branch. As stated before this value should be valid for [Fe/H]∼ −1.5 dex.
However, as the curve defining the shape of the HB is subjective to a certain extent the real error
of the HB’s absolute magnitude is somewhat larger. The absolute magnitudes and thus the distances
of the individual stars including those omitted earlier are obtained by adding their δMV to the mean
absolute magnitude of the HB.
3.2.4
P ROPER
MOTIONS AND POSITIONS
Positions and proper motions used in this work were taken from the Hipparcos catalogue (ESA 1997).
The mean error of the proper motions is below 1.5 mas/yr (see Table 3.2) which means an error in the
tangential velocity of 3.5 km s−1 for a star at a distance of 500 pc. As most of our stars have smaller
distances the error caused by the proper motion uncertainty is even smaller.
No star of the sample of HBA/B or sdB/O stars has an astrometric flag in the Hipparcos catalogue,
indicating there were no problems in the data reduction. The Hipparcos goodness-of-fit statistic is
below +3 in all cases, meaning that the astrometric data derived from the Hipparcos catalogue should
be reliable and there are no indications that our sample contains double stars.
43
3. K INEMATICAL TRENDS AMONG THE FIELD HORIZONTAL BRANCH STARS
Figure 3.2: Orbits of the HBA/HBB stars displayed in meridional cuts. The orbits shown here have
been calculated for 10 Gyr, in order to make the shape of the orbit better visible. For orbits of sdB
stars see de Boer et al. (1997b).
3.2.5
R ADIAL VELOCITIES
The radial velocities were taken from original sources (see Table 3.2), in part found from the Hipparcos Input Catalogue (Turon et al. 1992). The typical uncertainties are about 10 km s−1 , so that they
should not have a large effect on our results. The size of our sample was limited to a large extent by
the lack of radial velocities; for only about 30% of the HB-candidates radial velocities could be found.
Radial velocities can be affected by binarity of the star. We cannot absolutely exclude this possibility
for some of the stars, but as noted in Sect. 3.2.4 there are no indications for binary nature for any of
our stars.
44
3.3. Kinematics and orbits
For some stars, Corbally & Gray (1996) found drastically different values for the radial velocity. They
note however that in many of these cases their values may be affected for some reason (see their Sect.
4) as they show strong deviations with respect to values from the literature. We therefore used radial
velocities from Corbally & Gray only for HD 2857 for which no other value is available.
3.3
K INEMATICS AND ORBITS
In order to gain information about the nature and population membership of the stars we analyse their
kinematic behaviour and calculate their orbits.
3.3.1
C ALCULATING ORBITS AND
VELOCITIES
Before calculating the orbits the observational data have to be transformed into the coordinates of the
galactic system (X, Y, Z; U, V, W ). In this coordinate system X points from the Sun in direction of
the galactic centre with its origin in the galactic centre, Y points into the direction of the galactic
rotation at the position of the sun, and Z toward the north galactic pole. The same applies to the
corresponding velocities U , V , W .
The orbits are calculated using the model for the gravitational potential of our Milky Way by Allen
& Santillan (1991a) which was developed to be used in an orbit calculating program Odenkirchen &
Brosche (1992) This model has been extensively used in the studies of de Boer et al. (1997b), Geffert
(1998) and Scholz et al. (1996). There are several other models available which yield similar results as
long as the orbits do not extend to extreme distances from the galactic centre (Dauphole et al. 1996).
The model of Allen & Santillan (1991a) is based on ΘLSR = 220 km s−1 and RLSR = 8.5 kpc.
The values for the peculiar velocity of the Sun used in the calculations in this paper are Upec, = 10
km s−1 , Vpec, = 15 km s−1 , Wpec, = 8 km s−1 .
To determine the parameters zmax , the maximum height reached above the galactic plane and Ra and
Rp , the apo- and perigalactic distances, we calculated the orbits over 10 Gyr. This for certain does
not give true orbits as the orbits are probably altered in time by heating processes. However this long
timespan allows to better show the area the orbit can occupy in the meridional plane (see Fig. 2).
As in de Boer et al. (1997b), we also calculated the eccentricity ecc of the orbit, given by
ecc =
Ra − Rp
Ra + Rp
(3.3)
zmax
.
$(zmax )
(3.4)
and the normalised z-extent, nze, given by
nze =
The parameter nze is more relevant than zmax , since it accounts for the effect of diminished gravitational potential at larger galactocentric distance $.
To assign a star to a population often the U, V, W -velocities and their dispersions are used, as well
as the orbital velocity Θ. For stars near the Sun (small Y ), the V velocity is nearly the same as Θ.
However, for stars further away from the Sun’s azimuth, Θ becomes a linear combination of U and V .
Therefore Θ should be preferred. In order to make comparisons with results from other studies, we
use both U, V, W and Θ. The values for the velocities, angular momentums and orbital parameters of
our stars are shown in Table 3.3.
45
3. K INEMATICAL TRENDS AMONG THE FIELD HORIZONTAL BRANCH STARS
Table 3.4: Mean velocities (Φ, Θ, W , upper half) , angular momentum (IZ ) and orbital parameters
(ecc, nze, lower half) for various subsamples of HB stars
Types
subsample
HBA
HBB
sdB/O
sdB
RR Lyr
RR Lyr
RR Lyr
RR Lyr
RR Lyr
Types
this paper
this paper & Schmidt (1996)
this paper
this paper & de Boer (1997b)
all
[Fe/H] > −0.9
−0.9 >[Fe/H]> −1.3
−1.3 >[Fe/H]> −1.6
−1.6 <[Fe/H]
subsample
HBA
HBB
sdB/O
sdB
RR Lyr
RR Lyr
RR Lyr
RR Lyr
RR Lyr
this paper
this paper & Schmidt (1996)
this paper
this paper & de Boer (1997b)
all
[Fe/H] > −0.9
−0.9 >[Fe/H]> −1.3
−1.3 >[Fe/H]> −1.6
−1.6 <[Fe/H]
number
of stars
14
6
5
44
32
7
7
10
8
number
of stars
14
6
5
44
32
7
7
10
8
Φ
σΦ
−1
km s
−20 108
−22
96
+15
40
+9
59
−26 145
+34
35
−71 118
−51 181
−7 157
IZ σIZ
kpc km s−1
155 447
1382 558
1846
74
1660 312
721 968
1843 441
441 912
357 630
439 970
Θ
σΘ
−1
km s
+17
52
+151
55
+219
9
+194
48
+80
114
+218
37
+43
109
+32
74
+51
107
nze σnze
1.10
0.24
0.04
0.25
0.86
0.08
0.88
1.54
0.68
1.15
0.15
0.05
0.17
1.50
0.05
0.57
2.43
0.47
W
σW
−1
km s
−37
104
−4
43
+21
40
−3
54
−3
87
−14
31
−12
75
−12
110
+25
93
ecc σecc
0.74
0.41
0.12
0.15
0.59
0.19
0.64
0.68
0.65
0.16
0.27
0.08
0.11
0.33
0.13
0.38
0.40
0.30
We calculated the errors of the velocity components and the orbital velocity using Monte Carlo simulations of Gaussian distributions to vary the input parameters within their errors as described by
Odenkirchen (1991). This is neccesary rather than just calculating errors using Gauss error propagation laws because the parameters are significantly correlated. For the error calculation we used the
software of Odenkirchen (priv. comm.). The proper motion errors were taken from the Hipparcos
catalogue. The errors of the distances were calculated from the error in absolute magnitude as derived
in Sect. 3.2.3. We took the errors of the radial velocities as published in the respective articles. For
those radial velocities of Wilson (1953) and Evans (1967). having quality mark “e”, meaning the error
is larger than 10 km s−1 , we used 15 km s−1 as error. This is justified as can be seen by comparison
of these values with those of other studies. Generally the error in the velocity components is less than
10 km s−1 . Only a few stars have somewhat larger errors, the largest error in Θ being 12 km s−1 . For
the HBA/B stars the typical value of ∆Θ is about 7 km s−1 , for the on average closer sdB/O stars ∆Θ
is 1 to 2 km s−1 .
We estimated errors for nze, ecc, Ra and Rp because they have not been used individually in the
interpretation. Moreover the larger values of nze are very sensitive to small variations in the shape
of the orbit. This especially applies to stars having chaotic orbits. Variations in the input distance
modulus showed that the resulting variations in all of these quantities except nze are relatively small
in most cases. For a discussion of overall effects on a sample see de Boer et al. (1997b).
46
3.3. Kinematics and orbits
3.3.2
M ORPHOLOGY
OF THE ORBITS
The orbits of the HBA/B stars show a large variety of shapes. Nearly all of the cooler HBA stars
have a small perigalactic distance (Rp ≤ 3 kpc) and the most extreme case, HD 86986, reaches a
perigalactic distance of only 0.4 kpc. The single exception is HD 117880, which has a Rp of nearly 4
kpc.
Four stars have truly chaotic orbits, the rest has boxy type orbits, but some of these show signs of
chaotic behaviour as well. HD 79813 has an orbit staying very close to the disc, while HD 117880
orbits nearly perpendicular to the galactic plane. On the whole about half of our stars have orbits
which are chaotic or show signs of that. This agrees quite well with the results of Schuster & Allen
(1997) who analysed a sample of local halo subdwarfs.
Most of the stars have apogalactic distances of ' 8 to 11 kpc, just one star (HD 86986) goes well
beyond. The reason for this clumping in Ra is not physical but due to selection effects. Stars with
Ra ≤ 7.5 kpc never venture into the observable zone (at least observable by Hipparcos). On the other
hand the probability of finding the stars is greatest when they are near their major turning point, Rp .
So it is clear that the mean Ra , as well as to a lesser extent the eccentricity, are affected by selection
effects.
Stars belonging to the thin disk would have orbits with very small eccentricities and nze values (solar
values: ecc= 0.09, nze= 0.001, see de Boer et al. 1997b), while thick disk stars would have larger
values on average. Halo stars have generally orbits with large eccentricities while their nze show a
large range.
The eccentricities of the HBA star orbits are very large, ranging from 0.5 to nearly 1.0, the values for
nze vary by a huge amount, from 0.04 (HD 78913) to 5 (HD 117880). The stars BD +36 2242 and
Feige 86 are exceptions, their values for both parameters are more appropriate for disk objects. We
note that these two stars are the hottest of the HBA/B sample. The kinematics of the four HBB stars
from Schmidt (1996) show overall behaviour similar to that of BD +36 2242 and Feige 86 (Fig. 2).
All of these are hotter than 11000 K, the Teff of BD +36 2242.
The star HD 117880 features an orbit somewhat dissimilar from the others. While its nze is very high,
its eccentricity is by far the lowest of the sample of HBA stars.
3.3.3
V ELOCITY COMPONENTS AND
DISPERSIONS
The HBA stars (Teff ≤ 10,000 K) have a mean orbital velocity of Θ = 17 km s−1 , lagging about 200
km s−1 behind the local standard of rest. However, the velocity dispersions are large: 102, 53 and 95
km s−1 in U , V , W respectively. This shows that there are many stars with a non disk-like kinematical
behaviour in the sample of HBA/B stars. They therefore belong to the galactic halo population rather
than to the disk.
The orbital velocities of the HBA stars in the sample do not have a Gaussian distribution, as one might
have expected. Instead, they seem to have a somewhat flatter distribution (see Fig. 4). About 75%
of our stars have prograde velocities, four stars have retrograde orbits. However the exact distribution
cannot be studied reliably due to the limited number of stars at disposal.
Both the analysis of the kinematic properties and the shapes of the orbits imply that the HBA/B stars
mostly are members of the galactic halo population. However, there seems to be a difference in
kinematics and hence population membership between the cooler and the hotter stars. Stars cooler
than about 10,000 K have low orbital velocities and a large spread in nze. In contrast to this are the
hotter stars whose kinematics and orbits are consistent with those of disk objects. The HBB stars of
47
3. K INEMATICAL TRENDS AMONG THE FIELD HORIZONTAL BRANCH STARS
Figure 3.3: Kinematic trend of stars along the field horizontal branch characterised by eccentricity,
normalised z-extent and orbital velocity as plotted against effective temperature Teff and B−V . Upper
row, panels a) and b): eccentricity (ecc);
Middle row, panels c) and d): normalised z-extent (nze);
Bottom row, panels e) and f): orbital velocity (Θ).
The left side (panels a, c and e): versus Teff , showing the hotter part of the FHB.
Right side (panel b, d and f): versus B − V , highlighting the cooler part.
Filled symbols show the stars with Hipparcos data, open symbols the sdB and HBB stars from de Boer
et al. (1997) and Schmidt (1996). sdB/O stars are depicted by squares, HBB and HBA by hexagons.
The RR Lyraes are plotted with pentagons subdivided according to their metallicity (full: [Fe/H]<
−1.6 dex, half full: −1.6 <[Fe/H]< −1.3 and −1.3 <[Fe/H]< −0.9 dex, open [F e/H] > −0.9
dex).
48
3.4. RR Lyrae stars
Schmidt (1996) which are all hotter than 10,000 K behave like sdB stars, too.
3.3.4
K INEMATICS OF SD B/O
STARS
The sample of sdB/O stars show classical disk behaviour: Their mean orbital velocity is Θ = 219
km s−1 , meaning a negligible asymmetric drift. The V velocity dispersion (which is also the dispersion in Θ, because the stars are in the solar vicinity) is relatively small, similar to that of old thin
disk orbits, while the dispersion in U is much larger, fitting to thick disk values. The dispersion σW
is somewhere in between. These values are quite similar to those of the sdB star sample of de Boer
et al. (1997b). Until now no population of field sdB stars with halo kinematics has been found. Yet,
hot subdwarfs of the horizontal branches of halo globular clusters are, of course, well known (see e.g.
Moehler et al. 1997).
3.3.5
T REND OF KINEMATICS ALONG THE HB?
Given the results above there seems to be a trend in the kinematics of star types along the blue part of
the horizontal branch (see Fig. 3). The sdB/O stars have disklike orbits. The same probably applies
to the HBB stars hotter than about 10,000 K, though the statistics are rather poor for this part of the
HB. In contrast to that stand the cooler HBA stars which have much smaller orbital velocities, large
orbital eccentricities and large ranges of nze, thus showing a behaviour fitting more to halo than to
disk objects.
This result suggests to analyse the kinematics of the adjoining cooler stars of the HB, the RR Lyraes.
3.4
3.4.1
RR LYRAE STARS
A
SAMPLE OF
RR LYRAE STARS FROM
THE LITERATURE
Recently, Martin & Morrison (1998) carried out an investigation of the kinematics of RR Lyrae stars
which is mainly based on the study of Layden (1994). For our analysis we will use only those stars
having Hipparcos data. Six Hipparcos stars were excluded because they have a proper motion error
larger than 5 mas/yr.
The RR Lyrae stars present the observational difficulty in that they are variables with both V and
B − V changing continously. For most of the sample we were able to take the mean magnitudes from
Layden (1994). For the remaining stars we derived the intensity-mean magnitudes with help of the
formula given by Fitch et al. (1966) and revised by Barnes III & Hawley (1986) which is the same
method as used by Layden (1994) using the photometric data of Bookmeyer et al. (1977). The Layden
photometry was dereddened using the Burstein & Heiles (1982) reddening maps.
For later steps in this study it is necessary to know the mean B − V of the RR Lyrae stars. As the
colour curves of the stars are quite similar to the brightness curves, with the star being bluest when it
is near maximum brightness, we took the same formula as we used to calculate the mean magnitude.
This is not entirely correct but gives B − V close to the actual one. For six stars we did not have the
appropiate light curve data, so we could not determine the mean B − V for them. Therefore only 26
RR Lyraes are shown in Fig. 3.
As the RR-Lyrae stars are in most cases fainter and therefore farther away than our HBA/B stars they
have a rather large ∆π /π. For this reason we used the absolute magnitude derived in Sect. 3.2.3
49
3. K INEMATICAL TRENDS AMONG THE FIELD HORIZONTAL BRANCH STARS
Figure 3.4: Histogram showing the distribution of orbital velocities of the investigated stars. The
binsize is 20 km s−1 .
50
3.5. Selection effects
to calculate the distances for these stars. We thus have ignored the effects of metallicity on MV for
individual stars. Also possible evolutionary effects on MV (see Clement & Shelton 1999) have been
ignored, an aspect Groenewegen & Salaris (1999) did not consider in their determination of the RR
Lyrae MV either. Since we study the orbits of the RR Lyrae as a sample these limitations will not
affect our conclusions.
For most RR Lyrae stars we took the radial velocities from the sources mentioned in Sect. 3.2.5,
supplemented by radial velocities from Layden (1994).
The metallicities of the RR-Lyrae stars were taken from Layden (1994) as far as possible. A few
values come from Layden et al. (1996) and Preston (1959).
3.4.2
RR-LYRAE KINEMATICS
We calculated the orbits for the RR Lyrae stars in the same manner as for the HBA/B and sdB stars.
The RR-Lyrae stars show a spread in kinematical behaviour wider than that of the HBA/B stars. Many
stars have orbits similar to those of the HBA stars, others show disklike orbits with orbital velocities
in the vicinity of 200 km s−1 . Of the halo RR-Lyrae stars many have perigalactic distances smaller
than 1 kpc, as we also found for the HBA stars. The RR-Lyrae stars have orbital velocities typically
spanning the entire range found for disk and halo stars (see Fig. 3). Three members of our sample
of RR Lyr stars have orbits shaped somewhat different from those of the rest of halo orbits, looking
similar to that of HD 117880.
In Fig. 3 we have sorted the RR Lyr stars according to their metallicity using different plot symbols.
The stars with an [Fe/H]> −0.9 dex have high Θ like disk stars. The stars with lower metallicities
are more evenly distributed in Θ. There are several stars with disk-like kinematics with a very low
metallicity as low as [Fe/H]< −2.0 dex (see Table 3.4).
3.5
S ELECTION EFFECTS
The study of the spatial distribution of HB stars involves, unfortunately, several selection effects. The
general aspects have been reviewed by Majewski (1993) and will not be repeated in detail here. Yet,
for each stellar type discussed in this paper a few comments are in place.
HBA stars have in most cases been identified from photometry, notably because of a larger than
normal Balmer jump. This larger jump is mostly due to lower metallicity of the stellar atmosphere.
If the atmospheric metallicity is identical to the original one, then the criterion favours intrinsically
metal-poor stars, which are presumably the older ones. However, also stars starting with a little more
mass than the Sun and thus of solar composition will become HB stars and, when as old as the Sun,
by now are solar metallicity HB stars. If they were of HBA type, they would not have been recognised
in photometry of the Balmer jump. Such stars would be underrepresented in our sample. The HBA
stars considered here come from all galactic latitudes, so that selection effects due to galactic latitude
are not to be expected. However stars which have orbits going far away from the disk are always
underrepresented, as their fraction of time near the disk (and hence being observable) is much smaller
than for those which do not go far from the disk.
RR Lyraes, being variables, are not prone to such selection effects. Most of them are identified solely
by their variability. Metallicity or high velocity are generally not used as criteria for the identification
for RR Lyrae stars. For a discussion of selection effects due to galactic latitude we refer to Martin &
Morrison (1998) as our sample is a subsample of theirs.
51
3. K INEMATICAL TRENDS AMONG THE FIELD HORIZONTAL BRANCH STARS
The sdB/O stars were identified in surveys for quasars, e.g. the PG catalogue (Green et al. 1986) or
Hamburger Quasar Survey (Hagen et al. 1995). This means their blue colour is the criterion, rather
than proper motion, radial velocity or metallicity. Therefore we do not expect a selection bias towards
metal-poor halo stars. Moreover, de Boer et al. (1997b) showed that the sdB/O stars observed now
near the Sun come from widely differing locations in the Milky Way. As these catalogues only map
objects which are somewhat away from the galactic plane, they miss the majority of stars with solar
type orbits. sdO stars may be confused with pAGB stars descending down the HRD towards the white
dwarf regime.
The HBB stars of Schmidt (1996) are also taken from the PG catalogue, so that there should not be
noticeable selection effects, either. However HBB stars and main sequence stars have similar physical
properties such as log g, so that there may be confusion with the latter. Apart from this the selection
effects mentioned for the sdB/O stars apply to the HBB stars, too.
Finally, some words concerning the distribution of distances of the different samples are in place.
Generally, if one deals with stars having different absolute magnitudes, as in our case when the sdBs
are several magnitudes fainter than the HBAs, one gets samples with different mean distances. The
intrinsically fainter stars are on average much nearer than the brighter stars, if the two groups have
similar apparent magnitudes. This means that the spatial regions sampled differ depending on the
absolute magnitude of the stars. This would imply that the sdB sample is biased towards disk stars as
we do not sample them far enough from the galactic plane where there may be a higher concentration
of halo stars than further in. This is however not the case. As we include some of the results of de Boer
et al. (1997b) which come from a completely different source, namely mostly from the PG-catalogue
(Green et al. 1986) dealing with significantly fainter stars, the PG stars actually have on average larger
distances than any of our HBA stars. For this reason we do not expect that the difference in kinematics
arises from the distribution of the distances in the samples.
3.6
3.6.1
D ISCUSSION : TRENDS AND POPULATION MEMBERSHIP
OVERALL TRENDS
As shown in Figs. 3 and 4 the kinematics of the stars of horizontal branch type appears to have a trend
along the HB indeed.
The sdB stars have in general rather disk-like orbits and kinematical properties. The ones analysed
here (Table 3.4) show the same behaviour as those from the large sample of sdB stars investigated
previously (de Boer et al. 1997b)
The HB stars, the prime goal of our investigation, span a wide range in orbit parameters but when this
group is split in HBB and HBA stars a cut is present.
The (hotter) HBB stars behave rather like the sdBs with orbits of disk-like characteristics. However,
such stars are difficult to recognise and our sample is small. A much larger sample may show a larger
variation in kinematics.
The HBA stars have mostly halo orbits (mean Θ ' 17 km s−1 ). This is very similar to the value at
which most other studies concerning metal-poor stars in the solar neighbourhood arrive (see Table 2
of Kinman 1995). However, the known sample may be observationally skewed toward stars with low
atmospheric metallicity (large Balmer jump).
The RR-Lyrae stars have orbits spanning a large range in orbital parameters, too. However, a trend
seems to be present with metallicity. The metal-poor stars have halo orbits similar to those of the HBA
52
3.6. Discussion: trends and population membership
stars with rather low orbital velocities of less than 100 km s−1 , and large ecc and nze. The metalrich stars on the other hand have rather disk-like kinematical characteristics. A similar distribution
of metallicities and orbital velocities was also found in the studies of Chen (1999) and Martin &
Morrison (1998).
Although there are a few RR Lyraes having high orbital velocities (Θ ≥ 160 km s−1 ) and clearly
disk-like orbits (some of which are very metal-poor), HBA stars with such characteristics are not
found in our sample. On the other hand no RR Lyraes with [Fe/H]> −0.9 dex with halo-like orbits or
kinematics are present. This means that a high metallicity for a RR Lyr star is a good indicator that it
is a disk star. However, a low metallicity does not mean that a star neccessarily belongs to the halo.
For an overview of literature data on values for Θ (or asymmetric drift) for various star groups we
refer to Fig. 3 in the review of Gilmore et al. (1989).
3.6.2
D ISCUSSION
Since the sdB stars (and possibly the HBB stars) have disk-like orbits, these stars must be part of a
relatively younger, more metal-rich group among the HB stars. Majewski (1993) uses the expression
‘intermediate Population II’, other authors use the words ‘thick’ or ‘extended disk’. In addition to the
disk-nature of their orbits, the vertical distribution is consistent with a scale height of the order of 1
kpc (Villeneuve et al. 1995; de Boer et al. 1997b) Since the amount of metals in their atmospheres
may have been altered by diffusion it is not possible to estimate the true age from the metallicity.
The HBA stars have really halo orbits. This must mean they belong to a very old population. Their
atmospheric metal content is low indeed, the determinations showing a large scatter per star and from
star to star ranging between −1 and −2 dex. However, metal-rich HBA stars which are known to exist
in star clusters (see Peterson & Green 1998), would likely be underrepresented in the sample.
If the halo contains mostly old stars, like globular cluster stars, then the resulting halo HB stars should
occupy the HB in ranges related with metallicity as with the globular clusters (see Renzini 1983). The
very metal-poor ones ([M/H] ' −2 dex) would be HB stars of HBB and HBA nature as well as RR
Lyrae, the ones of intermediate metallicity ([M/H] ' −1.5 dex) would be very blue down to sdB
like, and the metal-rich ones ([M/H] ' −1 dex) would be RHB stars, perhaps including some RR
Lyrae. This behaviour may also explain the existence of the two Oosterhof groups (see van Albada
& Baker 1973 or Lee et al. 1990) of RR Lyrae, since only the very metal-poor and the relatively
metal-rich globular clusters contain RR Lyrae. Evolutionary changes of the HB stars may also affect
the location on the HB (Sweigart 1987; Clement & Shelton 1999).
However, sdB stars with halo kinematics have not been found (de Boer et al. 1997b). Instead, they
have only disk orbits. This must mean that the stars which originally formed in the halo had an initial
mass, a metallicity and a red giant mass loss such that RR Lyrae and HBA stars were the end product,
and not sdB stars.
As for the RR Lyrae stars, they show a wide range in kinematic behaviour, more or less in line with
the atmospheric metal content. The actual metallicity did not bias the identification of these stars,
since they are selected based on variability. One tends to divide the RR Lyrae sample into metal-poor
and metal-rich RR Lyrae (see Layden 1994). Here we recall that in the HB stars the contents of
heavier elements in their atmospheres may be altered (see Sect. 3.1). The RR Lyrae stars with the
continuous upheaval of the pulsation may stimulate mixing so that their atmospheres probably show
the true metallicity. Thus, for RR Lyraes the metallicity may be used as a general population tracer.
The observed range of metallicities would mean that there are old as well as younger RR Lyraes.
53
3. K INEMATICAL TRENDS AMONG THE FIELD HORIZONTAL BRANCH STARS
Old RR Lyrae must be very metal-poor and should have halo orbits. The majority of the RR Lyrae
included in our analysis fit these parameters. There are, however, a substantial number of RR Lyr
stars in our sample with disk-like kinematics but low metallicities, in several cases as low as −2 dex.
The origin of this group of stars, dubbed the ‘metal weak thick disk’, is still unknown (see Martin &
Morrison 1998 for a discussion).
Young (or younger) RR Lyrae should be relatively metal-rich and have disk orbits. The investigated
sample contains such stars. These objects should have an age, main-sequence mass, metallicity and
RGB mass loss such that RR Lyrae emerge, i.e. HB stars with a thicker hydrogen shell. They are,
being relatively metal-rich, also of slightly different MV than the metal-poor and old ones. In fact,
they are fainter and their distances should be based on the appropriate brightness-metallicity relation.
The dependence is, however, feeble and amounts to just 0.1 mag for 0.5 dex. We tested how serious
ignoring this effect is on the derived orbits by reducing the RR Lyr star distances by 10 %. It does not
lead to a change of significance in the histogram of Fig. 4.
3.6.3
S UMMARY
Our orbit studies allow to see a trend in the kinematics of the field HB stars along the horizontal
branch. This appears to give us access to the structure of the Milky Way and its halo as well as
information about possible formation scenarios. The trends related with age and history could only be
found using the kinematics, since it has become clear that the atmospheric metallicity in HB-like stars
has no relation to the one of the main sequence progenitor. The location of the stars on the HB must
be a complicated function of age, main-sequence mass, initial metallicity, and mass loss on the RGB.
For the HB-like stars of today indications for the age can be determined from the present kinematic
parameters. Only detailed models for metallicity dependent stellar evolution from main sequence
through the RG phase with mass loss should, in comparison with the observables of horizontal branch
stars, eventually be able to retrieve the true origin of the HB stars.
ACKNOWLEDGEMENTS :
We thank Oliver Cordes for supplying the values of log g and Teff for two stars. We are very grateful to Michael
Odenkirchen who supplied us the orbit calculating software. Furthermore we thank Michael Geffert for enlightening discussions, Wilhelm Seggewiss and Jörg Sanner for carefully and critically reading the manuscript. This
research project was supported in part by the Deutsche Forschungs Gemeinschaft (DFG) under grant Bo 779/21.
For our research we made with pleasure use of the SIMBAD in Strasbourg.
54
C HAPTER 4
K INEMATICS AND POPULATION
MEMBERSHIP OF SD B STARS
C OLLABORATORS : K LAAS S. DE B OER , H EINZ E DELMANN
A BSTRACT: We have analysed the kinematics of a sample of 114 sdB stars, the vast majority of which shows a kinetic
behaviour similar to that of Thick Disk stars; a minority, having solar-type orbits might be Thin Disk stars. 16 objects have
orbital velocities differing substantially from those of the mean.
In addition to a study of the kinematics, we calculated the orbits using a Galactic potential model. While most stars have
disk type orbits, a few venture far above the Galactic plane. Most orbits have eccentricities of less than 0.5, a few outliers
having more than 0.7, with the region inbetween underpopulated. This indicates that the (Thick) Disk and the Halo are
kinematically disjunct.
The statistics of the z-distance at given time intervals in the orbits of the stars leads to the z-probability distribution of the
sample. From the logarithmic histogram a scale height can be derived. In the histogram clearly two different slopes are
present, one showing the Disk and one the Halo component. For the Disk component we so find a scale height of 0.9 kpc,
which is consistent with the result of an earlier study, and also agreeing well with other results for the scale height of the
Thick Disk. The other component has a scale height of 7 kpc.
4.1
I NTRODUCTION
This chapter, the key part of this thesis, is an extension of the study by de Boer et al. (1997a) and
therefore significantly relies on this earlier work. We have increased the number of stars in the sample
almost by a factor of three, mainly adding objects slightly further away than before; these are, also
due to their generally much higher Galactic latitude, at noticeably larger distances from the Galactic
plane. Therefore we expect to have a greater probability of finding Halo objects; discovery of the
sdB Halo population is the most important motive for this extended analysis. Other relevant aspects
are deriving a (more) accurate scale height of the Thick Disk component analysed in de Boer et al.
(1997a), an analysis of the kinematics of sdB stars and as a collorary using the results found with our
sample of sdB stars to derive and discuss values of parameters describing the Galactic populations.
For a more detailed introduction to studies of kinematics and stellar distributions as well as Galactic
structure and Galactic populations, we refer to the general introduction in Chapter 1.
Before starting off, we first have to say a few words about the assembly of the sample, and discuss
some possible selection effects caused (or not) by the sample composition. This is accomplished in
the remainder of this section. Sect. 4.2 is an analysis of velocities and orbits, in Sect. 4.3 the vertical
probability distribution of the sample is derived and the resulting scale heights analysed and discussed.
55
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
The results are discussed in Sect. 4.4 and in a larger frame, incorporating the results of Chapters 3
and 5, in Chapter 6.
4.1.1
T HE SAMPLE
The sample of 114 sdB/OB1 stars is composed of objects taken from several sources. 59 stars, located
in the southern polar cap (SPC) of our Galaxy have been taken from the Hamburg-ESO-survey (HE).
For these new data have been obtained. We further included the 41 sdBs published in de Boer et al.
(1997a), which were mainly taken from the Palomar Green catalogue (Green et al. 1986). 17 stars
with Hipparcos data2 have also been included and one star (PG 1716+426) whose kinematics was
analysed by Geffert (1998). The data acquisition and reduction is described in detail in Chapter 2.
4.1.1.1
S ELECTION EFFECTS DUE TO SAMPLE COMPOSITION ?
The sample of sdB stars discussed in this paper is the collection of all relatively nearby stars we could
lay our hands on. The sole criterion was, that we should have or could obtain for each sdB star its
distance, its radial velocity and its proper motion. We have not aimed at obtaining and working with
an observationally unbiased sample. That this will not cause any problems in the end, is the goal of
the discussion of this section. For the present positions of the stars of the sample see Fig. 4.1.
The main sources of our objects were surveys for QSOs, such as the PG and HE. These surveys were
conducted at high Galactic latitudes, which means we miss objects at low Galactic latitudes in our
sample. They are also incomplete at the bright end (the PG at B ∼ 12 mag, the HS at ∼ 14 mag, the
HE at ∼ 13 mag)3 .
Thus nearby stars at high Galactic latitudes may be underrepresented. However, since nearby stars
may venture in time to almost any Galactic location (see Fig. 4.1), our sample will contain sufficient
distant stars which at other times would have been near the Sun and that bright, that they would have
escaped the PG, HS and HE surveys.
The stars we found in the H IPPARCOS data base, which are mainly from the SB-survey (Slettebak &
Brundage 1971) of blue SGP objects, are relatively bright and thus nearby.
The catalogues available normally do not contain stars presently at low Galactic latitudes. All of those
low b stars having Thick Disk or Halo kinematics would at other times have been detected in surveys
like PG, HS and HE (see Fig. 4.1). Stars with that kind of kinematics are thus not underrepresented
in our sample. Most of the stars currently in the disk (thus missing from our sample) and which do
have disk kinematics would always have been missed. Thus stars with Thin Disk like kinematics are
probably somewhat underrepresented in our sample.
Summarising, in spite of having used data from various special catalogues dealing with particular
observational selections of all stars available, our sample is only lacking (to an unknown amount) in
stars with Thin Disk kinematics.
1
In the following we do not discriminate between sdB and sdOB stars; therefore in this chapter sdB stands for both sdB
and sdOB.
2
Three objects (PG 1519+640 (Tycho), HD 205805 and CD −38 222) are in common with de Boer et al. (1997a),
however we use the Hipparcos proper motion data which was not yet available at the time of publication of de Boer et al.
(1997a).
3
These upper limits are not explicitly stated in Green et al. (1986) but for the Hamburg survey they are stated in the description of the catalogues available under http://www.hs.uni-hamburg.de/english/arbgeb/extgalqso
/surveys.html.
56
4.2. Kinematics and orbits
Figure 4.1: Current distribution of the stars of our sample (full hexagons) and approximately half
a revolution (100 Myr) earlier (open triangles) showing that our stars, now concentrated in a small
volume, come in fact from all over the Galaxy. The left panel shows the distributions on the Galactic
plane, the right panel shows the distributions perpendicular to the plane (along the X-axis). The filled
square and filled circle show the position of the Sun today and 100 Myr ago respectively. The circle
on the left panel has a radius of the present galactocentric distance of the Sun. The Galactic centre is
in the middle of both diagrams, and the dashed lines show the zero line for each coordinate.
4.2
4.2.1
K INEMATICS AND ORBITS
C ALCULATING VELOCITIES AND ORBITS
The observational quantities α, δ, d, µα , µδ , vrad are transformed into the X, Y, Z, U, V, W system
(for details, see Altmann & de Boer 2000, de Boer et al. 1997a or Chapter 3). Additionally the orbital
velocities Θ and the velocities towards the Galactic centre Φ, kinetic energies and angular momenta
are calculated4 .
Furthermore we calculated orbits for the stars of our sample using the Galactic gravitational potential
model of Allen & Santillan (1991a) backwards in time over 10 Gyr in steps of 1 Myr (for more details
see Altmann & de Boer 2000).
From the shape of the orbits we derived the apo- and perigalactic distances, Ra and Rp , and the
eccentricity (ecc) given by
Ra − Rp
(4.1)
ecc =
Ra + Rp
We also wish to consider the maximum distance a star reaches from the Galactic plane, zmax . However, since the gravitational potential diminishes at larger galactocentric distance, $, we calculated
nze =
zmax
,
$(zmax )
(4.2)
4
Because all of the stars are local (d < 5 kpc), U and W are quite similar to Φ and Θ; however, especially for stars
being well away from Y = 0 kpc, Θ and Φ become linear combinations of U and V .
57
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
the normalised z-extent of the orbit, which is more relevant than zmax alone.
Finally we stress that we calculated the orbits for the long timespan of 10 Gyr only because it gives a
better representation of the orbits’ shapes. This applies to low velocity Halo type stars taking a long
time to complete one revolution. The reader should be aware that orbits are subject to gradual change
over time due to gravitational interactions with local high density areas in the Galaxy. Therefore an
orbit calculated over a certain time is not necessarily a representation of the true orbit in the far past.
4.2.1.1
E RRORS
As in Chapter 3, we used a program (Pauli, priv. comm.) similar to that of Odenkirchen (priv. comm.)5
which we utilised in Chapter 3 to conduct an error analysis similar to that described in Sect. 3.3.1.
For the errors of the input quantities we used 5 mas/yr for the proper motions, 10% for the distances
and 30 km s−1 for the radial velocities (see Chapter 2).
For distances smaller than 1 kpc, the resulting errors for U, V, W are in the order of ∼10-20 km s−1 ,
with the influence of the radial velocity dominating. Unfortunately when calculated with the new
program (which was written to compute the errors for white dwarfs, which are much closer to the
Sun than 1 kpc) the derived errors of stars which are further away than approximately 1 kpc begin to
grow unrealistically large. The resulting values of ∆U, ∆V, ∆W were then far larger than 100 km s−1
which is not realistic and cannot be reproduced by determining the velocities with the input values
changed within the errors. We therefore extrapolate the results for the closer stars, taking into account
the errors of the input quantities. The errors for the velocities are estimated to be about 30 km s−1
for stars 1.5 kpc away (with both proper motion and radial velocity contributing equally to the error),
45 km s−1 for stars at 2 kpc distance, 60 km s−1 at 2.5 kpc and 70 km s−1 at 3 kpc distance (with
the proper motion error now dominating). Many of our stars are near the SGP; this means for these
objects that the value and error of W is dominated by those of the radial velocity. Therefore for many
of our stars ∆W is closer to 30 km s−1 , the error of most of the radial velocities.
In this error estimation we have not included the influence of intrinsically variable radial velocities of close binaries (see Sect. 2.3.1), which certainly are present for quite a few of the sdB stars.
Comparison with the values of the radial velocities taken from de Boer et al. (1997a) (from single
measurements) with those from Morales-Rueda et al. (2002) or Marsh (priv. comm.) show that the
differences between them is generally not overly large; often less than the error margin of the radial
velocities used in de Boer et al. (1997a). However for individual objects, whose radial velocities were
measured while near one of the extrema, there can be a large discrepancy between this measurement
and the systemic value. Unfortunately we do not have systemic radial velocities for most of our stars;
therefore we cannot quantitatively account for this effect.
The values for the errors described here apply only to those stars with proper motions, distances and
radial velocities derived as in Chapter 2; some of the stars have Hipparcos proper motions of radial
velocities from high resolution spectroscopy or even the systemic radial velocities from Marsh (priv.
comm.) or Morales-Rueda et al. (2002). These have of course far lower velocity errors than the other
objects. As in Chapter 3 we have not calculated the errors for the morphological quantities, such as
nze or ecc.
5
58
This program does not work on the Linux computers nowadays in use at Sternwarte Bonn.
Table 4.1: Positions, velocities (given in the Galactic euclidic system XY Z U V W and Φ, Θ) as well as the angular momentum Iz and morphological
orbital data (Ra , Rp , zmax and eccentricity (ecc), normalised z-extent (nze), see text) of all stars.
No. Name
X
Y
Z
U
V
W
Φ
Θ
Iz
Ra
Rp zmax
nze
ecc
−1
−1
−1
[kpc]
[km s ]
[km s ]
[kpc km s ]
[kpc]
1 HE 0000−2355 −8.399 +0.112 −0.750
−3 +165
+61
+5 +165
+1382
8.42 5.46
1.63
0.20 0.21
2 HE 0001−2443 −8.390 +0.108 −0.801
+42 +127 −23 −40 +127
+1067
8.68 3.46
0.93
0.11 0.43
3 HE 0004−2737 −8.394 +0.059 −0.696
−33 +184 −31
+34 +183
+1540
8.78 6.01
0.92
0.11 0.19
4 PG 0004+133
−8.775 +0.904 −1.046
+75 +100 −76 −65 +107
+941
9.43 2.92
3.48
0.41 0.53
5 HE 0021−2326 −8.347 +0.313 −2.698
−58 +171
+64
+64 +169
+1410
9.47 6.31
4.11
0.47 0.20
6 HE 0031−2724 −8.446 +0.033 −0.928
0 +273
+21
+1 +273
+2308 14.46 8.48
1.56
0.11 0.26
7 PG 0039+049
−8.769 +0.494 −0.887
−16 +214 −99
+28 +213
+1868 10.77 8.22
3.24
0.31 0.13
8 CD −38 222
−8.466 −0.038 −0.257
−40 +208
+69
+39 +208
+1761
9.48 7.40
1.53
0.16 0.12
9 HD 4539
−8.553 +0.088 −0.136
−2 +248
+17
+5 +248
+2120 11.09 8.55
0.30
0.03 0.13
10 HE 0049−2928 −8.460 −0.069 −2.200
−26
−6
+30
+26
−5
−45
9.34 0.08
7.24
3.07 0.98
11 HE 0049−3059 −8.459 −0.064 −1.213
−63 +169 −43
+62 +170
+1435
9.54 5.27
1.65
0.17 0.29
12 SB 410
−8.483 −0.062 −0.532
+50 +230
+66 −51 +230
+1950 11.42 7.66
1.78
0.16 0.20
13 Feige 11
−8.648 +0.183 −0.384
+25 +162 −42 −22 +163
+1410
8.87 8.31
3.03
0.25 0.10
14 SB 459
−8.499 −0.051 −0.438
+21 +250
+31 −23 +250
+2123 11.70 8.36
0.83
0.07 0.17
15 HE 0123−2808 −8.762 −0.224 −2.584
−31 +158 −17
+26 +159
+1392
9.23 5.55
2.66
0.30 0.25
16 HE 0127−4325 −8.411 −0.514 −1.626
−81 +237 −14
+67 +242
+2036 12.99 7.62
2.29
0.18 0.26
17 PG 0133+114
−8.882 +0.319 −0.587
−2 +107 −62
+6 +106
+946
8.90 2.88
1.49
0.18 0.50
18 PHL 1079
−8.859 +0.252 −0.681
+9 +159 −19
−4 +159
+1410
8.88 5.13
0.79
0.09 0.27
19 HE 0136−2758 −8.815 −0.254 −2.160
+56 −33 +194 −55 −35
−307 11.24 4.05 11.27
3.60 0.47
20 SB 707
−8.551 −0.020 −0.254
−43 +121
−3
+43 +121
+1034
8.79 3.18
0.26
0.03 0.47
21 PG 0142+148
−9.142 +0.504 −0.839 +156 +237
+80 +142 +245
+2245 20.76 6.91
3.90
0.19 0.50
22 SB 744
−8.584 −0.056 −0.446
−78
+31
+23
+78
+31
+268
9.25 0.51
5.23
0.91 0.89
23 HE 0151−3919 −8.614 −0.625 −2.008 +362
+25 +239 +363
−1
−10 84.83 0.02 85.51 29.18 1.00
24 PG 0212+148
−9.617 +0.614 −1.199
+25 +221 −86 −11 +222
+2143 11.84 9.69
3.42
0.30 0.10
25 PG 0212+143
−9.679 +0.636 −1.277 −103 +190 −22 +115 +182
+1769 13.48 5.79
1.70
0.13 0.40
26 HE 0218−3437 −8.646 −0.245 −0.761
+6 +211 −24 −12 +211
+1823
8.78 8.22
0.78
0.10 0.04
continued next page
4.2. Kinematics and orbits
59
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
No.
Name
27 HE 0218−4447
28 HE 0221−3250
29 HE 0230−4323
30 HE 0231−3441
31 PG 0242+132
32 HE 0258−2158
33 HE 0307−4554
34 HE 0315−4244
35 HE 0324−3749
36 HE 0340−3820
37 HE 0341−2449
38 PG 0342+026
39 HE 0343−4748
40 HE 0351−3536
41 HE 0405−1719
42 HE 0405−3839
43 HE 0407−1956
44 HE 0410−4901
45 HE 0419−2538
46 HE 0429−2448
47 HE 0442−1746
48 HE 0444−4945
49 HE 0447−3654
50 HE 0452−3654
51 HE 0500−3518
52 HE 0504−2041
53 HE 0505−2228
54 HE 0505−3833
55 HE 0510−4023
continued next page
X
−8.532
−8.834
−8.597
−8.714
−9.493
−9.269
−8.630
−9.478
−9.007
−8.917
−9.045
−8.781
−8.823
−8.798
−9.063
−8.964
−9.062
−8.778
−9.184
−9.150
−9.329
−8.774
−8.936
−8.837
−9.046
−9.414
−9.233
−8.847
−9.024
Table 4.1: Positions, velocities and morphological data of all stars (cont.)
Y
Z
U
V
W
Φ
Θ
Iz
[kpc]
[km s−1 ]
[km s−1 ]
[kpc km s−1 ]
−0.269 −0.584
−93 +149
+70
+88 +152
+1300
−0.457 −1.494
+89 −41 +153 −87 −45
−401
−0.442 −0.925
+91 +289
+88 +106 +284
+2442
−0.338 −0.936
−65 +306
+67
+53 +308
+2687
+0.344 −0.910
−47 +117
+9
+51 +116
+1099
−0.438 −1.549
−30 +235 −55
+19 +236
+2192
−0.540 −0.854
−19 +156
+99
+9 +157
+1357
−2.695 −4.347
+26
+46 −23 −38
+37
+367
−0.408 −0.942
+24 +173 −62 −31 +172
+1549
−0.758 −1.133
−28 +279
+75
+4 +280
+2445
−0.445 −0.881
−22 +143
+61
+15 +144
+1306
−0.022 −0.224
+16 +188 −15 −16 +188
+1647
−1.308 −1.638
+3 +158
+14 −26 +156
+1390
−0.455 −0.660
+17 +185 −43 −26 +183
+1616
−0.340 −0.631
−77 +262 −30
+67 +264
+2398
−0.869 −1.089
−6 +247
+65 −18 +247
+2220
−0.392 −0.665 −146 +318
+99 +132 +324
+2941
−1.152 −1.228
−81 +256
+46
+47 +264
+2339
−0.649 −0.883
+58 +205
+37 −72 +200
+1842
−0.609 −0.771
+50 +218 −35 −65 +214
+1963
−0.600 −0.737
−44 +290
−6
+25 +292
+2728
−1.136 −0.991 −185 +186
+3 +160 +208
+1842
−0.747 −0.712
+38
+51 −17 −42
+47
+423
−0.581 −0.535
−7 +275
+74 −11 +275
+2438
−0.881 −0.768
−93 +233
+51
+70 +241
+2193
−0.806 −0.758
−2 +222
+57 −17 +221
+2088
−0.695 −0.637
−1 +190
+91 −14 +190
+1758
−0.663 −0.547
−44 +189 −19
+30 +191
+1698
−1.113 −0.874
+32 +170
−6 −52 +165
+1497
Ra
9.92
10.08
20.41
20.21
9.90
12.48
8.67
11.90
9.27
16.80
9.11
8.87
9.18
9.02
15.98
12.97
38.12
13.71
11.36
11.45
19.23
14.95
9.24
16.46
13.82
10.74
9.54
9.23
9.71
Rp
[kpc]
4.54
1.32
7.92
8.59
3.76
9.16
6.49
0.72
6.25
8.85
4.80
6.50
5.17
6.50
8.38
8.76
8.20
8.63
6.82
7.58
9.29
5.54
0.94
8.84
8.17
9.14
8.01
6.74
5.34
2.13
7.97
4.22
3.35
0.98
2.69
2.41
6.20
2.01
3.12
1.93
0.31
1.69
1.19
1.27
2.06
9.11
1.85
1.34
1.38
1.35
1.41
4.43
2.80
2.07
1.73
2.71
0.65
0.95
zmax
0.22
1.50
0.20
0.19
0.11
0.22
0.38
0.72
0.22
0.22
0.22
0.03
0.19
0.13
0.08
0.20
0.25
0.18
0.12
0.12
0.07
0.11
0.67
0.17
0.15
0.16
0.29
0.07
0.10
nze
0.37
0.70
0.50
0.46
0.45
0.15
0.19
0.89
0.19
0.33
0.31
0.15
0.28
0.16
0.31
0.19
0.65
0.28
0.25
0.20
0.35
0.49
0.82
0.30
0.26
0.08
0.09
0.16
0.29
ecc
60
Name
56 HE 0516−2311
57 HE 0521−3914
58 HE 0523−1831
59 HE 0532−4503
60 HE 0539−4246
61 PG 0856+121
62 PG 0907+123
63 PG 0918+029
64 PG 0919+273
65 PG 1101+249
66 PG 1114+073
67 PG 1232−136
68 PG 1233+427
69 Feige 66
70 PG 1256+278
71 PG 1343−101
72 HD 127493
73 PG 1432+004
74 PG 1433+239
75 PG 1452+198
76 PG 1519+640
77 PG 1619+522
78 HD 149382
79 PG 1647+252
80 PG 1708+602
81 PG 1710+490
82 PG 1716+426
83 PG 1722+286
84 PG 1725+252
continued next page
No.
−9.882
−9.172
−9.697
−9.204
−8.901
−9.162
−9.470
−9.059
−8.736
−8.634
−8.575
−8.329
−8.559
−8.505
−8.483
−8.126
−8.415
−8.053
−8.338
−8.141
−8.580
−8.408
−8.432
−8.101
−8.482
−8.354
−8.125
−8.036
−8.114
X
Table 4.1: Positions, velocities and morphological data of all stars (cont.)
Y
Z
U
V
W
Φ
Θ
Iz
Ra
Rp
[kpc]
[km s−1 ]
[km s−1 ]
[kpc km s−1 ]
[kpc]
−1.393 −1.143 −114 +457 −88
+49 +468
+4672 161.35 9.94
−1.368 −0.995
−37 +407 −37 −24 +408
+3781
64.93 9.31
−1.037 −0.806
+74 +166
+16 −91 +157
+1531
11.31 5.28
−2.046 −1.359
+83 +305 +176 +147 +280
+2641
41.28 7.79
−1.025 −0.647
−34 +185 −26
+12 +187
+1678
9.05 6.77
−0.490 +0.549
−74 +116 −46
+68 +120
+1099
9.80 3.43
−0.749 +0.900
−6 +177
+86
−8 +176
+1676
9.53 7.44
−0.653 +0.586 −101
+89 −75
+94
+96
+874
9.46 6.88
−0.088 +0.243
+87 +221 −16 −89 +220
+1920
10.74 6.88
−0.086 +0.356
−33 +256 −56
+30 +256
+2209
13.02 8.47
−0.213 +0.389
0 +197
−4
−5 +197
+1688
8.60 7.15
−0.335 +0.429
−79 +135
+38
+73 +138
+1152
9.17 3.72
+0.062 +0.308
+17 +227
+74 −15 +227
+1942
10.11 8.47
−0.011 +0.182
+24 +217
+9 −24 +217
+1841
9.10 7.76
+0.018 +0.780
−71 +197
+75
+72 +196
+1666
10.68 6.33
−0.270 +0.553
−32 +149
+58
+27 +150
+1217
8.29 4.42
−0.046 +0.067
+10 +212
+15 −11 +212
+1780
8.53 7.71
−0.078 +0.609
+34 +143 −20 −36 +143
+1151
8.55 3.68
+0.096 +0.431
+14 +189 −44 −12 +189
+1574
8.41 6.47
+0.165 +0.707
+71 +169
+51 −67 +171
+1388
9.09 5.13
+0.443 +0.469
−54 +332 −93
+71 +329
+2826
29.98 8.36
+0.547 +0.534
−31 +199 −24
+44 +197
+1658
9.40 7.05
+0.014 +0.037
+13 +233
+11 −13 +233
+1966
9.64 8.33
+0.401 +0.429
−11 +265
+43
+24 +264
+2142
12.83 8.01
+1.450 +1.050 −108 +164
+95 +134 +143
+1232
12.05 3.78
+0.563 +0.424
+27 +208 −54 −13 +210
+1755
8.94 8.05
+0.913 +0.682 +128 +211 −44 +105 +230
+1877
12.73 6.27
+0.588 +0.442
−44 +222
+14
+61 +218
+1760
9.77 6.20
+0.432 +0.317
−51 +180
+33
+61 +177
+1435
10.08 8.01
26.79
7.35
0.88
18.28
0.82
1.33
2.81
4.77
0.30
1.53
0.41
0.82
1.78
0.22
2.19
1.31
0.20
0.69
0.90
1.48
4.89
0.63
0.13
1.14
3.75
1.00
1.38
0.50
1.64
zmax
0.17
0.11
0.08
0.47
0.09
0.14
0.31
0.28
0.03
0.12
0.05
0.09
0.18
0.02
0.21
0.16
0.02
0.08
0.11
0.16
0.20
0.08
0.01
0.09
0.31
0.13
0.10
0.06
0.06
nze
0.88
0.75
0.40
0.68
0.14
0.48
0.12
0.58
0.29
0.21
0.10
0.42
0.09
0.08
0.26
0.30
0.05
0.36
0.13
0.28
0.56
0.17
0.07
0.23
0.52
0.05
0.35
0.19
0.27
ecc
4.2. Kinematics and orbits
61
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
100
111
112
113
114
No.
PG 1738+505
UV0 1758+36
HD 171858
HE 2135−3749
HD 205805
HE 2154−4143
HE 2155−1724
HE 2156−1732
HE 2156−3927
HE 2201−2136
PG 2204+035
HE 2205−1952
HE 2213−4158
PG 2218+020
HE 2222−3738
PG 2226+094
PG 2259+134
Feige 109
Feige 108
PG 2337−070
HE 2337−2944
HE 2340−2806
SB 815
HE 2343−2944
HE 2349−3135
PG 2349+002
SB 884
HE 2355−3221
PG 2358+107
HE 2359−2844
Name
X
−8.322
−8.418
−8.341
−8.022
−8.366
−7.581
−7.840
−7.781
−7.646
−7.516
−8.108
−7.994
−6.247
−8.161
−7.759
−8.271
−8.434
−8.455
−8.450
−8.531
−8.277
−8.157
−8.430
−8.195
−8.018
−8.523
−8.418
−8.135
−8.625
−8.229
Table 4.1: Positions, velocities and morphological data of all stars (cont.)
Y
Z
U
V
W
Φ
Θ
Iz
[kpc]
[km s−1 ]
[km s−1 ]
[kpc km s−1 ]
+0.805 +0.511
−27 +241
+53
+50 +238
+1987
+0.158 +0.085
+5 +224
+33
−1 +224
+1889
+0.030 −0.021
+86 +227
0 −85 +227
+1894
+0.049 −0.543 −109 +244 +113 +110 +243
+1951
−0.016 −0.149
−82 +225
+3
+82 +225
+1880
−0.010 −1.172
−32 +270
−7
+32 +270
+2047
+0.510 −0.955
−54 +203
−18
+67 +199
+1563
+0.555 −1.053
−51 +136
+15
+61 +132
+1028
+0.044 −1.112 −153 +370 +141 +155 +369
+2822
+0.634 −1.471
−56 +183
−30
+71 +178
+1341
+0.817 −0.756
+20 +261
−85
+6 +262
+2132
+0.360 −0.797
−31 +172
+19
+38 +170
+1363
−0.080 −3.246 −104 +406
−71
+99 +407
+2544
+0.763 −0.790
+43 +201
−41 −24 +205
+1676
+0.067 −1.172 −227 +147
+12 +228 +145
+1123
+0.840 −0.720
−64 +184
0
+83 +177
+1468
+1.034 −0.911
+39
+20
−44 −14 +212
+1803
+0.751 −0.843
−7
+24
+63
+29 +240
+2033
+0.215 −0.327
+43 +238
−33 −37 +239
+2022
+0.478 −0.603 +138 +154
−28 +129 +162
+1381
+0.082 −0.839
−63 +241
+16
+65 +240
+1986
+0.170 −1.405
−38 +298
+24
+44 +298
+2428
+0.002 −0.242
+44 +238
−7 −43 +238
+2009
+0.110 −1.253
+20 +136
+2 −18 +137
+1120
+0.098 −2.021 +117 +254 −151 +114 +256
+2050
+0.423 −0.702
+76 +163
+61 −68 +167
+1422
+0.024 −0.363
−28 +191
−1
+28 +191
+1605
+0.042 −1.651
+78 +126
−43 −77 +126
+1026
+0.519 −0.635
+49 +193
−9 −37 +196
+1691
+0.116 −1.505
−23 +122 +125
+24 +122
+1002
Ra
11.56
8.89
11.74
16.11
11.48
13.04
9.42
8.33
61.63
8.93
13.74
8.33
62.40
8.56
16.53
12.30
8.79
12.50
10.95
11.60
11.96
18.82
10.89
8.31
22.52
9.69
8.69
9.00
9.18
8.35
Rp zmax
[kpc]
7.68
1.37
8.42
0.46
6.69
0.03
6.83
4.90
6.72
0.19
7.50
1.78
5.90
1.11
3.41
1.18
7.10 21.26
5.50
1.72
8.15
3.01
5.12
0.92
7.02 25.40
7.27
1.21
2.89
2.55
7.17
1.53
8.22
1.38
8.38
1.85
8.05
0.75
4.32
1.12
7.42
1.22
8.09
3.09
7.86
0.30
3.88
1.26
7.68 11.84
5.16
1.62
6.34
0.37
3.52
2.33
6.73
0.69
4.79
4.92
0.12
0.05
0.0025
0.32
0.02
0.16
0.12
0.14
0.37
0.20
0.22
0.11
0.44
0.14
0.16
0.08
0.16
0.19
0.07
0.10
0.10
0.17
0.03
0.15
0.61
0.17
0.04
0.26
0.08
0.70
nze
0.20
0.03
0.27
0.40
0.20
0.27
0.23
0.42
0.79
0.24
0.26
0.24
0.80
0.08
0.70
0.32
0.03
0.16
0.15
0.46
0.23
0.40
0.16
0.36
0.49
0.31
0.16
0.44
0.15
0.27
ecc
62
Table 4.2: Mean U V W, ΘΦ velocities, angular momentum, eccentricities and nze with their dispersions for the 114 star sample and for various
subsamples. The lines labelled e.g. Halo or Disk are attempts to extract subsamples containing only objects from that particular component while not
introducing too many biases (see text). For comparison the Sun’s values are also included.
Subsample
N
Ū σU
V̄
σV
W̄ σW
Θ̄ σΘ
Φ̄ σΦ
I¯z
σIz
ecc
¯
σecc nze
¯
σnze
−1
−1
[km s ]
[kpc km s ]
all
114
−8
74 +198
79 +12
64 +198
80
+6
74 +1700
705 0.33 0.22 0.51 2.74
R < 8.5 kpc
52 −13
60 +208
61 +10
53 +208
61 +22
62 +1698
465 0.28 0.18 0.18 0.42
R > 8.5 kpc
62
−3
70 +196
84 +13
72 +196
85
−7
79 +1761
902 0.35 0.23 0.30 0.49
ecc < 0.55
99
−5
59 +198
52 +10
55 +199
53
+5
58 +1707
460 0.26 0.13 0.19 0.36
ecc > 0.55
15 −29 136 +196 172 +31 102 +193
68 +15 138 +1655 1947 0.78 0.13 2.57 7.15
Z < 0.25 kpc
10 +23
46 +225
12
0
24 +225
12 −23
47 +1909
97 0.15 0.09 0.03 0.03
Disk:
Pure Thin Disk:
Z < 0.25 kpc
8
+8
38 +225
13
+2
26 +225
13
−7
38 +1910
108 0.11 0.06 0.04 0.05
∧ ecc < 0.2
Pure Thick Disk:
Z > 0.9 kpc
29 −23
64 +202
60 +2
60 +202
61 +22
64 +1729
649 0.32 0.13 0.24 0.15
∧ ecc < 0.55
∧ Θ > 50 km s−1
Halo:
ecc > 0.55
16 −24 133 +181 175 +41 107 +178 178 +11 135 +1532 1566 0.76 0.15 2.63 6.93
−1
∨ Θ < 50 km s
High velocity Halo:
ecc > 0.55
7 −75
76 +371
50 +18 108 +369
59 +48
96 +3175
570 0.73 0.10 0.29 0.13
∧ Θ > 220 km s−1
Low velocity Halo:
(ecc > 0.55
9 +16 153
+34
56 +59 102
+30
58 −18 153
+255
481 0.78 0.17 4.45 8.82
∨ Θ < 50 km s−1 )
∧ Θ < 220 km s−1
Sun
1 +10
− +235
−
+8
− +235
− −10
− +1998
− 0.08
− 0.01
−
4.2. Kinematics and orbits
63
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
Figure 4.2: Histogram of the orbital velocities for all 114 stars of the sample. The values for ΘThick disk
and σΘ (TD, Disk) have been taken from Ojha et al. (1994). The velocities of the two stars with rather
similar extreme kinematics (HE 0516−2311 and HE 0521−3914) have been labelled (see text).
Figure 4.3: Toomre diagram (Θ versus velocity perpendicular to Θ)pof the stars of our sample. Circles indicate vpec = Φ2 + W 2 + (Θ − ΘLSR )2 with values in
km s−1 . Note the asymmetry in the central condensation
of data points with vpec < 150 km s−1 . A star shows the
position of the LSR and a circle that of the Sun.
64
Figure 4.4: Bottlinger and
Θ − W diagram of the velocities of the stars of our sample.
As in Figure 4.3 a star denotes
the LSR and a circle the Sun’s
values.
4.2. Kinematics and orbits
4.2.2
A NALYSIS OF THE VELOCITIES AND VELOCITY DISPERSIONS
For the majority of the objects, the orbital velocities have values which are similar to those of disk
stars, which have been found before by other studies, e.g. de Boer et al. (1997a) or Thejll et al.
(1997). However a minor portion of the sample has orbital velocities that are significantly below or
above those expected for disk stars (see Fig. 4.2); some stars have even a near zero or even slightly
negative orbital velocity. As seen in earlier studies, the majority of the sdB stars have velocities rather
indicative of disk orbits, but with Θ̄ somewhat lower than that for Thin Disk stars, while the velocity
dispersions are larger (see Table 4.2).
σV is larger than expected for the Thick Disk alone, reflecting the fact that the Halo and Thin Disk
components are included. A significant old Thin Disk contribution can also be seen by looking at Θ̄
which is higher than what most studies of Thick Disk kinematics arrive at (see e.g. Ojha et al. 1994).
However, due to the composition of the sample, which is certainly lacking stars currently located at
low z-heights, we miss a fraction of the Thin Disk stars.
The stars with large Θ (between 250 and 300 km s−1 ) are also evident in the Toomre diagram (Fig.
4.3), which shows the kinematic divergence of a sample of stars with the orbital velocity plotted
against the velocity perpendicular to Galactic rotation. In our case most data points are located within
vpec ≤ 100 km s−1 , with the region of vpec ≤ 150 km s−1 also well populated for Θ ≤ ΘLSR .
This obvious asymmetry in the central condensation shows a behaviour usually known as asymmetric
drift. It means that kinematically hotter populations tend to rotate slower than kinematically cooler
populations. The reason for this effect lies in the greater eccentricity of the orbits of such objects
and will be discussed in greater detail in the analysis of the kinematic behaviour over the whole orbit
(Sect. 4.2.3.2). A few points lie further out, indicating a kinematic behaviour quite different from the
rest of our sdB stars. The central concentration is well filled to Θ ' 300 km s−1 . At very low peculiar
velocities (vpec ' 30 km s−1 ) only relatively few points are present.
The diagrams of Figure 4.4 show the Bottlinger diagrams with orbital velocity plotted against the two
other components namely the velocity towards the Galactic centre (Φ, top) and perpendicular to the
Galactic plane (W , bottom). Both diagrams show a concentration of stars at low values of Φ and W
respectively near ΘLSR . However the concentration of data points does appear to be slightly shifted
in respect to the Φ,W =0 axis. In both panels (but especially in one showing W, Θ) the points seem to
be somewhat inhomogeneously distributed. Again a few stars deviate from the general concentration
by a large degree.
The stars of our sample show a behaviour which is kinematically hotter than but not too different
from that of the Sun. This implies that the majority of our stars belong to the Thick Disk because
their orbital velocities are somewhat lower than those of stars with solar kinematics. A few stars have
orbital velocities which differ a lot from those of the rest, either being far higher or lower than those
of the rest. Two or three stars even have mildly retrograde orbits. These are presumably not disk stars
but members of a non-rotating Halo population. Whether the stars having a high velocity and those
with a low Θ are of similar or different origin will be discussed in the next section, when the orbits
are examined. This also applies to those disk stars which also have relatively high Θ values.
4.2.2.1
A NALYSIS OF THE VELOCITIES AND DISPERSIONS OF “ PURE ”
SAMPLES
Employing parameters like nze, ecc, Z etc., we can select subsamples which can then be analysed
in the same way as done in Sect. 4.2.2. One aim is to extract “pure” samples, containing only stars
belonging to one population.
65
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
Figure 4.5: The orbits of all 114 sdB stars. The orbits are depicted as meridional plots and calculated
over a timespan of 10 Gyr. Note that the most common types of orbits, the disk orbits, are grossly
underrepresented in this figure. The cross denotes the current position of the Sun and the triangle the
current position of the star. On the lower right panels of the first and last part of this figure the orbit
of our Sun is shown for comparison.
66
4.2. Kinematics and orbits
Figure 4.5: The orbits of all 114 sdB stars (cont.)
67
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
Figure 4.5: The orbits of all 114 sdB stars (cont.)
68
4.2. Kinematics and orbits
Figure 4.5: The orbits of all 114 sdB stars (cont.)
69
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
Figure 4.5: The orbits of all 114 sdB stars (cont.)
70
4.2. Kinematics and orbits
The normal way to achieve this is by using a non kinematic selection criterion such as metallicity. This
is however not possible for our stars due to their drastically altered chemical atmospheric composition.
For this reason we have to use kinematical criteria which unfortunately means introducing biases. First
of all we divided our sample with simple criteria (Table 4.2 upper section).
• A cut was made at R = 8.5 kpc, to see whether there are differences for stars inside and outside
the solar circle6 . For the group at R > 8.5 kpc Θ is somewhat lower than for the inner group
and the dispersions are larger. Because the subsamples still contain stars of all populations,
these differences are probably caused by outliers and do not have much significance.
• To separate the Disk and Halo component, we made a cut near the local minimum of the distribution of eccentricities (see Fig. 4.6). In this case Θ and the velocity dispersions behave as
expected for Disk and Halo populations. Closer inspection showed that the Disk sample was
still contaminated by the Halo. One star, HE 0136−2758, which has a negative Θ and a high
nze value still remains in the Disk sample due to its low eccentricity of 0.47. Furthermore the
two Disk components are still not separated in the Disk subsample.
• The third simple cut was to put all stars currently located at small distances from the Galactic
plane into a subsample – expecting that with this we would mainly choose the Thin Disk stars
(The subsample with z > 0.25 kpc is irrelevant, because it is the same mix of Thin and Thick
Disk and Halo as the original sample). The values of Θ and the velocity distributions are very
similar to other results for the Thin Disk, just σΦ is somewhat large – it better fits to the Thick
Disk. This value and the large Φ is caused by one object, HD 171858, which stays very close
to the plane during its entire orbit but has a large eccentricity – therefore it probably belongs to
the Thick Disk.
We see, that while such simple cuts7 are quite effective to separate different populations, each of
the parts has contamination. Therefore we introduced additional selection criteria in order to create
subsamples as large and pure as possible. These are combined by simple logical combinations (∧ and
∨). Due to the probable large overlap between the kinematics of Thin and Thick Disk it is impossible
to assign each Disk star to just one of the samples – here avoiding contaminations is more important.
The Halo stars, which are far less numerous, are more easily discriminated – here sample completeness
is the priority (see Table 4.2, lower section).
As can be seen in Table 4.2, less than half of the stars are sorted into the “pure” Thin Disk, Thick
Disk or Halo samples. This does not mean that the others cannot be assigned to one of those groups.
The criteria applied are very strict, leaving a wide margin at the borders of the parameter spaces
of the various groups. This especially holds true when distinguishing the two Disk samples, which
presumably have a considerable amount of overlap in kinematics. Nonetheless we cannot exclude that
there are stars having been assigned to the wrong group.
If one uses velocities as selection criteria when analysing mean velocities and velocity dispersions
the results are certainly biased. If the cut is not carefully made the results from an analysis of the
subsamples can be misleading. Therefore we only use velocities in uncritical dissections, e.g. when
discriminating between the high and low velocity Halo which are separated by more than 100 km s−1 ,
or when removing or adding an individual star which unambiguously belongs to one group such as
HE 0136−2758.
6
7
a discrimination often found in the literature.
cuts by only one selection criterion.
71
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
• The Thin Disk sample (see Table 4.2) shows velocities and dispersion similar to those expected
for stars of the Old Disk. The same applies to eccentricities and nze. σU is a little high, maybe
caused by some Thick Disk contamination. The criterion ecc < 0.2 is used to exclude possible
Thick Disk star HD 171858.
• To sort out most Thin Disk stars all objects closer than 0.9 kpc (three Old Thin Disk scaleheights) are excluded from the the Thick Disk sample. This subsample on the whole also
agrees with other studies (which is to be expected, because the full sample has values nearest to
those of the Thick Disk). However the orbital velocity is somewhat high; this might mean that
there still are Thin Disk contaminations in this subsample. In the Thick Disk subsample, there
is a quite significant offset in the mean U/Φ velocity amounting to over 30 km s−1 . Stars with
extreme kinematics cannot be the cause, because all probable Halo stars have been expunged
from this sample. The value is similar to what Fux (2001) found for Hipparcos Thick Disk stars.
Therefore we assume that this offset is real and will discuss it further in Sect. 6.2.3.2.
• The Halo has a mean Θ which is far higher than normally quoted for the Galactic Halo; it is
actually close to that of the Disk. The velocity dispersion in σΘ on the other hand is much larger.
The reason for this is the high velocity component, the few stars travelling at Θ far greater than
that of the LSR.
Therefore we divided this group into two sub groups, namely the “high velocity Halo” and the
“low velocity Halo”. The latter features a low orbital velocity of 34 km s−1 and the dispersions
are around 100 km s−1 , except σΘ which is lower. This could very well be caused by the
selection. The high velocity Halo has a Θ which is near 370 km s−1 . The velocity dispersions
are much lower than those of the low velocity component. One reason for this could be that
stars moving much faster than those of our sample would be expelled from the Galaxy and are
thus not part of our sample.
The high values of the mean U/Φ and W velocities are caused by small number statistics in
combination with extreme velocities of the stars in these subgroups, and are presumably of no
significance.
While Halo and Disk components can be separated quite clearly, it is questionable whether the two
Disk components are really kinematically disjunct. To a lesser extent, there could be some overlap in
kinematics of low inclined Halo stars and loose Thick Disk stars, but this seems to be rather small.
With more and better data the exact amount of overlap can be determined and corrected for.
So, while this way of selecting subsamples is rather problematic, we could still derive samples containing only one population type. However to really constrain the selection we need more and more
accurate data. In this case using selection criteria is potentially a quite powerful tool when assigning
stars to populations.
4.2.3
4.2.3.1
T HE ORBITS
O RBIT MORPHOLOGY
The orbits are shown in Figure 4.5; their morphologies show large varieties. However, the vast majority show box type orbits typical of Disk/Thick Disk stars. Six stars have chaotic orbits, or semi
chaotic orbits. These are the stars venturing very close to the Galactic centre, like most of the HBA
stars of Altmann & de Boer (2000). About the same number of stars have orbits going to very large
72
4.2. Kinematics and orbits
Figure 4.6: Histograms showing the distributions of ecc (left panel) and nze (right panel) for the
stars of the sample. Note the peaks at low values in in ecc and nze and the local minimum in the
distribution of the eccentricities near ecc=0.6
galactocentric distances, one having its apogalacticon at ∼160 kpc. These stars have an orbital velocity much higher than that of the LSR, in some cases approaching the escape velocity of the Milky
Way.
The stars have orbits with eccentricities (see Figure 4.6, left panel) spanning almost the complete
range, however more than 80% have ecc < 0.5. This is the region mainly populated by Disk and
Thick Disk stars. A minority has ecc > 0.7 with the intermediate zone somewhat underpopulated.
This might mean that the sdBs are part of two kinematically quite distinct groups, namely one with
orbits of small to medium eccentricity and another having very eccentric orbits.
The distribution of the normalised z-extents of our sample (see Figure 4.6, right panel) is more peaked
than that of the values for ecc, almost all of the stars having nze ≤ 0.4, but there is a long tail to high
values. We do not see a separation at intermediate nze values. However this is expected as nze is,
amongst others, a measure for the inclination of an orbit. A group of stars all having small orbit
inclinations will show up as a large peak at low values of nze in a histogram. In contrast to that, a
group of stars having orbits with more random inclinations will populate the range of nze without
any preferential value (except in the case of stellar streams or moving groups). This is basically what
can be seen in Figure 4.6, namely a peak of a population of low nze stars and a level distribution of a
group of stars with a large spread in orbit inclination.
4.2.3.2
A NALYSIS OF THE THE KINEMATICS OVER THE WHOLE ORBITS
The analysis of the current kinematics of the stars done in Sect. 4.2.2 gives important information
about the kinematical behaviour and population membership of the sample. However all of the velocities are not conserved quantities, and therefore change over time. Analysing a sample of stars solves
this problem because mean values of the velocity components and their dispersions are conserved
quantities. However they possibly suffer from selection effects. For example stars have, during a
73
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
Figure 4.7: Plots of Θ against ecc and log nze: On the left side the current values of Θ are plotted,
and on the right side the median Θ. On the upper right panel the maximal (open triangles) and minimal
(crosses) Θ are plotted as well. The Sun’s values are represented by the open circles and in the upper
right panel as the open square and star. log nze is used rather than nze to gain access to more detail
at low values. The dashed lines indicate the border between prograde and retrograde motion and the
ΘLSR at 220 km s−1
74
4.2. Kinematics and orbits
Figure 4.8: Diagram of Θ against the total kinetic energy (Ekin ): the open symbols represent the
current values of Θ and Ekin , the smaller filled hexagons the median values Θmed and Ekin,med . The
parabolic curves denote lines of equal orthogonal velocity (v⊥ , the velocity perpendicular to Θ). Most
of the stars cluster around the LSR along the low v⊥ . The medianised values lie more or less on a
straight line pointing from the LSR towards the lower left. The LSR is marked by a star, the Sun’s
current values by a circle and the medianised one by a triangle.
75
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
revolution around the Galactic centre, a considerable range in orbital velocity Θ (e.g. the Sun has a
Θmin of 203 km s−1 and a Θmax of 237 km s−1 ).
Furthermore, all stars spend a large part of the time at a galactocentric distance ($) which is near the
turning points of the orbit, i.e. near its peri- and especially apogalactic distance8 . For a sample of stars
this means that the distribution of velocities is not necessarily a Gaussian but may be a broader, even
possibly bimodal distribution, because the extreme values are more densely populated. The second
Keplerian law leads to the result that the high velocity part is less populated than the low velocity end.
Stars spend more time near apogalacticon than at perigalacticon. Because of the density structure of
our Galaxy there are more stars nearer to the centre than further away from it. Therefore the density
of stars is smaller towards the Galactic anticentrum, which is where many of the stars we see in
perigalacticon come from9 .
Another consequence of the second Keplerian law is the asymmetric drift, i.e. the effect that the
velocities of a sample of stars generally lag behind the orbital velocity of the local standard of rest.
This lagging behind depends on the eccentricity of a star’s orbit; the more eccentric it is the more
the mean orbital velocity deviates from ΘLSR , an effect that can be clearly seen in Fig. 4.7. For this
reason a sample of stars with moderately eccentric orbits is on average slower in Galactic rotation
than a sample of stars with kinematically cool orbits. The Toomre diagram (Fig. 4.3) shows this
effect especially well as the asymmetry of the distribution of data points, with more objects being at
Θ < ΘLSR than at Θ > ΘLSR .
In Sect. 4.2.2 we noted that there are quite a number of stars with relatively high orbital velocities
(Θ ≥ 250 km s−1 ). Looking at the orbits and Θ over the complete orbits of these stars shows that their
kinematics are very similar to those with values for Θ of less than 200 km s−1 . This means that every
sample of Thick Disk stars must have a number of objects having a Θ significantly faster than the
LSR (for solar like orbits the range in Θ covered is much smaller). Now looking again at Figure 4.2,
one sees that the histogram peaks at ∼220 km s−1 and has a plateau down to 150 km s−1 . The reason
for this could be that the stars come from two populations, namely a kinematically hotter one, i.e. the
Thick Disk, and a minority of stars, having much tighter orbits, which represent the Thin Disk.
In Figure 4.7 we plotted the current and median values of the orbital velocities Θ against the eccentricities and normalised z-extents of the stars. In the upper left panel of Figure 4.7 one can see that
most of the stars have low to moderate eccentricity orbits but a group has high ecc values with a less
populated region near ecc = 0.6 (which was already evident in the histogram of Figure 4.6). Moreover it is apparent that while there are more stars having a Θ smaller than ΘLSR , about 1/4 of the
objects have higher velocities. As the current Θ are only momentary values and change over time we
plotted the median of Θ over the whole orbit (We took the median rather than the mean because it
separates the values a little more, and for all except the highly eccentric orbits there is only a minor
difference between both values). To show the complete range of variation in Θ we also plotted the
maximum and minimum values in the upper right panel of Fig. 4.7. The Θmed all lie on a line, except
those of the retrograde orbits. Some deviate a little from this line. These are stars on somewhat more
inclined orbits having a higher W velocity component (which also adds to the velocity supporting the
orbit; a star on a higher inclined orbit can have a less eccentric orbit with the same orbital velocity,
8
in terms of analytic geometry: the orbit must be continuously differentiable in all parts (i.e. no kinks or jumps etc.).
Therefore as the star approaches one of the turning points of the orbit (either peri- or apogalacticon or a local zmax i.e.
zmax ($)) the velocity component in the direction will become smaller and smaller until it reaches zero. Therefore the
probability distribution in $ (or also z, see Sect 4.3) shows peaks near the extremes. As a consequence of the second
Keplerian law (Kepler et al. 1619) the peak for the perigalacticon becomes less pronounced with higher eccentricity orbits.
9
This is similar to our solar system. While the individual planets are more likely to be found near their aphel than their
perihel, there are more planets closer to the Sun.
76
4.2. Kinematics and orbits
because of its larger W velocity component). Again, the two groups of stars can be seen as well as
the division at ecc = 0.55. At ecc < 0.2 the trend in Θmed is small, and at higher values it gets more
pronounced. Again the Thin Disk part, if it exists, makes up a large part of this low ecc group.
In the lower two panels of Figure 4.7 plots of log nze (log nze because most values of nze are clumped
together at low values) against Θ, Θmed are shown. The left panel shows the distribution of nze of
our sample. The central condensation marks the majority of disk stars, and the outliers towards low
or very high Θ are the Halo stars. The spur towards low nze at LSR velocities consists of datapoints
of solar type orbits.
On the plot log nze − Θmed the different subdivisions of our sample can be seen even better, on the
left are the Halo stars, which have a low Θmed (the high velocity Halo stars also lie in the left of this
diagram). The bulk of the Thick Disk stars cluster around Θmed = 200 km s−1 , log nze = −0.9, and
the solar kinematics extension protrudes towards the bottom of the diagram. At values of log nze >
−0.7 there seems to be a gap appearing between ΘLSR and the data points. It is possible that the Thin
Disk population represented by the spur more or less ends at this point (which corresponds to a zmax
of ∼ 1.7 kpc or 5-6 Thin Disk scale heights). The stars having a Θmed of more than about 190 km s−1
and a nze of less than ∼0.2 (log nze = −0.7) are the prime candidates for the Thin Disk component.
However the region leftward of the spur might also be filled out with data points, because stars having
such kinematics may not be represented in sufficient quantity in our sample (see Sect. 4.1.1.1). In fact
there is one isolated data point in this region, belonging to the nearby star SB 707 (see Sect. 4.2.4).
So potentially the lower right plot of Figure 4.7 is a suitable tool to kinematically separate Thin and
Thick disk stars, if these populations are kinematically detached at all. However more stars at low z
must be included to see what really goes on in the low z range.
Another method of analysing the kinematics of stars is using the kinetic energy (or total velocity).
In Figure 4.8 we plotted the kinetic energy 2 · Ekin /m = U 2 + V 2 + W 2 against Θ. The parabolas
plotted in Figure 4.8 are lines of equal v⊥ (velocity orthogonal to Θ). This velocity is a measure of
kinetic temperature, the higher its value the more an object’s orbit deviates from a circular orbit. As
can be easily seen, most of the values cluster around the LSR on a banana shaped region alongside
the v⊥ = 0 km s−1 isovelocity line. This clustering means that the majority of them is kinematically
relatively cool. A few stars are located further away than the bulk, and in some cases quite far away
from the v⊥ = 0 km s−1 contour. These are the kinematically hot stars. The reason that most of our
stars have quite low v⊥ values is that most stars are near their orbital turning points, i.e. their apo- or
perigalacticon. In these orbital phases the Φ component is minimised.
As the current Θs and Ekin s are just snapshot values, we also calculated the median of both quantities
using the whole orbit and plotted these in Figure 4.8 as well. These data points lie nicely on a line
pointing towards lower Θ and lower Ekin away from the LSR. Those with the lowest values spread
out more than the others. Furthermore there is a gap near Θ = 110 km s−1 . Stars located to the left
of this gap have rather hot orbits. Their considerable dispersion in inclination is shown by the spread
along the line (caused by the W velocity component). They represent the Halo population. The stars
at Θ > 110 km s−1 are the Disk stars. Clearly the asymmetric drift of each star can be seen. The
warmer an orbit is kinematically (seen by increasing v⊥ ), the lower its orbital velocity is.
Considering Ekin and Θmed in Fig. 4.8, there is (similar to what we saw in Figures 4.6 and 4.7) a
clear division between the Halo and Thick Disk with the division line here being at Θ = 110 km s−1 .
Dividing Thick and Thin Disk is not so straightforward. Perhaps only the distribution of a sample
complete to the Galactic plane will lead to a separation of these two kinematical populations.
To conclude, analysing the kinematics of the whole orbits instead of just the current values gives
further insight into the kinematic behaviour of a group of stars. In our case the Halo and Disk com77
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
ponents of our sample are clearly discerned (see Figures 4.6, 4.7 & 4.8). Of the 114 stars, 16 (14%)
belong to the hitherto unknown Halo group, the rest are Disk stars10 . Thin and Thick Disk groups
cannot really be separated, at least not with the current sample, which is perhaps lacking in Thin Disk
stars. Possibly the kinematics of both disk components are not disjunct so that for a detailed analysis
statistically complete distributions are required.
4.2.4
N OTES ON INDIVIDUAL STARS
• SB 744: SB 744 is a sdB binary star intensively studied by Unglaub & Bues (1990) and probably the strongest evidence for the existence of Halo sdBs, because its proper motions come
from the Hipparcos catalogue. As the Hipparcos parallax is consistent with zero, the distance
was calculated using the values for Teff and log g derived by Unglaub & Bues (1990). The
brightness of the much fainter companion was not taken into account for the distance determination because it would shift the object further away by only a few percent. The radial velocity
was taken from Kilkenny & Muller (1989) and is consistent with the rather crude estimate of
Unglaub & Bues (1990). The orbital velocity is 31 km s−1 , its orbit is chaotic (see Fig. 4.5) and
it has a very small perigalactic distance. This is one of the stars with an orbit similar to those
shown in Altmann & de Boer (2000).
• HE 0136−2758 and HE 0221−3250: These objects are also very high probability Halo candidates. They are the only stars in the sample having a significantly retrograde orbit. The value
of Θ for these objects depends only weakly on their radial velocity, so in the case of having
measured an extreme value of variable radial velocities caused by binarity will most probably
not transform the stars’ kinematics into those of disk stars.
• HE 0516−2311 and HE 0523−3914: These two stars have very extreme orbits, bringing them
very far away from the Galactic centre or the solar vicinity. HE 0516−2311 has the most
extreme orbit of all of our stars and the highest value for Θ. While the photometry for this star
is only photographic (see Sect. 2.3.2), the resulting somewhat larger uncertainty for the distance
can however not be used to explain the extreme kinematics of this star.
Another striking property of the orbits of these two stars is that they are relatively similar. This
raises the question as to whether they have a common origin. Their orbital velocities which are
near the escape velocity of the Galaxy may lead to the speculation that these two stars come
from a stellar aggregate accreted relatively recently by the Milky Way. Although two objects
with relatively similar extreme kinematics is not very significant evidence, this coincidence is
surely notable. This aspect is discussed in greater detail in Sect. 6.2.4.
Apart from these two objects, there are a few more stars having an apogalactic distance of 30
kpc or more. These are HE 2156−3927, HE 0151−3919, HE 0407−1956, HE 0532−4503 and
PG 1519+640.
• HE 0218−4447: This star is the only sdO star in the sample. Although its value for Teff
(Teff =44500 K) is somewhat higher than the limit for an sdOB star, the star was kept in the
sample. A problem concerning sdO stars is that their evolutionary stage is ambiguous, because
stars can reach the sdO regime in different ways (EHB, AGB-manque, pAGB). The kinematics
of this star are inconspicuous; it has a disk orbit reaching a zmax of just over 2 kpc.
10
78
a further (unsure) candidate may be HE 2349−3135, see Section 4.2.4.
4.2. Kinematics and orbits
• HE 2349−3135: This star has a Θ of 256 km s−1 , and an eccentricity of 0.49, values rather
corresponding to stars of the Thick Disk. However it moves to nearly 12 kpc from the Galactic
plane. Therefore this object can either be an extreme Thick Disk star reaching a zmax of 12× the
scale height of this component, or it is a Halo star on a moderately eccentric but highly inclined
orbit, analogous to that of HE 0136−2758 (which clearly is a Halo object as it has a negative Θ).
The value Θmed places this star near the border between disk and Halo. The third possibility is
that it is one of the close binary sdBs with a highly variable radial velocity − its measured value
is quite high − if the measured radial velocity is far off the systemic one, it could mean that the
star might have a much closer orbit. But this is only speculation; certainly the radial velocity of
this (and other stars) has to be re-analysed. For the time being HE 2349−3135 is considered to
be part of the Halo part of our sample in the kinematic analyses and also in the determination
of the scale heights, but not in the number or the percentage of Halo stars in our sample.
• PG 1716+426: Its proper motion is based on Hipparcos data and its quality approaches that
of the Hipparcos data (Geffert 1998). The resulting orbit is a Thick Disk type orbit. This star
is one of those which are known to have a large amplitude variation in its radial velocity. The
systemic radial velocity that we used taken from Morales-Rueda et al. (2002) is only slightly
different to that used by Geffert (1998).
• SB 707: At first glance the orbit of this star is rather inconspicuous. However it has a very low
nze of 0.03, a high eccentricity of 0.47 and therefore a low Θ. The isolated datapoints of SB
707 can be clearly seen in the lower panels of Figure 4.7, well away from the remainder of data
points. As it is one of the stars with a Hipparcos proper motion, the velocity errors are small. So
the star is either a (Thick) Disk star with extreme kinematics or it is a low inclination Halo star.
On the other hand its Θ is similar to quite a number of other stars so it is possible that there are
more stars with the same combination of nze and Θ. Stars with low inclined orbits are out of
bounds of the parts of the sample taken from the HE-catalogue and from de Boer et al. (1997a)
so selection effects might come into play here once again (see Sect. 4.1.1.1).
4.2.5
S ELECTION
EFFECTS
Apart from the selection effects discussed in Sect. 4.1.1.1 which are mainly caused by the sample
composition, there are other effects resulting from the kinematics and orbital morphologies themselves. These therefore not only occur in studies of specific object types but in any kinematic study
such as the one presented here.
Stars with different vectors of motion (in respect to the Sun) have different probabilities of venturing
into the vicinity of the Sun (defined by the observable range of this study). An object with a motion
differing a lot from the solar motion will only stay in the solar vicinity for a short while; a star with
a solar like orbit will remain there for a very long time. One the other hand an object of the “fast
moving” type (i.e. relative to the Sun) has a greater probability of moving into the solar vicinity,
because a “solar like” object, once it is outside the solar range, will stay outside for a long time.
Presumably these two effects11 compensate each other or nearly do so; therefore we do not expect
significant skewness in our analyses caused by this. However stars with extreme kinematics might
very well be affected. This especially applies to stars on retrograde orbits or in principle to stars
orbiting significantly faster than the Sun. However stars with a Θ of 600 km s−1 or larger probably
do not exist in the Milky Way in great numbers (some of the stars of our sample already have rather
11
This is in principle the old problem of the two clocks: Which one is better, a clock being slow (or fast) one minute per
hour or one that is completely broken?
79
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
extreme orbital velocities) because they will escape from the Galaxy altogether. Stars with a retrograde
motion of −200 km s−1 (which is as far away from the 220 km s−1 of the Sun as Θ = 600 km s−1 )
may very well exist, but as they cross the solar vicinity in a very short time, it may be very difficult to
discover them.
A similar phenomenon could occur when looking at the motion perpendicular to the Galactic plane.
Here stars on polar orbits are presumably underrepresented in respect to stars travelling on an orbit
with a smaller inclination angle. Therefore spherical populations such as the Halo may appear flattened somewhat when examining the distributions of their stars using the kinematics. The effect on
disk-like populations such as the Disks should be of much smaller magnitude. Therefore we do not
take it into account in the present study.
Maybe the U /Φ component shows the most striking example of this differential motion bias. When
looking at our Halo sample one sees that there is a high velocity and a low velocity part (in Θ),
with very few stars inbetween. As shown in Fig. 4.8, there is no kinematic difference between these
two groups − they are just stars on different phases of their orbit. (The high velocity objects have
however, higher IZ values than the low velocity component, see Table 4.2). The bimodality of the
Halo arises from the effect that when they are near one of the turning points of their orbits (Θ maximal
or minimal, U/Φ near 0 km s−1 ) when near the Sun, they will stay there for a longer time (as far as
Θ and W permit them) than when they are on a intermediate phase of their orbits. This probably
explains most of the bimodality of the group of Halo stars.
We do not quantitatively analyse probable effects caused by the selection effects discussed in this
subsection, because the focus of this study was to determine quantities like the scale height of the
Disk, which is not as much affected by such a bias, and to find a possible Halo population. The
number of Halo stars is too small to give more than rather crude values for the scale height and other
quantities. However we do point out that in the future (when larger samples give us the opportunity of
a more detailed analysis of the Halo population) it is certainly worthwhile if not essential to analyse
and quantify the biases introduced by such phenomena.
4.3
D ETERMINING A SCALE HEIGHT FOR THE STARS USING THEIR OR BITS
4.3.1
z- PROBABILITY
PLOT AND SCALE HEIGHT
As done before in de Boer et al. (1997a) for 41 stars, we have derived the z-distribution12 using the
orbits of the stars of our sample of 114 stars. The program used to calculate the orbits does so for
a fixed time per step, in our case 1 Myr. Plotting a histogram of the orbit in $ or z leads to the $
resp. z probability distribution for the star, i.e. the probability to find the star at a certain $ or z
distance. Plotting the histogram for the whole sample (by adding up the individual histograms) leads
to the probability distribution for the complete group. From this the density gradient for the sample
can be deduced. One may now fit an exponential distribution and determine the scale height using the
relation
z
ln N (z) = ln N0 − ,
(4.3)
z0
12
z is the (positive) distance between the Galactic plane and a point (such as a star) while Z means the Z-coordinate
of the point in the XY Z, U V W system. Technically we are determining the Z-probability distribution, because we are
measuring the slope above and below the galactic plane, i.e. for Z < 0 kpc and Z > 0 kpc. Assuming the symmetry of the
disk in Z direction both slopes will have similar values and can therefore be averaged to one, namely the z-distribution.
80
4.3. Determining a scale height for the stars using their orbits
with N (z) being the number density at z, N0 being the density at z = 0 kpc, and z0 the scale height.
The scale height is the reciprocal value of the slope of the ln N distribution. As we do not have a
defined volume in which the stars are located we are unable to determine absolute values for N (z)
and N0 . The absolute values we obtain with this fit are arbitrary (they depend on the number of data
points in the sample, in our case (114 stars with 10000 data points per orbit) 114×106 ). However
what we can determine, are relative values of the form N1 (0)/N2 (0) in the case that there are two or
more slopes.
The method is described in greater detail in de Boer et al. (1997a). The z-distribution is depicted in
both linear and logarithmic form in Figure 4.9 (Panels a and b).
Panel b) of Figure 4.9 clearly shows that our distribution consists of two components with different zdistributions, a central one with a steep slope and an outer shallow distribution. Fitting linear equations
to the various regions leads us to scale heights of 1.0 (±0.1) kpc for the central (steep) part and
7 (±2) kpc for the outer (shallow) parts. For the fit of the steep slope we used a fitting interval of
[0.7,4] and [−4,−0.7] kpc and [7,17] resp. [−18,−7] kpc for the shallow slope13 The results for the
upper (Z > 0 kpc) and lower (Z < 0 kpc) half of the distribution are
z0,+ = 1.04 kpc and z0,− = 0.93 kpc for the central part
and z0,+ = 7.2 kpc, z0,− = 6.5 kpc for the outer parts.
The main reason for the greater uncertainty for the outer part is that this relies on only a small group
of stars and therefore suffers from small number statistics. On the whole the result for the component
with the steep slope is very similar that that of de Boer et al. (1997a) based on a sample only 1/3 of
the size of the present. The other component was not noticed by de Boer et al. (1997a), because their
sample has only a few data points at z > 2 kpc.
For small z the distribution is less well known. Here selection effects come into play (see Sect.
4.1.1.1). The volume of our sample containing the stars which only reach low z-heights is small. The
vast majority of our stars are located at z-heights of between 0.5 and 2 kpc, so that only a few stars
having a zmax < 0.5 kpc are included in our sample.
4.3.2
E FFECTS OF E RRORS
The effects of the errors of the input parameters, i.e. distance, radial velocities and proper motions on
the derived scale height were intensively analysed by de Boer et al. (1997a). They added the errors
to these quantities, calculated new orbits, and computed the scale heights anew. The most important
effect may be caused if there is a systematic error in the distances which would decrease the scale
height if the distances were systematically too low and increase the scale height if it is too high. The
effects of the other quantities are smaller, with the scale height being smallest when no error is added.
As we expect similar effects on our sample, we did not repeat the error analysis but refer to de Boer
et al. (1997a).
4.3.3
S CALE HEIGHT AND GALACTOCENTRIC DISTANCE
To see how the scale height results vary with galactocentric distance we cut the cumulative orbit file
of our whole sample into bins in galactocentric distance ($) and determined the scale heights for
each. In all bins (except the outermost bin $ ≥ 15 kpc, where the inner, steep distribution is missing)
both components were found, although the outer, shallow component was overwhelmed by the steep
13
The intervals used for this component are slightly different because of a disturbing spike in the one direction, which
would somewhat falsify the fit result.
81
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
Figure 4.9: Histogram of the z distance-statistics of the stars of the sample. a) and b) show the
histogram of all 114 stars in the sample. a) shows a linear representation of the z-distribution of the
stars, b) a logarithmic one. An exponential distribution can be fitted leading to a scale height (see
text). Two slopes can clearly be seen in the right panel. The binsize is 50 pc. The dashed lines in the
upper right panel show the exponential equations (linear in the logarithmic plot) fitted to the data, the
full lines the double exponentials. The dot-dashed vertical lines denote the fitting intervals of the two
double exponential functions. c) and d) show histograms of only the disk population (c, 97 stars), and
only the Halo population (d, 17 stars).
82
4.3. Determining a scale height for the stars using their orbits
component and thus hard to identify in the bins near $ ' 8.5 kpc. The results for the scale height
of the steep component is similar (however a little smaller) to the result derived from all data points.
Several aspects have to be taken into account such as the increase in scale height with $ and the
increase of solar like orbits in the central bins which counteract each other because the latter have a
smaller vertical extent. Therefore no significant trend with $ can be seen in the steep scale height.
The extended, high z distribution is based on only a few stars. For this reason one expects a large
spread in the derived scale heights of the subsamples. Apart from this there is a trend from small
to large scale heights with $. This is not surprising and is an effect of the diminishing gravitational
potential with galactocentric distance. Another reason is that because we are cutting slices into a
sphere when doing this kind of analysis, a star in one of the inner bins would have to reach a higher
and higher zmax to keep up a high scale height. Such a star would never venture near the Sun and
would never be part of our sample.
4.3.4
ROBUSTNESS
OF THE SCALE HEIGHTS , SEPARATING THE DIFFERENT POPULA -
TIONS
In order to test the stability of the values of our scale heights we made tests with changed fit interval
limits. Furthermore, to determine how the the various components influence each other, we derived
scale heights with various subsamples excluded.
Shifting the lower and upper border of the fit interval of the steep component, leads to a variation of
the result of about 100 pc. So, the interval used for fitting leads to an error of ∼ 50 pc, which means
that the derived slope and hence scale height is relatively robust in this respect. The fit intervals used
to determine the slope have a larger influence on the Halo component because of various peaks caused
by individual stars.
The presence of the Halo component has some influence on the obtained scale height. Without it
(selected using the results of Sect. 4.2) the scale height tends to be 100 - 150 pc lower. For the
complete disk sample without the 17 stars classified as Halo members, we find a scale height of the
steep component of 0.84(±0.1) kpc instead of the 0.98(±0.1) kpc for the whole sample. For this
reason the Halo component should be removed before calculating the scale height of the Thick Disk.
Histograms showing only the Disk and the Halo components of our distribution are shown in 4.9
(Panels c and d).
Removing the stars with the coolest, i.e. most solar-like, kinematics − those that are most likely Thin
Disk members − leads to a slightly higher scale height of a little over 0.9 kpc (for a sample having all
Halo and all stars with ecc < 0.15 and nze < 0.15 excluded). Obviously the influence of Thin Disk
stars is much lower. This becomes quite clear, when one considers that removing stars with a nze
lower than a certain value only changes the distribution in the middle. Therefore, the selection effects
described in Sect. 4.1.1.1 do not play a significant role for the determination of the scale height as
the central part is not used for the fit. If the sample were complete for the low z stars, the central part
would fill in and possibly result in a third perhaps still steeper component, representing the Thin Disk.
The end points of the fit are more significant for the Halo component than for the disk part. This
is expected as spikes in the distribution caused by individual stars are important − this subsample
contains only 17 stars. On the other hand the influence of the disk on the Halo scale height is small.
With the results of this analysis we conclude that the value of the scale height of the steep component,
representing the Disk is
0.84(±0.07) kpc, and that of the shallow part is
6.5(±0.2) kpc.
83
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
These errors are only based on the differences of the two derived values for the scaleheights (Z > 0
and Z < 0).
Another approach is not to separate the sample into a Disk and a Halo part but to use the whole
distribution and fit a 2-component function to this. The advantage of this is that one does not have
to rely on selection criteria, which are not without arbitrariness. This double exponential function
(which accounts for the overlap in the region where both components are of similar strength) has the
following form:
ln N (z) = ln(ND,0 · e−z/zD + NH,0 · e−z/zH )
(4.4)
with the indices D,H referring to the Disk and Halo respectively. The resulting fit of this equation to
the data is shown in Fig. 4.9 panel b). Here we used fitting intervals of [0.7,17] kpc and [−18,−0.7]
kpc (shown in Fig 4.9). Varying the fitting intervals lead to the following results: Raising the lower
limits caused the scaleheight to slowly rise. This trend was mainly caused by one side of the distribution, the other one did not change. The upper limit has the same difficulties caused by the spikes as in
the single exponential fits.
The resulting values for the scale heights are
zD =0.93(±0.09) kpc and zH =7.0 (±0.5) kpc.
This means that there is a difference of 0.09 kpc between the Disk scale heights derived using population separation and the 2-component fit. The difference between the two values for the Halo is as
large as 0.5 kpc; this may be related to the effect we see for the Disk scale height, but as the values
for the Halo are not very certain and depend much on the fit intervals, we do not further discuss the
differences of the Halo scale height values. Reasons for this small discrepancy could lie in the fit,
as the Halo component may have an influence on the derived value for the Disk, or in the point that
Disk and Halo may not have been completely separated using our selection criteria (Disk star being
incorporated in the Halo sample) in the method of the separate fits14 , which is however somewhat
unlikely. Fitting intervals could still play a role here.
To conclude, we consider the 2-component method the most trustworthy and finalise the value of the
scale heights as:
0.92+0.08
−0.12 kpc for the Disk (or 0.9±0.1 kpc)
and 6.8±1.5 kpc15 for the Halo component.
4.3.5
M IDPLANE NUMBER RATIO OF THE TWO COMPONENTS FOUND
The steep distribution has a peak value of ln N0 = 10.3 and the shallow part peaks at ln N0 = 6.5.
Therefore the relative density of the shallow with respect to the steep component is 1.25(±0.25)%.
The zero point of the broad distribution has of course a high uncertainty because it relies on the data
of only a few objects. Therefore the ratio of densities is only an estimate.
4.3.6
C ONSTRAINING
THE
T HIN D ISK COMPONENT
As said before, due to the selection of the stars forming our sample we do not get reliable information
about the z-distribution of the stars with zmax less than about 0.7 kpc (The reliability starts to deteriorate at even higher values). Therefore we cannot make definite statements about a possible Thin Disk
14
HE 2349−3135 is not the culprit, that has been tested.
This error is an estimate, but certainly more appropriate than the values shown above, derived from the difference of
the two fits (upper and lower half).
15
84
4.3. Determining a scale height for the stars using their orbits
Table 4.3: Compilation of our results for the scale heights (z0 )and mid plane densities N0 for Thin
Disk, Thick Disk and Halo. N0 of the Thick Disk is always set to 100%.
Method
(Old) Thin Disk Thick Disk
Halo
N0
z0 N 0
z0
N0
z0
[%]
[kpc] [%] [kpc] [%] [kpc ]
separate linear equations
–
– 100
0.98
1.3
6.8
populations separated by
–
– 100
0.84
1.3
6.5
selection criteria
2-component fit
–
– 100
0.93
1.2
7.0
a
a
a
a
3-component fit
330
0.30
100 0.93
1.2
7.0a
b
adopted values
–
– 100
0.92 1.25
6.8
a : This fit is solely used to give a constraint on the Thin Disk. All quantities marked with a are held
fixed.
b : These values mostly rely on the 2-component fit, but are shifted a little towards the result obtained
with the separated populations.
component, which mostly consists of stars at smaller zmax . We can however determine an upper limit
for this Thin Disk sdB population.
To accomplish this we need a three component distribution model (similar to the two component
function used in Section 4.3.4), having the form:
ln N (z) = ln(NOD,0 · e−z/zOD NTD,0 · e−z/zTD + NH,0 · e−z/zH )
(4.5)
The indices TD and OD mean Thick Disk and Old (Thin) Disk (assuming that the majority of the sdB
stars are old, and hence the bulk of the Thin Disk population belongs to the Old Disk) respectively.
The values for zTD , NTD,0 , NH,0 and zH are fixed to the values resulting from the fit in Section 4.3.4.
The scale height of the Old Disk is assumed to be 0.3 kpc, consistent with most results of star counts
(see Table 6.1). Thus the only free parameter of this fit is the z=0 kpc density of the Old Disk (NOD,0 ).
The resulting value for NOD,0 is:
NOD,0 = 3.4+0.9
−1.4 × NTD,0 .
The (not surprisingly) very large errors for this value result from the large differences in the derived
values of the fits to the upper and lower flank of the distribution.
This value, meaning the z = 0 kpc density of the Thick Disk normalised to that of the Old Disk is in
the order of not less than 30%, or if one takes into account the errors between 20% and 50%. This is
a much higher value than any result from other studies (see Table 6.1) which arrive at values for this
ratio of between 2 and at most 15 % (most between 4-8%).
Apart from problems arising from the fit itself (the lever for the Thin Disk component is very short
and therefore very prone to errors) there are probably two reasons for this:
1. The relative incompleteness of our data described in Section 4.1.1.1 begins earlier than z=0.7
or 0.8 kpc. That this has some influence is quite probable, because the majority of our stars are
at greater z-heights than 0.8 kpc. However the Thick Disk component does not appear to be
affected significantly because tests with increased lower fit limits do not lead to much different
results.
2. The other probable influence is an astrophysical one. In contrast to nearly all of the other studies
which dealt with mostly main sequence stars, or general star counts (i.e. counting mostly main
sequence stars) our study has a evolved star type as subject.
85
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
As far as we know the Thick Disk and Halo are populations which have completed their star
formation a long time ago. Moreover this period of star formation seems to have been during
a relatively well defined and also rather short timespan16 . This does not hold true for the Thin
Disk which has been forming stars since it came into existence about 9 Gyr ago (Knox et al.
1999) until the present. Therefore the ratio of the density of the Thin Disk and that of one of the
other components is higher when all stars or main sequence stars are taken into account, and
lower if only objects of an evolved star type are counted.
Now it can be argued that most types of evolved stars (in our case sdBs) can be formed from
stars of e.g. 2 M , i.e. from relatively young stars (∼ 1 Gyr). While this is in principle true,
there is another aspect that is to be considered: There are far more low mass stars than stars of
e.g. 2 M which means that the vast majority of our sdB stars (and accordingly any evolved
stars to which no predecessor of a well defined mass can be allocated) would be formed out of
stars near the lowest mass possible17 . Therefore it is expected that the density ratio between a
population with an ongoing star formation and a population which ceased forming stars depends
on the object used for the determination. This can very well explain our high Thick/Thin Disk
ratio.
Which of the two effects plays the dominant role can at present not be determined. However they
certainly influence the result of our study. The lesson to be learned from this is that it is crucial to
know what the subjects of study are especially when comparing the results with others.
4.3.7
D ISCUSSION OF RESULTS
Our scale height study resulted in finding two components, one with a large and one with a moderate
scale height. A compilation of the results with the different strategies described in the sections above,
is given in Table 4.3. The latter scale height is with z0 = 0.9 kpc very similar to that found for the
sdB stars by de Boer et al. (1997a). It is also similar to the determinations of the scale height of the
Thick Disk (see e.g. Ojha 1994, Kerber et al. 2001, Chen et al. 2001) and discussion below. Thus the
steep component in Fig. 4.9 (Panel b) can be identified with the Galactic Thick Disk population.
The analysis of the kinematics (Sect. 4.2) showed that there are some stars with solar kinematics.
These stand out in the histograms of Figure 4.9 as the extra double peak in the centre. Presumably
these and perhaps some more belong to the Old Thin Disk.
The shallow, high z component represents a drastically different population of stars. It is rather hard
to imagine a disk-like population with such a scale height if one considers the Galaxy’s radius being
of the order 15 kpc. So we speculate that this component is actually a spheroid or an ellipsoid. To
make significant quantitative statements about the shape of the distribution of this population more
stars are needed than the few which are discussed here. But we can say that this subsample consists
of members of the Halo.
The density ratio of the Halo to the Disk component extrapolated to the Galactic plane is 1.2%. This
value is of course quite uncertain. Kerber et al. (2001) found a density ratio of 0.2% for Halo and
Thin Disk. Chen et al. (2001) found a local relative density of the Halo against the Thin Disk of
0.125%. Our higher values for the Halo to Disk density is probably due to the fact that our Disk stars
are rather members of the Thick than the Thin Disk, or a mixture of both. The literature values for
16
Of course the early phases of the evolution, and hence star formation scenarios are still much under debate. A short
and early star formation phase of the Thick Disk is underlined by observational evidence Edvardsson et al. (1993) and also
theoretical models (see e.g. Burkert et al. 1992; Quinn et al. 1993).
17
This even more holds true when the SFR in the Galactic disk declined from the beginning to present.
86
4.4. Discussion: kinematics and the population membership of sdB stars
the Thick/Thin Disk density ratio range from about 5% to 10%. Assuming a Thick/Thin Disk relative
density of 7.5%, we obtain a Halo/Thick Disk ratio of 1.7%. This is rather similar to the value derived
from the sdB stars.
4.4
D ISCUSSION : KINEMATICS AND THE POPULATION MEMBERSHIP OF
SD B STARS
As shown in Sections 4.2 and 4.3, the sdB stars of our sample belong to different populations. In this
Section we discuss the different groups and implications for the evolutionary processes that lead to
the formation of sdB stars and questions of Galactic structure.
4.4.1
T HE D ISK
The vast majority of the sdB stars was found to belong to the Galactic Disk. While most stars have
orbits of moderate eccentricity and reach normalised z-heights (nze) of around 0.2, there are quite a
few which have near solar kinematics, and are therefore more likely to be associated with the Thin
Disk. Unfortunately, the sample composition prevents us from separating the two populations unambiguously if these are separate at all (see Sect. 4.1.1.1). The histogram in Figure 4.2 shows a Thick
Disk-like distribution with a Thin Disk peak. This implies that the stars of our sample come from both
Disk components. Because of our result for the scale height and the velocity dispersions, we conclude
that the majority of the sample belongs to the Thick Disk.
On the whole most other studies arrive at values similar to what we found for the scale height and
kinematics of the Thick Disk. There is however still some disagreement among these studies concerning the scale height and hence the local relative density. Kerber et al. (2001) derive a scale height for
the Thick Disk of between 0.8 and 1.2 kpc. Reylé & Robin (2001) favour a value of 0.8 kpc, Chen
et al. (2001) on the other hand arrive at 0.58 - 0.75 kpc but with a much higher local density of 6.5
- 13% of the density of the Thick Disk. In contrast to those results, Reid & Majewski (1993) find a
scale height of 1.4 kpc, in this case the local density being not large, ∼2%. As can be seen the values
differ by at least a factor of 2. Our value of 1 kpc is only a little above the values obtained in most
studies.
The velocities and velocity dispersions are under much less dispute than the scale height. Most studies
arrive at values near those of Ojha et al. (1994), i.e. ∼ 50 km s−1 for each U V W component and a
value of 175 km s−1 for the mean orbital velocity of the Thick Disk. Our larger value for V̄ /Θ̄ and
σV /σΘ is related to the Thin Disk and Halo contamination. When we only consider stars with ecc ≤
0.55 thus excluding most of the Halo objects, we obtain values for σV /σΘ of about 50 to 60 km s−1
(see Table 4.2).
In a recent study of the kinematics of local F and G main sequence stars, whose population membership was determined using their metal abundances (Fuhrmann 2000), an asymmetric drift of 80 km s−1
was derived, which is larger than the results for the asymmetric drift found by most other studies. Our
results indicate an asymmetric drift of ∼30-40 km s−1 the majority of the stars have orbital velocities
higher than 140 km s−1 and only a minority have a lower Θ. If one would aim at compatibility with
Fuhrmann (2000) the vast majority of our stars should be Thin Disk stars, which would mean that the
scale height and velocity dispersion of the Thin Disk are much higher than generally believed.
87
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
4.4.2
T HE H ALO
As described in Sect. 4.2 and 4.3, the Halo component stars can relatively easily be separated from
the Disk population. A number of 16 or 17 stars (see Sect. 4.2.4), i.e. ∼15% of the complete sample
of 114 stars, form our Halo sample. It is approximately divided in half, one part having small orbital
velocities, i.e. having orbits similar to those of the HB stars of Altmann & de Boer (2000), and the
other, the high velocity component, having Θ velocities far higher than that of the LSR. As can be
seen in Figure 4.8 there is no or only a small difference between the kinematics of the two groups.
They represent orbits in different phases − the low velocity ones are currently near their apogalacticon
and the others are close to the perigalacticon where Θ is highest. Therefore the orbits of both groups
of the stars of our sample cover different radial spaces in the Milky Way. That they form a bimodal
velocity distribution rather than a continuum in our sample is a consequence of the selection effects
discussed in Sect 4.2.5 and small number statistics.
However some of the orbits of the high velocity group extend very far out, further out than what
is generally considered to be the limits of the Galaxy. Their orbits are rather transient than bound
orbits. So one might speculate that the history of these stars is somewhat different than that of the low
velocity Halo stars.
It has long been known that stellar groups exist at distances large compared with what is regarded as
the normal extent of the Milky Way. Harris (1996) lists 9 globular clusters with a current galactocentric
distance of more than 30 kpc, the most remote objects being at 100 kpc or more. Dinescu et al. (1999a)
have 6 objects in their sample of 38 globulars with kinematic data which go beyond 30 kpc. With one
object (Pal 3) in common that makes 14 globular clusters of the 147 listed in Harris (1996), venturing
that far. However not only globular clusters but also field stars have been found that far from the
Galactic centre. Vivas et al. (2001) found ∼ 150 RR Lyrae stars at distances of about 50 kpc and
Yanny et al. (2000) found a large number of HBA stars forming a group or a stream at a similar
distance. So clearly this remote spatial regime is not unpopulated.
Our group of Halo and high velocity Halo stars is too small to state anything definite about the origin
and behaviour of distant stellar groups as a whole. However we speculate that two of our stars might
have a common origin because their trajectories are quite similar (see Sect. 4.2.4). Analysing a larger
sample might therefore give insight into moving streams of Halo stars which are being incorporated
into our Galaxy (see e.g. Helmi & White 1999).
4.4.3
A SPECTS OF THE STELLAR EVOLUTION HISTORY OF SD B
STARS
Apart from questions concerning the structure of the Galaxy, there are still aspects concerning the
evolution of stars to sdB stars which have not yet been satisfactorily solved. This especially applies
to their extreme mass loss leaving a He-core nearly completely stripped of all Hydrogen. It has been
suspected for a long time that a large part, or all, sdB stars are in fact products of binary evolution
(see e.g. Iben & Tutukov 1987), with their unusually thin H-shell being the result of mass transfer
from the evolving primary (the star later turning into the sdB star) to the secondary partner of the
system. In fact many sdBs show a secondary component in their spectrum and also in their colour
indices (see e.g. Thejll et al. 1994; Theissen et al. 1995; Aznar Cuadrado & Jeffery 2002 or Chapter 2
of this work). Quite a few have radial velocity variations which also hints at a binary nature of these
objects (Maxted et al. 2001, 2002; Morales-Rueda et al. 2002). Because most of these do not show
any sign of binarity in their spectra (neither as a spectral feature nor in the continuum), it is speculated
that their companions are faint white dwarf stars. The most recent (ongoing) studies for variable radial
velocities (Edelmann, Napiwotzki, priv. comm.) however find far less binary sdB stars than the earlier
88
4.5. Summary & Conclusions
studies. This means that it is certainly not clear whether close binary evolution is the only way sdB
stars are formed.
A kinematical study does not as such prove or disprove a theory about stellar evolution. However our
results show that sdBs occur in all locally observable older populations rather than only in one alone.
This means that it is unlikely that there are factors such as metallicity in play. Furthermore sdBs form
from stars of a quite significant spread in mass and hence in age, as the formation times of Halo, Thick
and Thin Disk are of ages differing by several Gyr. Therefore our results provide at least some support
for the binary scenario.
Dorman et al. (1993) have calculated models of horizontal branches for various metallicities ranging
from very metal-poor to supersolar metallicity. These show a thinning out of the occupation of the HB
in the middle, increasing with metallicity. D’Cruz et al. (1996) have further enhanced these models,
and tried to find an explanation for the extreme mass loss required to make HBB and sdB stars. The
models were calculated for masses of around 1 M and somewhat less massive for the metal-poor
models, to take into account that Halo stars are generally assumed to be older than the more metalrich stars of the Thick Disk and even more than those with solar metallicity.
This work shows that sdB stars can be found in all populations. Our earlier work (Altmann & de
Boer 2000), analysing the kinematics of all types of HB-stars in the temperature range between the
RR-Lyrae and the sdB regimes, came to the result, that very few if any HBA stars are Disk stars (with
normally relatively high metallicities) and few RR-Lyraes with near solar metallicities and disk-like
kinematics exist. This is well in line with the models showing the deficiency in stars of the middle
temperature range of the horizontal branch also in the data.
The bottom line is that our results actually fit to both scenarios, the binary evolution and the RGBpeel-off mechanism of D’Cruz et al. (1996). Therefore we cannot prove or disprove one or the other,
even both could be in play. A still larger low z-sample, which does not suffer from selection effects
against low zmax stars (see Sect. 4.1.1.1) could help answering this question. If the binary scenario
is the dominating process leading to the forming of sdB stars, then the ratio of sdB stars belonging
to the Halo, Thick and Thin Disk should be similar to that of other evolved stars. If, however, the
D’Cruz et al. (1996)-scheme holds true, then sdB stars in the Disk should be a little more numerous
than expected. A really large and complete sample is required to find such subtle differences.
4.5
S UMMARY & C ONCLUSIONS
In this Chapter we have shown that a Halo sdB population exists and determined the scale height,
density ratio, mean velocities and dispersions of the Disk and Halo components. Having been found
in all accessible populations sdB stars are unlike the field HBA stars, a type of which we only know
Halo objects. This implies a somewhat different formation history of these two otherwise relatively
similar stellar types. Possible reasons have been discussed in the previous section. The Halo/Thick
Disk ratio is more or less consistent with results of studies invoking other methods. The same applies
to the Thick Disk scale height. The density ratio between Thick and Thin Disk is in the contrary
larger than expected. In Chapter 6 we will address more aspects, adding the results of the other
studies flowing into this thesis.
ACKNOWLEDGEMENTS :
Special thanks to Tom Marsh (University of Southhampton) for sharing with us his systemic velocities of binary
sdB stars. This research project was supported in part by the Deutsche Forschungs Gemeinschaft (DFG) under
grant Bo 779/21. For our research we made with pleasure use of the SIMBAD in Strasbourg.
89
4. K INEMATICS AND POPULATION MEMBERSHIP OF SD B STARS
90
C HAPTER 5
T HE K INEMATICS OF HBB STARS
C OLLABORATORS : H. E DELMANN
A BSTRACT: Among the sample of sdB candidates were some stars which turned out to be HBB stars. Because these are
closely related to the sdB stars (Chapter 4) and HBA stars (Chapter 3) we analysed them further and present the results of a
study similar to that described in Chapter 4.
Because we have far less objects in this sample than in the sdB star sample our results are far less reliable and more
constricted than those for the sdB stars. Moreover the HBB stars are at the same apparent brightness further away than the
sdBs, making the tangential velocities less accurate.
Nevertheless we found some interesting results. While many of the stars show Halo like kinematics, similar to the HBAs
and the low velocity sdBs, some are disk stars. From this we conclude that probably the population membership is rather
similar to that of the sdB stars, maybe with a stronger Halo fraction. We find no HBB high velocity halo and in contrast to
some of the sdB stars all but one HBB stars do not venture very far out from the galactic centre.
The z-probability distribution of our HBB sample does unfortunately not allow us to fit accurate scaleheights to it. Comparison with the distribution of the sdB sample shows, however, remarkable agreement.
While much remains to be done in the study of HBB stars, this study gives us hints about the nature of the kinematic
behaviour and population membership of the HB stars between 10 000 and 20 000 K.
5.1
I NTRODUCTION
This Chapter deals with the kinetic behaviour of HBB stars, i.e the region in temperatures between
the HBA on the one side and the sdB regime on the other. As said before in Chapter 3 these objects
are more difficult to identify unambiguously than their hotter or cooler siblings because they can be
confused with B main sequence stars, at least as long as they are close to the galactic disk. This unfortunately also means those that are close to the Sun. At larger distances the risk of misidentification is
much smaller, as B main sequence stars do not normally exist in older populations1 . Therefore there
are almost no such objects in either the Halo or the Thick Disk.
As described in Chapter 3, there is a significant difference in the kinetic behaviour of sdB and HBA
stars, the former being mainly disk stars (the discovery of sdB halo stars described in Chapter 4 does
not significantly change this trend) and the latter halo members. It is thus of great interest to study the
part inbetween, where up to now we only have a few data points, because of the difficulties in proper
classification described above.
1
There are a few of examples of such stars occurring in the Halo. These were probably either ejected into the Halo by
some event such as the explosion of a companion or interactions between members of a cluster, or accreted into the Halo
from an assimilated dwarf galaxy etc. However these objects are very rare, so they can be neglected.
91
5. T HE K INEMATICS OF HBB STARS
5.2
S AMPLE COMPOSITION AND DATA REDUCTION
In the course of the observations for the study of sdB stars some sdB candidates turned out to be HBB
stars, which are now added to the few stars dealt with in Chapter 3. The sample of HBB stars now
contains 19 stars, an increase by a factor of three. Because the new stars come out of the same sample
as the sdB stars of Chapters 2 and 4 everything said there about the sample composition and selection
effects also applies for the HBB stars. Note however, that because these stars are intrinsically much
brighter in the optical regime2 they are much further away than the sdB stars of Chapter 4. This means
that their tangential velocity is considerably less accurate than that of the sdBs. The remainder of the
sample were taken from Altmann & de Boer (2000), among these 4 stars from Schmidt (1996) (see
Chapter 3).
The data for these objects were obtained using the same instruments as described in Chapter 2 during
the same observing campaigns. Data reduction was done in the same manner as well. Therefore we
refer to Chapter 2 where the obtaining and reduction of data is described in full detail. For the distance
determination we used a mass of 0.52 M instead of 0.5 M as for the sdBs to allow for the somewhat
more massive H-shell of the HBB stars.
Having obtained the proper motions, distances and radial velocities we transformed them into the
galactic XY Z, U V W coordinate system, derived Θ and Φ and calculated orbits again using the potential model of Allen & Santillan (1991a), just as described in Chapters 3 and 4.
5.2.1
S ELECTION
EFFECTS
Most of the selection effects discussed in Sect. 4.1.1.1 also apply to this sample. They are, however,
generally much more important, than for the sdB star sample. This is especially true for the stars
taken from the HE catalogue, because they are – being of similar brightness as the HE sdB stars –
due to their greater absolute magnitude at much greater distances. Therefore we miss stars with an
even larger range in kinematics, so here even Thick Disk stars may be underrepresented in comparison
with possible Halo objects, although not as strongly as in the case of Thin Disk stars with our sdB
sample (and of course Thin Disk stars in this sample). The significance of this selection effect can be
especially clearly seen in panel b) of Fig. 5.6.
5.3
5.3.1
K INEMATICS AND O RBITS
V ELOCITIES
To start with a word of caution: Because these stars are much further away than the sdBs discussed in
Chapter 4 their tangential velocities have far greater errors. Most HBB stars lie at a distance of just
under 3 kpc, while most of the sdB stars are between 1 and 1.5 kpc from the Sun. Therefore the HBB
stars should be looked primarily at as a sample rather than as individual objects.
The velocity components (see Table 5.1) of the stars of our sample indicate that they are a mixture of
Disk and Halo stars. Some of our objects clearly seem to be Halo objects, and one (BD +36 22423 )
even has a kinematic behaviour similar to that of the Sun. Looking at the mean velocities and their
2
not in terms of luminosity, where there is only a small decline towards higher temperatures caused by the ceasing of
hydrogen shell burning.
3
which lies relatively close to the Sun, so we can discuss this star as an individual object without risking overinterpretation.
92
HE 2134−4119
HE 2137−4221
HE 2203−3740
HE 2204−2136
HE 0023−2317
HE 0128−4311
HE 0225−4007
HE 0238−1912
HE 0255−1814
HE 0319−5105
HE 0420−1806
HE 0430−5341
HE 0519−3512
PG 0954+049
PG 1258−030
PG 2301+259
PG 2318+239
BD +36 2242
Feige 86
Name
Y
[kpc]
+0.02
−0.03
+0.15
+0.82
+0.47
−0.76
−0.49
−0.15
−0.54
−1.73
−2.17
−2.42
−0.68
−2.11
−0.97
+2.81
+3.57
+0.02
+0.04
X
−6.21
−6.61
−7.00
−7.22
−8.30
−8.38
−8.66
−8.90
−9.82
−8.70
−11.73
−8.84
−8.91
−10.06
−7.75
−8.74
−8.99
−8.58
−8.47
−2.56
−2.13
−2.07
−1.97
−4.14
−2.42
−1.18
−0.87
−2.43
−2.32
−3.35
−2.20
−0.51
+2.43
+2.09
−1.68
−2.45
+0.40
+0.25
Z
+138
+34
+91
+129
+176
−126
+11
+161
−20
−67
+46
+270
−53
−41
−82
+237
−29
+3
+76
U
+239
+155
+271
+22
−141
+80
+23
+232
−14
+15
+254
−93
+52
+213
+66
+80
+141
+227
+117
V
+37
−14
−9
+14
−97
+37
−57
+133
+12
−154
+58
+234
−118
+36
+55
−45
−69
+3
−7
W
[km s−1 ]
−137
−34
−85
−126
−184
+118
−12
−165
+20
+63
−92
−236
+49
−3
+73
−202
+79
−2
−76
Φ
+240
+155
+272
+37
−131
+90
+23
+230
−12
+28
+242
−161
+56
+217
+75
+148
+121
+227
+118
Θ
+1489
+1025
+1908
+268
−1090
+762
−198
+2044
−123
+246
+2883
−1474
+499
+2233
+587
+1363
+1167
+1945
+995
Iz
[kpc km s−1 ]
14.19
6.91
15.05
9.51
15.74
10.23
9.32
23.69
10.58
10.67
23.08
45.54
9.40
11.51
8.46
17.60
11.27
9.22
9.18
Ra
Table 5.1: Spatial and kinetic parameters for the 19 stars of our HBB sample
4.99
4.29
6.66
0.52
5.73
2.40
0.35
6.30
0.21
1.87
10.21
4.72
1.68
10.48
1.66
3.92
3.61
8.58
2.95
Rp
[kpc]
4.79
2.20
3.82
5.51
12.33
4.53
5.72
8.08
5.88
10.08
6.47
30.49
5.70
2.85
3.82
5.32
3.70
0.42
0.27
zmax
0.36
0.32
0.27
0.93
1.21
0.50
1.10
0.36
0.80
2.51
0.29
0.88
0.78
0.27
0.48
0.32
0.34
0.05
0.03
ecc
0.48
0.23
0.39
0.90
0.47
0.62
0.93
0.58
0.96
0.70
0.39
0.81
0.70
0.05
0.67
0.64
0.52
0.04
0.51
nze
5.3. Kinematics and Orbits
93
5. T HE K INEMATICS OF HBB STARS
Table 5.2: Mean U V W, ΘΦ velocities, angular momentum, eccentricities and nze with their dispersions for the 20 HBB star sample.
Subsample
N
all
R ≤ 8.5 kpc
R > 8.5 kpc
ecc ≤ 0.6
ecc ≥ 0.6
z ≤ 2.0 kpc
z ≥ 2.0 kpc
19
8
11
10
9
7
12
U σU
+50
+55
+55
+65
+33
+81
+33
109
100
114
73
136
94
112
V σV
+102
+101
+103
+171
+26
+107
+99
W σW
[km s−1 ]
Θ σΘ
116 +3 86 +104
121 +2 44 +107
112 +3 107 +102
115 +7 61 +169
51 −3 107 +32
83 −11 72 +120
131 +10 92 +95
120
117
122
112
81
80
137
Φ σΦ
−50
−56
−46
−70
−28
−76
−35
102
98
105
77
121
86
108
Iz σIz ecc σecc nze σnze
[kpc km s−1 ]
+870
+743
+962
+1460
+214
+988
+801
1093
842
1442
1019
1852
787
1379
0.56
0.53
0.57
0.36
0.77
0.61
0.52
0.26
0.19
0.30
0.18
0.12
0.28
0.24
0.62
0.51
0.70
0.35
0.92
0.51
0.69
0.55
0.36
0.65
0.31
0.61
0.40
0.62
dispersions shown in Table 5.2 leads to the following results: Θ has a value of ∼100 km s−1 , i.e.
the asymmetric drift is 120 km s−1 ; it thus lies between values expected for Halo and (Thick) Disk
populations. Three stars orbit in a retrograde manner, two of these have high negative Θ (Table 5.2).
The velocity dispersions are higher than those of the sdB sample but lower than the “low velocity”
Halo sdB subsample (see Table 4.2). This implies a mixture of Halo and Disk stars, with a larger
Halo fraction. The velocity component vertical to the galactic plane, W is near zero. What is striking,
however, is the relatively large value of Φ of almost −50 km s−1 . This value has the opposite sign
than what was derived for our “pure” sample of sdB Thick Disk stars (see Table 4.2) and what Fux
(2001) found for the Hercules moving group4 of old Disk stars. The value of Φ is even larger for
the less eccentric, i.e. more “disky” orbits. Far from zero mean values of the mean values of Φ and
W can be caused by single objects with extreme kinematics. Looking at the upper panel of 5.3 the
asymmetry of the distribution of the Φ values becomes apparent, even when cropping out the 2 or 4
smallest and largest values. In contrast to the sdB stars, a handful of stars of which have a orbital
velocity significantly higher than that of the LSR, this is not the case for the HBBs (see Figures 5.1,
5.2 and 5.3).
We divided the HBB sample into subsamples using selection criteria, similar to those described in
Sect. 4.2.2.1. Because of the small number of objects in our HBB sample we only invoked simple
selections using a single criterion.
Dividing along the solar circle leads to two subsamples with very similar characteristics. The stars at
R > 8.5 kpc have slightly larger velocity dispersions and larger spreads in ecc and nze. This could
mean that the percentage of Halo stars is a little larger in the outer group. Discriminating the sample
by eccentricity leads to a low ecc sample, which has a rather high mean orbital velocity of 170 km s−1
– containing most of the Thick Disk stars – and a high ecc sample, which has a low Θ typical for
samples of Halo stars. However σΘ of the low ecc sample is too high for the Thick Disk, and far
higher than our results for the Thick Disk sdB stars (Table 4.2). The reason for this could lie in Halo
contamination. A final experiment was made in which we divided the sample into two groups closer
and further away than 2 kpc to the Galactic plane. As expected the z < 2 kpc sample has a higher
mean orbital velocity and smaller velocity dispersions than the other group. This probably reflects
the percentage of Disk and Halo stars in each of the group, the z < 2 kpc group containing more
Disk stars and a lower fraction of Halo stars than the other subsample. However each of these groups
4
Please note that according to Fux (2001) the Hercules moving group is not only a small and local group of stars
with common motion such as a moving stream, but a rather large scale structure containing about 15% of all cooler stars
(B − V > 0.6 mag) in the Hipparcos catalogue.
94
5.4. The vertical probability distribution and the scaleheight
contains significant numbers of stars belonging to both populations, as can be seen from Table 5.2. To
conclude, while this method of dividing our sample into subdivisions gives us hints that there are stars
belonging to the Disk and Halo, we can not tell how large the fraction of stars of different populations
is; there are simply too large contaminations in every subsample. More and more accurate data might
improve the situation.
5.3.2
O RBITS
The orbits of all 20 stars are shown in Figure 5.4. The orbits show a large range in shape, from tight,
solar type orbits, to strongly halotic orbits extending to high z distances and highly eccentric orbits.
We cannot tell the fraction of stars belonging to the various populations but it seems (from the shapes
of the orbits (Fig. 5.4) and the orbital velocities (Table 5.1))Approximately half of the orbits are those
of Halo stars, ∼40% are rather disky, the rest are of intermediate type between Halo and Thick Disk.
The resulting values for the eccentricity and nze show the same tendency (see Table 5.2). Most stars
have ecc values near 0.6 (see Figure 5.5), which is the region in the according distribution of the
eccentricities of the sdB stars there seems to be a minimum. One reason for this could be the larger
errors in the velocities for the HBB stars. Large errors in the velocities (Θ) of disk stars would lead
to larger mean eccentricities. The maximum of the nze distribution is also at a larger value than that
of the sdBs. This can mainly be explained by the larger current z-distance and thus a generally larger
zmax of most of our HBB stars and the larger percentage of Halo stars.
It is quite astonishing that our sample of HBB stars only includes one star venturing extremely far (40
kpc or more) from the galactic centre whereas we have several of such examples in our sdB sample.
As noted in the previous section, we do not find HBB Halo stars with an orbital velocity much higher
than ΘLSR as it is the case for the sdBs. A possible reason could be sdB stars which are close binaries,
whose strongly variable radial velocities could imitate extreme kinematics. However in most cases it
is not (only) the radial velocity which mainly contributes to this kinetic behaviour. Furthermore for
some of those stars we do have the systemic radial velocity. Therefore sdB binarity cannot be the only
possible explanation.
It seems that while Halo sdB stars are rather evenly distributed among outer and inner Halo, Halo
HBB stars are more closely confined to the inner Galaxy. The HBA stars of Chapter 3 also have orbits
which indicate that they rather belong to the inner Halo.
5.4
T HE VERTICAL PROBABILITY DISTRIBUTION AND THE SCALEHEIGHT
The vertical probability distribution of our sample is shown in Fig. 5.6. The lack of nearby stars
is apparent in panel b) of this figure. For this reason and because our sample only consists of 19
objects, it is not sensible to fit equations to this histogram. However when lying the functions derived
for the sdB stars (see Sect. 4.3 and Fig. 4.9) over the distribution of the HBB stars they seem to fit
remarkably well. This implies that the HBB stars have a similar vertical distribution than the hotter
sdBs. Unfortunately most of the Disk part is cut off. The Halo component seems to be a little steeper
than that of the sdBs.
It would therefore be desirable to identify more local HBBs and do a similar study as conducted in
Chapter 4 on sdB stars. Here the abnormal atmospheric abundance patterns may be an advantage in
order to distinguish HBB stars from B main sequence stars.
95
5. T HE K INEMATICS OF HBB STARS
Figure 5.1: Histogram of the orbital velocities for
all 20 stars of the sample. The values for ΘThick disk
and σΘ (TD, Disk) have been taken from Ojha et al.
(1994). Binsize is 30 km s−1
Figure 5.3: Bottlinger and Θ−W diagram of
the velocities of the stars of our sample. As in
Figure 5.2 a star denotes the LSR and a circle
the Sun’s values.
Figure 5.2: Toomre diagram (Θ versus velocity
perpendicular to the galactic plane) of the stars of
our sample.
p The concentric dashed circles indicate
vpec = Φ2 + W 2 + (Θ − ΘLSR )2 with values in
km s−1 . The star indicates the position of the LSR in
this diagram and the circle the according values for
the Sun
96
5.4. The vertical probability distribution and the scaleheight
Figure 5.4: The orbits of all 19 stars shown in meridional cut. Calculation time is 10 Gyr backwards
in time. The crosses show the current position of the Sun and the triangles those of the stars. The orbit
of the Sun is shown in the lower right panel for comparison.
97
5. T HE K INEMATICS OF HBB STARS
Figure 5.5: Histograms showing the distribution of ecc and nze values for the 20 HBB stars
Figure 5.6: Histogram of the z distance-statistics of the 19 stars of the HBB sample. a) shows a linear
representation of the z-distribution of the stars, b) a logarithmic one. While the number of stars and the
lack of stars at z ≤ 2 kpc do not allow us to properly fit equations to this distribution the similarity to
the distribution of the sdB stars (see Fig. 4.9) as can be seen in panel b) in comparison to the functions
fitted to the sdB sample. The dashed lines in the right panel show the exponential equations (linear in
the logarithmic plot) fitted to the sdB data see Sect. 4.3, the full lines the double exponentials (These are
the same equations as in Fig. 4.9.). The dot-dashed vertical lines denote the fitting intervals of the two
double exponential functions. The binsize is 50 pc.
98
5.5. Discussion & conclusions
5.5
D ISCUSSION & CONCLUSIONS
While the amount and quality of the available kinematic data of HBB stars is insufficient to make
definite statements about their nature and origin, the newly obtained data of 13 stars does enable us to
make some constraints. It seems that the overall HBB star distribution is rather similar to that of the
sdB stars. Possibly the fraction of Halo objects is somewhat larger; however this impression can be
caused by the fact, that the HBBs are mostly further away from us than the sdBs, and hence at higher
z. A remarkable point is the lack of a “high velocity” halo component in the HBB sample which is so
apparent in the sdB sample.
The HBBs fill the part of the HB between the sdB and HBA stars. These two stellar types clearly
have different histories, the HBAs seemingly all originating in the Galactic Halo and the sdB being
found in all populations but predominantly in the (Thick) Disk. Therefore one may speculate that
the intermediate HBB5 stars might be a mixture of both, i.e. the “HBA” Halo population and the
“sdB” population overlapping in the HBB regime. This means that if the currently favoured close
binary evolution scenario for the formation of sdB stars holds true some of the HBB stars may also
have been formed this way, with the mass transfer ceasing somewhat earlier, leaving a HB star with a
slightly more massive envelope. Others are then probably descendants of stars with similar properties
than the predecessors of HBA stars. In order to settle this question the studies of sdB binarity should
also be extended into the HBB.
To conclude we feel that the HBB regime holds the answers to some of the important questions of
the kinematics, population membership of stars of the blue HB. Because they are much more difficult
to find and easier to be confused with main sequence stars they have been far less studied than the
adjoining HBA and sdB stars. However our results show that because they are the junction between
star types which are, while related in internal structure and evolutionary stage, of very different origin
they probably hold some of the clues we still need to find to explain the differences in kinematic
behaviour and population membership between HBA and sdB stars.
ACKNOWLEDGEMENTS :
Special thanks to Heinz Edelmann, who obtained and reduced the spectra of the HE-stars considered in this
Chapter.This research project was supported in part by the Deutsche Forschungs Gemeinschaft (DFG) under
grant Bo 779/21. For our research we made with pleasure use of the SIMBAD in Strasbourg.
5
This is certainly likely, because the definition of HBB stars is somewhat artificial and arbitrary and there is no reason
that the stars just across the border are of completely different origin. It is based on the same distinction between A and B
main sequence stars, i.e. at the temperature where He-lines appear if the star contains He in its atmosphere (which the HBB
stars normally do not). The upper limit of the HBB stars is defined to be near the Newell gap (Newell & Graham 1976) at
approximately 20 000 K.
99
5. T HE K INEMATICS OF HBB STARS
100
C HAPTER 6
D ISCUSSION OF THE RESULTS
A BSTRACT: In this chapter we analyse our results in a larger and more general frame. The parts which have already been
discussed in the previous chapters, are summarised. The first part deals with the trend in kinematics that has been found, and
its implications for stellar evolution scenarios, and the second part is a discussion of the results found for the populations.
In this section some more speculative topics are also addressed.
6.1
T HE KINEMATIC TREND REVISITED
In Chapter 3 (published as Altmann & de Boer 2000) we have analysed the kinematics of horizontal
branch stars from the RR-Lyrae regime to the sdB stars and found a clear trend in their kinematical
behaviour. It was found that, while the majority of the RR-Lyraes are Halo objects, the RR Lyrae
sample contains a significant Disk component as well. In contrast to that, all HBAs that we have
analysed were found to be Halo stars. The sdBs, on the other hand, were all classified as Disk stars.
How does this picture change with the discovery of Halo sdBs? The main point – the difference in
kinematics between sdBs and the HBA stars – is certainly still valid as can be seen in Figs. 6.1 and
6.2. Considering the results of our study of the kinematics of sdB stars (Chapter 4) we find that the
distribution of sdB stars among the Galactic populations is similar to that of other evolved low mass
stars. This means that the processes leading to the formation of sdB stars are likely to be independent
of factors like metallicity and, to a lesser extent, age and initial mass.
In contrast to this the HBAs are only found in the Galactic Halo. Even if one takes into account that
more metal-rich HBA stars may be missed due to selection effects (see Section 3.5), the number of
known HBA stars in the solar vicinity (d <
∼ 0.5 kpc) is much larger than the number of Halo sdB stars
(10 HBA versus 1 sdB star in our samples). In Figs. 6.3, 6.4, 6.5 the HBAs are clearly separated from
the bulk of the sdBs, only the distribution of the “low velocity” halo sdBs overlaps with that of the
HBAs. It is therefore very likely that the HBA stars represent an evolutionary stage of stars typically
found in the Halo, i.e. metal-poor stars which might also have been slightly less massive than the
progenitors of most sdBs.
This implies that there is probably a difference in the formation scenarios leading to HBA and to sdB
stars.
• The sdB stars could be formed by rather “accidental” processes (described in more detail in
Sect. 4.4.3), either by close binary evolution or the premature peel-off scenario suggested by
D’Cruz et al. (1996). The dispute as to which scenario is responsible for the formation of
most sdB stars, or whether both (or even additional theories) play a role is still going on. Both
101
6. D ISCUSSION OF THE RESULTS
Figure 6.1: The kinematic trend of stars along the HB revisited. This figure is based on Fig. 3.3,
with the new data (see Chapters 2, 4 and 5) added. The kinematic trend of stars along the field
horizontal branch characterised by eccentricity, normalised z-extent and orbital velocity as plotted
against effective temperature Teff and B − V . Upper row, panels a) and b): eccentricity (ecc);
Middle row, panels c) and d): normalised z-extent (nze);
Bottom row, panels e) and f): orbital velocity (Θ).
The left side (panels a, c and e): versus Teff , showing the hotter part of the FHB.
Right side (panel b, d and f): versus B − V , highlighting the cooler part.
Filled symbols show the stars with Hipparcos data, open symbols the sdB and HBB stars from de Boer
et al. (1997), Schmidt (1996) and Chapters 4 and 5. sdB/O stars are depicted by circles, HBBs by
triangles and HBA by hexagons. The RR Lyraes are plotted as pentagons, the filling of the symbols
is subdivided according to the stars’ metallicities (full: [Fe/H]< −1.6 dex, half full: −1.6 <[Fe/H]<
−1.3 and −1.3 <[Fe/H]< −0.9 dex, open[F e/H] > −0.9 dex).
102
6.1. The kinematic trend revisited
Figure 6.2: Histogram showing the distribution of Θ of all stars (see Chapters 3, 4 and 5).
The binsize is 20 km s−1 .
Figure 6.3: Bottlinger and Θ − W diagram
of the velocities of the stars of our sample. As
in Figure 6.4 the different symbols refer to the
various star types, a star denotes the LSR and
a circle the Sun’s values.
Figure 6.4: Toomre diagram of all stars; circles are the sdB stars (see Chapter 4), hexagons the
HBA stars (see Chapter 3) and triangles the HBB stars (see Chapters 3 and 5). The circle and the
star denote
p the Sun’s and the LSR position in the diagram. The concentric dashed circles indicate
vpec = Φ2 + W 2 + (Θ − ΘLSR )2 with values in km s−1 .
103
6. D ISCUSSION OF THE RESULTS
Figure 6.5: Diagram of Θ against total kinetic energy of all stars (sdB, HBB, HBA). Large open
symbols mean the current values, the small filled symbols the median values. The meaning of the
symbols is similar to that of the previous figure (Fig. 6.4). The parabolas show the velocity orthogonal
to Θ.
of these scenarios do not a priori require the stars to have a specific metallicity to form sdB
stars1 - therefore both explain that sdB stars seem to be formed in all populations. Evidence
has mounted recently that a large fraction of the sdB stars are indeed close binaries (Maxted
et al. 2001, 2002; Morales-Rueda et al. 2002); in the most recent programs the turnout of close
binary sdB stars was much lower than expected (Edelmann, Napiwotzki, priv. comm.), which
would mean that close binary evolution can probably not account for all sdB stars. A small
minority of sdB stars might also have formed through other evolutionary channels such as the
underluminous and low mass sdB star HD 188112 (Heber, priv. comm.).
• In contrast to this, the HBAs are probably formed in the “classical” way, i.e. through mass loss
during the preceding RGB phase. The fraction of the H-envelope lost almost certainly depends
on the initial metal content of the star, with metal-poor stars generally losing more of their
envelope than their more metal-rich siblings. According to D’Cruz et al. (1996), metal-rich
populations should also form HBB and sdB stars; this does not seem to be the case in metalrich globular clusters, all of which seem to have only red HBs (Harris 1996). For many clusters
the photometric data in the compilation of Harris (1996) is rather old and may not be deep
enough to separate sdB and main sequence stars in the faint part of the CMD. Indeed using new
data, sdB stars have been found in several high metallicity globular clusters (see e.g. Rich et al.
1997) and also the very old open clusters NGC 6791 and (possibly) NGC 188 (Liebert et al.
1994).
1
The peel off theory does depend on metallicity, but this mostly affects the middle part of the HB which thins out at
higher metal content; stars of the blue and red edges of the HB are formed predominantly independent of metallicity (D’Cruz
et al. 1996).
104
6.2. The populations of the Milky Way
The kinematic behaviour of the HBA and sdB stars can thus be explained by both the close binary
scenario and the peel off theory. How do the HBB stars fit into this picture? Fig. 6.2 seems to indicate
that they have a kinematic behaviour intermediate between that of sdB and HBA stars. Looking at
the Toomre (Fig. 6.4) and Bottlinger diagrams (Fig. 6.3) one sees that the datapoints representing
the HBBs overlap the distributions of both HBA and sdB stars. Along HBB stars there does not
appear to be a trend in kinematics with temperature (see Fig. 6.1). This leads us to the speculation
that stars with a similar history as the HBAs and as the sdB stars overlap the HBB regime rather
than a smooth transformation from halo-like to disk-like kinematics. This is not unexpected; the
discrimination between sdB, HBB and HBA stars is based on spectral features, temperatures, colours
etc., i.e. atmospheric criteria and has as such nothing to do with the evolution of these stars, prior to
becoming HB stars. Therefore one does not expect the kinematic behaviour of these stars to differ
abruptly at the transition from one type to another. The lack of disk HBA stars is presumably caused
by selection effects (see Chapter 3) – without these one would probably find a small disk component,
which is also present in the distribution among the populations of the even cooler RR-Lyrae stars.
To conclude our discussion about the kinematic trend and its origins we state the following main
hypotheses:
• The sdB stars have been formed by a process other than a normal strong stellar wind which
stripped the stars of almost all of their original H-envelope. Possible mechanisms at work could
be close binary evolution with mass transfer of premature departure of the RGB caused by
abnormally strong stellar winds (The peel off scenario by D’Cruz et al. 1996). They are found
in all populations, regardless of the initial metallicities, in number ratios more or less expected
for the various Galactic components.
• The adjoining HBB stars have more diverse histories: Some of them have been formed by
similar mechanisms to the sdB stars, others – mainly those that are members of the Halo – form
the hot end of single star HB formation.
• The cooler HBA stars are predominantly Halo objects. Whether there really is a Disk component remains to be seen. These stars were probably formed the classical way, similar to RHBs
and RR Lyrae stars, with the metal content of their main sequence predecessors being much
lower than most of those forming RHB stars.
6.2
T HE POPULATIONS OF THE M ILKY WAY
Many main points concerning our results for the Disk and Halo populations have been discussed in
Chapters 3 and 4. Here we summarise the results and discuss the synthesis of the single findings
described in the earlier parts. In order not to repeat too much, we keep the discussion on the Disk and
Halo rather short and then discuss some aspects concerning the Bulge which has not been a subject of
discussion until here, and conclude with a larger general discussion about relations between Galactic
populations as far as possible in the context of our own results.
6.2.1
T HE T HIN AND T HICK D ISK
Most of the stars of our sdB sample belong to the Disk. From the distances from the Galactic plane
and the kinematics we conclude that the majority of the stars in our sample are members of the Thick
Disk (see Chapter 4 for the discussion). We have, however, not found a method to unambiguously
105
6. D ISCUSSION OF THE RESULTS
separate Thin and Thick Disk stars; it may well be that these two Disk components are not entirely
kinematically discrete. There is probably a considerable overlap between their kinematics.
Our current sample is not suited to consider the question of the kinematic separation of Thin and
Thick Disk because of the selection effects discussed in Sect. 4.1.1.1. There are a number of stars
in our sample with very tight, sun-like, orbits. We think that these are Thin Disk stars. In order to
analyse the kinematics at low distances from the Galactic plane, i.e. where the Thin Disk dominates,
we need a different sample with only nearby and low Galactic latitude stars. We would then expect to
find a three slope distribution, such as Phleps et al. (2000) found in a study of the spatial distribution
of M main sequence stars. In Chapter 4 we have attempted to constrain the strength of the Thin Disk
component using a three component fit and we came to the conclusion that the Thin Disk component
(in respect to Thick Disk and Halo) is weaker than what is found from most other studies (Table 6.1).
The reason for this probably lies in the nature of the object of study, namely evolved stars in our case
and mainly main sequence stars in the case of most other studies; the effects leading to this difference
are discussed in detail in Sect. 4.3.6. On the other hand, we want to stress that our results are very
uncertain in this point, because we do not have access to most of the Thin Disk part, and our results
should thus be treated with great caution.
Apart from the problems caused by the composition of our sample there are possibly also physical
reasons preventing us from making a clean division between the Thin and Thick Disk. Each star in
the Disk has a slightly different kinetic behaviour; some are kinematically somewhat warmer2 than
others. In principle the stars of both Disk components are on similar orbits in the sense that they orbit
around the Galactic centre in a plane. The difference between Thin and Thick Disk is the degree of
deviation from perfect circular orbits. The latter stars have significant deviations from the circular
orbit, both in and perpendicular to the plane. But as each star has slightly different kinematics, this
means that these two components show an overlap in kinematical behaviour; there could be stars with
similar orbits and kinematics but with some belonging to the Thick and others belonging to the Thin
Disk.
To really separate the two Disks by kinematics, one needs a sample which is complete to the Galactic
plane (or at least to small z). Then one would expect to see two distributions in a Θ histogram and
also a third slope in the z probability distribution.
Another item that needs to be discussed is the shape of the disk. In Chapter 4 and de Boer et al. (1997a)
we have fitted exponentials to our data, assuming that the Disk is exponential. An exponential disk
is unphysical because at Z = 0 kpc the two exponentials meet and the whole distribution is not
continuously differentiable at this point. The Z-probability distribution of a disk-like orbit shows a
“horned” structure (see Fig. 3 of de Boer et al. 1997a), i.e. the star is more often further away from the
plane than near to it. Therefore the vertical density distribution becomes less steep near the plane. van
der Kruit & Searle (1981, 1982) proposed that an isothermal disk with a sech2 distribution is more
appropriate. They found that this distribution agrees well with the measured light profile of external
edge-on galaxies. Wainscoat et al. (1989) found the light distribution of a edge-on galaxy observed in
the near infrared is fit by a near-exponential rather than by an isothermal disk. van der Kruit (1988)
found that neither the sech2 nor the exponential distribution agree well with the observations, but a
sech distribution, which is intermediate to the two other slopes, does. The sech function approximates
an exponential if the argument becomes significantly larger than 1, i.e. in our case when the z-distance
becomes larger than the scale height, it is safe to use an exponential distribution. The fit conducted in
Chapter 4 started at approximately one scale height and ended at about four scale heights. Therefore
the use of an exponential function to fit to the data is justified. Because we do not have access to
2
are on more elliptical orbits, with velocities deviating more from those of the LSR.
106
6.2. The populations of the Milky Way
the part where the two distributions deviate most, we use the simpler exponential. An exponential
characterisation of the Disk makes comparisons with other studies easier, because most of them also
only assume an exponential Disk.
The values other studies found for the scale height of the Thick Disk and the density ratio of the two
Disk components are shown in Table 6.1. The studies whose results are presented in this table all rely
on star counts, mostly on general star counts not based on one particular stellar type. An exception to
this is the work by Phleps et al. (2000) who used M-type main sequence stars as tracers. Our value of
0.9 kpc lies somewhere in the middle of the range. The wide spread in the values for scale height and
density ratio are caused by a degeneracy between these two quantities. Most of these spatial studies
rely on a very small number of data points, to which a linear equation is fitted. The leverage of this
fit is rather small, which means that the slope/zero value combinations are not very constrained. This
effect can clearly be seen in Table 6.1, because large scale heights have small z = 0 density ratios and
vice versa. In some cases the authors only published a range of possible values with the lower scale
heights corresponding to higher densities and vice versa. While our results also suffer from this effect
(as can be seen in Table 4.3) we expect our values to be much less affected. The reason for this is that
we have far more points to support the fit3 , and our distribution extends further out than that of most
(if not all) studies.
Finally we summarise our main results for the Disk:
• the vast majority of the sdB stars of our sample belong to the Disk, probably mostly to the Thick
Disk.
• we did not find a method to distinguish Thin and Thick Disk stars unambiguously; it is quite
probable that there is some kinematic overlap between the two Disk components.
• the scale height of the Thick Disk is 0.9 kpc. This value is rather similar to the results of other
studies. Note that there is a large spread in values for the scale height in the literature.
• the initial density of a possible Thin Disk component in respect to that of the Thick Disk is
smaller than usually found for the Thick/Thin Disk density ratio. This is possibly caused by
the choice of an evolved star type as tracer rather than main sequence stars. The result for the
Thin/Thick Disk density ratio is unfortunately very unsure.
The implications of our results for Galaxy formation scenarios will be discussed in Sect. 6.2.5.
6.2.2
T HE H ALO
A significant number of the stars we studied belong to the Galactic Halo, namely 16 sdB stars, all 14
HBAs and a large fraction of the HBB stars4 . The stars belonging to this group feature orbits typically
associated with the Halo, i.e. high eccentricities, in many cases reaching to large distances from the
Galactic plane, sometimes retrograde orbits and mostly low orbital velocities. There is however a
group of sdB stars, which currently have very high orbital velocities. The mean orbital velocity of
the HBA stars is +17 km s−1 (see Chapter 4), that of the low velocity Halo component of our sdB
sample is +30 km s−1 (Table 4.2); if one takes the average of both values, Θ is +22 km s−1 . For the
HBB sample a positive Θ is also more likely. The more metal poor samples ([Fe/H]< −0.9 dex)
3
This does not mean more independent data.
Due to the less accurate kinematics and resulting difficulties in unambiguously assigning these objects to the populations, we do not consider the HBBs in the following discussion.
4
107
6. D ISCUSSION OF THE RESULTS
Table 6.1: Compendium of published scale heights (z0 ) and initial densities (N0 ) for Thin Disk, Thick Disk and Halo. N0 of the Thin Disk is always
set to 100% if applicable. The table is ordered alphabetical by author rather than chronological because some of the studies cited here are parts of
series, and present refinements and sample enlargements of the earlier studies or the same method used on different fields. Because the Halo does not
follow an exponential density law, there are only a few published scaleheights. This list is not intended to be complete. Those studies relying on “all
available stars” in a star field use galactic distribution and stellar evolution models etc. to derive the scale heights and densities.
Source
(Old) Thin Disk
Thick Disk
Halo
Star Type & remarks
N0
z0
N0
z0
N0
z0
[%]
[kpc]
[%]
[kpc]
[%] [kpc]
Amrose & Mckay 2001
—
—
—
1.8±0.5
—
— RR Lyr
Bahcall & Soneira 1984
100 0.25-0.35
0.0
N.A.
0.15
— all av. stars in SA51/68
Buser et al. 1998
100 0.29±0.05 5.4±1.5 1.15±0.15 0.05±0.03
— all av. stars in 14 fields
Buser et al. 1999
100 0.29±0.05 5.9±3
0.91 ± 0.3
—
— all av. stars in 7 fields
Chen 1996
—
—
—
1.17
—
— all av. stars in 2 square degr. field + proper motions
Chen 1997
100
0.34
2.0
1.3
—
— all av. stars in SA57/M3, reduced proper motion
Chen et al. 2001
100
0.33 6.5-13
0.58-0.75
0.125
— all av. stars in 279 square degrees, SDSS
Chiba & Yoshii 1997
—
—
—
∼ 1.0
—
— Hipparcos RR Lyr & metal-poor RGB
Gilmore & Reid 1983
—
0.30
—
1.45
—
— all av. stars in SGP field
Gilmore 1984
100
—
2.0
1.3
—
— reanalyses results from other publications
Kuijken & Gilmore 1989
100
—
4.0
1.0
—
— FV and KIII stars
Reid & Majewski 1993
—
—
—
1.3
—
— all av. stars in a field
Haywood et al. 1997
100
—
5.9
0.76
0.11
— all av. stars in SGP/NGP
Kerber et al. 2001
100
—
4-8
0.8-1.2
0.2 3-4.5 all av. stars in a HST field
Mendez & Guzman 1998
100
0.25
2-6
0.75-1.3
—
— all av. stars in & near HDF
Morrison et al. 1990
—
—
—
1.4 ± 0.7
—
— G&K giants
Ng et al. 1997a
460/100/39 0.1/0.25/0.5
5.3
1.0±0.1
0.4
— all av. stars in SGP/NGP
Ojha et al. 1996
100
—
6.1
0.76
—
— all av. stars in 3 fields + proper motions
Ojha et al. 1999
100
—
6.1
0.79
—
— all av. stars in 2 fields + proper motions
Phleps et al. 2000
100 0.28-0.36
2-8
1.0-1.5
—
— M-type dwarfs
Reylé & Robin 2001
100
—
6.2
0.8 ± 0.2
—
— all av. stars in several field, own & literature data
Robin et al. 1996
100
—
5.6 0.76±0.05
—
— all av. stars in 4 fields + literature data
Spagna et al. 1996
100 0.259±12
4.3 1.137±0.061
—
— all av. stars in NGP (20 square degrees)
von Hippel & Bothun 1993
— 0.29-0.33
—
0.86-0.95
— ≥4 mainly F&G stars, Stroemgren photom.
et al. (1997) have found evidence for four disk populations, the young, intermediate and old (thin) Disk and the thick disk
a :Ng
108
6.2. The populations of the Milky Way
of the RR Lyrae stars (Chapter 3) show positive values for Θ as well; they are however probably
contaminated by members of the Metal Weak Thick Disk (MWTD) (see Sect. 3.4.2). The dispersion
of the orbital velocity is rather low with about 55 km s−1 for both the HBA and sdB Halo samples.
The values for σΦ and σW are for subsamples much higher, at values of 100 - 150 km s−1 . Looking
at the velocity dispersions in the literature, one finds a strong spread in the values. Here probably
outliers and selection criteria play a strong role (see also Ryan & Norris 1993). Another striking point
is, that all Halo subsamples or subsamples containing a large number of Halo stars have a negative Φ
(see Tables 3.3, 4.2). The single exception is the “high velocity Halo” subsample of sdB stars. The
HBB stars show a similar trend to the other samples as the low metallicity RR Lyrae samples. This
phenomenon, which is also seen in stars of the Thick Disk (with the opposite sign) will be discussed
in Sect. 6.2.3.2. In W direction we do not see a clear tendency, neither for the Disk nor for the Halo.
The positive Θ for our Halo samples imply that the Galactic Halo is indeed slowly rotating in a
prograde manner. Many other studies also find slightly prograde rotation velocities, e.g. Martin &
Morrison (1998), Layden et al. (1996), Chiba & Yoshii (1998), Chiba & Beers (2000), Carney et al.
(1996) and Norris (1986). In some of these studies the positive rotation is very slight. Other studies
came to a negative result for ΘHalo . Among these are Reid (1990), Allen et al. (1991) and Majewski
(1992). A retrograde rotation of the Halo poses strong objections against all Galaxy formation models
which imply that the Disk formed out of the Halo. Studies of the kinematics of the whole Halo globular
cluster system show that it rotates in a prograde manner, however it can be split into a prograde “old”
part and a retrograde “younger” part (Majewski 1993). Thus the Halo possibly consists of more than
one part, with different evolutionary histories. Studies of field stars selected by metallicity can suffer
from contamination from MWTD stars, i.e. metal poor stars with disk-like kinematics.
As said before, our sdB Halo sample falls into two groups, namely a low velocity part, which has
similar kinematics to our HBA stars and many other Halo objects, and a high velocity component,
whose stars have orbital velocities far higher than that of the LSR (see Fig. 4.7). However, from a
purely kinematic point of view there is no difference between the two Halo components (see Fig. 4.7,
upper right panel and Fig. 4.8), because looking at mean or median values (i.e. when each star is
in the same phase of its orbit), one cannot distinguish between the low and high velocity Halo stars.
These two subgroups merely represent one group of stars on similar orbits which are currently in
different phases, i.e. some are near their peri- and some near their apogalacticon and some in between.
Because it is most probable to find a star when it is near one of the turning points (apogalacticon or
perigalacticon) we see this bimodal distribution. One might speculate that there is, in spite of this
kinematic similarity, a difference between the two groups. Most of the high velocity stars travel to
distances very far from the Sun or the Galactic centre. Moreover, two of them have rather similar
kinematic parameters - they might be part of a moving group (In Sect. 6.2.4 this is discussed in
detail). It may well be that all or most of these stars are remnants from minor merging events in the
past; at present we do not have any proof for this hypothesis, apart from the two stars with similar
kinematics.
The high velocity Halo was only found in the sdB sample. Apart from one or two of the RR Lyraes we
did not find other HB stars with such extreme kinematics. This raises the question, whether another
effect, such as large amplitude radial velocity variations in close binaries (and a large fraction of
the sdBs are close binaries), influences our measurement in such a way that these stars mimic high
velocity Halo stars? We think that this is not the case: in many cases the extreme kinematics are
caused by a large proper motion rather than the radial velocity or both. PG 1519+640 has both a
Tycho2 proper motion and a measured systemic radial velocity. But, are there other stars, apart from
our sdBs, with kinematics this extreme? One example is the famous Barnard’s star, which has a Θ
of 367 km s−1 and an angular momentum of 3000 kpc km s−1 . Its apogalactic distance is 36 kpc.
109
6. D ISCUSSION OF THE RESULTS
Chiba & Beers (2000) found some Halo stars with very large total velocities, almost up to the local
escape velocity5 at ∼ 500 − 550 km s−1 (Carney et al. 1988). Therefore we conclude that the high
velocity Halo indeed exists, which means that there are stars in the solar vicinity travelling to very
large distances. As stated before we can presently not say without doubt, whether there is really a
difference between the high and low velocity Halo based on the history of the Milky Way.
Finally some comments on the issue as to whether the Halo is disjunct from the Disk: strong evidence
in the kinematical analysis comes from the distribution of eccentricities shown in Fig. 4.6, which has
a region between ecc=0.5 and 0.7 which is clearly underpopulated. The analysis of the probability
distribution vertical to the Galactic plane shows clearly that our sample of sdB stars belong to two
distinct Galactic components: Disk and Halo.
To conclude this discussion, we summarise our main results for the Halo component:
• we found the sdB Halo population.
• a little more than half of the Halo sdB stars of our sample belongs to a group with low orbital
velocities similar to our HBA Halo stars, the remainder have high velocities and venture to very
large distances from the inner Galaxy, similar to Barnard’s star. Whether there is a difference
in origin between these two groups is unclear. Two of the high velocity stars have very similar
orbits (see Sect. 6.2.4).
• the Halo (i.e. low velocity sdB and HBA stars) rotates in a prograde manner with a net rotational
velocity of ∼ +20 km s−1 . The same tendency is also present for the HBB and RR Lyrae stars.
For most of these samples we find a negative value for Φ, while Thick Disk samples generally
show a positive tendency (see also Sect. 6.2.3.2).
• the density ratio of Halo to Disk sdB stars extrapolated to the Galactic plane is ∼ 1 %, which is
in the same order of magnitude as found in other studies.
• Halo and Disk are disjunct.
6.2.3
B ULGE AND BAR
As stated in the introduction, the present study does not reach into the Bulge region6 the implications
our results have for our understanding of the Bulge and a possible Galactic Bar are small.
The term “Bulge population” is somewhat problematic because it is very likely (but not absolutely
sure) that the Bulge is a distinct entity. It is not often regarded as the inner part of the Halo or one of
the Disk populations (for a discussion see Minniti 1996). Furthermore, there are only very few and
small observational “windows” with relatively low interstellar extinction where the stellar content of
the inner part of the galaxy and hence the Bulge can be studied. It means that relatively little is known
about the characteristics (kinematics, metallicity etc.) of the Bulge. There are however a few things
which can be said when comparing our findings with what has been published about HB stars in the
Bulge region.
A few of their stars had even vt ot > 550 km s−1 , however they discarded these as untrustworthy; our maximal vt ot is
∼480 km s−1 .
6
Bulge region; means the region where the Bulge is the dominant population, i.e. the inner few kpc of the Galaxy.
This stands in contrast to the Bulge population which means a group of stars having more or less similar properties and
generic history. It means that stars belonging to one of the other populations could be currently located in the Bulge region
without being a member of the Bulge population. This discrimination is especially important for the Bulge since all other
populations are present in the inner region as well.
5
110
6.2. The populations of the Milky Way
Figure 6.6: Plots of the parameters of the stars of the sample of Peterson et al. (2001).
upper left panel: histogram of the vlos distribution:
Note the peak at 100 km s−1 and the broad distribution centred at 0 km s−1 .
upper right: vrad against metallicity: Here a slight concentration can be seen at [Fe/H]=−1.5 dex
and vrad = 100 km s−1 . Most values for the metallicity are low.
lower left: distance against radial velocity: Again a very subtle concentration of data points can be
seen near vrad = 100 km s−1 .
lower right: distance against [Fe/H].
Please note that this sample contains some of the stars Peterson et al. (2001) discarded as RR Lyrae
stars. All data used for this figure are taken from Peterson et al. (2001).
111
6. D ISCUSSION OF THE RESULTS
6.2.3.1
BHB STARS IN THE G ALACTIC B ULGE – OR DO THEY BELONG TO THE H ALO ?
Recently Peterson et al. (2001) published the first part of a study dealing with hot HB stars in the
Bulge region. They have analysed a sample of 48 hot stars in a window of 1.3◦ × 1.3◦ located at
l = 3.3◦ , b = 6.7◦ or in 2000.0 coordinates centred on α = 18h 05m 17s , δ = −35◦ 100 5100 . Out of
these some were found to be A type main sequence stars, others possibly RR Lyraes7 which were
then sorted out. They final sample consists of 23 stars, 14 of which they claim to probably belong
to the Bulge. The kinematics show a small to negligible net vlos (≡ vrad ) velocity and a rather large
dispersion of σlos =100 km s−1 . The stars are mostly metal-poor, there are however a few with near
solar metallicity (see Figure 6.6, upper panels).
Compared to what is known about the Bulge, σlos is rather too high (usually measured to be about
60 km s−1 at the same angular distance from the Galactic centre, see Minniti 1996) and the bulk of
the [Fe/H] values is too low for the majority of these stars to be part of this population. However,
they may very well be Halo stars. The Halo does extend right to the Galactic centre, and its density is
highest in the inner part of the galaxy8 .
As we have seen in Chapter 3, many of the local halo stars venture to very small (in some cases
extremely small) distances to the Galactic centre. This means that some of them would at some times
show up in the space observed by Peterson et al. (2001), and some of the stars currently in Peterson’s
sample may well travel into the solar neighbourhood. Unfortunately (but understandably) there are no
proper motions currently available for any of the stars of Peterson et al. (2001), so we have no access
to the full kinematics, which would have made the discussion much easier. Given these arguments
and the kinetic and astrophysical properties of most stars not fitting to the Bulge, a membership of
the Halo for the majority is more than likely. Nevertheless there may be a few, particularly the more
metal-rich, objects which could be part of the Bulge population also indicated by the relatively low
vlos of some of these objects. It is possible that the situation is similar to that of the K-giants analysed
by Minniti (1996) who found that the more metal-rich stars show significant net vlos and a relatively
small dispersion while stars with [Fe/H]< −1.5 dex show only small mean vlos but a large dispersion.
Minniti (1996) interprets the two groups as part of the Halo (metal-poor) and Bulge (metal-rich).
To conclude, even if one considers the Bulge to be a separate component of the Galaxy (this discussion
is beyond the scope of this work, see Minniti 1996; Binney & Merrifield 1998) it is very likely that
the HBA stars found by Peterson et al. (2001) are part of the Halo population which then confirms our
results for the HBA kinematics as described in Chapter 3. However, once again a word of warning
cannot be avoided: the metal-rich HBA stars found by Peterson et al. (2001) indicate that these might
also exist in the solar neighbourhood, which might have been missed in the analysis conducted in
Chapter 3.
As can be seen in Figure 6.6 (upper left panel) there is a peak in the velocity distribution of the stars
in the Peterson sample at ∼ 100 km s−1 which may indicate a moving group or a similar entity. This
phenomenon is going to be discussed in Section 6.2.4.
6.2.3.2
D ISTURBANCE OF THE T HICK D ISK BY THE PRESENCE OF A G ALACTIC BAR ?
Unlike V resp. Θ that are per definition of non-zero mean value for most stellar groups (except maybe
the Halo), the mean values of U /Φ and W would be expected to be near zero for a stable homogeneous
feature. W 6= 0 km s−1 would mean that the sample as such is moving away from the Galactic plane,
7
RR Lyraes venture when hottest, i.e. near maximum, well into spectral class A, overlapping in Teff with HBA stars.
If the Halo density follows a power law e.g. ∝ r−3.5 , its density in the centre is several 1000× that of the solar
neighbourhood.
8
112
6.2. The populations of the Milky Way
i.e. a disk would bend. U /Φ 6= 0 km s−1 means that the stars are either moving inwards or outwards,
the feature would be contracting or expanding. Moving groups and (in small samples) stars with
extreme kinematics9 could of course be the cause of a net movement in a certain direction. To a
certain extent this effect could be taken care of by omitting the objects with the lowest and highest
velocity. If moving groups and extreme objects can be excluded, a non zero velocity could mean that
there is a net movement indeed, such as denting or buckling of e.g. the Galactic Disk.
In the early 1990’s it became clear, that the Milky Way has, like many other spiral galaxies, a bar (see
e.g. Weinberg 1992), having a semimajor axis of about 5 kpc. Fux (2001) modelled the influences this
bar could have on the local stellar populations and analysed the kinematics of samples taken from the
Hipparcos catalogue. Roughly 15 % of the sample are older stars belonging to what Fux (2001) called
“Hercules stream”. These stars have the asymmetric drift typical of the Thick Disk. Furthermore
they feature a net movement in X of Φ = 35 km s−1 . Theoretical modelling by Fux (2001) suggests
that this could possibly be caused by the presence of a bar. Our sdB sample (see Chapter 4) shows a
similar tendency too, though very slight, at least when the whole sample is considered. In fact the net
movement in W is even larger for our sample. Since our sample consists of a mixture of Halo, Thick
and probably Thin Disk stars, we divided the sample into subsamples which are shown in Table. 4.2.
The purest Thick Disk sample (see Table 4.2) shows the largest systematic Φ velocity of 22 km s−1 .
This is in the the same direction as the Hercules group and is thus consistent with the theoretical
results of Fux (2001).
All halo samples show a similar tendency in Φ, though in the other direction. This applies to the low
velocity halo sample of sdB stars, the HBB stars and the HBA stars. The more metal-poor subsamples
of the RR Lyraes show the same trend. The implications of this effect, are not clear. The local Halo
population seems to be generally moving outwards, away from the centre as if the Halo were inflating.
As the Halo is probably not expanding, we suspect that there is some instability which causes the Halo
to swing: in some areas, such as the solar neighbourhood, the net movement is outwards, the Halo
is expanding, in other parts of the galaxy the net movement of the Halo stars is inwards, these parts
of the Halo are contracting. The cause of this is unknown; one possibility could be interactions with
satellites, whose tidal forces pull out the stars somewhat at the nearest and farthest points. Or one
might speculate that an inhomogeneity, such as a spiral arm is the cause. It remains to be seen what
really is behind the offset in Φ in the Halo.
However the mean Φ and W velocities of many samples differ significantly from 0 km s−1 . This also
applies e.g. to our W which has an even larger value for the whole sample than Φ and some of the
subsamples (see Table 4.2). Martin & Morrison (1998) find a similar mean offset, but in the opposite
direction, a value which is again very similar to the result for our Hipparcos BHB stars (see Chapter
3). The HBB stars of Chapter 5 have a negligible mean movement in W direction.
Thus there are obviously effects at play which we do not really understand. Very basically, there
could be a systematic error in distance determination, however this is rather unlikely. For example
a systematically too low distance would result in too low velocity values; but the mean velocity of
a sample would not change in most cases because both positive and negative values for one of the
velocity components would become systematically too low causing little change for the mean value
in most cases. Sample composition has been discussed by Martin & Morrison (1998) for their sample
and they came to the conclusion that it does not play an important role. Another point could be that
disturbances imposed at different times upon the stars of a group lead to different effects, and we
probe these different groups with the different types of stars used for such studies. However a much
larger sample than the current one is required to make definitive statements about net movements of
9
compared with the rest of the sample.
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6. D ISCUSSION OF THE RESULTS
Galactic components. Small samples might have too many outliers included, while a sample useful
for this analysis should probably be at least as large as the one of Fux (2001).
6.2.4
M OVING GROUPS AND
STELLAR STREAMS
Moving groups and stellar streams are ensembles of stars moving in the same direction, which have a
similar history or origin and are however not as compact as clusters or associations. There is a large
range of varieties and forms of these groups.
Stellar streams of young stars in the Disk have been known for a long time, such as the Sirius- and
Pleiades stream (Eggen 1972) or Gould’s belt (Herschel 1847). More recently such aggregates have
been discovered in the older populations of the Galaxy. Unlike their younger counterparts, which have
left the gas cloud where they were born a relatively short time ago, or are the remainder of dissolving
open star clusters, they were usually formed long after the stars themselves were born. The origins of
these streams are usually dwarf galaxies such as the Sagittarius dwarf (Ibata et al. 1994) that were in
interaction with the Milky Way or globular clusters (Odenkirchen et al. 2001). In both cases the stars
are mostly lost by tidal forces occurring as they interact with the Galactic potential. The Sagittarius
dwarf stellar stream should be traceable for a rather long time (Ibata et al. 2001; Helmi & White 1999).
Thus finding such stellar streams of old stars can give us valuable information about the formation of
the Galactic Halo or at least a part of the Halo. If there are many of these streams it would mean that
the Milky Way suffered interactions with other, smaller galaxies on more than one occasion.
Because of the diversity of these stellar entities it is difficult to define stellar streams and moving
groups. In our context a moving group consists of a relatively small number of stars while a stellar
stream is a larger and more massive ensemble of stars such as the Magellanic stream or the Sagittarius
stream. A moving group can of course later turn out to be larger than originally thought.
However we want to emphasise that the samples used in the present work are not ideally suited for
this kind of investigation. First, they consist of a relatively rare stellar type, which means that there
are not many of these stars in the candidate moving group. Second, the radial velocities and proper
motions are mostly not good enough to achieve an accurate identification of (two) stars having so
similar kinematics that they can be considered to be part of such a moving group. Therefore this
discussion is rather meant to show peculiarities that hint at moving groups showing where one should
start to investigate in order to confirm or discard the idea that these objects are part of such an entity.
In Chapter 4 we have pointed out that there are two stars, namely HE 0516−2311 and HE 0521−3914,
which have
• a very extreme kinematic behaviour, seen in the value of Θ which is more than 400 km s−1 in
both cases,
• and rather similar kinematics, in the sense that they basically move in the same direction with a
Θ of 408 and 468 km s−1 respectively.
The distance between them is ∼700 pc, so that if they belong to a moving group it would have to be
a large structure. Their trajectories over 50 Myr are shown in Figure 6.7 (for comparison that of the
Sun is also shown). The orbits extend to a very large distance from the Galactic centre and the Sun,
with apogalactic distances of 60 and 160 kpc. These values and also the differences between them are
not significant, because we do not know what the Galactic potential looks like at such large distances
(this also applies to the eccentricities). The nze values of both stars are rather small. Thus these stars
travel through the Galaxy from an almost edge-on position. Apart from these two objects we have
114
-15
0
X [kpc]
5
10
-20
-15
Y [kpc]
-10
-10
-5
-10
-5
Y [kpc]
0
10
o
rotation: X: 60
-15
-5
5
0
5
X [kpc]
-5
-10
X [kpc]
Z: 135o
-10
0
-15
10
Figure 6.7: 3D plots of the of the orbits of HE 0516-2311 (full line) & HE 0521-3914 (long dashed line), two stars with a rather similar and very
extreme kinetic behaviour. Shown are the trajectories over 50 Myr and for comparison the trajectory of the Sun (short dashes). The rotations around
the X and Z axis are noted above the induvidual plots.
-10
-5
-15
0
0
0
5
5
-10
-10
Z: 315o
HE 0516-2311
HE 0521-3914
Sun
o
rotation: X: 60
-15
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Y [kpc]
10
-10
-5
10
-5
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Y [kpc]
-5
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-5
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rotation: X: 60o Z: 45o
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-5
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Z: 225o
Z [kpc]
o
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rotation: X: 60
6.2. The populations of the Milky Way
115
6. D ISCUSSION OF THE RESULTS
several more in our sample (in principle those part of the “Outer or High Velocity Halo” in Chapter 4)
which have high orbital velocities - though none of them that extreme - but their trajectories are very
different from those of HE 0516−2311 and HE 0521−3914.
Is there a real connection between these two stars? The reasons these stars were found to be peculiar
are both the extreme and relatively similar kinematics. Stars with velocities similar to each other but
having a disk-like kinematic behaviour would not be striking, because the kinematics of disk stars are
similar anyway. The differences in the trajectories and also Θ can be ascribed to errors in distance,
proper motion and radial velocity as well as the geometry (The stars are in the sky separated from
each other by ∼20◦ ). The distance of HE 0516−2311 is somewhat more unsure than that of other
stars, because we do not have CCD photometry for this object (see Section 2.3.2). However, these
errors do not explain the extreme kinematics as a whole.
To draw a line: We cannot prove that these stars are part of a moving group of stars or not. We
therefore consider them as being possible candidates which have to be further investigated. Their
motion through the Galaxy is however striking and certainly a piece of evidence that they are in fact
members of some stellar aggregate moving through our Galaxy but with the current data it cannot be
decided. More research is needed, on the one hand better data for the two stars themselves and an
investigation of the surroundings to see whether there are any stellar density enhancements at a similar
distance as these two stars are located at, i.e. ca. 2 kpc from the Sun. Analysing such moving groups
can give us clues how the outer Halo was build up; the other members of our High Velocity Halo are
possibly also remainders of some stellar group having been assimilated by the Milky Way.
Surprisingly there is another (just as weak) piece of evidence for a stellar stream or moving group in
the inner part of the Galaxy – at a place where it would not be suspected, because it would probably
not survive long in a very dense environment, which would disrupt such a stream rather quickly. As
has been mentioned in the previous section and can be seen in Figure 6.6 (upper left panel) there
is a peak in the velocity distribution of the stars in the Peterson sample. There also seems to be
an overdensity of stars with [Fe/H]=−1.5 dex at the velocity range of about 100 km s−1 (Figure 6.6
upper right). This can also be seen, although far less clearly, in the lower left panel of Figure 6.6
at vrad =100 km s−1 , while the fourth panel does not seem to show anything of this kind. This again
raises the question whether some of the stars found in this part of the parameter space, i.e. having a
vrad =100 km s−1 , [Fe/H]=−1.5 dex and a distance from the Sun of 7-9 kpc have a common history.
However, the number of objects is again very small, around five, and can therefore also be described
by a statistical fluctuation. Therefore such overdensities should be considered to be a mere hint and
by no means to be confirmations that such groups exist, something that may deserve a closer look.
Are these stars maybe the remainder of a merger torn apart by tidal forces and interactions with objects
in the Milky Way? If this is true, this group of stars has not been moving so close to the Galactic centre
very often, otherwise it would have been disrupted.
It would be very worthwhile to further follow these hints, because finding groups with common motion will give us important insight into how the Galaxy and thus any spiral galaxy is formed. More
observations, especially considering more numerous stars (main sequence), have to be conducted in
both cases to strengthen these points which are at the moment mere hints.
6.2.5
R ELATIONSHIPS OF THE COMPONENTS , EVOLUTION
OF OUR
G ALAXY
Our studies using stars of the blue and extreme HB came to the results discussed in Sect. 6.2.1 for the
Disk and Sect. 6.2.2 for the Halo. Furthermore we discussed some implications for the inner regions
(Sect. 6.2.3) and possible stellar streams (Sect. 6.2.4). We still need to consider the consequences for
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6.2. The populations of the Milky Way
various models of Galaxy formation.
The classical theory for the formation of the Galaxy is the ELS scenario of rapid collapse and subsequent spin up to the formation of a Disk as suggested by Eggen et al. (1962) (ELS). Because of the
difficulties for the ELS scenario to explain certain phenomena, such as the lack of a radial abundance
gradient for the outer globular clusters, Searle & Zinn (1978) added a second phase of collapse to
the ELS theory. In the outer regions of the protogalaxy the gas was according to the Searle & Zinn
(1978) (SZ) scenario far more inhomogeneous than in the inner part. It was organised in clumps,
which continued to rain onto the Galactic centre for quite a large timespan after the initial ELS like
collapse. Other models describing the formation of the Galaxy regard other – smaller – galaxies as
important agents. Merger processes are responsible for building up the Halo, creating the Thick Disk
etc, such as described in Quinn et al. (1993).
All of these models have been enhanced and supplemented over the years. Majewski (1993) has
compiled and reviewed eight of the more widespread theories (see his Table 1) for the formation of
the Thick Disk. He distinguishes between “top down” and “bottom up” models depending on what
formed first, Thin or Thick Disk.
According to our results, the Disk is disjoint from the Halo. This speaks against all models requiring a
continuous transition between Halo and Disk. Among these are the model by Sandage (1990), which
describes the formation of the Galaxy by continuous star formation during the collapse with the Thick
Disk being the part with beginning pressure support. Another model with a Disk Halo continuum
is the model by van der Kruit & Searle (1981) and Gilmore & Reid (1983) that describes the Thick
Disk as the Halo response to the disk potential. All other models in Majewski’s list pass this test; one,
regarding the Thick Disk as the debris of an accreted dwarf galaxy does not depend on the Halo being
disjunct or not.
A more stringent test on the models is the discreteness of the two Disk components. Unfortunately
our results do not give us an answer in this matter. Taking into account other results such as those
from Phleps et al. (2000) or Gilmore & Reid (1983), we consider the two Disks as being separate
entities rather than a continuous structure. This then rules out all of the “top down” models except the
“disk first” scenario (Jones & Wyse 1983) which suggests a disconnected formation of Disk and Halo.
Also challenged is a “bottom up” model which regards the Thick Disk to be formed by the diffusion
of Thin Disk orbits (Norris 1987).
Adding these two constraints, namely the disjunctness of Halo and Disk and the discreteness of the
two Disk components, only two models (both are “bottom up” scenarios) survive – both connected
with the interaction of the Galaxy and hence its Disk with another (smaller) galaxy. The first is the
model which constructs the Thick Disk from the remains of the intruder; in the second (see e.g. Quinn
et al. 1993) the Thick Disk is formed by the heated Thin Disk. The gas, which is also disturbed, later
relaxates and forms a new Thin Disk, the one that we have at present. Especially in the latter scenario
a large part of the dissolved intruding dwarf galaxy must have been incorporated into the Halo. Can
we observe such remains, even if the event happened in the distant past? The simulations of Helmi
& White (1999) show that the remnants of a dwarf galaxy would still be detectable as stellar streams
with approximately common motion even if the event happened several Gyr ago.
It is therefore very important to find such streams which would supply us with strong evidence for a
merger scenario. While this study presented here was not intended to search for moving groups we
have found some vague clues to their existence (see Sect. 6.2.4). However these are far too vague
to really make a statement in this respect. It is known that our Galaxy has swallowed (and does
so even today) other galaxies, e.g. the Sagittarius dwarf spheroidal which is in the process of being
incorporated by the Milky Way. For this reason we think that at least a part of the Galactic Halo
117
6. D ISCUSSION OF THE RESULTS
originates from interactions of the Galaxy with satellite dwarf galaxies.
But is the Halo completely formed by remnants of galaxies? Many Halo stars have highly eccentric
orbits taking them very close to the Galactic centre. This implies that at least a part of the Halo
was formed by some kind of collapse scenario, because, if the Halo was completely assembled from
infalling dwarf galaxies it would be hard to believe that most of them hit the Galactic centre with no
offset. If a dwarf galaxy etc. falls onto the Galaxy it has a velocity of its own, apart from the attraction
by the Galaxy’s gravitational potential which will cause the satellite to “miss” the Galactic centre and
start orbiting the centre on an elliptical orbit. This orbit will – in most cases – not take the object
very near to the Galactic centre. Therefore we presume that the stars having free fall orbits originate
from the initial collapse. This initial collapse must have occurred in the early phases of the history
of our Galaxy because the gas must somehow have settled into a disk as we observe it today. Other
Halo stars, such as those having a high inclination and a moderate eccentricity, e.g. HD 117880 or
HE 0136−2758 may well be remnants of early mergers. The same applies to at least some of the
“high velocity” Halo stars.
We suggest that the Halo was partly formed due to the initial collapse of the protogalactic cloud. Other
parts have been accumulated thereafter, either by accretion of satellite galaxies or by infall of debris
from a less inhomogeneous outer cloud, like Searle & Zinn (1978) described. In any case the Galaxy
has been accreting dwarf galaxies until the present, the Sagittarius dwarf being the latest “victim”.
The Disk was the endpoint of the collapse. For the reasons described above the Thick Disk does not
seem to be the immediate predecessor of the Thin Disk but formed later due to interaction of the Disk
with a (probably relatively massive) dwarf galaxy in a relatively early stage of the Galaxy (considering
the ages of Thick Disk stars from Edvardsson et al. (1993) this event can not have taken place too long
after the formation of the Halo). Whether the stars in the Thick Disk are the stars of the Disk which
have just been stirred up or the event caused an onset of star formation in the disturbed gas, is unclear.
The present Thin Disk then formed when the gas relaxed to form a thin and relatively dense gas disk,
forming the stars we now find in the Thin and Old Thin Disk.
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C HAPTER 7
O UTLOOK
7.1
F URTHER STEPS
In the study presented here we have shown that EHB/BHB stars are a useful tool for studies of Galactic
structure, and we finally identified the sdB Halo component. However this is just a beginning, and
many more steps must be taken until we find out how the Galaxy really works and how it has been
formed.
The size of the samples should be increased and the accuracy of the measurements improved, leading
us to a higher statistical relevance of our results and to better opportunities to separate the populations.
A part of the efforts should be directed to the outer Halo. We need to find out how large the Halo is,
how far it does extend. Another important aspect is the clumpiness of the Halo. The discussion in
the previous chapter made clear that this issue is of utmost importance for our understanding of the
early phases of our Galaxy. An important issue concerning sdB stars is their radial velocity, which in
some cases turned out to be variable due to close binarity. Therefore more of these objects should be
observed in order to determine their systemic radial velocity.
As time advances, more and more regions of the sky which have have been observed with CCDs over
a large time span will be available. In the same time the photographic plates such as the POSS and
other surveys get older and older – increasing the time baseline for proper motion determinations.
Adding new CCD data will within a few years will enable us to determine accurate proper motions
using CCD data as first epoch data. Due to the higher resolution and better PSF characteristics (the
PSF does not grow with object brightness, greater dynamic range etc.) of CCD data the time needed to
wait until a significant proper motion can be determined is drastically shortened. It would be possible
to measure an accurate proper motion within 5 years.
Another important point is the systematic compilation of sdB stars in the solar vicinity. We have seen
that we can not make any definite statement about the Thin Disk population of sdB stars with our
current sample. This was not intended in the first place, the primary aim was to find the Halo sdB
population. To include the Thin Disk we need a sample containing mostly nearby sdB stars and stars
at low galactic latitudes (which presents us with difficulties like extinction or crowding etc. that did
not play a significant role in our current moderate to high galactic latitude sample). A systematic
search in the literature for all known bright sdB stars (in preparation for the DIVA satellite mission)
has revealed that there are far more sdB stars in Hipparcos or Tycho 2 catalogues than previously
thought.
Apart from just studying sdB or HBA stars, one can conduct similar studies with other objects which
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7. O UTLOOK
have their own advantages. RR Lyraes have been a work horse for Galactic science for a long time.
With the increasing availability of precise proper motions and radial velocities the kinematics of these
objects certainly need to be re-analysed in a large sample. Such a study is currently underway (Maintz,
priv. comm.). Another star types especially suited for studies in the solar surroundings are DA white
dwarfs. They are numerous and are just as easily identified and analysed as sdB stars, but their major
drawback is their faintness – therefore they would not be the ideal subject of studies of the outer
Halo, but for studies of the Disk. Because of the importance in cosmology (double white dwarfs are
considered to be SN Ia progenitors) a large spectral survey of white dwarfs has been started, the SPY
survey (Koester et al. 2001). In the frame of this project, a study of the kinematics of white dwarfs is
in progress and has already first results (Pauli et al. 2002). Finally there are other objects such as RGB
stars which, while not being easy to access because of complicated spectra and overlaps in the CMD,
are important because they are the immediate progenitors of HB stars. We still do not know definitely
what effect drives the mass loss to be so different in stars as to form totally different HB stars in the
same population. Analysing the Galactic distribution of RGB stars with different properties, e.g. CN
strength, metallicity etc., would probably give us insight into this problem.
Purely spatial studies could also be extended to other Galaxies, such as M 31, where the confusion
of the different populations is presumably a little less severe, because we do not observe them from
the inside. In the immediate vicinity of the Galaxy, attempts are already made to determine proper
motions of dwarf galaxies (Mendez, priv. comm.). This would give us information about the motions
of the complete Milky Way system including its satellites and may answer some of the questions
concerning the formation of the outer Halo.
The circle has been closed again. In the introduction the importance of galaxies at various distances
has been described and the methods these are analysed; now we start to apply the methods we used
on the most nearby galaxy, the Milky Way, on objects of the next further category to gain more
information about a part of the local group.
7.2
T HE FUTURE : DIVA AND GAIA
This section deals with probably the most important step for astrometry – satellite missions. The
Hipparcos mission (ESA 1997, on which part of our work is based on) was a milestone being the
first astrometric space mission leaving behind all the problems of earth based astrometry, such as the
atmosphere, the Earth’s rotation. This project supplied us with proper motions mostly accurate to
∼ 1 − 1.5 mas/yr of 120,000 stars and accurate trigonometric parallaxes for thousands more. The
add on Tycho catalogue was the base of a new determination of about 2.5 million proper motions
published in the Tycho 2 catalogue (Høg et al. 2000) using ground based old catalogues as first epoch
data.
There are currently a number of satellite projects in the planning phase, which present – if they are
indeed realised – a major step in the accuracy and number of available proper motions. They will
furthermore increase the precision of distance measurements, with trigonometric parallaxes of unprecedented quality and quantity! The impact on Galactic science will be as big or even bigger than
that of the Hipparcos mission in 1997. Concerning our sample this would mean, that we will have
access to very precise proper motions for almost all our stars by 2010 and all stars to about 20 mag by
2020.
Among these new (second generation) missions are the DIVA, GAIA and FAME satellites.
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7.2. The future: DIVA and GAIA
Figure 7.1: Conceptual study of the DIVA satellite (left). Image taken from the DIVA project’s
homepage under URL.: http://www.ari.uni-heidelberg.de/diva/diva.html
Figure 7.2: Conceptual study of the GAIA mission (right). Image adapted from pictures taken
from the ESA’s GAIA homepage under URL.: http://astro.estec.esa.nl/GAIA/
The FAME1 (Full sky Astrometric Mapping Explorer) survey was supposed to measure very accurate
(0.05-0.5 mas/yr) proper motions parallaxes and magnitudes of 40 million stars. Unfortunately, this
mission ran into severe financial difficulties, when a large part of its funding was cancelled: It will
probably not be realised.
DIVA2 (Dual Instrument for Visual Astrometry) is a low budget successor of Hipparcos (Budget ∼
EUR 50 million (!)). It will measure proper motions and parallaxes of about 40 million stars brighter
than 16 mag with an accuracy of ∼ 0.25 mas/yr. Additionally, there will be accurate photometry and
a crude spectral classification system, using dispersed images. Probably this mission will contribute
significantly to solving some of the most important problems concerning the cosmic distance ladder,
such as the distances of δ Cep stars and RR Lyraes – something Hipparcos only partly managed to
achieve. DIVA is supposed to be launched in 2006, the data should be published in 2010. This
mission has already been postponed for one year3 and is under heavy financial pressure. At present
the future of DIVA is unsure.
Even further in the future, ESA will probably fund GAIA4 (Global Astrometric Interferometer for
Astrophysics), by far the most ambitious project. It will map all stars brighter than 20 mag (approximately 109 ) and measure proper motions with an error of down to 3µas, perform photometry on all
stars, and measure radial velocities for a brighter subset with an accuracy of 1 to 10 km s−1 . This will
give us the opportunity to conduct a similar study as the present one using a large percentage of the
stars in the Galaxy. GAIA will also allow us to measure significant proper motions for virtually every
galaxy in the local group. Launch date is about 2012, the data will probably be available in 2017 or
2018.
1
for further information, see: http://www.usno.navy.mil/FAME/
more information can be found at: http://www.ari.uni-heidelberg.de/diva/
3
original launch data was late 2004/early 2005.
4
see also: http://astro.estec.esa.nl/GAIA/
2
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7. O UTLOOK
Another mission, primarily focusing on extrasolar planets is the SIM5 (Space Interferometry Mission,
2009) interferometric mission. This project will also obtain very accurate astrometry for stars up to
20 mag, however only on somewhat more than 20,000 specially selected stars.
Every one of these missions, if successful, will provide us with a huge amount of extremely accurate
astrometric data. This would enable us to make studies similar to this one using samples of hundreds
or even thousands of objects. Many things that we could only vaguely determine would be easily
achieved in the future. We would finally be able to solve many of the remaining questions about
the structure and evolution of our Galaxy. We would know how the Halo formed, or whether the
Disk components are discrete or not, how many moving groups exist, and solve many other important
questions. There is just one big difficulty: one mission (FAME) is de facto cancelled, DIVA is in
serious financial difficulties, and the financing of the other two is also far from certain. If all goes
wrong, we might end up with nothing. Therefore we can only hope that at least one of them finally gets
approved and successfully completed and that not all fall victim to political and financial decisions.
We have seen what can be achieved with medium accuracy data of about 100 stars, namely the results
presented here. Therefore the thought, of what can be reached, when using the data of one of these
advanced space missions, is really tempting. They just have to be approved and financed by the
national and international science funding organisations and then completed successfully.
7.3
E PILOGUE
Apart from the scientific discussion, which was accomplished in Chapters 1 to 7 of this work, it is
becoming ever more important to invest in public outreach (especially if one wants the public to pay
expensive space missions).
For this reason I conclude with a picture (Fig. 7.3) showing some of the orbits of the stars we examined
superimposed on an edge-on galaxy similar to our own (NGC 4565). It shows us how our stars orbit
around our Galaxy, and how far they travel from the Galactic plane and centre. MPEG movie files of
the orbits can be downloaded under the URL:
http://www.astro.uni-bonn.de/maltmann/index.shtml.
Images of astronomical objects, such as galaxies, nebula, star clusters etc. (including most of those
displayed in Chapter 1) can be found under the following link:
http://www.astro.uni-bonn.de/maltmann/gallery.html.
5
see: http://planetquest.jpl.nasa.gov/SIM/sim index.html
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7.3. Epilogue
Figure 7.3: Orbits of Thick Disk and Halo sdB stars superimposed on NGC 4565, which is an edgeon galaxy probably quite similar to our galaxy. Note, that the scale of the orbits does probably not
accurately match the scale of the galaxy, it is just an approximation, showing the principle.
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7. O UTLOOK
124
A PPENDIX A
C ORRECTING LARGE GRADIENTS WITH
COMBINED DAWN / NIGHT SKY FLAT FIELD
EXPOSURES
The flat field correction of the DFOSC exposures presented us with problems: the large scale gradients
in the raw images could not be compensated with twilight flats – they were even worse than without the
flatfielding. Furthermore, the morning and evening flatfield exposures differed significantly. Dividing
a morning flat by an evening flat left a residual gradient of 4-5% (in some cases this gradient was even
as large as 10%). This resulted in a residual gradient in the object frames of about 2%. Therefore we
decided to utilise an alternative method which is briefly described here. The classical way of doing a
flatfield correction is using a sky flatfield exposure usually taken during dawn or dusk before/after the
night of observing. In stable optical systems, flats may be used from different nights1 . Less suited are
“dome flats” taken against an screen in the dome, because these screens are mostly not sufficiently
homogeneously illuminated. Buil (1989) describes a method of constructing a flat derived from the
night time object exposures by eliminating all stars with medianised adding up the individual object
frames. With this method the large scale structures in the flat field are represented correctly. On
the down side, the S/N ratio is low, so the small scale features (which are mostly rather subtle) are
only corrected inaccurately and a lot of unwanted noise is brought onto the corrected data image. The
method only works, if there are a sufficient number of frames with a high sky background (several 100
ADU on average), i.e. long exposure frames. Frames with a low sky background are not suitable –
any residual bias gradients left on the flatfield (even if the amplitude is less than 1 ADU) will influence
the large scale gradients by a large degree – let alone the very bad S/R ratio.
A flatfield exposure contains several kinds of information: there are large scale gradients, caused by
vignetting which is to some degree present in nearly every optical system, especially in focal reducers
(as in our case) or dust/dirt on optical surfaces far away from the focal plane, others are small scale
variations, such as pixel to pixel efficiency variation, dust specs on the chip, or the mechanical chip
structure. Unwanted information includes bad pixels (can be taken care of using bad pixel algorithms)
and statistical noise. Some exposures (especially in I band) show a fringing pattern which is difficult
to correct; however, our data does not suffer from this effect. To keep the additional noise introduced
to the corrected image small, one needs to get flat exposures with a S/N ratio which is as high as
possible.
1
provided no manipulation was done to the system, e.g. removal and replacement of the dewar, or filter wheels etc.,
because this would invalidate all previously taken flat field exposures for the next night.
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A. C ORRECTING LARGE GRADIENTS WITH COMBINED DAWN / NIGHT SKY FLAT FIELD
EXPOSURES
Our data consists of high galactic latitude star fields. Therefore the long exposures are ideal for
using them as flat fields. Unfortunately we do not have long B band exposures. Therefore we could
not enhance the B flats. The problem is that we have the dawn flats, which correct the small scale
structures accurately but not the large gradients and we have night flats which eliminate the gradients,
but add a lot of noise to the corrected image. Therefore we combined both keeping the advantages of
each and discarding the bad points using a method we call Skin Transplantation2 which resembles an
unsharp mask.
First a masterflat3 is created from all available dawn flatfield exposures using flatcombine. The
same is done for the object frames, using a clipping algorithm to discard the stars4 . Of the rejection
algorithms available in the IRAF software package, pclip5 has proven to be the most effective for this
type of problem. However, around the target star a residual structure remains. This is expected, since
the telescope is normally pointed towards the coordinates of the target stars, which means that unless
the pointing of the telescope is very bad, the target stars are near the same position on the frame.
Therefore we patch this position by cutting this area out and interpolating it (including the noise)
using the task imedit.
The second step is to normalise both masterflats, so that the signals (gradients and fine structures) are
of the same amplitude. Furthermore, it is necessary to correct for bad pixels, because they may spoil
the whole undertaking. Bad pixels have the tendency to show up as unwanted bright (or dark) stars on
the final flat. Therefore care should be taken to eliminate all bad pixels or lines before smoothing.
Having completed the preparations, both masterflats now have to be smoothed. In our case we used a
Gaussian algorithm (IRAF task gauss) to smooth the images. The σ of the Gaussian is not critical.
Tests with different σ revealed a negligible difference in the final flats. Even using a σ of 100 pix
does not change the result significantly. Subtracting or dividing the final flats only revealed a residual
of generally less than 0.1%; on some “hot spots” the difference was larger, though in every case less
than 0.5%. In most cases a sigma of 5-10 pixels should be used, in order to separate small scale and
large scale features optimally. It is important that both masterflats are treated with the same Gaussian.
Otherwise some features might be missing and others might be double in the final flat.
The smoothed object frame flatfield will correct the large scale structures. The other (twilight) flat is
used to correct the small scale structures. Therefore we flatten (“skin”) this image, so that only the
high frequencies are visible. This is done by simply dividing the unsmoothed twilight masterflat by
the smoothed one – the gradient is removed, the only features which are left are the fine variations.
The smoothed twilight flat and the untreated object flat may now be discarded.
Finally we only need to multiply the smoothed object flat to the “skinned” twilight image. The result
has both the correct large scale structure and high S/N small scale structure. This image can now be
applied to the object frames in the standard manner.
The process can be described in short using the following formula:
n
n
n
n
Ffin
= (Ftw
− g(Ftw
, σ)) × g(Fobj
, σ)
(A.1)
with Fxn being the (normalised) final, twilight and object frame flats, G(F, σ) the Gaussian.
2
We describe this method as done with tasks of the IRAF image reduction package. The basic methods are the same in
every other program; it may be that other packages do not have some of the particular tasks or it is more complicated to
accomplish the one or other step.
3
We assume, the flatfield images have been debiased etc. beforehand.
4
When assembling the twilight flats, it is wise to also use a clipping algorithm in order to remove possible stars (which
can even be unnoticed on the image); For this to be done successfully every exposure should be offset to the previous one
by 10-2000 , so that the stars are not always on the same position on the chip.
5
which rejects a certain percentile of pixels from a median formed before the clipping.
126
A PPENDIX B
D ATA OF THE STARS OF THE EQUATORIAL
FIELD
As mentioned in Chapter 2 we collected data on a field just north of the celestial equator at a right
ascension of between 22h 30m and 1h 50m taken from the Hamburg-Schmidt survey (Hagen et al.
1995). We did not use any of the obtained data for the main part of our work, because most of
the objects were found to be not suitable because they are either no sdB or HBB stars, or they had
an obvious cool companion (which means that the physical parameters could not have been derived
reliably). Only about 15-20 stars were in fact sdBs. Moreover they are very faint, and hence far away,
the tangential velocities would be much less accurate than for the brighter and therefore closer HE
stars.
Nevertheless, we include a data table of objects in this field in order to make the data available. Note
however that because these objects were not considered for our main study, the data are not complete
and in some cases not completely reduced. The proper motions are relative only, i.e. they have not
been calibrated to the extragalactic reference frame. Most of the positions are the 1950.0 positions
given in the HS catalogue precessed to 2000.0. The data for photometry, spectroscopy and astrometry
has been obtained at Calar Alto observatory, the first epoch coordinates of the proper motions have
been taken from the APM catalogue. Data reduction and analysis is described in Chapter 2.
The CCD images of these stars might be a good first epoch for a proper motion determination using
CCD data obtained in about 2008 or later as second epoch (the same applies to the CCD data of the
HE stars). Because most of the stars are just to faint to be observed by the DIVA satellite, such an
approach is still necessary if one wants to determine more accurate proper motions of these stars, than
possible today. The DIVA catalogue can serve as input catalogue.
More information about the data can be obtained, by mailing to: [email protected];
See also http://www.astro.uni-bonn.de/ maltmann/index.html for possible changes
in email address or other information.
127
B. DATA OF THE STARS OF THE EQUATORIAL FIELD
23 09 53.4
23 11 27.80
23 13 54.9
23 16 43.2
23 18 19.0
23 19 07.0
23 18 31.86
23 21 26.8
23 23 13.9
23 26 22.35
23 26 06.59
23 26 45.8
23 37 14.9
23 38 43.5
23 49 26.9
23 53 02.2
23 54 31.1
+01 12 14
+09 58 38.5
+07 12 51
+01 16 41
+09 11 48
+02 12 42
+09 34 03.9
+09 17 28
+08 56 43
+09 03 00.5
+05 16 15.8
+05 53 48
+02 0 49
+00 43 0
+04 21 4
+10 11 19
+07 6 26
16.55
15.91
14.45
15.68
16.77
12.88
15.71
13.98
14.40
15.70
16.23
16.88
16.78
15.47
16.94
15.14
14.41
16.68
17.01
17.41
14.58
17.00
15.56
16.30
16.15
15.84
16.95
16.06
16.84
−0.20
−0.06
−0.15
+0.04
+0.28
−0.29
+0.32
−0.16
−0.14
+0.04
−0.11
+0.02
+0.18
−0.06
−0.10
−0.11
−0.10
+0.39
−0.32
0.00
+0.33
+0.21
−0.08
−0.06
−0.12
−0.08
−0.10
+0.14
−0.18
−0.07
+0.01
−0.22
+0.08
+0.22
−0.09
−0.01
−0.19
−0.11
+0.03
−0.06
−0.01
sdB+x?
sdB
sdB
sdB
sdB
sdB+x
HBB
HBB/sdB
HBB
???
sdB
DA
DA
sdOB
sdB
sdB+x?
sdO
DA
sdB+x
DA
sdB+x
sdB/HBB
sdB
sdOB+x
sdB
sdB
sdB/HBB
sdOB
sdB+x
+14.3
−0.9
−4.5
−4.0
+1.8
+1.1
26250
32500
30000
30000
37500
5.20
5.15
5.18
5.00
5.12
YAS
YAS
YAS
YAS
YAS
Table B.1: Data of stars in the equatorial field: Positions, typology, relative proper motions, Teff and log g, if available. UH means Heber (priv. comm)
and YAS Aguilar-S’anchez (1998). A “p” in the magnitude column means that this is the photographic value from the HS.
No. Name
α(2000.0)δ
V
B−V
V − R Type
µα cos δ
µδ
Teff
log g Source
[hms ]
[◦ 0 00 ]
[mag]
[mas/yr]
[K]
22 34 16.56 +06 25 53.9
+0.30
−3.7
+3.8
22 40 14.3
+02 06 32
−0.15
22 42 52.5
+01 52 22
−0.17
32000
5.60
UH
22 49 27.0
+02 14 33
−0.22
33100
5.00
UH
22 52 15.94 +00 41 56.3
−0.22
−3.7
+2.1
22 54 02.03 +00 13 57.5
+0.63
+26.2 +25.3
22 54 23.36 +08 17 56.7
−0.16
+8.9
+7.6
22 56 01.1
+09 17 00
−0.04
23 04 22.98 +07 45 10.8
+0.49
+2.2
+1.9
+0.31
23 06 22.34 +02 09 05.9
−0.28
+0.6 +14.4 33700
5.71
−0.30
−0.11
−0.18
+1.7
+8.5 52000
5.2
UH
−0.16
+0.06
1 HS 2231+0610
2 HS 2237+0150
3 HS 2240+0136
4 HS 2246+0158
79 HS 2249+0026
5 HS 2251−0001
6 HS 2251+0801
7 HS 2253+0900
9 HS 2301+0728
9a HS 2302+0255
9b HS 2303+0152
9c HS 2306+0238
11 HS 2307+0055
12 HS 2308+0942
13 HS 2311+0656
14 HS 2314+0100
15 HS 2315+0855
16 HS 2316+0156
17 HS 2316+0917
18 HS 2318+0901
19 HS 2320+0840
21 HS 2323+0846
20 HS 2323+0459
22 HS 2324+0537
23 HS 2334+0144
24 HS 2336+0026
25 HS 2346+0404
26 HS 2350+0954
27 HS 2351+0649
continued next page.
128
129
Name
HS 2352+0415
HS 2357+0239
HS 0003+0632
HS 0007+0235
HS 0009+0026
HS 0009+0144
HS 0014+0000
HS 0014+0400
HS 0015+0024
HS 0016+0044
HS 0016+0216
HS 0019+0215
HS 0019+0318
HS 0033+0644
HS 0039+0030
HS 0041+0117
HS 0042+0927
HS 0043+0353
HS 0048+0026
HS 0055+0138
HS 0102+0024
HS 0105+0316
HS 0112+0244
HS 0116+0257
HS 0122+0239
HS 0123+0118
HS 0124+0311
HS 0129+0120
HS 0129+0333
HS 0145+0236
HS 0146+0217
No.
28
29
30
31
32
33
34
35
36
37a
37
38
39
41
42
43
44
45
46
47
48
49
51
52
53
54
55
56
57
59
60
Table B.1: Data of stars in the equatorial field (cont.)
α(2000.0)δ
V
B−V
V − R Type
µα cos δ µδ
hms
◦
0
00
[ ]
[
]
[mag]
[mas/yr]
23 55 21.4 +04 32 20 16.60
+0.82
+0.45 cool
23 59 35.3 +02 55 48 16.71
−0.28
−0.14 He−sdB/O
0 05 52.0 +06 49 20 16.80
−0.19
−0.05 sdB
0 10 09.0 +02 52 32 16.12
−0.24
−0.12 sdB
0 11 34.0 +00 43 15 16.48
+0.05
+0.10 HBB
0 12 04.4
+02 1 28 16.54
+0.14
+0.07 CV
0 16 52.4 +00 16 59 17.06
+0.37
+0.29 sdB
0 17 27.4 +04 16 57 14.62
+0.30
+0.18 HBB
0 17 42.2 +00 41 36 17.02
−0.03
−0.04 no sdB!
0 18 43.4
+01 1 21
sdB
0 18 43.3 +02 33 23 17.09
+0.17
+0.02 no sdB!
0 22 15.7 +02 31 56 17.61
0.00
−0.01 He−sdB
0 22 13.1
+03 35 5 16.98
0.00
+0.07 sdB+x
0 36 02.6
+07 0 48 16.76
−0.23
+0.16 DA
0 42 33.4 +00 47 18 17.40
−0.30
−0.32 sdB
0 44 04.9 +01 33 43 16.81
+0.06
+0.22 AGN
0 44 46.7 +09 43 51 16.02
−0.16
−0.11 sdB+x?
0 45 47.2 +04 10 22 15.85
+0.19
+0.27 AGN
0 51 06.7 +00 42 46 15.86
−0.30
−0.13 no sdB!
0 58 24.7 +01 54 33 15.14
−0.28
−0.14 sdB
1 05 30.5
+00 40 8 17.66
−0.21
−0.13 DA
1 08 16.9 +03 32 45 17.29
−0.24
−0.17 sdO/OB
1 14 42.3
+03 0 15 16.32
+0.56
+0.38 sdB+x
1 19 27.2 +03 13 29 17.22
−0.28
−0.14 sdB
1 25 20.2
+02 55 8 16.25
+0.56
+0.44 sdOB+x
1 26 21.1 +01 34 31 17.37
−0.17
−0.08 sdB
1 26 48.3
+03 27 8 16.90
+0.19
+0.20 AGN
1 32 24.0 +01 35 59 17.02
+0.02
+0.03 ???
1 32 26.1 +03 48 39 17.01
+0.30
+0.27 pec
1 47 51.5 +02 51 38 16.73
0.00
+0.06 ???
1 48 56.9 +02 32 26 16.68
+0.33
+0.18 AGN
5.12
5.00
5.12
5.37
5.12
27500
28750
32500
32500
log g
27000
Teff
[K]
YAS
YAS
YAS
YAS
YAS
Source
B. DATA OF THE STARS OF THE EQUATORIAL FIELD
130
A PPENDIX C
V ARIABLES AND D EFINITIONS USED IN
THIS STUDY
In this part all variables and definitions used in this work are listed and briefly explained. In this
compendium only short descriptions and explanations of the relevant quantities are given as a quick
reference. For more detailed information we refer to the literature.
C.1
P HOTOMETRIC QUANTITIES
• U, B, V, R, I: passbands of the Johnson-Cousins U BV RI system, the most well known and
widely used photometric system. It consists of wide passbands and is thus ideal for faint objects;
on the other hand Johnson photometry smears out more physical information than middle or
narrow band photometry. B − V is a colour index in the Johnson-Cousins system and (B −
V )0 represents the B − V index corrected for reddening. Also widely used is the Stroemgren
u, v, b, y middle passband photometric system.
• AV and EB−V : Interstellar absorption and reddening (in this case in V passband); these quantities are related to each other by AV =R × EB−V with R=3.1 for B − V . (In our case we
used IRAS maps taken from Schlegel et al. (1998), who recommend a slightly different value
of 3.315.)
• M, MV : absolute magnitude (V magnitude of the stars if it were at a distance of 10 pc.)
• δMV : quantity used in Chapter 3 to describe the difference between the actual absolute magnitude of a BHB star and the absolute magnitude of the horizontal part (at the B − V of RR
Lyrae). This is necessary to compensate the downward trend in MV for bluer stars.
C.2
S TELLAR PHYSICAL QUANTITIES
• log g: logarithm of the surface gravities in the CGS system.
• R: stellar radius
• Teff : effective temperature
131
C. VARIABLES AND D EFINITIONS USED IN THIS STUDY
C.3
S PATIAL AND KINEMATIC QUANTITIES
C.3.1
O BSERVED QUANTITIES
• α, δ: celestial coordinates are given in equinox J2000.0 throughout this study.
• µα cos δ, µδ : proper motions, usually given in mas/yr, 00 /100 yrs and other units are also found.
µα cos δ is actually 15µα cos δ, the 15 · cos δ translates µα from hms coordinates to ◦000 .
• vrad : radial velocity
• d: distance
C.3.2
S PATIAL QUANTITIES AND VELOCITIES
• XY Z, U V W : The euclidian galactic velocity coordinate system; XY Z are the spatial coordinates, and U V W the velocities. X points from the Sun to the Galactic centre (GC), the
zero point lies in the GC, which means that X =−8.500 kpc; the corresponding velocity is U .
Y points in the direction of Galactic rotation, its zero point also lies in the GC. The velocity
component in the Y direction is V . In the solar vicinity V contains most of the rotational velocity of the Disk. The Z axis lies perpendicular to the Galactic plane with its origin in the
GC. W is the corresponding velocity component. The coordinates of the GC are accordingly:
(X, Y, Z)=(0, 0, 0) kpc and the Sun’s (−8.5, 0, 0.007) kpc. Note: In many publications the V
velocity component has its origin at V = VLSR , i.e. at the rotational velocity of the disk at the
solar position. Others, such as in our case, non-rotation (V=0 km s−1 ) is used. As the resulting
values differ by the galactic rotational velocity, which is 220 km s−1 , therefore one should be
aware of the different definitions of V when comparing the results of different studies.
• z: z = |Z| is the (positive) distance of an object to the Galactic plane.
• $: (planar) Galactocentric distance, the distance between the Galactic centre and a point projected to the galactic plane, i.e. as given by
$=
p
X2 + Y 2
(C.1)
In some publications $ is also ρ and (depreciated) R, which actually refers to another (however
closely related) quantity.
• R: (Total) Galactocentric distance. In contrast to $, R stands for the total distance between the
Galactic centre and the object and is given by:
R=
p
X2 + Y 2 + Z2
(C.2)
In some studies R is also called Rgc .
• Θ: Orbital velocity; the (planar) orbital velocity lies perpendicular to the line object – Galactic
centre as well as orthogonal to Z resp. W . The name “orbital velocity” is used rather than
“rotational velocity” to avoid confusion with the rotational velocity (spin) of a star. Θ is one
of the most important indicators of the population membership of stars, because it indicates
whether an objects rotates with the Galactic Disk or not. This parameter can be computed
using:
Θ = V · cos η + U · sin η
(C.3)
132
C.3. Spatial and kinematic quantities
b)
Z
Z
v tot
v tot
Galactic Plane
Figure C.1: Spatial and velocity coordinates in the Galactic system. In panel a) the euclidian coordinates XY Z, U V W are presented, and in the right panel (b) the cylindrical velocity coordinates
ΦΘW are shown. The hexagon represents an example object, GC stands for Galactic centre. The
starred symbols refer to the object.
with η being arctan(Y /X). For small Y , Θ ' V .
• ΘLSR : the orbital velocity of the Local Standard of Rest (LSR), i.e. the local rotational velocity
of the Galactic Disk. At the Sun, ΘLSR is 220 km s−1 according to the current IAU values. This
value is also used throughout this study.
• Q and σQ (with Q = U, V, W, Θ, Φ, ecc, nze, IZ ): Mean value of the quantity and its dispersion
for an ensemble of objects. The mean value shows a typical value for some of these quantities,
e.g. a significantly non zero Θ means that the objects in this group show a significant net motion, i.e. rotation – they are probably part of a rotationally supported disk-like structure. Others,
such as Φ and W should be close to zero, if a disk is not expanding or warping. The dispersions give information about the uniformity of the motions in a group. In a disk-like structure,
i.e. stars moving at a velocity relatively near the rotational velocity of the disk on low inclined
orbits, the velocity dispersions are low, in a more disturbed group, where eccentricities and inclinations are spread over a larger range and the net rotation is slower, the dispersion is higher.
In non rotating, spherical structures, the mean velocities are near zero and the dispersions very
high. The dispersions are affected by the errors; the true dispersions are smaller than the observed ones. Given symmetrical errors, their influence on the mean value should be very small.
However outliers in the distribution could have a large effect.
• Θmed : This quantity is the median value of the orbital velocity (Θ) integrated over the whole
orbit. The current values of Θ are momentary, they change with time; currently high values
may become lower and vice-versa. Therefore Θmed was introduced to provide a characteristic
velocity of an individual orbit. In principle the mean Θ could also have been used, Θmed pulls
apart the datapoints a little more. Other characteristic points in an orbit include Θmax and Θmin ,
which are also plotted in Fig. 4.7.
• Φ: Centrifugal velocity; Φ is the velocity component pointing away from the Galactic centre.
In the solar vicinity Φ ' −U . Φ is computed by:
Θ = V · sin η + U · cos η
Θ✩
Φ✩
η
Z✩
90 o
Y✩
Φ✩
Galactic Plane
W✩
η
GC
ϖ
X✩
Y
X
Y✩
Z✩
U✩
Galactic Plane
W✩
X✩
Y
GC
X
Galactic Plane
W✩
V✩
a)
(C.4)
133
C. VARIABLES AND D EFINITIONS USED IN THIS STUDY
with η being arctan(Y /X).
• vpec : peculiar velocity; the amount the velocity of an objects deviates from that of the LSR,
i.e. from (Φ=0,Θ = ΘLSR ,W =0) km s−1 . vpec is an indicator of how “heated up” the orbit of
a star is.qThe Sun’s peculiar velocities are (+10,+15,+8) km s−1 , its vpec is thus 19.7 km s−1 .
(vpec =
Φ2 + (Θ − Θ2LSR + W 2 ))
• v⊥ : velocity perpendicular to the Galactic rotation (and to Θ). This parameter provides a measure for the degree an
√ orbit deviates from a circular orbit – it is an indicator of “kinematic
temperature” (v⊥ = Φ2 + W 2 .
√
√
• vtot : Total velocity, i.e. vtot = U 2 + V 2 + W 2 = Φ2 + Θ2 + W 2 .
• Iz : z-component of angular momentum – this quantity is a conserved quantity.
• Ekin : kinetic energy of an object (we actually use Ekin /2m).
Ekin = U 2 + V 2 + W 2
C.3.3
M ORPHOLOGICAL PARAMETERS OF THE ORBITS
• Ra ,Rp : Apo- (Ra ) and perigalactic (Rp ) distance. These are the maximal and minimal distances
from the Galactic centre reached by an individual object. In this work they are derived from the
orbital morphology.
• ecc: eccentricity; is a measure for the ellipticity of an orbit. It is computed by:
ecc =
Ra − Rp
Ra + Rp
(C.5)
• zmax : maximum distance to the Galactic Plane, that a star reaches during its orbit.
• nze: normalised z-extent; nze compensates for the diminished Galactic potential at larger distances from the Galactic centre. (the effect of which can be seen in any of the figures depicting
orbits in Chapters 3, 4 and 5, as the widening up of each orbit in Z with increasing $ – i.e.
further away from the Galactic plane.) nze was first introduced in de Boer et al. (1997a) and is
calculated using the following formula:
nze =
C.3.4
zmax
$(zmax )
(C.6)
S CALEHEIGHTS AND D ENSITIES
• z0 : The scale height of an exponential disk (sometimes also called h0 , hz ). z0 is the distance
from the plane of an exponential disk where the density is reduced to 1/e (' 36.8%) of the
initial density (at z0 ) of the distribution. Thus z0 , while being a measure of the thickness of
such a distribution, does not mean the thickness itself, as an exponential disk does not have a
limit as such. In practical, 3-5×z0 is more appropriate for the thickness as this encompasses
most of the stars in this particular disk-like structure.
134
C.3. Spatial and kinematic quantities
• N0 : Initial space density; this is the density of stars at the Galactic Plane, usually given in pc−3
or kpc−3 . In our case we cannot derive absolute values for N0 , but only relative density ratios.
Therefore we only use density ratios throughout the discussion, setting the N0 value of the Thin
Disk to 100%. In the discussion of our own sample, we set the Thick Disk’s N0 to 100%, since
we do not have an accurate relative value for the Thin Disk.
• N (z): Density at a distance z from the Galactic plane.
135
C. VARIABLES AND D EFINITIONS USED IN THIS STUDY
136
A PPENDIX D
L IST OF ABBREVIATIONS
ADS
ADU
AG
AGB
AGN
ALFOSC
APM
BAP
BD
BHB
CAHA
CAFOS
CCD
CD
CDS
CMD
CN
CV
DA
DAOPHOT
DB
DC
DO
DFG
DFOSC
DIVA
DLR
DSAZ
DSS
EHB
ESA
ESO
FAME
FHB
Astrophysics Data System
Analog Digital Unit
Astronomische Gesellschaft
Asymptotic Giant Branch
Active Galactic Nucleus
AndaLucia Faint Object Spectrograph
Automated Plate Measuring facility
Bonner Astrometrie-Programme
Bonner Durchmusterung
Blue Horizontal Branch
Centro Astronomico Hispano Aleman
Calar Alto Faint Object Spectrograph
Charge Coupled Device
Cordoba Durchmusterung
Centre de Données astronomiques Stellaires
Colour Magnitude Diagram
Carbon Nitrogen, or Cyano
Cataclysmic Variable
A-type White Dwarf
Dominion Astronomical Observatory PHOTometry
B-type White Dwarf
Cool White Dwarf
O-type White Dwarf
Deutsche Forschungsgemeinschaft
Danish Faint Object Spectrograph and Camera
Double Interferometer for Visual Astrometry
Deutsches Luft und Raumfahrtzentrum
Deutsch Spanisches Astronomie Zentrum
Digitized Sky Survey
Extreme/Extended Horizontal Branch
European Space Agency
European Southern Observatory
Fullsky Astrometric Mapping Explorer
Field Horizontal Branch
137
D. L IST OF ABBREVIATIONS
FWHM
GAIA
GC
GSC
HB
HBA
HBB
HD
HE
Hipparcos
HoLiCam
HS
HST
IC
IMEXAM
IPII
IR
IRAF
IRAS
IUE
LG
LMC
LTE
M
MCs
MIDAS
MPI
MW
MWTD
MS
NASA
NGC
NGP
NLTE
NOT
NPC
pAGB
PDMF
PDS
PG
PN
POSS
QSO
RGB
RHB
RR,RR-Lyr,RR-Lyrae
SB
138
Full Width Half Maximum
Global Astrometric Interferometer for Astrophysics
Globular Cluster
Guide Star Catalog
Horizontal Branch
Horizontal Branch type A
Horizontal Branch type B
Henry Draper
Hamburg Eso
HIgh Precision PARallax COllecting Satellite
HOher LIst CAMera
Hamburg Schmidt
Hubble Space Telescope
Index Catalogue
IMage EXAMine
Intermediate Population II (other name for the Thick Disk)
InfraRed
Image Reduction and Analysis Facility
InfraRed Astronomical Sattelite
International Ultraviolett Explorer
Local Group
Large Magellanic Cloud
Local Thermal Equilibrium
Messier
Magellanic Clouds
Munich Image Data Analysis System
Max-Planck-Institut
Milky Way
Metal Weak Thick Disk
Main Sequence
National Aeronautics and Space Administration
New General Catalogue
Northern Galactic Pole
Non Thermal Equilibrium
Nordic Optical Telescope
Northern Polar Cap
post Asymptotic Giant Branch
Present Day Mass Function
Photometric Data System
Palomar Green
Planetary Nebula (often referring to the central star)
Palomar Observatory Sky Survey
Quasi Stellar Object
Red Giant Branch
Red Horizontal Branch
RR Lyrae star
Slettebak Brundage
sdB
sdOB
sdO
SDSS
SExtractor
SGP
SIM
SPC
TAHB
TAMS
TWIN
USNO
VLT
WD
WFI
WWFPP
ZAHB
ZAMS
subdwarf B
subdwarf OB, i.e. hotter than sdB, cooler than sdO
subdwarf O
Sloan Digital Sky Survey
Source Extractor
Southern Galactic Pole
Space Interferometry Mission
Southern Polar Cap
Terminal Age Horizontal Branch
Terminal Age Main Sequence
TWIN spectrograph
United States Naval Observatory
Very Large Telescope
White Dwarf
Wide Field Imager
WeitWinkel Flächen-Photometer und -Polarimeter
Zero Age Horizontal Branch
Zero Age Main Sequence
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149
Z USAMMENFASSUNG
Z USAMMENFASSUNG
Die vorliegende Arbeit beschäftigt sich mit der Kinematik von Horizontalaststernen (HB-Sternen1 ),
wobei die heißen Unterzwerge (sdB-Sterne2 ) einen Schwerpunkt bilden. Das Hauptziel ist hierbei,
mit Hilfe dieser Sterne die Struktur der Milchstraße zu untersuchen.
Blaue Horizontalaststerne (d.h. alle HB-Sterne heißer als RR-Lyrae-Sterne) sind sehr gut für Studien
der älteren Komponenten der Milchstraße geeignet, da sie hell sind und eine blaue Farbe haben – im
Gegensatz zu fast allen anderen Objekten in alten Populationen, wie die der Dicken Scheibe und dem
Halo3 . Blaue Horizontalaststerne sind daher leicht und auch in großen Entfernungen aufzufinden.
Ihre Spektren sind relativ unkompliziert und daher leicht zu analysieren. Nachteilig sind Verwechslungsmöglichkeiten von den kühleren blauen HB-Sternen (insbesondere HBB-Sternen) mit Hauptreihensternen, und die veränderlichen Radialgeschwindigkeiten vieler sdB-Sternen. Diese zeugen
davon, dass es sich bei vielen sdB-Sternen um enge Doppelsterne handelt.
Bisherige Studien des kinematischen Verhaltens von sdB Sternen kamen zu dem Ergebnis, dass diese
Sterne vor allem oder sogar ausschließlich Mitglieder der Galaktischen Scheibe sind, und zwar der
Dicken Scheibe (siehe z.B. de Boer et al. 1997a). Ein Ziel dieser Arbeit ist es, die lange vermutete
Halo sdB Komponente zu finden.
D ER T REND IN DER K INEMATIK VON S TERNEN DES H ORIZONTALASTES
Wir haben eine Stichprobe (Kapitel 3) von HBA-, HBB- und sdB-Sternen untersucht, für die mit dem
Hipparcos Satelliten Eigenbewegungen und Parallaxen gemessen wurden. Aus den Parallaxen haben
wir, unter Berücksichtigung des Lutz-Kelker-Effektes, die Entfernung der HB-Sterne bestimmt4 . Es
wurde ein Trend im kinematischen Verhalten gefunden: Die HBA-Sterne nehmen nicht an der Galaktischen Rotation teil, sie haben sehr exzentrische Umlaufbahnen und erreichen mitunter große Entfernungen zu der Galaktischen Ebene. Sie sind alle Mitglieder des Galaktischen Halos5 . Im Gegensatz
dazu folgen die untersuchten sdB-Sterne der Galaktischen Rotation. Sie bleiben auch stets in der Nähe
der Galaktischen Ebene, und ihre Bahnen haben nur eine kleine bis mittlere Exzentrizität. Sie sind
also Mitglieder der Scheibe. Bei den HBB-Sternen haben wir kein klares Bild erhalten, da uns hier,
wegen den Verwechselungsmöglichkeiten mit Hauptreihensternen, nur wenige wirkliche HBB-Sterne
zur Verfügung stehen. Zur Ergänzung haben wir außerdem RR-Lyrae Sterne untersucht, die sich an
der kühleren Grenze des HBA Bereichs anschließen. Man findet sowohl der Scheibe wie auch dem
Halo zugehörige RR-Lyrae Sterne, wobei letztere die Mehrheit bilden. Es gibt also einen Trend in der
Kinematik der Sterne entlang des Horizontalastes.
1
HB: “horizontal branch”, also Horizontalast.
sdB: “subdwarf B”, also Unterzwerge des Spektraltyps B.
3
Die anderen, helleren Sterne in alten Populationen, Rote Riesen und RHB-Sterne, sind nur schwer voneinander zu
unterscheiden.
4
In unserem Falle reicht die Genauigkeit der Parallaxen in den meisten Fällen nicht zur Entfernungsbestimmung von
Einzelsternen aus; daher musste eine Methode angewandt werden, die die gesamte Stichprobe miteinbezieht.
5
Diese Sterne wurden an Hand ihrer Metallizität und Bewegung aufgespührt, was zu einer Bevorzugung von HaloSternen führt, da diese sowohl metallarm sind und meist eine große Eigenbewegung oder Radialgeschwindigkeit zeigen,
während potentielle HBA Sterne in der Scheibe deutlich unterrepräsentiert sind.
2
150
K INEMATIK VON SD B-S TERNEN
Den Hauptteil dieser Arbeit stellt eine erweiterte Studie der Kinematik heißer Unterzwergen dar6 .
Hierzu wurden in Zusammenarbeit mit H. Edelmann (Bamberg) neue astrometrische, photometrische
und spektroskopische Daten für 58 sdB-Sterne aus dem Hamburg-ESO- (HE-) Katalog gewonnen.
Mit weiteren Sternen, für die Eigenbewegungen aus dem Hipparcos Katalog zur Verfügung stehen,
und den Sternen aus der früheren Studie von de Boer et al. (1997a) wurde die Anzahl der insgesamt
untersuchten Sterne auf 114 erhöht – also fast eine Verdreifachung gegenüber dem Sample von de
Boer et al. (1997a).
Mögliche Auswahleffekte können die Ergebnisse einer Studie wie dieser stark beeinflussen. Daher
haben wir eventuelle auswahlbedingte Verfälschungen und ihre mögliche Folgen diskutiert. Einerseits ist unsere Stichprobe weitgehend frei von Auswahleffekten, die durch die Identifikationsmethode entstehen könnten. Andererseits beschränken sich diese Kataloge auf Objekte bei mittlerer und
hoher Galaktischer Breite, so dass in unserer Stichprobe zu wenig Sterne in der Nähe der Galaktischen Ebene zu finden sind – daher vermuten wir, dass Sterne der Dünnen Scheibe in unserer Probe
unterrepresentiert sind.
DATEN
UND
DATENREDUKTION
In Kapitel 2 wird die Datenbeschaffung und -reduktion beschrieben. Helligkeiten und Eigenbewegungen sind aus Daten, die mit dem 1.54m Teleskop der Europäischen Südsternwarte aufgenommen wurden, bestimmt worden. Die Photometrie haben wir mit den Photometriepaketen der IRAF
Datenverarbeitungssoftware (Aperturphotometrie) bewerkstelligt; die Eichung erfolgte mit Hilfe der
(während der Beobachtungen aufgenommenen) Standardsterne von Landolt (1992).
Für die Bestimmung von Eigenbewegungen ist ein Vergleich zwischen alten und neuen Aufnahmen7
notwendig. Als Erstepochendaten für die Bestimmung der Eigenbewegungen ist der DSS1 herangezogen worden, eine digitalisierte Version des Palomar Observatory Sky Surveys (POSS), bzw. seiner
südlichen Ergänzung, des UK-Schmidt Survey. Leider sind diese Daten relativ jung; sie stammen
zumeist aus den 70er Jahren, so dass sich eine mittlere Epochendifferenz von nur ca. 25 Jahren
ergibt. Größere Epochendifferenzen würden genauere Eigenbewegungen liefern. Die Plattenkoordinaten (XY-Positionen) sowohl der Erst- wie auch der Zweitepochendaten haben wir mit Hilfe des
Programms SExtractor (Bertin & Arnouts 1996) bestimmt, welches gegenüber anderen Programmen,
etwa DAOPHOT, deutliche Vorteile (etwa Geschwindigkeit, Genauigkeit8 ) besitzt. Die astrometrische
Reduktion erfolgte nach dem Standardverfahren: Zunächst werden für jede Aufnahme die Plattenkoordinaten im Vergleich zu einem Referenzkatalog bestimmt, anschlies̈end die Eigenbewegungen. Das
Ergebnis wird dann in einer weiteren Iterationsstufe als Referenzkatalog verwendet. Diese Reduktion
haben wir mit der BAP-Software von M. Geffert (siehe Geffert et al. 1997) durchgeführt. Da für
die erste Iterationsstufe der Reduktion keine Referenzkataloge mit gemessenen Eigenbewegungen zur
Verfügung standen, haben wir die Eigenbewegungen als 0 mas/yr angenommen, was zur Folge hat,
dass die gemessenen Eigenbewegungen nur relative, aber keine absolute Eigenbewegungen sind. Die
relativen Eigenbewegungen haben wir dann mit Hilfe der Hintergrundgalaxien zu absoluten geeicht.
6
Dieser Teil wird in den Kapiteln 2 und 4 behandelt. Aus didaktischen Gründen ist die Reihenfolge, in der in diesem
Abschnitt die Aspekte der Arbeit zusammengefasst werden, verändert.
7
Erst- und Zweitepochendaten.
8
Dies bezieht sich auf den Unterschied in der Methode mit der die Koordinaten bestimmt werden. DAOPHOT verwendet
eine PSF, die sich auf eine einzige Form der Lichtverteilung stützt, während SExtractor das Zentrum jeder Lichtverteilung
bestimmt – daher ist SExtractor für digitalisierte Photoplatten und Galaxien besser geeignet.
151
Z USAMMENFASSUNG
Da uns nur ein Erstepochendatensatz vorlag, können wir keine genauen Angaben bezüglich der Fehler
machen; wir schätzen sie auf etwa 5 mas/yr.
Die Spektren hat H. Edelmann mit der MIDAS Software reduziert und danach Modellspektren an
die Sternspektren angepasst, um Temperaturen und Schwerebeschleunigungen zu bestimmen. Daraus sind dann mit Hilfe von Standardmethoden der Astrophysik die Entfernungen bestimmt worden.
Außerdem haben wir aus den Spektren Radialgeschwindigkeiten ermittelt. Der Fehler der Entfernungen beträgt 10 % und der der Radialgeschwindigkeiten 30 km s−1 .
K INEMATIK UND BAHNEN
Die Messdaten wurden zunächst in die Positionen und Geschwindigkeiten des Galaktischen Euklidischen Koordinatensystems (XY Z, U V W ) umgewandelt und die Orbital- (Θ) und Zentrifugalgeschwindigkeit (Φ) berechnet. Desweiteren haben wir mit Hilfe des Potentialmodells von Allen & Santillan
(1991b) Galaktische Umlaufbahnen für jeden der Sterne berechnet.
Wie in Kapitel 4 dargestellt, zeigt sich, dass die große Mehrheit der Sterne, wie in vorherigen Studien
auch, Mitglieder der Dicken Scheibe sind, eine Minderheit jedoch ein ganz anderes kinematisches
Verhalten hat. Letztere Sterne erreichen z.T. große Höhen überhalb der Galaktischen Scheibe, und
ihre Geschwindigkeiten unterscheiden sich stark von der Rotationsgeschwindigkeit der Galaktischen
Scheibe. Die Kinematik dieser Sterne und die Form ihrer Bahnen lassen vermuten, dass diese Objekte
zum Halo gehören. Einige dieser Sterne haben weitaus höhere Θ als jene der Sonne oder anderer
Scheibensterne, andere zeigen hingegen erheblich kleinere Umlaufgeschwindigkeiten; zwei Objekte
bewegen sich sogar signifikant retrograd. Unsere Halogruppe besteht also aus zwei Untergruppen,
einem “Hochgeschwindigkeitshalo” und einem “langsam rotierenden Halo”. Betrachtet man jedoch
die Umlaufgeschwindigkeiten über die gesamte Bahn (ausgedrückt in z.B. Θ oder Θmed ), so verschwinden diese Unterschiede. In Diagrammen wie z.B. Abb. 4.8 sind die Sterne beider Gruppen in
derselben Region zu finden. Der Unterschied zwischen beiden liegt lediglich in der Phase des Orbits,
in der sich die Sterne derzeit befinden (z.B. in der Nähe des Perigalaktikons die “schnellen” und in der
Nähe der Apogalaktikons die “langsamen” Sterne). Ob es trotzdem einen Unterschied in der Herkunft
der Objekte dieser beiden Gruppen gibt, lässt sich derzeit nicht klären. Immerhin kommen die Objekte der langsamen Gruppe zum Teil sehr nah an das Galaktische Zentrum heran, während die der
anderen ihr Perigalaktikon in der Nähe des Sonnenkreises haben. Der Anteil der Haloobjekte in der
gesamten Stichprobe liegt bei ca. 15 %. Dünne und Dicke Scheibe konnten wir nicht trennen, einige
unserer Sterne haben jedoch Umlaufbahnen, die denen der Dünnen Scheibe, etwa der der Sonne, sehr
ähneln.
D IE S KALENH ÖHE DER SD B-S TERNE
Als nächstes haben wir die z-Aufenthaltswahrscheinlichkeitsverteilung erstellt. Mit Hilfe der berechneten Umlaufbahnen kann man beispielsweise die Aufenthaltswahrscheinlichkeit in z-Richtung (oder
auch einer anderen Richtung) bestimmen und in ein Histogramm auftragen. Macht man dieses für alle
Sterne, so erhält man die Aufenthaltswahrscheinlichkeitsverteilung für das gesamte Sample.
Wir haben die Verteilung in z-Richtung untersucht und dabei festgestellt, dass die Verteilung (an
jeder Seite) zwei Steigungen hat, im Gegensatz zur einer ähnlichen, von de Boer et al. (1997a) an
einer kleineren Stichprobe vorgenommenen Analyse, in der nur eine Steigung gefunden wurde (siehe
Abb. 4.9). Die steilere von beiden, in der Mitte des Histogramms, hat eine ähnliche Steigung, wie die
von de Boer et al. (1997a). Außerhalb dieser zentralen Komponente haben wir eine weitaus flachere
152
Verteilung gefunden. Die daraus resultierenden Skalenhöhen betragen 0.9 kpc für die steile Komponente und 7 kpc für die flache, das Dichteverhältnis Dicke zu Dünne Scheibe liegt bei 1.2 %. Letztere
stellt den Halo dar, erstere die Dicke Scheibe. Eine weitere, der Dünnen Scheibe zuzuordnende Komponente konnten wir nicht finden, haben wir eine Obergrenze für eine sdB Population in der Dünnen
Scheibe bestimmt: Diese ist erheblich geringer als vermutet (allerdings erwartungsgemäß nicht sehr
genau), vermutlich weil es sich bei sdB-Sternen um entwickelte Sterne handelt, welche in der Dünnen
Scheibe9 gegenüber Populationen, in denen die Sternentstehung schon lange abgeschlossen ist, unterrepresentiert sind.
Zusammenfassend kann man sagen, dass die Verteilung von sdB-Sternen im Prinzip ähnlich der
Verteilung anderer massearmer Sterne ist und somit sdB-Sterne also in allen Populationen vorkommen, d.h. die sdB Sterne besitzen Sterne unterschiedlicher Metallizität als Vorstufen10 . Daher kann
eine Eigenschaft, wie z.B. die Metallizität, bei der Frage, ob sich Sterne zu sdB-Sternen entwickeln,
allenfalls eine untergeordnete Rolle spielen. Zwei Entstehungstheorien, die derzeit diskutiert werden,
sind die Entstehung durch Masseaustausch in engen Doppelsternsystemen, oder der Verlust der Hülle
durch außergewöhnlich starke Sternwinde. Beide Szenarien sind mit unseren Ergebnissen vereinbar.
K INEMATIK VON HBB-S TERNEN
Unter den insgesamt 80 Sternen aus dem HE-Katalog, die für dieses Projekt beobachtet wurden,
befinden sich auch 13 HBB-Sterne. Die Kinematik dieser Sterne haben wir zusammen mit der von
weiteren Sternen aus der Literatur analysiert (siehe Kap. 5). Leider sind unsere Ergebnisse hier
weniger aussagekräftig als bei den sdB-Sternen, da die aus der größeren Entfernung dieser Sterne resultierenden Tangentialgeschwindigkeiten ungenauer sind und die Stichprobe wesentlich kleiner ist.
Die HBB-Sterne sind sowohl im Halo wie auch in der Scheibe zu finden, einen “Hochgeschwindigkeitshalo” wie bei den sdBs gibt es nicht. Die Menge der Sterne reicht nicht aus, um eine aussagekräftige
z-Aufenthaltswahrscheinlichkeitsverteilung zu bestimmen. Legt man aber die für die sdB-Sterne
gefundene Verteilung über das Histogramm, so findet man eine recht gute Übereinstimmung. Sie
sind also ebenfalls in allen Populationen präsent. Daher sind vermutlich HBB-Sterne teilweise durch
dieselben oder ähnliche Prozesse wie die sdB-Sterne entstanden. Möglicherweise gibt es auch HBBSterne, die ähnlich wie die kühleren HBA-Sterne entstanden sind und es somit in der HBB-Region
einen Überlapp beider Entstehungsszenarien gibt.
D ISKUSSION
S TELLARE A SPEKTE
Welche Konsequenzen haben die Ergebnisse unserer Studie an der größeren Stichprobe von sdBSternen für den in Kap. 3 gefundenen Trend? Die Grundaussage, dass HBA-Sterne Haloobjekte und
die sdB-Sterne vornehmlich Mitglieder der Scheibe sind, bleibt bestehen. sdB- und HBA-Sterne werden offensichtlich durch unterschiedliche Prozesse gebildet. HBA-Sterne sind wohl aus sehr massearmen Vorläufersternen entstandene “klassische” Horizontalaststerne, wohingegen die sdB-Sterne entweder durch Massenaustausch in engen Doppelsternsystemen oder aber durch aussergewöhnlich
9
in welcher auch heute noch Sternentstehung stattfindet.
Die Sterne der Populationen der Milchstraße besitzen im Mittel unterschiedliche Metallizitäten. Objekte des Halos
sind im Allgemeinen metallarm bis sehr metallarm, die Sterne der Dicken Scheibe besitzen eine mittlere Metallizität und
die Sterne der Dünnen Scheibe, etwa die Sonne, haben eine recht große Metallizität.
10
153
Z USAMMENFASSUNG
starke Sternwinde (wie in D’Cruz et al. 1996 beschrieben) entstanden sind. Die im Temperaturbereich zwischen sdB- und HBA-Sternen angesiedelten HBB-Sterne können möglicherweise durch beide
Szenarien gebildet werden.
G ALAKTISCHE A SPEKTE
Unser Ergebnis für die Skalenhöhe der Dicken Scheibe von 0.9 kpc liegt im Bereich der Resultate
anderer Studien. Allerdings ist die Streuung der in der Literatur gefundenen Werte für die Skalenhöhe
relativ groß; die Werte schwanken zwischen etwa 0.6 kpc und 1.7 kpc. Leider lassen sich auf Grund
der Zusammenstellung unserer Stichprobe11 Dicke und Dünne Scheibe nicht trennen. Es ist zu vermuten, dass diese beiden Scheibenkomponenten sich kinematisch beträchtlich überlappen. Andere
Arbeiten, die auf Sternzählungen beruhen, kommen zu dem Ergebnis, dass Dicke und Dünne Scheibe
getrennt sind (z.B. Phleps et al. 2000).
Die Halo-Population unserer sdB-Sterne besitzt eine Hoch- und eine Niedriggeschwindigkeitskomponente. Die Werte für die mittlere Umlaufgeschwindigkeit von letzterer Komponente, der HBA-Sterne
und der metallarmen RR-Lyrae-Sterne, sind sehr ähnlich, und zwar leicht positiv. Also rotiert der
Halo unseren Ergebnissen nach leicht prograd. Eine Hochgeschwindigkeitskomponente des Halos
haben wir nur bei den sdB-Sternen gefunden. Es stellt sich die Frage, ob es bei anderen Sternen
ebenfalls solch eine Gruppierung gibt. Bei Hauptreihensternen gibt es Objekte mit ähnlich extremer
Kinematik, z.B. Barnards Stern. Zwei der sdB-Sterne aus der Hochgeschwindigkeitsgruppe besitzen
nicht nur ein extremes kinematisches Verhalten, sondern auch recht ähnliche Bahnen. Es könnte sich
hierbei um Objekte gemeinsamen Ursprungs handeln. Möglicherweise handelt es sich bei den meisten
Objekten dieser Gruppe um Sterne, die aus anderen, kleineren Galaxien stammen und durch Wechselwirkungen dieser (Zwerg)galaxien mit der Milchstraße Teil unserer Galaxis geworden sind. Viele
Entstehungsszenarien sehen derartige Ereignisse vor.
Desweiteren fiel uns auf, dass sich die mittleren Geschwindigkeiten in Richtung Galaktisches Zentrum (also Φ) bei allen Proben der Dicken Scheibe von Null unterschieden; die der Haloproben unterscheiden sich ebenfalls von Null, nur mit entgegengesetzten Vorzeichen. Nach Fux (2001) ist diese
Verschiebung gegenüber dem Nullpunkt bei den Sternen der Dicken Scheibe auf die Gegenwart eines
Balkens zurückzuführen. Seine Stichprobe aus Sternen der Dicken Scheibe zeigte einen ähnlichen
Wert wie der unsrige.
Abschließend diskutieren wir unsere Ergebnisse im Zusammenhang mit einigen Entstehungstheorien
von Halo und Dicker Scheibe. Während ein Teil des Halos durch Akkretion von Zwerggalaxien entstanden sein könnte, spricht doch die große Anzahl der Sterne, deren Bahn sie unmittelbar in die Nähe
des Galaktischen Zentrums führt, dafür, dass ein weiterer Teil durch einen Kollaps einer Protogalaxie
entstanden ist ähnlich dem Szenario von Eggen et al. (1962). Die Entstehung der Dicken Scheibe
scheint nur durch Wechselwirkungen der Dünnen Scheibe mit Zwerggalaxien erklärbar zu sein. Die
anderen Szenarien (z.B. Entstehung der Dicken Scheibe während des Kollapses als Zwischenstufe zur
Entstehung der Dünnen Scheibe) werden durch die Beobachtungsergebnisse nicht bestätigt.
11
die Dünne Scheibe war auch nicht das Hauptziel dieser Untersuchung.
154
C URRICULUM VITAE
Name:
Date of birth:
Place of birth:
Nationality:
Address:
Martin Altmann
26th May 1970
Pretoria/Republic of South Africa
german
Dondertstr. 119, 47623 Kevelaer
School career:
1977–1980:
Deutsche Schule Pretoria (DSP), Pretoria
1980–1984:
Max-Stibbe School, Pretoria
1984–1990:
Kardinal von Galen Gymnasium, Kevelaer
1990:
Abitur (final school exams)
Military service:
1990–1991:
General military service at 3./FArtBtl. 111 (surveyance for artillery),
Oldenburg in Oldenburg
University career:
1991–1997:
Study of Physics (Diploma) at the Rheinische Friedrich-Wilhelms-Universität Bonn
1991–2002:
Study of Astronomy (Promotion) at the Rheinische FriedrichWilhelms-Universität Bonn
1994:
Prediploma in Physics
07/1996–10/1997:
studentische Hilfskraft at the Sternwarte of the Univ. Bonn
1996–1997:
Diploma in Physics. Thesis about “Proper Motions and Orbits of 12
sdB stars” (Supervisor: Prof. Dr. Klaas S. de Boer)
10/1997–02/1998:
wissenschaftliche Hilfskraft at the Sternwarte of the University Bonn
03/1998–04/2001:
Scientific employee at the Sternwarte of the Univ. Bonn (DFG funded)
Since 11/2001:
Scientific employee at the Dr. Remeis Sternwarte, Bamberg in the
frame of the DIVA-project (Univ. Erlangen-Nürnberg, DLR funded)
155
L EBENSLAUF
L EBENSLAUF
Name:
Geburtsdatum:
Geburtsort:
Nationalität:
Anschrift:
Martin Altmann
26. Mai 1970
Pretoria/Republik Südafrika
deutsch
Dondertstr. 119, 47623 Kevelaer
Schullaufbahn:
1977–1980:
Deutsche Schule Pretoria (DSP), Pretoria
1980–1984:
Max-Stibbe School, Pretoria
1984–1990:
Kardinal von Galen Gymnasium, Kevelaer
1990:
Abitur
Wehrdienst:
1990–1991:
Grundwehrdienst bei 3./FArtBtl. 111, Oldenburg in Oldenburg
Studium:
1991–1997:
Physikstudium (Diplom) an der Rheinischen Friedrich-Wilhelms-Universität
Bonn
1994:
Vordiplom in Physik
07/1996–10/1997:
studentische Hilfskraft an der Sternwarte der Univ. Bonn
1996–1997:
Diplom in Physik. Diplomarbeit über “Eigenbewegungen und Orbits von 12
sdB Sternen” (Betreuer: Prof. Dr. Klaas S. de Boer)
1991–2002:
Astronomiestudium (Promotion) an der Rheinischen Friedrich-WilhelmsUniversität Bonn
10/1997–02/1998:
wissenschaftliche Hilfskraft an der Sternwarte der Universität Bonn
03/1998–04/2001:
Wissenschaftlicher Mitarbeiter an der Sternwarte der Univ. Bonn (Drittmittel,
DFG)
seit 11/2001:
Wissenschaftlicher Mitarbeiter an der Dr. Remeis Sternwarte, Bamberg (Univ.
Erlangen-Nürnberg, Drittmittel, DLR)
156
ACKNOWLEDGEMENTS
So finally, after a long voyage through astronomy, one major personal goal is now achieved – the PhD.
thesis. This would not have been possible without the help of my dear colleagues and friends in Bonn,
Bamberg and elsewhere.
First of all I have to thank Prof. Dr. Klaas S. de Boer for giving me the subject, advising me, agreeing
to be the supervisor and referee of my work. I would also like to thank Klaas for the way he leads the
Sternwarte, the degree of freedom he gave us, and the advice that we all often profited from.
Many thanks to Prof. Dr. Wilhelm Seggewiß for being the co-advisor of this thesis. I thank Wilhelm
for granting me observing time at Hoher List Observatory, for the discussions about astronomy, the
Eifel area, the early days of institutions like ESO/Calar Alto and many other things – and last but not
least for the interest in my Hoher List Gallery of Astronomical Images.
I am deeply indebted to Prof. Dr. Uli Heber for giving me the DLR DIVA position and such a wealth
of freedom that I could complete my thesis without compromise. Thanks for many fruitful discussions
about hot stars and keen interest in my work. Also thanks for the three talks for which he invited me
to Bamberg.
The DFG for granting me the PhD project (Bo779/21) and several Calar Alto trips. The DLR for my
current position (grant No. 50 QD 0102). I thank the Astronomische Gesellschaft for the travel aids
for the meetings in Munich (JENAM) and Napoli.
(For the less formal part, starting here, names are given without academic titles.)
Michael Geffert for the astrometric software and a great deal of advice on astrometric questions and
everyday’s lively banter.
Heinz Edelmann for sharing his data on the HE stars and completing this project together with me.
Ralf Napiwotzki for supplying me with spectral models and software. I have to thank Ralf for many
other things: for the many discussions we had about hot stars, Galactic structure, and many other
subjects, for the many pubs we went to and the many beers we consumed in those pubs, the many
people he introduced me to. He showed me that astronomy is more than just a science – it is fun! My
impression of German geography1 has certainly changed since I met you.
ESO and DSAZ (operated by the Max-Planck Institute for Astronomy, Heidelberg, jointly with the
Spanish National Commission for Astronomy) for granting me observing time at their observatories at Calar-Alto and La Silla. The people on the two mountains for their help: Uli Thiele, Felipe
Hoyo, Manolo Alises, Jesus Aceituno, Manuel Aguirre, Ana Guijarro, Herr Frahm, Herr Wilhelmi and
others on Calar-Alto, Patrick Francois, Ivo Saviane, Francesco Selman, Tom Augusteijn, Hermann
Böhnhardt, Lisa Germany et al. on La Silla. Further thanks go to Valerio (the famous Calar-Alto Taxi
driver) and the people at the ESO guest house and Christa Euler for the travel reservations.
Tom Marsh (Southampton) for kindly supplying me with new systemic radial velocities of sdB binaries.
Marcio Catelan (Universidad Catolica de Santiago) for his interest in my work and enthusiasm in
helping me with my FONDECYT applications, and being my “investigador patrocinante”.
1
now I know that South-Germany starts at the Eider river.
157
ACKNOWLEDGEMENTS
René Méndez for offering me the 3 month stipend at ESO/Vitacura in 2003.
Steffen Mieske, Marcio Catelan, Michael Hilker, Matı́as & Carola Gomez for various pub evenings in
Santiago.
Kyril Panov and Wilhelm Seggewiss for arranging an opportunity for observing trips to Rozhen Observatory, Bulgaria in 1996-1998. The staff of the observatory for their support.
The organisers and participants of the conferences in Liège (1999), Puebla (2001) and Napoli (2002)
(and those of the AG-Tagungen, GK-meetings etc.) for the great job they did in organising these
memorable meetings. A special thanks to Stefan Dreitzler for the organisation of the mini symposium
during the JENAM-Meeting in 2001. And once again Klaas for giving me the opportunity to go to
Puebla.
Hans-Jörg Hagen, Dieter Engels and colleagues at Sternwarte Hamburg, for giving me access to the
HS-archive and assisting me during my stay in Hamburg.
Our system administrators Jochen M. Braun, Oliver-Mark Cordes, Horst Drechsel, Georg Drenkhahn,
Günter Lay, Ole Marggraf, Uwe Nass, Rainer Sterzer and Jean-Marie Will for keeping (at least) one
eye on the computer system of the Sternwarte.
Many thanks to the people of the workshop at Hoher List, namely Martin Polder, Günter Klink and
Franz Josef Willems for keeping the Telescopes in good shape, the dewars full, taking me with the
“Dienstwagen” to Gerolstein and Daun, some tools, and the newest news of what’s going on at the
HoLi.
Klaus Reif (also known as “Shutter Klaus”) and the CCD team, i.e. Henning Poschmann, Philipp
Müller and Christian Brauer for the CCDs and shutters, and the quick help if something went wrong
again.
The office staff, Elisabeth Danne, Alice Lindner, Kathy Schrüfer and Edith Day, for helping me with
so many administrative things; without this help most of would certainly have become hopelessly
stuck in the pitfalls of university and public service bureaucracy.
Lindsay King, Andrea Dieball, Ole Marggraf, Manuel Metz, Jörg Sanner, Philip Willemsen for reading parts of my work.
Peter Schneider for bringing in a “wind of change” when he moved here with his group, and many
new ideas.
Oliver Cordes for the fun we had during our observing trips to Calar-Alto and on the HoLi, the red
wine we consumed, and the holidays we has in Andalucia. Ole Marggraf (Taxi Ole) for driving me
home so many times after parties. And to both for helping me with my computer problems (apart
from their sysadmin duties). Jörg Sanner and Andrea Dieball for accompanying me over a long time
in the Sternwarte. Lindsay King for so many things, e.g. advice concerning applications/jobs, clothes
(for job interviews). Stay the way you are! Philip Willemsen and Thorsten Kaempf for asking me
233,000 questions (and still believing that I know something). Klaus Bagschik for discussions about
photography and much more, “Frau Generalstäbin”, Steffi Mühle for organising three (shortly it will
be four) new years “conventions” at Hoher List. Wolfgang Braun for his chocolate. Hanne Hämmerle
for her happy and lively “Bavarian2 ” nature, and the way she made us keep the institute kitchen tidy.
The board game gang, namely Olli Cordes, Ole Marggraf, Jörg Sanner, Thomas Erben, Wolfgang
Braun, Martina Kleinheinrich, Hanne Hämmerle, Klaus Bagschik, Steffi Mühle and all the others.
The current and former co-inmates of office 3.08: Jochen Braun, Wolfgang Braun, Steffen Mieske,
Philipp Richter, Manuel Metz, Andrea Kayser (and countless school practicants of Michael G.).
2
I know you’re a Swabian, but from Bavarian Swabia.
158
Thanks to the Xblast-players: Olli, Ole, Jörg, Jochen, Benny, Philipp, Dominik, Pfennich (Mark),
Holger, Thomas P., Gerd-Hans, Dimitris, Manuel, Wolfgang, Matı́as and “Lichtgestalt” (Hartmut).
The other people I met during my time at the Sternwarte, namely: Yolanda Aguilar Sánchez, Thilo
Bauer, Thomas Bausen, Hartmut Bluhm, Robert Breinhorst, Peter Brosche, Chen Li, Till Credner,
Nadja Dencheva, Boris Dirsch, Michaela Döllinger, Hildegard Domgörgen, Justina Engelmann, Edward H. Geyer, Matı́as Gomez, Dimitris Gouliermis, Eva K. Grebel, Benjamin (Benny) Greiner,
Daniel-Rolf Harbeck, Fabian Heitsch, Michael Hilker (and Yaneth), Pascal Hirsch, Peter Kahabka,
Andrea Kayser, Markus Kissler-Patig, Sven Kohle, Ralf Kohley, Gerd-Hans Krämer, Søren Larsen,
Gisela Maintz, Michael Odenkirchen (thanks for the software for the orbits etc.), Amelia OrtizGil, Thomas H. Puzia, Klaus Reif, Tom Richtler, Dominik Rosenbaum, Holger Schmidt, Jelena H.
Schmidt, Jürgen Schmoll, Jörg D. Schumann, Oliver Schwarz, Britta Seifert, Jörg Stegert, Armin
Theissen, Hans-Joachim Tucholke, Bernhard Wierig, Marc Wittlich, and Johannes Wünsch. It has
been a good feeling that everyone would spend a few minutes for questions and discussions at any
time.
The Dr. Remeis Sternwarte wouldn’t be half as friendly and nice place without the “Remeisen”,
namely Michael Bauer, Irmela Bues, Horst Drechsel, Heinz Edelmann, Sigi Falter, Uli Heber, Christian Karl, Thorsten Lisker, Sabine Moehler, Ralf Napiwotzki, Simon O’Toole, Eva-Maria Pauli, Zorica Pavcovic, Markus Ramspeck, Rainer Sterzer. Thanks also for the many nice evenings we spent
in Bamberg pubs. Special thanks to my Bamberg office mates Christian Karl, Zorica Pavcovic and
Thorsten Lisker.
The “lens group”: Lars Bähren, Maruša Bradač (keep on photographing), Douglas I. Clowe (“Uhhuh”, and the explanations of how the US system really works), Oliver Czoske, Jörg Dietrich (Thank
you for our combined (birthday/farewell) party on the roof), Thomas Erben (also for informations
about the EIS Survey and wide field imaging in General), Marco Hetterscheidt, Lindsay J. King,
Martin Kilbinger, Martina Kleinheinrich, Marco Lombardi (thank you for the pizza and the ESOtemplate), Joan-Marc Miralles, Abouzar Najafi, Peter Schneider, Mischa Schirmer (see also Thomas
Erben) and Patrick Simon.
Susanne Hüttemeister for the UGC 2855/66 project, and Eva Manthey for reducing the data.
Christian Henkel for his help in finding a place to print this thesis.
Bernhard and Susanne Wierig for their help in one of the more difficult times.
Ralf Belger, Angela Kreuels, Hans-Jörg Dirks and Mariana Panova for their friendship (even if mostly
per email nowadays).
My family.
This research has made use of NASA’s Astrophysics Data System Bibliographic Services (ADS), the
Centre de Données Astronomiques Stellaires (CDS) data archive in Strasbourg.
I have always been afraid of forgetting someone in the acknowledgements. I hope I did not. Probably
I did. Forgive me!
159