Parameter determination of a binary star system

Parameter Determination of a Binary Star System

Diploma Thesis

at the Institut für Theoretische Physik,
Technische Universität Graz
carried out at the Oddelek za Jiziko,
Univerza v Ljubljani

Fabian Gottfried Prilasnig

September 2001

Contents

Preface ... 6

1 Review of Binary Stars  ... 8
1.1 Introduction ... 8
1.2 Observational Classifieation of Binary Stars  ... 9
1.3 Visual Binaries ...  10
1.3.1 Orbital Elements ...  11
1.3.2 Mass Determination  ... 12
1.4 Astrometrie Binaries ... 14
1.5 Speetroseopie Binaries  ... 14
1.5.1 Orbital Elements ... 15
1.5.2 Double-lined Speetroseopie Binary Star  ... 15
1.5.3 Single-lined Speetroseopie Binary Star  ... 17
1.6 Eclipsing Binaries  ... 18
1.6.1 Phenomenologieal Classifieation  ...  19
1.6.2 Morphologieal Classifieation  ...  24
1.7 The Importanee of Data Derived from Eclipsing Binaries ... 28

2 Spectroscopy  ... 29
2.1 Astrophysieal Speetra  ... 30
2.2 Radial Veloeities ... 32
2.3 Speetrophotometry.  ... 32
2.4 Line-Profile Analysis  ... 33

3 Photometry  ... 35
3.1 Photoelectrie Photometry  ... 35
3.2 Two-Star Photometers ... 36
3.3 Photoeleetrie Observations.  ... 36
3.4 Imaging Data  ... 38

4 IRAF - Image Reduction and Analysis Facility  ... 39
4.1 A Short Introduetion to Analysis of Single Dispersion Speetra  ... 39
4.1.1 Philosophy and Praetiee of IRAF  ... 39
4.1.2 IRAF Set-up  ... 40
4.1.3 Aperture Extraction  ... 42
4.1.4 Wavelength Calibration  ... 44
4.1.5 Flux Calibration  ... 45
4.2 Reducing Echelle Spectra ... 46
4.2.1 Introduction ... 46
4.2.2 Processing Details ... 46

5 Binary System UV Leonis ... 52
5.1 UV Leonis ... 52
5.2 The 182-cm Telescope at Cima Ekar (Asiago) ... 52
5.2.1 Instrumentation of the Asiago 182-cm Telescope ... 53
5.3 The Pika Telescopes at Crni Vrh Observatory ... 54
5.3.1 Crni Vrh Observatory ... 54
5.3.2 The ACIT Imaging System  ... 54
5.3.3 The AlT Imaging System ... 55
5.4 Spectroscopical and Photometrical Results ... 56
5.4.1 Parameter Determination of UV Leonis ... 56
5.4.2 The Radial Velocity Curve of UV Leonis ... 57
5.4.3 The Band V Light Curves of UV Leonis ... 59
5.4.4 Discussion ... 61

Epilogue ... 68

Preface

The focus of this work about binary star systems is on model applications and selections of an algorithm to determine the parameters of individual binaries. It consists of four major parts: a general introduction to the theory of binary stars (Chapter 1); introductory material about spectroscopy and photometry (Chapter 2 and 3); a description of IRAF (Imaging Reduction and Analysis Facility) - this is a software program which allows the reduction and the analysis of gathered data of astronomical objects - and its application on parameter determination of such a binary system (Chapter 4); and the presentation of the two observatories Crni Vrh and Asiago, and of the spectroscopical and photometrical results of the binary system UV Leonis (Chapter 5).

Chapter 1 presents the ideas and concepts that are necessary to understand the interaction of binary systems and to get a physical overview of the field. First, the classical classification of binary stars based on observational results is given, followed by brief descriptions of each type of these systems. In particular, the issues of what can be derived from spectroscopic and eclipsing binary stars and why these data are relevant to astrophysics in general are considered. Further, the general concept of parameter determination for each type of binary systems and of equipotential surfaces in case of eclipsing binaries is introduced. Since binary star analysts need understanding of observational data, some background on the data base and methods of data acquisition is necessary. Therefore, Chapter 2 and 3 review the two most common methods of data analysis, spectroscopy and photometry. The intention is to summarize aspects of observational astronomy relevant to light curve acquisition and modeling.

Chapter 2 begins with an overview of astrophysical spectra and their two most important features: radiative transfer and spectrallines. In addition, the characteristics of radial velocities and the advantages of spectrophotometry are shortly explained. Finally, the most basic mechanisms of spectralline broadening, which originate in the star itself, are enumerated.

Chapter 3 intends to clarify the importance of photometry in optical astronomy. It reaches from photoelectric photometry, still the most precise and accurate means of obtaining flux measurements, via two-star photometers and the description of the process of standardization of photoelectric data to CCD ("charge couple device") photometry, whose main advantage is that it can detect many sources simultaneously and that detection of faint sources is possible even in the presence of bright sources.

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Chapter 1

Review of Binary Stars

1.1 Introduction

Binary stars are important, first, because they are numerous. The observed frequency of spectroscopic binaries detected in the galactic halo is not significantly different from that in the disk, despite differences in kinematic properties and chemical composition.

It is approximately 20% but the actual frequency is higher because many binaries remain undetected. In the solar neighbourhood the frequency is more than 50% - because of the advantage of proximity so that proper motion variations can be detected and several stars are in fact multiple systems.

The second reason for the importance of binaries is that they are the primary source of our knowledge of the fundamental properties of stars, for example, the direct determination of the mass of any astronomical object. This requires measurable gravitational interaction between at least two objects (galaxy-galaxy, star-star, star-planet, planet-satellite).

In galaxy-galaxy interactions, the distances and separations are so large that no detectable motion on the plane of the sky is possible. In star-planet interactions only the star′s motions are detectable, and the properties of that star must be assumed, mainly on the basis of previous binary star studies, in order to deduce the properties of the planet.

In star-star interactions, the variations in position and velocity caused by orbital motion are detectable for a wide range of stellar separations. It is often the case that both stars may be studied in any of several ways, depending on their distance, brightnesses, and motions.

Other basic properties of stars and of the systems they constitute can be determined through analysis of observational data, depending on the observational technique by which the interaction is studied. 

1.2 Observational Classification of Binary Stars

1. Optical double:

These systems are not true binaries but simply lie along the same line of sight. As a consequence of their large physical separations, they are not gravitationally bound and are not useful in determining stellar masses.

2. Physical double:

These systems are true binaries in gravitationally bound orbits. There are different types of such systems and the most common ones are listed below.

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