A study of binary star orbits using precise radial velocity measurements with the HERCULES spectrograph A dissertation submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Astronomy in the University of Canterbury by Siramas Komonjinda University of Canterbury New Zealand 2008 c Copyright by Siramas Komonjinda 2008 Acknowledgments Before the start of this dissertation, I would like to spend these pages to express my gratitude to many individuals and organizations who provide assistance during my PhD study. This dissertation could not have been written without them. Firstly, I would like to thank my supervisor, Prof. John Hearnshaw. John always gives me advice, guidance and suggestions, not only on my research work but also on how to live in New Zealand. He always patient in describing Astronomy to me as well as while he did the proof reading of this dissertation. Many suggestions on my research came from my co-supervisor, Dr. David Ramm, whom I also thank. David gave me many technical advice, and ideas on binary star re- search. Further, I would like to deserve my acknowledgment to my associated supervisor, Dr. William Tobin, and my mentor, Dr. Richard Watts. I would like to thank many people at Mt John University Observatory for all their help and support, including Alan, Pam, Maryrose, Nigel, Steve and Paul. I would like to acknowledge Alan and Pam, who helped me to solve problems during nights and observed all the photometric data in this research. I also thank David and Stuart for spectroscopic observations on the stars I studied in this research. There are staffs and students at the Department of Physics and Astronomy who helped me on so many things, particularly Gill Evans for her help on the first few days I arrived in New Zealand. I would like to thank Duncan for his great contribution of his MATLAB code for measuring the rotational velocity of a star and broaden the stars’ spectra. This research gratefully acknowledges the efforts and work of the CDS and NASA. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France and the NASA’s Astrophysics Data System Bibliographic Services. I would like to thank my Thai friends and the Thai communities in Christchurch who made me feel like home here. Many special thanks to Jimmy and Wast, Fon, Vi, Puin, Pear, and others, for all the days we had together. Thanks for all your support, especially for the last few months when I tried to finish this dissertation. During this research, I have financial support from a Thai Government Scholarship. I iv would like to thank the director of National Astronomical Research Institute of Thailand Assoc. Prof. Boonrucksar Soonthornthum, my MSc supervisor who encouraged me to come to New Zealand, for all his help. I also would like to thank the staff at the Department of Physics at Chiang Mai University, the Royal Thai Embassy in Wellington, the Office of Civil Service Commission in Bangkok and the Office of Education Affair in Canberra. Several trips to conferences and summer schools were supported by the D. W. Moore fund, the Frank Bradshaw & Elizabeth Pepper Wood fund, the IAU, the Vatican Ob- servatory, RSNZ, RASNZ and the Department of Physics and Astronomy. During those trips, I met several people and had an opportunity to discuss my research. Finally, I would like to thank my family for their understanding, unwavering support and belief that I would eventually finish this thesis. Many difficult times happened during this research, but they got me through to this day. Abstract of the Dissertation A study of binary star orbits using precise radial velocity measurements with the HERCULES spectrograph by Siramas Komonjinda Doctor of Philosophy in Astronomy University of Canterbury, 2008 Orbits of spectroscopic binary systems have been studied for more than a century. Over three thousand orbits of spectroscopic binary systems have been derived. These orbits are based on the radial velocities measured from the spectra recorded by a photographic plate to a high precision spectrum observed from a modern spectrograph. In many cases, the shape of the orbit was assumed to be circular, of hence the eccentricity is zero. This assumption is based on the fact that a small eccentricity (e < 0.1) measured from the observed data might be a result from the error of observations or from the intrinsic variation of a spectroscopic binary system. Sixteen southern spectroscopic binary systems, including twelve single-lined binaries and four double-lined binaries, were selected to study in this research program. These systems were assumed to have circular orbits or have very nearly circular orbits (e < 0.1) from their previous published solutions. The HERCULES spectrograph was used in conjunction with the 1-m McLellan telescope at Mt John University Observatory to collect the spectra of these systems. The observations, taken from October 2004 to August 2007, comprised about 2000 high-resolution spectra of spectroscopic binary systems and standard radial-velocity stars. Radial velocities of spectroscopic binary systems were measured from these spectra and orbital solutions of the systems were derived from these radial velocities. It was found that from HERCULES data, we are able to achieve high-precision orbital solutions of all the systems studied. The best-fit solutions can be improved as much as 70 times from the literature’s orbital solutions. It has been found that the precision of vi a system depends on the rotational velocities of the components as well as the level of their chromospheric activity. We are able to confirm the eccentricity in the orbit of only one of the selected spec- troscopic binary systems, HD 194215. Its eccentricity is 0.12329 0.000 78. The small ± eccentricities of other systems are not confirmed. There are four systems; HD22905, HD38099, HD85622 and HD197649, that have circular orbital solutions from the large errors in their measured eccentricities. Two systems, HD 77258 and HD 124425, have too small eccentricities, e =0.000 85 0.000 19 ± and 0.002 60 0.000 99 to be acceptable. ± An intrinsic variation is a presumed cause of the spurious eccentricities derived from the data of the other eight systems. Photometric data from Mt John University Obser- vatory service photometry program, as well as the photometric data from the Hipparcos satellite and information of these systems from the literature, using various methods and instruments, give a wider view on the systems’ behaviour. It is possible that the spurious eccentricities derived for these systems result from the eclipsing behaviour of a system (HD 50337), or from the nature of the components, such as, the distortion of their shape (HD 352 and HD 136905), their chromospheric activity (HD9053, HD3405, HD77137, HD101379 and HD155555), or stellar pulsation (HD 30021). Models of the active chromosphere system, HD 101379, have been simulated. An analysis of synthetic radial velocity data shows that spots on the star’s photosphere can cause a spurious eccentricity. The values of the spurious eccentricity and the longitude of periastron are dependent on the spot size, the spot temperature, and the position of the spots. Table of Contents 1 Introduction .................................... 1 1.1 Thestudyofbinarystars. 1 1.2 Classificationofbinarystars . ... 2 1.2.1 Visualbinaries ............................ 2 1.2.2 Spectroscopicbinaries . 3 1.2.3 Eclipsingbinaries ........................... 4 1.2.4 Binary systems by other methods . 5 1.3 Themotivationandgoalofthisstudy. ... 5 1.4 Thesiscontent................................. 7 2 Binary Star Systems .............................. 9 2.1 Geometryofbinarysystems . 9 2.1.1 Theequationofmotion. 10 2.1.2 Interpretation of spectroscopic binary radial velocity ....... 13 2.2 General perturbation in binary systems . ..... 16 2.2.1 The Roche model and the classification of binary systems..... 16 2.2.2 Apsidalmotion ............................ 19 2.2.3 Circularization and synchronization . .... 21 2.2.4 Thirdbody .............................. 23 3 Observations and Data reductions ...................... 26 3.1 Instrument: the HERCULES spectrograph . ... 26 3.1.1 Introductiontospectrographs . 26 3.1.2 HERCULESspectrograph . 27 3.2 Theprogrammestars............................. 29 3.3 Observational process and statistics . ...... 31 vii viii CONTENTS 3.4 The reduction of HERCULES spectra . 34 4 Methods of data analysis ............................ 38 4.1 Radial-velocity measurement . ... 38 4.1.1 Thecross-correlationmethod . 38 4.1.2 Selectionofspectralrange . 40 4.1.3 Cross-correlation peak and the radial-velocity measurements . 40 4.1.4 Two-dimensional cross-correlation . .... 44 4.1.5 Weighted-mean radial velocities . .. 46 4.1.6 Standardradial-velocitystars . .. 46 4.2 Orbital analysis from radial velocities . ....... 50 4.2.1 Least-squares differential correction . ..... 51 4.2.2 Errorestimation ........................... 53 4.2.3 Improvement of an orbital solution by fixing some elements and combining HERCULES data with historical data . 53 4.3 Problem of a small-detectable eccentricity . ....... 55 4.3.1 Systematic errors in a measured radial velocity . ...... 55 4.3.2 Statistical test of low-eccentricity orbital solutions......... 57 4.4 Inverse modelling of binary star systems . ..... 63 4.4.1 Spot model of a binary system ζ Trianguli Australis . 64 5 Orbital solutions of single-lined spectroscopic binaries ......... 67 5.1 Photometric observations of binary systems . ...... 67 5.2