This work is protected by copyright and other intellectual property rights and duplication or sale of all or part is not permitted, except that material may be duplicated by you for research, private study, criticism/review or educational purposes. Electronic or print copies are for your own personal, non- commercial use and shall not be passed to any other individual. No quotation may be published without proper acknowledgement. For any other use, or to quote extensively from the work, permission must be obtained from the copyright holder/s. Fundamental parameters of subgiant stars in detached eclipsing binary systems Jessica Ann Evans Doctor of Philosophy Keele University March, 2019 i Abstract Detailed studies of stars in long-period, detached eclipsing binary systems remain one of the best ways to test stellar evolutionary models. With so many detections of planets outside of the solar system, research has turned to the characterisation of these planets, which requires a good understanding of the planet host star. For the majority of single stars, determinations of mass and age must come from stellar evolutionary models. For the planet's characterisation to be correct, the stellar evolutionary models need to be correct, and uncertainties from any free parameters must be understood and calibrated. This thesis looks at determining fundamental parameters (mass, radius, temper- ature, composition) for four newly discovered detached eclipsing binary systems, each with a subgiant component, to calibrate the stellar evolutionary models. AI Phe, an- other such system, commonly used for this purpose, has also been studied and has updated parameters. A combination of high-precision ground-based photometry and UVES spectra has enabled the masses to be measured to a typical precision of 0.35% and the radii to 1.4%. Effective temperatures have been found for three of the new systems and AI Phe, while a metallicity has been found for two systems. Calculated distances are found to be in excellent agreement with those provided in the first data release from the Gaia mission. These parameters act as constraints in fitting GARSTEC stellar evolutionary models, to show how it is possible to start constraining the free parameters in these models. Here, the initial helium abundance and mixing length have been explored, but more detailed models are required to fully explore correlations between the two param- eters. These systems provide benchmark systems in a region of the Hertzsprung-Russell diagram that was previously empty, and highlight the need for further calibration work in preparation for upcoming space missions such as PLATO. ii Acknowledgements Firstly, I would like to say a huge thank you to my supervisor, Dr Pierre Maxted for all his advice, help and guidance, for his patience every time I asked a silly question, and likewise for the more puzzling questions. I would like to thank Dr Aldo Serenelli at the Institute of Space Sciences (ICE/CSIC-IEEC) in Spain, for all his help and patience running the stellar evolutionary models. His advice and opinions have been invaluable for the analysis. I would like to thank Dr Barry Smalley for helping me understand some of the complexities of stellar spectroscopy{I think there is much more to learn and understand, but I at least have a good starting point. Thanks to Dr John Southworth for the various bits of help with his codes and binary analysis. I would also like to thank any other people who have given me advice over the course of this project, even if it was small, it was still appreciated. I cannot write an acknowledgement section without thanking my soon-to-be hus- band, Daniel. From helping me use Linux and Python, to calmly pointing out the silly coding error that made it fail (again). He has supported me and helped me stay focused through the entire project. I cannot thank him enough. There are many other people who have supported me and given encouragement throughout the project, my Dad, my best friends, my brothers, you know who you are, thank you. Thank you to the Science and Technology Facilities Council (STFC) for the funding which has allowed me to carry out this research. Part of this work is based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programme 094.D-0190(A). WASP-South is hosted by the South African Astronomical Observatory and we are grateful for their ongoing support and assistance. This research has made use NASA's Astrophysics Data System,\Aladin sky atlas" (developed at CDS, Strasbourg Observatory, France, Bonnarel et al. 2000; Boch & Fernique 2014), the SIMBAD database, (operated at CDS, Strasbourg, France Wenger et al. 2000). Much of the work has used Astropy (a community-developed core Python iii package for Astronomy, Astropy Collaboration et al. 2013), NumPy (van derWalt, Colbert & Varoquaux 2011), Matplotlib (Hunter 2007), emcee (Foreman-Mackey et al. 2013) and corner (as both corner.py and triangle.py, Foreman-Mackey 2016). Also thanks to all those who have contributed to the development of the files needed for the LATEX template that has been used to write this thesis. It would have taken far longer without the template, your efforts are greatly appreciated. Now, enough of the mushy stuff. To the science! iv Contributions by others Thank you to the following people for their contributions towards the work in this thesis. • The telescope proposal for the UVES spectra (described in Section 2.1.4) was written by Dr P. Maxted. • Reduction of the SALT/HRS spectra was carried out by A. Kniazev. • The initial target selection (Section 2.3) and the analysis to obtain initial ephemerides for the systems (Section 3.1), were carried out by Dr P. Maxted. • The fitmag code and analysis of the system WASP0639-32, which appears in Chapter 4 and in Kirkby-Kent et al. (2017), were carried out by Dr P. Maxted. • All stellar evolutionary tracks used in Chapter 5, Kirkby-Kent et al. (2016) and Kirkby-Kent et al. (2017) were generated by Dr. A. Serenelli at the Institute of Space Sciences (ICE/CSIC-IEEC) in Spain. • The modvobs code, which is used in Chapter 5 and Kirkby-Kent et al. (2016) was written by Dr P. Maxted. • The code and fits presented in Section 5.2.4 of Chapter 5 and in Kirkby-Kent et al. (2017), have been generated by Dr A. Serenelli. • The photometric analysis of the star near to AI Phe in Section 3.2 of Kirkby- Kent et al. (2016) was carried out by D.F. Evans. v Contents Abstract ....................................... i Acknowledgements ................................ ii Contributions by others ............................. iv 1 Setting the scene ............................... 1 1.1 Introduction . .1 1.2 Introduction to eclipsing binary stars . .5 1.3 Subgiant stars and their place in stellar evolution . 12 1.4 Stellar evolutionary models . 17 1.4.1 Different evolutionary models . 18 1.4.2 Issues with current models . 19 2 The data and binary systems ....................... 21 2.1 Spectra . 21 2.1.1 What is a spectrum? . 22 2.1.2 Echelle´ spectra . 23 2.1.3 General spectra reduction . 24 2.1.4 VLT/UVES spectra . 28 2.1.5 SALT HRS spectra . 31 2.2 Photometry . 33 2.2.1 What is photometry? . 33 2.2.2 WASP photometry . 37 2.2.2.1 The WASP project . 38 2.2.2.2 WASP reduction in a nutshell . 39 2.2.2.3 Initial processing . 39 2.2.3 SAAO 1.0-m photometry . 42 2.2.3.1 Reduction . 44 2.3 The five targeted systems . 46 2.3.1 AI Phoenicis . 46 2.3.2 The WASP targets . 48 3 Mass and radius measurements ...................... 52 3.1 Ephemerides . 52 3.1.1 AI Phe . 52 3.1.2 WASP1046-28 . 55 3.1.3 WASP1133-45 . 60 3.1.4 WASP0928-37 . 60 3.2 Radial velocities & spectroscopic orbits . 60 3.2.1 Radial velocities . 61 3.2.1.1 Methods for measuring radial velocities . 63 vi 3.2.1.2 Chosen radial velocity techniques . 68 3.2.1.3 Measured radial velocities . 69 3.2.2 Fitting spectroscopic orbits . 74 3.2.2.1 The principle of radial velocity fitting . 76 3.2.2.2 Orbit fitting with SBOP . 76 3.2.2.3 Spectroscopic orbit parameters . 82 3.3 Lightcurve parameters . 87 3.3.1 Modelling codes . 87 3.3.2 Error analysis . 89 3.3.2.1 Checking for local minima . 90 3.3.2.2 Prayer-bead . 91 3.3.3 Choosing appropriate lightcurve parameters . 92 3.3.4 WASP detrending . 102 3.3.5 Priors - e cos !, e sin ! ....................... 104 3.3.6 Lightcurve parameter results . 106 3.3.6.1 AI Phe lightcurve parameters . 107 3.3.6.2 WASP0639-32 lightcurve parameters . 109 3.3.6.3 WASP0928-37 Lightcurve Parameters . 109 3.3.6.4 WASP1046-28 lightcurve parameters . 115 3.3.6.5 WASP1133-45 lightcurve parameters . 117 3.4 Combining orbital and lightcurve parameters . 120 3.5 Summary . 124 4 Temperatures and other spectroscopic parameters .......... 125 4.1 Techniques and parameters of spectroscopy . 126 4.1.1 Parameters though spectral fitting . 128 4.1.2 Parameters through equivalent widths . 129 4.1.3 Other methods . 131 4.2 My spectroscopic methods . 132 4.2.1 Disentangling . 132 4.2.2 Calculating equivalent widths . 139 4.2.3 Spectroscopic parameters from equivalent widths . 142 4.2.3.1 Ionisation and excitation balancing . 142 4.2.3.2 Equivalent width fitting . 143 4.2.3.3 EW-fitting testing . 145 4.2.4 Overall results . 151 4.2.4.1 Fitting Hα wings .