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This Work Is Protected by Copyright and Other Intellectual Property Rights 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 properties of M-dwarfs in eclipsing binary star systems Samuel Gill Doctor of Philosophy Department of Physics, Keele University March 2019 i Abstract The absolute parameters of M-dwarfs in eclipsing binary systems provide important tests for evolutionary models. Those that have been measured reveal significant discrepancies with evolutionary models. There are two problems with M-dwarfs: 1. M-dwarfs generally appear bigger and cooler than models predict (such that their luminosity agrees with models) and 2. some M-dwarfs in eclipsing binaries are measured to be hotter than expected for their mass. The exact cause of this is unclear and a variety of conjectures have been put forward including enhanced magnetic activity and spotted surfaces. There is a lack of M-dwarfs with absolute parameters and so the exact causes of these disparities are unclear. As the interest in low-mass stars rises from the ever increasing number of exoplanets found around them, it is important that a considerable effort is made to understand why this is so. A solution to the problem lies with low-mass eclipsing binary systems discovered by the WASP (Wide Angle Search for Planets) project. A large sample of these systems have been followed up with spectroscopic orbits that ultimately exclude them from the planet- hunting process. In this work I obtained follow-up photometry for 9 of these systems and used these data to measure the absolute parameters of each star. These will eventually be used to create empirical calibrations for low mass stars when the number of EBLMs (eclipsing binary, low-mass) measured within this framework increases. Breaking the mass degeneracy required supplementary information from evolutionary models and the primary stars atmospheric parameters. I successfully created, tested and de- ployed a spectral analysis routine which used wavelet decomposition to analyse the spectra of FGK stars in exoplanet/eclipsing binary systems. Careful selection of wavelet coeffi- cients filter out large systematic trends and noise typically observed in spectra. I used this principle to reliably measure Teff, V sin i and [Fe/H] from CORALIE spectra. My method had a systematic offset in [Fe/H] of −0:18 dex relative to equivalent-width measurements of higher-quality spectra. There is also a correlation between Teff and log g. The sample of eclipsing binary systems in this work highlight that only a fraction are suitable for empirical calibrations. I found that three of systems have primary stars which ii have evolved into the “blue-hook” part of their main-sequence evolution. They have two distinct solutions for mass and age which require supplementary information before they can be used in empirical calibrations. A further two systems have large impact parameters which increase the uncertainty in radius above the required precision of a few percent. I advocate the need for a volume-limited sample to avoid spending time observing and measuring such systems. The method used to measure low-mass eclipsing binaries is well-established, yet there is a dearth of well-studied F+M binaries. The EBLM project has provided spectroscopic orbits for 118 F+M binaries and I expect the absolute parameters for these systems to follow timely. However, there is a requirement for a hare-and-hounds style experiment to assess how absolute parameters differ between different research groups and methods of analysis. Using a subset of systems, I show that subtle choices in helium-enhancement and mixing- length parameters can introduce a 2-4% uncertainty in mass and age. A similar effect is seen for different limb-darkening laws and so an in-depth review into how this will affect empirical mass-radius calibrations is required. iii Acknowledgements “Results based on 12 mental health symptoms (GHQ-12) showed that 32% of PhD stu- dents are at risk of having or developing a common psychiatric disorder, especially depression.” – Levecque et al. (2017) I would like to thank my primary supervisor, Pierre Maxted, for always encouraging me do science better. No Journey through research is straightforward. The journey which produced this work involved scaling many mountains, crossing many riverines and navi- gating the thickest fog. You patiently nudged me in the right direction to ensure I never ventured too far from the beaten track, and for that I am exceptionally grateful. I would also like to thank my second supervisor, Barry Smalley, who always had an open ear to discuss all things spectroscopy. I thank Jessica Evans, Daniel Evans, John Southworth, David Ander- son, Leslie Hebb, Bruce Gary, Uffe Jørgensen, Martin Dominik, Colin Snodgrass, Penelope´ Longa-Pena˜ and Amaury Triaud for assisting in observations which feature in this work. Students in research degrees, and academia in general, face higher mental health risks than other professions. Stress and lone-working often leads to depression, guilt, isolation and negative thoughts. This often degrades ones self-confidence and the relationships with those closest to us. I would be fooling myself if I didn’t acknowledge that I have experienced some, if not all of the symptoms mentioned above whilst studying for my doctorate. I would never have been able to survive my Ph.D without the endless love and support of my fiance, Katie. Thank you for always bringing a smile to my face and helping me weather the harshest of storms. I thank my parents, Jean and Simon Gill. You provided me with emotional and financial support during my research, as well as invaluable guidance. For this I am eternally grateful. I would also like to honourably mention our beagle, Bruce McGill. You kept me company day and night, taxed all my crunchy goods and pestered me for walks. Those walks provided crucial down time which helped me relax and preserved my sanity. Thank you for needing so little and doing so much. iv Contents Abstract ......................................... i Acknowledgements .................................. iii 1 Introduction .................................... 1 1.1 Properties of M-dwarfs . .2 1.2 Absolute parameters of low-mass stars . .5 1.2.1 Interferometry . .5 1.2.2 Eclipsing binaries . .6 1.3 Tension with stellar models . .7 1.3.1 Magnetic activity . .9 1.3.2 Metalicity . 11 1.4 Empirical relations of M-dwarfs . 11 1.4.1 Luminosity relations . 14 1.4.2 Mass-radius-temperature relations . 21 1.5 Eclipsing binary, low mass . 25 1.6 Motivation . 27 2 Theory ....................................... 31 2.1 Stellar spectroscopy . 31 2.1.1 Effective temperature . 31 2.1.2 Broadening processes . 32 2.1.3 Surface gravity . 33 2.1.4 Composition . 33 2.2 Binary stars . 35 2.2.1 Positions of binary stars . 35 2.2.2 Radial velocity . 38 2.2.3 Light-curves . 40 2.2.4 Limb darkening . 43 2.3 Absolute parameters . 46 3 Observations ................................... 48 3.1 Photometric colours used for SED fitting . 50 3.2 Gaia colours and Interferometry used to estimate distance and evolutionary status . 53 3.3 WASP photometry for initial transit parameters . 53 3.4 SAAO 1-m follow-up transit photometry . 54 3.5 HAO follow-up transit photometry . 55 3.6 CTIO follow-up transit photometry . 57 3.7 K2 follow-up transit photometry . 59 3.7.1 Extraction . 60 v 3.7.2 De-trending . 60 3.8 CORALIE spectra used for radial velocities and atmospheric parameters . 63 3.9 INT spectra used for radial velocities and atmospheric parameters . 63 3.10 Lucky imaging used to identify nearby companions . 64 4 Atmospheric parameters of FGK stars using wavelet analysis ........ 66 4.1 Wavelet decomposition theory . 67 4.2 Bayesian measurements . 73 4.3 Self consistency . 76 4.4 Benchmark sample . 80 4.5 Results . 82 4.5.1 Systematic offset in [Fe/H]...................... 87 4.5.2 Systematic trend in log g ....................... 89 4.5.3 Precision of atmospheric parameters . 90 4.5.4 Spectrum quality . 90 5 Methods ...................................... 96 5.1 SED fitting . 96 5.2 Spectroscopic analysis . 97 5.2.1 CORALIE - wavelet analysis . 97 5.2.2 INT - synthesis . 99 5.3 First estimates for transit parameters . 99 5.4 Ephemerides . 100 5.5 Out-of-transit photometry . 101 5.5.1 WASP photometry . 102 5.5.2 K2 . 102 5.6 Orbital solution . 102 5.6.1 EBLMs with ground-based follow-up photometry . 104 5.6.1.1 Rossiter-McLaughlin effect . 105 5.6.1.2 Star shapes . 106 5.6.1.3 Primary eclipses . 107 5.6.2 EBLMs observed with K2 . 108 5.6.2.1 qpower2.......................... 109 5.6.2.2 Red noise model . 112 5.7 Masses, radii and age . 113 5.8 M-dwarf temperature for J0055−00 ..................... 115 6 Results ....................................... 117 6.1 J2349−32................................... 121 6.2 J2308−46................................... 123 6.3 J0218−31................................... 125 6.4 J1847+39................................... 127 6.5 J1436−13................................... 128 vi 6.6 J0055−00................................... 129 6.7 J0457+14................................... 131 6.8 J1652−19................................... 132 6.9 J2217−04................................... 134 7 Discussion ..................................... 154 7.1 The mass-radius diagram . 154 7.2 Bayesian measurements of radius inflation . 156 7.2.1 Effect of stellar metalicity . 159 7.2.2 Orbital period and stellar radii . 164 7.3 Systematic effects on determining mass, radius and age .
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