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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. i Fundamental Properties of Solar-Type Eclipsing Binary Stars, and Kinematic Biases of Exoplanet Host Stars Richard J. Hutcheon Submitted in accordance with the requirements for the degree of Doctor of Philosophy. Research Institute: School of Environmental and Physical Sciences and Applied Mathematics. University of Keele June 2015 ii iii Abstract This thesis is in three parts: 1) a kinematical study of exoplanet host stars, 2) a study of the detached eclipsing binary V1094 Tau and 3) and observations of other eclipsing binaries. Part I investigates kinematical biases between two methods of detecting exoplanets; the ground based transit and radial velocity methods. Distances of the host stars from each method lie in almost non-overlapping groups. Samples of host stars from each group are selected. They are compared by means of matching comparison samples of stars not known to have exoplanets. The detection methods are found to introduce a negligible bias into the metallicities of the host stars but the ground based transit method introduces a median age bias of about -2 Gyr. Part II describes a detailed analysis of V1094 Tau. Spectra were analysed by the cross-correlation software TODCOR to obtain radial velocities, and uvby photometric light curves were analysed by the JKTEBOP software. Precise measurements obtained were: Improved ephemeris - T(min,prim) = HJD 2 454 555.51836(25) + 8.98854775(102) days. Absolute masses: M = 1.0969 ± 0.0037 M , M = 1.0127 ± 0.0027 M . Absolute radii are 1 2 R = 1.406 ± 0.010 R and R = 1.099 ± 0.017 R . The apsidal period is (14.5 ± 3.7) × 103 1 2 years. The primary is somewhat evolved. The binary lies in an important region of the mass/radius/period grid for studying tidal interactions. These may introduce an important uncertainty when using eclipsing binaries to determine fundamental stellar parameters. iv Part III describes an observing run at SAAO Sutherland, aimed to survey detached eclipsing binaries. Light curves and two spectra each from two binaries were analysed, to determine masses and radii to the 10 to 30% level. This is a proof in principle that runs on 2-metre class telescopes can identify targets for detailed follow-up observations. v General Acknowledgements I would like to thank Dr. Pierre Maxted for all his help as a supervisor and for his prompt and detailed response to queries when I was working away from the University as a mature student. I would also like to thank other members of the Astrophysics Department, particularly Dr. John Taylor and Dr. Barry Smalley for their assistance. Technical acknowledgements appear at the end of the main text. vi Contents Abstract iii General Acknowledgements v Index of Contents vii List of Figures xv List of Tables xix List of Appendices xxii vii Aims and layout of thesis PART 1 Kinematic and temperature biases in ground based surveys of exoplanets 1 1. Introduction 3 2. Main features of detection methods 6 2.1 Main features of exoplanets 6 2.1.1 General description 6 2.1.2 Distribution of exoplanets 8 2.2 The transit method 11 2.2.1 Main features 11 2.2.2 Basic principles of analysis 13 2.2.3 Spin-orbit alignment 19 2.2.4 Experimental details 20 2.3 The radial velocity method 22 2.3.1 Main features 22 2.3.2 Experimental Difficulties and Limitations 24 2.4 Combination of methods 26 2.5 Other detection methods 27 3. Composition and comparison of exoplanet host star samples 28 3.1 Definition of samples 28 3.2 Restrictions on samples 29 3.3 List of sample stars 32 viii 3.4 Source and calculation of stellar parameters 33 3.5 Distance of star 33 3.6 Positions and velocities in the LSR 38 3.7. Positions and velocities in the absolute galactic frame 39 3.8 Calculation of Zmax 40 3.9 Homogenisation of Values of Stellar Parameters 42 3.9.1 Need for homogenisation 42 3.9.2 Homogenisation procedures 43 4. Comparison of Samples 47 4.1 Comparison of Actual Samples 47 4.2 Possible Explanations of Differences 51 4.2.1 Biases due to observational procedure 51 4.2.2 Biases due to the nature of exoplanet systems 54 4.3 Splitting of samples 55 4.4 Relation between period and distance 56 4.5 Construction and comparison of calibration samples 56 4.5.1 Parameters for constructing calibration samples 56 4.5.2 Method for constructing calibration samples 57 4.6 Method for comparing calibration samples 60 4.7 Results of comparisons 61 4.8 Sensitivity of conclusions to stellar data 63 5. Discussion and Conclusion 64 5.1 Discussion 64 5.2 Conclusion 66 ix PART II. Detailed study of the eclipsing binary V1094 Tau. 67 6. Introduction and justification of project 67 6.1 Reasons for studying dEB’s with periods in region 67 of 8 days 6.1.1 Importance of mass-radius relation 67 6.1.2 Importance of dEB observations 69 6.1.3 Reasons for studying V1094 Tau 70 6.1.4 Mass distribution of newly formed stars 71 6.2 Studies of dEB’s with similar periods 72 7. Background review 80 7.1 Stellar formation, evolution and models 80 7.1.1 Formation of stars 80 7.1.2 Main features of stellar models 84 7.1.3 Asteroseismology 89 7.2 The Mass/Radius/Metallicity Relation 91 7.2.1 Basic theoretical principles underlying the mass/radius relation 91 7.2.2 Discrepancies between observations and stellar models 92 - overview 7.2.3 Further details of papers discussing underprediction of 93 stellar radii 7.2.4 Reasons for discrepancies between observed radii and stellar 98 models 7.3 Description of Eclipsing Binaries 101 7.3.1 Classification of binaries 101 7.3.2 Formation and frequency of binaries 103 7.4 Importance of Eclipsing binaries 104 7.5 Limitations of dEB’s for providing accurate stellar 107 data 7.6 Literature and Data Review for dEB’s 108 x 8. Previous Knowledge and more Recent Data for 112 V1094 Tau 8.1 Main features of V1094 Tau 112 8.2 Previous studies 116 8.2.1 Discovery and period 116 8.2.2 Spectroscopic study by Griffin and Boffin (2003) 117 8.3 Spectroscopic observations 118 8.3.1 List of observations 118 8.3.2 CfA observations 119 8.3.3 INT spectra 119 8.4 Photometric observations 121 8.4.1 Principles 121 8.4.2 List of Light curves 122 8.4.3 NFO and URSA light curves 123 8.4.4 Strömgren Automatic Telescope (SAT) light curves 124 9. Analysis of data from V1094 Tau 126 9.1 Structure of analysis 126 9.1.1 Analysis sequence 126 9.1.2 Justification and further explanation of analysis sequence. 127 9.2 Derivation of new ephemeris 128 9.2.1 Sources of data 128 9.2.2 Times of minima 129 9.2.3 Fitting program 130 9.3 Apsidal motion 134 9.3.1 General description. 134 9.3.2 Apsidal motion in V1094 Tau 139 9.3.3 Comparison of observed and theoretical apsidal constants 141 9.3.4 Comparison with study of Wolf et al. (2010) 142 9.4 Determination of radial velocities and radial velocity 143 amplitudes 9.4.1 Radial velocities 143 9.4.2 Analysis by SBOP 146 9.4.3 Corrections to radial velocity 153 xi 9.5 Definitive analysis of orbital elements (Omdot) 155 9.5.1 Description 155 9.5.2 Results 157 9.6 Definitive Analysis of photometric light curves 161 (JKTEBOP) 9.6.1 Light curve plots 161 9.6.2 Input parameters 163 9.6.3 Additional constraints 166 9.6.4 Adjustment of error bars 174 9.6.5 Results 174 9.7 Values of Teff 176 9.7.1 Adjustment of temperatures of Torres 176 9.7.2 Temperature difference estimated from luminosity ratio 177 9.7.3 “Single star” temperature from Strömgren colour indices 179 9.7.4 Values finally adopted for Teff 180 9.8 Metallicity 181 9.8.1 Treatment of binary as a single system 181 9.8.2 Temperature determination for each individual star 187 9.8.3 Attempt to determine Teff by spectral disentangling 188 9.9 Final values of system parameters (jktabsdim) 188 9.9.1 Input data for jktabsdim 189 9.9.2 Definitive values of V1094 Tau parameters 190 9.10 Pseudosynchronisation 193 9.11 Are the tidal interactions significant? 195 9.12 Age and rough metallicity estimate (Analysis by modelplot) 195 9.12.1 Description of software 195 9.12.2 Estimate of age 196 9.12.3 Rough estimate of metallicity 198 9.13 Kinematics 200 9.13.1 Galactic coordinates and kinematics 200 9.13.2 Implications for stellar parameters 201 9.13.3 Plot of Galactic orbit 202 xii 10. Discussion and Conclusions 203 10.1 Summary of discussion of stellar properties 203 10.2 Recommendations for future work on V1094 Tau 204 10.3 Impact of future missions on studies of dEBs in 205 general 10.3.1 Description of missions 205 10.3.2 Comparison of mission specifications 208 10.3.3 Impact on future missions on the field of dEB studies 208 10.4 Relevance of future missions to V1094 Tau 211 xiii Part III Observations of Selected Eclipsing Binaries at SAAO Sutherland 212 11.
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