Sizing Up the Stars

Dissertation by Tabetha Suzanne Boyajian Georgia State University
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Georgia State University Digital Archive @ GSU Physics and Astronomy Dissertations Department of Physics and Astronomy 7-17-2009 Sizing Up the Stars Tabetha Suzanne Boyajian Recommended Citation Boyajian, Tabetha Suzanne, "Sizing Up the Stars" (2009). Physics and Astronomy Dissertations. Paper 34. http://digitalarchive.gsu.edu/phy_astr_diss/34 This Dissertation is brought to you for free and open access by the Department of Physics and Astronomy at Digital Archive @ GSU. It has been accepted for inclusion in Physics and Astronomy Dissertations by an authorized administrator of Digital Archive @ GSU. For more information, please contact digitalarchive@gsu.edu.

Sizing Up the Stars by Tabetha S. Boyajian Under the Direction of Harold McAlister Abstract For the main part of this dissertation, I have executed a survey of nearby, main sequence A, F, and G-type stars with the CHARA Array, successfully measuring the angular diameters of forty-four stars to better than 4% accuracy. The results of these observations also yield empirical determinations of stellar linear radii and effective temperatures for the stars ob- served. In addition, these CHARA-determined temperatures, radii, and luminosities are fit to Yonsei-Yale isochrones to constrain the masses and ages of the stars. These quantities are compared to the results found in Allende Prieto & Lambert (1999), Holmberg et al. (2007), and Takeda (2007), who indirectly determine these same properties by fitting models to observed photometry. I find that for most cases, the models underestimate the radius of the star by ∼ 12%, while in turn they overestimate the effective temperature by ∼ 1.5 − 4%, when compared to my directly measured values, with no apparent correlation to the star’s metallicity or color index. These overestimated temperatures and underestimated radii in

these works appear to cause an additional offset in the star’s surface gravity measurements, which consequently yield higher masses and younger ages, in particular for stars with masses greater than ∼ 1.3 M⊙ . Alternatively, these quantities I measure are also compared to direct measurements from a large sample of eclipsing binary stars in Andersen (1991), and excellent agreement is seen within both data sets. Finally, a multi-parameter solution is found to fit color-temperature-metallicity values of the stars in this sample to provide a new calibration of the effective temperature scale for these types of stars. Published work in the field of stellar interferometry and optical spectroscopy of early-type stars are presented in Appendix D and E, respectively. INDEX WORDS: Interferometry, Infrared, Stellar Astronomy, Fundamental Properties, Effective Temperatures, Stellar Radii

Sizing Up the Stars by Tabetha S. Boyajian A Dissertation Presented in Partial Fulfillment of Requirements for the Degree of Doctor of Philosophy in the College of Arts and Sciences Georgia State University 2009

Copyright by Tabetha S. Boyajian 2009

Sizing Up the Stars by Tabetha S. Boyajian Major Professor: Harold McAlister Committee: Nikolaus Dietz Douglas Gies Todd Henry Gerard van Belle Russel White Paul Wiita Electronic Version Approved: Office of Graduate Studies College of Arts & Sciences Georgia State University August 2009

iv –0– To Alex. Je t’m!

v –0– Acknowledgments A big, warm, and fuzzy hug to my family, friends, and colleagues. Alex, I know it has not been easy to deal with our growing family, with my head buried in the books and my eyes glued to the laptop. The magnitude of patience that you have to deal with a pregnant wife (and now a young child) can only be attributed to true love, and I am the luckiest person on Earth to have you as my husband and father of our son Jude. I also feel a need to thank Jude. Although he is only a few months old at the time of this writing, about 90% of his life has been spent staring at my bookshelf of old Physics and Astronomy books, notebooks, and papers. You deserve more attention than that of my left foot, which I used to rock you to sleep while I work at my desk. To my dear Kepler, I apologize for discovering a clever method of playing Frisbee with you (up our steep driveway), devised only to tire you out quickly so I could get back to work. Sincerest thanks to every member of my family that has had to miss my presence due my urgency in working to meet deadlines. Thank you for being so very understanding, for your never-ending support, and for your interest in my studies. I would also like to thank the people at the CHARA Array who work so hard so that everything runs smoothly for the scientists. I apologize that you may only hear of our problems when observing, you deserve to be acknowledged for the invaluable improvements that you make on a daily basis to make our work easier! To the night operators, thank you for dealing with us graduate students running the CHARA Array remotely from AROC. Special thanks to all of my committee members for spending your valuable time reviewing my progress reports and documents. In particular, to my dissertation advisor, Hal McAlister,

vi thank you for making the time to teach me all about interferometry, review my work in such a speedy manner, and encourage me to pursue any stray idea that came to mind. To Doug Gies, my masters advisor, thank you for allowing the opportunity to work with you researching the properties of massive stars. Thank you to all of the graduate students that have helped me along the way. Thank you Ginny McSwain, for your continuous encouragement to be an independent researcher, for inviting me to be a collaborator in your work, and for taking me observing with you and your team. Thank you Deepak Raghavan, David O’Brien, Yamina Touhami, and Noel Richardson for your support with CHARA observations and research. Thank you Ellyn Baines for teaching me how to drive the Array in the graduate winter observing sessions of 2007; I have (hopefully) succeeded in passing this experience onto other graduate students since then. Thank you Alvin Das, for making a dissertation template for future PhD students. Thank you Rajesh Deo and Justin Cantrell for your technical support. Finally, I would like to thank all the folks at the College of Charleston for encouraging me to pursue a career in Astronomy.

vii –0– Table of Contents Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Abbreviations and Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Stellar Radii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Stellar Effective Temperatures . . . . . . . . . . . . . . . . . . . . . 2 1.1.3 Angular Diameters of Main Sequence Stars . . . . . . . . . . . . . . 5 1.2 Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 The CHARA Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.1 Description of the Instrument . . . . . . . . . . . . . . . . . . . . . 7 1.3.2 Observing and Data Reduction . . . . . . . . . . . . . . . . . . . . 10 2 The Sample of A, F, and G Dwarfs . . . . . . . . . . . . . . . . . . . . . 13 2.1 Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.1 Resolution Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.2 Instrumental Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 The HIPPARCOS Catalogue Query . . . . . . . . . . . . . . . . . . . . . . 16 2.2.1 RECONS Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Interferometric Calibrators . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1 The Calibrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1.1 Calibrator Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2 Calibrating Interferometric Data . . . . . . . . . . . . . . . . . . . . . . . . 28

viii 3.3 Observing Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.1 When Is a Good Time to Align NIRO? . . . . . . . . . . . . . . . . 31 3.3.2 Classic Observing: 1×1 Versus 2×2 Pixels . . . . . . . . . . . . . . 31 3.3.3 Night-to-Night Repeatability . . . . . . . . . . . . . . . . . . . . . . 33 3.3.4 Object/Calibrator Brightness Offsets and Calibration . . . . . . . . 35 3.3.5 Observing with Two Calibrators . . . . . . . . . . . . . . . . . . . . 38 3.3.6 Signs of a Bad Calibrator . . . . . . . . . . . . . . . . . . . . . . . 40 3.4 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.4.1 The Baseline Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.4.2 Lab Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5 Stellar Diameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1 Diameter Fit to a Single Star . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.2 CHARA Versus Palomar Testbed Interferometer Diameters . . . . . . . . . 63 5.3 Systematics of CHARA Versus Other OLBI Diameters . . . . . . . . . . . 66 6 Luminosities and Temperatures . . . . . . . . . . . . . . . . . . . . . . . 71 6.1 Luminosities and Temperatures . . . . . . . . . . . . . . . . . . . . . . . . 71 6.2 Discussion of the CHARA Determined Fundamental Parameters . . . . . . 73 7 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 7.1 Comparative Analysis of Linear Radii . . . . . . . . . . . . . . . . . . . . . 84 7.2 Comparative Analysis of Effective Temperatures . . . . . . . . . . . . . . . 86 7.2.1 CHARA Versus Allende Prieto & Lambert (1999) . . . . . . . . . . 87 7.2.2 CHARA Versus Holmberg et al. (2007) . . . . . . . . . . . . . . . . 91 7.2.3 CHARA Versus Takeda (2007) . . . . . . . . . . . . . . . . . . . . . 92 7.3 Model Mass and Age Relations to Measured CHARA Data . . . . . . . . . 94 7.4 CHARA Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.5 Comparative Analysis to Eclipsing Binaries . . . . . . . . . . . . . . . . . . 109

ix 8 Yonsei-Yale Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 8.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 8.3 Comparative Analysis to Results from Other Works . . . . . . . . . . . . . 128 9 Effective Temperature Calibrations . . . . . . . . . . . . . . . . . . . . . 137 10 Summary and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 144 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 A Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 B Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 C Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 C.1 HD 4614 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 C.2 HD 5015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 C.3 HD 6582 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 C.4 HD 10780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 C.5 HD 16895 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 C.6 HD 19373 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 C.7 HD 20630 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 C.8 HD 22484 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 C.9 HD 30652 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 C.10 HD 34411 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 C.11 HD 39587 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 C.12 HD 48682 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 C.13 HD 48737 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 C.14 HD 56537 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

x C.15 HD 58946 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 C.16 HD 81937 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 C.17 HD 82328 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 C.18 HD 82885 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 C.19 HD 86728 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 C.20 HD 90839 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 C.21 HD 97603 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 C.22 HD 101501 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 C.23 HD 102870 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 C.24 HD 103095 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 C.25 HD 109358 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 C.26 HD 114710 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 C.27 HD 118098 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 C.28 HD 126660 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 C.29 HD 128167 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 C.30 HD 131156 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 C.31 HD 141795 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 C.32 HD 142860 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 C.33 HD 146233 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 C.34 HD 162003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 C.35 HD 164259 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 C.36 HD 173667 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 C.37 HD 177724 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 C.38 HD 182572 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 C.39 HD 185144 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 C.40 HD 185395 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

xi C.41 HD 210418 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 C.42 HD 213558 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 C.43 HD 215648 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 C.44 HD 222368 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 D Appendix D: Published Work in the Field of Stellar Interferometry . 362 E Appendix E: Published Work in the Field of Optical Spectroscopy . . 377

xii –0– List of Tables 1.1 CHARA Baseline Configurations . . . . . . . . . . . . . . . . . . . . . . . 12 2.1 Sample Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 The Sample of A, F, and G Dwarfs . . . . . . . . . . . . . . . . . . . . . . 22 2.3 Magnitudes and Colors of the Sample . . . . . . . . . . . . . . . . . . . . . 23 3.1 Calibrators Observed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2 Calibrator SED Diameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3 Bad Calibrators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.1 Observations of A, F, and G Dwarfs . . . . . . . . . . . . . . . . . . . . . . 52 4.2 Problem Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.1 Angular Diameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.2 CHARA Versus PTI Angular Diameters . . . . . . . . . . . . . . . . . . . 69 5.3 CHARA Versus PTI Calibrators . . . . . . . . . . . . . . . . . . . . . . . . 70 6.1 Bolometric Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.2 Luminosities and Temperatures . . . . . . . . . . . . . . . . . . . . . . . . 82 8.1 Y 2 Model Isochrone Results . . . . . . . . . . . . . . . . . . . . . . . . . . 135 C.1 HD 4614 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 C.2 HD 5015 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 C.3 HD 6582 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 C.4 HD 10780 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 C.5 HD 16895 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

xiii C.6 HD 19373 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 C.7 HD 20630 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 C.8 HD 22484 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 C.9 HD 30652 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 C.10 HD 34411 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 C.11 HD 39587 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 C.12 HD 48682 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 C.13 HD 48737 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 C.14 HD 56537 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 C.15 HD 59846 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 C.16 HD 81937 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 C.17 HD 82328 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 C.18 HD 82885 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 C.19 HD 86728 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 C.20 HD 90839 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 C.21 HD 97603 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 C.22 HD 101501 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 C.23 HD 102870 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 C.24 HD 103095 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 C.25 HD 109358 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 C.26 HD 114710 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 C.27 HD 118098 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 C.28 HD 126660 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 C.29 HD 128167 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 C.30 HD 131156 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 C.31 HD 141795 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

xiv C.32 HD 142860 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 C.33 HD 146233 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 C.34 HD 162003 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 C.35 HD 164259 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 C.36 HD 173667 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 C.37 HD 177724 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 C.38 HD 182572 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 C.39 HD 185144 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 C.40 HD 185395 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 C.41 HD 210418 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 C.42 HD 213558 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 C.43 HD 215648 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 C.44 HD 222368 Visibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

xv –0– List of Figures 1.1 The Two-Telescope Interferometer . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Mount Wilson Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Layout of the CHARA Array Facilities . . . . . . . . . . . . . . . . . . . . 10 2.1 Angular Size Versus Distance . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Angular Diameter as a Function of Temperature and Magnitude . . . . . . 17 2.3 Color Magnitude Diagram of Sample . . . . . . . . . . . . . . . . . . . . . 21 3.1 The Calibrator’s Diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Bad NIRO Alignment Effects . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 Bad NIRO Alignment Effects . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 NIRO 1×1 Versus 2×2 Pixels . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5 NIRO 1×1 Versus 2×2 Pixels . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.6 Night-to-Night Repeatability . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.7 Night-to-Night Repeatability . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.8 Two Calibrator Diameter Fit . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.9 Binary Calibrator Brackets . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.10 Lab Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.11 Lab Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5.1 SED Versus LD Diameters with Respect to (B − V ) Color . . . . . . . . . 61 5.2 Comparison of SED to LD Diameters with Respect to (B − V ) Color . . . 62 5.3 CHARA Versus PTI Diameters . . . . . . . . . . . . . . . . . . . . . . . . 64 5.4 Offsets in Various OLBI Data Sets . . . . . . . . . . . . . . . . . . . . . . 68

xvi 6.1 CHARA Luminosity Versus Temperature . . . . . . . . . . . . . . . . . . . 75 6.2 CHARA Luminosity Versus Temperature and Radius . . . . . . . . . . . . 75 6.3 CHARA Luminosity Versus Temperature and Metallicity . . . . . . . . . . 76 6.4 CHARA Luminosity Versus (B − V ) . . . . . . . . . . . . . . . . . . . . . 77 6.5 CHARA Luminosity Versus (B − V ) and Radius . . . . . . . . . . . . . . . 77 6.6 CHARA Luminosity Versus (B − V ) and Metallicity . . . . . . . . . . . . 78 6.7 CHARA Temperature Versus Radius . . . . . . . . . . . . . . . . . . . . . 78 6.8 CHARA Radius Versus (B − V ) . . . . . . . . . . . . . . . . . . . . . . . . 79 6.9 CHARA Luminosity Versus Radius . . . . . . . . . . . . . . . . . . . . . . 79 6.10 CHARA Temperature Versus (B − V ) and Metallicity . . . . . . . . . . . . 80 7.1 Measured Versus Model Radii . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.2 Effects of Metallicity on Radii Offsets . . . . . . . . . . . . . . . . . . . . . 86 7.3 Empirical Versus Model Effective Temperatures . . . . . . . . . . . . . . . 87 7.4 Empirical Versus Model Effective Temperatures . . . . . . . . . . . . . . . 88 7.5 Effects of Metallicity on Temperature Offsets . . . . . . . . . . . . . . . . . 89 7.6 Effects of (b − y) on Temperature Offsets . . . . . . . . . . . . . . . . . . . 90 7.7 Empirical Versus Model Effective Temperatures . . . . . . . . . . . . . . . 92 7.8 Empirical Versus Model Effective Temperatures . . . . . . . . . . . . . . . 93 7.9 Effects of Metallicity on Temperature Offsets . . . . . . . . . . . . . . . . . 94 7.10 Effects of (b − y) on Temperature Offsets . . . . . . . . . . . . . . . . . . . 95 7.11 Empirical Versus Model Effective Temperatures . . . . . . . . . . . . . . . 96 7.12 Empirical Versus Model Effective Temperatures . . . . . . . . . . . . . . . 97 7.13 Effects of Metallicity on Temperature Offsets . . . . . . . . . . . . . . . . . 98 7.14 Effects of (b − y) on Temperature Offsets . . . . . . . . . . . . . . . . . . . 99 7.15 Radius-Temperature-Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 7.16 Radius-Temperature-Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

xvii 7.17 Radius-Temperature-Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 7.18 Radius-Temperature-Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.19 Radius-Temperature-Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7.20 Radius-Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.21 Radius-Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.22 Radius-Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.23 Radius-Mass-Metallicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.24 Radius-Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 7.25 Radius-Mass-Metallicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.26 Radius-Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.27 Radius-Mass-Metallicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.28 Temperature-Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7.29 Temperature-Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.30 Temperature-Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 7.31 CHARA Masses Versus Model Masses . . . . . . . . . . . . . . . . . . . . . 117 7.32 CHARA Masses Versus Model Masses . . . . . . . . . . . . . . . . . . . . . 118 7.33 Eclipsing Binary and CHARA Radii Versus (B-V) . . . . . . . . . . . . . . 119 7.34 Eclipsing Binary and CHARA Masses Versus Radius . . . . . . . . . . . . 120 7.35 Eclipsing Binary and CHARA Luminosities Versus Radii . . . . . . . . . . 121 7.36 Eclipsing Binary and CHARA Mass Versus (B − V ) . . . . . . . . . . . . . 122 7.37 Eclipsing Binary and CHARA Mass Versus Luminosity . . . . . . . . . . . 123 8.1 Y2 Model Ages Versus Ages from Holmberg et al. (2007) and Takeda (2007) 129 8.2 Y2 Model Ages Versus Metallicity . . . . . . . . . . . . . . . . . . . . . . . 130 8.3 Y2 Model Masses Versus Masses from Allende Prieto & Lambert (1999), Holm- berg et al. (2007), and Takeda (2007) . . . . . . . . . . . . . . . . . . . . . 131 8.4 Y2 Model Masses Versus Masses Derived from log g . . . . . . . . . . . . . 132

xviii 8.5 Mass Versus Color Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 8.6 Mass Versus Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 9.1 Color-Temperature-Metallicity . . . . . . . . . . . . . . . . . . . . . . . . . 139 9.2 Comparing Color-Temperature-Metallicity Relations . . . . . . . . . . . . . 141 9.3 Residuals of Color-Temperature-Metallicity Relations . . . . . . . . . . . . 143 A.1 SED plot for HD 166 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 A.2 SED plot for HD 4614 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 A.3 SED plot for HD 5015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 A.4 SED plot for HD 6582 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 A.5 SED plot for HD 10780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 A.6 SED plot for HD 16895 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 A.7 SED plot for HD 19373 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 A.8 SED plot for HD 20630 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 A.9 SED plot for HD 22484 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 A.10 SED plot for HD 25457 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 A.11 SED plot for HD 27045 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 A.12 SED plot for HD 30652 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 A.13 SED plot for HD 33564 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 A.14 SED plot for HD 34411 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 A.15 SED plot for HD 35296 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 A.16 SED plot for HD 38858 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 A.17 SED plot for HD 39587 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 A.18 SED plot for HD 43042 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 A.19 SED plot for HD 43386 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 A.20 SED plot for HD 46588 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 A.21 SED plot for HD 48682 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

xix A.22 SED plot for HD 48737 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 A.23 SED plot for HD 50692 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 A.24 SED plot for HD 55575 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 A.25 SED plot for HD 56537 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 A.26 SED plot for HD 58855 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 A.27 SED plot for HD 58946 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 A.28 SED plot for HD 69897 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 A.29 SED plot for HD 78154 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 A.30 SED plot for HD 78209 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 A.31 SED plot for HD 81937 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 A.32 SED plot for HD 82328 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 A.33 SED plot for HD 82885 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 A.34 SED plot for HD 86728 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 A.35 SED plot for HD 87696 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 A.36 SED plot for HD 90089 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 A.37 SED plot for HD 90839 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 A.38 SED plot for HD 95418 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 A.39 SED plot for HD 97603 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 A.40 SED plot for HD 101501 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 A.41 SED plot for HD 102870 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 A.42 SED plot for HD 103095 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 A.43 SED plot for HD 103287 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 A.44 SED plot for HD 106591 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 A.45 SED plot for HD 109358 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 A.46 SED plot for HD 110897 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 A.47 SED plot for HD 114710 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

xx A.48 SED plot for HD 116842 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 A.49 SED plot for HD 118098 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 A.50 SED plot for HD 126660 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 A.51 SED plot for HD 126868 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 A.52 SED plot for HD 128167 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 A.53 SED plot for HD 131156 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 A.54 SED plot for HD 134083 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 A.55 SED plot for HD 140538 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 A.56 SED plot for HD 141795 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 A.57 SED plot for HD 142860 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 A.58 SED plot for HD 146233 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 A.59 SED plot for HD 157214 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 A.60 SED plot for HD 161868 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 A.61 SED plot for HD 162003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 A.62 SED plot for HD 164259 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 A.63 SED plot for HD 165777 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 A.64 SED plot for HD 168151 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 A.65 SED plot for HD 173667 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 A.66 SED plot for HD 177724 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 A.67 SED plot for HD 182572 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 A.68 SED plot for HD 185144 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 A.69 SED plot for HD 185395 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 A.70 SED plot for HD 187013 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 A.71 SED plot for HD 187691 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 A.72 SED plot for HD 195564 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 A.73 SED plot for HD 201091 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

xxi A.74 SED plot for HD 201092 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 A.75 SED plot for HD 210418 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 A.76 SED plot for HD 211336 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 A.77 SED plot for HD 213558 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 A.78 SED plot for HD 215648 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 A.79 SED plot for HD 222368 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 B.1 SED plot for HD 71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 B.2 SED plot for HD 6210 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 B.3 SED plot for HD 9407 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 B.4 SED plot for HD 20675 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 B.5 SED plot for HD 21790 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 B.6 SED plot for HD 22879 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 B.7 SED plot for HD 28355 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 B.8 SED plot for HD 30739 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 B.9 SED plot for HD 31295 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 B.10 SED plot for HD 34904 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 B.11 SED plot for HD 38558 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 B.12 SED plot for HD 42807 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 B.13 SED plot for HD 43042 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 B.14 SED plot for HD 43795 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 B.15 SED plot for HD 50277 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 B.16 SED plot for HD 58551 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 B.17 SED plot for HD 59037 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 B.18 SED plot for HD 65583 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 B.19 SED plot for HD 83951 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 B.20 SED plot for HD 87141 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

xxii B.21 SED plot for HD 88986 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 B.22 SED plot for HD 89389 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 B.23 SED plot for HD 91480 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 B.24 SED plot for HD 99285 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 B.25 SED plot for HD 99984 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 B.26 SED plot for HD 102124 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 B.27 SED plot for HD 102634 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 B.28 SED plot for HD 103799 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 B.29 SED plot for HD 110897 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 B.30 SED plot for HD 114093 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 B.31 SED plot for HD 120066 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 B.32 SED plot for HD 128093 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 B.33 SED plot for HD 129153 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 B.34 SED plot for HD 132254 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 B.35 SED plot for HD 135101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 B.36 SED plot for HD 139225 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 B.37 SED plot for HD 140775 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 B.38 SED plot for HD 145607 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 B.39 SED plot for HD 150177 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 B.40 SED plot for HD 154099 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 B.41 SED plot for HD 158352 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 B.42 SED plot for HD 158633 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 B.43 SED plot for HD 162004 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 B.44 SED plot for HD 167564 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 B.45 SED plot for HD 174897 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 B.46 SED plot for HD 176303 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

xxiii B.47 SED plot for HD 180317 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 B.48 SED plot for HD 183534 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 B.49 SED plot for HD 184499 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 B.50 SED plot for HD 189395 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 B.51 SED plot for HD 191195 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 B.52 SED plot for HD 193555 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 B.53 SED plot for HD 193664 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 B.54 SED plot for HD 195838 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 B.55 SED plot for HD 204485 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 B.56 SED plot for HD 210715 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 B.57 SED plot for HD 211976 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 B.58 SED plot for HD 214923 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 B.59 SED plot for HD 216735 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 B.60 SED plot for HD 218470 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 B.61 SED plot for HD 222603 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 B.62 SED plot for HD 225003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 C.1 Diameter fit for HD 4614 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 C.2 Y2 Model Isochrones for HD 4614 . . . . . . . . . . . . . . . . . . . . . . . 232 C.3 Diameter fit for HD 5015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 C.4 Y2 Model Isochrones for HD 5015 . . . . . . . . . . . . . . . . . . . . . . . 235 C.5 Diameter fit for HD 6582 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 C.6 Y2 Model Isochrones for HD 6582 . . . . . . . . . . . . . . . . . . . . . . . 238 C.7 Diameter fit for HD 10780 . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 C.8 Y2 Model Isochrones for HD 10780 . . . . . . . . . . . . . . . . . . . . . . 241 C.9 Diameter fit for HD 16895 . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 C.10 Y2 Model Isochrones for HD 16895 . . . . . . . . . . . . . . . . . . . . . . 244

xxiv C.11 Diameter fit for HD 19373 . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 C.12 Y2 Model Isochrones for HD 19373 . . . . . . . . . . . . . . . . . . . . . . 247 C.13 Diameter fit for HD 20630 . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 C.14 Y2 Model Isochrones for HD 20630 . . . . . . . . . . . . . . . . . . . . . . 250 C.15 Diameter fit for HD 22484 . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 C.16 Y2 Model Isochrones for HD 22484 . . . . . . . . . . . . . . . . . . . . . . 253 C.17 Diameter fit for HD 30652 . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 C.18 Y2 Model Isochrones for HD 30652 . . . . . . . . . . . . . . . . . . . . . . 256 C.19 Diameter fit for HD 34411 . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 C.20 Y2 Model Isochrones for HD 34411 . . . . . . . . . . . . . . . . . . . . . . 259 C.21 Diameter fit for HD 39587 . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 C.22 Y2 Model Isochrones for HD 39587 . . . . . . . . . . . . . . . . . . . . . . 262 C.23 Diameter fit for HD 48682 . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 C.24 Y2 Model Isochrones for HD 48682 . . . . . . . . . . . . . . . . . . . . . . 265 C.25 Diameter fit for HD 48737 . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 C.26 Y2 Model Isochrones for HD 48737 . . . . . . . . . . . . . . . . . . . . . . 268 C.27 Diameter fit for HD 56537 . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 C.28 Y2 Model Isochrones for HD 56537 . . . . . . . . . . . . . . . . . . . . . . 271 C.29 Diameter fit for HD 58946 . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 C.30 Y2 Model Isochrones for HD 58946 . . . . . . . . . . . . . . . . . . . . . . 274 C.31 Diameter fit for HD 81937 . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 C.32 Y2 Model Isochrones for HD 81937 . . . . . . . . . . . . . . . . . . . . . . 277 C.33 Diameter fit for HD 82328 . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 C.34 Y2 Model Isochrones for HD 82328 . . . . . . . . . . . . . . . . . . . . . . 280 C.35 Diameter fit for HD 82885 . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 C.36 Y2 Model Isochrones for HD 82885 . . . . . . . . . . . . . . . . . . . . . . 283

xxv C.37 Diameter fit for HD 86728 . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 C.38 Y2 Model Isochrones for HD 86728 . . . . . . . . . . . . . . . . . . . . . . 286 C.39 Diameter fit for HD 90839 . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 C.40 Y2 Model Isochrones for HD 90839 . . . . . . . . . . . . . . . . . . . . . . 289 C.41 Diameter fit for HD 97603 . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 C.42 Y2 Model Isochrones for HD 97603 . . . . . . . . . . . . . . . . . . . . . . 292 C.43 Diameter fit for HD 101501 . . . . . . . . . . . . . . . . . . . . . . . . . . 294 C.44 Y2 Model Isochrones for HD 101501 . . . . . . . . . . . . . . . . . . . . . . 295 C.45 Diameter fit for HD 102870 . . . . . . . . . . . . . . . . . . . . . . . . . . 297 C.46 Y2 Model Isochrones for HD 102870 . . . . . . . . . . . . . . . . . . . . . . 298 C.47 Diameter fit for HD 103095 . . . . . . . . . . . . . . . . . . . . . . . . . . 300 C.48 Y2 Model Isochrones for HD 103095 . . . . . . . . . . . . . . . . . . . . . . 301 C.49 Diameter fit for HD 109358 . . . . . . . . . . . . . . . . . . . . . . . . . . 303 C.50 Y2 Model Isochrones for HD 109358 . . . . . . . . . . . . . . . . . . . . . . 304 C.51 Diameter fit for HD 114710 . . . . . . . . . . . . . . . . . . . . . . . . . . 306 C.52 Y2 Model Isochrones for HD 114710 . . . . . . . . . . . . . . . . . . . . . . 307 C.53 Diameter fit for HD 118098 . . . . . . . . . . . . . . . . . . . . . . . . . . 309 C.54 Y2 Model Isochrones for HD 118098 . . . . . . . . . . . . . . . . . . . . . . 310 C.55 Diameter fit for HD 126660 . . . . . . . . . . . . . . . . . . . . . . . . . . 312 C.56 Y2 Model Isochrones for HD 126660 . . . . . . . . . . . . . . . . . . . . . . 313 C.57 Diameter fit for HD 128167 . . . . . . . . . . . . . . . . . . . . . . . . . . 315 C.58 Y2 Model Isochrones for HD 128167 . . . . . . . . . . . . . . . . . . . . . . 316 C.59 Diameter fit for HD 131156 . . . . . . . . . . . . . . . . . . . . . . . . . . 318 C.60 Y2 Model Isochrones for HD 131156 . . . . . . . . . . . . . . . . . . . . . . 319 C.61 Diameter fit for HD 141795 . . . . . . . . . . . . . . . . . . . . . . . . . . 321 C.62 Y2 Model Isochrones for HD 141795 . . . . . . . . . . . . . . . . . . . . . . 322

xxvi C.63 Diameter fit for HD 142860 . . . . . . . . . . . . . . . . . . . . . . . . . . 324 C.64 Y2 Model Isochrones for HD 142860 . . . . . . . . . . . . . . . . . . . . . . 325 C.65 Diameter fit for HD 146233 . . . . . . . . . . . . . . . . . . . . . . . . . . 327 C.66 Y2 Model Isochrones for HD 146233 . . . . . . . . . . . . . . . . . . . . . . 328 C.67 Diameter fit for HD 162003 . . . . . . . . . . . . . . . . . . . . . . . . . . 330 C.68 Y2 Model Isochrones for HD 162003 . . . . . . . . . . . . . . . . . . . . . . 331 C.69 Diameter fit for HD 164259 . . . . . . . . . . . . . . . . . . . . . . . . . . 333 C.70 Y2 Model Isochrones for HD 164259 . . . . . . . . . . . . . . . . . . . . . . 334 C.71 Diameter fit for HD 173667 . . . . . . . . . . . . . . . . . . . . . . . . . . 336 C.72 Y2 Model Isochrones for HD 173667 . . . . . . . . . . . . . . . . . . . . . . 337 C.73 Diameter fit for HD 177724 . . . . . . . . . . . . . . . . . . . . . . . . . . 339 C.74 Y2 Model Isochrones for HD 177724 . . . . . . . . . . . . . . . . . . . . . . 340 C.75 Diameter fit for HD 182572 . . . . . . . . . . . . . . . . . . . . . . . . . . 342 C.76 Y2 Model Isochrones for HD 182572 . . . . . . . . . . . . . . . . . . . . . . 343 C.77 Diameter fit for HD 185144 . . . . . . . . . . . . . . . . . . . . . . . . . . 345 C.78 Y2 Model Isochrones for HD 185144 . . . . . . . . . . . . . . . . . . . . . . 346 C.79 Diameter fit for HD 185395 . . . . . . . . . . . . . . . . . . . . . . . . . . 348 C.80 Y2 Model Isochrones for HD 185395 . . . . . . . . . . . . . . . . . . . . . . 349 C.81 Diameter fit for HD 210418 . . . . . . . . . . . . . . . . . . . . . . . . . . 351 C.82 Y2 Model Isochrones for HD 210418 . . . . . . . . . . . . . . . . . . . . . . 352 C.83 Diameter fit for HD 213558 . . . . . . . . . . . . . . . . . . . . . . . . . . 354 C.84 Y2 Model Isochrones for HD 213558 . . . . . . . . . . . . . . . . . . . . . . 355 C.85 Diameter fit for HD 215648 . . . . . . . . . . . . . . . . . . . . . . . . . . 357 C.86 Y2 Model Isochrones for HD 215648 . . . . . . . . . . . . . . . . . . . . . . 358 C.87 Diameter fit for HD 222368 . . . . . . . . . . . . . . . . . . . . . . . . . . 360 C.88 Y2 Model Isochrones for HD 222368 . . . . . . . . . . . . . . . . . . . . . . 361

xxvii –0– Abbreviations and Acronyms AROC Arrington Remote Operations Center BCL Beam Combination Labratory BSF Beam Synthesis Facility CCD Charge Coupled Device CHARA Center for High Angular Resolution Astronomy FBOL Bolometric Flux HST Hubble Space Telescope IDL Interactive Data Language IR infrared IRFM Infrared Flux Method km s−1 kilometers per second LBOI Long Baseline Optical Interferometry LO Lunar Occultation L⊙ Solar Luminosity mas milli-arcseconds MBOL Bolometric Magnitude MS Main Sequence M⊙ Solar Mass NASA National Aeronautic and Space Administration NIRO Near Infrared Observer

xxviii OLBI Optical Long Baseline Interferometry OPLE Optical Path Length Equalizer pc parsec R⊙ Solar Radius SED spectral energy distribution SNR Signal-to-noise ratio TEFF Effective Temperature

1 –1– Introduction 1.1 Motivation 1.1.1 Stellar Radii The stellar radius is a fundamental physical characteristic of a star. Unfortunately, this property of a star is not well known due to the difficulty to measuring it directly. In eclipsing binary systems, the radii are measured by the combination of the binary’s spectroscopic and photometric data, and absolute dimensions of their radii can be determined without the distance to the star being known. Although this is a straightforward approach to determining stellar radii, there are a limited amount of eclipsing binaries (52 individual components in the A, F, and G star range from the sample in Andersen 1991) to study in this manner. Radii measurements of single stars are more challenging. They require special observing techniques to measure directly their small angular size, θ. The combination of θ with trigono- metric parallax Π allows the linear radius to be determined. Thanks to the HIPPARCOS mission (ESA 1997; van Leeuwen 2007), we now know accurate parallaxes (out to a certain distance) to most of the bright stars in the sky. However, because stars are at such great distances from us, they are typically unresolved point sources of light, so their angular sizes can only be determined with clever techniques in astronomy such as using lunar or Jovian occultation (LO, JO) events, speckle interferometry, and long-baseline optical interferometry (LBOI).

2 The largest stars to be resolved in our sky are evolved stars (e.g. supergiants and giants), where although they reside at large distances from the Sun, their big intrinsic radii provide angular sizes that are large enough to be easily resolved by lunar occultation observations and by interferometers with modest baselines. Stars that have not evolved off the main sequence far outnumber the evolved stars is our sky, because ≈ 90% of a star’s life is spent on the main sequence. However, the radius of a main sequence star is typically one to three orders of magnitude (or 10 − 1000) smaller than that of an evolved star, making it much smaller in angular size, despite its close vicinity to the Sun. These main sequence stars are also intrinsically several magnitudes dimmer than giants, due to their smaller radii. The resolution limits to measuring the size of a single star using occultations (lunar or Jovian) or speckle interferometry depend on the size or diffraction limit of the telescope, and thus only the largest of stars may be observed with these techniques. Intensity inter- ferometery can measure the size of a star to great accuracy (dependent on the baseline), but is limited to bright stars as in the case of the Narrabri Stellar Intensity Interferometer (Hanbury Brown et al. 1974), which only observed stars brighter than B=2.5 mag). The CHARA Array, an amplitude (Michelson-type) interferometer, has the highest resolution of any interferometer in the world due to its long baselines, and, although the telescopes are only 1-meter in diameter, the sensitivity of the CHARA Array depends on the beam combiner and wavelength used for observation. 1.1.2 Stellar Effective Temperatures In addition to measuring the linear radius of a star, we may determine another fundamental property of a star, the effective temperature, TEFF . This property provides the link be-

3 tween the theory of stellar structure and evolution and model atmospheres. The effective temperature of a star is defined through the Stephan-Boltzmann law: 4 F = σTEFF (1.1) where F is the total emergent flux of the star and σ is the Stefan-Boltzmann constant. Transforming this equation to observables at Earth, we arrive at the expression: 1 FBOL = θ2 σTEFF 4 (1.2) 4 where FBOL is the bolometric flux received at Earth, and θ is the angular diameter of the star in radians. This is the only empirical method of determining a star’s temperature, and it mostly depends on the tricky task of measuring the angular diameter of the star. Fortunately, the error in the effective temperature is relatively insensitive to errors in θ or 1 4 FBOL . For instance, because TEFF ∝ θ−2 then σ(TEFF ) ∝ 2 σ(θ), and because TEFF ∝ FBOL 1 then σ(TEFF ) ∝ 4 σ(FBOL ) (Booth 1997). The renowned results from the survey of angular diameters of 32 stars conducted by the Narrabri Stellar Intensity Interferometer (Hanbury Brown et al. 1974; Code et al. 1976) extended from O to F type stars, eleven of which were on the main sequence. The average accuracy of these angular diameter determinations depended primarily on the brightness of the object, and was ≈ 6.5% for the 32 stars measured. Distance errors at the time were not of high accuracy, and only eleven of the stars had less than a 20% error in parallax, limiting the results of the linear radius derived from the angular diameter measurement as well. This survey (conducted more than three decades ago), has been a key resource in calibrating several less direct relationships to stellar properties.

4 One such relation was first established by Barnes & Evans (1976), with the use of angu- lar diameters of stars from lunar occultation (LO) measurements with other forms of direct measurements having been added to the calibration since this work was first published. It provides a relationship between the surface brightness of a star and its color index to the angular diameter of the star. Another technique, the Infrared Flux Method (IRFM), was first established by Blackwell & Shallis (1977). The IRFM embraces the idea that one can determine the angular diameter and temperature of a star simultaneously. A monochro- matic version of the method was developed by Gray (1967), where the observed spectral energy distribution is compared to a model spectral energy distribution of a star, so that by conservation of energy: 4πR2 F = 4πd2 FBOL (1.3) where R is the radius of the star, F is the total flux emitted at the surface of the star, and d is the distance to Earth. Because θ = 2R/d, then we have the relation: F = θ2 /4. (1.4) FBOL The IRFM performs this same task, but assumes that the flux in the ratio of F/FBOL holds for monochromatic wavelengths, in particular in the IR. In their work, Blackwell & Shallis (1977) justify this relation by arguing that there is a weak influence in the IR due to the temperature of the star versus the flux distribution (i.e., the monochromatic flux in the IR depends only on temperature to the first power, whereas the full integrated flux depends on the temperature to the fourth power). Smaller effects due to line-blanketing and opacity sources are more well known in this region as well. This method has developed sophistication

5 over the years to take these issues into account (see Gonz´lez Hern´ndez & Bonifacio 2009, a a and references therein) and boasts a 1% accuracy on effective temperature determinations. These relationships are extremely useful in extending our knowledge to a larger number of stars, at distances too far to resolve accurately their sizes. However, it has been noted over the years that in the absence of a more complete sample of stars, these relationships are only as good as the data upon which the calibrations were based (McAlister 1985). 1.1.3 Angular Diameters of Main Sequence Stars As mentioned before, the Narrabri Stellar Intensity Interferometer (Hanbury Brown et al. 1974; Code et al. 1976) measured the angular diameters of eleven main sequence stars, pro- viding the means to calibrate properties of stars on the hot, massive end of the main sequence. For several decades, luminosity class I, II, and III stars were observed with interferometry, but no main sequence star earlier than A7 was observed (Davis 1997). As an update, the CHARM2 Catalogue1 (Richichi et al. 2005) is a compilation of stellar diameters by means of direct measurements by high angular resolution methods, as well as indirect estimates. The CHARM2 Catalogue includes all results as of July 2004, a total of 8231 entries, for 3238 unique sources. Of these 8231 entries, 905 are from direct measurements, and 458 of these are unique sources. Of the latter sample, 242 have errors in the angular diameter measurements of <5%, and only 24 of these reside on the main sequence (luminosity class V or IV). In a recent work by Holmberg et al. (2008), they remark that measurements of the angular diameters of main sequence F and G stars need to be better than 2%, yielding temperatures to 1%, in order for offsets in the color-temperature calibrations to be minimal. 1 http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/A+A/431/773

6 At that time, only nine stars met this criterion. This accuracy limit reiterates the target accuracy proposed by Blackwell et al. (1979) for the limits to the Infrared Flux Method, that a good TEFF determination goal should be 1% to match the best atomic data available for abundance determinations and log g estimates (Davis 1985; Booth 1997). The determination of accurate temperatures also becomes an important issue when de- termining stellar ages. Holmberg et al. (2007) give several good examples of how an offset in effective temperature will, in turn, offset the metallicity [Fe/H] measurements, and that these effects double up when determining the ages of the stars, thereby producing false age- metallicity relations. With 1% errors in the effective temperature scale, it is also possible to challenge stellar models to achieve greater accuracy than now attainable, by constraining mixing length theory and convective overshooting, to name a few issues at hand. The long baselines of the CHARA Array are uniquely suited for observing diameters of main-sequence stars to great accuracy. 1.2 Interferometry We gain high spatial resolution in astronomical observations through the use of an interfer- ometer. An interferometer is an array of telescopes that synthesizes the aperture of a giant telescope with the diameter equal to the separation of the arms of the interferometer. Mount Wilson Observatory is famous for interferometry historically and at the present day. It is the site where interferometry was first used to measure the diameters of stars when Michelson & Pease (1921) observed the diameter of the star α Orionis (Betelgeuse) with the 20-foot Michelson interferometer, which was mounted to the frame of the 100-inch Hooker telescope.

7 The first operational two-telescope optical interferometer was developed by A. Labeyrie (Labeyrie 1975) who detected interference fringes on α Lyra (Vega) in 1974. In the cartoon of such an interferometer (Figure 1.1), light is collected by two telescopes, Tel. #1 and Tel. #2, separated by baseline B. The light emitted by the star reaches each telescope at different times, where the extra light travel to Tel. #2 is called the “delay”, and is quantified by the factor B sin θ. In order to detect interference fringes, this light delay to Tel. #2 must be compensated for, so the light collected from Tel. #1 must take a detour until the path lengths of light are equal. It is only then that interference fringes are formed when the beams are combined. The angular resolution of an interferometer is defined as λ/2B, where λ is the wavelength of observation. This is directly related to the condition of constructive interference in Young’s double slit experiment (where the slits in this case are telescopes). This is slightly better than the angular resolution of a single telescope established by the Rayleigh Criterion that is defined as 1.22λ/D, where D is the diameter of the telescope aperature. 1.3 The CHARA Array 1.3.1 Description of the Instrument The CHARA Array is a six-telescope optical/infrared interferometric array located at Mount Wilson Observatory in the San Gabriel mountains of southern California (see Figure 1.2). The funding to build the CHARA Array came from Georgia State University, the National Science Foundation, the W. M. Keck Foundation, and the David and Lucile Packard Foun- dation. Continued operation of the Array after ‘first fringes’ (November 1999) is provided by

8 Figure 1.1: The Two-Telescope Interferometer: Cartoon of a two-telescope long baseline interferom- eter. Image courtesy of H. McAlister. the College of Arts and Sciences of Georgia State University and the Division of Astronom- ical Sciences of the National Science Foundation. A detailed description of the instrument can be found in ten Brummelaar et al. (2005). The following text is a brief summary of the general elements and layout of the facility. The CHARA Array consists of six, 1-meter aperture telescopes in a Y-shaped configura- tion spread across the mountaintop of the Observatory (Figure 1.3). With the six telescopes, there are fifteen available baseline combinations, ranging from 34 to 331 meters, at a vari- ety of position angle orientations ψ (Table 1.1). There are two telescopes in each direction of South, East, and West, with the farthest telescope from the central OPLE building to which all light travels being named 1, the closer being named 2 (i.e. telescope S1 for the farthest southern telescope). The Array currently is the longest baseline optical/infrared interferometer in the world.

9 Figure 1.2: Mount Wilson Observatory: Pictorial overview of Mount Wilson Observatory. In the center of the image is the 100-inch Hooker telescope. CHARA telescopes are located at the right, bottom-left, and top-left of the image. (See also Figure 1.3.) Each of the CHARA telescopes is connected to an evacuated light pipe (Figure 1.3), which channels the light collected at the telescope into the central “L”-shaped Beam Synthesis Facility (BSF). It is here in the Optical Path Length Equalizer (OPLE) building that the extra delay in the light arriving at each telescope is matched down to µm precision level using delay carts that move along rails in a lateral direction. This movement along the rails is fully automated and actively controlled in real-time to follow the stars’ diurnal motion across the night sky. Adjacent to the OPLE building in the BSF is the Beam Combination Laboratory (BCL), where the fringes are formed and detected. There are several beam combiners available for

10 Figure 1.3: Layout of the CHARA Array Facilities the CHARA Array, and for this project observations were made using the CHARA Classic beam combiner in two-telescope mode. CHARA Classic is a pupil-plane beam combiner, which is used primarily in K ′ -band (central wavelength of λK ′ = 2.13 ± 0.01µm). Fringes are detected and recorded on the Near Infrared Observer (NIRO) camera, which is based upon a HgCdTe PICNIC Array read out at high speed. 1.3.2 Observing and Data Reduction Nearly all (98.5%) of the observing for this thesis was performed remotely from Georgia State University’s Cleon Arrington Remote Operations Center (AROC) in Atlanta, GA. Here, almost everything needed to drive the CHARA Array can be done. We are able to

11 align the beams on the NIRO chip and on the sky, acquire targets, move the delay carts, scan for fringes, and record data. We are also able to monitor the weather and open and close the telescope optics and dome slits at any time during the evening. Night operators are on-site to alleviate any issues that may (and will) arise that require human interaction such as rebooting servers when they crash. When observing, typically 200 scans are taken per data record, where the dither mirror scans the location of the last fringe offset2 . An ideal night of observing will yield approxi- mately 40 bracketed observations, but this is not typically the norm. Data recorded for each night of observing are stored on local machines at the Array. The main data reduction package used to reduce CHARA Classic data for this project is VisUVCalc, written in MathCAD by H. A. McAlister and A. Jerkstrand. To process the data, the raw fringe signal is normalized and filtered using a low-pass filter to eliminate low frequency modulations in the fringe scan. A bandpass filter is then applied to the power spectrum of the fringe and inverted to smooth the data. The fringe visibility is then measured by fitting a model fringe to the data. The Signal-to-Noise (S/N) of the fringe data is also measured for each of the 200 scans. Zero weight is applied to scans with fringe visibility measurements with low S/N ratio, scans with unrealistically high visibility measurements (visibility greater than 0.75), and scans that detect fringes in a location far from the last fringe offset3 . The total weight, mean and standard deviations of the individual visibilities are then calculated for the recorded data set. These outputs are stored in a text file to be calibrated (see Chapter 3 for details on calibrated observing methods and techniques). 2 The fringe offset depends on the astrometric and baseline solutions for the star and baseline configuration used. 3 The fringe servo keeps the fringe within the scan window while observing. In times of poor seeing, or other bad observing conditions, this tracking can be difficult, and scans can sometimes lose the fringe.

12 Table 1.1: CHARA Baseline Configurations Telescope B ψ Pair (m) (◦ ) S1/S2 34.08 350.1 E1/E2 65.89 236.5 W1/W2 107.93 97.5 W2/E2 156.28 63.3 S2/W2 177.44 340.2 S1/W2 210.96 341.8 E1/W2 221.84 241.2 S2/E2 248.13 17.7 S2/W1 249.39 317.0 W1/E2 251.34 77.6 S1/W1 278.50 320.9 S1/E2 278.77 14.5 S2/E1 302.33 25.5 E1/W1 313.54 253.2 S1/E1 330.67 22.1

13 –2– The Sample of A, F, and G Dwarfs 2.1 Selection Criteria The motivation for this project extends from a long-standing need for accurate angular diameters for (roughly) main sequence stars. I selected the target list by aiming to meet several criteria, described below in detail. As discussed in the Introduction, several sources indicate that at least a 2% accuracy on the measured angular diameter is needed to refine the effective temperature scale to better than 1%, because TEFF ∝ θ1/2 . This limit will also allow us to calibrate color-temperature relations to a high degree of accuracy, and enable us to extend our knowledge to large populations of stars throughout the Galaxy. For this project, we aim to measure the angular diameter of a star to better than 4%, only to arrive at a sample that is large enough for an initial analysis; however, most of the stars observed will be sufficiently resolved down to the 2% level. 2.1.1 Resolution Limits How accurately one can measure the angular diameter of a star depends on how far down the visibility curve you are able to sample. The visibility function of a single star is expressed as: 2J1 (x) V = , (2.1) x where x = πBθλ−1 , (2.2)

14 where B is the projected baseline, θ is the angular diameter of the star, and λ is the wave- length of observation. By knowing the λ and B utilized in a given observation, we can estimate the optimum resolution range resulting from the accuracy with which we can mea- sure the object visibility. For instance, assuming that we can readily measure the visibility of a star to 5% (McAlister, private communication), by evaluating Equation 2.1, we find that we must sample down to a visibility of V=0.55 to obtain better than 4% accuracy on the measured angular diameter of a star. To ensure that we will reach the resolution limit for our observations, we set the cutoff to obtain a visibility of 0.55 for CHARA’s third longest baseline (S2/E1=302.2m). Thus, the limiting resolution that meets this criteria is θ = 0.65 mas in K band and θ = 0.50 mas in H band. By binning the spectral types and taking the nominal values for linear diameters for the stars from Cox (2000), the maximum distance for each spectral type bin is found (Figure 2.1). I did not rely on assigned spectral types for stars because often it is difficult to find agreement from one catalogue to the next. Instead, in the HIPPARCOS Catalogue query, the ranges in spectral types were sampled by (B − V ) color indices, and luminosity classes were sampled by restricting the apparent V magnitudes of the stars to only admit roughly main sequence stars (Cox 2000). These sample criteria are listed in Table 2.1. 2.1.2 Instrumental Limits In this project, the instrumental limits for observing are restricted only by the target dec- lination, which must be greater than −10◦ . Stars approaching this declination suffer from baseline foreshortening. This is where the maximum projected baseline will never reach the full 330m on the longest S1/E1 baseline. Another factor in observing low-declination objects

15 2.0 A0 1.5 A5 F0 Angular Size (mas) F5 1.0 G0 G5 K0 0.5 0.0 10 20 30 40 50 Distance (pc) Figure 2.1: Angular Size Versus Distance: Plot of angular size of star by spectral type versus distance. The shaded region indicates distances where the star becomes too unresolved in H-band to achieve the goal of better than 4% accuracy on the angular diameter measurement. For example, we can observe a G0 dwarf to 20 pc using our adopted experimental setup. is that they do not remain at their highest elevations for very long. Stars that are observed at lower than ≈ 30◦ degrees elevation are thought to have calibration problems because one is observing through too much airmass, and seeing effects are more apparent at these low elevations. Additionally, the calibrator observed is likely to have a very different airmass, even if one is chosen to be very nearby, and these values change frequently when the objects are rising/setting. Last but not least, a very good reason not to observe a star too far south (and at low elevation) is that you are doomed to be glaring through the exhaust pipe of Los Angeles, which lies in the southern direction from Mount Wilson Observatory.

16 Magnitude limits are not a factor because of the resolution requirements set by the goals of the project (θ > 0.50 mas for better than 4% accuracy in H-band). These are set by the distances of the target stars, and their predicted linear sizes. For instance, an A0 star has an absolute magnitude MV = 0.65, so at the maximum distance of 33 pc it has an apparent magnitude of mV = 3.2. For the late end of the sample, a K0 star has an absolute magnitude MV = 5.9, so at the maximum distance of 16 pc this star has an apparent magnitude of mV = 6.9. These translate into apparent K magnitudes of mK = 3.2 and mK = 5.0 for the A0 star and the K0 star, respectively (assuming (V − K)A0 = 0.0 and (V − K)K0 = 1.96; Cox 2000). Very conservative limits for observing with the CHARA Classic beam combiner require a K magnitude to be brighter than 7, much fainter than these values. This fact also gives some relief in finding suitable calibrators for the target stars, which are preferred to be of similar spectral type as the object, but must also be an unresolved source (i.e., farther and dimmer). Figure 2.2 shows the relationship between a star’s angular diameter as a function of effective temperature and observed K magnitude in a graphical representation. This uses the results from Code et al. (1976) where the angular diameters and effective temperatures are measured for eleven luminosity class V and IV stars1 . For example, a K = 5 mag star with a temperature of ∼ 4000 K will have an angular diameter of ∼ 0.5 mas. 2.2 The HIPPARCOS Catalogue Query A query of the HIPPARCOS Catalogue was preformed to compile a large list of objects to observe in this survey of (roughly) main sequence (MS) A, F, and G-type stars. The 1 Computed K-magnitudes from line-blanketed model atmospheres developed by Robert Kurucz

17 10.00 K=0 K=1 K=2 K=3 K=4 1.00 K=5 Angular Diameter (mas) K=6 K=7 K=8 K=9 0.10 K=10 0.01 103 104 105 Effective Temperature (K) Figure 2.2: Angular Diameter as a Function of Temperature and Magnitude: The relationship between a star’s angular diameter as a function of effective temperature and observed K magnitude. The shaded region indicates the observable region for an approximate temperature range of this survey (5−10 kK), with an angular diameter cutoff of 0.5 mas (H-band; dark gray) and 0.65 mas (K ′ -band; light gray). HIPPARCOS Catalogue was queried through the online VizieR Service2 with the constraints listed in Table 2.1. A total of 132 possible targets resulted in the initial query. Next, each of these stars was individually scrutinized to find all relevant information that would prejudice good diameter measurements. For instance, each object was checked for entries in The 9th Catalogue of Spectroscopic Binary Orbits3 (SB9) and the Washington Double Star Catalogue4 (WDS) to determine whether or not it was a known binary. The primary object was rejected if it harbored a companion with a separation ρ of less than 2 2 http://vizier.u-strasbg.fr/viz-bin/VizieR 3 http://sb9.astro.ulb.ac.be/ 4 http://ad.usno.navy.mil/wds/

18 arcsec (with the exception of µ Cas, ρ = 1.3 arcsec). The primary object was flagged if the companion was 2−5 arcsec away. In this range, light from the secondary may contaminate the visibility measurements of the primary star, and/or make it hard for the telescope’s tip/tilt system to lock on the star. Detailed work was done in Boyajian et al. (2008) for the observations of µ Cas A to determine the contribution of light the secondary star contributes within our detector’s field-of-view (See Appendix D). In summary, the amount of contributing light from the secondary has to do with the system separation, delta magnitude, and the seeing conditions at the time of observation. A reference search for each target was also undertaken to determine if there were any extraordinary characteristics that could potentially hinder the accurate determination of the star’s diameter measurement. These objects were also flagged. This includes stars with spots, pulsating stars, and rapid rotators. The status of the duplicity of each star was also checked for completeness and accuracy in the above mentioned catalogues in this reference search. This is mostly relevant in the SB9 Catalogue, whereas the WDS is updated daily. Along with the reference search, stars with previously determined diameters via inter- ferometry were removed from the sample that I will observe for this project5 . Until very recently, main sequence stars in this range were unresolved, so very few fall into this cat- egory. However, the angular diameters of seven stars from Baines et al. (2008), who used the CHARA Array to measure the diameters of exoplanet host stars, fall within my sample criteria presented here and are eliminated from my sample in order not to be redundant. 5 For results prior to 2004, these entries are found in the CHARM2 Catalogue: An Updated Catalog of High Angular Resolution Measurements6 (Richichi et al. 2005).

19 These final candidates for the observing sample were sorted one last time. In order to estimate better angular sizes than ones merely defined by an estimated linear radius and distance to the star, I performed a fit of observed photometry to a model spectral energy distribution (SED). Information from this task also gives us a way to determine estimates of effective temperature, TEFF , and surface gravity, log g, which are then used to determine the limb darkening coefficients µλ used in the final diameter fits to the data (Claret et al. 1995). When available, the magnitudes (Johnson U BV , Johnson et al. 1966; Str¨mgren uvby, Hauck o & Mermilliod 1998; 2MASS JHK, Skrutskie et al. 2006) for each star were collected and then transformed into calibrated flux measurements using the methods described in Colina et al. (1996), Gray (1998), and Cohen et al. (2003). We then fitted a model SED7 to the observed flux-calibrated photometry to determine the angular diameters θSED for these stars. If the star has an observed infrared excess compared to the model, it was rejected because the presence of a companion is likely. A handful of stars also proved to be too small to be adequately resolved and were rejected as well. This unfortunate circumstance arose when we discovered that more often than not, the 2MASS JHK magnitudes had very large (>10%) errors due to saturation (usually occurring around K = +4 mag). In these cases, the fit was preformed with all data, and for any of the points with large errors that did not fit the SED for the star, the data in question were removed and the fit redone. The resulting sample size for the survey came to 77 stars, 13 of them flagged for reasons stated in the above paragraphs. Table 2.2 shows a list of the full sample names, coordinates, and spectral types. Table 2.3 shows the list of the magnitudes and HIPPARCOS parallaxes in 7 The model fluxes were interpolated from the grid of models from R. L. Kurucz available at http://kurucz.cfa.harvard.edu/

20 the final full sample, and Figure 2.3 plots these stars in a color-absolute magnitude diagram. The stars in Figure 2.3 range from spectral types A0V−K0V, and there is a nice intrinsic spread in the main sequence due to the evolutionary state of the stars within the band of the main sequence. The SED fit for each star can be found in Appendix A. 2.2.1 RECONS Stars The RECONS project8 is aimed at acquiring information about nearby stars, with particular emphasis on stars within 10 parsecs of the Sun. Given the selection criteria in this survey, all main sequence A, F, and G stars within 10 parsecs, and above −10◦ declination will now be observed with interferometry. Prior to this survey, Vega, Sirius, Altair, and Procyon were the only RECONS stars studied with interferometry (Aufdenberg et al. 2006; Kervella et al. 2003; Domiciano de Souza et al. 2005; Kervella et al. 2004b). In this survey, I will add an additional twelve stars, which will triple the number of RECONS stars with interferometric observations to date. All twelve stars have spectral types later than Procyon (F5IV-V, the latest spectral type of the above four mentioned), ranging from F6V−K0V. This leaves only four A, F and G RECONS stars (HD 98230, HD 98231, HD 161797, and HD 170153) in the northern hemisphere that will not be observed in this survey, due to their duplicity. 8 http://www.recons.org

21 0 2 MV 4 6 8 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 COLOR INDEX (B-V) Figure 2.3: Color Magnitude Diagram of Sample: This is a Color-Magnitude plot of the data in Table 2.3, showing the full sample selected for the CHARA observational program to determine angular diameters.

22 Table 2.1: Sample Criteria for HIPPARCOS Catalogue Querry† Spectral V (B − V ) π Distance # of Type (mag) (mag) (mas) (pc) stars A0V-A5V <6.0 −0.02-0.15 >30 <33 11 A6V-F0V <6.4 0.15-0.30 >34 <29 6 F1V-F5V <6.7 0.30-0.44 >41 <25 11 F6V-G0V <7.0 0.44-0.58 >47.6 <21 27 G1V-G5V <7.3 0.58-0.68 >58.8 <17 9 G6V-K0V <7.5 0.68-0.81 >62.5 <16 13 † Declination north of −10◦ . Table 2.2: The Sample of A, F, and G Dwarfs Other RA DEC Spectral Spectral HD HR HIP Namea (hh mm ss.xx) (dd mm ss) Typeb Typec 166 8 544 GJ 5 00 06 36.78 29 01 17.41 G8V K0V 4614 219 3821 24 η Cas A 00 49 06.29 57 48 54.67 F9V G0V 5015 244 4151 GJ 41 00 53 04.20 61 07 26.29 F8V F8V 6582 321 5336 34 µ Cas A 01 08 16.39 54 55 13.22 G5Vb G5Vp 10780 511 8362 GJ 75 01 47 44.84 63 51 09.00 G9V K0V 16895 799 12777 13 θ Per A 02 44 11.99 49 13 42.41 F7V F7V 19373 937 14632 ι Per 03 09 04.02 49 36 47.80 G0IV-V G0V 20630 996 15457 κ Cet 03 19 21.70 03 22 12.71 G5V G5Vvar 22484 1101 16852 10 Tau 03 36 52.38 00 24 05.98 F9IV-V F9V 25457 1249 18859 GJ 159 04 02 36.75 −00 16 08.12 F7V F5V 27045 1329 19990 50 ω Tau 04 17 15.66 20 34 42.93 ··· A3m 30652 1543 22449 1 π 3 Ori 04 49 50.41 06 57 40.59 F6IV-V F6V 34411 1729 24813 15 λ Aur 05 19 08.47 40 05 56.59 G1V G0V 33564 1686 25110 GJ 196 05 22 33.53 79 13 52.14 F7V F6V 35296 1780 25278 111 Tau 05 24 25.46 17 23 00.72 F8V F8V 38858 2007 27435 GJ 1085 05 48 34.94 −04 05 40.73 G2V G4V 39587 2047 27913 54 χ1 Ori 05 54 22.98 20 16 34.23 G0IV-V G0V 43042 2220 29650 71 Ori 06 14 50.88 19 09 23.21 F5.5IV-V F6V 43386 2241 29800 74 k Ori 06 16 26.62 12 16 19.79 F5V F5IV-V 48737 2484 32362 31 ξ Gem 06 45 17.37 12 53 44.13 F5IV-V F5IV 46588 2401 32439 23 H Cam 06 46 14.15 79 33 53.32 F8V F8V 48682 2483 32480 56 ψ 5 Aur 06 46 44.34 43 34 38.74 F9V G0V 50692 2569 33277 37 Gem 06 55 18.67 25 22 32.51 G0V G0V 55575 2721 35136 GJ 1095 07 15 50.14 47 14 23.87 F9V G0V 56537 2763 35350 54 λ Gem 07 18 05.58 16 32 25.38 ··· A3V 58946 2852 36366 62 ρ Gem 07 29 06.72 31 47 04.38 ··· F6V 58855 2849 36439 22 Lyn 07 29 55.96 49 40 20.87 F6V F6V 69897 3262 40843 18 χ Cnc 08 20 03.86 27 13 03.74 F6V F6V 78209 3619 44901 15 f UMa 09 08 52.26 51 36 16.73 ··· A1m 78154 3616 45038 13 σ 2 UMa 09 10 23.55 67 08 02.46 ··· F7IV-V 81937 3757 46733 23 h UMa 09 31 31.71 63 03 42.70 ··· F0IV 82328 3775 46853 25 θ UMa 09 32 51.43 51 40 38.28 F5.5IV-V F6IV 82885 3815 47080 11 LMi 09 35 39.50 35 48 36.48 G8+V G8IV-V 86728 3951 49081 20 LMi 10 01 00.66 31 55 25.22 G4V G3V 87696 3974 49593 21 LMi 10 07 25.76 35 14 40.90 A7V(n) A7V 90839 4112 51459 36 UMa 10 30 37.58 55 58 49.93 F8V F8V 90089 4084 51502 GJ 9330 10 31 04.66 82 33 30.92 F4V F2V 95418 4295 53910 48 β UMa 11 01 50.48 56 22 56.74 A1IV A1V 97603 4357 54872 68 δ Leo 11 14 06.50 20 31 25.38 A5IV(n) A4V Continued on Next Page. . .

23 Table 2.2 – Continued Other RA DEC Spectral Spectral HD HR HIP Namea (hh mm ss.xx) (dd mm ss) Typeb Typec 101501 4496 56997 61 UMa 11 41 03.02 34 12 05.89 G8V G8V 102870 4540 57757 5 β Vir 11 50 41.72 01 45 52.98 F8.5IV-V F8V 103095 4550 57939 CF UMa 11 52 58.77 37 43 07.24 K1V G8Vp 103287 4554 58001 64 γ UMa 11 53 49.85 53 41 41.14 A1IV(n) A0V 106591 4660 59774 69 δ UMa 12 15 25.56 57 01 57.42 A2Vn A3V 109358 4785 61317 8 β CVn 12 33 44.55 41 21 26.93 G0V G0V 110897 4845 62207 10 CVn 12 44 59.41 39 16 44.10 F9V G0V 114710 4983 64394 43 β Com 13 11 52.39 27 52 41.46 G0V G0V 116842 5062 65477 80 g UMa 13 25 13.54 54 59 16.65 A6Vnn A5V 118098 5107 66249 79 ζ Vir 13 34 41.59 −00 35 44.95 A2Van A3V 126660 5404 70497 23 θ Boo 14 25 11.80 51 51 02.68 F7V F7V 126868 5409 70755 105 φ Vir 14 28 12.14 −02 13 40.65 G2IV G2IV 128167 5447 71284 28 σ Boo 14 34 40.82 29 44 42.47 F4VkF2mF1 F3V 131156 5544 72659 37 ξ Boo 14 51 23.38 19 06 01.66 G7V G8V 134083 5634 73996 45 c Boo 15 07 18.07 24 52 09.10 F5V F5V 140538 5853 77052 23 ψ Ser 15 44 01.82 02 30 54.62 G5V G5V 141795 5892 77622 37 ǫ Ser 15 50 48.97 04 28 39.83 kA2hA5mA7V A2m 142860 5933 78072 41 γ Ser 15 56 27.18 15 39 41.82 F6V F6V 146233 6060 79672 18 Sco 16 15 37.27 −08 22 09.99 G2V G1V 157214 6458 84862 72 w Her 17 20 39.57 32 28 03.88 G0V G0V 162003 6636 86614 31 ψ Dra 17 41 56.36 72 08 55.84 F5IV-V F5IV-V 161868 6629 87108 62 γ Oph 17 47 53.56 02 42 26.19 A1VnkA0mA0 A0V 164259 6710 88175 57 ζ Ser 18 00 29.01 −03 41 24.97 F2V F3V 165777 6771 88771 72 Oph 18 07 20.98 09 33 49.85 A5V A4IVs 168151 6850 89348 36 Dra 18 13 53.83 64 23 50.23 ··· F5V 173667 7061 92043 110 Her 18 45 39.73 20 32 46.71 F5.5IV-V F6V 177724 7235 93747 17 ζ Aql 19 05 24.61 13 51 48.52 A0IV-Vnn A0Vn 182572 7373 95447 31 b Aql 19 24 58.20 11 56 39.90 ··· G8IV 185144 7462 96100 61 σ Dra 19 32 21.59 69 39 40.23 G9V K0V 185395 7469 96441 13 θ Cyg 19 36 26.54 50 13 15.97 F3+V F4V 187013 7534 97295 17 Cyg 19 46 25.60 33 43 39.35 F5.5IV-V F7V 187691 7560 97675 54 Aql 19 51 01.64 10 24 56.62 F8V F8V 195564 7845 101345 GJ 792.1 A 20 32 23.70 −09 51 12.20 G2V G2.5IV 210418 8450 109427 26 θ Peg 22 10 11.99 06 11 52.31 ··· A2V 211336 8494 109857 23 ǫ Cep 22 15 02.19 57 02 36.91 ··· F0IV 213558 8585 111169 7 α Lac 22 31 17.50 50 16 56.97 ··· A1V 215648 8665 112447 46 ξ Peg 22 46 41.58 12 10 22.40 F6V F7V 222368 8969 116771 17 ι Psc 23 39 57.04 05 37 34.65 F7V F7V Notes: a) Bayer-Flamsteed or GJ (Kostjuk 2004), b) Gray et al. (2001, 2003), c) SIMBAD (Wenger et al. 2000). Table 2.3: Magnitudes and Colors of the Sample V K (B − V ) π σ(π) MV HD (mag) (mag) (mag) (mas) (mas) (mag) 166 6.07 4.31 0.752 73.16 0.56 5.39 4614 3.46 1.99 0.587 168.01 0.48 4.59 5015 4.80 3.64 0.540 53.35 0.33 3.44 6582 5.17 3.51 0.704 132.40 0.60 5.78 10780 5.63 4.01 0.804 99.34 0.53 5.62 16895 4.10 2.70 0.514 89.88 0.23 3.87 19373 4.05 2.72 0.595 94.87 0.23 3.94 20630 4.84 2.96 0.681 109.39 0.27 5.03 22484 4.29 2.84 0.575 71.60 0.54 3.56 25457 5.38 4.18 0.516 53.09 0.32 4.01 Continued on Next Page. . .

24 Table 2.3 – Continued V K (B − V ) π σ(π) MV HD (mag) (mag) (mag) (mas) (mas) (mag) 27045 4.93 4.36 0.259 34.55 0.38 2.62 30652 3.19 1.60 0.484 123.94 0.17 3.66 33564 5.08 3.91 0.506 47.88 0.21 3.48 34411 4.69 3.04 0.630 79.18 0.28 4.18 35296 5.00 4.04 0.544 69.50 0.38 4.21 38858 5.97 4.41 0.639 65.90 0.41 5.06 39587 4.39 3.00 0.594 115.42 0.27 4.70 43042 5.20 4.13 0.430 48.06 0.34 3.61 43386 5.04 4.25 0.431 51.98 0.27 3.62 46588 5.44 4.14 0.525 55.95 0.27 4.18 48682 5.24 4.13 0.575 59.82 0.30 4.12 48737 3.35 1.69 0.443 55.55 0.19 2.07 50692 5.74 4.29 0.573 58.02 0.41 4.56 55575 5.54 4.12 0.576 59.21 0.33 4.40 56537 3.58 3.54 0.106 32.36 0.22 1.13 58855 5.35 4.18 0.470 49.41 0.36 3.82 58946 4.16 2.98 0.320 55.41 0.25 2.88 69897 5.13 3.87 0.487 54.73 0.32 3.82 78154 4.80 3.56 0.489 49.07 0.37 3.25 78209 4.46 4.04 0.288 34.70 0.25 2.16 81937 3.65 2.86 0.360 41.99 0.16 1.77 82328 3.17 1.97 0.475 74.18 0.13 2.52 82885 5.40 3.69 0.770 87.96 0.32 5.12 86728 5.37 3.82 0.676 66.47 0.32 4.48 87696 4.49 4.00 0.190 35.41 0.18 2.24 90089 5.25 4.27 0.399 46.51 1.40 3.59 90839 4.82 3.64 0.541 78.26 0.29 4.29 95418 2.34 2.29 0.033 40.89 0.16 0.40 97603 2.56 2.14 0.128 55.82 0.25 1.29 101501 5.31 3.59 0.723 104.03 0.26 5.40 102870 3.59 2.27 0.518 91.50 0.22 3.40 103095 6.42 4.37 0.754 109.98 0.41 6.63 103287 2.41 2.43 0.044 39.20 0.40 0.38 106591 3.32 3.10 0.077 40.50 0.14 1.36 109358 4.24 2.85 0.588 118.49 0.20 4.61 110897 5.95 4.47 0.557 57.55 0.32 4.75 114710 4.23 2.92 0.572 109.53 0.17 4.43 116842 3.99 3.15 0.169 39.91 0.14 2.00 118098 3.38 3.22 0.114 44.01 0.19 1.60 126660 4.04 2.74 0.497 68.83 0.14 3.23 126868 4.84 3.07 0.693 27.58 1.01 2.05 128167 4.47 3.34 0.364 63.16 0.26 3.47 131156 4.54 1.97 0.720 149.03 0.48 5.41 134083 4.93 3.86 0.429 51.14 0.31 3.47 140538 5.86 4.30 0.684 68.21 0.66 5.03 141795 3.71 3.43 0.147 46.28 0.19 2.04 142860 3.85 2.70 0.478 88.85 0.18 3.59 146233 5.49 4.19 0.652 71.93 0.37 4.77 157214 5.38 3.91 0.619 69.80 0.25 4.60 Continued on Next Page. . .

25 Table 2.3 – Continued V K (B − V ) π σ(π) MV HD (mag) (mag) (mag) (mas) (mas) (mag) 161868 3.75 3.62 0.043 31.73 0.21 1.26 162003 4.57 3.50 0.434 43.79 0.45 2.78 164259 4.62 3.64 0.390 42.44 0.33 2.76 165777 3.71 3.41 0.159 37.56 0.22 1.58 168151 4.99 3.94 0.440 43.63 0.17 3.19 173667 4.19 3.19 0.483 52.06 0.24 2.77 177724 2.99 2.88 0.014 39.27 0.17 0.96 182572 5.17 3.04 0.761 65.89 0.26 4.26 185144 4.67 2.90 0.786 173.77 0.18 5.87 185395 4.49 3.54 0.395 54.55 0.15 3.17 187013 5.00 3.83 0.476 47.11 0.26 3.37 187691 5.12 3.90 0.563 52.11 0.29 3.70 195564 5.65 4.00 0.690 40.98 0.33 3.71 210418 3.52 3.38 0.086 35.34 0.85 1.26 211336 4.18 3.54 0.278 38.17 0.97 2.09 213558 3.76 3.85 0.031 31.80 0.12 1.27 215648 4.20 2.96 0.502 61.37 0.20 3.14 222368 4.13 2.95 0.507 72.91 0.15 3.44

26 –3– Interferometric Calibrators 3.1 The Calibrator 3.1.1 Calibrator Selection I used the web interface of getCal1 for the preliminary calibrator search. This tool allows you to search for objects around your science star. It has many handy additional features such as limiting the luminosity classes or maximum angular diameters of the stars in the output. Very basic selection guidelines to find near-perfect calibrators (as the perfect calibrator is impossible to find) are as follows: they must be close to your target, normal (single stars with very boring atmospheric properties), and close to unresolved in angular diameter. Because the goal of this project is to determine very accurate, indisputable angular diameters, I paid very close attention to calibrator selection and often observed an object with more than one calibrator to ensure that the results on the science star were calibrated correctly. Details of this can be found later in this chapter in the section on Observing Techniques. Identifying calibrator stars that are close to your science target has many justifications. A good rule of thumb is to have the calibrator < 10◦ from the science target. This allows for quick transitions from calibrator to object and back to calibrator. Additionally, the effects from astronomical seeing change over time during the night, and could also vary greatly 1 http://nexsciweb.ipac.caltech.edu/gcWeb/gcWeb.jsp

27 depending on what part of the sky you are observing your objects. A long lapse of time between observations of the calibrator and object may ruin the data calibration. A second quality that we must have in the calibrator star is that it is normal, which is a very tough characteristic to find in stellar astronomy. Fortunately, much work has been done on the nearby bright stars (the ones we typically observe with LBOI), and the online catalogues are fairly up-to-date, so there are not many surprises from a star that appears to be normal but ends up not normal at all. I classify a normal star to be one that is not rotationally distorted, pulsating, or spotty. The normal calibrator star must also be single or have a companion with separation no less than 10 arcsec. This is to ensure that the companion does not contaminate the data collected, and that the measured visibilities will only be from the light of the primary star. Additionally, this separation limit will ensure us that the photometry collected for the SED fit to determine the calibrator’s angular diameter is only detected from the primary star. The final requirement in selecting a good calibrator is that it must be unresolved at the baselines that we are observing. The uncertainty in the calibrator star’s angular diameter propagates through in the final data calibration. If the calibrator is very unresolved, there is much less influence of the error of the estimated angular diameter with the calibration of the data. This is discussed in more detail in the paragraphs to follow. Typically, the output of getCal yields dozens of calibrators, depending on the selection criteria set by the user. Each star in the output must then be double checked for its goodness as a calibrator, taking into consideration the topics listed above. Table 3.1 lists the calibrators used in the thesis giving their right ascension RA, declination DEC, V and K magnitudes, and the relevant science object(s) it was observed with for this project. SED fits were

28 preformed on each of these calibrators to estimate their angular diameters in the same manner as the object SED fits (discussed in the previous chapter). Table 3.2 shows the calibrator HD number, effective temperature TEFF , gravity log g, and SED diameters θSED of the calibrator stars used in this work. The last column shows which targets were observed using each calibrator. Appendix B shows the plots of the SED fits for these calibrators. 3.2 Calibrating Interferometric Data Observations made with the CHARA Array, like all other optical interferometers, need to be calibrated to convert the data we record (the instrumental Visibility, or (Vi )) into the true Visibility (Vt ). The Vi is affected by several components of either the instrument and/or the observing conditions, which we assume to know very well, and we also assume to be somewhat stable and linear with time. In order to calibrate the data we take on an object, we make observations in a sequence bracketed with observations of a calibrator star. For example, to record one bracket, the sequence Calibrator−Object− Calibrator is performed, where Vi is recorded for both the calibrator’s observations (Vi,C ), and the object’s (Vi,O ). Calibration of interferometric data then uses the relation to find the true Visibility of the object (Vt,O ): Vi,O Vt,O = Vt,C × (3.1) Vi,C The angular diameter of the calibrator star is needed to calculate the true visibility of the calibrator Vt,C . We derive the angular diameter of the calibrator star by fitting flux-calibrated broad-band photometric observations to a Kurucz model spectral energy distribution (SED)

29 (see Table 3.2 and Appendix B). This method is much more precise than the simple technique of estimating the linear diameter of a calibrator star based on its spectral type, and converting this linear diameter to an angular diameter by applying the tiny triangle formula (θSp.Ty. = diameter/distance). Thus, once we have the estimated angular diameter of the calibrator star θSED , the true visibility of the calibrator star Vt,C at the time of observations is determined by evaluating the Bessel Function J1 for the θSED of the calibrator star (evaluated at the central wavelength of λ = 2.15 µm and the baseline at the time the object observation was made B): 2J1 (πBθSED λ−1 ) V = (3.2) πBθSED λ−1 Afterwards, we perform a linear interpolation of the calibrator’s visibilities to the times of the object observations, and solve Equation 3.1 above to get Vt,O . The errors in the final true visibility of the object are then a combination of the in- strumental errors in the object and calibrator visibilities, as well as the uncertainty in the calibrator’s true visibility (arising from the error in the estimated θSED of the calibrator star). Adding each of these errors in quadrature, we use the formula (derived from Equation 3.1) to get the calibrated visibility errors for the object δVt,O : 2 2 2 Vi,O Vt,O Vi,O Vt,C δVt,O = δVt,C + 2 δVi,C + δVi,O (3.3) Vi,C Vi,C Vi,C From simple inspection of the equations above, we can see that the largest error is that propagated from the uncertainty of the calibrator’s estimated diameter. The effect of the uncertainty of a calibrator’s diameter increases the more resolved (closer to zero visibility)

30 Figure 3.1: The Calibrator’s Diameter: The effect on the errors of a calibrator’s estimated diameter depend on its angular size. Seen here are visibility curves of two stars, one with a diameter of θ = 1.0 mas and the other with θ = 0.5 mas. With the same percentage uncertainty in the estimated diameter (5%), the error propagated (σ V/V) for the star of the smaller diameter is much smaller. Plot courtesy of H. A. McAlister. it is during observations. Figure 3.1 shows a graphical representation of this effect for two hypothetical stars of different sizes. At long baselines, where the θ = 1.0 mas star starts to become resolved, the corresponding values of σV/V start to rise much quicker than that for the smaller star which is still moderately unresolved at these baselines. If the calibrator is small enough, even a 100% error on the diameter does not yield noticeable effects at CHARA’s baselines. 3.3 Observing Techniques Many of the following sections describing observing techniques are typically topics for which the observer has a pre-chosen preference. However, each of these points has never been formally tested at the CHARA Array. Here, I show limits of several observing techniques and, in turn, how successful the data calibration process is with each method. This results in what should be referred to as “Tabby’s bona fide observing techniques ”.

31 3.3.1 When Is a Good Time to Align NIRO? The NIRO (Near InfraRed Observer) camera alignment is very important when it comes to calibrating interferometric visibilities. The input optics into the NIRO camera must allow for the light to fall on the center of the chip for data to be collected (in either 1×1 or 2×2 pixel arrays). Slight changes over time as an object moves across the sky during a short amount of time can offset the alignment of the system. For example, Figure 3.2 and Figure 3.3 show a sequence of bracketed observations for HD 215648 and a calibrator, HD 214923 (2007-07-21), taken over the course of approximately 2.5 hours. In Figure 3.2, one can see that just before 1.5 hours have passed, the system alignment starts to degrade, although the object and calibrator visibilities are still tracking one another. This sudden drop in the measured instrumental visibility for each is significant enough to show two effects in the object’s calibrated visibilities: (1) the visibility errors become increasingly larger, and (2) the calibrated visibility measurements fit to a single star visibility function show larger residuals (demonstrated in Figure 3.3, at baselines < 300 meters). NIRO alignment should not be done in the middle of a bracket, for the simple reason that it is an adjustment to the system, and calibration can be offset. The observer should complete the bracket, perform the alignment, then start a new bracket after the alignment is complete. 3.3.2 Classic Observing: 1×1 Versus 2×2 Pixels The light collecting area on the NIRO camera chip can be set to 1×1 or 2×2 pixels. During the start of my observing days with CHARA Classic, it was taught to be a good rule of thumb to observe with 2×2 pixels. In preparation for H-band observations (which need to

32 0.8 0.6 INSTRUMENTAL VISIBILITY 0.4 0.2 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 TIME (Hours) Figure 3.2: Bad NIRO Alignment Effects: Data for HD 215648 and its calibrator taken on 2007-07-21. Instrumental visibilities for the calibrator (plusses), object (crosses), and the object’s calibrated visibilities (diamonds) and 1-σ errors are shown with respect to time. The dotted line marks a time where NIRO should have been realigned. be done in 1×1)2 , I decided to perform a test of the calibration of the data made with the different pixel array sizes, mainly to see how poor seeing will affect the data quality on 2×2 pixel observing. On 2007-11-16, I observed 5 brackets of HD 90839 (with the calibrator HD 89389) in both 2×2 and 1×1 pixel arrays. Figure 3.4 shows the results of the test with data calibration, and Figure 3.5 shows the resulting diameter fit with data taken in each observing mode. Two things are learned from this test. The first is that the errors are smaller by a modest amount 2 The readout mode for H band is different than in K band, and saturation is an issue. If the camera is set to read out in 2×2 pixel arrays, saturation can occur on one pixel at a time during the scan, making data reduction hopeless.

33 1.0 0.8 VISIBILITY 0.6 0.4 0.2 0.0 280 290 300 310 320 330 BASELINE (METERS) Figure 3.3: Bad NIRO Alignment Effects: Limb darkened diameter fit to the calibrated visibilities of HD 215648 taken on 2007-07-21. In this case, Time= 0 in Figure 3.2 represents the points at the longest projected baseline shown here. Data obtained with baselines shorter than 300 meters are those where NIRO re-alignment should have been done (after 1.5 hours of observing, Figure 3.2). when observing with a 1×1 pixel array. The second is that the measured visibilities, and therefore the calibrated visibilities, are much more stable and have much less scatter in the diameter fit while observing with a 1×1 pixel array. Because of these results, it is thought that when the chip is set to read out in a 1×1 pixel array, it acts like a spatial filter. 3.3.3 Night-to-Night Repeatability The previous section shows the greatly improved stability in the measured visibilities for HD 90839 when observing with 1×1 pixels. An additional test was performed to investigate the night-to-night repeatability of the calibrated visibilities in 1×1 observing mode. Fig-

34 1.2 2x2 Pixels 1x1 Pixels 1.0 Calibrated Visibilities 0.8 INSTRUMENTAL VISIBILITY 0.6 Calibrator 0.4 Object 0.2 0.0 0.0 0.5 1.0 1.5 2.0 TIME (Hours) Figure 3.4: NIRO 1×1 Versus 2×2 Pixels: Data for HD 90839 and its calibrator taken on 2007-11-16. Instrumental visibilities for the calibrator (plusses), object (crosses), and the objects calibrated visibilities (diamonds) are shown with respect to time. The dotted line marks the time when NIRO was changed to collect data in 1×1 mode. ure 3.6 and Figure 3.7 show calibrated visibilities and the resulting diameter fit for HD 103095 taken on 2007-11-16 and 2007-12-24. In comparing the raw, instrumental visibilities of the calibrator and the object in Figure 3.6, we can see that they are offset by about 0.1 in the raw insturmental visibility from the November to the December observations. This offset in the raw visibilities is not a concern (rather expected), and is only an effect of the observing conditions. The results in the night-to-night repeatability are actually seen in Figure 3.7. Here, the values of the object’s calibrated visibilities for each night agree exceptionally well

35 1.2 2x2 Pixels 1x1 Pixels 1.0 0.8 VISIBILITY 0.6 0.4 0.2 0.0 220 230 240 250 260 270 280 290 BASELINE (METERS) Figure 3.5: NIRO 1×1 Versus 2×2 Pixels: Limb darkened diameter fit to the calibrated visibilities of HD 90839 taken on 2007-11-16. The scatter in the calibrated visibilities when observing with 2×2 pixels is apparent here. in the resulting diameter fit, proving that both the choice of calibrator was good and that the data calibration in this observing mode was successful. 3.3.4 Object/Calibrator Brightness Offsets and Calibration A good calibrator is unresolved at long baselines and thus is almost always intrinsically fainter than your science star (unless you use a very early-type calibrator). There exist four sampling rates to choose from when observing with CHARA Classic, namely 1000, 750, 500, and 250 Hz. The default is set to observe at 750 Hz, but for stars fainter than K ∼ 5 mag, a slower frequency (e.g. 500 Hz) may be desired, depending on the signal to noise of the data.

36 1.0 1.0 Calibrated Visibilities 0.8 0.8 INSTRUMENTAL VISIBILITY INSTRUMENTAL VISIBILITY 0.6 0.6 Calibrator 0.4 0.4 Object 0.2 0.2 2007-11-16 2007-12-24 0.0 0.0 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 2.0 2.5 TIME (Hours) TIME (Hours) Figure 3.6: Night-to-Night Repeatability: Data for HD 103095 and its calibrator taken on 2007-11- 16 and 2007-12-24. Instrumental visibilities for the calibrator (plusses), object (crosses), and the object’s calibrated visibilities (diamonds) are shown with respect to time. In the right panel, the asterisk symbol is a placeholder to indicate when NIRO was aligned. Almost all calibrators in this thesis are fainter than this limit, but 500 Hz was only used when seeing conditions were very poor. I performed a calibration check to ensure that although the counts appear low on the NIRO SUM window (on the NIRO server), the reduced data still calibrate well. The test bracket went as follows: • Calibrator at 500 Hz • Calibrator at 750 Hz • Object at 500 Hz

37 1.2 1.0 0.8 VISIBILITY 0.6 0.4 0.2 = 2007-11-16 = 2007-12-24 0.0 280 290 300 310 320 330 340 BASELINE (METERS) Figure 3.7: Night-to-Night Repeatability: Limb darkened diameter fit to the calibrated visibilities of HD 103095 taken on 2007-11-16 (diamonds) and 2007-12-24 (squares). Excellent agreement is seen in the resulting diameter fit for observations taken over a month apart. • Object at 750 Hz • Calibrator at 500 Hz • Calibrator at 750 Hz Calibrating the records of different frequencies independently (the error in the calibrated visibility is ∼ 10%), the calibrated visibilities when reduced with MathCAD are: V500 Hz = 0.82, and V750 Hz = 0.83 and the resulting calibrated visibilities when reduced in reduceir are: V500 Hz = 0.86, and V750 Hz = 0.85. This test shows that the calculated error of the visibilities

38 of ∼ 10% is much greater than the deviation in the two program’s calibrated visibilities (∼ 2%), as well as the difference produced by the two recording frequencies (∼ 1%). 3.3.5 Observing with Two Calibrators There exist several reasons to observe with more than one calibrator, as discussed in the beginning of this chapter. The typical observing cadence of observing with one calibrator is C-O-C-O-C-O-C. . . , where ‘C’ denotes a calibrator observation, and ‘O’ denotes an object observation. If you have chosen a good pair of calibrators, the object’s calibrated visibilities should agree with each other perfectly. The observer may choose to observe with one calibrator on one night, and another calibrator on the next, and rotate back to test if the calibrated data agree with one another. An alternative way to take brackets with two calibrators follows the sequence: C1-C2-O-C2-C1-O-C1-C2-O-C2-C1-O-C1-C2. . . Here, the object is always closely bracketed between either the first calibrator ‘C1’ or the second calibrator ‘C2’. This way of observing also allows you to track the calibrator’s visibilities against one another. The data can also be calibrated with both calibrators, giving higher weight to the calibrator data observed closer in time to the object. The downside of observing in this sequence is that a N IRO alignment is usually needed by the time the second or third bracket is completed. In Figure 3.8, I have illustrated the agreement of calibrated observations for HD 30652, taken on 2008-10-01. On this night, the object was observed with two calibrators, rotating 3 brackets with each one, taken in the order:

39 1.2 Calibrator: HD 31295 = 1.0 HD 28355 = 0.8 VISIBILITY 0.6 0.4 0.2 0.0 280 300 320 340 BASELINE (METERS) Figure 3.8: Two Calibrator Diameter Fit: Limb darkened diameter fit to the calibrated visibilities of HD 30652 taken on 2008-10-01. The diamonds represent data calibrated with the star HD 31295, and the squares represent the data calibrated with the star HD 28355. Excellent agreement is seen in the resulting diameter fit for observations calibrated with both calibrators. C1-O-C1-O-C1-O-C1 − C2-O-C2-O-C2-O-C2 − C1-O-. . . (aligning NIRO or moving carts where a ‘−’is indicated). Observing in this fashion has proven to be the most efficient and beneficial way to observe with two calibrators. In Figure 3.8, the calibrated visibilities for HD 30652 are shown in a single diameter fit. The agreement from one calibrator to the next (in an alternating observing pattern), is excellent, over a range of projected baselines.

40 3.3.6 Signs of a Bad Calibrator Estimates of the instrumental visibility Vi are recorded during observing by the Grand Wazoo for each data record. These numbers can help identify the use of a bad calibrator. This is especially the case if the calibrator you are observing has visibilities smaller than those of the object, and the estimated size of the calibrator is thought to be smaller (i.e., unresolved). It is then the likely case that your calibrator is a previously undetected binary, or the observer did a poor job checking the calibrator’s ‘goodness ’. Another hint that the calibrator is bad (a binary) is that the calibrator visibility estimates change drastically over the few hours you are taking brackets, while the object visibility estimates stay constant. Although detecting this pattern can also mean that the object could also be a previously undetected binary, or the instrumental system and/or seeing is unstable, one can deduce the real source of the variability by looking at the entire night’s data set. Figure 3.9 shows the unmistakable signature of a bad calibrator (HD 41074), taken with the target star HD 48682 on 2007-12-24. In this data set, Figure 3.9 shows that the calibrated visibilities reach values >1, purely indicative of a calibrator star that is a binary, and the calibrated visibility observations for this star need to be thrown away. Bad calibrators may appear less conspicuous when observing over the course of a few hours if there is not much change in position angle of the baseline projected on the sky during the time when the object is observed. More subtle effects may also arise if the chosen calibrator is single, but not round (i.e., rapidly rotating or has a disk). The four stars in Table 3.3 were observed and have been identified as bad calibrators, or in other words, newly discovered binaries.

41 1.5 1.0 INSTRUMENTAL VISIBILITY Calibrated Visibilities 0.5 Calibrator Object 0.0 0.0 0.5 1.0 1.5 2.0 TIME (Hours) Figure 3.9: Binary Calibrator Brackets: Brackets of HD 48682 and its calibrator taken on 2007-12-24. Instrumental visibilities for the calibrator (plusses), object (crosses), and the object’s calibrated visibilities (diamonds) are shown with respect to time. The change in the calibrator visibilities with respect to time are a good indicator that this calibrator (HD 41074) is a binary. Also note that the calibrated visibilities reach values greater than 1.0, a tell-tale sign that the calibrator used is a binary. 3.4 Miscellaneous 3.4.1 The Baseline Test Due to the fact that the star is moving across the sky when observing, the moving delay cart must compensate for this motion to obtain interference fringes. Each data record takes ≈200 scans, with shutter sequences in the beginning and end of the record to enable us to remove background and noise from the data. The time it takes to take one data record depends on scan length (short, medium, or long), and the sampling rate (250, 500, 750, or 1000 Hz), all

42 of which are chosen by the observer3 . The amount of change in projected baseline depends on where the object is in the sky and which baseline is being used. The combination of these conditions can change the projected baseline calculated from the beginning of the record to the end of the record by an amount on the order of meters. In our diameter fits for stars in this thesis, the projected baseline at the time of mid-observation is used. We tested this effect on the diameter fit for the calibrated visibilities when we used the projected baseline at the start of the record versus the projected baseline at the end of the record for observations of HD 6582 taken on 2007-7-17. These data were taken at 500 Hz (slower than the normal 750 Hz sampling rate) using a long scan (which also contributes to a longer observation record), where each data record is ≈ 7.1 minutes in duration. There is an average difference of three meters of projected baseline between the beginning to the end of each observation4 . Performing diameter fits to each set of calibrated points (one using B from the beginning of the observations and one using B from the end of the observation), we find that the baseline motion during observing is an insignificant contribution (about 0.2% out of 1.5%) to the overall uncertainty in diameter. 3.4.2 Lab Vibrations Vibrations in the lab may cause spurious visibility measurements and lead to calibration errors. They are likely to manifest while observing due to cooling fans in electrical devices or due to mechanical devices in the lab being moved in some manner. Things that have caused issues in the past are: the PICO #3 micrometer driven control box, the HVAC 3 Time for one observation takes place over ≈ 3−8 minutes 4 The change in baseline also depends on where the object is in the sky and the bsaeline used for obser- vation.

43 (which sits on a bed of springs to alleviate most of the effects), and the vacuum pumps for the vacuum light tubes. Figure 3.10 and Figure 3.11 show data taken on lab fringes that T. ten Brummelaar obtained and analyzed on 2007-01-27. Here, we can clearly see that in Figure 3.11, where the HVAC unit is turned on, the power spectrum is much lumpier and wider than the power spectrum of the data when it is turned off in Figure 3.10. Relocation of the offending components and the adoption of appropriate observing practices can nearly completely eliminate these problems.

44 Figure 3.10: Lab Vibrations: Plot of data reduced from lab fringes with the HVAC units turned off. Figure 3.11: Lab Vibrations: Plot of data reduced from lab fringes with the HVAC unit turned on.

45 Table 3.1: Calibrators Observed Calibrator RA DEC V K Target (s) HD (hh mm ss.xx) (dd mm ss) (mag) (mag) HD 71 00 05 39.73 55 42 36 7.0 4.2 4614 6210 01 04 19.45 61 34 49 5.8 4.4 4614, 5015, 6582, 10780 9407 01 34 33.26 68 56 53 6.5 4.9 4614 20675 03 21 52.53 49 04 15 5.9 4.9 16895, 19373 21790 03 30 37.06 −05 04 31 4.7 4.9 20630, 22484, 25457 22879 03 40 22.06 −03 13 01 6.7 5.2 20630, 22484, 25457 28355 04 28 50.16 13 02 51 5.0 4.5 30652 30739 04 50 36.72 08 54 00 4.3 4.2 30652 31295 04 54 53.73 10 09 03 4.6 4.6 30652 34904 05 22 50.31 41 01 45 5.5 5.1 34411 38558 05 47 26.20 17 43 45 5.5 4.5 39587 42807 06 13 12.50 10 37 38 6.4 4.6 48737 43042 06 14 50.88 19 09 23 5.2 4.1 39587 43795 06 20 16.04 42 47 60 7.7 5.4 48682 50277 06 52 49.47 08 22 49 5.8 5.1 48737 58551 07 26 50.25 21 32 08 6.5 5.2 56537 59037 07 29 20.44 28 07 06 5.1 4.7 58946 65583 08 00 32.13 29 12 44 6.9 5.1 58946 83951 09 42 42.70 35 05 36 6.1 5.2 82885, 86728 87141 10 04 36.32 53 53 30 5.7 4.5 82328 88986 10 16 28.08 28 40 57 6.5 4.9 86728 89389 10 20 14.79 53 46 46 6.5 5.0 90839, 95418 91480 10 35 09.69 57 04 57 5.2 4.3 81937, 90839, 95418 99285 11 25 36.37 16 27 24 5.6 4.6 97603 99984 11 41 34.26 31 44 45 5.7 4.5 103095 102124 11 45 17.04 08 15 29 4.8 4.4 102870 102634 11 49 01.28 00 19 07 6.2 4.9 102870 103799 11 57 14.58 40 20 37 6.6 5.3 101501, 103095, 109358 110897 12 44 59.41 39 16 44 6.0 4.5 109358 114093 13 08 02.41 24 49 52 6.8 4.6 114710 120066 13 46 57.12 06 21 01 6.3 4.9 118098 128093 14 34 11.71 32 32 04 6.3 5.2 128167 129153 14 40 42.39 13 32 04 5.9 5.4 131156 132254 14 56 23.04 49 37 42 5.6 4.4 126660 135101 15 12 43.48 19 17 10 6.7 5.0 131156 139225 15 36 29.23 16 07 09 5.9 5.0 142860 140775 15 45 23.48 05 26 50 5.6 5.4 141795 145607 16 12 07.32 −08 32 51 5.4 5.1 146233 150177 16 39 39.13 −09 33 17 6.3 5.0 146233 154099 16 56 16.74 73 07 40 6.3 5.6 162003 158352 17 28 49.70 00 19 49 5.4 4.8 164259 158633 17 25 00.10 67 18 24 6.4 4.5 168151 162004 17 41 58.11 72 09 25 5.8 4.5 162003 167564 18 15 59.93 −03 37 05 6.3 5.8 165259 174897 18 52 18.64 14 32 08 6.5 4.1 182572 176303 18 59 05.74 13 37 20 5.3 3.9 173667, 177724, 182572, 187691 180317 19 15 17.36 21 13 56 5.7 5.3 173667, 177724 Continued on Next Page. . .

46 Table 3.1 – Continued Calibrator RA DEC V K Target (s) HD (hh mm ss.xx) (◦ ′ ′′) (mag) (mag) HD 183534 19 27 25.96 52 19 13 5.7 5.7 185395 184499 19 33 27.08 33 12 07 6.6 5.1 187013 189395 19 58 37.98 30 59 01 5.5 5.6 187013 191195 20 06 13.85 53 09 56 5.9 4.8 185395 193555 20 20 15.38 15 32 34 6.8 5.5 187691 193664 20 17 31.33 66 51 13 5.9 4.5 185144 195838 20 34 11.70 −13 43 16 6.1 4.8 195564 204485 21 28 08.25 32 13 31 5.8 5.0 201091, 201092 210715 22 11 09.89 50 49 24 5.4 5.0 213558 211976 22 20 55.80 08 11 12 6.2 5.0 210418, 215648 214923 22 41 27.72 10 49 53 3.4 3.6 215648 216735 22 55 13.67 08 48 58 4.9 4.8 215648, 222368 218470 23 07 45.38 49 17 45 5.7 4.6 213558 222603 23 42 02.80 01 46 48 4.5 4.1 222368 225003 00 02 29.70 08 29 08 5.7 4.9 222368 Table 3.2: Calibrator SED Diameters Calibrator TEFF log g θSED Target (s) HD (K) (cgs) (mas) HD 71 4500 4.50 0.682 ± 0.024 4614 6210 6100 3.80 0.519 ± 0.012 4614, 5015, 6582, 10780 9407 5800 4.50 0.430 ± 0.017 4614 20675 6600 4.20 0.415 ± 0.012 16895, 19373 21790 11500 3.70 0.308 ± 0.009 20630, 22484, 25457 22879 6250 4.25 0.342 ± 0.021 20630, 22484, 25457 28355 8000 4.00 0.425 ± 0.030 30652 30739 9450 3.90 0.461 ± 0.018 30652 31295 8800 4.10 0.439 ± 0.043 30652 34904 7900 4.00 0.345 ± 0.013 34411 38558 7100 3.50 0.422 ± 0.008 39587 42807 5850 4.45 0.429 ± 0.016 48737 43042 6650 4.25 0.591 ± 0.030 39587 43795 5000 2.50 0.376 ± 0.008 48682 50277 7400 4.00 0.346 ± 0.011 48737 58551 6200 4.00 0.357 ± 0.009 56537 59037 8450 4.20 0.389 ± 0.018 58946 65583 5550 4.50 0.406 ± 0.033 58946 Continued on Next Page. . .

47 Table 3.2 – Continued Calibrator TEFF log g θSED Target (s) HD (K) (cgs) (mas) HD 83951 6750 4.00 0.360 ± 0.006 82885, 86728 87141 6400 4.00 0.476 ± 0.022 82328 88986 5850 4.00 0.432 ± 0.013 86728 89389 6100 4.20 0.398 ± 0.013 90839, 95418 91480 7050 4.25 0.518 ± 0.014 81937, 90839, 95418 99285 6800 3.90 0.456 ± 0.017 97603 99984 6200 3.80 0.483 ± 0.020 103095 102124 7950 4.20 0.466 ± 0.022 102870 102634 6350 4.25 0.404 ± 0.010 102870 103799 6300 4.50 0.343 ± 0.013 101501, 103095, 109358 110897 6150 4.25 0.492 ± 0.022 109358 114093 4900 4.40 0.572 ± 0.014 114710 120066 6000 4.50 0.428 ± 0.013 118098 128093 6600 4.10 0.351 ± 0.011 128167 129153 7650 4.25 0.309 ± 0.010 131156 132254 6350 4.00 0.520 ± 0.015 126660 135101 5750 4.40 0.409 ± 0.014 131156 139225 6900 4.00 0.380 ± 0.122 142860 140775 9000 4.00 0.275 ± 0.013 141795 145607 8400 4.00 0.325 ± 0.020 146233 150177 6250 4.00 0.391 ± 0.019 146233 154099 7300 4.00 0.283 ± 0.005 162003 158352 7450 3.90 0.407 ± 0.013 164259 158633 5400 4.50 0.542 ± 0.043 168151 162004 6250 4.20 0.498 ± 0.015 162003 167564 7500 4.00 0.259 ± 0.004 165259 174897 4950 3.50 0.652 ± 0.038 182572 176303 6200 4.25 0.659 ± 0.016 173667, 177724, 182572, 187691 180317 8050 4.00 0.309 ± 0.007 173667, 177724 183534 9500 4.00 0.241 ± 0.012 185395 184499 6050 4.50 0.383 ± 0.019 187013 189395 10650 3.50 0.235 ± 0.006 187013 191195 6650 4.25 0.432 ± 0.014 185395 193555 6150 4.00 0.328 ± 0.006 187691 193664 6100 4.50 0.494 ± 0.019 185144 195838 6300 4.25 0.421 ± 0.017 195564 204485 7100 4.25 0.381 ± 0.011 201091, 201092 210715 7950 4.20 0.366 ± 0.015 213558 211976 6600 4.00 0.373 ± 0.013 210418, 215648 214923 10100 3.75 0.611 ± 0.029 215648 Continued on Next Page. . .

48 Table 3.2 – Continued Calibrator TEFF log g θSED Target (s) HD (K) (cgs) (mas) HD 216735 10150 3.50 0.321 ± 0.022 215648, 222368 218470 6650 4.00 0.462 ± 0.014 213558 222603 7750 4.00 0.577 ± 0.032 222368 225003 7200 4.00 0.386 ± 0.017 222368 Table 3.3: Bad Calibrators RA DEC HD (hh mm ss.xx) (dd mm ss) Reason 41074 06 05 03.38 42 58 54 visibility modulation 43153 06 15 25.13 16 08 35 separated fringe packet binary 101606 11 41 34.26 31 44 46 separated fringe packet binary 181655 19 19 39.00 37 19 50 separated fringe packet binary

49 –4– Observations Observations were taken using the CHARA Array, located on Mount Wilson, CA, and re- motely operated from the Georgia State University AROC1 facility in Atlanta, GA. Observ- ing proposals for the full-year durations of 2007 and 2008 were submitted, and sufficient time was assigned to the project to collect data on forty-four stars to determine their angular di- ameters. This observed sample includes 7 A-type stars, 19 F-type stars and 18 G-type stars (also includes spectral type K0). Observations were made using the CHARA Classic beam combiner in the K ′ -band (λ = 2.15 ± 0.01 µm). The target sample was selected on the assumption that we could also observe many of these stars in H-band, which provides higher resolution than observing in K-band because of the shorter wavelength. H-band observations were desired for approximately half of the sample, allowing us to extend farther down the visibility curve to measure their diameter with better than 4% accuracy. A combination of H- and K-band observations were to be made for ∼10 of the objects, useful for comparison of data from different filters. The remaining objects are sufficiently resolved in the K-band only. H-band observations were attempted on several occasions; however, the brightness of the targets restricted us from taking any useful data2 . Ideally, observations of the stars use a combination of the longest baselines for diameter determinations. In particular, the use of CHARA’s longest baseline, S1/E1, is crucial to 1 Arrington Remote Operations Center 2 The faintest of the stars in the sample were observed in the fastest readout mode (1000 Hz) and the chip was still saturating three quarters of the way through the scan.

50 this work due to the small angular sizes of the targets. The length of the projected baseline changes naturally throughout the night due to the diurnal rotation of the Earth, so a large range in projected baselines (and thus visibility curve coverage) are obtainable with one pair of telescopes. In order to take advantage of an available orthogonal baseline configuration for better UV plane coverage for the observations, we found that either S1/W1 or E1/W1 provides a suitable complement to S1/E1. The UV plane can also be represented by the position angle of the baseline with respect to the object in the sky and it also changes throughout the night similar to the projected baseline length. Table 1.1 shows the current baseline configurations (2007) for the CHARA Array for each telescope pair’s maximum projected baseline B and position angle ψ of the baseline on the sky. Remote observing at AROC allows for easy data acquisition without travel to Mount Wilson, CA. Although a telescope operator must still be present on the mountain to do necessary lab alignment and other such things, nearly all the tasks to be done during the night can be done independently from AROC. This facility also allows for parallel observing of two independent programs using separate beam combiners and baselines. The data collected on my targets were promptly reduced and calibrated within a few days of the observations being made. Table 4.1 lists the identifications of all (52) stars made for this work (column 1), UT date (column 2), the baseline used (column 3), the number of bracketed observations (column 4), and the calibrator(s) used on that date (column 5). The abbreviation (H) denotes H-band observations, which proved to be impossible to reduce and use for this work. Observations made with a bad calibrator are denoted with a † . Stars that are incomplete in their analysis †† to this date are labeled with a in Table 4.1. Table 4.2 lists these eight stars and gives a

51 reason why those analyses are incomplete. ‘Binary (or Disk)’ indicates that the star shows dramatic changes in visibility, either during single night of observations, or over a period of time. Stars that ‘Need more data’ are not sufficiently resolved to meet the goals of this project. Omission of these eight stars leaves 44 stars with sufficient observations for the final analysis. Tables of the resulting calibrated visibilities for each star can be found in Appendix C, along with a plot of the final diameter fits.

52 Table 4.1: Observations of A, F, and G Dwarfs Object UT Number of Calibrator HD Date Baseline Brackets HD 4614 2007/06/29 W1/E1 2 6210 2007/06/30 W1/E1 5 6210 2007/07/01 W1/E1 3 6210 2007/07/18 S1/E1 3 6210 2007/07/19 S1/E1 3 6210 2007/11/16 S1/E1 4 6210 2008/10/02 W1/E1 4 6210, 9407 5015 2007/10/10 W1/E1 10 6210 2007/11/03 W1/E1 7 6210 2007/11/17 S1/E1 8 6210 6582 2007/07/01 W1/E1 3 6210 2007/07/17 S1/E1 6 6210 2007/07/18 S1/E1 8 6210 2007/09/08 S1/E1 10 6210 10780 2007/06/29 W1/E1 2 6210 2007/07/19 S1/E1 10 6210 2007/10/10 W1/E1 10 6210 16895 2007/09/08 S1/E1 7 20675 2007/11/03 W1/E1 8 20675 2007/12/24 S1/E1 6 20675 19373 2007/01/25 S1/E1 8 20675 2007/08/28 W1/S1 2 20675 2007/09/08 S1/E1 10 20675 2007/11/04 W1/E1 6 20675 20630 2007/09/09 S1/E1 9 21790 2007/09/10 S1/E1 6 (H) 21790 2008/10/01 S1/E1 4 22879 2008/11/17 S1/E1 5 22879 2008/11/18 S1/E1 5 21790, 22879 22484 2006/12/05 S1/E1 1 21790 2006/12/07 S1/E1 3 21790 Continued on Next Page. . .

53 Table 4.1 – Continued Object UT Number of Calibrator HD Date Baseline Brackets HD 2007/09/09 S1/E1 8 21790 2008/10/01 S1/E1 6 22879 2008/10/02 W1/E1 4 22879 25457†† 2008/11/17 S1/E1 6 22879 2008/11/18 S1/E1 3 21790, 22879 30652 2007/11/05 S1/E1 16 30739 2008/10/01 S1/E1 10 28355, 31295 2008/10/02 W1/E1 3 31295 34411 2007/01/26 S1/E1 5 34904 2007/11/03 W1/E1 8 34904 2007/11/15 S1/E1 4 34904 2007/11/17 S1/E1 7 34904 39587 2006/12/07 S1/E1 3 38558 2007/03/06 S1/E1 8 38558 2008/11/18 S1/E1 11 38558, 43042 48682 2007/12/24 S1/E1 6 41074† 2008/09/17 S1/E1 6 43795 2008/10/02 W1/E1 3 43795 2008/11/16 S1/E1 6 43795 48737 2006/12/07 S1/E1 4 50277 2008/11/17 S1/E1 12 42807, 50277 2008/11/18 S1/E1 11 42807, 50277 55575†† 2007/11/03 W1/E1 5 56221 2007/11/07 S1/E1 5 56221 2007/11/17 S1/E1 1 + 1 (H) 56221 56537 2007/02/21 S1/E1 1 58551 2007/02/25 S1/E1 7 58551 2007/03/11 S1/E1 6 58551 2007/11/04 S1/E1 5 58551 2007/12/23 S1/E1 5 58551 58946 2007/01/25 S1/E1 6 65583 Continued on Next Page. . .

54 Table 4.1 – Continued Object UT Number of Calibrator HD Date Baseline Brackets HD 2007/11/16 S1/E1 7 59037 2007/11/17 S1/E1 7 59037 81937 2007/11/29 S2/E2 9 91480 82328 2007/11/02 W2/E2 9 87141 82885 2007/02/03 S1/E1 2 83951 2007/11/03 W1/E1 7 83951 2007/11/07 S1/E1 9 83951 2007/12/24 S1/E1 5 83951 86728 2007/11/15 S1/E1 10 83951 2007/11/16 S1/E1 2 83951 2007/12/24 S1/E1 6 83951 2008/11/16 S1/E1 10 83951, 88986 90839 2007/11/16 S1/E1 10 89389 2008/04/17 W1/S1 5 89389, 91480 95418†† 2007/04/04 S1/E1 7 91480 2007/11/07 S1/E1 6 91480 2008/04/17 W1/S1 5 89389, 91480 97603 2007/02/21 S1/E1 10 99285 2007/03/10 S1/E1 1 99285 2007/03/11 S1/E1 5 99285 101501 2007/11/15 S1/E1 7 103799 2007/12/24 S1/E1 3 103799 102870 2007/03/09 S1/E1 6 102124 2007/12/23 S1/E1 4 102124 2008/04/19 W1/S1 8 102124 2008/04/22 S1/E1 9 102124 2008/04/23 S1/E1 7 102634 103095 2007/11/16 S1/E1 7 103799 2007/12/24 S1/E1 10 103799 Continued on Next Page. . .

55 Table 4.1 – Continued Object UT Number of Calibrator HD Date Baseline Brackets HD 109358 2007/05/26 S1/E2 3 110897 2008/04/18 W1/S1 5 103799, 110897 114710 2008/04/21 W1/S1 10 114093 2008/06/27 S1/E1 6 114093 118098 2007/03/10 S1/E1 6 120066 2007/03/30 S1/E1 5 120066 2007/12/23 S1/E1 2 120066 126660 2007/05/24 W1/S1 5 132254 2007/07/16 S1/E1 6 132254 2008/07/25 S1/E1 4 132254 128167 2008/06/28 S1/E1 5 128093 2008/07/06 S1/E1 12 128093 2008/07/24 S1/E2 10 128093 131156 2007/03/12 S1/E1 5 135101 2008/04/18 W1/S1 5 135101, 129153 2008/04/19 W1/S1 6 135101 2008/06/27 S1/E1 9 135101, 129153 141795 2008/07/22 S1/E1 8 140775 142860 2007/07/20 S1/E1 3 139225 2007/07/21 S1/E1 6 139225 2008/04/21 W1/S1 10 139225 146233 2008/04/19 W1/S1 11 145607, 150177 2008/04/21 W1/S1 6 145607, 150177 2008/04/22 S1/E1 9 145607, 150177 2008/04/23 S1/E1 6 145607, 150177 2008/05/16 W1/E2 4 150177 162003 2007/07/17 S1/E1 8 154099 2007/07/18 S1/E1 2 162004 2007/10/10 W1/E1 6 162004 2007/11/17 S1/E1 4 162004 2008/06/26 S1/E1 5 162004 Continued on Next Page. . .

56 Table 4.1 – Continued Object UT Number of Calibrator HD Date Baseline Brackets HD 164259 2008/04/22 S1/E1 6 167564, 158352 2008/04/23 S1/E1 3 158352 2008/06/20 W1/S1 3 158352 2008/06/28 S1/E1 5 158352 2008/07/27 W1/S1 6 158352 168151†† 2008/07/21 S1/E1 4 158633 173667 2007/07/20 S1/E1 3 180317 2007/07/21 S1/E1 9 176303 2007/09/10 S1/E1 12 (H) 176303 2008/04/21 W1/S1 3 176303 2008/06/28 S1/E1 8 176303 2008/07/07 W1/S1 1 176303 2008/07/21 W1/S1 1 176303 2008/07/22 S1/E1 6 176303 2008/07/23 W1/E1 6 176303 177724 2008/06/28 S1/E1 10 176303 2008/07/07 W1/S1 5 176303 2008/07/21 W1/S1 4 176303 2008/07/22 S1/E1 6 176303 2008/07/23 W1/E1 6 176303 2008/10/01 S1/E1 4 176303 182572 2007/07/21 S1/E1 6 174897 2007/09/09 S1/E1 10 174897 2008/07/22 S1/E1 5 174897 2008/07/24 S1/E2 5 174897 2008/09/30 S1/E1 7 176303 185144 2007/05/24 W1/S1 3 193664 2007/05/25 W1/S1 4 193664 2007/06/28 W1/E1 1 193664 2007/06/29 W1/E1 4 193664 2007/06/30 W1/E1 1 193664 2007/07/01 W1/E1 2 193664 185395 2007/05/26 S1/E2 3 183534 Continued on Next Page. . .

57 Table 4.1 – Continued Object UT Number of Calibrator HD Date Baseline Brackets HD 2007/07/19 S1/E1 11 191195 2007/11/02 W1/E2 5 191195 2008/07/25 S1/E1 8 191195 187013†† 2008/04/17 W1/S1 2 181655† 2008/07/23 S1/E1 10 184499, 189395 2008/07/24 S1/E2 5 184499 187691†† 2007/09/09 S1/E1 8 193555 2008/06/27 S1/E1 7 193555 2008/09/30 S1/E1 3 176303 195564†† 2008/06/20 W1/S1 3 196838 2008/06/27 S1/E1 11 196838 210418 2008/06/28 S1/E1 6 211976 2008/07/22 S1/E1 9 211976 2008/07/24 S1/E2 4 211976 2008/10/01 S1/E1 3 211976 211336†† 2008/10/02 W1/E1 4 204965 213558 2007/09/08 S1/E1 7 218470 2007/10/10 W1/E1 10 210715 2007/12/24 S1/E1 6 218470 2008/07/21 S1/E1 5 218470 215648 2007/07/16 S1/E1 4 211976 2007/07/21 S1/E1 14 214923 2008/07/24 S1/E2 5 214923 2008/09/30 S1/E1 4 211976 2008/10/01 S1/E1 8 211976, 216735 222368 2006/12/07 S1/E1 4 222603 2007/07/20 S1/E1 11 222603 2007/09/09 S1/E1 5 222603 2007/09/10 S1/E1 5 (H) 222603 2008/09/30 S1/E1 10 222603, 225003 2008/10/01 S1/E1 8 216735

58 † †† Bad calibrator used. Incomplete. Table 4.2: Problem Stars Star Reason 25457 Need more data 55575 Binary? 95418 Binary and/or Disk? 168151 Need more data 187013 Need more data 187691 Binary? 195564 Need more data 211336 Need more data

59 –5– Stellar Diameters 5.1 Diameter Fit to a Single Star Angular diameters for each star were determined by fitting the calibrated visibilities to the visibility curve for a single star’s uniform-disk and limb-darkened angular diameters. We calculate the uniform-disk θUD (Equation 5.1) and limb-darkened θLD (Equation 5.2) angular diameters from the calibrated visibilities by χ2 minimization of the following relations from Brown et al. (1974): 2J1 (x) V = , (5.1) x −1 1 − µλ µλ J1 (x) π 1/2 J3/2 (x) V = + × (1 − µλ ) + µλ , (5.2) 2 3 x 2 x3/2 and x = πBθλ−1 , (5.3) where Jn is the nth -order Bessel function and µλ is the linear limb darkening coefficient at the wavelength of observation. In Equation 5.3, B is the projected baseline in the sky, θ is the UD angular diameter of the star when applied to Equation 5.1 and the LD angular diameter when used in Equation 5.2, and λ is the central wavelength of the observational bandpass (λ = 2.15 µm). The error of the diameter fit is based upon the values on either side of the minimum for which χ2 = χ2 + 1 (Press et al. 1992; Wall & Jenkins 2003). We find in most cases that min

60 the value of the reduced χ2 is less than 1.0, meaning that we have overestimated the errors on the calibrated visibilities for the star. In the results presented here, we adjusted those error estimates to force the reduced χ2 to unity to compensate for the uncertainty in the visibility error estimates. These measured angular diameters are converted to limb darkened angular diameters θLD using the limb darkening coefficients in K-band µK found in Claret et al. (1995). Although observations with CHARA Classic are in the K ′ -band, to find the limb darkening coefficients here we assume that K ≈ K ′ , since there is a negligible difference in limb darkening correc- tions in this wavelength region. Overall, for stars of these spectral types, the correction from θUD to θLD is ≈ 2%, and therefore we expect little offset due to the dependence of stellar models in determining the limb darkening coefficients used. Table 5.1 shows the input TEFF and log g used for generating the model SED fit for each program star. The Claret et al. (1995) limb darkening coefficients (µK ) are then found through a bilinear interpolation of these TEFF and log g estimates. Table 5.1 also shows the θSED , θUD , and θLD for the stars observed in this project. Finally, we are able to determine the linear radii R of each of the stars observed by simply combining the measured parallax from van Leeuwen (2007) and the measured limb darkened angular diameter θLD (column 9). Note that this table includes only the 44 stars that meet the criteria of better than 4% accuracy on the measured angular diameter (i.e., excludes problem stars). The mean percentage error of the measured limb darkened angular diameter is 1.5%, with 0.2% as the best and 3.5% the worst. A short summary of the results for each star can be found in Appendix C, which includes tables of the calibrated visibilities for each star and plots of their diameter fits.

61 In Figure 5.1, the θSED values are plotted against the θLD angular diameters, with the color corresponding to the (B − V ) color index of the star. Here we see that most stars lie above the 1:1 ratio line, meaning that the θSED is typically underestimated for the sample, especially for stars under ≈ 0.9 mas, and for the bluer stars in the sample. Figure 5.2 shows the percent difference in the measured θLD and the θSED versus the (B − V ) color index. The average offset is ∼ 10% for all 44 stars, while diameters of stars bluer than (B − V )=0.2 are all overestimated. 2.0 1.5 LD Diameter (mas) 1.0 0.5 0.0 0.0 0.5 1.0 1.5 2.0 SED Diameter (mas) Figure 5.1: SED Versus LD Diameters with Respect to (B − V ) Color: Plot of SED versus LD angular diameters and the dependence on color index (B − V ). The color of the data point corresponds to the (B − V ) color index of the star, where blue indicates the bluest star in the sample (B − V ) = 0.013), and red indicates the reddest star in the sample (B − V ) = 0.804). The dotted line shows a 1:1 ratio.

62 Figure 5.2: Comparison of SED to LD Diameters with Respect to (B − V ) Color: Plot of the percentage difference between the angular diameters found by SED fits and observational data (∆θ), and the dependence on color index (B − V ).

63 5.2 CHARA Versus Palomar Testbed Interferometer Diameters The sample of stars for this project was selected in terms of how resolved they would be with the longest baselines of the CHARA Array. Recently, angular diameters of a few dozen main sequence stars measured with the Palomar Testbed Interferometer (PTI) were released in van Belle & von Braun (2009). This work provides measurements of 14 stars in common with the CHARA stars measured in this work and is the only alternate source of angular diameter measurements of these stars. The longest baseline obtainable with PTI is 110 m, a factor of three shorter than those of the CHARA Array, and accurate measurements are quite difficult with this instrument due to the small angular sizes of these stars. Table 5.2 lists the 14 stars in common with the van Belle & von Braun (2009) work, the limb darkened angular diameters and errors, and how many σ the two values differ from each other. For these stars, the errors on the PTI angular diameters are anywhere from 2−12 times (with an average of 6.5 times) the errors on the CHARA angular diameters presented here. However, this comparison can still point to any systematic offsets in the results from each instrument. Comparing the angular diameters from this work and van Belle & von Braun (2009), I find that the weighted mean ratio of CHARA to PTI diameters is θCHARA /θPTI = 1.052 ± 0.062. van Belle & von Braun (2009) make this same comparison of their diameters compared to diameters from Baines et al. (2008), who used the CHARA Array to measure the diameters of exoplanet host stars, and find that the ratio of the four stars they have in common is θCHARA /θPTI = 1.06 ± 0.06, very similar to the results found here, indicating again that there is a slight preference for smaller PTI diameters, and larger

64 Figure 5.3: CHARA Versus PTI Diameters: TOP: Plot of CHARA versus PTI limb-darkened angular diameters for the stars in common from this work (CHARA) and van Belle & von Braun (2009) (PTI). The dotted line shows a 1:1 ratio. BOTTOM: Plot showing the fractional difference between the CHARA and PTI limb-darkened angular diameters. The dotted line shows an equal agreement of both measurements.

65 CHARA diameters. Figure 5.3 shows this comparison in a graphical representation for the stars in common in each work, where most of the stars fall below the 1:1 line, but typically agree within 1-σ of each other. This is also seen in Boyajian et al. (2009), where I measure the diameters of the four Hyades giants with the CHARA Array. In that work, two of the stars, ǫ Tau and δ 1 Tau, were measured previously with other interferometers (Mark III, NPOI, and PTI), all which lead to smaller diameters than those measured with CHARA. However, we find that models for the Hyades age and metallicity match flawlessly with the CHARA observations, and the smaller angular diameters from other works in turn lead to temperatures that are much too hot for these stars. A main distinction that could lead to offsets in measured diameters are the estimated sizes of the calibrator stars. van Belle & von Braun (2009) also discuss their calibrator selection in their work compared to Baines et al. (2008). van Belle & von Braun (2009) set a limit to a sufficiently unresolved calibrator at CHARA to be < 0.5 mas in diameter, a criterion which all but a few calibrators in this work meet. The stars that were observed with calibrators > 0.5 mas were also observed with calibrators < 0.5 mas in order to catch any inconsistencies in the calibration process. The reality of this < 1-σ systematic displacement is questionable. To investigate the possibility that the estimated size of the calibrators in this work are offset to the calibrators used in van Belle & von Braun (2009), I compare the estimated sizes of the calibrators in the Palomar Testbed Interferometer Calibrator Catalog (PTICC, van Belle et al. 2008) to the ones derived here. Twenty-nine of the 63 calibrators used in

66 this work are included in the PTICC. Overall, the ratio of the estimated diameter of the calibrator in this work to the PTICC is 0.97 ± 0.06, a less than 1-σ difference. Twelve of the 14 stars in common with both works were observed with calibrators whose diameters are also included in the PTICC. For each of these 12 calibrators, the estimated angular diameter θSED is presented in Table 5.3, along with the ratio of the CHARA to PTI SED diameters. The object that the calibrator was observed with is also listed in Table 5.3 along with the ratio of the CHARA to PTI measured limb darkened diameters. Here, there is no pattern in the calibrator SED diameter ratio and the object diameter ratio. In fact, the effects of a slight offset in the calibrator’s estimated diameter listed above (ratio θCHARA /θPTI = 0.97±0.06) would actually contribute counterproductively to the slight offset in the diameter measurements (ratio θCHARA /θPTI = 1.05 ± 0.06). For instance, for the case of my data, the size of the calibrator θSED is typically smaller, thus the true visibility of the calibrator would be bigger (i.e., it would be more unresolved). If the true visibility of the calibrator is bigger, it would in turn make the true visibility of the object bigger in the calibration process (see Equation 3.1). Thus, the object would appear more unresolved (having larger calibrated visibilities) if I were using a SED diameter of the same calibrator but with a larger value. Because we do not see the case of smaller CHARA diameters, then this indicates that the calibrators are not the cause of any offset, if present, in each data set. 5.3 Systematics of CHARA Versus Other OLBI Diameters The diameters measured in this project are ∼ 5% larger than what is expected from SED fits, as well as compared to the measurements of some of the same stars in van Belle & von

67 Braun (2009). Here, we utilize a version of the surface brightness relation (for example, see Kervella et al. 2004a) to compare the diameters measured with CHARA Classic to diameters measured with other Optical Long Baseline Interferometry (OLBI) to determine whether there are systematic differences in our measurements. On this relation: 5 log θLD = −(KObs − ∆KTEFF ) + C (5.4) the θLD is the limb-darkened angular diameter, KObs is the observed K magnitude, and C is the constant relating your measured K magnitude to the angular diameter. The term ∆KTEFF = KTEFF − K10kK are the Kurucz model K magnitudes including a temperature correction term relative to a 10 kK, log g = 4.5 star. The big problem is getting good K mags for bright stars, since the 2M ASS mags are saturated and unreliable. However, there is an old Two-Micron Sky Survey1 that is good for northern targets to K < 3 mags (Neugebauer & Leighton 1969). Thus, the collection of interferometric diameters used for this fit includes only BAFGK dwarfs with TEFF > 5000 (so that the Kurucz relation is valid) and with K < 3 mags (so they are listed in Neugebauer & Leighton 1969). There are 55 stars that meet this criteria, and Figure 5.4 shows the plot (K − ∆KTEFF , 5 log θLD ). The solution for the fit of Equation 5.4 finds a mean trend for a constant C = 2.49626. We can see that CHARA Classic (the set of stars in this work) is a little high, but falls well within 1 σ of the constant. The PTI values are on the low side, but also within 1 σ of the constant. Note that the single SUSI point for β Vir is probably 1 made at Mount Wilson; http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=II/2B

68 not meaningful since the errors here are dominated by its K mag (±0.06 mag), so it is likely within errors of the main trend. 4 3 5 log θ LD (mas) 2 1 -0.022+/-0.081 Narrabri II +0.038+/-0.099 CHARA Classic -0.001+/-0.033 CHARA FLUOR/MIRC -0.050+/-0.118 PTI +0.034+/-0.023 VLTI 0 +0.085 SUSI -1 -2 -1 0 1 2 3 K - ∆K(Teff) (mag) Figure 5.4: Offsets in Various OLBI Data Sets: Plot showing the solution to the relation in Equa- tion 5.4 for a constant C = 2.49626 (dotted line). The legend presents the symbols indicating data sets from each OLBI, and the relative offset and standard deviation to this constant for each data set. Table 5.1: Angular Diameters Star TEFF † log g † θSED θUD θLD θLD Radius HD (K) (cgs) µλ (mas) (mas) (mas) % error (R⊙ ) 4614 6000 4.4 0.255 1.656 ± 0.076 1.592 ± 0.004 1.632 ± 0.004 0.2 1.044 ± 0.004 5015 6250 4.0 0.239 0.771 ± 0.019 0.850 ± 0.010 0.866 ± 0.010 1.2 1.746 ± 0.023 6582 5450 4.5 0.287 0.973 ± 0.127 0.951 ± 0.009 0.973 ± 0.009 0.9 0.791 ± 0.008 10780 5650 4.5 0.276 0.659 ± 0.016 0.747 ± 0.018 0.763 ± 0.019 2.5 0.819 ± 0.024 16895 6200 4.5 0.246 1.127 ± 0.047 1.082 ± 0.009 1.105 ± 0.009 0.8 1.322 ± 0.011 19373 6150 4.3 0.246 1.130 ± 0.034 1.222 ± 0.007 1.249 ± 0.008 0.6 1.415 ± 0.009 20630 5850 4.5 0.265 0.914 ± 0.039 0.918 ± 0.024 0.937 ± 0.025 2.7 0.922 ± 0.025 22484 6050 4.0 0.249 1.092 ± 0.029 1.060 ± 0.014 1.082 ± 0.014 1.3 1.625 ± 0.024 30652 6600 4.5 0.227 1.477 ± 0.042 1.494 ± 0.004 1.526 ± 0.004 0.3 1.325 ± 0.004 34411 5850 4.5 0.265 1.000 ± 0.049 0.961 ± 0.015 0.982 ± 0.015 1.5 1.334 ± 0.020 39587 6100 4.5 0.251 1.013 ± 0.031 1.031 ± 0.009 1.053 ± 0.010 0.9 0.981 ± 0.009 48682 6350 4.3 0.236 0.606 ± 0.014 0.825 ± 0.012 0.841 ± 0.012 1.4 1.511 ± 0.023 Continued on Next Page. . .

69 Table 5.1 – Continued Star TEFF † log g † θSED θUD θLD θLD Radius HD (K) (cgs) µλ (mas) (mas) (mas) % error (R⊙ ) 48737 6550 3.8 0.222 1.366 ± 0.025 1.375 ± 0.009 1.402 ± 0.010 0.7 2.715 ± 0.021 56537 9000 4.0 0.166 0.673 ± 0.030 0.827 ± 0.013 0.838 ± 0.013 1.6 2.784 ± 0.048 58946 6600 4.3 0.225 0.952 ± 0.050 0.840 ± 0.013 0.855 ± 0.014 1.6 1.659 ± 0.038 81937 7000 4.0 0.209 1.016 ± 0.041 1.312 ± 0.042 1.334 ± 0.043 3.2 3.496 ± 0.078 82328 6400 4.0 0.231 1.586 ± 0.039 1.671 ± 0.050 1.702 ± 0.051 3.0 2.467 ± 0.074 82885 5550 4.5 0.281 0.797 ± 0.023 0.806 ± 0.013 0.824 ± 0.013 1.6 1.008 ± 0.016 86728 5850 4.3 0.263 0.694 ± 0.022 0.755 ± 0.012 0.771 ± 0.013 1.7 1.247 ± 0.021 90839 6400 4.3 0.234 0.731 ± 0.025 0.782 ± 0.014 0.796 ± 0.014 1.8 1.093 ± 0.020 97603 8150 4.0 0.190 1.267 ± 0.051 1.309 ± 0.009 1.330 ± 0.009 0.7 2.563 ± 0.020 101501 5650 4.6 0.277 0.805 ± 0.037 0.890 ± 0.009 0.911 ± 0.009 1.0 0.941 ± 0.010 102870 6150 4.2 0.245 1.419 ± 0.029 1.401 ± 0.006 1.433 ± 0.006 0.4 1.684 ± 0.008 103095 5500 4.5 0.284 0.594 ± 0.011 0.677 ± 0.008 0.692 ± 0.008 1.2 0.677 ± 0.008 109358 6100 4.5 0.251 1.077 ± 0.041 1.214 ± 0.030 1.239 ± 0.031 2.5 1.125 ± 0.028 114710 6150 4.5 0.248 1.057 ± 0.026 1.105 ± 0.011 1.128 ± 0.011 1.0 1.107 ± 0.011 118098 8800 4.0 0.170 0.777 ± 0.031 0.849 ± 0.014 0.860 ± 0.014 1.6 2.102 ± 0.036 126660 6450 4.0 0.229 1.020 ± 0.023 1.090 ± 0.007 1.111 ± 0.007 0.6 1.735 ± 0.011 128167 6650 4.4 0.224 0.818 ± 0.038 0.827 ± 0.013 0.842 ± 0.013 1.5 1.434 ± 0.023 131156 5500 4.5 0.284 1.256 ± 0.096 1.168 ± 0.014 1.196 ± 0.014 1.2 0.863 ± 0.011 141795 8250 4.2 0.188 0.728 ± 0.032 0.759 ± 0.017 0.770 ± 0.017 2.2 1.789 ± 0.040 142860 6450 4.3 0.231 1.159 ± 0.036 1.195 ± 0.005 1.219 ± 0.005 0.4 1.475 ± 0.007 146233 6050 4.5 0.253 0.601 ± 0.013 0.766 ± 0.017 0.781 ± 0.017 2.2 1.167 ± 0.026 162003 6650 4.0 0.221 0.753 ± 0.023 0.853 ± 0.028 0.868 ± 0.029 3.3 2.131 ± 0.074 164259 6800 4.0 0.215 0.710 ± 0.019 0.764 ± 0.027 0.776 ± 0.027 3.5 1.967 ± 0.071 173667 6650 4.0 0.221 0.892 ± 0.021 0.983 ± 0.009 1.000 ± 0.009 0.9 2.066 ± 0.021 177724 9950 4.0 0.154 0.790 ± 0.027 0.887 ± 0.016 0.897 ± 0.017 1.9 2.457 ± 0.047 182572 5400 4.5 0.290 1.009 ± 0.070 0.823 ± 0.024 0.842 ± 0.024 2.9 1.374 ± 0.040 185144 5550 4.5 0.281 1.118 ± 0.062 1.224 ± 0.012 1.254 ± 0.012 1.0 0.776 ± 0.007 185395 6900 4.0 0.212 0.732 ± 0.029 0.848 ± 0.015 0.862 ± 0.015 1.7 1.699 ± 0.030 210418 8550 4.0 0.177 0.740 ± 0.035 0.852 ± 0.017 0.864 ± 0.018 2.1 2.629 ± 0.083 213558 9350 4.2 0.160 0.594 ± 0.034 0.628 ± 0.021 0.635 ± 0.021 3.3 2.197 ± 0.076 215648 6350 4.1 0.235 1.015 ± 0.032 1.072 ± 0.008 1.093 ± 0.009 0.8 1.915 ± 0.016 222368 6350 4.0 0.234 1.032 ± 0.030 1.063 ± 0.009 1.084 ± 0.009 0.8 1.598 ± 0.014 † Kurucz model estimates for SED fit. Table 5.2: CHARA Versus PTI Angular Diameters CHARA error PTI error † HD θLD ± σ (%) θLD ± σ (%) ∆θLD /σC 16895 1.105 ± 0.009 0.8 1.086 ± 0.056 5.2 0.3 19373 1.249 ± 0.008 0.6 1.331 ± 0.050 3.8 −1.6 20630 0.937 ± 0.025 2.7 0.895 ± 0.070 7.8 0.6 22484 1.082 ± 0.014 1.3 0.911 ± 0.123 13.5 1.4 30652 1.526 ± 0.004 0.3 1.409 ± 0.048 3.4 2.4 39587 1.053 ± 0.010 0.9 1.124 ± 0.056 5.0 −1.2 97603 1.330 ± 0.009 0.7 1.198 ± 0.053 4.4 2.5 109358 1.239 ± 0.031 2.5 1.138 ± 0.055 4.8 1.6 114710 1.128 ± 0.011 1.0 1.071 ± 0.057 5.3 1.0 126660 1.111 ± 0.007 0.6 1.130 ± 0.055 4.9 −0.3 Continued on Next Page. . .

70 Table 5.2 – Continued CHARA error PTI error † HD θLD ± σ (%) θLD ± σ (%) ∆θLD /σC 142860 1.219 ± 0.005 0.4 1.161 ± 0.054 4.7 1.1 185144 1.254 ± 0.012 1.0 1.092 ± 0.057 5.2 2.8 215648 1.093 ± 0.009 0.8 1.022 ± 0.059 5.8 1.2 222368 1.084 ± 0.009 0.8 1.062 ± 0.057 5.4 0.4 † Here, ∆θLD is the difference between PTI and CHARA limb darkened angular diameters, and σC is the combined error, σC = (σCHARA + σPTI )0.5 . 2 2 Table 5.3: CHARA Versus PTI Calibrators Calibrator CHARA PTI Calibrator SED Object Object Measured HD θSED (mas) θSED (mas) θCHARA /θPTI HD θCHARA /θPTI 20675 0.415±0.012 0.424±0.020 0.98±0.05 16895 1.02±0.05 20675 0.415±0.012 0.424±0.020 0.98±0.05 19373 0.94±0.04 22879 0.342±0.021 0.369±0.009 0.93±0.06 20630 1.05±0.09 22879 0.342±0.021 0.369±0.009 0.93±0.06 22484 1.19±0.16 28355 0.425±0.030 0.401±0.012 1.06±0.08 30652 1.08±0.04 30739 0.461±0.018 0.544±0.025 0.85±0.05 30652 1.08±0.04 31295 0.439±0.043 0.470±0.022 0.93±0.10 30652 1.08±0.04 38558 0.422±0.008 0.442±0.033 0.95±0.07 39587 0.94±0.05 43042 0.591±0.030 0.655±0.017 0.90±0.05 39587 0.94±0.05 99285 0.456±0.017 0.454±0.026 1.00±0.07 97603 1.11±0.05 110897 0.492±0.022 0.504±0.009 0.98±0.05 109358 1.09±0.06 132254 0.520±0.015 0.542±0.013 0.96±0.04 126660 0.98±0.05 193664 0.494±0.019 0.552±0.011 0.89±0.04 185144 1.15±0.06 211976 0.373±0.013 0.377±0.009 0.99±0.04 215648 1.07±0.06 214923 0.611±0.029 0.552±0.094 1.11±0.20 215648 1.07±0.06 216735 0.321±0.022 0.330±0.020 0.97±0.09 215648 1.07±0.06 216735 0.321±0.022 0.330±0.020 0.97±0.09 222368 1.02±0.06 222603 0.577±0.032 0.533±0.014 1.08±0.07 222368 1.02±0.06

71 –6– Luminosities and Temperatures 6.1 Luminosities and Temperatures The absolute luminosity of a star may be determined by several methods. The simplest, and albeit the most model dependent, is the use of bolometric corrections (BCs). For instance, the absolute magnitude of a star at a particular photometric band Mλ is determined by knowing the parallax of the star Π and the apparent magnitude mλ (what we observe from Earth). The BC is a scalar number that converts this Mλ to compensate for all light not accounted for in the spectrum of that waveband into the bolometric magnitude MBOL . The luminosity in solar units (assuming MBOL,⊙ = 4.74) is then found using the equation: L = 10(MBOL −4.74)/−2.5 . (6.1) However, BCs depend on several stellar parameters not easily determined (such as metallicity and log g) and there exist offsets from one source to the next (see discussion in Torres et al. 1997). A more thorough method to determine the absolute luminosity of a star is by collect- ing flux calibrated photometry (or spectrophotometry) covering the entire stellar spectrum. However, this approach is also impractical because it is impossible to measure the flux of a star at all wavelengths of the electromagnetic spectrum. Therefore, models are typically fit

72 to the available data, and by integrating the flux over the spectrum, the bolometric flux FBOL is determined. Incorporating the distance to the star d, the luminosity is found through: L = FBOL 4πd2 . (6.2) For this work, published values of BC and/or FBOL are averaged and used to determine the absolute luminosity of the star. Table 6.1 shows the values for the resulting bolometric flux with each reference and the standard deviation of the values for each star. Interstellar extinction is negligible for all of the stars in the sample due to their close proximity to the Earth. Table 6.2 lists the absolute luminosity L of each of the stars. Errors are added in quadrature, where the standard deviation of the FBOL for each star is applied as well as the HIPPARCOS parallax error. For stars with only one measurement of FBOL , we apply a 3% error to the flux measurement, which corresponds to the average percentage standard deviation of the other stars with more than one value for FBOL . By measuring the angular diameter of a star, we can calculate the effective temperature in a purely empirical manner. Beginning with the expression of luminosity: L = 4πr2 σTEFF 4 (6.3) we divide both sides of the equation by the square of the distance, which then produces the relation: 1 2 4 FBOL = θLD σTEFF (6.4) 4

73 where θ is the angular diameter of the star and σ is the Stefan-Boltzmann constant. Solving for temperature we arrive at the expression: 1 2 TEFF = 2341(FBOL /θLD ) 4 (6.5) where θ is in units of milliarcsec, and FBOL in 10−8 erg cm−2 s−1 . Effective temperatures are found for all stars using Equation 6.5 and are presented in Table 6.2. For the whole sample, I have reached an average error on the effective temperature of 1.2%, where 20 of the stars observed have temperature errors of <1%. My goal to measure temperatures to better than 2% was achieved for all but 2 of the 44 stars (which have errors of 2.1%). 6.2 Discussion of the CHARA Determined Fundamental Parameters Figure 6.1 through Figure 6.10 show the relationships between all the fundamental quantities measured for the stars in this survey. The information is displayed for parameter pairs with two methods. The first shows the errors of the measurements (for example, see Figure 6.1). The second shows no errors, but has the additional information of either the stellar size or metallicity which is represented as the size or color (respectively) of the data point (for example, see Figure 6.2 or Figure 6.3). In Figure 6.1 and Figure 6.4, the two most metal poor stars (µ Cas A = HD 6582 and Gmb 1830 = HD 103095), are labeled. In Figure 6.1, where temperature is the x-axis, the two points are not offset from the ZAMS line of the rest of the sample. However, in Figure 6.4, we plot luminosity against the color index (B − V ), which is much bluer for these

74 stars because of their low metal abundances. As a result of this, they lie below the ZAMS for the rest of the sample, appearing under-luminous for their apparent (B − V ) color index. It is thus safe to say that the use of the color index (B − V ) by itself is not a good indicator of a star’s effective temperature. Also shown in Figure 6.1 are lines of constant radius from the relation: L = 4πr2 σTEFF 4 (6.6) where stars of the same radius fall on this line on the logarithmic luminosity-temperature plane: L TEFF R log = 4 log + 2 log . (6.7) L⊙ TEFF,⊙ R⊙ Evolution within the main sequence band is clearly apparent from these figures. For instance, in Figure 6.2 and Figure 6.5, we can see that in both the (B − V ) and temperature dependent plots, there is a significant amount of evolution where the stars evolve to larger radii in the direction of up and to the right on these plots. Figure 6.3 and Figure 6.6 show that the nearby main sequence stars observed in this survey span a range of metallicities at all stages of evolution within the main sequence band. Figure 6.7 demonstrates evolution from the main sequence in a different manner, showing that even the star with the largest radius is not the hottest star in the sample. The spread in these plots due to evolution is remarkable. For instance, in Figure 6.7 and Figure 6.8, at any given point on the x-axis (TEFF or color index), several different values of radius appear, with the error bars close to overlapping (very pronounced at log TEFF ≈ 3.78, where there are stars of both 1 R⊙ and

75 3.5 R⊙ ). Figure 6.9 beautifully shows the thickening of the main sequence with increasing mass (up and right) and consequently accelerated evolution. 2 1 LOG Luminosity (LSol) 4 RSol 3 RSol 2 RSol 0 1 RSol HD 6582 HD103095 -1 0.5 RSol 4.00 3.90 3.80 3.70 3.60 LOG Teff (K) Figure 6.1: CHARA Luminosity Versus Temperature: The luminosities and temperatures of the stars in the survey are plotted with their 1-σ errors. Lines of constant radii are plotted as dotted lines. 2 1 LOG Luminosity (LSol) 0 -1 4.00 3.95 3.90 3.85 3.80 3.75 3.70 LOG Teff (K) Figure 6.2: CHARA Luminosity Versus Temperature and Radius: The luminosities and temper- atures of the stars in the survey are plotted. The size of the symbol represents the linear radius of the star.

76 -1.5 +0.4 2 [Fe/H] 1 LOG Luminosity (LSol) 0 -1 4.00 3.95 3.90 3.85 3.80 3.75 3.70 LOG Teff (K) Figure 6.3: CHARA Luminosity Versus Temperature and Metallicity: The luminosities and tem- peratures of the stars in the survey are plotted. The shading of the symbols represents the metallicity of the star [Fe/H] from Holmberg et al. (2007). For stars without metallicity estimates from Holmberg et al. (2007), the [M/H] values from Gray et al. (2003, 2006) (HD 82885, HD 97603, HD 118098, HD 131156, HD 177724, HD 210418), and Takeda et al. (2005) (HD 182572) are used. Stars without metallicity measurements have [Fe/H]=0 (HD 56537, HD 141795, HD 213558).

77 2 1 LOG Luminosity (LSol) 0 HD 6582 HD 103095 -1 0.0 0.2 0.4 0.6 0.8 1.0 COLOR INDEX (B-V) Figure 6.4: CHARA Luminosity Versus (B − V ): The luminosity and color index (B − V ) of the stars in the survey are plotted with their 1-σ errors. 2 1 LOG Luminosity (LSol) 0 -1 0.0 0.2 0.4 0.6 0.8 1.0 COLOR INDEX (B-V) Figure 6.5: CHARA Luminosity Versus (B −V ) and Radius: The luminosity and color index (B −V ) of the stars in the survey are plotted. The size of the symbol represents the linear radius of the star.

78 -1.5 +0.4 2 [Fe/H] 1 LOG Luminosity (LSol) 0 -1 0.0 0.2 0.4 0.6 0.8 1.0 COLOR INDEX (B-V) Figure 6.6: CHARA Luminosity Versus (B − V ) and Metallicity: The luminosity and color index (B − V ) of the stars in the survey are plotted. The shading of the symbol represents the metallicity of the star [Fe/H] (with the same references as in Figure 6.3). 0.8 0.6 0.4 LOG Radius (RSol) 0.2 0.0 -0.2 -0.4 4.00 3.90 3.80 3.70 3.60 LOG Teff (K) Figure 6.7: CHARA Temperature Versus Radius: The effective temperatures and radii of the stars in the survey are plotted with their 1-σ errors.

79 0.8 0.6 0.4 LOG Radius (RSol) 0.2 0.0 -0.2 -0.4 0.0 0.2 0.4 0.6 0.8 1.0 COLOR INDEX (B-V) Figure 6.8: CHARA Radius Versus (B − V ): The color index (B − V ) and radii of the stars in the survey are plotted with their 1-σ errors. 2.0 1.5 1.0 LOG Luminosity (LSol) 0.5 0.0 -0.5 -1.0 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 LOG Radius (RSol) Figure 6.9: CHARA Luminosity Versus Radius: The absolute luminosities and radii of the stars in the survey are plotted. The symbol size is proportional to the linear radius of the star.

80 4.00 -1.5 +0.4 3.95 [Fe/H] 3.90 3.85 LOG TEFF (K) 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 1.0 COLOR INDEX (B-V) Figure 6.10: CHARA Temperature Versus (B − V ) and Metallicity: The temperature and color index (B − V ) of the stars in the survey are plotted. The shading of the symbol represents the metallicity of the star [Fe/H] (with the same references as in Figure 6.3).

81 Table 6.1: Bolometric Fluxes† Star AAMR95, Average Std. Dev. HD BLG98†† BG89†† AAMR96†† APL99†† TOSKS05†† Flux Flux 4614 ··· 119.3 114.0 111.8 118.2 115.8 3.51 5015 ··· ··· 31.4 30.2 32.8 31.5 1.31 6582 25.0 ··· 25.3 ··· ··· 25.2 0.21 10780 ··· ··· 15.9 ··· 17.1 16.5 0.85 16895 ··· ··· 59.7 59.8 62.0 60.5 1.30 19373 64.1 ··· 63.7 60.9 ··· 62.9 1.77 20630 32.2 ··· 31.8 31.7 33.1 32.2 0.68 22484 51.3 ··· 51.9 49.3 53.5 51.5 1.76 30652 137.8 ··· 137.0 136.9 ··· 137.2 0.49 34411 35.2 ··· 35.1 34.4 37.4 35.5 1.28 39587 ··· ··· 46.4 47.9 49.3 47.9 1.42 48682 ··· ··· 20.8 21.5 ··· 21.1 0.53 48737 ··· ··· ··· 114.9 ··· 114.9 ··· 56537 ··· ··· ··· 91.6 ··· 91.6 ··· 58946 52.8 ··· 55.2 54.5 ··· 54.2 1.22 81937 ··· ··· ··· 84.0 ··· 84.0 ··· 82328 ··· ··· 141.0 138.2 148.8 142.6 5.47 82885 ··· ··· 20.9 ··· 20.5 20.7 0.24 86728 ··· ··· 19.3 18.7 20.0 19.3 0.63 90839 ··· ··· 30.6 30.8 ··· 30.7 0.15 97603 ··· ··· ··· 233.6 ··· 233.6 ··· 101501 ··· 23.2 21.0 ··· 22.5 22.2 1.12 102870 95.9 ··· 94.2 91.3 100.1 95.4 3.68 103095 8.3 ··· 8.4 ··· 9.1 8.6 0.44 109358 ··· 54.1 53.2 ··· 57.6 55.0 2.33 114710 52.6 55.1 52.4 54.0 56.0 54.0 1.56 118098 116.6 ··· ··· 110.8 ··· 113.7 4.12 126660 ··· ··· ··· 60.3 ··· 60.3 ··· 128167 40.9 ··· 43.3 42.1 44.1 42.6 1.41 131156 ··· ··· ··· ··· 45.8 45.8 ··· 141795 ··· ··· ··· 82.3 ··· 82.3 ··· 142860 ··· ··· 75.9 73.9 78.8 76.2 2.47 146233 ··· ··· 16.6 17.2 ··· 16.9 0.44 162003 ··· ··· 37.7 36.7 ··· 37.2 0.73 164259 ··· ··· 36.6 34.4 ··· 35.5 1.59 173667 53.2 ··· 53.8 52.5 56.6 54.0 1.76 177724 ··· ··· ··· 178.0 ··· 178.0 ··· 182572 24.5 ··· 23.7 23.6 25.1 24.2 0.73 185144 ··· 42.5 40.1 ··· ··· 41.3 1.69 185395 40.1 ··· 41.5 40.6 ··· 40.7 0.70 210418 ··· ··· ··· 99.2 ··· 99.2 ··· 213558 ··· ··· 79.4 85.6 ··· 82.5 4.38 215648 55.7 ··· 55.6 53.0 57.6 55.5 1.88 222368 ··· ··· 58.7 55.0 60.9 58.2 2.97 † units in 10−8 erg cm−2 s−1 . †† Blackwell & Lynas-Gray (1998) (BLG98), Bell & Gustafsson (1989) (BG89), Alonso et al. (1995, 1996) (AAMR95,AAMR96), Allende Prieto & Lambert (1999) (APL99), Takeda et al. (2005) (TOSKS05).

82 Table 6.2: Luminosities and Temperatures Star L TEFF % error HD (L⊙ ) (K) TEFF 4614 1.27 ± 0.04 6011 ± 46 0.8 5015 3.43 ± 0.14 5959 ± 71 1.2 6582 0.445 ± 0.004 5315 ± 27 0.5 10780 0.52 ± 0.03 5400 ± 97 1.8 16895 2.32 ± 0.05 6211 ± 42 0.7 19373 2.17 ± 0.06 5899 ± 46 0.8 20630 0.834 ± 0.018 5760 ± 83 1.4 22484 3.11 ± 0.10 6028 ± 65 1.1 30652 2.7707 ± 0.0098 6486 ± 10 0.2 34411 1.76 ± 0.06 5767 ± 68 1.2 39587 1.11 ± 0.03 6001 ± 53 0.9 48682 1.83 ± 0.05 5473 ± 52 1.0 48737 11.5 ± 0.3 6474 ± 54 0.8 56537 27.2 ± 0.8 7912 ± 85 1.1 58946 5.47 ± 0.12 6869 ± 68 1.0 81937 14.8 ± 0.4 6137 ± 109 1.8 82328 8.0 ± 0.3 6201 ± 110 1.8 82885 0.8300 ± 0.0098 5501 ± 46 0.8 86728 1.36 ± 0.04 5590 ± 65 1.2 90839 1.554 ± 0.008 6176 ± 55 0.9 97603 23.3 ± 0.7 7936 ± 65 0.8 101501 0.64 ± 0.03 5326 ± 72 1.4 102870 3.53 ± 0.13 6111 ± 60 1.0 103095 0.221 ± 0.011 4821 ± 68 1.4 109358 1.21 ± 0.05 5726 ± 94 1.6 114710 1.40 ± 0.04 5976 ± 52 0.9 118098 18.2 ± 0.7 8243 ± 100 1.2 126660 3.95 ± 0.11 6190 ± 50 0.8 128167 3.31 ± 0.11 6518 ± 74 1.1 131156 0.639 ± 0.019 5567 ± 53 1.0 141795 11.9 ± 0.4 8035 ± 107 1.3 142860 2.99 ± 0.09 6264 ± 52 0.8 146233 1.01 ± 0.02 5373 ± 68 1.3 162003 6.02 ± 0.11 6205 ± 108 1.7 164259 6.1 ± 0.3 6487 ± 134 2.1 173667 6.2 ± 0.2 6347 ± 59 0.9 177724 35.8 ± 1.1 9029 ± 109 1.2 182572 1.73 ± 0.05 5660 ± 91 1.6 Continued on Next Page. . .

83 Table 6.2 – Continued Star L TEFF % error HD (L⊙ ) (K) TEFF 185144 0.424 ± 0.017 5299 ± 60 1.1 185395 4.24 ± 0.07 6369 ± 62 1.0 210418 24.6 ± 0.7 7948 ± 102 1.3 213558 25.3 ± 1.3 8854 ± 188 2.1 215648 4.57 ± 0.15 6111 ± 58 0.9 222368 3.39 ± 0.17 6211 ± 83 1.3

84 –7– Analysis 7.1 Comparative Analysis of Linear Radii Thirty-seven out of the 44 stars that I observed were also included in the work from Allende Prieto & Lambert (1999). Allende Prieto & Lambert (1999) identified several fundamen- tal parameters by fitting model evolutionary tracks from Bertelli et al. (1994) to observed photometry. The directly determined linear radii found for our stars are compared with the results Allende Prieto & Lambert (1999) in Figure 7.1, where the dotted line indicates the 1:1 ratio of radii (top panel) or 0% difference of radii (bottom panel). We can see that for stars larger than ≈ 1R⊙ , the model radii are under-predicted by an average of ≈ 12% (and up to 28%) of the radius. Figure 7.2 shows the percent difference in the Allende Prieto & Lambert (1999) radii ver- sus the CHARA radii plotted against metallicity values [Fe/H] from Holmberg et al. (2007). For stars without [Fe/H] measurements from Holmberg et al. (2007), [M/H] abundances are used from Gray et al. (2003, 2006) (HD 97603, HD 118098, HD 177724, HD 210418) and Takeda et al. (2005) (HD 182572). The stars HD 56537, HD 141795, and HD 213558 have no published values of metallicity, and their values are set to zero for this plot. Figure 7.2 shows that only one star above solar metallicity ([Fe/H]=0.0) has an accurately predicted radius from the models used in Allende Prieto & Lambert (1999). The most populated region in this plot ranging from solar metallicity down to [Fe/H]≈ −0.3 has a few stars which do have accurately predicted radii, but most points fall well above the line even in this region.

85 4.0 3.0 RAP99 (RSol) 2.0 1.0 0.0 0.2 (RAP99-RCHARA)/RCHARA 0.0 -0.2 -0.4 -0.6 0 1 2 3 4 RCHARA (RSol) Figure 7.1: Measured Versus Model Radii: TOP: The data plotted show the difference between model radii determined by Allende Prieto & Lambert (1999) (AP99) and radii measured for this project, along with 1-σ errors for each. The dotted line marks a 1:1 relation between the two values. BOTTOM: The percent difference between model radii determined by Allende Prieto & Lambert (1999) (AP99) and radii measured for this project.

86 0.2 -0.0 (RAP99-RCHARA)/RCHARA -0.2 -0.4 -0.6 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 [Fe/H] Figure 7.2: Effects of Metallicity on Radii Offsets: The data plotted show the differences between model radii determined by Allende Prieto & Lambert (1999) (AP99) and radii measured for this project, and the metallicities of the stars. The dotted line marks a 0% difference between the measured and model radii values. 7.2 Comparative Analysis of Effective Temperatures There are three surveys of nearby stars that I will compare my results to in this analysis: Allende Prieto & Lambert (1999); Holmberg et al. (2007); Takeda (2007). While each of these covers a large number of stars, none encompasses all the stars I have observed with the CHARA Array for this work. The number of stars in common with each survey are 37, 34, and 25 for Allende Prieto & Lambert (1999); Holmberg et al. (2007); Takeda (2007), respectively. Effective temperatures for stars from each of these surveys are compared to my direct measurements and are discussed in the sections to follow.

87 7.2.1 CHARA Versus Allende Prieto & Lambert (1999) The new empirical effective temperatures are compared here to those determined by models in Allende Prieto & Lambert (1999), where available. Figure 7.3 shows the relationship be- tween the two temperature determinations, where the dotted line indicates the 1:1 ratio. For most cases seen here, Allende Prieto & Lambert (1999) overestimates the effective tempera- ture of the star through the entire range of effective temperatures by about 5%, up to 15% (Figure 7.4). Figure 7.5 and Figure 7.6 show the dependence on metallicity and (b − y) color index (respectively) of the star versus the fractional offset from each method. It is apparent that neither the metallicity nor the color index influences the offset in temperature. 10000 9000 8000 TAP99 (K) 7000 6000 5000 5000 6000 7000 8000 9000 10000 TCHARA (K) Figure 7.3: Empirical Versus Model Effective Temperatures: The data plotted show the differences between model temperatures determined by Allende Prieto & Lambert (1999) (AP99) and the empirical values determined in this project. The dotted line marks equal temperatures from each source.

88 0.30 0.20 (TAP99-TCHARA)/TCHARA 0.10 0.00 -0.10 5000 6000 7000 8000 9000 10000 TCHARA (K) Figure 7.4: Empirical Versus Model Effective Temperatures: The data plotted show the fractional difference between model temperatures determined by Allende Prieto & Lambert (1999) (AP99) and the empirical values determined in this project.

89 0.30 0.20 (TAP99-TCHARA)/TCHARA 0.10 0.00 -0.10 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 [Fe/H] Figure 7.5: Effects of Metallicity on Temperature Offsets: The data plotted show the differences between model temperatures determined by Allende Prieto & Lambert (1999) (AP99) and the empirical values determined in this project versus metallicity. The dotted line marks a 0% difference between the temperature values from each source.

90 0.30 0.20 (TAP99- TCHARA)/TCHARA 0.10 0.00 -0.10 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 (b-y) Figure 7.6: Effects of (b − y) on Temperature Offsets: The data plotted show the differences between model temperatures determined by Allende Prieto & Lambert (1999) (AP99) and the empirical values determined in this project versus (b − y) color index. The dotted line marks a 0% difference between the temperature values from each source.

91 7.2.2 CHARA Versus Holmberg et al. (2007) We now compare the temperatures from the Geneva-Copenhagen survey (GC07; Holmberg et al. 2007) to the empirically determined temperatures found here. The stars that are not included in the Holmberg et al. (2007) sample that were observed with CHARA are the A stars HD 56537, HD 97603, HD 118098, HD 141795, HD 177724, HD 210418, and HD 213558, and three G8 stars HD 82885, HD 131156, and HD 182572. Figure 7.7 shows the differences in the effective temperatures of the two data sets (there are no errors given for the GC07 temperatures). The agreement between the two is much better than that with Allende Prieto & Lambert (1999), but there is still a slight trend seen in the temperature offsets of the models to prefer higher temperatures than what we measure with CHARA, with the largest deviation in temperature value of 13% (Figure 7.8). Figure 7.9 shows the fractional deviation between the two values and the dependence on metallicity measured for each source in Holmberg et al. (2007), where again, there is no trend seen in the offset in temperatures of each source due to the metallicity of the star. Figure 7.10 displays the relationship between the (b − y) color index and the fractional temperature offsets, showing again that the color index of the star has no relation to the offset in temperature from models to observations. The stars with the largest offsets in the effective temperatures are HD 81937 (13%), HD 48682 (10%) and HD 146233 (7%). Interestingly enough, these stars also have high deviations in the SED diameter versus the limb darkened diameter measured with CHARA (See Figure 5.2). However, stars such as HD 10780 and HD 109358 also have high deviation in the SED diameter versus the limb darkened diameter measured with CHARA, but their

92 8000 7000 TGC07 (K) 6000 5000 4000 4000 5000 6000 7000 8000 TCHARA (K) Figure 7.7: Empirical Versus Model Effective Temperatures: The data plotted show the differ- ences between model temperatures determined by Holmberg et al. (2007) (GC07) and the empirical values determined in this project. The dotted line marks a 1:1 ratio between the temperature values from each source. agreement with the temperature from Holmberg et al. (2007) is at the ≈1% level. It is interesting to note that the star HD 146233 (18 Sco), that was first identified by Porto de Mello & da Silva (1997) to be a solar twin, is one of these stars with a large offset in effective temperature. 7.2.3 CHARA Versus Takeda (2007) CHARA stars that do not overlap with the study by Takeda (2007) are HD 19373, HD 48682, HD 48737, HD 56537, HD 58946, HD 81937, HD 90839, HD 97603, HD 118098, HD 126660, HD 146233, HD 162003, HD 164259, HD 177724, HD 210418 and HD 213558. Figure 7.11

93 0.20 0.15 0.10 (TGC07-TCHARA)/TCHARA 0.05 0.00 -0.05 -0.10 4000 5000 6000 7000 8000 TCHARA (K) Figure 7.8: Empirical Versus Model Effective Temperatures: The data plotted show the fractional differences between model temperatures determined by Holmberg et al. (2007) (GC07) and the empirical values determined in this project. shows the differences in the effective temperatures of the two data sets (there are no errors given for the Takeda 2007 temperatures). The agreement between the two is under the 6% level, much better than that of Allende Prieto & Lambert (1999) and Holmberg et al. (2007), but again temperature estimates from Takeda (2007) are higher than the value we measure with the CHARA Array. The largest outliers in temperature offsets are HD 128167 (6.5%), HD 103095 (5.4%), and HD 86728 (4.3%) (Figure 7.12). Comparing these outliers to the Holmberg et al. (2007) outliers, there are no two stars in each that show large deviations from the model versus CHARA temperature, with the exception of the very metal poor star HD 103095. The metallicities measured in Takeda (2007) are compared to the fractional

94 0.20 0.15 0.10 (TGC07-TCHARA)/TCHARA 0.05 0.00 -0.05 -0.10 -1.5 -1.0 -0.5 0.0 [Fe/H] Figure 7.9: Effects of Metallicity on Temperature Offsets: The data plotted show the differences between model temperatures determined by Holmberg et al. (2007) (GC07) and the empirical values deter- mined in this project versus metallicity. The dotted line marks a 0% difference between the temperature values from each source. deviation in the temperature values for Takeda (2007) and CHARA in Figure 7.13, and the (b − y) color index is compared to the fractional deviation in the temperature values for Takeda (2007) and CHARA in Figure 7.14. Again, it does not appear that a star’s metallicity or color index is related to the deviation in temperatures of each source. 7.3 Model Mass and Age Relations to Measured CHARA Data The work done by Allende Prieto & Lambert (1999), Holmberg et al. (2007) and Takeda (2007) all use model isochrones to determine the masses and ages of each star. Here, I show

95 0.20 0.15 0.10 (TGC07-TCHARA)/TCHARA 0.05 0.00 -0.05 -0.10 0.1 0.2 0.3 0.4 0.5 0.6 (b-y) Figure 7.10: Effects of (b−y) on Temperature Offsets: The data plotted show the differences between model temperatures determined by Holmberg et al. (2007) (GC07) and the empirical values determined in this project versus (b−y) color index. The dotted line marks a 0% difference between the temperature values from each source. relationships using these quantities for the stars observed in each survey that overlap with the CHARA stars. In Figure 7.15, Figure 7.16, and Figure 7.17, the CHARA determined temperatures and linear radii are plotted with the symbol size proportional to the model mass of the star. The most massive of the stars observed are also the biggest in linear size. The sample in Figure 7.15 includes the largest dispersion in mass, temperature and radius. It is most apparent here that a star with a linear radius of R = 2R⊙ has quite a large range in mass, as well as a potential 3000◦ K range in temperature. On the other hand, a star with TEFF = 6200 K ranges from 1 − 3.5R⊙ at a range in masses as well. This is an important

96 8000 7000 TTak07 (K) 6000 5000 4000 4000 5000 6000 7000 8000 TCHARA (K) Figure 7.11: Empirical Versus Model Effective Temperatures: The data plotted show the differences between model temperatures determined by Takeda (2007) (Tak07) and the empirical values determined in this project. The dotted line marks a 1:1 ratio between the temperature values from each source. effect resulting from stellar evolution on the main sequence where the more massive stars evolve to be cooler and have larger radii. The temperatures and radii of the stars are compared with the model-determined ages in Figure 7.18 and Figure 7.19 (Allende Prieto & Lambert 1999 do not determine ages in their work). In Figure 7.18 we can see that for stars hotter than ≈ 6300 K, only younger stars were observed, but interestingly enough, they exhibit a range in stellar radii. For the later type stars with an effective temperature of less than ≈ 6300 K, the stars observed cover a full range of ages and show a moderate spread in radii. In Figure 7.18, only the oldest stars

97 0.20 0.15 0.10 (TTak07-TCHARA)/TCHARA 0.05 0.00 -0.05 -0.10 4000 5000 6000 7000 8000 TCHARA (K) Figure 7.12: Empirical Versus Model Effective Temperatures: The data plotted show the fractional differences between model temperatures determined by Takeda (2007) (Tak07) and the empirical values determined in this project. are observed at temperatures cooler than ≈ 5500 K, whereas a mixture of observations are made for the remainder of the sample.

98 0.10 0.05 (TTak07- TCHARA)/TCHARA 0.00 -0.05 -0.10 -1.0 -0.5 0.0 0.5 [Fe/H] Figure 7.13: Effects of Metallicity on Temperature Offsets: The data plotted show the differences between model temperatures determined by Takeda (2007) (Tak07) and the empirical values determined in this project versus metallicity. The dotted line marks a 0% difference between the temperature values from each source.

99 0.10 0.05 (TTak07- TCHARA)/TCHARA 0.00 -0.05 -0.10 0.1 0.2 0.3 0.4 0.5 0.6 (b-y) Figure 7.14: Effects of (b − y) on Temperature Offsets: The data plotted show the differences between model temperatures determined by Takeda (2007) (Tak07) and the empirical values determined in this project versus (b−y) color index. The dotted line marks a 0% difference between the temperature values from each source.

100 4 3 RCHARA (RSol) 2 1 0 10000 9000 8000 7000 6000 5000 4000 TCHARA (K) Figure 7.15: Radius-Temperature-Mass: The CHARA radii and temperatures (and the 1-σ errors) are plotted for stars in common with the Allende Prieto & Lambert (1999) (AP99) survey. The size of the circle is proportional to the mass of the star determined from models in Allende Prieto & Lambert (1999). To show the scale of the plot, a star of 1 MSol is plotted on the lower left.

101 4 3 RCHARA (RSol) 2 1 0 10000 9000 8000 7000 6000 5000 4000 TCHARA (K) Figure 7.16: Radius-Temperature-Mass: The CHARA radii and temperatures (and the 1-σ errors) are plotted for stars in common with the Holmberg et al. (2007) (GC07) survey. The size of the circle is proportional to the mass of the star determined from models in Holmberg et al. (2007).

102 4 3 RCHARA (RSol) 2 1 0 10000 9000 8000 7000 6000 5000 4000 TCHARA (K) Figure 7.17: Radius-Temperature-Mass: The CHARA radii and temperatures (and the 1-σ errors) are plotted for stars in common with the Takeda (2007) (Tak07) survey. The size of the circle is proportional to the mass of the star determined from models in Takeda (2007).

103 4 3 RCHARA (RSol) 2 1 0 8000 7000 6000 5000 4000 TCHARA (K) Figure 7.18: Radius-Temperature-Age: The CHARA radii and temperatures are plotted for stars in common with the Holmberg et al. (2007) survey. The size of the circle is proportional to the age of the star in Gyr determined from models in Holmberg et al. (2007). Errors in our measurements are not shown here for clarity.

104 4 3 RCHARA (RSol) 2 1 0 8000 7000 6000 5000 4000 TCHARA (K) Figure 7.19: Radius-Temperature-Age: The CHARA radii and temperatures are plotted for stars in common with the Takeda (2007) survey. The size of the circle is proportional to the age of the star in Gyr determined from models in Takeda (2007). Errors in our measurements are not shown here for clarity.

105 Figure 7.20 and Figure 7.21 show the radius-age relation for stars in common in the Holmberg et al. (2007) and Takeda (2007) surveys and this one. Figure 7.20 shows that the smaller the star is, the larger the error on the model age. It also shows that stars above ≈ 2R⊙ , are all under ≈ 2.5 Gyrs old. Age errors are not listed for Takeda (2007), but we can see that the large spread in age for the smaller stars is similar to the spread in Holmberg et al. (2007) for stars of these types. This can be attributed to the lifetime of a star on the main sequence and slower evolution of the less massive stars. Thus, there are more stages of evolution on the main sequence seen in these types of stars. The more massive stars that evolve quicker have shorter main sequence lifetimes, and thus there are few seen at very different ages in this range (before they become giants). The relationship between stellar radius and mass is explored in Figure 7.22, Figure 7.24, and Figure 7.26 with stars in common in the Allende Prieto & Lambert (1999), Holmberg et al. (2007) and Takeda (2007) surveys, respectively. Again, Takeda (2007) does not present errors on mass, so they are not included in the plot. All of these figures show fairly tight correlations between observed radii and model masses from each reference. In Figure 7.22 (CHARA versus Allende Prieto & Lambert 1999), the spread in masses for stars larger than 2R⊙ becomes two times greater than that for stars of smaller radii. The upwards trend is consistent in each figure, but it is unclear whether or not the curve levels out at around 2R⊙ (Figure 7.26) or continues to rise (Figure 7.24) due to lack of data in this range of higher mass stars. Figure 7.23, Figure 7.25, and Figure 7.27 show the same relation of the CHARA measured stellar radius versus mass for the stars in common in the Allende Prieto & Lambert (1999), Holmberg et al. (2007), and Takeda (2007) surveys. Here, the metallicity of each

106 4 3 RCHARA (RSol) 2 1 0 -2 0 2 4 6 8 10 12 AGEGC07 (GYR) Figure 7.20: Radius-Age: The CHARA radii are plotted for stars in common with the Holmberg et al. (2007) survey. The 1-σ errors on radius and age (asymmetric in most cases) are plotted. point is shaded to a grayscale value corresponding to the metallicity estimate determined from each reference. Temperature and mass relations of the three surveys versus the new CHARA results are presented in Figure 7.28, Figure 7.29, and Figure 7.30. Each of these figures shows that, in general, there is a range of ≈ 0.3M⊙ for a given temperature. They also show that for main sequence stars of these types, the relation between temperature and mass is somewhat linear.

107 4 3 RCHARA (RSol) 2 1 0 -2 0 2 4 6 8 10 12 AGETak07 (GYR) Figure 7.21: Radius-Age: The CHARA radii are plotted for stars in common with the Takeda (2007) survey. Each point is represented by a circle, and the 1-σ errors in radius are shown (Takeda 2007 does not provide age errors). 7.4 CHARA Masses With the linear radii known for all stars in the CHARA sample, I am able to determine the mass of a star using log g estimates found in Allende Prieto & Lambert (1999) and Takeda (2007) using the relation: GM⋆ g⋆ = 2 (7.1) R⋆ where G is the gravitational constant, M⋆ is the mass of the star, R⋆ is the radius of the star, and g⋆ is the surface gravity of the star. Figure 7.31 and Figure 7.32 show the results of this

108 4 3 RCHARA (RSol) 2 1 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 MassAP99 (MSol) Figure 7.22: Radius-Mass: The CHARA radii and model masses are plotted for stars in common with the Allende Prieto & Lambert (1999) survey (AP99). The 1-σ errors on radius and mass are also shown. approach, and compares these derived masses to the masses derived by Allende Prieto & Lambert (1999) and Takeda (2007). The errors on the CHARA derived masses are hard to determine, but are suspected to be quite high due to the uncertainty in log g estimates used in the determination of the masses. It is interesting to note that in Figure 7.31, the CHARA masses are larger than AP99 for stars more massive than ≈ 1.3M⊙ , and the more massive the star, the more deviation there is from the 1:1 ratio line. The reason for this discrepancy is likely to be because the Allende Prieto & Lambert (1999) stars are also underestimated in radius (Figure 7.1), which in turn, leads models to predict a smaller mass. It could also be caused by an offset in the log g estimates for these more massive stars by some unknown

109 4 -1.5 +0.4 [Fe/H] 3 RCHARA (RSol) 2 1 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 MASSAP99 (MSol) Figure 7.23: Radius-Mass-Metallicity: The CHARA radii and model masses are plotted for stars in common with the Allende Prieto & Lambert (1999) survey (AP99). The grayscale color corresponds to the metallicity [Fe/H] of the star. property in the stellar atmosphere. This could tie into the model temperatures used to fit the star’s gravity (that is overestimated in most cases). The relation in Figure 7.32 shows much more scatter, but points seem to follow the 1:1 trendline. The two outliers (different from the ones in Figure 7.31), are the hottest stars in the Tak07 survey that overlap with the CHARA stars. 7.5 Comparative Analysis to Eclipsing Binaries Andersen (1991) provides a compilation of data on all eclipsing binaries (EB) known at the time - a total of 90 stars, most of which are on the main sequence. Section 4 in Andersen

110 4 3 RCHARA (RSol) 2 1 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 MASSGC07 (MSol) Figure 7.24: Radius-Mass: The CHARA radii and model masses are plotted for stars in common with the Holmberg et al. (2007) survey (GC07). The 1-σ errors on radius and mass are also shown. (1991) argues that the motivation for compiling the EB data is to aid in the prediction of single star properties where masses and radii are unobtainable by direct measurements for a large number of stars. We use these data on eclipsing binaries to compare with our results for single stars in this section. Effective temperatures of EB stars are not able to be determined directly because the distances to the systems are not known to great accuracy. Due to the fact that the stars are in binaries, their parallaxes could be difficult to determine because the orbital motion of the binary in the sky around the center of mass of the system is particularly difficult to deconvolve from the parallactic displacement. In addition, interstellar reddening is also a

111 4 -1.5 +0.4 [Fe/H] 3 RCHARA (RSol) 2 1 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 MASSGC07 (MSol) Figure 7.25: Radius-Mass-Metallicity: The CHARA radii and model masses are plotted for stars in common with the Holmberg et al. (2007) survey (GC07). The grayscale color corresponds to the metallicity [Fe/H] of the star. factor in the distant systems when converting observed photometry to absolute magnitudes. Thus, a primary advantage of measuring the angular diameters of single stars for which we know the distances with great accuracy is that reddening can be ignored. Nearby stars will provide the means to calibrate the temperature relations for EB’s and can also be applied to a large number of stars. Also, in Andersen (1991) the luminosities are derived via the Stefan-Boltzmann equation, using the measured EB radii and model derived TEFF . In the discussions to follow, keep in mind that these EB luminosities and temperatures might have systematic offsets due to the indirect determination of these quantities.

112 4 3 RCHARA (RSol) 2 1 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 MASSTak07 (MSol) Figure 7.26: Radius-Mass: The CHARA radii and model masses are plotted for stars in common with the Takeda (2007) survey (Tak07). Each point is represented by a circle, and the 1-σ errors in radius are shown (Takeda 2007 does not provide mass errors). Eclipsing binary star and single star radii versus (B − V ) color index are compared in Figure 7.33. The general direction of evolution off the main sequence is marked in the top right of the plot. One can see that for stars even on the main sequence there is quite a spread in radius for a given (B − V ). It is interesting to note that for stars redder than B − V ≈ 0.5, EB stars are more evolved than CHARA stars (although the data are sparse in this region for EBs). For stars bluer than B − V ≈ 0.5, the CHARA stars are more evolved than the EB stars. This might be from a selection effect that all nearby stars observed with CHARA are field stars, and hence older than EBs found in dense young clusters. The important conclusion here is that there is no systematic offset seen when comparing the radii from

113 4 -1.5 +0.4 [Fe/H] 3 RCHARA (RSol) 2 1 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 MASSTak07 (MSol) Figure 7.27: Radius-Mass-Metallicity: The CHARA radii and model masses are plotted for stars in common with the Takeda (2007) survey (Tak07). The grayscale color corresponds to the metallicity [Fe/H] of the star. eclipsing binary and single stars. This supports the conclusion that models are doing a poor job of predicted radii for single stars (§7.1). Exploring the mass-radius relations in single versus binary stars, we find a similar re- lationship. Figure 7.34 shows that there is still much scatter in the mass-radius relation for main sequence stars and that there is no systematic offset when comparing values from binary to single stars. The masses used here are the masses derived from our measured CHARA radii and log g estimates. In the previous section, Figure 7.31 and Figure 7.32 showed that for stars of larger masses, there were increasingly larger differences between the model masses from the references, and our derived CHARA masses. In the region of higher

114 10000 9000 8000 TCHARA (K) 7000 6000 5000 4000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 MASSAP99 (MSol) Figure 7.28: Temperature-Mass: The CHARA temperatures and model masses are plotted for stars in common with the Allende Prieto & Lambert (1999) survey (AP99). The 1-σ errors on temperature and mass are also shown. masses in Figure 7.34, the derived CHARA masses are very consistent with the EB values, so perhaps the errors in gravity are not as large as previously thought, and the techniques for determining masses from the models need to be tweaked. The mass-radius relation of R ∝ M 0.8 is shown as the dotted line, which holds for both binary and single main sequence stars of less than ≈ 3.5M⊙ . Figure 7.35 is the radius-luminosity relation for both the EB stars and the single CHARA stars. The larger the radii, the more spread in luminosity is found in these stars. For the main sequence stars observed with CHARA this spread is minimal. For the eclipsing binary stars, whose spectral types range from O8−M1, the spread on the luminosity-radius plane

115 10000 9000 8000 TCHARA (K) 7000 6000 5000 4000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 MASSGC07 (MSol) Figure 7.29: Temperature-Mass: The CHARA temperatures and model masses are plotted for stars in common with the Holmberg et al. (2007) survey (GC07). The 1-σ errors on temperature and mass are shown. is significant. Within the range of radii measured with CHARA (log R/R⊙ ≈ −0.2 to 0.6), there is a tight relation of binary stars to single stars up to log R/R⊙ ≈ 0.15. For stars larger than this radius, there is a minimum luminosity for a given radius consistent within each data set, but the spread to higher luminosities of the EB sample increases significantly more than the single stars. Figure 7.36 shows the mass to color index (B − V ) relation for EB and CHARA stars with masses derived from log g estimates. For the sample of EBs, Andersen (1991) points out that stellar evolution on the main sequence can be seen by the fact that for a certain color index, there is a range of masses (EB mass error is typically ≈ 1.4%). This effect is

116 10000 9000 8000 TCHARA (K) 7000 6000 5000 4000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 MASSTak07 (MSol) Figure 7.30: Temperature-Mass: The CHARA temperatures and model masses are plotted for stars in common with the Takeda (2007) survey (Tak07). Each point is represented by a circle, and the 1-σ errors in temperatures are shown (Takeda 2007 does not provide mass errors). most apparent in spectral types A-F (0.0 B−V 0.5), where for the EB data points, there is a spread in the right direction of the plot (the direction of stellar evolution). For the CHARA stars, the error in mass is much larger. However, the same trend seen in Figure 7.33 (radius versus color index) is seen with respect to stellar mass versus color index, where the stars bluer than B − V 0.45 are more evolved than the stars in the EB sample. There does seem to be a systematic offset between EB masses and CHARA masses derived from gravity when plotted against luminosity, as seen in Figure 7.37. Although the scatter is large, the systematics appear for stars with M ≥ 1.5M⊙ , the same position as in Figure 7.31, where the CHARA masses are larger than they should be if log g estimates are

117 4 3 MAP99 (MSol) 2 1 0 0 1 2 3 4 MCHARA (MSol) Figure 7.31: CHARA Masses Versus Model Masses: The CHARA masses derived from measured radii and log g estimates from Allende Prieto & Lambert (1999) (AP99) compared to model masses of the same stars included in Allende Prieto & Lambert (1999). The dotted line shows the 1:1 relation. Errors are not shown, however the errors for the CHARA derived masses are ≈ 20% due to uncertainty in gravity estimates. overestimated. However, the errors in CHARA derived masses may diminish the significance of this effect. An equally likely contributor to this effect is that this could be a problem with the derived EB luminosities.

118 4 3 MTak07 (MSol) 2 1 0 0 1 2 3 4 MCHARA (MSol) Figure 7.32: CHARA Masses Versus Model Masses: The CHARA masses derived from measured radii and log g estimates from Takeda (2007) (Tak07) compared to model masses of the same stars included in Allende Prieto & Lambert (1999). The dotted line shows the 1:1 relation. Errors are not shown, however the errors for the CHARA derived masses are ≈ 20% due to uncertainty in gravity estimates.

119 = EB 1.0 = CHARA LOG Radius (RSol) 0.5 0.0 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 COLOR INDEX (B-V) Figure 7.33: Eclipsing Binary and CHARA Radii Versus (B-V): The CHARA radii (filled circles) and eclipsing binary radii (open circles) are plotted against color index (B − V ). In most cases, the errors in radii are smaller than the data points. The arrow in the top right side of the plot indicates the direction of evolution off the main sequence.

120 1.5 = EB = CHARA / AP99 = CHARA / Tak07 1.0 LOG Radius (RSol) 0.5 0.0 -0.5 1.5 1.0 0.5 0.0 -0.5 LOG Mass (MSol) Figure 7.34: Eclipsing Binary and CHARA Masses Versus Radius: The EB radii and masses (open circles) are from Andersen (1991). CHARA data from this work are plotted, where the mass is derived from the log g estimates combined with CHARA radii for stars in Allende Prieto & Lambert (1999) (AP99) and Takeda (2007) (Tak07). In most cases, the errors in radii are smaller than the data points. Mass errors for EB’s are typically smaller than the data point. A representative error in CHARA mass is plotted on the bottom left of the plot window. The dotted line is the mass-radius relation for main sequence stars R ∝ M 0.8 .

121 6 4 LOG Luminosity (LSol) 2 0 -2 0.0 0.5 1.0 LOG Radius (RSol) Figure 7.35: Eclipsing Binary and CHARA Luminosities Versus Radii: The EB data are from Andersen (1991) and are plotted as open circles. CHARA data from this work are plotted as closed circles. In most cases, the errors in radii and luminosities are smaller than the data points.

122 1.5 = EB = CHARA / AP99 = CHARA / Tak07 1.0 LOG Mass (MSol) 0.5 0.0 -0.5 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 COLOR INDEX (B-V) Figure 7.36: Eclipsing Binary and CHARA Mass Versus (B − V ): The EB data are from Andersen (1991) and are plotted as open circles. The mass is derived from the log g estimates combined with CHARA radii for stars in Allende Prieto & Lambert (1999) (AP99) and Takeda (2007) (Tak07) are plotted as green and blue filled circles, respectively. In most cases, the errors in color index (B − V ) are smaller than the data point. Mass errors for EB’s are typically smaller than the data point. A representative error in CHARA mass is plotted on the bottom left of the plot window. The arrow in the upper right position of the plot points in the direction of stellar evolution.

123 6 = EB = CHARA / AP99 = CHARA / Tak07 4 LOG Luminosity (LSol) 2 0 -2 1.5 1.0 0.5 0.0 -0.5 LOG Mass (MSol) Figure 7.37: Eclipsing Binary and CHARA Mass Versus Luminosity: The EB data are from Andersen (1991) and are plotted as open circles. The mass is derived from the log g estimates combined with CHARA radii for stars in Allende Prieto & Lambert (1999) (AP99) and Takeda (2007) (Tak07) are plotted as filled green and blue circles, respectively. In most cases, the error in luminosity is smaller than the data point. Mass errors for EB’s are typically smaller than the data point, whereas the error in CHARA masses are much larger (representative CHARA mass error shown in the bottom left position of the plot window). The dotted line is the relation: M ∝ L3.8 . The arrow in the upper right position of the plot points in the direction of stellar evolution.

124 –8– Yonsei-Yale Models 8.1 Introduction The previous chapter compares ages of our stars in common with the stars in the survey work from Holmberg et al. (2007) and Takeda (2007). In those works, Holmberg et al. (2007) use the Padova models (Girardi et al. 2000; Salasnich et al. 2000), and Takeda (2007) uses the Yonsei-Yale (Y2 ) stellar isochrones (Yi et al. 2001; Kim et al. 2002; Yi et al. 2003; Demarque et al. 2004). Holmberg et al. (2007) demonstrate that these model isochrones (among others) show minimal differences when compared to each other (also seen in Boyajian et al. 2008). In order to determine ages of all the CHARA stars observed in this work, the Yonsei- Yale (Y2 ) stellar isochrones, which apply the color table from Lejeune et al. (1998), are fit to the temperatures and luminosities determined here. To run the model isochrones, input estimates are required for the abundance of iron [Fe/H] and α-elements [α/Fe], both of which contribute to the overall heavy-metal mass fraction Z. Table 8.1 shows the model input values used in generating its isochrones for each of the 44 stars. For each star, model isochrones are generated for every 0.1 Gyr, in the range of 0.1−15 Gyr, and Table 8.1 has the resulting best fit age isochrone (in the temperature-luminosity plane), along with the associated mass for this best fit isochrone. Appendix C shows the results for the Y 2 model isochrones for each star. There are four plots generated, all with 0.1, 1, 5, and 10 Gyr isochrones lines1 along with the best fit 1 Isochrone lines for 15 Gyr are also plotted for the stars HD 6582, HD48682, HD 101501, HD 103095, HD 109358, and HD 146233

125 isochrone line for the star’s measured temperature and luminosity (also plotted with the 1-σ errors). The results for each star are also presented in Table 8.1, which includes the star name, best fit model isochrone age in Gyr, and the mass that corresponds to the position of the star on the fitted isochrone. The stars HD 6582 and HD 103095 are the only two stars which require non-zero [α/Fe] estimates as inputs to the model. Still, however, the solution for the best fit isochrone age is unphysical (>15 Gyr) showing that the models need further adjustment to match observations (see the discussion in Boyajian et al. 2008 for details on HD 6582). The star HD 146233 also shows a solution for an age >15 Gyr, unexplainable with the data at hand here. 8.2 Discussion We fit the model isochrones in the theoretical temperature-luminosity (T-L) plane, where the solutions from the model are purely from the theory of stellar structure. In Appendix C, we also show the these results from the model isochrones and observations with respect to the observational color index (B − V )-luminosity ((B − V )-L) plane. For almost all of the stars, the solutions are offset, and different ages can be inferred by matching the isochrone to the data in the observational plane of the color index (B − V ). For instance, the age of HD 4614 in the T-L plane is 5.7 Gyr, however in the (B − V )-L plane, the age would be closer to ∼10 Gyr. The opposite is true for HD 86728, where the age in the T-L plane is 9.2 Gyr, and the (B − V )-L plane the age is closer to ∼5 Gyr. Very rarely do the two ages agree with one another. I suspect that this is due to an offset in the color table used in transforming the model isochrone temperatures to (B − V ) colors (Lejeune et al. 1998). In

126 the next chapter, I will determine a color-temperature relation for the stars observed here with CHARA. It is worth noting that the metallicity input for the model isochrones has an impact on the derived age (and in turn also on the derived mass). Lower metallicity isochrones shift down and to the left on these diagrams, so for a star with a true metallicity less than the input value, a higher isochrone age would be found. The opposite is true for stars with higher values of metallicity, where a younger age would result. For stars on the cool end of the main sequence, the isochrone lines are not very sensitive to age. For example, see HD 185144, a K0V, which has an age of 7.6 Gyr. Here, the errors in the temperature and luminosity alone (which are at the 1% level) result in acceptable values for its age from ∼ 1 − 10 Gyr. An uncertainty in its metallicity value makes this acceptable range in age even wider. Because of this, no age errors are computed for these stars, and only fixed values of metallicity measured from a uniform source are used in the model input for computations. Thus relative ages may be correct while absolute ages are highly uncertain. There are a few additional items to mention with respect to fitting these model isochrones to our measurements. The most metal poor stars observed, HD 6582 and HD 103095, have large deviations of the model compared to the observations, where the model overestimates the temperatures and underestimates the radii for each star and even 15 Gyr isochrones do not fit the data (see Boyajian et al. 2008 for details on HD 6582). The star HD 146233 (18 Sco) also has this issue, and the isochrone age found for this star is >15 Gyr. I find this result very puzzling and interesting because HD 146233 is identified as a solar twin (Porto de Mello & da Silva 1997). Solar twins as defined in Cayrel de Strobel (1996) are stars that 1) have a temperature within ∼ 10◦ K, of the Sun, 2) have a metallicity

127 within ∼ 0.05 dex of the Sun, 3) have an age within ∼ 1 Gyr of the Sun, and 4) have no known stellar companion. We measure an angular diameter of this star as θLD = 0.781 ± 0.017 mas, much larger than the expected SED diameter of θSED = 0.601±0.013 mas. It was extensively observed over five nights, with three different baselines and using two calibrators, for a total of 25 data points used in the final diameter fit. The observed angular diameter forces this star to have a temperature much less than that of the Sun, TEFF = 5373±68 K (TEFF,⊙ = 5777 K). While the luminosity of HD 146233 is very similar to the Solar value, L = 1.01 ± 0.03L⊙ , the radius is measured to be ≈ 17% larger, indicating that it is much more evolved. Mel´ndez e & Ram´ ırez (2007) recently determined that indeed HD 146233 is more luminous than the Sun (L = 1.06 ± 0.09L⊙ ), and while still finding the temperature close to solar, the radius is then predicted to be larger than solar by 0.03R⊙ , still showing a large discrepancy to our measurements. The best explanation of this offset may be from an undetected stellar companion, making the star appear more resolved by interferometry. Although long-term, high-resolution spectroscopic surveys have been conducted on HD 146233 to determine its abundances as well as radial velocity searches for exo-planets, a low-mass star could be undetected if it is far enough separated from the primary, producing no radial velocity changes over time. A hidden companion (nearly identical to the primary) would also mask the true abundance of the star, raising the continuum and making the absorption lines of the primary star appear weaker than they truly are. Further work should be done on HD 146233 to uncover the real reason for this discrepancy and possibly rule out its status of being a solar twin.

128 8.3 Comparative Analysis to Results from Other Works For the stars in common in Holmberg et al. (2007) and Takeda (2007), I compare in Figure 8.1 the model ages I find with the Y 2 isochrones fits to my observations, to the ages they derive. The ages found for each reference compared to mine are significantly different, with the most pronounced differences in the ages from Holmberg et al. (2007), where their ages are typically lower than the my values. Because we are using the metallicity values from Holmberg et al. (2007) in computing the model isochrones in this work, we can assume that the difference is from one of two things. First, if the temperatures they are fitting to the models are higher (as seen in the last chapter when comparing the our temperatures to theirs), then a younger age will be found. Secondly, the models used are different in each work, but this effect should not contribute to such a high difference in the ages derived. We associate the effect seen to be a consequence of overestimating the temperature for the stars in Holmberg et al. (2007). The youngest ages we find for the stars in the sample do not agree with the Holmberg et al. (2007) or Takeda (2007) ages, where we find ages of 0.2 Gyr, while their ages are significantly higher, at 1.5 to 6.5 Gyr. These outliers are on the cool end of the sample (HD 10780; K0V and HD 20630; G5V), where the best isochrones are extremely sensitive to the data. To investigate the possibility of an age-metallicity relation I plot the Y 2 isochrone age versus metallicity in Figure 8.2. The overall scatter in the diagram shows that for the nearby stars observed, there is no correlation between age and metallicity. Also shown in this figure is the color index for each star, coded to indicate its (B − V ) color, ranging from HD 177724 (bluest; (B − V ) = 0.013; A0Vn) to HD 10780 (reddest; (B − V ) = 0.804; K0V), where the

129 1.5 = GC07 = Tak07 1.0 LOG Age (Gyr): Reference 0.5 0.0 -0.5 -1.0 -1.0 -0.5 0.0 0.5 1.0 1.5 LOG Age (Gyr): Y2 Isochrones Figure 8.1: Y2 Model Ages Versus Ages from Holmberg et al. (2007) and Takeda (2007): Ages derived from the Y 2 isochrones compared to ages of stars in common with Holmberg et al. (2007) and Takeda (2007). The dotted line shows a 1:1 relation. color of the Sun ((B − V ) = 0.64; G2V; shown as black in the figure) is yellow. For the reddest stars in the sample, we find stars ranging from the extreme of ages and metallicities. The bluest stars in the sample plotted do seem to show a slight downwards trend towards younger ages at higher metallicities. However, these bluest stars are also rapid rotators, which may make determining the [Fe/H] values difficult due to the rotational broadening of their spectral lines. The masses I found from the best fit Y 2 isochrones compared to the masses derived for the stars in common in Allende Prieto & Lambert (1999), Holmberg et al. (2007), and Takeda (2007) are compared to each other in Figure 8.3. There is excellent agreement here for each

130 1.5 1.0 0.5 LOG Age (Gyr) 0.0 -0.5 -1.0 -1.5 -1.0 -0.5 0.0 0.5 Metallicity [Fe/H] Figure 8.2: Y2 Model Ages Versus Metallicity: Ages derived from the Y 2 isochrones as a function of metallicity for each star observed. The Sun is shown as ⊙. The color-scale represents the (B − V ) color index of each star, where the (B − V )min = 0.013 is the bluest shade, (B − V )max = 0.804 is the reddest shade, and (B − V )⊙ is yellow for an age of 4.57 Gyr (Bonanno et al. 2002). reference, with a slight tendency for the mass in each reference to be higher than my derived mass. This is likely because the ages derived for the stars are mostly overestimated in each reference compared to these new results, a cause which links back to the temperature offsets. An overestimated temperature will lead to a slightly more massive star, because hotter stars on the main sequence are more massive than their cooler counterparts, as well as a younger age. In the previous chapter, I derived masses using the CHARA measured radius of a star in combination with log g estimates for stars in common with Takeda (2007) and Allende Prieto

131 0.6 = GC07 = Tak07 = AP99 0.4 LOG Mass (MSol): Reference 0.2 0.0 -0.2 -0.4 -0.4 -0.2 0.0 0.2 0.4 0.6 LOG Mass (MSol): Y2 Isochrones Figure 8.3: Y2 Model Masses Versus Masses from Allende Prieto & Lambert (1999), Holmberg et al. (2007), and Takeda (2007): Masses derived from the Y 2 isochrones compared to masses of stars in common with Allende Prieto & Lambert (1999), Holmberg et al. (2007), and Takeda (2007). The dotted line shows a 1:1 relation. & Lambert (1999). Figure 8.4 shows the relation between the masses derived from the Y 2 isochrones, compared to the masses found from the combination of log g and CHARA radii. There is significant scatter in the plot, especially for the stars in common with the Takeda (2007) survey. The stars in the Allende Prieto & Lambert (1999) work show an interesting trend for masses bigger than ∼ 1M⊙ , where the derived mass from log g and radii are larger than the model mass solutions from the Y 2 isochrones. This can be attributed to the log g values being overestimated, producing in turn higher masses than expected. It is possible that the reason why the log g values are being overestimated is a consequence of stars’

132 overestimated temperatures. If the model temperature that is used to fit the spectral lines to determine log g values for the stars is offset, it will in turn lead to spurious values of log g for the stars. This idea is enforced in the previous chapter that showed that the temperatures in Allende Prieto & Lambert (1999) are much more offset to higher temperatures than the temperatures for stars in Takeda (2007), especially for the hotter (more massive) stars. 0.6 = CHARA / Tak07 = CHARA / AP99 0.4 LOG Mass (MSol): From log (g) and CHARA Radius 0.2 0.0 -0.2 -0.4 -0.4 -0.2 0.0 0.2 0.4 0.6 LOG Mass (MSol): Y2 Isochrones Figure 8.4: Y2 Model Masses Versus Masses Derived from log g: Masses derived from the Y 2 isochrones compared to masses of stars calculated from the combination of log g estimates and our CHARA Radii. Reference for log g estimates are for stars in common with the Allende Prieto & Lambert (1999), and Takeda (2007) surveys. The dotted line shows a 1:1 relation. In Figure 8.5, I show the relation between (B −V ) color index and stellar mass. Eclipsing binary data from Andersen (1991) are plotted, as well as the masses for stars in this project derived from the Y 2 isochrones, and masses derived from the combination of the CHARA

133 radii and log g estimates from each source (AP99 or Tak07). In the previous chapter, in- spection of this plot revealed that the stars observed in this survey were slightly evolved compared to eclipsing binary systems. Introducing the Y 2 masses in this figure, I find that that result is likely misinterpreted. The Y 2 masses I found are in excellent agreement with the unevolved sample of eclipsing binaries from Andersen (1991). The higher masses found from the log g/radii method made the stars appear to be more evolved than they really are. This offset of higher log g estimates (forcing higher derived masses) also ties into the reference’s results for slightly higher model masses (Figure 8.3), leading to younger ages (Figure 8.1), all factors that are results of overestimated temperatures. 1.5 = EB = CHARA / Y2 = CHARA / AP99 = CHARA / Tak07 1.0 LOG Mass (MSol) 0.5 0.0 -0.5 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 COLOR INDEX (B-V) Figure 8.5: Mass Versus Color Index: Mass versus color index for eclipsing binaries plotted with masses derived from the Y 2 isochrones, and masses of stars calculated from the combination of log g estimates and our CHARA radii. Reference for log g estimates are for stars in common with the Allende Prieto & Lambert (1999), and Takeda (2007) surveys. The arrow points in the direction of evolution.

134 The mass-luminosity relation for the stars in this project are plotted against the sample of eclipsing binaries in Andersen (1991) in Figure 8.6. Masses found from the Y 2 isochrones are again in excellent agreement with the eclipsing binaries. The masses derived from the CHARA radii/log g method again show an offset to prefer higher masses, forcing them to appear under-luminous compared to the EB sample. This effect leads to a false sense of younger ages, along with the higher log g’s and under-predicted radius values from Allende Prieto & Lambert (1999). 6 = EB = CHARA / Y2 = CHARA / AP99 4 = CHARA / Tak07 LOG Luminosity (LSol) 2 0 -2 1.5 1.0 0.5 0.0 -0.5 LOG Mass (MSol) Figure 8.6: Mass Versus Luminosity: Mass versus luminosity for eclipsing binaries and CHARA masses derived from the Y 2 isochrones, as well as masses of stars calculated from the combination of log g estimates and our CHARA radii. Reference for log g estimates are for stars in common with the Allende Prieto & Lambert (1999), and Takeda (2007) surveys. The arrow points in the direction of evolution. The dotted line is the relation M ∝ L3.8 .

135 Table 8.1: Y 2 Model Isochrone Results † † † Star [Fe/H] [α/Fe] Age Mass HD (Gyr) (M⊙ ) 4614 −0.30 0.0 5.7 0.97 5015 0.00 0.0 5.4 1.18 6582 −0.83 0.3 >15.0 0.71 10780 0.05 0.0 0.2 0.94 16895 −0.12 0.0 3.5 1.17 19373 0.09 0.0 6.0 1.12 20630 0.00 0.0 0.2 1.04 22484 −0.09 0.0 5.5 1.15 30652 −0.03 0.0 1.6 1.27 34411 0.05 0.0 8.0 1.04 39587 −0.16 0.0 1.6 1.04 48682 0.01 0.0 12.0 0.98 48737 0.04 0.0 1.7 1.71 56537 0.00 0.0 0.8 2.10 58946 −0.31 0.0 2.2 1.35 81937 0.06 0.0 2.0 1.70 82328 −0.12 0.0 2.6 1.49 82885 0.06 0.0 9.3 0.93 86728 0.20 0.0 9.2 1.02 90839 −0.16 0.0 2.3 1.10 97603 0.00 0.0 0.8 2.03 101501 −0.12 0.0 14.9 0.82 102870 0.11 0.0 3.4 1.32 103095 −1.36 0.3 >15.0 0.61 109358 −0.30 0.0 12.8 0.87 114710 −0.06 0.0 4.0 1.06 118098 −0.02 0.0 0.7 1.95 126660 −0.14 0.0 4.6 1.20 128167 −0.36 0.0 3.2 1.19 131156 −0.33 0.0 9.8 0.83 141795 0.00 0.0 0.6 1.80 142860 −0.19 0.0 4.2 1.17 146233 −0.02 0.0 >15.0 0.88 162003 −0.17 0.0 3.8 1.30 164259 −0.14 0.0 2.5 1.42 173667 −0.15 0.0 3.3 1.36 177724 −0.68 0.0 1.2 1.79 182572 0.33 0.0 5.6 1.15 Continued on Next Page. . .

136 Table 8.1 – Continued † † † Star [Fe/H] [α/Fe] Age Mass HD (Gyr) (M⊙ ) 185144 −0.24 0.0 7.6 0.80 185395 −0.04 0.0 2.8 1.34 210418 −0.38 0.0 1.1 1.86 213558 0.00 0.0 0.5 2.13 215648 −0.24 0.0 5.0 1.18 222368 −0.08 0.0 3.4 1.27 † [Fe/H] values from Holmberg et al. (2007), when available. For stars without metallicity estimates from Holmberg et al. (2007), the [M/H] values from Gray et al. (2003, 2006) (HD 82885, HD 97603, HD 118098, HD 131156, HD 177724, HD 210418), and Takeda et al. (2005) (HD 182572) are used. Stars without metallicity measurements have [Fe/H]=0.0 (HD 56537, HD 141795, HD 213558). † † The [α/Fe] for all stars are zero, except for HD 6582 and HD 103095 where we set [α/Fe] = 0.3 (the average value for stars with [Fe/H]< −0.6 (Carney 1996)).

137 –9– Effective Temperature Calibrations Obtaining an empirical effective temperature scale provides the means to estimating the temperatures of a large number of stars at great distances where they are too unresolved to measure their temperature directly with interferometry. This is particularly important when studying clusters of stars, allowing the transformation of their observed properties on a color-color diagram to the theoretical version of a temperature-luminosity diagram. There exist theoretical color-temperature relations as well as empirical color-temperature relations (and some semi-empirical). The most robust methods implement the metallicity of the star into the relation as well, for this is a contributing factor to the observed color index of a star along with the effective temperature. The typical expression used to fit the temperature, color, and metallicity is expressed in Equation 1 of Alonso et al. (1996): θEFF = a0 + a1 X + a2 X 2 + a3 X[Fe/H] + a4 [Fe/H] + a5 [Fe/H]2 (9.1) where θEFF = 5040/TEFF , X is the color index (B − V ), [Fe/H] is the metallicity, and ai (i = 0 . . . 5) are the coefficients of the fit. This formula has been used in temperature calibrations derived from the Infrared Flux Method (IRFM, Blackwell & Shallis 1977) in more recent works including Ram´ & Mel´ndez (2005); Casagrande et al. (2006); Gonz´lez ırez e a Hern´ndez & Bonifacio (2009). a

138 In this work, the solution of coefficients ai is found using a nonlinear, least-squares fit imple- menting the Levenberg-Marquardt algorithm in M athematica. The stars in this sample are bright, and 2M ASS K magnitudes are typically saturated and have a photometric quality flag grade of C, or worse. For this reason, I derive a calibration using the well-determined (B − V ) colors. The data were fit in the full range of color index (0.013 ≤ (B − V ) ≤ 0.804) and full range in metallicity (−1.36 ≤ [Fe/H] ≤ 0.33) to arrive at the solution: θEFF = 0.563 + 0.629(B − V ) − 0.209(B − V )2 − 0.100(B − V )[Fe/H] (9.2) 2 +0.050[Fe/H] + 0.049[Fe/H] where the standard deviation of the fit is σ(θEFF ) = 0.025. Ordinarily, there are several iterations performed of the fit, with outliers greater than 2.5σ clipped out of the following fit (see Gonz´lez Hern´ndez & Bonifacio 2009, and references therein). This solution includes a a all data points (one iteration for the fit), and there are two outliers: HD 48682 (368◦ K) and HD 81937 (363◦ K). Following the accepted policy of clipping data with fit residuals > 2.5σ, a second iteration is performed with a resulting σ(θEFF ) = 0.018 and, according to policy, only one outlier must be removed HD 146233 (282◦ K) for the next (and final) iteration. In the final iteration, all the data have fit residuals within 2.5σ, with a standard deviation of the fit of σ(θEFF ) = 0.0156. This is the final form of the solution: θEFF = 0.561 + 0.585(B − V ) − 0.152(B − V )2 − 0.094(B − V )[Fe/H] (9.3) 2 +0.022[Fe/H] + 0.032[Fe/H] .

139 -1.5 +0.4 [Fe/H] Figure 9.1: Color-Temperature-Metallicity: The star temperature θEFF = 5040/TEFF versus (B − V ) color index, with grayscale levels indicating the metallicity [Fe/H]. The three stars clipped in the final solution are plotted as open circles. The final solution is plotted for lines of constant metallicity values (see legend). Figure 9.1 shows the new results and the relation I derived for lines of constant metallicity. There are three stars in the sample with very low metallicity, HD 6582, HD 103095, and HD 177724 ((θEFF , (B − V ),[Fe/H]) = (0.948, 0.695, −0.83), (1.045, 0.751, −1.36), (0.558, 0.013, −0.68), respectively). The metallicity dependence for metal-poor, late-type stars is mostly defined by HD 6582 and HD 103095, and there are several dozen other stars used in the fit for this region to define the characteristics for stars of various higher metallicities. There is a paucity of data in the hotter region of this sample that includes only the 7 A-type stars observed with CHARA. One star in particular, HD 177724, is one of the most rapidly rotating A-stars known, with a projected rotational velocity v sin i = 317 km s−1

140 (Royer et al. 2006). For this work, I give the average diameter of all measurements, which agrees exceptionally well with the predicted mean angular diameter of the star from Absil et al. (2008)1 . However, although we measure a mean angular diameter of the star, there are several issues that manifest due to its rapid rotation. The star will have apparent gravity darkening (in addition to limb darkening), which results in hotter temperatures at its pole than at its equator. Due to this temperature gradient (which is likely to be on the order of a few hundred degrees Kelvin), its spectra will contain the absorption lines of elements with different ionization states corresponding to both the hotter and cooler regions of the star. The spectral lines are also very rotationally broadened, making abundances measured from equivalent widths difficult. I suspect that the low metallicity of HD 177724 ([Fe/H]=−0.68; Gray et al. 2003) is a product of these circumstances. It is more probable that HD 177724 has a metallicity nearer to solar, because it has such a young age (AgeISO = 1.2 Gyr). With this in mind, the solution derived above is likely close to the truth for low-metallicity hot stars, because metal lines become weak at hotter temperatures, and so there would be less dependence of a stars metallicity on both the (B − V ) color and bolometric flux (the basis for temperature). Figure 9.2 shows a visual representation of the fit compared to the solutions from other publications. Code et al. (1976) derived a relation of temperature versus color for the main sequence stars they observed (assuming solar metallicity) for the bluer end of the range. However, most works following this do not apply their calibration for stars bluer than (B − V ) ∼ 0.3. The relation from Lejeune et al. (1998) (red dashed line) is based upon synthetic 1 Further work on this star is warranted, and is discussed in the chapter on Conclusions and Future Work.

141 colors and model atmospheres, and extends through the whole range of temperature and colors. Figure 9.2: Comparing Color-Temperature-Metallicity Relations: The solutions for color temper- ature calibrations for 4 different metallicities. The lines correspond to the following: this work (thick-solid), Code et al. (1976) (solid), Alonso et al. (1996) (blue dotted), Ram´ ırez & Mel´ndez (2005) (green dashed), e Gonz´lez Hern´ndez & Bonifacio (2009) (lime dotted-dashed), Casagrande et al. (2006) (orange triple-dotted- a a dashed), and Lejeune et al. (1998) (red long-dashed). For a solar metallicity relation, my solution predicts cooler temperatures compared to Code et al. (1976) and Lejeune et al. (1998) by ∼ 200◦ K on the bluest end of the sequence, converging to a difference of only around ∼ 100◦ K at (B − V ) ∼ 0.3. The overall spread in temperature for all other relations on the red end of the sequence is ∼ 100◦ K, where my temperatures are typically cooler for stars bluer than the Sun and hotter for stars redder than the Sun (where θEFF,⊙ = 0.872). The same applies for a metallicity [Fe/H]= −0.5,

142 although the spread in temperatures here approaches ∼ 300◦ K for the stars of (B − V ) ∼ 0.8. At a metallicity of [Fe/H] = −1, the solution from this work predicts temperatures cooler than most of the other references compared here for the whole range of colors. The solution for the lowest metallicity of [Fe/H] = −1.5 is quite interesting. My temperatures are ∼ 200◦ K lower than any of the other temperature scales it is compared to here. To compare my results to solutions in previous works, I use the color-temperature- metallicity scales presented in Alonso et al. (1996), Ram´ & Mel´ndez (2005), and Gonz´lez ırez e a Hern´ndez & Bonifacio (2009) to determine the residuals when my data are applied to their a solution (only valid for stars in the ranges of (B − V ) 0.3). Figure 9.3 shows the residual in the predicted temperature of the polynomial solution for each star’s color and metallicity versus the CHARA temperature found from interferometry (δT ). The results for this work are also shown (top panel), and the standard deviation of the residuals is also displayed in the lower left hand corner of each panel. Each solution reproduces the CHARA tempera- tures with a mean error of < 100◦ K, however, slight systematic residuals are seen for stars bluer than (B − V ) ∼ 0.5, where the predictions in the published references lead to hotter temperatures. Cooler temperatures are predicted (with a significant amount of scatter) for the redder stars in this region, most pronounced in the Alonso et al. (1996) and Ram´ & ırez Mel´ndez (2005) temperature scales. e

143 Figure 9.3: Residuals of Color-Temperature-Metallicity Relations: The color-temperature- metallicity relations in Alonso et al. (1996) (AAMR96), Ram´ & Mel´ndez (2005) (RM05), and Gonz´lez ırez e a Hern´ndez & Bonifacio (2009) (GHB09) are used to predict the temperature of each star and are compared a with the measured CHARA temperature (δT ). The standard deviation in the predicted versus measured temperature residuals is shown in the lower left region of each plot.

144 – 10 – Summary and Future Work During the 2007-2008 observing seasons, I observed a total of 69 nights with the CHARA Array. A total of 943 bracketed observations were collected for 44 of the 77 stars chosen for this survey; this includes 7 A-stars, 19 F-stars, and 18 G-stars. The measurements of these 44 stars meet the main goal of the project, to determine their angular diameters to better then 4% accuracy. These results also yield linear radii of the 44 stars to better than 4% accuracy. Twenty of these stars have effective temperatures measured to <1% accuracy, all of which are measured to better than 2.1%. Contact has been established with several different groups who are interested in using these results to refine the effective temperature scale of main sequence stars of these types to better improve models and color-temperature transformations. The temperatures and luminosities presented here were used in conjunction with Yonsei- Yale model isochrones to derive ages and masses for these 44 stars, and excellent agreement is seen with the results from a large sample of eclipsing binary stars. On the other hand, in- direct determination of stellar parameters (exclusively using photometric observations) show a discrepancy compared to my results. For most cases, the indirectly determined proper- ties lead the models to underestimate the radius of the star by ∼ 12%, while in turn they overestimate the effective temperature by ∼ 1.5 − 4%, with no apparent correlation to the star’s metallicity or color index. The overestimated temperatures and underestimated radii in these works appear to cause an additional offset in the star’s surface gravity measure-

145 ments, which consequently yields higher masses and younger ages, in particular for stars with masses greater than ∼ 1.3 M⊙ . To fully take advantage of the excellent accuracy available on measuring the angular diameters with the CHARA Array, a few things need to be studied further. The first is the effective wavelength of the CHARA Classic filter. Modeling of the transmission of the filter, mirror reflection properties and incorporating the flux distribution of the star in the K ′ waveband, McAlister et al. (2005) concluded that we know the effective wavelength as λ = 2.15 ± 0.01 µm. A project is underway by Ms Emily Bowsher to characterize the properties of the filter. Her investigation will cover a range in spectral types from O to M, at different luminosity classes, and is anticipated to be completed by Spring 2010. Next, a more robust method for determining the bolometric flux for each star is needed. Lacking this improvement, we will ultimately make the errors on the TEFF determination through the angular diameter of the star be limited by the FBOL error, which for these stars is currently at the 3% level, on average. A collaboration with Dr Gerard van Belle (ESO) has been established to determine the bolometric flux’s for these stars in the same way as described in van Belle et al. (2008). Briefly put, this implies fitting a template SED from Pickles (1998) to observed photometry, in addition to accounting for additional wavelength dependent reddening factors (assumed to be zero in this work). Due to time constraints, we performed only a test run to estimate FBOL for these stars using van Belle’s routine. For this test run, the SED template from Pickles (1998) was fixed to the spectral type given in Table 2.2 (majority of spectral types from Gray et al. 2001, 2003). However, a main drawback from this approach is that incorrect spectral typing is possible, and if the star is off by a subclass (or two) in spectral type, this

146 can lead to spurious results. Likewise, there is a nasty degeneracy between incorrect spectral typing and apparent reddening, which can also lead to inaccurate results. When the time comes for the final analysis, we plan to search through a larger grid of suitable spectral type templates to find the best fit solution of FBOL estimates for each star. The FBOL estimated from a test run of van Belle’s routine compared with the literature values in I used for this work (summarized in Table 6.1) have an average absolute difference of 5.1%1 . Although these new values need to be scrubbed, it is quite decent to say that the errors estimated for the FBOL in Chapter 6 are likely to be underestimated. This is in part because the rms value of multiple measurements was taken as the error, and the values without multiple measurements were assigned the mean percentage error (3%) for the stars with more than one FBOL estimate. To view the consequences of this mishap, we impose a conservative 4.5% error on the average literature values for FBOL in Table 6.1 (where 4.5% is the median absolute difference between the various values found in Table 6.1). Overall, this is an increased error of FBOL for almost all of the stars (which is directly proportional to the error on the absolute luminosity, quoted here in Table 6.2). This increase in FBOL error, also changes the errors in temperature because the error of FBOL is propagated through to the final error in temperature (along with the error of the angular diameter). The effective temperature errors for the 44 stars now range from 1.1−2.1% (compared to 0.2−2.1% with the old method), with an average error of 1.4% (compared to 1.2% with the old method). This simple exercise provides us with solid proof that picking FBOL values from the literature 1 However, taking into account the issues described in the previous paragraph, we suspect that in the end the agreement will not fall below ∼ 3%

147 to determine the stellar temperature is the weakest point in our method, and attention to revising this matter is currently underway. Also, special attention of the following stars is required: • Rapid rotators A-type stars are approaching the range at which stars begin to be seen with the highest rotational velocities (B-type stars). HD 177724 was observed for this project and its average diameter is given. However, it is among one of the fastest rotating A- stars, with a rotational velocity of vsin i = 317 km s−1 (Royer et al. 2006), which leads to a predicted apparent oblateness of 1.307 (Absil et al. 2008). This oblateness factor depends on the limb-darkened angular diameter, vsin i and mass of the star (see Equation 5 in (Absil et al. 2008)). Our mean angular diameter of HD 177724 of θ = 0.897 ± 0.017 mas is in excellent agreement with their predicted mean angular diameter of θ = 0.880 ± 0.018 mas. In fact, the rotational velocities for all of the A-type stars in this project (except for HD 141795) are fairly high (HD 56537 = 154 km s−1 , HD 97603 = 180 km s−1 , HD 118098 = 222 km s−1 , HD 210418 = 144 km s−1 , and HD 213558 = 128 km s−1 , Royer et al. 2006). Although their predicted oblateness is likely to be undetectable with the precision of our measurements we should consider the angular diameter measured for these stars as the mean angular diameter. • Visual and/or spectroscopic binaries The diameters of the primary stars in several binary systems were measured in this survey. The work for the population II binary HD 6582 has been published already by

148 Boyajian et al. (2008). The other systems observed are widely separated (ρ >10 arc- sec), and have fainter late K to M dwarf companions (HD 4614, HD 16895, HD 39587, HD 131156, and HD 162003). These orbits have not been updated in several decades, despite data continually being collected on the systems. An effort needs to be made to update the orbital parameters for these stars to obtain dynamical masses. In combina- tion with the results from these interferometric observations of their angular diameters, we will be able to determine all of the fundamental properties of these stars, the masses, luminosities, temperatures and radii, providing a more powerful probe into models of stellar theory, star formation, and evolution. • Visibility Binaries There are several stars that I observed for this work having visibility measurements that do not lead to an angular diameter for a single star, namely, HD 55575, HD 95418, and HD 187691. These stars are likely previously undetected binaries, and more ob- servations may confirm their multiplicity status, as well as enable us to define their orbital motions. • Incomplete diameter determination The stars HD 25457, HD 168151, HD 187013, HD 195564, and HD 211336 presently have an insufficient amount of data to reliably determine their angular diameters to the accuracy goals of this project. New improvements to the CHARA Array will allow for H-band observations of brighter targets that were previously saturating. Observations at a shorter wavelength will adequately resolve these targets to meet the goal of better than 4% accuracy.

149 I would also like to build a database (similar to the CHARM2 Catalogue) of stars with diameter measurements. Georgia State University could be known as “Diameter Central ” because the CHARA Array has enabled us to advance the field of fundamental stellar properties. I have received a Hubble Fellowship to further pursue the determination of fundamental properties of main sequence stars with the CHARA Array. In the fellowship proposal, I aimed to carry out a program encompassing several astrophysically interesting stars to determine their diameters to great accuracy. I have selected stars with special astrophysical significance in three primary areas: exoplanet host stars, low-mass, main-sequence K and M stars, and metal-poor stars. By successfully measuring the angular diameters for all objects described in this project, the fundamental properties of effective temperature, stellar radius, and absolute luminosity will be determined. Stellar ages will then be able to be determined by fitting the data to model evolutionary isochrones as well as activity isochrones. With these quantities in hand, I will explore the connection between activity rates and the deviation between model pre- dictions about radius and temperature. The ranges of ages and metallicities of these nearby stars will in turn help reveal details about the star formation history of the local region of the Galactic disk. These relevant issues are fundamentally connected to the NASA Cosmic Ori- gins themes. I will accomplish a foundation for establishing an empirical temperature scale for late-type, main sequence stars, enabling the means for calibrating less direct relationships to extend our knowledge to a larger number of stars. This includes the practical applica- tion of plotting positions of stars in the temperature-luminosity version of the H-R diagram through newly established color-temperature-metallicity transformations. By accomplishing

150 a survey of the very oldest metal-poor stars, to the typical local population of nearby stars, and to those stars that have known exoplanets, we will better understand the processes of star formation, chemical enrichment, planetary formation, and Galactic evolution to the present day, all important themes for the NASA Cosmic Origins Missions.

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156 Appendices

157 –A– Appendix A SED plots for the all objects in the sample. The solid line is the Kurucz model atmosphere for the star’s effective temperature and gravity and the diamonds are flux calibrated photometry.

158 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.1: SED plot for HD 166. 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.2: SED plot for HD 4614.

159 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.3: SED plot for HD 5015. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.4: SED plot for HD 6582.

160 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.5: SED plot for HD 10780. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.6: SED plot for HD 16895.

161 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.7: SED plot for HD 19373. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.8: SED plot for HD 20630.

162 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.9: SED plot for HD 22484. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.10: SED plot for HD 25457.

163 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.11: SED plot for HD 27045. WAVELENGTH X FLUX (erg cm-2 s-1) 10-6 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.12: SED plot for HD 30652.

164 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.13: SED plot for HD 33564. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.14: SED plot for HD 34411.

165 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.15: SED plot for HD 35296. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.16: SED plot for HD 38858.

166 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.17: SED plot for HD 39587. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.18: SED plot for HD 43042.

167 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.19: SED plot for HD 43386. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.20: SED plot for HD 46588.

168 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.21: SED plot for HD 48682. 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.22: SED plot for HD 48737.

169 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.23: SED plot for HD 50692. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.24: SED plot for HD 55575.

170 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.25: SED plot for HD 56537. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.26: SED plot for HD 58855.

171 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.27: SED plot for HD 58946. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.28: SED plot for HD 69897.

172 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.29: SED plot for HD 78154. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.30: SED plot for HD 78209.

173 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.31: SED plot for HD 81937. WAVELENGTH X FLUX (erg cm-2 s-1) 10-6 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.32: SED plot for HD 82328.

174 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.33: SED plot for HD 82885. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.34: SED plot for HD 86728.

175 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.35: SED plot for HD 87696. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.36: SED plot for HD 90089.

176 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.37: SED plot for HD 90839. WAVELENGTH X FLUX (erg cm-2 s-1) 10-6 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.38: SED plot for HD 95418.

177 WAVELENGTH X FLUX (erg cm-2 s-1) 10-6 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.39: SED plot for HD 97603. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.40: SED plot for HD 101501.

178 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.41: SED plot for HD 102870. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.42: SED plot for HD 103095.

179 WAVELENGTH X FLUX (erg cm-2 s-1) 10-6 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.43: SED plot for HD 103287. WAVELENGTH X FLUX (erg cm-2 s-1) 10-6 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.44: SED plot for HD 106591.

180 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.45: SED plot for HD 109358. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.46: SED plot for HD 110897.

181 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.47: SED plot for HD 114710. 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.48: SED plot for HD 116842.

182 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.49: SED plot for HD 118098. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.50: SED plot for HD 126660.

183 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.51: SED plot for HD 126868. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.52: SED plot for HD 128167.

184 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.53: SED plot for HD 131156. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.54: SED plot for HD 134083.

185 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.55: SED plot for HD 140538. 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.56: SED plot for HD 141795.

186 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.57: SED plot for HD 142860. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.58: SED plot for HD 146233.

187 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.59: SED plot for HD 157214. 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.60: SED plot for HD 161868.

188 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.61: SED plot for HD 162003. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.62: SED plot for HD 164259.

189 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.63: SED plot for HD 165777. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.64: SED plot for HD 168151.

190 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.65: SED plot for HD 173667. WAVELENGTH X FLUX (erg cm-2 s-1) 10-6 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.66: SED plot for HD 177724.

191 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.67: SED plot for HD 182572. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.68: SED plot for HD 185144.

192 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.69: SED plot for HD 185395. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.70: SED plot for HD 187013.

193 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.71: SED plot for HD 187691. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.72: SED plot for HD 195564.

194 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.73: SED plot for HD 201091. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure A.74: SED plot for HD 201092.

195 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.75: SED plot for HD 210418. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.76: SED plot for HD 211336.

196 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.77: SED plot for HD 213558. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.78: SED plot for HD 215648.

197 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure A.79: SED plot for HD 222368.

198 –B– Appendix B SED plots for the calibrators used in the thesis. The solid line is the Kurucz model atmo- sphere for the star’s effective temperature and gravity and the diamonds are flux calibrated photometry.

199 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.1: SED plot for HD 71. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.2: SED plot for HD 6210.

200 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.3: SED plot for HD 9407. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.4: SED plot for HD 20675.

201 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.5: SED plot for HD 21790. WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.6: SED plot for HD 22879.

202 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.7: SED plot for HD 28355. 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.8: SED plot for HD 30739.

203 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.9: SED plot for HD 31295. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.10: SED plot for HD 34904.

204 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.11: SED plot for HD 38558. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.12: SED plot for HD 42807.

205 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.13: SED plot for HD 43042. WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.14: SED plot for HD 43795.

206 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.15: SED plot for HD 50277. WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.16: SED plot for HD 58551.

207 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.17: SED plot for HD 59037. WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.18: SED plot for HD 65583.

208 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.19: SED plot for HD 83951. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.20: SED plot for HD 87141.

209 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.21: SED plot for HD 88986. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.22: SED plot for HD 89389.

210 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.23: SED plot for HD 91480. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.24: SED plot for HD 99285.

211 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.25: SED plot for HD 99984. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.26: SED plot for HD 102124.

212 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.27: SED plot for HD 102634. WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.28: SED plot for HD 103799.

213 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.29: SED plot for HD 110897. WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.30: SED plot for HD 114093.

214 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.31: SED plot for HD 120066. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.32: SED plot for HD 128093.

215 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.33: SED plot for HD 129153. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.34: SED plot for HD 132254.

216 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.35: SED plot for HD 135101. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.36: SED plot for HD 139225.

217 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.37: SED plot for HD 140775. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.38: SED plot for HD 145607.

218 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.39: SED plot for HD 150177. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.40: SED plot for HD 154099.

219 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.41: SED plot for HD 158352. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.42: SED plot for HD 158633.

220 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.43: SED plot for HD 162004. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.44: SED plot for HD 167564.

221 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.45: SED plot for HD 174897. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.46: SED plot for HD 176303.

222 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.47: SED plot for HD 180317. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.48: SED plot for HD 183534.

223 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.49: SED plot for HD 184499. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.50: SED plot for HD 189395.

224 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.51: SED plot for HD 191195. WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.52: SED plot for HD 193555.

225 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.53: SED plot for HD 193664. 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.54: SED plot for HD 195838.

226 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.55: SED plot for HD 204485. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.56: SED plot for HD 210715.

227 10-7 WAVELENGTH X FLUX (erg cm-2 s-1) 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.57: SED plot for HD 211976. 10-6 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10000 WAVELENGTH (ANGSTROMS) Figure B.58: SED plot for HD 214923.

228 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.59: SED plot for HD 216735. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.60: SED plot for HD 218470.

229 WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.61: SED plot for HD 222603. WAVELENGTH X FLUX (erg cm-2 s-1) 10-7 10-8 10000 WAVELENGTH (ANGSTROMS) Figure B.62: SED plot for HD 225003.

230 –C– Appendix C C.1 HD 4614 Table C.1: HD 4614 Visibilities B ψ MJD (m) (◦ ) V σV 54280.969 270.8 −23.2 0.212 0.016 54280.990 280.7 −16.0 0.162 0.009 54281.943 259.3 −31.6 0.239 0.014 54281.954 264.5 −27.7 0.229 0.023 54281.964 269.5 −24.1 0.186 0.019 54281.974 274.7 −20.4 0.168 0.014 54281.988 281.1 −15.8 0.147 0.012 54282.889 234.7 −52.4 0.337 0.038 54282.903 240.9 −46.4 0.288 0.033 54282.938 258.1 −32.5 0.253 0.017 54300.928 275.7 40.4 0.200 0.009 54300.940 280.7 42.9 0.176 0.010 54300.950 285.0 45.2 0.163 0.007 54301.869 244.8 28.1 0.309 0.014 54301.879 251.3 30.4 0.282 0.015 54301.891 258.3 33.0 0.264 0.015 54420.695 306.7 27.4 0.092 0.009 54420.714 309.9 22.9 0.100 0.009 54420.720 310.9 21.3 0.084 0.006 54420.732 312.3 18.6 0.078 0.008 54741.743 286.3 101.9 0.145 0.018 54741.759 292.6 96.8 0.124 0.013 54741.775 298.1 92.0 0.097 0.013 54741.826 310.3 76.5 0.087 0.014

231 Figure C.1: Diameter fit for HD 4614

232 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.2: Y2 Model Isochrones for HD 4614: HD 4614 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.3.)

233 C.2 HD 5015 Table C.2: HD 5015 Visibilities B ψ MJD (m) (◦ ) V σV 54383.903 312.2 47.3 0.629 0.048 54383.908 311.8 45.4 0.618 0.040 54383.915 311.3 43.3 0.594 0.108 54383.921 310.8 41.2 0.660 0.047 54383.927 310.3 39.1 0.688 0.053 54383.978 305.8 21.7 0.603 0.057 54383.984 305.4 19.5 0.662 0.039 54383.990 304.9 17.3 0.619 0.059 54383.996 304.6 15.2 0.638 0.064 54384.009 303.9 10.5 0.697 0.061 54407.614 269.1 119.5 0.585 0.121 54407.620 272.0 117.1 0.692 0.151 54407.627 274.6 114.8 0.708 0.124 54407.634 277.5 112.3 0.726 0.097 54407.668 290.5 100.9 0.587 0.080 54407.674 292.7 98.8 0.590 0.078 54407.681 295.2 96.3 0.697 0.093 54421.671 294.5 34.0 0.605 0.057 54421.676 295.9 32.6 0.665 0.040 54421.682 297.3 31.2 0.599 0.038 54421.688 298.6 29.7 0.654 0.044 54421.694 299.8 28.2 0.624 0.039 54421.700 301.0 26.8 0.565 0.053 54421.706 302.0 25.4 0.640 0.040 54421.711 303.0 24.1 0.650 0.048

234 Figure C.3: Diameter fit for HD 5015

235 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.4: Y2 Model Isochrones for HD 5015: HD 5015 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.0).

236 C.3 HD 6582 Results on this star have been published in Boyajian et al. (2008). To re-iterate the important information, we give the calibrated visibilities and Diameter fit below. Table C.3: HD 6582 Visibilities B ψ MJD (m) (◦ ) V σV 54282.917 233.2 135.0 0.739 0.093 54282.929 239.8 130.0 0.692 0.071 54282.954 253.8 120.4 0.652 0.065 54298.915 266.4 234.3 0.682 0.038 54298.929 274.0 231.4 0.672 0.023 54298.942 280.7 228.6 0.638 0.024 54298.957 287.1 225.6 0.625 0.020 54298.971 292.7 222.7 0.580 0.024 54298.986 298.0 219.4 0.550 0.026 54299.885 249.2 239.9 0.636 0.027 54299.896 256.2 237.8 0.629 0.023 54299.905 262.2 235.8 0.694 0.030 54299.917 268.9 233.4 0.639 0.028 54299.961 290.0 224.1 0.583 0.035 54299.973 294.6 221.5 0.568 0.038 54299.984 298.2 219.2 0.549 0.026 54299.996 301.9 216.6 0.547 0.035 54351.787 275.7 219.2 0.566 0.037 54351.795 279.4 220.8 0.612 0.030 54351.802 282.8 222.3 0.605 0.026 54351.809 285.9 223.8 0.618 0.040 54351.816 288.9 225.3 0.660 0.045 54351.831 294.5 228.4 0.569 0.034 54351.839 297.3 230.2 0.604 0.047 54351.851 301.3 232.9 0.576 0.036 54351.875 307.6 238.3 0.601 0.055

237 Figure C.5: Diameter fit for HD 6582

238 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.6: Y2 Model Isochrones for HD 6582: HD 6582 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.3, [Fe/H]=−0.83).

239 C.4 HD 10780 Results on this star have been published in Boyajian et al. (2008). To re-iterate the important information, we give the calibrated visibilities and Diameter fit below. Table C.4: HD 10780 Visibilities B ψ MJD (m) (◦ ) V σV 52922.857 235.2 137.4 0.890 0.092 52922.867 233.3 140.4 0.947 0.076 54280.952 256.8 138.4 0.730 0.063 54280.979 266.4 127.5 0.738 0.043 54301.903 230.1 248.9 0.834 0.037 54301.913 236.4 246.2 0.879 0.053 54301.924 242.5 243.4 0.819 0.054 54301.935 248.7 240.5 0.802 0.062 54301.946 254.3 237.7 0.758 0.056 54301.957 259.4 235.0 0.780 0.035 54301.968 264.5 232.2 0.787 0.062 54301.979 269.0 229.5 0.783 0.072 54301.989 273.2 226.8 0.856 0.058 54302.000 276.9 224.2 0.824 0.059 54383.935 313.2 220.9 0.742 0.059 54383.943 312.8 223.7 0.694 0.069 54383.950 312.5 226.2 0.614 0.059 54383.958 312.1 228.7 0.688 0.071 54383.971 311.3 233.2 0.627 0.045 54384.017 308.5 249.0 0.692 0.078 54384.025 308.1 251.6 0.582 0.145 54384.031 307.8 253.9 0.708 0.077

240 Figure C.7: Diameter fit for HD 10780

241 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.8: Y2 Model Isochrones for HD 10780: HD 10780 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.05).

242 C.5 HD 16895 Table C.5: HD 16895 Visibilities B ψ MJD (m) (◦ ) V σV 54351.917 310.9 36.0 0.518 0.050 54351.936 315.5 32.0 0.461 0.019 54351.946 317.5 29.9 0.408 0.026 54351.956 319.3 27.7 0.413 0.026 54351.966 320.9 25.5 0.403 0.028 54351.973 321.8 24.0 0.365 0.027 54351.983 323.0 21.6 0.471 0.031 54407.710 266.5 106.1 0.544 0.074 54407.718 271.3 103.8 0.470 0.073 54407.725 276.0 101.4 0.517 0.052 54407.733 280.3 99.3 0.551 0.049 54407.741 284.7 97.0 0.455 0.060 54407.765 296.4 90.2 0.396 0.049 54407.775 300.3 87.5 0.489 0.080 54407.783 303.0 85.4 0.465 0.061 54458.694 323.3 21.1 0.383 0.025 54458.702 324.1 19.1 0.415 0.023 54458.711 324.8 17.1 0.406 0.019 54458.719 325.4 15.2 0.379 0.033 54458.728 325.9 13.2 0.381 0.027 54458.737 326.3 11.0 0.396 0.029

243 Figure C.9: Diameter fit for HD 16895

244 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.10: Y2 Model Isochrones for HD 16895: HD 16895 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.12).

245 C.6 HD 19373 Table C.6: HD 19373 Visibilities B ψ MJD (m) (◦ ) V σV 54125.655 325.5 76.7 0.290 0.037 54125.666 326.0 79.3 0.282 0.028 54125.676 326.4 81.6 0.288 0.029 54125.686 326.6 83.9 0.292 0.029 54125.709 326.9 89.4 0.260 0.024 54125.718 326.9 −88.2 0.261 0.034 54125.728 326.8 −85.9 0.268 0.035 54340.996 277.1 147.6 0.399 0.023 54341.007 276.3 144.8 0.366 0.027 54351.902 299.9 42.4 0.416 0.034 54351.909 302.3 41.1 0.378 0.034 54351.923 307.0 38.3 0.334 0.033 54351.939 311.7 35.0 0.326 0.022 54351.949 314.1 32.9 0.347 0.018 54351.959 316.3 30.8 0.314 0.026 54351.976 319.4 27.0 0.310 0.024 54351.987 320.9 24.7 0.294 0.026 54351.993 321.7 23.3 0.293 0.025 54351.999 322.5 21.9 0.308 0.019 54408.699 249.2 114.9 0.621 0.170 54408.715 260.6 109.4 0.619 0.172 54408.728 269.2 105.1 0.542 0.059 54408.735 273.1 103.2 0.457 0.047 54408.741 277.0 101.3 0.473 0.048 54408.751 282.6 98.4 0.441 0.083

246 Figure C.11: Diameter fit for HD 19373

247 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.12: Y2 Model Isochrones for HD 19373: HD 19373 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.9).

248 C.7 HD 20630 Table C.7: HD 20630 Visibilities B ψ MJD (m) (◦ ) V σV 54352.907 324.4 38.5 0.560 0.080 54352.938 314.6 35.5 0.604 0.106 54352.953 308.6 33.6 0.682 0.106 54352.964 303.9 32.0 0.660 0.079 54352.978 297.7 29.7 0.786 0.115 54352.989 292.7 27.7 0.804 0.121 54353.003 286.6 25.0 0.750 0.101 54353.013 282.3 22.9 0.697 0.083 54353.020 279.4 21.2 0.570 0.072 54740.872 316.2 36.0 0.614 0.060 54740.883 312.0 34.7 0.621 0.079 54740.902 304.2 32.1 0.577 0.057 54740.912 299.8 30.5 0.560 0.087 54787.776 303.3 31.8 0.548 0.081 54787.794 295.3 28.8 0.613 0.075 54787.823 282.5 22.9 0.557 0.067 54787.836 277.3 19.9 0.638 0.067 54788.780 300.0 30.6 0.446 0.064 54788.792 294.6 28.5 0.586 0.101 54788.811 286.5 25.0 0.619 0.068 54788.827 279.5 21.3 0.536 0.049 54788.849 271.5 15.8 0.762 0.138

249 Figure C.13: Diameter fit for HD 20630

250 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.14: Y2 Model Isochrones for HD 20630: HD 20630 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.0).

251 C.8 HD 22484 Table C.8: HD 22484 Visibilities B ψ MJD (m) (◦ ) V σV 54074.707 310.8 36.8 0.505 0.074 54076.692 314.7 37.7 0.361 0.038 54076.705 309.3 36.4 0.413 0.051 54076.717 303.7 35.0 0.413 0.062 54076.729 297.9 33.4 0.431 0.041 54352.911 323.1 39.5 0.479 0.050 54352.919 320.7 39.1 0.481 0.043 54352.950 308.9 36.3 0.513 0.078 54352.961 303.7 35.0 0.510 0.055 54352.975 296.8 33.1 0.603 0.073 54352.986 291.2 31.4 0.655 0.131 54353.000 284.1 29.0 0.611 0.090 54353.010 278.9 27.1 0.594 0.063 54740.842 324.9 39.9 0.382 0.038 54740.858 320.4 39.0 0.472 0.055 54740.863 318.5 38.6 0.447 0.050 54740.879 312.7 37.3 0.400 0.054 54740.898 304.1 35.1 0.506 0.052 54740.909 299.1 33.8 0.490 0.066 54741.854 286.8 74.3 0.514 0.031 54741.865 294.4 74.7 0.501 0.032 54741.874 300.1 75.0 0.483 0.051 54741.886 305.8 75.4 0.543 0.048

252 Figure C.15: Diameter fit for HD 22484

253 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.16: Y2 Model Isochrones for HD 22484: HD 22484 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.09).

254 C.9 HD 30652 Table C.9: HD 30652 Visibilities B ψ MJD (m) (◦ ) V σV 54409.942 284.5 17.0 0.259 0.047 54409.948 282.7 15.5 0.264 0.035 54409.953 281.1 14.0 0.282 0.036 54409.959 279.6 12.4 0.296 0.048 54409.966 278.2 10.8 0.285 0.044 54409.976 276.3 7.9 0.269 0.027 54409.982 275.4 6.2 0.263 0.029 54409.990 274.6 4.0 0.260 0.035 54409.996 274.3 2.4 0.246 0.041 54410.001 274.1 0.9 0.211 0.033 54410.032 276.3 172.1 0.237 0.040 54410.038 277.3 170.5 0.244 0.040 54410.045 278.6 168.7 0.221 0.033 54410.051 280.0 167.1 0.249 0.033 54410.056 281.6 165.6 0.204 0.045 54410.023 275.1 174.7 0.262 0.036 54740.927 322.7 36.3 0.088 0.010 54740.934 320.9 35.5 0.108 0.010 54740.940 318.9 34.7 0.115 0.011 54740.973 307.4 30.0 0.181 0.025 54740.985 302.7 27.8 0.182 0.020 54740.992 300.0 26.5 0.178 0.023 54741.038 283.7 16.3 0.247 0.039 54741.049 280.6 13.5 0.254 0.037 54741.056 278.9 11.7 0.220 0.029 54740.951 315.5 33.3 0.114 0.014 54740.957 313.3 32.5 0.118 0.012 54740.963 311.2 31.6 0.122 0.014 54741.004 295.5 24.2 0.177 0.027 54741.010 293.3 22.9 0.218 0.041 54741.016 291.0 21.6 0.200 0.030 54741.025 287.8 19.5 0.217 0.021 54741.946 307.4 76.9 0.151 0.011 54741.955 310.4 76.6 0.152 0.014

255 Figure C.17: Diameter fit for HD 30652

256 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.18: Y2 Model Isochrones for HD 30652: HD 30652 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.03).

257 C.10 HD 34411 Table C.10: HD 34411 Visibilities B ψ MJD (m) (◦ ) V σV 54126.812 330.6 −86.8 0.566 0.105 54126.823 330.7 −84.3 0.470 0.046 54126.833 330.7 −81.9 0.428 0.063 54126.846 330.7 −78.8 0.463 0.051 54126.862 330.6 −75.2 0.391 0.059 54407.809 253.5 102.5 0.619 0.053 54407.819 261.2 100.1 0.595 0.048 54407.833 272.6 96.3 0.595 0.078 54407.840 277.3 94.7 0.698 0.163 54407.853 286.4 91.4 0.673 0.224 54407.865 293.0 88.7 0.686 0.191 54407.873 297.2 86.9 0.616 0.138 54419.718 269.2 52.3 0.563 0.104 54419.753 292.0 47.9 0.489 0.062 54419.778 304.4 44.4 0.507 0.060 54419.793 310.3 42.1 0.574 0.060 54421.730 281.6 50.2 0.661 0.031 54421.738 286.6 49.1 0.631 0.031 54421.747 291.7 48.0 0.535 0.043 54421.755 295.9 46.9 0.599 0.027 54421.763 299.8 45.8 0.569 0.041 54421.771 303.5 44.7 0.560 0.046 54421.778 306.7 43.6 0.587 0.042

258 Figure C.19: Diameter fit for HD 34411

259 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.20: Y2 Model Isochrones for HD 34411: HD 34411 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.05).

260 C.11 HD 39587 Table C.11: HD 39587 Visibilities B ψ MJD (m) (◦ ) V σV 54076.960 309.3 0.1 0.498 0.045 54076.970 309.5 −87.2 0.503 0.033 54076.981 310.0 −84.7 0.483 0.043 54165.694 310.1 84.3 0.533 0.051 54165.709 309.4 88.2 0.462 0.052 54165.725 309.4 −87.9 0.493 0.053 54165.734 309.8 −85.5 0.493 0.045 54165.744 310.5 −83.1 0.467 0.034 54165.753 311.4 −80.7 0.417 0.037 54165.763 312.5 −78.4 0.400 0.047 54165.775 314.2 −75.5 0.390 0.035 54788.874 327.6 30.3 0.398 0.058 54788.881 326.5 29.1 0.413 0.060 54788.891 324.9 27.3 0.440 0.111 54788.899 323.7 25.9 0.476 0.111 54788.906 322.3 24.5 0.372 0.066 54788.914 320.9 22.9 0.483 0.072 54788.927 318.6 20.3 0.438 0.051 54788.934 317.2 18.7 0.416 0.058 54788.941 316.1 17.2 0.502 0.061 54788.948 315.0 15.6 0.461 0.061 54788.954 314.0 14.2 0.344 0.044

261 Figure C.21: Diameter fit for HD 39587

262 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.22: Y2 Model Isochrones for HD 39587: HD 39587 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.16).

263 C.12 HD 48682 Table C.12: HD 48682 Visibilities B ψ MJD (m) (◦ ) V σV 54458.756† 308.2 41.6 0.663 0.053 54458.766† 311.5 39.9 0.736 0.050 54458.775† 314.5 38.1 0.735 0.055 54458.785† 317.1 36.4 0.745 0.047 54458.793† 319.1 34.8 0.807 0.049 54458.802† 320.9 33.1 0.836 0.067 54458.810† 322.5 31.5 0.989 0.076 54458.818† 323.8 29.9 1.060 0.115 54458.827† 325.0 28.1 1.091 0.149 54726.971 284.1 49.7 0.682 0.073 54726.979 288.6 48.6 0.734 0.105 54726.987 292.9 47.3 0.697 0.065 54726.995 297.0 46.0 0.615 0.053 54727.004 301.3 44.5 0.666 0.044 54727.036 313.1 39.0 0.690 0.048 54741.978 272.5 98.8 0.740 0.110 54741.989 280.0 95.8 0.654 0.093 54742.001 287.3 92.7 0.683 0.088 54786.827 294.7 46.8 0.679 0.056 54786.838 299.9 45.0 0.669 0.031 54786.846 303.7 43.6 0.648 0.042 54786.855 307.0 42.1 0.610 0.044 54786.922 324.0 29.6 0.848 0.089 † represents data calibrated with a bad calibrator.

264 Figure C.23: Diameter fit for HD 48682

265 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.24: Y2 Model Isochrones for HD 48682: HD 48682 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.01).

266 C.13 HD 48737 Table C.13: HD 48737 Visibilities B ψ MJD (m) (◦ ) V σV 54076.900 308.4 66.8 0.192 0.027 54076.911 305.2 69.1 0.248 0.015 54076.923 302.1 71.7 0.253 0.016 54076.933 299.5 74.2 0.256 0.021 54787.943 312.1 25.8 0.280 0.036 54787.951 309.8 24.2 0.221 0.022 54788.026 293.0 6.3 0.262 0.039 54788.034 292.3 4.2 0.298 0.029 54788.050 291.7 90.0 0.263 0.029 54787.966 305.4 21.0 0.226 0.027 54787.974 303.2 19.2 0.193 0.020 54787.982 301.1 17.3 0.273 0.035 54787.996 297.8 14.0 0.222 0.024 54788.013 294.6 9.7 0.242 0.030 54788.970 303.5 19.5 0.233 0.031 54788.976 301.9 18.1 0.348 0.039 54788.985 299.6 15.9 0.287 0.028 54788.991 298.2 14.4 0.289 0.027 54789.003 295.8 11.4 0.280 0.031 54789.010 294.7 9.8 0.308 0.048 54789.016 293.8 8.2 0.294 0.040 54789.022 293.1 6.6 0.299 0.033 54789.029 292.4 4.8 0.263 0.034 54789.035 292.0 3.0 0.221 0.024 54789.041 291.8 1.4 0.212 0.025

267 Figure C.25: Diameter fit for HD 48737

268 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.26: Y2 Model Isochrones for HD 48737: HD 48737 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.04).

269 C.14 HD 56537 Table C.14: HD 56537 Visibilities B ψ MJD (m) (◦ ) V σV 54156.743 306.6 75.8 0.581 0.066 54156.754 304.7 78.5 0.613 0.051 54156.765 303.1 81.3 0.663 0.076 54156.777 302.0 84.3 0.690 0.081 54156.789 301.2 87.5 0.676 0.080 54156.801 301.1 −89.5 0.665 0.085 54156.812 301.4 −86.7 0.677 0.053 54170.746 301.5 4.3 0.644 0.083 54170.760 301.1 0.7 0.661 0.056 54170.772 301.2 177.5 0.648 0.052 54170.784 301.9 174.4 0.648 0.063 54170.797 303.3 171.0 0.557 0.066 54409.003 317.6 25.1 0.720 0.066 54409.013 315.3 23.1 0.702 0.049 54409.018 322.4 22.8 0.919 0.066 54409.038 309.5 17.7 0.642 0.074 54409.048 307.6 15.5 0.584 0.058 54457.879 315.4 23.2 0.604 0.056 54457.889 313.1 21.2 0.561 0.041 54457.914 307.6 15.5 0.658 0.045 54457.923 306.0 13.4 0.672 0.049 54457.933 304.4 11.0 0.601 0.042 54457.947 302.5 7.4 0.699 0.096

270 Figure C.27: Diameter fit for HD 56537

271 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.28: Y2 Model Isochrones for HD 56537: HD 56537 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.0).

272 C.15 HD 58946 Table C.15: HD 58946 Visibilities B ψ MJD (m) (◦ ) V σV 54125.881 326.5 87.6 0.609 0.046 54125.896 326.4 −88.9 0.461 0.070 54125.907 326.6 −86.2 0.507 0.094 54125.925 327.1 −82.0 0.689 0.061 54125.936 327.5 −79.5 0.564 0.054 54125.953 328.4 −75.5 0.542 0.040 54420.805 286.1 48.1 0.746 0.100 54420.815 291.9 47.4 0.694 0.072 54420.821 295.7 46.9 0.534 0.074 54420.842 306.7 44.9 0.666 0.077 54420.848 309.7 44.3 0.586 0.072 54420.854 312.2 43.6 0.585 0.045 54420.861 314.5 42.9 0.665 0.048 54421.800 284.2 48.3 0.761 0.059 54421.807 289.0 47.8 0.711 0.052 54421.815 293.9 47.2 0.656 0.064 54421.828 301.4 46.0 0.664 0.065 54421.836 305.3 45.3 0.654 0.063 54421.844 309.0 44.4 0.608 0.052 54421.852 312.5 43.5 0.622 0.054

273 Figure C.29: Diameter fit for HD 58946

274 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.30: Y2 Model Isochrones for HD 58946: HD 58946 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.31).

275 C.16 HD 81937 Table C.16: HD 81937 Visibilities B ψ MJD (m) (◦ ) V σV 54433.982 213.9 33.1 0.575 0.048 54433.991 215.5 31.0 0.629 0.050 54433.999 216.9 29.1 0.487 0.043 54434.010 218.7 26.4 0.543 0.050 54434.020 220.0 24.0 0.490 0.037 54434.033 221.7 20.7 0.599 0.052 54434.041 222.6 18.7 0.552 0.046 54434.052 223.6 16.0 0.565 0.047 54434.061 224.3 13.9 0.690 0.048

276 Figure C.31: Diameter fit for HD 81937

277 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.32: Y2 Model Isochrones for HD 81937: HD 81937 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.06).

278 C.17 HD 82328 Table C.17: HD 82328 Visibilities B ψ MJD (m) (◦ ) V σV 54406.988 130.600 97.8 0.705 0.1 54406.994 132.670 95.9 0.675 0.1 54407.001 134.650 94.0 0.687 0.1 54407.007 136.490 92.3 0.674 0.1 54407.013 138.260 90.5 0.658 0.1 54407.019 140.110 88.6 0.671 0.1 54407.027 142.220 86.4 0.717 0.1 54407.034 143.800 84.6 0.739 0.1 54407.041 145.340 82.8 0.750 0.1

279 Figure C.33: Diameter fit for HD 82328

280 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.34: Y2 Model Isochrones for HD 82328: HD 82328 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.12).

281 C.18 HD 82885 Table C.18: HD 82885 Visibilities B ψ MJD (m) (◦ ) V σV 54134.908 329.9 11.3 0.643 0.071 54134.921 329.7 8.2 0.530 0.065 54407.992 255.7 98.1 0.767 0.074 54408.004 265.9 95.4 0.734 0.064 54408.012 272.3 93.7 0.716 0.074 54408.020 278.8 91.8 0.725 0.062 54408.034 288.4 88.8 0.719 0.061 54408.042 293.2 87.2 0.756 0.066 54408.050 297.4 85.5 0.631 0.057 54411.935 289.8 48.3 0.655 0.064 54411.943 294.2 47.5 0.731 0.114 54411.951 298.5 46.6 0.748 0.136 54411.958 302.3 45.7 0.720 0.087 54411.966 305.9 44.7 0.726 0.075 54411.974 309.2 43.8 0.671 0.080 54411.981 312.3 42.7 0.685 0.080 54411.989 314.9 41.7 0.706 0.085 54412.009 321.1 38.6 0.610 0.091 54458.854 312.8 42.6 0.694 0.068 54458.866 316.9 40.8 0.704 0.060 54458.878 320.4 39.0 0.618 0.048 54458.889 323.1 37.3 0.611 0.058 54458.901 325.3 35.4 0.575 0.045

282 Figure C.35: Diameter fit for HD 82885

283 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.36: Y2 Model Isochrones for HD 82885: HD 82885 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.06).

284 C.19 HD 86728 Table C.19: HD 86728 Visibilities B ψ MJD (m) (◦ ) V σV 54419.878 259.1 50.1 0.727 0.076 54419.889 268.6 49.6 0.697 0.067 54419.901 277.0 49.0 0.704 0.096 54419.912 285.1 48.3 0.801 0.087 54419.924 292.6 47.4 0.722 0.084 54419.944 303.5 45.6 0.693 0.060 54419.955 308.7 44.5 0.705 0.069 54419.968 314.2 43.0 0.658 0.077 54419.976 316.9 42.1 0.640 0.083 54419.984 319.5 41.1 0.598 0.069 54420.889 270.1 49.5 0.710 0.087 54420.895 275.0 49.2 0.586 0.081 54458.846 307.9 44.7 0.684 0.035 54458.863 314.6 42.9 0.727 0.044 54458.875 318.7 41.4 0.612 0.052 54458.886 321.9 39.9 0.647 0.048 54458.897 324.5 38.4 0.668 0.050 54458.908 326.6 36.7 0.714 0.047 54786.948 307.8 44.7 0.660 0.059 54786.957 311.6 43.7 0.643 0.064 54786.965 314.7 42.8 0.682 0.068 54786.983 320.5 40.6 0.764 0.065 54786.991 322.7 39.5 0.655 0.053 54787.007 326.0 37.3 0.704 0.055 54787.029 329.0 33.7 0.706 0.046 54787.042 330.0 31.6 0.648 0.056 54787.051 330.4 30.0 0.767 0.068

285 Figure C.37: Diameter fit for HD 86728

286 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.38: Y2 Model Isochrones for HD 86728: HD 86728 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.2).

287 C.20 HD 90839 Table C.20: HD 90839 Visibilities B ψ MJD (m) (◦ ) V σV 54420.922 231.2 65.5 0.732 0.069 54420.928 235.6 64.2 0.819 0.050 54420.935 240.8 62.7 0.820 0.069 54420.951 251.7 59.3 0.710 0.054 54420.957 255.4 58.1 0.721 0.045 54420.968 262.5 55.6 0.784 0.046 54420.975 266.1 54.3 0.786 0.047 54420.980 269.2 53.1 0.759 0.052 54420.987 272.5 51.8 0.734 0.049 54420.993 275.8 50.4 0.727 0.039 54573.688 311.4 25.3 0.718 0.097 54573.688 311.4 25.3 0.639 0.138 54573.710 314.6 20.1 0.690 0.119 54573.710 314.6 20.1 0.667 0.140 54573.741 317.6 12.6 0.714 0.064 54573.741 317.6 12.6 0.808 0.178 54573.760 318.7 8.2 0.662 0.064 54573.760 318.7 8.2 0.656 0.095 54573.777 319.2 3.8 0.714 0.085 54573.777 319.2 3.8 0.625 0.066

288 Figure C.39: Diameter fit for HD 90839

289 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.40: Y2 Model Isochrones for HD 90839: HD 90839 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.16).

290 C.21 HD 97603 Table C.21: HD 97603 Visibilities B ψ MJD (m) (◦ ) V σV 54152.901 316.7 72.6 0.303 0.025 54152.912 315.0 74.9 0.323 0.025 54152.923 313.4 77.6 0.275 0.029 54152.934 312.0 80.3 0.278 0.020 54152.945 311.0 82.8 0.263 0.016 54152.958 310.2 86.2 0.252 0.012 54152.970 309.8 89.3 0.258 0.012 54152.981 309.9 −88.1 0.231 0.020 54152.992 310.4 −85.2 0.255 0.014 54153.003 311.1 −82.5 0.246 0.020 54169.825 322.0 66.2 0.268 0.038 54170.864 314.8 75.3 0.284 0.038 54170.876 313.2 78.0 0.270 0.023 54170.887 304.6 78.4 0.291 0.024 54170.901 310.6 84.4 0.284 0.034 54170.915 310.0 87.7 0.272 0.037

291 Figure C.41: Diameter fit for HD 97603

292 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.42: Y2 Model Isochrones for HD 97603: HD 97603 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.0).

293 C.22 HD 101501 Table C.22: HD 101501 Visibilities B ψ MJD (m) (◦ ) V σV 54420.003 294.4 47.3 0.620 0.054 54420.014 300.4 46.2 0.645 0.068 54420.023 304.9 45.2 0.605 0.045 54420.040 312.1 43.2 0.612 0.056 54420.050 315.6 41.9 0.594 0.068 54420.059 318.6 40.7 0.559 0.050 54420.071 321.9 38.9 0.571 0.043 54458.940 314.5 42.4 0.555 0.045 54458.963 321.5 39.1 0.539 0.040 54458.992 327.2 34.6 0.586 0.041

294 Figure C.43: Diameter fit for HD 101501

295 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.44: Y2 Model Isochrones for HD 101501: HD 101501 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.12).

296 C.23 HD 102870 Table C.23: HD 102870 Visibilities B ψ MJD (m) (◦ ) V σV 54168.947 256.5 87.5 0.370 0.040 54168.959 256.3 −88.9 0.342 0.024 54168.970 257.0 −85.5 0.326 0.037 54168.982 258.7 −81.9 0.325 0.026 54168.994 261.4 −78.4 0.327 0.033 54169.017 268.6 −72.2 0.277 0.034 54458.001 314.0 36.3 0.207 0.019 54458.010 310.3 35.3 0.205 0.018 54458.026 303.5 33.3 0.208 0.024 54458.034 299.6 32.0 0.259 0.024 54575.660 197.9 154.7 0.329 0.177 54575.673 205.1 150.6 0.629 0.058 54575.681 209.8 148.3 0.568 0.072 54575.690 215.2 146.0 0.520 0.067 54575.697 219.8 144.2 0.510 0.066 54575.707 225.9 142.0 0.529 0.090 54575.715 230.7 140.4 0.478 0.062 54575.722 235.4 138.9 0.433 0.062 54578.665 316.0 36.9 0.186 0.034 54578.674 312.9 36.0 0.211 0.028 54578.682 309.6 35.1 0.223 0.031 54578.691 305.5 33.9 0.245 0.026 54578.699 302.0 32.8 0.235 0.021 54578.707 298.2 31.5 0.248 0.030 54578.722 290.9 28.9 0.287 0.034 54578.730 287.1 27.4 0.278 0.025 54578.738 283.4 25.9 0.295 0.031 54579.653 319.5 37.8 0.170 0.029 54579.674 311.8 35.7 0.186 0.032 54579.683 308.0 34.6 0.194 0.031 54579.690 304.7 33.6 0.221 0.029 54579.706 297.3 31.2 0.234 0.033 54579.714 293.7 30.0 0.247 0.025 54579.722 289.8 28.5 0.262 0.028

297 Figure C.45: Diameter fit for HD 102870

298 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.46: Y2 Model Isochrones for HD 102870: HD 102870 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.11).

299 C.24 HD 103095 Table C.24: HD 103095 Visibilities B ψ MJD (m) (◦ ) V σV 54421.009 288.2 48.7 0.773 0.090 54421.018 293.6 47.6 0.776 0.056 54421.032 300.7 45.9 0.769 0.066 54421.040 304.7 44.8 0.761 0.064 54421.047 307.5 43.9 0.755 0.057 54421.053 310.1 43.0 0.756 0.064 54421.060 312.5 42.1 0.752 0.073 54458.927 299.9 46.1 0.757 0.036 54458.935 304.1 45.0 0.759 0.043 54458.950 310.3 42.9 0.734 0.055 54458.959 313.5 41.7 0.714 0.053 54458.978 319.5 38.6 0.748 0.042 54458.996 323.7 35.6 0.733 0.031 54459.005 325.2 34.1 0.691 0.051 54459.013 326.5 32.6 0.724 0.047 54459.022 327.5 31.1 0.696 0.053 54459.030 328.5 29.4 0.820 0.071

300 Figure C.47: Diameter fit for HD 103095

301 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.48: Y2 Model Isochrones for HD 103095: HD 103095 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−1.36).

302 C.25 HD 109358 Table C.25: HD 109358 Visibilities B ψ MJD (m) (◦ ) V σV 54246.844 275.2 -68.4 0.469 0.033 54246.858 274.0 -65.7 0.537 0.046 54246.869 272.7 -63.5 0.498 0.042 54574.650 274.3 174.1 0.478 0.086 54574.666 274.8 169.6 0.424 0.049 54574.677 275.3 166.4 0.592 0.081 54574.688 275.8 163.5 0.452 0.066 54574.699 276.4 160.6 0.536 0.100 54574.666 274.8 169.6 0.332 0.040 54574.677 275.3 166.4 0.430 0.058 54574.688 275.8 163.5 0.353 0.048 54574.699 276.4 160.6 0.434 0.074

303 Figure C.49: Diameter fit for HD 109358

304 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.50: Y2 Model Isochrones for HD 109358: HD 109358 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.3).

305 C.26 HD 114710 Table C.26: HD 114710 Visibilities B ψ MJD (m) (◦ ) V σV 54644.693 322.3 4.2 0.370 0.035 54644.700 322.1 2.4 0.378 0.034 54644.707 322.1 0.8 0.400 0.044 54644.713 322.1 179.3 0.444 0.040 54644.721 322.2 177.3 0.420 0.034 54644.727 322.3 175.9 0.362 0.043 54577.646 254.9 0.5 0.659 0.134 54577.664 255.2 175.4 0.560 0.084 54577.675 256.1 171.8 0.501 0.071 54577.688 257.3 168.1 0.578 0.114 54577.701 259.2 164.2 0.542 0.105 54577.714 261.4 160.5 0.548 0.104 54577.734 265.3 154.9 0.515 0.079 54577.743 267.1 152.6 0.484 0.076 54577.751 268.8 150.6 0.537 0.054 54577.760 270.5 148.5 0.565 0.072

306 Figure C.51: Diameter fit for HD 114710

307 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.52: Y2 Model Isochrones for HD 114710: HD 114710 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.06).

308 C.27 HD 118098 Table C.27: HD 118098 Visibilities B ψ MJD (m) (◦ ) V σV 54169.888 298.3 33.7 0.644 0.064 54169.903 290.6 31.4 0.678 0.097 54169.922 280.6 28.0 0.718 0.105 54169.937 273.2 24.9 0.670 0.097 54169.952 265.9 21.4 0.647 0.091 54169.970 258.4 16.7 0.599 0.117 54189.808 310.0 36.7 0.582 0.058 54189.819 305.1 35.5 0.635 0.055 54189.831 299.3 34.0 0.627 0.073 54189.843 293.2 32.2 0.671 0.071 54189.854 287.6 30.5 0.745 0.086 54458.058 316.3 38.2 0.596 0.064 54458.071 311.2 37.0 0.691 0.102

309 Figure C.53: Diameter fit for HD 118098

310 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.54: Y2 Model Isochrones for HD 118098: HD 118098 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.02).

311 C.28 HD 126660 Table C.28: HD 126660 Visibilities B ψ MJD (m) (◦ ) V σV 54244.833 254.0 −31.9 0.572 0.030 54244.847 248.1 −28.6 0.561 0.029 54244.860 242.0 −25.5 0.623 0.030 54244.873 235.6 −22.6 0.598 0.045 54244.884 229.6 −20.1 0.677 0.044 54297.681 324.3 7.3 0.423 0.040 54297.711 324.7 90.0 0.396 0.026 54297.721 324.7 177.5 0.377 0.027 54297.747 324.2 172.1 0.415 0.019 54297.771 323.7 169.4 0.404 0.024 54297.795 323.1 166.8 0.397 0.022 54672.774 320.0 158.7 0.411 0.042 54672.781 319.2 157.1 0.444 0.053 54672.788 318.2 155.6 0.409 0.051 54672.795 317.2 154.0 0.422 0.053

312 Figure C.55: Diameter fit for HD 126660

313 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.56: Y2 Model Isochrones for HD 126660: HD 126660 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.14).

314 C.29 HD 128167 Table C.29: HD 128167 Visibilities B ψ MJD (m) (◦ ) V σV 54645.762 324.3 0.8 0.602 0.068 54645.767 324.3 179.4 0.610 0.068 54645.774 324.4 177.9 0.558 0.069 54645.780 324.5 176.3 0.676 0.075 54645.787 324.7 174.7 0.632 0.079 54653.703 325.4 9.5 0.575 0.109 54653.710 325.1 8.0 0.541 0.062 54653.717 324.8 6.3 0.596 0.080 54653.723 324.6 4.8 0.602 0.080 54653.730 324.5 3.2 0.634 0.073 54653.736 324.4 1.7 0.673 0.100 54653.743 324.3 90.2 0.644 0.104 54653.756 324.4 176.8 0.638 0.059 54653.762 324.6 175.5 0.630 0.053 54653.768 324.8 174.1 0.659 0.078 54653.774 325.0 172.6 0.633 0.076 54653.780 325.3 171.1 0.584 0.052 54671.674 276.3 177.9 0.710 0.072 54671.680 276.4 176.4 0.698 0.100 54671.686 276.5 175.1 0.633 0.128 54671.693 276.6 173.8 0.851 0.137 54671.706 276.9 171.0 0.709 0.120 54671.713 277.1 169.3 0.814 0.127 54671.720 277.3 167.8 0.659 0.081 54671.737 277.9 164.4 0.586 0.124 54671.749 278.3 161.9 0.677 0.151

315 Figure C.57: Diameter fit for HD 128167

316 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.58: Y2 Model Isochrones for HD 128167: HD 128167 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.36).

317 C.30 HD 131156 Table C.30: HD 131156 Visibilities B ψ MJD (m) (◦ ) V σV 54171.968 320.6 65.8 0.406 0.044 54171.983 317.6 68.8 0.425 0.044 54171.997 315.0 71.7 0.392 0.035 54172.011 312.5 74.9 0.417 0.040 54172.024 310.4 78.1 0.428 0.036 54574.861 267.1 141.9 0.466 0.051 54574.874 270.7 139.4 0.414 0.059 54574.914 277.8 133.1 0.417 0.023 54574.925 278.4 131.7 0.347 0.027 54574.943 278.0 129.6 0.466 0.021 54574.874 270.7 139.4 0.453 0.050 54574.914 277.8 133.1 0.499 0.029 54574.925 278.4 131.7 0.443 0.033 54574.943 278.0 129.6 0.472 0.024 54575.779 242.6 161.7 0.599 0.072 54575.792 246.2 157.9 0.538 0.059 54575.802 249.1 155.1 0.525 0.060 54575.817 254.0 151.2 0.531 0.083 54575.826 256.9 149.0 0.496 0.069 54575.842 262.0 145.4 0.503 0.050 54575.806 250.5 153.9 0.564 0.063 54644.751 308.1 7.2 0.521 0.078 54644.757 307.6 5.6 0.519 0.055 54644.764 307.2 4.0 0.465 0.055 54644.769 307.0 2.5 0.388 0.057 54644.775 306.9 1.1 0.445 0.044 54644.782 306.9 179.4 0.403 0.049 54644.796 307.3 175.8 0.408 0.041 54644.803 307.7 174.1 0.374 0.055 54644.810 308.4 172.2 0.350 0.050

318 Figure C.59: Diameter fit for HD 131156

319 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.60: Y2 Model Isochrones for HD 131156: HD 131156 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.33).

320 C.31 HD 141795 Table C.31: HD 141795 Visibilities B ψ MJD (m) (◦ ) V σV 54669.677 282.0 20.6 0.750 0.094 54669.684 279.1 18.8 0.753 0.097 54669.692 276.4 16.8 0.795 0.119 54669.701 273.8 14.7 0.701 0.081 54669.713 270.5 11.2 0.786 0.094 54669.722 268.7 8.9 0.752 0.079 54669.729 267.4 6.7 0.762 0.083 54669.738 266.4 4.2 0.768 0.083

321 Figure C.61: Diameter fit for HD 141795

322 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.62: Y2 Model Isochrones for HD 141795: HD 141795 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.0).

323 C.32 HD 142860 Table C.32: HD 142860 Visibilities B ψ MJD (m) (◦ ) V σV 54301.760 298.9 89.4 0.379 0.036 54301.770 299.0 −87.9 0.396 0.034 54301.781 299.7 −84.9 0.349 0.042 54302.690 307.7 72.4 0.344 0.044 54302.696 306.3 73.9 0.353 0.030 54302.711 303.3 77.5 0.390 0.029 54302.718 302.2 79.3 0.381 0.026 54302.725 301.2 81.0 0.385 0.035 54302.734 300.2 83.3 0.385 0.041 54577.781 226.5 173.2 0.617 0.089 54577.789 227.6 170.5 0.575 0.120 54577.798 229.1 167.8 0.611 0.099 54577.805 230.7 165.3 0.603 0.057 54577.814 233.0 162.5 0.577 0.067 54577.822 235.3 160.1 0.570 0.066 54577.834 239.3 156.5 0.571 0.084 54577.842 242.1 154.2 0.590 0.065 54577.850 245.3 151.9 0.533 0.072 54577.859 248.6 149.7 0.562 0.084

324 Figure C.63: Diameter fit for HD 142860

325 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.64: Y2 Model Isochrones for HD 142860: HD 142860 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.19).

326 C.33 HD 146233 Table C.33: HD 146233 Visibilities B ψ MJD (m) (◦ ) V σV 54578.901 267.1 236.9 0.819 0.069 54578.923 252.2 241.1 0.786 0.085 54577.877 195.8 132.0 0.849 0.076 54577.903 216.5 136.6 0.823 0.107 54578.829 309.5 229.5 0.733 0.069 54578.837 305.9 229.9 0.715 0.075 54578.890 274.4 235.2 0.720 0.052 54578.912 259.7 238.8 0.815 0.059 54579.828 308.8 229.5 0.660 0.105 54579.856 293.6 231.6 0.748 0.099 54579.881 278.0 234.4 0.827 0.088 54577.891 206.7 134.6 0.823 0.086 54577.950 249.5 141.2 0.687 0.107 54575.877 190.8 130.6 0.837 0.064 54575.926 230.0 138.8 0.787 0.041 54575.954 248.8 141.1 0.790 0.033 54575.980 262.7 142.2 0.753 0.068 54575.863 179.3 126.9 0.894 0.066 54575.889 200.6 133.2 0.811 0.042 54575.914 221.0 137.4 0.802 0.047 54575.941 240.7 140.2 0.833 0.047 54575.966 255.7 141.7 0.833 0.059 54575.996 269.4 142.4 0.779 0.080 54602.945 196.3 187.6 0.741 0.076 54602.961 180.4 187.5 0.855 0.094

327 Figure C.65: Diameter fit for HD 146233

328 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.66: Y2 Model Isochrones for HD 146233: HD 146233 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.02).

329 C.34 HD 162003 Table C.34: HD 162003 Visibilities B ψ MJD (m) (◦ ) V σV 54300.844 282.9 179.4 0.586 0.044 54300.854 282.8 176.6 0.687 0.055 54383.728 312.9 265.8 0.637 0.080 54383.742 312.9 90.9 0.734 0.064 54383.751 312.9 94.1 0.592 0.056 54383.763 312.9 98.3 0.591 0.087 54383.775 313.0 102.2 0.763 0.070 54383.786 313.1 106.4 0.641 0.074 54421.599 276.3 115.0 0.590 0.083 54421.609 274.8 117.8 0.602 0.099 54421.622 272.5 121.3 0.659 0.072 54421.632 270.5 124.1 0.663 0.090 54643.850 281.0 256.2 0.713 0.080 54643.859 281.6 258.5 0.780 0.072 54643.867 282.0 260.7 0.727 0.067 54643.874 282.4 262.8 0.675 0.096 54643.843 280.3 254.3 0.528 0.081

330 Figure C.67: Diameter fit for HD 162003

331 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.68: Y2 Model Isochrones for HD 162003: HD 162003 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.17).

332 C.35 HD 164259 Table C.35: HD 164259 Visibilities B ψ MJD (m) (◦ ) V σV 54579.938 298.0 233.9 0.693 0.118 54578.954 290.6 235.7 0.636 0.062 54578.979 276.8 239.5 0.766 0.084 54578.940 298.4 233.8 0.847 0.134 54578.954 290.6 235.7 0.841 0.093 54578.965 284.4 237.3 0.890 0.102 54578.990 270.3 241.6 0.765 0.102 54578.997 266.4 243.1 0.806 0.085 54645.714 317.9 230.2 0.691 0.101 54645.721 315.2 230.6 0.625 0.078 54645.728 312.3 231.1 0.664 0.112 54645.735 309.5 231.6 0.663 0.135 54645.744 305.3 232.4 0.617 0.124 54673.681 202.7 127.5 0.789 0.102 54673.689 208.6 129.4 0.826 0.075 54673.697 214.5 131.1 0.849 0.092 54673.705 220.2 132.6 0.833 0.120 54673.713 226.1 134.0 0.935 0.116 54673.722 232.5 135.4 0.782 0.064

333 Figure C.69: Diameter fit for HD 164259

334 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.70: Y2 Model Isochrones for HD 164259: HD 164259 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.14).

335 C.36 HD 173667 Table C.36: HD 173667 Visibilities B ψ MJD (m) (◦ ) V σV 54301.827 313.8 193.1 0.537 0.032 54301.838 312.5 190.7 0.482 0.026 54301.848 311.4 188.1 0.507 0.033 54302.755 325.4 207.5 0.467 0.047 54302.765 323.9 205.8 0.486 0.052 54302.773 322.5 204.2 0.506 0.059 54302.781 321.1 202.7 0.521 0.030 54302.789 319.7 201.1 0.433 0.029 54302.796 318.3 199.4 0.458 0.034 54302.805 316.8 197.6 0.484 0.035 54302.813 315.5 195.6 0.494 0.040 54302.821 314.3 193.8 0.506 0.031 54577.971 255.6 117.8 0.606 0.115 54577.987 260.5 121.8 0.566 0.170 54577.998 263.8 124.3 0.697 0.312 54645.817 325.4 242.5 0.556 0.102 54645.827 323.8 244.2 0.684 0.130 54645.836 322.2 246.1 0.550 0.081 54645.848 320.1 248.4 0.519 0.043 54645.857 318.4 250.5 0.493 0.098 54645.881 314.5 255.8 0.512 0.058 54645.891 313.1 258.2 0.595 0.093 54645.905 311.5 261.5 0.576 0.093 54654.777 260.5 121.8 0.490 0.043 54668.833 278.5 138.6 0.569 0.059 54670.718 302.6 189.8 0.648 0.042 54670.730 307.6 191.1 0.610 0.063 54670.740 310.7 192.3 0.561 0.061 54670.759 313.4 194.7 0.505 0.028 54670.769 313.4 195.9 0.522 0.038 54670.776 312.7 196.8 0.532 0.044 54669.807 315.9 253.8 0.472 0.062 54669.821 313.7 257.1 0.563 0.098 54669.833 312.2 260.0 0.655 0.102 54669.852 310.5 264.6 0.492 0.072 54669.864 310.0 267.6 0.494 0.065 54669.875 309.9 90.4 0.565 0.081

336 Figure C.71: Diameter fit for HD 173667

337 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.72: Y2 Model Isochrones for HD 173667: HD 173667 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.15).

338 C.37 HD 177724 Table C.37: HD 177724 Visibilities B ψ MJD (m) (◦ ) V σV 54645.803 324.3 32.7 0.534 0.092 54645.810 322.8 31.6 0.606 0.132 54645.823 319.6 29.6 0.557 0.084 54645.833 317.1 27.9 0.499 0.066 54645.844 314.1 25.9 0.529 0.055 54645.854 311.3 23.9 0.595 0.074 54645.871 306.6 20.2 0.551 0.077 54645.877 305.0 18.9 0.519 0.081 54645.887 302.7 16.6 0.557 0.075 54645.901 299.6 13.3 0.551 0.078 54654.772 242.2 151.1 0.753 0.066 54654.784 247.0 148.1 0.756 0.060 54654.790 249.5 146.7 0.748 0.056 54654.797 252.4 145.1 0.757 0.059 54654.803 254.9 143.8 0.687 0.077 54668.827 274.9 133.4 0.689 0.080 54668.845 277.6 131.4 0.629 0.102 54668.857 278.4 130.2 0.588 0.047 54668.864 278.5 129.6 0.719 0.072 54670.713 294.3 79.7 0.602 0.056 54670.726 301.6 78.9 0.633 0.071 54670.736 306.5 78.2 0.718 0.052 54670.756 312.1 76.7 0.656 0.035 54670.766 313.3 75.9 0.639 0.044 54670.780 313.1 74.6 0.628 0.051 54669.801 307.8 21.2 0.587 0.079 54669.817 303.7 17.7 0.619 0.105 54669.829 301.1 15.0 0.670 0.089 54669.848 297.5 10.3 0.638 0.088 54669.859 295.9 7.3 0.631 0.067 54669.871 294.9 4.3 0.457 0.053

339 Figure C.73: Diameter fit for HD 177724

340 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.74: Y2 Model Isochrones for HD 177724: HD 177724 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.68).

341 C.38 HD 182572 Table C.38: HD 182572 Visibilities B ψ MJD (m) (◦ ) V σV 54302.840 298.0 73.4 0.613 0.042 54302.847 296.3 75.0 0.678 0.052 54302.854 294.8 76.7 0.742 0.061 54302.862 293.2 78.7 0.756 0.065 54302.869 292.0 80.5 0.703 0.063 54302.875 291.0 82.2 0.719 0.047 54352.663 309.8 25.5 0.644 0.054 54352.670 307.7 24.2 0.654 0.093 54352.677 305.6 22.8 0.727 0.095 54352.684 303.6 21.3 0.615 0.087 54352.690 301.8 19.9 0.598 0.066 54352.697 300.0 18.4 0.596 0.068 54352.706 297.6 16.3 0.627 0.073 54352.712 296.1 14.8 0.646 0.060 54352.719 294.7 13.2 0.653 0.060 54352.726 293.2 11.3 0.737 0.068 54669.763 319.4 31.2 0.771 0.154 54669.769 317.5 30.1 0.586 0.080 54669.776 315.7 29.1 0.747 0.141 54669.782 313.8 27.9 0.657 0.090 54669.789 311.8 26.7 0.701 0.119 54671.787 260.2 17.9 0.602 0.081 54671.793 259.0 16.6 0.448 0.062 54671.800 257.8 15.2 0.536 0.066 54671.807 256.6 13.6 0.717 0.110 54671.814 255.6 12.2 0.630 0.093 54739.637 300.1 18.6 0.782 0.067 54739.644 298.3 16.9 0.789 0.072 54739.655 296.4 9.5 0.710 0.068 54739.671 294.5 5.3 0.762 0.101 54739.680 291.1 7.9 0.775 0.122 54739.686 290.3 6.3 0.685 0.108 54739.693 289.7 4.4 0.724 0.099 54739.700 289.3 2.5 0.846 0.080 54739.707 289.1 0.7 0.846 0.098

342 Figure C.75: Diameter fit for HD 182572

343 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.76: Y2 Model Isochrones for HD 182572: HD 182572 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.33).

344 C.39 HD 185144 Results on this star have been published in Boyajian et al. (2008). To re-iterate the important information, we give the calibrated visibilities and Diameter fit below. Table C.39: HD 185144 Visibilities B ψ MJD (m) (◦ ) V σV 54244.974 252.1 134.9 0.532 0.097 54244.984 250.1 131.7 0.575 0.051 54244.997 247.3 127.8 0.528 0.044 54245.971 252.0 134.7 0.522 0.050 54245.984 249.6 131.0 0.550 0.051 54245.995 247.2 127.7 0.520 0.053 54246.007 244.6 124.3 0.564 0.059 54279.838 303.2 268.9 0.380 0.016 54280.715 275.4 131.8 0.492 0.036 54280.860 307.1 260.5 0.346 0.034 54280.872 308.6 256.6 0.293 0.022 54280.884 309.9 252.5 0.307 0.020 54281.725 278.4 127.1 0.394 0.034 54282.675 267.4 145.5 0.472 0.056 54282.687 270.1 140.5 0.434 0.048

345 Figure C.77: Diameter fit for HD 185144

346 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.78: Y2 Model Isochrones for HD 185144: HD 185144 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.24).

347 C.40 HD 185395 Table C.40: HD 185395 Visibilities B ψ MJD (m) (◦ ) V σV 54246.951 268.1 198.5 0.779 0.062 54301.708 290.5 226.4 0.738 0.047 54301.720 295.6 224.1 0.579 0.045 54301.736 301.7 221.0 0.563 0.067 54301.748 305.8 218.6 0.668 0.098 54301.760 309.3 216.2 0.609 0.070 54301.772 312.6 213.5 0.588 0.050 54301.784 315.2 211.0 0.598 0.059 54301.801 318.3 207.4 0.637 0.063 54301.811 319.8 205.2 0.720 0.077 54301.825 321.7 201.9 0.696 0.082 54301.836 322.8 199.5 0.667 0.050 54406.670 233.7 233.2 0.734 0.078 54406.677 232.1 235.8 0.737 0.079 54406.686 230.1 239.2 0.712 0.085 54406.693 228.6 241.7 0.737 0.091 54406.700 227.3 244.4 0.754 0.080 54672.812 322.3 249.2 0.612 0.051 54672.819 323.0 250.7 0.625 0.056 54672.826 323.6 252.3 0.646 0.044 54672.833 324.1 254.0 0.560 0.061 54672.840 324.6 255.6 0.550 0.053 54672.846 325.0 257.2 0.582 0.048 54672.853 325.3 258.7 0.535 0.053 54672.860 325.6 260.3 0.528 0.069

348 Figure C.79: Diameter fit for HD 185395

349 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.80: Y2 Model Isochrones for HD 185395: HD 185395 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.04).

350 C.41 HD 210418 Table C.41: HD 210418 Visibilities B ψ MJD (m) (◦ ) V σV 54645.929 316.1 34.1 0.704 0.096 54645.938 312.8 32.9 0.723 0.159 54645.954 306.7 30.4 0.599 0.129 54645.966 301.9 28.3 0.824 0.130 54645.975 298.6 26.8 0.648 0.099 54645.983 295.2 25.1 0.591 0.066 54669.935 288.2 21.2 0.634 0.077 54669.948 283.8 18.2 0.611 0.094 54669.955 281.5 16.5 0.706 0.126 54669.962 279.6 14.8 0.650 0.125 54669.968 277.8 13.1 0.662 0.123 54669.979 275.4 10.3 0.717 0.071 54669.985 274.2 8.6 0.644 0.080 54669.991 273.2 6.8 0.647 0.090 54669.997 272.5 5.0 0.724 0.096 54671.846 264.6 28.6 0.677 0.094 54671.856 262.0 27.2 0.729 0.094 54671.865 259.5 25.7 0.688 0.105 54671.877 256.1 23.6 0.817 0.120 54740.683 311.0 32.2 0.674 0.075 54740.691 307.9 30.9 0.703 0.095

351 Figure C.81: Diameter fit for HD 210418

352 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.82: Y2 Model Isochrones for HD 210418: HD 210418 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.38).

353 C.42 HD 213558 Table C.42: HD 213558 Visibilities B ψ MJD (m) (◦ ) V σV 54351.681 285.8 48.2 0.900 0.090 54351.717 301.3 41.2 0.833 0.066 54351.723 303.6 39.9 0.851 0.081 54351.731 306.0 38.4 0.807 0.104 54351.749 311.1 34.7 0.922 0.089 54383.812 304.4 46.3 0.826 0.052 54383.819 302.8 44.0 0.859 0.077 54383.825 301.4 41.9 0.771 0.079 54383.834 299.4 39.2 0.781 0.091 54383.840 297.9 37.1 0.786 0.084 54383.850 295.6 33.6 0.866 0.096 54383.856 294.2 31.6 0.835 0.070 54383.862 292.8 29.4 0.864 0.066 54383.879 289.2 23.2 0.742 0.092 54383.886 288.0 20.8 0.746 0.073 54383.872 290.6 25.7 0.841 0.086 54458.614 326.3 178.7 0.835 0.146 54458.625 326.2 175.9 0.722 0.096 54458.636 326.0 173.3 0.837 0.122 54458.648 325.6 170.5 0.837 0.079 54458.659 325.1 167.8 0.748 0.074 54458.672 324.3 164.8 0.823 0.086 54668.972 324.6 14.3 0.666 0.067 54668.979 325.0 12.7 0.626 0.078 54668.986 325.3 11.1 0.652 0.064 54668.993 325.6 9.5 0.712 0.066 54668.999 325.8 7.9 0.634 0.074

354 Figure C.83: Diameter fit for HD 213558

355 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.84: Y2 Model Isochrones for HD 213558: HD 213558 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=0.0).

356 C.43 HD 215648 Table C.43: HD 215648 Visibilities B ψ MJD (m) (◦ ) V σV 54298.116 326.3 228.4 0.414 0.028 54298.140 328.5 228.8 0.322 0.027 54298.166 330.0 229.5 0.329 0.029 54298.192 330.6 230.4 0.340 0.038 54302.910 318.8 210.6 0.442 0.025 54302.919 316.3 209.1 0.446 0.028 54302.925 314.4 208.0 0.435 0.027 54302.932 312.3 206.8 0.465 0.027 54302.944 308.7 204.5 0.461 0.020 54302.953 306.1 202.7 0.475 0.024 54302.961 303.6 200.9 0.479 0.034 54302.969 301.4 199.1 0.500 0.028 54302.978 299.0 197.1 0.541 0.030 54302.984 297.5 195.6 0.510 0.047 54302.991 296.0 194.0 0.569 0.049 54302.997 294.6 192.4 0.532 0.068 54303.004 293.3 190.6 0.523 0.055 54303.011 292.3 189.0 0.455 0.041 54671.891 267.7 245.4 0.597 0.097 54671.897 266.3 246.5 0.536 0.067 54671.903 265.1 247.6 0.538 0.071 54671.910 263.9 248.7 0.603 0.090 54671.916 262.7 249.9 0.510 0.051 54740.748 308.2 245.8 0.506 0.064 54740.773 300.8 251.4 0.402 0.055 54740.791 296.4 255.6 0.472 0.043 54740.801 294.2 258.1 0.521 0.045 54740.817 291.7 262.1 0.467 0.056 54740.699 322.2 237.4 0.411 0.050 54740.707 320.2 238.6 0.404 0.053 54740.714 318.2 239.7 0.431 0.049 54739.840 289.9 267.5 0.573 0.059 54739.849 289.7 180.0 0.519 0.054 54739.857 289.9 92.1 0.484 0.048

357 Figure C.85: Diameter fit for HD 215648

358 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.86: Y2 Model Isochrones for HD 215648: HD 215648 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.24).

359 C.44 HD 222368 Table C.44: HD 222368 Visibilities B ψ MJD (m) (◦ ) V σV 54076.624 285.5 200.6 0.518 0.078 54076.635 281.5 197.8 0.446 0.065 54076.646 278.1 195.1 0.467 0.074 54076.658 275.0 192.0 0.678 0.095 54301.904 323.7 217.3 0.437 0.030 54301.914 320.9 216.3 0.454 0.030 54301.927 316.7 214.8 0.478 0.035 54301.942 311.5 212.8 0.447 0.023 54301.956 306.0 210.7 0.489 0.025 54301.971 300.0 208.1 0.496 0.028 54301.978 297.0 206.7 0.494 0.027 54301.986 293.6 205.1 0.488 0.035 54301.994 290.6 203.6 0.509 0.032 54302.001 287.9 202.0 0.557 0.042 54302.007 285.6 200.6 0.602 0.051 54352.768 323.0 233.0 0.355 0.053 54352.775 321.3 233.6 0.351 0.053 54352.781 319.4 234.3 0.429 0.050 54352.787 317.4 235.0 0.480 0.094 54352.793 315.2 235.8 0.495 0.067 54739.753 308.0 238.5 0.389 0.054 54739.763 304.1 240.1 0.429 0.073 54739.771 300.9 241.5 0.414 0.068 54739.778 298.0 242.8 0.417 0.037 54739.788 294.0 244.7 0.454 0.066 54739.795 291.2 246.1 0.457 0.084 54739.803 287.9 248.0 0.614 0.104 54739.726 317.8 234.8 0.452 0.048 54739.734 315.3 235.8 0.459 0.080 54739.741 312.9 236.7 0.390 0.056 54740.727 316.7 235.3 0.453 0.040 54740.740 312.2 236.9 0.467 0.066 54740.752 307.6 238.7 0.561 0.069 54740.781 295.8 243.8 0.548 0.059 54740.794 290.2 246.6 0.459 0.056 54740.805 286.2 249.0 0.452 0.058

360 Figure C.87: Diameter fit for HD 222368

361 1.5 1.5 1.0 1.0 Log L (Lsol) Log L (Lsol) 0.5 0.5 0.0 0.0 -0.5 -0.5 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) 0.6 0.6 0.4 0.4 Log R (Rsol) Log R (Rsol) 0.2 0.2 0.0 0.0 -0.2 -0.2 4.00 3.95 3.90 3.85 3.80 3.75 3.70 0.0 0.2 0.4 0.6 0.8 Log Teff (K) COLOR INDEX (B-V) Figure C.88: Y2 Model Isochrones for HD 222368: HD 222368 data (and 1-σ errors) plotted against Y2 models isochrones ([α/Fe]=0.0, [Fe/H]=−0.08).

362 –D– Appendix D: Published Work in the Field of Stellar Interferometry This appendix includes published work in the general topic of stellar interferometry with the CHARA Array.

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377 –E– Appendix E: Published Work in the Field of Optical Spectroscopy This appendix includes published work in the general topic of optical spectroscopy of early-type stars.

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400 Publications of the Astronomical Society of the Pacific, 119: 742–746, 2007 July ᭧ 2007. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A. Radial Velocities of Six OB Stars T. S. Boyajian,1 D. R. Gies,1 E. K. Baines, P. Barai,2 E. D. Grundstrom,1 M. V. McSwain,1,3,4 J. R. Parks, R. L. Riddle,1,5 W. T. Ryle, and D. W. Wingert1 Center for High Angular Resolution Astronomy, and Department of Physics and Astronomy, Georgia State University, Atlanta, GA; tabetha@chara.gsu.edu, gies@chara.gsu.edu, baines@chara.gsu.edu, pabar56@phy.ulaval.ca, erika@chara.gsu.edu, mcswain@astro.yale.edu, parksj@physics.emory.edu, riddle@astro.caltech.edu, ryle@chara.gsu.edu, wingert@chara.gsu.edu Received 2007 May 21; accepted 2007 June 7; published 2007 July 24 ABSTRACT. We present new results from a radial velocity study of six bright OB stars with little or no prior measurements. One of these, HD 45314, may be a long-period binary, but the velocity variations of this Be star may be related to changes in its circumstellar disk. Significant velocity variations were also found for HD 60848 (possibly related to nonradial pulsations) and HD 61827 (related to wind variations). The other three targets, HD 46150, HD 54879, and HD 206183, are constant-velocity objects, but we note that HD 54879 has Ha emission that may originate from a binary companion. We illustrate the average red spectrum of each target. Online material: extended table 1. INTRODUCTION 2. OBSERVATIONS AND RADIAL VELOCITIES Radial velocity measurements exist for many of the bright Red spectra were collected with the KPNO 0.9 m coude feed´ OB stars because of their usefulness for binary mass deter- telescope during two observing runs in 2000 October and De- mination and cluster dynamics. However, of the 227 stars listed cember. The spectra were made using the long collimator, grat- by Mason et al. (1998) in a survey of the multiplicity of bright ing B (in second order, with order-sorting filter OG 550), cam- O stars, 17 lacked sufficient radial velocity data to determine era 5, and the F3KB CCD, a Ford Aerospace 3072 # 1024 whether or not they were members of spectroscopic binaries. device. The setup yielded a resolving power of R p l/dl ≈ We observed six of these targets with unknown spectroscopic ˚ 9500, with a spectral coverage of 6440–7105 A. The exposure duplicity in two extended observing runs of high dispersion times were less than 30 minutes, yielding a S/N ≈ 200 pixelϪ1. and high signal-to-noise ratio (S/N) spectroscopy at the Kitt We obtained between 22 and 62 spectra of each star. Peak National Observatory (KPNO) coude feed telescope in ´ The spectra were extracted and calibrated using standard 2000. We have already reported on discoveries made during routines in IRAF,6 and then each continuum-rectified spectrum these runs, of new single-lined spectroscopic binaries (HD was transformed onto a uniform heliocentric wavelength grid 14633, HD 15137; Boyajian et al. 2005) and double-lined spec- for analysis. We removed atmospheric lines by creating a li- troscopic binaries (HD 37366, HD 54662; Boyajian et al. 2007). brary of spectra from each run of the rapidly rotating A star Here we present our results on the six stars with mainly “un- z Aql, removing the broad stellar features from these, and then known” spectroscopic binary status from the list of Mason et dividing each target spectrum by the modified atmospheric al. (1998). We describe the observations, measurements, and spectrum that most closely matched the target spectrum in a analysis in § 2 and then discuss the individual targets in detail selected region dominated by atmospheric absorptions. in § 3. Our results are summarized in Table 2 of § 2. We measured radial velocities in two ways. For targets with absorption lines, we formed a cross-correlation function (CCF) between a given spectrum and a single reference spectrum of 1 the star (usually the first observation). These relative velocities Visiting Astronomer, Kitt Peak National Observatory, National Optical were then transformed to an absolute velocity scale by adding Astronomy Observatory, operated by the Association of Universities for Re- search in Astronomy, Inc., under contract with the National Science a mean velocity measured by parabolic fits to the lower halves Foundation. of the absorption lines in the reference spectrum. Two of the 2 Current address: Departement de Physique, de Genie Physique et d’Op- targets have spectra dominated by emission lines, and in these tique, Universite Laval, Quebec, QC, Canada. ´ ´ cases we measured bisector velocities for the extreme line 3 Current address: Astronomy Department, Yale University, New Haven, CT. 4 NSF Astronomy and Astrophysics Postdoctoral Fellow. 6 IRAF is distributed by the National Optical Astronomy Observatory, which 5 Current address: Thirty Meter Telescope, Pasadena, CA. is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. 742

401 RADIAL VELOCITIES OF SIX OB STARS 743 TABLE 1 Radial Velocity Measurements Date Vr j Star Name (HJD Ϫ2,450,000) (km sϪ1) (km sϪ1) HD 45314 ...... 1817.942 Ϫ31.3 … HD 45314 ...... 1818.945 Ϫ32.2 … HD 45314 ...... 1819.936 Ϫ31.2 … HD 45314 ...... 1820.931 Ϫ32.0 … HD 45314 ...... 1821.931 Ϫ32.2 … HD 45314 ...... 1822.926 Ϫ31.9 … HD 45314 ...... 1823.866 Ϫ32.0 … HD 45314 ...... 1823.987 Ϫ32.5 … HD 45314 ...... 1824.888 Ϫ31.4 … HD 45314 ...... 1825.004 Ϫ30.6 … HD 45314 ...... 1830.956 Ϫ34.2 … Note.—Table 1 is published in its entirety in the electronic edition of the PASP. A portion is shown here for guidance re- garding its form and content. Fig. 1.—Mean red spectrum of HD 45314 in the rest frame. Line identi- wings, using the method of Shafter et al. (1986). All these fications are marked by vertical lines. velocities are shown in Table 1, which lists the star name, Heliocentric Julian Date of midexposure, radial velocity, and 3. NOTES ON INDIVIDUAL STARS the line-to-line standard deviation j (where multiple lines were measured). In § 3, we give a more detailed description of the 3.1. HD 45314 radial velocity analysis performed on the individual stars. The star HD 45314 (O9 pe, Conti 1974; B0 IVe, Negueruela We checked for evidence of temporal variations in the ve- et al. 2004) has a speckle interferometric companion at a sep- locity data by comparing the external scatter between obser- aration of 50 mas (corresponding to a period of ≈30 yr; Mason vations E (equal to the standard deviation of the individual et al. 1998). The average red spectrum illustrated in Figure 1 velocities in Table 1) with an estimate of the internal error I. shows that Ha and He i ll6678, 7065 are double-peaked emis- The internal error is the average of the line-to-line standard sion lines. This suggests that the emission forms in a disk and deviation j for all but the cases of HD 45314 and HD 60848, that the line wings form in the gas closest to the star. Thus, where only one spectral feature was measured. For these two we can use measurements of the Ha wings as a proxy for the cases, we estimated I by the average of FVi Ϫ Viϩ1F/ͱ2 for ob- motion of the underlying star. We measured radial velocities servations closely spaced in time. We then computed the F- using the wing bisector method of Shafter et al. (1986). statistic to determine the probability that the observed scatter Our results indicate that there was a significant change in is due to random noise (Conti et al. 1977a). We assume that velocity from Ϫ32.0 ‫ 9.0 ע‬to Ϫ21.6 ‫ 9.1 ע‬km sϪ1 between the variations are significant if this probability is below 1% the runs. This may indicate that the Be star is a spectroscopic (Conti et al. 1977a). The results are summarized in Table 2, binary with a period of months. However, the emission profiles which lists the star name, number of observations, the mean changed in shape between the runs (see Fig. 2 for the Ha velocity, E and I, the derived probability, and a short description averages from each run), so it is also possible that the changes of the probable source of the variations if present. Details for in bisector velocity result from physical changes in the gas each target follow in the next section. distribution in the disk rather than orbital motion. We rec- TABLE 2 Radial Velocity Summary AVrS E I Prob. Star Name N (km sϪ1) (km sϪ1) (km sϪ1) (%) Status HD 45314 . . . . . . . 33 Ϫ25.1 5.2 0.4 0 Long-period SB or disk variation HD 46150 . . . . . . . 30 33.8 3.8 1.3 0.6 Constant HD 54879 . . . . . . . 26 35.4 1.4 0.6 3.1 Constant HD 60848 . . . . . . . 62 5.5 3.2 1.0 0.3 Short-period variation HD 61827 . . . . . . . 25 70.2 5.4 0.5 0 Wind-related variation HD 206183 . . . . . . 22 Ϫ7.8 1.4 0.6 3.4 Constant 2007 PASP, 119:742–746

402 744 BOYAJIAN ET AL. Fig. 3.—Mean spectrum of HD 46150. Fig. 2.—HD 45314 mean Ha line profiles observed during the first (solid line) and second (dotted line) observing runs. line scatter in j for the first run). Thus, the velocity variations ommend a program of blue spectroscopy of this star to distin- are probably not significant and are consistent with constant guish between the binary and disk variation explanations. radial velocity over the interval of our observations. 3.2. HD 46150 3.3. HD 54879 The spectroscopic binary status of HD 46150 (O5 V((f)); The target HD 54879 (B3 V, Neubauer 1943; O9.5 V, Morgan Underhill & Gilroy 1990) remains inconclusive, even though et al. 1955; B0 V, Claria 1974) has only a few spectroscopic it has a history of radial velocity measurements spanning eight measurements over the past century. The mean spectrum shown decades (Plaskett 1924; Abt 1970; Conti et al. 1977b; Garmany in Figure 4 indicates that it has Ha emission and is thus a Be et al. 1980; Liu et al. 1989, 1991; Underhill & Gilroy 1990; star, which has historically never been observed in emission Fullerton 1990; Stickland & Lloyd 2001). The measured radial until now. We made CCF velocity measurements using the lines velocities fall in the range of Vr p 14 –51 km sϪ1. Stickland & He i ll6678, 7065, C ii ll6578, 6583, and Si iv ll6667, Lloyd (2001) suggest that this range is significantly larger than 6701. expected for diverse measurements of a single star. The most Our Vr measurements show no evidence of Doppler shifts in extensive analysis of this star by Garmany et al. (1980) covered the absorption lines over both short and long timescales. The four observing seasons, with a mean of Vr p 39 km sϪ1 and a external error E p 1.4 km sϪ1 is somewhat larger than the range of 26 km sϪ1. They conclude that the scatter results from atmospheric rather than orbital variations (see also Underhill & Gilroy 1990). The mean red spectrum in Figure 3 shows a strong He ii spectrum associated with a very early type star. We measured CCF velocities of the Ha, He i ll6678, 7065, and He ii ll6683, 6890 features. The error in the mean velocity from closely spaced pairs is I p 1.3 km sϪ1, while the standard deviation among the mean velocities is E p 3.8 km sϪ1. A standard F-test (Conti et al. 1977a) indicates that a temporal variation this large is expected from random variations with a probability of 0.6%; i.e., the observed variation is probably significant. However, most of the variance comes from the first run, in which there appear to be relatively large night-to-night variations that are absent in the second run. This may indicate that the observational errors were larger in the first run com- pared to our estimate of I from the scatter in measurements from the second run (also consistent with the larger line-to- Fig. 4.—Mean spectrum of HD 54879. 2007 PASP, 119:742–746

403 RADIAL VELOCITIES OF SIX OB STARS 745 Fig. 5.—Mean spectrum of HD 60848. ˚ Fig. 6.—Mean spectrum of HD 61827. Features in the 6830–6870 A region are incompletely removed atmospheric lines. internal error I p 0.6 km sϪ1. The F-test indicates that a scatter between observations of this size is expected with a probability ond run, but with a higher sampling rate (as frequent as of 3.1%, so this star is radial velocity constant over the duration 15 minute intervals during some nights). The mean red spec- of the runs. The only other radial velocity measurement on trum (Fig. 5) shows that Ha and He i ll6678,7065 all display record, Vr p 15.6 ‫ 4.1 ע‬km sϪ1, from Neubauer (1943), is double-peaked emission. smaller than our mean of Vr p 35.4 ‫ 4.1 ע‬km sϪ1. We caution We measured relative radial velocities by determining CCF that this discrepancy may be caused by measuring different offsets from the first spectrum for the He i l6678 region, and lines in the blue part of the spectrum, or by long-term changes these were then placed on an absolute scale by finding the in the spectrum. bisector velocity of the profile in the first spectrum, using the The mean spectrum has very narrow lines of He i, C ii, method from Shafter et al. (1986). The external error of N ii, O ii, and Si iv. These apparently sharp absorption lines E p 3.2 km sϪ1 is larger than the internal error of I p 1.0 km are unexpected in Be stars that are normally rapid rotators with sϪ1, and the F-test indicates that this scatter has a probability broad lines. One possibility is that HD 54879 is a rare Be star of 0.3% for an origin in random variations. Furthermore, there that is seen almost pole-on, so that the rotation is tangential to is clear evidence of systematic trends within some nights. We the line of sight and the lines do not suffer rotational broad- used the CLEAN algorithm from Roberts et al. (1987) to find ening. Another possibility is that HD 54879 is a Be shell star evidence of two periodic signals with periods of 3.51 ‫30.0 ע‬ in which the narrow absorptions form in a circumstellar disk and 3.74 ‫ 30.0 ע‬hr (both with peak power far above the 1% that is projected against the star. The star might have a strong false-alarm probability defined by Scargle 1982). These periods magnetic field that controls the gas outflow and has spun down are much too small to be related to binary motion. They may the star. Finally, the spectrum may be that of a long-period be due to changes in disk density or illumination caused by binary consisting of a bright, narrow-lined B star and a fainter nonradial pulsations in the underlying star (Rivinius et al. Be star (although no companion was found in the speckle sur- 2003). vey by Mason et al. 1998). This explanation is supported by the fact that the Ha emission does vary in strength and shape 3.5. HD 61827 on short and long timescales in our observations, while the The star HD 61827 (O8–9 Ib, Houk 1982; B3 Iab, Garrison absorption lines are constant. et al. 1977; B3 Ia, Turner 1977) is a luminous object in an association surrounding the cluster NGC 2439 (Turner 1977). 3.4. HD 60848 We found no evidence of a prior radial velocity measurement The star HD 60848 is another Be-type object (O9.5 IVe; in the literature. The star’s red spectrum (Fig. 6) shows Ha in Negueruela et al. 2004) that may be a runaway star because emission, as is often the case for B supergiants. The lack of of its position well out of the Galactic plane (de Wit et al. He ii l6683 and the relative strength of C ii ll6578, 6583 2005). It was recently observed with moderate-dispersion blue support the later subtype adopted by Garrison et al. (1977) and spectra by McSwain et al. (2007), who found no evidence of Turner (1977). We used the C ii ll6578, 6583 and He i ll6678, velocity variability. We observed this star only during the sec- 7065 absorption lines in the CCF to determine radial velocities 2007 PASP, 119:742–746

404 746 BOYAJIAN ET AL. for this star. The ratio of the external to the internal error indicates that the star is a velocity variable. Our spectra show dynamic Ha emission changes, with var- iable red and blue peaks appearing to vary on a timescale of 5–10 days. We suspect that these variations are related to struc- tures in the stellar wind that are modulated by rotation and temporal changes in the outflow. These emission variations in Ha appear to affect the velocities measured for the absorption lines of C ii and He i through subtle effects of emission filling that are not apparent to the eye. For example, during the first run, we observed the emergence of a strong redshifted Ha peak during the time when the absorption velocities attained their minimum value, and the appearance of a strongly blueshifted Ha peak occurred at the time when the absorption velocities reached a maximum. This correlation indicates that the ab- sorption lines we measured (C ii and He i) are probably also partially filled in by weak emission that shifts the line center away from the location of the emission. Thus, we suggest that Fig. 7.—Mean spectrum of HD 206183. the apparent velocity variations in HD 61827 are due to the effects of variations in the star’s wind. 7065. The mean velocities show no evidence for velocity var- iability over the two runs. 3.6. HD 206183 We thank Daryl Willmarth and the staff of KPNO for their HD 206183 (O9.5 V; Daflon et al. 2003) resides in the Tr assistance in making these observations possible. This work 37 cluster in the Cep OB2 association. Mason et al. (1998) list was supported by the National Science Foundation under grants two visual companions but assign the star to the “unknown” AST 02-05297, AST 05-06573, and AST 06-06861. Institu- status as a spectroscopic binary, since only one other velocity tional support has been provided from the GSU College of Arts measurement exists (Sanford & Merrill 1938). The average red and Sciences and from the Research Program Enhancement spectrum (Fig. 7) shows that the lines are narrow (V sin i p fund of the Board of Regents of the University System of 19.2 ‫ 9.1 ע‬km sϪ1; Daflon et al. 2003). We measured CCF Georgia, administered through the GSU Office of the Vice radial velocities for HD 206183 using Ha and He i ll6678, President for Research. REFERENCES Abt, H. A. 1970, ApJS, 19, 387 Liu, T., Janes, K. A., & Bania, T. M. 1991, AJ, 102, 1103 Boyajian, T. S., et al. 2005, ApJ, 621, 978 Mason, B. D., Gies, D. R., Hartkopf, W. I., Bagnuolo, Jr., W. G., ten ———. 2007, ApJ, 664, 1121 Brummelaar, T., & McAlister, H. A. 1998, AJ, 115, 821 Claria, J. J. 1974, A&A, 37, 229 McSwain, M. V., Boyajian, T. S., Grundstrom, E. D., & Gies, D. R. Conti, P. S. 1974, ApJ, 187, 539 2007, ApJ, 655, 473 Conti, P. S., Garmany, C. D., & Hutchings, J. B. 1977a, ApJ, 215, Morgan, W. W., Code, A. D., & Whitford, A. E. 1955, ApJS, 2, 41 561 Negueruela, I., Steele, I. A., & Bernabeu, G. 2004, Astron. Nachr., Conti, P. S., Leep, E. M., & Lorre, J. J. 1977b, ApJ, 214, 759 325, 749 Daflon, S., Cunha, K., Smith, V. V., & Butler, K. 2003, A&A, 399, Neubauer, F. J. 1943, ApJ, 97, 300 525 Plaskett, J. S. 1924, Publ. Dom. Astrophys. Obs., 2, 285 de Wit, W. J., Testi, L., Palla, F., & Zinnecker, H. 2005, A&A, 437, ˇ Rivinius, T., Baade, D., & Stefl, S. 2003, A&A, 411, 229 247 Roberts, D. H., Lehar, J., & Dreher, J. W. 1987, AJ, 93, 968 ´ Fullerton, A. W. 1990, Ph.D. thesis, Univ. Toronto Sanford, R. F., & Merrill, P. W. 1938, ApJ, 87, 517 Garmany, C. D., Conti, P. S., & Massey, P. 1980, ApJ, 242, 1063 Scargle, J. D. 1982, ApJ, 263, 835 Garrison, R. F., Hiltner, W. A., & Schild, R. E. 1977, ApJS, 35, 111 Shafter, A. W., Szkody, P., & Thorstensen, J. R. 1986, ApJ, 308, 765 Houk, N. 1982, Catalogue of Two-Dimensional Spectral Types for Stickland, D. J., & Lloyd, C. 2001, Observatory, 121, 1 the HD Stars, Vol. 3 (Ann Arbor: Univ. Michigan) Turner, D. G. 1977, AJ, 82, 805 Liu, T., Janes, K. A., & Bania, T. M. 1989, AJ, 98, 626 Underhill, A. B., & Gilroy, K. K. 1990, ApJ, 364, 626 2007 PASP, 119:742–746

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