ON THE ANALYSIS OF TWO LOW-MASS, ECLIPSING BINARY SYSTEMS IN THE YOUNG ORION NEBULA CLUSTER By Yilen G´omezMaqueo Chew Dissertation Submitted to the Faculty of the Graduate School of Vanderbilt University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Physics August, 2010 Nashville, Tennessee Approved: Prof. Keivan G. Stassun Prof. David J. Ernst Prof. Robert A. Knop Prof. Robert C. O’Dell Prof. Andrej Prˇsa Prof. David A. Weintraub ACKNOWLEDGEMENTS This research would not have been possible without the financial support of CONACYT and Keivan Stassun. I am very grateful to the people from Villanova’s Astronomy Department for shar- ing their knowledge on eclipsing binaries, for their hospitality, and for always proving excellent espresso. I would like to also thank those in the Physics and Astronomy Department at Vanderbilt that helped me through this journey, specially the other grad students, Leslie who always had words of encouragement, and Bob who believed in me. Special thanks to Gilma and Martha for sharing with me all these years, with their ups and downs. I am also grateful for the good time spent at the Fortress, with the other members of the garrison: Talia and Yonah. Thank you Brittany, for being Thing 1 or Thing 2, as required, and also to Stacey for Hana Club. I would like to thank Jeff for good food, and words. And I would also like to thank Ponch for being a good friend. Finally, I would like to thank my parents and sister, Yuyen, for being patient and never doubting that I could accomplish this, as well as the Agraz GM family for feeding me and keeping me well caffeinated when I visited. ii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS . ii LIST OF TABLES . vi LIST OF FIGURES . vii Chapter I. INTRODUCTION . 1 II. OBSERVATIONS AND DATA REDUCTION . 7 II.1 The JHKS Photometric Observations . 8 II.1.1 NIR Data Reduction . 12 II.1.2 I Season: Undithered Calibrations . 17 II.1.3 The NIR Bad Quadrant . 18 II.2 The BV IC Photometric Observations . 19 II.2.1 ANDICAM BV IC Data Processing . 20 II.3 The Spectroscopic Observations . 21 II.3.1 Spectra of Par 1802 . 21 II.3.2 Spectra of 2M0535−05 . 24 III. LIGHT AND RADIAL VELOCITY CURVES . 26 III.1 Generating the Light Curves . 26 III.1.1 JHKS Light Curves . 28 III.1.2 BV IC Light Curves . 33 III.2 Radial Velocity Curves . 33 III.2.1 Radial Velocities of Par 1802 . 36 III.2.2 Radial Velocities of 2M0535−05 . 37 IV. METHODOLOGY OF THE ANALYSIS . 39 IV.1 Periodicity . 39 IV.1.1 Orbital Period Determination . 39 IV.1.2 Low-Amplitude Photometric Variability . 42 IV.2 Eclipsing Binary Modeling . 50 IV.2.1 Overview of the Model . 50 IV.2.2 Setting Up . 59 IV.2.3 Radial Velocity Solution . 61 IV.2.4 LC Solution . 63 iii IV.2.5 LC+RV Solution . 65 IV.2.6 Including Surface Spots . 67 IV.2.7 Joint Confidence Intervals . 70 IV.2.8 Determination of the Parameter Uncertainties . 73 V. PARENAGO 1802 . 78 V.1 Observations and Data Reduction . 79 V.1.1 Photometric Observations . 79 V.1.2 Near-Infrared Data Reduction . 80 V.1.3 Spectroscopic Observations . 85 V.2 Analysis . 86 V.2.1 Periodicity . 86 V.2.2 Spectral Veiling: Evidence for a Third Light in Par 1802 . 95 V.2.3 Characterization of the Third Light . 98 V.3 Results: Orbital and Physical Parameters of Par 1802 . 101 V.4 Discussion . 112 V.4.1 Eccentricity, Rotation Period and Tidal Evolution . 113 V.4.2 The Third Stellar Component . 115 VI. ECLIPSING BROWN DWARFS . 119 VI.1 Near-Infrared Light Curves . 121 VI.1.1 Near-Infrared Photometric Observations . 122 VI.1.2 Data Reduction . 122 VI.2 Light Curve Analysis . 126 VI.2.1 Rotation periods . 126 VI.2.2 Orbital and Physical Parameters of 2M0535−05 . 133 VI.3 Surface Spots . 140 VI.4 Discussion . 149 VII. CONCLUSIONS . 152 VII.1 Summmary . 152 VII.2 Results in Context . 158 VII.3 In Progress and Future Work . 162 Appendices A. PHOEBE: CONFIGURATION FILE . 166 B. PHOEBE: MODELING SCRIPT . 175 C. PHOEBE: PARAMETER CROSS SECTION SCANNING SCRIPT . 183 D. PHOEBE: UNCERTAINTY DETERMINATION SCRIPT . 186 iv E. PAR 1802: ABRIDGED VIC JHKS LIGHT CURVES . 193 F. PAR 1802: DISTANCE ESTIMATION SCRIPT . 198 G. 2M0535−05: ABRIDGED JHKS LIGHT CURVES . 201 BIBLIOGRAPHY . 204 v LIST OF TABLES Table Page 1. Physical Properties of the Low-Mass, PMS Eclipsing Binaries . 4 2. ANDICAM Detector Characteristics . 9 3. ∆χ2 as a Function of Confidence Level and Number of Parameters of Interest ν .................................. 72 4. Photometric Time Series Observations of Par 1802 . 82 5. Timings of Eclipse Minima in the IC Light Curve . 87 6. Periodicity in the Light Curves of Par 1802 . 89 7. Orbital and Physical Parameters of Par 1802 . 111 8. Photometric Time Series Observations of 2M0535−05 . 123 9. Periodicities Detected by Season and Passband . 132 10. Orbital and Physical Parameters of 2M0535−05 . 134 11. Differential V band Light Curve of Par 1802 . 193 12. Differential IC band Light Curve of Par 1802 . 194 13. Differential J band Light Curve of Par 1802 . 195 14. Differential H band Light Curve of Par 1802 . 196 15. Differential KS band Light Curve of Par 1802 . 197 16. Differential J band Light Curve of 2M0535−05 . 201 17. Differential H band Light Curve of 2M0535−05 . 202 18. Differential KS band Light Curve of 2M0535−05 . 203 vi LIST OF FIGURES Figure Page 1. NIR Atmospheric and Passband Transmission . 10 2. ANDICAM’s Optical Layout . 11 3. JHKS Data Reduction Flowchart . 12 4. JHKS Master Sky Frames . 15 5. J-band Bad Quadrant Dither and Co-Added Image . 18 6. Rectified, Out-of-Eclipse J Light Curve . 31 7. Histograms of the JHKS Light Curves’ Residuals and Photometric Errors 32 8. RV Determination via the Broadening Function . 38 9. V -band Lomb-Scargle Periodogram of Par 1802 . 43 10. Maximum Periodogram Peak Distribution from Monte Carlo Method . 45 11. Identifying Independent Periodicities from their Aliases . 47 12. Period Uncertainty via Post-Mortem Analysis . 48 13. Orbital Geometry and Orientation . 52 14. Orbital Phase and Quantities . 53 15. Observed and Modeled VIC JHKS Light Curves of Par 1802 . 81 16. OFE VIC JHKS Lomb-Scargle Periodograms . 88 17. Low-Amplitude, Photometric Variability . 90 18. OFE IC and Synthetic Periodograms . 94 19. Observed and Model Spectrum of Par 1802 . 96 20. Effects of the IC Third Light on the System’s Parameters . 104 21. RV+LC Joint Confidence Levels for e − ω . 107 22. LC Joint Confidence Levels for e − ω . 108 vii 23. Joint Confidence Levels for (Teff,1/Teff,2)–(R1/R2) . 110 24. JHKS light curves of 2M0535−05 . 125 25. Lomb-Scargle Periodograms of 2M0535−05 . 128 26. Out-of-Eclipse IC JH-band Light Curves . 131 27. Joint Confidence Interval between i and Ω1 . 137 28. Joint Confidence Interval between (Teff,2/Teff,1) and (R2/R1) . 138 29. Modeling of the Wavelength-Dependent Photometric Variability Using an Analytical Inversion Technique . 142 30. Degeneracy Between Large Polar Spots on the Primary and the Sec- ondary Components of 2M0535−05 . 146 31. Light Curve Modeling Including Treatment of Spots . 148 32. Comparison of Physical Properties of Par 1802 with Theoretical Models 157 33. Observed and Theoretical Mass-Radius Relationship . 160 34. Observed and Theoretical Effective Temperature-Radius Relationship . 161 35. Spitzer IRAC and new J Light Curves of Par 1802 . 164 viii CHAPTER I INTRODUCTION Empirical measurements of the masses, radii, temperatures, and luminosities of pre-main sequence (PMS) stars and brown dwarfs are valuable for the understanding of star formation. They delimit the Initial Mass Function, defining the outcome of star formation and providing the energy scale for the formation process. They represent an observational tie to the theoretical evolution models that describe the chronology of stellar evolution, and set the timescales for circumstellar disk evolution and planet formation. In order for these models to accurately describe the physics of PMS evolution, they must be tested against observed properties of young stars and brown dwarfs (e.g., Mathieu et al., 2007). Mass is the physical property of stars that is most important in determining the course of their evolution. Most stellar masses, however, are derived from evolu- tionary tracks based on converting the measured spectral types and magnitudes to model-dependent calculations of temperatures and luminosities. Thus, the empirical determination of PMS masses represents the link between observations and theoreti- cal evolutionary models. The calibration of these models can be done by measuring the dynamical masses, with precisions of at least a few percent, and jointly obtaining stellar properties like luminosities and effective temperatures or radii (Torres et al., 2010). Only three systems allow for dynamical mass measurements to be acquired: 1 young stars with a circumstellar disks, binary systems with both double-lined spec- troscopic and astrometric orbits, and double-lined eclipsing binary (EB) systems. In the case of the first type of system mentioned above, the dynamical mass of the parent star can be determined from the disk’s rotation curve (e.g., Prato et al., 2002). The derived mass depends on the inclination of the disk with respect to the observer, which can be estimated from the morphology of the observed disk emission. In the second case, direct mass measurements for both binary components is possible. The spectroscopic orbit solution provides the mass ratio of the system, as well as the period and information about the size and eccentricity of the orbit.