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Analysis of Exoplanetary Transit Light Curves Joshua Adam Carter

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Analysis of Exoplanetary Transit Light Curves by Joshua Adam Carter B.S., Physics, University of North Carolina at Chapel Hill, 2004 B.S., Mathematics, University of North Carolina at Chapel Hill, 2004 Submitted to the Department of Physics in partial fulfillment of the requirements for the degree oft MASSACHUSETTS INSTITUTE Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY ARCHIVES September 2009 © Massachusetts Institute of Technology 2009. All rights reserved. Author ................ .............. Department of Physics 31, 2009 7A .August Certified by....... Joshua N. Winn Assistant Professor of Physics Class of 1942 Career Development Professor Thesis Supervisor A Accepted by ............................ TlW rs J. Greytak Lester Wolfe Professor of Physics Associate Department Head for Education Analysis of Exoplanetary Transit Light Curves by Joshua Adam Carter Submitted to the Department of Physics on August 31, 2009, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract This Thesis considers the scenario in which an extra-solar planet (exoplanet) passes in front of its star relative to our observing perspective. In this event, the light curve measured for the host star features a systematic drop in flux occurring once every orbital period as the exoplanet covers a portion of the stellar disk. This exoplanetary transit light curve provides a wealth of information about both the planet and star. In this Thesis we consider the transit light curve as a tool for characterizing the exoplanet. The Thesis can divided into two parts. In the first part, comprised of the second and third chapters, I assess what ob- servables describing the exoplanet (and host) may be measured, how well they can be measured, and what effect systematics in the light curve can have on our estimation of these parameters. In particular, we utilize a simplified transit light curve model to produce simple, analytic estimates of parameter values and uncertainties. Later, we suggest a transit parameter estimation technique that properly treats temporally correlated stochastic noise when determining a posteriori parameter distributions. In the second part, comprised of the fourth and fifth chapters, I direct my at- tention to real exoplanetary transit light curves, primarily for two exoplanets: HD 149026b and HD 189733b. We analyze four transits of the ultra-dense HD 149026b, as measured by an instrument on the Hubble Space Telescope, in an effort to properly constrain the stellar and exoplanetary radius. In addition, we assess a detection of strong, wavelength dependent absorption, possibly due to an unusual atmospheric composition. For HD 189733b, we utilize seven ultra-precise Spitzer Space Telescope transit light curves in an effort to make the first empirical measurement of asphericity in an exoplanet shape. In particular, we constrain the parameters describing an oblate spheriod shape for HD 189733b and, attributing oblateness to rigid-body rotation, we place lower bounds on the rotation period of the exoplanet. Thesis Supervisor: Joshua N. Winn Title: Assistant Professor of Physics Class of 1942 Career Development Professor Acknowledgements Many people contributed to this work and to the completion of this degree. I want to thank both my parents for instilling in me the virtues of perseverance, self-reliance, and humility which have time and again helped me succeed at any endeavor. I want to thank my Dad for being so proud of every good thing I have done, no matter how small. Dad, thanks for all the life lessons and for sharing all those baseball games together. I want to thank my Mom for shaping my mind from an early age to succeed in academics, science and life. Mom, thanks for the love and Legos. I also want to thank my siblings, Troy, Jason and Stephanie, for all their support and guidance. I want to thank my surrogate parents, John and Janet Mustonen, for accepting me so completely into their family. Over the years they have given me tremendous support ranging from great advice to good company. I also want to thank Pete, my brother-in-law, for all his help and for bravely subjecting himself to endless good- natured competition despite my clear intellectual edge. To my Boston family, Carly, Sarah, Stephanie and Eric, thanks for making my life away from MIT particularly awesome. To all my current and past officemates of 37-602, thanks for making every day at work fun, even if no work was getting done. A special thanks goes to Ryan Lang whose friendship over the years left an indelible mark on my career and life as a graduate student at MIT. Thanks to my advisor, Josh Winn, for making my last few years of graduate school exciting, stimulating and an excellent learning experience. I also want to thank Jean Papagianopoulos, Arlyn Hertz and the rest of the staff at MKI and the physics department for helping me so much over my time as a graduate student. Most of all, I want to thank my perfect wife Erica for being so much more than just my wife; for being my drive, my motivation, and my purpose for reaching this goal. Without her, all of this work would be pointless. Thank you Erica for being so patient through all my ups and downs during my graduate career. Thank you for taking such good care of me. Thank you for being so beautiful even without trying. Thank you for making me feel so special and loved; I honestly feel so very lucky to have met and married you. I dedicate this work and, much more importantly, all the good I can offer in my entire life to you and our family to come. I love you so very much. Contents 1 Introduction 17 1.1 Planets near and far . .. .. ... .. .. .. .. .. ... ... .. 17 1.1.1 Our own Solar System . ... .. .. .. .... .... .. 17 1.1.2 Extrasolar planets: Planets outside our own Solar System . .... .... .... 18 1.2 Detecting extrasolar planets .. .. .. ... .. ... ... .. .. 2 1 1.2.1 Detection via radial velocity .. .. .. .. .. .. .. .. 22 1.2.2 Detection via transit . .. ... .. .. ... ... .. ... 23 1.3 Characterizing extrasolar planets that transit . .... .... ... 27 1.3.1 The exoplanetary transit light curve: From top to bottom . .. ... .. .. .. .... .... 28 1.4 Thesis overview . ... .. .. ... .. .. .. .. .... .... .. 36 2 Analytic approximations for transit light-curve observables, uncer- tainties, and covariances 43 2.1 Introduction .. ... .. ... ... ... ... .. ... ... ... .. 43 2.2 Linear approximation to the transit light curve . ... ... ... .. 45 2.3 Fisher information analysis . .. .. ... .. ... .. .. ... .. 49 2.4 Accuracy of the covariance expressions .. .... .... ... .... 56 2.4.1 Finite cadence correction . .... ... ... .... ... .. 58 2.4.2 Comparison with covariances of the exact uniform-source model 58 2.4.3 The effects of limb darkening ... .. ... ... ... ... 60 2.5 Errors in derived quantities of interest in the absence of limb darkening 65 2.6 Optimizing parameter sets for fitting data with small limb darkening 66 2.7 Sum m ary . ... .. ... .. ... .. ... .. ... .. ... .. .. 75 3 Parameter Estimation from Time-Series Data with Correlated Er- rors: A Wavelet-Based Method and its Application to Transit Light Curves 81 3.1 Introduction .... ...... .... .. .. .. 81 3.2 Parameter estimation with "colorful" noise ..... .... ... .. 84 3.3 Wavelets and 1/f noise .. ....... ...... .... ... .. 89 3.3.1 The wavelet transform as a multiresolution analysis . .. .. 91 3.3.2 The Discrete Wavelet Transform .. ...... ... .. .. 93 3.3.3 Wavelet transforms and 1/fy noise . ..... ... ... .. 94 3.3.4 The whitening filter ........ ......... .. .. .. 95 3.3.5 The wavelet-based likelihood .. ...... ..... ... .. 97 3.3.6 Some practical considerations .... ...... .. .. .. 98 3.4 Numerical experiments with transit light curves ... ... .. .. 99 3.4.1 Estimating the midtransit time: Known noise parameters . .. 99 3.4.2 Estimating the midtransit time: Unknown noise parameters 105 3.4.3 Runtime analysis of the time-domain method .... .... 108 3.4.4 Comparison with other methods .. .... .... .... ... 111 3.4.5 Alternative noise models . ..... .... .... ..... .. 114 3.4.6 Transit timing variations estimated from a collection of light curves .... ..... ..... ..... .... ..... ... 118 3.4.7 Estimation of multiple parameters ..... ...... ..... 122 3.5 Summary and Discussion ...... ..... ...... ...... .. 123 4 Near-infrared transit photometry of the exoplanet HD 149026b 133 4.1 Introduction ...... ..... ...... ...... ...... ... 133 4.2 Observations and Reductions ..... ...... ..... ...... 135 4.3 NICMOS Light-Curve Analysis ... ...... ..... ...... 137 4.3.1 Results from NICMOS photometric analysis ..... ..... 146 4.4 Stellar Parameters ... ... ... ... ... ... ... ... .. 153 4.5 Joint Analysis with Optical and Mid-Infrared Light Curves . 157 4.6 Ephemeris and transit timing . ... .. .. .. ... .. .. .. 159 4.7 Discussion of broadband results ... .. ... .. ... .. ... 161 4.8 Transmission spectroscopy ... .. ... .. ... .. ... .. .. 166 5 An Empirical Upper Limit on the Oblateness of an Exoplanet 177 5.1 Introduction . .. ... .. ... .. ... .. .. ... .. ..... 177 5.2 Physical review ... ... ... ... .. ... ... ... 180 5.2.1 Relevant timescales . .. ... ... .. ... .. .. 180 5.2.2 Oblateness and rotation .. ... ... .. ... .. 182 5.2.3 Competing effects in the transit light curve .. ... 185 5.3 A numerical method for computing transit light curves of ellipsoidal exoplanets .. .... ... .... ... .... ... ... 187 5.4 Spitzer transits of HD 189733b: An oblate analysis .. .. 195 5.4.1 Observations and data
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